[Advances in Chemistry] Anaerobic Biological Treatment Processes Volume 105 || Dynamic Modeling and Simulation of the Anaerobic Digestion Process

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  • 8 Dynamic Modeling and Simulation of the Anaerobic Digestion Process

    JOHN F. ANDREWS and STEPHEN P. GRAEF

    Department of Environmental Systems Engineering, Clemson University, Clemson, S. C. 29631

    One of the major problems associated with the anaerobic digestion process is its poor record with respect to process stability. Dynamic modeling and simulation are useful tools for investigating process stability and can be used to quantify operation and improve design. Some key features to be included in a dynamic model are: (1) an inhibition function to relate volatile acids concentration and specific growth rate for the methane bacteria; (2) consideration of the unionized acid as the growth limiting substrate and inhibiting agent; (3) consideration of the interactions which occur in and between the liquid, gas, and biological phases of the digester. Simulation studies can provide qualitative evidence for the validity of the model by predicting the dynamic response of those variables most commonly used for process operation.

    '"phe anaerobic digestion process is used widely for treating municipal A waste sludge and is finding increasing use in treating industrial wastes

    which contain high concentrations of organic materials. The process has significant advantages over other methods of waste treatment. Among these are a low production of waste sludge, low power requirements for operation, and formation of a useful product, methane gas, which is a form of energy that is easily transported and stored. The digested sludge is a good soil conditioner and has some fertilizer value. It should see increasing use in land reclamation. Unfortunately, even with all these advantages the process has not enjoyed a good reputation in general because of its poor record with respect to process stability as indicated through the years by the many reports of "sour" or failing digesters. The major problems appear to lie in the area of process operation as evi-

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    In Anaerobic Biological Treatment Processes; Pohland, F.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

  • 8. A N D R E W S A N D G R A E F Modeling and Simulation of Digestion 127

    denced by its more successful performance in larger cities where skilled operation is more prevalent. At present operating practice consists only of a set of empirical rules, and there is a great need for a dynamic model to put process operation on a more quantitative basis. This would lead ultimately to the development of better control procedures for preventing process failure and for optimizing process performance. A dynamic model would also be valuable in improving process design since it would allow comparison of the different versions of the process with respect to process stability. The incorporation of improved control systems in the design would also improve process stability and decrease the need for oversizing.

    Most mathematical models currently used to describe the process are steady-state models and therefore cannot be used to predict process performance during start-up operations or under transient conditions resulting from changes in process inputs. Dynamic models can be used to make these predictions, and the importance of such models is realized when one considers that a failing digester is definitely not at steady state. Andrews (I) has developed a dynamic model for the process which is based on continuous culture theory but incorporates several important modifications. The two key features of his model are: (1) use of an inhibition function in lieu of the Monod function to relate volatile acids concentration and specific growth rate for the methane bacteria; (2) con-sideration of the unionized volatile acids as both the growth-limiting substrate and inhibiting agent. The use of an inhibition function is an important modification since it enables the model to predict process failure by high concentrations of volatile acids at residence times exceed-ing the wash-out residence time. Consideration of the unionized acids as the inhibiting agent resolves the conflict which has existed in the litera-ture as to whether inhibition is caused by high volatile acids concentra-tion or low pH. Since the concentration of unionized acids is a function of both total volatile acids concentration and pH, both are important. Andrews (I) presented experimental evidence and evidence from the microbiological literature to support his model. He also presented the results of computer simulations which provide additional supporting evi-dence by predicting results which have been commonly observed in field studies on digesters.

    Since the process is complex and poorly understood, this first model was a simplified one with several limitations. The primary limitation was its restriction to digesters with a constant pH. The model presented in this paper removes this limitation by considering the interactions which occur in and between the liquid, gas, and biological phases of the digester. Consideration of these interactions permits the development of a model which predicts the dynamic response of the five variables most commonly used for process operation: (1) volatile acids concentation, (2) alka-

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    In Anaerobic Biological Treatment Processes; Pohland, F.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

  • 128 A N A E R O B I C B I O L O G I C A L T R E A T M E N T P R O C E S S E S

    Unity, (3) pH, (4) gas flow rate, (5) gas composition. The results of simulations of batch cultures and the simulated responses of continuous flow cultures to step changes in substrate concentration and flow rate are presented and compared qualitatively with results commonly ob-served for field digesters. Even though the model still has several limita-tions, it should be useful in guiding experimentation and investigating the effect of different control actions and design procedures on the dynamics of the process.

    Since this paper is primarily based on computer simulation, a rela-tively new technique, a brief discussion of this is in order. Simulation is not new since physical models have long been used to simulate processes. Many laboratory experiments are attempts to simulate physically the real system. Computer simulation has many of the same advantages and disadvantages of physical simulation. Among the advantages are con-siderable insight into the process mechanisms and savings in time and money. Much knowledge can be obtained about the process through the development of a mathematical model and the subsequent computer simulations using this model. Considerable monetary savings are usually realized since experimentation on the computer is less expensive than construction of a full scale plant or physical model with subsequent experimentation. Time can be compressed on the computer with simula-tions being conducted in minutes. This is especially important for proc-esses such as the anaerobic digestion process where rates are slow and physical experimentation may require weeks and even months.

    There are, of course, disadvantages to computer simulation. The simulation results are no better than the mathematical model on which they are based, and many first simulations therefore give only qualitative answers. Simulation with physical models does not have this disadvan-tage since no mathematical model is required. However, physical simu-lations do have the problem of scale-up from the model to the real system. This disadvantage of computer simulation can be overcome by working back and forth between mathematical modeling, computer simulation, and field observations since these complement one another. Experimen-tation with physical models may also be incorporated into this iterative procedure. Knowledge gained in simulation is useful for modifying the mathematical model and guiding physical experimentation. The model should be considered evolutionary in nature since it will change as more knowledge is gained about the system through simulation, field observa-tion, or physical experimentation.

    In the past, even simple models of biological processes have pre-sented a computational bottleneck since they are largely made up of sets of nonlinear differential or partial differential equations for which ana-lytical solutions are not usually available. However this bottleneck has

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    In Anaerobic Biological Treatment Processes; Pohland, F.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

  • 8. A N D R E W S A N D G R A E F Modeling and Simulation of Digestion 129

    been largely removed by the availability of analog computers and con-tinuous systems modeling programs for digital computers. The simula-tions presented in this paper were performed using CSMP-360 (2) on the IBM 360/40 computer.

    The anaerobic digestion of complex organic wastes is normally con-sidered to consist of reactions occurring in series as illustrated in Figure 1. This is an approximation since many different microbial species may participate in the process, and their interactions are not always clearly defined. For example, recent evidence (3) indicates that some non-methanogenic bacteria may be involved in the conversion of volatile acids to methane and carbon dioxide. However, since most species of methane bacteria have much lower growth rates (4, 5) than the acid-producing bacteria, the over-all conversion of the intermediate products, volatile acids, to methane and carbon dioxide is usually considered to be the rate-limiting step in the process and will be the only reaction con-sidered herein. The methane bacteria also appear to be more sensitive than the acid-producing bacteria to changes in environmental conditions such as pH, temperature, and inhibitory substances.

    Stoichiometry

    Buswell and co-workers (fj) have studied the anaerobic decomposi-tion of many organic materials and have presented a general formula (Equation 1) for the conversion of complex organic materials

    to carbon dioxide and methane. However, this formula does not include the fraction of substrate that is converted to microorganisms which, although small, is necessary for the development of a dynamic model of the process. A more general formula (Equation 2) for converting organic material to microorganisms, carbon dioxide, and methane is shown below:

    Theory

    |_2 8 ^

    Organics F x / s [C 6Hi 20 6] + 1

    [C02)T + 1

    [CHJ (2) ^co2/x

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    In Anaerobic Biological Treatment Processes; Pohland, F.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

  • 130 A N A E R O B I C B I O L O G I C A L T R E A T M E N T P R O C E S S E S

    where:

    Yx/s = moles organisms produced/mole substrate consumed

    ^co2/x = moles C 0 2 produced/mole organisms produced

    F C H 4 / X = moles C H 4 produced/mole organisms produced

    Equation 3 is a more specific formula for the metabolism of acetic acid and is developed from an oxidation-reduction balance using the appro-priate yield "constants" as defined.

    CH3COOH - * 0.02 C 6 H 1 2 0 6 + 0.94 [C0 2]T + 0.94 C H 4 (3) The empirical composition of the microorganisms is assumed to be C 6 H i 2 0 6 . The value of YX/s for acetic acid was estimated from the data of Lawrence and McCarty (5). All quantities are expressed in moles for ease of manipulation in the model.

    The simulations presented are for the conversion of acetic acid to microorganisms, methane, and carbon dioxide. Yields will be different for other volatile acids, especially noticeable being the increased ratio of methane to carbon dioxide produced as the length of the carbon chain increases. For field digesters utilizing complex substrates it would also be necessary to include the carbon dioxide generated by the acid-producing bacteria.

    The carbon dioxide produced is indicated as (C0 2 ) r since it can remain dissolved in the liquid, react chemically to form bicarbonate or carbonate, be transported into the gas phase, or precipitated as carbonate. The extent to which these reactions occur will be influenced by the interactions between volatile acids, alkalinity, pH, gas flow rate, and gas composition and are considered in the model with the exception of pre-cipitation as carbonate. The methane produced does not undergo any chemical reaction and being slightly soluble is transported quantitatively into the gas phase.

    Kinetics of the Steady State

    Current design practice is based mostly on empirical procedures determined from experience. However, in recent years there has been a trend toward a more rational basis for design through the application of continuous culture theory. This theory can be expressed as a mathemati-cal model which is based on material balances of substrate and organisms for a continuous flow, complete-mixing reactor using the three basic relationships given in the following equations. Andrews (4), among others, has discussed the assumptions involved in the development of this model.

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    In Anaerobic Biological Treatment Processes; Pohland, F.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

  • 8. A N D R E W S A N D G R A E F Modeling and Simulation of Digestion 131

    Growth Rate

    Monod Function

    ( 4 )

    (5)

    Yield dX v dS Ht = ~ 7 x / s = - F x / s ^ (6)

    Organism Balance

    Accumulation = Input Output + Reaction

    ^ = ~ X0 ^ Xi + \LXI (7)

    Substrate Balance Accumulation = Input Output + Reaction

    dSi F Q F e \L Y ~dT = v ~ v 1 ~ T^s 1 w

    where:

    X = organism concentration, moles/liter = substrate concentration, moles/liter F = liquid flow rate to reactor, liters/day V = reactor liquid volume, liters [x = specific growth rate, day - 1 jl = maximum specific growth rate, day - 1 K8 = saturation constant, moles/liter 0 = subscript denoting reactor influent 1 = subscript denoting reactor effluent

    Solutions for the steady state are obtained from Equations 7 and 8 by setting the derivatives equal to zero and solving the resulting alge-braic equations for substrate and organism concentrations in the reactor effluent. The effects of other factors such as endogenous respiration, utilization of substrate for maintenance energy, a...

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