Dynamic simulator for anaerobic digestion processes

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  • Dynamic Simulator for Anaerobic Digestion Processes

    C. KLEINSTREUER and T. POWEIGHA, Department of Chemical and Environmental Engineering, Rensselaer Polytechnic Institute,

    Troy, New York 12181

    Summary A transient, two-culture model simulating methane production from biomass has been devel-

    oped. The simulator, based partially on the work by Andrews and McCarty, is capable of calcu- lating the hydrolysis products of several common organic materials, accommodating various substrate feeding modes, and simulating the transient physico-biochemical transport and con- version processes occumng in the biological, liquid, and gaseous phases of a well-mixed reactor. The mathematical representation of this bioconversion system consists of a set of 11 coupled, nonlinear first-order rate equations based on the principles of mass conservation and biochemi- cal reaction kinetics. The model can be used in conjunction with laboratory investigations and as a simulator for evaluating process control strategies and cost developments.


    Anaerobic digestion is the reduction of biomass by microorganisms in the absence of free oxygen. Economically suitable biomass includes manure, mu- nicipal organic waste, dairy waste, and aquatic plants. Biogas produced con- tains reduced species such as methane (the desirable pipeline gas), hydrogen sulfide, and the main oxidized species, carbon dioxide. The digestion process is believed to occur in three main steps, each involving a distinct group of bacteria. As described by Bryant,' in the first step biomass is broken down to alcohols, organic acids, C02, and hydrogen by fermentative bacteria. In the second step, the H2-producing process, acetogenic bacteria metabolize these products to acetate and hydrogen. In the final step, methanogenic bacteria catabolize the products of the two earlier steps to the predominant end prod- ucts, methane and carbon dioxide. These three steps occur simultaneously rather than in sequence as described. The fermentative bacteria are robust and fast. In contrast, the methanogenic bacteria are relatively slow in growth and in metabolism to produce CH4 and C02. In addition, they are very sensi- tive to temperature changes and to a low pH environment (less than 6.5) which might be caused by a buildup of acid formers in response to heavy organic loading. The potential for process failure, in the absence of a proper control system, is the main drawback of anaerobic digestion which is other- wise economically attractive when the plant is located near the source of suit- able feedstock. Mathematical modeling can help to mitigate the problems

    Biotechnology and Bioengineering, Vol. XXIV, F'p. 1941-1951 (1982) 0 1982 John Wiley & Sons, Inc. CCC ooO6-3592/82/091941-11$02.10


    associated with anaerobic digestion systems. In particular, computer simula- tions can aid in 1) planning cost-intensive laboratory experiments, 2) inter- preting data sets, and 3) developing generalized equations which describe important subprocesses such as growth and metabolism of methane formers. Furthermorc, a calibrated dytiainic simulator is a useful tool for 1) predicting digestor performance, 2) testing appropriate process control options, and 3) analyzing static as well as transient cost developments.

    An excellent review on anaerobic digestion and other biomass conversion processes was given by Bungay.2 The overview by DeRenzo3 concentrates on anaerobic digestion of waste materials, in particular-sewage, and crops to generate methane as a fuel gas. The current status of methane cultures and their microbial interactions was reviewed by Z e i k ~ s . ~ The conceptualization of basic physical, transport, and biochemical conversion phenomena was given by Andrew~,~ Pfeffer,6 and M~Car ty .~ Christensen and McCarty8 developed BIOTREAT which is a steady-state, one-culture computer code with special subroutines for calculating yield and rate coefficients as well as stoichiometric formulae of common substrates. In contrast, Andrews and co- workers developed a dynamic one-culture process model which was used and improved by Graef and A r d r e w ~ , ~ Collins and Gilliland,lo Smith and Roesler," Buhr and Andrews,12 and Hill and N0rd~tedt.l~ Buhr emphasized the modeling of thermophilic process operation which might lower the deten- tion time, improve sludge drying, and increase the destruction of pathogenic organism. These advantages entail higher heating requirements and closer process control to maintain system stability. Hill developed an agricultural waste treatment simulator using the special-purpose language C S M P (IBM, 1968) for long-term prediction of typical process variables for anaerobic lagoons, digesters, and mass-culture algae production units. Kleinstreuer, Vasudevan, and Poweigha14 discussed mathematical models and their per- formance as compared to experimental observations.

    Experimental data for model calibration and verification was obtained from the open literature.15-17


    A complete process simulation of anaerobic biomass digestion would in- clude l8 1) biomass generation, collection, and transportation; 2) physical and chemical pretreatment of substrate; 3) controlled gas production; and 4) gas separation, effluent dewatering, drying, and disposal. Such global modeling studies for the purpose of cost predictions were done by Pfeffer et al.I9 and by Milne et al.*O

    The mathematical model presented herein focuses on the acetogenic and methanogenic stages of the three-stage overall anaerobic digestion process. It is assumed that the hydrolysis of a typical complex waste has occurred in a pretreatment step in a separate reactor, and that the resulting soluble or- ganic compounds are the input for the main reactor (Figs. 1 and 2). Christen-



    C I Alcohols

    5 H2. Cop

    > e . g . Acids,

    + a " ELs




    Acetogenic Acetate' Methanogeni c B a c t e r i a B a c t e r i a

    Hqs CO2 - . +


    sen and McCarty8 have developed a model (BIOTREAT) which calculates the hydrolysis products of several typical complex organic wastes. BIOTREAT has been adapted as an optional preprocessor into the current model to extend its applicability to various substrates. Besides this feature of accommodating a wide range of substrates, the model can also simulate the use of different cul- tures simply by accepting as input the kinetic data for the corresponding microorganisms (maximum specific growth rate, inhibition constant, and half -velocity constants).

    Other physical phenomena that are accounted for by the model include the well-known sensitivity of the methagonic bacteria. to environmental factors



    Fig. 2. System conceptualization.


    like pH, temperature, toxic substances, and inhibition due to nonionized volatile acids. The requirement for an appropriate balance of nutrients (N, P) in relation to the carbon source is also incorporated. In general, the system is very sensitive to changes of parameter which affect the performance of the methanogenic bacteria. The limiting detention time is three to five days in order to avoid washout of the bacteria from the digester. Practical detention periods, however, range from 6-30 days.

    The mathematical modeling framework is depicted in Figure 2. The op- tional preprocessor provides all input requirements for the main program. Given a specific feedstock, the number of moles of substrate compounds and associated yield coefficients are calculated from stoichiometric relationships. Additional input data include initial conditions for startup, mesophilic or thermophiiic parameters, and an interactive symbol indicating which feed in- put or reactor effluent pattern (pulse, continuous, stochastic, etc.) is desired. The anaerobic digestion process can be conceptually viewed as interrelated transport and conversion phenomena between biological, liquid, and gaseous phases in a well mixed, two-phase reactor. This study has represented the biomass energy system as a set of 11 coupled, nonlinear first-order rate equa- tions based on the principles of mass conservation and biochemical reaction kinetics21 :

    aci - + (v- V ) C ~ = V *DVci + CSj at

    which can be reduced to

    dc, I- - csj dt

    where ci is the concentration of the ith process variable; CSj is the sum of the sources minus the sum of the sinks; Si = Si(cT, time); m = -1, 1, 2. Spe- cific forms of eq. (2) for the biological, liquid, and gaseous phases are sum- marized in the Appendix.

    The number of governing equations can be easily extended in order to ac- commodate more nutrients, dissolved constituents, and gases as well as the temperature. 21

    The system of process equations (Appendix) constitutes a nonlinear initial value problem (IVP) of the form:

    subject to

    Y(0) = g[yl(o),yz(o), * .,ym(O)1 (4)

    It was solved with a modified Runge-Kutta-Verner routine which allows large time steps, necessary in simulating full-scale plant operations.



    Stable, acceptable results from computer simulations were obtained with feedstock rates and model parameter values which fall into the range of published data. Small changes in KLa (overall mass transfer coefficient for C 0 2 ) , NT/CT ratio (total nitrogen to carbonic species concentrations), and loading and discharge patterns (batch, pulse, continuous, etc.) influenced the biogas production, in particular carbon dioxide, significantly. The prin- cipal process variables (gas flow rates, pH, and rate of volatile acid destruc- tion) are, of course, also sensitive to changes in substrate concentration, growth and decay parameters of the microorganisms, detention time, and amount of inhibitors present. Gross process failure simulated with the RPI one-culture computer code14 was confirmed with laboratory model studies conducted by Williams.22

    Sample outputs of the dynamic two-culture model are given in Figures 3-6. Figures 3(a) and 3(b) show the transient response of the principal vari- ables to plant startup for a continuous feed mode. The plant startup is similar to a step function initiated at time t = 0. With an initial amount of acid and methane formers in the reactor, drastic changes of all system pa- rameters occur basically during the first week. The initial concentration of methane formers (curve No. 5) reduces to a level corresponding mainly to the balancing amount of volatile organic acids (curve No. 3) available and the stabilized effluent concentration of substrate (curve No. 2). The pH (curve No. 6) stays within a favorable range. The other variables or parameters fol- low the expected dynamic dependence. Figures 4-6 depict the response to different step inputs of the feed substrate after steady state was reached. Sys- tem parameters and a time scale were chosen in order to reestablish steady- state behavior following the transient response. Without time delay (CSTR concept), the gas production rate (curve Nos. 4 and 5) begins to increase un- til the critical pH of approximately 5.5 (curve No. 3) is reached, at which point the growth rate of the microorganisms drops sharply. A further drop in the pH value causes reactor failure. Figures 5 and 6 are similar to Figure 4 except for the fact that milder increases in feed substrate concentration allow process recovery. It is interesting to note that the second transient response of the gas production rate (curve Nos. 4 and 5 in Figures 5 and 6, respectively) with the dynamic reestablishment of the (optimal) process pH (curve No. 3) follows the patterns of the volatile acids concentration with time. A signifi- cantly higher initial concentration of methane formers than acid formers had to be present in the reactor to assure stable developments.

    The computer simulation model is more sensitive to parameter changes than laboratory and pilot plants as various reports6,u indicate. One reason might be the use of the submodel for microbial growth taken from A n d r e w ~ ~ , ~ J ~ (Appendix). If the specific growth rate p for methane formers is plotted ver- sus the concentration of the substrate S considering inhibition, Andrews submodel predicts one peak (maximum growth rate) whereas laboratory observations indicate that pmax is maintained for a wide range of substrate



    Fig. 3. (a) Response of system parameters to plant startup. (b) Response of additional sys- tem parameters to plant startup. Curves here and in following figures: (CU) excitation (feed); (-) response.

    concentration; i.e., p ( S ) exhibits a plateau rather than a peak. Furthermore, the Monod equation and some extended submodels for microbial growth are not applicable during transient states when microorganisms are responding to sudden upset^.^-^

    An important indicator of anaerobic digester performance is the ratio of methane gas volume to mass of volatile organic solids utilized, i.e., m3 CH4 /kg VOS. The authors advanced two-culture mode1 predicts mean values rang- ing from 0.15 to 0.21 which compares favorably with pilot-plant measure-


    Fig. 4. Process failure due to sudden finite increase of feed substrate.

    ments, 0.09-0.4 reported by Pfeffer and Khan,I7 Jewell, l6 and Pfeffer.I5 Even closer agreement was obtained for the ratio of CH4/C02 production rates where the simulator predicted values of 1.2-1.3 for input data given by Pfef- fer and KhanI7 who measured a ratio of 1.16. The set of input data used to produce the computer results are given in the Appendix.


    An advanced dynamic model simulating the physical and biochemical phenomena of an anaerobic digestion process was developed. The computer

    0 0 0 0 0

    Fig. 5. Step input of feed substrate and process recovery I.


    0 0 000 Fig. 6. Step input of feed substrate and process recovery 11.

    code is adaptable to bench-scale or commercial-size CSRT reactors for the prediction of major process variables versus time and the effects of adverse conditions leading to process failure. It was found that biogas production from anaerobic digestion is very sensitive to small changes of certain input parameters as well as environmental factors. Hence, proper pretreatment and accurate process control are a requirement for successful operations. In- deed, pilot-plant or full-scale digesters which operate satisfactorily for an extended period of time (> 6 months) work either with well pretreated sub- strates and close process control or with primary/activated sludge where ac- climated microbial cultures always enter the reactor with the feedstock so that a steady-state biogas production is almost guaranteed.


    Governing Equations

    Kinetics apd ionics D20 = 24.0 TABS =THETA + 273.0 DTHETA = D20*TABS/293. DELT= THETA - 35.0 MUHCH4zO. 19S*EXP( -0.06*(DELT**2)) MUHVOA=0.325*EXP( -0.06*(DELT**2)) KDCH4= 0.02*EXP( - 0.06*(DELT**2)) KDVOA=O.O4*EXP( -O.O6*(DELT**2)) KH=EXP( -8.1403+(842.9/(THETA+ 151.5)))/760.0 PH20= 760.O*EXP( 12.0 - (4014.O/(THETA + 234.6))) PKSMA= -3.1649+( 1170.4WTABS) +(0.013399*TABS) PKA = 0.6322 + (2835.76/TABS) + (0.001225*TABS) PK1= - 14.8435+ (3404.7UTABS) +(0.032786*TABS)


    TABLE A1 Basic Input Data

    Parameter/Variable Value Source

    YXCH4 0.0320 mol/mol Graef and Andrews (ref. 8) YXVOA 0.3200 mol/mol trial value YCH4XM 45.7 mol/mol Buhr and Andrews (ref. 11) YVOAXA 31.25 mol/mol trial value YC02XM 32.4 mol/mol trial value YCO2XA 5.0 mol/mol trial value YNX 1.0 mol/mol Buhr and Andrews (ref. 11) KSA 0.00133 mol/L trial value KSM 0.00075 mol/L trial value KIM 0.24300 mol/L trial value KLA 10.000 mol/L trial value MUHVOA 0.325 day-' Hill and Barth MUHCH4 0.195 day-' trial value

    Rate equations







    IF(Y(8) .GT. 0.25) GO TO 111 IF(Y(8) .LT. 0.25 .AND. Y(8) .GT. 0.10) GO TO 112 IF(Y(8) .LE. 0.10) GO TO 113 KTM=MUCH4- KDCH4 KTA= MUVOA- KDVOA GO TO 1 KTM=(Y(8)-O.lO)*(MUCH4- KDCH4V0.15 KTA=(Y(8)-O0.1O)*(MUVOA- KDVOA)/O.15 GO TO 1 KTM=O.O KTA=O.O YPRIME(l)=(FD( l)*FD(3)--(2)*Y(l))/Y( lo)+ MUCH4*Y( 1)- KDCH4*Y(l)- KTM*Y(l) YPRIMEX2)=(FD(l)*FD(4)-FD(2)*Y(2))/Y(lO)+ MUVOA*Y(2)- KDVOA*Y(2)- KTA*Y(2) YPRIME(3)=(FD( 1)*FD(6) - FD(2)*Y(3))/Y( 10) -(MUVOA- KDVOA-

    YPRIME(4) =(FD( 1)*FD(5) - FD(Z)*Y(4)))/Y( 10) - YNX*((MUCH4 - KDCH4-KTM)*Y(l) +(MUVOA- KDVOA- KTA*Y(2)) YPRIME(S)=(FD(l)*FD(S) - FD(2)*Y(S))/Y(lO) + RB- RG YPRIME(6) = (FD(l)*FD(7) - FD(2)*Y(6))/Y( 10) - (MUCH4 - KDCH4- KTM)*Y(l)/YXCH4 + (MUVOA - KDVOA - KTA)*Y(Z)*YVOA YPRIME(7) = (FD( l)*FD(9) - FD(2)*Y(7))/Y( 10) YPRIME(8)=(FD(l)*FD( 10) -FD(2)*Y(8))/Y( 10) - KTA*Y(8) - KTM*Y(8)


    IF(IC0DE .EQ. 2) GO TO 10 YPRIME(9) =O.O GO TO 15 YPRIME(9)= (FD( l)*FD( 11) - FD(2)*Y(9))/Y( 10) - DELH*(YPRIME( 1) +YPRIME(2))/(DENSfCP) YPRIME(lO)=FD(l)-FD(2) VG = VX-Y( 10) YPRIME( 11)= 760.0*DTHETA*RG*Y( 10)/VG - Y( 11)*760.0*(QCH4+ QC02)/ ((760.0- PH20)*VG)

  • 1950

    Feed variables



    inflow rate (L/day) outflow rate (L/day) methane formers (mol/L) acid formers (mol/L) nitrate (ammonia) (mol/L) glucose (mol/L) acetic acid (mol/L) dissolved COz (mol/L) total cation (mol/L) toxic material (mol/L) temperature (K)

    State variables methane formers (mol/L) acid formers (mol/L) glucose (mol/L) nitrate (ammonia) (mol/L) dissolved C02 (mol/L) acetic acid (mol/L) net cation (mol/L) toxic material (mol/L) temperature (K) liquid volume (L) pressure C 0 2 (mm Hg)

    Yield coefficients YXCH4 YXVOA rnol acid formers/mol glucose YCH4XM rnol CH,/mol methane formers YVOAXA rnol acetic acid/mol acid formers YCO2XM rnol C02/mol methane formers YCO2XA rnol CO2/mol acid formers YNX rnol N2/mol microorganism

    rnol methane formers/mol acetic acid

    Kinetic and ionic parameters KIM inhibition constant, methane formers (mol/L) KSM half-velocity constant, methane formers (mol/L) KTM toxic death rate, methane formers (day-') KIA inhibition constant, acid formers (mol/L) KSA half-velocity constant, acid formers (mol/L) KTA toxic death rate, acid formers (day-') MUHCH4 maximum specific growth rate, methane formers (day-') MUCH4 effective specific growth rate, methane formers (day-') MUHVOA maximum specific growth rate, acid formers (day-') MUVOA effective specific growth rate, acid formers (day-') KDCH4 specific death rate of methane formers (day-') KDVOA specific death rate of acid formers (day-') KH Henry's Law constant for C 0 2 (dimensionless) KSMA ionization constant for acetic acid (dimensionless) KA ionization constant for ammonia (dimensionless) K1 ionization constant for carbonic acid (dimensionless)

    *The preprocessor, an adaptation of BIOTREAT developed by McCarty,' is not included here.


    Professor Andrews (University of Houstpn, Houston, TX), Professor Buhr (University of Rondebasch, South Africa), Professor McCarty (Stanford University, Stanford, CA), and Dr. Smith (EPA, Cincinnati, OH) provided the authors with computer codes and/or other valuable material. Their encouragement and help is greatly appreciated. The authors also wish to thank Professor Bungay (Rensselaer Polytechnic Institute, Troy, NY) for reading the manuscript and offering very helpful suggestions.


    1. M. P. Bryant, J. Animal Sci., 48, 193-201 (1979). 2. H. R. Bungay, Energy. The Biomass Options (Wiley, New York, 1981). 3. D. J. DeRenzo, Enerafrom Bioconversion of Waste Materials (Noyes Data Cop., 1977). 4. J. G. Zeiikus, Bacteriol. Rev., XX, 514 (1977). 5. J. F. Andrews, J. Sanit. Eng. Div. Roc . ASCE, 99, SA1, (1959). 6. J. T. Pfeffer and J. C. Liebman, Semi-Annual Progress Report UILV-ENG-75-2001,

    7. P. L. McCarty, BIOTREAT, Dept. of Civil Eng., Stanford University, Stanford, CA, 1974. 8. D. R. Christensen and P. L. McCarty, J. Water Pollut. Control Fed., 47, ( l l ) , (1975). 9. S. P. Graef and J. F. Andrews, MChE Symp. Ser., 70, 136 (1973).

    10. A. S. Collins and B. E. Gilliland, ASCE, 100, EE2, 487-506 (1974). 11. R. Smith and J. F. Roesler, Time-Dependent Computer Model for Anaerobic Diges-

    12. H. 0. Buhr and J. F. Andrews, Water Res., 11, 129 (1977). 13. D. T. Hill and R. A. Nordstedt, Modeling Techniques and Computer Simulation of

    Agricultural Waste Treatment Processes, Univ. of Fla., Gainesville, paper given at 1977 Ann. Mtg. ASAE, N.C. State Univ., Raleigh, NC, June 26-29, 1977.

    14. C. Kleinstreuer, C. Vasudevan, and T. Poweigha, in Proceedings of Second International Conference on Mathematical Modeling, X.J.R. Avula et al., Eds. (Univ. of Missouri-Rolla, 1979), Vol. 11.

    15. J. T. Pfeffer, Proceedings 3rd Annual Biomass Energy Systems Conference, SERI, June

    16. W. J. Jewell, in Second Annual Symposium on Fuels from Biomass (Rensselaer Poly- technic Institute, Troy, NY, 1978), p. 701.

    17. J. T. Pfeffer and K. A. Khan, Biotechnol. Bioeng., 18, 1179 (1976). 18. L. J. Ricci, Chem. Eng., 81, (1974). 19. National Academy of Sciences, Methane Generation from Organic Wastes, Commis-

    20. T. A. Mdne et al., Final Task Report, SERIITR-33-067, 1978. 21. T. Poweigha and C. Kleinstreuer, Water Res., to appear. 22. J. Williams, Mathematical and Physical Modeling of Anaerobic Digestion, Masters

    23. REFCOM, Waste Management, Inc., 900 Jorie Blvd., Oak Brook, IL 60521. 24. S. Elmaleh and R. Bentim, Chem. Eng. Sci., 33, 365 (1978).

    NSF/RANN, University of Illinois, Urbana, IL, 1975.

    tion, U.S. EPA, Cincinnati, OH 45268, 1976.

    5-7, 1979.

    sion on Int. Rel. (JH215), NAS-NRC, Washington, DC, 1977.

    thesis, Rensselaer Polytechnic Institute, Troy, NY, 1978.

    Accepted for Publication February 4, 1982


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