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Two-phase methanation of lactose in biofilm reactors Yu, Jian 1991

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TWO-PHASE METHANATION OF L A C T O S E IN BIOFLLM REACTORS By Jian Y u B . Sc. Zhejiang Institute of Technology, 1982 M . Sc. Zhejiang University, 1985  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in  THE FACULTY OF GRADUATE STUDIES CHEMICAL ENGINEERING We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April 1991 © Jian Y u , 1991  In  presenting this  degree at the  thesis  in  University of  partial  fulfilment  of  the  British Columbia, I agree that the  freely available for reference and study. I further copying  of  department  this or  thesis for by  his  or  requirements  representatives.  an advanced  Library shall make  it  agree that permission for extensive  scholarly purposes may be her  for  It  is  granted  by the  understood  that  head of copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department  of  tmrtteA^  &l&2Aje&Z24tfr  The University of British Columbia Vancouver, Canada  DE-6 (2/88)  Abstract  Anaerobic methanation of lactose, the main component of cheese whey, is an attractive alternative for the disposal of this wastewater because of its added benefit of recovering energy as methane.  T w o advances in this technology have been the separation of the  bacteria in two reactors according to their substrates and the retention of the anaerobic bacteria in the form of bacterial biofilms on solid supports.  T h e mass transfer rate  of the substrates within the active biofilms must be known for the determination of an optimum biofilm thickness. A prerequisite for the investigation of substrate mass transfer rate in an active biofilm is the knowledge of intrinsic kinetics of the substrate utihzation by the embedded bacterial cells. Start-up of symbiotic methanogenic biofilms was also investigated on inert supports. In recycled reactors, mesophihc (35 ° C ) acid-producing bacteria or methane-producing bacteria,  cultured with lactose at a p H of 4.6 for the former or cultured with mixed  acids (acetate, propionate and butyrate) at a p H of 7.1 for the latter , attached P V C sheets, forming thin acidogenic or methanogenic biofilms, respectively.  onto  After the  external mass transfer resistance had been eliminated by increasing the recycle rate and the internal mass transfer resistance was minimized by using thin biofilms, the intrinsic kinetics of lactose acidogenesis and methanogenesis  of organic acids were investigated  in the newly formed acidogenic and methanogenic biofilms, respectively.  T h e lactose  digestion rate as well as the production of two main products, acetate and butyrate, can be described by Michaelis-Menten equations.  T h e production of propionate, as a  minor product, was depressed in the culture environment. The digestion of acetate could also be modelled by a Michaelis-Menten equation while the dissimilation of propionate  n  and butyrate was affected by propionate concentration, the propionate digestion being promoted but the butyrate digestion being inhibited at high propionate concentrations. Two models have been proposed for their utilization. Substrate mass transfer in the active biofilms was investigated with a diffusion cell. After symmetric biofilms formed on the two membrane filters of the cell, the substrate concentrations on the biofilm surfaces and inside the cell were measured at steady state. T h e effective diffusivities of substrates in the active biofilms were estimated by numerically solving the diffusion-reaction equations using the intrinsic kinetics and the substrate concentrations as the boundary conditions. T h e effective diffusivity of lactose in an acidogenic biofilm was about 65.3 % of its diffusivity in water, and the diffusivities of acetate, propionate and butyrate in a methanogenic biofilm were reduced to about 30.2  % of  the values in water. Comparing the fractional void volumes in the two types of biofilms showed that the methanogenic biofilm, which grew more slowly, had a more tortuous structure of channels than did the acidogenic biofilm. Studies on the build-up of symbiotic methanogenic biofilms were conducted using supports of wood, ceramic rings, P V C and stainless steel, which gave a range of water contact angle from 0° to 9 9 . 7 ° . The accumulation of acetate-, propionate- and butyratedegrading bacteria on the supports were monitored by measuring the substrate utilization rates of each bacterial group in a standard batch culture which was seeded by the supports with the attached biofilms.  T h e three types of bacteria had different preference to a  hydrophilic support surface, butyrate degrader > acetate degrader > propionate degrader Based on the analysis of the process of biofilm formation, a model has been proposed. T h e parameters which depict the attachment of free cells onto clean surfaces were found to have a linear relationship with the water contact angles of the support surfaces. iii  Acknowledgement  T h e author expresses here his sincere appreciation to D r . K . L . Pinder for his advice, direction and support throughout this research project.  He is also grateful to Dr.  R.  M . R. Branion and Dr. K . V . Lo, two members of his supervision committee, for their constructive criticisms and review of this thesis. T h e author is obliged for financial support of this research  to the Foundation of  Pao Z h a o - L o n g and Pao Y u - G a n g Scholarship and the Natural Science and Engineering Research Council of Canada. Special thanks go to his family and parents for their understanding and support.  iv  T a b l e of C o n t e n t s  Abstract  ii  Acknowledgement  iv  List of Tables  xi  List of Figures 1  Introduction  1  1.1  Utilization of Lactose in W h e y  1  1.2  Anaerobic Methanation of Lactose  3  1.3  More Considerations on Two-phase Methanation of Lactose . .  6  1.3.1  Kinetics in Each Phase Reactor  8  1.3.2  Mass Transfer in the Biofilms  9  1.3.3  Start-up of Anaerobic Biofilms  1.4 2  xiv  Research Objectives and Scope  11 12  Theoretical Aspects and Previous Studies  14  2.1  Process Biochemistry and Microbiology  14  2.1.1  Lactose Acidogenesis  15  2.1.2  Methanogenesis of Fatty Acids  24  2.1.3  Acetogenesis of Fatty Acids  28  2.2  . .  Start-up of Anaerobic Biofilms  32  2.2.1  32  Mechanism of Build-up of Bacterial Biofilms  v  2.2.2 2.3  2.4  3  Startup of Methanogenic Biofilms  Mass Transfer in Anaerobic Biofilms  39  2.3.1  Structure of Anaerobic Biofilms  41  2.3.2  Mass Transfer within Biofilms  43  Intrinsic Kinetics of Substrate Utihzation in Anaerobic Biofilms  47  2.4.1  Expression of Intrinsic Kinetics  47  2.4.2  Ehmination of External and Internal Mass Transfer Resistances  2.4.3  Kinetics of Acidogenesis and Methanogenesis  Experimental Conditions and Setup 3.1  3.2  3.3  3.4  36  .  49 51  54  Experimental Conditions  55  3.1.1  Culture Temperature  55  3.1.2  Culture p H  56  3.1.3  Growth Nutrients  57  Experimental Setups  59  3.2.1  General Setup  60  3.2.2  Reactor  62  Biofilm Supports  . .  66  3.3.1  Supports for Kinetic Studies  66  3.3.2  Supports for Mass Transfer Studies  67  3.3.3  Supports for Studies of Biofilm Start-up  69  Experimental Analysis  70  3.4.1  Sohd Sample Analysis  70  3.4.2  Liquid Sample Analysis  72  3.4.3  Gaseous sample analysis  73  vi  4  5  I n t r i n s i c K i n e t i c s of L a c t o s e U t i l i z a t i o n  74  4.1  Experiments on Lactose Acidogenesis  74  4.2  Development of an Acidogenic Biofilm  78  4.3  Utilization Rate of Lactose  84  4.4  Production of Organic Acids  89  4.5  Responses of Acidogenic Biofilms to Disturbances  S t a r t - u p of S y m b i o t i c M e t h a n o g e n i c B i o f i l m s o n I n e r t S u r f a c e s  104  5.1  Wettability of a Support Surface  104  5.2  Experimental Steps  107  5.3  A Kinetic Model of Biofilm Start-up  Ill  5.3.1  Attachment on Clean Surfaces  Ill  5.3.2  Growth of Attached Bacteria  113  5.3.3  Attachment on Fixed Biomass  113  5.3.4  Detachment  114  5.4 6  101  Estimation of Model Parameters  116  I n t r i n s i c K i n e t i c s o f M e t h a n o g e n e s i s of O r g a n i c A c i d s  128  6.1  Experiments of Organic A c i d Methanogenesis  129  6.2  Development of Methanogenic Biofilms  136  6.3  Interaction of Organic Acids  140  6.3.1  Influence of Acetate Concentration  140  6.3.2  Influence of Propionate Concentration  141  6.3.3  Influence of Butyrate Concentration  142  6.4  Utihzation Rates of Organic Acids  145  6.4.1  Propionate Utihzation Rate  146  6.4.2  Utihzation Rate of Butyrate  150  vii  6.4.3 6.5  7  154  Distribution of Bacterial Groups in Balanced Biofilms  M a s s Transfer  158  in Biofilms  166  7.1  Diffusivities of Substrates in Water  166  7.2  Principle of Mass Transfer Measurement within Biofilms  168  7.3  Experimental Setup  173  7.4  Diffusivity of Lactose in Acidogenic Biofilms  175  7.5  Effective Diffusivities of Organic Acids in Methanogenic  7.6 8  Acetate Utilization Rate  Biofilms  Biofilms  181  7.5.1  Formation of Symbiotic Methanogenic  7.5.2  Effective Diffusivities of Propionate and Butyrate in the Biofilms .  182  7.5.3  Effective Diffusivity of Acetate in Methanogenic  187  7.5.4  Effect of Support Properties on the Measurement of Diffusivities .  Influence of Biofilm Structure on Diffusivities  Conclusions  and Recommendations  181  Biofilms  191 196 203  8.1  Conclusions  203  8.2  Recommendations  208  8.2.1  Concentration Effect  208  8.2.2  Controlling Biofilm Thickness  208  8.2.3  A Compromised Physical Method  211  Bibliography  213  Appendices  230  A  Fermentation Pathways  230  A.l  230  Four Fermentation Pathways of Glucose to Pyruvate  vm  A. 2  B  Formation of Organic Acids from Pyruvate  231  Analysis Methods  241  B. l  Determination of Lactose  241  B.l.l  Reagents and Apparatus  241  B.1.2  Procedure  242  B.2  B.3  B.4  B.5  B.6  Determination of Lactate  242  B.2.1  Reagents and Apparatus  243  B.2.2  procedure  244  Determination of Volatile Fatty Acids and Ethanol  244  B.3.1  Reagents and Apparatus  245  B.3.2  Procedure  246  Gas Composition  247  B.4.1  Apparatus  247  B.4.2  Procedure  249  Determination of Carbon Content in a Liquid Sample  251  B.5.1  Sample Preparation  251  B.5.2  Reagents and Apparatus  252  B.5.3  Procedure  252  Analysis of a Biofilm  253  B.6.1  D r y Biomass and Carbon Content of a Biofilm  253  B.6.2  A s h Content of a Biomass  253  B.6.3  Water Volume. Density and Thickness of a Biofilm  253  C Results of Lactose Acidogenesis  255  D Results of Buildup of Methanogenic Biofilms  257  ix  E  R e s u l t s of O r g a n i c A c i d M e t h a n o g e n e s i s  259  F  D e r i v a t i o n o f U t i l i z a t i o n R a t e M o d e l s of P r o p i o n a t e a n d B u t y r a t e  261  F.l  Utihzation Rate Model of Propionate  261  F. 2  Utihzation Rate Model of Butyrate  262  G  Numerical Methods  265  G. l  Direct Search Method  265  G.2  Runge-Kutta-Fehlberg  G.3  T h e Computer Programs in Pascal Language  Method  266  x  269  List of Tables  1.1  Major components of a typical whey  2  1.2  Pilot- and full-scale plants of two-phase anaerobic treatment of wastewaters  8  2.3  Main genera of acid-producing bacteria imphcated in first phase  18  2.4  Classification of seven genera of methanogenic bacteria  24  2.5  Currently known mesophilic obligate proton-reducing bacteria  30  2.6  Growth rate of obhgate H^-producing actogens  30  2.7  Ratios of effective diffusivities measured in inactive biomass to diffusivities in water  .  46  2.8  Growth constants of anaerobic cultures at 35 °C  52  3.9  Chemical components and concentrations in culture medium  59  3.10  Comparison of experimental conditions for each phase  60  3.11  Properties of biofilm supports for studies of biofilm formation  70  4.12  Experimental conditions of lactose acidogenesis  79  4.13  M a x i m u m lactose digestion rate and half velocity concentration  87  4.14  Reactions of Lactose Conversion  90  4.15  Rate parameters of the products in lactose fermentation  94  4.16  Comparison of production rates of organic acids at two p H levels  101  5.17  Results of screening kinetic models of biofilm start-up  118  5.18  Linear relations between specific attachment rates and water contact angles 125  xi  6.19  Methanogenic reactions of organic acids  128  6.20  V F A distribution in anaerobic digestion process  129  6.21  Experimental conditions for organic acid methanogenesis  136  6.22  Properties of methanogenic biofilms  140  6.23  Methanogenesis of organic acids  157  6.24  Fractional mass of bacterial groups and utihzation rates of fatty acids . .  165  7.25  Diffusivities in water at 35 °C  168  7.26  Effective diffusivity of lactose within acidogenic biofilms at 35 ° C  7.27  Sensitivity of lactose effective diffusivity to experimental error  181  7.28  Effective diffusivities of propionate and butyrate  187  7.29  Effective diffusivity of acetate in methanogenic biofilms  190  7.30  Distribution of bacterial species in biofilms forming on nitrocellulose mem-  . . . .  180  branes  194  7.31  Effect of bacterial species distribution on the measurement of diffusivities  195  7.32  Comparison of acidogenic and methanogenic biofilms  201  8.33  Organic carbon fraction of each bacterial group in methanogenic biofilms on P V C and nitrocellulose membrane filter supports  207  C.34 Accumulation of acidogenic biofilms on removable P V C slides  255  C . 35 Results of lactose acidogenesis  256  D . 36 Accumulation of acetate-degrading  bacteria on inert supports  257  D.37 Accumulation of propionate-degrading bacteria on inert supports  258  D . 38 Accumulation of butyrate-degrading bacteria on inert supports  258  E . 39 Accumulation of methanogenic biofilms on removable P V C shdes  259  xii  E.40 Methanogenesis of acetate, propionate and butyrate E.41 Gas production rate and composition of organic acid methanation  xm  260 . . . .  260  List of Figures  1.1  Illustration of configurations of anaerobic filter (A),  fluidized/expanded  bed (B) and upflow anaerobic sludge blanket ( C )  5  1.2  Two-phase process of anaerobic digestion of organic wastes  7  2.3  Illustration of lactose structure  15  2.4  Illustration of two types of glycosidic links  16  2.5  Structure of lac operon  17  2.6  Bacterial fermentation  products of pyruvate.  Pyruvate formed by the  catabolism of glucose is further metabolized by pathways which are characteristic of particular organisms. E n d products of fermentations are shown in boxes and intermediates in dash boxes. " - " refers to consumption and "+"  to production  22  2.7  Structure of biofilms  43  2.8  Illustration of substrate concentration profiles in biofilms  50  3.9  Illustration of temperature influence on growth rate of microbes  56  3.10  Illustration of general experimental setup.  1-feed tank, 2-pump, 3-head  tank, 4-microvalve, 5-rotameter, 6-break tube, 7-reactor, 8-biofum support, 9-refrigerated  bath, 10-heat exchanger,  bath, 1 3 - p H controller,  11-pump,  12-thermostat  1 4 - p H adjusting solution, 15-gas collector,  16-  thermoregulator  61  3.11  Illustration of reactor configuration  63  3.12  A removable sampling slide  63 xiv  3.13  Effect of recycle ratio on reactor's behavior. A - r e c y c l e ratio 3.8,  x-recycle  ratio 7.6 3.14  65  P V C biofilm support for kinetic studies of lactose or organic acids fermentation  3.15  67  A thin biofilm (the black up-layer) on a P V C support, magnified by 100 times  3.16  68  A biofilm support device for mass transfer studies of lactose or organic acids in biofilms  4.17  68  External mass transfer resistance on lactose utihzation in biofilms is tested by changing recycle rate  77  4.18  Lactose digestion rate of whole reactor changes with time  78  4.19  Specific lactose digestion rate changes with biofilm thickness  79  4.20  Biomass distribution in the fermenter  80  4.21  Biomass on removable shdes increases with time  81  4.22  Carbon content in the biomass  82  4.23  Total carbon content developed on the supports. T h e hne was calculated from Equation 4.16  4.24  83  Effect of lactose concentration on lactose digestion rate. T h e hne is calculated from Equation 4.20  4.25  85  Influence of lactose concentration on acetate production rate. The hne is calculated from Equation 4.24 and the parameter values in Table 4.15 . .  4.26  Influence of lactose concentration on butyrate production rate.  T h e hne  is calculated from Equation 4.24 and the parameter values in Table 4.15 4.27  91  92  Influence of lactose concentration on ethanol production rate. T h e hne is calculated from Equation 4.24 and the parameter values in Table 4.15 . .  xv  92  4.28  Influence of lactose concentration on propionate production rate. T h e hne is calculated from Equation 4.25 and the parameter value in Table 4.15  4.29  93  Influence of lactose concentration on lactate production rate. T h e hne is calculated from Equation 4.25 and the parameter value in Table 4.15  4.30  .  Pathways of acidogenesis of lactose.  . .  93  Sign (-) refers to consumption, and  (+) refers to production. T h e intermediates are in dash boxes and products in sohd boxes  95  4.31  Production rate of acetate versus digestion rate of lactose  98  4.32  Production rate of butyrate versus digestion rate of lactose  99  4.33  Production rate of ethanol versus digestion rate of lactose  99  4.34  Production rate of propionate versus digestion rate of lactose  100  4.35  Production rate of lactate versus digestion rate of lactose  100  4.36  Responses of the acidogenic biofilm reactor to flow rate change. T h e sohd hne represents lactose concentration and the dash hne lactate concentration. 103  5.37  Schematic illustration of a spreading drop of liquid in contact with a solid surface, showing the relations between the contact angle, 6, and three interfacial free energies  5.38  105  Illustration of calculating contact angle, assuming the drop being a spherical segment  5.39  107  Organic acids degradation in a batch culture, o - acetate, A - propionate, x - butyrate  5.40  Build-up of acetate-degrading  110 bacteria in the biofilms. T h e lines are cal-  culated from the model. Surfaces: o - wood, x - ceramic, A - P V C , • steel  120  xvi  5.41  Build-up of propionate-degrading bacteria in the biofilms.  T h e lines are  calculated from the model. Surfaces: o - wood, x - ceramic, A - P V C , • - steel 5.42  121  Build-up of butyrate-degrading bacteria in the biofilms The lines are calculated from the model. Surfaces: o - wood, x - ceramic, A - P V C , • steel  5.43  122  Ease of attachment of bacteria on substrata as shown by model parameter k  5.44  123  Attachment factor, k, as a function of water contact angle of surface. Line is the least square fit. o-butyrate degrading bacteria, A-acetate degrading bacteria, X-propionate degrading bacteria  5.45  124  Spreading factor, s, as a function of the water contact angle of the surfaces for all bacteria  126  6.46  Influence of recycle rate on acetate utihzation  133  6.47  Influence of recycle rate on propionate utihzation  134  6.48  Influence of recycle rate on butyrate utihzation  134  6.49  Influence of biofilm thickness on acetate digestion rate  135  6.50  Biomass on slides increases with culture time  138  6.51  Total organic carbon on slides increases with culture time  138  6.52  Relationship between organic carbon and dry biomass of biofilms  6.53  Effect of acetate concentration on propionate digestion (HPr=880-996 mg/l)141  6.54  Effect of acetate concentration on butyrate digestion (HBu=48-66 mg/1)  6.55  Effect of propionate concentration on acetate utihzation (HAc=700-1000 mg/1)  . :  . . . .  139  142  143.  xvn  6.56  Effect of propionate concentration on butyrate utilization (HBu=50-80 mg/1)  143  6.57  Effect of butyrate concentration on acetate digestion (HAc=1400-3000 mg/l)144  6.58  Effect of butyrate concentration on propionate digestion (HPr=700-900 mg/1)  6.59  145  Dependence of propionate digestion rate on propionate concentration. T h e dash hne represents Equation 6.54.  T h e sohd hne is calculated from Equa-  tion 6.56 6.60  147  Dependence of butyrate digestion rate on butyrate concentration.  The  dash hne is calculated from the Michaelis-Menten equation 6.60;  The  points ( x ) are calculated from Equation 6.62 6.61  Influence of butyrate concentration on butyrate digestion (HPr = 690-900 mg/1)  6.62  152  Dependence of acetate utihzation rate on acetate concentration. The hne is calculated from Equation 6.65  7.63  155  Substrate concentration distribution within a biofilm at steady state, T h e elemental volume has a thickness Al and an area A  7.64  Influence of D  e  171  e  T h e biofilms symmetrically fixed on the two membrane filters of the diffusion-measuring cell  7.66  170  on substrate concentration distribution within a biofilm,  D' > D" > D™ 7.65  151  174  A steady-state lactose concentration inside the cell was established after a dilution. T h e lactose concentration outside the cell ranged from 1750 to  7.67  1900 mg/1  177  A controlled change in the lactose concentration of bulk culture solution .  178  xvm  7.68  Dynamic response of lactose concentration inside the cell to the controlled change in the outside lactose concentration  7.69  Effect of recycle rate on the lactose concentration inside the cell.  178 The  lactose concentration in the bulk solution ranged from 1857 to 1750 mg/1 7.70  Establishment of a steady state propionate concentration inside the cell (o) after a dilution. • - propionate concentration outside the cell . . . .  7.71  183  Establishment of a steady state butyrate concentration inside the cell (o) after a dilution. • - butyrate concentration outside the cell  7.72  184  Effect of recycle rate on propionate concentration inside the cell (o), • porpionate concentration outside the cell  7.73  Effect of recycle rate on butyrate concentration inside the cell (o), •  185 -  butyrate concentration outside the cell 7.74  185  Effect of recycle rate on the acetate concentration inside the cell (o), • acetate concentration outside the cell  7.75  179  189  Establishment of a steady state acetate concentration inside the device (o) after a dilution, • - acetate concentration outside the cell  189  7.76  Top view of a methanogenic biofilm, (x 400)  197  7.77  Experimental determination of biofilm void fraction  199  7.78  Straight vertical channels (along the black and white boundary) in a section of an acidogenic biofilm (x  100).  T h e down black part is biofilm and  P V C support 8.79  8.80  200  Illustration of an optimum operation of biofilm reactors. No back- mixing of medium is assumed  209  Illustration of a process of three stages of cheese whey treatment  211  xix  A.81 E M P pathway of glucose conversion to pjTuvate. Key to the enzymes: E C 2.7.1.1: hexokinase; E C 5.3.1.9: glucosephosphate isomerase; E C 2.7.1.11: phosphofructokinase;  E C 4.2.1.13:  fructosebisphosphate aldolase; E C -  5.3.1.1: triosephosphate isomerase; E C 1.2.1.12: glyceraldehyde 3-phosphate dehydrogenase; E C 2.7.2.3: phosphoglycerate kinase; E C 2.7.5.3: phosphoglyceromutase;  E C 4.2.1.11:  Enolase; E C 2.7.1.40:  pyruvate kinase.  Source is [52]  232  A.82 Schematic representation of the cyclic (pentose shunt) and non-cyclic nature of the H M P pathway. Source is [52]. . A.83 H M P pathway of glucose utihzation.  233  S 7-P: sedoheptulose 7-phosphate;  G A 3 - P : glyceraldehyde 3-phosphate; D H A P : dihydroxy-acetonephosphate; E 4-P: erythrose 4-phosphate; tose 1,6-bisphosphate. 1.1.1.49:  F 6-P: fructose 6-phosphate;  K e y to the enzymes:  glucose 6-phosphate  dehydrogenase;  EC2.7.1.1:  F D P : fruc-  hexkoinase; E C  E C 3.1.1.17:  gluconolac-  tonase; E C 1.1.1.44: 6-phosphogluconate dehydrogenase; E C 5.1.3.1: ribulosephosphate 3-epimerase: EC  2.2.1.1:  transketolase;  E C 5.3.1.6: E C 4.1.2.13:  ribose 5-phosphate  isomerase;  fructose bisphosphate aldolase;  E C 3.1.3.11: hexose diphosphatase; E C 5.3.1.9: glucose 6-phosphate isomerase. Source is [52]  234  A.84 E D pathway of glucose utihzation. T h e abbreviations as in H M P pathway.  K e y to the enzymes: E C 2.7.1.1: hexokinase; E C 1.1.1.49: glucose  6-phosphate dehydrogenase; E C 3.1.1.17: gluconolactonase; E C 4.2.1.12: phosphogluconate dehydratase;  E C 4.1.2.14:  phospho-2-  keto-3-deoxy-  gluconate aldolase; E C 2.2.1.1: transketolase;  E C 2.2.1.2:  transaldolase;  E C 5.1.3.1: ribulosephosphate 5- phosphate isomerase. Source is [52]. . .  xx  235  A.85 P K pathway of hexose and pentose utihzation. K e y to the enzymes: E C 2.7.1.1: hexokinase; E C 1.1.1.49: glucose 6-phosphate dehydrogenase; E C 3.1.1.17:  gluconolactonase;  E C 1.1.1.44:  phosphogluconate dehydroge-  nase; E C 5.1.3.1: ribulose phosphate 3-epimerase; E C 2.7.1.15: ribokinase; E C 5.3.16: ribosephosphate isomerase; E C 5.3.1.3:  arabinose isomerase;  E C 2.7.1.47: ribulokinase; E C 5.3.1.5: xylose isomerase; E C 2.7.1.17: xylulokinase; E C 4.1.2.9: phosphokeitolase; E C 2.7.2.1: acetokinase. Source is [52]  236  A.86 Formation of acetate from pyruvate.  1, Degradation of fructose via the  Embden-Meyerhof-Parnas pathway; 2, pyruvate-ferredoxin oxidoreductase; 3, phosphotransacetylase plus acetate kinase; 4, formate dehydrogenase; 5, formyl-tetrahydrofolate synthetase; 6, methenyl-tetrahydrofolate cyclohydrolase; 7, methylene- tetrahydrofolate  dehydrogenase; 8, methylene-  tetrahydrofolate reductase; 9, tetrahydrofolate: B i methyltransferase; 10, 2  C O dehydrogenase; 11, acetyl-CoA-symthesizing enzyme; [CO], enzymebond. Source is [54]  237  A.87 Butyrate formation from pyruvate by Clostridia.  K e y to the enzymes: 1,  pyruvate-ferrodoxin oxidoreductase; 2, acetyl-CoA-acetyl transferase; 3, 3hydroxybutyryl-Co A dehydrogenase; 4, 3-hydroxyacyl-CoA hydrolyase; 5, butyryl-CoA dehydrogenase; 6, fatty acid C o A transferase. A.88 Formation of mixed products (ethanol, lactate, etc.).  Source is [52].  238  1, enzymes for the  E M P pathways; 2, lactate dehydrogenase; 3, pyruvate- formate lyase; 4, formate-hydrogen lyase; 5, acetaldehyde dehydrogenase; 6, alcohol dehydrogenase; 7, phosphotransacetylase;  8, acetate kinase; 9, P E P carboxy-  lase; 10, malate dehydrogenase, fumarase and fumarate reductase. is [54]  Source 239  xxi  A.89 Formation of propionate from pyruvate or lactate. nase; 2, pyruvate-ferredoxin oxidorecuctase; 4, acetate kinase; 5, Ds-methylmalonyl-  1, lactate dehydroge-  3, phosphoacetyl transfrase;  CoA-pyruvate transcarboxylase;  6, malate dehydrogenase; 7, fumarase; 8, fumarate reductase; 9, succinylC o A transferase; 10, L R - methylmalonyl-CoA mutase; 11, methylmalonylC o A racemase;  12, pj^ruvate-phosphate dikinase; 13, PEP-carboxytrans-  phosphorylase. Source is [52]  240  B.90 Standard curve of lactose concentration vs absorbance at 480 nm, T h e line is calculated from the equation: S i  act0  j , e = 120.3369 'absorbance' - 0.07461. 243  B.91 Standard curve of lactate concentration vs absorbance. T h e line is calculated from the equation: S i  a c t a t e  = 12.0048 'absorbance 4 - 0.005522.  . . .  245  B.92 A typical calibration curve of acetate  247  B.93 A typical calibration curve of propionate  248  B.94 A typical calibration curve of butyrate  248  B.95 A typical volatile fatty acid chromatogram. Residence time (min): ethanol (0.20); acetic acid (0.47); propionic acid (1.03); iso-butyric acid (2.10); butyric acid (3.01)  249  B.96 A typical chromotogram of gaseous samples. (0.26); methane (0.38); carbon dioxide (1.86) G.97 Flow chart of the direct search method  xxn  Residence time (min): air 250 267  Chapter 1  Introduction  Lactose, a major constituent of cheese whey, influences the technologies apphed to treatment of whey.  Whey is the residual watery portion of milk after removal of the curd  (cheese) during the cheese-making process. It is an opaque, greenish-yellow hquid with about 6 to 6.5 percent total sohds and a biological oxygen demand ( B O D ) of 32000 mg/1 or higher [1]. Treatment of this by-product is a really challenging problem to cheese manufacturers considering that 9 kilograms of whey are produced for each kilogram of cheese and over 277 million kilograms of cheese were produced in Canada and over 3 billion kilograms in North America in 1987  [2].  In recent years, growing concern about environmental  pollution has forced the manufacturers  to give up the conventional disposal methods  such as direct discharge into receiving waters [3], landfills [4], municipal sewage system [5] and adopt other more suitable methods. Obviously, the most satisfactory method is to re-use the organic components to reduce or ehminate the cost of treatment and disposal of whey.  1.1  U t i l i z a t i o n of L a c t o s e i n W h e y  As shown in Table 1.1, lactose is the principal component of whey, and consequently, utihzation of whey actually becomes  the utihzation of lactose although processes for  obtaining milk proteins by ultrafiltration techniques to allow their utihzation have been developed [6]. 1  2  Chapter 1. Introduction  Table 1.1: Major components of a typical whey Component  Composition (w/w %)  water  93.1  lactose  4.9  protein  0.9  lacto-globuhn lacto-albumin lummune-globuhns fat  0.3  lactic acid  0.2  ash  0.6  oxides of K N a Ca Mg Fe phsophrous pentoxide chlorine oxide sulfur trioxdde total solids  6.9  Source is [7].  Whey powders are produced by drying whey [8]. Also lactose can be separated from whey by the processes of concentration and crystallization. These products can be used as feed for animals or as substrate for biological processes (e.g. penicillin production) [9]. Obviously, a great amount of energy is consumed for the removal of about 93 percent water. Use of whey as a substrate for fermentations can upgrade the raw material into useful products such as yeast, alcohol, organic acids, vitamins, alcohohc beverages and vinegar by employing microorganisms that are able to utilize lactose [1]. A variety of procedures have been suggested for the growth of yeast (Saccharomyces fragilis)  i n whey [10], producing food- and feed-grade yeast or yeast-whey products  which, if properly produced, are highly nutritious, nontoxic sources of protein and vitamins and under the right circumstances  can find apphcation in human and animal  Chapter 1. Introduction  nutrition.  3  Whey has also been used to grow microorganisms which produce useful en-  zymes, including /3  — galactosidase [11].  Anaerobic growth of lactose utilizing yeast  (Kluyveromyces species) in whey converts lactose into ethanol [12], but a simple fermentation of whey produces a solution containing only ca 2% of ethanol, which is uneconomic to distill. Some dried whey permeate has been added to liquid whey giving a high concentration of lactose and thus of ethanol. It is clear that only economical reasons prevent the use of these approaches to treat whey. First of all, not all the whey produced is available for the uses mentioned above, since much cheese is made in small factories at scattered locations, making it impractical to transport the bulky whey to a centralized plant for processing. Moreover, for recovery systems the capital and operation costs are comparatively high because of the low concentration of lactose.  Finally, the supply of whey for re-use often exceeds the demand.  This situation has left many smaller cheese plants in an insecure position with regard to whey disposal, because economically acceptable alternatives to the re-use options have not been identified [13].  1.2  Anaerobic Methanation of Lactose  Anaerobic methanation is a biological digestion process in which various anaerobic bacterial species cooperate to convert organic materials (carbohydrates,  fats, proteins, etc) to  organic acids and finally a gaseous mixture of methane and carbon dioxide in the absence of molecular oxygen. In the past, broad scale applications of this process, a well known process in waste management  area, have been largely with the treatment of municipal  sewage sludge and animal residues to achieve waste stabilization and solid reduction. Compared with the processes of whey fermentation to products such as alcohol, yeasts, as mentioned above, the most distinctive advantage of whey anaerobic methanation is  Chapter  1.  4  Introduction  that the final product, methane, naturally separates from the hquid waste to save energy in downstream processing and is also useable in large quantities as a fuel without major modification to existing furnaces in the plants. Other advantages include no requirement for sterilization of the wastewater, low nutrient requirement  etc.  Compared to the aerobic treatment, lactose utihzation by anaerobic sludge also offers several distinctive advantages including: 1. lower sohds/sludge production, 2. highly stabilized waste biological sludge that, as a rule, can be easily dewatered, 3. no energy requirement for aeration, 4. production of methane, a useful end product. However, the conventional anaerobic processes suffer from a slow digestion rate and poor process stability (unstable performance,  susceptibility to shock loading) and rela-  tively long periods of time required to start up the process or recover from an unstable condition. To overcome these problems encountered in a convertional process of anaerobic digestion, the key role of cell immobihzation has been recognized and it was found that success of a biological treatment was directly related to the efficiency of cell immobihzation and/or retention because of the higher cell concentration which resulted in a lower reactor volume requirement and better stability. T h e use of biomass immobihzation has led to development of different configurations of anaerobic digesters such as anaerobic filter [14], fluidized/expanded bed reactor [15], and the upflow anaerobic sludge blanket ( U A S B ) digester [16] as illustrated in Figure 1.1. T h e bacteria attach and grow on an inert support material which is static in anaerobic filters (e.g.  rocks, plastics) and movable in fluidized/expanded bed reactors (e.g.  Chapter 1. Introduction  5  gas  -effluent  static supports^  effluent  particles recycle  influent  influent  (A)  (B)  effluent  granules •>> .1  (C) Figure 1.1: Illustration of configurations of anaerobic filter (A), fluidized/expanded bed (B) and upflow anaerobic sludge blanket (C)  Chapter 1.  Introduction  6  sands), forming slime bacteria films on the support and resulting in a long retention time and a high concentration of bacteria in the digesters. In U A S B reactors, under favorable chemical and physical conditions the bacteria flocculate to form granules with superior settling characteristics, bacteria in the reactors.  which gives a high concentration and a long retention time of For anaerobic methanation of whey or lactose, Switzenbaum  and Danskin [17], Boeing and Larsen [18] utilized the fluidized or expanded bed reactors.  Dehaast et al [19], van den Berg and Kennedy [20], Wildenauer and Winter [21]  applied upflow or downflow fixed film reactors. Reynolds and Colleran [22] used a hybrid sludge-bed/fixed-bed reactor which was actually a combination of a U A S B reactor and an anaerobic filter. Further understanding of the microbiology and biochemistry involved in the anaerobic methanation of soluble organic materials which will be discussed in the following chapter in detail has led to a two-phase process in which acid-producing bacteria and methane-producing bacteria are cultured in separated reactors because it is believed that the acidogens and methanogens have different biological properties and thus culture requirements.  Also in a two-phase process, more opportunities are offered for controlling  the flow of the substrates between the distinct groups of bacteria, and thus, producing a better match between them [23].  1.3  M o r e Considerations on Two-phase Methanation of Lactose  In a two-phase process, the first phase reactor contains acid-forming bacteria which ferment lactose to a mixture of mainly acetic, propionic and butyric acids. fast-growing bacteria (minimum doubling time around 30 min).  T h e y are  In the second phase  reactor, the bacteria can be divided into two groups, acetate-forming bacteria which convert propionic and butyric acids to acetate, and methane-forming bacteria which  Chapter 1. Introduction  utilize acetate and H2/CO2 to produce methane.  7  A l l of them grow very slowly, the  former having minimum doubhng times of 1.5-4.0 days and the latter of 2-3 days [24]. Figure 1.2 illustrates the concept of two-phase anaerobic digestion of wastes.  Gas " (CH + C0 ) 4  Influent (whey, lactose)  Intermediates (HAc, H B u , H P r ) Methane-forming Acid-forming Reactor Reactor  2  Effluent  Figure 1.2: Two-phase process of anaerobic digestion of organic wastes  A number of researchers have investigated the two-phase processes.  Some efforts  were focused on the methods of separating methanogenic from acidogenic species and on achieving and characterizing the resulting environment in each phase. Pohland and Ghosh [23] washed the methanogens out of the first phase reactor using kinetic controls. Investigations [25,26,27,28,29] have indicated that the environmental requirements of acidogenic and methanogenic (acetogens plus methanogens) phases are quite different from each other in terms of p H and oxidation-reduction potentials ( O R P ) . After comparing the performance of a conventional single-phase and a two-phase anaerobic digestion of soft-drink waste, Ghosh et al [30] indicated that phase separation could improve the operation stabihty as well as quality of product gas. Table 1.2 hsts the apphcations of the two-phase process in the treatment of various wastewaters. In design and operation of a two-phase biofilm process of anaerobic digestion of whey,  Chapter  1.  Introduction  8  Table 1.2: Pilot- and full-scale plants of two-phase anaerobic treatment of wastewaters Year  Industry  Location  Type  1977  Distillery  Belgium  Pilot  Capacity (kg C O D / d a y ) 180  (enzyme, alcohol) 1980  Beet sugar  West Germany  Pilot  45  1980  DistiUery  Belgium  Pilot  135  1981  Beet sugar  Belgium  Pilot  170  1981  Citric acid  West Germany  Pilot  120  1981  Beet sugar  West Germany  Pilot  1980  Flax retting  Belgium  Full-scale  350  1982  Starch-to-glucose  West Germany  Full-scale  20,000  1983  Yeast-alcohol  Netherlands  Full-scale  20,000  1984  Baker's yeast  France  Full-scale  7,000  (yeast, alcohol)  45  Source is [13,30,31].  further consideration are needed on several points, especially, the fermentation kinetics in each phase, mass transfer of substrates in the biofilms and build-up of anaerobic biofilms.  1.3.1  Kinetics in Each Phase Reactor  W h e n steady state operation in a two-phase system is estabhshed, the production of organic acids in the first phase reactor must be balanced by their consumption in the second phase reactor, otherwise, accumulation of these acids would lead to a "sour" process if the p H is uncontrolled. In this case more caustic solution will be consumed for controlling the p H of the second phase reactor i n a narrow neutral range with more organic acids appearing in the effluent in the form of salts.  Therefore, the knowledge  of yield and consumption rates of organic acids are essential for process development. Furthermore, the effluent from a cheese plant, as is well known, has a variable flow rate and B O D strength [3]. This requires the process have an operation range over which it  Chapter 1. Introduction  9  can withstand the normal feed fluctuations. T h e response of each phase reactor to feed fluctuations may be used for the determination of this operation range. Most of the experiments  conducted to date on the anaerobic methanation of lactose  or whey were designed to evaluate the performance of the process [17,18,19,20,21,22,32, 33,34,35]. Detailed biochemical kinetic information is virtually non-existent.  For other  substrates, some kinetic results of anaerobic methanation are available. However, most of them were obtained in single-phase processes which differ greatly from two-phase processes considering the effects of phase separation which results in a constant production of organic acids (e.g. propionic and butyric acids) i n the first phase, and correspondingly, a healthy population of obligate hydrogen-producing acetogens ( O H P A ) and associated hydrogen-oxidizing methanogens  ( H O M ) which ensured the rapid assimilation of those  acids in the second phase reactor [36].  1.3.2  Mass Transfer in the Biofilms  As discussed above, the biomass must be retained in reactors to make a long solid retention time (SRT) possible even at short hydrauhc retention times ( H R T ) and to maximize biomass concentrations  in the reactors, which has been fulfilled by developing three ma-  jor types of reactor configurations as shown in Figure 1.1. As biomass accumulates in the form of biofilms (anaerobic filters and fluidized/expanded beds) or granules ( U A S B ) in a reactor of specified volume, two problems may arise.  One is that the biomass will  form a solid phase in which the substrates are gradually consumed as they diffuse into the biomass, and so, the bacterial cells embedded in the film see different substrate concentrations. T h e combination of the consumption and the diffusion rates determines a effective thickness of biofilm beyond which no substrate is available to the bacteria.  Secondly,  since the living bacteria are continuously growing with the consumption of substrates even though the growth rate is relatively slow i n anaerobic processes, the actual H R T  Chapter 1. Introduction  10  majr be reduced to impractically low values due to the accumulation of active biomass (within an effective thickness) and/or dead biomass which reduce the available reactor volume. Because of these considerations, a knowledge of mass transfer within the acidogenic and methanogenic biofilms is necessary for the estimation of the most effective biofilm thickness for maximizing the biomass concentration as well as a long term stable operation. Compared with fluidized/expanded bed and U A S B , an anaerobic filter is more affected by mass transfer limitations because the biomass can be almost completely retained. This problem has been recognized by literature reports of phenomena caused by plugging and channehng in laboratory scale anaerobic filters [37,38].  In a full scale downflow  anaerobic reactor which contained three layers of clay blocks with square vertical channels as supports, treating an effluent from a dairy plant (1500 to 1800 m / d a y , 2000-3000 kg 3  BOD  5  or 4000-6000 kg C O D per day), the C O D removal decreased from a range of 60-80  % after the start-up period to 50 % and less at the end of 2 years when it was found that the active reactor volume had declined by 80 percent [3]. Based on observations of the long term performances of an anaerobic filter and a U A S B reactor and their abilities to prevent the accumulation of excess biomass, a hybrid reactor configuration (combination of these two types of reactor) was developed in Wastewater Technology Centre, Canada, in order to minimize the excess biomass accumulation and its impact on reactor hydraulics [39]. Obviously, a growing biofilm should be controlled at its optimum thickness so as to maintain effective and long term stable operation i n an anaerobic digestion process. Knowledge of mass transfer rates of substrates in anaerobic biofilms is essential to estimate this optimal biofilm thickness.  T h e majority of the studies on mass transfer in  biomass, however, has been concerned with aerobic microbial aggregates, because it was  Chapter 1.  Introduction  11  easy to recognize that O2 supply is limiting due to its low solubility in water. Few works have been conducted on anaerobic bacterial aggregates and to the author's knowledge, no report on the transport of lactose and organic acids in anaerobic microbial aggregates exists.  1.3.3  Start-up of Anaerobic Biofilms  One disadvantage of anaerobic digestion processes is that a relatively long time is needed for start up due to the very slow growth rate of anaerobic bacteria, especially the acetogens and methanogens.  A mature reactor is characterized by a well developed, immo-  bilized biomass (granules or biofilms). During the process of biofilm formation the first step is attachment of bacteria onto inert solid supports, which is affected by many factors such as bacterial strain, limiting nutrients, physio-chemical properties of the solid surfaces. T h e n the attached bacteria proliferate forming microcolonies, and a biofilm by the merging of these colonies. Start-up of an anaerobic process to a great extent nowadays still relies on industrial experience because of the complexity of the process. In a two-phase system, the acidogens grow fast and also form a biofilm more easily. T h e formation of a methanogenic biofilm (including acetogens), thus, becomes the ratelimiting step. Furthermore, it would also be interesting if the properties of solid supports would affect the relative attachment rates of each type of bacteria (acetate-, propionate-, and butyrate-degrading bacteria) when the supports are immersed in the mixture of these microorganisms. Choice of a solid supporter would then in part depend on the knowledge of its effect on the ease with which each group of bacteria attach on it. A number of studies on methanogenic film development have been conducted. Most of them were based on the total consumption rate of organic carbon [40], methane production rate [41], or total protein content of a biofilm [42], which can not answer the  Chapter 1. Introduction  12  question whether or not and how the surface properties influence the attachment of various bacterial types in a mixed culture.  Some researchers [43] used a single substrate  (acetate) to investigate the influence of sohd surfaces on biofilm development. This approach can only give partial information because it neglects the symbiotic relationship between bacteria.  1.4  Research Objectives and Scope  T h e two-phase anaerobic methanation of whey has been, as indicated above, demonstrated as a potentially successful process.  However, some further studies are needed,  especially on the three topics discussed above, if it is to become an economic, reliable, and stable alternate for the treatment of high B O D wastewaters. Kisaahta, L o and Pinder [44,45] have studied the acidogenesis of lactose in a continuous stirred reactor ( C S T R ) in which the bacteria were suspended. They found that the dilution rate and p H would affect the acidogenic product distribution which was assumed to be caused by a shift in the bacterial population. T h e present research is an extension of their effort to introduce the two-phase method for whey treatment and will be mainly focussed on immobihzed acidogenic and methanogenic bacteria. Specifically, the present study includes the following major topics:  1. Intrinsic kinetics of lactose acidogenesis and methanogenesis Under selected conditions (temperature,  p H , nutrients) which are based on the  results of Kisaahta [46] and others, investigate the utihzation rate of lactose and production rates of organic acids in a fixed-film acidogenic reactor, and conduct studies on the utilization rates of organic acids in a fixed-film methanogenic reactor. These results should be obtained under conditions where there is negligible effect  13  Chapter 2. Introduction  of external and internal mass transfer resistance. Also, some studies will be made on the responses of these two reactors to feed fluctuations. 2. Mass transfer of lactose in acidogenic biofilms and organic acids in methanogenic biofilms Mass transfer within active biofilms is a very comphcated process because it involves both mass transfer and reactions. Some researchers have described the influence of mass transfer on reaction with macro-kinetics which included both intrinsic kinetics as well as mass transfer and gave an overall reaction of half order [47]. Some studied a simplified biofilm which was deactivated to eliminate the influence of reaction on mass transfer. T h e present research will use a speciaUy designed device to measure directly the substrate concentration drop within living biofilms. of substrates (lactose,  T h e diffusivities  acetate, propionate and butyrate) in their corresponding  biofilms will be found by using a reaction-diffusion model which describes the mass transfer process of these substrates in anaerobic biofilms. 3. Start-up of symbiotic methanogenic biofilms Considering that many factors can effect the start-up of biofilms, this research will concentrate on the effect of sohd surfaces, in terms of their water contact angles (0 - 1 0 0 ° ) , on the attachment of acetogenic and methanogenic bacteria groups. Some efforts will be made to estabhsh a model to describe the start-up of a symbiotic methanogenic biofilm.  Chapter 2  Theoretical Aspects and Previous Studies  2.1  Process Biochemistry and Microbiology  Anaerobic digestion is usually considered to be a two-phase process consisting of acidformation (acidogenesis)  and methane-formation (methanogenesis).  It has been known  that at least three large, physiologically different, bacterial populations must be present for the overall conversion of organic matter to methane and carbon dioxide to occur. In the first phase, organic matter (proteins, hpids, carbohydrates)  are converted by a  heterogeneous group of microorganisms into fatty acids by hydrolysis and fermentation. In the second phase, the end-products of the first phase fermentation are converted to methane and carbon dioxide by strict obligate anaerobic bacteria (methanogenic bacteria) with the assistance  from another group of bacteria termed acetogenic  bacteria.  The  latter can convert the compounds the methanogenic bacteria cannot digest into acetate, dihydrogen and carbon dioxide which can be utilized by methanogenic bacteria. If the hydrolysis of biopolymer molecules is the slowest step (e.g. cellulose hydrolysis) in the whole process, the fatty acids produced in the first phase would not be accumulated in the culture medium due to their being digested by methanogenic bacteria. the organic matter, however, is readily hydrolyzed (e.g.  If  lactose which can be directly  transported into microbial cells), the slowest step becomes the methanogenesis of fatty acids. It would then be possible that the fatty acids may not be digested rapidly enough by methanogenic bacteria and their accumulation in the culture medium would lead to  14  Chapter 2.  Theoretical  15  Aspects and Previous Studies  HO-CH2  HO-CH  2  6(1-4) D-Galactose  D-Glucose  Figure 2.3: Illustration of lactose structure an undesirable 'sour' process and no gas is produced [46]. 2.1.1  Lactose Acidogenesis  Lactose, a reducing disaccharide, is constructed from a galactose residue and a glucose residue. The glycosidic hnk is 8(1 —• 4), which means that the OH group on the anomeric carbon atom of galactose is in /3 position as shown in Figure 2.3. Although the anomeric atom on galactose residue is involved in the glycosidic bond, the anomeric carbon atom (Cl) on the glucose residue can still participate in forming a free aldehyde group and thus the free carbonyl oxygen can reduce a number of substances, for example, divalent copper ( C u ) to the monovalent species (Cu ). This reducing ++  +  capacity of lactose has been used in this study to measure its concentration in a culture medium. The /3(1 —> 4) glycosidic hnk may have a significant effect on the properties of lactose, which can be projected by comparing the properties of cellulose and amylose (a type of starch having straight carbon chains). Cellulose is constructed from repeating units of D glucose held together by 3(1 —> 4) glycosidic bonds and amylose by a(l —> 4) glycosidic  Chapter 2.  16  Theoretical Aspects and Previous Studies  a (1-4)  £ (1—4)  Figure 2.4: Illustration of two types of glycosidic links bonds (Figure  2.4).  This subtle difference, however, results in a significant difference in the physical properties of the two types of polysaccharides; starch, a storage form of cellular fuel which is quite easily digested by mammals, yeasts or bacteria, and cellulose, a structural element of plant cells which cannot be hydrolyzed by most mammals, including humans. microorganisms  capable of secreting the enzyme cellulase can hydrolyze the 8(1  The —> 4)  link of cellulose into D-glucose. Breakage of the lactose 8(1  —* 4) glycosidic bond involves a special enzyme, 8  -  galactosidase, coded and controlled by a segment of D N A in bacteria termed lac operon. Studies of the structure of the lac operon in Escherichia coli clearly demonstrated  the  whole process for producing the enzymes required for lactose transport and metabolism. A diagram of the lac operon is shown in Figure 2.5  [48].  Chapter 2.  17  Theoretical Aspects and Previous Studies  i  control sil .es i P  i  structural genes  o  a  section of prokaryotic D N A  Lactose operon  I-  L,Operator gene: 1  binds repressor protein  —Promotor site: binds R N A polymerase  ' — Regulatory gene: codes for repressor protein  Figure 2.5: Structure of lac operon  T h e lac operon consists of three distinct parts: the regulatory gene (i), the operator gene (o) and the structural genes (z, y, a).  T h e structural genes (z, y, a) code for  three separate enzymes involved with lactose metabolism. T h e 'z' gene codes for (3 — galactosidase, the enzyme that hydrolyzes lactose into glucose and galactose for further use in energy production.  CHaQH  CH OH  ChfepH  HO  ^ 6  2  Galactosidase HO  1  z  Lactose  Galactose  Glucose  T h e 'y' gene codes for galactoside permease, the enzyme that mediates the transport of lactose into the cell, which means that the hydrolysis of lactose occurs in the cell's cytoplasm rather than in the culture medium. T h e 'a' gene codes for galacoside acetylase (function unknown). A textbook [48] should be consulted for how the E coli cell mediates the transport and metabolism through the regulatory and operator genes. T h e glucose  Chapter 2.  Theoretical Aspects and Previous Studies  Table 2.3:  Aerobes Facultative Anaerobes  Obligate Anaerobes  18  M a i n genera of acid-producing bacteria implicated in first phase Genus  Substrate  Products  Pseudomonas Micrococcus Bacillus Lactobacillus Escherichia Clostridia Ruminococcus Bacteroides Butyrivibrio Megasphera Selenomonas Desulfobibrio Bifidobacteria Propionibacterium Anaerovibrio  nutritionally highly versatile starch  lactate  starch maltose  lactate  numerous sugars  acetate  numerous sugars succinate, acetate cellulose, cellobiose  ethanol, hydrogen  hemicellulose, pectin  formate  starch  butyrate, lactate  lactate, glucose  branched V F A , hydrogen  sugars  acetate, propionate  lactate, malate  acetate  proteins  VFA  amino-acids  propionate  Source is [49].  and galactose in the bacterial cells undergo further various reactions depending on the bacterial species present. T h e bacteria isolated from the anaerobic digestion mixture of the first phase include a wide range of physiological groups as shown in Table 2.3. Whether all the different isolates obtained by various workers are physiologically significant in the digestion process still remains to be determined. However, the presence of various genera in a mixed culture can supply various enzymes crucial to the hydrolysis and fermentation of various organic materials.  This is especially desirable in a process  for wastewater treatment which may contain many kinds of organic wastes. Moreover, whether a bacterial species can survive and dominate in a digester depends greatly on the environmental conditions (temperature, p H , nutrients, etc.) ing energy from the environment.  and its efficiency of extract-  T h e more energy it is able to get from the nutrients,  Chapter 2.  Theoretical Aspects and Previous Studies  the faster it will grow.  19  Presence of aerobes and facultative anaerobes in anaerobic di-  gesters was explained by McKinney [50] by the ease of growth of the facultative bacteria which gives them an edge over the strict anaerobes and so the acid-formers are made up predominantly of facultative bacteria with a few strict anaerobes.  T h e oxygen needed  for growth of facultative anaerobic bacteria may come from the dissolved oxygen in the feed solution. After they developed a method to enumerate obhgate anaerobic acidogenic bacteria in digesters, Toerien et al [51] reported 3 9 x l 0 non-methanogenic and 8 x l 0 in several digesters.  5  to 1 x 1 0  s  7  to 1 5 x l 0  9  obhgate anaerobic  aerobic and facultative anaerobic bacteria per ml  T h e anaerobic counts were usually 100 or more times greater than  the aerobic counts. Post et al [52] also reported the presence of a large obhgate anaerobic bacterial population in anaerobic digester. While so many bacterial species are present in a digester, glucose and its epimers (galactose, mannose etc.) recognized routes  are catabolized to pyruvate anaerobicaUy by four currently  [53].  ct Embden-Meyerhof-Parnas ( E M P ) pathway. • Hexose monophosphate ( H M P ) pathway, o Enter-Doudoroff ( E D ) pathway. • Phosphoketolase ( P K ) pathway. Through the use of  1 4  C tracers, M c C a r t y et al [54] concluded that both E M P glycolysis  and hexose phosphate pathways probably mainly occurred in anaerobic digesters receiving carbohydrates.  Among the four pathways, the E M P pathway provides bacteria with  the greatest amount of A T P under anaerobic condition [53].  Glucose + 2 A T P + 2 N A D + — • 2Pyruvate + 4 A T P + 2 N A D H +  2H+  Chapter 2,  Theoretical Aspects and Previous Studies  20  But it does not produce the important precursors for purine, pyrimidine, D N A and R N A biosynthesis.  In contrast, the H M P pathway produces all the precursors necessary for  these important biomolecules, giving half the amount of A T P . Microorganisms growing on simple defined media such as glucose (or lactose) plus mineral salts must use other pathways such as the H M P pathway if they are not supplied with growth factors. T h e ratio of usage of the E M P and H M P pathways can vary greatly depending on environmental conditions. Biological activities of living cells involve catabolic and anabobc pathways. Catabolic pathways are the degradative reactions through which nutrient molecules are degraded into simpler molecules, releasing chemical energy. processes in which various cellular constituents  Anabolic pathways are biosynthetic  are synthesized from simpler precursor  molecules and require the input of chemical energy. T h e whole process is accomplished by what are known as coupled reactions usually catalyzed by enzymes.  T h e released  chemical energy is trapped in the form of an energy-rich intermediate and used to drive a second reaction. Adenosine triphosphate ( A T P ) is the primary energy carrier in all life forms. As nutrients are broken down, some of the free energy contained in those molecules is conserved in the form of A T P . W h e n cells must synthesize various molecules, free energy is required to make the new bonds; this energy is supplied by the A T P molecules. Specifically, A T P hydrolyses into adenosine diphosphate ( A D P ) and inorganic phosphate, releasing a significant amount of free energy.  A T P + H 0 — » A D P + Pi 2  ( A G = - 7 . 3 kcal/mol) 0  T h e standard conditions specified in this thesis are; one atmosphere for each  gaseous  components, all other compounds in aqueous solution at 1 M activity at p H of 7.0 and 25 °C. Details of the four routes can be found in Appendix A . T h e other points of importance  Chapter 2.  Theoretical Aspects and Previous Studies  21  in the sequence of the E M P glycolysis are emphasized here because its product, pyruvate, is the key component for further reactions in acidogenesis. • Glucose has first to be activated and converted to a phosphated fructose by consuming two A T P molecules. • After the fructose is split into two triosephosphates, is coupled to the reduction of a electron/hydrogen  the oxidation of the trioses  carrier, nicotinamide adenine  dinucleotide ( N A D ) o In the subsequent steps to pyruvate, a total of 4 moles of A T P are formed. T h e reduced N A D  must be regenerated by some mechanism, which to a great extent  +  determines the final fermentation product distribution. In addition to 2 moles of pyruvate and A T P , the glycolysis gives 2 moles of reduced NAD  +  ( N A D H ) which must be reoxidized under anaerobic conditions for repeated use.  NAD+ + H  2  ^ NADH +  H+  Depending on the mechanisms by which they oxidize the reduced N A D , the acidogenic bacteria give rise to a diversity of products by further metabolism of pyruvate (see Figure 2.6).  These reactions permit an overall oxidation-reduction balance to be preserved  under anaerobic conditions. The change in free energy during the reoxidation of N A D H into N A D comes negative only when the partial pressure of hydrogen drops below 1 0  -3  +  and H  2  be-  atmospheres  [180]. Thus a low hydrogen partial pressure can pull the overall metabohsm towards the formation of H , C 0 2  2  and acetate.  O n the other hand, higher values of hydrogen par-  tial pressure will inhibit the oxidation of N A D H and then it must be reoxidized by the reduction of pyruvate or acetyl-CoA, forming reduced products such as lactate, ethanol,  Chapter 2.  Theoretical Aspects and Previous Studies  Acrylate \»  Lactate  -2H  Pyruvate  22  A Acetaldehyde -2H  j Oxaloacetate j -2H  Ethanol  ! Malate j  ! Formate i -f I Acetyl C o A i 4 -2H H, I Succinate j  Propionate Acetone  IButyryl C o A l -  -f A T P Butyrate  Figure 2.6:  Bacterial fermentation  products of pyruvate.  Pyruvate formed by the  catabohsm of glucose is further metabolized by pathways which are characteristic of particular organisms. E n d products of fermentations are shown in boxes and intermediates in dash boxes. " - " refers to consumption and "+"  to production.  Chapter 2.  Theoretical Aspects and Previous Studies  propionate and butyrate.  23  Among them, some products (acetate, butyrate) give rise to  additional energy by substrate-level phosphorylations, e.g. the conversion of an acetylC o A derivative to free acid,  C H 3 C O - S C 0 A + A D P + Pi — • C H 3 C O O H + A T P +  C H C H C H C O - S C o A + A D P + P; —> 3  2  2  SCoA  CH CH CH COOH + ATP + 3  2  SCoA  2  Some reactions (formation of lactate, ethanol, etc), however, can not produce extra A T P and only keep oxidation-reduction in balance by oxidizing the reduced N A D . +  C H 3 C O C O O H + N A D H + H+ — • C H 3 C H O H C O O H +  The effect of environments (pH, temperature, tion products is also quite significant.  etc.)  NAD+  on the distribution of fermenta-  As the culture p H drops, it becomes more and  more difficult to reoxidize N A D H from the point of view of energetics.  Therefore, the  production of acetate as sole end product would not be satisfied, and bacteria will utihze pyruvate not only to form acetate but also butyrate, a weaker acid than acetate. If the p H drops below 4, some neutral compounds are produced such as butanol and acetone. If the environmental conditions are not favorable to a bacterial species, its characteristic product from the fermentation of pyruvate apparently would not occur. Hungate [56] first expressed the idea that hydrogen production and utihzation could profoundly influence the course of a fermentation in anaerobic ecosystems.  T h e regulatory  role of hydrogen in the course of anaerobic fermentations is effected by interspecies hydrogen transfer, induced by hydrogen-trophic organisms (methanogenic bacteria), to pull the reactions toward the direction in which more hydrogen is produced. In a two-phase process, the acid-formation and methane-formation phases are physically separated and the hydrogentrophic methanogens are not present in the first phase reactor because of some  Chapter 2.  Theoretical Aspects and Previous Studies  24  Table 2.4: Classification of seven genera of methanogenic bacteria Order I  Substrate  Genus  Morphology  Gram  Methanobacterium  long rods to  +  H /C0 ,  formate  +  H /C0 ,  formate  -  H2/CO2,  formate  filaments M ethanobrevibcter  short rod to lancet cocci irregular and  2  2  2  2  II  M ethanococcus  III  M ethanomicrobium  short rods  -  H /CO2-,  formate  M ethanogenium  irregular  -  H /C0 ,  formate  -  H2/CO2,  formate  +  H /C0 ,  methanol  small 2  2  2  small cocci Methanospirillum  short to long wavy spirilla  M ethanosarcina  pseudosarcina  2  2  acetate, methylamine  Source is [57].  deliberately chosen conditions (low p H , low hydraulic residence time etc.). Therefore, it is essential to investigate the rate and product distribution of lactose fermentation in a separated acidogenic biofilm reactor without effects from hydrogentrophic methanogens.  2.1.2  Methanogenesis of Fatty Acids  Methanogenic bacteria are members of a very distinct group of bacteria with respect to their physiology and ecology. T h e y are present in extremely anaerobic environments like the rumens, sewage sludge digesters and anoxic muds and sediments. They are the terminal organisms in the anaerobic transformation of the substrates available in such environments.  A taxonomy, to replace an old one based on bacterial morphology, has  been recently adopted which is based on the structure of their 16S ribosomal R N A (see Table 2.4). This molecule has changed very slowly during evolution, so any significant differences that are observed must indicate a very long evolution history.  Chapter 2. Theoretical Aspects and Previous Studies  25  Table 2.4 indicates that, based on the structure of 16S r R N A , there is a very great diversity among the methanogens. group of bacteria.  They are not a homogeneous and closely related  T h e unifying characteristic  of this bacterial group is that all mem-  bers are able to reduce carbon dioxide into methane as final product of their energetic metabohsm.  Growth on CO2 as carbon source is autotrophy, but the autotrophic  growth of the methanogens is totally different from that of virtually all phototrophs and chemoautotrophs  because it does not involve the ribolase bisphosphate (Calvin) cycle.  As a consequence, they have been classified into a group of bacteria called archbacteria which is distinct from the "Classical" procaryotes.  In this group, extreme halophiles  (Halobacteriaceae ) and thermoacidophiles (Sulfolobus) have also been placed [58]. T h e methanogens  are strict  obhgate anaerobes,  but they are capable of existing  well in close association with other classes of bacteria which are capable of removing oxygen.  Kiener and Leisinger investigated the sensitivity of five methanogenic  bacte-  ria (belonging to four genera) to oxygen [59]. T h e death curves of Methanobacterium  thermoautotrophicum , Methanohrevibacter arboriphilus and Methanosarcina barkeri were biphasic. For these strains, exposure to air for 10 to 30 hours was without effect on their survival. U p to a critical time of contact, oxygen apparently caused no or only reversible damage on these organisms. For the two methanococci species ( M . voltae and M. vannielii), however, the number of surviving cells upon exposure to air dropped exponentially without lag. T h e three comparatively robust strains were originally isolated from sludge digesters, i.e. ecosystems which are periodically subjected to oxygen stress and therefore may favour the development of air-tolerant methanogenic bacteria. In contrast to them, the two Methanococci strains were highly sensitive to oxygen.  Sea and  lake sediments, the natural habitats of Methanococci , are not exposed to oxygen thereby providing a safe environment for these highly oxygen sensitive methanogens. This information is very useful for judging the extent to which strictly anaerobic conditions should  Chapter 2.  Theoretical Aspects and Previous Studies  26  be kept in handling methanogens. A l l methanogenic bacteria are capable of extracting  energy from the oxidation of  dihydrogen under anaerobic conditions using carbon dioxide as electron acceptor. 4H  2  + H C O J + H+ —>  C H + 3H 0 4  ( A G ° = - 1 3 8 . 9 kJ)  2  (2.1)  T h e initial reduction of carbon dioxide to the level of formaldehyde is thermodynamically unfavorable whereas further reduction of formaldehyde to methane is very favorable, and the standard free energy change of the reaction would theoretically support the formation of two molecules of A T P . T h e dihydrogen-dependent reduction of C 0  2  requires an  anaerobic electron transport pathway. The exact nature of the electron carriers involved in this pathway has not yet been determined. A methyl carrier, coenzyme M , has been detected in all methanogenic bacteria and appears to be unique to this group of organisms [60].  A n early labelled reduction product of  1 4  C0  2  that can be detected in whole  cells or in the extract of methanogenic bacteria is methyl-coenzyme M . It is believed that this compound is the substrate for the final step in methane production catalyzed by m e t h y l - C o M reductase  [61].  CH -SCoM + H 3  2  —• CH + 4  HSCoM  Methanogens differ from other autotrophs (organisms that proliferate with C 0 sole carbon source) in that their C 0  2  2  as the  metabohsm involves both fixation to cell carbon  and reduction to methane. A t present, httle is known about the initial reactions involved in C 0  2  reduction to methane and fixation into cellular intermediates.  The biochemical mechanism of methane formation from organic acids (the major products of the acid-formation phase) and its couphng to A T P synthesis is virtually unknown. Recently, a fluorescent electron transfer coenzyme (coenzyme F found in all methanogens but has not been detected  elsewhere.  F  4 2 0  4 2 0  ) has been  participates  as  an electron carrier in the nicotinamide adenine dinucleotide phosphate ( N A D P ) hnked  Chapter 2.  Theoretical Aspects and Previous Studies  27  hydrogenase and formate dehydrogenase systems in methanogens  [62].  Thus, formate  and hydrogen are essentially equivalent sources of electrons for the reduction of carbon dioxide to methane. In anaerobic digesters, the major source of methane appears to be acetate rather than carbon dioxide or formate even though only a few methanogenic species are able to use acetate as their energy and carbon source.  Estimations based on carbon isotope  labelling indicate that 67 to 75 per cent of the methane is derived from acetate [63,64]. Methanosarcina  barkeri,  one of a few species having a wider substrate spectrum, has  shown its ability to use acetate, methanol and methylated amines as sole carbon and energy source instead of H / C 0 . 2  2  It has been confirmed by labelling acetate that its  methyl group during the fermentation is transferred intact into methane; evidence of the acetate being oxidized first to C 0 CH3COOH — • C*H  4  + C0  2  [65,66]. ( A G ° = - 3 2 kJ/mol)  2  there is no  (2.2)  Conservation of the protons in the methyl moiety strongly suggests that methane production from acetate was attained via a single reduction step by a single organism. Under standard conditions, the acetate conversion to methane can only offer limited energy. Therefore, acetate-fermenting  methanogens would be inherently slow growing, and it  would be questionable if fermentation of acetate alone would sustain the energy requirements for growth.  Values reported for the free energy of A T P hydrolysis have been  estimated to range from -34.4  to -52.4  k J / m o l at physiological conditions. Normal ef-  ficiencies of energy transfer in bacteria are 30 to 50 per cent.  Thus, the reactions that  yield less than -49 k J / m o l at standard conditions makes the formation of an energy-rich compound via substrate level phosphorylation unhkely and is insufficient for cell growth [67]. "Highly purified" cultures of Methanosarcina showed a very slow acetate fermentation [68].  barkeri and Methanococcus species  Isotopic tracer studies by Zeikus et al  [69] indicated that hydrogen was required for the metabolism of acetate to methane by  Chapter 2.  Theoretical Aspects and Previous Studies  28  several pure cultures. Comparing the energy formed per mole of methane produced from reactions 2.1 and 2.2 shows that approximately four times as much energy is available from respiration of hydrogen than that from acetate fermentation.  Adding hydrogen to  pure acetate fermentation cultures not only raises the actual free energy released from the acetate fermentation due to decreased CO2 concentration but also supplies more free energy for bacterial growth from the reduction of carbon dioxide.  Alternatively, The  methanogenic species which are capable of utilizing acetate may possess a mechanism through which sufficient free energy can be accumulated from the fermentations of more than one acetate molecule and then the energy is used to produce A T P . As a result, up to 70 per cent methane is produced from the reaction of acetate fermentation. In mixed cultures, more complexly, the acetate utilization was affected by many factors such as ions strength, redox potential of the culture [71] and even the presence of sulfate-reducing species  [70]  2.1.3  Acetogenesis of Fatty Acids  As discussed above, the substrate spectra of methanogenic bacteria are very narrow, only including H / C 0 , formate, 2  methanol, methylamide and acetate, while the end  2  products from the first phase (acids-formation) include a large number of organic acids containing more than two carbon atoms (propionate,  butyrate,  etc.)  which can not  be directly utilized by methanogenic bacteria. A third group of bacteria must exist as a bridge between the acidogenic and the methanogenic microbes. These obligate hydrogenproducing bacteria,  acetogens, are able to convert the chemical compounds (ethanol,  propionate, butyrate, etc.) that the methanogens cannot utilize to acetate, C 0  C H C H O H + H 0 —-> C H 3 C O O - + H+ + 2 H 3  2  2  C H C H C O O - + 3 H 0 —> 3  2  2  C H C O O - + H+ + 3 H 3  2  2  + HCOJ  ( A G = +9.6 0  2  and H . 2  kJ)  (Ac7° = +76.1  kJ)  Chapter 2.  Theoretical Aspects and Previous Studies  C H C H C H C O O - + 2 H 0 —> 3  2  2  2  2 C H C O O - + H+ + 2 H 3  29  2  ( A G = +48.1 0  kJ)  Thermodynamically, however, these reactions are unfavorable under standard conditions (AG  0  > 0) and move towards the right only under a very low partial pressure of hydrogen  (below 10~  atmospheres)  4  [72].  This can be accomplished by the action of hydrogen-  trophic bacteria such as methanogens or sulfate-reducing bacteria.  Thus, the acetogens  and methanogens constitute a symbiotic association; the former needs the latter to remove H  2  to create a favorable environment and the latter can obtain their  (acetate, H / C 0 ) from the metabolic products of the former. 2  2  substrates  This advance in the  knowledge of anaerobic digestion goes back to the classical studies of Bryant, Wolin and Wolfe [73] who reported in 1967 that "Methanobacillus omelianskii''\ a species capable of producing methane from ethanol, was actually a symbiotic association of two different species. Microscopic observations suggested that M. omelianskii consisted of two organisms of different shape.  W h e n the organisms were separated, one, a methanogen later  named Methanobacterium bryantii, grew on hydrogen and carbon dioxide but no other substrates. The  T h e other species, S organism oxidized ethanol to acetate and hydrogen.  electrons generated from this oxidation were transferred to a pyridine nucleotide  carrier ( N A D  +  ) and ultimately used to reduce protons to molecular hydrogen. T h e sig-  nificance of this study is their speculation that alcohols other than methanol and fatty acids other than acetate and formate are not catabobzed by methanogens, but by another group of nonmethanogenic bacteria.  Later, Mclnerney et al (1981) [75] obtained  Syntrophomonas wolfei, an anaerobic butyrate-oxidizing bacterium in co-culture with either a hydrogenotrophic sulfate reducer or a hydrogenotrophic methanogen.  A syn-  trophic association of an anaerobic propionate oxidizer in co-culture with a hydrogentrophic organism was reported by Boone and Bryant (1981) [76]. currently known mesophilic acetogens.  Table 2.5 lists the  Chapter 2.  Theoretical Aspects and Previous Studies  30  Table 2.5: Currently known mesophilic obligate proton-reducing bacteria  Organisms  Co-culture with  Habitat  Substrate  Syntrophobacter  Desulfovibrio  digester  propionic acid  digester,  monocarboxylic saturated  sediments  fatty acids (14-8 C )  digester,  Benzoic acid  wolinii  Gil or  M. hungatei 4 - D.  Syntrophomonas  Desulfovibrio  wolfei  M. hungatei  Syntrophus  Desulfovibrio  buwellii  Gil,  M. hungatei + D. Desulfovibri  Gil  Gil,  Gil  digester,  monocarboxylic fatty  M. hungatei M1H  sediments  acids (to 11 C)  Strain Gra I val  Desulfovibrio E70  marine  isovaleric acid  Strain Go I val  Desulfovibrio  digester  Strain SF-1,  M. hungatei or  digester  Clostridium bryantii  E70,  sediments  sediment NSF-2  Desulfovibrio sp. Strain BZ-2  Desulfovibrio PS-1  isovaleric acid monocarboxylic saturated fatty acids (4-6 C )  digester  benzoic acid  Methanosporillum sp. Source is [74].  A direct cell count of co-cultures of Syntrophomonas wolfei with Methanospirillum hungatei fed with butyrate indicated that the former made up 30 per cent of the population versus the latter 70 per cent [78]. T h e growth rate of acetogens is very low as shown in Table 2.6 with or without sulfate-reducing bacteria (SRB) as co-culture.  Table 2.6: Growth rate of obligate H - p r o d u c i n g actogens 2  Organism  Substrate  p, (day  l  )  p (day  l  )  Reference  with S R B  without S R B  Syntrophobacter wolinii propionate  0.192.  0.103  [76]  Syntrophomonas wolfei  butyrate  0.307  0.185  [75]  Syntrophus buswillii  benzoate  0.127  0.101  [77]  Chapter 2. Theoretical Aspects and Previous Studies  Obviously, the sulfate-reducing bacteria  31  can promote the growth of obhgate  Re-  producing acetogens because of a much faster removal of the hydrogen released at the expense of some energy and carbon source ( H , acetate, etc.) 2  consumed by sulfate-  reducing bacteria. Hardly any information is presently available on the biochemical pathways in acetogens, as pure cultures are not yet available. Tracer studies with enrichment cultures that converted propionate to methane and acetate [79] showed that the C - l a b e l e d car14  boxyl group exclusively appeared in carbon dioxide whereas the accumulated acetate was practically free of labeled carbon. Both [ 2 - C ] and [3- C]-propionate lead to the 14  14  production of radioactive acetate. T h e methyl group and the carboxyl group of the acetate produced were equally labeled, regardless of whether [ 2 - C ] or [3- C]-propionate 14  14  had been used. These observations suggested that propionate was degraded through a randomizing pathway. O f the three reactions mentioned above, propionate oxidation is thermodynamically the most unfavorable, and so, propionate is not easily digested in the methanogenesis phase and occurs i n the effluent in quite high concentrations, especially when the acidogenesis phase is producing a large amount of propionate due to some disturbance caused by changes in load, p H , temperature etc.. T h e anaerobic oxidation of butyrate in S. wolfei has been postulated to go via 3oxidation [75], but detailed labehng studies are lacking. However, the observation that the conversion of normal monocarboxylic saturated four to eight carbon fatty acids yields H  2  and acetate, or H  2  and acetate plus propionate is consistent with a /3-oxidation  mechanism for the degradation of fatty acids by Syntrophomonas wolfei. Selective lysing of cells of Syntrophomonas wolfei recently allowed Mclnerney and co-workers  [78] to  demonstrate the presence of enzyme activities consistent with a /3-oxidation pathway for butyrate degradation.  Chapter 2. Theoretical Aspects and Previous Studies  2.2  32  Start-up of Anaerobic Biofilms  T h e operational principle of anaerobic biofilm reactors is based on the fact that attachment of anaerobic bacteria which grow very slowly, to support surfaces prevents them from being washed out of the reactor. T h e startup of anaerobic biofilm reactors, however, is generally time consuming and often difficult partly because of the low growth rate of anaerobes, especially the methanogenic and acetogenic bacteria, and also due to the lack of understanding of the mechanisms underlying the process and the factors affecting the attachment of bacteria onto support surfaces.  T h e present status of the understanding  of the start-up of an anaerobic biofilm reactor is more experimental than theoretical [80].  2.2.1  Mechanism of Build-up of Bacterial Biofilms  Biofilm formation is the net result of depositional, metabohc and removal processes [81], including: 1. Cellular particles transport from bulk hquid to support surfaces. Bacteria, as particles (d = 1 pm) suspended in culture medium, can be transported to a surface by any one, or a combination of, the following mechanisms:  motihty  and chemotaxis; gravity; molecular diffusion (in laminar flow); and eddy diffusion (in turbulent flow). It is doubtful, in a nutrient-rich fermenter,  that chemotaxis  and gravity would play a significant role in transport of bacterial cells which have a density (1.05-1.1 g / c m ) very close to that of the medium. A n d so, molecular dif3  fusion and/or eddy diffusion may be the dominating mechanisms for cell particles transport in a laminar or turbulent flow situation [82,83]. T h e fluid flow velocity has two principal effects on the formation of biofilms; the shear stress which increases with increased velocity and a change in the flux of cells/nutrients across the boundary layer or viscous sub-layer which is compressed as the velocity increases.  Chapter 2. Theoretical Aspects and Previous Studies  Moreover, the concentration  33  of cells in the bulk aqueous phase may also play a  role to some extent. Bryers and Characklis [86] reported that under turbulent flow the deposition rate increased by a factor of 4.5 for a 5 times increase in cell mass concentration. 2. Microbial adhesion. Once bacterial cells are close to or on the surface, then irreversibly.  they adhere reversibly and  Zobell (1943) [84] observed that bacterial attachment was of-  ten reversible-that bacteria which appeared to have settled on a substratum could be washed off by a stream of water, and that firm attachment appeared to occur only after a bacterium had remained settled for several hours. T h e investigations of Marshall et al (1971) [85] supported this two-stage attachment theory, called 'reversible' and 'irreversible sorption' respectively. Reversible sorption is the initial stage of bacterial attachment when the bacterium, exhibiting Brownian motion, is only weakly held at the surface while irreversible sorption was a time- dependent stage, which is due to the synthesis of exocellular polymers bridging the bacterial and substratum surfaces. T h e fixed bacterial cell does not exhibit Brownian motion and is not removed by washing. 3. Colonization of the surface by growth of the organism and formation of a biofilm. After becoming firmly attached,  the cells multiply and are joined by additional  attaching cells, which leads to the formation of microcolonies. These isolated points of growth eventually unite to form a continuous layer of microbial mass, i.e. a biofilm. 4. Detachment of the microbial film due to shear force and sloughing.  Chapter 2.  Theoretical Aspects and Previous Studies  34  Generally, sloughing and/or biomass decay more likely occur in a thick biofilm due to lack of nutrients in deeper layers while in the period of startup of biofilm or of a thin biofilm, the removal caused by shear force may predominate [87]. A dynamic equilibrium is maintained when steps 3 and 4 are occurring at the same rate. T h e attachment of bacteria to sohd surfaces in aqueous solution is affected by many factors since it involves three components: the bacterial surface, the sohd substratum, and the surrounding liquid phase.  A factor which can directly or indirectly affect one  of them would play a significant role in the process of attachment.  T h e influence of  bacterial cell surface on attachment, for example, is reflected in the fact that the attachment depends upon the growth conditions of the cells, such as the medium components [85], the hmiting nutrients [88], the dilution rate in a continuous culture [89] and growth phase in batch culture [90]. Some factors can influence more than one component, such as electrolyte concentration [85], presence of dissolved substances which are adsorbed onto the surfaces modifying the surface properties [91], p H of the medium [92] as well as temperature [90].  Obviously, the intrinsic properties of the substratum and the bac-  terial surface have significant influence on attachment.  The physicochemical properties  (surface charge, surface free energy) of a potential substratum have been imphcated in influencing attachment  [93].  Recently, the hydrophobicity of bacterial cell surfaces has  been studied [95,96] as an overall parameter for the measurement of the adhesion potential to sohd surfaces, because in low-ion-strength environments the microbial surface hydrophobicity and charges are of greater importance [97] while most previous studies on bacterial attachment were conducted in a marine environment [98]. Initial attempts were made to model the adhesion phenomenon on the basis of colloid stabihty theory ( D E L V O theory) since the small size, low derisity and net negative charge of bacterial cells are similar to those of colloidal particles.  This approach has achieved  Chapter 2. Theoretical Aspects and Previous Studies  35  some success in the explanation of general features and 'long range' interactions between cells and surfaces [99]. A n alternative phenomenological approach involving the study of free energies employs an analysis of the thermodynamic potential for cell adhesion on the basis of known interfacial tensions [100] and has also been in some measure successful in modeling cell-surface contact events in terms of decreases in surface free energies resulting from adhesion [102]. T h e weakness of the physico-chemical models lies in their failure to take account of biological reactions since the cells are treated as solid inert particles rather than as bving systems. Marshall [101] proposed a two-stage model based on experimental observations.  T h e first stage involves cell deposition in which the bacterial cell is held  a small but finite distance from the solid surface, and this situation is maintained by the existence of an energy barrier.  T h e second stage occurs when the energy barrier is  breached allowing intimate surface contact and permanent adhesion. Three bridging mechanisms have been suggested: short-range physico-chemical forces such as chemical bonds or hydrophobic bonding [100]; specialized bacterial holdfasts, such as pili, fimbriae; and 'polymer bridging' through the mediation of bacterial extracellular polymers.  Since most bacteria have no obvious structures for attachment, it is widely  believed that the existence or 'in situ' synthesis of extracellular adhesives is required for permanent adhesion, the polymer occurring as an acidic polysaccharide [103], glycoproteins [104] etc. Polymer bridging was the mechanism proposed by Marshall for the time dependent second stage in which irreversible sorption awaits polymer synthesis.  How-  ever, it has been observed that some bacteria have the ability to bind rapidly to surfaces — this spontaneous binding suggests that bridging may depend on the compatibility of biopolymers (exuded prior to reversible adsorption) with the sohd surface.  It is further  observed that the initial, rapid attachment of a marine pseudomonad was mediated by a compact acidic polysaccharide followed by synthesis of a 'second' fibrous polysaccharide responsible for biofilm consolidation [103].  Chapter 2.  Theoretical Aspects and Previous Studies  36  Many bacteria (Gram-positive and Gram-negative) can produce layers of polysaccharide outside their cell wall (capsules or shmes).  T h e degree of capsulation and the  production of extracellular polysaccharides by a particular organism can be markedly influenced by the growth conditions. T h e nature of the linkage to the underlying wall structures  remains unknown.  However, the biosynthesis of several capsular polysac-  charides is known to require the participation of lipid intermediates  [105]. In terms of  structure, capsules and shme layers are in general highly hydrated. Capsules of aerogenes  Klebsiella  strains A l and A 3 were reported to give a viscous solution containing only 1  to 2 per cent polysaccharide material [106]. Therefore, a bacterial cell can be imagined as a small ball around which a layer of hydrated adhesive exists.  2.2.2  Startup of Methanogenic Biofilms  In the anaerobic treatment of cheese whey, the methanogenic and acetogenic  bacteria  grow much more slowly than do acidogens. Therefore, the start-up of the methanogenic biofilm is more time consuming than that of acidogenic biofilm.  Moreover, in the  methanogenic phase a symbiotic community is involved which includes methanogens and acetogens.  It is essential to know whether the properties of support surfaces would affect  the attachment  of each bacterial type — that is whether or not the attached biomass  would have the same bacterial composition as that in the bulk culture medium. Shapiro and Switzenbaum [107] investigated the initial anaerobic biofilm development in a mixed culture fed with sucrose. T h e methanogen accumulation was monitored by F o 42  fluorescence content of the biofilm material. T h e ratio of methanogens to total anaerobic biomass was found to remain constant throughout 25 days for high organic space loadings. Longer solid residence time (SRT), higher concentrations of anaerobic microorganisms and higher organic space loadings were beneficial to the startup of anaerobic biofilms. M a n y investigations have been conducted on the effect of support surface on startup  Chapter 2.  Theoretical Aspects and Previous Studies  of methanogenic biofilms.  37  Murray and van den Berg [43] studied the development of  methanogenic fixed films on pieces of polyvinyl chloride ( P V C ) plastic, etched glass and baked clay and the results showed that support material markedly affected the rate of attachment and growth of bacteria converting acetic acid to methane. Scanning electron micrographs showed that the film of bacteria attached to clay was thick and uniform, while the bacterial film attached to P V C plastic was thin but still uniform. Attachment to etched glass was spotty. That the clay was superior was attributed to its rough porous surface and the presence of minerals in it. particularly iron which is known to stimulate methanogenesis and growth. More supports were tested by van den Berg and co-workers [109]. Comparing methane production rates of anaerobic biofilms on four supports, needle punched polyester, red draintile clay, gray potters clay and P V C , they found that needle punched polyester was one of the most effective in developing an active biomass film even though it could not offer the microbes extra nutrients like clay. A series of packing materials, non porous and porous, were compared by Huysman et al [110] in a mixed anaerobic biofilm reactor in order to elucidate the most important factors for biofilm formation.  Their results indicate that surface roughness and  total porosity plus pore size have the largest effect on the colonization velocity, and a reticulated polyurethane foam appeared an excellent colonization matrix. However, the study of attachment  of methanogenic bacteria to solid supports with various porosities  performed by K u r o d a et al [40] revealed that methanogens adhered to moderately rough surfaces that had pores measuring a few tenths of a micron in diameter more than to polished and rough surfaces, and also preferably adhered to solid supports made of carbon material.  Obviously, the roughness of a support surface is playing a significant role in  the development of biofilms because a rough surface either offers more area for microbes to attack or entrap the fixed biomass by preventing them from being detached by shear stress of fluid flow.  In this sense, the porosity of a surface is a common factor to all  Chapter 2.  Theoretical Aspects and Previous Studies  bacterial attachment  38  (not only beneficial to methanogens and acetogens). Furthermore,  it should be controUed because in thick biomass entrapped in the channels of supports (e.g.  foam) the resistance to mass transfer would become significant, resulting in more  dead volume in digesters. A fundamental study was conducted by Verrier and Albagnac [111]  to investigate  adhesion of methanogenic bacteria onto inert sohd surfaces, P V C and glass shdes. Again the experiments showed that bacterial attachment  on glass shdes was very spotty, and  remained always low, while it was higher and increased constantly with time on P V C shdes.  It was calculated that 7 x l 0  3  bacteria adhered per m m  2  of P V C per day. T h e  predominant bacteria were filaments with septa and irregular surfaces tentatively identified to be Methanothrix soehngenii.  A strong influence of calcium concentration on  bacterial adhesion was observed with an optimal effect at about 2 m M of C a  + +  .  Above  this concentration a negative effect appeared due to bacterial aggregation. Sodium addition was less effective. Verrier and co-workers conducted more research on the adhesion of methanogens onto surfaces [112]. This time, 4 pure methanogenic cultures were used to investigate their initial adhesion on polymeric surfaces with different hydrophobicities.  Methanothrix soehngenii adhered preferentially to hydrophobic polymers while  Methanospirillum hungatei preferred hydrophilic surfaces and Methanobrevibacter arboriphilicus adhered onto all the supports. These results suggest that initial adhesion may influence the start-up rate of anaerobic fixed film reactors and is a function of the support hydrophobicity. It is interesting that Methanosarcina rnazei, an acetate-degrading species, did not adhere to any support even though Methanosarcina spp can always be found in large amounts in methanogenic biofilms, which may imply that some symbiotic function is involved when a mixed bacterial population attaches onto support surfaces. T h e importance of support materials on anaerobic biofilm formation was also pointed out by Switzenbaum et al [113], but their effort to enhance the rate of initial anaerobic  Chapter 2.  Theoretical Aspects and Previous Studies  39  biofilm accumulation by precoating support media with denitrifying bacteria biofilms (biological precoating) and various polymers (chemical precoating), failed. Recently, Wollersheim [42]  investigated the adhesion and biofilm development of  methanogenic biofilms on glass.  T h e experiments  carried out with an undefined cul-  ture as well as with a propionate-degrading anaerobic culture revealed that the primary adhesion was a passive process while the following biofilm development was an active one, which was accompanied by excretion of polysaccharides.  T h e primary adhesion of  bacteria may be controlled by the hydrophobicity and the surface charge of the supporting material.  T h e adsorption of acetogenic and methanogenic bacteria to wood chips,  studied by Moo-Young and co-workers [114], has been assessed in terms of adsorbed particulate organic nitrogen ( P O N ) representing a total amount of symbiotic biomass. It was found that the adsorbed P O N / m  2  of support could be related to the cell concentration  in solution by a Freundlich-type isotherm. It seems that the installation of the first bacterial layer may be of major importance for further biofilm growth and, stability. To this author's knowledge, however, no study has been conducted on the effect of support materials on the bacterial composition of an attached microbial biomass in a symbiotic bacterial community (methanogens plus acetogens) because of the difficulty in differentiating the specific substrate-degrading bacterial type from a mixed culture.  2.3  Mass Transfer in Anaerobic Biofilms  Once an anaerobic biofilm forms on a support surface, two major phases exist in the fermenter, an aqueous medium phase and a concentrated biomass phase. T h e sequence of steps occurring during substrate utihzation by the biofilm can be simplified into two important steps:  (1) substrates are transported from the bulk medium solution to the  Chapter 2. Theoretical Aspects and Previous Studies  40  interface between the liquid and the biofilm (external mass transfer),  (2) diffusion and  consumption of substrates within the biological slime (internal mass transfer plus reaction). These two steps are in series, and so the slower one becomes the rate-limiting step of the overall process. film-fluid  T h e transport  rate of substrates from the bulk solution to the  interface can be represented by the equation below  N = k (S -S ) L  b  (2.1)  s  where N is the rate (flux) of mass transfer ( m g / s e c / c m ) , kr, is the mass transfer co2  efficient (cm/sec), Sb and S  e  are the substrate concentrations  at the biofilm surface ( m g / c m ) , respectively. 3  in the bulk solution and  If the mass transfer coefficient is so large  that the external mass transfer rate is much faster than the rate of internal mass transfer plus reaction,  at any particular value of 5b, the overall rate will depend only on the  kinetics of internal mass transfer plus reaction.  This hmiting regime has been termed  kinetic regime, or reaction-controlled regime [115]. It is the only case i n which the actual reaction kinetics of the biological film can be directly measured, provided the internal diffusional effects are reduced to neghgible level. Frequently, the external mass transfer coefficient, kj, is incorporated in the dimensionless Sherwood number, Sh, which is predicted as a function of Reynolds number, Re, and Schmidt number, Sc, characterizing hydrodynamic conditions and molecular diffusion, respectively,  Sh = f(Re,Sc)  (2.2)  where Sh = k^djDi,] Re = ud/v; and Sc = u/Dr,.  For creeping flow (Re < 1), the  theory developed by Levich [116] shows that:  Sh = 0 . 9 9 # e  1/3  Sc  1/3  (2.3)  Chapter 2. Theoretical Aspects and Previous Studies  41  In the range 10 < Re < 10 , 4  Sh = 0 . 9 5 # e  1/2  Sc  (2.4)  1/3  More empirical or semi-empirical equations can be found for other fluid patterns [117]. Use of stagnant film theory, i.e., estimation of a liquid/solid mass transfer coefficient as the quotient of a diffusivity and diffusion layer thickness (fcf, = D /6 ) is an alternative W  W  method which gives a lower bound for ki when Re number is less than 0.01 [118]. T h e stagnant diffusion layer can be taken, for example, to be the ratio of the liquid volume to media surface area. Obviously, the external mass transfer coefficient is markedly affected by fluid flow pattern in a fermenter. Experimentally, the external mass transfer resistance can be minimized or eliminated by increasing the fluid velocity over the biofilm [119].  2.3.1  Structure of Anaerobic Biofilms  B y using light, U V , scanning and transmission electron microscopy, Robinson et al [120] examined the structure of anaerobic biofilms sampled from eight anaerobic  fixed-film  digesters fed with swine waste which had been in operation for 12 months at the University of Florida Swine Research Unit. Although the biofilm samples were collected from various support materials (different shapes of plastics and blocks of pine, cypress, oak), the biofilms did not differ significantly in microbial or overall appearance.  T h e overall  surface of the biofilms was rough and uneven. Protuberances resembling volcanoes were observed with openings of 100 to 500 / u n in diameter with a smooth microbial lining. Cross-sections of biofilms revealed a high density of material containing a heterogeneous bacterial population toward the base of the biofilms.  Various cell types were found in  small, loosely packed congregates or microcolonies. Some microcolonies contain only one morphological type of coccus, but most microcolonies contained several different types of cells (perhaps symbiotic communities). Large aggregations of sarcina-containing cysts  Chapter 2. Theoretical Aspects and Previous Studies  42  were the most prevalent microbe found in thin sections cut from the biofilms. Individual cells were enclosed by a dark-staining wall closely associated with an amorphous matrix material 180 n m thick that extended throughout the cyst. Cells on the periphery of the cyst were covered by a capsule-like material or by a honeycombed netword of dead cells. Transmission electron micrographs of thin sectioned biofilm samples fixed with ruthenium red, an electron dense marker which can stain the extracellular  polysaccharides,  revealed that at least three types of matrix material or glycocalyx existed in biofilms [121]. Around individual cells is glycocalyx type II w hich is a flexible integral microcapr  sule and glycocalyx III envelopes microcolonies containing morphologically similar sister cells. T h e type I, rigid peripheral glycocalyx, appears to be spatially extensive and possesses interstices which have different cross sectional size. A clear demarcation was seen between the interstices and their boundary walls; suggesting that the interstices may be channels within the type I glycocalyx. Large vacant areas in some of the interstices were observed and it was attributed to dead cells which once occupied these areas and left their 'foot print' in the rigid matrix [98]. T h e glycocalyx also contain mineral precipitates containing C a , P and a small amount of M g [120]. concentrations  In a methanogenic biofilm on a needle-punched polyester support, the of C a and P in the extracellular  matrix were 92 and 28 times higher,  respectively, than in the cells [122]. In the sense of internal mass transfer, a biofilm may be described as an assemblage of bacterial cells, biological catalytic  centers,  that are  distributed in an extracellular fibrous polysaccharide-containing matrix and connected by tortuous channels of various size as shown in Figure 2.7.  Chapter 2.  Theoretical Aspects and Previous Studies  Channel  43  Embedded cell  Figure 2.7: Structure of biofilms 2.3.2  Mass Transfer within Biofilms  Because of the gelatinous character of biofilm matrix it is thought that convective transport contributes little to the movement of reactive constituents within biofilms and substrate molecules transport towards the inner layers of biofilms along the tortuous channels by a mechanism of diffusion. Simultaneously, they also transport, by some mechanisms (passive and/or active transfer etc.), into the embedded microbes (see Figure 2.7) where utihzation reactions occur. It should be pointed out here that this latter mass transfer is a part of the intrinsic kinetics of substrate utihzation by microorganisms because it involves some characteristic enzymes of the bacteria even though immobihzation of living cells may produce a layer of exocellular polymers (glycocalyx type II) around the cells which affects the mass transfer rate. It is almost impossible to determine the actual transfer mechanism and rate of diffusion within the tortuous pores of the biofilms, and therefore, some workers have defined an effective diffusivity D in such a way that the e  Chapter 2. Theoretical Aspects and Previous Studies  44  substrate molecules may be thought of as diffusing through an equivalent homogeneous medium as is done in the study of porous catalysts.  N — —D (dS/dx) e  (2.5)  Unhke in homogeneous systems such as water solutions where the major diffusional resistance comes from the collision of solute molecules with water molecules, the diffusion of substrate molecules in biofilms will be further retarded because they must move through the gelatinous matrix. In addition to the factors which influence the diffusivity in pure water, D , such as temperature,  molecule size and viscosity, the effective diffusivity, by  its definition, must be influenced by the structures of biofilms. Therefore, investigation of internal mass transfer within a biofilm comes to be the measurement of the effective diffusivity, D , of substrate molecules in the biofilm. e  Effective diffusion coefficients of some substrates have been measured in aerobic microbial aggregates (films, blocs) because the supply of oxygen to aerobes embedded in microbial aggregates is believed to be the rate-hmiting step. These are reported in several papers which have been reviewed by Libicki and coworkers (1988) [123]. In contrast, no report has been found by this writer on the internal mass transfer in fermentative biofilms. Actually, as discussed in Chapter 1, the knowledge of effective diffusion coefficients in fermentative biofilms and then, an optimum biofilm thickness, becomes essential when the anaerobic technology is apphed to industry where a long term stable and optimal operation is required. To evaluate the internal mass transfer parameter under a neghgible external transfer resistance, three approaches have been taken: (1) evaluation of intrinsic reaction rates from a separate experimental study or literature and the internal transfer rate by fitting them simultaneously to the reactor breakthrough data (indirect method) [124], (2)  Chapter 2. Theoretical Aspects and Previous Studies  45  evaluation of internal mass transfer rate by measuring a concentration gradient through an active biofilm and coupling it with the flux of material into the biofilm [125], (3) evaluation of internal mass transfer rate from the flux across an inactive biofilm in a two chamber device (direct method) [127]. T h e biofilm is often killed by chemicals (mercuric chloride) or radiation (ultraviolet) [128]. In the first method by w hich most diffusivities r  in active microbial aggregates have been measured, the effective diffusivities have been used as fitting parameters in substrate utilization models and it is likely that error would be introduced into their results if the reactor hydrodynamies was not exactly the same as predicted by their model. T h e second method is a direct method to measure effective diffusivities in active biofilms, but measuring a concentration profile within an active biofilm needs special probes which should be very small in size and able to detect the target molecules. This method has been used by Bungay and co-workers for oxygen diffusion into laboratory-grown [125] and actual trickling filter films [126]. T h e third method may be able to avoid the effects of non-ideal reactor deviations on the measurement of effective diffusivities because it focuses on the two sides of the target biofilm. B u t it usually uses an 'inactive' biofilm to avoid the uncertainty caused by the kinetics of substrate utihzation.  T h e measurements involve the concentration changes in the chambers with  time after a pulse input is given to one chamber.  Not only must it be certain that the  biofilm is completely killed and so no reaction will occur [128] but also some factors of importance in a hving biofilm like gaseous products released in small bubbles, symbiotic relationship and interaction between active bacterial species are neglected. Furthermore, the process of deactivating a biofilm may introduce some changes in the structure of the biofilms. Table 2.7 summarizes some experimentally determined diffusivities in inactive biomass. Variability i n these results is substantial even in this narrow sample of experiments.  Chapter 2. Theoretical Aspects and Previous Studies  46  Table 2.7: Ratios of effective diffusivities measured in inactive biomass to diffusivities in water  DJD Oxygen  Glucose  NHj  Reference  Biofilm  W  NO;  NO;  preparation  0.85  -  0.8-0.87  0.86  0.93-1.0  Na+ -  0.2-1.0  0.3-0.5  -  -  -  -  1.2  0.15-1.2  0.7  settled, filtered  [129]  0.6  -  -  -  -  0.6  grown in place  [130]  0.3  -  -  -  -  -  centrifuged  [131]  filtered  [127]  centrifuged,  [128]  pressed  This may be due in part to the differences in biomass growth conditions but it is probably also due to the different techniques that have been used to prepare the biofilms. For example, O n u m a and Omura [129] have reported variance in film diffusivities with carbon to nitrogen ratio in the media in which the biomass was grown.  Matson and  Charackhs [128] grew mixed cultures of bacteria on glucose in completely mixed reactors, concentrated them by centrifugation, and formed them into films by spreading them onto a template with a spatula. T h e biofilm was then sandwiched between two membrane filters prior to its placement in the diffusion apparatus. It is possible that some artificial effects may be introduced by the process of preparing such a biofilm because the major difference in diffusivities in water and i n hydrated biofilms is caused by the matrix made of exocellular polymers. In order to avoid the possible effects introduced by artificially treating biofilms, a nonreactive solute has been used to measure its effective diffusive permeability in intact microbial cell aggregates [123]. Because of the difficulties associated with the direct measurement  of the effective  diffusivity, most studies on the modehng of fixed-film reactors have used assumed values. Based on their previous work on prepared biofilms of aerobic, autotrophic, nitrifying bacteria [127], subsequent studies by Williamson, M c C a r t y and their co-workers [132,133]  Chapter 2.  Theoretical Aspects and Previous Studies  47  have assumed effective diffusivities of 80 percent of the free values for a larger number of substances in various biofilms. T h e effective diffusivity of acetate in a methanogenic biofilm was also taken as 80 percent of the value in free water, based on that same work [134].  Harris and Hansford [135] assumed that the effective diffusivity of glucose was  equal to the value in water because of the results of Atkinson and Daoud [1.36]. It is one purpose of the present study to measure the effective diffusivities of lactose in active acidogenic biofilms, and organic acids in active symbiotic methanogenic biofilms in a two-chamber device which can offer a more direct measurement.  However, in situ  measurement of effective diffusivities in an active biofilm needs firstly the knowledge of intrinsic kinetics of substrate utihzation by the biofilm.  2.4  Intrinsic Kinetics of Substrate Utilization in Anaerobic Biofilms  T h e so-called intrinsic kinetics describe the relationship between the utihzation rates and substrate concentrations in biofilms without interference from external and internal mass transfer resistances.  Thus, the focus is on the process by which the substrate molecules  are transported into microbial cells and dissimilated in the cytoplasm of the cells rather than on the transport of substrates from bulk solution to individual cells. As discussed in Section 1, this process involves various enzymes, and each of them is responsible for the catalysis of a specific chemical reaction. Generally, the slowest reaction catalyzed by a key enzyme becomes the rate-limiting step and determines the overall rate of substrate utihzation.  2.4.1  Expression of Intrinsic Kinetics  Michaehs and Menten proposed a theory of enzyme action. substrate 5, forming an enzyme-substrate complex (ES  Enzyme E can bind to  complex).  Chapter 2. Theoretical Aspects and Previous Studies  E + S  i  ES  48  P + E  This E S complex breaks down to yield free enzyme and product (P). T h e k  are rate constants that define how fast the individual steps proceed.  2  and  They further  assumed that the ES complex does not easily reform from free enzyme and products, and more importantly, that the rate of formation of the ES complex was equal to its rate of degradation - that is, that the formation of the ES complex has reached a steady state. In this case, the concentration of the ES complex will be constant.  Using these  assumptions, Michaelis and Menten derived Equation 2.6,  K = (k +k_ )/ki, e  2  1  indicating the affinity of the substrate for the enzyme active site. This  classical equation is identical to the empirical M o n o d equation which depicts microbial growth and has been used as a theoretical basis for the Monod equation since growth is the result of a number of enzymatically catalyzed biosynthetic steps. Another advantage of this mechanistic model is that modifying the reaction pathways can give rate equations describing some unusual phenomena such as substrate inhibition [137]. Cell growth and substrate utihzation are generally considered to be coupled reactions, i.e., substrate removal occurs because of cell growth. T h e proportionahty constant is the true growth yield, Y . Intrinsic rates of biological reactions are generally expressed on g  the basis of a unit of biomass, e.g. the intrinsic rate of substrate removal is expressed as the mass of substrate removed per unit time per unit of biomass.  The unit can be  based on some biomass volumetric property, such as dry weight, carbon content, protein  Chapter 2.  Theoretical Aspects and Previous Studies  49  content. T h e substrate removal rate is related to the specific growth rate of microbes by  r = p/Y  (2.7)  g  T h e Monod expression for the specific growth rate is  and so, r  max  =  p. /Y . max  g  These definitions assume that all substrate utihzation is channeled into cell synthesis and that cell maintenance needs are met by decay. Another approach would be to assume that a portion of the substrate was channeled directly into cell maintenance.  Although  there are differences in the fundamental mechanisms employed by the two models both yield the same result and can be considered to be equivalent [138].  2.4.2  Elimination of External and Internal Mass Transfer Resistances  In an active biofilm, reaction and diffusion are occurring at the same time, which creates various substrate concentration profiles within the film as illustrated in Figure 2.8. Figure 2.8 also illustrates that external mass transfer resistance, which is modeled with a diffusion layer, effects the substrate concentration at the biofilm surface. Having lower concentrations entering into the biofilm means that the reaction rate per unit biomass may dechne as the biomass is located further away from the outer biofilm surface. Indirect evidence for the importance of external mass transfer 'resistance has been obtained by observing changes in the reaction rate when the fluid velocity past a biofilm is changed. As introduced in the last section, the external mass transfer resistance can be minimized or eliminated by increasing the fluid velocity over the biofilm. a rotating annular reactor,  B y using  L a M o t t a [119] found that the reaction rate increased until  the velocity past the biofilm was around 0.8 m/s, but that thereafter it was constant.  Chapter 2.  Theoretical Aspects and Previous Studies  50  Figure 2.8: Illustration of substrate concentration profiles in biofilms Since the external mass transfer is in series with the diffusion plus reaction, whether the external mass transfer resistance is important and what velocity past the biofilm can ehminate the external mass transfer resistance depend upon the potential (intrinsic) reaction rates in the biofilm. The slower the intrinsic reaction rates, the more easily the external mass transfer resistance is minimized. In contrast to external mass transfer resistance, the internal mass transfer resistance is more difficult to ehminate because it occurs simultaneously with reaction. The distribution of substrate concentration within the biofilm, as shown in Figure 2.8, depends on the relative rates of diffusion and intrinsic reaction. Fast diffusion with slow reaction gives a shallow substrate concentration profile while slow diffusion with fast consumption causes a deep profile where substrate concentration reaches zero at or before the support surface. A strategy, widely applied in reaction engineering to minimize the internal mass transfer resistance of porous catalysts, is to reduce the thickness of the biofilm so that  Chapter 2.  Theoretical Aspects and Previous Studies  51  the concentration drop in the biofilm is not substantial and can be represented by the concentration at the surface. Experimentally, this has been achieved by L a M o t t a [124] in aerobic utilization of glucose and by Shieh and Mulcahy [139] in biological denitrification with methanol as the organic carbon source. It should be noted that much faster intrinsic reactions were involved in these studies than in lactose and organic acid fermentations. Shieh and Mulcahy observed that for each feed concentration, a critical biofilm thickness existed, beyond which the observed denitrification rate, on a per unit biomass basis, decreased sharply. A n d then, the denitrification rates obtained from experimental runs in which the biofilm thickness was less than the critical value were used to determine the intrinsic kinetic parameters.  To what extent a biofilm thickness should be reduced,  obviously, depends upon the relative rates of diffusion and intrinsic reaction, and can only be determined by experiments.  Therefore, an ideal support surface should give a  uniform, thin biofilm for a relatively long period of time. Considering the effects of support materials on the thickness of biofilms, as discussed in Section 2, smooth polyvinyl chloride ( P V C ) sheet may be a good support material for the studies of intrinsic kinetics of lactose and organic acid fermentations in anaerobic biofilms.  2.4.3  Kinetics of Acidogenesis and Methanogenesis  M a n y laboratory experiments have been performed on the anaerobic methanation of whey or lactose to evaluate the performance of reactors using immobihzed bacteria [35,140,19, 18,17,33,32], but kinetic data of the process are virtually non-existent.  Kisaahta  [46]  investigated mainly the reaction pathways of lactose acidogenesis as well as the effects of dilution rate and p H on the pathways in a suspended culture.  But the growth rate  expression for acidogenic bacteria was not satisfied due to considerable wall growth which would cause a more serious problem at high dilution rates. In contrast  to lactose  acidogenesis, more kinetic studies have been conducted on  Chapter 2.  Theoretical Aspects and Previous Studies  52  Table 2 . 8 : Growth constants of anaerobic cultures at 3 5 °C y*  Culture day"  gVSS/gCOD  Acetic acid producing bacteria  max  1  ''mm  fl'max/Ymax  gCOD/gVSS/day  gCOD/1  2.0  0.15  13  0.2  producing bacteria  0.4  0.03  13  0.05  Combined culture  0.4  0.18  2  -  Methane  Source is [144].  methanogenesis  of organic acids.  Lawrence and M c C a r t y investigated the kinetics of  methane production in cultures enriched by acetate, propionate and butyrate  [142].  After  a calculation was made that the specific utihzation rate of one acid was based only on the fraction of biomass which was responsible for the bioconversion of that acid, their results showed that the three bacterial groups responsible for degradation of three organic acids had the same specific growth rate,  0.37-0.4  ( d a y ) . In a suspended methanogenic -1  culture stirred by bubbling of recycled gas, L i n et al [143] studied the kinetics of the methanogenesis of mixtures of organic acids, and expressed the Michaelis-Menten model as a function of the C O D concentration of total organic acids. Many results on the anaerobic treatment  of wastewater  in fixed film reactors can  be found in a comprehensive review by Henze and Harremoes  [144].  After reviewing  the results of theoretical and experimental studies on various anaerobic systems, they proposed growth constants of anaerobic cultures as hsted in Table 2 . 8 . However, this author has found no report on intrinsic kinetics of lactose acidogenesis and methanogenesis of organic acids.  In most of the kinetic studies, the  researchers  had made no effort to ehminate external and/or internal mass transfer resistance nor  Chapter 2.  Theoretical Aspects and Previous Studies  53  have they described clearly in their reports their handling of this problem even though microbial aggregates (biofilms, blocs) were involved in their investigations. If the possible effects of bacterial immobilization on the metabolic behavior of the attached  microbes  are considered, such as the exocellular glycocalyx around the wall of individual cells, it will further reduce the available information on intrinsic kinetics of lactose methanation by immobilized bacteria. From the,discussions on these topics; attachment of symbiotic communities of acetogens and methanogens  onto inert sohd supports; effective diffusivities of lactose in  acidogenic biofilms and organic acids in methanogenic biofilms; intrinsic fermentation kinetics of lactose and organic acids by anaerobic biofilms, it can be seen that related information is available but no previous work has been conducted specifically on these topics. This study will concentrate on these topics and some fundamental investigations will be made which may be valuable for a better understanding of the complex process of lactose anaerobic methanation in fixed biofilms.  Chapter 3  Experimental Conditions and Setup  It has been indicated in Chapter 1 that this study, as an extension of studies of lactose acidogenesis in suspended cultures conducted by Kisaahta [46], will concentrate on lactose utihzation in two-phase anaerobic biofilms. Although a great deal of research has been carried out on anaerobic digestion of organic substrates, some problems still need more investigations which are crucial for an optimal design and operation of a process in which lactose is utihzed in two-phase anaerobic biofilm reactors. A m o n g these, five have been selected as the present research objects: intrinsic kinetics of lactose utihzation and organic acids production in acidogenic biofilms, attachment  and build-up of symbiotic  methanogenic biofilms, intrinsic kinetics of organic acids dissimilation in methanogenic biofilms, lactose transfer in the acidogenic biofilms and organic acids transfer in the methanogenic biofilms. Mass transfer  data are prerequisites for estimating and controlling the optimum  biofilm thickness so that a stable operation can be achieved in a fermenter with growing biofilms.  T h e intrinsic kinetics of substrate utihzation by anaerobic biofilms not only  give fundamental knowledge on how fast the sugar and the acids can be digested by the responsible microbes embedded in the biofilms but also are needed to estimate  the  diffusion properties of substrates in hving biofilms. A l l the five research subtitles will involve different microbial species, substrates, culture conditions and biofilm supports, which will be detailed in each of the following chapters.  However, some common conditions and setups which will be used in all these  54  Chapter 3. Experimental Conditions and Setup  55  investigations are described in this chapter.  3.1  Experimental Conditions  Experimental conditions mainly include culture temperature,  culture p H , composition  and concentration of growth nutrients.  3.1.1  Culture Temperature  Microbial growth rate, and thus substrate utihzation rate caused by the biological activities of microorganisms, as with all chemical reactions, are a function of temperature.  It  has been found that in nature microorganisms can grow at temperatures below 0 °C and above 93 °C — the primary requirement is for liquid water. According to their biological activities in different temperature  ranges, bacteria can be classified into three groups,  psychrophiles, mesophiles and thermophiles. There are three generalizations that can be made concerning the effect of temperature on growth rate as shown in Figure 3.9 [210]. First, growth only occurs over a 30 °C range for any group of microorganisms; second, growth rate increases slowly with raising temperature is reached; and third, at temperatures  until the maximum growth rate  above the maximum, growth rate falls rapidly.  In general, the maximum growth rate of each group of microorganisms increases with temperature.  It can be seen in Figure 3.9 that the maximum substrate utihzation rates  occur over a very narrow temperature  range.  Psychrophiles are able to grow at lower  temperatures, but few of them are found in industrial practice due to their low biological activity, especially anaerobic microbes which have very low intrinsic growth rates. Thermophiles have attracted research interests recently in anaerobic treatment of wastewater because of their faster growth rates.  Compared with mesophiles, however, they have  two disadvantages, worse process stability and more energy is needed to maintain the  56  Chapter 3. Experimental Conditions and Setup  2-i  psychrophile  mesophile  thermophile  x E  a.  Temperature (degree) Figure 3.9: Illustration of temperature influence on growth rate of microbes. culture at a higher temperature.  Cheese whey, when it is discharged from the plant, has  a temperature which is suitable for mesophilic bacterial growth and little or no energy is needed to heat the culture.  Moreover, in the temperature  range of 32-38 ° C , the  mesophiles behave actively [144]. This study will adapt and use mesophilic bacteria at 35 ± 2 °C to investigate the fermentation kinetics, mass transfer of lactose and organic acids in biofilms and build-up of methanogenic biofilms.  3.1.2  Culture p H  T h e p H , a measure of the hydrogen ion (H ) +  activity, is particularly important as a  parameter of microbial growth. Most microorganisms grow over a p H range of 3-4 units; this represents a 1000 to 10000 fold range of hydrogen ion concentration. However, they have an optimum biological activity around p H 6.5-7.5.  Chapter 3. Experimental Conditions and Setup  57  T h e acidogens responsible for lactose fermentation grow in a quite wide p H range of 48. T h e studies conducted by Kisaalita et al [44] on the influence of culture p H on lactose acidogenesis revealed that the utilization rate of lactose was not significantly affected by p H in the p H range of 4-7 and the p H had a great influence on the distribution of the acids producted by the fermentation. A low p H value can not only depress the production of propionic acid which is the product most difficultly digested in the following methanogenic phase [145] but can also save caustic solution which is needed for maintaining the culture p H at a higher value due to the accumulation of acid products of lactose acidogenesis. Although the methane-producing bacteria have been found in alkaline (pH 9.7) lake sediments [146] and in acidic peat (pH 3.6) [147] , the favorable p H range of methanogenic bacteria in a digester is narrow, 6-8,  as proposed by Zehnder et al [148]. In their in-  vestigations on methane production from organic acids in immobilized cell bioreactors, Scharer and co-workers [114] found a narrower optimum p H range of 6.5-7.5 over which no significant differences in the rate of methane production occurred. In this study, the p H value of lactose acidogenesis will be controlled at 4.6 ± 0.2 and the p H value for methanogenesis of organic acids at 7.1 ± 0.2 .  3.1.3  Growth Nutrients  In this study, the utihzation of lactose and organic acids in anaerobic biofilms were investigated separately.  T w o types of medium were used which contained lactose or  organic acids respectively. It is desirable that only the carbon source, lactose or organic acids, is the growth limiting component in the culture medium. In addition to the carbon source, lactose or organic acids, the bacteria also need N , P, S, as well as trace elements for their growth. A m m o n i u m is the preferred nitrogen source for methanogenic bacteria [149], although for one species of Methanobacterium it could be replaced by glutamine [150]. Nitrate is not a suitable nitrogen source for methanogens.  Chapter 3. Experimental Conditions and Setup  58  In addition, it increases the redox potential of the media and may result in overgrowth of enrichment cultures by nitrate-reducing bacteria, van den Berg and Lentz [151] found a suitable C O D / N (or C / N ) ratio to be 420/7 (or 158/7) and a good N / P ratio can be considered to be 7 [152]. Sulfide has often been used as both sulphur source and reducing agent since the redox potential of the media for methanogenesis should be reduced to E h < -200 mv, but in high concentrations sulfide may inhibit growth [153]. Theoretically, it is beheved that enrichment media must usually be free of sulfate because methanogens may otherwise be outcompeted by sulfate reducing bacteria at least for the most common substrates H  2  and acetate.  However, assimilatory sulfate reduction was also described  for methanogens by Daniels et al [154]. A n d the concentration of sulfide produced from the reduction of sulfate would not be high enough to inhibit bacterial growth. Sulfates of M g , Fe, Z n and C u added to the medium supply both the metal ions and sulphur. For mixed cultures used for acidogenic and methanogenic bacteria, a ratio of C : N : P (158:7:1) was required for balanced biological growth [152,155,156]. B u t little work has been done on the growth requirements for single phase systems.  Into the lactose acido-  genesis medium having the same C : N : P ratio as mentioned above, Kisaahta [46] added, as growth nutrients for the acidogens, the same inorganic salts which were used by M c Carty [157] and Speece et al [158] i n their mixed cultures.  Concentrations of calcium  and sodium were kept at 100 - 200 mg/1 while potassium and magnesium concentrations were at 200-250 mg/1. It was beheved that under such concentrations of growth nutrients the carbon source (lactose) was the only growth hmiting component.  It would be ex-  pected that the inorganic salts which satisfy the growth requirements of mixed cultures of acidogenesis and methanogenesis should also supply enough nutrients to a separated culture, acidogenesis or methanogenesis.  Table 3.9 hsts the chemical components and  their concentrations used i n this study which are similar to those used by Kisaahta. T h e concentrations of inorganic salts are based on a lactose concentration of 12 g/1  Chapter 3. Experimental Conditions and Setup  59  Table 3.9: Chemical components and concentrations in culture medium Component  Concentration (g/1)  Substrates  12  Lactose HAc : HPr : H B u  6:3:3  Macro elements 0.42  NH C1 4  (NH ) HP0 4  2  0.8  4  0.35  MgS0 .7H 0 4  2  0.7  KC1 CaCl .2H 0 2  0.5  2  Micro elements Fe(NH ) S0 4  2  0.2  4  ZnS0 .7H 0  0.005  MnCl .4H 0  0.005  4  2  2  2  0.002  CuS0 .5H 0 4  2  NaB O .10H O  0.002  NaMo0 .2H 0  0.002  4  2  2  4  2  for lactose acidogenesis or a mixed solution of organic acids for organic acid methanogenesis where acetic acid is 6 g/1, propionic acid 3 g/1 and butyric acid 3 g/1. If the substrate concentrations were changed, the concentrations of the nutrients were also adjusted correspondingly. N o growth factors (vitamins, yeast extract etc.) were added to this chemically defined medium. A l l the chemicals were reagent grade and supphed by B D H unless otherwise indicated. Table 3.10 summerizes the experimental conditions used in each type of fermentation.  3.2  Experimental Setups  Experimental setups include the general experimental setup, the configuration and operation properties of the reactor, and the biofilm supports used in three types of experiments.  Chapter  3.  Experimental  Table 3.10:  Conditions  and  Setup  60  Comparison of experimental conditions for each phase  Phase  Substrate  pH  Temp.  p H adj. soln.  Acidogenesis  Lactose  46  35 ° C  KOH+NaOH  experiments kinetics mass transfer  Methanogenesis  HAc,HPr,HBu  7.1  35 °C  HC1  kinetics mass transfer build-up of biofilms  3.2.1  General Setup  A reactor and some auxiliary facilities are needed to keep the bacteria, methanogens,  acidogens or  in a defined environment and to investigate their biological behavior in  the environment.  Figure 3.10 illustrates the general setup which allowed the control of  culture temperature,  p H , feed, recycle rate etc. needed for this study.  Lactose (or salts of organic acids) was mixed with the inorganic nutrient solutions (see Table 3.9) and diluted to a desired concentration with tap water. T h e feed was stored in the feed tank and cooled to 1-4  °C by a refrigerated  circulating bath ( N E S L A B ) .  Nitrogen was bubbhng through the feed to maintain a positive oxygen-free  atmosphere  in the tank, which is necessary for anaerobic microbes, especially for the strict anaerobic methanogens.  A Masterflex pump ( C O L E P A R M E R ) recycled the feed between the feed  tank and the head tank, mixing the feed and maintaining a constant hquid head over the reactor to give a stable feed flow rate.  T h e feed flow rates were controlled with a  micro-valve and monitored with a rotameter at high flow rates or with a break tube at low flow rates by counting the feed drops over a period of time.  The break tube also  prevented contamination of the feed in the tanks by the microbes in the fermenter. T h e desired p H values of the cultures were controlled by a p H / p u m p system (Cole Parmer Series 7142). As p H adjusting solutions, an equimolar K O H and N a O H solution  Figure 3.10: Illustration of general experimental setup. 1-feed tank, 2-pump, 3-head tank, 4-microvalve, 5-rotameter, 6-break tube, 7-reactor, 8-biofilm support, 9-refrigerated bath, 10-heat exchanger, 11-pump, 12-thermostat bath, 13-pH controUer, 14-pH adjusting solution, 15-gas collector, 16-thermoregulator  Chapter 3. Experimental Conditions and Setup  (total concentrations  0.5-2  (concentrations  N) for organic acids fermentation.  0.3-1  62  N) was used for lactose fermentation and a HC1 solution T h e culture temperature  was  maintained at 35 ± 2 °C by heating the recycled culture medium with hot water from a ultra thermostat  ( C O L O R A ) . T h e temperature of the thermostat  was in turn adjusted  according to the culture temperature by the thermoregulator inserted in the reactor. T h e production rates (volume/time) of gaseous products from lactose fermentation (C0 , H 2  2  etc.)  and from organic acids fermentation ( C H , C 0 4  with the gas collector.  2  etc.)  were measured  T h e two liquid surfaces in the collector were kept at almost the  same level when the gas was collected. A layer of oil was added on the liquid surface in the scaled tube to prevent the soluble gaseous components (e.g.  C 0 ) from absorbing 2  into the water.  3.2.2  Reactor  For studies on anaerobic biofilms, the properties of biofilms must be known during the experiments.  A common practice is to measure a biofilm on a removable support slide  which is identical to the biofilm supports immersed in a reactor.  Unhke investigations  on aerobic biofilms where a reactor is open to air and a biofilm which is attached to a removable slide can be repeatedly measured, anaerobic biofilms on a shde can not be put back into the reactor after it has been exposed to the atmosphere for a long time. Therefore it is required that the reactor can hold enough sampling slides for multiple measurements.  T h e reactor is made of a half Plexiglass tube as shown in Figure 3.11.  35 sampling ports could be arranged on the large surface area of the top and the curved bottom minimized the accumulation of bacterial sludge in the reactor.  T h e removable  shdes were fixed in slots cut in rubber stoppers which in turn were fixed in the samphng ports in the reactor cover as shown in Figure 3.12. Recycling the culture medium by a Masterflex pump ( C O L E P A R M E R ) is another  Chapter 3. Experimental Conditions and Setup  Figure 3.11: Illustration of reactor configuration  rubber stopper  slide  i Figure 3.12: A removable sampling slide  63  Chapter 3. Experimental Conditions and Setup  64  significant characteristic of this reactor, which offers a means for controlling the culture temperature by heating the recycled medium. More importantly, it was possible to reduce and even ehminate the influence of external mass transfer on the substrate utihzation rates by increasing the recychng rate, i.e. increasing the linear velocity over the biofilms without changing the feed rate.  This is a critical requirement for the investigation of  the intrinsic kinetics of substrate digestion in biofilms and will be explained in detail in following chapters which describe the experiments.  Another important advantage of the  recycle flow is that the reactor behavior approaches, and can be modelled as, a continuous stirred tank reactor ( C S T R ) . For the ideal C S T R reactor model, the concentration substrate (temperature etc.)  of  in the reactor is uniform and is equal to the concentration  in the effluent, which greatly reduces the complexity of modehng the reactor. Generally, when the ratio of recycle rate to the fresh feed rate is above 10, the reactor can be approximated as a C S T R . A pulse test was used to confirm this behavior. In a continuous completely mixed reactor, the concentration change of tracer in the effluent with the time after a pulse input of the tracer can be described as foUows:  C = C e0  where Co is the concentration  (3.9)  t / ( v / F )  at the beginning of measurement,  V the reactor volume  and F the constant flow rate. Equation 3.9 can be rewritten as,  -logC =  (l// P)(lo )<-logC7 J  ge  0  (3.10)  HC1 solution was used as the tracer in a flow of tap water and the p H change in the effluent should have a hnear relationship with time if the reactor could be taken as a C S T R at a high enough recycle ratio.  Chapter 3. Experimental Conditions and Setup  65  - \og[H ] = (V/F)(\og e)t - \og[H }  (3.11)  pH = At - B  (3.12)  +  +  0  and,  where A, B are constants. At afixedrecycle rate, theflowrate of tap water was changed to test the influence of the recycle ratio on mixing behavior in the reactor. Figure 3.13 indicates that as long as the recycle ratio was kept above 8, the reactor behaved like a CSTR. It was found in the kinetic tests (see Chapters 4 and 6) that the recycle rate had to be kept above 14 1/hr to minimize the effect of external mass transfer resistance on substrate utihzation in biofilms, therefore, the feed flow rate had to be kept below 1.7  Chapter 3.  Experimental  Conditions  66  and Setup  1/hr. This requirement was satisfied in all experiments.  3.3  Biofilm Supports  In addition to a controlled environment, the microbes must also be given a sohd support on which to form biofilms, only then can the biofilms be investigated in detail; fermentation kinetics of substrates in biofilms, mass transfer in biofilms and build-up of biofilms. Each of these themes requires a special biofilm support because of its different focus. Three kinds of supports were designed and used in this study.  3.3.1  Supports for Kinetic Studies  T h e investigation of the intrinsic kinetics of lactose utihzation in acidogenic biofilms or methanogenesis of organic acids in methanogenic biofilms needs as much biofilm as possible so that the biofilms contain most of the biomass in the reactor and the contribution from suspended microbes may be neglected. Intrinsic kinetic data can be obtained only after both the external and internal mass transfer resistance have been greatly reduced. Generally, the internal mass transfer resistance can be minimized by using a thin biofilm. Kennedy and Droste [159] used several materials as anaerobic biofilm supports, including needle-punched polyester, polyvinyl chloride sheet ( P V C ) , glass and two types of clay, and found that P V C supported biofilms gave a relatively low methane production rate due to small mass of the biofilm (a thin biofilm) and this low methane production rate was stable and could last up to 80 days. Obviously, it is desirable for a thin biofilm to be able to last a long time during the experiments.  T h e biofilm supports used in kinetic  studies of lactose or organic acids fermentation, therefore, were made of P V C sheets as shown in Figure 3.14.  T h e material has other advantages as well such as no physiological  effect on the bacteria [43] and ease of fabrication. T h e total support surface had an area  Chapter 3.  Experimental Conditions and Setup  67  Figure 3.14: PVC biofilm support for kinetic studies of lactose or organic acids fermentation of 1280 cm . The picture (Figure 3.15) shows a section of a thin and uniform biofilm on 2  the PVC support as seen under a microscope (NIKON). 3.3.2  Supports for Mass Transfer Studies  In the investigation of substrate mass transfer in biofilms, attention was focussed on a part of a biofilm in the reactor and the measurement of substrate concentration difference on the two sides of the biofilm. The configuration of the biofilm support is shown in Figure 3.16. The reasons for this design will be given in Chapter 7 on mass transfer in biofilms. Since it was made from a section of Plexiglass tube, the device had a symmetrical structure. On each side a nitrocellulose membrane filter, which has no biological effect on the bacterial growth, was sandwiched by rubber gaskets and fixed by two stainless steel flanges, forming a closed volume of 30 ml. The porosity of the filters (d=0.45 pm) kept the microbes (generally, d = 1 /zm) from entering the device while the substrate molecules  Chapter 3.  Experimental Conditions and Setup  68  Figure 3.15: A thin biofilm (the black up-layer) on a P V C support, magnified by 100 times.  pump  Figure 3.16: A biofilm support device for mass transfer studies of lactose or organic acids in biofilms  Chapter 3. Experimental Conditions and Setup  69  could enter it freely. W h e n the device was immersed in a culture medium, some biofilm formed on its two membrane filters. A higher substrate concentration outside the device than inside the device caused a substrate transfer into the device by the mechanism of molecular diffusion through the biofilms and filters. T h e medium inside the device was recycled with a Masterflex pump ( C O L E P A R M E R ) to promote estabhshment of a uniform concentration inside it. A t steady state, the concentrations of substrates outside and inside the device were measured and used to estimate the mass transfer properties of the substrates within the biofilms. In order to avoid convective mass transfer through the biofilms, the pressure as well as the hquid levels outside and inside the cell were kept the same. T h e hole on the top of the cell was not only to maintain a zero pressure difference but also to ehminate any mechanical disturbance to the filters caused by the recycle.  3.3.3  Supports for Studies of Biofilm Start-up  Attachment and build-up of symbiotic methanogenic biofilms were investigated on 4 types of sohd materials; wood, ceramic Rasching rings, P V C and stainless steel. These materials have a wide range of surface wettability as can be seen in Table 3.11 and also are widely used in industry. Except for the ceramic rings, which are often used as packing material in separation towers and reactors to give a large surface area, the other three materials have the same shape, like microscope shdes, and so, they could be fixed on rubber stoppers as mentioned before. Suspending a ceramic ring in the culture medium as a removable support was done by hanging the ring on a hook which was made from a thin steel wire and fixed on a rubber stopper. After the surfaces were immersed in a culture medium, the accumulation of biologically active materials on these inert sohd supports was measured and used to follow the build-up of biofilms.  Chapter 3. Experimental Conditions and Setup  Table 3.11:  Properties of biofilm supports for studies of biofilm formation Size  Water contact angle  mm X mm X mm  Degrees  15 x 35 x 2  0.0  (010 - c/>6) x 9  56.6  15 x 35 x 1.5  88.0  15 x 35 x 1  99.7  Substratum W o o d (fir) Ceramic ring PVC Stainless steel  3.4  70  Experimental Analysis  Many samples were collected during the experiments for analysis. T h e samples can be classified into three groups; sohd, liquid and gas, and hence different methods of analysis were needed, which are briefly described here while the details are given in Appendix B .  3.4.1  Solid Sample Analysis  Sohd samples were taken of acidogenic or methanogenic biofilms.  For the studies on  substrate fermentation and mass transfer in anaerobic biofilms, the properties of the biofilms such as dry weight, total organic carbon content, density and thickness of the biofilms were needed. o D r y weight of a biofilm sample: A sample of biofilm attached on a P V C shde as described in Figure 3.12 or taken from a support was dried at 70 ° C to a constant weight. T h e low temperature used to avoid any disturbance from the plastic material.  was  After the dried biomass  with the shde or in a container was weighed, it was dissolved away in distilled water which had been acidified with sulfuric acid to p H 1. T h e cleaned and dried shde or container was weighed again. T h e difference of two weights was taken as the dry weight of the biofilm sample.  Chapter 3. Experimental Conditions and Setup  71  • Total organic carbon of a biofilm sample: T h e total organic carbon of the dissolved biomass, the dry weight of which had been measured, was analyzed with a carbon analyzer ( A S T R O ) . Thus, the total organic carbon content in the biofilm sample was known directly. • Density of a biofilm: T h e density of a biofilm refers to the dry weight (or carbon content) of biomass in a unit volume of the biofilm. A n intact biofilm was scraped from a support surface and put into a glass tube (d=6 mm), and then, was centrifuged at 4000 rpm to have a constant total volume (height) consisting of a sohd volume at the bottom and a clean water volume above.  After the total volume, V , was measured, the  sohd biomass was dried for dry weight  (Wd)  analysis and the T O C content  (M^oc)  of this biofilm sample was measured.  Pa = W /V  (3.13)  d  Ptoc =  W  t o e  /V  (3.14)  o Thickness of a biofilm: This measurement is crucial to the measurement of diffusion properties of substrates (lactose and organic acids) i n biofilms. T h e total biomass attached on a membrane filter of the device as shown in Figure 7.65 was carefully scraped into a container and dried to measure the dry weight and T O C content.  Based on the area of  the filter from which the biomass was collected and the density of the biofilm, the  Chapter  3. Experimental  Conditions  and Setup  72  biofilm thickness could be estimated as following:  PdA  ptocA  where Wd — total dry weight of a biofilm, Pd = biofilm density based on dry weight of biomass, W  toc  — total organic carbon content of a biofilm,  Ptoc — biofilm density based on organic carbon content of biomass, A = filter area  Obviously, this thickness is an average value over the whole surface.  3.4.2  Liquid Sample Analysis  Liquid samples were collected in all three parts of the study (kinetics, mass transfer and biofilm build-up).  Analysis of these samples was done with a spectrophotometer  and a  gas chromatograph ( G C ) . T h e components analyzed by the spectrophotometer included lactose and lactate and those by the G C were acetic, propionic, butyric acids and ethanol. o Lactose and lactate analysis: Lactose  contains a reduced group which can give an orange-yellow color when  treated with phenol and concentrated  sulfuric acid. Lactate in a very diluted so-  lution can be converted to acetaldehyde when heated in the presence of sulfuric acid.  T h e acetaldehyde acting with p-hydroxydiphenyl gives a purple color.  a characteristic  At  wave length, absorption of a monochromatic light is proportional  to the color strength of a solution which is placed between the light source and a hght receiver.  T h e more lactose (lactate) in a sample solution, the stronger  the  color produced, and thus the more hght that is absorbed. T h e concentration  was  Chapter 3. Experimental Conditions and Setup  73  found from a standard curve which was obtained by analyzing several samples with known concentrations. • Organic acids and ethanol analysis: T h e organic acids in their free form and ethanol are easily vaporized and can be analyzed with a G C ( C A R L E ) equipped with a flame-ion detector samples were acidified to below p H 2.5 with a H P 0 3  4  (FID). T h e  solution since acetic acid, the  strongest acid compound, is in free form below this p H value. • Solid carbon content in a hquid sample: T h e sohd carbon content in a hquid sample is needed to determine the mass of free microbes in the culture medium. Half the volume of a hquid sample was analyzed with a carbon analyzer to find the original carbon content of the sample. T h e rest of the sample was filtered through a membrane filter (d = 0.45  pm)  to remove  the suspended microbes in the medium, and then the total carbon content of the filtrate was measured under the same instrument conditions. T h e difference in total carbon content of these two parts reflected the free microbe content in the liquid sample.  3.4.3  Gaseous sample analysis  Gaseous samples were mainly collected during the studies of the methanogenesis of organic acids ( C H , CO2 etc.) while much less gas was produced from lactose acidogenesis 4  (CO2 etc.). T h e concentrations of the gas components are needed when a carbon balance around the reactor is made. Therefore, only methane and carbon dioxide were analyzed by using a G C ( C A R L E ) equipped with a thermal conductivity detector  (TCD).  Chapter 4  Intrinsic Kinetics of Lactose Utilization  Anaerobic digestion of lactose in a two-phase process consists of acidogenesis and methanogenesis which are carried out in series reactors.  In the acids-forming reactor, lactose  is utihzed by acidogens with the main products of acetates, propionates and butyrates. Then, these intermediates are converted to methane and CO2 by the methanogens in the following methanogenic reactor.  This chapter describes the intrinsic kinetics of lactose  utihzation in acidogenic biofilms.  4.1  Experiments on Lactose Acidogenesis  T h e general experimental setup is as shown in Figure 3.10.  T h e feed consisted of lactose  as the limiting organic substrate and inorganic salts as the stimulating nutrients which are listed in Table 3.9.  T h e lactose concentration of the feed ranged from 5 to 10 g/1  in order to control its level in the fermenter with the experimental dilution rates used. This range of lactose and nutrient concentrations made lactose the only possible limiting substrate [46].  T h e methods used to keep the feed from fermenting in the storage tank  include:  • Low temperature,  the medium was maintained in 1 to 4 ° C in the tank;  • Low oxygen partial pressure, nitrogen was slowly bubbled through the medium; • Small amount of feed was stored at one time, enough for only 4 to 5 days operation.  74  Chapter 4. Intrinsic Kinetics of Lactose Utilization  T h e feed concentration  75  was determined from the first and final day sample  analyses  during the storage of 4 to 5 days. T h e fermenter had a working volume of 1,000 m l . T h e flow rate of feed, measured from the effluent collected over a period of time (3-8 hours), was controlled at above 150 m l / h r (D = 0.15 h r  - 1  ) so that the suspended bacteria were washed from the reactor and  this part of the biomass, compared with the fixed bacteria,  could be neglected.  Henze  and Harremoes reviewed the hterature on anaerobic processes and reported a maximum specific growth rate of acetic acid producing bacteria at 35 °C of 2 d a y hr ) - 1  - 1  (or D = 0.083  [144]. T h e carbon content of the solids in the effluent under these conditions was  found to be neghgible when the carbon contents of both the effluent and their filtrate from a membrane filter (d = 0.45/im) were analyzed and compared by using a T O C analyzer ( A S T R O ) . This indicated that no significant amount of biomass was suspended in the reactor. T h e p H of the culture was controlled at 4 . 6 ± 0 . 2 with 0.5 to 2 N equimolar N a O H and K O H solutions. T h e caustic concentration was adjusted on the basis of lactose utihzation rates to produce a neghgible influence on the dilution rates. T h e inoculum was obtained from the first phase reactor of a two-phase mini-plant which had been fed with cheese whey for two years. T h e experiment can be divided into four stages.  1. Adaptation; T h e fermenter was filled with a diluted lactose solution (2 g/1) and N was continuously introduced to strip the dissolved oxygen. W h e n the temperature reached 35 °C, the fermenter was seeded (200 m l inoculum) and then operated in batch mode.  After lactose had been used up, < 0.01 g/1, half the volume of the  culture (500 ml) was replaced by fresh feed (4 g/1 lactose) and this was repeated five times.  2  Chapter 4. Intrinsic Kinetics of Lactose Utilization  76  2. Build-up of biofilm; The operation, then, was shifted to continuous mode while the flow rate was controlled at less than 50 m l / h r to prevent the suspended bacteria from washout. It was observed that a white slimy biofilm gradually started to form on the grey P V C supports. 3. Steady state operation; After the build-up of biofilms, the flow rate was gradually increased to greater than 150 m l / h r . T h e temperature was maintained at 35 and the p H of the medium at 4.6.  °C,  To investigate the influence of lactose concen-  tration on the rates of lactose utilization and organic acid production, the lactose concentration in the reactor was controlled by adjusting either the feed flow rate (residence time) or the feed concentration, sometimes both of them. These two control modes had the same effect in a reactor in which the bacteria were immobilized. A dynamic response caused by a change in flow rate is described and discussed in Section 4.5.  A t each desired concentration level, a steady state during which  there was no significant lactose concentration change (< 10 %) in the effluent, was maintained more than 2 days to collect experimental data. T h e concentration was adjusted from a low to a high level , and after a set of desired levels had been investigated, the tests on the same set of levels were repeated. Since the biofilm thickness increased with time, the lactose utihzation rate at each of the concentration levels was obtained with acidogenic biofilms having different thickness.  Therefore, by  comparing the data, the influence of internal mass transfer resistance on lactose digestion rate could be estimated. 4. Influence of p H change; After the kinetic experiments had been completed, the culture p H was gradually increased from 4.6 to 6.5 while the flowrate and temperature were maintained at 220 m l / h r and 35 ° C , respectively.  Chapter 4. Intrinsic Kinetics of Lactose UtiEzation  77  3-1  o  CO  0  60  100  160  200  260  300  360  400  Recycle rate (ml/mln) Figure 4.17: External mass transfer resistance on lactose utilization in biofilms is tested by changing recycle rate. Before the intrinsic kinetic data could be collected, the influence of external mass transfer was tested by varying the recycle rate.  Figure 4.17  shows that the lactose  utihzation rate would not be affected by the external mass transfer resistance as long as the recycle rate was kept above 228 m l / m i n , corresponding to a hnear velocity over the biofilm of 3.3 c m / m i n . T h e influence of internal mass transfer is often reduced by using a thin biofilm which is available in the early stage of biofilm development. To extend the experimental time during which the effect of internal mass transfer resistance could be minimized even though the biofilms were getting thicker, the experiments were arranged in such a way that the concentration levels were adjusted from low to high for a test recycle. A t higher bulk concentrations the internal concentrations were also relatively high, which would give all the bacterial cells embedded in a thick biofilm the maximum utihzation rate,  78  Chapter 4. Intrinsic Kinetics of Lactose UtiEzation  3000  n  oH 0  1  10  1  20  1  30  1  40  1  60  1  60  Culture time (day)  1  70  1  80  1  90  Figure 4.18: Lactose digestion rate of whole reactor changes with time C  thereby, the influence of concentration distribution could be reduced. Figure 4.18 indicates that the lactose digestion rate based on the whole reactor gradually increased and then leveled off because of the gradually thickening biofilm, which means that more bacteria saw lower substrate concentration. Since the experiments were repeated at several concentration levels from low to high, it can be assumed that the kinetic data obtained on days 0 to 55 were not markedly affected by the internal mass transfer resistance. This becomes clear if the lactose digestion rates based on unit weight of biomass (mgCarbon) are plotted versus biofilm thickness (Figure 4.19). The experimental conditions are summarized in the Table 4.12. 4.2  Development of an Acidogenic Biofilm  As discussed in the previous chapters, the presence of sohd supports helps the retention of biomass in a reactor, and so the total amount of biomass in the reactor will increase  er 4.  Intrinsic Kinetics of Lactose Utilization  o.e-i  0.6  0.4  0.2  1  0.8  Biofilm thickness (mm)  Figure 4.19: Specific lactose digestion rate changes with biofilm thickness  Table 4.12: Experimental conditions of lactose acidogenesis Parameter  Condition  Temperature  35 ± 2 °C  pH  4.6 ± 0.2  Lactose feed  5-10 g/1  Flow rate  > 150 m l / h r (2.5 ml/min)  Dilution rate  > 0.15  Biomass  acidogens  Recycle rate  > 230 m l / m i n  hr-  1  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  80  Figure 4.20: Biomass distribution in the fermenter slowly with the digestion of substrates. To estimate the lactose utihzation rate based on unit mass of biomass, it is essential to know the total mass of biomass retained in the reactor during the experimental time. Three types of biomass existed in the reactor as shown in Figure 4.20; • suspended bacteria, • attached bacteria on the supports, • sludge. The suspended bacteria, compared with the fixed ones, were negligible as mentioned above. The biomass in the biofilms was the major part of the total biomass retained in the fermenter, and measured during the experiments by analyzing the biomass on the removable slides at given time intervals. The time when the first kinetic data were  Chapter 4. Intrinsic Kinetics of Lactose Utilization  81  160-1 140•  E  120-  CO <o  100-  "M  80-  TJ  c  o  (0 w < ED o  CQ  6040-  2orj 0-  —I— 10  —I— 20  30  —i— 40  —i— 60  —i— 60  —I— 70  —I— 80  —i  90  Culture time (day)  Figure 4.21: Biomass on removable slides increases with time collected was recorded as zero time, and then, after each time interval (5 to 8 days) one or two shdes which had been immersed at different positions in the reactor were removed and analyzed. It was found that the two shdes immersed at different positions in the reactor had very close biomass accumulations and hence, the distribution of biofilms was quite uniform in the fermenter. Figure 4.21 shows that the biomass on the shdes increased gradually with time. The carbon content and the dry biomass weight had a very good linear relationship as shown in Figure 4.22 and the slope was 0.382, which means that the dry biomass of the biofilm contained 38.2 per cent organic carbon. In general, the carbon content in a single cell ranges from 45 to 50 percent. The decrease in carbon content of the biofilm is probably due to the considerable amount of inorganic salts trapped in the films. Turakhia and Characklis [161] reported that a major portion of calcium was immobilized in the extracellular components of the biofilm matrix.  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  82  70-i  60-  140  B i o m a s s (mg)  Figure 4.22: Carbon content in the biomass The total carbon (TC) content of biofilms retained in the fermenter was obtained by multiplying the carbon content on a slide by the area ratio of the total supports to the shde, and its development with time is shown in Figure 4.23. A good correlation of total carbon with time is given by an exponential expression as follows and shown in Figure 4.23.  TC = 5.697e Where  002S9t  A/a = 1813.8e  00259  '  (4.16)  was the time, 'A' the total support area and V the shde area. An exponential  function was used since in a thin biofilm the bacteria could get enough food from the environment and so grow exponentially. The biomass deposited on the reactor walls was estimated based on three assumptions. Firstly, the experimental period was in the early stage of biofilm development and so no significant sloughing occurred because sloughing is believed to be due to lack of nutrients  Chapter 4. Intrinsic Kinetics of Lactose Utilization  83  24-i  20-  0-) 0  1  1  1  1  1  1  1  1  10  20  30  40  60  60  70  80  Culture time (day)  1 90  Figure 4.23: Total carbon content developed on the supports. T h e hne was calculated from Equation 4.16 in a thick biofilm [160]. Secondly, the biomass detached by fluid stress was continuously washed out by the high dilution rates. Hence, the sludge was attributed to the biofilm formed on the reactor walls. Finally, this part of the biofilm had the same growth rate as that on the supports. Experimentally, before the first kinetic data were collected, all the sludge which formed i n the first two stages of adaptation and biofilm start-up as mentioned above were removed by discharging the medium in the reactor. A t the end of experiments the biomass on the reactor wall was collected and measured. It contained only 1.5 g of carbon compared with 15.0 grams in the biomass on the supports. Including this part of biomass Equation 4.16 becomes  TC = (1813.8 + 1 7 5 ) e  002S9t  (4.17)  This correlation predicted the final biomass in the reactor at 86 days within 7 percent.  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  4.3  84  Utilization Rate of Lactose  T h e lactose concentration in the fermenter, which the bacteria actually saw, was the same as that in the effluent since the reactor was operated in a completely mixed mode. A t a steady state, the amount of lactose in the reactor was balanced as following;  Flow in = Flow out + Consumption due to reaction  that is, FS  in  = FS  out  + Wr  (4.18)  or, r = F(S -S )/W in  (4.19)  out  Where r is the lactose utihzation rate based on unit weight of carbon content (mgC) of biomass (mg S / m g C / h r ) , F the feed flow rate (ml/hr), Si and Sout the lactose concentran  tions in the feed and the effluent respectively (mg/ml), W is the total amount of biomass carbon content retained in the reactor at that time and is estimated from Equation 4.17. T h e right side of Equation 4.19 can be experimentally measured and thus, the lactose utihzation rate, r , at the lactose concentration of S  ou4  can be found.  Figure 4.24 indicates that the lactose digestion rate at various lactose concentrations can be correlated very well with the lactose concentration by a Michaelis-Menten type equation as  r =  (4.20)  For a non-linear model like Equation 4.20, it is better in general to estimate the parameters  (r  , K ) by using a direct search method since the fit errors of the model  max  t  with the experimental data are not then affected by the methods used to linearize the  Chapter 4. Intrinsic Kinetics of Lactose Utilization  85  0.6-1  -eii-  •  1000  2000  3000  •  o  4000  6000  Lactose Concentration (mg/l)  Figure 4.24: Effect of lactose concentration on lactose digestion rate. The hne is calculated from Equation 4.20 model. However, a direct search method is very sensitive to the selection of the initial search points which often give local optimal points. Therefore, many more calculations are needed by a direct search method to determine a 'real' optimal point from many initial search points. In the present work, if an initial point could be estimated by linearizing a non-linear model, the direct search, then, was started from that initial point to get a set of optimal parameters. Otherwise, the parameters could only be determined by searching from various initial points. The initial estimation of the two parameters in Equation 4.20, r  max  and K,, was made  by a linear least-square method after a transformation of Equation 4.20 to, S _  K.  |  S  (4.21)  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  86  and then, a direct search (see Appendix G ) was carried out to optimize the fit of Equation 4.20 to the experimental data. T h e results were r  mffit  K  s  = 0.3144  mg lactose/mgC/hr  = 201  mg lactose/1.  To compare these data with the literature data which are summarized in Table 4.13, the units were converted to k g C O D / k g V S S / h r and k g C O D / m , respectively, assuming 1 3  kg lactose equivalent to 1.067 kg C O D for complete oxidation of lactose and 1 kg biomass carbon equivalent to 2.61 kg V S S .  Ci H 2  2 2  0 n + 120  2  — • 12C0  2  + 11H 0 2  Compared with Kisaalita's data, the second set in Table 4.13 which were obtained in suspended cultures, the maximum lactose utihzation rate was much lower and the half velocity constant higher. Kisaalita noticed that bacteria attached and grew on the walls of his reactor and auxiliary internal parts and this might have caused errors if the fixed biomass had not been included, especially under high dilution rates with fewer free cells [46]. Another possible reason was that the immobilized bacteiral cells excreted more extracellular polymers than the free cells. Therefore, the lactose utihzation rate based on unit weight of immobilized biomass (carbon or suspended solids) was lower than that based on unit weight of free cells. T h e difference may also be attributed to the fact that immobilization of bacteria has a large influence on the substrate digestion rate. It has been found that, in nature where the substrate concentration was relatively low, attached bacteria are often more active than free cells due to the concentrating function of the supports [167,168,169]. In a fermenter where substrate level is quite high, however, this kind of concentrating function plays no significant role. Very recently, V a n Loosdrecht and coworkers [170] reviewed the  Chapter 4. Intrinsic Kinetics of Lactose Utilization  87  Table 4.13: Maximum lactose digestion rate and half velocity concentration  K  Temp/pH  s  kgCOD/kgVSS/hr  kgCOD/m  2.63  -» 0  3  Culture/Substrate  Reference  suspended anaerobic  [145]  °C 30/6  /glucose 2.28  0.022  35/4.5  suspended anaerobic  [46]  /lactose 2.14  0.37  1.52  0.0053-  35/6.6-7.3  mixed anaerobic  [162]  /glucose 35/6  suspended anaerobic  [46]  /lactose  0.008 0.564  18.3  35/6.6-7.3  mixed anaerobic  0.545  30.9  35/6.6-7.3  mixed anaerobic  0.395  37  36/5.8  mixed anaerobic  [162]  /sewage sludge [162]  /cellulose [26]  /activated sludge 0.313  0.192  35/7.0  theoretical model  [163]  /glucose 0.145  0.214  35/4.5  fixed anaerobic  This study  /lactose 38/5.6-7.2  > 0.103  anaerobic sludge /dextrose,  [164]  tryptone  0.0917  2.0  35/6.3-8.1  fixed films  0.0417  0.15  35/6.3-8.1  fixed films  0.0367  0.25  20-35/> 6  anaerobic filter  [165]  /dextrose, protein [165]  /dextrose /starch  [166]  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  88  literature on the influence of immobilization on the bacterial activity and concluded that so far neither experimental nor theoretical evidence exists that immobilization of cells directly affects their metabolism. For the phenomena of decreased substrate utilization, growth rate, assimilation etc. in a community of immobilized bacteria, various explanations existed such as less cell surface available for substrate uptake [171,172], higher maintenance coefficient [172], substrate transport limitation [173], and desorption limitation [174,175]. Around fixed cells quite a lot of extracellular polysaccharides have been found under the microscope, which connects i the cells forming a network of channels as described in Chapter 2 while on free cells there is less extracellular polysaccharides (only a thin capsule if any). Therefore, the mass transfer from outside to inside of cells, which is a part of intrinsic kinetic process, has more resistance due to the extra polysaccharides on the cell wall which is excreted by the bacteria during the immobilization of the free cells. Moreover, part of a cell surface may be unavailable for the mass transfer due to very close proximity between some cells. O n the basis of activity measurements on attached and free living Vibriosp.,  Jeffrey  and Paul [171] suggested that not only the maximum substrate consumption rate but also the apparent substrate affinity of attached cells are different from suspended cells. A decrease in substrate affinity or an increase in the half saturation constant, K , for s  adhered cells has often been reported [173,176,177]. [176], there are two possible explanations:  According to Bright and Fletcher  (1) the difference is due to changes in the  environment of the cell, or (2) the higher K„ values for surface-associated  cells is a  reflection of a real difference in assimilation behavior. Independent experimental evidence that the results of the present study are more reliable can be obtained from the experimental data of lactose transport through active acidogenic biofilms (see Chapter 7). B y using Kisaahta's kinetic data and assuming that the diffusivity of lactose in free solution is its effective diffusivity within the biofilms, the  Chapter 4. Intrinsic Kinetics of Lactose Utilization  89  lactose concentration found from the reaction-diffusion model very quickly dropped to less than 1 0  - 3  at a biofilm thickness 0.5 m m while the measured lactose concentration  was about 50 mg/1 at a biofilm thickness 1.3 m m (Table 7.26).  If Kisaahta's kinetic  data and the measured lactose concentrations on the two sides of a biofilm were used to estimate the effective diffusivity of lactose in the biofilm, the lactose effective diffusivity was found to be in a range of 15 to 25 times higher than its value in free solution. However, the estimated lactose diffusivity by the kinetic data of the present study was quite reasonable, D e / D < 1.  4.4  Production of Organic Acids  A t the same time the lactose digestion rate was measured, the products were also analyzed and measured. T h e detectable products included acetate, propionate, butyrate, ethanol and lactate, the major ones being acetate and butyrate (see Appendix C ) . Some organic acids with carbon number more than 4 (Ce, Cg) were also detected in transient processes (change in dilution rate, feed concentration etc. ), but at steady state they disappeared. Table 4.14  hsts the reactions  standard free energy.  of lactose being converted to those products and their  Although the standard free energy of the reaction for butyrate  formation is the least, butyrates were produced in large amounts in this experiment. This must have been affected by the experimental conditions. A carbon balance on conversion of lactose to these products ranged from 52.1 to 67.7 percent as shown in Appendix C , a reasonable range considering the fact that the carbon converted to CO  2  and to biomass had not been included in the balance. If carbon leaving  the reactor in gaseous bubbles, or dissolved in the effluent was estimated according to the reactions in Table 4.14 (e.g. 1 mole of acetate accompanied with 1 mole of H C O j ) , the carbon balance was between 85 and 102 percent.  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  90  Table 4.14: Reactions of Lactose Conversion Reactions C  1 2  H  2 2  AG  0 i i + 9H 2 0 - » 4 C H C O O - + 3  4HCO3 + 8H+ + 8H  C  1 2  H  2 2  0 „ + 4H -» 4 C H C H C O O - + 3 H 0 + 4H+  1 2  H  2 2  0 n + 5H 0 - » 2 C H C H C H C O O - + 4 H C 0  Ci H  2 2  0 n + 5H 0 - » 4 C H O H + 4 H C 0  Ci H  2 2  2  2  2  3  2  2  2  3  2  5  -716.2  2  2  2  3  3  + 6H+ + 4H  + 4H+  Q „ + H 0 -+ 4 C H C H O H C O Q - + 4H+ 2  (kJ)  -412.6  2  C  0  3  2  -50.92 -451.8 -396.6  Source is [156].  Similar to the utilization of lactose, each of the products was balanced around the reactor at a steady state.  Produced from the reactions + Flow in = Flow out  The 'flow i n ' amount was zero because no digestion of lactose occurred in the feed tank under the measures mentioned before. So, for the ith component, at steady state, Production rate = Flow out that is, TiW = Fd  (4.22)  or, r< = FCJW  (4.23)  Where r{ is the production rate of the ith component based on the unit weight of carbon content of biomass (mg i / m g C / h r ) , F the feed flow rate (ml/hr), Ci the concentration of the component in the effluent (mg i/1) and W the total amount of biomass carbon content within the reactor at that time. T h e right side of Equation 4.23 can be calculated from the experimental data of F, Ci and W, and thus the production rate of the ith product can be found.  Chapter 4. Intrinsic Kinetics of Lactose Utilization  91  0.12  ^  0.10-  o E D)  co  «  k_  0.08-  •  0.06-  O)  •  •  T ?  1  c ff  0.04-  o " <  0.02  0.00  1000  2000  3000  4000  6000  L a c t o $ e c o n c e n t r a t i o n (mg/l)  Figure 4.25: Influence of lactose concentration on acetate production rate. The hne is calculated from Equation 4.24 and the parameter values in Table 4.15 As discussed in Chapter 2, lactose fermentation proceeds via the Embden-Meyerhof pathway and pyruvate is the key intermediate from which other products are formed. The rates of these parallel reactions were dependent on the concentration of pyruvate and thus lactose concentration. The dependence of the production rate of each product on lactose concentration is shown in Figures 4.25,4.26,4.27, 4.28,4.29. The products can be divided into two groups according to the pattern of influence of lactose concentration on their production rates; acetate, butyrate and ethanol one group (Figures 4.25, 4.26, 4.27), lactate and propionate another (Figures 4.28, 4.29). The first group can be described with a Michaelis-Menten type equation;  Where r  . - is the maximum production rate of the ith component (acetate, butyrate and  maa t  Chapter 4.  Intrinsic Kinetics of Lactose Utilization  92  Figure 4.26: Influence of lactose concentration on butyrate production rate. T h e hne is calculated from Equation 4.24 and the parameter values i n Table 4.15  0.014  0.000  1000  2000  3000  4000  6000  Lactose concentration (mg/l) Figure 4.27: Influence of lactose concentration on ethanol production rate, T h e hne is calculated from Equation 4.24 and the parameter values i n Table 4.15  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  93  0.010-1  Figure 4.28:  Influence of lactose concentration  on propionate production rate. T h e hne  is calculated from Equation 4.25 and the parameter value in Table 4.15 0.014-,  o  0.012-  6000  L a c t o s e c o n c e n t r a t i o n (mg/l) Figure 4.29:  Influence of lactose concentration  on lactate production rate.  calculated from Equation 4.25 and the parameter value in Table 4.15  T h e hne is  Chapter 4. Intrinsic Kinetics of Lactose Utilization  Table 4.15:  94  Rate parameters of the products in lactose fermentation Tmaxj  K  k  Bti  F test  {  0 95  (m /mgC/hr)  (mg s/1)  0.0599  89  3129  2.1  Butyrate  0.115  532  1246  2.1  Ethanol  0.0101  929  556  2.1  g l  Acetate  IP"  F.  6  Lactate  2.18  1383  2.1  Propionate  1.25  705  2.1  ethanol) (mg i / m g C / h r ) , S the lactose concentration (mg/1) and K ^ B  concentration  (mg/1).  T h e two parameters,  r  maXt  i and K i,  the half velocity  were estimated with the  s  same method as for lactose utihzation rate, i.e. by a linear least-square method after a transformation of Equation 4.24 to a hnear expression hke Equation 4.21, and then by the direct search method to optimize the fit of Equation 4.24 to the experimental data. T h e estimated values of parameters are listed in Table 4.15 T h e production rates of the second group, including propionate and lactate, has a hnear relationship with the lactose concentration.  (4.25)  r = hS {  Where k{ is the specific reaction rate (mg i / m g C / h r ) ( m g / l )  _ 1  which is the production  rate when lactose concentration is 1 mg/1. T h e estimated values of ki are also listed in T a ble 4.15.  T h e statistical tests (F test) indicate that the influence of lactose concentration  is significant on the yield rates of these 5 products. Cohen and co-workers [178] investigated acidogenesis of glucose in a suspended culture and found that propionate and butyrate were formed by at least two different species, and thus two types of fermentation occurred under different environments: • butyrate type fermentation; production of mainly butyrate, acetate, C O 2 , H2 and  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  95  low E h values, • propionate type fermentation; valerate,  mainly propionate and acetate, minor amounts of  low or no gas production consisting solely of C O 2 , relatively high E h  values.  Under the present experimental conditions as summarized in Table 4.12,  the butyrate  type fermentation predominated.  Lactose  Propionate  i  +1/3 A T P Lactate  +2ATP -2H  -4H  +2H  j Pyruvate j +H  Ethanol  Propionate  Glucose I  -4H  A Succinate j +ATP 8  :  -4H Acetyl C o A \ ' +ATP  Butyrate  +ATP Acetate  Figure 4.30:  Pathways of acidogenesis of lactose. Sign (-) refers to consumption, and  (+)  refers to production. T h e intermediates are in dash boxes and products in sohd boxes.  Chapter 4. Intrinsic Kinetics of Lactose Utilization  96  Many reaction pathways are known which lead to a great variety of fermentation products for carbohydrate  anaerobic digestion as reviewed in Chapter 2.  Figure  4.30  gives a simple relationship between the substrate and the products as well as production of A T P and transfer of electrons/hydrogen by which the reduced co-enzyme, N A D , can be reoxidized. T h e possibility of producing various products is especially high in a mixed culture because the presence of so many bacterial species offers the potential to induce a great variety of enzymes which are needed for various reactions.  It is well known that het-  erotrophic bacteria degrade carbohydrate for energy and carbon which are necessary for their reproduction and life maintenance.  T h e energy released from the chemical bonds  of the substrate is stored in A T P , an energy-rich molecule.  T h e more A T P a reaction  pathway can yield, the more likely it is that it would predominate.  T h e fact that only  butyrate and acetate were the main products under the present conditions implied that their formation could give more energy to the bacteria than could the other pathways. Thauer and co-workers [179] have extensively reviewed energy conservation in chemotrophic anaerobic bacteria.  It seems that, in many anaerobic bacteria, the amount of  A T P formed per mole of energy supplying substrate can be regulated, thus, permitting the organism to optimize the thermodynamic efficiency of energy transformation. T h e formation of lactate can only give 4 moles of A T P per mole of lactose utilized, because no energy is available from the conversion of pyruvate to lactate even though it accepts the electrons/hydrogen produced.  Conversion of pyruvate, however, to acetyl-  C o A , the primary energy-rich intermediate, can offer more A T P , which is obtained during its further conversion to butyrate and acetate, and so the bacteria prefer the butyrate type fermentation. Furthermore, acetate, butyrate and ethanol have the same precursor, acetyl-CoA. T h a t may be why they have the same type of production rate equation since acetyl-Co A is formed from pyruvate via pyruvate:ferredoxin oxidoreductase or pyruvate  Chapter 4. Intrinsic Kinetics of Lactose Utilization  97  formate lyase [179]. As with the formation of lactate, no extra A T P is produced during acetyl-Co A conversion to ethanol, and thus, the amount of ethanol, as a minor product, had the same level as lactate in the fermenter (Figures 4.27 4.29). 8 moles of A T P are produced per mole of lactose utilized via the pathway to acetate, 6 moles A T P to butyrate and 4 moles A T P to ethanol. T h e preference of bacteria on these pathways are also reflected in their affinity coefficients or half velocity K i. e<  T h e first choice was the pathway to acetate (K  s  concentrations,  = 89 mg/1) and then to butyrate  (K, = 532 mg/1) and finally to ethanol (K„ = 929 mg/1). There are two pathways for propionate formation; in the acrylate pathway lactate is reduced stepwise to propionate, i n the succinate-propionate pathway pyruvate is converted to propionate via succinate [180]. T h e present experimental conditions may have been unfavorable to the bacterial species so that the necessary enzymes could not be induced to convert pyruvate to propionate via the succinate pathway even though the formation of propionate in this way also offers an extra production of A T P . In the next section it will be shown that changes in the environment had an effect on the production of propionate. T h e thermodynamic efficiency of energy transfer from substrate to products explains why acetate and butyrate were the major products of lactose acidogenesis under the present conditions. It cannot, however, explain why the bacteria could not convert lactose solely to acetate which gives more A T P than do conversions to other products. T h e energy required for the synthesis of A T P from A D P and P i is generally provided by reductionoxidation (Redox) process. Anaerobic energy metabolism is often intramolecular, that is, electron-donating and electron-accepting steps are not only linked by the electron carrier ( N A D ) but also by the electron acceptor, which must be formed as a product from the substrate.  During the formation of pyruvate from lactose the dehydrogenase required  N A D as an electron/hydrogen acceptor and its reduced form, N A D H , must be reoxidized  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  98  0.12-j  o  o.io-  O)  E  O)  0.08-  E  0.4  L a c t o s e - u s i n g rate (mg/mgC/hr)  Figure 4.31: Production rate of acetate versus digestion rate of lactose to NAD for the next redox cycle, otherwise digestion of lactose could not be carried on. In the acidogenic phase, the reoxidation of NADH is conducted by transferring the electron/H from NADH to products of fermentation. Among the 5 products, only the formation of acetate cannot accept the electron from NADH. So, the bacteria must find other ways to compensate this enzyme cofactor. This may be the major reason why the formation of acetate remained constant with increase in the amount of lactose digested by unit weight of bacteria in one hour as shown in Figure 4.31, because the amount of NAD is a constant in unit weight of bacteria while conversion to acetate can not reoxidize the reduced NAD. However, formation of other products could transfer electrons from NADH to themselves, and thus, as shown in Figures 4.32, 4.34, 4.33, 4.35, their production rates increased dramatically with increase in lactose digestion rate on unit weight of biomass.  er 4.  Intrinsic Kinetics of Lactose Utilization  0.14  o.oo  o.o  0.1  0.2  0.3  0.4  L a c t o s e - u s i n g rate (mg/mgC/hr)  Figure 4.32: Production rate of butyrate versus digestion rate of lactose  0.014  o.ooo  0.1  0.2  0.4  L a c t o s e - u s i n g rate (mg/mgC/hr)  Figure 4.33: Production rate of ethanol versus digestion rate of lactose  Chapter 4.  Intrinsic Kinetics of Lactose Utihzation  0.010  0.000  o.o  0.1  0.2  0.3  L a c t o s e - u s i n g rate (mg/mgC/hr)  0.4  Figure 4.34: Production rate of propionate versus digestion rate of lactose  0.014-,  cj  0.012  CD  E  "OJ  0.010  S ®  0.008H  C  0.006  >S  i  0.004  •J  0.002  CO  0.000 0.0  rbB: 0.1  0.2  0.3  0.4  L a c t o s e - u s i n g rate (mg/mgC/hr) Figure 4.35: Production rate of lactate versus digestion rate of lactose  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  Table 4.16:  101  Comparison of production rates of organic acids at two p H levels Relative production rate H  Acetate  Propionate  Butyrate  Lactate  4.6  1  1  1  1  6.6  1.08  17.16  1.15  0.97  P  4.5  Responses of Acidogenic Biofilms to Disturbances  Immobilized bacterial communities are quite stable.  A change in p H of the culture  medium from 4.6 to 5.1 did not affect the lactose utihzation rate nor its product distribution. However, when the p H of the culture medium jumped up to 6.5 and stayed at this level, it affected not only the product distribution but also the biofilm itself.  The  amount of biofilm attached on the support was reduced from a density of 4.1 m g C / c m to 2.4 m g C / c m  2  2  and it was observed that the biomass on the bottom of the reactor  increased and a lot of foam was produced on the medium surface. So, a dramatic change in p H could make the environment very unfavorable to some bacterial species.  Unhke  a suspended culture where a bacterial species will be washed out quickly if its growth rate is less than the dilution rate, these bacteria are trapped in the biofilm so that their death and lysis caused the biofilm thinning and the medium foaming. T h e change in the p H of culture medium gradually affected the distribution of the bacterial species and/or their fermentation mechanism, which was reflected in the change of the yield rates of organic acids, especially propionate formation. Table 4.16 compares the production rates of acetic, propionic, butyric and lactic acids at two p H levels, where the production rates at the p H of 4.6 are taken as one unit for the ease of comparison. It is clear that the propionate production rate was increased considerably. Its concentration in the reactor effluent jumped from about 30 mg/1 to 450 mg/1. This proves that low p H depresses the formation of propionate which is generally the least desirable  Chapter 4. Intrinsic Kinetics of Lactose Utihzation  102  fermentative product for the following methane-producing bacteria. A n acidogenic reactor even under normal operation can become unstable because of load changes which are caused by fluctuations in feed concentration and/or flow rate. For a fixed film reactor these two factors produce the same results, a change in substrate concentration, because of negligible washout of cells. Figure 4.36 shows the response of the biofilm reactor after a change in flow rate, from 120 m l / h r to 280 m l / h r . T h e input concentration of lactose was constant at 5500 (mg/1). A t the first steady state (flow rate 120 m l / h r ) , lactose was almost completely digested (100 concentration (10-20 mg/1).  mg/1) with very low lactate  T h e flow rate jump resulted in an increase in lactose and  lactate concentrations in the fermenter. After reaching a peak value where its conversion was only about 24 per cent, the lactose concentration returned to a new low steady value (400  mg/1) corresponding to the new flow rate.  In parallel, the lactate concentration  returned to a new steady value (20 mg/1), too. This response may be due to some kind of temporary physiological slowdown of the bacteria at high concentrations of substrates or products because the bacteria could return to another stable state after a period of time for adaptation. From the results of kinetic studies discussed in the previous sections it can be predicted that an increase in lactose concentration  should result in higher production rates of  butyrate, propionate, lactate etc., and thus an increase in their concentrations  in the  fermenter. Recently, van den Heuvel and co-workers investigated the effect of free butyric acid on the acidogenic dissimilation of glucose in anaerobic continuous cultures by adding extra acetate and butyrate to the culture medium and found that only free butyric acid inhibited bacterial activity and the inhibition was more obvious at lower p H values [181]. In the culture medium, butyrate is in equihbrium with its free molecule at steady state,  CH CH CH COOH ^ 3  2  2  CH CH CH COO3  2  2  + H+  Chapter 4. Intrinsic Kinetics of Lactose Utilization  103  Legend  Time (hr)  Figure 4.36: Responses of the acidogenic biofilrn reactor to flow rate change. The sohd hne represents lactose concentration and the dash hne lactate concentration. The dissociation constant, K, is only a function of temperature, [CH CH CH COO-}[H ] 3  2  +  2  [CH CH CH COOH] 3  2  2  Lower pH values (higher [H ]) and/or higher butyrate concentration can lead to +  more free butyric acid. It is widely accepted that free fatty acids will pass through the plasma membrane easily and may dissociate intracellularly, thereby abohshing the transmembrane pH-gradient which is a part of proton motive force necessary for bacterial functions [182].  Chapter 5  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  Compared with the start-up of acidogenic biofilms by which lactose is converted to organic acids, the build-up of methanogenic biofilms is more time consuming because of the much slower growth rate of methanogens and acetogens. and acetate-producing  Moreover, since methane-  bacteria form a symbiotic microbial community and collectively  convert the fermentative products from the first acid-producing phase to methane, it would be valuable to know if support materials have some kind of selective function on the attachment of various bacterial species responsible for different substrate utihzation. As discussed in Chapter 2, many properties of a support material may be able to influence the attachment of bacteria.  One of them is wettability or hydrophobicity of the  surface which has been shown by Verrier et al [112] to affect the attachment of different methanogenic bacteria.  5.1  Wettability of a Support Surface  Wettability measurement of a sohd surface is an old technique. Compared with some new surface-sensitive techniques which probe the sohd/vacuum interfaces like E S C A (electron spectroscopy for chemical analysis) and S E M (scanning electron microscopy), however, wettabihty measurements  that probe the solid/liquid interface have some  such as great surface sensitivity (5-10  advantages  A), inexpensive, simple and compatible with most  samples including organic materials and hquids [183]. W h e n a hquid drop comes in contact with a sohd, the liquid may wet the sohd very 104  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  105  Figure 5.37: Schematic illustration of a spreading drop of hquid in contact with a sohd surface, showing the relations between the contact angle, 6, and three interfacial free energies. well, and thus spread completely across the surface, or not so well, with a result that the drop edge expands to a maximum extent which is dependent on the strength of interaction between sohd and hquid surfaces. T h e contact angle, 6, as illustrated in Figure 5.37, is an important thermodynamic quantity that characterizes this interaction between a sohd and a hquid surface at the interface with gas. It is generally agreed to give the name of contact angle to the angle within the hquid, i.e. 6 as shown in Figure 5.37. This angle is an experimental representation of an important thermodynamic relationship known as the Young equation, which relates the cosine of the angle, 6, to the interfacial free energies of the three interfaces, sohd-vapor (sv), sohd-hquid (si) and liquidvapor (lv). A t equilibrium,  f cos6 - f„ - j lv  ai  (5.26)  Obviously, the contact angle, 0 can be interpreted only in terms of differences and ratios  Chapter 5.  106  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  of surface free energies rather than as a direct measure of interfacial tension or free energy between sohd and liquid surface. However, with comparisons of measurements in similar systems rather than the interpretation of absolute values obtained from only one system, this technique of contact angle measurements  is applicable to the characterization  of  solid-liquid interfaces. Roughness of a surface also affects the "equilibrium" contact angles. Every groove, valley or scratch on a sohd surface acts as a capillary tube in which the liquid rises if the contact angle is less than 9 0 ° or descends if this angle is greater than 9 0 ° [184]. Hence, a rough surface usually is better wetted than a smooth surface by a well-wetting liquid, while a poorly wetting liquid should spread on a smooth surface better than on a rough one.  T h e liquid thus acts as a sensitive probe of the surface by interacting chemically  with functional groups at the surface, or physically with surface asperities. The contact angle formed by a drop on a horizontal sohd surface can be computed from the dimensions of the drop. T h e computation is simple if the drop is so small that it can be treated as a spherical segment.  As illustrated in Figure 5.38, the angle 6 can  be calculated from the volume, v, of the drop and the diameter, a, of its base. If the drop is so small as to be nearly spherical, the relation between v and a is given by the equation [184],  a  V  3  _  24Sm fl 3  ~ TT(2 - ZCosO + Cos 9) 3  ^'  5 2  Four types of material have been used in this study as the supports for symbiotic methanogenic biofilms (wood, ceramic, P V C and stainless steel) because they not only are widely used in industry but also give a quite wide range of hydrophobicity.  The  contact angle between a clean surface and a small water drop (1 pi) was measured with a 30 power microscope. For the base length, a, of a small drop, the average of the values  '  Chapter 5.  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  V  Figure 5.38:  107  X  Illustration of calculating contact angle, assuming the drop being a spherical  segment. measured at 0, 45 and 9 0 ° was used. T h e water contact angle on each material which is hsted in Table 3.11 in Chapter 3, is an average of measurements on more than 10 drops.  5.2  Experimental Steps  T h e general setup has been illustrated in Chapter 3. T h e film attachment experiments were conducted in the continuous flow reactor as shown in Figure 3.10. mixture of organic acids (acetate : propionate : butyrate = 6 : 3 : 3  T h e feed was a  g/1) plus growth stim-  ulating inorganic salts as hsted i n Table 3.9. It was stored at 4 °C under an oxygen-free atmosphere provided by nitrogen bubbling. T h e inoculum was taken from a continuous flow methanogenic reactor which was fed with the same feed. Firstly, the reactor was filled with 500 m l of feed and 500 m l of tap water and the temperature solution was adjusted to 35 °C by the heat exchanger  of the medium  on the recycle hne with nitro-  gen bubbhng through the solution. After the temperature  was constant at 35 °C7 and  the p H of the medium was controlled at 7.1 by the automatic p H controller (with 0.2N  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  108  hydrochloric acid solution), the reactor was seeded with 400 m l of inoculum under a nitrogen atmosphere and operated in batch mode for 2 days with a recycle rate of 152 ml/min.  T h e operation was then shifted to a continuous mode with a hydrauhc reten-  tion time at 7 to 8 days controlled with the microvalve. Under this hydrauhc retention time, the recycle ratio was greater than ten and hence, the reactor could be treated as a completely mixed continuous flow reactor with uniform nutrient concentration and temperature profiles being maintained in the reactor.  Also this long retention time gave a  considerable concentration of free bacterial cells suspended in the medium, which was essential for the investigation of attachment of free cells on support surfaces. A t steady state, the concentrations of acetate, propionate and butyrate in the reactor were about 1,800, 1,000 and 100 mg/1, respectively.  A t this time, the four support materials men-  tioned above were inserted into the culture medium from the top of the reactor and the time was recorded as zero time for start-up of biofilms on the supports. A run started with a total of 32 samples which had been washed with detergent and distilled water before their being immersed into the medium. After some time (6 - 10 days) one of each type of surface was removed and the biomass accumulated on it was measured in a batch culture till all the samples were used. A key, and also the most difficult, problem in this investigation was how to discriminate and describe quantitatively each bacterial group responsible for special substrate degradation in a mixed bacterial community.  T h e usual methods such as by morpho-  logical difference, by protein content, or by special co-enzyme (e.g.  .F420)  not capable of discriminating the mixed bacterial species from each other.  content are Based on a  principal that the bacterial species responsible for a special substrate assimilation can be lumped into a group (such as acetate-degrading,  propionate-degrading and butyrate-  degrading bacteria), the shde samples with attached biomass were immersed in a "standard" medium which was prepared by diluting the feed to one fifth and the utihzation  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  rates of each organic acid in the batch culture were measured.  109  50 ml of the standard  medium which was used throughout this investigation was placed in a 150 ml Erlenmeyer flask immersed in a water bath at 35 °C and nitrogen gas bubbled through the medium to give good mixing and an oxygen free atmosphere. Each support shde with fixed biomass was placed in a flask and the concentrations of acetate, propionate and butyrate in the medium samples taken at regular intervals were measured by gas chromatography (see Appendix B ) . A sample of medium ( 1 - 5 ml) from the continuous flow reactor was treated in the same way in order to estimate the number of free cells in the fermenter.  To be  certain that the constant growth rate assumption would hold during the batch test, the run time of batch tests was controlled to maintain a high substrate concentration. T h e mass of bacteria carrying out dissimilation of each of the three organic acids was monitored by foUowing the degradation rates of the organic acids i n the standard cultures.  Substrate consumption is related to the growth and survival of the bacterial  type using that particular substrate,  [dS/ dt] i — [dSIdrouth + [dS'/dt] tota  maintenance  (5.28)  or, V[dS/dt]  total  = (fi/Y + m)X  where, V = volume of batch culture medium (1) t = culture time (hr) S — concentration of a substrate in the batch culture (mg/1) p — specific growth rate of a bacterial group ( h r ) - 1  Y — yield coefficient of a bacterial group (mg/mgS) m = maintenance coefficient (mgS/mg hr) X — total mass of bacteria which degrade that substrate (mg).  (5.29)  Chapter 5.  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  110  c  o c CD O  c  o o —I— 60  100  Time (hr)  —i— 160  200  Figure 5.39: Organic acids degradation in a batch culture, o - acetate, A - propionate, x - butyrate. In a nutrient rich environment the microorganisms have sufficient food supply so that p is a constant. Thus the total mass of a bacterial type is proportional to the utihzation rate of that substrate. p/Y + m  v  '  Figure 5.39 shows that the concentrations of the three organic acids decreased linearly with culture time (i.e. [<i5/ti£] / = constant). The slopes are the utihzation rates for tota  each acid. Therefore, it was assumed that the total number of bacteria remained constant during the tests. It was also assumed that the fixed bacteria had the same phsiological properties (p, Y and m) as those of the free cells in the continuous flow reactor, which gives X fixed X free  [dS/dt]fixed [dS/dt]free  (5.31)  Chapter 5.  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  111  where the subscripts "fixed" and "free" represent the biomass samples from fixed biofilms on the supports and from the medium of the continuous flow reactor.  5.3  A Kinetic Model of Biofilm Start-up  In general it can be deduced from the work which has been reported on bacterial attachment that the formation of a biofilm is the net result of several steps  [81].  1. bacterial attachment on a clean surface 2. growth of fixed microorganisms 3. suspended cells attaching onto bacterial colonies/films 4. detachment of fixed ceUs into the aqueous environment  5.3.1  Attachment on Clean Surfaces  In the absence of external forces, bacterial ceUs dispersed in a fluid exhibit Brownian motion and touch the support surface randomly. In a flowing fluid they may be entrained in the fluid streamlines and be brought into contact with the surface as the fluid moves past it. If a cell contacts a surface for a long enough time for the cell to produce adhesive polymers [98] which bridge between the cell and the substratum, the ceU is fixed to the support. Marshall et al [85] observed reversible and then irreversible attachment  of  bacteria at a surface. Thus two steps are involved; firstly, a bacterial cell approached the surface to form a reversible bacterium-substratum complex and secondly, the complex becomes a fixed cell.  x + A  fcj/fe-i  x-A  xA  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  112  where, x = concentration of the suspended cells (cells/1) A = fractional clean surface area available to bacterial cells x — A = density of cell-substratum complex (cells/cm ) 2  xA = density of fixed cells (cells/cm ) 2  T h e rate of complex formation is determined by the concentration of suspended cells [90] and the available clean area [  1  d t  =k [x]A  (5.32)  1  It is assumed that the fixation of a cell-substratum comples is the rate limiting step since it involves some physiological activities for the cell to produce exopolymers. Therefore, the disappear rate of the complex is mainly due to the detachment of the complex into aqueous medium again. -  d  ^  ^  = k_ [x-A]  (5.33)  l  At equilibrium, the attachment and detachment rates will be equal  ki[x]A - k-^x-A]  (5.34)  or,  [x-A] k  1  and k_i are the specific attachment  = (ki/k_i)[x]A  (5.35)  and detachment  rate constants.  T h e rate of  bacterial ceUs attaching onto a clean surface (cells/cm .hr) is; 2  n  = k2[x-A]  = k[x]A  (5.36)  where  k = kiki/k-i  (5.37)  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  This overall rate constant,  fc(l/cm .hr)  113  indicates whether the rate of attachment is fast or  2  slow. Thus, the value of k may be used as an indicator of the ease of bacterial attachment on a surface.  5.3.2  Growth of Attached Bacteria  Growth of the bacteria immobihzed on a surface makes a major contribution to the development of biofilms [185]. T h e rate of growth may be expressed as r  2  = fi[xA]  (5.38)  T h e specific growth rate, fi ( h r ) , is a constant if the fixed cells are able to get enough -1  nutrients from their environment (thin biofilms at high substrate  5.3.3  concentrations).  Attachment on Fixed Biomass  Attachment onto fixed biomass can be described by a similar set of steps to those of attachment on a clean surface,  X +  >  k  A  ^  x  -  A  > J ^  x  A  where A' is the fractional area occupied by fixed colonies/films and A + A'=l  (5.39)  Again assuming that the forward and backward rates easily reach equilibrium because of the very slow fixation of the complex, x — A', k [x}A' 3  = k_ [x-A'}  (5.40)  = {k /k- )[x]A'  (5.41)  3  and so, [x-A']  3  3  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  114  T h e rate of accumulation of fixed cells due to attachment of free cells on the biomass already fixed on the sohd support is r where K = k k /k_ 3  4  3  = k [x-A'] = K[x]A' = K(l - A)[x]  3  (5.42)  A  ( l / c m . h r ) , signifying the ease with which bacterial cells attach onto 2  biomass already present. Obviously, i n contrast to k, K is not affected by the properties of support surfaces.  5.3.4  Detachment  T h e mechanisms of detachment of immobihzed biomass previously has not been investigated throughly as was indicated in Chapter 2. T h e major possible reasons for detachment of fixed biofilms are sloughing (for thick biofilms) and shearing caused by fluid flow. In the latter case, the detachment may occur not only on the outer layer but also at some locations inside the biofilm depending on the bridging strength between the cells. T h e thicker the biofilm, the more connections there are between cells, and the greater is the probabihty that the connections may be broken. Therefore, the rate of detachment of fixed cells has been set proportional to the amount of biomass on the surface, r  4  - K'[xA)  (5.43)  T h e parameter K' ( h r ) is influenced by the shear stress caused by culture medium - 1  flow, by the bacterial species, and by other factors which influence the structure and homogeneity of the biofilm, e.g. the concentration of cations such as C a  2 +  , and M g  2 +  .  T h e total rate of accumulation of one bacterial subgroup is the sum  r = r + r + r - r 1  2  3  4  which gives, = k[x]A + K[x](l - A ) +  dt  p[xA] - K'[xA)  (5.44)  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  115  or, ^  1  dt  = {k- K)[x)A + K[x] + (p-  K')[xA)  (5.45)  where A , the fractional area of clean surface, is a function of time,  A = 1  at  t=0  and A —> 0  as  It was observed during the experiments  t —> oo that the bacterial colonies, rather than a  uniform biofilm with one- or two-cell thickness, were scattered on the surface and had different thickness. As the fixed microorganisms grew they spread slowly over the surface thus reducing the clean surface area left.  Therefore, the clean surface area should be  inversely proportional to the growth rate of the fixed bacteria which is an exponential function of time in a nutrient rich environment. This can be expressed as;  A = e-'  (5.46)  1  T h e parameter s ( h r ) indicates the ease with which the colonies can spread over a sur- 1  face and may be a function of rugosity of the surface. Substitute for A in Equation 5.45,  ={k- K ^ e -  1  + K[x] + {u- K')[xA]  (5.47)  dt Integrating with the initial conditions,  [xA] = 0  at  t=0  gives (5.48)  Chapter 5.  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  116  T h e density of fixed bacteria on a support shde, x A , and the concentration of free cells in the fermenter, x, were measured with the 'standard' batch cultures as discussed above. T h e left side of Equation 5.48  =A] _ X [x]  becomes,  ^ volume of sample  fixed  Xf  area of support  Tee  where the volume of sample refers to the volume of medium taken from the continuous flow reactor (1-5 ml) and the area of support is the area of the removable support sample. Using Equation 5.31, Equation 5.48  [dS/dt}  fixed  [dS/dt]  free  x area  x volume  =  =  becomes  k-K  {  u- ')t K  _  -.  ,  t]  s+p-K'  [  J  K  r>-*')< _ -n  p - K<  1  J  ,~ ~ K  '  Q )  J  Now, the left side of Equation 5.50 can be experimentally determined with the data from the batch cultures as shown in Figure 5.39.  5.4  Estimation of Model Parameters  Equation 5.50  is a general equation which can be apphed to each substratum; wood,  ceramic, P V C and stainless steel, and also to each bacterial group; propionate-degrading and butyrate-degrading.  acetate-degrading,  Hence in all, 12 equations hke Equa-  tion 5.50 can be written down with different parameters.  Not all the parameters, however,  in these 12 equations should be different since they may be independent of the surface type or the bacterial type. Since it was impossible, a priori, to determine which values were common to all equations, a direct search method [186] (see Appendix G) was used to search for a set of optimum parameters  which would best fit one of the models with  13, 16, 21 and 22 parameters to the 12 curves (108 experimental data points as hsted in Appendix D ) . T h e optimum parameters for each model were determined by comparision  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  117  of the local minimum fit errors obtained from different initial search points and by the significance of the values (e.g.  the parameter  values should be positive).  Table 5.17  summarizes the results of screening the models by comparing the sum of absolute error between the experimental values and the values predicated by a model. In the table, K represents the attachment  of free cells onto fixed biomass already  on the support surfaces; K' the detachment of immobilized cells into the medium; p the specific growth rate of attached biomass; k the attachment of free cells onto clean surfaces and s the expansion of attached microbial colonies on support surfaces.  T h e subscripts  indicate the surfaces and the bacterial types Since start-up of a biofilm is the net result of several steps hke attachment,  growth  and detachment, a mechanistic model which describes these steps always contains more parameters than an empirical correlation. If the consideration is limited to one bacterial and one support type, 5 parameters and 4 freedoms (freedom = number of parameters number of equations) are involved in Equation 5.48.  In this case, some of the parameters  may be highly correlated. However, when the number of types of bacteria and supports was increased, even though the total number of parametrs were increased, the freedom for each of bacterial and support type was decreased. Furthermore, since the steps described by the model always occur simultaneously during the build-up of a biofilm and could not be separated experimentally, changing one factor hke support surface wettabihty which would affect one of the steps (free cells attaching onto clean surfaces),  and thus, the  value of the parameter (k) describing this step, may be the only practicable method to investigate this complicated process. T h e simplest model, model 1, assumed that the surface characteristics  had the same  effect on the three bacterial groups, and thus there were only 13 parameters 12 equations.  in the  T h e sum of absolute errors for this model was 5.53 as compared to the  experimental data.  Model 2 tested whether the attachment-detachment  of bacteria to  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  Table 5.17: Results of screening kinetic models of biofilm start-up 1  2  3  4  Unit  13  16  21  22  cm/day  0.001125  day' day' day' day' day' day' day' day' day' day' day' day' day' day' day' day'  0.02225  0.02225  0.02148  >)  0.02938  cm/day cm/day  Model Parameters K K'w  1  1  K  P  1  K K pwa Ppa P-sa Pea P'wp  thp  1  1  1  1  1  1  Vcp Pwb  fhb P-Bb  Pcb k  ""wa h  1  1  1  1  1  0.003194 0.05192  0.02819  !) )) ))  0.03444  0.03963  0.03581  0.06651  ii ii ii  >) ;)  ii ii ii  0.06364  »)  1  1  0.00225 . 0.000275  0.03062  0.02806  0.0330  j)  >) >)  )> ii  >;  )) )>  0.06118 0.06151  0.03415  0.05481  1!  0.06005  11  0.05788  11  0.05192  0.03875  0.0445  0.03504  0.07236  !) )) !)  j)  )>  0.06632  >)  >j  0.05319  0.04738  0.05596  0.06729  ))  j)  0.03396  jj  0.082  ;>  0.03356  0.02966  0.02968  ii ii  0.07156 0.06757  k b w  cm/day  kpa  cm/day  0.0245  j) 0.02794  kpp  cm/day  kpb k  cm/day  )> >)  ea  cm/day  ii ii 0.0210  0.02844  0.02909  0.03119  kgp  cm/day  )>  kb kca kep  cm/day  )) 0.03481  ii ii  0.02628  cm/day  )!  0.03769  0.04202  cm/day  JJ  kb  )> 0.04731  )! ))  0.03071  cm/day  0.06306  0.05218  0.07837  0.05675  0.06788  0.08931  0.09576  0.05069  0.06638  0.0908  0.1082  0.0595  0.06975  0.08536  0.05146  5.533  5.271  2.783  4.249  t  c  day' day' day' day'  1  Sp  Ss  1  1  1  sum of error  0.04191  0.03786  j) 0.03234  0.06597  >)  w,p,s,c: surfaces of wood, P V C , stainless steel and ceramic ring a,p,b: bacteria degrading acetate, propionate and butyrate  118  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  119  the biomass was influenced by the substrata. This added 3 parameters and only reduced the sum of absolute error to 5.27. Model 4 tested the possibihty that the specific growth rate of each species was influenced by the characteristics  of the substrata.  Although the  number of parameters was increased to 22, the sum of absolute error was only reduced to 4.25.  Model 3 which was used to describe the results was based on the assumption that  each bacterial type attached differently to each surface, but their specific growth rates were independent of the surface properties because the support materials used in this study were inert (wood is not biodegradable to any extent in the short time period used) and fixed microbes could get enough nutrients from the culture medium with no help from the sohd surfaces.  Twenty one parameters in 12 equations gave a sum of absolute  error of only 2.78 probably due to the reasonable assumptions which were made. Figures 5.40, 5.41 and 5.42 show how well this model fits the experimental points. Mathamatically, although 22 parameters were estimated simultaneously and the total degree of freedom (22 - 12) of the search was 10, for each of the equations the degree of freedom was less than 1 (10/12) (a hnear equation i n general has one degree of freedom). Therefore, for each combination of bacterial and support type, the fit of the equation with the experimental data was made by adjusting less than one parameter,  so, there  was very low correlation between the parameters. In addition to the assumption mentioned above that a special bacterial group (say, acetate- degrading bacteria) has the same specific growth rates on four different supports, the three bacterial groups have almost the same specific growth rates, 0.035  (day ). -1  Lawrence and M c C a r t y [142] obtained a similar result in their study on the kinetics of methanogenic cultures - that is, acetate-, propionate- and butyrate-degrading bacteria had the same specific growth rates.  Moreover, a value of specific growth rate for  methanogenic anaerobes was calculated from the data given by Verrier et al [111] as 0.027 (day ). -1  This is good agreement considering that they used a different technique  Chapter 5.  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  120  Figure 5.40: Build-up of acetate-degrading bacteria in the biofilms. T h e lines are calculated from the model. Surfaces: o - wood, x - ceramic, A - P V C , • - steel  Chapter 5.  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  121  Figure 5.41: Build-up of propionate-degrading bacteria in the biofilms. The lines are calculated from the model. Surfaces: o - wood, x - ceramic, A - PVC, • - steel  Chapter 5.  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  122  4-1  Time (day)  Figure 5.42: Build-up of butyrate-degrading bacteria in the biofilms The lines are calculated from the model. Surfaces: o - wood, x - ceramic, A - PVC, • - steel  Chapter 5.  Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  123  10-1  WOOD  CERAMIC PVC S u r f a c e type  STEEL  Figure 5.43: Ease of attachment of bacteria on substrata as shown by model parameter k. to measure the growth rate on different substrates. The other two factors which were considered to be independent of surface type are K and K', the attachment and detachment to and from fixed biomass, respectively, since the surface involved was a biomass surface. The parameter k, defined in Equation 5.36, is a proportionality factor which takes into account the ease with which bacteria can attach and remain on a surface. Figure 5.43 shows the same data graphically. It can be found that the acetate and butyrate degrading bacteria had obvious surface preferences of, wood > ceramic > PVC > stainless steel The propionate degrading bacteria, however, attached less easily and had almost no surface preference. The spreading factor, s, was calculated for all the bacteria lumped together but for  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  124  0.10-1  120  C o n t a c t angle (degree)  Figure 5.44: Attachment factor, k, as a function of water contact angle of surface. Line is the least square fit. o-butyrate degrading bacteria, A-acetate degrading bacteria, X-propionate degrading bacteria each support surface. Here it can be seen that, once attached, the ease with which the microorganisms spread on the surface by growth was in the order, stainless steel > PVC > ceramic > wood This is exactly the reverse of the ease of attachment order. Figure 5.44 is a plot of the attachment factor, k, against the water contact angles for the four surfaces tested. There appears to be a relationship between these two factors which can be fitted very well by a hnear least square method. The fitting parameters are hsted in Table 5.18.  It was  reported by van Loosdrecht et al [187] that on a single surface (sulfated polystyrene), attachment of 16 bacterial strains could be linearly correlated with the bacterial wall hydrophobicity (water contact angle between 15° and 70°). There have been some contradictory reports on the relationship between wettabihty and attachment as reported by Dexter et al [93], and by Pringle and Fletcher [188].  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces  125  Table 5.18: Linear relations between specific attachment rates and water contact angles Intercept  Slope  (cm/day)  (cm/day.degree)  (%)  Acetate-degrading  0.05632  -2.646 X l O "  99.6  Propionate-degrading  0.03422  -6.659xl0-  0.0847  -4.546 x l O  Bacteria  Butyrate- degrading  r- squared 4  5  88.1  - 4  94.9  Bright and Fletcher [176] found that amino acid assimilation and respiration by attached and free-living marine Pseudomonas spp decreased with increasing water contact angle of the support surface while Fletcher and Leob [189] observed that lower hydrophobicity, i.e. smaller contact angles, promoted attachment of marine bacteria. Absolom [190] has reported that bacterial attachment depends not only on the hydrophobicity of the substrata but also on the hydrophobicity of the bacterial wall [191]. T h e bacteria with hydrophilic surfaces have smaller contact angles and larger  contact  areas on hydrophilic support surfaces. Thus they are deformed more and may be able to remain on the surface for a longer time because more adhesive extracellular glycocalyces (capsules or s layers) are in contact with the substrate [192,100].  If bacterial cells can  stay in contact with a substratum for a long time the physiological functions of the cells can produce more extracellular polysaccharide materials which bridge the cells and the substratum [85,189]. If it is assumed that the initial contact and attachment is a function of the relative hydrophobicity of the surface and the bacteria, the nature of the three bacterial types can be summarized as follows: 1. T h e butyrate degrading bacteria have the most hydrophilic wall surfaces since their specific attachment rate, k, decreases most rapidly with increasing hydrophobicity of the substrata.  Chapter 5. Start-up of Symbiotic Methanogenic Biofilms on Inert Surfaces126  0.10-1  C o n t a c t angle (degree) Figure 5.45:  Spreading factor, s, as a function of the water contact angle of the surfaces  for all bacteria. 2. T h e propionate degrading bacteria are least hydrophilic since the support surface wettability has only a small effect on their attachment. 3. T h e acetate degrading bacteria have somewhat hydrophihc wall surfaces. Thus, since the surface of the three bacterial types have different hydrophobicities, it should be possible to some extent to influence the composition of a methanogenic biofilm by purposely choosing a substratum. T h e coefficient of spread, s , defined by the film attachment model has also been shown to be affected by the substrata wettability.  Figure 5.45  shows graphically this  model parameter, which describes the rate of colony spreading on a surface, as a function of the wetting angle of surfaces. Fixed cells divide within a hydrated exopolysaccharide cells are trapped in a juxtaposition  matrix so that the daughter  that results in the formation of microcolonies  as  Chapter  5.  Start-up  of Symbiotic  indicated in Chapter 2.  Methanogenic  Biofilms  on Inert  Surfaces  127  In a fluid flow environment, as found in this study, solid sup-  ports offer shields for bacterial colonies fixed on them because the flow stagnates on the surface due to the fluid viscosity.  However, on hydrophobic surfaces the solid surfaces  do not strongly attract the water molecules and there is a greater possibility of slip. It is expected that this phenomenon will have an influence on the size of microcolonies. Flattening would result in a spreading of the microcolonies in the flow direction. Since the flow velocity approaches zero at a hydrophilic surface the microcolonies would be less flattened and the spreading would, be slower than on a hydrophobic substratum. T h e more hydrophobic the surface, the more rapid is the spread of bacteria. Pfaender [193]  Shimp and  have also observed the spreading phenomena of microbial colonies as a  function of flow rate.  Chapter 6 Intrinsic Kinetics of Methanogenesis of Organic Acids  Flow from the acidogenic phase reactor, where lactose was converted to organic acids by the acidogens, enters the second phase reactor where the symbiotic methanogenic bacteria convert these intermediates into gaseous products, methane and carbon dioxide. As discused i n Chapter 2, many species of methane-producing bacteria have been identified and maintained in pure culture. A U known species can utihze carbon dioxide and hydrogen as substrates for methane generation whereas a few of them can use acetate as their substrate to produce methane.  Except for these two types of substrates (CO2/H2 and  acetate), the methanogens must rely on the biological activities of acetogens,  who can  convert other substrates such as ethanol, propionic and butyric acids to acetate, carbon dioxide and hydrogen. Table 6.19 lists the four main reactions occurring in fatty acid methanogenesis reported by Thauer et al [179].  Table 6.19: Methanogenic reactions of organic acids Reactions CH3COO-  A G (kJ) + H 0 -> C H + 2  4  HCO3  C H C H C O O - + 3 H 0 -> C H C O O - + H C O j + H+ + 3 H 3  2  2  3  C H C H C H C O O - + 2 H 0 -> 2 C H C O O - + H+ + 2 H 3  4H  2  2  2  + HCO3  2  + H  +  3  -» C H + 4  3H 0 2  2  2  +76.1 +48.1 -135.6  Source is [179].  However, the acetogens cannot do this job at all at high hydrogen partial pressures,  128  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  Table 6.20:  129  V F A distribution in anaerobic digestion process  Substrate  H A c : H P r : H B u (w:w:w)  Reference  Sewage sludge  1 : 0.6 : 0.2  [201]  Raw sludge  1 : 0.9 : 0.7  [202]  Primary sludge  1 : 0.8 : 0.4  [203]  Sewage sludge  1 : 0.3 : 0.3  [204]  1 : 0.3 : 0.3  [26]  1 : 0.4 : 0.6  [44]  1 : 0.1 : 0.2  [44]  Sewage sludge Lactose (D=0.25 Lactose (D=0.1  1/hr) 1/hr)  and thus must rely on the methanogens to remove the produced hydrogen, too. In contrast to the case of lactose acidogenesis where all the bacterial species could be lumped as a single group from the point of view of lactose consumption, the methanogenic community includes at least four groups of bacteria classified by their substrates;  butyrate-,  propionate-, acetate-, and hydrogen-utilizing bacteria.  6.1  Experiments of Organic A c i d Methanogenesis  T h e experimental setup was the same as for lactose acidogenesis; the general setup was as shown in Figure 3.10 and the biofilm support surface was made from P V C sheets as described in Chapter 3. T h e feed was a mixture of acetate, propionate and butyrate in a ratio of 1 : 0.5 : 0.5 by weight. This ratio was determined from the ratios of volatile fatty acids ( V F A ) concentrations produced in the conventional anaerobic digestion process and the two-phase digestion process as hsted in Table 6.20. The studies on lactose acidogenesis described in Chapter 4 revealed that under those experimental conditions the major products were acetate and butyrate with propionate being a minor product. However, propionate was still used in this study for more information about its rate of utihzation, and its influence on the digestion of other components.  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  130  T h e necessary growth nutrients for the microorganisms were added as inorganic salts as shown in Table 3.9.  The feed had an acetate concentration ranging from 2 to 5 g/1, and  hence the acetate concentration in the fermenter could be controlled at different levels under the desired experimental dilution rates.  Correspondingly, the concentrations  of  propionate and butyrate in the fermenter were also controlled at their own levels at the experimental dilution rates because the concentrations of propionate and butyrate in the feed had a fixed ratio to that of acetate ( H A c : H P r : H B u =  1 : 0.5  : 0.5).  The  oxygen dissolved in the feed was stripped off with N . T h e feed was then kept under a 2  N  2  atmosphere by bubbling N through the feed because the methane-producing bacteria 2  are obhgate anaerobes.  To avoid evaporating the volatile fatty acids the p H of the feed  was adjusted to 7.0 - 7.2 by the addition of equimolar sodium hydroxide and potassium hydroxide. Every batch of feed was analyzed at least two times during the experiments to determine the feed concentrations. T h e fermenter had a working volume of one liter.  T h e flow rate, measured by col-  lecting effluent during a period of time (3-4 hours), was controlled at above 30 m l / h r to maintain the dilution rate, D , greater than 0.72 d a y . In their review of the anaerobic - 1  digestion hterature,  Henze and Harremoes [144]  concluded that the maximum specific  growth rate of methanogenic bacteria at 35 ° C was 0.4 d a y . - 1  Under the chosen hy-  drauhc conditions the bacterial cells suspended in the culture medium were washed out and this fraction of biomass retained in the reactor could be neglected in comparison with the biomass fixed on the supports. T h e neghgible amount of free bacterial biomass was confirmed by analyzing the sohd carbon content in the effluents as was done in the experiments of lactose acidogenesis. T h e p H of the fermenter was controlled by an automatic p H controller at 7 . 1 ± 0 . 2 with 0.3 to 1 N hydrochloric acid solutions. T h e HC1 concentration was adjusted according to the strength of the methanogenic activity to have as low an influence on flow rate and  Chapter  6.  Intrinsic  Kinetics  of Methanogenesis  of Organic  131  Acids  local p H in the fermenter as possible. The inoculum was obtained from the secondary phase reactor of a two-phase mini-plant which had been in continuous operation for two years. T h e experiments  on the methanogenesis  of organic acids can be divided into four  stages: 1. Adaptation; T h e feed used during this period was a mixture of acetate (3 g/1), propionate (1.5 g/1) and butyrate (1.5 g/1) so that the bacterial community would have a balanced population, containing acetate-, propionate-, butyrate-, and hydrogenutilizing groups.  T h e fermenter was filled with the feed (500 ml) and tap water  (300 ml). Nitrogen was continuously bubbling through the medium for 2 hours to remove the dissolved oxygen. W h e n the temperature reached 35 ° C , the fermenter was inoculated with 200 ml of inoculum and then operated in batch mode. After the three acids had been used up, half the volume of the culture (500  ml) was  replaced by fresh feed and this was repeated 5 times. 2. Build-up of a symbiotic biofilm; Adaptation of the microorganisms to the mixture of fatty acids gave a balanced microorganism population which was suspended in the culture medium. At that time the supports made of P V C sheets were immersed in the medium under N  2  atmosphere.  T h e operation, then, was shifted to continuous  operation mode with the flow rate controlled below 6 m l / h r (dilution rate D < d a y ) to avoid washout of the free cells. - 1  0.15  After about 60 days a uniform black  biofilm could be observed on the grey P V C sheets. 3. Steady state operation; W i t h build-up of the biofilm the flow rate was gradually increased to above 30 m l / h r to wash out the suspended cells. T h e temperature of the culture medium was kept at 35 ° C and the p H at 7.1. T h e fatty acid concentrations in the fermenter were controlled by adjusting the feed concentration and flow  Chapter 6.  Intrinsic  Kinetics  of Methanogenesis  of Organic  Acids  132  rate. A t each of the desired concentration levels, a steady state (effluent concentration fluctuation < 10 %) was maintained at least 3 days to get experimental data. Similar to the procedures for lactose acidogenesis, after a set of concentration levels had been investigated, the experiments were repeated on the same set of levels again and again. Therefore, the utilization rates of fatty acids could be obtained at each of the concentration levels but on different thickness of methanogenic biofilms. B y comparing these data, the effect of internal mass transfer resistance could be estimated, and only those data not affected by the biofilm thickness were taken as the intrinsic data. 4. Interaction  of fatty acids; Following the kinetic studies, the interaction of fatty  acids was investigated in the "mature and balanced" methanogenic biofilms which contained aU the bacterial types responsible for the utihzation of three organic acids.  In this stage, the concentration of one acid in the feed was adjusted at  different levels while those of other two acids and other conditions were unchanged. Therefore, any change in the utihzation rates of these two acids might be attributed to the effect of the acid with changed concentrations.  T h e acetate concentration in  the fermenter was adjusted from 800 to 1,100 mg/1, the propionate concentration from 0 to 2,000 mg/1, and the butyrate concentration from 100 to 1,500 mg/1. T h e culture temperature and p H were maintained at 35 ° C and 7.1, respectively. T h e intrinsic kinetics of biofilms must be investigated under neghgible external and internal mass transfer resistance.  In this study the influence of external mass transfer  was reduced as low as possible by increasing the recycle rate, and thus the linear velocity over the biofilm, which effectively reduced the external mass transfer resistance as indicated in the studies made on lactose digestion by acidogenic biofilms in Chapter 4. It should be easier to minimize the external and internal mass transfer resistance during  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  133  I.6-1  E  < x 0  1  0  '  '  '  •  I  60  I  100  160  •  '  •  •  I  200  , .  260  i  .  [  .  .  .  .  300  ,  360  R e c y c l e rate (ml/min) Figure 6.46:  Influence of recycle rate on acetate utilization  the methanogenesis because the physiological activities of methanogens are much weaker than those of acidogens. Figure 6.46, Figure 6.47 and Figure 6.48 indicate that as long as the recycle rate was above 190 m l / m i n , i.e. a hnear velocity of 2.8 c m / m i n over the biofilm, the utihzation rates of acetate, propionate and butyrate should not be affected by external mass transfer. This conclusion was confirmed later by the relationship between these reaction rates and the bulk substrate concentrations. Grady and L i m [205] showed that the presence of external mass transfer resistance prevents the rate expression from exhibiting a Michaelis-Menten type of a dependence on the bulk substrate concentration even when the true kinetics were assumed to do so. T h e influence of internal mass transfer resistance is always present if the mass transfer rate, based on the mechanism of molecular diffusion, is not much greater than the consumption rate, and if the bulk substrate concentration is taken as representative of the internal substrate concentrations within the biofilms. Obviously, the thinner the biofilm,  Chapter 6.  Intrinsic Kinetics of Methanogenesis of Organic Acids  Figure 6.47: Influence of recycle rate on propionate utilization  Figure 6.48: Influence of recycle rate on butyrate utilization  134  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  135  0.20  CJ cn  o» E  —  0.16  0.12  CO  • TJ  c O  Q  r P ^  L^Lp  0.08  Ui  0.04-  < 0.00 0.10  0.16  0.20  0.26  0.30  0.36  0.40  Biofilm t h i c k n e s s (mm)  0.46  — i 0.60  1  0.66  Figure 6.49: Influence of biofilm thickness on acetate digestion rate the less the influence of internal mass transfer resistance.  The kinetic data collected  during the early stage of biofilm development are considered to be the result of pure bacterial reaction because a very thin biofilm had developed at that time. Figure 6.49 shows that the acetate utihzation rate per unit weight of biomass carbon gradually decreased with an increase of the methanogenic biofilm thickness because the bacterial cells embedded in the thicker biofilms saw lower substrate concentrations. Therefore, the experiments were arranged in such a way that the experiments at low substrate concentrations were conducted first and those at high concentrations later. Corresponding to higher bulk concentrations, the concentrations inside the biofilms were also higher, and hence, all the bacterial cells embedded in a thick biofilm might have their maximum utihzation rates which was determined by the Michaelis-Menten type kinetics of the bacteria. Thereby, the effect of internal mass transfer resistance could be reduced. As shown in Figure 6.49, the internal mass transfer resistance in a biofilm  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  Table 6.21:  136  Experimental conditions for organic acid methanogenesis  Parameter  Unit  Temperature  Condition 35 ± 2  °C  pH  7.1 ±  Flow rate  ml/hr  >  Dilution rate  day'  0.72  Recycle rate  1/hr  Biomass Feed for biofilm buildup for kinetics  1  0.2  30  11.4 methanogenic  g/1  HAc : HPr : HBu 3 : 1.5 : 1.5 2-5.5  : 1-2.7  :  1-2.7  having a thickness less than 0.3 m m could be considered to be minimal, and hence, the intrinsic kinetic data should be collected during this period (about 100 days). Mixtures of acetate, propionate and butyrate in the ratio of 1 : 0.5 : 0.5 (weight) were used as the feeds for biofilm build-up and kinetic studies. However, investigations on the interaction between fatty acids were also conducted on the balanced biofilms with the feeds having different ratios of acetate, propionate and butyrate.  T h e concentrations of  each acid wiU be listed in the description of each test. Table 6.21 hsts the experimental conditions for fatty acid methanogenesis.  T h e recycle ratio, the ratio of recycle rate  to flow rate, was up to 380, that is, much greater than 10.  Therefore, the fermenter  could be taken as a completely mixed continuous flow reactor ( C S T R ) and the effluent concentration was the same as that in the fermenter.  6.2  Development of Methanogenic Biofilms  T h e amount of biomass retained in a fermenter has a large effect on the performance of this reactor.  In this study all the utihzation rates of the organic acids were based  on unit weight of active biomass. Therefore, the total amount of biomass in the reactor  Chapter  6. Intrinsic Kinetics of Methanogenesis  must be known during the experiment.  of Organic Acids  137  As was discussed in Chapter 4 for the acidogenic  biomass, the methanogenic biomass also existed in three forms: biofilms, the major part of the retained biomass; free cells, a minor fraction under the experimental dilution rates; and the sludge on the reactor walls which was taken as biofilm on the walls as shown in Figure 4.20. W h e n the P V C biofilm supports as described in Figure 3.14 were immersed into the medium, about 30 removable P V C slides were also inserted into the fermenter.  The  biomass on these shdes was measured at different times and was believed to be the same as those on the supports. Each time one or two shdes were analyzed and it was observed that a uniform biofilm was forming on the supports because the two shdes randomly taken from different locations in the reactor had almost the same amount of biomass. Figure 6.50 time.  shows that the biomass on the shdes increased gradually with the culture  Correspondingly, the carbon content of the biomass on the shdes also increased  with the culture time as shown in Figure 6.51.  T h e carbon content of the biofilms gave  a very good linear relationship with their dry biomass as shown in Figure 6.52.  The  slope of the straight hne in Figure 6.52 is 0.353 (mg carbon/mg dry biomass). From the carbon content of the biomass on a removable shde and the areas of the supports and the shde, the total carbon content of biofilms fixed on the supports at that time could be calculated. T h e biomass on the reactor walls was not easily measured.  T h e sludge which was  introduced into the fermenter as seed and had reproduced during the period of biofilm development was removed by discharging the culture medium under a N  2  atmosphere  after a visible black biofilm had formed and before the kinetic data were collected. Thus the biomass left on the reactor walls was taken to be the biofilm attached on the walls. Based on the same assumption used for acidogenic biomass, this part of biomass should have the same growth rate as the biomass on the supports. After the experiments  were  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  40  Figure 6.50:  80  120  138  240  160  Culture time (day)  Biomass on slides increases with culture time  26-i  160  200  240  Culture time (day) Figure 6.51:  Total organic carbon on slides increases with culture time  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  139  26-|  20-  00  E  B i o m a s s (mg)  Figure 6.52: Relationship between organic carbon and dry biomass of biofilms finished the biomass on the reactor walls was carefully collected and measured, and the initial amount of biomass was estimated by using this data and the growth rate of biofilms on the supports. The total biomass, in terms of total organic carbon, of the biofilms on the supports and reactor walls can be predicted by using the following equation.  TC = 1678.9e  00 0 9 0 t  (6.51)  Table 6.22 lists some analysis results of biomass samples taken from biofilms on the supports and 'sludges' on the reactor walls. The 'biofilms' on the reactor walls contained more ash and less organic carbon because more inorganic salts (metal ions) were deposited on the bottom of the reactor. That is why the total carbon content, of the biofilm, instead of the dry biomass, was used in this study.  Chapter  6.  Intrinsic  Kinetics  Table 6.22:  of Methanogenesis  of Organic  140  Properties of methanogenic biofilms  Item A s h content (w%) T O C content (w%)  6.3  Acids  Sample 1  Sample 2  38.1  37.7  biofilm sludge  58  59  biofilm  34.4  35.2  sludge  15.2  17.3  Interaction of Organic Acids  T h e methanogenesis of fatty acids depends on a symbiotic microorganism community which consists of at least four groups of bacteria.  Each of them has its own substrate.  Generally the substrate concentration affects the biological activity of the bacterial group responsible for the utihzation of this substrate.  One example is the dependence of lac-  tose utihzation rate on the lactose concentration as discussed in lactose acidogenesis. However, one substrate may also affect other groups of bacteria because of the symbiotic properties of the bacterial community.  Scharer and Moo-Young [206] found that  the kinetic information obtained using single substrates could not be used for predicting methane generation from a mixture of acids and when equimolar mixtures of acetate, propionate and butyrate were used, propionate was not consumed at all. This may be caused by the high substrate and/or product concentrations being toxic or beneficial to the bacterial activities, but may also be caused by inhibition or competition from other substrates in a feed of mixed organic acids. T h e following experiments were conducted by using the feeds with different concentrations of organic acids.  6.3.1  Influence of Acetate Concentration  Methanogenesis of organic acids was investigated in immobilized cell bioreactors  by  Scharer et al [114]. Their results indicated that acetic acid was consumed very rapidly  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  141  0.04-1  o  |*  0.03  •  X I  CO  «  •  TJ  3  0.02  c o  CO  CO  O)  0.01  TJ  w O. X  0.00 760  800  860  900  960  1000  1060  — i 1100  1  1150  A c e t a t e c o n c e n t r a t i o n (mg/l) Figure 6.53: Effect of acetate concentration on propionate digestion (HPr=880-996 mg/1) in comparison to propionic and butyric acids and the presence of acetic acid had an inhibiting effect on the utihzation of either propionic or butyric acid. Therefore, it seems possible that acetogenesis of these two organic acids could be inhibited by their product, acetate.  To test this hypothesis, the concentrations  of propionate and butyrate were  maintained in narrow ranges, 880-996 mg/1 and 48-66 mg/1 respectively, and only the acetate concentration was adjusted in the fermenter.  Figure 6.53 and Figure 6.54  re-  veal that the digestion of neither propionate nor butyrate was inhibited by the presence of acetate.  This means that in a balanced bacterial community the acetogens are not  inhibited by the products of their metabolic activities.  6.3.2  Influence of Propionate Concentration  Propionate is the component most difficult for the bacteria to digest.  Hence, it often  appears in high concentrations in the effluent of an unstable digester.  Its influence on  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  142  0.04  (J o> f=  •—*  0.03  JE <D  «  TJ  0.02  c o  •  LT  • "TJ  co CD  .5? •o  0.01  3  CO X 0.00 760  800  860  900  960  1000  1060  1100  1160  Acetate concentration (mg/1) Figure 6.54: Effect of acetate concentration on butyrate digestion (HBu=48-66 mg/1) the utilization rates of acetate and butyrate was investigated by maintaining acetate and butyrate concentrations  in the fermenter in narrow ranges, 700-1000 mg/1 and 50-80  mg/1 respectively, while the propionate concentration was adjusted from 150-2300 mg/1. A n y change observed in the utihzation rates of acetate and butyrate would then be due to the changes in the propionate feed composition.  Figure 6.55 shows no influence of  propionate on acetate utihzation. Figure 6.56, however, indicates that high propionate concentrations could inhibit the digestion of butyrate.  6.3.3  Influence of Butyrate Concentration  T h e bacteria responsible for the conversion to butyrate belong to the same group of microorganisms, acetogens, as do those which utihze propionate. T h e possible influence of butyrate concentration on acetate and propionate utihzation was checked by adjusting butyrate concentrations  in the fermenter while acetate and propionate  concentrations  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  143  0.20-1  E o E — <D  0.12  C  o  •  0.08|  CO  CD 0.04  < 0.00 400  800  1200  1600  2400  2000  Propionate concentration (mg/l) Figure 6.55:  Effect of propionate concentration on acetate utilization  (HAc=700-1000  mg/1) 0.06  £  0.04H  E -»» o> ~  O  0.03  0.02-  TJ  03 CD  B  ai "°  0.01  CD X 0.00 400  800  1200  1600  2000  2400  . Propionate concentration (mg/l) Figure 6.56: mg/l)  Effect of propionate concentration on butyrate utilization  (HBu=50-80  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  144  0.20  cj  0.16  O)  E E —  0.12  CO  c O  0.08  XL  m—SF—•  •D  CO CO  O)  ~° O < X  0.04  0.00 200  400  600  800  1000  1200  1400  1600  Butyrate concentration (mg/l) Figure 6.57:  Effect of butyrate concentration on acetate digestion (HAc=1400-3000 mg/l)  were kept in a relatively narrow range, 1400-3000 m g / l and 700-900 m g / l respectively. Although the acetate concentrations changed from 1400 to 3000 m g / l no significant influence of butyrate concentration was observed on acetate digestion as shown in Figure 6.57. This was because at high substrate concentrations acetate-digesting bacteria had reached their maximum metabolism rate and hence further increase in acetate concentration had little effect on the utihzation rate. Figure 6.58 shows no influence of butyrate concentration on propionate utihzation even though the later inhibited the former's digestion. This may be an indirect evidence that conversion of these two fatty acids involves different bacterial species. T h e interaction of substrates or bacterial groups of a balanced microorganism community can be summarized as follows: • Acetate has no influence on the biological activities of acetogens which are responsible for the conversion of propionate and butyrate to acetate and H2, and also,  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  145  0.03  o O)  E  O)  0.02  E CD *-< <D w  •  C  o «  0.01  •  ll  -43-  •  CD  O)  CL  0.00  0  200  400  600  800  1000  1200  1400  1600  Butyrate c o n c e n t r a t i o n (mg/l) Figure 6.58:  Effect of butyrate concentration on propionate digestion (HPr=700-900  mg/1) neither propionate nor butyrate affects the methane-producing bacteria which can use acetate directly as substrate. • Propionate-utilizing bacteria are not affected by acetate and butyrate, but propionate can inhibit the activity of butyrate-utilizing bacteria.  • Butyrate, hke acetate, does not influence other fatty acids utilizing bacteria.  6.4  Utilization Rates of O r g a n i c A c i d s  T h e kinetics of organic acid digestion were investigated on feeds having a fixed ratio of acetate, propionate and butyrate. Therefore, each acid was always present in the fermenter so that a balanced bacterial community could be maintained. Various steady state levels of fatty acid concentration were obtained by changing  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  146  feed concentrations or residence time or both of them. A steady state which was judged from the concentration fluctuation in the effluent (< 10 was collected, such as the total amount of dry biomass, the total organic carbon, the gaseous production rate and composition, the culture medium flow rate and composition. T h e carbon recovery for these experiments ranged from 77 to 86 percent (see Appendix E ) which included the gaseous carbon ( C H and C 0 ) and carbon in the liquid phase (organic 4  acids, C02)-  2  This balance is quite reasonable since the sohd carbon contained in  biomass either as free cells or as biofilms, was not calculated, nor were some minor fermentative products hke valeric acid.  6.4.1  Propionate Utilization Rate  A t steady state, a material balance of propionate around the fermenter gives  FS  iiP  = FS ,  e p  + Wr  (6.52)  p  or,  r  p  where r  p  =  F  {  S  i  *  w  S  °*  (6.53)  ]  is the consumption rate of propionate ( m g / m g C / h r ) , S ; , S , iP  e  p  the propi-  onate concentration in the feed and effluent (mg/1). For each steady state the right side on Equation 6.53 could be determined experimentally, and thus the propionate consumption rate. A Michaelis-Menten type equation was firstly used to describe the effect of propionate concentration on the propionate utihzation rate.  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  The  two parameters,  r  maa  .  and K ,  ]P  p  147  were estimated by using the direct search  method (see Appendix G ) while the initial search point was determined from the least-square estimation of the linearized equation.  ' max,p K  p  However, a plot of r  p  = 0.021  = 99  mg/mgC/hr mg/l  against propionate concentration shows that a Michaelis-  Menten type model, as represented by the dash hne in Figure 6.59, can not describe the effect of propionate concentration on propionate utihzation rate very well over the tested concentration range, especially from 200 to 800 m g / l .  0.030-,  o . o o o - l — • — i — . — i — • — i — • — i — • — i — • — i — • — i — • — i — • — i — • — i 0 200 400 600 800 1 0 0 0 1200 1400 1 6 0 0 1 8 0 0 2 0 0 0  Propionate concentration (mg/l)  Figure 6.59:  Dependence of propionate digestion rate on propionate concentration. T h e  dash hne represents Equation 6.54.  T h e sohd hne is calculated from Equation 6.56  It may be proposed that the propionate utihzation rate was promoted by higher  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  propionate concentration.  Because acetate and butyrate  propionate-digesting bacteria  148  have no influence on  as discussed before, the only possible influence is  from propionate itself. Digestion of propionate may involve many reactions promoted by various enzymes. It is generally assumed that there exists a slowest reaction step, or rate-limiting step, which is catalyzed by a key enzyme. T h e reaction mechanism can be assumed to be as follows:  E + S f E S - ^ P  + E  (1)  ES + S ^  .  (2)  P + ES  T h e first reaction is the weU known Michaelis-Menten reaction. mation of the ES  During the for-  complex, the enzyme molecule is twisted, which places some  strain on the geometry of the substrate molecule. This strain renders it susceptible to attack by H  +  or O H  -  ions or by specific active groups of the enzyme.  this manner the substrate molecule is converted to its product.  In  W i t h increase in  substrate concentration more and more enzyme will form the complex ES  and the  rate of reaction will increase until, finally, virtually all the enzyme is in the form of ES.  Introducing the second reaction is based on the assumption that ES  complex  can still be attacked by another substrate molecule to form a product molecule. Therefore, the total substrate consumption rate is  (*;_! + k )lk 2  x  + S  (6  .55)  T h e detailed derivation of Equation 6.55 can be found in the Appendix F . Similar to the apphcation of a Michaelis-Menten equation which describes the rate of  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  149  a key enzyme reaction to an overall substrate utilization rate, Equation 6.55 is transformed to give the overall propionate utihzation rate by propionate-degrading microorganisms,  r p  K  =  S  p +  ( 6  -  5 6 )  This is a non-hnear equation containing three unknown parameters, two of them, r  max,p  a  n  d K , having the same significance as those in a Michaelis-Menten type p  equation. These three parameters were estimated by using the direct search method to best fit the experimental data with Equation 6.56. T h e sohd hne in Figure 6.59 is calculated from the model with the following parameter values,  ' max,p = 0.0162  mg/mgC/hr  K = 50  mg/l  8 = 0.0002  1/mg  p  T h e question of concern is whether it is worth adding another independent parameter, /?, to the two-parameter  model, Equation 6.54.  Statistically,  this can  be answered by calculating the marginal effect of 8 in reducing the variability in predicting the propionate utihzation rates when the other two parameters are already in the model.  T h e marginal effect is measured by a coefficient of partial  determination which is defined as [207],  SSEi — SSE  2 ri  Where SSEi  and SSE  2  -'  =  SSE  X  SSE  2 =  1  - S S E  1  2  , ( 6  N  -  5 7 )  are the error sum of squares of the two models, respec-  tively. T h e coefficient of partial determination was found to be 0.522, which means that, by adding the third parameter 8, the error sum of squares of the modified  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  model could be reduced by 52.2  150  %, compared with the Michaelis-Menten model.  Further statistial test can be made to determine whether or not there is a relation between the propionate utilization rate and the three paramenters in the modified Michaelis-Menten model. T h e F value was found to be 25.7 while F0.95 = 5.79 [207]. Hence, it can be concluded that all three parameters are significant in describing the propionate utihzation rate.  6.4.2  Utilization Rate of Butyrate  At the same steady state a butyrate balance around the fermenter leads to the foUowing equation,  FS  i t b  =  FS  e t b  +  rW b  (6.58)  or,  n = Where r  b  F  {  S  i  *  Si w  '  b)  (6.59)  is the butyrate utihzation rate ( m g / m g C / h r ) , F the flow rate (1/hr), W  the total amount of biomass in terms of total organic carbon in the fermenter (mgC) and 5t,b, S ,fc the butyrate concentrations (mg/1) in the feed and effluent, respece  tively. T h e rate, r , experimentally determined from the right side of Equation b  6.59,  is plotted vs the butyrate concentrations in the fermenter. Firstly, the effect of butyrate concentration on butyrate utihzation rate was modeled by a Michaelis-Menten model,  Chapter 6.  Intrinsic Kinetics of Methanogenesis of Organic Acids  151  0.08-,  £  0.05  E °>  E  •*-* to  0.04  k. c o  0.03  co CD  0.02-  3  0.01  CO I 0.00)£ 100  200  300  400  600  eoo  Butyrate concentration (mg/l)  Figure 6.60: Dependence of butyrate digestion rate on butyrate concentration. The dash hne is calculated from the Michaelis-Menten equation 6.60; The points (x) are calculated from Equation 6.62 Equation 6.60 was linearized to give an initial estimation of the two parameters, r  MAII  6 and Kb, and then, the direct search method was used, with the initial esti-  mation as the start point, to further optimize the fitness of the model equation to the experimental data. fmox.b  K  b  = 0.0334  = 20  mg/mgC/hr mg/l  Figure 6.60 shows that the butyrate utihzation rate is not predicted satisfactorily by the Michaelis-Menten type equation 6.60 represented by the dash hne because the rate is depressed at higher butyrate (propionate) concentrations.  There are  two explanations for this phenomenon. One is that the rate is inhibited by propionate, as indicated earlier in the discussion about the interaction of substrates,  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  152  0.10-1  »  00 8  o.oeCD H—*  <0  c  O co  •  0.04-  •  •  •  CD  O) •°  0.02-  D  CO X 0.00  200  400  600  —i 800  '  1  1000  •  1  1200  •  1  1400  •  1  •  1600  1  1800  Butyrate c o n c e n t r a t i o n (mg/l)  Figure 6.61: Influence of butyrate concentration on butyrate digestion (HPr = 690-900 mg/1) since the feeds, having a fixed weight ratio of fatty acids, contained also a large amount of propionate at high butyrate concentrations. It may also, on the other hand, be attributed to high butyrate concentrations, i.e., a substrate inhibition. An experiment was designed to check the latter possible mechanism. The propionate concentration was controlled in a narrow range, 690-900 (mg/1), the butyrate concentration in the fermenter was adjusted from 100 to 1500 (mg/1). As shown in Figure 6.61, the high butyrate concentration did not inhibit its utihzation by the responsible bacteria, at least in the present experimental concentration range. Therefore, the only mechanism to explain why the butyrate digestion rate is inhibited is the effect of propionate. This result also indicates that the inhibition of butyric acid in anaerobic digestion processes, as reported by van den Heuvel [181], is caused by the effect of the acid on acidogenic microbes instead of methanogenic  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  bacteria.  153  It appears that an increase in propionate concentration can promote its  own utihzation rate but wiU inhibit the butyrate digestion rate.  T h e inhibition  mechanism is assumed to be of the form:  k  h  E + S ^ E S ^ P  + E  (1)  h ESb + S  p  k-3  S ESb  (deactivation)  p  (2)  In addition to the main reaction (1), a Michaelis-Menten reaction, the enzymebutyrate complex, ESb may also be attacked by a propionate molecule, S , which p  results in a deactivated active enzyme center, S ESb- A reaction rate expression is p  derived from this mechanism (see Appendix F for detailed derivation).  r =  ^  (6.61)  (&_! + A; )/fci + S + {k /k^)S Sp 2  b  3  b  V  ;  Correspondingly, the overaU butyrate utihzation rate, rj,, has a similar expression,  ,„ « \  Tmax,bSb  = K + S + KrS Sp  r b  Where r  maxb  0  b  b  b  <- ) 6  62  is the maximum butyrate digestion rate ( m g / m g C / h r ) , Kb the half  velocity concentration  (mg/l).  Kj is a equilibrium constant of the deactivation  reaction and has a unit of reciprocal of concentration (1/mg).  T h e direct search  method was used to estimate the optimum parameter values to fit the experimental data with Equation 6.62. rmax,b = 0.0473  mg/mgC/hr  K = 27  mg/l  Ki = 0.000296  1/mg  b  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  154  T h e points marked by the sign ' x ' in Figure 6.60 are predicted by Equation 6.62 with these parameters at different propionate concentrations  (20-1700 mg/1).  Again, the addition of the third independent parameter, Kj, into the two-parameter model 6.60 was statistically tested by calculating the coefficient of partial determination, and its value was 0.53.  Therefore, the introduction of Kj into the model re-  duced the error sum of squares by 53 % compared with the two-parameter MichaelisMenten equation 6.60.  T h e F test shows that F = 241 > F(0.95: 2, 13) =  3.81,  which means that the butyrate utihzation rate is significantly related with all three parameters.  6.4.3  Acetate Utilization Rate  At steady state, the amount of acetate which was introduced into the reactor should be balanced by the amount consumed by the bacteria plus that in the effluent. T h e acetate introduced into the reactor could be divided into direct and indirect input. T h e direct input was the amount fed into the reactor as feed and the indirect part was the amount converted from propionate and butyrate by the acetogens. Generally one mole of propionate produces one mole of acetate and one mole of butyrate produces two moles of acetate as shown in Table 6.19.  T h e material  balance gives  FS  iA  + W(^rp  M„  + ^r ) b  Mb  = FSe,a  + raW  (6.63)  and it is re-arranged as  FiSi^-S^) W  Ma +  M /  2M p  +  M  a  b  (6.64) V  b  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  155  0.16-1  A c e t a t e c o n c e n t r a t i o n (mg/l) Figure 6.62:  Dependence of acetate utilization rate on acetate concentration.  T h e hne is  calculated from Equation 6.65 Where F is the flow rate of medium (1/hr), S  i a  , 5  e j a  the acetate  concentrations  (mg/l) in the feed and effluent, respectively, W the total amount of biomass retained in the fermenter in terms of total organic carbon (mgC), M , a  M , Mb the molecular p  weight of acetate, propionate and butyrate, r , r , r the utihzation rates of acetate, a  p  b  propionate and butyrate ( m g / m g C / h r ) , respectively. of Equation 6.64  can be determined experimentally.  against the acetate concentrations  in the fermenter,  T h e items on the right side T h e rate, r , a  5  e>a  was plotted  , since in a completely  mixed continuous flow reactor the effluent concentration equals the concentration within the reactor. Figure 6.62  indicates that the dependence of acetate utihzation rate on acetate  concentration  can be described quite well by a Michaelis-Menten type equation.  Also it had previously been shown that the acetate utihzation rate is affected by  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  156  neither propionate nor butyrate as discussed in the section on interaction between substrates.  K  a  '  (6.65)  a S  + S  a  T h e two parameters are estimated by linearizing the non-linear Equation 6.65 as  S  fn  f  +  (6.66) 7*n  m n rr n  and then by using the least square method to fit Equation 6.66 with the experimental data. T h e initial estimation of the parameters was then used as the first search point from which a direct search was conducted on Equation 6.65 to optimize its fitness to the experimental data. The results are r  max  ,  a  = 0.098  K = 160 a  where r  maa  .  ja  mg/mgC/hr mg/l.  is the maximum utihzation rate of acetate and K  a  acetate concentration which characterizes  is the half velocity  the affinity of acetate-utihzing  bacteria  on acetate. In order to confirm the assumption of stoichiometry of propionate and butyrate conversion to acetate, a feed containing only acetate (14828 m g / l ) was used. T h e acetate digestion rate at steady state was 0.093 ( m g / m g C / h r ) and acetate concentration in the fermenter was 5611 (mg/l). This rate was obviously the maximum rate since it was very close to the value of  r  . Therefore, it is further  mana  confirmed (1) that the presence of propionate and butyrate has no influence on acetate-utilizing bacteria;  (2) that the stoichiometry of propionate and butyrate  conversion to acetate was reasonable; (3) that the dependence of the acetate utihzation rate on acetate concentrations follows the Michaelis-Menten equation up  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  157  to 5600 (mg/1). Table 6.23 summarizes the utilization rates and half velocity constants  for the  methanogenesis of organic acids obtained in this study and reported in the literature.  For the sake of comparison with other data, organic acids are converted to  equivalent C O D content using the ratios of 1.07 (mg C O D / m g acetic acid), 1.51 (mg C O D / m g propionic acid) and 1.86 (mg C O D / m g butyric acid). Table 6.23: Methanogenesis of organic acids Substrate  Culture  Temp.  pH r  c° Acetate  H A c enrichment  m a x  mgCOD  K„  Reference  mgCOD/1 165  [142]  35  7  mqV SS.hr 0.36  35  7  0.6  34  [142]  35  7  1.21  5  [142]  35  7  0.11-  35  7  sludge Propionate  H P r enrichment sludge  Butyrate  H B u enrichment sludge  Acetate  H A c enrichment biofilms  Acetate  H A c enrichment  0.21  sludge Acetate  H A c enrichment  [208] [144]  0.450.54  38  0.045  [144]  0.26  246  [209]  166  [143]  sludge Propionate  mixed sludge  33  Mixed acids  mixed biomass  35  7.2  0.712  Mixed acids  mixed biofilms  37  7  0.02-0.24  [114]  Mixed acids acetate  mixed biofilms  35  7.1  0.3  171  this study  propionate  mixed biofilms  35  7.1  0.04  77  this study  butyrate  mixed biofilms  35  7.1  0.22  39  this study  It should be pointed out here that various measures of biomass have been used by researchers as a base for calculating the substrate utihzation rates; suspended sohd [143], suspended sohd nitrogen [142], particulate protein content [114] and total  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  organic carbon (this study).  158  Moreover, the cultures had different distributions of  bacterial groups in the fermenter,  some containing much more  acetate-degrading  bacteria due to acetate enrichment, some containing a distribution determined by substrate concentrations in the feed. A n d thus the substrate digestion rate would be different if the rate is based on whole biomass.  T h e next section will discuss  this problem further.  6.5  Distribution of Bacterial Groups in Balanced Biofilms  As indicated repeatedly, conversion of a mixture of acetate, propionate and butyrate to methane and carbon dioxide needs contributions from at least four distinct functional bacterial groups.  This balanced microorganism community con-  tains acetogens which convert propionate and butyrate to acetate and H2, and methanogens which utihze acetate and CO2/H2 to produce methane and carbon dioxide. Whenever the biomass retained in a fermenter is referred to as the basis for the determination of the utilization rates of these organic acids, all four groups of bacteria are included. Obviously, the distribution of these bacterial species in biofilms has a great effect on the determination of digestion rates of each acid. It is almost impossible, experimentally, to measure this distribution because so many species are involved in the biological process and no convenient method exists to identify and count them. Even in a defined mixed culture the distribution of each species would change corresponding to changes in the environment, such as availability of substrates and nutrients, temperature, toxic components.  p H , alkahnity, dilution rate and  This may be one reason why the kinetic information obtained  on a single acid could not be used to predict the digestion rates of mixtures of organic acids as found by Scharer and Moo-Young [206]. In the present study, a  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  159  mixture of three acids with a fixed ratio has been used in the adaptation of the inoculum, formation of biofilms and kinetic experiments with an attempt to have and maintain a balanced bacterial community by a sufficient supply of substrates. In this section, an effort will be made to estimate the distribution of the bacterial groups in a mixed and undefined biofilm. Lawrence and M c C a r t y [142] used a single acid as substrate to investigate the methanogenesis  of fatty acids.  In the case of acetic acid, the culture was quite  simple and it was believed that only acetate utihzing methanogens existed. B u t for propionate or butyrate, at least three functional groups were involved, propionateor butyrate-utilizing bacteria, hydrogen removing bacteria and acetate fermentation bacteria, even though they did not consider the fraction of microorganisms responsible for the generation of methane from CO2/H2. This approach might be explained by the fact that it is only recently that the important symbiotic function of this fraction of bacteria has been discovered.  Their estimation of the bacteria  distribution in the 'two-components' sludge was based on thermodynamic principles.  T h e more free energy available as a result of biochemical transformations  of substrate, the more bacteria, growth responsible for this substrate dissimilation. More researchers, however, just took the mixed culture as a pure one, and so, their results were based on total volatile suspended solids [143,211,212], on adsorbed particulate organic nitrogen ( P O N ) [114], or on volatile film solids [213]. Some of them only used the reactor volume as the basis for the evaluation of various types of fermenters such as upflow sludge bed reactors and fixed bed reactors [214] even though the retained biomass was the key parameter for these reactors. In a nutrient-rich environment, all bacterial species get enough food supply and grow at their intrinsic maximum growth rate, correspondingly, each substrate is  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  consumed at its maximum dissimilation rate, r  160  ^. Experimentally, this situation  max  can be confirmed by using much higher concentrations of substrates in the fermenter than their half velocity concentrations, Ki. If this rate is based on 1 mg of biomass and only four major functional groups are considered, this one mg of biomass contains m , a  m , m , nth mgs of bacteria responsible for the utihzation of acetate, p  b  propionate, butyrate and hydrogen, respectively.  m  + m  a  p  + rn + m b  = 1  h  (mgC)  (6.67)  that is,  m  m  p  m (l a  h  + — -f m„ m„  or, m„ =  m  b  ) = 1  1  (6.68)  m„ 1  1 + m jm p  + m /m  a  b  a  +  m jm h  (6.69)  a  T h e investigation on build-up of symbiotic methanogenic biofilms revealed that the acetate-, propionate- and butyrate-utihzing bacteria had the same intrinsic maxim u m growth rate, and this was also reported by Lawrence and M c C a r t y [142] in their studies on single acid methanogenesis.  Therefore, the distribution of these  three specific bacterial groups in a biofilm mainly depends on their initial attachment on the biofilm supports because the initial attached ceUs simultaneously multiply, forming colonies and biofilms. group was expressed as  fcja:];,  T h e attachment of each specific bacterial  where [x]- is the free cell concentration in the cult  ture medium and ki the specific attachment rate affected by the physicochemical properties of the supports.  k [x]a a  (6.70)  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  161  and  771f,  — m  fcfcfllf,  = .T « [Ta ;lj  Q  a  6  a  '  7  1  If the number of bacterial cells in unit volume of medium was so high that the attachment rate became a quasi-Oth order rate,  TTir)  — - =  m  p  a  fan  ,  _  ,  (6.72)  K  a  and ^  m  = £  (6.73)  k  a  a  In the nutrient-rich environment, acetate, propionate and butyrate are being consumed at their maximum rates ( m g / m g C / h r ) ;  r  p  = >°"*S (l+0S ) r  p  -ftp  ~ ^  P  ~ K + S + KrfbSt b  i + .00045 ) 0  r  T"Tnax,bSb n  (  p  (6.75)  ~T  b  m a x  b  ~ 1 + 0.00015S  . —„\ P  1  "  '  If propionate concentration in the environment is controlled under 1000 mg/1, but still much higher than 50 mg/1, the half velocity propionate concentration of the propionate dissimilation rate, Equations 6.75 and 6.76 simplify to,  r  p  r  maXt  p  (6.77)  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  162  anc  n = r  (6.78)  max<b  W h e n propionate and butyrate are digested by the bacteria at the above rates, hydrogen is produced as shown in Table 6.19, one mole of propionate to 3 moles of hydrogen and one mole of butyrate to 2 of moles hydrogen. In a mature balanced biofilm, these 5 moles of hydrogen must be removed by the H -utiHzing bacteria to 2  keep the H2 concentration in the fermenter very low.  AH  2  + HCO3  + H  +  -> CH +  ZH 0  A  2  Therefore, the hydrogen removal rate is  3 2 h — ~~^~ max,p + ~j^ max,b r  r  r  (6.79)  where r/, is the hydrogen removal rate by symbiotic bacteria ( m m o l / m g C / h r ) , M , p  Alb the molecular weight of propionate and butyrate.  Correspondingly, according  to the conversion of CO2/H2 to methane above, the methane production rate from C0 /H 2  2  utihzation, r h m<  ( m m o l / m g C / h r ) , can be expressed as follows,  rm.h  rh  . 4  3 ., r p r  AM  maX  -\-  P  2 4.M  r  m a x  b  (0.8UJ  b  Another source of methane production is from acetate fermentation, one mole of acetate being converted to one mole of methane.  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  where r ,  m a  163  is the methane production rate from acetate digestion ( m m o l / m g C / h r ) .  Acetate conversion includes the reduction of the methyl group of acetic acid [142]. T h e dissimilation of acetic acid to methane requires the net transfer of one electron and the free energy decrement of the conversion is small. However, the formation of a methane molecule by carbon dioxide reduction requires a net transfer of eight electrons.  Hence, the free energy decrement  of the conversion of hydrogen and  carbon dioxide to methane is approximately three times the free energy decrement of the dissimilation of acetic acid to methane and carbon dioxide as reported by Smith and M a h [64]. If formation of one mmole of methane from acetate gives A G (J) free energy, and then, the energy production rates ( J / m g C / h r ) reactions  for these two  are  r,  e h  = 3r , AG m  h  (6.82)  and r ,a = r , A G e  m  (6.83)  a  T h e basic mechanism by which the free energy available from the two reactions may be utilized is by the trapping of this energy through the formation of the energy-rich intermediate, A T P . It has been shown that the yield of cells (cell mass mg) with respect to the amount of A T P (mmole) used is a constant, typically 10.5 (mg/mmol A T P ) [210]. Assume these two groups of methane-producing  bacteria  having the same energy utihzation efficiency, then the efficiency to store the free energy available from the reactions into A T P is  Yxrp (mmol A T P / k J free energy).  T h e ratio of the bacterial biomass responsible for CO2/H2 utihzation to that responsible for acetate conversion is proportional to their A T P yield rates from their own substrate utihzation.  Chapter 6.  164  Intrinsic Kinetics of Methanogenesis of Organic Acids  m  _ l0.5Y  h  m  l0.5Y  a  r  ATP  ATP  _  eth  r  r  eA  r  e>a  eA  This equation imphes that the group which can obtain more energy from its substrate utihzation would predominate in the methanogenic sub-community. Replacing Equations 6.82, 6.83, 6.80 and 6.81 into Equation 6.84 gives  rn  _ 9/M r  h  p  +  maXiP  6/M r b  max.b  m  i  r\r\  n  4/M r  a  a  maXia  Put Equations 6.72, 6.73, 6.85 into Equation 6.69 and get Equation 6.86 for estimating the amount of biomass (mg organic carbon) responsible for acetate digestion within one mg organic carbon of biofilm in a nutrient-rich environment.  1 4 - k Ik  771(1 =  1  4 - hulk  ^ "'PI ^a  v Kb/ " - o  4 - (ZM^r i ^  o4-  ' max,P  '  \\~U^r M  ^' ^ 86  maxjb )/ ^' max,a  b  Using Equations 6.72, 6.73, 6.85 and the estimated m expression above gives the a  mp, mb and m/j, respectively.  kp/k  a  1 "1" k / k p  a  + k /k b  + (  a  r  h/k m  b =  , , /,. 1 + kp/k a  _ 771/1  , ,. / , . + kb/k a  M;,  max  Mi,  r  i  ~ 1 J- 4 ~-k "-p/Ik > V a A~ hulk "•bl " " a ~ ^ ^  M  p  b  1  m o i , o  1  TT ,/A  r  ,  jo II  a  , ,9M„_ T6M+ ( ^ max,p 4 - 6 M a r  V. Mp ' max,p -  (6.87)  max,p  • max:,b ) /^ ' "  max  4.T  jo 1  1  (- ) 6  r  1  maxa  In  '  4 - 6 M a'r max.o.W4' mox,p ~ / / ^ ' max.a  Table 6.24 hsts the maximum utihzation rates of fatty acids, r  maX)  88  raoi,a  O  Q  \  ^°- ' 0 y  t , based on the  integrated biomass of a methanogenic biofilm, the fractional biomass responsible  Chapter 6. Intrinsic Kinetics of Methanogenesis of Organic Acids  165  for each acid digestion in one mg of the integrated biomass and the recalculated maximum dissimilation rates of the organic acids, r'  maxi  based on only a fractional  biomass being responsible for the specific dissimilation reaction.  T h e hydrogen  removing rate is estimated from the Equation 6.79.  Table 6.24: Fractional mass of bacterial groups and utihzation rates of fatty acids  ''raoi  mi  (mg/mgC/hr)  (mgC,i/mgC)  ( max mg/mgC,i/hr)  Acetate  0.098  0.26  0.38  Propionate  0.0162  0.22  0.074  Butyrate  0.0473  0.32  0.148  H  0.0035  0.20  0.018  Substrate  2  r'  Chapter 7  Mass Transfer in Biofilms  Immobilization of microorganisms results in two distinctive phases in a fermenter, the liquid medium phase and the sohd phase of biofilms or bioflocks. Different mechanisms of substrate transfer are involved in these two phases. T h e hydraulics, the macro-transport of water and substrates within the hquid phase, differs very much from one reactor type to another, just as the significance of a possible hquid film layer which is adjacent to the sohd phase does. However, common to all types of reactors is the process of mass transfer within the sohd phase which is a combination of bacterial ceUs, extracellular polysaccharides and some inorganic salts trapped in the biofilms. Fick's laws of diffusion form the basis for the current theoretical approaches to the mass transfer within the biofilms.  7.1  Diffusivities of Substrates in Water  Fick (1855) developed the laws of diffusion by analogy to Fourier's work and defined a one dimensional flux JA as:  JA = D  A  B  J  1  (7.90)  Where JA is the flux of solute, A , through unit area across which diffusion is occurring, c is the concentration of the solute and / the distance in the solvent B . T h e quantity DAB,  which Fick called "the constant depending on the nature of the substance" is the  diffusion coefficient of solute A in solvent B . To estimate the diffusivities of various solutes 166  Chapter 7. Mass Transfer in Biofilms  167  in solvents, prediction methods have been developed based on a variety of theories, such as hydrodynamic theory, kinetic theory and statistical mechanics, as reported i n several reviews [194,195,196]. Among them the Stokes-Einstein equation [197]  RT D  A B  = ~„  =-  (7.91)  6-MIBRA  has found wide application which considers the solute A as large spherical molecules diffusing in a dilute solution. Many researchers have used it as a starting point in developing their correlations [197]. In Equation 7.91 T)B is the viscosity of the solvent and R^4 is the radius of the 'spherical' solute. used correlation for DAB  M  In the present study an old but still widely  infinite dilution, the Wilke-Chang (1955) estimation method  [198], was used to estimate the diffusivities of lactose, acetic, propionic and butyric acids in the culture mediums.  7.4*  lO- (<j>M y' T 8  VBV  B  2  J  where D°AB  =  diffusivity of solute A at very low concentrations in solvent B , c m / s 2  </> = association factor of solvent B, dimensionless M  B  = molecular weight of solvent B , g/mole  T = temperature, K TJB = viscosity of solvent B, cp VA = molar volume of solute A at its normal boiling temperature, c m / m o l . 3  Table 7.25 lists the estimated diffusivities of the concerned solutes and experimental values if available. T h e values of VA were calculated from Le Bas' additive method [197]. T h e diffusivity of sucrose is also listed i n the table since to this author's knowledge the experimental value of lactose diffusivity i n water solutions is unavailable while sucrose has  Chapter 7. Mass Transfer in Biofilms  168  Table 7.25: Diffusivities in water at 35 °C Solute  v  D x 10  A  5  D  x 10  exp  5  Reference  (cm /mol)  (cm /sec)  Lactose  291.2  0.72  Sucrose  294.7  0.71  0.75  [199]  Acetic acid  68.4  1.71  1.74  [199]  Propionic acid  90.6  1.45  Butyric acid  112.8  1.27  3  2  (cm /sec) 2  the same molecular weight and equivalent molecular size as lactose.  Equation 7.92 was  also used to convert the experimental data measured at other temperatures  to those at  35 ° C . Comparing the calculated diffusivities of acetate and sucrose with those measured experimentally indicates that Wilke-Chang equation 7.92 has a satisfying accuracy. T h e diffusivity of a solute in infinite dilution implies that each solute molecule is in an environment of pure solvent. From an engineering viewpoint this value might be used to represent  the diffusion coefficient for concentrations  10 mole percent  [197].  of solute up to 5 and perhaps  This reported finding may be due to the fact that the solute  molecules in an aqueous solution are densely packed and strongly affected by the force fields of neighboring molecules and even in a dilute solution the major influence still comes from the water molecules.  T h e concentrations  of substrates i n this study were  not higher than 10 g/1. Although other components hke nutrients and products exist in the culture medium, the substrate molecules are still mostly surrounded by the water molecules, and hence the medium can be thought of as a dilute solution.  7.2  Principle of Mass Transfer Measurement within Biofilms  As indicated in Chapter 2, the biofilms contain many irregular channels through which the substrates transport from outer to inner layers by molecular diffusion to replenish  Chapter 7. Mass Transfer in Biofilms  the consumed substrates.  169  The channels have very complicated structures, tortuous and  even dead-ends. Therefore, it is almost impossible to describe them mathematically.  It  is common, analogous to reactions in a porous catalyst, to express the diffusion in the biofilm by a parameter,  De, the effective diffusion coefficient.  In this way, the transfer  of substrate molecules in the biofilm can be imagined as proceeding in a homogeneous medium and still can be described by Fick's law,  (7.93) Compared with Equation 7.90, this modified Fick's law only replaced the diffusivity, DAB, with the effective diffusivity, De. W h e n an active biofilm slab is immersed in a culture medium, the substrate molecules transport from the bulk solution to the outer face of the biofilm, and then, at the same time they penetrate into the biofilm, some of them are digested by the bacteria embedded in the biofilm. Finally a steady state is achieved and the substrate concentration has a distribution within the biofilm as shown in Figure 7.63. Since in an active biofilm the substrate diffusion and digestion occur simultaneously, a diffusion-reaction model could be deduced by making a material balance around the elemental volume i n Figure 7.63.  Usually, biofilms are quite thin with the thickness  ranging from tens to several hundreds of micrometers and thus the mass transfer from the side areas is negligible. A diffusion-reaction model with one dimensional diffusion is deduced as follows;  Diffusion in = Diffusion out + Consumption by reaction  AD ^(S e  - ^-Al) = -AD ~ e  +  AlAp r c  (7.94)  Chapter 7. Mass Transfer in Biofilms  170  Figure 7.63: Substrate concentration distribution within a biofilm at steady state, T h e elemental volume has a thickness Al and an area A .  AD —Al  = AlA r  e  (7.95)  Pc  dS 2  D —=p r e  Where D  e  (7.96)  c  is the effective diffusion coefficient of substrate molecules i n the biofilm  (cm /sec), S the substrate concentration ( m g / c m ) , p the density of the biofilm (mgC 2  3  c  / c m ) , r the substrate utilization rate based on unit weight of biofilm (mg/mgC/sec). 3  Al and A are the thickness and area of the elemental volume respectively. T h e left side of Equation 7.96 is the net amount of substrate transported into a unit volume of the biofilm and which should be digested by the bacteria embedded i n this volume at steady state as represented by the right side of the equation. In situ measurement of substrate transport in active biofilms requires the knowledge of the intrinsic kinetics of substrate  Chapter 7. Mass Transfer in Biofilms  171  S  Figure 7.64:  > D' ' > e  Influence of D  e  on substrate concentration  distribution within a biofilm, D'  e  D?.  utihzation by the target bacteria. T h e previous two chapters have described the intrinsic kinetics of lactose digestion in acidogenic biofilms and of organic acids degradation in methanogenic biofilms. Mathematically, Equation 7.96 can be solved by a numeric method when two boundary conditions are determined. S = Si  at / = L  dS/dl = 0  at / = 0  (biofilm surface) (due to the symmetry of biofilms)  Therefore, a family of curves can be obtained which describe the substrate  concentra-  tion distribution depending on the values of effective diffusion coefficient as shown i n Figure  7.64.  Theoretically, if another experimentally determined value can be found, for example,  Chapter 7. Mass Transfer in Biofilms  S, e  the substrate concentration  172  at the center of the biofilm slab, the substrate distri-  bution within the biofilm can be determined uniquely, and thus, the effective diffusion coefficient. In this sense, the effective diffusion coefficient, D , becomes a model paramee  ter of the reaction-diffusion model rather than a physical parameter determined only by the properties of the solute and the pseudo-homogeneous solvent (medium plus biofilms). However, as long as the assumption of one dimensional diffusion holds for the actual processes such as substrate diffusion in thin biofilms or bioflocks, the possible error caused by the assumption can be minimized or eliminated. Putting the utihzation rate expressions for lactose and organic acids into the diffusion-reaction model, Equation 7.96, gives a second-order ordinary differential equation;  d  <1P= <-K-TS P  '  (7 97)  A numerical method must be used to solve this equation. If the boundary conditions at / = 0 (S  e  and dS/dl) are known, the boundary condition problem can be solved as an  initial value problem and the value of D can be determined by fitting the experimental e  value of Si, the substrate concentration on the biofilm surface, with the calculated value from Equation 7.97. In this study, the Runge-Kutta-Fehlberg ( R K F ) method, was selected from many available numerical methods [200] to solve this initial value problem. T h e R K F method (see Appendix G ) has the advantages of requiring fewer calculations and having the abihty to control local truncation error and its local error is less than h  6  (h is the step size). So, the key point in the present work is how to measure the substrate concentration at the center of a biofilm, S , as well as the concentration on the biofilm surface, Si, and e  also how to meet the boundary condition at the center of the biofilm, dS/dl = 0.  Chapter 7. Mass Transfer in Biofilms  7.3  173  Experimental Setup  T h e general experimental setup has been described in Chapter 3, the same one as for the kinetic studies.  T h e major difference is the support on which biofilms formed. In  the kinetic experiments the support surface was made of many P V C sheets (1.5  mm  thick) and thus the biomass on the supports was a major part of whole biomass retained in the reactor.  In the measurement of substrate diffusivities within biofilms, however,  a diffusion cell was used since the attention was focused on the biofilm growing on the membrane filters and other biomass was not very important. T h e device's structure has also been described in Chapter 3. O n the each side of the cell a cellulose nitrate membrane filter (pore size =  0.45  /xm, Sartorius, W . Germany) was fixed by sandwiching it between two rubber gaskets, and hence, the bacteria (d =  1 pm)  could not enter into the cell while the substrates  could be transported into the cell through the layers of biofilm and the membrane filters. This was confirmed by the observation that there was no water leakage after replacing the membrane filters with plastic films. Biofilms (acidogenic or methanogenic ) formed uniformly on the filters and had the same thickness on each side of the cell as shown in Figure 7.65. Because no bacteria was inside the cell due to the pore size of the filters, the substrates which moved into the cell would not be further digested, therefore, the substrate concentration within the cell, S , e  equals that on the other side of the membrane filter,  S' , if a steady state was maintained. e  This condition could exist only at steady state  because at unsteady states, mass transfer occurred across the filter, and thus, S  e  ^  S' . e  T h e medium within the cell was recycled to promote a uniform concentration as well as the establishment of steady state. Moreover, because of the symmetry of both the cell's  Chapter 7. Mass Transfer in Biofilms  174  S  S  b  = Sj  Biofilm  Figure 7.65:  T h e biofilms symmetrically fixed on the two membrane filters of the diffu-  sion-measuring cell structure and the biofilms formed on the two membrane filters, the substrate concentration indice the divice, S , e  was the concentration at the biofilm center as mentioned in  the last section if the two biofilms on the membranes were thought of as the two half biofilms shown in Figure 7.63.  T h e symmetrical characteristics of the diffusion cell also  gave another boundary condition at steady state, dS/dl = 0, at each membrane filter. T h e two boundary conditions at 1=0 are known or experimentally available from the discussion above. T h e third one, the substrate concentration on the biofilm surface, Si, can be determined from the bulk concentration if the (imagined) hquid film thickness adjacent to the biofilm is known.  Experimentally, the hquid velocity over the biofilm  can be increased to such an extent that the hquid film or its effect is neghgible and the substrate concentration on the biofilm surface approaches that of the bulk solution.  Chapter 7. Mass Transfer in Biofilms  7.4  175  Diffusivity of Lactose in Acidogenic Biofilms  As in the experiments made to measure the kinetics of lactose utilization, the feed contains lactose as the limited organic substrate (listed in Table 3.9).  and inorganic salts as growth nutrients  T h e lactose concentration in the feed was 5-6  g/1.  To prevent  lactose from being digested in the feed tank, the same measures as mentioned in lactose acidogenesis kinetics were used, i.e. low temperature,  low oxygen partial pressure  and small amount of feed prepared each time. T h e p H of the culture was controlled at 4 . 6 ± 0 . 2 with 0.5 N N a O H solution. T h e medium in the reactor was recycled to produce a uniform concentration and temperature distribution in the reactor, and also, to reduce the external mass transfer resistance by increasing the recycle flow rate. T h e temperature was maintained at 3 5 ± 2  °C.  In situ measurement of lactose diffusivity in acidogenic biofilms was carried out in two stages, formation of biofilms on the cell's membrane and measuring lactose concentrations outside and inside the cell at steady state. T h e fermenter was first fed with a diluted feed (2 g lactose/1) and N was introduced 2  to strip off the oxygen dissolved in the medium. After the temperature  and p H of the  medium were adjusted to 35 °C and 4.6, respectively, the diffusion device which had a capacity of 30 c m was immersed in the medium. Gradually the medium penetrated into 3  the device through the membranes. W h e n the hquid outside and inside the cell reached the same level, recycle of the hquid within the cell was started. showed the same concentrations  outside and inside the cell.  Analyses for lactose  Under a N  2  atmosphere  the fermenter was seeded with 50 ml of inoculum collected from the effluent of lactose acidogenesis.  T h e fermenter was then operated in batch mode.  To obtain qualitative  information on the formation of the biofilms, when the cell was immersed in the reactor some P V C shdes, used as in the kinetic studies, were also immersed into the medium  Chapter 7. Mass Transfer in Biofilms  176  since it was believed that biofilm formation was easier on the membranes than on P V C sheets.  After the lactose had been used up, half the volume of the culture (500 ml) was  replaced by a fresh feed (5 g lactose/1) and this was repeated until a biofilm had formed on the membranes. After biofilms were observed on the removable P V C shdes the reactor operation was shifted to continuous mode. Every seven days the biofilm on a removable P V C shde was measured and the second stage started when a thick biofilm (ca.  1 mm)  had formed. T h e second stage was to measure the steady-state lactose concentrations outside and inside the cell. To ensure that a steady-state concentration was being measured, a disturbance was given to the concentration inside the ceU while the outside concentration was maintained as stable as possible. This was done by replacing 20 ml of the hquid within the cell with the same volume of distilled water which had been stripped of dissolved 0  2  by N , and then the lactose concentration within the cell was monitored until there was 2  no further change in the concentration. Figure 7.66 shows that the lactose concentration inside the device, after dilution with oxygen-free distilled water, approached a constant value, which means that a steady state was reached.  T o confirm this, the dynamic behavior of the device was further  investigated. W h e n the lactose concentrations inside and outside the cell were at a steady state, the feed flow rate, and thus the outside concentration was gradually reduced to a new level, and then returned to the original flow rate as shown in Figure 7.67.  It was found that  the inside lactose concentration, corresponding to the change in the lactose concentration of the bulk solution, also decreased to a lower value of 30 m g / l from a steady-state of 46 m g / l and then it returned to the original level of 45 m g / l as shown in Figure  7.68.  This indicated that the dynamic response of the cell was quite good and that as long as  Chapter 7. Mass Transfer in Biofilms  177  100-i  o H — i — i — i — i — • — i — * — i — • — i — i — i — ' — • — ' — i — • — • — ' — i — • — • — • — i 0 40 80 120 160 200 240  Time (hr)  Figure 7.66:  A steady-state lactose concentration inside the cell was established after a  dilution. T h e lactose concentration outside the cell ranged from 1750 to 1900 mg/1. a steady-state outside concentration was maintained longer than 5 hours, a corresponding  steady-state inside lactose concentration could be obtained because under normal  operating conditions the inside lactose concentration fluctuation was not more than 15 mg/1. This dynamic behavior also made it possible to use reliable operating conditions since fluctuations in the outside lactose concentration was unavoidable, however it was relatively easy to keep it at a steady state for 5 - 8  hours. Moreover, during this short  period of time the biofilm thickness (see Chapter 4) would not increase markedly and a quasi-steady state biofilm thickness could be assumed. As  shown in the experimental results of the kinetic studies in Chapter 4, the external  mass transfer could be reduced to a negligible extent by increasing the recycle velocity, and  thus the velocity over the biofilms. Under this condition the lactose concentration  Chapter 7. Mass Transfer in Biofilms  178  4000-,  100  Time ( h r )  Figure 7.67:  A controlled change in the lactose concentration of bulk culture solution  40  eo  80  100  Time ( h r ) Figure 7.68:  Dynamic response of lactose concentration inside the cell to the controlled  change in the outside lactose concentration  Chapter 7. Mass Transfer in Biofilms  179  80-i  . .  70-  a E  60-  -  c  o  50-  G-  -o  -e-  en  l_ *->  40-  o  30-  OS  c  o o CD  20-  •  o  CO  _1  10-  010  12  14  16  —i—  — i —  18  20  22  R e c y c l e rate (l/hr) Figure 7.69:  Effect of recycle rate on the lactose concentration inside the cell. T h e lactose  concentration in the bulk solution ranged from 1857 to 1750 m g / l on the biofilms, S;, was very close to the concentration, Sb, in the bulk solution which was measurable.  Figure 7.69 indicates that under different recycle rates the steady-  state lactose concentration inside the cell did not change markedly when the outside concentration was kept within a narrow range.  This fact implies:  (1) that the major  resistance to lactose transfer from the bulk solution to the cell was in the biofilm and (2) that the mass transfer resistance between the bulk solution and the biofilm surface was neghgible. Therefore, with a recycle rate of 220 m l / m i n the bulk solution, Sb, was a reasonable approximation of Si. Finally after steady-state lactose concentrations outside and inside the cell had been measured and judged to be satisfactory, the diffusion cell was taken out of the fermenter and the biofilms on the membrane filters were carefully collected and analyzed according to the procedures described in Chapter 3. T h e biofilms on the two membrane filters had  Chapter 7. Mass Transfer in Biofilms  180  Table 7.26: Effective diffusivity of lactose within acidogenic biofilms at 35 °C Parameter  Unit  Value  s  b  mg/1  2114  Se  mg/1  45  L  mm  1.3  Pc  mgC/ml  29.7  ^max  mg/mgC/hr  0.3144  mg/1  201  K.  xlO  - 5  cm /sec 2  De/D  0.47 0.653  almost the same thickness, 1.32 m m and 1.29 m m respectively, which means that the biofilms were symmetrical.  Therefore, the prerequisite on the boundary conditions at I  = 0 as discussed in the last section was satisfied and the conditions were reliable. B y using these data and the numerical solution method, the diffusivity of lactose within the acidogenic biofilms was estimated and the results are listed in Table 7.26. Obviously, the value of lactose effective diffusivity i n acidogenic biofilms estimated in this way depended on many factors even if the calculating error of the numerical method was controlled to within a reasonable range (< 1 0 ) . -4  It was affected not only by the  calculated values of the intrinsic lactose utihzation rate in biofilms, K„ and r  max  , but  also by the biofilm thickness and density, L and p , as well as the lactose concentrations c  inside and outside the diffusion cell, S  e  and S . b  Table 7.27 compares the influence of  these data on the effective diffusivity, De, (the sensitivity of De to the possible error of these data) by giving one of them a 10 % fluctuation while the rest are unchanged. T h e most sensitive parameter was the biofilm thickness which could give a 15 % error and the least sensitive ones were concentration inside the device, S  e  K  s  and the kinetic parameter  since they gave a corresponding error less than 5 % . T h e error caused in the other  parameters was not amplified or reduced. Therefore, experimentally, more attention was  Chapter 7. Mass Transfer in Biofilms  Table 7.27:  Sensitivity of lactose effective diffusivity to experimental error  Parameter Value  Error  mg/l  mg/l  mm  Pc mgC/ml  Tmax m  g/ gC/hr m  K  s  mg/l  45  2114  1.3  29.7  0.314  201  + 10  +10  + 10  +10  +10  (%)  +2.9  -7.1  +15.9  +10  +10  -4.8  -10  -10  -10  -10  -10  -10  (%)  -3.1  +8.4  -14.9  -10  -10  +5.2  (%)  De error  L  +10  (%)  De error  s  b  Unit Error  181  given to the measurement of the sensitive parameters like the biofilm thickness, density, and the maximum utihzation rate to reduce the possible error.  7.5  Effective Diffusivities of Organic Acids in Methanogenic Biofilms  Using the same diffusion-measuring device and the fermenter as described before, the process for measuring the effective diffusivities of organic acids in methanogenic biofilms could also be divided into two stages, formation of the biofilms on the two membrane filters of the ceU and then measuring the organic acids concentrations inside and outside the cell.  7.5.1  Formation of Symbiotic Methanogenic Biofilms  In order to build up balanced methanogenic biofilms which comprised acetate-, propionate- and butyrate-utihzing bacteria, on the membranes of the device, an inoculum was collected from a methanogenic phase reactor which was being fed with a mixture of organic acids.  Also, the feed was a mixture of acetate, propionate and butyrate  at  concentrations of 5, 2.5, 2.5 (g/1), respectively, which could supply enough substrates to each bacterial group in the fermenter. as growth nutrients.  T h e inorganic salts hsted in Table 3.9 were used  Chapter 7. Mass Transfer in Biofilms  182  T h e reactor was firstly filled with 500 ml of tap water and 500 ml of culture medium and nitrogen was introduced to strip out the dissolved oxygen. T h e cell was immersed into the solution, and the hquid penetrated into the cell through the membrane filters. After the hquid surface inside the cell reached the same level as that of the culture medium outside the cell, recycling was started.  T h e p H and temperature  in the reactor were  adjusted to 7 . 1 ± 0 . 2 , 3 5 ± 2 ° C , respectively. Under a nitrogen atmosphere the reactor was seeded with 50 ml of the inoculum then operated in a batch mode. After the organic acids had been used up by the bacteria, 500 m l of culture medium was replaced by 500 m l of fresh feed, which was repeated till black bacterial colonies were observed on a removable P V C shde which was inserted into the reactor at the same time as the ceU was immersed into the medium. Afterwards, the reactor was shifted to continuous flow mode. The flow rate was gradually changed to and maintained at 40 m l / h r (dilution rate ~ 0.04 h r ) . - 1  A t this rate the organic acids concentrations in the fermenter were kept high enough, 3 g/1, 1.5 g/1 and 0.5 g/1 for acetate, propionate and butyrate respectively, to support the bacterial growth at their maximum rates.  7.5.2  Effective Diffusivities of Propionate and Butyrate in the Biofilms  As indicated previously the diffusion-reaction model, Equation 7.96, which describes a substrate concentration distribution within a biofilm can be solved numerically or analytically and the model parameter, D , can be determined if three boundary conditions e  are measured experimentally; the substrate concentration on the biofilm surface, S{, and the substrate concentration inside the device, S , and the concentration gradient, dS/dl, e  at the membrane filters. T h e last one (dS/dl = 0) can be assumed confidently as long as the biofilms on the two membrane filters have the same thickness, which was to a great extent dependent on the symmetrical structures of the device and the fermenter. Thickness measurements of the biofilms on the two membrane filters at the end of the  Chapter 7. Mass Transfer in Biofilms  2400  183  n  2200-  E  2000;=  ioooH  1  0  1 20  .  1 40  .  1 60  .  1 80  Time (hr)  Figure 7.70: Establishment of a steady state propionate concentration inside the cell (o) after a dilution. • - propionate concentration outside the cell experiments confirmed the accuracy of this assumption. Using the substrate concentration inside the cell as the value at the interface between the biofilm and the membrane filter would be rehable only when a steady state throughout the biofilm was estabhshed and no microbes existed inside the cell. Estabhshment of a steady state was checked by displacing 20 ml of the medium inside the cell with the same volume of oxygen-free distilled water and then monitoring the concentration change while the outside concentration was kept as constant as possible. That the concentrations of propionate and butyrate inside the cell, after dilution with the oxygen-free distilled water, gradually approached a constant as shown in Figure 7.70 and Figure 7.71 implied that a steady state was estabhshed. This dilution operation was repeated eight times both to confirm the estabhshment of a steady state in the films and to minimize the biological activity inside the cell. It  Chapter 7.  Mass Transfer in Biofilms  184  800-1  700-  100-  0-| 0  .  1  20  •  i 40  '  1  60  •  1 80  Time (hr)'  Figure 7.71: Establishment of a steady state butyrate concentration inside the cell (o) after a dilution. • - butyrate concentration outside the cell was beheved that the number of microbes inside the cell could be neglected because of the filtering action of the membrane filters (pore size 0.45 pm) and the dilution of the medium inside the dive with oxygen-free water. The bulk substrate concentrations were taken as those on the biofilm surface. This assumption, however, was reliable only when the external mass transfer resistance was small. The effect of external mass transfer resistance was to reduce the substrate concentration on the biofilm surface and thus the substrate concentration inside the cell. If this resistance is minimized or the external mass transfer is far faster than the rates of substrate digestion and internal mass transfer within the biofilms, the substrate concentration on the biofilm surface would be very close to the bulk concentration, and correspondingly the inside concentration would reach its maximum value. Experimentally this was checked by increasing the recycle rate to a value above which the inside  Chapter  7.  Mass  Transfer  in  185  Biofilms  2100-1  ^  2000-  E  1900-  c o  L3-  co  £ c  1800-  O U  1700-  CD O  -€>  1600-  1500-  8  10  12  14  16  R e c y c l e rate (l/hr)  Figure 7.72:  18  Effect of recycle rate on propionate concentration inside the cell (o),  •  porpionate concentration outside the cell. 800-i  700 |»  600-  §  500-  B-  -B-  CO  £ c  400-  C O  300  CD  O 3  -e-  -O  200-\  m X  100 8  10  12  14  16  18  R e c y c l e rate (l/hr) Figure 7.73:  Effect of recycle rate on butyrate concentration inside the cell (o), •  butyrate concentration outside the cell.  -  Chapter 7.  Mass Transfer in Biofilms  186  concentrations leveled off. Figure 7.72 and Figure 7.73 show that when the recycle rate was raised above 11.4 l / h r , (superficial velocity = 3 cm/min), the concentrations of propionate and butyrate inside the cell approached their constant values, which indicated that the external mass transfer resistance had been minimized and was not a rate limiting step. Thereby, the bulk substrate concentrations  could be reasonably taken as those on ts  the biofilm surface. Steady state concentrations  of propionate and butyrate inside and outside the cell  were averaged for four measurements which were conducted at a recycle rate of 16 l / h r . Substituting the intrinsic utihzation rates of propionate and butyrate, Equations 6.75 and 6.76, for the reaction rate on the right side of the diffusion-reaction model (Equation 7.96) gives the following equations which describe diffusion and dissimilation of these two acids in the methanogenic biofilm, dS 2  n  ^~dP  D  D  ^  =  r . 5p(l 4 -  p  maa  =  P  iP  3S ) P  * — K p T S p —  < K  b  +  Sb  +  K SblSp  Where the subscripts, p and 6, refer to propionate and butyrate.  ( 7  ( 7  -  '  9 8 )  9 9 )  T h e reaction rates  for each of the acids are based on an integrated biomass ( m g / m g C / h r ) , i.e., a biomass containing a mixture of bacterial groups responsible for the utihzation of various substrates, as discussed in Chapter 6. Correspondingly the density of the biomass, p , has c  units of carbon content in unit volume of the integrated biomass ( m g C / m l ) . T h e density and thickness of the biofilms on the membrane filters were measured according to the steps described in Chapter 3. For each of the equations above, three boundary conditions were known; Sp = Se  iP  and dSp/dl = 0,  at I = 0,  Chapter 7. Mass Transfer in Biofilms  187  Table 7.28: Effective diffusivities of propionate and butyrate Item  Unit  Propionate e  Butyrate  s S  mg/l  1805  515  mg/l  1725  326  Pc L  mgC/ml  26.8  26.8  mm  0.78  0.78  Tmax  mg/mgC/hr  0.0162  0.0473  K.  mg/l  50  27  D DJD  xl0 cm /sec  0.60  0.357  0.41  0.281  b  e  5  e  s = S b  s  P  2  and dS /dl = 0,  Eib  = S  b  and S - s ,  biP  b  Where L is the biofilm thickness, S  e<p  and outside the device, S cell.  Cib  and S  bjb  :  and S  bib  b<p  a U = 0, at I = L.  are the propionate concentrations inside  the butyrate concentrations inside and outside the  T h e same programs as were used for lactose diffusion were used for solving the  differential Equations 7.98, 7.99 and searching for optimum values of effective diffusion coefficients of propionate and butyrate in the biofilms by fitting the calculated values from the model with the experimental values of the concentrations butyrate on the biofilm surface, S  btP  7.5.3  of propionate and  and S . T h e outcome is summarized in Table 7.28. bib  Effective Diffusivity of Acetate in Methanogenic Biofilms  Acetate, as discussed in the kinetic studies of organic acids digestion, is an intermediate product of propionic and butyric acids dissimilation by the acetogens.  T o develop a  balanced bacterial community, the kinetic investigation used a feed mixture of acetate, propionate and butyrate i n a weight ratio of 1 : 0.5 : 0.5. In situ measurement of diffusivities of fatty acids i n an active biofilm needs a knowledge of the intrinsic kinetics of the dissimilation of these acids in the biofilm.  It was, therefore,  necessary  to use  Chapter 7. Mass Transfer in Biofilms  188  the same feed composition as was used for the kinetic studies to develop methanogenic biofilms on the two membrane filters so that the bacterial community had the same distribution of bacterial species in the two cases.  W h e n the measurement of effective  diffusivities of propionate and butyrate was made, the concentration of acetate was also analyzed. T h e data, however, could not be used to calculate the effective diffusivity of acetate in the biofilm because the two longer chain acids were converted to acetate and thus their diffusion would affect the acetate concentration inside the cell. Instead, a feed which contained only acetate was used to measure the effective diffusivity of acetate. T h e time of this feed shift was made short so that it could be assumed that this shift did not cause a considerable change in the distribution of bacterial species in the biofilm. T h e input of acetate into the elemental volume of biofilm as shown in Figure 7.63 was only by diffusion, and Equation 7.96 is still vahd for acetate diffusion and reaction.  dS  a  r  m a x a  S  ,„  a  '^ 'KTr~s:  D  i n n  \  -  (7 100)  =p  Figure 7.74 indicates that the external mass transfer resistance could be neglected as long as the recycle rate was above 12 l / h r . Figure 7.75 shows the estabhshment of steady-state acetate concentration throughout the biofilm after a disturbance to the acetate concentration inside the cell was made by diluting it with oxygen-free distilled water. For the above differential equation (Equation 7.100), three boundary conditions are;  S  a  - S a and dSa/dl = 0  S = a  ei  Sb,  a  at I = 0, at  I =  L.  T h e effective diffusivity of acetate in the methanogenic biofilm is estimated by solving Equation 7.100 with the three boundary conditions. Table 7.29 summarizes the results of the numerical solution.  189  Chapter 7. Mass Transfer in Biofilms  Figure 7.74:  Effect of recycle rate on the acetate concentration inside the cell (o), •  acetate concentration outside the cell 2400-1  21001800i  Cx—B-  §  -B-  43-  43  -G-  -O  1500  *^ CO  Z c  1200  CO  o  C 900 o o o eoo <  o f '  300H —I—  20  —I—  40  —I—  60  —i  80  Time (hr) Figure 7.75:  Estabhshment of a steady state acetate concentration inside the device (o)  after a dilution, • - acetate concentration outside the cell.  Chapter 7. Mass Transfer in Biofilms  Table 7.29:  190  Effective diffusivity of acetate in methanogenic biofilms Item  Unit  Value  S  mg/l  1760  Se  mg/l  1390  Pc  mgC/ml  26.8  L  mm mg/mgC/hr  0.78  mg/l  160  b  max D De/V e  x 10 cm /sec 5  2  0.098 0.54 0.31  During the period of this measurement, it was assumed that the bacterial components in the biofilm had not changed considerably even though an acetate-only feed was used, because the experimental time was held short and bacterial growth was very slow. Experimentally, in order to check this assumption, a repeat experiment was conducted by using the previous feed mixture of three acids again (5, 2-.5, 2.5 g/1 for acetate, propionate and butyrate respectively).  T h e propionate and butyrate concentrations inside the ceU were  analyzed at steady state and no significant change was found in the inside concentrations while the outside concentrations were very close to the values shown in Figures 7.70 and 7.71.  A n d also, the steady states were achieved in an equivalently short period of time  after a disturbance was given to the concentrations inside the device.  These facts im-  plied that the bacterial components in the biofilm had not changed significantly during the acetate-only feed test. As is well known, the bacterial species distribution in a mixed culture is to a great extent dependent on their environment, especially the substrate concentrations if other conditions such as p H , temperature and inorganic salt growth nutrients are unchanged. A t the beginning of this subsection it was explained that to produce a bacterial community as similar as possible to the one used in the kinetic studies, the same feed composition  Chapter 7. Mass Transfer in Biofilms  191  was used in the measurement of effective diffusivities. It is assumed that as long as aU the bacteria can obtain enough food from their environment they will grow at their own maximum rate and thus the fraction of each species in a mixed culture would be determined uniquely. This idea was proposed and used when the distribution of bacterial species in a biofilm was estimated in the last chapter even though high propionate concentrations had some influences on the utihzation rates of propionate and butyrate, and thus may affect the growth'rates of bacteria responsible for these two reactions (see sections "Interaction of organic acids" and "Distribution of bacterial groups in balanced biofilms" in Chapter 6).  For bacterial biofilms which are built up in situ, however, the effect of the  properties of the support materials should be considered, too. This will be discussed in next subsection.  7.5.4  Effect of Support Properties on the Measurement of Diffusivities  In the previous subsections, measurement of the effective diffusivities of acetate, propionate and butyrate in biofilms was discussed. T h e measurement was conducted in situ on active methanogenic biofilms which formed on two nitroceUulose membrane filters using as substrate a mixture of acetate, propionate and butyrate.  T h e intrinsic kinetics  used in the diffusion-reaction model were obtained on active methanogenic biofilms which formed with a feed of the same fatty acids composition and ratio.  Therefore the effect  of substrates on the distribution of bacterial species could be eliminated. T h e influence of the properties of the biofilm support, however, had been ignored when the utihzation rates of organic acids obtained in the biofilms forming on P V C supports were used for the biofilms forming on the nitroceUulose membrane. This assumes that the composition of bacterial species in the biofilms forming on P V C supports was the same as that in the biofilms forming on nitroceUulose membranes. T h e change in composition of bacterial species in a biofilm may have no great physical  Chapter 7. Mass Transfer in Biofilms  192  effect on the structure of biofilm channels through which the substrates transfer into the inner part of the biofilm. However, it may have considerable effect on the consumption rate of a special substrate in a unit volume of the biofilm because the content of the bacterial species responsible for this reaction properties  on the composition of bacterial  may change.  T h e influence of support  species in a biofilm is mainly due to  the  influence of the support surfaces on the attachment of bacterial species when the supports are immersed in a nutrient-rich culture medium. This is because acetate-, propionate- and butyrate-utihzing bacteria have almost the same growth rate in a nutrient-rich medium as indicated in Chapter 5 as well as in the kinetic studies conducted by Lawrence and M c C a r t y [142]. M a n y properties of support surfaces may affect the attachment of free microbes onto the support. It was found that the wettabihty of the surface was an important parameter and that a significant relationship existed between this parameter and the attachment rates of acetate-, propionate- and butyrate- utihzing bacteria in the formation of symbiotic biofilms on different inert surfaces as discussed in Chapter 5. butyrate-  utihzing microbes prefer surfaces with high wettabihty  membrane filters used as biofilm support in the measurement quite pure cellulose nitrate,  a derivative of cellulose.  For example,  such as wood.  the The  of diffusivities is made of  Surfaces made of cellulose have  very high wettabihty because the wettabihty of a surface depends mainly on its interaction with water at the surface.  T h e celluloses, especially the amorphous ones, contain  a great number of "free-hydroxyls" available for site adsorption of water molecules, and thus strong interaction occurs through the formation of hydrogen bonds between water molecules and the surface. Therefore, the nitrocellulose surface has a wettabihty similar to a wood surface because it is made of the same macro-molecules,  cellulose, and thus  the water contact angle on the nitroceUulose surface is taken as zero. As proposed in Chapter 6, on the distribution of bacterial groups in a balanced  Chapter 7. Mass Transfer in Biofilms  193  symbiotic methanogenic biofilm, Equations 6.86, 6.87 and 6.88 could be used to estimate, in one mg of organic carbon of the biofilms on the nitrocellulose membrane filters, the fractions of biomass, m , m , mf,, responsible for dissimilation of acetate, propionate and a  p  butyrate.  m  1 + KIK + hIK + ( ^ r  a  T  + ^r )/(4r  p  + ^r )/(4r 6  m a x  p  + ^r. )/(4r  m a x  b  m a x  , ) a  k /k p  =  mr,  p  1 + k /k p  a  + hlk  a  a  + (*M±r  , )  ( 7  '  1 0 1 )  (7.102)  Q  kb/k  a  ^  =  1 + k /k p  + h/K  a  + ( ^ r  f c  , ) a  ( 7  -  1 0 3 )  T h e propionate concentrations inside and outside the cell were above 1000 mg/1 (Table 7.28) and so its effect on the utihzation rates of propionate and butyrate should not be neglected.  r  p  = r  maXj  p(l  + 0.00025 )  (7.104)  p  and  A n average propionate concentration inside and outside the cell was taken as its representative concentration within the biofilm, since the difference between the concentrations on the two sides was small. T h e specific attachment rates of acetate-, propionateand butyrate-degrading bacterial species on wood surface, k i, are used as those on a Wi  hydrophilic nitrocellulose surface. Table 7.30 lists the results of calculations using Equations 6.86, 6.87 and 6.88. Rewriting the diffusion-reaction model (Equation 7.96) gives  Chapter 7. Mass Transfer in Biofilms  194  Table 7.30: Distribution of bacterial species in biofilms forming on nitrocellulose membranes Item  Unit  Values  K  cm / day  5.596  K h  cm/day  3.396  cm/day  8.20  mg/mgC/hr  0.0219  mg/mgC/hr  0.0311  a  mgC/mgC  0.263  p  mgC/mgC  0.160  h  mgC/mgC  0.375  n m m m  ^max,am g / m g C / h r  0.098  mg/mgC/hr  0.0162  mg/mgC/hr  0.0473  mg/mgC,a/hr r' rnaXyQ. mg/mgC,p/hr r' max,p mg/mgC,b/hr r1  0.373 0.101 0.126  max ,6  D ^= e  P c  m r' j  (7.106)  j  where the subscription, j, refers to acetate, propionate and butyrate  respectively,  p is the density of an integrated biomass which contains the four types of bacteria c  responsible for utihzation of acetate, propionate, butyrate and CO2/H2 ( m g C / m l ) , m,j the fraction of the biomass which is responsible only for the degradation of the j t h substrate,  r'- is the dissimilation rate of the j t h substrate based on the biomass only  responsible for the utihzation of the j t h components values of r'j are also hsted in Table 7.30.  (mg/mgCj/hr).  T h e maximum  T h e dependency of reaction rates on the  substrate concentrations would generally not be affected by the distribution of bacterial species in the biofilms. Therefore, for each one of the organic acids, a diffusion^reaction equation can be estabhshed similar to those discussed i n the previous subsections.  Chapter 7. Mass Transfer in Biofilms  195  Table 7.31: Effect of bacterial species distribution on the measurement of diffusivities Biofilm on P V C supports Substrate  D  m  Biofilm on membrane supports  D /B  e  gCj/mgC  x 10 cm / sec  0.31  0.263  0.558  0.32  0.601  0.41  0.160  0.437  0.30  0.357  0.28  0.375  0.421  0.33  xl0 cm /sec  Acetate  0.255  0.541  Propionate  0.220  Butyrate  0.318  2  D,  e a  D  e,p  d Sg  dP  =  dP •  ™Z  d 2Sb  m  s  2  2  c  pm c  a  f  (7.107)  K + S a  pm  dP  D,e,b-  m  e  mgCj/mgC  5  Kp  a  (7.108)  + Sp  'm.ax,b Sb  r  pmT  r  T  b  °Kb  + Sb +  KiSbSp  (7.109)  Using the three boundary conditions for each acid and the programs for solving the differential equations as well as for searching optimum parameter values gives the effective diffusivity of each acid in the methanogenic biofilms.  T h e results are summarized in  Table 7.31 and compared with the diffusivity values calculated under the assumption that there was no difference in the bacterial distribution in the biofilms forming on the P V C support or on the nitrocellulose membranes. In Table 7.31, 'biofilm on P V C supports' refers to the methanogenic biofilms which formed on P V C support, and correspondingly the effective diffusivities are obtained by using the utihzation rates of organic acids in these biofilms while 'biofilm on membrane supports' means that the bacterial components in the biofilms forming on the membranes have been corrected according to the hydrophilic properties of the nitrocellulose filter, and also the effective diffusivities.  As indicated in the study of build-up of symbiotic  Chapter 7. Mass Transfer in Biofilms  196  methanogenic biofilms on various inert supports, the physiochemical properties of the support surface affect the attachment of free microbes, especiaUy the propionate- and butyrate-utihzing bacteria.  T h e former is most insensitive to the wettabihty of the sup-  port surface while the latter prefers hydrophilic surfaces. The P V C supports on which the kinetic investigation of organic acids digestion was conducted was very weakly wettable (88  0  water contact angle), but the nitrocellulose membranes are very hydrophihc (0  water contact angle).  0  Therefore, the fractional biomass of propionate-utihzing bacteria  on the membrane was less than that on the P V C support because of the increase in fractional biomass responsible for conversion of butyrate.  If this difference of bacterial  components in the biofilms forming on various supports is ignored, the influence of solute size on effective diffusivities calculated from the diffusion-reaction model as shown in Table 7.31 can not be explained. T h e bigger propionate molecule has a faster molecular diffusion rate than the smaller acetate molecules. This error, however, can be corrected by considering the change in bacterial compositions in the biofilms forming on different support surfaces.  Influence of Biofilm Structure on Diffusivities  7.6  Figure 7.76  shows a top view of a methanogenic biofilm magnified 400 times with a  microscope ( N I K O N ) after a water layer on the biofilm was carefully absorbed by a filter paper. W h e n such a porous biofilm composed of irregular channels of various sizes is immersed in an aqueous solution, the channels are filled with water and solute molecules are transported i n these channels just as they are in free solution. However, the presence of sohd biomass would certainly affect the motion of a solute molecule.  There are two  mechanisms by which a solute molecule may lose momentum in the axial direction.  Chapter 7. Mass Transfer in Biofilms  Figure 7.76:  Top view of a methanogenic biofilm, (x  197  400)  1. By direct transfer to the wall as a result of molecule-wall collisions 2. B y transfer to water molecules as a consequence of collisions between solute and solvent molecules  T h e first mechanism, Knudsen diffusion, will predominate when the diameter of a channel is small compared with the molecular mean free path lengths (the distance between two molecular collisions). In this situation, molecule-wall collisions are much more frequent than molecule- molecule collisions. This is true, especiaUy for gas mixtures low pressures and high temperatures.  at  Unlike the diffusion in gases a solute molecule is  surrounded by water molecules in a diluted solution and even in a channel of micropore size the collisions between solute and water molecules are more frequent than those between solute molecules and wall. Hence, it is reasonable to suggest that the fluxes, just as in the bulk diffusion, are described by the second mechanism, and will still be described  Chapter  7. Mass  Transfer  in  Biofilms  198  by Fick's law since inter-molecular collisions still dominate over molecule-wall collisions. But, the diffusion coefficient must be replaced by an effective diffusion coefficient,  D  = KiD  e  D. e  (7.110)  Where Ki is a factor determined by the geometry of the pore structure only. K ; should be independent of the pore size, provided this is large compared with the mean free path lengths, but it should be proportional to the void fraction, and should reflect the fact that the available directions for molecular drift are constrained by the orientation of the pores. Thus it is common to find K\ expressed in the form  Kt = -  (7.111)  T  and so,  D  e  = -D  (7.112)  T  e  D  r  Where r is a tortuosity factor determined by the statistics of pore orientations, and e is the biofilm void fraction occupied by the channels or fractional area through which solute molecules can enter into the biofilms by diffusion. T h e value of e can be determined experimentally provided the biofilm can be assumed to have a uniform void traction.  Some biomass collected from intact biofilms was filled  into a small K i m a x tube (diameter = 4 mm) and then centrifuged at 4000 rpm until the dense biomass volume became a constant as shown in Figure 7.77.  Chapter 7. Mass Transfer in Biofilms  199  Water Biomass Dense biomass  Figure 7.77:  Experimental determination of biofilm void fraction  T h e water volume is thought of as the total volume of channels, because they were full of water and collapsed into sohd biomass under the centrifugal force, while the water is left. T h e void fraction of the biofilm is calculated by the following equation.  *w ~  where V  w  is the water volume and V  matl  'mixta  the sohd biomass volume. For the acidogenic  biofilms, e = 0 . 6 6 ± 0 . 0 4 , on the basis of 4 samples. From Equation 7.113 the tortuosity of acidogenic biofilms  D 0.72 T = e— = 0.66 x — — = IL 0.47  1.03  (7.115)  This value of r means that the influence of acidogenic biofilm structure on lactose effective diffusivity is mainly from the fractional area occupied by the sohd biomass which reduced the area available to lactose diffusion into the biofilm, and also that the biofilms  Chapter 7. Mass Transfer in Biofilms  200  Figure 7.78: Straight vertical channels (along the black and white boundary) in a section of an acidogenic biofilm ( x 100). T h e down black part is biofilm and P V C support. had almost straight channels. Observation of biofilms on a P V C slide with a microscope revealed that some vertical channels existed in the biofilms as shown in Figure 7.78 T h e channels shown in this picture are the macro-channels which were formed during the development of the biofilm, and so might be affected by the production and release of gaseous fermentation products, such as CO2. More numerous are the micro-channels through which the substrate molecules are transported to microbial cells embedded i n the exopolysaccharide matrix. T h e same measurements were made on methanogenic biofilms.  T h e fractional area  available for organic acid transfer in the methanogenic biofilms, e, is calculated from Equation 7.114, £ = 0 . 5 4 ± 0 . 0 3 . Another structure parameter of the biofilms, tortuosity factor, can be obtained from the values of e, D and D with Equation 7.113. For each acid, e  the parameter r is calculated from the ratio of its effective diffusivity to free diffusivity.  Chapter  7.  Mass  Transfer  in Biofilms  201  Table 7.32: Comparison of acidogenic and methanogenic biofilms Parameter  Unit  Acidogenic  Methanogenic  P  g dry mass / m l  0.087  0.076  Carbon content  m g C / m g . d r y mass  0.342  0.348  Pc  g carbon/ml  0.030  0.027  e  0.66  0.54  T  1.03  1.69  Color  milk white  black  0.0259  0.0090  mgC/mgC.day  Growth rate  r  = e(D/D )  = 0.54/0.32 = 1.69  (7.116)  T = e(D/D )  p  = 0.54/0.30 = 1.80  (7.117)  Tf, = e(D/D )  b  = 0.54/0.34 = 1.59  (7.118)  a  e  p  a  e  e  T h e subscripts mean that the tortuosity is estimated from the diffusivity ratios of acetate, propionate and butyrate, respectively.  Because the organic acids are transported  in the same methanogenic biofilms the difference in the values of tortuosity is due to experimental and calculation errors. A n average value of 1.69 is taken as representative. T h e relative error is less than 7 percent. Table 7.32 summarizes some parameters describing the acidogenic and methanogenic biofilms. Comparisons between these two types of biofilms gives some interesting properties of the biofilms. In the experiments it was observed that the methanogenic biofilms were obviously different from the acidogenic biofilms. T h e former was black and the latter milk white since the sulfate-reducing bacteria in the methanogenic biofilms reduced S  + 6  to S  - 2  some of which formed insoluble black FeS while the sulfate-reducing bacteria  Chapter 7. Mass Transfer in Biofilms  202  could not survive in the acidogenic environment even though the acidogenic biofilms were also fed with the same sulfate solution. T h e methanogenic biofilms, however, have almost the same carbon content as the acidogenic biofilms per unit weight of dry biomass. This means that the bacterial species composing these two functionally distinctive bacterial groups have almost the same carbon content.  T h e differences in the values of e and  r obtained from the methanogenic and acidogenic biofilms reflect the difference in the structure of these two kind of biofilms, the methanogenic biofilms having more tortuous channels and less void area for internal mass transfer than those of acidogenic biofilms. T h e difference in the void fractional volume, e, of the biofilms may be attributed both to biofilms' growth rates, the net accumulation rate of acigogenic biofilms being 3 times faster than that of methanogenic biofilms, and to biofilms' appearance since it could be observed that the acidogenic biofilms had numerous stringy filaments extending outward into the hquid while the methanogenic biofilms had soomther surface. W h e n the biofilms were taken out from the medium, the filaments collapsed to hold up some water.  In  methanogenic biofilms, the release of great amount of methane which is sparingly soluble in water produced lots of tiny bubbles which arised at the direction almost perpendicular to the direction of substrate transport, which gave higher mass transfer resistance and thus, more tortuous channels than those in acidogenic biofilms.  Chapter 8  Conclusions and  Recommendations  Conclusions After it was confirmed that the external and internal mass transfer resistance had no significant influences on lactose fermentation in acidogenic biofilms under the conditions of these experiments,  the intrinsic kinetics of lactose degradation and  production of acetate, propionate, butyrate, lactate and ethanol were investigated in a continuous flow reactor ( C S T R ) at 35 °C and p H of 4.6. T h e culture medium was chemically defined. T h e major fermentative  products of lactose under these  conditions were acetate and butyrate while the minor products were propionate, ethanol and lactate. The utihzation rate of lactose, as a function of lactose concentration, S (mg lactose/1), can be described by a Michaelis-Menten type equation as can the formation rates of acetate, butyrate and ethanol; _  0.3144S,  ac  (mg  r  acetate  _ -  butyrate  r  Tethanol -  0.0599S g  9  Lactose/mgC/hr)  iac  +  (mg H A c / m g C / h r )  0.115S  Iac  ', c  532  c  ^  o  +  o  +  (mg H B u / m g C / h r )  ^  (mg E t h / m g C / h r ) 203  Chapter 8.  Conclusions and Recommendations  204  The formation rates of two other minor products, propionate and lactate, have linear relationships with lactose concentration under the experimental conditions;  "propionate  = 1.25 x 10~ S  (mg H P r / m g C / h r )  6  lactate  = 2.18 x 1 0 - S 6  tac  (mg H L a / m g C / h r )  ioc  A l l these rates are based on a milligram of carbon of attached biomass. T h e low p H value (4.6) of the culture medium could depress the formation of propionate, an intermediate the following methanogenic bacteria cannot digest easily. A dramatic change in p H (5 to 6.5) caused lysis of some embedded bacteria with the acidogenic biofilm thinning and the fermenter foaming. 2. T h e rate of formation of a methanogenic biofilm is slower than that of an acidogenic biofilm. A study on build-up of symbiotic methanogenic biofilms on different inert supports was conducted by culturing a mixture of methane-producing bacteria in a nutrient rich medium in the presence of four types of supports; wood, ceramic ring,  PVC  and stainless steel.  T h e three groups of bacteria,  propionate-degrading and butyrate-degrading,  acetate-degrading,  were found to attach at different  rates to different substrata. A semi-theoretical kinetic model has been proposed to depict the process of bacterial attachment.  For attachment of each of three bacterial  types onto each of four support surfaces, the accumulation of fixed biomass on unit area of support surface, [xA], with time can be expressed as following;  [x] - +p.-K> s  [  l +  u-K>  [  1  A model with 21 parameters has been found to be able to fit 12 equations hke the equation above. For each type of bacteria, a linear relationship is found between  Chapter 8.  Conclusions and Recommendations  205  the model parameter, k. which is a specific attachment rate of free bacterial cells onto clean surfaces, and the wettabihty of the surfaces.  If it is explained that  the bacteria with more hydrophilic surfaces attach more easily to more hydrophihc supports, then the order of decreasing hydrophobicity of bacterial wall surfaces is;  butyrate degraders > acetate degraders > propionate degraders  T h e rate of spread of bacterial microcolonies on support surfaces was also found to be influenced by the wettabihty of the substrata.  In this case, the spreading  factor, s, that is, the ease with which the microcolonies spread on surfaces, was found to increase with the hydrophobicity of the surfaces. Compared with the rate of attachment of bacteria onto a clean surface and that of fixed bacterial growth, the attachment  of free ceUs onto immobilized biomass already on the surface was  neghgible. T h e specific growth rates of the three types of bacteria were found to be the same, and therefore, the composition of a fixed biomass, i.e., the distribution of each group of bacteria in the fixed bacterial community, is to a great extent dependent on the initial attachment rate of each type of bacteria which is affected by the wettabihty of the supports. 3. Again after external and internal mass transfer resistance had been experimentally minimized and/or eliminated, biomethanation kinetics of organic acids in methanogenic biofilms were investigated at a p H of 7.1 and 35 °C.  T h e substrate  was a mixture of organic acids containing acetic, propionic and butyric acids at a weight ratio of 1 : 0.5 : 0.5 (mg/l).  T h e degradation rate of acetate can be  expressed by a Michaelis-Menten equation,  HAc  r  =  0.0985/f 160 +  Ac  S Ac H  (mg H A c / m g C / h r )  Chapter 8.  Conclusions and Recommendations  206  However, the degradation of propionate and butyrate are affected by the concentration of propionic acid in the medium, and so, two modified Michaelis-Menten equations are used for the assimilation rates of propionic and butyric acids.  For  propionic acid utilization, higher propionic acid concentration promotes its degradation, 0 . 0 1 6 2 S P r ( l + 0.0002Stfp ) zrit c H  r Pr  =  H  r  50  +  ( § HPr/mgC/hr) m  b PT H  O n the other hand, the utihzation of butyric acid is inhibited by high concentrations of propionate, 0.0473SgB„ =  27  +  S ., 0.000296 g  +  W „ ,  ( m g HB  "/ « / > m  C  hr  In the three equations above, the rates are based on unit weight of carbon in the methanogenic biofilms and the concentrations of fatty acids in mg/1. To check the interaction between the three organic acids, feeds having various ratios of the three organic acids were also used and it was found that only propionic acid concentration had promotional and inhibitory influences as described above. 4. A methanogenic biofilm is a symbiotic bacterial community including four fundamental types of bacteria, acetate degraders, propionate degraders, butyrate degraders and hydrogen-utihzing bacteria. A method has been proposed to estimate the distribution of each bacterial group in a methanogenic biofilm from the knowledge of the attachment rate of methanogens and acetogens on clean surfaces, the kinetics of utihzation of the organic acids, and the hydrogen and the energy balance in mature methanogenic biofilms. T h e compositions (mg carbon of the ith bacterial type per mg carbon of total biomass) of mature symbiotic methanogenic biofilms  Chapter 8.  Table 8.33:  Conclusions and Recommendations  207  Organic carbon fraction of each bacterial group in methanogenic biofilms on  P V C and nitrocellulose membrane filter supports Substrate  Acetate  Propionate  Butyrate  Hydrogen  degraders  wt%  wt%  wt%  wt%  on P V C  25.5  22.0  31.8  20.7  on membrane  26.3  16.0  37.5  20.2  on P V C supports and nitrocellose membrane filters were estimated and hsted in Table 8.33. 5. Based on the intrinsic kinetics of lactose fermentation in acidogenic biofilms and organic acids digestion in methanogenic biofilms, in situ measurements  of mass  transfer of lactose and organic acids were conducted in active biofilms.  Effective  diffusivities of lactose and organic acids, defined by a modified Fick's law and a diffusion-reaction model, were estimated from steady state concentration drops through an active biofilm by numerically solving a diffusion-reaction model. T h e effective diffusivity of lactose in an acidogenic biofilm is 0 . 4 7 x l O is 65.3%  of its diffusivity in pure water.  - 5  cm /sec that 2  After a correction was made to allow  for the fact that the composition of bacterial types might be somewhat different in methanogenic biofilms fixed on both P V C and nitroceUulose filter supports, the effective diffusivities of acetate, propionate and butyrate were found to be 0.558 x l O  - 5  , 0.4374xl0  -5  and 0.421 x l O  - 5  cm /sec, respectively, which means that 2  diffusivities of acetate, propionate and butyrate in methanogenic biofilms have been reduced to about 30.2 % of the values in pure water. B y using these data and the experimentaUy measured fractional void volume of biofilms, tortuosity factor r , a parameter describing the structure of channels formed in biofilms, was estimated for acidogenic biofilms (r = 1.03)  and methanogenic biofilms (r = 1.69) respectively.  Chapter 8.  Conclusions and Recommendations  208  A comparison was also made between other properties of these two kind of biofilms.  8.2  Recommendations  Going back to the questions put froward in Chapter 1, two problems have been tentatively solved in this study, i.e. the measurement of the intrinsic kinetics and mass transfer of lactose and organic acids in the corresponding biofilms, and so it may be possible to calculate an optimum biofilm thickness.  Further studies are, however, needed on how  to control a growing biofilm at a steady state thickness so as to maintain an optimum operation for a long time.  8.2.1  Concentration Effect  Obviously, an optimum biofilm thickness with which a fermenter can hold up the largest amount of active biomass without dead volume caused by excess biomass is dependent on substrate concentrations in the bulk medium and at the interface between a biofilm and a support.  T h e former mainly depends on the flow pattern in a reactor while the  latter would be determined mainly by the process designer, e.g, a concentration which gives a half maximum reaction rate, (K„).  From the effect of concentration on optimum  biofilm thickness, a biofilm should have a thickness which gradually decreases with the reduced substrate concentration from the inlet to the outlet.  Therefore, a plug flow of  medium over a biofilm with decreasing thickness as shown in Figure 8.79 may be an ideal for optimum operation.  8.2.2  Controlling Biofilm Thickness  To this author's knowledge, few studies have been conducted on how to control a growing biofilm at a constant film thickness though some investigations have been conducted  Chapter 8- Conclusions and Recommendations  209  S  So  Inlet  Reactor  Outlet  Figure 8.79: Illustration of an optimum operation of biofilm reactors. No back- mixing of medium is assumed. on the influence of shear stress of fluid flow on biofilms. Most of investigations were concentrated on the formation of biofilms or on the possibility of biofilm technology being apphed to a special wastewater. It may be thought that a steady state biofilm would be established automatically by the action of fluid flow stress and sloughing. However, in most cases of present industrial applications, the fluid flow rates are quite low due to the long residence time required for the slow utihzation rate of substrates and so it can not be used purposely to control the biofilm thickness. In some fluidized bed reactors the biofilm on sand carriers are very thin due to strong turbulent flow, and hence, the thickness is controlled, but not kept at an optimum value. Sloughing is not a good method, either, because it occurs randomly with a result that block biomass would be lost and a bare support left.  Moreover, it has been observed in this investigation that an over thick  acidogenic biofilm (3-4  mm) could hold quite strongly on a membrane filter even though  Chapter 8.  Conclusions and Recommendations  210  the substrate concentration within the biofilm had fallen to zero at a thickness of about 2 mm.  Another experimental observation which shows that sloughing does not occur  easily was that anaerobic biofilms, especially the acidogenic biofilms, could stand in a pure water for a very long time (up to 7 days) without falling off. Although there are many factors which can influence attachment and formation of biofilms (genetic, physiological, environmental, chemical factors) as discussed in Chapter 2, those which can be used to control the size of microbial aggregations  (thickness of  biofilms, size of granules) are generally limited to chemical or physical methods. T h e chemical methods utilize some chemicals  such as p H , chelating agents (hke  E D T A ) , to redisperse the fixed biomass into the medium, or, a decrease in the amount of chemicals in a medium which are beneficial for the formation of the extracellular polymer matrix such as Ca  ++  could also reduce film thickness. T h e most striking advantage of a  chemical method is that it would not cause extra back-mixing in a fermenter and thus an approach to the ideal flow pattern shown in Figure 8.79 can be attained. However, it may not be easy for an operator to use chemicals to control biofilm thickness by redispersing immobilized biomass, and also, the lysis of bacteria which have been damaged by the chemicals may introduce extra operational difficulties such as foaming in a fermenter as observed in this study. Another method is by physical means as have been utilized in fluidized bed fermenters. As indicated above, the active biofilm on supports (usually sand) can be kept very thin due to the interactions among particles and/or between particles and liquids, but it is difficult to control the biofilm thickness at a desirable value by this method. Moreover, with this method the turbulence of fluid flow and thus the back-mixing in the fermenter must be increased, which greatly decreases the thickness of an active biofilm and the holdup of active biomass in the fermenter while the bulk medium concentration the outlet concentration due to the back-mixing.  approaches  Chapter 8.  Conclusions and Recommendations  Gas  211  ,Gas  Gas  III  -a  -a  Support size Figure 8.80:  8.2.3  Illustration of a process of three stages of cheese whey treatment  A Compromised Physical Method  W i t h a physical method to control the biofilm thickness, the excess biomass can be easily removed from the fermenter, thus, a long term stable operation can be estabhshed. First of all, considering the concentration effect on biofilm thickness and the complete backmixing caused by fluid flow, it is suggested that the process of cheese whey treatment be divided into several stages connected in series, not only two stages (or two phases) and each stage can be operated with a small amount of back-mixing. Figure 8.80 shows a process of three stages. T h e distribution of acidogens and methanogens (with acetogens) is flexible. It may be possible for the first stage to act as the acidogenic phase and the following two stages as the methanogenic phase. One recommended support is balls of porous materials such as natural sponge or polyurethane foam which can entrap the active biomass within their pores.  T h e size  Chapter 8.  Conclusions and Recommendations  212  of the balls, however, should be controlled according to the optimum biofilm thickness calculated for the special conditions in a stage. In general, the first stage has the balls with the biggest diameter, with gradually decreased ball size in the following stages. T h e last stage may use sand as its support if the desirable biofilm thickness is very thin. T h e excess biomass produced by the growing biofilms can be removed from the surface of the balls by fluidizing the reactors as with sand fluidized beds while the biomass within the balls will always be active throughout the balls because of their controlled sizes. As is well known, the microbial growth in the first one or two stages will be the fastest because of the faster intrinsic growth rate of acid-producing bacteria and the higher substrate concentrations. these stages.  Therefore most of the excess biomass should be removed in  Another arrangement  is recommended in which the first two stages are  operated in a fluidized bed mode having supports as suggested above, while the last stage is operated in a plug flow mode with stationary supports such as needle-punched P V C . T h e removal of excess biomass from the stationary supports may be performed periodically by recychng the medium which would add a stress on the biofilm or by adding stripping chemicals. In conclusion, a long term optimal and stable operation of fermenters using immobilized microorganisms depends to great extent on whether the excess biomass due to microbial growth can be removed from the reactors smoothly and continuouly to maintain the size of microbial aggregates at an optimum value. 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Smith "Colorimetric method for determination of surgars and related substrances",  Analytical Chem-  istry, 28(3):350-356 R . L . Markus, "Colorimetric determination of lactic acid in body fluids utihsing cation exchange of deproteinization", Archives of Biochemistry, 29:159-165  Appendix A  Fermentation Pathways  A.l  Four Fermentation Pathways of Glucose to Pyruvate  1. Embden-Meyerhof-Parnas ( E M P ) pathway of glucose utihzation is considered to be widely used among fungi, yeasts and bacteria and has the overall reaction  Glucose + 2 A T P + 2 N A D +  2Pyruvate + 4 A T P + 2 ( N A D H +  H+).  Figure A.81 shows the reaction intermediates and the enzymes which catalyses the formation of these intermediates. 2. Hexose monophosphate ( H M P ) pathway is largely concerned with biosynthetic metabohsm because of its provision of pentoses which are needed for the synthesis of nucleic acids and nucleotide-containing prosthetic groups. can be operated in two different variations.  T h e H M P pathway  T h e first variation is referred to as  the em pentose shunt or pentose cycle which does not lead directly to pyruvate as shown in Figure A.82 [53]. T h e overall reaction is Glucose + 1 2 N A D P + + 7 H 0 + A T P — • 2  6CO2 + 1 2 ( N A D P H + H ) + H P 0 +  3  4  + ADP.  Another variation is used by oxidative microorganisms, the partly complete cycle to produce pyruvate from glyceraldehyde 3-phosphate, catalyzed by the same enzymes as the E M P pathway. T h e sum of reactions for this second variation is  230  Appendix A. Fermentation Pathways  3Glucose + 6 N A D P + + A T P —>  231  2Ffructose 6-P + Glyceraldehyde 3-P +  3C0  2  + A D P + 6 ( N A D P H + H+) + H P 0 . 3  4  and the pathway is shown in Figure A.83. 3. T h e Entner-Doudoroff ( E D ) pathway was discovered by Entner and Doudoroff during metabohc studies of Pseudomonas saccharophila as shown in Figure A.84. 4. In addition to the well known E M P , H M P and E D pathways, there is another pathway, phosphoketolase ( P K ) pathway as shown in Figure A.85. It is, however, possessed by only a small group of bacteria, the heterofermentative  A.2  Lactobacilli.  Formation of Organic Acids from Pyruvate  T h e following figures show the mechanisms of the formation of acetate (Figure  A.86),  butyrate (Figure A.87), mixed products (Figure A.88) and propionate (Figure A.89) from glucose via the common intermediate, pyruvate.  Appendix A. Fermentation Pathways  232  GLUCOSE EC 2. 7.  1. 1.  glucose 6-phosphate EC 5. 3. 1. 9. fructose 6-phosphate ' "  A  T  *  ?  S-ADP  —  /  fructose 1,6-bisphosphate  dihydroxyacetonephosphate  - glyceraldehyde 3phosphate EC 1.2.1.12.  ^•NADH+H*  1,3-bisphosphoglycerate methylglyoxal  EC  •ADP  2. 7. 2. 3.  ^ATP  3-phosphoglycerate D-lactate -NAD* ••NADH + H*  EC 2.7.5. 3.  ?  t  2-phosphoglycerate EC 4. 2.1.11.  phosphoenolpyruvate L-Al  EC 2.7.1.40 I  •ATP  2 ATP  PYRUVATE  Figure A.81: EMP pathway of glucose conversion to pyruvate. Key to the enzymes: E C 2.7.1.1: hexokinase; EC 5.3.1.9: glucosephosphate isomerase; EC 2.7.1.11: phosphofructokinase; EC 4.2.1.13: fructosebisphosphate aldolase; EC 5.3.1.1: triosephosphate isomerase; EC 1.2.1.12: glyceraldehyde 3-phosphate dehydrogenase; EC 2.7.2.3: phosphoglycerate kinase; EC 2.7.5.3: phosphoglyceromutase; EC 4.2.1.11: Enolase; EC 2.7.1.40: pyruvate kinase. Source is [52].  233  Appendix A. Fermentation Pathways  glucose  i glucose 6-phosphate •*  T  "  I  ribulose 5-phosphate Pentose phosphates i • glyceraldehyde 3 - P „  dihydroxyacetone-P  fructose 1,6-bisphosphate fructose 6 - P • E M P pathway  I  phosphoenolpyruvate  pyruvate  Figure A.82: Schematic representation of the cychc (pentose shunt) and non-cychc nature of the HMP pathway. Source is [52].  Appendix A. Fermentation Pathways  234  GLUCOSE ,-ATP "ADP glucose 6-phosphate NADP* 'NADPH + H  EC 1. 1.1.49  +  glucono-lactone 6-phosphate EC 3.1.1.17 6-phosphogluconate U-NADP* 1 1 1 " L. ADPH+H* N  ribulose 5-phosphate / EC 5.1.3.1 xylulose 5-phosphate  glyceraldehyde  NAD*^L-ADP NADH+H*«7>»-A' ,  \ E C 5. 3. 1. 6 |ribose 5-phosphate|  fructose 6 - P \  X  fructose 6-P \  I ECS.3.  1.9  glucose 6-phosphate-  IT  PYRUVATE  Figure A.83: HMP pathway of glucose utihzation. S 7-P: sedoheptulose 7-phosphate; GA 3- P: glyceraldehyde 3-phosphate; DHAP: dihydroxy-acetonephosphate; E 4-P: erythrose 4- phosphate; F 6-P: fructose 6-phosphate; FDP: fructose 1,6-bisphosphate. Key to the enzymes: EC2.7.1.1: hexkoinase; EC 1.1.1.49: glucose 6-phosphate dehydrogenase; EC 3.1.1.17: gluconolactonaise; EC 1.1.1.44: 6-phosphogluconate dehydrogenase; EC 5.1.3.1: ribulosephosphate 3-epimerase: EC 5.3.1.6: ribose 5-phosphate isomerase; EC 2.2.1.1: transketolase; EC 4.1.2.13: fructose bisphosphate aldolase; EC 3.1.3.11: hexose diphosphatase; EC 5.3.1.9: glucose 6-phosphate isomerase. Source is [52].  Appendix A. Fermentation Pathways  235  G L U C O S E  glucose  6-phosphate  gluconate  L—NADP* EC 1.1. 1.49 f K^NADPH + H* glucono-lactone  6-phosphate  EC 3.1.1.17 6-phosphogluconate  EC 4. 2. 1. 12 2- keto- 3- d e x y -  6-phosphogluconate  EC4.1.2.14 fructose P Y R U V A T E  glyceraldehyde  *  3-phosphate  6-P  / ~V  EC 2. 2.1.1 2 ATP 2 ADP erythrose  A T P '  4-  phosphate  . P O O L /  fructose  6-P xylulose  5-  phosphate  |ECJ. 1.3. 1  sedoheptulose 7-phosphate  L  glyceraldehyde 3-phosphate  EC2.2.1.1  ribose  ribulose  5-  phosphate  |  5-phosphate  Figure A.84: ED pathway of glucose utilization. The abbreviations as in HMP pathway. Key to the enzymes: EC 2.7.1.1: hexokinase; EC 1.1.1.49: glucose 6-phosphate dehydrogenase; EC 3.1.1.17: gluconolactonase; EC 4.2.1.12: 'phosphogluconate dehydratase; EC 4.1.2.14: phospho-2- keto-3-deoxygluconate aldolase; EC 2.2.1.1: transketolase; EC 2.2.1.2: transaldolase; EC 5.1.3.1: ribulosephosphate 5- phosphate isomerase. Source is [52].  Appendix A. Fermentation Pathways  glucose  236  L-arabinose  D-ribose  L-ATP  ^-ATP EC 2 . 7 . 1 . 1 5  k»-ADP  ^-»-ADP  EC 5.  D-xylose  EC 5. 3. 1 . 5  3.1.3  glucose 6 - P U-NADP* E C 1 1 1  "'  p>NADPH + H*  glucono-lactone 6 - P  D-ribose 5 - P  L-ribulose  D- xylulose  ATP  EC 3 . 1 . 1 . 1 7  ATP  "•ADF  6-phosphogluconate  >-*-ADP  EC 5 . 3 . 1 . 6  U-NADP+ EC 1. 1 . 1 . 44 L  NADPH-H*  ribulose 5-phosphate  xylulose 5-phosphate IEC4. 1.2. 9 ADP ATP  glyceraldehyde 3 - P 1  acetyl-phosphate — ^ ^ » acetate  «tEMP  pyruvate  Figure A.85: PK pathway of hexose and pentose utihzation. Key to the enzymes: EC 2.7.1.1: hexokinase; EC 1.1.1.49: glucose 6-phosphate dehydrogenase; EC 3.1.1.17: gluconolactonase; EC 1.1.1.44: phosphogluconate dehydrogenase; EC 5.1.3.1: ribulose phosphate 3-epimerase; EC 2.7.1.15: ribokinase; EC 5.3.16: ribosephosphate isomerase; EC 5.3.1.3: arabinose isomerase; EC 2.7^1.47: ribulokinase; EC 5.3.1.5: xylose isomerase; EC 2.7.1.17: xylulokinase; EC 4.1.2.9: phosphokeitolase; EC 2.7.2.1: acetokinase. Source is [52].  Appendix A. Fermentation Pathways  237  fructose 2ADP + 2P;-  2NAD • 2NADH + 2H*  2ATP-  r  pyruvate  pyruvate CoA•Fd • FdH  •FdH,  2  1  acetyl-CoA  C0  ADP + Pj  acetyl-CoA  CO,  2  r  ATP  CoA-  -Fd  CoA-  XH  ADP + Pj  ' 3  2  ATP  CoA  XH, 10  acetate  X+ H 0 2  ICO]  formate  ATP—-X ADP + P j - ^ 1  H F4  methyl-B -E  5  12  10-formyl-H F 4  ^ - CoA acetyl-CoA S- ADP + ^  5, 10-methenyl-H F  CoA  4  NADH + rT  ATP  J acetate  NAD* -*-A 5, 10-methylene-H<F -methylene FdH 2  FdS-methyl-r^F  Figure A.86: Formation of acetate from pyruvate.  B„-E  1, Degradation of fructose via the  Embden-Meyerhof-Parnas pathway; 2, pyruvate-ferredoxin oxidoreductase; 3, phosphotransacetylase plus acetate kinase; 4, formate dehydrogenase; 5, formyl-tetrahydrofolate synthetase; 6, methenyl-tetrahydrofolate cyclohydrolase; 7, methylene- tetrahydrofolate dehydrogenase; 8, methylene-tetrahydrofolate reductase; 9, tetrahydrofolate: B  i 2  methyl-  transferase; 10, C O dehydrogenase; 11, acetyl-CoA-symthesizing enzyme; [CO], enzymebond. Source is [54].  Appendix A. Fermentation Pathways  C H  3  - C O - C H  2  C H  CH —CO-SCoA  - C O - S C o A  3  acetoacetyl-CoA - NADH + H  238  >co  3  - C H  2  - C H  2  - C O - S C o A  butyryl-CoA 3  +  NAD*-*N  >• NAD* NADH + H*  CH3-CO-COOH pyruvate C H  3  - C H - C H  2  - C O - S C o A  OH  • C H  — HjO  3  - C H = C H - G O - S C o A crotonyl-CoA  (J-hydroxybutyryl-CoA  Figure A.87: Butyrate formation from pyruvate by Clostridia. Key to the enzymes: 1, pyruvate-ferrodoxin oxidoreductase; 2, acetyl-Co A-acetyl transferase; 3, 3-hydroxybutyryl-CoA dehydrogenase; 4, 3-hydroxyacyl-CoA hydrolyase; 5, butyryl-CoA dehydrogenase; 6, fatty acid CoA transferase. Source is [52].  Appendix A. Fermentation Pathways  239  glucose  (H)  succinate"] • ^ - • ^  CO, oxaloacetate - 4—^—  -(H) ADP A ' TP LADP  P E P  X*-ATP S  lactate  5  acetaldehyde  (H)  ethanol  (H)  —^  (H) pyruvate  X  •I: X  formate  acetyl-CoA  CoA  acetyl- (?) :etylADP  CO,  ATP  Figure A.88: Formation of mixed products (ethanol, lactate, etc.). 1, enzymes for the EMP pathways; 2, lactate dehydrogenase; 3, pyruvate- formate lyase; 4, formate-hydrogen lyase; 5, acetaldehyde dehydrogenase; 6, alcohol dehydrogenase; 7, phosphotransacetylase; 8, acetate kinase; 9, PEP carboxylase; 10, malate dehydrogenase, fumarase and fumarate reductase. Source is [54].  Appendix A. Fermentation Pathways  240  ADP C H j - C O - P O j  1  "  ATP  -  C H  3  - C O O H  acetate •  C H j - C H j - C O S C o A p r o p i o n y l - C o A  C H  3  - C O ~ S C o A  acetyl-CoA  - C H j - C O - C O O H  H O O C - C - C O - S C o A  I  H  pyruvate  Ds-methylmaJonyl-CoA  - C H , - C H O H - C O O H lactate  /-ATP ^ A M P • Pj  H O O C - C H  H O O C - C - C O - S C o A I C H  2  - C O - C O O H  fi  Ln-methylmalonyl-CoA  C H j = C - C O O " O  oxalacetate  3  L—NADH • H*  pofphosphoenolpyruvate  ' r* NAD* H O O C - C H j - C H O H - C O O H malate r  H O O C - C H , - C H  2  H,0  H O O C - C H = C H - C O O H  - C O - S C o A  fu m a r a t e  s u c c i n y l - C o A  i^-ADP • p  t  C H j C H , C O O H  -  H O O C ^ C H , - C H , - C O O H  propionate  Figure A.89: Formation of propionate from pyruvate or lactate. 1, lactate dehydrogenase; 2, pyruvate-ferredoxin oxidorecuctase; 3, phosphoacetyl transferase; 4, acetate kinase; 5, Ds-methylmalonyl- CoA-pyruvate transcarboxylase; 6, malate dehydrogenase; 7, fumarase; 8, fumarate reductase; 9, succinyl-CoA transferase; 10, L R - methylmalonyl-CoA mutase; 11, methylmalonyl-CoA racemase; 12, pyruvate-phosphate dikinase; 13, PEP-carboxytransphosphorylase. Source is [52].  Appendix B  Analysis Methods  The first two sections describe the analysis of a liquid sample for lactose, lactate, acetate, propionate, butyrate,  and ethanol.  T h e third section covers the measurement  production rate and compositions of the gaseous products.  of the  T h e last one explains the  analysis of sohd samples including total organic carbon ( T O C ) , dry weight and ash content of a biomass, etc.  B.l  Determination of Lactose  T h e lactose concentration  in the feed mixtures or the fermenter effluents was assayed  with a colorimetric method. Simple sugars, oligosaccharides, polysaccharides, and their derivatives, including the methyl ethers with free or potentially free reducing groups, give an orange-yellow color when treated with phenol and concentrated  sulfuric acid.  T h e method is simple, rapid, and sensitive, and gives reproducible results because the color produced is permanent. Therefore, it is unnecessary to pay special attention to the control of the analytical conditions [215].  B.l.l  Reagents and Apparatus  • Phenol solution, 5 % by weight, prepared by adding 20 grams of reagent grade phenol ( B D H ) to 380 grams of distilled water, which was used throughout experiments.  241  the  Appendix B. Analysis Methods  242  • Sulfuric acid, reagent grade 95.5 % ( B D H ) , specific gravity 1.84.  B.l.2  Procedure  1. Five m L of filtrate of the hquid sample filtrated with a membrane filter (d = 0.45 /x, Sartorius, W . Germany) were diluted to such that it contained between 10-100 mg lactose/1. 2. After one m L of the phenol solution and one m L of the diluted solution was pipetted into a test tube (15 m L ) , five m L of sulfuric acid were added rapidly, the stream of acid being directed against the hquid surface to obtain good mixing. 3. T h e tube was allowed to stand 10 minutes in air, and then, was shaken in a water bath to be maintained at 20-30 ° C for 10 minutes. 4. In parallel, two such samples were prepared for one sugar solution. A blank was prepared by substituting distiUed water for the sugar solution. 5. P u t the samples and the blank in three colorimeter tubes and read the absorbance of the samples at a wave length of 480 n m after the meter's zero point was adjusted on the blank. 6. T h e concentration of lactose was then determined from the readings by reference to the standard curve in Figure B.90 which had been obtained by analyzing a few lactose solutions with known concentration.  B.2  D e t e r m i n a t i o n of Lactate  When a very dilute solute solution of lactic acid is heated in the presence of a high concentration of sulfuric acid, it is converted to acetaldehyde.  T h e acetaldehyde can  Appendix B. Analysis Methods  243  Absorbance  Figure B.90: Standard curve of lactose concentration vs absorbance at 480 nm, The hne is calculated from the equation: S ^ ^ e = 120.3369 'absorbance' - 0.07461. then be assayed by a sensitive color test employing p-hydroxydiphenyl which gives the sample a purple color [216]. This method was modified by adding of sulfuric acid to the aqueous samples so rapidly that a large amount of reaction heat released could be used to supply sufficient heat for the conversion of lactate to acetaldehyde. B.2.1  Reagents and Apparatus  • CuS0 solution; 4 grams of CuS0 .5H 0 (BDH) were dissolved in 100 mL of 4  4  2  distilled water. • Hydroxydiphenyl solution; 1 gram of p-hydroxydiphenyl (BDH) was dissolved in 100 mL of 0.08N NaOH solution and stored in a brown bottle in a refrigerator till needed. • Sulfuric acid; reagent grade 95.5 % (BDH).  Appendix B. Analysis Methods  • Spetronic 70 ( B A U S H & L O M B )  B.2.2  244  spectrophotometer.  procedure  1. Five m L of filtrate of reactor effluent filtered through a membrane filter (d =  0.45  p) were diluted to give 1-9 mg lactate pre m L . 2. After one m L of the diluted solution and 50 pL CUSCM were added into a test tube (15mL), 5 m L of sulfuric acid was added rapidly into the sample by directing the stream of the acid onto the liquid surface. 3. T h e sample was allowed to stand in air for 20 minutes and then cooled below 20 ° C in tap water. 4. 50 pL of hydroxydiphenyl solution were added without touching the tube's wall, mixed thoroughly, and the sample was allowed to stand for 6 hours. 5. In paraUel, two such samples were prepared for each effluent solution. A blank was also prepared by replacing the effluent solution with distilled water. 6. Put the two samples and the blank in three colorimetric tubes of the spectrophotometer.  T h e lactate concentration  was then determined from the readings at a  wave length of 570 nm, after the meter's zero point had been adjusted using the blank, by reference to the standard hne of lactate concentration  vs absorbance  as  shown in Figure B.91.  B.3  Determination of Volatile Fatty Acids and Ethanol  Acetic acid, propionic acid, butyric acid and ethanol are easily vaporized. they can be assayed with a gas chromatograph.  Therefore,  Appendix B. Analysis Methods  245  lO-,  Absorbance  Figure B.91: Standard curve of lactate concentration vs absorbance. The hne is calculated from the equation: Sioctate — 12.0048 'absorbance + 0.005522. B.3.1  Reagents and Apparatus  • 0.2N Phosphoric acid solution. • 9 standard samples having known concentrations of ethanol (8-600 mg/l), acetic acid (500-7200 mg/l), propionic acid (200-1300 mg/l), butyric acid (600-1800 mg/l), iso-butyric acid (7-20 mg/l) and valeric acid (0-2000 mg/l). • Analytical gas chromatograph (GC)-Model 311 (CARLE), equipped with both a TCD and a FID. • Gas cylinders of air, hydrogen and He (UNION CARBIDE). • A 60/80 Carbopack C/0.3 Carbowax 20 M/0.1 % H P 0 3  4  column, 30" x 1/8"  stainless steel (SUPELCO).  0  Appendix B. Analysis Methods  246  • A computing intergrator-SP 4100 ( S P E C T R A - P H Y S I C S ) .  B.3.2  Procedure  1. Five m L of filtrate of the reactor effluent, filtered through a membrane filter (d = 0.45 p), was titrated with 0.2N phosphoric acid solution until the p H value of the sample was below 2. It was calculated by Kisaalita [46] that the p H value of a sample must be acidified below 2.73 if the strongest acid in the sample, acetic acid, could be in free form. T h e amount of added acid solution was recorded to calculated the dilution factor. 2. T h e air, hydrogen and He regulators were set at 12, 20, and 23 psig respectively since it is advised by the G C manufacture  that these pressures would give an  optimal ratio of air to hydrogen and a suitable residence time of the components. The oven temperature was set at 120 ° C . 3. After the G C was maintained at the desired state, the F I D was turned on and 5-10 minutes were allowed for stabihzing the basehne of the computing integrator. 4. 0.5 pL of the acidified sample was injected for each run. Each sample was analyzed at least three times and then an average was reported. 5. For each sample, 0.5 pL of a standard sample which had the nearest composition to the unknown sample, was also injected. Therefore, the composition of the unknown sample was determined from the concentration factors calculated from the standard sample, /,-, (the concentrations, S  devided by the peak areas, A  standardti  standard<i  the peak areas of the components in the sample,  Q  ^unknowriji  •  r  -™~unkn.own i t  X  J{  A known,i un  •  . —  s\unknown,i  Sstandard,! X —-  •™-Btandard,i  )  and  Appendix B.  Analysis Methods  247  46-] 40-  c  TJ  36-  C  30-  CO 3  26-  <0 .o c  4-* CD CD  20-  i_  16-  «J  10-  CD  CD 0 .  6-  oF  0  500  1000  1500  2000  2600  3000  3600  4000  4600  C o n c e n t r a t i o n (mg/l) Figure B.92: A typical calibration curve of acetate. As shown in Figures B.92, B.93 and B.94, the concentrations of acetate, propionate and butyrate have a hnear relationship with their peak area at a steady operation state of the G C . In order to avoid the possible effect on the concentration factors caused by change in the operation state of the G C , a standard sample was injected at each time of the analysis. Figure B.95 is a typical volatile fatty acid chromatogram.  B.4  Gas Composition  B.4.1  Apparatus  • Analytical gas chromatograph ( G C ) - Model 311 ( C A R L E ) , equipped with both a T C D and a F I D . • Hehum as the carrier gas.  Appendix B. Analysis Methods  800  1200  1600  200  Concentration (mg/l)  Figure B.93: A typical calibration curve of propionate.  TJ  c to  CO 3  o CO  CO  CO CO  0.  300  600  900  1200  Concentration (mg/l)  Figure B.94: A typical calibration curve of butyrate.  160  Appendix B. Analysis Methods  INJECT  TIME  249  B2:50:47  746  T702  3. © B  Figure B.95: A typical volatile fatty acid chromatogram. Residence time (min): ethanol (0.20); acetic acid (0.47); propionic acid (1.03); iso-butyric acid (2.10); butyric acid (3.01). • A 10 % carbowax 20 M on chromosorb W-HF 80/100 mesh column, 8' x 1/8" stainless steel (CHROMTOGRAPHIC SPCIALITIES). • A computing integrator - SP 4100 (SPECTRA PHYSICS). • Standard gas sample (UNION CARBIDE); C H = 59.97 %, C 0 = 30.0 %, others 4  2  = 10.03 %. • A gas tight syringe (1 ml, GASTIGHT, #1001).  B.4.2  Procedure  1. The carrier gas, He, was set at 12 psig and the oven temperature was controlled at 35 °C. After the GC had reached a steady state, the thermal conductivity detector (TCD) was turned on, and then, 10 minutes were allowed to let the base hne of the integrator stabihzed.  Appendix B. Analysis Methods  INJECT  TIME  81:24:51  2E  r  250  TTET 1. 6 6  Figure B.96: A typical chromotogram of gaseous samples. Residence time (min): air (0.26); methane (0.38); carbon dioxide (1.86). 2. Repeat injecting 1 ml of the standard gas with the gas tight syringe three times, an average concentration factor (a ratio of the concentration and the peak area of a component) was obtained for each component. This single point method to calculate the concentration factor was reliable in this study because the standard gas composition was very close to the compositions of the reactor gaseous effluents which showed no markedly change in the compositions (see Appendix E). 3. Repeat injection of 1 ml, for three times, of the gaseous sample which was directly collected with the same syringe from the gas collector as shown in Figure 3.10 in Chapter 3. The composition of the gas sample was determined from the peak areas of the components (CO2, CH4) as shown in Figure B.96 as well as the concentration factors obtained from the standard gas as depicted in step 2.  Appendix  B.5  B.  Analysis  251  Methods  Determination of Carbon Content in a Liquid Sample  T h e carbon content in a hquid sample was assayed by a total carbon analyzer which can convert the organic carbon dissolved or suspended as small particles in the aqueous solution to CO2 with a strong oxidizing agent hke sodium persulfate ( I M ) . T h e produced carbon dioxide is then carried by a stream of oxygen to an infrared analyzer which is specially designed to measure the concentration of the carbon dioxide.  This analysis  was used for determining both the concentration of free bacterial ceUs in the culture medium and the total carbon content of a biofilm, by preparing these two types of samples differently.  B.5.1  Sample Preparation  • Concentration of free bacterial ceUs in the culture medium: T w o samples were needed for analyzing the concentration of free cells in a culture medium. Sample 1 was obtained directly from the effluent of the fermenter and sample 2 was a filtrate prepared by filtering the same effluent solution through a membrane filter (pore size 0.45 p).  T h e concentration of free bacterial cells was determined from the  difference in the carbon contents of these two samples because the free cells in the sample 2 had been removed before the carbon analysis. • Carbon content of a biofilm: A mass of wet biofilm was dried at 70 ° C to a constant weight.  T h e dried biomass, after weighing, was dissolved in 50 m L of distilled  water. To promote the dissolution of the biomass and removal of inorganic carbon, the solution was first adjusted to a p H below 1 with sulphuric acid and then, heated and mixed on a hot plate ( T H E R M I X , F I S H E R ) at about 80 ° C for 5 hours. Finally, the solution was cooled to room temperature  and distilled water was added into  the solution to a volume of 100 m l for carbon content analysis.  Appendix B. Analysis Methods  B.5.2  Reagents  252  and Apparatus  • Total carbon analyzer ( A S T R O ) . • Sodium persulfate solution; 238 grams of ultra-pure reagent grade sodium persulfate ( B D H ) was dissolved in one bter of distilled water. • Standard solutions; (1) 2360 mg carbon/1 - 5.5 m L of ethylene glycol ( B D H ) was dissolved in one hter of distilled water, (2) 429 mg carbbn/1 - 1 m L of ethylene glycol was dissolved in one hter of distilled water, (3) 86 mg carbon/1 - 0.2 m L of ethylene glycol was dissolved in one hter of distilled water.  • Oxygen cyhnder ( U N I O N C A R B I D E )  B.5.3  Procedure  1. T h e total carbon analyzer was operated in the total carbon and manual mode and an analysis range was chosen (100 ppm, 500 p p m or 2500 ppm), depending on the strength of a sample. A standard solution mentioned above was chosen so that its concentration was about 70 % of the full range. 2. T h e analyzer was stabihzed for 4 hours with an oxygen flow rate of 300 m l / m i n and distilled water as a hquid carrier. 3. After the sodium persulfate solution was used as the hquid carrier,  30 minutes  were aUowed to stabilize the machine, and then 20 m l of the standard solution was injected.  A t least three injections of the standard solution were needed to let the  analyzer determine an average concentration factor. 4. After following the startup instructions, 20 m L of a sample prepared by the methods discussed above was injected. A n average carbon content of the sample was reported  Appendix  B.  Analysis  Methods  253  from three injections.  B.6  Analysis of a Biofilm  T h e analysis of a biofilm consisted of (1) dry biomass, (2) carbon content, (3) ash content, (4) water volume of a wet biomass, (5) density and (6) biofilm thickness.  B.6.1  Dry Biomass and Carbon Content of a Biofilm  A wet biofilm attached  on a removable P V C shde was dried in a oven at 70  0  to a  constant weight. This low temperature was used to avoid any influence from the plastic which might decompose at a high temperature. a desiccator  After coohng to room temperature in  and weighing, the dry biomass with the P V C shde was put in a flask to  be dissolved in distilled water as explained in the last section. was then dried again, cooled to room temperature  T h e cleaned P V C shde  in the desiccator and weighed. T h e  difference between the two weights was the dry biomass of the biofilm.  T h e carbon  content of the biofilm was calculated from the carbon content of the biomass solution (100 m L ) which was determined with the carbon analyzer as described in the last section.  B.6.2  Ash Content of a Biomass  A weighed dry biomass was ignited in a oven at 550 ° C for 5 hours.  After cooled to  200 °C in the oven and then to room temperature in a desiccator, the ash was weighted.  B.6.3  Water Volume, Density and Thickness of a Biofilm  A n intact biomass of a wet biofilm which was taken out of the fermenter was carefully and immediately scraped into a small K i m a x test tube ((f) = 4 mm) ana then was centrifuged at 4000 rpm to a constant volume of dense biomass at the bottom of the tube.  Appendix B. Analysis Methods  254  After the water volume and the total volume were measured, the dense biomass was assayed as described before for the dry biomass and carbon content. T h e densities of the biofilm sample , dry biomass or carbon content per unit volume of the biofilm, were then calculated from the total volume of the biofilm sample and the dry biomass or carbon content. W h e n the thickness of a biofilm was concerned, two methods were employed. For a thick biofilm, the biomass sample was collected from an exactly known area of a support. Following the same steps as above, the total volume was measured and the thickness was determined by dividing the total volume by the area.  However, for a thin biofilm,  to minimize the error caused by the operation, the dry biomass and carbon content of a biofilm sample which was collected from on an exactly known support area was determined, and then by using the densities of the biomass which were determined from a large amount of biomass, the volume of the biofilm sample as well as the thickness of the biofilm were calculated.  Appendix C  Results of Lactose Acidogenesis  Table C.34: Accumulation of acidogenic biofilms on removable P V C slides T i m e (day)  Dry Biomass (mg)  Carbon Content (mg)  0  18.8  5.33  9  25.3  6.69  16  25.8  8.60  16  23.5  6.48  23  37.2  14.50  23  25.9  6.87  30  48  13.42  30  43.3  15.54  38  42.6  13.54  38  49.1  18.33  46  60.2  22.50  51  58.8  18.30  51  70.8  27.89  61  70.3  30.5  65  64.6  24.3  65  70.9  27.80  76  103.1  43.00  76  110.8  47.60  84  116  46.60  84  117  39.40  255  Appendix C. Results of Lactose Acidogenesis  256  Table C.35: Results of lactose acidogenesis  No.  Biofilm  Flow rate  mg C A001  p  Sout mg/l  HLa  Ethol  HAc  HPr  HBu  mL/hr  Sin mg/l  mg/l  mg/l  mg/l  mg/l  mg/l  1931.6  100  9992  4000  180  160  1165  93  1887  67.2  A002  1982.3  102  9992  3783  169  175  1088  107  2060  67.7  ^recov  %  A004  2198.7  113  9992  3883  178  170  1170  102  1944  67.6  A006  2256.4  111  9108  2935  137  150  1289  73  1882  65.8  A007  2315.6  94  9108  1725  89  184  1668  68  2158  64.6  A101  2635.7  90  8957  1249  75  160  1767  55  2221  63.4  A103  2775.9  103  7329  600  25  107  1391  134  1650  56.0  A203  3787.7  168  4591  402  16  66  1038  18  833  52.1  A301  3989.1  115  5004  201  10  91  1476  25  1308  67.6  A302  4093.8  112  5004  261  11  92  1422  23  1081  61.2  A303  4201.2  121  5004  250  8  115  1369  35  971  57.8  A305  4782.0  236  5004  390  30  68  891  14  1450  61.9  A403  5168.4  273  5053  514  14  60  1042  18  1367  63.2  A405  5586.0  308  5053  582  18  78  1080  22  1318  64.2  A501  5732.6  313  8384  3080  99  134  1006  57  1734  66.5  A502  5883.0  329  8384  3073  105  125  1001  55  1704  65.5  A601  6525.2  230  7807  706  25-  121  1598  23  1712  55.4  A603  7052.4  279  7807  1040  70  118  1315  21  1771  55.9  A803  8238.1  275  7752  809  65  128  1574  30  2116  64.7  A804  8238.1  288  7752  797  71  126  1468  23  2052  61.9  A805  8454.2  318  7752  830  43  112  1402  26  1957  58.9  A806  8454.2  313  7752  888  52  118  1404  27  2020  60.9  Appendix D  Results of B u i l d u p of M e t h a n o g e n i c Biofilms  T h e experimental data of buildup of symbiotic methanogenic biofilms on the four types of supports (wood, ceramic, P V C and stainless steel) are listed, as a ratio of the concentration of bacterial cells fixed on the supports to the concentration of free cells suspended in the medium ([jus]/[a;] cm), in the following three tables.  Table D.36: Accumulation of acetate-degrading Time day  bacteria on inert supports  Wood  Ceramic  PVC  Steel  cm  cm  cm  cm  0  0  0  0  0  7  0.348  0.159  -  0.139  12  0.330  0.279  -  0.336  14  -  -  0.140  -  20  0.830  0.433  0.392  0.381  32  -  -  0.274  -  37  -  0.707  43  1.310  -  -  0.635  -  45  -  -  0.517  -  51  1.982  0.884  0.721  0.502  57  1.700  0.810  -  0.603  66  1.860  1.207  1.098  0.656  84  3.032  1.563  1.035  0.978  98  -  -  1.322  -  257  endix D. Results of Buildup of Methanogenic Biofilms  Table D.37: Accumulation of propionate-degrading bacteria on inert supports Time  Wood  Ceramic  PVC  Steel  cm  cm  cm  cm  0  0  0  0  0  7  0.297  0.182  -  0.221  0.38  0.147  -  0.143  day  12 14  -  -  0.236  -  20  0.576  0.303  0.259  0.219  32  -  -  0.427  -  37  -  0.512  -  -  43  0.768  -  -  0.441  45  -  -  0.484  -  51  1.033  0.697  0.593  0.511  57  1.148  0.712  -  0.561  66  1.288  0.771  0.687  0.594  84  1.368  0.856  0.913  0.780  98  -  -  1.065  -  Table D.38: Accumulation of butyrate-degrading bacteria on inert supports Time  Wood  Ceramic  PVC  Steel  cm  cm  cm  cm  0  0  0  0  7  0.558  0.197  0 -  0.193  0.35  0.187  -  0.214  day  12 14  -  -  0.236  -  20  1.164  0.543  0.354  32  -  -  0.524  0.39 -  37  -  1.575  -  -  43  1.992  -  -  45  -  -  0.800  0.597 -  51  2.764  1.684  0.881  0,790  57  2.874  1.750  -  0.819  66  3.270  1.538  1.070  0.921  84  3.751  1.716  1.350  1.158  98  -  -  1.564  -  Appendix E  Results of Organic A c i d Methanogenesis  Table E.39: Accumulation of methanogenic biofilms on removable P V C shdes Time  Number  day  Dry Biomass  Carbon Content  mg  mg  0  B02  6.0  1.95  0  B18  6.4  2.27  18  B29  8.0  2.8  43  B32  11.3  3.1  52  B26  12.0  3.5  60  B21  12.9  5.7  75  B12  12.9  5.5  89  B09  16.0  4.0  102  B14  16.7  4.0  110  B36  16.1  4.6  140  B27  28.4  8.7  156  B35  26.1  11.2  170  B31  32.9  12.6  170  B07  33.2  11.0  193  B37  35.9  14.0  193  B25  34.5  11.3  208  B17  45.2  16.5  208  B24  45.6  15.6  259  Appendix E. Results of Organic Acid Methanogenesis  260  Table E.40: Methanogenesis of acetate, propionate and butyrate  Biofilm  Flow rate  mg C  ml/hr  mg/l  mg/l  mg/l  mg/l  mg/l  mg/l  n ^recov  B21  1887.3  35.6  2791  654  1531  728  1004  23  82  B23  1921.6  59.9  2791  1608  1531  924  1004  101  B24  1939.0  75.6  2791  1962  1531  1026  1004  148  B31  No.  HAc  i n  HAc  o u t  HPr  HPr  t n  o u f  HBu  i n  HBu f OU  %  78  2342.4  69.0  1646  476  985  449  640  22  B32  2363.6  59.0  1646  353  985  422  640  13  B42  2563.0  33.2  1646  133  985  104  640  4  B45  2633.1  34.0  1646  154  985  85  640  5  B57  2933.4  63.0  900  105  500  75  360  5  B65  3180.9  59.7  4094  2511  2474  1425  2109  419  78  B67  3297.5  53.6  4094  1999  2474  1173  2109  177  79  B68  3327.3  57.0  4094  2156  2474  1230  2109  144  B69  3357.4  57.5  4094  2123  2474  1295  2109  244  B72  3480.5  62.4  4094  2142  2474  1354  2109  257  B75  3575.7  68.6  4925  3102  2719  1655  1969  463  B77  3740.3  68.6  4925  3122  2719  1629  1969  377  B78  3774.1  72.9  4925  3068  2719  1701  1969  424  The carbon recovery includes the carbon of CH T h e C0  2  4  and C0  2  in gas and C0  2  77  86  in the effluent.  in the effluent is calculated from the gas composition as a saturated solution.  Table E.41: Gas production rate and composition of organic acid methanation Temperature  Pressure  ml/hr  °C  mrnHg  %  %  %  133.3  24.5  767.6  72.1  18.6  10.2  106.4  23.3  743.0  70.9  15.2  14.4  80.1  22.7  750.0  73.6  16.2  10.2  51.0  22.9  750.0  81.5  13.8  5.3  144.4  23.2  765.0  74.1  17.6  7.8  189.6  23.4  762.0  71.7  22.8  3.5  201.9  20.6  748  74.7  25.0  3.0  Rate  Composit ion CH  4  CC-2  Others  Appendix F  Derivation of Utilization Rate Models of Propionate and Butyrate  F.l  Utilization Rate Model of Propionate  T h e utihzation of propionate in a symbiotic methanogenic biofilm is assumed to have a mechanism as follows:  E + S  ES  ES + S ^  P +E  (1) (2)  P + ES  T h e sum of the fractions of active enzyme centers, [E], and of the substrate-enzyme complex centers,  [ES], should equal one because the total amount of enzyme active  centers is a constant in a given amount of biomass,  [E] + [ES] = 1  (F.119)  B y using the Michaelis-Menten assumption that the concentration of the substrateenzyme complex is unchanged at steady state, i.e.,  ^p-  = h[E][S] - k^[ES] - k [ES] = 0 2  (F.120)  or,  k [E][S] = {k_ i  1  + k )[ES] 2  Hence, the fraction of the empty active enzyme centers can be expressed by  261  (F.121)  Appendix F. Derivation of Utilization Rate Models of Propionate and Butyrate  w^^r^i  262  <- > F1 2 2  Substituting Equation F.122 for the fraction of active enzyme centers in Equation F.119 gives  ^  - w  r  r  a  <  F123  >  From reactions (1) and (2), the consumption rate of the substrate can be written as follows:  r = ~  = KIE^S]  - k^[ES} + 8k [ES}[S] 2  (F.124)  Put Equation F.121 into Equation F.124 to give  r = k [ES)(l + 8[S])  (F.125)  2  Finally, replacing the fraction of the substrate-enzyme by its expression,Equation F.123, the substrate (propionate)  complex in Equation F.125 utihzation rate can be ex-  pressed as a function of substrate concentration, S,  r  =  , T/,  k S(l+8S) 2  (fc_ + k )/ki + S  F.2  x  o  2  v  F.126 '  Utilization R a t e M o d e l of B u t y r a t e  The utihzation of butyrate by acetogens in the methanogenic biofilms is affected by the presence of propionate, especially at the high concentrations  of the latter. T h e reaction  mechanism is assumed as follows: E + S  b  ^  E S  b  - ^ P + E  (1)  Appendix F. Derivation of Utilization Rate Models of Propionate and Butyrate  ESb + Sp  ^  SpESb  (deactivation)  263  (2)  W i t h the assumptions that the sum of the fractions of the three types of active centers (E, ESb  a  n  d SpESb) should equals one, and that the fraction of deactivated centers is a  constant at steady state,  [E] + [ES ] + [SpESb] = 1  (F.127)  b  and,  d[S ES ] p  b  k [ES ][S ] - k_ [SpES ] = 0 3  dt  b  p  3  (F.128)  b  or,  p-[ES ][S ]  [SpESb] =  b  (F.129)  p  "-3  T h e Michaelis-Menten assumption that the substrate-enzyme complex is a constant at steady state gives d[ES] dt  k^Sb]  - k^ESb] ~ k [ES ] - k [ES ][S ] + k_ [S ES ] = 0 2  b  3  b  p  3  p  k [E][S ] = (k- + k )[ES ] 1  b  1  i  b  b  (F.130)  T h e fraction of active empty enzyme centers, [E], can be expressed by  ll = W £  1 £ S t l  (F131)  Put the expressions for [E] and [S ESb], Equations F.129 and F.131 into Equap  tion F.127 to give the expression of [ESb] s the foUowing, a  Appendix F. Derivation of Utilization Rate Models of Propionate and Butyrate  [s + (k /k_ )[s ][s ] + (*,. +  [ESb]  b  3  [ b  3  p  264  fc )/fc a  ( F  x  '  1 3 2 )  T h e substrate b is consumed by the reaction (1) only, and its utihzation rate is  n  =  ~lt  ^ ]  =  fcl  5fc  k-i\ES ]  _  (F.133)  h  B y using Equation F.130, the rate expression becomes  r = k [ES ] b  2  (F.134)  b  Substituting Equation F.132 for [ESb] in Equation F.134, the digestion rate of butyrate is expressed as a function of the concentrations of butyrate and propionate, Sb and S , p  T b  + k )/k 2  t  + S + (k /k_ )S S b  3  3  p  b  ( F  '  1 3 5 )  Appendix  G  Numerical Methods  T h e numerical methods used in this study include a direct search method for the estimation of parameters in a non-linear function and the Runge-Kutta-Fehlberg  (RKF)  method for the numerical solution of a differential equation.  G.l  Direct Search M e t h o d  T h e estimation of several parameters in a non-hnear function is generally converted to an optimization problem, minimizing the difference between the experimental results and the data predicted by the model (a non-hnear function) by changing the values of the parameters.  For a non-hnear function of several variables, it is common that a direct  search method is used because of the complexity of the differentiations of the function. There have been several methods devised which comprise two major stages in a direct search, an exploratory stage and a pattern stage. One of the simplest methods is due to Hooke and Jeeves [186] which has been used in this study. T h e algorithm is designed to seek the best direction of search and move fast in that direction as shown in Figure G.97. First of all, a base camp is estabhshed at x ° .  For this first stage of the expedition,  this point is also the advanced camp x , from which explorations are made. 1  a given length, d, is taken in each of the coordinate directions in turn.  A step of  If a success is  encountered in a direction insofar as a lower objective function value is achieved, progress has been made.  If it is not, the step in this direction is decreased by d from the start  point and tested again; if it still produces no decrease, stay at the start point. W h e n all  265  Appendix G. Numerical Methods  266  variables are thus dealt with, the exploratory state is complete.  It is deemed a success  if the value of the function at the latest point, x', is less than f ( x ° ) .  Otherwise it is a  failure. If successful, the base camp is moved to x' and the advanced camp is moved to x  1  = x' + (x' - x ); 0  process repeated.  A new search is carried out from the new advanced camp and the A computer program in Pascal language is attached here which has  been successfuUy used in a personal computer with Turbo Parscal.  G.2  Runge-Kutta-Fehlberg Method  Since there are relatively few differential equations arising from practical problems like the reaction-diffusion model for which analytical solutions are known, one must resort to numerical methods. In general, an mth-order differential equation,  y  {m)  =  f(x,y,y',y",---,y ~ ) {rn  1)  with initial conditions  y(xo) = yo y'M  = y'  y^ixo)  0  =  can be rewritten as an equivalent system of m first-order equations. To do so, a new set of dependent variables yi(x), y2(x), . . . , y ( x ) are defined by m  yi=y 2/2 = y'  endix G. Numerical Methods  267  (START) INPUT  BASE  STEP  SIZE  |EVALUATE  POINT X  (  0  >  D A N DD MIN  F U N C T I O N A T X<°>  |  • 1 PUT  X  <  0  = X^'FOR START  PHASE  r  [PUT I = I I  I OUTPUT RESULTS | f STOP) Figure G.97: Flow chart of the direct search method  Appendix  G.  Numerical  268  Methods  2/3=2/  Therefore, a mth-order differential equation (e.g.  the reaction-diffusion model is a  2nd-order differential equation) can be numerically solved like m first-order differential equations. R u n g e - K u t t a methods are expbcit algorithms that involve evaluation of the function f at points i n a small interval, between x,- and x ; i . In order to estimate the errors occurring +  during computation, a local error would be calculated from the difference between u * and U i i where u i is calculated using a step-size of h and u * +  J +  1 + 1  t + 1  using a step-size of  h / 2 . Since the accuracy of the numerical method depends upon the step-size to a certain power, u *  2 + 1  will be a better estimate for y ( x \z i i+  -  U  i  + l  ) than U i  I + 1  |<  \z i i+  -  + 1  . Therefore,  u \ i+1  and so,  e  t +  l=  z  ~  u  i  + l  —  + l  u  — i  +  u  l  R u n g e - K u t t a formulas, if two half-step procedure is used, would need many computations.  A better procedure is Runge-Kutta-Fehlberg's  method [200], which uses a  R u n g e - K u t t a formula of higher-order accuracy than used for u i to compute u * l +  l + 1  . In  this study, the R u n g e - K u t t a - F e h l b e r g fourth-order method was used and the pari of formulas is U;  +i  1 + 1  u* i i+  = u  {  = li; -f  +  . 25 , L  . 16 ,  216  Ki  H  1408, 2565  6656 ,  + —  k  « 3  H  2197, 4104  28561,  3  + —  k  4  1, ,  KA  -  5 9 ,  -k  5  K  5  e, i = +  J  +  2 ,.  + -k ] 6  ,..  0(/l ) n  V  e  i+1  '  =  n  .  0(h  f 6  .  )  Appendix G. Numerical Methods  269  where fcj =  hf(xi,Ui)  k = hf(xi + \h,Ui 2  k = hf(xi + lh,Ui  -  3  k  A  k  5  - hf(xi  +  ^h,u  = hf(xi  + h,Ui +  {  k = hf(x{ + \h,Ui 6  n  -  40  Notice that the formula for U{ i is fourth-order accurate but requires five function +  evaluations as compared with the four of the R u n g - K u t t a - G i U method, which is of the same order accuracy.  However, if e j  + 1  is to be estimated, the half-step method using the  R u n g e - K u t t a - G i l l method requires eleven function evaluations while the R K F method requires only six. T h e following computer program , written in Pascal language, was used to solve numerically the reaction-diffusion model which has been described in Chapter 7 on mass transfer in active biofilms.  G.3 The  The Computer Programs in Pascal Language direct search program (Procedure M U L T I V A R ) and the R K F program (Procedure  RungeKutta) are called by a main program (Program S E A R C H ) . T h e main program reads the experimental data from a D O S file 'Data' (Procedure G E T D A T A ) ,  calculates  the value of the objective function at a set of estimated parameters (Procedure S U M ) , determines if a search is successful by comparing the values of the objective function at two search points (Procedure T E S T A R R Y ) and completes the search for a set of parameters which give the minimum value of the objective function (Procedure  MULTIVAR).  Appendix G. Numerical Methods  270  The objective function used in this study was a sum of square errors between the experimental data and the values predicted by a model at a set of estimated  parameters.  For the model of build-up of symbiotic methanogenic biofilms, the predicted values could be directly calculated from the model. However, for the reaction-diffusion model, the program (Procedure RungeKutta) of Runge-Kutta-Fehlber's method must be called in by the procedure S U M to calculate the substrate concentrations on the biofilm surface with the model, and then, by comparing the calculated values with the experimentally measured values, a set of optimal parameters (diffusion coefficients) were determined.  PROGRAM SEARCH; {The main program} CONST dimen = 1 ; { d i m e n s i o n s of p a r a m e t e r s e t } n e q u a t n = 1;{number of e q u a t i o n s } n t i m e = 1;{number of e x p e r i m e n t a l d a t a of} { i n d e p e n d e n t v a r i a b l e x} nmax = 2; {number of dependent v a r i a b l e s y p l u s TYPE {type of v a r i a b l e s ; r e a l , l n t e g r , a r r y 2 = A R R A Y [ 1 . . n t ime, 1 . . n m a x ] OF paramet = A R R A Y [ 1 . . d i m e n ] OF r e a l ; a r r y l = A R R A Y [ 1 . . n e q u a t n ] OF r e a l ; -'VAR {names of t h e variables} d a t a : arry2; paraO : p a r a m e t ; s t e p , stepm: r e a l ; i: integer; f i l v a r : text; PROCEDURE GETDATA(VAR d a t a : a r r y 2 ) ; {read d a t a f r o m a d i s k f i l e } VAR i , J  :  integer;  etc} real;  1}  Appendix G. Numerical Methods  271  BEGIN { r e a d d a t a f r o m the DOS f i l e ' D a t a ' } assIgn(fi1var, 'Data'); {$!-} {turn o f f e r r o r checking} reset(f ilvar); {$!+} { t u r n i t back on} FOR i := 1 TO ntlme DO BEGIN {Data f i l e } FOR j := 1 TO nmax DO {x, y} read(fi1var,data[i,j]); {x, y} readln(filvar) {....} END {x, y} END;  PROCEDURE S U M ( x : p a r a m e t ; VAR y v a l u e : R E A L ) ; { c a l c u l a t e the v a l u e s of t h e o b j e c t i v e f u n c t i o n } {x g i v e s the p a r a m e t e r s } { y v a l u e sends out the c a l c u l a t i o n r e s u l t } VAR equatn : a r r y l ; i , j : integer; y: r e a l ; {$i RungKuta.pas} { R u n g e - K u t t a method t o s o l v e a d i f f e r e n t i a l e q u a t i o n } {It s h o u l d be removed i f d i f f e r e n t i a l e q u a t i o n s not i n v o l v e d } BEGIN RungeKutta yvalue END;  ( y ) ; { s o l u t i o n of a d i f f e r e n t i a l e q u a t i o n } := s q r ( y - d a t a [ l , l ] ) {sum of e r r o r }  PROCEDURE T E S T A R R Y ( x l a r y , x 2 a r y : p a r a m e t ; V A R r 1 , r 2 : I N T E G E R ) ; {compare the v a l u e s of t h e o b j e c t i v e f u n c t i o n at two p o i n t s } {and d e t e r m i n e i f a s e a r c h i s s u c c e s s } VAR i : BEGIN r l :=  r2  :=  INTEGER;  1; 1;  FOR i := 1 TO dimen DO BEGIN IF x l a r y C i ] = x 2 a r y [ i ] THEN r e s u l t 1 := i ELSE r e s u l t 2 := 0 END END;  272  Appendix G. Numerical Methods  {$i m u l t i v a r . p a s } {the d i r e c t s e a r c h  program}  BEGIN {main program} w r i t e l n ( ' i n p u t your i n i t i a l FOR I := 1 TO dimen DO BEGIN WRITECp'.l, '='); readln(paraO[i]) END; write('step length ='); readln(step); wr i t e ( ' m i n i m u m s t e p l e n g t h readln(stepm); getdata(data); multivar; writeln('a perfect e x i t ' ) END.  guess  =');  of  parameters');  Appendix  G. Numerical  273  Methods  PROCEDURE MULTIVAR; {the d i r e c t s e a r c h method} VAR p a r a , p a r a l , p a r a 2 : p a r a m e t ; i , xlexO,xlnexO: integer; fvalue, fvalueO, f v a l u e l , fvalue2,  £:  real;  BEGIN{procedure m u l t i v a r } FOR i := 1 TO dimen DO begi n p a r a [ i ] := p a r a O [ i ] ; p a r a l [ i ] := p a r a O t i ] end; REPEAT { r e d u c e s t e p l e n g t h l o o p } f o r i := 1 t o dimen do p a r a [ i ] := p a r a O C i ] ; FOR i := 1 TO dimen DO BEGIN {N p a r a m e t e r s ' exploration} p a r a C i ] := p a r a l [ i ] + s t e p ; SUM(para,f); f v a l u e := f ; SUM(paral,f); f v a l u e l := f ; IF f v a l u e >= f v a l u e l THEN BEGIN {backward one s t e p } p a r a [ i ] := p a r a l [ i ] - s t e p ; IF p a r a C i 3 < 0 THEN p a r a [ i ] : = 0; SUM(para,f); f v a l u e := f ; SUM(paral,f); f v a l u e l := f ; IF f v a l u e >= f v a l u e l THEN p a r a 2 [ i ] := p a r a l [ i ] ELSE p a r a 2 [ i ] := p a r a [ i ] END {end badkward one s t e p } ELSE para2[i] : = para[i] END; {end n p r a m e t e r s ' exploration} SUM(para2, f ) ; f v a l u e 2 := f ; SUM(paraO, f ) ; f v a l u e O := f ; wr 1 1 e l n ( f u n c t i o n v a l u e f v a l u e O = ' , f v a l u e O ) ; IF f v a l u e 2 >= f v a l u e O THEN BEGIN 1  Appendix G. Numerical Methods  TESTARRY(paral,paraO, xlexO, xlnexO); I F x l e x O = x l n e x O THEN s t e p := s t e p / 2 ELSE FOR i := 1 T O d i m e n DO p a r a l [ i ] := p a r a O [ i ] END ELSE FOR i := 1 T O d i m e n DO BEGIN p a r a l C i ] := p a r a 2 [ i ] + p a r a 2 [ i ] - p a r a O [ i ] ; paraO[i ] : - para2[i ] END; I F ( 2 * s t e p ) < s t e p m THEN BEGIN W R I T E L N ( ' T H E MINIMUM F U N C T I O N = ' , f v a l u e O ) ; writeln('N parameters'); FOR i := 1 T O d i m e n DO wr i t e l n ( ' p a r a [ ' , ! , ' ] = ' , p a r a O [ i ] ) END; FOR i := 1 T O d i m e n DO WRITEC ',paraO[i]); wr i t e 1 n UNTIL <2*step) < stepm END;  274  Appendix G. Numerical Methods  PROCEDURE R u n g e K u t t a (VAR S i n i t i a l {Runge-Kutta-Fehlberg's method}  :  real);  label start; const a l l = 25/216; a l 3 = 1408/2565; a l 4 = 2197/4104; a21 = 1 6 / 1 3 5 ; a23 = 6 6 5 6 / 1 2 8 2 5 ; a24 = 2 8 5 6 1 / 5 6 4 3 0 ; a25 = 9 / 5 0 ; a26 = 2 / 5 5 ; b31 = 3 / 3 2 ; b32 = 9 / 3 2 ; b41 = 1 9 3 2 / 2 1 9 7 ; b42 = 7 2 0 0 / 2 1 9 7 ; b43 = 7 2 9 6 / 2 1 9 7 ; b51 = 4 3 9 / 2 1 6 ; b53 = 3 6 8 0 / 5 1 3 ; b54 = 8 4 5 / 4 1 0 4 ; b61 = 8 / 2 7 ; b63 = 3 5 4 4 / 2 5 6 5 ; b64 = 1 8 5 9 / 4 1 0 4 ; b65 = 1 1 / 4 0 ; m = 4; 12 t i m e s t h e number of d i f f e r e n t i a l e q u a t i o n s } e l t = 0 . 0 0 0 0 1 ; { e r r o r of l a c a l t r u n c t i o n } ex = 0 . 0 0 1 ; { e r r o r of f i n a l l e n g t h } d i v i s i o n = 1000; { d i v i s i o n of a b i o f i l m t h i c k n e s s } t h i c k n e s s = 0 . 0 7 8 ; { b i o f i l m t h i c k n e s s (cm)} Var yO, y , z , u : a r r a y [ l . . m ] of r e a l ; step, lmark: r e a l ; k: a r r a y [ 1 . . 6 , 1 . . m ] of r e a l ; i: integer; { y 0 , u : HBu, d H B u / d x , H P r , d H P r / d x } {Four  functions  a r e d e f i n e d as  following}  FUNCTION F l ( a , b , c , d : r e a l ) : real; { a , b , c , d are f a l s e v a r i a b l e s } begin F l := b ; end;  276  Appendix G. Numerical Methods  FUNCTION F 2 ( a , b , c , d : r e a l ) : real; { a , b , c , d are f a l s e v a r i a b l e s } begl n F2 :=x[l]*a/(0.027+a+0.296*a*c); {the u t i l i z a t i o n r a t e of b u t y r a t e } end; FUNCTION F 3 ( a , b , c , d : begi n F3 := d ; end;  real):  real;  FUNCTION F 4 < a , b , c , d : r e a l ) : real; begin F4 :=27.l*c*(l+0.2*c)/(0.05+c); {the u t i l i z a t i o n r a t e of p r o p i o n a t e } end; Begin s t e p := t h i c k n e s s / d i v i s i o n ; ltnark := 0; y0[l] := 0 . 3 2 6 ; {HBu c o n c e n . (mg/ml) i n s i d e y 0 [ 2 ] := 0; { d s / d x of HBu i n s i d e t h e c e l l } y 0 [ 3 ] := 1 . 7 1 5 ; {HPr c o n c e n . (mg/ml) i n s i d e y 0 [ 4 ] := 0; { d s / d x of HPr i n s i d e t h e c e l l } {Four i n i t i a l c o n d i t i o n s } s t a r t : f o r i := 1 t o m do u [ i ] := y 0 [ i ] ; k [ l , l ] := s t e p * F l ( u [ l ] , u C 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ l , 2 ] := s t e p * F 2 ( u [ l ] , u [ 2 ] , u t 3 ] , u [ 4 ] ) ; k [ l , 3 ] := s t e p * F 3 ( u [ l ], u [ 2 ] , u C 3 ] , u [ 4 ] ) ; k [ l , 4 ] := s t e p * F 4 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; f o r I := 1 t o u do u [ i ] .: = y 0 [ i J + k [ l , i ]/4; k [ 2 , l ] := s t e p * F l ( u [ l ] , u [ 2 ] , u [ 3 ] u t 4 ] ) ; k [ 2 , 2 ] := s t e p * F 2 < u [ l ] , u t 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ 2 , 3 ] := s t e p * F 3 ( u [ l ] , u [ 2 ] , u [ 3 ] u [ 4 ] ) ; k [ 2 , 4 ] := s t e * F 4 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; f o r i := 1 t o m do u [ l ] := y 0 [ i ] + b 3 1 * k [ l , i ]+b32*k[2, i ] ; k [ 3 , l ] := s t e p * F l ( u [ l ] u [ 2 ] , u [ 3 ] , u t 4 ] ) ; k [ 3 , 2 ] := s t e p * F 2 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ 3 , 3 ] := s t e p * F 3 ( u [ l ], u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ 3 , 4 ] := s t e p * F 4 ( u [ l ] , u [ 2 ] , u [ 3 ] , u t 4 ] ) ; f o r i : = 1 t o m do J  J  P  >  the c e l l } the  cell}  Appendix G. Numerical Methods  u [ i ] := y O [ i ] + b 4 1 * k [ l , i ] - b 4 2 * k [ 2 , i ] + b 4 3 * k [ 3 , i ] ; k [ 4 , l ] := s t e p * F l ( u [ l ] , u [ 2 ] , u [ 3 ] , u t 4 ] ) ; k [ 4 , 2 ] := s t e p * F 2 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ 4 , 3 ] := s t e p * F 3 ( u [ l ] , u [ 2 ] , u [ 3 ] , u t 4 ] ) ; k [ 4 , 4 ] := s t e p * F 4 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; f o r i := 1 t o m do u [ i ] := y O [ i ] + b 5 1 * k [ l , 1 ] - 8 * k [ 2 , i ] + b 5 3 * k [ 3 , i ]-b54*k[4, 1 ]; k [ 5 , l ] := s t e p * F l ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ 5 , 2 ] := s t e p * F 2 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 3 ) ; k [ 5 , 3 ] := s t e p * F 3 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ 5 , 4 ] := s t e p * F 4 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; for i : = l t o m d o u [ i ] := y O [ i ] - b 6 1 * k [ l , i ] + 2 * k [ 2 , i ] - b 6 3 * k [ 3 , i ]+b64*k[4, i ] - b 6 5 * k [ 5 , 1 ] ; k [ 6 , l ] := s t e p * F l ( u [ l ] , u [ 2 ] , u C 3 ] , u [ 4 ] ) ; k [ 6 , 2 ] := s t e p * F 2 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ 6 , 3 ] := s t e p * F 3 ( u t l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; k [ 6 , 4 ] := s t e p * F 4 ( u [ l ] , u [ 2 ] , u [ 3 ] , u [ 4 ] ) ; f o r i := 1 t o m do b e g i n y[i]:=yO[i]+all*k[l,i]+al3*k[3, i]+ 14* k[4, i ]-k[5, i ]/5; z[i]:=yO[i]+a21*k[l,i]+a23*k[3,i]+a24 * k [ 4 , i ] - a 2 5 * k [ 5 , i ]+a26*k[6, i ] ; end; i f a b s ( y [ l ] - z [ l ] ) > e l t then begin s t e p := s t e p / 2 ; goto s t a r t ; end; i f a b s ( y [ 2 ] - z [ 2 ] ) > e l t then begin s t e p := s t e p / 2 ; goto s t a r t ; end; lmark := lmark + s t e p ; i f a b s ( t h i c k n e s s - l m a r k ) > ex t h e n begin f o r i := 1 t o m do y O [ i ] := z [ i ] ; i f ( l m a r k + 2 * s t e p ) <= t h i c k n e s s t h e n begin s t e p := 2 * s t e p ; goto s t a r t ; end; s t e p := t h i c k n e s s - l m a r k ; goto s t a r t ; end; wr i t e l n ( ' c o n c n = z[l]); w r i t e l n ( ' d s / d x =•',- z [ 2 ] ) ; S i n i t i a l := z [ l ] ; a  end;  

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