two-stage anaerobic digestion for the treatment of cellulosic wastes

The Chemrcal Engzneenng Journal, 33 (1986) Bl - BlO Bl

Two-Stage Anaerobic Digestion for the Treatment of Cellulosic Wastes

P GIRARD*, J M SCHARER and M MOO-YOUNG

Department of Chemzcal Engmeerrng, Unwerslty of Waterloo, Waterloo, Ontano N2L 3Gl (Canada)

(Received January 10, 1985)

ABSTRACT

The feaslballty of two-stage anaerobic dlgestlon systems for methane genemtlon from celluloslc wastes was studied The microflora comprised a heterogeneous bac- tenal culture at mesophlhc temperature (39 “C) In the first stage, optimum organic acid production from cellulose concentrations ranging from 0 5% to 2 3% cellulose feed (w/v basis) occurred at carbon to nitrogen ratios of 4 to 1 High loading mtes favoured butyrlc aczdproductlon, while at low loading rates (0 5 g I-’ day-‘) acetic and proptonlc acids were predominant

Both fuced film and suspension cultures were utilized to study methanogenesls from organic acid muctures (second stage) Acetate utdlzatlon by methanogens followed a Monod-type kinetic model, the maximum specific growth rate p,,, and the half satum- tlon constant K, were found to be 0 17 day-’ and 8 46 X 1 OA3 M acetate respectively Proplonate and bu tyrate u tlhzatlon were mhlblted by acetate The mhlbltlon resembled classical competltwe mhlbltlon patterns The mechanlstlc models derived from the experimental data were applicable for acid matures m both downflow fmed film and suspensions cultures

1 INTRODUCTION

Anaeroblc digestion of organic matter has become very attractive as a means of stablllzmg highly concentrated wastes (m- dustnal and agncultural residues) The

*Present address Biotechnology Research Institute, NatIonal Research Council of Canada, 750 Bel-Air Street, Montreal, Quebec, H4C 2K3, Canada

0300-9467/86/$3 50

pnmary advantages of the anaerobic process include a higher degree of digestion of hgno- celluloslc matenals at high loading rate [l], reduction of pollution m terms of COD or BOD, production of energy m the form of methane gas and recovery of residues as fertlhzer Currently, anaerobic digestion 1s viewed as a three-stage process [ 21. The first stage mvolves acldogenlc bacteria which hydrolyse and ferment carbohydrates, protems and lipids to alcohols, volatile fatty acids, Hz and COZ. The second stage mvolves aceto- geruc bacteria which produce acetate, CO* and Hz from the alcohols and higher fatty acids Finally, m the thu-d stage, methanogemc bactena utlhze the products of the previous stages, mamly acetate, CO* and Hz, to produce CH4 and CO* Owing to the different nutrltlonal and envu-onmental requirements of the microbial groups, stage separation seems to be a rational approach to optlmlzmg the process [3]. The two stages of the anaerobic process mclude an acldo- gemc and a methanogemc stage.

Previous anaerobic reactor designs were based on emplrlcal models [4 - 61 which correlate the experimental data on gas production with some space-loading variable These models do not take mto account the mechanism of the anaerobic process and, therefore, cannot predict gas production outside the realm of experunental conditions or digester falure. Mathematical models representing steady-state condltlons [7 - 91 are more fundamental than emplncal models smce they attempt to explam methane production from some mtermedlates present during the fermentation However, anaerobic reactors are seldom at steady state For this reason, the dynamic characterlzatlon of the process seems the best approach m order to understand, quantify and predict methane

0 Elsevler Sequola/Prmted in The Netherlands

B2

production The dynamic models of Andrews and Graef [lo] and the modification by Hill and Barth [ 111, however, have only considered acetate as a malor mtermediate for methane production. This approach does not take mto account the different kmetics mvolved m the utihzation of higher fatty acids such as propionic and butync acids These higher volatile fatty acids are not used directly for methane production, but are degraded by acetogemc bacteria m syntrophic association with methanogens [ 21.

The research described here focussed on both acid production and methane generation from cellulose. Volatile fatty acid production and acid distribution were assessed as a function of the cellulose loading rate and carbon- to-nitrogen ratio m suspension cultures. Both downflow fixed-film and stirred bioreactors were used to study the kmetics of acid utmzation and methanogenesis.

2 MATERIALS AND METHODS

2 1 Orgamc acid production m suspension culture

The experimental studies were performed m both 500 ml bioreactors and 30 1 digester vessels. The 30 1 apparatus, shown m Fig. 1, consisted of an upright glass cyhnder 23 cm m diameter equipped with a conical-bottomed recirculation pump, temperature controller and wet test meter Cellulose (cr-floe) and urea were used as the primary carbonaceous substrate and the nitrogen source respectively. The concentrations of other organic and morgamc constituents were based on levels found m normal swine manure [ 121. The moculum comprised a mixed culture of bacteria from a fed-batch system adapted to the cellulose substrate The fermentations were carried out at 39 “C. The pH was ad- Justed to an u-&ml value of 6.0 with HCl. These studies included both batch and fed- batch fermentations with dsuly addition of fresh medium.

2 2 Organrc aced utakataon and methane generation

Kmetic studies on acid utilization and methanogenesls were performed m 500 ml bioreactors (suspension culture) and fixed- film reactors. The fixed-film reactors, shown

&d.

.51609.“05 pk.S= m.thanop.mc Plus*

Fig 1 Schematics of the two-stage anaeroblc dlgestlon apparatus

m Fig 1, consisted of glass columns (length, 85 cm, diameter, 6.5 cm) packed randomly with ceramic Raschig nngs of diameter 1.25 cm to a height of 62 cm The hquid level was mamtamed 10 cm above the film support and the surface area to volume ratio (243 cm2 me3) was near optimum as reported by Van den Berg and Kennedy [13] The reactors were operated m a downflow manner at a recuculation rate of 6 hquid volumes h-’ Inocula for both the suspension and fixed-film reactors were denved from a 20 1 methanogenic fermenter, fed continuously with a fatty acids, urea and salts solution The reactor temperature was mamtamed at 39 + 1 “C! The pH was controlled at the desired level with an automatic pH controller. Approximately 4 months were required to establish a satisfactory biofilm of methano- genie bacteria m the fixed-film reactors.

Analytical techniques included cellulose determmations by a modified Updegraff [14] method, ammoma measurements by specific ion electrode, carbon dioxide evolu- tion by adsorption m 0.1 N BaOH solution [ 151, particulate orgamc mtrogen by the KJelfoss method, organic acids and biogas analysis by gas chromatography [ 71

3 RESULTS AND DISCUSSION

3 1 Orgamc acd productwn Fermentations of cellulose to orgamc acids

were performed at carbon to mtrogen [C]/[N] ratios rangmg from 4 to 24. In Table 1, the product yields, expressed m gramme- equivalents of acetic acid per gramme of

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TABLE 1

Effect of carbon to mtrogen rat.10 on volatile acid yield

Znztzal cellulose C/N ratzo Fermentatzon Cellulose Fznal pH Yzeld content (%) tz me (days) utzlzzatzon (%) (g equw acetic acid (g cellulose)-‘)

05 4/l 5 82 1 61 0 57 0 55 24/l 5 87 3 58 0 47 10 4/l 7 93 5 61 0 75 10 24/l 7 79 8 55 0 32 23 411 11 92 8 62 0 87 23 24/l 11 68 4 50 0 45

TABLE 2

Effect of cellulose loading rate on cellulose uthzatlon and acid dlstrlbutlon

Loadzng rate Retentzon tzme g 1-l day-’ (days)

05 5 10 5 23 5 23 11

Aczd dzstrzbutzon

Acetate Propzonate

(W (M)

0 0250 0 0026 0 0410 0 0183 0 0480 0 0196 0 1030 0 0330

Butymte

(M)

0 0014 0 0028 0 0026 0 0267

Cellulose utzlzzatzon

(%)

82 1 72 6 27 4 92 2

cellulose added, are compared at low and high (24) [C ] / [ N] ratios at various cellulose concentrations m the fermentation broth At low cellulose content m the medium, both the cellulose utlhzatlon efflclency and the product yield were essentially independently of the [C]/[N] ratio At high cellulose con- centratlon, however, both the cellulose utlhzatlon efflclency and the product yield dechned slgmflcantly as the [C] /[N] ratio mcreased. This declme IS beheved to be due to the depressed pH condltlons expenenced mth higher [C] /[ N] ratios Durmg the fermentation, the pnmary mtrogen source, urea, was readily hydrolyzed to ammonia and carbon dioxide. At high [Cl/ [N] ratios coupled with high cellulose levels, the ammomum ion product was msufflclent to poise the pH (z e , neutrahze acids) m the optimum range for cellulose hydrolysis and acid generation.

The effect of cellulose loadmg rate on acid production and acid dlstnbutlon at a [C]/[N] ratio of 4 1s shown m Table 2 At a constant hydraulic retention time (5 days), the cellulose utlllzatlon efflclency dechned with mcreasmg loading rate The mcrease m the retention tnne from 5 to 11 days, however, was beneficial with regard to

the cellulose utlhzatlon efficiency. As the loadmg rate increased, butyrlc and higher carbon fatty acids (Valerie, caprolc acids) became progressively more promment m the fermentor effluent

3 2 Orgamc acid utduatlon and methane generation

Kinetic studies were performed with synthetic acid mixtures as well as acids produced from various carbohydrates. On the basis of these studies, a set of dlfferentlal equations was denved to model acetate, proplonate and butyrate utlhzatlon m both suspension cultures and fured film reactors.

Acetate 1s the major, but by no means the only mtermedlate produced from the degradation of celluloslc materials.. However, most of the previous studies involved either acetate only m ennchment cultures or higher acids were expressed as acetate equvalents. Prehmmary results mdlcated substantial dlf- ferences between the kmetlcs of acetate and other fatty acid utlhzatlon.

3 3 Kmetzcs of acetate utlllzatzon Using Methanosarcma stram 227, Smith

and Mah [16] have shown that the rate of acetate utlhzatlon can be expressed by a Monod model as follows.

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0 024

-PredIcted 0 Expenment 1 l Experiment 2

0 1 2 3 4 5

Time (days)

Fig 2 Observed and predicted acetate utlllzatlon m free suspensions T= 39 “C!, mltlal pH 7 uncontrolled

dA ---pmax AX _= dt &a + A)Y,

(1)

The concentration of methane bactena can be related to acetate concentration through the growth yield [3] m the followmg manner

dA -~maxA~(A,- A) + -WY,1 _=- dt Wea + A)

(2)

The mam advantage of eqn. (2) 1s that the biomass production 1s replaced by a more readily measurable terms, z e acetate concentration The expenments reported were performed with acetate as the pnmary carbon source for methanogenesls with both stirred suspended cultures and fixed-film reactors. The maximum specific growth rate pmax and the half-saturation constant K,, were evaluated for this data by numencally mte- gratmg eqn (2) and comparmg it with the experunental data by non-linear regression The parameters obtamed m this manner were 0.17 day-’ for /.L,,, and 8.46 X 10e3 M for &a Virtually identical parameter values

032 t 02

02

02

01 1 OExperlmental

0 0 25 0 50 0 75 I D 1 25 15

Time (days)

Fig 3 Observed and predwted acetate utlhzatlon m the fixed film bed reactor T = 39 “C, pH 7 uncontrolled

were obtamed m suspension cultures and fured-film reactors The parameter values of the two systems differed only with respect to the active biomass levels The fixed-flm reactors contamed approximately 4 tnnes more biomass than the free suspensions on a unit volume basis. This was expected, since the support retamed more biomass than the conventional reactor The expenmental data are compared with the snnula- tlons m Fig 2 for the suspension cultures and m Fig. 3 for the fured-hhn reactor 1rutm.l acetate concentrations m these expenments were approxnnately 2 g 1-l No inhibition by acetate was observed at concentrations m excess of 10 g 1-l

In Table 3, the kinetic parameters obtamed m this study are compared with published data The generally hgher values reported for E.c,,, m suspension cultures may be due to several factors It has been observed by Lawrence and McCarty [9] that acetate utlhzmg bactena adhere to solid surfaces (wall growth) and if neglected m the calcu- lations, could result m apparently high specific growth rate and acid utlhzatlon, particularly m contmuous culture With the

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TABLE 3

Comparison of reported maximum speclflc growth rate prnax and half-saturation constant K,, for acetate utlhzatlon m anaeroblc dIgesters

T (“C) Anax (day-‘) Ksa (M) Type of drgestzon PH Reference

35 0 360 3 88 x 10-3 Swine manure 75 Smith et al [24 ] 2 stages

35 0 356 2 57 x 10-3 Enrichment culture Near neutrahty Lawrence [ 231

37 0 45 5 x 10-3 Enrichment culture - Smith and Mah [ 161 (smgle orgamsm)

37 - 10 x 10-J Digestion sludge 68 Ghosh and Pohland [ 81 (2 stages)

38 0 400 3 33 x 10-5 Simulation - Andrews and Graef [lo]

39 0 170 8 46 x 1O-3 Enrichment culture 7 00 This study

0 0025

0

0 0 0025 0 005 0 0075 0 010 0 0125 0 015

Concentration of Proplonate (M)

E’lg 4 Effect of acetate concentration on the rate of proplonate utlllzatlon m the fixed film bed reactor

exception of data given by Andrews and terns These higher volatile fatty acids, how- Graef [lo], the reported half-saturation ever, are not directly utilized by methanogens constants range from 2.5 X 10m3 M to 10d2 Rather, they are degraded by acetogenic M acetate. In addition to acetate, propionate bacteria to acetate and other products in and butyrate are also present m significant syntrophic association with methano- concentrations m anaerobic digestion sys- gens

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3 4 Kmetm of proptonate and butyrate u t&a tlon

The expenmental results have shown that the rate of utlllzatlon of proplonate and butyrate are more complex than the rate of acetate uttizatlon. In Fig 4, the rate of proplonate utlhzatlon 1s plotted at various acetate concentrations. These results were obtamed m the fixed f&n bloreactor at controlled pH values of 7 0. At acetate concentrations, as low as 0 01 M, the rate of proplonate utlllzatlon m 0 005 proplonate solutions declined more than two-fold m comparison to acetate-free solutions Acetate concentrations of 0 04 M resulted m approximately 90% reduction of proplonate utilization rates. Accordmg to a model dlscrlmmatlon study [ 171, the effect of acetate on proplonate degradation could best be expressed by a competltlve mhlbltlon model with acetate A as an m- hlbltor.

ClP P -= dt -k* K, + P + A/k,’ (3)

To examine the kmetlcs of multiple acids utllzatlon, the flow of fresh medium to contmuously operating digesters was mter- rupted and the effluent recycled at a hquld reclrculatlon rate of 6 liquid volumes h-’ Figure 5 gives typical results of acids utlh- zation in acetatepropionate solutions. At high acetate concentrations, the rate of proplonate d=appearance 1s relatively low m comparison with that of proplonate. As the acetate concentration declines, proplonate 1s catabohzed at progressively higher rates m accordance with the mhlbltlon model rep- resented by eqn (3) Although not shown, butyrate uttizatlon was affected by acetate m a manner sun&r to proplonate. Accordmg- ly, a model dlscnmmatlon procedure was performed for butyrate-acetate solutions as well and the followmg model was found to be the best m the least squares error sense

dB B _= dt -k, Ksb + B + A/k,,’ (4)

In eqns. (3) and (4), the maximum rates of proplonate and butyrate catabohsm (kp and k,,) are the products of the specific growth rate pmax, the acetogenlc biomass concentration X’ and the growth yield of

0 012

0 010

0 004

0 002

0

-Predrcted Expenmental

@Acetate

AProplonate

lime (days)

Fig 5 Observed and predxted acetate and proplonate uthzatlon In free suspensions T = 39 “C, mtlsl pH 7 uncontrolled

acetogenlc bactena Y,‘. In theory, the de- pendence of the rates on the acetogemc population density could be expressed ex- phcltly as for the methanogenlc bactena (see eqn. (1)) This procedure, however, gave insignificant improvements m predlctmg the reaction rates, hence, it was deemed unnecessary

It 1s well known, that the catabolism of propionate and butyrate by acetogenlc bactena gives nse to acetate formation. Accordmg to Thauer et al [ 181 and Bryant [ 191, bacterial action on proplonate and butyrate results m the formation of Hz as well as acetate and CO2 The free energy change associated with this reaction is posl- tlve. The reaction proceeds m the forward dn-ectlon only if the partial pressure of Hz 1s kept low by Hz-utlllzmg methanogemc bactena m syntrophlc assoclatlon with acetogenlc population. This reaction sequence for proplonate can be summarized as follows.

acetogehs CH,CH,COO- + 3H20 -

CH,COO- + 3H, + HCO3 + H+ (5) AG” = +18.07 kcal (reaction)-l

TABLE 4

Kmetlc coeffmenb of acid utdmtlon

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dp -= -k,P

dt K,, + P + A/k,’ (19)

I-(max K X2Yg 2 k;' kb K sb kb’

0 17 day-l 8 46 x lo+ M 0 0469 M 1 372 x 10s3 M day-’ 1765 x lo-’ M 0 5936 1 6 x 10q3 M day-’ 3 718 x lo-* M 1 042

HCOs- + 4Hz + H+ methanogy CH,, + 3HsO

AG” = -32.4 kcal (reaction)-’ (8)

Hydrogen was not detected m the gas phase dunng anaerobic digestion of propionate and butyrate, either with mdlvidual acids or with acid mixtures. The stoicluometry of acetate formation from butyrate and propionate could best be expressed m the followmg manner:

CH,CH,COO- + 0.5HsO + 0.5c02---

175CHsCOO- + 0 75H+ (7) AG”= -1.02 kcal (reaction)-’

CHsCH&H2COO- + 0.5HC0, -

2 5CHsCOO- + H+ + 0.5HsO + 0 5COs

AG” = -1.38 kcal (reaction)-’ (8)

Although eqns (7) and (8) do not imply a mechanism, it is sigmficant that the free energy changes associated with the reactions are negative, hence, they could proceed without simultaneous methanogenic activity. Taking into account the stoichiometry of acetate formation from the higher volatile acids, the followmg differential equations can be derived

d[Al= -Pmax A

dt K,+A {(A, -A) + 1.75(P, - P)

dP + 2.5(Bo -B) + X,,/YJ - 1.75 dt

-25; (9)

dB -k,B -= dt Ksb + B + A/kb’ (11)

In eqn. (9), the contributions of proplomc and butync acid degradation to the acetic acid pool are mcluded m the first term. It can be shown by material balance that the methanogemc biomass is

X = X0 + Y.&A, -A) + 1.75(P,-P)

+ 2.5(B0 - B)} (12)

The second and the third terms of eqn. (9) give the rate of acetate formation from propiomc and butync acids. The coefficients correspond to the stoicluometry given by eqn. (7) and eqn (8).

3 5 Pammeter estlmatzon To obtam numerical values for the con-

stants, these non-lmear differential equations were numerically mtegrated by usmg the Adams-Moulton algorithm [20] The subroutme NLDEQD from the University of Waterloo [21] was used for the numerical integration. The parameters were estimated by mminuzmg the total sum of squares between observed and predicted acid concentrations by combmmg the Gauss (Taylor senes) method and the method of steepest descent usmg Marquardt’s algorithm [22]. The calculation procedure was iterative. First, the mtegratlon was performed with assumed parameter values. The mitral parameter values were obtamed by varymg one parameter of the model at a time and by selecting the value at which the mnnmum total sum of squares was obtamed. Sub- sequently the parameter values were re- evaluated by the Marquardt algorithm and the mtegration repeated.

The approach based on mltial parameter estimates was necessary because of the high correlation between the parameters. In fact, almost identical mmunum residual sum of squares could be obtained with widely drffer- mg parameter values. Some of the parameter values were clearly unreahstic for the anaerobic digestion system.

The cntena for model fitting were that the convergence of the total sum of squares to

B8

0 016

0 014

0 012

0 010

x

E 0 008

? ;' : 6 u

0 006

- Predlcted

EXpWlmental

- Qredlcted .

Experrmental

l Acetate

A Propronate

4 wyrate

0 Acetate

A Proplonate

A Butyrate

Time (days)

0 05 10 15 20 25 30

Time (days)

Fig 6 Observed and predicted acetate, proplonate Fig 7 Observed and predlcted acetate, proplonate and butyrate utlhzatlon m free suspensions T = and butyrate utlhzatlon III fixed-film bed reactor 39 “C, lnbd pH 7 uncontrolled T = 39 “C, ph 7 controlled

less than 10S5 and the parameter convergence to less than 10m5 between two successive iterations. The best parameter estimates are compiled m Table 4

The application of the models and the results of the simulation for the suspension culture and fixed-film reactor are illustrated m Figs. 5 - 7 Of the nme parameters required to model the fate of orgamc acids, three of the parameter values (X,/Y,, k, and k,,) depend on the particular bloreactor system. For example, for the simulation shown m Fig. 7, the methanogemc biomass level X,, was approximately SIX times higher, while the rates of propionate k, and butyrate kb degradation were about 10 tunes higher m fured film reactors than m free suspensions (Fig. 6). These dynamic models gave good agreement between predicted and observed acid concentrations m a number of widely dlffermg acid mixtures.

3 6 Methane generataon To predict the rate of methane generation,

acetate has been considered as the sole precursor of methane. Consequently, the rate of methane formation, expressed as moles CH4 formed per htre per day, could be directly obtamed by consldermg the first term of eqn. (9).

d[CHd -~maxA - = K dt sa

+A {(A,-A) + 175(P,--p)

+ 2.5(&--B) + X,,/Y8} (13)

In Fig 8, methane formation from an acetate-proplonate-butyrate mixture m a fixed-film reactor is shown The apphcabihty of the model to predict methane generation is self-evident. The difference between

- Predlcte _

0 CH4

0 05 10 15 20 25 30

Time (days)

Fig 8 Observed and predlcted methane production from an acetate-proplonate butyrate mixture m a fixed-f&n reactor

observed and predicted values was generally less than 10%. By using the rate expressions (eqns. (9) - (11) and (13)), these predlctlons of methane generation m acid mixtures were essentially the same as those m a much simpler system such as acetate only m the dlgestlon liquor. This supports the present approach with regard to modelhng the fate of higher volatile acids durmg anaerobic digestion

4 CONCLUSIONS

Optimum conversion of cellulose to organic acids was obtamed at a carbon to nitrogen ratio of 4 to 1. Only a small fraction of the nitrogen was mcorporated into biomass The ammomum ion product was pmanly required to prevent pH depression to m- hlbltory levels The acid dlstrrbutlon was a function of the loading rates. Acetic and proplonrc acids were predommant at low loadmg rates while at high loadmg rates butync acrd productron was favoured. Pro- plonate and butyrate were always present m

B9

srgmflcant concentrations m the range of cellulose concentrations mvestlgated. To predict methane generation, the fate of the acids was analyzed m detarl.

Both fixed-frhn and suspensron cultures were utilized to study methanogenesls from organic acid mrxtures Monod kmetlcs could be used to predict the rate of acetate utrliza- tlon No substrate mhlbltlon was observed with acetate only Proplonate and butyrate utilization were mhlblted by acetate and followed a competltlve mhlbltlon pattern. The agreement between observations and predlctlons supported the hypothesis that acetogemc bactena produce 1.75 mol acetate from 1 mol proplonate and 2 5 mol acetate from 1 mol butyrate. The differences between acetate, proplonate and butyrate utlhzatlon and methanogenesls imply that bactena utlhzmg higher volatile acids (acetogens) compnse a metabohc group drfferent from methanogenlc bactena.

ACKNOWLEDGMENTS

The authors are grateful to the Natural Sciences and Engmeermg Research Council of Canada for the fmancial support to perform this work The assistance of MS Veronlque Devlesaver m experunents on acid productron from cellulose IS also acknowledged.

REFERENCES

J T Pfeffer, J Water PoNut Contr Fed, 40 (1968) 1920 G T Taylor, Progr Ind Mzcrobzol , 16 (1982) 231 S Ghoeh and D L Klass, Process Bzochem , 13 (1978) 15 A G Hashunoto, Bzotechnoi Bzoeng, 25 (1983) 185 G R Moms, W J Jewels and R C Loehr, Food, Fertzlzzer and Agrzcultural Reszdues, Ann Arbor Science, New York, 1977 R K Smgh, MA SC Theszs, Umverslty of Mam- toba, Wmmpeg, 1977 J M Scharer, M FuJita and M Moo-Young, Waste Treatment and Utzlztatzon, Theory and Practzce of Waste Management, vol 2, Pergamon, Oxford, 1982 S Ghosh and F G Pohland, J Water Pollut Contr Fed, 46 (4) (1974) 748 A W Lawrence and P L McCarty, J Water Pollut Contr Fed, 41 (1969) Rl

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21

22

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24

J F Andrews and S P Graef, Adwm Chem Ser , 105 (1971) 126 D T Hill and C L Barth, J Water Poll& Contr Fed, 49 (1977) 2129 H M Lapp, A Study of the Feaslbzhty of Usmg Methane Gas Produced from Anzmal Waste for Energy Purposes, Agriculture Canada, 1977 L Van den Berg and K J Kennedy, J Chem Techn Blotechnol , 32 (1982) 427 D M Updegraff, Anal Bzochem , 32 (1969) 420 A I Vogel, A Textbook of Quanktatzve Znorgan- IC Analyses, Longman, London, 1962, 3rd edn M R Srmth and R A Mah, Appl Envzron Mzcrobrol, 36 (1978) 870 P Gerard, J M Scharer and M Moo-Young, Proc 6th Symp on Waste Water Treatment, Montreal, 1983 R K Thauer, J Jungermann and K Decker, Bactenol Rev, 41 (1977) 100 M P Bryant, J Anzm Scz, 48 (1979) 193 P Henncl, Discrete Vanable Methods zn Ordznary Equations, Wdey, New York, 1962 NLDEOD, Fortran IV Subroutme, Umverslty of Waterloo, Waterloo, Ontano (1965) D W Marquardt, J Sot Znd Appl Math, 2 (1963) 431 A W Lawrence, Aduan Chem Ser , 105 (1971) 163 R E Smith, M J Reed and J T K&er, Tmns ASAE, 20 (1977) 1123

APPENDIX A NOMENCLATURE

A

Ao B

Bo

dA

dt

concentration of acetate (M) mltial concentration of acetate (M) concentration of butyrate (M) mltlal concentration of butyrate tM)

rate of acetate uttilzatlon (M day-l)

dB - dt

d[Cbl

dt

dP

dt kb

kb’ kP

k,’ Ksa

Ksb

KSP

P

PO

X

x0

ys

rate of butyrate utlllzatlon (M day-‘)

rate of methane production (M day-‘)

rate of proplonate utlhzatlon (M day-‘) maximum rate of butyrate utlllzatlon (M day-‘) mlubltion constant for butyrate maxnnum rate of propionate utih- zatlon (M day-‘) mhlbltlon constant for proplonate half-saturation constant for acetate (M) half-saturation constant of butyrate (M) half-saturation constant of proplonate (M) concentration of proplonate (M) mitial concentration of propionate (M) concentration of methane bactena (g biomass 1-l) mltkl concentration of methane formers (g biomass I-‘) growth yield of methanogens (g biomass (mol acetate)-‘)

Greek symbol P max maximum specific growth rate of

methanogens (day-‘)

two-stage anaerobic digestion for the treatment of cellulosic wastes

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