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Modelling oxygen delignification in pulp processing operations Susilo, Jacky 2005

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M O D E L L I N G O X Y G E N DELIGNIFICATION IN PULP PROCESSING OPERATIONS by JACKY SUSJXO B.A.Sc, University of Indonesia, 2002  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS OF THE DEGREE OF MASTER OF APPLIED SCIENCE  in  THE FACULTY OF GRADUATE STUDIES (CHEMICAL AND BIOLOGICAL ENGINEERING)  THE UNIVERSITY OF BRITISH COLUMBIA APRIL 2005  ©JACKY SUSILO, 2005  Abstract  A mathematical model of oxygen delignification for pulp processing operations has been developed to predict the kappa number (lignin content) and pulp strength (CED viscosity) as a function of system operation variables. The model incorporates a set of appropriate chemical reaction kinetics chosen from those available in the literature and gas-liquid mass transfer resistances for pulp suspension mixing and pulp suspension flow through retention towers as measured in our laboratory. This thesis reviews the available kinetic and mass transfer data incorporated in the model and discusses several important issues related to model development and interpretation, including kappa number measurement, the molecular size distribution of the lignin remaining in the pulp and lignin leaching from the fibre. The model is compared with laboratory experimental data from several sources as well an industrial oxygen delignification system.  ii  Table of Contents  Abstract  ii  Table of Contents  iii  List of Tables  vii  List of Figures  viii  Nomenclature  xi  Acknowledgements.  xiv  Chapter 1  1  General Introduction  1  1.1  Pulping and Bleaching  1  1.2  Oxygen Delignification  2  1.3  Objectives and Scopes of Thesis  4  Chapter 2  5  Literature Review  5  2.1  Oxygen Delignification Process  5  2.2  Chemistry of Oxygen Species and Oxygen Delignification  7  2.3  Lignin: Structure and Compositions  2.3.1  10  Lignin Model Compounds  15  iii  2.3.2 2.4  Lignin Reactions  17  Issues in Industrial Oxygen Delignification Systems  20  2.4.1  Lignin Leaching  21  2.4.2  Kappa Number Determination  25  2.4.3  Molecular Weight Distribution  30  2.5  Kinetics and Process Variables  32  2.5.1  Time and temperature  35  2.5.2  Alkali Charge  40  2.5.3  Oxygen Pressure  41  2.5.4  Consistency  42  2.5.5  Washing and black liquor solids carry-over  42  2.6  Oxygen and Alkali Consumption  45  2.7  Mass Transfer in Oxygen Bleaching  46  2.7.1  Gas-Liquid mass transfer in medium consistency mixers  51  2.7.2  Gas-Liquid mass transfer in pulp retention towers  52  2.8  Maximum Lignin Removal in Oxygen Delignification  Chapter 3  55  57  Model Development  57  3.1  Introduction  57  3.2  Model Formulations  60  3.3  Delignification Kinetics  63  iv  3.4  Model Development  67  3.5  Assumptions  71  3.6  Governing Equations  78  3.6.1  Oxygen and Alkali Balances  78  3.6.2  Gas-liquid Mass transfer, Tower Pressure & Temperature  82  3.6.3  Carbohydrate Degradation  83  3.7  Effect of Black Liquor Solids Carry-Over  85  Chapter 4  S9  Simulations Results and Discussions 4.1  89  Simulations  89  4.1.1  Effect of Temperatures  92  4.1.1  Effect of Tower Pressure  98  4.1.2  Effect of Alkali Charge  99  4.1.3  Effect of Oxygen Charge  102  4.1.4  Effect of Suspension Consistency  104  4.1.5  Effect of Black Liquor Solids Carry-Over  105  4.1.6  Effect of Mixing Power  106  4.1.7  Effect of Gas-Liquid Mass Transfer Coefficient in the Retention Tower  109  4.2  Model Validation  111  4.2.1  Howe Sound Pulp & Paper Simulations  111  4.2.2  Mill Survey  113  Conclusions  116  v  Recommendations (Future Work)  117  Bibliography  118  Appendix A: LMC Delignification Kinetics  126  A.l  Stilbene Structures  126  A.2  P-aryl Ether Structures  130  A.3  Vinyl (enol) Ether Structures  131  A.4  Diphenyl-Methane (5-5) Structures  132  Appendix B: Molecular Weight Distribution Experiments Appendix C: Kappa number & Leaching Experiments. AppendixD: MATLAB Programming Codes D. 1  134 137 142  Non-linear Fitting of Lignin Model Compound Kinetics  142  D. 1.1  Stilbene Structure  144  D. 1.2  Vinyl (Enol) Ether Structure  145  D. 1.3  Beta Aryl Ether Structure  146  D.l .4  Dipropylbiguaiacol (5-5) Structure  147  D.2  LMC Oxygen Delignification Model  148  D.3  LMC Model (with Iribarae & Schroeder's Carbohydrate Degradation Kinetic)  152  Appendix E: Gas-liquid Mass Transfer in Tower Appendix F: Simulations Results  156 162  vi  List of Tables  Table 2.1 Oxygen species present in oxygen delignification systems  8  Table 2.2 Proportions of common types of linkages in native lignin [Sjostrom, 1993] Table 2.3 Changes in frequency  13  of linkages (%) of residual lignin as it moves from native wood to oxygen  bleached [Northey, 2001; Gellerstedt, 2001] Table 2.4 Approximate fractions  14  of softwood residual lignin in pulp [Ala-Kaila,  2001]  Table 2.5 Fraction of apparent and actual birch residual lignin as kappa number [Ala-Kaila, Table 2.6 Summary of delignification Table 2.7 Summary of carbohydrate  Table 3.3 Characteristic  2003]  kinetic studies, listing the determined exponents and parameters. degradation kinetic studies with fibre suspension  Table 3.1 Proposed composition of residual lignin going into oxygen delignification Table 3.2 Kinetic parameters  24 27 34 38  stages  acquired from lignin model compound studies  rate of oxygen consumption and diffusion for all model compounds  62 66 76  Table 3.4 The contents of lignin and its high molar mass in black liquors  85  Table 4.1 Range of operating conditions used in the simulations  89  Table 4.2 Oxygen and alkali consumption per unit kappa number reduction during oxygen bleaching of softwood kraft pulp at medium consistency (laboratory and commercial systems)  94  Table 4.3 Input variables for Howe Sound Pulp & Paper Simulations  Ill  Table 4.4 Over-all industrial process conditions from mill survey of Bennington and Pinault [1999]... 113  vii  List of Figures  Figure 2.1 Typical schematic diagram of industrial oxygen delignification  system  6  Figure 2.2 Reactions of oxygen species under alkaline bleaching conditions [Argyropoulos, Figure 2.3 Steps in the mechanism of oxygen bleaching [McDonough, Figure 2.4 Substitutedphenylpropane  2001]  1996]  9  unit [Sjostrom, 1993]  10  Figure 2.5 Proposed lignin structures [Brunow, 1998] Figure 2.6 Common linkages between phenylpropane  11 units [Sjostrom,  1993]  12  Figure 2.7 Relative reactivity of lignin model compounds under alkali-Oj conditions [Ljunggren  et al,  1994]  16  Figure 2.8 Initial reactions that lead to oxygen delignification Figure 2.9 Reactions of intermediate  hydroperoxides  [McDonough,  1996]  that lead to lignin fragmentation  18 [McDonough,  1996] Figure 2.10 Representation  9  19 of the tortuous pathway for a lignin macromolecule  to diffuse out in the wood  cell wall [Goring et al, 1984] Figure 2.11 Theoretical delignification  21 vs delignification  efficiency achieved by surveyed mills  [Bennington & Pineault, 1999] Figure 2.12 Molecular size distribution  28 of unbleached kraft (—-) and oxygen delignified  (—)  lignin of Eucalyptus Globulus [Lachenal et al, 2001]  31  Figure 2.13 Effect of successive oxygen stages to molecular weight distribution Figure 2.14 Two-stage model of oxygen delignification  residual  [Lachenal et al, 2004] 32  [Olm and Teder, 1979]  Figure 2.15 Effect of temperature on oxygen delignification  35  rate [Harder et al, 1970]  36  Figure 2.16 Viscosity of the oxygen bleached pulp versus kappa number [Hsu and Hsieh, 1987]  37  Figure 2.17 Effect of Alkali Charge on oxygen delignification  40  viii  rate [Liebergott  et al, 1985]  Figure 2.18 Effect of alkali charge on viscosity drop [Liebergott et al, 1985] Figure 2.19 Effect of oxygen pressure on delignification  rate [Hsu andHsieh,  Figure 2.20 Effect of cooking carry-over to kappa number and delignification kraftpulp,  41 1987, 1988]  42  (kappa #16.7 HW  10% consistency, 2% NaOH, 3% 0 , 60 minutes reaction, 100°C) [Iijima & Taneda, 1997]. 43 2  Figure 2.21 Profile of residual alkali and pH during oxygen delignification kraft pulp, 10% consistency, 2% NaOH, 3%02,  reaction (kappa #16.7 HW  60 minutes reaction, 100°C)  [Iijima & Taneda, 1997] 44  Figure 2.22 Effect of temperature on oxygen consumption [Berry et al, 2002]  45  Figure 2.23 Mass transfer in oxygen delignification  47  Figure 2.24 Effect of mixing on oxygen solubilization  [Iribarne & Schroeder, 1997]  in water and NaOH solution [Berry et al, 2002]. 48  Figure 2.25 Effect of secondary mixing (mixing after initial high-intensity mixing at 2400rpm) on the degree of delignification:  Mode 1, no mixing; Mode 2, mixing at 240 rpm for 4 seconds after 20 minutes;  Mode 3, mixing at 400 rpm for 4 seconds every 5 minutes; Mode 4, mixing at 400 rpm for 4 seconds every 20 seconds; Mode 5, mixing at 60 rpm continuously [Berry et al, 2002]  49  Figure 2.26 Mixing intensity vs degree of delignification  50  [Iijima & Taneda, 1997]  Figure 2.27 k a vs pulp consistency (C„) at different mixing rotational speed [Rewatkar & Bennington, L  2000]  52  Figure 2.28 k a vs superficial gas velocity at various pulp consistency C [Rewatkar & Bennington, L  m  2002]  53  Figure 2.29 Gas residence time distribution in an industrial oxygen tower [Hornsey et al, 1998]  54  Figure 3.1 Model representation of the actual lignin structures [Jurasek, 1995]  61  Figure 3.2 Degradation of stilbene model compound at different pH (left) with first order plot of the model compound reaction rate vs reaction time (right) [Ljunggren & Johansson, 1990a]  64  Figure 3.3 Differentiation of native lignin into four distinct reactive lignin structures  68  Figure 3.4 Schematic flowsheet of the model (model inputs are shown in bold)  69  Figure 3.5 Representation of mixer and retention tower in the model  70  ix  Figure 3.6 Medium consistency oxygen tower [left, White and Larsson, 1996] and pulp RTD of an upflow CIO2 bleaching tower [right, Bennington, 2000]  73  Figure 4.1 Effect of temperature on kappa number during oxygen bleaching  92  Figure 4.2 Dissolved oxygen concentration profile at different temperature vs. bleaching time  93  Figure 4.3 Profile of a decreasing alkali concentration as reaction progresses  95  Figure 4.4 Effect of temperature on viscosity drop during oxygen bleaching  96  Figure 4.5 Effect of temperature on viscosity drop during oxygen bleaching  (estimated  using carbohydrate degradation kinetics of fibre suspension [Iribarne & Schroeder, 1997])  97  Figure 4.6 Effect of oxygen pressure on kappa number during oxygen bleaching  98  Figure 4.7 Effect of alkali charge (%) on kappa number during oxygen bleaching  99  Figure 4.8 Alkali exhaustion profile that limit the extent of delignification  (ymoH  =  1.9 grams/ kg  pulp, kappa)  101  Figure 4.9 Oxygen exhaustion during oxygen bleaching (yo2  =  0.55 grams/ kg pulp, kappa)  102  Figure 4.10 Dissolved oxygen concentration profile at different oxygen charge vs. bleaching time  103  Figure 4.11 Effect of consistency on kappa number during oxygen bleaching  104  Figure 4.12 Effect of black solids carry-over on kappa number during oxygen bleaching  105  Figure 4.13 Effect of mixer power on delignification  106  during oxygen bleaching  Figure 4.14 Effect of mixer power on kappa number during the first 10 minutes reaction  707  Figure 4.15 Effect of mixer power on oxygen concentration in the liquid phase  108  Figure 4.16 Effect ofk a  109  L  (tower) on kappa number during oxygen bleaching.  Figure 4.17 HSPP simulation result and measured kappa number with 95% confidence intervals shown 112 Figure 4.18 Actual vs. Predicted outgoing kappa number  x  114  Nomenclature  Symbol 2  3  a  specific gas-liquid interfacial area [m Im ]  A  pre-exponential factor constant  A  alkali charge [% on pulp]  c  E  activation energy [kJ/mol]  C  concentration [mol/L]  Cm  pulp consistency [%]  D  oxygen diffusivity inside the fibres [m A]  A  D  diameter of oxygen retention tower [m]  DP  degree of polymerization of cellulose  t  DP  initial degree of polymerization of cellulose  ECCSA  effective capillary cross-sectional area constant  h  height of oxygen retention tower to be evaluated [m]  H  total height of oxygen retention tower [m]  k  delignification kinetic rate constant  0  initial-stage delignification kinetic rate constant final-stage delignification kinetic rate constant  k  2  oxygen solubility constant h  gas-liquid mass transfer coefficient [m/s]  kia  volumetric gas-liquid masss transfer coefficient [s' ] ]  DP  cellulose (carbohydrate) degradation kinetic rate constant lignin model compound substrate or kappa number  L  m  number-average of moles of cellulose per metric ton of pulp  Mw  molecular weight [gram/mol]  n  dissolved oxygen concentration in the liquid phase [mol/L]  o,, 2 a  saturated (maximum) dissolved oxygen concentration [mol/L]  xi  [Off]  hydroxide ion concentration [mol/L]  [0 ]  oxygen concentration [mol/L]  p  oxygen charge [% on pulp]  p  pulp production rate [ton/day]  2  p  oxygen partial pressure at top of retention tower [kPa]  p  oxygen partial pressure at bottom of retention tower [kPa]  top  bottom  oxygen partial pressure [kPa or atm] o>  r  oxygen consumption rate [mollLls]  R  ideal gas constant [J/mol.K]  R  coefficient of determination [%]  t  reaction time [minutes, hours, or seconds]  T  temperature [°C or K]  T.  temperature at bottom of retention tower [°C or K]  T  temperature at top of retention tower [°C or K]  2  in  out  u  superfical gas velocity [m/s]  V  pulp suspension velocity [mlmin]  V  volume [m or L]  W  fibre wall thickness (m)  X  lignin model compound composition [%]  y  oxygen consumed per kg pulp per kappa number drop [glkg.K  yNaOH  NaOH consumed per kg pulp per kappa number drop [glkg.K]  s  3  0l  Superscripts/subscripts  b  exponent of the correction in the k a at elevated temperature  i  at particular lignin model compund  j  total number of lignin model compound in the model  m  reaction rate constant with respect to oxygen concentration  n  reaction rate constant with respect to alkali concentration  q  reaction rate constant with respect to kappa number  L  xii  Greek Letter K  kappa number  K°  initial kappa number  K  final kappa number  K"  floor kappa number  o\  fast kappa number  (  K  slow kappa number  02  K  TAPPI/CED pulp viscosity [mPa.s] M  intrinsic viscosity of pulp [cc/g]  Mo  initial intrinsic viscosity of pulp [cc/g] liquid water viscosity [N.s/m ] 2  ML  mixer power dissipation [ Wlm ] 3  £  gas void fraction rate of oxygen diffusion across the fibre walls [g O^kg pulpls] o  rate of oxygen reaction (consumption) [g O^kg pulpls] rxn  Acronyms AOX  absorbable organic halide  BLS  black liquor solids [kg/ton of pulp]  BOD  biological oxygen demand  CED  cupri-ethylene-diamine  COD  chemical oxygen demand  CSTR  continuous stirred tank reactor  HMML  high molecular mass lignin  HW  hardwood  L/D  length to diameter aspect ratio  PFR  plug flow reactor  PMS  peroxymonosuphate  SW  softwood  xiii  Acknowledgements  I gratefully acknowledge the following for their contribution to this project:  Dr. C.P.J. Bennington, my research supervisor, for his guidance, kind support, suggestion, and helpful discussion throughout the course of this research. Dr. B.D. Bowen and Prof. C.W. Oloman, members of my advisory committee, for their helpful advice. R.M. Berry, for his valuable discussion. G.L. Pageau and members at the Howe Sound Pulp and Paper Ltd., for their support during our mill tests and supplying the pulp samples used in this research. Dr. J.F. Kadla and members of biomaterials chemistry laboratory at the Department of Wood Science, for obtaining the molecular weight distributions of residual lignin through enzymatic isolation procedures. Members of the Pulp and Paper Centre and Chemical and Biological Engineering Department for their help in many aspects of this research. My family, my mother, brother and sister, and all my friends, thank you for your help and never ending support.  xiv  Chapter 1 General Introduction  1.1  Pulping and Bleaching Pulp and paper mills generally are made up of a wide variety of processes which  transform fibrous raw material into pulp and paper products. Complicated physical and chemical phenomena take place in many of the unit operations involved in these processes. There are several different methods of converting wood chips into unbleached or fully bleached pulp. Chemical pulping using the kraft process is a typical example. The most important unit operations involved in the kraft process are digesting for pulping, brown stock washing for chemical recovery, and a series of bleaching towers for brightening the pulp. There are also many other smaller units that play an important role and are an integral part of the pulp and paper mill such as pumping, mixing, stock chests for storage and blending, sensors and control systems, etc. During pulping with chemicals and heat in the digester, lignin and other alkalisoluble constituents of wood are dissolved in the cooking liquor and fibres are liberated. The mixture of pulp and spent cooking liquor after the digestion process, referred as brown stock, is fed to a series of washers, where spent cooking liquor is washed out from the pulp using either fresh or recycled water or some combination of the two. The spent cooking liquor, called weak black liquor, is then delivered to the recovery system where the valuable spent cooking chemicals and the energy content of the liquor are recovered. The washed pulp is transferred to the bleach plant where it is subjected to a series of bleaching stages involving different chemical  Chapter 1: Introduction  2  treatments to increase pulp brightness while maintaining pulp strength. Fully bleached or 'white' pulps, are then produced. Chemicals that have been used for bleaching include, but are not limited to, oxygen, ozone, chlorine, chlorine dioxide, sodium hydroxide, and hydrogen peroxide. Figure 1.1 shows a rough schematic of a typical kraft pulp mill starting from the wood chip to the fully bleached pulp. Wood Chips  1  Digestion  Cooking Liquor I Make-up Chemicals  H  Z  •-1  Fresh/Reused water  Brown Stock Washing  Alkali Oxygen  Black liquor  Recovery  Energy  System  Oxygen Delignification  Post-0  Fresh/Reused water  2  Washing  Bleaching chemicals  B l e a c h Plant  ir  Bleached Pulp  Figure 1.1 Schematic diagram of kraft pulp process with oxygen delignification  1.2  Oxygen Delignification For over the last decade, there have been quite a number of efforts attempting to optimize  the extent of pulp delignification before it enters the bleach plant. One of the processes that has  Chapter 1: Introduction  3  received considerable attention is oxygen delignification. This is the process that takes place between the cooking and the bleaching processes. The fact that the chemicals applied to oxygen delignification are compatible with the kraft recovery system has made this process desirable and relatively easy to integrate into an existing kraft mill. However, it was not until 1970 in South Africa that the first commercial oxygen delignification system was commissioned. Many mills have incorporated oxygen delignification into their process lines since then. Figure 1.2 shows how the worldwide production capacity of pulp made via oxygen delignification has increase since 1970.  140 2?  120  A  5c 100 4 2 -6  CO o o o  80  111 Single-stags systems |  | Two-stage systems  60 40  9  O.  20  4  (0  U  1970  1975  1980  1985  1990  1995  Figure 1.2 Growth of Oxygen Delignification Worldwide (Dence & Reeve, 1996)  The main unit operations in the oxygen delignification system are the mixing of chemicals into a pulp slurry, the reaction stage, and the washing of pulp after the reaction stage. Optimization of oxygen delignification must take into account the mass transfer of oxygen to the reactive lignin sites within the fibre and the subsequent chemical reaction kinetics. Also, there Chapter 1: Introduction  4  are some other critical issues that are of concern, including accurate kappa number determination, lignin leaching, mass transfer limitations, and the floor kappa number. A l l these topics have been the subject of research and publication. Any model of an oxygen delignification system needs to consider all of these issues.  1.3  Objectives and Scopes of Thesis Computer simulation can be of considerable help in solving design and, more  importantly, operational problems. This has been the reason why there is an interest in developing better computer models that are not only able to predict what could happen in the actual process but also able to underline the significance of the particular unit operation being used in the mill as well as, if possible, to help optimize the system. The industrial oxygen delignification processes can be modeled mathematically based on mass and energy balances and appropriate reaction kinetics. In this project, a set of mathematical ordinary differential equations are developed which incorporate the appropriate reaction kinetics of several lignin model compounds as well as mass transfer and consumption of both oxygen and alkali in the mixer and oxygen tower. The model can be used to study the response of the final kappa number, viscosity, and residual chemicals to changes in various process variables both in the medium-consistency mixer and in the retention tower that follows. The model is compared with data from several operating mills as well as from batch operated laboratory systems.  Chapter 1: Introduction  5  Chapter 2 Literature Review  2.1  Oxygen Delignification Process Oxygen delignification is a well-known and well-established technology for removing a  substantial portion of the residual lignin in unbleached pulp using oxygen and alkali. The dissolved lignin can then go to the recovery furnace instead of to the bleach plant where it would be a potential source of environmental problems. The environmental benefits that oxygen delignification processes offer, together with the more stringent environmental regulations being imposed, has made oxygen delignification one of the most important technologies that can be incorporated in modern pulp and paper mills. In addition to its environmental advantages, the development of oxygen delignification has also been driven by economic considerations such as operational cost savings and the desire to improve pulp properties. Lower chemical costs result from the decreased requirement for delignifying oxidizing chemicals in the bleach plant (e.g., chlorine, chlorine dioxide, hydrogen peroxide, and ozone). This is because oxygen is less expensive, and oxidized white liquor usually provides the necessary alkali for the oxygen stage at low cost. Further savings result from a decrease in the chlorine dioxide charge needed for the final bleaching stages [McDonough, 1996]. Improvements in pulp quality, such as higher brightness [McDonough, 1995], higher delignification without sacrificing pulp selectivity, and higher yield, have all been reported using the proper adjustment of operating conditions [Bokstrom, 1999].  Chapter 2: Literature  Review  Oxygen delignification is typically carried out under medium-consistency  conditions  with either softwood or hardwood pulps using sodium hydroxide as an alkali source (1 to 4% NaOH on pulp) and with an oxygen pressure of 400 to 1000 kPa. Three phases are present in the reaction vessel: the solid pulp fibres, the aqueous phase around the fibers and within the fiber pores, and the oxygen gas phase distributed throughout the mixture. The pulp at 8 to 12% consistency is heated to about 80 to 100°C in a steam mixer, oxygen is injected in a high-shear mixer(s), and retention times of 20 to 90 minutes are normally achieved using an up-flow oxygen tower(s). Figure 2.1 illustrates the flowsheet of a typical industrial oxygen delignification system.  Figure 2.1 Typical schematic diagram of industrial oxygen delignification system  The rate of oxygen bleaching is determined by both physical and chemical phenomena [McDonough, 1986]. Physical factors govern the movement of the reacting species within the  Chapter 2: Literature  Review  pulp (mass transfer), while chemical factors govern the rate at which the pulp and bleaching chemicals react with one another once they are in contact (chemical kinetics). It is therefore obvious that, to understand the oxygen bleaching process, two key obstacles must be overcome: the tendency of the process to be chemically nonselective and the difficulty in achieving efficient mass transfer. The selectivity problem arises from the natural tendency of oxygen to form reactive free radicals that can attack cellulose and other carbohydrates as well as lignin. Limitations in mass transfer derive from the fact that oxygen bleaching processes involve threephase systems, and depending on the conditions, the rate of oxygen transport can limit the rate of the overall process [McDonough, 1996]. Key parameters in any commercial oxygen delignification system are the temperature, alkali charge, oxygen pressure, and the degree of mixing for efficient mass transfer of oxygen [McDonough,  1986;  Bennington and Pineault,  1999].  Surveys  of  industrial  oxygen  delignification systems show that the overall extent of delignification varies from mill to mill, with an average of 36.0% for softwoods and 36.6% for hardwoods, with system delignifications ranging from a low of 21% to a high of 48% for softwoods and from 26% to 46% for hardwoods [Bennington and Pineault, 1999].  2.2  Chemistry of Oxygen Species and Oxygen Delignification The fundamental interactions of oxygen in aqueous alkali with lignin moieties have been  the subject of various structural and kinetic enquiries. However, the conclusions of such studies cannot fully describe the events that occur when oxygen interacts with lignin macromolecules. It is likely that the multitude of branching and cross-linking variations that occur within lignin may  Chapter 2: Literature  Review  8  cause significant accessibility variations of reactive moieties towards even the same functional group [Argyropoulos, 1997]. Under the conditions typically used in oxygen bleaching, there are a large number of oxygen species present (Table 2.1).  Table 2.1 Oxygen species present in oxygen delignification systems  Anionic Form  Oxygen Species Oxygen  °2  Hydroperoxy Radical  HO  Hydrogen Peroxide  H0  Hydroxyl Radical  Superoxide Anion Radical  r  2  2  HO-  Hydroperoxy Anion  HO~  Oxyl Anion Radical  ~0-  The reaction of oxygen with lignin moieties under alkaline conditions generates a superoxide radical anion through a one-electron transfer from the lignin active site to oxygen. This is generally the rate-determining step of the oxidation and requires the presence of metal ions or elevated temperatures. This superoxide radical can undergo a metal catalyzed dismutation forming hydroperoxide and a hydroxy radical [Argyropoulos, 2001]. Of the oxygen species listed in Table 2.1, only the hydroxyl radical and its conjugate base are strong oxidants; the oxygen itself is a weak oxidant. Therefore oxygen bleaching is usually run under alkaline conditions so that ionized phenolic hydroxyl groups on the lignin will furnish the high electron density needed to initiate an electron transfer. A listing of some of the interconversion reactions between oxygen species is shown in Figure 2.2. Certain of these reactions are extremely rapid under oxygen bleaching conditions  Chapter 2: Literature Review  9  while others may require the presence of metals or protons to catalyze the reaction [Argyropoulos, 2001]. •0 ~  + HO'  -> HO~ +  0  H0 ~  + HO'  -> HO~ +  *0  2  2  HO•0 ~  + *0  2  + H0  2  '0  2  H0 2  2  + HO'  ->  2  2  H0 2  2  -> HO~ +0 +  2  2  + H0  -> HO~ + HO' +  + H0 ~  -> H 0  2  2  2  + HO- +  2  HO~  0  2  '0 ~ 2  Figure 2.2 Reactions of oxygen species under alkaline bleaching conditions [Argyropoulos, 2001]  The complex oxidation processes that occur in the oxygen-bleaching reactor include radical chain reactions involving a variety of organic species derived from both lignin and carbohydrate. Figure 2.3 shows likely initiation, propagation, and termination steps.  Initiation  Propagation  RO + 0  2  ->  RH + 0  2  ->  R» + 0  ->  (1)  2  R. + H O . z  R0  (2) (3)  2  R 0 . + RH -> R0 H + R.  (4)  R O + R« -> ROR  (5)  2  Termination  2  RC+0 -  2  Figure 2.3 Steps in the mechanism of oxygen bleaching [McDonough, 1996]  In oxygen bleaching, the substrate is activated by providing alkaline conditions to ionize free phenolic hydroxyl groups in the residual lignin. The resulting anionic sites are electron-rich  Chapter 2: Literature  Review  10  and therefore vulnerable to attack by oxygen. A n electron is abstracted, forming a superoxide anion and a phenoxy radical (Figure 2.3, reaction 1). A n alternate pathway for initiation of the radical chain reaction is abstraction of a hydrogen atom from an unionized phenolic group or other functional group to give the corresponding organic radical (Figure 2.3, reaction 2). Propagation of the chain reaction occurs by reactions such as the one between oxygen and an organic radical to form a peroxy radical which, in turn, may abstract a hydrogen atom to regenerate a new organic radical (reactions 3 and 4). The chain is terminated by coupling reactions.  2.3  Lignin: Structure and Compositions Lignin is a heterogeneous polymer that is made up of substituted phenylpropane, i.e.  coniferyl alcohol (softwood) or a mixture of coniferyl and sinapyl alcohol (hardwood) units. Although various studies have been conducted, the exact structure of lignin is still not known. Brunow [1998] proposed a widely accepted model for the structure of softwood lignin (Figure 2.5). Softwood lignin has an average molecular weight of 20,000 while the molecular weight of hardwood lignin is lower [Sjostrom, 1993]. Due to its complexity, most researchers have simplified lignin into a basic substituted phenylpropane unit (Figure 2.4).  R = H.OCH>CR' = H.CR  Figure 2.4 Substituted phenylpropane unit [Sjostrom, 1993]  Chapter 2: Literature  Review  11  Figure 2.5 Proposed lignin structures [Brunow, 1998]  The aromatic ring on lignin structures has one or two methoxy substituents (carbon-3 and carbon-5, see position designation in Figure 2.4), a C-C linkage (carbon-5), and an ether or a hydroxy substituent (carbon-4). Different wood species will have different types and numbers of these basic lignin units. These individual units can be linked through the R-groups (Figure 2.4) and the a-P double bond to form both C-C and C-O-C (ether) bonds by radical reactions [Sjostrom, 1993]. The ether linkages dominate approximately two-thirds or more and the rest are  Chapter 2: Literature  Review  12  of the carbon-to-carbon type. Some of the common linkages between the phenylpropane units in lignin are shown in Figure 2.6. The most abundant linkage between these units in native lignin is the ether P-O-4 bond. The list of all common linkages in native lignin with their approximate proportions can be seen in Table 2.2.  4-0-5  P-5  P-1  P-P  Figure 2.6 Common linkages between phenylpropane units [Sjostrom, 1993]  During alkaline pulping, most of the ether bonds having p-0-4 and a-O-A structures are cleaved by hydroxide ions promoting efficient lignin fragmentation by generating new free phenolic hydroxyl groups. A minor portion of lignin during alkaline pulping can also be ascribed to the cleavage of carbon-carbon bonds forming formaldehyde that may initiate lignin condensation reactions.  Chapter 2: Literature Review  13  Table 2.2 Proportions of common types of linkages in native lignin [Sjostrom, 1993]  Linkage type  D i m er Stru c t u re  3-0-4 a-o-4 p-5  Percent of the total linkages Softwood  Hardwood  Ary lgly cerol-B^ary 1-ether  50  6o  Noncyclic benzyl aryl ether  2-8  7  Phe ny lc ou ma ra n  9-12  6  p-1  l , 2-Diary 1 propane  lO-ll  5  5-5  Biphenyl  4  7  4-0-5  Diarylether  7  7  P-P  Linked through side chains  2  3  In kraft pulping, the majority of condensation reactions occur in the unoccupied C-5 position of the phenolic unit. Therefore, condensation occurs more easily in softwood than hardwood and is part of the reason why hardwood pulps are normally easier to bleach than softwood pulps. Moreover, it has been found that, during conventional kraft pulping, significant structural changes occur in the residual lignin with the progressive enrichment of carboxylic acid and condensed phenolic hydroxyl groups. Toward the end of pulping, residual lignin contains much more C-5 condensed phenolic hydroxyl groups than were present in the native wood. Both C-5 and C-6 condensed phenolic units were found to be relatively stable toward oxygen delignification [Jiang and Argyropoulos, 1999]. The approximate proportions of changes in composition of residual lignin as it moves from native wood to oxygen delignified pulp are given in Table 2.3. As can be seen from Table 2.3, a variety of reactions that take place during a kraft cook lead to the formation of new structures, i.e. stilbene and enol-ether structures. These structures exist in negligible amounts in native lignin; however, the amount of stilbenes following cooking has been estimated using U V analysis to increase to approximately 3-5% of the total linkages  Chapter 2: Literature Review  14  [Northey, 2001]. A n increase in the amount of vinyl (enol) ether structures was also observed which could be up to 0.5-2% of the total linkages.  Table 2.3 Changes in frequency of linkages (%) of residual lignin as it moves from native wood to oxygen bleached [Northey, 2001; Gellerstedt, 2001]  Type  Linkage 0-O-4 0-5 5-5  4-O-5 ff - O -4  M m "  (% of linkages)  Kraft lignin (%)  2 )  0 delignified (%)  uncondensed  48  8  12  condensed uncondensed condensed condensed  10  12  13-2  7  lO  5  n  15 8  17 8.8  5  uncondensed uncondensed  5  -  -  2  2  -  fi-P Stilbenes  highly reactive  -  reactive  Negligible Negligible  3-5  Vinyl Ethers  2  -  diPhenyl Methane  condensed  Negligible  40  44  88  97  lOO  Total  3 )  2  milled wood lignin a )  approximate value for a residual kraft lignin from a 30 kappa pulp  ;,)  approximate value after an O-stage kappa 9.3  Another noticeable change in the residual lignin composition shown in Table 2.3 is in the condensed structure of diphenylmethane (DPM). The exact amount of these structures is a matter of debate, as the analysis of residual lignin samples using various methods have generated values from roughly 5% to as high as 60%) of the total linkages [Argyropoulos et al, 1998; Chiang and Funaoka, 1990]. Studies have shown that residual lignin undergoes structural changes creating new functional groups and new compositions following the kraft cooking process. Studies with lignin model compounds were needed to determine how these new functional groups and linkages react under oxygen delignification conditions.  Chapter 2: Literature  Review  15  2.3.1 Lignin Model Compounds In order to get a better and more complete understanding of the reactivity and mechanisms involved in oxygen delignification, model compounds containing the linkages and functional groups assumed to represent the native lignin structures found in the residual lignin of kraft pulps were studied. The selection of which functional groups and linkages to investigate was based upon the presumed structure of residual lignin. Today, lignin model compounds have been extensively developed using the results of wet chemical procedures such as permanganate oxidation, acidolysis, Resonance (NMR), and also  3 1  1 3  C Nuclear Magnetic  P N M R [Northey, 2001]. However, since native lignin is  comprised of various different functional groups, one lignin model compound can only represent a small portion of the native (actual) lignin present in the fibre wall. Numerous studies with individual model compounds have demonstrated that only those structures containing a free phenolic hydroxyl groups react to any extent under oxygen bleaching conditions. Because of the lack of reactivity of non-phenolic model compounds, the majority of studies on ring cleavage by oxygen have focused on compounds with free phenolic hydroxyl groups. However, a non-phenolic model compound has been degraded by oxygen in the presence of a compound containing a free phenolic hydroxyl group and excess iron. This increase in reactivity of the non-phenolic hydroxyl model compound was caused by the generation of oxygen radical species in the reaction of oxygen with the free phenolic model compound [Argyropoulos, 2001]. The most reactive lignin model compounds are of the stilbene type closely followed by the vinyl (enol) ether structures. Stilbene structures are rapidly degraded by oxygen under  Chapter 2: Literature  Review  16  alkaline condition even at temperatures as low as 45°C [Ljunggren, 1986; Ljunggren & Johansson, 1990]. A series of lignin model compounds are listed in Figure 2.7 in relative order of their susceptibility to oxidation.  diguaiacol stilbene  CHOH  (\  >  i  /^-hydroxy stilbene  y=s  CHaO  > CHs  CHa  H  phenolic p-aryl ether  CHs  OH  dipropylbiguaiaco!  Figure 2.7 Relative reactivity of lignin model compounds under a l k a l i - 0 conditions [Ljunggren et al., 1994] 2  When subjected to alkaline oxidation conditions, degradation of phenolic stilbenes occurs across the double bond forming phenolic aldehydes [Gierer and Nivebrant, 1986]. Vinyl ether structures also cleave across the double bond. Although still quite reactive, vinyl ethers oxidize over one hundred times slower than their stilbene counterparts. The remaining structures listed in Figure 2.7, other than stilbene and vinyl (enol) ether, are significantly less reactive with oxygen under typical oxygen bleaching conditions. All of these compounds react, by an order of magnitude or more, slower than the vinyl-ether structures. The P-O-4 and P-1 linked compounds react fairly slowly, with the diphenylmethane, 5-5, and  Chapter 2: Literature  Review  17  P-5 linked compounds being the slowest. It is important to note that all of these compounds were reacted alone and so any effects of multiple branching and crosslinking that exist in native lignin were eliminated.  2.3.2 Lignin Reactions Studies of the mechanisms of lignin removal during oxygen bleaching have been made since the 1960s and still continue up to now [Gierer, 1993]. The reason for this is because reactions of lignin during oxygen delignification are complex and not completely understood. Model compounds have provided considerable insight about the effects of the process and structural features of both residual and dissolved lignin into the physical and chemical aspects of the reaction mechanism involved in the oxygen degradation of lignin [Gierer, 1993; Ljunggren and Johansson, 1990 & 1994; Northey, 2001; Argyropoulos, 2003]. McDonough [1996] summarized studies of lignin reactions under oxygen alkaline conditions. He showed that free phenolic hydroxyl groups play a major role in oxygen delignification. The phenolic group is ionized forming a phenoxy radical under strong alkaline conditions, generating a site with high electron density, which undergoes transfer of a single electron to molecular oxygen or any of the available radical species. The resulting phenoxy radical is a resonance hybrid of structures which, in several ways, could be transformed into the hydroperoxy  radical,  an  intermediate  structure  which  can  subsequently  undergo  an  intramolecular nucleophilic reaction at its adjacent site leading to the formation of oxirane, muconic acid, and carbonyl structures. The last step corresponds to breakage of a bond joining two lignin monomeric units and therefore leads to lignin fragmentation. The other step  Chapter 2: Literature Review  18  corresponds to the introduction of hydrophilic groups, imparting a polar character. Both types of reactions may be expected to enhance the solubility of lignin in an alkaline medium. The degradation products from oxygen delignification are predominantly organic acids and carbon dioxide. The suggested mechanisms of oxygen delignification are illustrated in Figure 2.8 and Figure 2.9.  Figure 2.8 Initial reactions that lead to oxygen delignification [McDonough, 1996]  Studies employing pulp suspensions have confirmed, to a large extent, the conclusion drawn from model compound studies. Gellerstedt [1986, 1987] and Argyropoulos [1997]  Chapter 2: Literature Review  19  investigated the structure of the lignin in oxygen-bleached pulp and concluded that oxygen bleaching reduces the content of free phenolic units. Lignin remaining in pulp after oxygen bleaching was enriched with biphenyl-type condensed structures and p-hydroxyphenyl-type lignin. It was further confirmed that the number of phenolic hydroxyl groups in the pulp lignin decreased and the number of carboxylic acid groups increased the lignin solubility.  Figure 2.9 Reactions of intermediate hydroperoxides that lead to lignin fragmentation [McDonough, 1996]  A final point concerning the chemistry of lignin reactions during oxygen bleaching is the role of covalent linkages between lignin and one or more of the carbohydrate components. Researchers have found that a lignin-carbohydrate complex extracted from pulp after oxygen delignification contained about half of the residual lignin, and that it was extensively degraded [McDonough, 1996]. They concluded that cleavage of a bond between xylan and lignin would allow more extensive oxygen delignification.  Chapter 2: Literature  Review  20  2.4  Issues in Industrial Oxygen Delignification Systems Often, positive results obtained in laboratory systems are not duplicated in commercial  operations and hence the expected return of investment is not delivered to the customer by the vendor. Some of this discrepancy could be caused by using laboratory reactors that allow the chemistry of the oxygen delignification reaction to proceed without taking into account some of the physical constraints that exist in a commercial system [Berry et al, 2002]. Some of the differences between commercial systems and many laboratory reactors are: •  A specific charge of oxygen is applied in a commercial system whereas a large excess of oxygen is used in many laboratory reactors.  •  Commercial systems have variations in pressure because of a changing hydrostatic head in the retention tower while laboratory reactors are commonly used with a constant oxygen pressure.  •  There is generally only one opportunity to mix oxygen with pulp in a commercial system whereas mixing is either intermittent or continuous in laboratory reactors.  •  The pulp volume to reactor surface area is very much larger in a commercial system than in laboratory reactors.  •  The effect of carry-over is normally neglected in laboratory experiments. Depending on the washing efficiency, the carry-over in commercial systems could be quite significant.  Despite all of the differences mentioned above, there are some other critical issues that may affect the performance of an industrial oxygen delignification system. Some of the issues are lignin leaching and kappa number determination. Understanding these issues is essential for the modeling of industrial oxygen delignification systems.  Chapter 2: Literature Review  21  2.4.1 Lignin Leaching Leaching of lignin can be defined as the transport of the lignin macromolecule out of the fibre wall into the bulk liquid. This process normally takes place in the washing system with the addition of fresh or reused water. During oxygen delignification, residual lignin reacts with oxygen gas under alkaline conditions, after which the degraded lignin must diffuse out of the fibre wall before it can be dissolved in the bulk liquor. As illustrated in Figure 2.10, the degraded lignin macromolecule has to traverse a tortuous path across the fibre wall before it can dissolve in the bulk liquor, which makes the pathway of a particular molecule being leached from the fibre considerably longer than the distance measured directly across the fibre wall [Goring et al., 1984]. Moreover, the distance between adjacent lamellae in the fibre wall may vary so that a lignin macromolecule may then be trapped in a pore of the fibre wall (pore restriction). Another restriction on the leaching of lignin is the possible viscous drag force between the macromolecule and the walls of the pore which will reduce the rate at which the lignin can diffuse out [Goring et al., 1984].  Figure 2.10 Representation of the tortuous pathway for a lignin macromolecule to diffuse out in the wood cell wall [Goring et at., 1984]  Chapter 2: Literature Review  22  Several publications [Yean et ah, 1976; Favis et ah, 1981; 1983; 1984] on the leaching of lignin during the washing stage have been published and all have described the slow diffusion of lignin macromolecules from the fibre wall into the wash liquid. It was reported that the diffusion coefficient observed during these leaching experiments was several orders of magnitude smaller than that corresponding to free diffusion in water. It is likely that the interaction of lignin with the cellulose hydrogel (mainly hemicellulose) must greatly restrict the diffusion of the lignin macromolecules out of the fibre. Diffusion or leaching of lignin will always take place whenever there is free liquor between the fibres and a concentration difference between this bulk liquid and the immobile liquor inside the fibre wall. Diffusion is retarded at high pulp consistency because of the limited amount of free liquor between the fibres. The speed at which diffusion take place is a strong function of pH and temperature [Favis et ah, 1983]. The size (molecular weight) of the diffusing lignin, type of wood species, free liquor turbulence, and process configuration also affects the diffusion phenomenon [Favis et ah, 1984; Ala-Kaila et ah, 1997]. After a kraft cooking process, the residual lignin in pulp fibres consists of different types of chemical fractions [Northey, 2001]. As in kraft cooking, oxygen delignification also proved to promote certain aromatic structures in residual lignin over some other structures [Gellerstedt et ah, 1986; 1987]. The vast variety of lignin moieties formed during pulping and oxygen bleaching, depending on the process conditions used in the digester and oxygen delignification system, differ in their degree of oxidation. A certain portion of the residual lignin could be partially oxidized or fragmentized, another portion could be fully oxidized, while the remaining residual lignin could be left un-oxidized. Partially oxidized lignin molecules following the cooking and oxygen delignification processes, depending on their size and location within fibre  Chapter 2: Literature  Review  23  wall, are trapped inside the fiber wall and over time could be leached out from the fibre to the surrounding liquor. However, the partially oxidized lignin will consume permanganate during a kappa number test and, hence, contribute to what is called 'transient' material. The term 'transient' for residual materials left in the pulps, i.e. residual lignin, comes from fact that a considerable amount of residual material could be leached out from the fiber to the free liquor surrounding the fiber providing sufficient time is allowed. Consequently, the measurement of how much lignin is actually left inside the fiber wall would depend on when the kappa number test is conducted. In other words, there are situations where the kappa number test does not measure the actual lignin requiring oxidation during the oxygen delignification process. This issue will have a significant impact when examining the performance or overall efficiency of an industrial oxygen delignification system. The transient behavior of the residual lignin components in chemical pulps has been the subject of intensive study [Crotogino, 1987; MacLeod, 1993 & 1996; Ala-Kaila, 1996 & 2001]. Mill-produced kraft pulp fibres hardly ever represent a state of equilibrium with respect to residual alkali-soluble lignin. When examining the overall performance or efficiency of a particular process, this time-dependent behavior of residual lignin components should be taken into consideration in order to get a precise evaluation on the efficiency of the process. The group of Ala-Kaila [1996, 2001, 2003] did extensive research on lignin leaching, particularly during the oxygen delignification stage. From leaching experiments with softwood kraft pulp, they found that residual material in the pulp could be divided into four different fractions: wash loss, easily leachable, slowly leachable, and stagnant. The wash loss fraction is specified as kappa number drop after 5 minutes washing. The easily leachable lignin is the amount of kappa number that was removed after 30 minutes leaching. The third fraction, slowly  Chapter 2: Literature Review  24  leachable lignin, was removed after 24 hours of leaching. Stagnant lignin was defined as the kappa number that remains following 24 hours of leaching. The sum of the four fractions is equal to the total kappa number of the original pulp sample before leaching. The leaching rate was also found to accelerate with increased pulp temperature, alkali content (pH), and the presence of oxygen gas or air. These results were in agreement with the previous experiments of Goring [1983] and MacLeod [1993; 1996]. The approximate fractions of residual lignin in the pulp samples are shown in Table 2.4. Leaching experiments were performed at low consistency at 85-100°C under nitrogen bubbled through the suspension to prevent oxidation during leaching. Pulp samples were centrifuged up to 38% consistency before leaching was started to remove any dissolved solids or impurities [Ala-Kaila, 2001].  Table 2.4 Approximate fractions of softwood residual lignin in pulp [Ala-Kaila, 2001] Approximated fractions Initial kappa number  BSW 2 2 . 9  Wash loss fraction Kappa after.5-min washing  19.7  13  blow'  5.5 7.6  0.4 11.1  1.1 17.5  2  5.3  1.1  Stagnant fraction 15  16.8 i.1.5  18.6  Slowly leachable fraction Kappa after 24-h leaching  0  3.2  Easily leachable fraction Kappa after 30-mm leaching  Oj b l o w '  0.2 7.4  1.1 10  17.5  0.6 6.8  10  6.8  T=85°C, 10% Consistency, 3.5% NaOH, 15% 0 , 45 minutes retention 2  2)  T=100°C, 10% Consistency, 0.4% NaOH,.l% 0 , 45 minutes retention 2  From the results of the leaching experiments shown in Table 2.4, most of the leached lignin was present in the wash loss fraction that took place during the first 5 minutes period of washing with de-ionized water at 2% consistency. These results underline the importance of thorough washing in the mill to achieve maximum delignification in an oxygen-alkali  Chapter 2: Literature Review  25  delignification process. Moreover, despite a decrease in total kappa number, there is a noticeable reduction in the amount of the easily leachable fraction from 1.1 to 0.4 kappa, from the brown stock washer to the 1 oxygen blowline (Oi blow, Table 2.4). This finding suggested that both st  leaching phenomena and oxidation reaction are occurring in the 1 oxygen tower as the pulp st  suspension moves upward through the tower. Furthermore, when compared with the result following the 2  nd  reactor ( O 2 blow, Table 2.4), lower amounts of easily and slowly leachable  fraction are observed. This suggested that in the 2  nd  oxygen reactor (tower), the structure of the  lignin is becoming less reactive towards oxygen, possibly being more condensed in structure as has been measured by Argyropoulos [1997] and the effect of leaching could be more predominant in the second oxygen retention tower.  2.4.2 Kappa Number Determination Kappa number is defined as the volume (in milliliters) of 0.1N potassium permanganate solution consumed by one gram of moisture-free pulp under conditions specified in the standard kappa method (TAPPI T-236 cm-85 or PAPTAC G.18). The method can be used for all types and grades of chemical pulp obtained in yields under 60%. The standard kappa number test is widely employed and uses the rapid oxidation of lignin by acid potassium permanganate to estimate the residual lignin content in pulp fibres. The method has been used both in mill operations and in laboratory work since 1934 as a measure of the degree of delignification of chemical pulps in pulping, oxygen delignification, and bleaching stages. However, recent studies [Gellerstedt, 1998a] on the kinetics and mechanisms of the kappa number test have pointed out a drawback and an improper definition given in the standard  Chapter 2: Literature  Review  26  kappa test (T-236 cm-85), which could lead to erroneous kappa number values. Gellerstedt reported that during kappa number determinations, the lignin structure is oxidized by the addition of permanganate to the aromatic rings followed by the degradation of the rings that requires about one minute. He mentioned that the ten minutes reaction time given in the standard kappa number procedure is unnecessarily long and may give an uncertain kappa number value because of uncontrolled oxidation of e.g. carbohydrate structures. Gellerstedt [1998a] also reported that the definition of the 30-70% permanganate consumption range used in the standard kappa test would result in erroneous kappa numbers since there is no permanganate remaining in the solution at above 60% consumption of added permanganate. Furthermore, studies in the last few years have also shown that the kappa number reflects not only lignin but also carbohydrate structures sensitive to oxidation by permanganate, notably hexenuronic acid structures linked to xylan [Gellerstedt, 1997 & 1998b]. A more accurate way of estimating the actual residual lignin content is therefore necessary. One such measurement is the oxymercuration-demercuration (Ox-Dem) kappa number, which reflects only the contribution from the residual lignin [Gellerstedt, 2002a]. However, the meticulous procedures required for this test are impractical in the mill environment. Nevertheless, oxymercuration-demercuration kappa number could be a useful way to validate the importance of results taken from laboratoryscale research. One interesting example of utilization of Ox-Dem kappa number was reported by Gellerstedt et al. [2002b, 2002c]. They measure the relationship between the kappa number and oxidizable structures [2002b] and its distribution [2002c] in E C F - and TCF-bleached kraft pulps. They found that even though the normal kappa number indicates only about 45-55% and 30-40% reduction across the oxygen stage for both softwoods and hardwoods respectively, the degree of  Chapter 2: Literature Review  27  'actual' lignin dissolution is, in fact, about 73% and 60%>. The reason for these large differences are because a standard kappa number measurement also includes contributions from hexenuronic acid and other non-lignin structures that are not eliminated in the oxygen stage. Ala-Kaila [2003] also included Ox-Dem kappa number measurements to characterize the 'apparent' and 'actual' delignification responses of birch pulp in the two oxygen reactors as shown in Table 2.5.  Table 2.5 Fraction of apparent and actual birch residual lignin as kappa number [Ala-Kaila, 2003] Brownstock  O, b l o w  G blow  )  }  2  A p p r o x i m a t e d fractions Apparent  Actual  Apparent  Actual  Apparent  Actual  -  5-5  -  5-5  -  Easily leachable fraction  5-4 0.8  0.3  0.2  0  0.3  0  Slowly leachable fraction  2  .1-4  0.9  0-7  0.6  0.3  Stagnant fraction  13-9  6.5  11.6  4-7  10.4  3-7  Total kappa  22.1  8.2  l8.2  54  16.8  4  Wash loss fraction  no.  D i=92''c, 10% Consistency, 1,65% NaOH, 0.4% 0 , 1 5 minutes retention 2  ) T=96°C, 10% Consistency, 0% N a O H , 2%  2  65.minutes retention  As can be seen in Table 2.5 above, the 'apparent' and 'actual' kappa numbers for each approximated fraction of hardwood (birch) pulp shows a similar trend. However, the magnitude of actual lignin removal showed a lower value. Also, in terms of the stagnant fraction of apparent lignin, birch kraft pulp showed a much lower percentage decrease (25%) compared to softwood kraft (60%>) shown previously in Table 2.4. The transient, or time-dependent behavior of 'apparent' lignin, which depends on the washing treatment received before the analysis, may have a significant effect on the delignification response measured in an industrial oxygen bleaching process. Results of Ala-  Chapter 2: Literature Review  28  Kaila open an opportunity that pulp can always be in a transient state where it contains a considerable amount of 'apparent' lignin, not 'actual' lignin and has not had a chance to leach out of the fiber. Consequently, there will always be a risk that bleached or unbleached pulp may be characterized on the basis of a pulp sample that still contains leachable apparent lignin that has been affected in reaction but has not yet had the right conditions or enough time to be removed from the pulp fibres. The result of this finding underlines how the applied experimental (measurement) procedure may have a noticeable effect on the performance characteristics measured for an industrial oxygen-alkali delignification process. The procedure for measuring kappa number may have a noticeable effect on the performance characteristics reported for an industrial oxygen delignification system. One such example of quantifying industrial delignification performance in oxygen bleaching was reported in the survey of Bennington and Pineault [1999].  20  30  40  50  Delignification, (%) Figure 2.11 Theoretical delignification vs delignification efficiency achieved by surveyed mills [Bennington & Pineault, 1999]  Chapter 2: Literature  Review  29  In Figure 2.11, theoretical delignification was plotted against the reported (and normally quoted) delignification achieved in all systems. Theoretical delignification was calculated by taking into account the existence of a floor level of lignin ( K ) that could not be exceeded under n  normal working conditions. More about the floor level of lignin and the limit of oxygen delignification (maximum lignin removal possible) will be presented later in this chapter. Delignification (%) and theoretical delignification (%) were calculated as:  % Delignification  [2-1]  % Theoritical Delignification =  [2-2]  The floor lignin levels used in the calculation were kappa 10.5 for softwoods and kappa 7 for hardwoods. As can be seen from Figure 2.11, some mills, such as mill C and mill F, despite having low measured delignification efficiency, are close to the theoretical ceiling (>85% theoretical delignification). Mills with low theoretical delignification should be able to increase their system performance if desired and mills that are close to the theoretical ceiling have less room to improve [Bennington & Pineault, 1999]. Part of the floor level of lignin and the limiting behaviour of theoretical delignification could be due to the non-lignin structures measured during the kappa number test. Moreover, the exact location of pulp sampling and pulp treatment prior to the kappa number test will affect the comparison of reported delignification between each system. Quite significant leaching of lignin can occur during washing or when the pulp is subjected to alkaline conditions; this will reduce the lignin content of pulp even in the absence of oxygen as we discussed earlier.  Chapter 2: Literature  Review  30  2.4.3 Molecular Weight Distribution The molecular weight distribution can be used to help understand how different processes or different treatments affect the physical characteristics, i.e., degradation rate of cellulose and both residual and dissolved lignin. There are two ways of measuring the molecular weight distribution: using ultrafiltration or using chromatographic techniques. Ultrafiltration has been widely used for the characterization (fractionation) of organic material in bleach plant effluents. It can be used to determine both the relative molecular weight and molecular weight distribution. However, the more suitable methods for these purposes are ones based on chromatographic techniques such as size exclusion (SEC) or gel permeation chromatography (GPC). Size exclusion or gel permeation chromatography measures the distribution of molecular weight using a spiral column filled with little beads. The beads have different sizes of pores or holes so that when the lignin solution is injected into the column, the lignin molecules will move into the pores on their way through the column. Some lignin molecules take longer than others to elute through the column. High molecular weight lignin cannot fit in the smaller holes and because there are fewer pores that they can enter, they are eluted through the column more rapidly. However, the smaller lignin molecules having lower molecular weight can move in and out the small pores and, consequently, take longer to move trough the column. Molecular weight distribution of carbohydrate (polysaccharides) is a fast and widely used indicator to measure pulp physical strength. This parameter is normally measured across the pulping and bleaching processes to study the response of changes in process conditions to pulp properties. On the other hand, the measurement of molecular weight distribution of both residual and dissolved lignin helps understand the mechanism and effectiveness of particular process in modifying lignin structures and removing them from the fiber cell wall.  Chapter 2: Literature Review  31  0.06 0.05 .2  0.04  I  0.03  Q  0.02  03  c  0.01 0 5  10  15  20  25  30  Elution volume, ml Figure 2.12 Molecular size distribution of unbleached kraft (—) and oxygen delignified (—) residual lignin of Eucalyptus Globulus [Lachenal et al., 2001]  As can be seen from Figure 2.12, there is a change in the distribution of molecular weight (size) of residual lignin following the oxygen bleaching. The oxygen delignified residual lignin has a slightly smaller average molecular mass than the unbleached one [Lachenal et al, 2001]. These results are in agreement with those of Gierer [1993] who showed that residual lignin undergoes cleavage of C-a and C-p bonds during the oxygen bleaching stage. However, the molecular mass distribution pattern shown in Figure 2.12 does not reflect the true molecular mass distribution of the original residual lignin in the pulps. The reason for this is because residual lignin samples were normally isolated from the pulp using acid hydrolysis and the original lignin could undergo degradation and rearrangement under the conditions of their isolation [Chang, 1992]. Lachenal [2004] further investigated how successive oxygen stages affected the molecular weight distribution of softwood kraft pulp. He concluded that residual lignin had a lower molecular weight after oxygen bleaching. However, the molecular size of the lignin did not vary significantly after the second and the third oxygen stage as shown in Figure 2.13.  Chapter 2: Literature Review  32  0.014 n  Elution volume, mL Figure 2.13 Effect of successive oxygen stages to molecular weight distribution [Lachenal et al., 2004]  2.5  Kinetics and Process Variables The response of an oxygen delignification system to changes in process variables, i.e.,  temperature, alkali and oxygen charge, consistency, and oxygen pressure, is a manifestation of the kinetics of the component chemical reactions and mass-transfer processes.  Studies of the  kinetics of oxygen delignification with fiber suspensions have been well documented [Iribarne and Schroeder, 1997; Hartler, 1970; Evans, 1979a; Olm and Teder, 1979 and 1981; Kovasin et al, 1987; Hsu and Hsieh, 1987 and 1988; Myers and Edwards, 1989b; Vincent et al,  1994;  Perng and Oloman, 1994; Argawal et al, 1999]. Such kinetic studies provide a useful framework for predicting the effect of process variables on delignification performance. All of the kinetic models that have been developed are empirical and the rate of delignification is considered to be proportional to the lignin content expressed as the kappa number {K), the hydroxide ion concentration [OH"], and either the oxygen partial pressure (P02)  Chapter 2: Literature Review  33  or the oxygen concentration in the liquid phase [O2] expressed in the form of a "power law". This is given by an equation of the form:  [2-3]  The constant m, n, and q are determined empirically from experimental data. The reaction rate coefficient k depends on the temperature and is given by Arrhenius equation:  [2-4]  where A is the pre-exponential factor, EA is the activation energy (kJ/mole), R is the gas constant (kJImole.K), and Tis the absolute temperature (K).  The kinetic parameters obtained for delignification by previous workers using pulp fibre suspension studies are summarized in Table 2.6. Both one (equation [2-3]) and two (parallel) stages of kinetic equations have been proposed. In the two-stage models, investigator treated oxygen delignification by considering that the kappa drop (lignin removal) takes place over two distinct time periods, an initial rapid reaction (initial stage) followed by a slower reaction (final stage). Normally, a two-stage model will give a better correlation coefficient R compared to a single-stage model. The general form of the rate expression for a two-stage model is:  •dKldt = *, [ 0 f [OH'J 2  [tcf +k [ 0 f [OH-J 2  2  [K]  [2-5]  Some publications added a unit step function to equation [2-5] to imply the time period of the first term and second term, i.e. Hsu and Hsieh (1987, 1988) defined the first 2 minutes of reaction by the first term (k ) and the rest of the reaction is described by the second term (k ). x  Chapter 2: Literature Review  2  34  Table 2.6 Summary of delignification kinetic studies, listing the determined exponents and parameters  Stage •  Reference  P u l p Type  Hartler{1970)  Sulphate (Pine)  Edwards and Norberg (1973)  Kraft (Hemlock)  Reaction O r d e r  A  Ea (kj/mole)  Alkali  Oxygen  Kappa  -  n.a.  n.a.  n.a.  69.03  n.a  2  n.a.  1  48.6  4.00E+03  Jarrehult and Samuelson (1978)  Kraft (Pine)  -  1  n.a.  n.a.  n.a.  n.a.  Evans etal. (1979)  Kraft Southern  -  1  1.23  1  49.1  1.00E+05  Olm and Teder(1979)  Kraft Softwood  Initial  0.1  0.1  1  10  n.a.  Final  , 0.3  0.2  1  45  n.a.  Olm and Teder (1981)  Kraft Softwood  0.6  0.5  3.2  70  n.a.  0.13  0.5  1  18.6  n.a.  1  0.89  6.27  8.30E+07  0.24  Initial  0.78  0.35  3.07  3.60E+07  2.46  Final  0.7  0.74  3.07  7.10E+07  143.9  Initial  0  0.43  1  31.6  1.51 E+05  Final  0.875  0.43  1  61.4  1.68E+07  Kovasin et.al (1987)  -  Kraft (Eucalyptus) Kraft (Pine)  Hsu and Hsieh (1988) . Myers and Edwards (1989)  Kraft SW & HW Kraft (Eucalyptus)  Vincent et.al. (1994) Pemg and Oloman (1994)  Kraft Softwood  Argawal et. al. (1996)  Kraft Hardwood  Iribameand Schroeder(1997)  Kraft (Pine)  Iribarne and Schroeder (1997)  Kraft (Pine)  Initial  0  0.4  1  24.2  27.5  Final  0.39  0.38  1  46.3  7667  -  0.4  0.5  4.8  60  1.8  0.92  0.53  7.7  107.2  2.36E+06  0.7  0.7  2  51  3.00E+06  Initial  1.2  1.3  1  67  6.00E+11  Final  0.3  0.2  1  40  6.00E+04  The most widely accepted two region kinetic model is that of Olm and Teder (1979) who assumed pseudo-first-order kinetic equations in terms of kappa number. They defined the initial kappa number as the sum of fast ( K ) and slow ( K ) lignin: M  02  tc = /c +/c ox  [2-6]  Q2  Equation (2-5) was applied to the two regions in the form of two parallel first-order kinetic expressions:  = *, [OH-]° '  [P f 02  K  m  +  k  2  [OH-f  [P f 02  K  02  where kj and k are the rate constant in the initial and final phases respectively, 2  [2-7]  and K are 2  the "easily eliminated" and "slowly eliminated" lignin. In the initial stage, the reaction rate was  Chapter 2: Literature  Review  35  reported to be about 20 times higher than in the final stage. The initial and final phase of delignification profile of Olm and Teder's model can be depicted in Figure 2.14.  S. ' •  ol 0  L  I  i  1  10  20  30  40  Tim©, min  SO  Figure 2.14 Two-stage model of oxygen delignification [Olm and Teder, 1979]  2.5.1 Time and temperature As previously mentioned, the decrease of kappa number with time exhibits two distinct stages, both of which are first-order rate processes. There is an initial rapid kappa number drop followed by a slower one. This is usually interpreted as being caused by the presence of two types of lignin that differ in ease of removal. In addition to this, through lignin model compound studies, it has been found that the structures of residual lignin leaving the cooking stage exhibit different reactivities when exposed to oxygen delignification conditions [Ljunggren and Johanson, 1994]. The different reactivities are assumed to be related to the various lignin linkages comprising its structures (more on lignin model compounds study will be discussed later in this chapter).  Chapter 2: Literature Review  36  A consequence of the first-order nature of the delignification process is that, given enough alkali, the kappa number will continue to drop indefinitely [McDonough, 1986]. However, this is in contrast to the normal observation that the process appears to stop when a limiting kappa number is reached, as shown in Figure 2.15. The latter behavior results when the alkali charge is exhausted [McDonough, 1986] or when the lignin structures become highly condensed forming stable lignin moieties (i.e. biphenyl, diphenylmethane), causing it to react very slowly under typical oxygen bleaching conditions [Argyropoulos et al, 2001]. In commercial oxygen delignification processes, the temperature ranges from 80°C to 105°C for medium consistency and from 100°C to 115°C for high consistency [Bennington and Pineault, 1999; McDonough, 1996]. Pulp residence time varies from one mill to another, depending on the number of stages and the particular process conditions chosen. Many newer mills have two-stage systems with 20-30 minute residence times in their 1 stage followed by an st  additional 30-65 minutes in the 2  nd  stage, providing a total of 50-95 minutes retention time.  40 J  0  1  2  3  Reaction time, h  Figure 2.15 Effect of temperature on oxygen delignification rate [Hartler et al., 1970]  Chapter 2: Literature Review  37  As Figure 2.15  shows, the delignification or kappa number reduction is strongly  influenced by temperature. However, increasing temperature will substantially accelerate both delignification and cellulose degradation rates. Consequently, the degree to which lignin can be delignified is normally limited to a certain level to prevent undesirable viscosity (pulp strength) loss. Figure 2.16 shows the relation between the intrinsic viscosity of the pulp and the kappa number where there is a marked tendency for the viscosity to decrease at high temperatures.  , :i 5  5  _  _  _  _  10  15  20  25  _  30  K A P P A N U M B E R , mUg Figure 2.16 Viscosity of the oxygen bleached pulp versus kappa number [Hsu and Hsieh, 1987]  The loss in pulp viscosity across the oxygen system is used to describe the extent of carbohydrate degradation that accompanies the delignification reactions. As in delignification kinetics, carbohydrate degradation kinetics are generally expressed in the form of a power law. This is done by monitoring the increase in the number-average moles of cellulose per metric ton of pulp (m ). Each time a cellulose bond is broken, one more chain is formed and the number of n  moles of cellulose chains in the pulp increases. The higher the value of m the greater the extent n  of cellulose degradation. The general carbohydrate degradation kinetic expression has the following form:  Chapter 2: Literature Review  38  dmJdt = k [0 } [OH-^[m ] m  c  [2-8]  q  2  n  The reaction orders m, n, and q are shown in Table 2.7, the reaction rate coefficient k is given c  by the Arrhenius equation:  k =Aexp(-^A  [2-9]  c  where A is the pre-exponential factor, E is the activation energy (kJ/mole), R is the gas constant A  (kJImole.K), and Tis the absolute temperature (K).  Table 2.7 Summary of carbohydrate degradation kinetic studies with fibre suspension Reference  Pulp Type  Hartler (1970)  Sulphate (Pine)  dm and Teder (1979)  Kraft Softwood  Perng and Oloman (1994)  Kraft Scflvvood  Iribarne and Schroeder (1997)  Kraft (Pine)  Reaction Order  Stage -  E a (kJ/mole)  A  n.a.  86  n.a  0.8  0  40  n.a.  0.6  0.1  0  53  n.a.  0.7  2.1  -5.3  94  4.8 x 10  0.3  0.4  0  78  7x10  Alkali  Oxygen  Kappa  -  n.a.  n.a.  Initial  0.2  Final  -  Using the number-average moles of cellulose (m ) n  12  10  estimated in equation [2-8], the  change in degree of polymerization (DP) is calculated by dividing the weight of the pulp (1 ton) by the known molecular weight of an anhydro-glucose unit (162 glmoles) times m , i.e., n  10 DP = —— 162m„ 6  [2-10]  The degree of polymerization is further correlated to the TAPPI/CED viscosity (rj, mPa.s, T-230 om-94) using the following correlation of Godsay and Pearce [1984]:  DP = 961.38 log(7) - 245.3  Chapter 2: Literature  Review  [2-11]  39  Another way that researchers [Zou et al, 1994; Marcoccia et al, 1993; Emsley and Heywood, 1997; Soares et al, 2001] have used to describe cellulose degradation has been through first-order kinetic expressions of the form:  1  ={k ){t)  1  [2-12]  DP  (DP) (DP)  o  where (DP) , o  k ,  and t denote the initial value of DP, the rate constant for cellulose  DP  degradation (min ), and time (min), respectively. 1  Furthermore, Argawal [1997] proposed an alternative way of modeling viscosity loss in oxygen delignification in terms of pulp residence time in the oxygen tower (t, min) as follows:  log  {-5.8265x10" r [OH]° P 7  2  S  02 O2  }log(r)  [2-13]  \M„j  where /u is the intrinsic viscosity of the pulp in cc/g [ASTM Standard D1795-62 similar to SCAN-C 15:62], ju is the initial pulp intrinsic viscosity, T is temperature in °C, [OH] is the 0  alkali concentration in g/L, and P ^ the oxygen pressure inpsig. The intrinsic viscosity (p.) can 0  then be correlated to the conventional TAPPI viscosity (n) [Argawal, 1997] as follows:  r) = 3 x 1 0 ~ V - 0.392// + 175.7  Chapter 2: Literature Review  [2-14]  40  2.5.2 Alkali Charge As for temperature, increasing alkali concentration by increasing the alkali charge at constant consistency will result in higher delignification and lower selectivity. Figure 2.17 and Figure 2.18 illustrate these relations.  5  15  30  60  80  Time, m Figure 2.17 Effect of Alkali Charge on oxygen delignification rate [Liebergott et at., 1985]  The amount of alkali charged into the oxygen tower of an industrial oxygen system is fixed depending on the capacity of the mill's particular chemical recovery plant. A n industrial survey found that the amount of alkali charge could vary from one mill to another. Depending on mill process configuration, the amount ranged from a low of 0.3 up to 2.7 (% on pulp) [Bennington and Pineault, 1999]. As we mentioned earlier in section 2.3.2 on lignin reactions, alkali availability is critical for delignification reactions to proceed. The amount of residual alkali left in the retention tower over time will determine the extent of the reactions. As Figure 2.17 shows, extending pulp retention beyond 60 minutes did not result in a significant decrease of kappa number. Once the alkali is exhausted, reaction will stop and the kappa number levels out.  Chapter 2: Literature  Review  41  Consistency #25% 07% Temperature 110*0 ppO 0.68MPa 2  1  JO-  %  N  a  (  3  H  O  2.5% NaOH > , o "O-  5  15  60  30  3.5% NaOH  80  Time, m Figure 2.18 Effect of alkali charge on viscosity drop [Liebergott et al., 1985]  Similar to temperature, alkali has also been found to have a strong impact on cellulose degradation. Increasing alkali charge will decrease pulp viscosity significantly as shown in Figure 2.18. Moreover, the effect of suspension consistency is minor, as shown in Figure 2.17 and Figure 2.18. Increasing C from 7% to 25% only increases delignification slightly. m  2.5.3  Oxygen Pressure In general, the effect of oxygen pressure is small in comparison with the effects of alkali  charge and temperature [McDonough, 1986]. However, increasing oxygen pressure will increase oxygen solubility in the liquid phase and thus the driving force for oxygen mass transfer, both in the oxygen mixer and in the retention tower. Maintaining a high oxygen pressure will maximize the delignification rate. The latter will depends on the tower specifications that limit the operating pressure allowed. The increase in delignification rate as O2 pressure is increased is shown in Figure 2.19.  Chapter 2: Literature Review  42  TIME, frrtri  «~f  o.o  1  too  r  1  20.0 so.o  1  *o.o  TIME (MIN)  T  1  50.0 60.0  Figure 2.19 Effect of oxygen pressure on delignification rate [Hsu and Hsieh, 1987,1988]  2.5.4 Consistency Consistency is a process variable that is less likely to be adjusted due to its far-reaching process design implications. In spite of that fact, the effect of consistency at fixed alkali charge is relatively small. Increasing consistency results in a moderate increase of both the delignification and carbohydrate degradation as a result of the associated increase in alkali concentration. These effects were shown previously in Figure 2.17 and Figure 2.18.  2.5.5  Washing and black liquor solids carry-over One of the important objectives of oxygen delignification is to reduce the environmental  impact of bleach plant effluent as described by A O X , COD, color, and BOD. However, in order to achieve the maximum benefit of oxygen delignification, good washing is required to remove any dissolved material from the digester that would affect the reaction selectivity [Iijima and  Chapter 2: Literature  Review  43  Taneda, 1997; Allison et al, 2000; Genco et al, 2000; Vuorenvirta et al, 2001]. Figure 2.20 shows the effect of cooking carry-over to performance of an oxygen delignification stage. The organic materials in the carry-over did not affect the delignification rate in the first (initial) phase because the rate of delignification is still high and there are excess alkali and oxygen in the system. However, the delignification rate in the second (final) phase would be lower than in the first because the excess alkali was consumed.  17  ! 1 1  1 >  15  50  with c arryov sr  1%  <B -O  1  &S40 c o 30  w i t h o i t c a m ./over  E 13 \  z RJ Q. Q.  •> . .  20 • •) 1. . . . - • - l l  1  2  —  i  3  4  A* * " ^ • ^ without carryover  10  9 7  iI  %  11  ro b£  i «n  •  0  carryover ( p H 1 3 )  4—  ••  10  5  ""A., carryover ( p H 7 )  :  20  30  40  50  60  70  Reaction time (min)  NaOH on pulp (%)  Figure 2.20 Effect of cooking carry-over to kappa number and delignification (kappa #16.7 HW kraft pulp, 10% consistency, 2% NaOH, 3% 0 , 60 minutes reaction, 100°C) [Iijima & Taneda, 1997] 2  Iijima and Taneda [1997] further investigated the effect of C O D carry-over both from the cooking filtrate (black liquor) and from the oxygen-stage filtrate. They reported that at the same level of COD, the filtrate from the cooking stage has a more detrimental effect on delignification than the filtrate from the oxygen stage (the filtrate recycled after the oxygen stage has already seen an oxygen stage and is more oxidized than that coming from the brown stock system). Therefore, the delignification efficiency is not only dependent on the C O D level of the carryover but also on the character of the dissolved organic material in the carry-over. The reason for these effects can be explained as competitive consumption of both oxygen and caustic between  Chapter 2: Literature Review  44  the lignin in the pulp and dissolved materials in the entrained liquor. Black liquor carry-over contains unoxidized structures (dissolved lignin) that competes with pulp for oxygen and sodium hydroxide.  13 without carryover  12  "*k. carryover (pHl3)  .29 3  <  •A., carryover (pH7)  11  X Q.  as  •  10  r  without carryover "^k carryover (pH 13) ***.. carryover (pH7)  _  1  ~o 'in  9  0  10  20  30  40  50  60  70  8  k• 0  10  20  30  40  ~  50  i  | . 1  60  70  Reaction time (min)  Reaction time (min)  Figure 2.21 Profile of residual alkali and pH during oxygen delignification reaction (kappa #16.7 HW kraft pulp, 10% consistency, 2% NaOH, 3% 02, 60 minutes reaction, 100°C) [Iijima & Taneda, 1997]  In addition, Iijima and Taneda also observed that even though cooking carry-over provides additional alkali shown as a higher value of residual alkali (Figure 2.21 left), the alkalinity (pH) of the solution was significantly lower than that of the carry-over free system as shown in Figure 2.21 (right). These effects suggest that there would be a buffering effect of the dissolved organics in the carry-over, possibly carbonate [CO3 "] and bicarbonate [HCO3"] carried 2  over from the cooking stage. From Figure 2.21, it can also be concluded that if the pH of the system were less than 9.5, a pH at which most of the phenols are not ionized, the oxygen delignification would not proceed further. The presence of carry-over from the cooking stage will also increase the overall oxygen requirement due to its consumption by the dissolved organic and inorganic compounds, including sulphur compounds [Iijima and Taneda, 1997].  Chapter 2: Literature Review  45  2.6  Oxygen and Alkali Consumption While there have been intensive studies describing the reaction of pulp with oxygen and  alkali, not much research has focused on consumption of the chemicals, particularly the alkali consumption. This is due to the complex nature of the chemistry of oxygen delignification and the lack of suitable methods for following the changes in alkalinity. Berry et al. [2002] calculated oxygen consumption in a laboratory-scale oxygen reactor by measuring the decrease in pressure as the reaction progresses. As can be seen in Figure 2.22, the overall oxygen consumption per unit kappa number reduction gradually decreased from 0.087% to 0.055% as the temperature increased from 75 to 110°C. No explanations were provided as to why higher reaction temperatures consumed less oxygen.  3 % oxygen; 618 K P a ; 3 % N a O H  0.10  r  0.0S5  75  85  95  110  Temp. ° C  Figure 2.22 Effect of temperature on oxygen consumption [Berry et al, 2002]  Berry et al. [2002] also reported that 60% of the oxygen consumption occurred in the initial reaction phase and that most of the change in the measured oxygen consumption occurred in the initial phase. The initial phase of kappa number reduction consumes more oxygen per unit  Chapter 2: Literature  Review  46  kappa number reduction than the second phase. These results suggest that the second phase of reaction is predominantly alkali leaching and the effectiveness of delignification is dependent on the extent of reactions occurring in the initial phase. The industrial oxygen delignification survey by Bennington and Pineault [1999] showed that the oxygen charge applied in industrial systems varied from 0.7% to 2.5% on pulp. Oxygen consumption in a laboratory reactor was reported to vary from 0.05 to 0.064%> kg oxygen per unit kappa number reduction per kg pulp [Corbett, 1976; Berry, 2002] while the reported oxygen consumption in commercial systems varies from 0.08 to 0.19% per unit kappa number decrease [Seifert, 1980; Evans, 1979b; McDonough, 1996]. This is expected since in commercial systems, there are losses due to reactor venting and entrainment with the pulp leaving the reactor [McDonough, 1996]. Also, significant quantities of spent cooking liquor are carried forward to the oxygen stage which will consume additional oxygen as was discussed previously. Violette [2003] reported that 0.135%) NaOH was consumed per kappa number drop. A recent publication by Jiang et al. [2004] who measured alkalinity in filtrates from oxygen delignification stages reported a significantly higher value of alkali consumption up to 0.19%. Both of these results were measured using laboratory reactors. As was the case for oxygen consumption, these values of alkali consumption are expected to be higher in the commercial processes due the presence of spent cooking liquor carry-over.  2.7  Mass Transfer in Oxygen Bleaching Mass transfer is an important consideration in most of oxygen bleaching stages because  the reaction system consists of three phases [Hsu and Hsieh, 1988; Yaldez and Stark, 1996;  Chapter 2: Literature Review  47  Iijima and Taneda, 1997; Bennington and Pineault, 1999]. Oxygen must cross the gas-liquid interface, diffuse through the liquid film surrounding the fiber, and finally diffuse into the fiber wall before reacting. Any of these steps can be rate determining depending on the relative rates of mass transfer and chemical reaction. The mass transfer problem is aggravated by the low solubility of oxygen in aqueous solutions containing sodium hydroxide [McDonough, 1996]. To ensure that sufficient oxygen is available during the course of reaction, the partial pressure of oxygen in the gas phase must be maintained at a high enough level to ensure increased solubility in the liquid phase. Initial oxygen pressures at the mixer range from 400 kPa to 1000 kPa, with the pressure differential between the top and bottom of the tower being 200-400 kPa.  Figure 2.23 Mass transfer in oxygen delignification [Iribarne & Schroeder, 1997]  The rate of mass transfer of dissolved oxygen to the liquid phase is determined by the gas-liquid interfacial area (a), which would depend on the tower design, oxygen charge, consistency, and oxygen pressure. In the case of a medium consistency mixer, it is difficult to obtain contact between oxygen gas molecules and the fibres at 10% consistency because the  Chapter 2: Literature Review  48  fibres are surrounded by an immobile water layer. Therefore, fluidization of the pulp suspension during mixing/contacting with oxygen is considered a prerequisite for oxygen delignification. Figure 2.23 shows the path oxygen needs to follow in a pulp suspension before it reacts with a lignin macromolecule inside the fiber wall. Berry et al. [2002] have studied the effect of mixing on oxygen solubilization and consumption. They investigated how the mode of mixing, the period of mixing, and mixing intensity affected the rate of oxygen dissolution and also the delignification performance of a single-stage oxygen delignification system using a laboratory oxygen reactor. Two types of experiments were conducted using an alkaline solution to measure oxygen dissolution and using a pulp suspension to measure the extent of delignification.  750 700  f 1500 RPM (4 sec) with water  no high shear mixing with water of  650  S  600  550 500  2400 RPM (4 sec) with water  1  2  3 4 Time, min.  2400 RPM (4 sec) wfth 3.5% NaOH  5  6  7  Figure 2.24 Effect of mixing on oxygen solubilization in water and NaOH solution [Berry et at., 2002]  In the first experiment, they recorded the solubilization of oxygen in water and 3.5% NaOH solution from the decrease in total pressure in the reactor immediately after mixing was started. They measured an immediate distribution of the oxygen using high intensity mixing at 2400 rpm as illustrated above in Figure 2.24. At 1500 rpm, there is good but not complete initial  Chapter 2: Literature Review  49  mixing and it took another 2 minutes to achieve the same oxygen uptake as was achieved with initial mixing rate of 2400 rpm. Also, without initial high intensity mixing, 5 minutes of continual mixing at 100 rpm was required to achieve the same uptake of oxygen.  60  49.7  50  44.6  o  47.2  41.1 40 4  "O  29.1  g. 30 Q_ to  20 <D  4  ro Q 104  Mode of mixing applied following an initial mixing Figure 2.25 Effect of secondary mixing (mixing after initial high-intensity mixing at 2400rpm) on the degree of delignification: Mode 1, no mixing; Mode 2, mixing at 240 rpm for 4 seconds after 20 minutes; Mode 3, mixing at 400 rpm for 4 seconds every 5 minutes; Mode 4, mixing at 400 rpm for 4 seconds every 20 seconds; Mode 5, mixing at 60 rpm continuously [Berry et al, 2002]  In their second experiment, using Canadian interior softwood pulp (kappa number, 32; CED viscosity, 51.2 mPa.s), Berry et al. [2002] investigated how the mode of mixing during oxygen delignification could affect the degree of delignification achieved (Figure 2.25). Experiments were conducted at 95 °C, 618 kPa oxygen pressure, 3% oxygen charge, and 2% NaOH charge. They reported that delignification was 29.1% when no further mixing was used after the initial high-intensity mixing at 2400 rpm (mode-1 in Figure 2.25), while 49.7% delignification was obtained when the pulp was mixed every 20 seconds at 400 rpm for 4  Chapter 2: Literature  Review  50  seconds for the 30 minutes duration of the reaction time (mode-4). A comparable 47.2% delignification was obtained when the pulp was continuously mixed at 60 rpm after initial high intensity mixing (mode-5 in Figure 2.25).  43  !  !  |41  I  40  |  39  ro  i  5 s mixing 10 s mi>ing  42  .,„_«  ........  *  j§) 38 Q 37 36  500  1000 1500 2000  2500  3000  Mixing speed (rpm)  Figure 2.26 Mixing intensity vs degree of delignification [Iijima & Taneda, 1997]  Moreover,  Iijima and Taneda [1997] (Figure 2.26)  also reported that  37.1%  delignification (using hardwood kraft) could be attained without any mixing or pulp fluidization through 30 minutes reaction with 1% NaOH, 1.5% oxygen charge, 10% consistency, and 100°C reaction temperature. However, they reported that when using high-intensity mixing, an increase of mixing speed from 1000 rpm to 3000 rpm could increase delignification up to 2%; this effect is more pronounced at longer mixing periods, up to 10 seconds. Also, Bennington and Peneault [1999] have shown that improving gas contacting during mixing has enabled a number of mills to increase oxygen delignification performance, obtaining significant chemical savings in subsequent bleaching stages. Studies by Iijima and Taneda [1997], Bennington and Peneault [1999], and Berry et al. [2002] all underline the significance of mixing in supporting delignification, however initial  Chapter 2: Literature Review  51  high-intensity mixing alone is not good enough to drive the delignification reaction to completion, therefore mass transfer in both industrial oxygen mixers and oxygen towers determine the degree of delignification achieved in industrial systems. Gas-liquid mass transfer is normally characterized using the volumetric gas-liquid mass transfer coefficient {kid). This coefficient depends on the gas-liquid mass transfer coefficient (kf) and the specific gas-liquid interfacial area (a). However, as it is difficult to measure ki and a independently, their product is usually measured. Together, kia and the concentration driving force determine the rate of mass transfer per unit volume from the gas to the liquid phase.  2.7.1 Gas-Liquid mass transfer in medium consistency mixers Rewatkar and Bennington [2000] measured the volumetric gas-liquid mass transfer coefficient for low and medium consistency gas-fibre suspensions contacted in a commercial laboratory-scale pulp mixer. They found that gas-liquid mass transfer was significantly reduced in pulp suspensions, even for low suspension concentrations. Part of this reduction was associated with dissolved components leached from the fibres to the liquid phase which could account up to 30% reduction when compared with distilled water. A correlation for kyoi was developed for fully bleached kraft (FBK) fiber suspensions:.  k a = 1.17 x 10  -4  L  V  26  g  exp {-0.386 * C }  [2-15]  m  where s is the mixer power dissipation (W/m ), <j) is the gas void fraction, and C is the fibre g  m  mass concentration (as a fraction) covering the range from 0.0 < C < 0.1 (up to 10%) m  consistency. As we can see from equation (2-6), ki.a will increase with increasing power  Chapter 2: Literature Review  52  dissipation (achieved by increasing the impeller rotational speed) at all fibre concentrations. Figure 2.27 shows an increase in kia as the rotational speed of the mixer increased for all fibre concentrations. However, kia became less sensitive to mixer speed as the suspension mass concentration increased. This was attributed to the increase in apparent viscosity of the suspension, which reduced the level of turbulence in the liquid and favored formation of stable gas cavities behind the rotor blades. Together these factors decrease the interfacial area and caused a reduction in kia [Rewatkar and Bennington, 2000].  0.8  0.6  0.2  0.0 0.00  0.02  0.04  0.06  0.08  0.10  C (W/w) m  Figure 2.27 k a vs pulp consistency (C ) at different mixing rotational speed [Rewatkar & Bennington, 2000] L  m  2.7.2 Gas-Liquid mass transfer in pulp retention towers Berry et al. [2002] have shown that initial high-intensity mixing alone is not sufficient to drive the reaction to completion; therefore, understanding the role of oxygen mass transfer in the retention tower is critical to maximize the delignification potential of industrial oxygen systems. Information on the oxygen mass transfer rate in the liquid phase of pulp retention towers is not  Chapter 2: Literature Review  53  well documented and thus the extent to which gas-liquid mass transfer in residence tower influences oxygen delignification is unknown. The only information on this has been reported by Rewatkar and Bennington [2002] for a tower configured as a bubble column. Rewatkar and Bennington [2002] measured the gas hold up and gas-liquid mass transfer coefficient  in a pilot-scale  column as a function of suspension  mass concentration  (0.0 < effraction) < 0.09) and superficial gas velocity (0.0015 < U , mls< 0.05). Tests were g  conducted at room temperature and atmospheric pressure. They reported the gas-liquid mass transfer coefficient increasing as suspension mass concentration increased from C = 0.06 to m  0.09 (6 to 9%) as shown in Figure 2.28.  0.1  0.01  42. •* 1E-3  1E-4 0.0 0  0.01  0.02  0.03  0.04  0.05  0.06  U (m/s) g  Figure 2.28 k a vs superficial gas velocity at various pulp consistency C [Rewatkar & Bennington, 2002] L  m  Based on industrial data, the average gas superficial velocities relative to a stationary pulp suspension are expected to vary from zero to 0.004 m/s. In this range, as can be seen from Figure 2.28, the gas-liquid mass transfer coefficient (kLa) in a pulp retention tower could change  Chapter 2: Literature Review  54  dramatically with changes in superficial gas velocity, from a low of 0.001s  1  to a high of  0.007 s . Changes infaawith superficial gas velocity could mean that the in-tower mass transfer -1  would be sensitive to changes in both oxygen charge and tower operating pressure. However, the extent of non-uniform gas flows through industrial towers in not known. In the laboratory, gas flow was well distributed across the column cross section, but this may not be the case in industrial oxygen towers [Rewatkar and Bennington, 2002].  Hornsey et al. [1998] measured gas-phase residence times in industrial oxygen towers. They reported that gas phase residence time was only 20-40% that of the pulp. Gas was found to travel rapidly through the tower and was detected after only three minutes of the full 62-minutes pulp residence time as illustrated in Figure 2.29. As a result, the superficial gas velocity in industrial towers is expected to vary as was mentioned previously. However, at this time we have no way of knowing how the non-uniformity of gas flow through industrial oxygen tower  Chapter 2: Literature Review  55  affects the gas-liquid mass transfer (k a). The effects of gas-liquid mass transfer in retention L  tower will be further investigated and discussed later in chapters 3 and 4. Due to the complex nature of lignin reactions coupled with several critical issues in pulp bleaching such as lignin leaching and kappa number (lignin) determination, it has been difficult to quantify the relative significance of mass-transfer in oxygen mixers and retention in oxygen towers to industrial delignification. The residence time in an industrial mixer is typically around one second, with kia about 1 s" for medium consistency mixer operated at 10 W/m . On the 1  6  3  other hand, kia in retention towers could be as low as 0.001 s" with typical residence times in 1  the order of an hour. Overall, the actual mass transfer achieved will depend on the net reaction rate of the pulp which depends on the amount and nature of the remaining lignin in fibre and other mass transfer resistances in the system. Therefore, it is part of the objective of this modelling work to gain a better understanding on the role of both oxygen mixers and retention towers in industrial oxygen delignification systems.  2.8  Maximum Lignin Removal in Oxygen Delignification Ways to maximize lignin removal using oxygen delignification has been a subject of  interest as it would allow reducing of the expensive chemicals needed in subsequent bleaching stages. However, extending industrial oxygen delignification beyond 50% can cause severe cellulose degradation resulting in the deterioration of pulp viscosity and strength characteristics [McDonough, 1995]. A number of studies have focused on elucidating the mechanisms responsible for limiting the oxygen delignification process. Studies with fibre suspension using a laboratory-scale oxygen reactor have shown that residual lignin or lignin-like compounds, i.e.,  Chapter 2: Literature Review  56  hexenuronic acid, cannot be removed beyond 75% of the original level, although the first-phase of the oxygen delignification reaction is able to remove nearly half of the original resident kraft residual lignin [Lucia, 2003]. Moreover, Lucia [2004] further demonstrated that the kappa number of softwood kraft pulp could not drop below 7 without incurring cellulose degradation during oxygen delignification despite the application of selectivity enhancement agents. The main factor limiting lignin removal during the oxygen delignification process is the penetration of oxygen and oxygen-active species into the lignin matrix along the microfibrils in the pulp. The matrix structure of carbohydrate and the lignin carbohydrate complex constitute the main barriers against oxidative reactions. The hemicellulose in the pulp is part of the lignincarbohydrate complex, and the robust nature of the native cellulose crystal structure in the pulp fiber is partly responsible for the barrier to lignin removal during oxygen-alkali treatment [Lucia, 2003]. Furthermore, Chirat and Lachenal [1998] have also reported that a fraction of residual lignin in kraft pulp will never dissolve in multi-stage oxygen treatment carried out under conventional oxygen delignification conditions. They performed oxygen delignification for both softwood and hardwood, and in all cases they found that delignification almost stopped and reached its floor kappa level after 3 successive oxygen stages with total of 75%> of delignification for softwood and 60%) for hardwood pulps, respectively. They proposed that the presence of lignin-carbohydrate linkages as the main reason of this limits of delignification which agrees with the results of Lucia [2003, 2004].  Chapter 2: Literature  Review  57  Chapter 3 Model Development  3.1  Introduction Modeling of oxygen delignification processes in pulp processing operations has been  described in several earlier studies covering both steady-state and dynamic simulations [Kovasin et al, 1987; Myers et al, 1989a; Ulinder, 1995; Kumar & Gustafson, 1998; Genco et al, 1998; Pageau, 2000; Gendron et al, 2002, and van Heiningen et al, 2003]. A l l of the models were developed using fiber suspension delignification kinetics to model the behavior of industrial oxygen delignification systems. In the first steady-state modeling approach, by Kovasin et al [1987], mass transfer effects were not taken into consideration due the lack of correlations for mass transfer coefficients in oxygen delignification reactors. Kovasin et al. assumed that mass transfer effects were implicitly included in the reaction kinetic model of Olm & Teder [1981]. On the other hand, Myers et al. [1989a] and Ulinder [1995] used dynamic versions of existing steady-state simulation packages such as GEMS and I D E A S ™ to model a retention tower for oxygen delignification. No specific type of delignification kinetics was described in the work of either Myers or Ulinder as they were focusing more on control issues. Kumar & Gustafson [1998] used statistical modeling based on multivariate techniques (i.e. factor analysis) to control process variables in oxygen delignification. They found that the kappa number variability out of the digester was the major source of kappa variability in oxygen delignification. They suggested that better digester control could lead to an improved oxygen  Chapter 3: Model Development  58  reactor performance. Genco et al. [1998] later on followed the approach of Kovasin et al. [1987] to model industrial oxygen delignification systems of mixed southern hardwood pulp using reaction kinetics developed in their own laboratory [Guven et al., 1996]. The delignification kinetic expressions of Olm & Teder [1981] and Guven et al. [1996] were developed in laboratory batch tank reactors. Olm and Teder [1981] used separate oxygenation of the liquor and ultra-low consistency (0.5%) fibre suspensions while Guven [1996] applied constant mixing throughout the whole experiment to overcome mass transfer limitations. A characteristic of the kinetic expressions developed using pulp suspensions is to lump mass transfer and reaction kinetics into a single global kinetic model. The equations obtained in this way are inherently biased toward the mixing conditions present in the actual oxygen delignification systems used. Consequently, the modeling work of Kovasin et al. [1987] and Genco et al. [1998] would unlikely be able to capture the effects of gas-liquid mass transfer in industrial mixers or oxygen retention towers where the mass transfer rates could be significantly different. Further modeling work on industrial oxygen delignification was done recently by van Heiningen et al. [2003]. They extended the work of Kovasin et al. [1987] and Genco et al. [1998] by examining the effect of mass transfer (faa) on delignification in both medium-consistency mixers and oxygen retention towers, which form part of an industrial oxygen delignification system. In their model, van Heiningen et al. used the delignification kinetics measured for a pulp suspension as obtained by Iribarne and Schroeder [1997] and the gas-liquid mass transfer effect measured for pulp suspensions by Rewatkar and Bennington [2000, 2002]. They reported an unmeasurable amount of kappa number decrease across the high-intensity mixer (~10" kappa) 4  and a negligible decrease in kappa number at the outlet of the oxygen retention tower, despite a  Chapter 3: Model Development  59  10-fold increase in mixer power from 1x10  W/m to 1x10  W/m . They concluded that  industrial oxygen mixers are not effective in dissolving oxygen and further suggested that mixing is not an important unit operation in industrial oxygen delignification processes. Past oxygen delignification modeling work has incorporated the delignification kinetics of pulp suspensions to model kappa number reduction in industrial systems. The reduction in kappa number occurs via a rapid initial delignification step followed by a longer period in which the kappa number decreases fairly slowly. One can postulate that the rate of delignification would vary greatly, depending on the type and composition of the lignin being reacted. Structures such as stilbene would react with oxygen on the order of seconds whereas condensed structures like propylguaiacol could take up to hours to react. The fast reacting types of lignin structures most likely account for the early rapid delignification step while the slow structures account for the long slow reaction period. In the development of delignification kinetics with pulp suspensions, studies normally were focused on determining the effect of process conditions, i.e., reaction time, temperature, oxygen pressure, alkali and oxygen concentration, on the extent of delignification achieved. This was done by varying one of the process variables while keeping the others constant. A nonlinear relationship between the kappa number and the process conditions was then developed using nonlinear least-squares programming techniques. The reaction period, the sampling interval, and the time at which the first sample was taken vary from one experiment to another. Iribarne and Schroeder [1997] took their first sample at 6 minutes, Myers and Edwards [1989] give a data point after 2 minutes, Guven et al. [1996] measured their first kappa number after 5 minutes of reaction. The time interval taken after first sampling also varied, which was typically in the range of 5 to 10 minutes; some researchers [i.e.  Chapter 3: Model Development  60  Guven, 1996] even reported that only two data points were used, i.e., the first one at 5 minutes and the second one at the end of reaction period. With the nature of the development of delignification kinetics described above, a fitting correlation of experimental data into single or parallel equations for the delignification kinetics would not be able to capture any early rapid delignification rate. The reason for this is because no experimental points fall within the region of rapid delignification, particularly in the first minute and more importantly, the first second of reaction where the reaction of fast lignin is likely taking place in the high-intensity mixers. To overcome the limitation of pulp suspension kinetics in capturing the phenomena that take place during the brief period of initial high-intensity mixing (which has been reported to have significant impact on the dissolution of oxygen in the liquid phase and the final degree of delignification achieved [Iijima & Taneda, 1997; Bennington & Pineault, 1999; Berry et al., 2002]), general lignin model compound kinetics are developed in this work using the experimental results of Ljunggren and Johansson [1990a, 1990b, 1994].  3.2  Model Formulations We developed our model using the kinetics developed for lignin model compounds. The  actual residual lignin structure left in fiber wall was modeled as a series of lignin compounds connected to one another as illustrated in Figure 3.1, with their compositions approximated using information available in the literature. For simplicity, we divided the residual lignin structures into five distinct lignin groups based on reactivity under oxygen-alkali conditions. The first lignin group is called 'very fast  Chapter 3: Model Development  67  lignin', this group was represented by the kinetics of stilbene model compounds and their relative abundance in kraft pulp. The second structure was 'moderately fast lignin' that was taken also from known kinetics of enol-ether model compounds. The third and fourth structures were called 'slow lignin' and 'very slow' lignin that were taken from available kinetics of P-aryl-ether and dipropyl-biguaiacol model compounds, respectively. The last group was defined as 'stagnant lignin' to account for the non-reactive lignin structures that are not removable under typical commercial oxygen delignification conditions.  Figure 3.1 Model representation of the actual lignin structures |Jurasek, 1995]  The reason we decided to break down the actual native lignin structures into five different lignin groups is because there was not enough information in the literature to generate more than five distinct kinetic expressions. Each lignin model compound group requires a separate kinetic expression. However, as the number of studies using lignin model compounds increases, the total number of model compound groups incorporated in the model can be increased accordingly.  Chapter 3: Model Development  62  The ratio of lignin in the five model compound groups is proportional to the composition of the native lignin and also to the initial pulp kappa number. Table 3.1 shows the proposed composition (x,) that we use in the model. The stilbene (very fast) and vinyl-ether (fast) group compositions were specified using information of their relative abundance following kraft pulping (see Table 2.3). They account for x,= 5% and x = 2% of the total residual lignin, 2  respectively. Similarly, using the data in Table 2.3, the composition of 'moderately slow lignin' was specified by summing compositions from three uncondensed types of linkages: (3-0-4, (3-1, and P-P. It accounts for x = 20% of the total residual lignin. 3  Table 3.1 Proposed composition of residual lignin going into oxygen delignification stages Linkage  Type  Group  Proposed (*,)  1  Stilbene  highly reactive  very fast  5  2  Vinyl Ether  reactive  fast  2  uncondensed  slow  20  3 4  5-5  condensed  very slow  48  5  Stagnant  not reactive  stagnant  25  Total  lOO  Furthermore, in order to specify the 'very slow' and 'stagnant' lignin compositions, we used the available literature studies of Chirat et al. [1998] and Lucia [2003] who found that typical oxygen delignification processes cannot remove softwood lignin beyond 75%> of the original  level  without  incurring  cellulose  degradation  (see  section  2.8  on maximum  delignification). Hence, the composition of 'stagnant' lignin was specified as x ~ 25% of the 5  total residual lignin. Thus, 48%> of residual lignin (the balance of the so-far unspecified lignin, x ) 4  was assumed to have condensed structures and was grouped in the 'very slow lignin' category.  Chapter 3: Model Development  63  The kinetics of the 'very fast' stilbene, 'fast' vinyl ether, and 'moderately slow' P-arylether structures were developed from studies of 4,4'-dihyroxy-3,3'-dimethoxy-stilbene, guaiacoxy-4-hydroxy-3-methoxy-styrene,  and  4-hydroxy-3-methoxy-phenyl-glycol  [3-  model  compound, respectively [Ljunggren & Johansson, 1990a]. The 'very slow' 5-5 linkage was taken from 4,4'-di-n-propyl-6,6'-biguaiacol model compound study [Ljunggren & Johansson, 1990b].  3.3  Delignification Kinetics Ljunggren and Johansson [1990a, 1990b] investigated the effect of process conditions,  i.e., temperature, oxygen pressure, and pH on the observed reaction rate of lignin model compounds. The studies were done using the constant-concentration method in which all reaction conditions except for the model compound concentration, were kept nearly constant. A buffer solution was added to keep the pH constant during the reactions. Continuous bubbling of oxygen was used to maintain a constant oxygen concentration throughout the course of reaction. Experiments were conducted at both low and high oxygen partial pressures. At atmospheric oxygen pressure, the oxidation of model compounds was performed in a polyethylene bottle equipped with a gas sparger, several condensers, and a magnetic stirrer placed in a thermostatically controlled water bath. The model compound was dissolved in an organic solvent (7% ethanol or 10% dimethylformamide, DMF) to assure solubility. Reaction was started by adding the substrate solution containing model compound to the temperature-controlled oxygen-saturated pH-buffered pre-adjusted aqueous solution. For the high oxygen pressure experiments, an autoclave equipped with gas and liquid inlet and liquid outlet sample port was used. In this case, the reaction was started immediately after the high-pressure oxygen gas was introduced into the reactor.  Chapter 3: Model Development  64  The  extent of reaction was monitored by measuring the amount of lignin model  compound remaining as a function of time and the amount of certain reaction products formed. Samples were withdrawn from the reaction mixture and measured for concentration using liquid chromatography. The lignin model (L) reacts with oxygen at the rate of the reaction given by:  d[L']_  Rate  k.[o ][r]  [3-1]  2  dt  Under constant oxygen concentration, the reaction becomes a pseudo-first-order-reaction with the rate equation:  4l r  The  r  i  [3-2]  logarithm of the percentage of substrate reactants remaining is plotted against  reaction time and in every case it should give a straight line indicating afirst-orderreaction. From the slope of the plotted lines (e.g. as in Figure 3.2), the pseudo-first-order rate constants for each lignin model can be determined. The pseudo-first-order behavior was further confirmed by the linear correlations of it =0.991 in most of the runs [Ljunggren and Johansson, 1990a; 1990b]. 2  Remaining stilbene, % Yield Vanillin , mol %  16 20 Reaction time, min  k  6  8  10  Reaction time (minutes)  Figure 3.2 Degradation of stilbene model compound at different pH (left) with first order plot of the model compound reaction rate vs reaction time (right) [Ljunggren & Johansson, 1990a]  Chapter 3: Model Development  65  We used the first-order reaction rate constant data reported by Ljunggren and Johansson [1990a, 1990b] and developed general delignification kinetic expressions that were a function of temperature, alkali concentration, and oxygen concentration in the liquid phase of the form:  -d[L]ldt = k[0 ] [OH-J [L]  [3-3]  m  2  The reaction rate coefficient, k, depends on the reaction temperature and is given by Arrhenius equation:  k = A exp  \  [3-4]  RT  All of the required kinetic parameters, i.e., A, EA, m, and n in equations (3-3) and (3-4) were determined using standard non-linear least-squares  fitting techniques. A separate kinetic  expression was developed for each lignin group using a representative model compound. Hence, the number of lignin groups determines the number of kinetic expressions used in the model. The following equations illustrate the basic set up of our delignification kinetic model:  4 A] - A exp x  dt  d[L ] 2  dt  d[L„]_ dt  = A exp 2  A exp n  RT _ -EAI  RT  -E •in  RT  [(trior? fc] [3-5]  [(tJ"[OH-f[L„]  with the total delignification calculated as: d[L]_ dt  r  d[L^ dt  +\  Chapter 3: Model Development  l 2]] + dt d L  . . +  \ 44]1 dt  [3-6]  66  As can be seen from Equations (3-5) and (3-6), the total number of lignin model compounds that could be incorporated into the model is unlimited; it could be up to any number with each lignin model compound having its own composition (x ..x ) and corresponding v  n  kinetic expression. However, in this work, we will use only five lignin model compounds as was mentioned previously in section 3.2. The five groups chosen represent the range of reaction rates expected for oxygen delignification reactions in pulp. We could not find sufficient experimental results in the literature to generate more than five model compound kinetic expression (four reactive lignins plus one un-reactive stagnant lignin). Nevertheless, with its capability to be easily expanded to a greater number of model compounds, a more robust and accurate prediction of the delignification behavior of actual residual lignin is possible in future studies, not only for oxygen bleaching stages, but also in other pulp processing operations.  Table 3.2 Kinetic parameters acquired from lignin model compound studies Frequency factor (A )  Activation energy  Very fast  1.21E+15  77.O  Fast  2.19E+15  Slow Very slow  Lignin Group  (£ ),kJ/mol  Reaction order (ra/n/q) [OHT  W  O.63  0.28  1  80.1  1-37  0.45  1  3.17E+10  56.1  1.46  0.31  1  3.25E+08  43-3  1-73  0.12  1  A  [OJ  m  q  Table 3.2 gives the kinetic parameters for each lignin model compound used in the model. The parameters are acquired by performing least-squares fitting of the observed first-order reaction rate constants to the process conditions as reported by Ljunggren and Johansson [1990a, 1990b]. The reaction order with respect to lignin was set to unity (q = 1) in the four model compound used. More details on the fitting procedures, plots, and results are available in Appendix-A.  Chapter 3: Model Development  67  3.4  Model Development The basic idea of the model was to group lignin structures based on their reactivities  toward oxygen. We call this approach the Lignin Model Compound (LMC) method. Using this approach, the wide distribution of reactivities between lignin structures, rather than universally averaged into one single expression (as is typically done for the kinetics developed for pulp suspensions), are treated concurrently and independently giving a better representation of the behavior of the actual residual lignin structures. However, by using the lignin model compound approach, we have to neglect the branching and crosslinking nature of native lignin. These natural characteristics of native lignin might cause variations in terms of accessibility of particular reactive lignin moieties toward oxygen and alkali resulting in somewhat different rates of delignification. Moreover, native lignin-linkages are heterogeneously distributed over the lignin and are connected in a wide variety of differently branched configurations. Depending on how these lignin-linkages are connected to the bulk lignin, the reactivity of each individual linkage could be different from one to the next, even if the linkages are of the same type. The reason for this is because lignin reactivities are affected not only by their own distinct structure but also by the structures adjacent to them. Even so, due to the large differences in the magnitude of the rate of delignification each lignin model compounds has, these effects can be considered insignificant compared to the intrinsic variability that each lignin model possesses. Another advantage of using the L M C approach is that it allows the composition of the lignin to be changed to suit differences that each type of wood (hardwood, softwood) species might have. Also, since the composition of lignin is found to change with the type of process that it experienced (see Table 2.3), depending on the conditions and chemicals that a particular  Chapter 3: Model Development  68  process used, adjustment to the lignin composition can be done appropriately in the model to give a precise prediction between the actual and the predicted delignification profile. As has been mentioned before, we divided the native residual lignin into five (four reactive and one un-reactive) distinct lignin structures which have large differences in reactivity towards oxygen from one structure to another. We can see a representation of these reactive groups of lignin in Figure 3.3 where each of the lignin fractions, i.e., very fast, fast, slow and very slow lignin are treated independently.  Figure 3.3 Differentiation of native lignin into four distinct reactive lignin structures  The total composition of lignin shown in Figure 3.3 adds up to 75% with the remaining 25%o considered as stagnant or 'floor' lignin. This 25% of stagnant lignin was taken from the work of Lucia [2003] who reported that residual lignin, under typical oxygen bleaching conditions, cannot be removed beyond 75%> of their original levels. The work of Chirat and  Chapter 3: Model Development  69  Lachenal [1998] also supports these findings. Another consideration for specifying one portion of lignin as stagnant lignin was based on the fact that the kappa number used as a measure of delignification can also measure the non-lignin structures (i.e. hexenuronic acid) which are not removed under O 2 delignification conditions. Acknowledging the presence of 'stagnant' lignin, provides justification in the model that some portion of 'lignin' cannot be delignified, not only due to the intrinsic nature of the remaining residual lignin itself, but also because a portion of the kappa number does not correspond to lignin and so will not react during oxygen delignification. The detailed schematic flowsheet of the model can be seen in Figure 3.4 below.  Wood/Pulp  X Carbohydrate  Lignin  Veiy Fast  (Viscosity in)  Residual  Dissolved  (Kappa in)  (Carry Over in)  Slow  Fast  Stagnant  Delignification Kinetics  Very Slow  Operating Condition  Carbohydrate Degradation  Final Output  Figure 3.4 Schematic flowsheet of the model (model inputs are shown in bold)  The methodology of the model is to divide the wood (pulp) into its major components, i.e., lignin and carbohydrate. Lignin itself will be divided into two major fractions, one is residual lignin that is left in the fiber and the other is dissolved lignin that is carried over from the cooking  Chapter 3: Model Development  70  stages to the oxygen delignification stages (known as black liquor solids carry-over). The residual lignin will be further grouped into five major lignin constituents that we described earlier, namely the very fast, fast, slow, very slow and stagnant lignin. Similarly, dissolved lignin will also contribute to the very fast, fast, slow, very slow lignin and no stagnant lignin. Each type of lignin constituent will be treated independently according to its delignification kinetics that we developed from the lignin model compound studies. Figure 3.5 shows a schematic representation of the model. The variables that are required as inputs to the model are the kappa number and viscosity coming in to the oxygen delignification stage together with the operating conditions of both the high shear mixer(s) and oxygen tower(s). The operating parameters of the mixer include mixer power and mixer residence time. The operating variables of the retention tower include temperature, alkali and oxygen charge, pressure at the top and bottom of the tower, tower dimensions, and pulp consistency. The pulp residence time was calculated from the production rate, consistency, and tower dimensions. Retention T o w e r  h Out  Alkali Steam Oxygen  r  P u l p in  """""  v  r  - r  i  f  XX Mixer  Figure 3.5 Representation of mixer and retention tower in the model  Chapter 3: Model Development  71  We modeled the up-flow retention tower by dividing it into a large number of layers in which each layer was treated as continuous stirred tank reactor (CSTR). The implications of this CSTR approach will be discussed later in section 3.5. Calculations in both the mixer and retention tower were performed independently and sequentially, meaning the output from the mixer would become the input to the first layer of the tower and the output from the first layer of the tower would become the input to the second layer of the tower, and so on. Calculations were continued repetitively, one layer at a time, until the desired total pulp residence time (calculated from the pulp production rate and consistency) was reached. The volume of each CSTR layer was determined by the tower volume (calculated from the tower dimensions) divided by total number of layers in the model. Typically, the total number of layer was fixed at 100 since further increase will not give any significant changes to the output of the calculations obtained.  3.5  Assumptions Several assumptions were made in the governing equations used, including: the kappa  number and lignin composition relationship, oxygen and alkali consumptions, gas and pulp distribution in the high-shear mixer and retention tower, and oxygen mass transfer resistances. The decrease in the amount of lignin left in the pulp suspension as it reacts with oxygen is typically measured using the kappa number (K ) test. The kappa number is linearly correlated with the lignin content by the following relationship (TAPPI T-236 cm-85):  %Lignin = K * 0.147  [3-7]  Since the correlation of kappa number and lignin content is linear, we assumed that the correlation of kappa number and the amount of each lignin model compound is linear. For  Chapter 3: Model Development  72  example, if we specified that the amount of 'very fast' lignin in the pulp entering the oxygen delignification stage is 5% of the total lignin content in the pulp, then the amount of kappa number corresponding to that 'very fast' lignin will also be 5% of the incoming kappa number. Similarly, linear correlations were used in specifying the relationship between the kappa number and the composition of the 'fast', 'slow', 'very slow' and 'stagnant' lignin groups. As lignin was removed from the fibre, measured as a kappa number drop, chemicals, i.e., oxygen and alkali, were consumed in the delignification reactions. The rates of chemical consumption were assumed to be proportional to the rate of delignification expressed as grams of oxygen (yo ) and alkali (yNaOH) consumed per kappa number drop per kg of pulp. The specific 2  consumption rates were fixed throughout the simulation and were based upon typical values reported in the literature (see section 2.6). Much of the delignification reactions in oxygen bleaching take place in the retention tower following the mixer. Consequently, the oxygen retention tower is designed to achieve a certain residence time to complete the bleaching reactions and plug flow to obtain maximum bleaching uniformity. The tower L/D (length/diameter) aspect ratio is designed to ensure critical minimum stock velocity, the velocity at which the internal shear of the stock exceeds the wall friction, necessary to minimize channeling and maintain plug flow (Bodenheimer, 1969). Typical tower dimensions for a 1000 admt/day production rate are 4.5 m in diameter by 24 m high. A survey of industrial oxygen delignification units shows that the tower aspect ratios for medium consistency pulp vary from 5.9 to 16.7 with the majority of the systems being between 9 and 12 [Bennington and Pineault, 1999]. The inlet of the oxygen tower can contain a rotating distributor to help improve pulp distribution and facilitate plug flow of the stock in the tower. The stability of the pulp-gas  Chapter 3: Model Development  73  dispersion is also aided by the buoyancy imparted by the trapped oxygen which reduces the likelihood of bed compaction. At the top of the reactor, a fully submerged rotating scraper-type discharger prevents plugging and channeling and directs the pulp through a blow valve to the blowline where pressure is relieved (White and Larsson, 1996). In modeling the retention tower, we assumed that the pulp flow is uniformly distributed across the tower cross-sectional area (pure plug-flow) resulting in a uniform pulp residence time in the tower. This pure plug-flow assumption has also been used in most previous models of steady-state bleaching process in retention towers [Ackert et al, 1975; Kovasin et al,  1987;  Myers and Edwards, 1989b; Ulinder, 1995; Genco et al, 1998; and van Heiningen et al, 2003].  1$  Pulp Out  mid way along up/low tube  Pulp In  0 Tracer injection  t  0  1  2  t, hr  Figure 3.6 Medium consistency oxygen tower [left, White and Larsson, 1996] and pulp R T D of an up-flow C 1 0 bleaching tower [right, Bennington, 2000] 2  Chapter 3: Model Development  74  The  plug flow behavior inside the pulp retention tower is confirmed from the R T D  diagram for an up-flow medium-consistency CIO2 tower shown in Figure 3.6 (oxygen towers have similar characteristics as the CIO2 bleaching towers). A series of continuous stirred tank reactors (CSTRs) is commonly used to model plug-flow reactors. As the number of tanks becomes very large, the behavior of the system approaches that of perfect plug-flow [Levenspiel, 1972;Fogler, 1999]. We chose the CSTR-in-series approach to model the oxygen retention tower(s) since this model is governed by simple ordinary differential equations that can be solved readily. We did not take into account the axial dispersion that could occur due to variations of pulp flow velocity and friction losses caused by fluid viscosity and wall drag.  At present, we have no way of  knowing the behavior of pulp in the industrial retention tower. The consequence of taking this plug-flow assumption is that the pulp will be uniformly distributed and have uniform residence times. Also, due to the large tower aspect ratio and the variability of incoming kappa number from the digester, axial dispersion will not significantly affect the uniformity of delignification. Moreover, oxygen gas is found to travel much faster than pulp in industrial retention towers. The actual behavior of gas traveling through an industrial retention tower is not known. Mills have reported that typical oxygen gas residence times are only about 25 to 37% [Miller et al, 1993] or 20 to 40%> [Hornsey et al, 1998] of that of the pulp. Increasing the oxygen gas flow rate was also found to decrease the gas residence time and does not always increase delignification [McDonough, 1996; Hornsey et al, 1998]. In the retention tower, we assumed that there is no segregation of gas that could lead to a non-uniform distribution of gas and a change in the gas void fraction (<f> ). Bennington and g  Pineault [1999] investigated the flow of gas through a medium-consistency fibre suspension in a  Chapter 3: Model Development  75  laboratory model column. They observed that the gas forms channels and bypass through the fibre network as it flows upward in the column. The presence of bypass which indicate formation of channels coupled with the large amount of oxygen that industrial oxygen delignification process typically use, justify the assumption of a constant void fraction (^ ). Moreover, in the g  continuous operation of commercial oxygen systems, the relative movement of oxygen will replenish the consumed oxygen and maintain the constant gas void fraction and oxygen concentration inside the tower. As long as there is oxygen in bubbles near the fibers, the oxygen concentration in the liquor will remain relatively constant. Mass transfer is an important consideration in most of oxygen bleaching stages because the overall mass transfer process consists of three steps (see section 2.7). Oxygen must cross the gas-liquid interface, diffuse through the liquid film surrounding the fiber, and finally diffuse into the fiber wall before reacting. Any of these steps can be rate determining depending on the relative rates of mass transfer and chemical reaction. The liquid-fibre mass transfer rate is roughly 150 times faster than the gas-liquid mass transfer rate due to a much larger surface area [Hsu and Hsieh, 1988]. Therefore, depending on the mixing conditions, the transfer of oxygen gas to the liquid phase could be a limiting factor. This will be investigated and further discussed in chapter 4. To do that, we need to investigate the intra-fibre diffusion in comparison to the intrinsic reaction rate at the lignin sites. The rate of oxygen diffusion across the fibre wall can be estimated as follows:  ®oi = where Q?  Diff  D*ECCSA*C  n  *V*Mw  ^  [3-8]  is rate of oxygen diffusion (g/kg pulp/.?) across the fibre wall, D is the bulk diffusion  coefficient of oxygen in the alkaline liquor at 95°C (1.32xl0~ m ls), E C C S A is the so- called 8  Chapter 3: Model Development  2  76  effective capillary cross sectional area (~0.07) which accounts for tortuosity and limited open area for diffusion in the fiber wall [van Heiningen et al., 2003], C  Q sot  is the saturated  (maximum) concentration of oxygen at typical oxygen delignification conditions (800 kPa and 95°C) and is found to be 6.152xl0" moles O2/L water, V is the volume of water inside the 3  swollen fibre wall (1.5-2.5 Llkg pulp), M is the molecular weight of oxygen (32 glmoT), and W is w  the fibre wall thickness (3><10" m). Insertion all of the values into Eq. (3-8) gives a rate of 6  oxygen diffusion, O  o g f  , of 40.5 grams O^kg pulp/5.  The diffusion limitation in the fiber wall is negligible when the rate for oxygen reaction (consumption) (O  r a  «  is an order of magnitude smaller than the rate for oxygen  diffusion  0 ). The highest rate of oxygen reaction occurs at the 'very fast' stilbene lignin Diff  group. This can be calculated as:  <J> =^* ~ ra  V  \  [3-9]  )stilbene  where y ^ is the grams of oxygen consumed per kg pulp per kappa drop, taken as 0.55 based on 0  a reported value in literature (see section 2.6). The delignification rate (-dL/dt) is calculated using the typical oxygen delignification conditions shown in Table 3.3 below.  Table 3.3 Characteristic rate of oxygen consumption and diffusion for all model compounds Model Compound  -dL/dt  lype  "  kappa/s  rt> rxn a)  <f>  3)  gr 02/kgpulp.s gr 02/kgpulp.s  ^rxn/^diff  Stilbene  Very fast  4.34U+OO  2.39E+OO  4.04E+OI  5.91E-02  Vinyl Ether  Fast  3.96E-02  2.18E-02  4.04E+01  5.39E-04  Slow -  1.35E-03  7.42E-04  4.04E+01  •I.84K-O5  4.08E-04  2.24E-04  4.04E+OI  5-55E-06  5-5  Very Slow  1)  delignificationrateconstant at T=95°C, P=800kPa, Cm=10%, Alkali=2%, Oxygen=2%  3  rate of oxygen consumption by reaction; rate of oxygen diffusion across fibre wall 3)  Chapter 3: Model Development  77  As Table 3.3 shows, the rate of oxygen reaction (consumption) was found to be an order of magnitude or more smaller than the rate for oxygen diffusion. Moreover, the ratio of reaction to diffusion rates ( O  w n  / 0 ) for stilbene was found to be 0.06 meaning reaction consumes only Diff  6% of the available oxygen supplied through diffusion. The above analysis concludes that there is no mass transfer resistance for oxygen to diffuse from the fiber surface to the lignin reaction sites inside the fiber wall. This is in agreement with work of Hsu & Hsieh [1988] and van Heiningen et al. [2003]. Moreover, intra-fiber diffusion resistance has also been assumed to be insignificant in many other laboratory-scale oxygen delignification studies [Myers and Edwards, 1989b; Vincent et al, 1994; Argawal et al., 1996; Iribarne and Schroeder, 1997].  To summarize, the following assumptions have been made in the governing equation used: 1. The relationship between kappa number (lignin content) and the composition (amount) of lignin model compounds (x ) is linear. t  2. The consumptions of oxygen and alkali are proportional to the total rate of delignification expressed as grams of oxygen or alkali consumed per kappa number drop. 3. Steady-state operation. 4. Perfect contact between oxygen and the pulp suspension (no segregation) in both the mixer(s) and retention tower(s). 5. Uniform distribution of pulp (plug flow) which results in uniform pulp residence time in retention tower(s). 6. No mass transfer resistance of oxygen inside the fiber walls.  Chapter 3: Model Development  78  7. Pressure drop in up-flow tower because of friction (shear) is negligible and only hydrostatic pressure head is considered. 8. The gas phase is pure oxygen.  3.6  Governing Equations Apart from the kinetic equations described earlier in section 3.3, a number of governing  equations describing the oxygen and alkali balances, oxygen solubility in alkali solutions, decreasing pressure during reaction in the retention tower, gas-liquid mass transfer coefficient for high-shear medium-consistency mixers, and carbohydrate degradation rate were incorporated in the model.  3.6.1 Oxygen and Alkali Balances The oxygen balance is taken from general mass balance for a continuous stirred tank reactor (CSTR). The oxidation reactions are taking place in the pulp suspension inside the fibre wall; therefore the pulp volumetric flowrate will not change due to reaction. Also, as oxygen consumption, as a result of reaction with lignin in the liquid suspension, provides minimal changes in the gas volume, the gas void fraction (^ ) in the retention tower will be considered g  constant. The initial amount of oxygen in the gas phase ( 0 ) was determined by the oxygen g  2  charge (% on pulp) injected to the system. Oxygen consumption by reaction with lignin sites determines the remaining oxygen gas available for gas-liquid mass-transfer. The mass balance of oxygen dissolved in the liquid phase (O ) for a pulp suspension going into a single continuous 1  stirred tank can be described in general as follows:  Chapter 3: Model Development  79  ACC = IN- OUT + GEN - CONS  [3-10]  Writing Eq. [3-10] for the oxygen balance in the liquid phase:  flow of  flow of  [Accumulation] = O into  O out of +  l  rate of O'  transfer of  2  2  the system  the system  Of ->  [3-11]  consumption  1  O'  by reaction  Since we are evaluating the system at steady state  flow of  flow of —  0' out of  transfer of  O into l  2  Of ->  2  the system  the system  0'  rate of 0' 2  —  [3-12]  consumption by reaction  Thus, we can write the total mass balance given by Eq. [3-12] in the form of a differential equation as follows: d(CV)  k a{AC)V-r y  =  dh  [3-13]  o  L  Where v is the pulp suspension velocity moving through the retention tower and h is the height of a single slice CSTR in the tower. At steady state, the pulp suspension moves at a constant rate through the system (v=dhldt). As a result, the relationship in Equation [3-13] can be expressed directly as a function of pulp residence time in the tower (r, min) as follows:  d(CV)  k a(AC)V-r V L  dt  [3-14]  0  Writing Eq. [3-14] for the pulp suspension gives:  d[0> ]  lv(l-0 ) = k a[O  2  dt  g  L  -O ]Vl  2tSat  2  Chapter 3: Model Development  ^ | 100-0.333C v  d[L] my  dt  •V(\-<t> ) s  [3-15]  80  Dividing Eq. [3-15] by V(\-(j)) gives:  4^L dt  d[L]  ka r L  "(1-^)  L  2  " ' ra  2  100-0.333C,  [32  j  m  [3-16]  dt  J  where (J is dissolved oxygen concentration in the liquid phase (moles O 2 / L liquid) and 0 2  2 sal  is  the saturated (maximum) amount of oxygen that can be dissolved in the liquid phase at a given oxygen partial pressure, k a is the volumetric gas-liquid mass transfer coefficient of oxygen to L  the liquid phase, <j> is the gas void fraction, y z  Q  is the coefficient specifying the amount (g) of  oxygen consumed per kappa number drop per kg of pulp, and C is pulp consistency in percent. m  The pulp residence time (At, min), the time at which lignin reactions are taking place in a single slice of CSTR, is determined from the tower dimensions, consistency (C , %), gas void m  fraction (^ ), and pulp production rate. It is calculated as: g  Af =  360xD?HC (l-* ) m  g  «i (100-0.333C )  [3-17]  >  m  where D is the tower diameter (m), H is the tower height (m), n is the total number of equal sized t  layer in which the tower is divided, and P is the pulp production rate (ton/day).  The saturated oxygen concentration is obtained using the Henry's law coefficient reported by Tromans [2001] which is a function of the oxygen pressure (atm) and system temperature (K). The equation is given as follow:  O  - P k  ^2,sal ~  where  Chapter 3: Model Development  [3-18]  0 '0  1  n  1  2  81  -3 0.0467 + 203.357/ln(77 298) - (299.378 + 0.0927/) (7/ - 298) - 20.591 x 10 72  k  0i  = exp  (8.3144)7/  "N  [3-19]  The oxygen solubility correlation developed by Tromans is valid for oxygen pressures up to 60 atm and temperatures up to 342°C. Tromans [2001] also investigated the effect of alkali on oxygen bleaching solutions. He concluded that, at the typical alkali concentrations used in oxygen bleaching, the oxygen solubility curve lies very close to that of the pure water. Thus, the 0  2 sal  concentration is controlled primarily by temperature and oxygen pressure as described in  Equations [3-18] and [3-19]. The change in alkali or hydroxide concentration (mol/L liquid) was calculated using the following equation:  d[L\  'aOH  dt where y  Na0H  40  dt  100-c,  m J  [3-20]  is a coefficient that relates the amount of alkali consumed per kappa number drop  per kg pulp. It can be adjusted to reflect measured or theoretical consumption. The initial (t=0) hydroxide concentration in the liquid phase will depend on the alkali charge (%) injected into the system and the pulp consistency, i.e.:  [OH-],__ = 0  [3-21]  40(100-C ) m  where A is the NaOH charge (% on pulp) and C is pulp consistency (%). c  Chapter 3: Model Development  m  82  3.6.2 Gas-liquid Mass transfer, Tower Pressure & Temperature The volumetric gas-liquid mass transfer coefficient (k a, s") under high-shear mixing 1  L  conditions was determined by Rewatkar and Bennington [2000] as a function of fibre suspension consistency, C (%), as: m  k a = 1.17 x 10" ^ V g exp {-0.3 86 * C } 4  [3-22]  6  L  m  where s is the mixer power (W/m ) and <j> is the gas volume fraction inside the mixer. <f> is 3  g  g  calculated from the oxygen charge p (% on pulp), temperature (K), and the oxygen pressure P02 (kPa) using:  * = g  =  ^C xpxT m  8 . 3 1 4 C x j r ? x r + 3.2(100-0.333C )P m  m  O2  In the case of the retention tower, the gas liquid mass transfer coefficient was taken from the experimental results of Rewatkar and Bennington [2002] which gives k a as a function of the L  superficial gas velocity. Values for typical industrial conditions were reported to vary from 0.001 s" to 0.007 s" based on measurement in laboratory at room temperature (25°C). Consequently, in 1  1  the model, the measured gas-liquid mass transfer coefficients (&/,«), both in the mixer and oxygen tower, were corrected to take into account the temperature dependency. The gas-liquid mass transfer coefficient (kid) at 100°C is approximately three times higher in the high-shear mixer, and about four times higher in the retention tower than at the room temperature values (see Appendix E for details on kia corrections and calculations). Furthermore, we assume that the total pressure inside the oxygen retention tower decreases linearly from the bottom to the top, i.e.:  P(h) = Pbottom -(P b  \  Chapter 3: Model Development  -P  )  bottom lop J  [3-24]  83  where h is the height at which the pressure is going to be evaluated and H is the total height of the retention tower. The oxygen partial pressure is calculated by subtracting the total pressure with the water-vapor pressure calculated using Antoine correlation. Similarly, even though the magnitude of the increase in temperature is minimal (1-2 °C) due to a mild exothermic reaction of oxygen with lignin, we incorporate temperature changes by assuming that temperature inside oxygen retention tower(s) increases linearly from the bottom to the top of the tower, i.e.:  T(h) = T +  ~h  m  [3-25]  Both oxygen pressure and temperature at the bottom and at the top are specified as inputs to the model. In the case of temperature, if there are no information on temperature coming into and going out of the tower(s), constant temperature throughout the reactions was assumed.  3.6.3 Carbohydrate Degradation Cellulose and hemicellulose in wood cells are composed of several sugar units, i.e., glucose,  mannose, xylose,  galactose, rhamnose, arabinose, and their derivatives. As in  delignification, the preferable way of modeling the carbohydrate degradation is through studies with carbohydrate model compounds representing each of the individual sugar units. This could be a long-term project to understand the reactions occurring in the carbohydrates during oxygen delignification.  Studies  of oxidative alkaline degradation involving carbohydrate model  compounds today are not as extensive as for lignin model compounds. Guay [2000] suggested that hydroxyl radicals are the major oxygen species to attack carbohydrates at anomeric positions.  Chapter 3: Model Development  84  On the other hand, Yasumoto et al. [1996] reported that methyl-P-D-glucopyranoside (model carbohydrate) was not degraded by oxygen but degraded in the presence of guaiacol and catechol types of model lignin compounds. The extent of its degradation was strongly dependent on the structure and the amount of the lignin model compound. Up to the time that this thesis was written, we could not find sufficient data to generate carbohydrate degradation kinetics using model compound studies. Therefore, the carbohydrate degradation profile was developed using the information available, based either on fiber suspension studies or on industrial experience [Liebergott, et al., 1985; Marcoccia et al., 1993; McDonough, 1996]. We coupled the decrease in degree of polymerization (DP) with the decrease in kappa number (lignin content). A constant k  DP  was specified to measure how much carbohydrate was  degraded as lignin was removed, i.e.:  d[L\  djUDP)_  dt  dt  ~  (D?ho=fM  The rate constant for cellulose degradation (k ) DP  [3-26]  was found to be in the range of 10" min , in 5  1  agreement with results of Marcoccia et al. [1993] who reported the carbohydrate degradation constant using photo-enhanced oxygen delignification to vary from 3.5 xlO" up to 5xl0" min' . 5  5  1  The number average degree of polymerization (DP) of cellulose was related to the CED viscosity (77) using the correlation developed by Godsay and Pierce [1984]:  DP = 961.381og (^)-245.3 10  [3-27]  with the initial (t = 0) degree of polymerization calculated from the viscosity (mPa.s) entering the oxygen delignification stage.  Chapter 3: Model Development  85  3.7  Effect of Black Liquor Solids Carry-Over Carry-over of black liquor from the cooking stage and recycled post-oxygen filtrates are  normally encountered in industrial oxygen delignification processes. This carry-over contains organic and non-organic components in different proportions, with post-oxygen filtrate having less COD compared with the black solid filtrate counterpart. In our model, we consider only black liquor solids carry-over and neglect the post-oxygen filtrate since unoxidised lignin consumes far more chemicals, lowers pH, and consequently slows fibre delignification [Allison et al., 2000]. We modeled black liquor solids carry-over as being involved in the reactions with oxygen and alkali; they will consume both oxygen and alkali, lowering both chemical concentrations available for lignin reactions. Consequently, they will also lower the rate of delignification, and ultimately reduce the overall delignification achieved. In the model, black liquor solids carry-over was assumed to contribute only to reactive lignin, i.e., the 'very fast', 'fast', 'slow', 'very slow' lignin, and not for stagnant lignin. The reaction of the carry-over lignin structures was assumed to take place simultaneously and competitively with the reaction of the residual lignin in fiber walls. Four sets of delignification kinetics were therefore added to the governing equations corresponding to the four groups of lignin carry-over. They were solved simultaneously together with the oxygen and alkali balances.  Table 3.4 The contents of lignin and its high molar mass in black liquors Type of pulp  lignin content  HMML'  1  Polysaccharides  % of.BLS (dry)  % of lignin  %ofBLS(dry)  Hardwood Kraft  33  3-5  2-5  Softwood Kraft  36  9 - 12  i -3  Bagasse, Soda  35-'6  n.a.  n-5  High Molar Mass Lignin (molar mass -above-1.0,000)  Chapter 3: Model Development  86  To incorporate the effect of black liquor solids into the overall delignification reaction, we need to quantify the amount of lignin that is contained in the black liquor solids (kg/ton of pulp) carried forward to the oxygen delignification stages. We used data for the composition of black liquor reported by Soderhjelm and Sagfors [1992] as shown in Table 3.4. The amount of 'carry-over' lignin in the black liquor solids (BLS) from a softwood kraft pulping is 36% (by mass), which means about one third of black liquor solids are dissolved lignin. We converted the amount of black liquor solids (kg/ton of pulp) into lignin content expressed as the kappa number as follows:  _ 036*BLS L lcairy_aver  0.147*1000  Moreover, we assumed that the distribution of dissolved lignin reactivity is the same as in native lignin and use the same kinetic expressions as described in section 3.3 with the exception that carry-over contains no 'stagnant' lignin (L ). The composition of 'very fast' and 'fast' types 5  of lignin carry-over are x = x = 5%> and x = x = 2%>, respectively. The 'slow' and 'very slow' ]  6  2  7  types of lignin were specified based on their relative distribution in residual lignin i.e. x = 30% 8  and x - 63% of the dissolved lignin. 9  ["As]  "^6  []carry_over  ^  29]  ["^7]  ^7  carry-over  ^  30]  [*4J  "^8  [^Icorry _over  ^  ^  ^Z.(jJ  Xg  \.^\carry_over  ^ 32]  t^lrc'A/t/wo/  ["^Iro/a/  where  l L, L  dual  =  IA ] [4 ] +  +  t"Scarry_over  [4 ] + [L< ] + [L5 ];  Chapter 3: Model Development  ^  [L]  carryover  33]  = [4 ] + [ L, ] + [ L  87  The compositions of the lignin groups in residual lignin (x , x , x , x ) need to be x  2  3  4  adjusted appropriately in the presence of black solids carry-over, i.e.:  '  v  ~[L]  l  d  L  r-5 •JAl  1 residual  ,+[L]  Xmw  J residual I  L  J  scarry _over  -*2 '\ ] ; , I 1 residual new ~ T -[ residual r T^ L  ro T C ]  1  v  2  X  L --' J J  T  I  3  X  J  [3-36]  s residual  J carry _ over [^3residual \.^\c  *l  X  rn 171  residual  residual  [L]  +  carry _over  Similarly, the compositions of the lignin groups in the dissolved lignin ( x , x , x , x ) were 5  6  7  8  also adjusted as follows:  x,  Y L  v.  L scarry _over  U  ^residual L Jcorryover  x *[Z] 7  '  -  L Scarry over  WTML]  7 NEW  "  [3  J residual L Jca/vj^over  L  39]  x *[Z] 8  *-" ~[L]  ,+[L]  ew  L  v[4  _ A  99 new new  _  r  d  L  J  A residual L scarry over  T  Iii  1  .  Jca/7y_over . f r l  . + \ L ,  41]  n  L  J n  1  J  Jcarry _over  As a result of the addition of black liquor solids, the total number of kinetic expressions adds up to eight (see Equation 3.42), the first four expressions corresponds to 'residual lignin'  Chapter 3: Model Development  88  and the last four expressions are for 'carried-over' dissolved lignin in the aqueous phase. These sets of delignification kinetic expressions are summarized as follow:  d[L ] = A exp dt x  x  d[L ] _ 2  A exp 2  dt  d[L,]_ A exp dt i  4, exp  dt  = 4 exp  dt  d[L ]_ ^ exp dt  RT  [o;]>/rJ'[ ] A  [O'TIOH-J^]  RT RT  d[L ] g  dt  = A exp 3  Total  [;]-[o/f-]-[z,]  RT  0  [4]  W'[OH-]'[L,]  ,  tA],  3_new * [^] otal  =  X  = 0  T  =  =0  X  4_  Total  n e W  RT  1  dt  Total  RT  [0[f[0H-J[ ] Ll  ;  [Z L 7  0  = x  7  n  e  w  7bto/  *[Z]  RT [3-42]  = A exp 4  RT  [^f  [OH~f[L ] 9  ;  [I ], 9  = 0  = x _ _ * [ l ] 7bta/ 9  The above set of delignification kinetic expressions can be written in the simplified form:  d[L,] _  A exp t  dt  "AJ  RT  [0' J'[0H-J[L,) ; [4L = 2  0  Total  [3-43]  with total delignification calculated as:  _d[L\ dt  +  d[Lj] dt  where j is the total number of model compounds used in the model  Chapter 3: Model Development  [3-44]  89  Chapter 4 Simulations Results arid Discussions  4.1  Simulations The simulation was started by providing the known oxygen delignification operating  conditions to the model. We investigated the role of mass transfer in both the high shear mixer(s) and oxygen retention tower(s) by examining the degree of delignification achieved for different process conditions. In the case of a medium-consistency mixer, the effect of mixer power was examined over the range of power inputs commonly seen [Bennington, 1996]. The significance of gas-liquid mass transfer (kid) was evaluated as well as how changes in process variables, i.e., temperature, alkali and oxygen charge, tower pressure, consistency, and black liquor solids carry-over, affect the overall delignification efficiency. The ranges of operating conditions examined are shown in Table 4.1.  Table 4.1 Range of operating conditions used in the simulations Level  T y p e s o f Variables  Base Case  Low  High  Reaction temperature, °C  lOO  80  120  Bottom Tower pressure , kPa  850  600  lOOO  Charge of Alkali, % of pulp  2  1  4  Charge of Oxygen, % of pulp  2  0.5  3  Pulp consistency, %  10  8  H  Mixer Power , W/m  10  10  xo  !)  2)  3  J  6  8  Pulp Residence Time in Mixer, s  0.5  -  Pulp Residence Time in Tower, min  60  -  -  k(.a (retention tower), s"  0.007  0.004  0.014  1  Tower pressure differential (top-bottom) was maintained at 400 kPa No pressure drop across the medium-consistency mixer(s)  Chapter 4: Simulations Results and Discussions  90  Changes of the operating conditions listed in Table 4.1 will have a direct impact on the lignin model compound apparent kinetics. The delignification kinetics themselves are governed by the kinetic parameters shown earlier in Table 3.2. For the simulations presented here, the kinetic parameters were fixed and no changes were made throughout the simulations. However, they could be changed to model the specific bleaching kinetics of specific pulps. To make this more convenient, the parameters were written in separate Matlab function file so that they can be changed without interfering with the main script file (see Matlab codes in Appendix D). We modeled the high-intensity mixer as one single independent continuous stirred tank where the reactions of model compounds take place simultaneously within the specified mixer residence times. Depending on the mixer volume and pulp production rate, the range of pulp residence time in most industrial medium-consistency mixers could vary from 0.05 s to 0.9 s [Bennington, 1996]. We fixed the pulp residence time in the mixer at 0.5 s for our base-case simulations. Oxygen pressure and gas void fraction inside the mixer were kept constant as oxygen was consumed in the reaction. This is a good approximation for the typical mediumconsistency mixers used in oxygen delignification applications. Prior to mixing, the initial oxygen concentration in the liquid phase was set to zero. The mixing power consumed in the mixer determines the volumetric gas-liquid mass transfer coefficient kia (Eq. E-6) and the partial pressure of oxygen determines the driving force for dissolution of oxygen (Eq. 3-18). These factors determine oxygen dissolution and hence the dissolved oxygen available for reaction. Following the mixer, tower calculations were performed as in the mixer. The retention tower was divided into a large number of layers, each one represented as a CSTR, for which the pulp production rate and tower dimensions determined the amount of time that the pulp spent in  Chapter 4: Simulations Results and Discussions  91  each layer. The initial conditions used for the tower calculation, i.e., kappa coming into the tower, pulp viscosity coming into the tower, residual chemical concentrations, etc., were taken from the output of the mixer calculation. The outputs from first layer calculation were passed onto the next layer of the tower. Calculations for each layer of the tower were made sequentially as the pulp move through the tower. Calculations were stopped when the total number of layers or the desired pulp residence time was  achieved. Moreover, there is no quantitative information available on gas  hydrodynamics in industrial oxygen tower. Therefore, the gas void fraction inside the retention tower was assumed to be constant at <j> = 0.1 for all simulations conducted based on g  measurements in laboratory column by Rewatkar & Bennington [2002] (see section 3.5). The tower pressure decreased linearly from the bottom to the top depending on the pressure set at the top of tower. The saturated oxygen concentration was adjusted at each CSTR to match the tower pressure at that location. We tested the model by changing one specific operating condition that we would like to investigate while keeping the rest constant at their base case values. The model was formulated using the steady-state assumption. Therefore, it does not account for any process disturbances (although it could be modified to do so). The model only considered black solids liquor carry-over and assumed that the recycle materials from dilution and post-oxygen washing did not consume chemicals. This was based on fact that oxidized lignin has far less chemical demand than raw black liquor solids [Allison et al., 2000; Genco et al, 2000; Vuorenvirta, 2001]. Also, the reaction temperatures were taken as input parameters since an energy balance is not included in the model. This aspect was found not to be critical, although, it could be incorporated into the simulation at a later date if the need should arise.  Chapter 4: Simulations Results and Discussions  92  4.1.1 Effect of Temperatures The influence of temperature on kappa number reduction is shown below in Figure 4.1 as a function of time. It can be seen that, during the first 2-3 minutes of reaction, the kappa number drops fairly fast. As expected, the delignification rate in the second (final) phase of the reaction showed a lower rate controlled by the 'slow' and 'very slow' lignin, with the largest reduction being obtained at the highest temperature. The extent of delignification predicted by the model is comparable with kinetic studies made using fiber suspensions [Hartler et al, 1970; Olm and Teder, 1979; Hsu and Hsieh, 1987]. At longer bleaching times (t > 60 minutes) and severe operating condition, i.e., temperature >120°C, delignification will eventually reach its floor kappa, which has been set as 25% of the incoming kappa number. However, to minimize carbohydrate degradation, industrial mediumconsistency oxygen delignification systems limit the temperature range from 80°C to 100°C.  32  1  30 Temperature 80°C  28 26 (D  E Z  CO Q. Q.  -  90°C  \  24  N  "'-^  \  \ \  22  •  100°C 120°C  v  -  *. '  N  \  V m  20  ro  18  ** *" -  Bottom Pressure 850 kPa Top Pressure 450 kPa NaOH Charge 2% 0 Charge 2% Consistency 10%  16  _  *"*"*•-. "* ** - _  2  14 12  0  10  20  30  40  50  60  Time (minutes) Figure 4.1 Effect of temperature on kappa number during oxygen bleaching Chapter 4: Simulations Results and Discussions  93  Figure 4.2 below gives the concentration profile of dissolved oxygen in the liquid phase. In the first minutes of reaction, oxygen is consumed mainly by reaction with the 'very fast' stilbene and the 'fast' vinyl ether lignin structures, leaving its concentration nearly zero. As reactions proceeds, most of the 'fast' and 'very fast' structures have been oxidized, leaving only the slower ones to react further. At this point, the high oxygen partial pressure at the bottom of the tower creates a high oxygen solubility, which together with the gas-liquid mass transfer coefficient (kia), cause an increase of dissolved oxygen concentration in the liquid phase. The model assumes a constant kia in the tower and negligible gas-side mass transfer resistance as pure oxygen is used. Consequently, the declining oxygen concentration illustrated in Figure 4.2 is determined solely by oxygen consumption. At the later stage (Y>10 minutes), constant oxygen consumption together with the decreasing tower pressure reduces the oxygen solubility and lowers the amount of dissolved oxygen progressively approaching the saturated concentration.  0.007  1  1  Saturated 0  0.006  .." - -  2  80°C 90°C  o E  0.005  -  100°C 120°C  0.004 -  /' //  ^"^-*T  •  /' /  0.003  "*  :  /; • ;'(•/  0.002  •  ~~  / '  7 • i  Temperature 100°C Bottom Pressure 850 kPa Top Pressure 450 kPa NaOH Charge 2% 0 Charge 2% Consistency 10%  0.001  Dissolved 0  100°C 120°C  •  0  10  20  30  -  90°C  2  0.000  2  80°C  40  50  60  Time (minutes) Figure 4.2 Dissolved oxygen concentration profile at different temperature vs. bleaching time Chapter 4: Simulations Results and Discussions  94  During the lignin oxidation reaction, oxygen and sodium hydroxide (alkali) were consumed reducing their concentrations proportionally with the decreasing kappa number. The magnitude of the consumption was governed by the input parameters, i.e., y  Na0H  andy ^, the 0  grams of chemicals consumed per kappa number drop per kg pulp. In the simulations, the alkali consumption parameter (y  Na0H  ) was fixed at 0.7 grams per kappa number reduction based on the  measurement of Evans [1979b]. Similarly, oxygen consumption constant (y ^) Q  was set at 0.55  grams per kappa drop based on the reported literature values shown in Table 4.2 below. These input chemical consumption parameters can be changed to suit different pulp characteristics.  Table 4.2 Oxygen and alkali consumption per unit kappa number reduction during oxygen bleaching of softwood kraft pulp at medium consistency (laboratory and commercial systems) Oxygen Consumption (y ) 02  Alkali Consumption (y^m)  Reference  System  Berry et al., 2002  lab reactor  O.55-O.64  n.a.  Corbett era/., 1976  lab reactor  0.5 -0.6  n.a.  grams chemical per unit kappa reduction per kg of pulp  Iijima & Taneda, 1997  lab reactor  1.38  n.a.  Seifert et al.  commercial  1.2 - 1.9  n.a.  McDonough, T.J., 1996  commercial  1.4  1-3  Evans, J.C, 1979  commercial  0.8 -0;9  0.6 - 0.8  Violette, S., 2003  lab reactor  n.a.  1-35  Jiang era/-., 2004  lab reactor  n.a.  1.57-1.9  Figure 4.3 illustrates the decreasing profile of the residual alkali concentration left in the liquid phase as a function of time; the trend was much more pronounced at high temperature. The initial hydroxide concentration was estimated from the sodium hydroxide charge to the oxygen reactor. In reality, the initial alkali concentration depends also on the residual alkali carried forward from the cooking stage and the recycled post-oxygen filtrate.  Chapter 4: Simulations Results and Discussions  95  Figure 4.3 Profile of a decreasing alkali concentration as reaction progresses  Moreover, large numbers of inorganic species are present in the oxygen bleaching filtrate solution. As a result, although alkali was consumed during the reaction, the pH of the suspension might not drop below -10 due to the buffering capacity of carbonate-bicarbonate present in the alkaline white liquor. The alkalinity of the bleaching liquor itself depends on the acid/base properties of inorganic and organic compounds and on the temperature. In order to determine the exact value of hydroxide ion concentration, equilibrium calculations have to be made using estimates of the bleaching liquor compositions. Due to complexities described, we have not modeled pH in this work.  Chapter 4: Simulations Results and Discussions  96  The effect of temperature on viscosity loss is presented in Figure 4.4. As has been mentioned in the literature [Hartler et al, 1970; Hsu and Hsieh, 1987; Iribarne and Schroeder, 1997], the reaction temperature has a significant impact on carbohydrate degradation. We modeled selectivity by coupling the carbohydrate degradation rate with the lignin delignification rate to give a direct inter-relation between the two. Consequently, a certain portion of the carbohydrates will always be degraded as lignin is removed resulting in a viscosity drop. The extent to which the carbohydrate degraded is governed by the cellulose degradation rate constant (k ). This value was fixed throughout the simulations and was acquired using available DP  industrial viscosity loss data. However, several ways of improving oxygen delignification have been proposed, for example Bouchard et al. [2001] reported that by combining oxygen with peroxymonosulphate (PMS) higher delignification could be achieved without sacrificing selectivity. In this case, an adjustment to the cellulose degradation rate constant (hop) would have to be made in the model.  Time (minutes)  Figure 4.4 Effect of temperature on viscosity drop during oxygen bleaching Chapter 4: Simulations Results and Discussions  97  Temperature 80°C 90°C '  \  ' •  \  v  100°C  '  '•._  \  "  120°C  N  Temperature 100°C Bottom Pressure 850 kPa Top Pressure 450 kPa NaOH Charge 2% 0 Charge 2% Consistency 10%  ^ ^ ^ ^  2  0  10  20  30  40  50  60  Time (minutes) Figure 4.5 Effect of temperature on viscosity drop during oxygen bleaching (estimated using carbohydrate degradation kinetics of fibre suspension [Iribarne & Schroeder, 1997])  Iribarne and Schroeder [1997] developed degradation (see  a kinetic expression  for carbohydrate  section 2.5.1) using fibre suspensions. We compared our carbohydrate  degradation kinetics (Equation 3-24) with Iribarne & Schroeder's correlation (see Equation 2-8 & Table 2.7). This was done by modifying the Matlab function file (see Appendix-D). Figure 4.5 illustrates the effect of temperature on viscosity loss estimated using Iribarne & Schroeder's correlation. Compared with Figure 4.4, the Iribarne & Schroeder's carbohydrate degradation kinetics shows a much larger dependency on temperature. The model correlation seems to work well at temperatures up to 100°C. However, at the higher temperature of 120°C, the viscosity dropped significantly below the critical value of 15 mPa.s. This does not agree well with experimental results for oxygen bleaching using fiber suspensions [Hartler et al., 1970; Hsu and Hsieh, 1987]. Further work is needed to develop a better correlation with a range of carbohydrate model compounds to improve the predictive capabilities of the model (see section 3.6.3). Chapter 4: Simulations Results and Discussions  98  4.1.1 Effect of Tower Pressure  Time (minutes) Figure 4.6 Effect of oxygen pressure on kappa number during oxygen bleaching  The effect of tower pressure on the delignification achieved is shown in Figure 4.6 above. Here, the pressure drop across the tower is fixed, but a back pressure is applied to increase the pressure throughout the tower. The delignification increases strongly with increasing pressure. This is due to the increase in oxygen solubility, which is a function of the oxygen partial pressure and temperature. As a consequence, for a given gas-liquid mass transfer coefficient, increasing the pressure will increase the driving force for oxygen dissolution in the liquid phase, i.e., higher dissolved oxygen concentration and thus enhances delignification. Typically, bleaching at medium-consistency (10-15%) pulp consumes 24 times as much oxygen as can be present in the liquid phase at any one time [McDonough, 1986]. Therefore, ensuring that the partial pressure of oxygen in the gas phase and that the gas-liquid mass-transfer coefficient are sufficiently large is crucial for achieving the maximum delignification possible. Chapter 4: Simulations Results and Discussions  99  4.1.2 Effect of Alkali Charge  32  Studies of oxygen delignification with fibre suspensions have found a substantial increase in delignification with increasing alkali charge at constant consistency (Figure 2.17 and Figure 2.18). However, these results were not predicted in our model simulations. As Figure 4.7 shows, increasing alkali charge by a factor of four resulted in a decrease of only about 1 to 2 kappa units which does not correspond to lab or industrial practice. There could be a number of possible reasons for this discrepancy. Studies of oxygen delignification with lignin model compound did not a show large dependency on the alkali charge (pH) as is normally seen with fibre suspensions, resulting in a low reaction order with respect to the alkali concentration. The role of alkali in the oxidation reaction with fibre suspensions does not seem to be well-captured using lignin model compounds.  Chapter 4: Simulations Results and Discussions  100  High alkalinity is known to cause fibres to swell, increasing the fibre wall thickness, allowing better accessibility for dissolved oxygen and alkali to reach the lignin sites within the fibre wall. However, the effect of minimizing the mass transfer resistance inside the fibre wall is negligible in comparison with the intrinsic reaction rate. Similar results were obtained previously by Hsu and Hsieh [1988] who varied the mixer rpm throughout the course of the reaction and did not see a noticeable kappa number reduction. Based on this rationale, higher delignification as a result of fibre swelling caused by higher alkali charge does not hold. The complete role of alkali in the oxygen delignification chemistry during the oxidation of native lignin is apparently not well-captured using lignin model compound studies. The branched and cross-linked nature of native lignin might be one of the obvious differences between native lignin and the lignin model compounds. Further research is required to find out why the studies with lignin model compound did not show large dependency with respect to the alkali charge, as it occurs in fibre suspensions. In industrial oxygen delignification operations, for economic reasons, the extent of reaction is frequently limited by the availability of alkali charged to the system. The reaction will literally stop when the alkali is exhausted. As a result, given enough alkali, the kappa number will continue to drop indefinitely [McDonough, 1986]. However, this is not the case for the laboratory observations where the process appeared to stop when a limiting kappa number was reached as reported by Lachenal [1998] and more recently by Lucia [2003] (see section 2.8). To handle this issue, we limited our maximum possible delignification to 75%. The remaining 25%> was specified as stagnant or 'floor' lignin. Moreover, we set the amount of alkali consumption per kg of pulp per kappa drop as an adjustable input parameter that we could change to model the actual alkali exhaustion phenomenon observed in industrial oxygen practice, thereby limiting the extent of delignification. Chapter 4: Simulations Results and Discussions  101  Time (minutes) Figure 4.8 Alkali exhaustion profile that limit the extent of delignification  (y H Na0  =  1-9 grams/ kg pulp.kappa)  The decrease in kappa number shown in Figure 4.8 is limited by the availability of alkali. Once the alkali becomes exhausted, delignification reaction cannot proceed any further and the kappa number no longer changes with time. In this case, the higher the alkali charge applied the greater the extent of delignification would be. The delignification profiles shown in Figure 4.8 were obtained by increasing the alkali consumption parameter set in the model (y  Na0H  ) by a  factor of 2.7, i.e., from 0.7 to 1.9 gram of alkali consumed per kg of pulp per kappa number drop. Note that, while the model then predicts the observed alkali dependencies shown in Figure 2.17, the value of y  Na0H  needed to achieve this is the highest value reported in the literature (see  Table 4.2). Consequently, the model can only predict an alkali dependency by exhausting it. Further work on the lignin model compound kinetics is needed to better mimic the larger extent of delignification observed in fibre suspension studies.  Chapter 4: Simulations Results and Discussions  102  4.1.3  Effect of Oxygen Charge The rate of oxygen delignification is affected by the oxygen solubility (concentration) in  the liquor, and the application of the oxygen charge does not affect the rate of reaction as long as there is enough oxygen to last until the end of retention tower. However, in the extreme case where oxygen does run out, the delignification simply stops [Pageau G.L., 2000]. We developed the model based on the assumption that there is a uniform distribution (perfect mixing) of oxygen at any given point in the oxygen tower. Gas-liquid mass transfer will take place as soon as there is a concentration difference between the dissolved oxygen (0 ) and saturated oxygen 2  (0 ) 2sal  concentrations. However, oxygen is consumed as it reacts with the lignin sites.  Depending on the quantity (% on pulp) of oxygen charged into the system, it could get exhausted at some point in the tower. At that point, no further oxygen can be transferred to the liquid phase and the delignification is subsequently driven only by the dissolved oxygen in the liquor.  32  30  Oxygen Charge 0.2 %  28  0.4 % 0.6 % 2 %  26 24  •  22  • Temperature 100°C Bottom Pressure 850 kPa Top Pressure 450 kPa NaOH Charge 2% 0 Charge 2% Consistency 10%  20  18  — .  2  16 •  •  i  0  10  20  30  40  50  60  Time (minutes) Figure 4.9 Oxygen exhaustion during oxygen bleaching ( y = 0.55 grams/ kg pulp.kappa) 02  Chapter 4: Simulations Results and Discussions  103  "  0.006  I  •  I  Oxygen Charge  0.5 % 0.005  Temperature 100°C Bottom Pressure 850 kPa Top Pressure 450 kPa NaOH Charge 2%; 0 Charge 2% Consistency 10%  1 % 1.5% 3% Saturated  ;  E 0.004  c  o 2  0.003  O  0.002  c <D o c  <D OJ ^  0.001  0.000 10  20  30  40  50  60  Time (minutes) Figure 4.10 Dissolved oxygen concentration profile at different oxygen charge vs. bleaching time  The oxygen exhaustion phenomenon is illustrated in Figure 4.9 and Figure 4.10. The initial (t = 0) amount of oxygen gas available for reaction was determined by the oxygen charge (% on pulp). Depending on the oxygen consumption parameter (y  0  ), the amount of oxygen  available for gas-liquid mass transfer decreases over time. In the model, we calculated a simple oxygen gas mass balance for which the consumption of oxygen was determined from the kappa number reduction, and set the gas-liquid mass transfer to zero (k a = 0) as soon as the available L  oxygen gas ran out. Figure 4.10 shows the oxygen concentration profile at different oxygen charges. As can be seen, at 0.2 to 0.6% oxygen charge with_y = 0.55 grams per kappa drop per 02  kg pulp, oxygen became exhausted which is shown as the abrupt decrease in the dissolved oxygen concentration. In reality, the drop in oxygen concentration is not expected to be so abrupt, because as the oxygen becomes consumed, the gas void fraction will decrease which  Chapter 4: Simulations Results and Discussions  104  reduces the gas-liquid mass transfer coefficient (k a), producing a less pronounced change in L  dissolved gas oxygen concentration.  4.1.4  Effect of Suspension Consistency  12 I  1  0  •  1  10  •  1  20  •  1  1  30  1  40  •  1—I 50  1  1  60  Time (minutes) Figure 4.11 Effect of consistency on kappa number during oxygen bleaching  Increasing the suspension consistency has only a slight effect on delignification. As Figure 4.11 shows, at constant alkali and oxygen charges, increasing consistency leads to a moderate increase in delignification as a result of the associated increase in alkali concentration in the liquid phase. In addition, at a constant production rate, with the same tower specification, increasing consistency not only increases the alkali concentration, but also increases the pulp residence time in the oxygen tower due to the lower water content of the system, resulting in a longer reaction time promoting higher delignification. Even so, consistency is not likely to be adjusted due to equipment (e.g. pump) limitations and other process implications it may cause. Chapter 4: Simulations Results and Discussions  105  4.1.5 Effect of Black Liquor Solids Carry-Over  0  10  20  30  40  50  60  Time (minutes) Figure 4.12 Effect of black solids carry-over on kappa number during oxygen bleaching  Good brown stock washing is essential for oxygen delignification, because dissolved lignin carried forward (dissolved black liquor solids) will consume both alkali and oxygen through competitive reactions with the lignin in the fibre (residual lignin), reducing the extent of delignification and may also adversely effect selectivity [Genco et al., 2000; Vuorenvirta et al., 2001]. Depending on the washing efficiency, the amount of black liquor solids carry-over could vary from 0 up to about 50 kg per ton of pulp (McDonough, 1996). With little information available on chemical consumption rate of black liquor solids in industrial oxygen delignification systems, lignin carry-over was assumed to consume oxygen and alkali on the same rate as residual lignin, i.e., 0.55 grams of oxygen per kappa drop and 0.7 grams of alkali per kappa drop. Figure 4.12 above shows the effect of the amount of black liquor Chapter 4: Simulations Results and Discussions  .  ^  ^  ^  . . . . . . .  ...  7  0  6  solids on the kappa number. As can seen, even with a small amount of carry-over, the presence of black solids carry-over can lower the delignification by up to two kappa numbers.  4.1.6 Effect of Mixing Power  32  30  28  26 i  CD  E  24  C  o . 22 ro 20  18  16  0  10  20  30  40  50  60  Time (minutes) Figure 4.13 Effect of mixer power on delignification during oxygen bleaching  Mixing in oxygen delignification is usually conducted in a high-shear mixer just prior to the retention tower. Increasing the mixer power affects kia during mixing and consequently C  £.  •?  delignification as shown in Figure 4.13. At mixer powers of 10 to 10 W/m , not much change in kappa number could be seen. However, as the power was increased to 10  W/m ,  approximately one to two kappa drop could take place within the mixer itself. In addition, although mixing was done very briefly (< 1 second) in the high-shear mixer, its effect could propagate through the 60 minutes of reaction time in the tower. Chapter 4: Simulations Results and Discussions  107  The importance of mixing is more pronounced at the early stages of the reaction where rapid delignification is taking place. Maximizing the amount of oxygen dissolved in the liquid phase will ensure maximum delignification is achieved by the time the pulp exits the tower.  30  Mixer Power 10  W/m  5  10 W/m 6  29  10  W/m  7  10 W/m 8  CD  28  3  3  3  3  E 27  26  25  Temperature 100°C Bottom Pressure 850 kPa Top Pressure 450 kPa NaOH Charge 2%; 0 Charge 2% Pulp residence time in mixer = 0.5s Consistency 10% 2  24  0  2  4  6  8  10  Time (minutes) Figure 4.14 Effect of mixer power on kappa number during the first 10 minutes reaction  The initial kappa drop that takes place during the mixing process is depicted in Figure 4.14 above. Depending on the operating conditions in the mixer (mixer power, oxygen partial pressure, temperature, oxygen charge/gas void fraction, and consistency), up to about a 1.5 kappa drop could occur within the mixer itself followed by a gradually decreasing delignification rate. Highly reactive stilbene structures together with the fast vinyl-ether lignin are responsible for this sudden kappa drop across the mixer. A mixer residence time of 0.5 seconds was used in the simulation. Chapter 4: Simulations Results and Discussions  108  •  1  •  •  0.006  i  Mixer Power 10 W/m  3  10 W/m  3  10 W/m  3  5  _J  6  0.005  7  o E, c o  """"•••-...^ 0.004  .  10 W7m saturated 8  •  3  TO c  O <D  c o O c  0.003  0.002  „  CD  O  0.001  !  ! f:" ;;0-n: .'0 100°C Bottom Pressure 850 kPa Top Pressure 450 kPa NaOH Charge 2%; 0 Charge 2% Pulp residence time in mixer = 0.5s Consistency 10%  • i  1  : i  2  :i 0.000 0  2  4  6  8  10  Time (minutes) Figure 4.15 Effect of mixer power on oxygen concentration in the liquid phase  High mixing power provides the oxygen required to oxidize the lignin structures particularly the fast lignin ones. As can be seen in Figure 4.15, at mixer powers of 10 to 10 5  6  W/m , more oxygen was consumed by reaction than the mixer could supply resulting in a near 3  zero concentration of dissolved oxygen as the pulp exited the mixer. On the other hand, at mixer powers of 10 to 10 W/m , excess oxygen is delivered, with the liquid phase oxygen cone, reach up its highest value and allowing the reaction to take place at the highest possible rate. More importantly, as we can see from Figure 4.15, it requires 8 to 10 minutes retention in the oxygen tower after mixing at 10 to 10 W/m to achieve approximately the same level of 5  6  3  8  3  dissolved oxygen in the liquid phase as it would for mixing using a mixer power of 10 W/m . This is one reason why we observe a higher delignification as the mixer power is increased. It is clear from this simulation that, even though most of the delignification occurs in the retention tower, the high-shear mixer plays a crucial role in supporting efficient industrial Chapter 4: Simulations Results and Discussions  109  oxygen delignification. Moreover, while little can be done to change the tower specifications, ensuring high quality of mixing of pulp at the reactor entrance will give maximum amount of gas-liquid mass transfer possible allowing the maximum delignification level to be attained. The mixing quality exiting the high-shear mixer may also determine the average gas-liquid mass transfer coefficient (kid) in the tower.  4.1.7 Effect of Gas-Liquid Mass Transfer Coefficient in the Retention Tower  64.  -  30  k a Tower  fx  L  V\\'- \ V'. 's  28  s  26  V. \  24  E  1  0.007 s"  1  0.01 s"  1  0.014 s"  \ \ • \ \ '.  22  0.004 s"  X  1  \  -  20 18 16  •  Temperature 100°C Bottom Pressure 850 kPa Top Pressure 450 kPa NaOH Charge 2%; 0 Charge 2% Consistency 10% 2  14 0  10  20  30  40  50  60  Time (minutes) Figure 4.16 Effect of k a (tower) on kappa number during oxygen bleaching L  Rewatkar and Bennington [2002] found that the gas-liquid mass transfer coefficient (kid) in a laboratory retention tower could vary from 0.001 s" to 0.007 s" under medium-consistency 1  1  conditions. Figure 4.16 shows how these variations of fact affect the delignification. As we can see, oxygen mass transfer in the retention tower can dramatically impact delignification. Chapter 4: Simulations Results and Discussions  110  The tower allows the slower lignin reactions to continue and permits leaching of reacted lignin out from the fibre. The flow of oxygen through the tower is much faster than that of the pulp. Gas phase residence times are reported to be only 10 to 37% of that of the pulp [Bennington and Pineault, 1999]. The relative movement between oxygen gas and the pulp through the tower contributes to the gas-liquid mass transfer and replenishes the consumed oxygen. However, the behaviour of the gas phase in industrial oxygen towers and how it contributes to the gas-liquid mass transfer are not known. The quality of the gas distribution in the tower right after it leaves the mixer has never been measured. This simulation suggests that sufficient mixer power is needed to supply the necessary rate of oxygen transfer to the liquid phase, thus maximizing the initial rapid delignification rate. The mixer will closely saturate the liquid phase with oxygen under the prevailing conditions (temperature and pressure). Most of the fast lignins are immediately oxidized following the mixer, whereas the slower lignin reactions subsequently consume the dissolved oxygen in the tower. The gas-liquid mass transfer in the tower will then renew the consumed oxygen allowing the reaction to go further towards completion. Bennington and Pinault [1999] observed that the flow of gas through a mediumconsistency fibre suspension using a laboratory column. They reported that at consistencies greater than 3%>, the gas forms channels as it flows through the fibre network. Once the channels are formed, the gas preferentially follows them. If this is the case in industrial towers, it could restrict the amount of gas-liquid mass transfer in some regions of the tower.  Chapter 4: Simulations Results and Discussions  Ill  4.2  Model Validation Simulation of an industrial oxygen delignification system was carried out to validate the  model. The oxygen delignification system at Howe Sound Pulp and Paper, Port Mellon, BC, was simulated. Also, we used tabulated data from the industrial survey of Bennington and Penault [1999] to further test the model by comparing the actual reported outgoing kappa numbers against the predicted values calculated from the model for the reaction conditions reported.  4.2.1 Howe Sound Pulp & Paper Simulations Howe Sound Pulp and Paper has a two-stage oxygen delignification system with one high-shear medium-consistency mixer prior to each tower. The pulp is fed into the first mixer followed by the first retention tower operating at an inlet (gage) pressure of 925 kPa and a temperature of 85°C. A second mixer was placed prior the second retention tower operating at an inlet pressure of 700 kPa and a temperature of 90°C. A l l of the alkali is added prior to the 1  st  mixer, while the oxygen charge is distributed over the two mixers. The inlet conditions used are: pulp production rate 1060 odt/day, 8.5% consistency, kappa number of 26.5, and pulp viscosity 29 mPa.s. Other operating conditions used in the simulation are listed in Table 4.3.  Table 4.3 Input variables for Howe Sound Pulp & Paper Simulations #i Mixer (BSW)  Variables Inlet Tower pressure, kPa Outlet Tower pressure, kPa Charge of Oxygen, % of pulp  -  #1 Tower #2 Mixer #2 Tower 925  -  700  430  -  140  0.74  -  Charge of alkali, % of pulp  1.4  Mixer Power, W/m Pulp Residence time in mixer, s  10  0.5  -  Tower Residence time, min  -  27  Kappa in  26.49  25-13  18.55  -  Kappa out  2513  -  -  16.43  3  Chapter 4: Simulations Results and Discussions  0.92  6  10  6  0.5  27  112  28  26  24  CD XI  E  22  C CO  a  20  ro  18  16  0  10  20  30  40  50  60  Time (minutes) Figure 4.17 HSPP simulation result and measured kappa number with 95% confidence intervals shown  Howe Sound Pulp & Paper mill uses two identical towers in their two-stage system with large height/diameter ratios of 11.4. The pulp residence time in each tower, depending on the consistency and production rate, varies between 25-30 minutes. Simulations were performed at 27 minutes residence time in each tower. We also accounted for the 1.5 minute time lag between the first and second sampling points, i.e., from brown stock washer to the 1 mixer. st  The result of the simulation is shown in Figure 4.17. There are four pulp sample locations available in the industrial system: at the brown stock washers, immediately after the 1 mixer, at st  the exit of the 1 tower, and at the exit of the 2 st  nd  tower. We time-tracked the samples throughout  the process to minimize process disturbances that could lead to kappa variability. It can be seen that the model is able to predict the delignification in this industrial system very well. The gasliquid mass transfer coefficient used in both towers was 0.007 s" (estimated from superficial gas 1  velocity, see Appendix-E), which is in the region obtained by Rewatkar and Bennington [2002]. Chapter 4: Simulations Results and Discussions  113  4.2.2 Mill Survey Bennington and Pineault  [1999] compiled a mill  survey  of industrial oxygen  delignification practice in North America in an effort to capture process and design information. There are 14 mills involved in the survey representing 19 separate systems. The survey provides information on the overall delignification performance, chemical uses, and operating conditions in both mixers and retention towers. Details of the survey are shown in Table 4.4. With the information taken from the survey, we further validated the model by using the known operating variables in our model and compared the outgoing (predicted) kappa number with that reported in the survey. No changes were made in the kinetic parameters used (Table 3.2). It should be noted that typical values were supplied in the survey, not time-tracked pulp samples. Thus, the accuracy of the survey data is not as good as the time-tracked case.  Table 4.4 Over-all industrial process conditions from mill survey of Bennington and Pinault [1999] Mill  Wood type  Kappa No. in  Delign.  Prod. Rate T w r Hgt. Res. T i m e C o n s . T e m p . Pressure T o p Pres. C h e m i c a l Charge (%)  leaving Aclual (%) (BD(/day)  -  A-l  SW  A-2  SW  30 -  18  B  SW  29  17  (m)  (nun)  32.9  25  32;9  25 58  (°q  (kl'aj)  (kPag)  o  84  925  430  0:92  90  700  140  0.74  0  9  95  640  373.3  1.6  1.6  (%) 8.5  2  NaOH 1.4  40.0  1060  41.4  585  29.3  980  27.4  56  11  90  630  340  1.3  -  35:7  74  12  86  517  230  1.6  1.7 1.7  C  HW  12  8.2  31.7  D,  SW  23.2  12  48.3  D  900-1260  HW  17  9.9  41.8  35.7  74  10-14  86  517  230  1.6  E  SW  27  16  40.7  1080  38.7  88  12  96  570  300  1.6  -  Fi  SW  19.8  12.3  37.9  1015  35.0  85  12  95  500  350  1.3  1.6 1.4  a  ;  Pa  HW  10  7.4  26.0  1360  35;0  -  12  95  500  350  1.2  G,  SW  23  13  43.5  1330  32.3  95  10  99  532  400  1.2  2  G  HW  12.5  8  36.0  1670  32.3  75  10  99  532  400  1.3  1.3 0.85  2  H  SW  19  15  21.1  765  35.7  25  11  80  800  450  1.1  I  SW  23  11.5  50.0  500  10.7  -  25  115  472  470  2.1  1.1  J,  SW  30  18  40.0  900  36.0  62  98  720  340  2.5  2.7  J  1Q  SW  35  23  34.3  -  36.0  20  3.4  SW  23  15  34.8  -  36.0  55  Ki IO>  SW  30  22  26.7  350  22.0  34  SW  30  22  26.7  650  27.0  l>i  SW  26.5  17.8  32.8  600  25:6  L M  HW  16.9  9.2  45.6  650  SW  28.9  20  30.8  850  N-l  SW  28.5  -  SW  -  17.5  2  2  *' S W = Softwood  386  1044  H W = Hardwood  Chapter 4: Simulations Results and Discussions  82-84  957  690  1.8  84-100  694  380  -  -  9  80  690  400  1.1  0.66  25  10  80  690  400  1.1  0.48  56  11  85  1000  400  2.5  -  25;6  25  10.5  88  670  300  1.5  -  30.5  54  10  95  800  440  2  2  27.4  22  11.5  97.5  1000  650  1.5  1.2  43.0  84  11  99  650  200  0.8  0.3  10.5  114  A plot of the predicted kappa number against the actual kappa number shows that the points are clustered around the 45° line (Figure 4.18). The coefficient of determination of the model predictions R = 85.3% or about ±1.3 kappa units. In an actual industrial application, the 2  model would be specifically adjusted to account for a specific pulp, and the predictions would be better. In addition, predicted kappa numbers showed in Figure 4.18 were calculated from raw data provided in the survey. When simulating industrial processes, time-tracked samples are critical since kappa number coming into oxygen delignification fluctuates due to non-uniform cooking in the digester. As expected, the model predictions from the survey are not as accurate as in the Howe Sound Pulp and Paper Mill simulations where we used time-tracked pulp samples.  Chapter 4: Simulations Results and Discussions  115  The gas-liquid mass transfer coefficient (k a) used on the surveyed mill simulations was L  calculated from the gas superficial velocity relative to the actual pulp velocity. The reason for this is because Rewatkar and Bennington [2002] used stationary pulp in a laboratory column to measure the k a for an oxygen tower. In the calculation, gas was assumed to move 3.3 times L  faster than the pulp, this was based on the reported gas residence time distribution in industrial tower that is only 20-40% of that of the pulp [Hornsey et al., 1998]. Moreover, we corrected the k a in the retention tower to account for the temperature difference between the laboratory L  measurements (room temperature, 25°C) and the actual industrial retention tower (80-100°C). More details on the k a in retention tower graphs and calculations are available in Appendix E . L  We modeled hardwood pulp by changing the pulp composition used by the model. The 'very fast' and 'fast' lignin groups were kept the same as in softwood pulp at 5%> and 2%> of the total lignin, respectively. The 'stagnant' lignin was specified at 40%>, this was based on reported value of maximum 60%> delignification achieved after 3 successive oxygen stages [Chirat and Lachenal, 1998] (see maximum lignin removal in section 2.8). The 'slow' and 'very slow' lignin compositions were estimated using the relative proportion of their compositions in softwood lignin and were found to be 15%> and 38%> respectively. By doing adjustment to the pulp compositions between softwood and hardwood, the model was found to give a better prediction of the delignification achieved (calculated as the outlet kappa number) in industrial oxygen delignification systems. This yielded an improvement in the coefficient of determination (R ) of the mill-surveyed simulations from 76.8%) to 85.3%. The pulp species adjustability adds a new essential feature in the model, particularly in the case where mills are using more than one type of species in their woodchip feedstock.  Chapter 4: Simulations Results and Discussions  116  Conclusions  The purpose of this thesis was to develop an oxygen delignification computer model that could capture the significance of gas-liquid mass transfer both in industrial oxygen mixers and retention towers. To do so, we developed the appropriate oxygen delignification kinetics based on lignin model compound studies and coupled them with the gas-liquid mass transfer in both the mediumconsistency mixer [Rewatkar and Bennington, 2000] and in pulp retention towers [Rewatkar and Bennington, 2002] as measured in the laboratory. The model predicted the residual alkali and oxygen concentration in the retention tower. We also incorporated carbohydrate degradation to account for viscosity drop during the reaction. The results of the study are summarized as follow:  1. The oxygen delignification model developed based on the 'Lignin Model Compound' approach can be used effectively to predict mill-scale oxygen delignification performance. 2. Both intense initial high-intensity mixing and good gas-liquid mass transfer in the tower play an important role in the performance of an oxygen bleaching system. 3. Reaction temperature, alkali charge, and O2 partial pressure all have significant impact on increasing delignification, while consistency and black liquor carry-over play minor roles. 4. The simulations suggest that more efficient  mixing could improve delignification by  maximizing the initial period of rapid delignification. 5. The wide range of delignification performance achieved in industrial systems opens an opportunity for the mill to improve their systems using appropriate adjustment in their mixing and tower operating strategies.  Conclusions  117  Recommendations (Future Work)  The following recommendations are suggested for future work in the modeling of oxygen delignification systems:  1. The incorporation of carbohydrate model compounds representing the individual sugar units of cellulose and hemicellulose to model the carbohydrate degradation (pulp strength). This would allow using the model to optimize for improved selectivity while maintaining good delignification. 2. Further investigation on gas hydrodynamic (segregation) within oxygen retention tower. This would allow for developing a better oxygen delignification (tower) model that helps understand roles of gas-liquid mass transfer in the retention tower. 3. Investigating the changes in the structure of residual lignin more thoroughly not only in kraft pulp but also other type of bleached pulps. This would permit application of the model not only to oxygen delignification stages but also for other pulp bleaching operations. 4. Incorporating washing stages (pre- and post- oxygen) in the model to better represent an industrial oxygen delignification system. This would allow a thorough examination of the effectiveness of washing and recycling of post oxygen filtrates. 5. Development of an accurate model for predicting pH within oxygen delignification systems. This would be helpful in achieving optimum chemical charge and other process conditions in industrial oxygen bleaching operations.  Recommendation (future work)  118  Bibliography  Ackert, J.E., Koch, D.D., and Edwards, L.L., "Displacement Chlorination of Kraft Pulps-An Experimental Study and Comparison of Models", TAPPI Journal, 58(10), 141-145, 1975. Ala-Kaila, K., Vehmaa, J., Gullichsen, J., and Stromberg, B., "Leaching of Organic Material from Kraft Pulps", Pulp Washing Conference, 147-154, 1996. 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Yean, W.Q., Goring, D.A.I., Choi, P.M.K.," Removal of Lignin from Kraft Pulp During Washing", Transaction of the Technical Section (Canadian Pulp and Paper Association), 2(2), 5862, 1976. Wang, R.D., Tessier, P.J.-C, and Bennington, C.P.J., "Modeling and Dynamic Simulation of a Bleach Plant", AIChE Journal, 41(12), 2603-2613, 1995. White, D.E., and Larsson, R., "Towers and Reactors", in Pulp Bleaching: Principle and Practice, Dence, C.W. and Reeve, D.W., Section VI, Chapter-4, TAPPI Press, 1996. Yaldez, R., and Stark, H., "The Limitations of Influencing the Mass Transfer during the Oxygen Bleaching Process", Non-Chlorine Bleaching Conference, 1-16, 1996. Yasumoto, M . , Matsumoto, Y . , and Ishizu, A . , "The Role of Peroxide Species in the Carbohydrate Degradation During Oxygen Bleaching", Journal of Wood Chemistry and Technology, 16(1), 95-107, 1996. Zou, X., Gurnagul, N . , Uesaka, T., and Bouchard, J., "Accelerated Aging of Papers of Pure Cellulose: Mechanism of Cellulose Degradation and Paper Embrittlement", Polymer Degradation and Stability, 43, 393-402, 1994.  Bibliography  126  Appendix A: LMC Delignification Kinetics  Oxygen delignification kinetics for representative  lignin model compounds were  developed using the experimental results of Ljunggren and Johansson [1990a, 1990b, 1994]. A l l of the kinetic parameters required in the kinetic expression, i.e., frequency factor (A), activation energy (Ed), and reaction order with respect to oxygen (m) and hydroxide concentration (n) were acquired from non-linear, multi-variable least-square fitting techniques.  A.1  Stilbene Structures Ljunggren and Johansson [1990a] reported the reaction rate constant of 4,4'-dihydroxy-  3,3'-dimethoxy-stilbene with oxygen under alkaline conditions as shown in Table A . l .  Table A . l Observed pseudo-first order rate constant of stilbene Temp [°C]  pH  P02 [kPa]  kobs [10 min" ] 3,  26  9  100  36  26  10  100  320  26  11.5  100  322  26  12.1  100  230  26  13.5  100  38  25  9  250  25  26  9  600  115  27  9  250  36  27  9  300  77  30  9  210  37  30  9  300  138  33  9  100  76  33  12.1  100  320  40  9  100  160  40  10  100  633  40  11.5  100  840  12.2  100  810  40  Appendix A:LMC Delignification Kinetic  1  127  They observed that the stilbene structure reacts very quickly and almost instantaneously under typical oxygen-alkaline oxidation conditions. They measured the reaction rate of stilbene at low temperatures (between 25-40°C) to slow the reaction rate down, making the measurement of stilbene  concentration possible.  However, we were interested  in developing a general  delignification kinetic expression that covered reaction temperatures up to 100°C. To do so, an appropriate assumption was made and several linear interpolations were employed. As can be seen in Table A . l , the reaction rate of stilbene increases strongly with temperature. At the same degree of alkalinity and oxygen pressure, the rate constants were more than doubled for every 10°C increase in temperature. Therefore, for us to estimate the stilbene rate constants at higher temperatures, an assumption that stilbene reaction rate doubles with every 10°C increase in temperature was made.  Table A.2 Estimation of stilbene rate constants up to 110°C Temp  kobs (10 , min" ), P 3  1  0 2  = 100 k P a  °C  pH = 9  pH = 11.5  pH = 12.1  26  36  322  230  33  76  530  320  40  160  840  810  50  320  1680  1620  60  640  3360  3240  70  1.28E+03  6.72E+03  6.48E+03  80  2.56E+03  1.34E+04  1.30E+04  90  5.12E+03  2.69E+04  2.59E+04  100  1.02E+04  5.38E+04  5.18E+04  110  2.05E+04  1.08E+05  1.04E+05  A linear assumption was also made to estimate the stilbene rate constant at three different oxygen pressures. This assumption was based on the reported data of Ljunggren and Johansson  Appendix A:LMC  Delignification  Kinetic  128  [1990a] shown in Table A . l where at a constant pH of 9 and a temperature of 26°C, the reaction rate constant of stilbene increased linearly as the oxygen pressure was increased from 100 kPa to 0.6 kPa. This linear correlation is depicted at Figure A . l by linear regression.  Table A.3 Linear extrapolation to estimate rate constant at oxygen pressure of 300 & 600 kPa P02. kPa  PH  100  9  k  (10 , min" ) 3  o b s  1  T = 26°G  T = 100°C  36  1.02E+04  kobs (10 , 3  PH  min ) 1  T = 26°C  T = 100°C  12.1  230  5.38E+04  linear extrapolation 300  9  77  2.19E+04  12.1  462  1.08E+05  600  9  115  3.27E+04  12.1  690  1.61E+05  Appendix A:LMC Delignification Kinetic  129  Non-linear multi-variable least-square fitting was employed by inputting the reported rate constants of Ljunggren and Johansson together with the estimated rate constants at temperatures up to 100°C and oxygen pressure up to 600 kPa. A complete listing of the Matlab codes used in these non-linear fittings are available in Appendix D.  Results of the fitting:  Actual stilbene rate constant (min" ) 1  Figure A.2 The actual vs predicted stilbene rate constant  Exponential factor (A) = 1.213 x l O  ± 4.62><10  15  14  Activation Energy (Ed) = 76.99xlO ± 10.94xlO J/mole 3  2  Reaction order with respect to oxygen (m) = 0.280 ± 0.0045 Reaction order with respect to alkali (n) = 0.598 ± 0.008 Coefficient of Determination (R ) = 0.999 2  Appendix A:LMC Delignification Kinetic  130  A.2  P-aryl Ether Structures The observed rate constants  of 4-hydroxy-3-methoxy-phenyl-glycol ((3-aryl-ether)  reported by Ljunggren and Johansson [1990a] that were used in non-linear fitting are shown in Table A.4. Table A.4 Observed pseudo-first order rate constant of fi-aryl-ether P  [kPa]  k  [10 'min' ] 3  T e m p [°C]  PH  60  11  1100  3.85  80  11  1100  14  100  10  1100  23  100  11  400  6.1  100  11  600  19.33  100  11  900  41.5  100  11  1100  120  11  1100  0 2  obs  1  47.25 • 125  Fitting results:  Figure A.3 The actual vs predicted beta-aryl-ether rate constant  Appendix A:LMC  Delignification  Kinetic  131  Exponential factor (A) = 3 . 1 6 x l 0  10  ± 8.91 x l O  10  Activation Energy (Ed) = 56.11 x l O ± 88.34xlO J/mole 3  2  Reaction order with respect to oxygen (m) = 1.464 ± 0.54 Reaction order with respect to alkali (n) = 0.312 ± 0.173 Coefficient of Determination (R ) = 0.992 2  A.3  Vinyl (enol) Ether Structures Ljunggren and Johansson [1990a] reported the reaction rate constant of P-guaiacoxy-4-  hydroxy-3-methoxy-styrene (vinyl-ether structures) as shown in Table A. 5. As in the stilbene structures, non-linear multi-variable least-square fitting was applied using the reported reaction conditions and observed rate constants.  Table A.5 Observed pseudo-first order rate constant of vinyl-ether  Temp [ ° q  PH  22  13  40  11  100  5  40  11  600  15  60  11  600  65  60  11  1100  61  80  11  600  128  80  11  1100  187  90  11  600  150  100  10  1100  309  100  11  220  27  100  11  400  147  100  11  600  500  100  11  900  650  100  11  1100  850  Appendix A:LMC Delignification Kinetic  P  0 2  [kPa]  1100  k  [10 ' 3  o b s  14  min" ] 1  132  Fitting results:  0  150  300  450  600  750  900  Actual vinyl-ether rate constant (10 , min" ) 3  1  Figure A.4 The actual vs predicted vinyl-ether rate constant  Exponential factor (A) = 2.19 x 10 ± 1.65 x 10 15  16  Activation Energy (Ea) = 80.12xlO ± 22.28xlO J/mole 3  2  Reaction order with respect to oxygen (m) = 1.372 ± 0.324 Reaction order with respect to alkali (n) = 0.448 ± 0 . 1 5 8 Coefficient of Determination (R ) = 0.966 2  A.4  Diphenyl-Methane (5-5) Structures The observed rate constants of lignin model compound of 4-hydroxy-3-methoxy-phenyl-  glycol (5-5 structure) that were used in non-linear fitting are shown in Table A.6 [Ljunggren and Johansson 1990b].  Appendix A:LMC Delignification Kinetic  133  Table A.6 Observed pseudo-first order rate constant of dipropylbiguaiacol  T e m p [°C]  pH  P02 [kPa]  60  11  1100  4  80  11  1100  12  100  10  1100  22  100  10.5  1100  32  100  11  420  7  100  11  600  8  100  11  800  19.67  100  11  950  25.67  100  11  1100  38  110  11  1100  43  0  10  20  k  [10 mm ] 3  o b s  30  1  40  50  Actual dipropylbiguaiacol rate constant (10 , min" ) 3  1  Figure A.5 The actual vs predicted dipropylbiguaiacol rate constant  Exponential factor (A) = 3.245 x 10 ± 1.957 x 10 8  9  Activation Energy (Ea) = 43.33 xlO ± 15.99x10 J/mole 3  3  Reaction order with respect to oxygen (m) - 1.730 ± 0.786 Reaction order with respect to alkali (n) = 0.118 ± 0.148 Coefficient of Determination (R ) = 0.934 2  Appendix A:LMC Delignification Kinetic  134  Appendix B: Molecular Weight Distribution Experiments  We measured the molecular weight distribution of the residual lignin in the pulp samples that we took at the Howe Sound Pulp and Paper to see whether there are any extents of reactions that change the molecular weight as the pulp moves from brown stock washer, exiting the first mixer, exiting the first and second tower. We chose enzymatic method over acid hydrolysis in isolating the residual lignin from the pulp due to possible changes in lignin structure when using acid hydrolysis. The following are the procedures for lignin isolation and molecular weight distribution measurement using Gel Permeation Chromatography (GPC):  Procedure for Lignin Isolation from pulp (Enzymatic Method): 1. The pulp to be treated with cellulolytic enzymes is washed with tap water to remove any dissolved chemical that might affect the pH of the pulp to be isolated. 2. A pH 4.8 acetate buffer solution is prepared by dissolving 5.8 ml of glacial sodium acetate in 900 ml distilled water. The solution is adjusted to pH 4.8 by adding approximately 70 ml 1M (4gr/100ml) NaOH solution. Once the target pH is reached, volume is adjusted to 1 litre and stored at 4°C. 3. In each of two 2000-ml Erlenmeyer flask with screw caps, a 20-g (OD) specific sample of pulp at a consistency of approximately 2% is prepared by diluting wet pulp of known moisture content with acetate buffer solution to a final volume of 1000 ml. 4. An anti-biotic is added to the pulp sample to prevent bacteria growth. It is prepared by dissolving 400 mg tetracycline hydrochloride (Sigma) and 300 mg cycloheximide (Sigma) in 10 ml acetate buffer solution. 1.5-3 ml of anti-biotic solution is then added to each of 1000-ml pulp sample. 5. The pulp slurry of consistency 2% is then treated with 20 ml [per gr. of dry pulp substrate] of Fibrilase H D L 160 (65 FPU - Iogen Corporation, Ontario) and 6 ml [per gr. of dry pulp substrate] ofNovozym 188 (341 FPU - Novozym North America, Inc.) commercial enzymes.  Appendix B: Molecular  Weight Distribution  Experiments  135  6. After incubation under agitation at 45°C for 48 hr, the hydrolyzates are removed by centrifugation, the residues are washed using distilled water and centrifuged once again to get a cleaner residue of lignin. 7. The residues from the two flasks are combined and placed in a different flask and subjected to a second enzyme treatment by adding 20 ml of the Fibrilase H D L and 6 ml of Novozym 188 enzyme and using the acetate buffer solution to bring the final volume to 1000 ml. 8. Again, the hydrolyzates are separated from the precipitates by centrifugation at 4000 rpm for 2 hours. 9. The residue from the second treatment is then washed twice and then freeze-dried from a water suspension for 3 days to give a water-insoluble residual lignin.  Procedure for measuring molecular mass distribution of lignin: 1. The Cellulolytic Enzyme Lignin (CEL) residual lignins were acetylated with pyridine/acetic anhydride (1/1) for two days. 2. The acetylated lignin samples were then dissolved in 0.1 M LiCl in dimethylformamide (DMF) solvent with concentration 1 mg. lignin/ml. solvent. 3. The sample was then placed in an ultrasonic bath for 1 hr to disperse the bulk lignin into the solvent solution. 4. The partly dissolved lignin in D M F is then filtered prior to column injection using a 0.45 um membrane filter to remove any insoluble fractions that might affect the performance of the Gas Permeation Chromatography column. 5.  150 pi of filtered sample was then chromatographed on the GPC system (Waters Associates, U V and RI detectors) using two styragel columns (HR1 and HR5E) at 50°C with 0.1 M LiCl solution in D M F as the eluting solvent (flowrate, 0.5 ml/min) and monitored with an U V detector at 280 nm. The GPC system was calibrated using standard polystyrene sample.  6. It requires 1 hr for each sample to go through the column and the elution time data is then plotted against intensity (concentration) to give the molecular mass distribution curve.  Appendix B: Molecular  Weight Distribution  Experiments  136  0.30  k  0.25  Brown Stock Pulp Post 1 Oxygen Mixer st  0.20  l  0.15  U  Post 2  nd  Oxygen Tower  cz o  '"*-» CD  i_ •t—»  o O  0.10  0.05  0.00  20  30  40  50  60  Elution Time (minutes) Figure B . l Molecular weight distribution of residual lignin from GPC experiment  Molecular weight of residual lignin following oxygen delignification was found to decrease in size (see section 2.4.3). Lower (smaller) molecular weight lignin is represented by longer elution time in the Figure B . l above. As can be seen, residual lignin sample taken from post oxygen mixer has slightly lower molecular weight (DP) compared to the brown stock one. However, this result of molecular weight distribution is not accurate due to poor solubility of the C E L residual lignin in the molecular weight determination experiment using gel permeation chromatography (GPC). The different concentrations shown in Figure B . l is caused by a small amount of lignin (particularly post-oxygen lignin) dissolved in the solvent prior to injection to GPC column. We experienced experimental limitation where the isolation of lignin using enzymatic procedure did not give sufficient solubility required for GPC measurement.  Appendix B: Molecular  Weight Distribution  Experiments  137  Appendix C: Kappa number & Leaching Experiments  Leaching Procedure: 1. Preheat water bath to 90°C ± 3°C (use hot/pre-boiled water instead of cold water to accelerate the heating process). 2. Weight 7.58 gram of oven-dried pulp and blend it with approximately 50 ml deionized water in a Waring Blender for 1 minute. 3. Weight 0.3 gram Sodium Hydroxide NaOH and dilute it into approximately 700 ml deionized water. 4. Preheat the 700 ml NaOH solution in a hot plate up to 90°C ± 3°C. 5. Add the 50 ml pulp suspension to the preheat alkali solution to form 1% consistency pulp suspension and immediately start the stopwatch. 6. Put the 750 ml pulp-alkaline solution into the 1 L Erlenmeyer flask and immersed it in the water bath at constant temperature of 90°C ± 3°C. 7. Introduce N2 gas to the surface of the suspension and start the laboratory mixer [CaframoRZR1, 60 Hz, 35-2200 rpm] at constant speed of 250 rpm. 8. Keep the pulp suspension in the water bath for 30 minutes. 9. After 25 minutes, pour out the pulp suspension into a mesh and washed it 3 times followed by hand-pressing to form approximately 20% consistency. 10. Put the sample in 4°C storage room or directly to the oven for further kappa number determination.  Appendix C: Kappa Number & Leaching  Experiments  138  Kappa number measurement (TAPPI T-236 cm-85) procedure: 1. Measure required bone dry pulp in grams from the oven 2. Measure 425 ml of deionized water 3. Put the dry pulp into Waring mini container (MC2, 110ml) with some deionized water and disintegrate the pulp using Waring blender (Catalogue No. A-04244-85) for 1 minute 4. Measure 25 ml of 8N sulfuric acid (H2SO4) into the beaker with the pulp. 5. Measure 50 ml of 0. IN potassium permanganate (KMnC^) 6. Put KMnC>4 into beaker and immediately start the timer (for 10 minutes) 7. After 5 minutes, measure the temperature using thermometer 8. Prepare 15 ml of potassium iodide solution (KI) 9. At exactly 10 minutes, put KI into the beaker 10. Add starch indicator for titration (color will turn dark brown) 11. Start the titration using 0.1N sodium thiosulfate (Na2S2C»3) solution 12. Stop the titration when the mixture turns to colorless and record the reading 13. Carry out a blank determination using exactly the same method described above only without the pulp  Calculations: Calculate kappa number ( K ) as follow:  log K = log £  + 0.00093Q? - 50)  [C-l]  [C-2]  Appendix C: Kappa Number & Leaching Experiments  139  If the temperature is not higher than 30°C and not lower than 20°C, correct kappa number as follow:  [C-3]  P=  (b-a)N 0.1  Where: K = kappa number w = weight of moisture-free pulp in the specimen (grams) p = amount of 0. IN potassium permanganate consumed in the blank determination (ml) b = amount of sodium thiosulfate consumed in the blank determination (ml) a = amount of sodium thiosulfate consumed by the test specimen (ml) N = normality of the sodium thiosulfate T = reaction temperature (°C)  Appendix C: Kappa Number & Leaching Experiments  [C-4]  140  Table C . l Kappa number measurement data (unleached and leached pulp samples) No.  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  Sample  point  Kappa  #  Average  K  Sigma  26.92 BrownStock (BSW)  Post 1 Mixer (AMi) st  Post 1 Tower (POi) st  Post 2  n d  Tower (POW)  BSW (leached)  A M i (leached)  POi (leached)  POW (leached)  26.47 26.18 26.43 25.20 24.79 25-52 25.02 18.92 18.31 18.84 18.44 16.03 16.63 16.52 16.55 24.00 23.32 23.62 20.51 20.62 21.08 15.46 1505 14.95 1352 13-38 13.26  Appendix C: Kappa Number & Leaching Experiments  26.50  0.31  2513  0.31  18.63  0.30  16.43  0.27  2365  o.34  20.74  0.30  15.15  0.27  1339  0.13  141  28 Brown Stock Washer  26  V Pulp Sample -•— Unleached -•— Leached  24  i-  CD  22  n  \  E =j 20 ca CL  a. 18 ca  f  Tower  16 2  n d  Tower  14 12 I  L.  10  20  30  40  50  60  Time (minute) Figure C l kappa number of unleached and leached pulp sample taken from HSPP  As expected, the kappa number of the leached pulp sample is lower at all sample points, indicating that a portion of the lignin was not removed during washing (pulp samples were washed thoroughly prior to leaching experiments). The kappa drop of the leached sample from the brown stock washer to post-mixer was 2.91 kappa compared to 1.37 kappa of the unleached one. The increase in kappa drop after leaching could indicate that some partially oxidized lignin that had reacted in the mixer did not have enough time to diffuse out of the fibre (see lignin leaching in section 2.4.1). However, the exact structure of leached material is not know due to the fact that kappa number test measured not only lignin but also other non-lignin structures i.e. hexenuronic acid (see kappa number determination in section 2.4.2).  Appendix C: Kappa Number & Leaching  Experiments  142  Appendix D: M A T L A B Programming C o d e s  D.1  Non-linear Fitting of Lignin Model Compound Kinetics  Three general Matlab function files were required to do the non-linear least-square fitting: •  'fiit.m', this function file was used to define the power-law curve fitting relationship  •  'dffit.m', this function file was used to define the partial derivatives of the power-law curve fitting relationship  •  'marqrt.m', this function file was used to calculate the fitting parameter, the fitted values, variance, 95% confidence interval, and number of iteration required to reach the desired tolerance.  function y=ffit(x,k) % ' f f i t . m ' i s a f u n c t i o n m - f i l e t h a t d e f i n e s t h e power law curve % Input arguments: % x = s c a l a r o r v e c t o r o f independent x v a l u e s % k = v e c t o r o f f i t t i n g parameters % Output argument: % y = s c a l a r or vector of f i t t e d y values  fitting  relationship.  y=k(l) *exp(-k(2) / ( 8 . 3 1 4 * x ( l ) ) ) * ( x ( 2 ) k ( 3 ) ) * ( x ( 3 )k ( 4 ) ) ; A  A  function dy=dffit(i,x,k) % ' d f f i t . m ' i s a f u n c t i o n m - f i l e t h a t d e f i n e s the p a r t i a l d e r i v a t i v e s o f t h e % power law curve f i t t i n g r e l a t i o n s h i p w.r.t. the f i t t i n g parameters a l and a2. % Input arguments: % i = index i n d i c a t i n g p.d. w.r.t. a l o r a2 % x = s c a l a r o r v e c t o r o f independent x v a l u e s % k = v e c t o r o f f i t t i n g parameters % Output argument: % dy = s c a l a r o r v e c t o r o f p a r t i a l d e r i v a t i v e v a l u e s a = k ( l ) ; b=k(2); c = k ( 3 ) ; d=k(4); i f i==l d y = e x p ( - b / ( 8 . 3 1 4 * x ( l ) ) ) * (x (2) c ) * (x (3) d ) ; e l s e i f i==2 dy=(-a*exp(-b/{8.314*x(l)))*(x(2) c)*(x(3) d))/(8.314 *x(l) ) ; e l s e i f i==3 d y = a * e x p ( - b / ( 8 . 3 1 4 * x ( l ) ) ) * (x (2) c ) * l o g (x (2) ) * (x (3) d ) ; else dy=a*exp(-b/(8.314*x(l)))*(x(2) c)*(x(3) d)*log(x(3)) ; end A  A  A  A  A  A  A  Appendix D:MATLAB  Programming  Codes  A  143  function  [a,yfit,var,k,AA,int]  =  marqrt(W,a,f,df)  % A s s i g n v a r i a b l e s r e q u i r e d by t h e f i t t i n g [c,m]=size(W); cm=2:c; c p = l : c - l ; y=W(l,:); x ( c p , :)=W(cm, :) ; t o l = l e - 4 ; maxit=50000; r e l a x = l ; n=length(a) ; lamda=le-3; maxda=lelO; i t e r = 0 ; f l a g = l ; k ( l , : ) = a ;  procedure  % Calculating y f i t f o r i=l:m xx=x(:,i); yl(i)=feval(f,xx,a) ; end % C a l c u l a t e e r r o r term S SSQ=sum((y-yl). 2 ) ; A  % U s i n g c o m b i n a t i o n Marquardts and Newton method w h i l e maxda>tol iter=iter+l; i f iter>maxit f p r i n t f ( ' M a r q u a r d t s method f a i l e d t o converged i n %2.0f i t e r a t i o n s return end i f flag==l alpha=coef f 2 ( f , d f , x , y , a ) ; for j=l:n diag(j)=alpha(j,j); end end % U s i n g marquardt's method, i n t r o d u c i n g lamdap=lamda+l; for j=l:n alpha(j , j)=diag(j)*lamdap; end  lamda  % U s i n g Newton's method t o f i n d a new f i t t i n g parameter da=gauss(alpha); %d=alpha(:,5); dd=[alpha(:,1) a l p h a ( : , 2 ) a l p h a ( : , 3 ) a l p h a ( : , 4 ) ] ; %d=alpha(:,3); dd=[alpha(:,1) a l p h a ( : , 2 ) ] ; dda=dd\d; da=dda'; a new=a+relax*da; maxda new=max(abs(da./a)); f o r i=l:m xx=x(:,i) ; y f i t ( i ) = f e v a l ( f , x x , a new) ; end  dda=dd\d; da=dda';  % C a l c u l a t e t h e new e r r o r term SSQ_new=sum((y-yfit) . "2) ; % Check whether t h e new e r r o r i s l a r g e r o r l e s s % I f l a r g e r , i n c r e a s e lamda by t e n , o t h e r w i s e d e c r e a s e lamda by t e n . i f SSQ_new<SSQ a=a new; lamda=0.l*lamda; SSQ=SSQ_new; maxda=maxda new; flag=l; else 1amda=10*1amda; flag=0; end k(iter+l,:)=a; end  Appendix D:MATLAB  Programming  Codes  \n',iter)  144  % C a l c u l a t i n g the v a r i a n c e var=SSQ/(m-n); % C a l c u l a t e 95% c o n f i d e n c e i n t e r v a l o f the paramater d=length(alpha)-1; AA=inv(alpha(1:d,1:d)); for i = l : d tk ( i ) =sqrt (var) * s q r t ( A A ( i , i ) ) ; ' •• i n t ( i ) = 1 . 9 6 * t k (i) ; end  D.1.1  Stilbene Structure  % Stilbene Structure % S p e c i f y the known independent v a r i a b l e s (temperature, p r e s s u r e , a l k a l i % and oxygen c o n c e n t r a t i o n ) and dependent v a r i a b l e (observed r e a c t i o n r a t e ) yl=[36 76 160 320 1280 2560 10240 20480 322 530 840 1680 6720 13440 53760 107520 5475.56 . 8177.78 21902.22 32711.11 26996.87 40320 107987.48 161280.00]./1000; % R e a c t i o n c o n s t a n t [min-1] x l c = [ 2 6 33 40 50 70 80 100 110 26 33 40 50 70 80 100 110 80 80 100 100 80 ... 80 100 1 0 0 ] ; % Temperature [ C e l c i u s ] xl=xlc+273.15; % Temperature [ K e l v i n ] x2c=[9 9 9 9 9 9 9 9 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 9 9 9 9 11.5 11.5 11.5 11.5]; % pH x2=l./(10. (14.-x2c)); % A l k a l i Concentration [mol/ltr] x3c=[0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.3 0.6 0.3 ... 0.6 0.3 0.6 0.3 0.6]; % Oxygen P r e s s u r e [Mpa] x3cc=(x3c*1000)/101.325; % Oxygen P r e s s u r e [atm] x3=(exp(((0.046.*xl."2)+(203.35.*xl.*log(xl./298))-(299.378+0.092.*xl).*(xl-298)2 0 . 5 9 1 * 1 0 3 ) . / ( 8 . 3 1 4 4 . * x l ) ) . * x 3 c c ) ; % Oxygen s o l u b i l i t y [mol/Kg H20] N=(yl;xl;x2;x3] ; A  A  % A s s i g n i n i t i a l e s t i m a t e s o f t h e f i t t e d parameter k= [ 1 1 1 1 ] ; % Use Marquart's method t o c a r r y out t h e n o n - l i n e a r f i t , o u t p u t r e s u l t s i n c l u d e % the f i t t e d c o e f f i c i e n t ( b ) , f i t t i n g v a l u e ( y f i t ) , and v a r i a n c e ( v a r i ) [b,yfit,vari, its,A,int]=marqrt(N,k,'ffit','dffit'); % Determine t h e c o e f f i c i e n t o f D e t e r m i n a t i o n o f t h e a c t u a l and f i t t e d v a l u e s ya=sum(yl)/length(yl); r = l - s u m ( ( y l - y f i t ) . " 2 ) / s u m ( ( y l - y a ) . 2) ; A  % Output r e s u l t s result=[yl;xl;x2;x3;yfit;yfit-yl]; f p r i n t f C\n F i t t e d parameters a r e : \n\n') fprintfC k(%1.0f) =%8.6f \n',[ 1: l e n g t h (b) ;b] ) fprintfC C o e f f i c i e n t o f D e t e r m i n a t i o n (R 2) = %8.6f \n',[r]) f p r i n t f ( ' \ n \ n " R e a c t i o n r a t e f o r L i n i n Model Compound ( S t i l b e n e ) " \n') fprintf ( | I I I I I I \n' ) fprintfCI y I xl I x2 | x3 I yfit I yfit-y I\n') fprintf! 'I I I I I I I \n' ) fprintfC| %6.2f | %5.1f I %1.4f | %1.5f I %6.2f | %10.6f | \ n ' , r e s u l t ) fprintf ( 'I I I I I I I \n' ) f p r i n t f C \ n C o n f i d e n c e l e v e l i n t e r v a l k ( % 1 . 0 f ) = +/- %8 . 6 f ,[ 1: l e n g t h (b) ; i n t ] ) % P l o t r e s u l t s o f c a l c u l a t e d d a t a vs e x p e r i m e n t a l d a t a figure(1) p l o t ( y l , y f i t , ' * ' , [0 800], [0 800]) xlabel('Actual'), ylabel('Model') t i t l e ( 'Stilbene') A  1  Appendix D:MATLAB Programming Codes  145  D.1.2 Vinyl (Enol) Ether Structure  % Vinyl  (enol) E t h e r S t r u c t u r e  % S p e c i f y the known i n d e p e n d e n t v a r i a b l e s (temperature, p r e s s u r e , a l k a l i % and oxygen c o n c e n t r a t i o n ) and dependent v a r i a b l e (observed r e a c t i o n r a t e ) yl=[14 5 15 65 61 128 187 150 309 27 147 500 650 850]./1000; % R e a c t i o n c o n s t a n t [min-1] xlc=[22 40 40 60 60 80 80 90 100 100 100 100 100 100]; % Temperature [ C e l c i u s ] xl=xlc+273.15; % Temperature [ K e l v i n ] x2c=[13 11 11 11 11 11 11 11 10 11 11 11 11 11]; % pH x2=l./(10. (14.-x2c)); % A l k a l i Concentration [mol/ltr] x 3 c = [ l . l 0.1 0.6 0.6 1.1 0.6 1.1 0.6 1.1 0.22 0.4 0.6 0.9 1.1]; % Oxygen P r e s s u r e [Mpa] x3cc=(x3c*1000)/101.325; % Oxygen P r e s s u r e [atm] x3=(exp(((0.04 6 . * x l . 2 ) + ( 2 0 3 . 3 5 . * x l . * l o g ( x l . / 2 9 8 ) ) - ( 2 9 9 . 3 7 8 + 0 . 0 9 2 . * x l ) . * ( x l - 2 9 8 ) 20.591*10 3)./(8.3144.*xl)).*x3cc); % Oxygen s o l u b i l i t y [mol/Kg H20] N=[yl;xl;x2;x3]; A  A  A  % Assign i n i t i a l k= [ 1 1 1 1 ] ;  e s t i m a t e s o f the f i t t e d  parameter  % Use Marquart's method t o c a r r y out the n o n - l i n e a r f i t , o u t p u t r e s u l t s % the f i t t e d c o e f f i c i e n t (b), f i t t i n g v a l u e ( y f i t ) , and v a r i a n c e ( v a r i ) [ b , y f i t , v a r i , i t s , A , i n t ] =marqrt (N, k, ' f f i t ' , ' d f f i t ' ) ; % Determine the c o e f f i c i e n t ya=sum(yl)/length(yl) ;  o f D e t e r m i n a t i o n o f the a c t u a l  and  fitted  include  values  r=l-sum((yl-yfit). 2)/sum((yl-ya)."2); A  % Output  results  result=[yl; xl; x 2 ; x 3 ; y f i t ; y f i t - y l ] ; f p r i n t f ! ' \ n F i t t e d p a r a m e t e r s a r e : \n\n') fprintf(' k(%1.0f) = %8.6f \n' ,[ 1: l e n g t h (b) ; b] ) fprintf(' C o e f f i c i e n t o f D e t e r m i n a t i o n (R 2) = %8.6f \n',[r]) f p r i n t f ( ' \ n \ n " R e a c t i o n r a t e f o r L i n i n Model Compound (Enol - E t h e r ) " \n') fprintf(' I I I I I l\n' ) fprintf(' I y I xl | x2 | x3 I yfit l\n' ) f p r i n t f (' I I I I I l\n' ) fprintfC I %6.2f | %5.1f | %1.4f | %1.5f | %6.2f | %10.6f f p r i n t f (' I I I I I I \n' ) fprintf('\n Confidence l e v e l i n t e r v a l k(%1.0f) = +/- % 8 . 6 f , [ 1 : l e n g t h ( b ) ; i n t ] ) A  % P l o t r e s u l t s o f c a l c u l a t e d d a t a vs e x p e r i m e n t a l d a t a figure(1) p l o t ( y l * 1 0 3 , y f i t * 1 0 3 , ' * ' , [0 900], [0 900]) xlabel('Actual'), ylabel('Model') t i t l e ( ' E n o l - Ether') A  A  Appendix D.MATLAB Programming Codes  I |  yfit-y  I |\n',result) I  146  D.1.3  Beta Aryl Ether Structure  % Beta A r y l E t h e r S t r u c t u r e % S p e c i f y the known independent v a r i a b l e s (temperature, p r e s s u r e , a l k a l i % and oxygen c o n c e n t r a t i o n ) and dependent v a r i a b l e (observed r e a c t i o n r a t e ) yl=[3.85 14 23 6.1 19.33333333 41.5 47.25 125]./1000; % R e a c t i o n c o n s t a n t [min-1] xlc=[60 80 100 100 100 100 100 120]; % Temperature [ C e l c i u s ] xl=xlc+273.15; % Temperature [ K e l v i n ] x 2 c = [ l l 11 10 11 11 11 11 11]; % pH x2=l./(10. (14.-x2c)); % A l k a l i Concentration [mol/ltr] x 3 c = [ l . l 1.1 1.1 0.4 0.6 0.9 1.1 1.1]; % Oxygen P r e s s u r e [Mpa] x3cc=(x3c*1000)/101.325; % Oxygen P r e s s u r e [atm] x3=(exp(((0.04 6 . * x l . 2 ) + ( 2 0 3 . 3 5 . * x l . * l o g ( x l . / 2 9 8 ) ) - ( 2 9 9 . 3 7 8 + 0 . 0 9 2 . * x l ) . * ( x l - 2 98)20.591*10 3)./(8.3144.*xl)).*x3cc); % Oxygen s o l u b i l i t y [mol/Kg H20] N=[yl;xl;x2;x3]; A  A  A  % Assign i n i t i a l k= [ 1 1 1 1 ] ;  e s t i m a t e s o f the f i t t e d  parameter  % Use Marquart's method t o c a r r y out the n o n - l i n e a r f i t , o u t p u t r e s u l t s i n c l u d e % the f i t t e d c o e f f i c i e n t (b), f i t t i n g v a l u e ( y f i t ) , and v a r i a n c e ( v a r i ) [b,yfit,vari,its,A,int]=marqrt(N,k, ' f f i t ' , ' d f f i t ' ) ; % Determine the c o e f f i c i e n t ya=sum(yl)/length(yl);  o f D e t e r m i n a t i o n of the a c t u a l and  fitted  values  r=l-sum((yl-yfit). 2)/sum((yl-ya). 2); A  % Output  A  results  result=[yl; xl; x2;x3;yfit;yfit-yl]; f p r i n t f C \ n F i t t e d parameters a r e : \n\n') fprintfC k(%1.0f) = %8.6f \n',[ 1: l e n g t h (b) ; b] ) fprintf(' C o e f f i c i e n t o f D e t e r m i n a t i o n (R 2) = %8.6f \n',[r]) f p r i n t f ( ' \ n \ n " R e a c t i o n r a t e f o r L i n i n Model Compound (Beta - A r y l - E t h e r ) " \n') f p r i n t f (' I I I I I I l\n' ) fprintfC I y I xl | x2 | x3 I yfit | yfit-y I \n' ) fprintfC I I I I I I l\n') fprintfC I %6.2f I %5.1f | %1.4f | %1.5f | %6.2f | %10.6f | \ n ' , r e s u l t ) fprintfC I I I I I I l\n' ) f p r i n t f C\n Confidence l e v e l i n t e r v a l k(%1.0f) = +/- %8 . 6 f ,[ 1: l e n g t h (b) ; i n t ] ) % P l o t r e s u l t s o f c a l c u l a t e d d a t a vs e x p e r i m e n t a l d a t a f i g u r e (1) p l o t ( y l * 1 0 3 , y f i t * 1 0 3 , ' * ' , [0 140], [0 140]) xlabel( 'Actual'), ylabel('Model') t i t l e ( ' B e t a - A r y l - Ether') A  A  Appendix D:MATLAB  A  Programming  Codes  147  D.1.4 Dipropylbiguaiacol (5-5) Structure  % Beta D i p r o p y l b i g u a i a c o l S t r u c t u r e % S p e c i f y t h e known i n d e p e n d e n t v a r i a b l e s (temperature, p r e s s u r e , a l k a l i % and oxygen c o n c e n t r a t i o n ) and dependent v a r i a b l e ( o b s e r v e d r e a c t i o n r a t e ) yl=[4 12 22 32 7 8 1 9 . 6 6 6 6 6 6 6 7 25.66666667 38 43]./1000; % R e a c t i o n c o n s t a n t [min-1] xlc=[60 80 100 100 100 100 100 100 100 110]; % Temperature [ C e l c i u s ] xl=xlc+273.15; % Temperature [ K e l v i n ] x 2 c = [ l l 11 10 10.5 11 11 11 11 11 11]; % pH x2=l./(10. (14.-x2c)); % A l k a l i Concentration [mol/ltr] x 3 c = [ l . l 1.1 1.1 1.1 0.42 0.6 0.8 0.95 1.1 1.1]; % Oxygen P r e s s u r e [MPa] x3cc=(x3c*1000)/101.325; % Oxygen P r e s s u r e [atm] x3=(exp(((0.046.*xl."2)+(203.35.*xl.*log(xl./298))-(299.378+0.092.*xl).*(xl-298)2 0 . 5 9 1 * 1 0 ^ 3 ) . / ( 8 . 3 1 4 4 . * x l ) ) . * x 3 c c ) ; % Oxygen s o l u b i l i t y [mol/Kg H20] N=[yl;xl;x2;x3]; A  % Assign i n i t i a l k=[1 1 1 1] ;  e s t i m a t e s o f the f i t t e d  parameter  % Use M a r q u a r t ' s method t o c a r r y out t h e n o n - l i n e a r f i t , o u t p u t r e s u l t s i n c l u d e % the f i t t e d c o e f f i c i e n t ( b ) , f i t t i n g v a l u e ( y f i t ) , and v a r i a n c e ( v a r i ) [b,yfit,vari,its,A,int]=marqrt(N,k,'ffit','dffit'); % Determine t h e c o e f f i c i e n t ya=sum(yl)/length(yl) ;  of Determination  o f the a c t u a l  and f i t t e d  values  r=l-sum((yl-yfit). 2)/sum((yl-ya). 2); A  A  % Output r e s u l t s rf ep sr ui ln t =f [( y' l\ ;n x lF;i x2; y lr]e;: \n\n') t t e dx 3p;ayrfaimte; ty ef ri st - a fprintfC k(%1.0f) =%8.6f \n',[ 1: l e n g t h (b) ; b] ) fprintf(' C o e f f i c i e n t o f D e t e r m i n a t i o n (R 2) = %8.6f \n',[r]) f p r i n t f ( \ n \ n " R e a c t i o n r a t e f o r L i n i n Model Compound ( D i p r o p y l b i g u a i a c o l ) " \n' ) fprintfC I I I I I I l\n') fprintfC I y I xl | x2 | x3 I yfit I yfit-y |\n') fprintfC I I I I I I l\n') fprintfC I %5.2f | %5.1f | %1.4f | %1.5f I %5.2f | %10.6f | \ n ' , r e s u l t ) fprintfC I I I I I I I \n ' ) fprintf('\n Confidence l e v e l i n t e r v a l k(%1.0f) = +/- % 8 . 6 f , [ 1 : l e n g t h ( b ) ; i n t ] ) A  1  1  % P l o t r e s u l t s o f c a l c u l a t e d d a t a vs e x p e r i m e n t a l figure(1) p l o t ( y l * 1 0 3 , y f i t * 1 0 3 , ' * ' , [0 5 0 ] , [0 5 0 ] ) x l a b e l ( ' A c t u a l ) , ylabel('Model') title{'Dipropylbiguaiacol ) A  A  1  1  Appendix D.MATLAB Programming Codes  data  a,  % % % %  b  g l o b a l 0 2 s a t k i a T Cm  TO  S c r i p t f i l e t h a t c a l c u l a t e s the kappa number, r e s i d u a l a l k a l i , r e s i d u a l oxygen and v i s c o s i t y drop d u r i n g oxygen d e l i g n i f i c a t i o n r e a c t i o n . A s e t o f ODEs a r e s o l v e d s i m u l t a n e o u s l y u s i n g b u i l t - i n matlab ODE s o l v e r ODE23s by c a l l i n g f u n c t i o n f i l e r h s k i n e t i c . m where a l l of the ODE are put t o g e t h e r . 1  1  Xg  T_V = [80 90 100 120]; for a=l:length(T_V)  to "a  ro  O  % I n v e s t i g a t e the e f f e c t of temperature  [C]  % A s s i g n known o p e r a t i n g c o n d i t i o n s i n both mixer and r e t e n t i o n tower TDS = 0; % Amount o f B l a c k l i q u o r s o l i d c a r r y over (kg/ton of p u l p ) e = le6; % M i x e r power (W/m 3) T = T_V(a); % Temperature (C) Ac = 2; % A l k a l i Charge [%] p = 2; % Oxygen Charge (%) Cm = 10; % Pulp c o n s i s t e n c y [%] K i n = 30; % Kappa Number Coming i n t o the mixer P = 1000000/(24*60); % Pulp p r o d u c t i o n r a t e [1000 odt/day] (o.d. kg/min) Xg_t = 0 . 1 ; % V o i d f r a c t i o n i n the oxygen tower ( f i x e d ) H = 42; % Tower h e i g h t (m) AR = 11.4; % Tower A s p e c t ratio D = H/AR; % Tower i n t e r n a l diameter (m) V = pi*D 2*H/4; % Volume o f the tower (m 3) n = 100; % T o t a l number o f l a y e r i n w h i c h the tower i s d i v i d e d dV = V*1000/n; % Volume o f each s i n g l e l a y e r o f tower ( L i t e r ) dH = H/n; % H e i g h t o f each s i n g l e l a y e r o f tower (m) dt = dV*(1-Xg_t)*Cm/(P*(100-0.333*Cm)) ; % Residence time of each l a y e r (min) A  a'  Co  A  A  dm = 0.5/60; m = 1; dt_m = dm/m; OH = 10*Cm*Ac/(40*(100-Cm)); 02Av = 10*p; PWV = 10 (7.96681-(1668.21/(T+228)))*0.1333; P02_b = 850-PWV; P02_t = 450-PWV; Vc = 29; SW = [5 2 20 48 2 5 ] ; SW TDS = [SW(1) SW(2) 30 6 3 ] ; A  % % % % % % % % % %  M i x e r r e s i d e n c e time [min] T o t a l number of l a y e r i n which mixer i s d i v i d e d Residence time of each s i n g l e l a y e r i n M i x e r [min] I n i t i a l Hydroxide C o n c e n t r a t i o n [ m o l / L t r Suspension] I n i t i a l Oxygen a v a i l a b l e f o r r e a c t i o n [gr 02/min] Water-vapor p r e s s u r e [kPa] - A n t o i n e E q u a t i o n Oxygen p a r t i a l p r e s s u r e (gage) a t the bottom of the tower [kPa] Oxygen p a r t i a l p r e s s u r e (gage) a t the top of the tower [kPa] I n i t i a l CED V i s c o s i t y (mPa.s) C o m p o s i t i o n s o f LMC i n Softwood K r a f t r e s i d u a l l i g n i n [%] % C o m p o s i t i o n s of d i s o l l v e d l i g n i n i n b l a k l i q u o r s o l i d s c a r r y - o v e r [%]  % B l a c k L i q u o r S o l i d C a r r y Over E f f e c t [% mass d r y s o l i d c o n t e n t ] % C a r r y o v e r from post-02 washer i s i g n o r e d due t o much l e s s d e t r i m e n t a l compare t o BLS BLS = TDS/1000; % Amount o f BLS c a r r y over [kg d.s./kg p u l p ] B L S _ l i g n i n = 0.36*BLS; % Amount o f d i s s o l v e d l i g n i n c a r r y over i n the BLS [kg l i g n i n / k g p u l p ] B L S _ v e r y _ f a s t = SW_TDS(1)*BLS_lignin; % Amount o f v e r y f a s t l i g n i n i n l i g n i n c a r r y over [% l i g n i n / k g p u l p ] B L S _ f a s t = SW_TDS(2)*BLS_lignin; % Amount o f f a s t l i g n i n i n l i g n i n c a r r y over [% l i g n i n / k g pulp] BLS_slow = SW_TDS(3)*BLS_lignin; % Amount o f slow l i g n i n i n l i g n i n c a r r y over [% l i g n i n / k g p u l p ] [Mass f r a c t i o n of l i g n i n ] B L S _ v e r y _ s l o w = SW_TDS(4)*BLS l i g n i n ; % Amount o f v e r y slow l i g n i n i n l i g n i n c a r r y over [% l i g n i n / k g p u l p ]  O x *< <a  CD 3  D  JD  <5" o o 3 O  CL  CD  TO a Si.  X'  b  ta  3' Op  TO  TDSKappa_very_fast = BLS_very_fast/0.147; % C o r r e s p o n d i n g k a p p a o f TDS TDSKappa_fast = BLS_fast/0.147; % C o r r e s p o n d i n g k a p p a o f TDS TDSKappa_slow = BLS_slow/0.147; % C o r r e s p o n d i n g k a p p a o f TDS TDSKappa_very_slow = BLS_very_slow/0.147; % C o r r e s p o n d i n g k a p p a o f TDS K i n _ t d s = TDSKappa_very_fast+TDSKappa_fast+TDSKappa_slow+TDSKappa_very_slow; c o r r e s p o n d t o b l a c k s o l i d c a r r y over) al=(SW(l)*Kin)/(Kin+Kin_tds) ; bl=(SW(2)*Kin)/(Kin+Kin_tds) ; cl=(SW(3)*Kin)/(Kin+Kin_tds) ; dl=(SW(4)*Kin)/(Kin+Kin_tds); el=(SW(5)*Kin)/(Kin+Kin_tds) ; fl=TDSKappa_very_fast*100/(Kin+Kin_tds) ; gl=TDSKappa_fast*100/(Kin+Kin_tds) ; hl=TDSKappa_slow*100/(Kin+Kin_tds); dl=TDSKappa_very_slow*100/(Kin+Kin_tds); SW_new = [ a l b l c l d l e l f l g l h i i l ] . / 1 0 0 ; [mass f r a c t i o n ]  c a r r y over with respect t o very fast l i g n i n c a r r y over w i t h respect t o fast l i g n i n c a r r y over w i t h r e s p e c t t o slow l i g n i n c a r r y over with respect t o very slow l i g n i n % New k a p p a n u m b e r ( r e d u a l k a p p a + k a p p a  New S t i l b e n e C o m p o s i t i o n New V i n y l _ E t h e r C o m p o s i t i o n New B e t a - a r y l - E t h e r C o m p o s i t i o n New D i p r o p y l g u a i a c o l ( 5 - 5 ) C o m p o s i t i o n New S t a g n a n t ( f l o o r k a p p a ) C o m p o s i t i o n Stilbene Composition i n d i s s o l v e d l i g n i n Vinyl_Ether Composition i n d i s s o l v e d l i g n i n Beta-Aryl-Ether Composition i n dissolved l i g n i n D i p r o p y l g u a i a c o l (5-5) C o m p o s i t i o n i n d i s s o l v e d l i g n i n New c o m p o s i t i o n o f S o f t w o o d K r a f t r e s i d u a l l i g n i n ( t a k i n g i n t o  account  BLS)  % A S S I G N I N I T I A L CONDITION O 2 s a t = ( P O 2 _ b / 1 0 1 . 3 ) * e x p ( ( 0 . 0 4 6 * ( T + 2 7 3 ) 2 + 2 0 3 . 3 5 * ( T + 2 7 3 ) * l o g ( ( T + 2 7 3 ) /298) - ( 2 9 9 . 3 7 8 + 0 . 0 9 2 * ( T + 2 7 3 ) ) * ( ( T + 2 7 3 ) - 2 9 8 ) 20.591e3)/(8.3144*(T+273))); t ( l ) = 0 ; O2(l)=0; 02s(1)=02sat; 02g(l)=02Av; % S p e c i f y i n g i n i t i a l c o n d i t i o n s o f oxygen c o n c e n t r a t i o n s K ( l ) = K i n + K i n _ t d s ; Kl(1)=SW_new(1)*K(1); K2(1)=SW_new(2)*K(1); K3(1)=SW_new(3)*K(1); K4(1)=SW_new(4)*K(1); % Specifying i n i t i a l c o n d i t i o n s o f r e s i d u a l kappa K 5 ( l ) = T D S K a p p a _ v e r y _ f a s t ; K6(1)=TDSKappa_fast; K7(1)=TDSKappa_slow; K8(1)=TDSKappa_very_slow; % Specifying i n i t i a l conditions of d i s s o l v e d kappa DP(1)=1/(961.38*logl0(Vc)-245.3); % I n i t i a l degrees of p o l y m e r i z a t i o n o f p o l y s a c c h a r i d e chains A  %MIXER Xg=l.206*Cm*p*(T+273)/(1.206*Cm*p*(T+273)+3.2*(100-0.333*Cm)*PO2_b*0.145); % Gas v o i d f r a c t i o n WV_T1=8.9e-4; % W a t e r v i s c o s i t y a t T = 25C [N.s/m2] % W a t e r V i s c o s i t y a t T = T2 [F] [N.s/m2] WV_T2=exp(-0.942268218-25.61273 6036/(T*9/5+32)-1.324553216*log(T*9/5+32)) ; D_T1=2.5e-5; % D i f f u s i o n c o e f f i c i e n t o f o x y g e n i n w a t e r a t T = 25C [ c m 2 / s ] D T2=D T l * ( ( T + 2 7 3 ) / 2 9 8 ) * ( W V Tl/WV T 2 ) ; % E i n s t e i n r e l a t i o n t o e s t i m a t e d i f f u s i o n c o e f f i c i e n t o f o x y g e n a t T = T2 [K] % G a s - l i q u i d mass t r a n s f e r c o e f f i c i e n t i n m i x e r ( m i n - l ) kla=60*l.17e-4*e*Xg 2.6*exp(-0.386*Cm)*(D_T2/D_T1) 0.8; % S o l v i n g a s e t o f ODE i n t h e h i g h i n t e n s i t y m i x e r f o r q=2:m+l options=odeset('RelTol',le-6, 'Stats','off'); [ x , y ] = o d e 2 3 s ( ' r h s k i n e t i c ' , [ 0 d t _ m ] , [ K l ( q - 1 ) K2(q-1) K3(q-1) K4(q-1) K5(q-1) K6(q-1) K7(q-1) K8(q-1) OH(q-l) 02(q-1) DP(q1)],options); j=length(x); K l ( q ) = y ( j , 1) ; K2 (q) =y ( j , 2) ; K3 (q) =y ( j , 3) ; K4 (q) =y ( j , 4 ) , K ( q ) = K 1 ( q ) + K 2 ( q ) + K 3 ( q ) + K 4 ( q ) + ( S W ( 5 ) / 1 0 0 ) * K i n ; K 5 ( q ) = y ( j , 5 ) ; K 6 ( q ) = y ( j , 6) ; K7 (q) =y ( j , 7) ; K8 (q) =y ( j , 8) ; t ( q ) = t ( q - l ) + x ( j ) ; OH (q) =y ( j , 9) ; 02 (q) =y ( j , 10) ; DP (q) =y ( j , 11) 0 2 s ( q ) = 0 2 s a t ; V c ( q ) = 1 0 ( (1/(DP(q)(+24 5.3)/961.38) ; 02g(q)=02g(q-1)-0.55*(K(q-l)-K(q)) ; end A  A  A  A  A  so  TO : Si.  %TOWER %Output from m i x e r c a l c u l a t i o n i s used as an i n p u t the tower c a l c u l a t i o n kla=0.007*60; % G a s - l i q u i d Mass t r a n s f e r c o e f f i c i e n t i n tower [ m i n - l ] Xg=Xg_t; % Gas v o i d f r a c t i o n of r e t e n t i o n tower f o r i=q+l:n+q % S o l v i n g a s e t of ODE i n the r e t e n t i o n tower l a y e r by l a y e r options=odeset(' R e l T o l , l e - 6 , ' S t a t s ' , ' o f f ' ) ; [ x , y ] = o d e 2 3 s ( ' r h s k i n e t i c \ [0 dt] , [KI (i-1) K 2 ( i - 1 ) K 3 ( i - 1 ) K 4 ( i - 1 ) K 5 ( i - 1 ) K 6 ( i - 1 ) K 7 ( i - 1 ) K 8 ( i - 1 ) O H ( i - l ) 0 2 ( i - l ) D P ( i 1)],options); j=length(x); KI(i)=y(j,1); K 2 ( i ) = y ( j , 2 ) ; K3 ( i ) =y (j , 3) ; K 4 ( i ) = y ( j , 4 ) ; K ( i ) = K 1 ( i ) + K 2 ( i ) + K 3 ( i ) + K 4 ( i ) + (SW (5)/100) * K i n ; K5 ( i ) =y (j , 5) ; K 6 ( i ) = y ( j , 6) ; K7 ( i ) =y (j , 7) ; K 8 ( i ) = y ( j , 8 ) ; t ( i ) = t ( i - l ) + x ( j ) ; 0H(i)=y ( j , 9) ; 02 ( i ) =y (j , 10) ; DP ( i ) = (y (j , 11) ) ; 02s ( i ) =02sat; Vc(i)=10 ((1/(DP(i))+245.3)/961.38) ; % V i s c o s i t y changes from p r e v i o u s l a y e r t o the n e x t l a y e r P02=P02_b-(P02_b-P02_t)*(dH*(i-q)/H); % P r e s s u r e changes from p r e v i o u s l a y e r t o the next l a y e r O2sat=(PO2/101.3)*exp((0.04 6*(T+273)"2+203.35*(T+273)*log((T+273)/298)-(299.378+0.092*(T+273))*((T+273)-298)20.591e3)/(8.3144*(T+273))); O2g(i)=O2g(i-l)-0.55*(K(i-l)-K(i) ) ; i f 0 2 g ( i ) <= 0 kla=0; end end K ( l ) = K i n ; KK(a,:)=K; OHH(a,:)=OH; 022(a,:)=02; 022s(a,:)=02s; DPP(a,:)=1./DP; Vcc(a,:)=Vc; t t ( a , : ) = t ; end A  1  to  A  TO to  % P l o t R e s u l t s i . e . kappa number, a l k a l i & oxygen c o n c e n t r a t i o n , figure(1) p l o t (t,KK(l, :),t,KK(2,:),'d',t,KK(3,:),'v ,t,KK(4,:), o') xlabel('Time [minutes] ) y l a b e l ( ' K a p p a Number ) ,  and v i s c o s i t y a g a i n s t time  ,  1  1  legend('Temperature  = 80C', Temperature = 90C','Temperature = 100C','Temperature = 120C',0) 1  figure(2) p l o t ( t , 022(1, : ) , ' : ' , t , 0 2 2 s ( 1 , : ) , ' : ' , t , 0 2 2 ( 2 , : ) , ' - . ' , t , 0 2 2 s ( 2 , : ) , '. ' , t,022 (3, :) , 'o' , t,022s (3, : ) , 'o' , t,022 (4, : ) , ' v', t , 022s (4, :) , 'V ) x l a b e l f ' T i m e [minutes]') y l a b e l ( ' D i s s o l v e d Oxygen C o n c e n t r a t i o n [ m o l / l t r s u s p e n s i o n ] ' ) legend!'Temperature = 80C','Temperature = 90C','Temperature = 100C','Temperature = 120C',0) figure(3) p l o t ( t , O H H ( 1 , :),':',t,OHH(2, :),'-.',t,OHH(3, : ) , 'o',t,OHH(4, : ) , 'v') x l a b e l ( ' T i m e [minutes]') y l a b e l ( ' H y d r o x i d e Concentration [ m o l / l t r suspension]') figure(4) legend('Temperature = 80C','Temperature = 90C','Temperature = 100C','Temperature = 120C',0) plot(KK(1,:),Vcc(1,:),':',KK(2,:),Vcc(2,:),'-.',KK(3,:),Vcc(3,:),'o',KK(4,:),Vcc(4,:),'v') x l a b e l ( ' K a p p a Number') y l a b e l ( ' C E D V i s c o s i t y [mPa.s]') legend!'Temperature = 80C','Temperature = 90C','Temperature = 100C','Temperature = 120C',0)  % rhskinetic.m function L = rhskinetic(x,y) g l o b a l 0 2 s a t k i a T Cm R = 8.314;  Xg % I d e a l Gas Constant  [J/mole.K]  % S t i l b e n e model compound A l = 1213240903060715; % Pre-exponential factor E a l = 76989.169767; % A c t i v a t i o n Energy [J/mol] ml = 0.28002; % R e a c t i o n o r d e r w i t h r e s p e c t t o A l k a l i Charge n l = 0.629768; % R e a c t i o n order w i t h r e s p e c t t o Oxygen P r e s s u r e -Al*exp(-Eal/(R*(T+273)))*(y(9)"ml)*(y(10) nl)*y(1) ; % 1 s t o r d e r r x n c o n s t a n t f o r S t i l b e n e [min-1] L(l) A  % E n o l - E t h e r model compound A2 = 2188320815066909.7; % Ea2 = 80119.023814; . . % m2 = 0.447651; % n2 = 1.372502; % L(2) = -A2*exp(-Ea2/(R*(T+273)))* ( y ( 9 ) % B e t a - A r y l - E t h e r model compound A3 = 31664581945.410217; % Ea3 = 56114.186203; % m3 = 0.312195; % n3 = 1.464752; % L(3) = -A3*exp(-Ea3/(R* ( T + 2 7 3 ) ) ) * ( y ( 9 )  A  A  Pre-exponential factor A c t i v a t i o n Energy [J/mol] R e a c t i o n o r d e r w i t h r e s p e c t t o A l k a l i Charge R e a c t i o n o r d e r w i t h r e s p e c t t o Oxygen P r e s s u r e m2)*(y(10) n2)*y(2); % 1st order rxn constant f o r Enol-Ether A  [min-1]  Pre-exponential factor A c t i v a t i o n Energy [J/mol] R e a c t i o n o r d e r w i t h r e s p e c t t o A l k a l i Charge R e a c t i o n o r d e r w i t h r e s p e c t t o Oxygen P r e s s u r e m3)*(y(10) n3)*y(3); % 1 s t o r d e r r x n c o n s t a n t f o r B e t a - A r y l - E t h e r [min-1] A  % D i p r o p y l b i g u a i a c o l model compound A4 = 324504027.121509; % Pre-exponential factor Ea4 = 43334.405927; % A c t i v a t i o n Energy [J/mol] m4 = 0.118397; % R e a c t i o n o r d e r w i t h r e s p e c t t o A l k a l i Charge n4 = 1.730276; % R e a c t i o n o r d e r w i t h r e s p e c t t o Oxygen P r e s s u r e 1,(4) = - A 4 * e x p ( - E a 4 / ( R * ( T + 2 7 3 ) ) ) * ( y ( 9 ) m 4 ) * ( y ( 1 0 ) n 4 ) * y ( 4 ) ; % 1 s t o r d e r r x n c o n s t a n t f o r D i p r o p y l b i g u a i a c o l [min-1] A  A  % D i s s o l v e d C a r r y o v e r Model Compound L(5) = - A l * e x p ( - E a l / ( R * ( T + 2 7 3 ) ) ) * ( y ( 9 ) m l ) * ( y ( 1 0 ) n l ) * y ( 5 ) L(6) = -A2*exp(-Ea2/(R* (T+273)))*(y(9) m2)*(y(10) n2)*y(6) L(7) = -A3*exp(-Ea3/(R* (T+273)))*(y(9) m3)*(y(10) n3)*y(7) L(8) = -A4*exp(-Ea4/(R* (T+273)))*(y(9) m4)*(y(10) n4)*y(8) A  A  A  A  A  A  A  A  % % % %  1st 1st 1st 1st  order order order order  rxn rxn rxn rxn  constant constant constant constant  for for for for  S t i l b e n e TDS [min-1] E n o l - E t h e r TDS [min-1] B e t a - A r y l - E t h e r TDS [min-1] D i p r o p y l b i g u a i a c o l TDS [min-1]  % Oxygen and A l k a l i Consumption r a t e L(9) = - ( 0 . 7 / 4 0 ) * ( C m / ( 1 0 0 - C m ) ) * ( - L ( 1 ) - L ( 2 ) - L ( 3 ) - L ( 4 ) - L ( 5 ) - L ( 6 ) - L ( 7 ) - L ( 8 ) ) ; 1,(10) = k i a * ( 0 2 s a t - y (10) ) / (1-Xg) - (0 . 55/32) * (Cm/ (100-0 . 333*Cm) ) * (-L (1)-L (2)-L (3) -L (4)-L (5)-L ( 6) -L (7)-L ( 8 ) ) ; % Carbohydrate degradation rate 1,(11) = 0.00001* ( - L ( l ) - L ( 2 ) - L ( 3 ) - L ( 4 ) - L ( 5 ) - L ( 6 ) - L ( 7 ) - L ( 8 ) ) ; L = [ L (1) ; L ( 2 ) ; L ( 3 ) ; L ( 4 ) ; L ( 5 ) ; L ( 6 ) ; L ( 7 ) ; L ( 8 ) ; L ( 9 ) ; L ( 1 0 ) ;  L(ll)];  :  TO  to  % % % %  S c r i p t f i l e t h a t c a l c u l a t e s the kappa number, r e s i d u a l a l k a l i , r e s i d u a l oxygen and v i s c o s i t y drop d u r i n g oxygen d e l i g n i f i c a t i o n r e a c t i o n . A s e t o f ODEs a r e s o l v e d s i m u l t a n e o u s l y u s i n g b u i l t - i n matlab ODE s o l v e r ODE23s by c a l l i n g f u n c t i o n f i l e ' r h s k i n e t i c . m ' where a l l o f the ODE a r e put t o g e t h e r .  % U s i n g I r i b a r n e S Schroeder F i b e r S u s p e n s i o n Carbohydrate D e g r a d a t i o n K i n e t i c  o  g l o b a l 0 2 s a t k i a T Cm Xg  o a  I n v e s t i g a t e the e f f e c t o f temperature  T_V = [80,90,100,120]; for a=l:length(T_V)  % As s i g n known o p e r a t i n g c o n d i t i o n s i n b o t h mixer and r e t e n t i o n tower % Amount o f B l a c k l i q u o r s o l i d c a r r y over (kg/ton of pulp) TDS = 0; % M i x e r power (W/m 3) e = le6; % Temperature (C) T = T_V(a) ; % A l k a l i Charge [%] Ac = 2; % Oxygen Charge (%) P = 2; % Pulp c o n s i s t e n c y [%] Cm 10; % Kappa Number Coming i n t o the m i x e r K i n = 30; % Pulp p r o d u c t i o n r a t e [1000 odt/day] (o.d. kg/min) P = 1000000/(24 6 0 ) ; % V o i d f r a c t i o n i n the oxygen tower ( f i x e d ) Xg_t = 0.1; H = 42; % Tower h e i g h t (m) AR % Tower Aspect ratio 11.4; D = H/AR; % Tower i n t e r n a l d i a m e t e r (m) V = pi*D 2*H/4; % Volume o f the tower (m"3) n = 100; % T o t a l number o f l a y e r i n which the tower i s d i v i d e d dV = V*1000/n; % Volume o f each s i n g l e l a y e r o f tower ( L i t e r ) dH = H/n; % H e i g h t o f each s i n g l e l a y e r o f tower (m) dt = dV*(1-Xg_t *Cm/(P*(100-0.333*Cm)) , % Residence time o f each l a y e r (min);  <r>  A  : a'  :  TO Co  :  A  dm = 0.5/60; m = 1; dt_m = dm/m; OH = 10*Cm*Ac/(40*(100-Cm)) ; P02_b = 850; P02_t = 450; Vc = 29; SW = [5 2 20 48 2 5 ] ; SW TDS = [SW(1) SW(2) 30 63];  % % % % % % % %  M i x e r r e s i d e n c e time [min]; T o t a l number o f l a y e r i n which mixer i s d i v i d e d Residence time o f each s i n g l e l a y e r i n M i x e r [min] I n i t i a l Hydroxide C o n c e n t r a t i o n [ m o l / L t r Suspension] Oxygen p r e s s u r e i n the bottom o f the tower [KPa] Oxygen p r e s s u r e i n the top o f t h e tower [KPa] I n i t i a l CED V i s c o s i t y (mPa.s) Compositions o f LMC i n Softwood K r a f t r e s i d u a l l i g n i n [%] % Compositions o f d i s o l l v e d l i g n i n i n b l a k l i q u o r s o l i d s c a r r y - o v e r [%]  % B l a c k L i q u o r S o l i d C a r r y Over E f f e c t [% mass d r y s o l i d c o n t e n t ] % C a r r y o v e r from post-02 washer i s i g n o r e d due t o much l e s s d e t r i m e n t a l compare t o BLS BLS = TDS/1000; % Amount o f BLS c a r r y over [kg d.s./kg p u l p ] B L S _ l i g n i n = 0.36*BLS; % Amount o f d i s s o l v e d l i g n i n c a r r y over i n the BLS [kg l i g n i n / k g p u l p ] B L S _ v e r y _ f a s t = SW_TDS(1)*BLS_lignin; % Amount o f v e r y f a s t l i g n i n i n l i g n i n c a r r y over [% l i g n i n / k g p u l p ] B L S _ f a s t = SW_TDS(2)*BLS_lignin; % Amount o f f a s t l i g n i n i n l i g n i n c a r r y over [% l i g n i n / k g p u l p ] BLS_slow = SW_TDS(3)*BLS_lignin; % Amount o f slow l i g n i n i n l i g n i n c a r r y over [% l i g n i n / k g p u l p ] [Mass fraction of lignin] B L S _ v e r y _ s l o w = SW_TPS(4)*BLS l i g n i n ; % Amount of v e r y slow l i g n i n i n l i g n i n c a r r y over [% l i g n i n / k g p u l p ]  or fl> 3 CD J?o  0) o  3" -» O CD  Q. <D  —i  to  o a>  CT O  3" *< a ~i s> r*  CD  o  (P  to  ft) a 0) r*  o  3 3 CD  TO 3  to "a  a TO On  TDSKappa_very_fast = BLS_very_fast/0.147; % C o r r e s p o n d i n g kappa o f TDS TDSKappa_fast = BLS_fast/0.147; % C o r r e s p o n d i n g kappa of TDS TDSKappa_slow = BLS_slow/0.147; % C o r r e s p o n d i n g kappa o f TDS TDSKappa_very_slow = BLS_very_slow/0.147; % C o r r e s p o n d i n g kappa of TDS K i n _ t d s = TDSKappa_very_fast+TDSKappa_fast+TDSKappa_slow+TDSKappa_very_slow; c o r r e s p o n d t o b l a c k s o l i d c a r r y over) al=(SW(1)*Kin)/(Kin+Kin_tds) , bl=(SW(2)*Kin)/(Kin+Kin_tds) , cl=(SW{3)*Kin)/(Kin+Kin_tds) , dl=(SW(4)*Kin)/(Kin+Kin_tds) , el=(SW(5)*Kin)/(Kin+Kin_tds) , fl=TDSKappa_very_fast*100/(Kin+Kin_tds); gl=TDSKappa_fast*100/(Kin+Kin_tds); hl=TDSKappa_slow*100/(Kin+Kin_tds); il=TDSKappa_very_slow*100/(Kin+Kin_tds) ; SW_new = [ a l b l c l d l e l f l g l h i i l ] . / 1 0 0 ; [mass f r a c t i o n ]  c a r r y over with respect t o very f a s t l i g n i n c a r r y over with respect t o f a s t l i g n i n c a r r y o v e r w i t h r e s p e c t t o slow l i g n i n c a r r y o v e r w i t h r e s p e c t t o v e r y slow l i g n i n % New kappa number ( r e d u a l kappa + kappa  New S t i l b e n e C o m p o s i t i o n New V i n y l _ E t h e r C o m p o s i t i o n New B e t a - a r y l - E t h e r C o m p o s i t i o n New D i p r o p y l g u a i a c o l (5-5) C o m p o s i t i o n New S t a g n a n t ( f l o o r kappa) C o m p o s i t i o n S t i l b e n e Composition i n d i s s o l v e d l i g n i n V i n y l _ E t h e r Composition i n d i s s o l v e d l i g n i n B e t a - A r y l - E t h e r Composition i n d i s s o l v e d l i g n i n D i p r o p y l g u a i a c o l (5-5) C o m p o s i t i o n i n d i s s o l v e d l i g n i n New c o m p o s i t i o n o f Softwood K r a f t r e s i d u a l l i g n i n ( t a k i n g i n t o a c c o u n t BLS)  %ASSIGN INITIAL CONDITION O2sat=(PO2_b/101.3)*exp((0.04 6*(T+273)"2+203.35*(T+273)*log((T+273)/298)-(299.378+0.092*(T+273))*((T+273)-298)20.591e3)/(8.3144*(T+273))) ; t ( l ) = 0 ; O2(l)=0; 02s(l)=02sat; % S p e c i f y i n g i n i t i a l c o n d i t i o n s o f oxygen c o n c e n t r a t i o n s K ( l ) = K i n + K i n _ t d s ; Kl(1)=SW_new(1)*K(1); K2(1)=SW_new(2)*K(1); K3(1)=SW_new(3)*K(1); K4(1)=SW_new(4)*K(1); % Specifying i n i t i a l c o n d i t i o n s o f r e s i d u a l kappa K5(1)=TDSKappa_very_fast; K6(1)=TDSKappa_fast; K7(1)=TDSKappa_slow; K8(1)=TDSKappa_very_slow; % Specifying i n i t i a l conditions of d i s s o l v e d kappa DP(1)=961.38*logl0(Vc)-245.3; % I n i t i a l degrees o f p o l y m e r i z a t i o n o f p o l y s a c c h a r i d e chains mn(l)=le6/(162*DP(l)); %MIXER Xg=l .206*Cm*p*(T+273)/(1.206*Cm*p*(T+273)+3.2*(100-0.333*Cm)*PO2_b*0.145) ; % Gas v o i d f r a c t i o n WV_T1=8.9e-4; % Water v i s c o s i t y a t T = 25C [N.s/m2] WV_T2=exp(-0.942268218-25.612736036/(T*9/5+32)-1.324553216*log(T*9/5+32)) ; % Water V i s c o s i t y a t T = T2 [F] [N.s/m2] D_Tl=2.5e-5; % D i f f u s i o n c o e f f i c i e n t o f oxygen i n water a t T = 25C [cm"2/s] D_T2=D_T1*((T+273)/298)*(WV_T1/WV_T2); % E i n s t e i n r e l a t i o n t o e s t i m a t e d i f f u s i o n c o e f f i c i e n t o f oxygen a t T = T2 [K] kla=60*l.17e-4*e*Xg"2.6*exp(-0.386*Cm)*(D JT2/D_T1)"0.8; % G a s - l i q u i d mass t r a n s f e r c o e f f i c i e n t i n m i x e r (min"-l) f o r q=2:m+l % S o l v i n g a s e t o f ODE i n the h i g h i n t e n s i t y mixer options=odeset('RelTol ,le-6, 'Stats' , ' off ' ) ; [x, y ] = o d e 2 3 s ( ' r h s k i n e t i c 2 2 c m c ' , [0 dt_m], [Kl(q-1) K2(q-1) K3(q-1) K4(q-1) K5(q-1) K6(q-1) K7(q-1) K8(q-1) OH(q-l) 02(q-1) mn(q-1)],options); j=length(x); K l ( q ) = y ( j , 1 ) ; K 2 ( q ) = y ( j , 2 ) ; K 3 ( q ) = y ( j , 3 ) ; K4(q)=y(j,4) ; K(q)=K1(q)+K2(q)+K3(q)+K4 (q) + (SW ( 5 ) / 1 0 0 ) * K i n ; K5(q)=y (j,5) ; K 6 ( q ) = y ( j , 6) ; K7 (q) =y (j , 7) ; K8 (q) =y (j , 8) ; t ( q ) = t ( q - l ) + x ( j ) ; OH (q) =y (j , 9) ; 02 (q) =y (j , 10) ; mn (q) =y (j , 11) ; 02s (q) =02sat; DP(q)=le6/(162*mn(q)); Vc(q)=10"((DP(q)+245.3)/961. 38) ; end 1  TO a  %TOWER %Output from m i x e r c a l c u l a t i o n i s used as an i n p u t the tower c a l c u l a t i o n kla=0.004*60; % G a s - l i q u i d Mass t r a n s f e r c o e f f i c i e n t i n tower [ m i n ~ - l ] Xg=Xg_t; % Gas v o i d f r a c t i o n of r e t e n t i o n tower f o r i=q+l:n+q % S o l v i n g a s e t of ODE i n the r e t e n t i o n tower l a y e r by l a y e r options=odeset('RelTol',le-6,'Stats', off ) ; [x,y]=ode23s( ' r h s k i n e t i c 2 2 c m c ' , [0 d t ] , [ K l ( i - l ) K 2 ( i - 1 ) K 3 ( i - 1 ) K 4 ( i - 1 ) K 5 ( i - 1 ) K 6 ( i - 1 ) K 7 ( i - 1 ) K 8 ( i - 1 ) O H ( i - l ) 0 2 ( i - l ) mn(i-1)],options); j=length(x); K l ( i ) = y ( j , 1); K 2 ( i ) = y ( j , 2 ) ; K 3 ( i ) = y ( j , 3) ; K 4 ( i ) = y ( j , 4 ) ; K ( i ) = K 1 ( i ) + K 2 ( i ) + K 3 ( i ) + K 4 ( i ) + (SW(5)/100)*Kin; K 5 ( i ) = y (j,5) ; K 6 ( i ) = y ( j , 6) ; K7 ( i ) =y (j , 7) ; K 8 < i ) = y ( j , 8 ) ; t ( i ) = t ( i - l ) + x ( j ) ; O H ( i ) = y ( j , 9 ) ; 02 ( i ) =y (j , 10) ; mn ( i ) = (y (j , 11) ) ; 0 2 s ( i ) = 0 2 s a t ; DP(i)=le6/(l62*mn(i)); Vc(i)=10 ((DP(i)+245.3)/961.38); % V i s c o s i t y changes from p r e v i o u s l a y e r t o the next l a y e r P02=P02_b-(P02_b-P02_t)*(dH*(i-q)/H); % P r e s s u r e changes from p r e v i o u s l a y e r t o the next l a y e r O2sat=(PO2/10lT3)*exp((0.04 6*(T+273)"2+203.35*(T+273)*log((T+273)/298)-(2 99.378+0.092*(T+273))*((T+273)-298)20.591e3)/(8.3144*(T+273))); end 1  to "a  1  A  O • o  STO Co  K ( l ) = K i n ; KK(a,:)=K; -OHH(a, :)=OH; 022(a, :)=02; 022s(a, :)=02s; DPP(a, :)=1./DP; V c c ( a , :)=Vc; t t ( a , :)=t; end % P l o t R e s u l t s i . e . kappa number, a l k a l i & oxygen c o n c e n t r a t i o n , figure(1) plot (t,KK(l,:) t,KK(2,:),'d ,t,KK(3,:),'v',t,KK(4,:), o') x l a b e l ( ' T i m e [minutes]') y l a b e l ( ' K a p p a Number') ,  and v i s c o s i t y a g a i n s t time  ,  (  l e g e n d ( ' T e m p e r a t u r e = 80C','Temperature = 90C','Temperature = 100C','Temperature = 120C',0) figure(2) p l o t ( t , 0 2 2 ( 1 , : ) , ':',t,022(2, :) , '-.', t,022(3, : ) , 'o',t,022(4, : ) , ' v ' , t , 0 2 s , 'd') x l a b e l ( ' T i m e [minutes]') y l a b e l ( ' D i s s o l v e d Oxygen C o n c e n t r a t i o n [ m o l / l t r s u s p e n s i o n ] ) 1  l e g e n d ( ' T e m p e r a t u r e = 80C','Temperature = 90C','Temperature = 100C', Temperature = 120C',0) 1  figure(3) p l o t ( t , O H H ( 1 , :),':',t,0HH(2, : ) , '-.', t,0HH(3, :) , 'o' , t,OHH(4, :) , 'v') x l a b e l ( ' T i m e [minutes]') y l a b e l ( ' H y d r o x i d e Concentration [ m o l / l t r suspension]') l e g e n d ( Temperature = 80C ,'Temperature = 90C','Temperature = 100C','Temperature = 120C',0) 1  1  figure(4) p l o t ( K K ( 1 , :) , V c c ( 1 , : ) , ' : ' , KK(2,:),Vcc(2, : ) , ' - . ' , K K ( 3 , : ) , V c c ( 3 , : ) , 'o , KK(4, :),Vcc (4, : ) , ' v' ) x l a b e l ( Kappa Number') y l a b e l ( ' C E D V i s c o s i t y [mPa.s]') l e g e n d ( ' T e m p e r a t u r e = 80C','Temperature = 90C','Temperature = 100C','Temperature = 120C',0) 1  1  ••V  TO  to  3 STO  f u n c t i o n L = r h s k i n e t i c 2 2 c m c ( x , y) g l o b a l 0 2 s a t k i a T Cm Xg R = 8.314;  % I d e a l Gas C o n s t a n t  [J/mole.K]  % S t i l b e n e m o d e l compound A l = 1213240903060715; % Pre-exponential factor E a l = 76989.169767; % A c t i v a t i o n Energy [J/mol] ml = 0.28002; % Reaction order w i t h respect t o A l k a l i Charge n l = 0.629768; % R e a c t i o n o r d e r w i t h r e s p e c t t o Oxygen P r e s s u r e L(l) -Al*exp(-Eal/(R* (T+273)))*(y(9)"ml)*(y(10)"nl)*y(1); % 1st order rxn constant  for Stilbene  % E n o l - E t h e r m o d e l compound A2 = 2 1 8 8 3 2 0 8 1 5 0 6 6 9 0 9 . 7 ; % Pre-exponential factor Ea2 = 8 0 1 1 9 . 0 2 3 8 1 4 ; % A c t i v a t i o n Energy [J/mol] m2 = 0 . 4 4 7 6 5 1 ; % Reaction order w i t h respect t o A l k a l i Charge n2 = 1 . 3 7 2 5 0 2 ; % R e a c t i o n o r d e r w i t h r e s p e c t t o Oxygen P r e s s u r e L(2) = -A2*exp(-Ea2/(R*(T+273)))*(y(9)"m2)*(y(10)"n2)*y(2); % 1st order rxn constant  f o r Enol-Ether  % B e t a - A r y l - E t h e r m o d e l compound A3 = 3 1 6 6 4 5 8 1 9 4 5 . 4 1 0 2 1 7 ; % Pre-exponential factor Ea3 = 56114.186203; % A c t i v a t i o n Energy [J/mol] m3 = 0 . 3 1 2 1 9 5 ; % Reaction order with respect t o A l k a l i Charge n3 = 1.464752; % R e a c t i o n o r d e r w i t h r e s p e c t t o Oxygen P r e s s u r e L(3) = -A3*exp(-Ea3/(R*(T+273)))*(y(9)"m3)*(y(10)"n3)*y(3); % 1st order rxn constant  f o r B e t a - A r y l - E t h e r [min-1]  % D i p r o p y l b i g u a i a c o l m o d e l compound A4 = 3 2 4 5 0 4 0 2 7 . 1 2 1 5 0 9 ; % Pre-exponential factor Ea4 = 4 3 3 3 4 . 4 0 5 9 2 7 ; % A c t i v a t i o n Energy [J/mol] m4 = 0 . 1 1 8 3 9 7 ; % Reaction order w i t h respect t o A l k a l i Charge n4 = 1 . 7 3 0 2 7 6 ; % R e a c t i o n o r d e r w i t h r e s p e c t t o Oxygen P r e s s u r e L(4) = -A4*exp(-Ea4/(R*(T+273)))*(y(9)"m4)*(y(10)"n4)*y(4) , % 1st order rxn constant  f o r D i p r o p y l b i g u a i a c o l [min-1]  % D i s s o l v e d C a r r y o v e r M o d e l Compound L(5) = - A l * e x p ( - E a l / ( R * (T+273)))*(y(9)"ml)*(y(10)"nl)*y(5) L(6) = -A2*exp(-Ea2/(R* (T+273)))*(y(9)"m2)*(y(10)"n2)*y(6) L(7) = -A3*exp(-Ea3/(R* (T+273)))*(y(9)"m3)*(y(10)"n3)*y(7) L(8) = -A4*exp(-Ea4/(R* (T+273)))*(y(9)"m4)*(y(10)"n4)*y(8)  for for for for  % % % %  1st 1st 1st 1st  order order order order  rxn rxn rxn rxn  constant constant constant constant  [min-1]  [min-1]  S t i l b e n e TDS [ m i n - 1 ] E n o l - E t h e r TDS [ m i n - 1 ] B e t a - A r y l - E t h e r TDS [ m i n - 1 ] D i p r o p y l b i g u a i a c o l TDS [ m i n - 1 ]  % Oxygen and A l k a l i Consumption r a t e L(9) = - (0.7/40)*(Cm/(100-Cm))*(-L(1)-L(2)-L(3)-L(4)-L(5)-L(6)-L(7)-L(8) ) ; L(10) = k i a * ( O 2 s a t - y ( 1 0 ) ) / ( 1 - X g ) - ( 0 . 5 5 / 3 2 ) * ( C m / ( 1 0 0 - 0 . 3 3 3 * C m ) ) * ( - L ( l ) - L ( 2 ) - L ( 3 ) - L ( 4 ) - L ( 5 ) - L ( 6 ) - L ( 7 ) - L ( 8 ) ' % Carbohydrate degradation rate Acd = 7 e l 0 ; % Pre-exponential factor Eacd = 78000; % A c t i v a t i o n Energy [J/mol] mcd = 0.3; % Reaction order with respect to A l k a l i n c d = 0.4; % R e a c t i o n o r d e r w i t h r e s p e c t t o Oxygen L(ll) = Acd*exp(-Eacd/(R*(T+273)))*(y(9)"mcd)*(y(10)"ncd); L =  [L(1);  L ( 2 ) ; L ( 3 ) ; L(4); L(5); L(6); L(7); L(8); L(9); L(10);  L(ll)];  Charge Pressure  156  Appendix E: Gas-liquid Mass Transfer in Tower  The volumetric gas-liquid mass transfer coefficient  for the oxygen retention tower  used in the model was taken from laboratory measurement of Rewatkar and Bennington [2002]. The measurements were performed using pilot-scale retention column where gas (air or nitrogen) was distributed over the column cross-section filled with stationary pulp (unbleached kraft). The gas-liquid mass transfer rate was found to depend on the pulp suspension consistency (C ) and m  the superficial gas velocity (U ) as shown in Figure E . l . g  0.1  0.01 P JO 1E-3fc • water (Nj) —•— water (Q,) •0013 —&-0.03 •006 —O-0.09 _i 1E-4 0.00  I  .  0.01  I  0.02  |  .  i  0.03  U  I  0.04  0.05  0.06  U (m/s) g  Figure E . l Gas-liquid mass transfer coefficient as a function of superficial gas velocity and pulp consistency  Appendix E: Simulations Results  157  We validated the model using data from survey of oxygen delignification practice in North America collected by Bennington and Pineault [1999]. In the survey, the superficial pulp velocity (U ) in the retention tower was calculated using the reported pulp production rate and p  tower dimensions. In order to estimate the gas-liquid mass transfer coefficient (kia) in the surveyed retention tower, we need to estimate the gas velocity inside the tower. We assumed that gas residence time is only 30% of the pulp; this was based on the reported average gas residence time measured in industrial oxygen tower by Hornsey et al. [1998] who found gas residence time vary between 20 to 40%> of the pulp. As a result of this assumption, gas velocity in the retention tower is 3.33 times higher than that of pulp. We then further calculated the actual gas velocity relative to pulp (gas void fraction, </>, was assumed constant at 10%>) to account for the relative g  movement between the oxygen gas and the pulp suspension as they traveled in the retention tower as follow:  U.  (relative  g aclual  to the pulp) =  (3.33 - 1 W P  V  The actual gas velocity relative to the pulp,  U tuai, g>ac  \ [m/s]  [E-l]  Yg)  calculated from (E-l) was used to find the  corresponding gas-liquid mass transfer coefficient (kia) in Figure E . l . However, since kia in Figure E. 1 was plotted against the superficial gas velocity measured in the lab, we first need to convert the superficial gas velocity into actual gas velocity using the known gas void fraction (factual  =  Ug/(/)g). This was done for every point in the graph since gas void fraction (</>) change g  with superficial gas velocity at particular pulp consistency (C ). The correlation of gas void m  fraction and superficial gas velocity is illustrated in Figure E.2. The resulted reconstruction of xaxis of Figure E . l is shown in Figure E.3 at pulp suspension concentration C =0.09. m  Appendix E: Simulations Results  158  0.20  0.15 r*  0.10h  -e0.05 h  0.00 0.00  0.03 U (m/s)  0.02  0.01  0.04  0.05  g  Figure E.2 Gas void fraction  versus superficial gas velocity as a function of pulp consistency.  As we can see in Figure E.2, at pulp consistency of 0.09 (fraction) and superficial gas velocity (U ) of 0-0.02 m/s, the gas void fraction is fairly constant at 0.08. At higher U > 0.03 m/s, the g  g  gas void fraction relatively constant at 0.1.  0.01 k  1E-3t  1E-4 0.0  0.125  0.25  0.3  0.4  0.5  0.6  U (actual, m/s) g  Figure E.3 Gas-liquid mass transfer coefficients as a function of actual gas velocity at 9% pulp consistency  Appendix E: Simulations Results  159  Table E . l below shows the calculated actual gas velocity relative to the pulp for all the mills surveyed by Pineault and Bennington [1999]. The volumetric gas-liquid mass transfer coefficients (kia) taken from Figure E.3 were found to vary from 0.001 to 0.0035 s". 1  Table E . l Gas-liquid mass transfer coefficient (k a) in industrial oxygen retention towers estimated at 25°C L  Wood  Up (superficial)  type**  A-l A-2 B C  m/s  Up (actual) ' m/s  Ug (actual) rel. to pulp ' m/s  SW SW SW HW  0.022 0.022 0.007 0.008  0.024 0.024 0.008 0.009  0.06 0.06 0.02 0.02  ki,a tower ' -l s 0.003 0.003 0.001 0.001  Di  SW  0.008  0.009  0.02  0.001  D E  HW SW  0.007  0.008  0.02  0.001  Fi  SW  0.007  0.008  0.02  0.001  F  HW  0.009  0.010  0.02  0.001  Mill  2  2  1  2  3  SW  0.006  0.006  0.01  0.001  0.007 0.002 -  0.008 0.003 -  0.02 0.01 -  0.001 0.001 -  Ji  HW SW SW SW  0.010  0.011  0.02  0.001  J  SW  0.010  0.011  0.02  0.001  SW  0.010  0.011  0.02  0.001  Ki  SW  0.030  0.033  0.08  0.0035  K  2  SW  0.018  0.020  0.05  0.0025  Li  SW  0.008  0.008  0.02  0.001  L M  HW SW  0.017 0.009  0.019 0.010  0.04 0.02  0.002 0.001  N-l  SW  0.021  0.023  0.05  0.003  N-2  SW  0.009  0.009  0.02  0.001  Gi G H I  2  2  J  3  2  SW = Softwood  HW = Hardwood  assumed contant gas void fraction (<fi =0.l) g  assumed gas travels 3.33 times faster than of pulp (gas res. time is 30% that of pulp) taken from figure E.3  Up to this point, we have not yet taken into account the effect of temperature on the kia (Rewatkar & Bennington [2002] measured kia  Appendix E: Simulations  Results  at room temperature).  Industrial oxygen  160  delignification system operates at temperature range of 80-120°C. In order to estimate the volumetric gas-liquid mass transfer coefficient (kid) at elevated temperature, we assumed that k a L  is correlated proportionally to the liquid-phase diffusion coefficient (D) as follows:  D,(T )  [E-2]  2  where the exponent b is a constant that may range from about zero to 1.0 depending on the Reynolds number and the type of flow [Treybal, 1981]. We fixed the exponent b at 0.8 in the high-shear medium-consistency mixer and at b = 1.0 in the oxygen retention tower (laminar flow). Moreover, the liquid-phase diffusion coefficients can be estimated from a base temperature T\ to another temperature Tj by using the Einstein correlation [Perry, 1997]:  (T )  ~  D  2  [E-3]  (T,)  D  where T is temperature [K] and JU. is the liquid viscosity. The liquid viscosity decreases with increasing temperature, and can be approximated accurately using the following correlation [Perry, 1997]:  \np =A + j + ClnT  [E-4]  L  The constant A , B, and C were found by regressing the available liquid (water) viscosity data i.e.:  In p = -0.942 L  -1.324 In T  [E-5]  where p. is liquid water viscosity [N.s/m ] and T\s temperature [F]. L  The diffusion coefficient of oxygen in water at temperature 7>25°C is 2.5xlO" cm /s. 5  2  Insertion of this values into [E-2], [E-3], and [E-5] will give the volumetric gas-liquid mass  Appendix E: Simulations  Results  161  transfer coefficient (kid) of oxygen in water as a function of temperature. The gas-liquid mass transfer coefficient (kid) at r=100°C is approximately three times higher in the high-shear mixer, and about four times higher in the retention tower than at the room temperature values. In the model, we corrected the k a correlation for high-shear mixer as follows: L  ka L  where Z )  (r)  cm /s; Z )  (r)  = 1.17 x 1 (T ^ ' V  2 6  4  (Ti)  g  exp {-0.386 * C } * m  a 2)  [E-6]  is essentially the diffusion coefficient of oxygen in water at T = 25°C i.e. 2.5x10" x  is the diffusion coefficient of oxygen in water at elevated temperature T and is 2  approximated using both equations of [E-3] and [E-5] as we mentioned previously. Similarly, for oxygen retention tower, the estimated kia was corrected to account for temperature dependency. Prior to correction, as shown earlier in Table E . l , the estimated kia in industrial oxygen tower was found to vary in the range of 0.001 to 0.0035 s", these cover the 1  range of temperature as low as 80°C to a high of 115°C, with majority of mill operated at 9099°C. At this temperature range, the volumetric gas-liquid mass transfer coefficient (kid) would approximately be 3.5 to 4 times higher than that at room temperature; this correspond to kia being as low as 0.0035 up to a high of 0.014 s". In the model, the volumetric gas-liquid mass 1  transfer coefficient (kid) was fixed at 0.007 s" for all the simulations performed. Further research 1  is needed to investigate the hydrodynamics of pulp and gas flows in retention towers and to measure the exact volumetric gas-liquid mass transfer coefficients.  Appendix E: Simulations Results  162  Appendix F: Simulations Results  Table F.lSimulations data at different temperatures Variables Kappa Alkali Concentration [mole/L] Oxygen Concentration [mole/L] Viscosity [mPa.s]  In/Out  T = 80°C  T = 90°C  T = 100°C  T =120°C  In  30  30  30  30  Out  19.446  17.715  16.182  14.240  In  5.56E-02  5.56E-02  5.56E-02  5.56E-02  Out  3.50E-02  3.17E-02  2.87E-02  2.49E-02  In  0  0  0  0  Out  3.04E-03  2.79E-03  2.55E-03  1.92E-03  In  29  29  29  29  Out  21.412  20.500  19.749  18.868  Table F.2 Simulations data at different oxygen partial pressures Variables Kappa Alkali Concentration [mole/L] Oxygen Concentration [mole/L] Viscosity [mPa.s]  In/Out  P  0 2  In  = 600kPa  P  30  Kappa Alkali Concentration [mole/L] Oxygen Concentration [mole/L] Viscosity [mPa.s]  = 700kPa 30  P02 = 850kPa 30  P  O2  = 1000kPa 30  Out  21.422  19.184  16.182  13.682  In  5.56E-02  5.56E-02  5.56E-02  5.56E-02  Out  3.89E-02  3.45E-02  2.87E-02  2.38E-02  In  0  0  0  0  Out  7.95E-04  1.49E-03  2.55E-03  3.66E-03  In  29  29  29  29  Out  22.547  21.270  19.749  18.628  Table F.3 Simulations data at different alkali charges (yN„0H Variables  0 2  =  0-7 grams/kg pulp, kappa)  In/Out  Alkali = 1%  In  30  30  30  30  Out  17.366  16.182  15.738  15.470  In  2.78E-02  5.56E-02  8.33E-02  1.11E-01  Out  3.20E-03  2.87E-02  5.56E-02  8.29E-02  In  0  0  0  0  Out  2.58E-03  2.55E-03  2.55E-03  2.55E-03  In  29  29  29  29  Out  20.324  19.749  19.541  19.418  Appendix E: Simulations Results  Alkali = 2%  Alkali = 3%  Alkali = 4%  163  Table F.4 Simulations data at different alkali charges (}>NaOH  =  Variables Kappa Alkali Concentration [mole/L] Oxygen Concentration [mole/L] Viscosity [mPa.s]  In/Out  Alkali = 1%  1-9 grams/kg pulp, kappa)  Alkali = 1.5%  Alkali = 2%  Alkali =3%  In  30  30  30  30  Out  24.735  22.066  19.474  16.349  In  2.78E-02  4.17E-02  5.56E-02  8.33E-02  Out  0.00E+00  0.00E+00  0.00E+00  1.13E-02  In  0  0  0  0  Out  2.81 E-03  2.81 E-03  2.81 E-03  2.58E-03  In  29  29  29  29  Out  24.710  22.940  21.427  19.828  Table F.5 Simulations data at different oxygen charges Variables Kappa  In/Out  Oxygen = 0.2%  Oxygen = 0.4%  Oxygen = 0.6%  Oxygen = 3%  In  30  30  30  30  Out  24.343  20.644  17.602  16.182  Alkali Concentration [mole/L]  In  5.56E-02  5.56E-02  5.56E-02  5.56E-02  Out  4.46E-02  3.74E-02  3.14E-02  2.87E-02  Oxygen Concentration [mole/L]  In  0  0  0  0  Out  1.60E-04  4.01 E-04  1.01 E-03  2.55E-03  In  29  29  29  29  Out  24.436  22.087  20.443  19.749  Viscosity [mPa.s]  Table F.6 Simulations data at different black liquor solids carry over Variables Kappa Alkali Concentration [mole/L] Oxygen Concentration [mole/L] Viscosity [mPa.s]  In/Out  BLS  =0  BLS  = 25  BLS  = 35  BLS  = 50  kg/ton pulp  kg/ton pulp  kg/ton pulp  kg/ton pulp  In  30  30  30  30  Out  16.182  16.868  17.132  17.515  In  5.56E-02  5.56E-02  5.56E-02  5.56E-02  Out  2.87E-02  2.31 E-02  2.10E-02  1.81 E-02  In  0  0  0  0  Out  2.55E-03  2.48E-03  2.44E-03  2.40E-03  In  29  29  29  29  Out  19.749  18.462  18.026  17.442  Appendix E: Simulations Results  164  Table F.7 Simulations data at different mixer powers Variables Kappa Alkali Concentration [mole/L] Oxygen Concentration [mole/L] Viscosity [mPa.s]  In/Out  e = 10 W/m  In  30  30  30  30  Out  16.241  16.211  15.981  15.611  In  5.56E-02  5.56E-02  5.56E-02  5.56E-02  Out  2.88E-02  2.87E-02  2.83E-02  2.76E-02  In  0  0  0  0  Out  2.54E-03  2.54E-03  2.55E-03  2.56E-03  In  29  29  29  29  Out  19.777  19.763  19.654  19.482  s  3  e = 10 W/m 6  3  e = 10 W/m 7  3  e = 10 W/m 8  Table F.8 Simulations data at different gas-liquid mass transfer coefficients (k a) in the tower L  Variables Kappa Alkali Concentration [mole/L] Oxygen Concentration [mole/L] Viscosity [mPa.s]  In/Out  k a = 0.002 L  s-  1  k a = 0.002 L  s-  1  k a = 0.002 L  s-  1  k a = 0.002 L  s  1  In  30  30  30  30  Out  17.799  16.182  15.464  14.965  In  5.56E-02  5.56E-02  5.56E-02  5.56E-02  Out  3.18E-02  2.87E-02  2.73E-02  2.63E-02  In  0  0  0  0  Out  2.36E-03  2.55E-03  2.62E-03  2.65E-03  In  29  29  29  29  Out  20.542  19.749  19.415  19.188  Appendix E: Simulations Results  3  

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