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Simulation of the kinetics of an SBR for animal wastewater treatment Jung, Jinki 1994

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SIMULATION OF T H E KINETICS OF A N SBR FOR A N I M A L WASTEWATER T R E A T M E N T By Jinki Jung B. Sc. Yeungnam University, Gyeongsan, Korea  A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E EO F M A S T E R OF SCIENCE  in T H E F A C U L T Y O F G R A D U A T E STUDIES DEPARTMENT OF BIO-RESOURCE ENGINEERING  We accept this thesis as conforming to the required standard  T H E UNIVERSITY O F BRITISH DECEMBER, 1994  © Jinki Jung, 1994  COLUMBIA  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study.  I further agree that permission for extensive copying of this  thesis for scholarly purposes may be granted by the head of my department or by his or her representatives.  It is understood that copying or publication of this thesis for  financial gain shall not be allowed without my written permission.  Bio-Resource Engineering The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V 6 T 1W5  Date:  ABSTRACT  A mathematical model for SBR(Sequencing Batch Reactors) system treating swine wastewater is developed and a non-linear method and a linear method to estimate the kinetic coefficients, /j, , K m  s  and kj, are compared. The coefficients determined by the non-linear  method appeared to better fit the experimentally observed data. Based on the proposed model and the kinetic coefficients estimated by the non-linear method, a computer simulation is performed. The assumption of constant biomass in the fill period and the react period for the determination of kinetic coefficients is valid for the simulation of C O D and biomass. The effects of changes in the yield factor, Y , on the efficiency of C O D removal and biomass change were examined. Sensitivity analysis demonstrates that C O D removal is more sensitive to the change of Yield factor than the biomass change. The effect of idle period on the system performance must be considered in modeling of biomass change when idle period is considerably long to improve the accuracy of the model.  11  Table of Contents  ABSTRACT  ii  List of Tables  v  List of Figures  vi  Acknowledgement  viii  1  INTRODUCTION  1  2  OBJECTIVES  4  3  LITERATURE REVIEW  5  3.1  Characteristics of Animal Waste  5  3.2  Fundamentals of Biological Wastewater Treatment  7  3.2.1  Removal of Organic Matter  7  3.2.2  Removal of Nitrogen  9  3.3  3.4  Biological Wastewater Treatment by the Activated Sludge Process . . . .  11  3.3.1  Mass Balance and Kinetics of Batch Processes  11  3.3.2  Mass Balance and Kinetics of Continuous Processes . . . . . . . .  15  3.3.3  Determination of Kinetic Coefficients  17  SBR Process  18  3.4.1  Technology Description and Previous Works  19  3.4.2  Mass Balance and Kinetics of SBR Process  24  iii  4  5  6  METHODS  28  4.1  Data Acqusition  28  4.2  Mathematical Model  33  4.2.1  Fill Period . .  33  4.2.2  React Period  34  4.3  Determination of the Kinetic Coefficients  35  4.4  Computer Simulations  36  4.5  Statistical Analysis  36  RESULTS A N D DISCUSSIONS  37  5.1  Fill Period  37  5.2  React Period  43  5.3  Sensitivity Test  49  5.4  Test of Model  .  CONCLUSION  54 57  Bibliography  58  Appendices  61  A  Nomenclature  61  A  Source C o d e  63  IV  List of Tables  3.1  Manure production and characteristics per 1000kg live animal mass per day  6  3.2  Comparision between a batch SBR and a continuous system  19  4.1  Comparison of experimental conditions of Fernandes[7] and Lo &z Liao[l].  29  4.2  Data selected for the simulation of C O D change. The C O D in the influent of COD-1, COD-2, COD-3 and COD-4 are 9500, 19000, 28500 and 38000 mg/L, respectively. (Fernandes[7j)  4.3  31  Data selected for the test of proposed model simulating the change of C O D . C O D in the influent of COD-1, COD-2, COD-3 and COD-4 was 7896 mg/L. Lo & Liao[l]  4.4  31  Data selected for the simulation of biomass change. Mass-1, Mass-2, Mass3 and Mass-4 are corresponding to COD-1, COD-2, COD-3 and COD-4 in Table 4.2, respectively  4.5  32  Data selected for the test of model simulating the change of biomass Mass1, Mass-2, Mass-3 and Mass-4 are corresponding to COD-1, COD-2, C O D 3 and COD-4 in Table 4.3, respectively  32  5.1  The kf values of fill period  38  5.2  Comparison of kinetic coefficients for react period determined by linear models and a non-linear model  44  v  List of Figures  3.1  Schematic structure of typical continuous activated sludge process . . . .  15  3.2  Schematic of the total cycle of each reactor in an SBR process  20  5.1  Simulation of C O D in fill period when C O D of the influent is 9500mg/L .  39  5.2  Simulation of Biomass in fill period when C O D of the influent is 9500mg/L 39  5.3  Simulation of C O D in fill period when C O D of the influent is 19000mg/L  5.4  Simulation of Biomass in fill period when C O D of the influent is 19000mg/L 40  5.5  Simulation of C O D in fill period when C O D of the influent is 28500mg/L  5.6  Simulation of Biomass in fill period when C O D of the influent is 28500mg/L 41  5.7  Simulation of C O D in fill period when C O D of the influent is 38000mg/L  5.8  Simulation of Biomass in fill period when C O D of the influent is 38000mg/L 42  5.9  Simulation of C O D in react period when C O D of the influent is 9500mg/L  40  41  42  45  5.10 Simulation of Biomass in react period when C O D of the influent is 9500mg/L 45 5.11 Simulation of C O D in react period when C O D of the influent is 19000mg/L 46 5.12 Simulation of Biomass in react period when C O D of the influent is 19000mg/L 46 5.13 Simulation of C O D in react period when C O D of the influent is 28500mg/L 47 5.14 Simulation of Biomass in react period when C O D of the influent is 28500mg/L 47 5.15 Simulation of C O D in react period when C O D of the influent is 38000mg/L 48 5.16 Simulation of Biomass in react period when C O D of the influent is 38000mg/L 48 5.17 C O D profile by change of Yield factor when the influent is 9500mg/L . .  50  5.18 Biomass profile by change of Yield factor when the influent is 9500mg/L  50  5.19 C O D profile by change of Yield factor when the influent is 19000mg/L  vi  .  51  5.20 Biomass profile by change of Yield factor when the influent is 19000mg/L  51  5.21 C O D profile by change of Yield factor when the influent is 28500mg/L  .  52  5.22 Biomass profile by change of Yield factor when the influent is 28500mg/L  52  5.23 C O D profile by change of Yield factor when the influent is 38000mg/L  .  53  5.24 Biomass profile by change of Yield factor when the influent is 38000mg/L  53  5.25 Simulation of C O D and biomass for the test of proposed model(reactor one) 55 5.26 Simulation of C O D and biomass for the test of proposed model(reactor two) 55 5.27 Simulation of C O D and biomass for the test of proposed model(reactor three)  56  5.28 Simulation of C O D and biomass for the test of proposed model(reactor four) 56  vn  Acknowledgement  I would like to thank the following people for this thesis: Dr. Lau Anthoney for his good guidance and Dr. Lo and Dr. Branion for their useful critiques. Dr. Lee, JaeGwang, Dr. K i m , WooYong and Dr. Nam, YunSoon for their technical supports. Mr. K i m , SungHo, Dr. Chung Chul, Mr. Ra, ChangSix and Mr. Ahn, OkHyun for their generous help. I especially wish to thank Prof. Lee, KyunKyung in Kyungpook Nat'l University who simplified my problem. I have a friend who is suffering from a cancer. He kindly lended his computer to me to finish this thesis. I wish him a quick recovery. Lastly, I would like to thank our parents and my wife, her parents and my two sons, SungYong and DaeYong.  viii  Chapter 1  INTRODUCTION  Sustainable development is an underlying principle of global water policy, directed at maintaining the delicate balance between human activities and the health of our aquatic ecosystem. The challenge of sustainable development requires the action of individuals and society as well as technical support. In the science community, a multidisplinary approach to scientific research is essential these days to obtain a sound knowledge base for decision-making because the effect of environmental degradation is not confined to a specific area [4]. Water quality management is one of major tasks of concern since well managed water quality will lead to a successful sustainable developement. The treatment of wastewater is especially important in this view. Over the last few decades, numerous studies have been carried out on the treatment of the wastewater from municipalities and various industries, whereas the treatment of wastewater from the agri-food industry has been less studied, for its size is comparatively small and its impact has appeared rather indirectly. However the significance of its treatment has increased considerably. Animal wastewater is becoming a special problem source. Often the facilities are remotely located and the wastewater from those facilities flow into reservoirs resulting in a deterioration in drinking water quality. Besides this, the ever increasing size of the agri-food industries demands more studies on its specific wastewater treatment. Agri-food wastewater can be distinguished from municipal and industrial wastes by its chemical composition and its seasonal characteristics. Land application, animal feed  1  Chapter 1.  INTRODUCTION  2  and biological treatment have been widely practiced to treat wastewater from the agrifood industries. As environmental regulations becomes more stringent, the landfill and animal feed options have become unfavorable due to the problems associated with them, for example, the cost for transportation and labor for handling, limited land capacity, odour and health problems, etc. Biological treatment systems have been adapted primarily for reducing organic carbon pollutants. The activated sludge system has been especially widely used in both municipal and industrial wastewater systems for over 60 years.  Consequently, the study of the such systems is well developed as compared to  other systems. Generally speaking, the size of agri-food industries is medium to small and it is often not economical to maintain and operate conventional continuous treatment sytems, due to their large space requirements and relatively high operating costs. Also the seasonal characteristics of agri-food waste generate the need to find a reliable alternative which is comparatively low cost, simple in operation, reliable and less space occupying. The SBR(Sequencing Batch Reactors) system is one of the revived systems which has the potential to meet the demand. The term SBR was coined by Irvine and his colleagues in the early 1970s. The classical fill-and-draw batch system, which had been abandoned because of its labor intensiveness, was successfully modified mainly due to the development of operational technology. It is its simple and flexible operational abilities which attracted much attention to the SBR process since its revival. In the late 1980s a number of full scale applications were constructed and it is reported that these facilities have been performing the task successfully [2]. However, the application of SBR systems has mostly focused on municipal wastewater treatment and has had limited use for agri-food wastewater mainly because of a lack of accumulated technical information. Consquently a large portion of an SBR system for agri-food wastewater treatment remains undeveloped.  One of the  Chapter 1.  INTRODUCTION  3  essential items needed for system design and operation is knowledge of the kinetics of the system. This thesis presents an attempt to summarize and quantify the available data on carbon removal kinetics and examines the available models of the SBR as applied to the treatment of agri-food wastewater. Finally, a new model is developed and computer simulations are carried out based on this suggested model.  Chapter 2  OBJECTIVES  The overall goal of this study is to predict the performance of an SBR system for treating animal waste, with emphasis placed primarily on swine wastewater.  The specific  objectives are: 1. to develop or refine mathematical models that describe growth kinetics and substrate removal in an SBR system. 2. to estimate values for the kinetic coefficients. 3. to perform a computer simulation for validating the model by comparing the predicted results with existing experimental data. 4. to predict the effects of changes in important design parameters on system performance.  4  Chapter 3  LITERATURE REVIEW  3.1  Characteristics of A n i m a l Waste  Knowledge of animal waste and its characteristics is essential for the selection of an appropriate waste management technology. Animal wastes are composed of organic materials and animal manure is much more concentrated than domestic sewage having B O D values 50 to 100 times higher, typically 25,000 - 35,000 mg/L[16]. It has been found that manure production is proportional to animal age, weight and feed intake. On the average, in the case of swine, the weight of manure produced is 1.75kg/day/100kg of swine weight, and the moisture content is about 92% which gives the manure fluid characteristics. Animal housing, floor washing and the manure collection technology also influence the quality of manure [7]. Major constituents of animal wastes are carbohydrate (30 to 50%, practically all cellulose and hemicellulose), organic nitrogen(14 to 30% protein equivalent,!.e. N*6.25), lignin(5 to 12%), and inorganic salts(10 to 25%). Table 3.1 summarizes the composition of typical animal wastes[9]. The main water pollution hazards are associated with a) inadequate manure storage facilities, b) winter application on frozen soil, c) excessively high rates of spreading manure on land[33]. The high concentration of organic solids limits the location of an animal-rearing operations, land application of the waste, or use of traditional municipal waste treatment techniques.  5  Chapter 3. LITERATURE  REVIEW  6  Table 3.1: Manure production and characteristics per 1000kg live animal mass per day[9] Parameter Total Manure BOD COD Total Solids Volatile Solids Urine Total Nitrogen Total Phosphorus pH Potassium Calcium Magnesium Sulfur Sodium Chloride Iron Manganese Boron Molybdenum Zine Copper Cadmium Nickel Lead 5  c  Units kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/1000kg. day kg/1000kg. day kg/1000kg. day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day kg/lOOOkg.day  Dairy 86 1.6 11 12 10 26 0.45 0.094 7.0 0.29 0.16 0.071 0.051 0.052 0.13 0.012 0.0019 0.0071 0.00007 0.0018 0.00045 0.000003 0.00028 **  Beef 58 1.6 7.8 8.5 7.2 18 0.34 0.092 7.0 0.21 0.14 0.049 0.045 0.030 ** 0.0078 0.0012 0.0008 0.00004 0.0011 0.00031 ** ** **  Swine 84 3.1 8.4 11 8.5 39 0.52 0.18 7.5 0.29 0.33 0.070 0.076 0.067 0.26 0.016 0.0019 0.0031 0.00003 0.0050 0.0012 0.000027 **  0.32 0.28 0.072 0.055 0.078 0.089 0.0081 0.0014 0.0006 0.00025 0.0016 0.00022 0.000007 **  0.000084  0.000084  Sheep 40 1.2 11 11 9.2 15 0.42 0.087 **  Chapter 3. LITERATURE  3.2  REVIEW  7  Fundamentals of Biological Wastewater Treatment  3.2.1  Removal of Organic Matter  The organic matter and nutrient compounds can be effectively removed from wastewater through biological treatment processes given a favorable environment for the living microorganisms which do the treatment. The stabilization of organic matter by biological means is possible because the biological reactions are irreversible.  organic matter + Oi  CO% + H^O + energy -+• cell mass  The above equation 3.1 shows the input and final output of the biochemical reactions involved in microbial growth. Yet this equation is overly simplified and not detailed enough since it is only qualitative, no quantitative information is included, and significant elements have been omitted. For example sources of nitrogen and phosphorus and small amounts of many other elements are needed both in the reactions, which form new cell components and in the reactions by which waste is degraded. The organic matter in the waste serves primarily as carbon source, but depending upon the waste in question, it may also contain some nitrogen and phosphorus which are metabolically available to the cells.  Organic matter  02  CO2 + H 2 0 + ATP  (respiration)  (COHNS) ATP  New C e l l s (C5H7N02)  (synthesis)  (3-1)  Chapter 3. LITERATURE  REVIEW  8  The biological stabilization of organic matter in liquid wastes consists of two processes, synthesis and respiration. These two processes are interrelated and cannot be considered as separate, distinct functions. The above diagram shows that a portion of the organic matter which is used for respiration is oxidized to CO2 and H2O producing energy by converting A D P to ATP. Heterotrophic microorganisms utilize organic matter to support their life and growth functions. Bacteria use hydrolytic enzymes to convert complex, high molecular weight organic substances into simple, souble components, which are diffusable through the cell membrane. The substrate is then oxidized by the enzymatic removal of hydrogen from the substrate molecule.  The final hydrogen acceptor is determined by the aerobic or  anaerobic nature of the surrounding medium. Aerobic processes are used effectively in wastewater treatment.  In these processes  a heterogeneous microbial community or sludge, composed mostly of bacteria, fungi, protozoa and rotifers, metabolizes organic matter in the presence of oxygen and the resulting end products are carbon dioxide, water and new cells. Under food-limiting conditions, however, the microorganisms are forced to consume their own cellular mass until they lyse and lose their viability and the ability for reproduction. When lysing predominates the cell nutrients are released into environment and become available to the other active organisms as substrate. Equation 3.2 is an empirical chemical equation describing the endogenous respiration reaction.  C H N0 5  7  2  + 0  ^ l^ e  2  5CO2 + 2H 0 + NH 2  3  + energy  (3.2)  The principal significance of oxygen as the external electron acceptor is that aerobic heterotrophs oxidize the substrate completely and therefore the maximum amount of 1  A heterotroph requires organic matter for both energy and carbon source  1  Chapter 3. LITERATURE  REVIEW  9  energy is generated. Whereas anaerobic microorganisms produce reduced compounds but the energy yield is much lower than aerobic process. For an example, the difference in energy yield from anaerobic and aerobic metabolism of glucose is 31 and 686 Kcal/mol, respectively [7]. Because of their fast growing characteristics, aerobic microorganisms and aerobic treatment system have been preferred where reaction time is an important operating parameter.  3.2.2  R e m o v a l of N i t r o g e n  Ammonia removal from wastewater streams is an important part of maintaining the integrity of the environment. Nitrogen in the form of ammonia is a pollutant that exerts a number of adverse effects on receiving water resources. Ammonia is toxic to fish and when present with phosphorus, can stimulate undesirable aquatic growth that causes the eutrophication of natural waters. Ammonia also represents an oxygen demand in streams and its presence can result in lower dissolved oxygen(DO) concentration in the aquatic environment. Currently, a number of biological and physico-chemical processes are available to remove ammonia from agri-food, municipal and industrial wastewater. Of these processes, biological nitrification/denitrification has been favored for economical reasons. The term nitrification refers to the sequential biological oxidation of ammonia, first to nitrite and then to nitrate mostly by autotrophs  2  and to lesser extent by certain heterotrophic  bacteria. The term denitrification refers to a sequential reduction reaction of nitrate to nitrogen gas under anoxic conditions . The following diagram illustrates these concepts: 3  Autotroph: a class of microorganism which do not utilize organic matter but oxidize inorganic compound for energy and use CO2 as carbon source. Anoxic condition: the condition in which the dissolved oxygen concentration is very low but not necessarily zero. It especially refers to the condition when the dissolved oxygen concentration is less than 2% of saturation.[10] 2  3  Chapter 3. LITERATURE  Organic Nitrogen  >  REVIEW  J^°P + *°J!^°™°  Hete  h  10  ~ Nitrobacter  Ni  NH  ^——.  Ammonification  N  *  Q  N  Q  Anae.Heterotreph  v  _^  v  Nitrification  Denitrification  .  In untreated wastewater nitrogen is present principally in the form of organic nitrogen and ammonia which is produced during the decomposition of organic compounds and exists, at neutral pH, as ammonium ion. Ammonia is the most reduced form of inorganic nitrogen and serves as the starting point for a biological nitrogen removal process. Under aerobic conditions, ammonia is oxidized in two sequential biochemical reactions which together constitute the nitrification process.  The first one is oxidation of ammonia to  nitrite by the genera Nitrosomonas and the second process is further oxidation of nitrite to nitrate by the genera Nitrobacter. The stoichiometry for nitrification can be expressed as [10]:  55NH+ + 5 C 0 + 760 2  400A/O " + 5C0 2  2  N 2  i  l^°^  a  s  CH0N 5  7  + NH+ + 1950 + 2H 0 2  2  + 54NO; + 52H 0 + 109#+  2  J^ ^  N  (3.3)  2  b  r  CH0N 5  7  2  + 400iVOj + H  +  (3.4)  In conjunction with the nitrification process, denitrification is an important nitrogen removal mechanism by which nitrate nitrogen is reduced to nitrite and subsequently to nitrous oxide and nitrogen gas (dissimilation) or to cell material (assimilation) at low concentrations of dissolved oxygen. Although some autotrophic bacteria are able to reduce nitrate by using it as electron acceptor, denitrification is carried out mostly by facultative anaerobic heterotrophs.  Four enzymes, nitrate reductase, nitrite reductase,  nitric oxide reductase and nitrous oxide reductase are the catalysts which permit the denitrification process to occur under anoxic condition, which is inhibited by the presence of oxygen [12]. The denitrification reaction can be used in conjunction with the nitrification reaction utilizing both suspended growth and attached growth microorganims.  Chapter 3. LITERATURE  REVIEW  11  Electron donors in denitrification may be either influent organic materials or microbial intracellular endogenous reserve compounds [13]. The overall stoichiometric equations for denitrification using methanol as the carbon source have been calculated as [14]: Overall nitrate removal: NOs + \MCH OH z  + H  +  —• 0.0Q5C H O N  + 0.47A/ + 0.76CO + 2.UH 0  (3.5)  —• 0.04C H O N  + 0A8N + 0.47CO + 1.7 H 0  (3.6)  5  7  2  2  2  2  Overall nitrite removal: NO; + 0.67CH OH 3  + H  +  5  7  2  2  2  2  Denitrification kinetics vary widely and depend on the starting concentration of nitrate or loading rate[12, 15].  3.3  Biological Wastewater Treatment by the A c t i v a t e d Sludge Process  Activated sludge is a sludge of activated microorganisms capable of stabilizing waste under aerobic conditions [17]. Upon continued feeding sludge develops into a flocculent suspension that settles readily and possesses excellent clarification and oxidation properties. The process was developed in England in 1914 by Ardern and Lockett and was named so because it involved the production of an activated mass of microorganisms. Activated sludge has been used in many systems, but fundamentally they are all similar. This literature review will focus on conventional continuous and batch systems.  3.3.1  M a s s Balance and Kinetics of B a t c h Processes  The kinetics of biological reactions in an activated sludge system consists of the two fundamental expressions: the rate of change of biomass and the rate of disappearance of limiting substrates. In the exponential growth phase it has been found that the rate of  Chapter 3. LITERATURE  REVIEW  12  increase of biomass is directly proportional to the initial cell concentration and it can be represented by a first order reaction as follows:  £  =  <-> 3 7  where the first order rate constant // is known as specific growth rate ( £ ) and X is the _ 1  concentration of active biomass. If the active biomass concentration at t=0 is ^(0), and after time t has elapsed the biomass at that time will be: X(t) = X{0)exp(fit)  (3.8)  The specific growth rate of a given microorganism growing in a given medium can be calculated graphically from the result of batch growth experiments which determine the increase in biomass with time. As for substrate degradation, a number of rate expressions has been reported and Monod kinetics is considered general purpose kinetics[20] and is widely used to represent the degradation of an individual substrate in a pure culture system:  fl^L dt  ] x  =  Zi  S  i  K i + Si  (3.9)  Sj  where 5,- is the concentration of ith substrate(mg/L), ki is the Monod rate constant of ith substrate {mg .mg~ .day~ ) and K j is the Monod half-saturation constant of the ith l  l  s  substrate ( m g / ) . -1  However, the choice of the rate of substrate degradation is highly  dependent on the characteristics of the behaviour of a system. When a multicomponent substrate is allowed to degrade in a batch reactor, the variation of the combined substrate concentrations against time follows a smooth curve which can be approximated by a first order law [18] or some other nth order rate law[19]. This pseudo first order reaction is actually a summation of mutiple zero order reactions and this can be symbolically expressed as:  Chapter 3. LITERATURE  When the assumption that K  REVIEW  s  «  13  S is applied, multicomponent substrate degradation  rate can be expressed as a first order reaction in terms of active biomass and this is the same form as equation 3.7. Therefore, the integration of eqn 3.10 will provide a frame in which to estimate the concentration of substrate at time t. However, estimation in this way will be only valid over a small range of time, since the estimation is made under an assumption of first order reaction. Besides, unlike a continuous system, the significance of substrate concentration will be considerably increased as time elapses in a batch system. This fact leads to the production of other frames which includes the substrate factor.  S(t) = S(0)exp(—£-Xt) S(t) = 5(0) - kXt kXt = K \n(S(0)/S(t)) s  + S(0) - S(t)  (when K  s  (when K  «  s  (when K  s  »  S)  (3.11)  S) > S or K  (3.12)  s  < S)  (3.13)  It is useful to be able to estimate how much biomass will be produced from a given amount of substrates consumed. A cell yield factor is used for this purpose and it is defined as mass of biomass produced per unit mass of substrate removed as shown in eqn 3.14. There are many factors which have an influence on the magnitude of the yield coefficient, of which the most important is the oxidation hhtate of carbon source. Other factors likely to affect the yield coefficient include: the formation of storage products such as glycogen and/or polyphosphate and changes in fraction of maintenance energy used for cell. Although the value of the yield factor will vary depending on the nature of substrate. It is usually assumed to be constant for heterogeneous populations growing on a agri-food or municipal wastewater. The relationship between the rate of biomass change and substrate degradation and yield factor is defined as:  dS/dt  AS  k  1  '  Chapter 3. LITERATURE  REVIEW  14  where \x is a specific growth rate of biomass and k is a specific removal rate of substrates. Typical heterotrophic microorganisms have values of yield coefficient in the range 0.4 0.6 g biomass/g substrate, which indicates that up to 60% of substrate utilized has been used for the purposes other than biomass production. In bacterial systems used in wastewater treatment the distribution of cell ages is such that not all the cells in the system are in the exponential growth phase. Consequently, the expression for the rate of growth can be modified to account for the energy required for cell maintenance. Other factors, such as death and predation, must also be considered. These factors are usually lumped together and it is assumed that the decrease in the cell mass caused by them is proportional to the concentration of the organisms present. This decrease is often identified as the endogenous decay. The rate of growth(eqn. 3.7) is reformulated to include the endogenous decay term as follows:  — = fiX-k X d  = (ti-  k )X d  (3.15)  In turn, the integrated forms of biomass and substrate derivatives are:  (3.16) (3.17)  Chapter 3. LITERATURE  3.3.2  REVIEW  15  Mass Balance and Kinetics of Continuous Processes  The ease of automation has been a major advantage of continuous systems over batch systems for many years but sacrificing flexibility to shock loading and large space requirements.  A |  waste  influent  F i g . 3.1 Schematic s t r u c t u r e of t y p i c a l continuous a c t i v a t e d sludge process. A conventional continuous system utilizing activated sludge consists of three parts as shown in Figure 3.1: primary sedimentation, aeration and secondary sedimentation. Some of the biomass settled in the final clarifier is returned to the aeration basin to keep a desired concentration of organisms. The excess cells produced in the conversion process are wasted to the primary clarifier for disposal with primary solids. Mixing in the reactors is accomplished by blowing compressed air through porous media or perforated pipes, or by mechanical aerators. The formulation of a completely mixed continuous system requires a few assumptions: • uniform distribution of biomass or substrate in reactor • constant yield • steady state operation A mass balance is necessary for a kinetic analysis of a continuous system, Thus  Chapter 3. LITERATURE  REVIEW  16  A mass balance is necessary for a kinetic analysis of a continuous system, thus  rate of change  rate of incoming  rate of production  of biomass/  of biomass/  of biomass/  substrate  substrate  substrate  substrate  in the system  in the system  in the system  in the system  rate of removal  +  of biomass/substrate  In the case of biomass change, assuming the concentration of biomass in incoming flow is negligible, the symbolic expression will be:  dX  V = fiXV - QX ~~dt  (3.18)  where V is working volume, pL is specific growth rate and Q is outflow rate. Analysis of the above eqn 3.18 can provide critical information for system design and operation. By the assumption of steady state m o d e , ^ = 0 and  Q  (3.19)  V  The term (Q/V) is known as the dilution rate and the reciprocal of the dilution rate is known as mean cell residence time which is also sludge age. The dilution rate is of profound importance in the control of bacterial growth under continuous cultivation as it shows the dependence of specific growth rate on the flow rate of substrate into reactor. Thus by controlling the flow of medium into a reactor at a constant, known rate, the growth of organism could be regulated, provided the growth rate does not exceed its maximum growth rate [22]. The change of substrate concentration in a continous system can be expressed as dSi  — QinSi.i  QeSi.e  yXV  (3.20)  Chapter 3. LITERATURE  REVIEW  where 5, is zth substrate, Qi  n  17  is flow rate into the reactor, Su is the concentration of  ith substrate in Qi , Q is the outflow rate and Si, is the concentration of ith substrate n  in Q . e  e  By assumption, Qi  e  n  is equal to Q  e  and Si. is same as the concentration of ith e  substrate in a reactor of continuous systems. In steady state conditions,  - S. ) = t e  (3.21)  From this, knowing the yield factor and the concentrations of the ith substrate in the influent and effluent, it is possible to estimate the amount of biomass in the systems. Having known values for biomass concentration and yield factor, it is possible to estimate the amount of time required to complete treatment and vice versa utilizing one of the equations 3.11, 3.12, 3.13.  3.3.3  D e t e r m i n a t i o n of K i n e t i c Coefficients  The equations described in the previous sections require kinetic coefficients which have to be determined. There are several methods available for their determination. The underlying principle of all the methods is linearization. By algebraic operations, the primary kinetic expressions can be transformed to linear forms which are assumed to have a uniform gradient and specific intercept points. The Lineweaver-Burk(eqn 3.22), Hans(eqn 3.23) and Edie-Hofstee (eqn 3.24) methods are all derived from Monod kinetics:  - = — + — -z  (3.22)  ^ = — + —5  (3.23)  li = fi -K £  (3.24)  m  e  Another way of linerization is by integration of the rate of substrate degradation in Monod kinetics and in turn transformation to a linear form. Hence,  Chapter 3. LITERATURE  REVIEW  M  18  f --*»(ii); M  t  K,  5(0) - 5 ( 0  ^  m  (S(0)\  1  ^ S(t))  5(0) - S(t)  '  °  [6  ;  The methods of determination of coefficients introduced so far are good for rough estimation without accounting for the endogenous decay factor. To increase the accuracy of the estimation, the endogenous decay factor should be estimated. One possible method is via the linearized expression from eqn 3.17.  Y  m _ _ m ^ _  k  d  (  ,  2  7  )  where kj, is endogenous decay factor. The other way of the determination wil be one by non-linear regression. The method will be disscussed in detail in the Section 4.3.  3.4  T h e S B R Process  The SBR process is neither a continuous system nor a batch system, rather it is a hybrid of both systems. In terms of overall influent and effluent flow it can be considered as a continuous system but from each reactor's point of view it is a batch system utilizing an activated sludge. Historically, it has generally been considered to be a batch system, probably because for historical reasons. The original sludge system was a batch process. Later, however, despite a better degree of treatment, this fill-and-draw, batch system was replaced by continuous flow systems primarily because a high degree of manual operater attention was required. Clogging problems associated with its air diffusers were also a drawback. Reliable process, valving, timing and switching technology were then not available. Development of new hardware; such as motorized valves, pneumatically actuated valves, electronic and mechanical timers, solenoids, level sensors, flow meters,  Chapter 3. LITERATURE  REVIEW  19  Table 3.2: Comparision between a batch SBR and a continuous system.* added by author  Concept Inflow Outflow Loading Condition D.O Aeration Flexibility Flow pattern Sludge cycle Yield factor* Monitoring Operation mode  Batch Time Sequence Periodic Periodic Cyclical Varies in time Varies Intermittent High  SBR* Time Sequence Periodic/Continuous Periodic/Continuous Cyclic/Continuous Varies in time Varies Intermittent High for shack load  -  -  No Varies End of cycle Non-steady state  Yes/No Varies End of cycle Non-steady state  Continuos Spatial Sequence Continuous Continuous Even(ideal) Varies in space Constant Continuous Limited Plug flow Yes Does not vary Continuous Steady state  and microprocessers, has made it possible to revitalize batch treatment technology [23]. The first notable resurgence of interest, though short lived, occured in the early 1950's at the Eastern Regional Laboratory.  It was primarily directed at the dairy industry.  The second resurgence was led by Irvine and his co-workers, It was this group that standardized the terminology of the SBR process [24]. A concise comparision between batch and continuous systems is presented by Barth [25] with an SBR section added by the author it appears in Table 3.2.  3.4.1  Technology Description and Previous Works  The SBR process can consist of one or more reactors. Theoretically there is no limit to the number of reactors but practically a 3-4 reactor system has been preferred. Each reactor is operated in single sludge processing under repeated cycles of aeration and nonaeration. A typical cycle for each SBR reactor is divided into the following five discrete periods as shown in Figure 3.2. These are fill, react, settle, draw and idle [2].  Chapter 3.  LITERATURE  F i g u r e 3.2  REVIEW  Schematic of the t o t a l c y c l e of each r e a c t o r i n an SBR process  20  Chapter 3. LITERATURE  REVIEW  21  • Fill: During the fill period, the reactor is gradually filled with raw wastewater or primary effluent over a set period of time to a predetermined volume. Prior to filling, the reactor contains activated sludge remaining in the reactor from the previous cycle. Mixing and/or aeration can be supplied during this period. • React: The reaction that begins during the fill period is completed during the react period. The range of cycle, times for this period is 35-80% of total cycle time [26, 29, 30, 31]. Depending on the objective, aerobic/anoxic environments can be supplied. Towards the end of this period, sludge wasting can be done to maintain the sludge age.  The sludge age in days would be equal to the reciprocal of the  fraction of the maximum volume wasted each day. • Settle: In this period, separation of liquid and solids is carried out under quiescent conditions. The time for settling is usually between 0.5 and 1 hour. • Draw: During the draw sequence, the clarified supernatant is discharged. Arora et al.[2] have reported that floating or adjustable weirs are the most popular decanting mechanisms in current use. The percent of the cycle time can range from 5 to more than 30%. • Idle: The idle period is used whenever the influent wastewater flow is irregular. It can also function as a pause in a multi-tank system, by providing time for one reactor to complete its full cycle before switching to another unit. The length of time in idle will be determined by the wastewater flow rate pattern. Provision for aeration mixing and sludge wasting are optional in this stage. In this period, the microbial population is maintained by endogenous respiration and can be readily activated by the incoming wastewater during the fill period. SBR systems have been applied to the treatment of wastewater from various sources  Chapter 3. LITERATURE  REVIEW  22  with good results [3, 6, 5, 23, 27, 32, 28]. Compared to a CFSTR(Continuous Flow Stirred Tank Reactor) the SBR offers the advantage of reliable effluent quality under shock loading and fluctuating influent concentrations, high oxygen transfer efficiency, nitrogen removal via nitrification/denitrification and phosphorous removal without addition of chemicals, and less reactor volume [2, 23]. Irvine and Richter [24] compared the volumes required for CFSTRs and SBRs of multiple-tank systems to treat a given influent. The results showed that with the exception of a 2 tank system, the volume required for a batch process for all cases is less than 50% of the volume requirement of a C F S T R . In addition the reactor design must consider maximum flows. When the maximum flow is three times that of average flow, the SBR required a reactor volume that was less than 60% of the volume of the C F S T R . This means a substantial reduction in the requirements for reactor volume and space occupied by the reactor. Milking center wastewater treatment by SBR was studied by Lo et al.[5, 26]. Three bench-scale SBRs of 5L working volume were operated at three different temperatures(29.8, 21.8 and 10.5°C). The results indicated that very high B O D , C O D , ammonia-nitrogen 5  and suspended solids removal were achieved. There was no noticeable difference in the treatment efficiency between reactors operating at 29.8 and 2 1 . 8 ° C , whereas the reactor operating 10.5°C showed significantly lower treatment efficiency. An existing aerated lagoon treating piggery waste was converted into an aerobic SBR by Wong and Choi [6]. The SBR was operated on a 24-h cycle: fill(3h), aerate(18h), settle(lh) and withdraw(2h). After the commissioning period, the SBR was reported to perform efficiently as evidenced by effluent data over a 15-week period. The average B O D removal efficiency was in excess of 99%; resulting in effluent B O D concentrations ranging from 10-30 mg/L(infment B O D concentration is 2000-4000mg/L), which was below the required effluent standard of 50 m g / L . Shock loading to the plant was not  Chapter 3. LITERATURE  REVIEW  23  found to be a problem. Lo and Liao studied the treatment of poultry processing wastewater using benchscale sequencing batch reactors [3]. A 4-hour cycle was adopted, which consisted of fill(8 min), react(120 min), settle(105 min), draw(4 min) and idle(15 min). The reactors were operated at three different temperatures(10, 22 and 3 5 ° C ) . The mean HRT(Hydraulic Retention Time) was 10 hour for each reactor. Sludge removal was undertaken once a day during the last 30 minutes of the aeration period, by wasting 50 ml out of 5.0 liters of the mixed liquor to make the mean cell residence time (SRT) 10 days. BOD5 removal efficiency for the 10°C reactor was 89% compared to 95% for the 2 2 ° C and 3 5 ° C reactors, though C O D removal efficiency of 89% was practically the same for all 3 reactors. Applying first-order kinetics to substrate removal, the reported kinetic coefficients, which is ^pwere 0.0014, 0.0098, 0.0109 L/mg*t, respectively for the 3 ascending temperatures. The settling characteristics of sludge were found to be good with a sludge volume index(SVI) ranging from 70 to 108. A full scale system of 3 sequencing batch reactors was used to treat diluted swine wastewater [1]. The reactor design was based on the results of a bench-scale study of swine wastewater. A 4- hour cycle consisted of the following sequence: aerated fill(6min), react (200min), settle(30min), draw(6min) and no idle time was allowed. The volume of wastewater treated and discharged each cycle amounted to 1400 liters. The SRT was maintained at 14 days after the fifteenth week. The results indicated that very high B O D 5 removal(91%) was achieved. In general, effluent B O D 5 levels were below 50 mg/L. Fernandes and McKyes tested different strength influents, measured in terms of C O D , of swine manure (9500, 19000, 28500, 38000mg/L). A mathematical model was developed to describe the changes in concentration with time of C O D , ammonia, nitrate and nitrite. Total cycle time was 24 hours: fill(3.0h), react(19.Oh), settle(l.Oh), draw(0.5h) and idle(0.5h). The results showed that the single reactor SBR process is capable of reducing  Chapter 3. LITERATURE  REVIEW  24  the potential polluting carbon and nitrogen components of a concentrated wastewater to a high degree when it is operated with 7 to 9 days of H R T and 20 days of SRT. The prediction of C O D removal in the fill periods showed good agreement with observed values but this study failed to reproduce the prediction using their data and model and proposed coefficients. Overall efficiency of C O D removal was 96% [31]. The effects of H R T on piggery wastewater effluent were investigated by Ng [32]. Ng tested 15, 10, 5, 3, 1 days of H R T as a system parameter and the removal efficiency increased with H R T up to 10 days but sharply decreased at HRT of 15 day. Fernandes used SRT and H R T as one of the system parameters. The effects of SRTs of 10, 20, 30 days and HRTs of 3, 5, 7, 9 days on the effluent quality were tested. No significant effects on the system performance by the change of SRT were observed, on the other hand, the substrate removal rate of H R T of 3 days was significantly lower than that of HRT of 5, 7 and 9 days. H R T of 3 days showed removal efficiency of 70% whereas H R T of 5, 7 and 9 days showed 90% above.  3.4.2  Mass Balance and Kinetics of S B R Process  Fill and react periods are normally selected for SBR models since over 90% of kinetic change takes place in these two periods which constitute more than 90% of operation time. In this section, Fernandes's simulation model is taken as a sample case for the description of an SBR mass balance. The environmental conditions for the simulation are temperature of 2 0 ° C , 8 days of H R T , 20 days of SRT, 19 hours of aeration [7].  Fill Period The model discussed in this section is the model of Fernandes[7]. The change of substrate in a reactor during the fill period can be expressed by doing a mass balance on the  Chapter 3. LITERATURE  REVIEW  25  substrate. There is no outflow from an SBR reactor in the fill period, so the symbolic expression for quantification of the fill period will be:  ^p-  = QinS .i-Vk XS i  f  (3.28)  i  where V is working volume of reactor, Si is ith substrate in a reactor, Qi is the influent n  flow rate, Si.i is the ith substrate concentration in Qi , n  kj is the first order kinetic  coefficient for Si. The model's variation comes from the term for substrate degradation in eqn 3.28. The second term on the right hand side of eqn 3.28 is essentially the same as the one of the models describing the activated sludge system and it is a speical case of Monod kinetics where S << K  and therefore kj in equ 3.28 should be:  s  Utilizing eqn 3.28, Fernandes and McKyes [31] made two assumptions for simplification; constant volume and constant biomass. However, the Fernandes's model based on the assumption of constant volume is incorrect and the new model will be suggested in the 'Method section'. The concentration of biomass(MLVSS) was found not to change significantly •(> 5%) during the fill period[7, 31], thus the second term on the right hand side of eqn 3.28 becomes fist order only with respect to substrate concentration.  ^  — y Si.i  kf Si  (3.30)  tX  where kf = p^- and Si.i is considered as a constant. The analytical solution of equ 3.30 J  tX  is given as:  s ( t )=  f;^  +{So  ~ ft^  )exp(  -^  -  (3 31)  Chapter 3. LITERATURE  REVIEW  26  where 5o is the initial concentration of ith substrate.  Using measured data, kj can iX  be estimated by curve fitting. Fernandes carried out a simulation and reported a kj  yX  of 0.4 ( / i r ) for C O D degradation in the fill period. The simulation of 3 hour's C O D _1  degradation at different concentrations showed the accuracy of 93.7%, 94.8%, 93.1%, and 91.9% for each set of influent and initial concentrations of ( 9500mg/L and 328 mg/1), (19000mg/L and 601mg/L), (28500mg/.L and 903 mg/L) and (38000mg/L and 1203mg/L), respectively. A l l the simulations were carried out for a reaction volume of 2.625L and a flow rate to the reactor of 0.125 L/hr.  React P e r i o d Since there is no inflow and no outflow during a react.period, the mass balance for a react period is same as one for a batch activated sludge processes. As in fill period, Fernandes assumed K  s  »  S, constant volume, constant biomass and first order reaction with  respect to the concentration of substrate. Again, these assumptions will be examined at the results and discussion section.  —jj- = —k Si  (3.32)  2tX  k , is a first order kinetic coefficient. The analytical solution for eqn 3.32 is given as: 2  x  S(t) = S exp(-k , t) 0  1  2 x  Using eqn 3.33 and an empirically determined k  2>x  (3.33)  value, simulated effluent C O D  results were claimed to be within 20% of measured values, for influent and initial C O D concentration of 9500mg/L and 328mg/L, respectively.  When the influent concentra-  tion was increased to 19000mg/L and 28500mg/L, the discrepancy between measured and computed C O D becomes very large(50-80%). However, the accuracy of prediction  Chapter 3. LITERATURE  REVIEW  27  got better (within 35%) when the influent C O D concentration was further increased to 38000mg/L. The inconsistent accuracy of prediction could be due to two reasons. One possible reason might be the assumption of K  s  >>  S since reported K  s  values from  literature range from 100 to 1500 m g / L and the initial concentration of C O D used in the simulation has a range of 330 - 1200mg/L. The other possible reason might be that the model does not include all the factors involved in the experiments, such as H R T , SRT, temperature or the endogenous decay factor.  Chapter 4  METHODS  4.1  Data Acquisition  The data presented by Fernandes [7] was chosen for the simulation study and the works of Lo and Liao[3] was selected for testing of the proposed model. Fernandes performed an integrated experiment for the study of the treatment of swine wastewater using a sequencing batch reactor system with four different influent C O D concentrations, 9500, 19000, 28500 and 38000mg/L. The experimental focus was laid on the feasibility of SBR for the removal of C O D and nitrogen compounds in high strength wastewater with the operational parameters of H R T of 3, 5, 7, 9 days and SRT of 10, 20, 30days. Furthermore, the researcher examined the theoretical aspects of the system and developed a kinetic model for an SBR systems. Total cycle was 24 hours: nonaerated fill(3h), aerated react(19h), settle(lh), draw(0.5h) and idle(0.5h). The objective of Lo and Liao's experimental works was to find the optimized operating conditions of SBR for the treatment of swine wastewater. Different cycle time(4, 8, 24hr) were tested as well as alternating aeration and non-aeration mode. The specific conditions for the data selected are 4 days of H R T , 16 days of SRT and 24hr of total cycle time. Total cycle of 24hr is consisted of: aerated fill(O.lhr), aerated react(18hr), settle(1.5hr), draw(O.lhr) and idle(4.3hr). The summary and comparison of experimental conditions of both data of Fernandes and Lo Sz Liao are presented in Table 4.1.  28  o  CO  0.125  a  at t=0  2.625  X  a o  EH CD o  React (hr)  Period Settle (hr)  o ^  CM  o  oo  1.5  J-H  NoAir  Fill (hr)  c6  <  Fernandes  CD  (L)  CD CO  (L)  a o o Inflow Rate (L/hr)  O  Reactor Volume  a  Volume  CO  Total Cycle Time (hr)  •x)  SRT (day)  o  HRT (day)  Draw (hr) NoAir 0.5 NoAir 0.1  4.3  Idle (hr) NoAir 1.5 NoAir  Chapter 4. METHODS  < ^  < ©  co  CM  o ,—1  CO  eg  O CO i—i  o  o  Chapter 4.  METHODS  30  Both studies were carried out in a bench scale(3L, 4L). The conditions and the length of react period of both experiments are nearly identical, whereas the length of fill periods of both experiments are significantly different. In case of Lo & Liao's experiment, fill period of O.lhr is unlikely to happen in real situation and, by the same token, the inflow rate of lOL/hr is unrealistic for the size of 4 Liters. The difference in H R T and SRT between both experiments must be mentioned: according to the result of Fernandes's work, the change of SRT from 10 days to 30 days showed no significant difference in treatment ability. The change of HRT, however, showed a significant difference in terms of C O D removal. The data of C O D change for the simulation and the test of proposed model are presented in Table 4.2 and 4.3. Unlike Fernandes's work, the data of hourly base track analysis were not available in Lo & Liao's work. Instead, C O D data measured at every beginning and end of each cycle were available. Table 4.3 shows the C O D data from an one-week long operation of four SBR reactors with the same influent. The data of the second, third and fourth day of operation were not available. Nevertheless, from operational point of view, the hourly base track analysis is only a tool to predict the quality of effluent. Providing there was no change of operational condition during the second, third and fourth day of operations, the C O D data of the fifth day(120hr) and sixth day(144hr) can be used to test the proposed model. The simulation of biomass was also carried out and the data for the simulation and the test are shown in Table 4.4 and 4.5. The biomass change which is corresponding to the C O D change of of COD-1, COD-2, COD-3 and COD-4 in Table 4.2 are presented in Table 4.4. In Table 4.5, the biomass change corresponding to the change of C O D in Table 4.3 is presented.  Chapter 4.  METHODS  31  Table 4.2: Data selected for the simulation of C O D change. The C O D in the influent of COD-1, COD-2, COD-3 and COD-4 are 9500, 19000, 28500 and 38000 m g / L , respectively. (Fernandes [7]) Time (hr) 0 1 2 3 5 8 12 16 18 22 Average  COD-1 (mg/L) 328 566 684 769 535 407 335 320 296 283 452  COD-2 (mg/L) 601 1100 1530 1790 1390 1000 775 635 620 610 1005  COD-4 COD-3 (mg/L) (mg/L) 903 1203 1600 2250 2250 3000 2430 3250 1950 2750 1500 2380 1140 1990 990 1850 960 1800 930 1750 1465 . 2222  Table 4.3: Data selected for the test of the proposed model simulating the change of C O D . C O D in the influent of COD-1, COD-2, COD-3 and COD-4 was 7896 mg/L. Lo k Liao[l] Time (hr) 0 24  COD-1 (mg/L) 1262 1318  COD-2 (mg/L) 1060 1143  COD-3 (mg/L) 1089 1162  COD-4 (mg/L) 1462 1532  120 144 Average  1234 1184 1250  910 830 986  827 811 972  946 808 1187  Chapter 4.  METHODS  32  Table 4.4: Data selected for the simulation of biomass change. Mass-1, Mass-2, Mass-3 and Mass-4 are corresponding to COD-1, COD-2, COD-3 and COD-4 in Table 4.2, respectively. Time (hr) 0 1 2 3 5 8 12 16 18 22 Average  Mass-1 (mg/L) 9000 8800 8550 8400 8900 9500 9100 8950 8750 8600 8855  Mass-2 (mg/L) 11800 11450 11000 11100 11280 11700 12200 11870 11500 11210 11511  Mass-3 (mg/L) 14700 14400 14150 14100 14800 15210 14900 14500 14150 13800 14471  Mass-4 (mg/L) 16400 16200 15950 15700 16450 17700 17100 16700 16300 15700 16420  Table 4.5: Data selected for the test of the proposed model simulating the change of biomass. Mass-1, Mass-2, Mass-3 and Mass-4 are corresponding to COD-1, COD-2, COD-3 and COD-4 in Table 4.3, respectively. Time (hr) 0 24  Mass-1 (mg/L) 10223 10636  Mass-2 (mg/L) 9370 9260  Mass-3 (mg/L) 10030 10256  Mass-4 (mg/L) 10143 10187  120 144 Average  9942 9890 10173  9644 9906 9545  10188 10535 10252  10052 10248 10158  Chapter 4.  4.2  METHODS  33  Mathematical Model  A n ideal model of an SBR should be able to respond to changes in every operating parameter, such as temperature, SRT, H R T as well as the concentration of biomass and substrate. However, building a perfect model with the inclusion of all the possible parameters will not be possible. Rather, this thesis attempts to focus on the most basic parameter C O D as a substrate as well as biomass. A n attempt was also given to a proper procedure for the estimation of the kinetic coefficients.  4.2.1  Fill Period  Fernandes's model assumed the reacting volume in fill period constant, but it is possible to make a system without the assumption of constant reacting volume.  Since dV/dt is inflow rate(Qi ), n  dVS n r  „dS =  i [  v  „ +  Q  *  n s  ( 4  -  2 )  On the other hand, the mass balance of substrate in fill period can be formulated as  ^  = QinSo - Vk S  (4.3)  f  where S is the C O D in the influent and kj is a first order kinetic coefficient of fill period. 0  The S is considered constant. Combining eqn 4.2 and 4.3 0  V  1I  +  Q  i  n  S  Arranging eqn 4.4 with respect to dS/dt,  =  Q  m  S  ° ~  V  k  f  S  ( 4  -  4 )  Chapter 4.  METHODS  34  m  =  Q* _(Q*  )  SO  +FC/  S  ( 4 - 5 )  Analytical solution of eqn 4.5 is  _ ( ( » + k ) 5(0) - % * S ) * exp ( - ( & » + fc,) *) + % 5 f  0  g  where S(0) is the C O D concentration at time is zero. Biomass can be simulated using eqn.3.14 whereby dX/dt is related to dS/dt via a specific yield factor,Y, for the fill period.  4.2.2  React Period  Monod kinetics was adopted and the assumption that K  s  »  S was not used to simulate  the transient phase. The endogenous decay factor, kd, was included and assumed to be constant.  d  S  X  (  S  , \  where kj, is the endogenous decay factor. The change of biomass with decay coefficient is :  The analytical solution of equation 4.7 is  S(t) - 5(0)  *?XK.  (ftX-**X)S(t)  +  %XK.\  Chapter 4.  4.3  METHODS  35  D e t e r m i n a t i o n of the K i n e t i c Coefficients  The kinetic coefficients must be determined for the simulation of the time change of substrate and biomass, using the rate expressions derived in the previous section. Curve fitting was used for this purpose. In fill period, the first order coefficient, fc/, was determined by fitting observed data to eqn.4.6 and eqn.3.14 was used for the determination of yield factor,Y. In react period, linear and non-linear models were tested. The linear models were introduced in section 3.3.3. Both data of substrate change and biomass change can be used in non-linear method for the determination of coefficients. Firstly, to use the data of biomass change, the integrated form of eqn. 4.8 was transformed to a linear form  S(t)fi  m  where A is In (X(t)/X(0))/t.  - K,A - S(t)k - K k d  s  d  = S(t)A  (4.10)  At a known time t, the right hand side of eqn. 4.10 is also  known and therefore the problem can be generalized as  axi — bx — 0x3 — dx\ = e  (4.11)  2  where a=c=S'(t), b=A, d = l , e=a*b, x is fj, , x is K , x is k and x is the product of x  x and £3(1.e. K *k ). 2  s  d  m  2  s  3  d  4  The solution of eqn.4.11 can be obtained by solving simultaneous  equations with one constraint. However, it could be difficult to determine the coefficients of SBR system with this method because the biomass increased in the first part and decreased in the second part of react period. Secondly, for the purpose of the determination of coefficients, it is conceivable to use the data of substrate change by fixing biomass concentration in eqn 4.9. It is not right to fix substrate concentration because its range of change is around 60% and the influence of the change to the system performance is not neglibible, whereas the range of change  Chapter 4.  METHODS  36  of biomass is within 10% and the influence of the change to the system performance may be considered negligible in the process of the determination of kinetic coefficients.  4.4  Computer Simulations  Based on the estimated kinetic coefficents in the previous section, computer simulation was performed and the results were compared with experimentally observed data. A numerical software package,DSS(Differential Systems Simulator), was used for simulation using a Runge-Kutta, Euler algorithm for integration [11]. The computer code is included in Appendix B.  4.5  Statistical Analysis  For statistical analysis of the results, the RMSE(Root Mean Square Error) method was used. R M S E is a measure of the deviation of the predicted values from the measured data. It is defined as:  (4.12) where y,- is ith experimentally obtained data and X{ is simulated result of y,-. The R M S E is always positive and a perfect prediction will have a null R M S E .  Chapter 5  RESULTS A N D DISCUSSION  5.1  Fill Period  The observed C O D data[7] showed that C O D increased with time during the three hours of fill period; the first hour of the fill period exhibited the highest gradient and that gradient got lower during the second and the third hour.  This phenomenon can be  possibly explained from mechanical and biochemical point of view.  The mechanical  reason is that, during the first hour, since there is not enough agitation, the anaerobic organisms have, less chance to contact the soluble substrate and that chance gets better slowly and reaches its maximum. Therefore, mixing and operation mode factors should be included in the model of the fill period, however, to do so would overly complicate the model and such an inclusion is impractical. The biochemical reason comes from the fact that all the biological reactions are catalyzed by regulatory mechanisms. In turn, a part of the regulatory system is the surrounding environment which provides the information for maintaining an equilibrium. After the previous react period, the biomass undergoes exposure to non-aeration and non-mixing periods. During these settle, draw and idle periods, the enzyme regulatory system could reduce the amount of enzyme necessary to maintain the equilibrium. But when the concentration of the substrate increases sharply in the fill period conditions become far from equilibrium and the enzyme concentration increases in correspondence. Prior to the simulation of a fill period, the coefficients of the proposed model(eqn.4.5)  37  Chapter 5. RESULTS  AND  DISCUSSION  38  Table 5.1: The kj values of fill period Influent C O D */(l/br) (mg/L) Author Fernandes 9500 0.4 0.46(± 0.0029) 19000 0.4 0.34(± 0.0053) 28500 0.4 0 . 4 0 ( ± 0.0128) 38000 0.4 0 . 4 0 ( ± 0.0128) Average 0.4 0 . 4 0 ( ± 0.0081)  need to be determined. The coefficient of fill period was determined by curve fitting observed data to the proposed model(eqn.4.6) for kj . The average value of kj is nearly same as the one reported by Fernandes, but at low C O D concentration(9500,19000 mg/L) the coefficient values are considerably different (Table 5.1). The simulations of C O D in fill period were graphically presented in Figs. 5.1, 5.3, 5.5 and 5.7. The statistical analysis of discrete data points via R M S E shows that the simulation by eqn. 4.5(Author) has better predictability than eqn.3.30(Fernandes[7]). The average R M S E value of the simulations of C O D by eqn.4.5 and eqn. 3.30 were 27.02 and 51.09, respectively. The simulated values of biomass in the fill period were presented in Figs. 5.2, 5.4, 5.6 and 5.8. The average R M S E value of the simulations of biomass by eqn 4.5(Author) and the reported simulation of Fernandes - Fernandes's biomass model was not explicitly expressed - were 74.34 and 1409.05, respectively. The predictability of biomass concentration was improved when constant reacting volume was not assumed. It may therefore be conculded that without the assumption of constant volume in fill period the precision of simulation can be improved.  RESULTS AND DISCUSSION  Chapter 5.  39  1000  800  OX)  600  B  &  400  H O  Observed Author, Eqa4.5 - Fernandes, Eqa3.30  200  0  0.5  1  1.5  2  25  3  3.5  Time(hr) Figure 5.1 Simulation of C O D in f i l l period when C O D of the influent is 9500 mg/L.  10000  8000 OX)  —•—  Observed^ Biomass) Eqn.4.8 --+-- Author, — o~ -Fernandes  6000  3 a o (3  4000  2000  1  0  l i _  3.5  0.5  Time(hr) Figure 5.2 Simulation of Biomass in fill period when C O D of the influent is 9500 mg/L.  Chapter 5. RESULTS  40  AND DISCUSSION  0.5  1  1.5  2  2.5  3  3.5  Time(hr) Figure 53 Simulation of C O D in Fill period when C O D of the influent is 19000 mg/L.  20000  15000 h  6 S  10000 f"  S o 5000 h  0.5  1.5  2  3.5  Time(hr) Figure 5.4 Simulation of Biomass in fill period when C O D of the influent is 19000 mg/L.  Chapter 5. RESULTS  0  41  AND DISCUSSION  1.5  0.5  3.5  2  Time(hr) Figure 5.5 Simulation of COD in fill period when COD of the influent is 28500 mg/L. 10000 j — *  8000 Oft  •£ IT. £ c s  —  — Observed(Biomass) - - + - - Author, Eqn. 4.8 — D - - Fernandes  6000  4000  2000  0 I 0  i 0.5  i 1  1  1.5  1  2  Time(hr)  -i 2.5  ' 3  1  3.5  Figure 5.6 Simulation of Biomass in fill period when COD of the influent is 28500 mg/L.  42  Chapter 5. RESULTS AND DISCUSSION  3500 3000 2500  B  u  2000  -  — • — - ObservedCOD) .  --+- - Author, Eqa4.5 — D - - Fernandes, Eqn.3.30  1500  -  1000 500 0 0.5  1.5  3.5  2  Time(hr) Figure 5.7 Simulation of C O D in fill period when C O D of the influent is 38000 mg/L.  20000  —  15000  00 6 o  -a  •  -—•— — Obsen'edf Biomass) Y- - Author. Eqn.4.8 — D - - Femancbs  10000  S 5000  0.5  1.5  2  3.5  Time(hr) Figure 5.8 Simulation of Biomass in Fill period when C O D of the influent is 38000 mg/L.  Chapter 5. RESULTS  5.2  AND  DISCUSSION  43  React Period  The react period was studied to simulate the behaviour of an SBR system. Since there is no inflow and outflow, batch kinetics can be applied. The proposed model adopts Monod's kinetics including an endogenous decay factor. Table 5.2 shows the values of [j, , K , kd determined by linear and nonlinear method. Yield factor, Y is assumed 0.5. m  s  All the fi  m  values determined by the various linear methods were an order of magnitude  smaller than the value derived from the nonlinear method, whereas all the K values by s  linear methods were 2-4 times greater then the values obtained by the nonlinear method. Using the nonlinear method that accounts for the decay factor, it may be deduced from the average values of fi  m  and k that 27% of digested energy is used for the maintenance d  in exponential growth phases. The \x  m  of 0.09(l/hr) reported by Koh et al[35] agrees  with the results of the author, however, Ross's[36] /u  m  of 0.4 (1/hr) as obtained by  regression analysis against volatile solids data is about ten times larger. The values of K ranging from 960 to 2860 m g / L is an order of magnitude greater than the typical value s  of 150 m g / L for municipal sewage. This could be due to the high C O D concentration of animal wastewater, as compared to Yoo et al[37] who reported a K  s  of 3000mg/L  under high substrate concentration conditions. The simulation of C O D in react period are graphically presented in Figs. 5.9, 5.11, 5.13 and 5.15.  The statistical analysis of  R M S E shows that the simulation method by eqn.4.7(author) has better preditability than eqn.3.32(Fernandes[7]). The average R M S E values of the simulation by eqn.4.7 and eqn.  3.32 were 27.47 and 149.89, respectively.  Thus, it may be concluded that with  the inclusion of decay factor the accuracy of C O D simulation can be improved. The simulation of biomass in react period are depicted in Figs. 5.10, 5.12, 5.14 and 5.16. The average R M S E value of the simulation by eqn 4.8 and Fernandes's model were 596.91 and 603.62, respectively.  Chapter 5. RESULTS  AND  DISCUSSION  c6  -d a  CD  (=1  O  1=1  CM •O rpl COoo — enI i—i CO t00LOC 1 — o o o T P O 3 < = > s o o O o ,_: CM o CM O co o CM O r< o o 05  -d  -H  i—I  -H  -H  CD  13 O  CO oo CM' CO rj< oo LO LO  SH  C D  CM  i-3  o CO  o o  C D C D  -H  0 5  LO CM  co oo  oo LO oo  .2  C D  oo  CO o  C O C O CM  £  oo  05  to oo <—I  CO I—I  o o o o LO CO  LO CO  LO  r-l  o n3  C D C D SH  co oo LO CM  CO CM CO CO  C O CO  | o  a  C D C D O  o o o  'G O  C D  'C cc3 OH  o  O  O  a  CM  a =a a  C D ~CD  11  o d  o o CM CM  o o  o LO o o o o o  CD  ^o  o  LO  o o o  o o LO oo CM  a 3  CJ  C D CD CD  o  a  C O oo  o o  CO  oo o o  O CD  co CM CO  a  a o  CD  13  1  CD  CD  a,  <J  CO  cc3  co  c3  SH  a  CD  O  CO  a  a C D a .> '5b  CM CM  CD SH  a  cr  1  CD  a .2  a .2  AH SH  a  m !H  «3  1  CT3  13  a  CD  <D CD  a SH  13  a  o o o oo CO  C D bfj OS IC -D l > cci  <  -d a  cc3  w  a  CD  t-t  CD  a o ^a  03 i-i OH  13  03 a SH  03 03 -d 03 03 SH  a  03 • 0) o CJ H ^  03 a  'M a  03  Q  CD _>  O  CD CD  oo  CO  a  a  CD  u u  SH  cc3  05  CD  cr  1  a .2  _a o -d  a cd CO  a o cj  a o  CD CH  a cr  03 SH  -a 5  o n3  CJ  cr CD  >>  u  •>  H J  a  3  a  a  Q  O  ^o  o  C O CO o  a  CO  CM  cr  -H  -H  o T—( CM°. o co = >d ° < = > o" o -H ° "H ° -H ° -H fCO o I® d LO 05 LO -H o r~ LO o o o o LO o o o o o o  SH  _a  a  CD  OOoo COo LO O CO CO l CC t-- CMO C O C = 5 CM O C O o CO o I CM O  PH -S^>  PH  CM CO  -u ,co <H-H  -H ^ -H  CM  -d  a o  'co CO  a o  _Q -d C D a  44  cd  <D  a a o a  CT3  6 o  o a  03  .ja  CO  J0 =3! 03  a -d  Chapter 5. RESULTS AND DISCUSSION  800  600 500 400 u  .  -  300 200 100 0  10 .  15  25  20  Time(hr) Figure 5.9 Simulation of C O D in"react period when C O D of the influent is 9500 mg/L.  10000  1—— i — i rI  1  -i—i—i—r e-  ' ' I  1  -  8000 S3 OK  g  -4k— Observed 6jio w\  6000  -B—  -0 O  M ; W Ey\ +.8 Fe.r r\^"n des  4000  2000  0  •  0  •  •  •  I  5  I  i  i  •  I  i  i | | | | i_ J I  10 15 Time(hr)  20  J  I  I  l _  25  Figure 5.10 Simulation of Biomass in react period with Yield of 0.5 when COD of the influent is 9500 mg/L.  Chapter 5. RESULTS AND DISCUSSION  2000  ObservedtCOD)  I- - - Author. Eqa4.7  1500  — O- - Fernandes,E^rv3-32 ;  a 1000  500  -a  10  25  20  15  Time(hr) Hgure 5.11 Simulation of G O D in react period when C O D of the influent is 19000 mg/L.  14000  -I—i—i—i  1  1—i  1—i 1 — — i r— — ii1 — — i i 1—i—i 1—t—i—i-  12000 10000  a o  8000  Cbservedf Biomass)  - 0 — Author, Eqn.4.8 o Fernandss  6000 4000 2000 0 0  _i i i i_  < • ' i  t ii ii i 10 15 i imc(hr)  i i i  i  1 20  ii  L _ J — '  25  Figure 5.12 Simulation of Biomass in react period with Yield of 0.5 when C O D of the influent is 19000 mg/L  Chapter 5. RESULTS AND DISCUSSION 2500  2000 h  1500 h  1000 r-  500  5  10 15 Trme(hr)  20  25  Figure 5.13 Simulation of COD in react period when COD of the influent is 28500 mg/L,  16000 14000 12000 10000  -A—Observed; Biomass) -B—Author, Bqn.4.8 -s— Fernandes  8000 o  • #4 -  6000 4000 2000 0  •  lit  I i i i i  1,. i i  i  i J j  10 15 Time(hr)  i—i—i—L  20  25  Figure 5.14 Simulation of Biomass in react period with Yield of 0.5 when COD of the influent is 28500 mg/L  Chapter 5. RESULTS AND DISCUSSION  3500 ,  ,  48  r—=  r  1  Time<Qr)  Figure 5.15  20000  -T  1  1  1  Simulation of C O D in react period when C O D of the influent is 38000 mg/L.  1  1  1  1  1  1  1  1  1  1  [  1  >  I  1  |  1  —  1  '  *~  15000 e  -A—• CteervedE Biomass) - B — Author, Eqn.4.8 - o — Fernandes  10000 o  (5 5000  • • i • i • i • <i • • i i I — i t—i—i—I—i—i—i—t-  0 0  5  10 15 Time(hr)  20  25  figure 5.16 Simulation of Biomass in react period with Yield o f 0.5 when C O D of the influent is 38000 mg/L  Chapter 5. RESULTS  5.3  AND  DISCUSSION  49  Sensitivity Test  The effects of the changes in the kinetic coefficients on the treatment efficiency have been studied. Yield factor was allowed to vary from 0.4 to 0.6, in order to study the effect of yield level on the C O D removal and the biomass growth. The results are shown in Figs. 5.17 - 5.24. In the case of C O D , the lower yield led to higher removal rate. This can be explained from eqn. 4.7 in the 'Method section'. The substrate removal rate can be expressed as [i /Y. m  Since Y is less than 1, the smaller  Y-value will cause faster substrate removal rate. Unlike C O D , the change of biomass with Y did not show considerable difference. For instance, for an influent C O D of 9500 and 19000 m g / L , the difference is hardly distinguishable. Even though the simualtion did not simulate the growth and decay phases of react period, the overall prediction of the final values are successful.  Chapter 5. RESULTS  AND DISCUSSION  800  a Q  o u  1—1—I—I—I—|—I—I—I—I—|—i—I—r-  700  A observed (coia)  600  a—coV#=o<5;  500  A—COT)  =o, C  400 300 200 100 0  i-  i—  J  i  o  i.  i  i  i  < t  5  t  i  I  I  20  10 15 Time(hr)  25  figure 5.17 C O D profile by change of Y i e l d factor when the influent is 9500 m g / L  10000  -i—i—i—i—|—i—i—i—i—|—i—i—i—i  j  -I—i—i—I  1  r—1  I  1  1  1—r-  8000  °f 6000 o  4000  5  2000 I  ]  1  I  I  I  I  I  I  1  1  I  t  1  I  1  1  L_X25  10 15 20 Timeihr) Figure5.18 Biomass profile by change of Yield factor when ihe influent is 9500 m^/L  Chapter 5. RESULTS  AND  2000  DISCUSSION  -i—i—i—r  -  ~ J — I — l — i — i — j — r — i  p  COD .(x=o.sJ  ~B  1500  1—I  - o — C O D 6< = < V on  a, Q O  1000  •u 500  ()  I  0  I  I  I  I  J  I  1  I  I  5  I. I . I  I  •  10  I  15  1  1  i  I—I—1—I—1—1  20  25  Time(hr) Figure 5.19 C O D profile by change o f Y i e l d factor when the influent is 19000 m g / L  14000  '  '  I  -i—i—i—r  T — i — i — r -  12000 _ 10000 S  8000  CO 05 6  6000  o  4000 2000 0 10 15 Timet hr)  20  25  Figure 5.20 Biomass profile by change o f Y i e l d factor when the influent is 19000 m g / L  Chapter 5. RESULTS  2500  AND DISCUSSION  T—'—'— —'—I ' '  p •o u  »i  1  -B  2000  a  52  r i | i i  ' i  COD oV=c\>5]  1500 U 1000  -«-  500  . i. 1  0  i •  10 15 Time<hr)  20  25  Figure 5.21 C O D profile by change of Y i e l d factor when the influent is 28500 m g / L  16000  ~t—I—I—i—|  i— ii I— — j— i— i— i I— — | I—I—I—I—p—1—I— — i r-  '14000 12000' 10000 C3  8000  o  6000 4000 2000 0  5  10  15  20  25  Timet hr) Figure 5Z2 Biomass profile by change of Y i eld factor when Ihe influent"is 28500 mg/L  Chapter 5.  RESULTS  AND  DISCUSSION _  3500 3000 2500 on S  2000  Q O  1500  u  1000 -e—Coj> ft* 0.5")  500 0  I — 1 _  _J  10  15  Time<hr)  25  20  Figure 5.23 C O D profile by change of Y i e l d facror when the influent is 38000 m g / L  20000  — |— i t ii—j—i—i—r—i—|—i—i—i—i—|—'—>—>—i-  15000  •J oij  a  \  a  I'QOOO  O —"Bto^ctss C< Q3 e  o 5 5000  0 L i !• • ' • • ' • 10 0 5 1  1  1  1  1  1  J  1  Timet hr)  15  20  J  L .  1  1-  25  Figure 5.24 Biomass profile by change of Yield factor when the influent is 38000 ina/L  Chapter 5. RESULTS  5.4  AND  DISCUSSION  54  Test of M o d e l  The study made by Lo and Liao[3] was selected for testing of the proposed model. However, the fill period of Lo and Liao's experiment was not attempted in simulations because its short duration of O.lhr constitued only 0.4% of the total cycle time, thus, the flow rate of lOL/hr for the size of 4L of working volume does not seem to be very practical. For simulation of the react period, the kinetic coefficients previously determined from an influent C O D of 38000mg/L were used, since at this level, the substrate strength of both experiments was compatible. Simulation results of are shown in Figs. 5.25 - 5.28. Using Y of 0.5, the prediction of biomass at the end of each cycle was successful; the overall performance of the biomass modeling was 92% accurate. The simulation of C O D was not as successful as biomass. In all four reactors, the simulated CODs were higher than the observed values. The overall prediction accuracy of C O D was 48%. This discrepancy may stem from error sources such as long idle period(4.3hr) and inaccurate estimate of kinetic coefficients.  In particular, when the idle period lasts longer than one hour the  effect of the period should be studied to improve the accuracy of the model.  Chapter 5. RESULTS  12000 10000  AND DISCUSSION  ~ > i < i i— i— i— i— | <—— i— ii— i— i— i— i— i— |— i— i— i— i— i— i— i— i r~ I 4f  8000 —I  Q O  U  6000  A •  COD Simulated (mg/L) Biomass Simulated (mg/L) Observed (COD) (mg/L) Observed (Biomass) (mg/L)  4000  50  100  150  Time(hr) Figure 5,2 5 Simulation of C O D and Biomass for the test of proposed model (reactor one)  12000  "T—i—i—i—i—i—i—r~r  — i- — i— i— i— i— i— ir  — ]— i— i— i— i— ir  10000 8000  e, Q  o V  -. A •  6000  COD Simulated (mg/L) Biomass Simulated (mg/L) Observed (COD)( mg/L) Observed (Biomass) (mg/L)  4000 2000 0  J  i i i i i i i i i i i_J i i i i i i i i i i i i i i i i_ 50  Time(hr)  100  150  Figure 5.2 6 Simulation of C O D and Biomass for the test of proposed model (reactor two)  Chapter 5. RESULTS  AND DISCUSSION  12000 10000 o  3  •P.  ti  3  0  50  100  150  Time(hr)  Figure 5.2 7 Simulation of C O D and Biomass for the test of proposed model (reactor three)  12000 1  1  ' ' i  i i-» i  i. i i i i  ii  »i i  |ii  i i  ii  i i  i  loooo <k" 8000  a Q  O U  6000  A •  o  COD Simulated (mg/L) Biomass Simulated (mg/L) Observed (GOD)(mg/L) Observed (Biomass)(mg/L)  B %  'ji  ?  4000  :  Ore r  2000  L 0  •  '  '  i—i—'—i—i—I—i—i—i—i  i  i  i  50  i  i,.I , i  100 Time(hr)  150  Figure 5. 2 8Simulation of C O D and Biomass for the test of proposed model (reactor four)  Chapter 6  CONCLUSION  Based on the objectives and the findings of this study, the following conclusions may be made: • The mathematical model developed by the author consistently yields more accurate estimates of effluent data when compared to the actual data, than Fernandes' model during both the fill period and react period. • The kinetic coefficients may be used as design parameters for the SBR process. The kinetic coefficients determinded using non-linear regression method lead to more realistic simulation than the linear regression method. A summary of the range of kinetic coefficient for the fill period and the react period have been tabulated in Table 5.1 and 5.2. In most cases, the variation of their magnitudes are within three-folds. • The assumption of constant biomass in fill period and react period for the determination of kinetic coefficients is valid for the simulation of C O D , biomass change. • If the length of idle period is long(> lhr), the effect of the idle period on system performance must be considered in modeling. • Sensitivity analysis results demonstrate that the removal of C O D is more sensitive to the change of yield factor than biomass change. The analysis shows that yield factor is inversely proportional to the C O D removal rate.  57  Bibliography  [1] Lo K . V . , Liao P.H. and Kleeck van R.J. (1991). 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Sequencing batch reactor activated sludge processes for the treatment of municipal landfill leachate: removal of nitrogen and refractory organic compounds. Water Science Technology, 21:1651-1654. [28] Decreon A . , Therien N. and Jones J.P. (1985). The application of sequencing batch treatment to an industrial wastewater. Water Pollution Research Journal, Canada, 20(1): 42-53. [29] Ng W . J . and Tan J . C . (1990). Some observation on organic removal in an SBR. Biological Wastes, 33:169-179. [30] Dennis R . W . and Irvine R . L . (1979). Effect of filhreact ratio on sequencing batch biological reactors. Journal of W P C F , 51(2):255-263. [31] Fernandes L . , McKyes E.(1991) Theoretical and experimental study of a sequencing batch reactor treatment of liquid swine manure. A S A E transaction, 34(l-2):597-602. [32] Ng W . J . (1989). A sequencing batch anaerobic reactor for treating piggery wastewater. Biological Wastes, 28:39-51. [33] Canada Animal Waste Management Guide.1972. [34] Robinson J . A . and Characklis W . G . (1984). Simultaneous estimation of V , K and the rate of endogenous substrate production(R) from substrate depletion data. Microb. Eco. (10):165 -178 m  m  [35] Koh W . K . , Ng W . J . and Ong S.L.(1989) A Bio-oxidation study of methanol synthetic wastewater using the SBR. Biological Wastes, 27:101-113.  Appendix A  Nomenclature  COD  Chemical Oxygen Demand(mg/L).  BOD  Biological Oxygen Demand(mg/L).  RMSE  Root Mean Square Error.  X  The concentration of biomass(mg/L).  S  The concentration of substrate(mg/L).  5  The concentration of substrate in influent(mg/L).  51  The concentration of the ith substrate(mg/L).  Si i  The concentration of the ith substrate in the inflow to a reactor(mg/L).  Si  The concentration of the ith substrate in the outflow(mg/L).  S'(O)  The concentration of substrate at time 0(mg/L).  S(t)  The concentration of substrate at time t(mg/L).  V  The reactor volume(L).  0  t  te  Qi  The inflow rate to a reactor(L/hr).  Q  e  The outflow rate(L/hr).  K  s  Monod half saturation constant of substrate(mg/L).  Kj  Monod half saturation constant of the ith substrate(mg/L).  k  Monod rate constant of substrate(l/hr).  ki  Monod rate constant of the ith substrate(l/hr).  kj  Monod rate constant for the fill period of SBR(l/hr).  n  s  kf  jX  Monod rate constant for the fill period of SBR when the constant  61  Appendix A.  Nomenclature  biomass was assumed(l/hr). k, 2  x  Monod rate constant for the react period of SBR when the constant biomass was assumed(l/hr). The specific growth rate(l/hr).  ji H  The maximum specific growth rate(l/hr).  kd  The endogenous decay factor (l/hr).  Y  The yield factor  Xi  In R M S E , the ith simulated result.  yi  In R M S E , the zth experimentally obtained data.  N  In R M S E , the number of data.  m  62  Appendix B  Source C o d e  PROGRAM DSS2S C C C C  Ordinary Differential Systems Simulator DSS Version 2 Special Application to Sequencing Batch Reactor System Simulation C0MM0N/SYSTM1/TO,TF,TP,H,ERROR,N,MAX,NTYPE,NPRINT,IRRTYP COMMON/T/T,NFIN,NORUN C0MM0N/I0/NI,NO,INPUT2,0UTPUT2 C0MM0N/Y/Y(250) C0MM0N/F/F(250) C0MM0N/RK1/K1(250) C0MM0N/RK2/K2(250) C0MM0N/RK3/K3(250) C0MM0N/RK4/K4(250) C0MM0N/RK5/K5(250) C0MM0N/RK6/E(250) C0MM0N/RK7/Y0(250) C0MM0N/RK8/F0(250) C0MM0N/SYSTM2/NVAR, INTERR.C250) C0MM0N/SYSTM3/NACC,INTACC(250) C0MM0N/ABSERR/ABSERR(250) COMMON/RELERR/RELERR(250) COMMON/ ERR/ ERR(250)  C  Following i s localized section for SBR Simulation  C C C  COMMON/LOCAL/Q,VO,SO,SI,KFILL,KREACT,TFR,S1PRE REAL Q,V0,SO,SI,KFILL,KREACT,TFR,S1PRE Above i s localized section Q —> Flow Rate (L/day) V —> Reactor Volume (Liter) 63  Appendix B. Source Code  C C C  1  2 8 9 10  3  12  SO —> COD concentration in Raw wastewater (mg/L) KFILL —> Reaction Coefficient i n F i l l Period KREACT —> Reaction Coefficient i n React Period REAL K1,K2,K3,K4,K5 DIMENSION TITLE(20),XTITLE(3),YTITLE(2) CHARACTER TITLE*4, XTITLE*4, YTITLE*4, IHREL*3 DATA XTITLE/'END ','OF R','UNS '/ DATA YTITLE/'REPE','ATS '/ DATA IHREL/'REL'/ Y(3) = 11100 NI=10 N0=12 OPEN(NI,FILE='paraml') OPEN(NO,FILE='output') N0RUN=0 S1PRE=0.0 N0RUN=N0RUN+1 NFIN=0 NRPT=0 READ(NI,900)(TITLE(I),1=1,20) DO 2 1=1,3 IF(TITLE(I).NE.XTITLE(I))GO TO 8 CONTINUE GO TO 500 DO 9 1=1,2 IF(TITLE(I).NE.YTITLE(I))GO TO 3 CONTINUE READ(NI,902)NRPTS NRPT=NRPT+1 T0=T0S GO TO 12 READ(NI,901)T0,TF,TP T0S=T0 READ(NI,90 2)N,NMAX,NTYPE,NPRINT,IRRTYP,ERROR,ML,MU WRITE(N0,903)N0RUN,(TITLE(I),1=1,20) WRITE(NO,904)TO,TF,TP  Appendix B. Source Code  6 4  5  7  14 11  13 900  WRITE(NO,905)N,NMAX,NTYPE WRITE(N0,908) WRITE(NO,909)NPRINT,IRRTYP,ERROR WRITE(N0,919) T=T0 CALL INITAL IF(ABS(NTYPE)-.GT.15)G0 TO 13 NACC=0 DO 6 1=1,N INTACC(I)=0 CALL PRINT IF(NFIN.NE.O)GO TO 5 IF(T.GT.(TF-O.5*TP))GO TO 5 TO=T CALL INT1 S1PRE=Y(1) GO TO 4 IF((NPRINT.EQ.0).AND.(NRPT.EQ.0))GO TO 1 IF((NPRINT.EQ.O).AND.(NRPT.NE.O))GO TO 11 IF((NACC.EQ.O).AND.(NRPT.EQ.0))G0 TO 1 IF((NACC.EQ.O).AND.(NRPT.NE.O))GO TO 11 J=0 DO 7 1=1,N IF(INTACC(I).EQ.O)GO TO 7 J=J+1 INTACC(J)=I CONTINUE WRITE(NO,906)(INTACC(I),1=1,NACC) WRITE(N0,907) IF(NRPT.EQ.O)GO TO 1 IF(NRPT.EQ.NRPTS)GO TO 1 N0RUN=N0RUN+1 NFIN=0 GO TO 10 WRITE(N0,913) GO TO 14 FORMAT(20A4)  65  Appendix B. Source Code  901 902 903 904  905  66  F0RMAT(3E10.0) FORMAT(415,2X,A3,E10.0,215) FORMAT(1H1,10X.8HRUN NO. ,I2,3H- ,20A4,/) FORMAT(1IX,24HINITIAL VALUE OF TIME = ,El1.4,//, 1 11X,22HFINAL VALUE OF TIME = ,El1.4,//, 2 11X,25HPRINT INTERVAL OF TIME = ,El1.4,/) FORMAT( 1 1IX,47HNUMBER OF FIRST-ORDER DIFFERENTIAL EQUATIONS = ,13,//, 2 11X.46HPRINT INTERVAL/MINIMUM INTEGRATION INTERVAL = ,15,//, 3 11X,24HINTEGRATI0N ALGORITHM = ,13,/, 4 16X.54H 1 - RUNGE KUTTA EULER 1, 5 16X,54H 2 - RUNGE KUTTA NIESSE 1, 6 16X,54H 3 RUNGE KUTTA MERSON 1, 7 16X,54H 4 RUNGE KUTTA TANAKA - 4 1, 8 16X,54H 5 RUNGE KUTTA TANAKA - 5 /, 9 16X,54H 6 - RUNGE KUTTA CHAI ) FORMAT( A 16X.54H 7 - RUNGE KUTTA ENGLAND /, B 16X.54H 8 - RUNGE KUTTA WES - 4/1 1, C 16X,54H 9 - RUNGE KUTTA WES - 4/2 /, D 16X.54H10 - RUNGE KUTTA WES - 4/3 1, E 16X.54H11 - RUNGE KUTTA WES - 4/4 /, F 16X.54H12 RUNGE KUTTA WES - 4/5 1, G 16X.54H13 RUNGE KUTTA WES - 5/1 /, H 16X,54H14 RUNGE KUTTA WES - 5/2 /, I 16X,54H15 - RUNGE KUTTA FEHLBERG - RKF45 /) FORMAT( I 11X,15HPRINT OPTION = ,11,/, J 16X,36HN0 INTEGRATION ERROR DIAGNOSTICS - 0,'/, K 16X,36HSUMMARY OF INTEGRATION ERRORS - 1,//, L 11X.28HTYPE OF INTEGRATION ERROR = ,A3,//, M 11X.28HMAXIMUM INTEGRATION ERROR = ,E10.3,/) FORMAT(1H1,10X,55HINTEGRATI0N ERROR FOR THE FOLLOWING DEPENDENT VA 1RIABLES,/,11X,10I5,/) FORMAT(1IX,95HDEPENDENT VARIABLES REPORTED IN THE ERROR SUMMARY AR IE NUMBERED IN THE SAME ORDER AS THEY APPEAR,/,1IX,97HIN THE /Y/ SE 2CTI0N OF LABELLED COMMON (SEE THE COMMON AREA OF SUBROUTINES INITA 9  9  9  9  9  9  9  9  9  9  9  9  9  9  909  906 907  Appendix B. Source Code  913  919 500  67  3L, DERV AND PRINT)) FORMAT( 1 16X,54HALG0RITHM NUMBER READ FROM THIRD DATA LINE IS OUTSIDE , /, 2 16X,54HTHE INTERVAL -15 TO 15 SO THE CURRENT RUN IS TERMINA- , /, 3 16X,54HED , /) FORMAT(1H1) continue stop END  C********************* **************************************************** C Subroutine for Differential Systems Definition * C************************************************************************* SUBROUTINE DERV COMMON/T/T,NFIN,NORUN/Y/Y(2)/F/F(2)/E/NCALL COMMON/LOCAL/Q,VO,SO,SI,KFILL,KREACT,TFR,S1PRE REAL Q,VO,SO,SI,KFILL,KREACT,TFR,S1PRE IF(T .LE. TFR) THEN F(l)= ((Q*S0)/(V0+Y(2))) - KFILL*Y(1) F(2)= q ELSE F(l) = -0.0739*Y(1)/(961.6+Y(1))*Y(3) + 362.11 F(3) = (0.0739*Y(1)/(961.6+Y(1)) - 0.0287)*Y(3) END IF NCALL=NCALL+1 RETURN END C************************************************************************* C Subroutine for I n i t i a l i z a t i o n * C************************************************************************* SUBROUTINE INITAL COMMON/T/T,NFIN,NORUN/Y/Y(2)/F/F(2)/E/NCALL COMMON/IO/NI,N0,INPUT2,0UTPUT2  Appendix B. Source Code  68  COMMON/LOCAL/Q,VO,SO,S1,KFILL,KREACT,TFR,S1PRE REAL Q,VO,SO,S1,KFILL,KREACT,TFR,S1PRE INPUT2 = 20 OPEN(unit=INPUT2,file='param2',status='OLD') READ(unit=INPUT2,fmt=100) Q READ(unit=INPUT2,fmt=100) VO READ(unit=INPUT2,fmt=100) SO READ(unit=INPUT2,fmt=100) SI READ(unit=INPUT2,fmt=100) KFILL READ(unit=INPUT2,fmt=100) KREACT READ(UNIT=INPUT2,fmt=100) TFR READ(UNIT=INPUT2,fmt=100) Y(2) CLOSE(unit=INPUT2,status='KEEP') IF(NORUN .Eq. 1) THEN  100  Y(l) = SI ELSE Y(l) = S1PRE END IF NCALL=0 format(E10.4) RETURN END  Q************************************************************************  C  Subroutine for Print  3|c 3^C S|C }fc l|c l|c 3|c 3|c 3^C sfc l|c ?|C S|c 3fc 3^C  1  3(c 3|c 3|c 3|c l|C 3|c 3|C 3|c l|c 3|c ?|c 3JC SfC  * l|C l|C )|C 3|C 3|C ?|c 3|c 3|c 3|c 3|c 3^C 3fc }fc 3fc ?|C  3§C  ?|C  ?{C 3|c 3|c 3JC 3§C 3|c 3fC 3fC 3|c ?|c 3|c 3|c sfc 3|c 3|c 3|c 3fc 3^C  SUBROUTINE PRINT COMMON/T/T,NFIN,NORUN/Y/Y(2)/F/F(2)/E/NCALL COMMON/IO/NI,NO,INPUT2,0UTPUT2 INTEGER INPUT2, 0UTPUT2 0UTPUT2=21 OPEN(UNIT=0UTPUT2,FILE='GRAPH') WRITE(*,2) T+((N0RUN-1)*25),Y(1),Y(3) WRITE(0UTPUT2,2) T+((N0RUN-1)*25),Y(l) WRITE(NO.l) T,Y(1),Y(2). FORMAT('T \f4.1,' COD(YCD) \f5.0,' Y(2) \f5.0)  3^C *f(  Appendix B. Source Code  2  69  FORMAT(f4.1, ' \ 2fl0.1) RETURN END  C************************************************************************ C Subroutine for Integration, Runge-Kutta * C************************************************************************ SUBROUTINE INT1 REAL K1,K2,K3,K4,K5 C0MM0N/SYSTM1/T0,TF,TP,H,ERROR,N,NMAX,NTYPE,NPRINT,IRRTYP C0MM0N/SYSTM2/NVAR,INTERR(250) COMMON/SYSTM3/NACC,INTACC(250) COMMON/T/T,NFIN,NRUN CDMM0N/Y/Y(250) C0MM0N/F/F(250) C0MM0N/RK6/E(250) C0MM0N/RK7/Y0(250) C0MM0N/RK8/F0(250) COMMON/IO/NI,NO,INPUT2,0UTPUT2 DATA IHREL/3HREL/ DMAX=1.0E+38 YMIN=1.0E-20 IF (NPRINT.EQ.O) GO TO 2 DO 1 1=1,N IF (ABS(Y(I)).LE.DMAX) GO TO 1 WRITE (NO,500) I,Y(I),T NFIN=1 1 CONTINUE IF (NFIN.EQ.O) GO TO 2 WRITE (NO,600) RETURN 2 NVAR=0  Appendix B. Source Code  DO 3 1=1,N 3 INTERR(I)=0 HMIN=TP/FLOAT(NMAX) NEND=0 T1=T0+TP H=TP/8.E+00 5 IF (T+H.LT.T1) GO TO 6 H=T1-T NEND=1 6 CALL DERV IF (NFIN.NE.O) GO TO 16 DO 7 1=1,N YO(I)=Y(I) 7 FO(l)=F(I) TO=T 8 DO 9 1=1,N 9 Y(I)=YO(I)+FO(l)*H T=TO+H CALL DERV IF (NFIN.NE.O) GO TO 16 DO 10 1=1,N 10 E(I)=(F(I)-F0(l))*H/2.E+00. SCALE=l.E+00 TEST=O.E+00 IF (H.LE.HMIN) GO TO 14 DO 11 1=1,N IF (IRRTYP.EQ.IHREL) SCALE=1.E+00/(Y(I)+YMIN) ERR=ABS(SCALE*E(I)) IF (ERR.GE.ERROR) GO TO 13 11 TEST=AMAX1(TEST,ERR) DO 12 1=1,N 12 Y(I)=Y(I)+E(I) T=TO+H IF (NEND.EQ.1) GO TO 16 IF (TEST.LT.ERROR/4.E+00) H=H*2.E+00 GO TO 5 13 H=H/2.E+00  Appendix B. Source Code  71  NEND=0 GO TO 8 14 DO 15 1=1,N IF (IRRTYP.EQ.IHREL) SCALE=1.E+00/(Y(I)+YMIN) ERR=ABS(SCALE*E(I)) IF (ERR.GE.ERROR) INTERR(I)=I 15 Y(I)=Y(I)+E(I) T=TO+H IF (NEND.EQ.l) GO TO 16 H=H*2.E+00 GO TO 5 16 J=0 DO 17 1=1,N IF (INTERR(I).EQ.O) GO TO 17 J=J+1 INTERR(J)=I IF (INTACC(I).NE.O) GO TO 17 INTACC(I)=I NACC=NACC+1 17 CONTINUE NVAR=J RETURN 500 FORMAT(//,20H DEPENDENT VARIABLE ,I4,15H HAS THE VALUE ,E10.3,38H XWHEN THE INDEPENDENT VARIABLE EQUALS ,E10.3) 600 FORMAT( X 58H ERROR CONDITION IN SUBROUTINE INTEG. RUN IS TERMINATED. , /, X 58H THE USER SHOULD CHECK THAT ALL OF THE DEPENDENT VARIABLES, /, X 58H IN COMMON/Y/ ARE INITIALIZED AND THAT THE PROGRAMMING IN , /, X 58H SUBROUTINE DERV IS CORRECT I.E., ALL OF THE DERIVATIVES , /, X 58H IN COMMON/F/ ARE SET TO GOOD VALUES BEFORE EXITING FROM , /, X 58H SUBROUTINE DERV , /) END  C************************************************************************** C Sample input, paraml * C**************************************************************************  Appendix B. Source Code  72  TWO SIMULTANEOUS NONLINEAR FIRST-ORDER ODE, RUNGE KUTTA EULER 0. 24.0 1.0 3 1000 1 1 REL 0.0001 END OF RUNS C************************************************************************** C Sample input, param2 * C************************************************************************** 0.125 2.625 19000.0 601.0 0.35 0.06 3.0 0.0  Flow Rate(q) L/hr Volume(V) L Concentration of substrate in raw wastewater(mg/L) Beginning concentration of substrate in the reactor(mg/L) Coefficient of F i l l Period Coefficient of Reacto Period End Time of F i l l Period/ Starting Time of React Period Delta Volume in F i l l Period  Q********************************  END * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  

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