A dynamic simulation of a two-phase anaerobic digestion system for solid wastes

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A Dynamic Simulation of a Two-Phase Anaerobic Digestion System for Solid Wastes Joan Mata-Alvarez Department of Chemical Engineering, University of Barcelona, Marti i Franques 08028, Barcelona, Spain Accepted for publication November 3, 1986 In this article, a two-phase system for the digestion of wastes with a high solid content is simulated. The solids are charged to the hydrolyzer and then leachate recirculation is activated until biodegradation is nearly complete. Several parameters are tested, namely moisture , l eacha te recirculation flow rate, and hydrolyzer-methanizer volume ratio. The results show that recirculation rate is an important parameter subject to optimization, with optimal values corresponding to hydrolyzer hydraulic retention times below 1 day. The quantity of recirculating water must be the highest possi- ble. As a consequence, the organic load to the methanizer is reduced, making thus possible the use of a smaller methanizer volume. INTRODUCTION Anaerobic digestion processes are natural biological pro- cesses in which groups of microorganisms in absence of free oxygen cooperate to convert waste organic matter into bio- gas. The biogas contains reduced species such as methane, hydrogen sulfide and the main oxidized species, carbon dioxide. Six distinct steps may be identified in an anaerobic digester,' although usually it is described as a two-phase biological process. In the first phase, complex organic com- pounds are broken down and subsequently metabolized by fermentative bacteria to produce mainly volatile fatty acids (VFA) and carbon dioxide. In the second phase, VFA are converted to acetate and hydrogen. Methanogenic bacteria remove these compounds, together with carbon dioxide, to form methane. The two main microbial groups involved in the anaerobic digestion differ significantly with respect to physiology, nutritional requirements and growth rate.' Phase separation in anaerobic digestion appears to be warranted from the kinetic as well as the process control point of view, thus being possible the maintenance of an optimum environment for each phase. Two phase digestion processes can be used advantageously to treat solid wastes, i.e., those with a total solid content (dry matter) over 20%. Included into this group are agricultural and municipal solid wastes. An example of the application of this technology is the digestion processes proposed for agricultural solid Biotechnology and Bioengineering, Vol. 30, Pp. 844-851 (1987) 0 1987 John Wiley & Sons, Inc. wastes by Colleran et al.3 and Rijkens et aL4 In this approach the solid organic matter is broken down in the first reaction step (first digester) by acid forming anaerobic bacteria, under percolation of recycled process water. The soluble organic matter and VFA are pumped into a specific methane reactor (second digester), containing a high concentration of methanogenic bacteria, which can effectively treat the water, producing biogas. The treated water is recycled to the first digester (see Fig. 1). The procedure to operate such a system is as follows: 1) to load the reactor with the solid waste; 2) to bring water to the hydrolyzer until the desired level is reached (this water could come from another hydro- lyzer or from a buffer tank, and is used repeatedly cycle after cycle); 3) to start the water recirculation; 4) once the di- gestion is completed, to remove the water from the hydro- lyzer (pumping it to another hydrolyzer which could be starting the cycle or, alternatively, to a buffer tank); and 5 ) to unload the digested solids. These digested solids could be dried with the exhaust gas of a cogenerator set - working with the produced biogas-so that they can be packed and sold as soil conditioners. It is important to point out that ' C H ~ B1oGAS h t I lYDROLYZER 7 VH ( B A T C H L O A D E D ) V O L R = !! V H H H R T = !? 9 M H R T = !!! 9 Q [IVM 2 R - LEACHATE RECIRCULATION Figure 1. Schematic of the simulated two-phase system for the anaerobic digestion of solid wastes. Hydrolyzer is loaded in a batch fashion whereas methanizer is operated continuously. CCC 0006-35921871070844-08$04.00 those systems do generate a certain amount of wastewater. Leachate recirculation line must have a drain point after the methanizer in order to keep the salt contents under allowable levels (The volume of water removed during the solids unloading - part of the liquid is inevitably retained - will not probably be enough to achieve this goal). As a con- sequence, it is also necessary to add some make-up water in order to keep the optimum levels of the overall moisture. However, these amounts of water are much smaller than those required to slurry the solids. The problem posed by this wastewater must be balanced with the solid waste removal. In this article, a two-phase digestion process similar to the one described above has been simulated to study quali- tatively the effect of several parameters involved in the process. The simplified mathematical model presented fo- cuses on the hydrolytic and methanogenic steps. The model framework consists of the principles of mass conservation law and biochemical reaction kinetics. MODEL SETUP The system is composed of a hydrolyzer of volume VH and a methanizer of volume VM (see Fig. 1). The volume ratio VM/VH will be denoted by V,,,. Leachate is re- circulated with a flow rate Q from the hydrolyzer to the methanizer and from the latter to the former. In this sim- plified model neither liquid drain nor make up water is considered. The waste in the hydrolyzer has an initial total solid content of TSo, an initial total volatile solids of VSo, and an initial biodegradable volatile solids content of BVS,,. In order to keep the moisture level above critical values, a recirculating water volume Wv (L) is added per gram of substrate added to the hydrolyzer. If in an overall system a moisture level H (%) is desired, Wv will be: TSO/(100 - H ) - 1 1000 W" = (where a density of 1 kg/L is assumed for the liquid). Hydrolysis The hydrolysis essentially is the conversion of the bio- degradable volatile solids to volatile fatty acids, that is, hydrolysis and acidification steps are considered together. As a first approach it is assumed that all the biodegradable matter is converted into acids. The fraction being converted into C 0 2 , H2, and cellular matter is not differentiated. The refinement of considering two methanogenic cultures, i.e., including also the homoacetogenic bacteria, would compli- cate the model resolution, affecting only the absolute re- sults, but not the relative ones. Kinetics of the hydrolysis step are considered first order,IS2 since the rate of disappearance of the biodegradable volatile solids is proportional to their concentration. This concen- tration is expressed as milligrams of BVS to milligrams of initial sample weight. Table I presents the kinetic equation. It has also been assumed that the rate of hydrolysis is pH dependent. According to different authors in the literature, a pH of ca. 6 is optimal for hydr~lysis .~-~ Based on these data, the hydrolysis first-order constant has been expressed as a pH function (Table I). Table I1 presents the numerical values assumed for the rate constant at pH 6.8-9 The pH is expressed in relation to the VFA concentration. The formula has been based on our own experimental data using straw and cow manure as a substrate: Table I. Two-phase digester simulation, with kinetic models used for the hydrolytic and meth- anogenic step in the hydrolyzer and in the methanizer. First-order kinetic constant and maximum substrate removal rate have been assumed pH dependent, with maximum values at pH 6.0 and 7.5, respectively. Hydrolytic Step Rate equation First-order kinetic constant as a pH function kk = k,(-0.5pH; + 6.1pHh - 17.6) Methanogenic Step Substrate removal rate Yield equation Maximum substrate removal rate as a pH function Maximum substrate removal rate as pH function Hydrolyzer Methanizer Steady state assumed (X,,, = 1.5 x lo4 mg/L) rrh = Y r , - kdXk Hydrolyzer k , = kd(-0.501pH2 + 7.319pHh - 25.701) Methanizer k,. = kmo(-0.501pH2 + 7.139pHm - 25.701) MATA-ALVAREZ: A TWO-PHASE ANAEROBIC DIGESTION SYSTEM 845 Table 11. Two-phase digester simulation, with kinetic constant values used for the hydrolytic and methanogenic step in accordance with the literature (see references in text). Initial values of microorganism and solid concentrations used in the program runs. Hydrolysis km = 3 day-' Methanization kd = kmmo = 7 mg VFA/mg microorganisms day K, = 400 mg/L k, = 0.02 day-' Y = 0.04 mg/mg day Initial Conditions TSo = 90% VSo = 80% BVS, = 35% X, = 10 mg/L X, = X, = 1.5 x lo4 mg/L pH = -log,," + 10.23)] where S applies for the VFA concentration in the methanizer or in the hydrolyzer, that is, for Se or S,. Methanization Methanization can take place in both the hydrolyzer and methanizer, provided that the VFA concentration is low enough. Kinetics for methanization have been assumed to follow a Monod equation.'.' In the methanizer the model is simplified considering the amount of active microorganism concentration constant. This hypothesis is acceptable pro- vided that the methanizer is a high rate digester in which the microorganisms are attached to some kind of support. The kinetic equations are shown in Table I, for both the hydrolyzer and methanizer. The maximum substrate re- moval rate constants have been assumed as a function of the digester pH. These functions present a maximum at pH 7.5, and have been fitted after the data published by Ishida et al? The constant numerical values have been extracted from the literature'-'* and are presented in Table 11. MATHEMATICAL MODEL The dynamic model of a two-phase digester is based on the equations which express the mass conservation law. Thus, mass balances for BVS in the hydrolyzer and VFA in both hydrolyzer and methanizer have been carried out. They are presented in the following sections. BVS Balance Only two terms are present in the balance: the rate of accumulation and the disappearance rate. Taking into ac- count the kinetic equation (Table I), the final expression for this balance is: The boundary conditions are t = 0 and BVS = BVSo. VFA Balances VFA in the Hydrolyzer There are four terms in the balance: the rate of VFA accumulation, VFA input and output, and VFA generation. There are two sources of VFA generation. A VFA produc- tion coming from the hydrolysis of the BVS and a possible methanization provided that pH is high enough (a negative generation). The resulting equations for the VFA hydrolyzer balance are: (The numerical constant 10 is a unit coherence requirement) VFA Balance in the Methanizer In a similar way, a material balance for VFA in the meth- anizer can be deduced. But in this digester there is only one term which accounts for generation, the one corresponding to the conversion to methane. The final expression is: 4 S e ) - s a - S e krnrnsexrn dt MHRT K,, + S, Methane Production Assuming that all the acids are transformed into acetic acid, the potential methane production is: BVSo 100 - M00.373 (mL STP CH,) Thus, the ultimate methane yield as defined by Chen and Hashimoto'' will be: Bo = -0.373 BVSo (mL STP CHa/mg VS added) vso The equations to compute the methane production rate in the hydrolyzer and in the methanizer referred to the volatile solids added, together with the accumulated methane pro- duction are presented in Table 111. In Table 111, the equations to evaluate the percentage of the maximum methanization achieved are also given. This parameter will later be used for comparison of the process performance. PROCEDURE A program has been written in FORTRAN 77 to solve the above set of non-linear differential equations. The Runge-Kutta method with variable step length has been used. The program has been run to simulate the fermentation of a solid with the characteristics presented in Table 11. The 846 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 30, NOVEMBER 1987 Table Ill. Two-phase digester simulation, with equations used to evalu- ate methane yields in the hydrolyzer and in the methanizer. Overall system methanization is obtained by adding the percentages of maximum methane production achieved in both digesters. Hydrolyzer Methanizer Methane production rate referred to QCQh = the VS added rmh Wv0.373 r,. Wv0.373 VSOlO QcH4l = VS~~O/VOLR Accumulated I- I- methane production at time ? B, = J, QcH, dt B , = I, QcH, dt B , B Bo Bo (%Irn = - 100 Percentage of maximum methane (a), = 100 production achieved process parameters studied have been the overall system moisture, H , the hydraulic retention time in the hydrolyzer, HHRT, and the volume ratio methanizer/hydrolyzer, VOLR. The desired moisture is achieved by the addition of the required quantity of recycling water. Table IV shows the levels tested of the studied parameters. RESULTS AND DISCUSSION Figures 2 and 3 show some of the results studied from a run of the program. In the depicted situations, the simulated systems operate with an overall moisture of 95%, a VoLR of 0.2, and HHRTs of 0.5 and 1 day, respectively. As can be seen the parameters 1) methanization percentage in hydro- lyzer, methanizer, and in the overall system, and 2) VFA concentration at the methanizer inlet (S,) are represented as a function of the elapsed time. The VFA concentrations at - _ _ _ T 0 T Q M E T H R N I Z R T I 0 N - WETHQN. I N METHRN. ~ YETYRN. 1N HYDFI0L. PERCENTRGE OF METHRNIZRTIBN 1% 1 100 70 60 50 I 10 0- 0 Table IV. values used in the different runs of the program. Two-phase digestion simulation, with parameters and their Parameter Tested values Overall system moisture, H (%) Volume ratio, VoLR Hydrolyzer HRT, HHRT (day) 75, 80, 85, 90, 95, 97 1, 0.5, 0.3, 0.2, 0.1, 0.05 15, 10, 5 , 4 , 3, 2, 1.0.9, 0.7, 0.5, 0.3, 0.1, 0.09, 0.07, 0.05, 0.03, 0.01 the methanizer outlet (S,) are nearly negligible and are not represented. Comparing Figures 2 and 3, it is clear that they present similar profiles, the main difference being the level of methanization achieved in the hydrolyzer as a con- sequence of the different VFA concentrations, s,, in both situations. Subsequent results are analyzed mainly on the basis of methanization percentages obtained at day 21. It has been considered that this value is representative enough of the fermentation process as the particular profiles are similar from one set of conditions to another (Figures 2 and 3). Nevertheless the rest of parameters are considered, when necessary, in the subsequent discussion. A summary of the obtained results is presented in Figures 4, 5, and 6 . Figure 4 presents the percentage of methanization achieved on the 21st day in the overall sys- tem and in the hydrolyzer using a volume ratio VoLR of 0.3, as a function of 1) the HHRT used and 2) the overall system moisture, H . As can be seen, it is very important to work with a high moisture level and with rather low HHRT (say below one day, depending on the moisture value). High moisture levels favor methanization in the first digester, as a logical consequence of a reduction of the VFA concen- - VFR RT METHANIZER I N L E T ( S , ) VFR CBNCENTRRTIBN [MG/Ll I I I I I I I I I 1 I _ _ _ _-- --- _ _ _ _ _ - --- - - 100 ,__--- ,/ , 90 - 80 - / 70 60 50 - 40 - 30 - 20 - 10 , - I - I / , - - , / ................................. _~~~_._...._.._..-------- - 0- I I I I I I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 1.000 800 600 400 200 0 TIME (DRYS1 Figure 2. HHRT = 0.5 days; moisture, H = 95%; and volume ratio, VoLR = 0.2. Two-phase digester simulation results. Profiles were obtained with the following parameters: MATA-ALVAREZ: A TWO-PHASE ANAEROBIC DIGESTION SYSTEM a47 T 0 T R L METHRNIZRTIBY METHRN. I N METHRN. ~ YETHRN" I N HYDFBL. - VFR A T HETHRNIZER INLET ( S a ) PERCENTRGE OF METHRNIZRTIBN 1'4 1 VFR CBNCENTRRTIBN IMG/LI I I I I I I I I I --- --- 1 on 90 - - . . . . ................ ............. - - - - - - 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 1.600 1 .400 1.200 1 * 000 000 600 400 200 0 T I M E (DAYS1 Figure 3. HHRT = 1.0 days; moisture, H = 95%; and volume ratio, VoLR = 0.2. Two-phase digester simulation results, with profiles obtained with the following parameters: METHRNIZRTIBN [%I RFTER 21 DRYS M0ISTURE 80 M0ISTURE 85 MBISTURE 90 MBISTURE 95 ~ MBISTURE 97 .__. - _ _ _ ...... 100 90 80 70 60 50 40 30 20 10 0 0 0.5 1.0 I 5 2.0 2.5 3.0 3.5 1.0 4.5 5.0 HHRT IDRYSl Figure 4. working with a volume ratio VoLR = 0.3, as a function of the HHRT and the overall system moisture H . Two-phase digester simulation results, with overall and hydrolyzer methanization achieved in 21 days 848 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 30, NOVEMBER 1987 7,000 - 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 DRYS - Figure 5. working with an overall system moisture H = 90% and with a volume ratio V,, = 0.5. Two-phase digester simulation results, with VFA concentration at the methanizer inlet (So) profiles I I I I I I - ._ -.. --_. - _ - _ -. --.. - _ -. -. .. -._ -._ -._ -.. ._ -.---__ -._. - _ -.--- - --. .. -...--- - - - - 6 - : 2 - 2 - I - - Figure 6. Two-phase digester simulation results, with maximum load achieved during the digestion period as a function of the HHRT, for different moisture levels, H, and volume ratios, VOLR. _ - _ _ _ _ _ _ - 1 ' , , I \ , ~ 1 ', ,' , c , , \ , , , /' , , ---, -_ , - , , -.- - ... ,' ~~ - - - I I I 1 I I I I I MATA-ALVAREZ: A TWO-PHASE ANAEROBIC DIGESTION SYSTEM 849 tration in this reactor. At a given mifiimum moisture, there is an optimum HHRT which promotes a maximum of meth- anization in the first digester. The appearance of this maxi- mum is a consequence of two opposite trends: As the HHRT increases 1) there is more time for VFA to degrade, and 2) ?here is more VFA accumulation, so that a more un- favorable environment for microorganisms is developed. A maximuin for the overall system methanization also exists at a given moisture level and recirculation rate. This fact is also a consequence of two opposite trends: as the re- circulation rate increases (or the HHRT decreases), 1) the VFA concentration, S,, increases (see Fig. 5 ) allowing more methanization in the second digester, and 2) the rate at which VFA are conveyed to the methanizer, and thus methanized, decreases. The limit for methanization is im- posed by the maximum methanizer allowable load. This load mainly depends on the volume ratio and moisture. At this point it is interesting to look at Figure 6, where the maximum organic load achieved during the digestion pe- riod, is represented as a HHRT function for two differ- ent values of H and V,,,. The HHRT dependence is not very strong, the profiles being rather smooth. It can also be seen that. there is a local maximum for the load at a given HHRT, The absolute maximum appears at theoretical HHRT zero. These profiles suggest that at certain conditions - those corresponding to the local maximum-a critical HHRT could exist, for which the methanization collapses. However, and in order to avoid problems, the operating HHRT should be chosen far from this point, using lower HHRT which maximize the overall system performance. The HHRT at which the overall methanization maximum appear: is not the same as the HHRT for a maximum meth- anization in the hydrolyzer, this HHRT being lower for the latter case. The differences between both HHRTs at which the respective overall system or hydrolyzer meth- anization is maximum, is due to the fact that the VFA level to allow methanization in the hydrolyzer needs a lower HHRT than that required for a maximum methanization in the whole system. Although not represented, it appears that approximately the same level of total methanization is observed indepen- dent of the volume ratio V,, applied, if this level is over a certain critical value which depends on the moisture. This means that the second digester would work under its maxi- mum capacity in those simulated situations. The limit is imposed by the maximum organic Ioad allowed for the methanizer. Over a value around 25 kg VFA/L day the system begins to acidify and the yield begins to decrease. This value is a function of the biomass present in the digester and also of the microorganism yield for the subtrate fed to it (in this case supposedly acetate). The organic load is directly dependent on the H and V,,, as discussed earlier (see Fig. 6). A practical consequence of these results is that by working with higher moisture levels, a small methanizer is required. It therefore appears advisable to work with the maximum allowable water quantity, which will be dictated by the physical characteristics of the system. Figure 5 represents the evolution of the VFA concen- tration at the methanizer inlet, S,, for various HHRTs. As can be seen a maximum exists, appearing on days 6-7 for HHRTs up to 4-5 days. With higher HHRTs, the appear- ance of this maximum is delayed. This is quite normal as the hydrolyzer with high HHRTs tends to behave as a batch- single-phase digester. Low HHRT values present the addi- tional advantage of a more smooth S, profile. This is very convenient for a better methanizer behavior. It is also easier to integrate a system with more than one hydrolyzer, which, on the other hand, would be the more frequent situation in systems like that studied here. CONCLUSIONS Although the results of this simulation work must be regarded from the qualitative point of view, due to the un- derlying hypothesis, some conclusions can be drawn: 1) In systems like that represented in Figure 1, large quantities of recirculating water (high overall moistures) favor the rate of methanization in both the hydrolyzer and the overall system. 2 ) The hydrolyzer/methanizer volume ratio has a simi- lar effect to that of the moisture. Therefore, similar results can be obtained using a smaller methanizer, but a higher moisture, 3) At a certain level of moisture, there is a leachate re- circulation flow rate that maximizes the solids bio- degradation rate. That is to say, there is an optimum HHRT that reduces the necessary time to achieve a given bio- degradation level. These optimal hydrolyzer hydraulic re- tention times are less than one day. 4) If only the methanization in the hydrolyzer is consid- ered, there is also an optimum HHRT which promotes the highest rate of VFA removal in the hydrolyzer. This HHRT value does not coincide with that promoting an overall maxi- mum methanization (former conclusion). However, it could be better to operate with this HHRT value, with several hydrolyzers working in parallel, in order to reduce the meth- anizer load. Finally, the procedure to design a full-scale unit would be to use the maximum quantity of recirculating water allow- able by the physical characteristics of the system, so that to reach the highest possible overall moisture. Once the mois- ture is set up, the next step would be to select a leachate recirculation rate in accordance with the optimum values pointed out in steps 3 and 4. Finally, and using plots like those of Figure 6, the volume ratio VOLRAT would be chosen, in accordance with the maximum allowable loading rate of the chosen type of methanizer. NOMENCLATURE B, B , Bo BVSo accumulated methane production in the hydrolyzer (mL STP CH,/mg VS added) accumulated methane production in the methanizer (mL STP CH,/mg VS added) ultimate methane yield (mL STP CH,/mg VS added) initial biodegradable volatile solids content (a) 850 RIOTECHNOLOGY AND BIOENGINEERING, VOL. 30, NOVEMBER 1987 BVS H HRT HHRT k, T QCH, r h biodegradable volatile solids (%) overall system moisture (%) hydraulic retention time hydrolyzer hydraulic retention time (day) microorganism decay rate constant for methanization (mg VFA/L) first-order hydrolysis kinetic constant (day-) first-order hydrolysis kinetic constant at pH 6 (day-) maximum substrate removal rate in the hydrolyzer (mg VFA/mg microorganisms day) maximum substrate removal rate in the methanizer (mg VFA/mg microorganisms day) maximum substrate removal rate in the hydrolyzer at pH 7.5 (mg VFA/mg microorganisms day) maximum substrate removal rate in the methanizer at pH 7.5 (mg VFA/mg microoganisms day) saturation constant for methanization (mg VFA/L) methanizer hydraulic retention time (day) initial substrate mass (mg) hydrolyzer pH (dimensionless) methanizer pH (dimensionless) leachate recirculation flow rate (dm/day) methane production rate in the hydrolyzer (mL STP CH,/mg VS added day) methane production rate in the methanizer (mL STP CH,/mg VS added day) hydrolysis rate (mg biodegradable volume of solids/initial mg substrate day) methanization rate in the hydrolyzer (rng VFA/L day) methanization rate in the methanizer (mg VFA/L day) microorganism growth rate (mg microorganisms/L day) VFA concentration at the methanizer inlet (mg VFA/L) VFA concentration at the methanizer outlet (mg VFA/L) time (day) initial total solids content (%) volatile fatty acids hydrolyzer volume (dm) methanizer volume (dm3) volume ratio, VM/VH (dimensionless) VS volatile solids VSo Wv Xh X, X , Y initial volatile solid content (56) water volume added per gram of substrate initially fed (L/g) methanogenic bacteria concentration in the hydrolyzer (mg microorganisms/L) initial methanogenic bacteria concentration in the hydrolyzer (mg microorganisms/L) methanogenic bacteria concentration in the methanizer (mg microorganisms/L) methanization yield constant (mg microorganisms/mg VFA) References 1. W. Gujer and A. J. B. Zehnder, Conversion processes in anaerobic 2. W. Verstraete, L. De Baere, and A. Rozzi, Trib. Cebedeau, 3 . E. Colleran, A. Wilkie, M. Barry, G . Faherty, N. OKelly and P. J. Reynolds, One and two-stage anaerobic filter digestion of agricultural wastes, Third International Symposium on Anaerobic Digestion, August 14-19, 1983, Boston, MA, pp. 285-312. 4. B. A. Rijkens, J. W. Voetberg, G. Hofenk, and S. J. J . Lips, Two phase anaerobic digestion of solid organic wastes yielding biogas and compost, Final report, E.C. Contract No. ESE-E-R-040-NL, IBVL Wageningen, The Netherlands, 1984. 5 . M. Ishida, Y. Odaware, T. Gejo, and H. Okumura, Biogasification of municipal waste, in Recycling Berlin, K. J. Thome-Kozmiensky, Ed. (Publisher, E. Berlin, 1979). 6. R. J. Zoetemeyer, A. J. C. M. Matthijsen, J. C. van den Heuvel, A. Cohen, and C. Boelhouwer, Biomass. 2(3), 201 (1982). 7. H. J. Amtz, E. Stoppok, andK. Buchholz,Biotechnol. Left., 7(2), 113 (1985). 8. M. Henze and P. HarremoEs, Water Sci. Technol., 15, 1 (1983). 9. J. A. Eastman and J. F. Ferguson, J . Water Pollut. Control Fed., 53, 352 (1981). 10. F. E. Mosey, Kinetic descriptions of anaerobic digestion, Third In- ternational Symposium on Anaerobic Digestion, August 14- 19, 1983, Boston, MA. 11. Y. Chen and A. Hashimoto, Biotechnol. Bioeng., 22, 2081 (1980). digestion, IAWPRC Seminar, Copenhagen, Denmark, 1982. 453-454(34), 367 (1981). MATA-ALVAREZ: A TWO-PHASE ANAEROBIC DIGESTION SYSTEM 851

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