pavlostathis, gossett - 1986 - a kinetic model for anaerobic digestion of biological...

8/15/2019 Pavlostathis, Gossett - 1986 - A Kinetic Model for Anaerobic Digestion of Biological Sludge-Annotated

1/12

A Kinetic Model for Anaerobic Digestion ofBiological Sludge

Spyros G. Pavlostathis and James M. Gosset t

School of Civil and Enviro nmental Engineering, Cornell Universi ty, l thaca,New York 14853

Accepted for publ ica t ion Nov emb er25 1985

The principal objective of this stud y was th e dev elopmentand evaluation of a comp rehen sive kinetic model capa bleof predicting digester performance whenfed biologicalsludge. Preliminary conversion mechanism s such a s celldeath, lysis, and hydrolysis resp onsible for rend ering vi-able biological sludge organisms to available substratewere studied in depth. T he results of this study indicatethat hydrolysis of the dead, particulate biomass-pri-marily consisting of protein-is the slowest ste p, andtherefore kinetically controls the overall process of an-aerobic digestion of biological sludge.A kinetic m odelwa s developed which could accurately describe digesterperformance and predict effluent quality.

INTRODUCTION

Previou s studies’,* dealing with the anaerob ic diges-tion of activated sludge (AS) have shown that kineticmodels which assu me that m ethanogen esis is the solerate-limiting step are inapplicable in the case of bio-

logical sludges. Anaerobic degradation ofA S requiresthat the potentially-degradable portion of viableASorganisms must first be converted to available sub-strate by preliminary conversion mechanisms such ascell death , lysis, and/or hydrolysis. I t was show n2 h atfor solids retention times(@‘IG) values of practical in-terest, acidogenesis an d m ethanoge nesis are not pro-cess-controlling s tep s in digeste rs receiving biologicalsludges. The predominant degradable constituent inthe effluents of such digesters is particulate protein,indicating that hydrolysis and/or other preliminaryconversion mechanism(s) is(are) Limiting from the pointof view of subs trate availability.

Which of the postulated, preliminary-conversionmechanisms is most kinetically limiting can only beinferred from these previous investigations. T heir di-rect study was not undertaken. Examination of con-tinuous-flow anaerob ic digestion data2 from digesterswhich were fed autoclaved sludge showed thata sig-nificant preliminary barrier rem ains, even after auto -claving. Sinc e autoclaving induces cell de ath and lysis,these dat a suggest that the m ost kinetically limiting of

the possible preliminary conversion me chanism s maybe hydrolysis and not cell death o r lysis.

Th e purpose of this article is to e xam ine directly th epreliminary conversion step in detail, consideringmechanisms such as cell death, lysis and hydrolysis,so as to evaluate their relative importance in thean-

aero bic digestion of biological sludges. T his is don e inthe context of a conc eptua l model fo r biological sludgedigestion, which is here presented a nd evalua ted.

MODEL DEVELOPMENT

Conceptual Mod el of Biological Sludge Digestio n

A conceptual representation of the processes in-volved in the anaerobic digestion ofAS is shown inFigure 1. Gossett and Belser ’ demonstrated that thebiodegradable fraction of AS consists almost exclu-

sively of the biodegradable portio n of viable, activate dsludge organisms. Th e biodegradable portion of viableAS cells may be thought of as comprising two s ubstr atepools: one particulate and one soluble. Upon death,the cell mem brane ruptures (i .e. lysis occu rs), and partof the intracellular, s oluble, degradable CO D (i.e. sol-uble BOD) (presumably the lowest molecular weightcomponents) is immediately released. Then, the re-maining intracellular soluble BOD pool ofa dead cellchanges with time b ecause of soluble B OD productionvia intraceliular hydrolysis (IH) and loss of solubleBOD du e to diffusion. Much of the IH may be d uetoremaining, native intracellular enzymes, uncontrolled

upon cell death. Contribution s toIH f rom exoenzymesproduced by the anaerobic microflora may also be sup-posed. The dead cell particulate BOD is additionallysubject to extracellular hydrolysis(EH), presumed tobe primarily induced by the active digester microor-ganisms. Th e extracellular soluble B OD pool is su bjectto decrease because of uptake by the digester micro-flora, especially by the acid-forming bacteria. Fromthat point on the model follows the classical two-phase

Biotechnology and Bioengineer ing, Vol. XXVIII,Pp. 1519-1530 (1986)1986 John Wiley & Sons, Inc. CCC 0006-3592/86/101519-12$04.00


2/12

EXTRACELLULAR

A C I W ~ E S I S

M * . co,

k

Figure 1. Conceptual model for anaerobic digestion of biologicalsolids (I.H. is intracellular hydrolysis; E.H. is extracellular hydrol-ysis; kd is the death rate coefficient; kh, and kh, are the intra- andextracellular hydrolysis rate coefficients; k , is the soluble BOD dif-fusion rate coefficient; and y is the cell soluble BOD immediatelyreleased, fraction of total BOD).

Dum/LysIs

anaerobic digestion scheme: acidogenesis and meth-anogenesis.

Validation of the above-outlined model requires thedirect estimation of all constants and parameters in-volved. Due to the complexity of the system, difficul-ties are encountered in developing analytical tech-niques to accomplish this without simplification. Forexample, note that the conceptual model equates deathand lysis. From the point of view of substrate avail-ability, cell lysis is more important than death. How-ever , lysis is difficult to ass ay, compared with the quan-tification of death. Certainly, all cells which lyse aredead. If death results from predation by anaerobic pro-tozoa, “ lysis” may be said to be pretty much concur-rent with death. But for other, nonlytic causes of death,how soon does lysis follow death?

Attempts were made in the present study to measurecell lysis rate, but they were not successful, as is dis-cussed in a later section. On the other hand, it is be-lieved that once the cell is dead, the permeability bar-rier provided by the plasma membrane is rapidlydestroyed, and most of the soluble cell contents (pre-sumably the lowest molecular weight components) leakout.3 Thus, from the point of view

ofsubstrate avail-

ability, we assume here that there is practically no lagbetween death and lysis. Hence, we refer to both as asingular death/lysis mechanism.

Upon cell death/lysis a good portion of the intra-cellular soluble BOD is believed to be released almostimmediately. The remaining intracellular soluble BOD-originally present in the viable cell and al so producedvia intracellula r hydrolysis of particulate BOD follow-ing cell death-must diffuse out of the dead cell if the

oRocyys ,

k h

cell membrane, although ruptured, still provides a bar-rier. Whether or not the damaged membrane providesa significant barrier to release depends on the relativesize of the membrane perforations compared with thesize of the material leaking out. Evidence is presentedin a later section which suggests that diffusion fromwithin a damaged cell membrane is not a significant,kinetic limitation with respect to substrate release.

If diffusion limitations are ignored, then the intra-

and extracellular hydrolysis rates are additive and maybe collectively referred to as “hydrolysis.” Accord-ingly, the conceptual model presented in Figure 1 canbe simplified as is shown in Figure 2.

SUBSTRATEREQUIRINGHYDROLYSIS

Equations

The following assumptions and premises were con-sidered in the derivation of model equations: 1) allvariables are expressed on a COD unit basis; in fact,all except microorganism concentrations are expressedas degradable COD; 2) the inherent, net biodegradablefraction fd) of viable AS organisms and anaerobic mi-

croflora is the same; 3) we do not differentiate betweencell death and lysis, but we assume that lysis occurssoon after death; 4) upon death/lysis, all soluble intra-cellular material is released as “soluble” substrate,and it is taken as a constant fraction of the total celldegradable COD (i.e., diffusion of soluble material outof the damaged cell is rapid-this assumption is jus-tified later); and 5 ) facultative AS bacteria which mayultimately survive are not considered as part of theacid-phase, active biomass.

The death/lysis rate is considered to be first-order:

- k d X f sd = p -d X f s

dt

1520 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 28, OCTOBER 1986


3/12

where X t S is the viable AS biomass concentration inthe digester (g/L) and kd is the death/lysis rate coeffi-cient (day-').

The hydrolysis rate is assumed to be a first-orderreaction with respect to the concentration of degrad-able particulate COD:

where F is the degradable, particulate (nonviable) CODconcentration (g/L) and kh is the hydrolysis rate coef-ficient (day-'). In terms of the complex conceptualmodel (Fig. 1)-and given our assumption that thereis no diffusional limitation for transport of solubilizedmaterial out of the damaged cell-then this kh is reallythe sum of intracellular and extracellular hydrolysisrate coefficients.

The microbial growth rate and substrate utilizationrate for any particular group of digester bacteria arebased on the Monod equation4:

dX YkSXr x = bXd t K , S

kSXK , + S~S

dt" = - -

(3)

(4)

where X is the active microorganism concentration (g/L);S is the substrate concentration (g/L); Yis the microbialgrowth yield coefficient (g biomass produced/g sub-strate utilized); k is the maximum specific substrateutilization rate (day- '); K , is the half-velocity coeffi-cient (g/L); and b is the microorganism decay coeffi-cient (day - .

For the case of a completely mixed, continuous-flowreactor without recycle, at steady-state, the followingmass balances can be derived (definitions of termsfollow):

Mass Balance on D egradable Portion of Viable ASMicroorganisms (fdXts)

( 5 )f d (X:', X t s ) VfdkdX:' = 0

Mass Balance on Nonviable Substrate RequiringHydrolysis (F)

Q(F0 F) VkhF + V(I 7 ) dkdx,"' = O (6)

Mass Balance on Soluble Substrate for Ac idPhase (9 )

Q SS S A )+ VkhF + VYfdk&fiSk A S A X i

Kf + SA = 0 (7)

Mass Balance on Degradable Portion of ActiveAcidogenic Biomass (fdX )

erAX2 X 3YAkASAX$vfd[ K:' c SA b A X t ] = 0 (8)

Mass Balance on Products

We may define (as did Eastman and Ferguson5) aquantity, P , which is the concentration of volatile acidsformed by acidogenic bacteria, plus any influent vol-atile acids. Parameter P differs from the actual, ob-served concentration of volatile acids remaining, dueto their consumption by methanogenic bacteria. Thus,P is the sum of observed volatile acids, plus methaneformed, plus methanogenic biomass formed, all in CODunits. The mass balance on P then becomes:

VkASAX2 VYAkASAX2Kf SA Kf + SAPo PI

where Q is the hydraulic flow rate (L/day); V is thereactor volume (L); X;p,Sis the influent, viable AS bio-mass COD concentration (g/L); Fo is the influent de-gradable particulate (nonviable) COD concentration(g/L); y is the fraction of total degradable COD inX,"' released as soluble COD upon deathilysis; SSis the influent soluble substrate COD to the reactor(g/L); X i ois the influent active acidogenic microorgan-ism concentration (g COD/L) ; Po is the influent productconcentration (g COD/L); and fd is the net biodegrad-

able fraction of active biomass. (Note that superscriptA S refers to activated sludge and superscript A refersto the acid phase).

The last mass balance was derived based on thefollowing reasoning: COD is conserved in an anaerobicdigestion system and the utilized substrate COD is eitherincorporated into cellular material or converted toproducts for microbial energy. Therefore, the differ-ence between the substrate utilized and the net cellularCOD produced represents the amount of product

By adding the five steady-state equations and divid-COD.^,^

ing by Q the following expression is obtained:

The hydraulic retention time ( 6 )(equal to solids reten-tion time for systems without biomass recycle) ap-

PAVLOSTATHIS AND GOSSETT: ANAEROBIC DIGESTIONOF SLUDGE 1521


4/12

pearing in the eq uation is equal to V/Q. From eq. (8),we obtain:

which substi tuted into Equation (10) gives:

fAX$rjj XCS)+ (Fa F ) + ( S t S A ) + xtoX:[1 + (1 - f d P f 9 ] (Po P ) = 0 (IOa)

The influent, viable AS biomass concentration is givenby the following equation’:

D COD,,f d

X$rjj =

where D is the ultimate biodegradability of AS (frac-tion) and CODi, is the influent COD concentration g/L).An explicit solution for each variable can be found byalgebraic manipulation of the five steady-state equations:

Model Equations

The model equations are as follows:

-X:[1 + (1 d ) b A O ] (17)In the last phase, i.e. methanogenesis, we make useof the Monod model for substrate and biomass con-centrations (Note that superscript B refers to meth-anogenesis). Ignoring X:a,

where SB is the effluent soluble COD (i.e., volatile acidCOD) (g/L); K is the composite, half-velocity coef-

bB is the decay coefficient for methanogens (day- I ) ;YB s the yield coefficient for methanogens (g biomassCOD/g substrate COD utilized); kB is the maximumspecific substrate utilization rate for methanogens (g

ficient ( = Kyetic + Kyopionic or this case, g COD/L);

substrate COD/g biomass COD day-’) ; X f s the totalmethanogenic biomass (g COD/L); (Sg)effec s the ef-fective influent volatile acid COD to th e methane phase(g/L); and the rest of the symbols are as defined inprevious sections.

The connection between t he acid phase and methanephase of the present model is made via the productformed in the former phase, which is essentially the“influent” to the last phase, i.e., = P. Sincethe product equation includes a correction for acido-genic biomass produced in the system, the only cor-rection of the processed COD for the digester per-formance equation [i.e., percent of COD destroyed(%COD,,,,)] is the methanogenic biomass:

The four basic equations of the model [Eqs. ( I3) ,(14), I S ) , and (16)] can be linearized in order to de-termine the kinetic constants involved. However, t hebiggest analytical difficulty faced in the present study,which was the inability to differentiate (and measure)AS biomass from the acidogenic and methanogenicbiomass produced in the digester, made such a deter-mination impossible. To overcome these problems, anumber of batch experiments were conducted, to in-dependently provide important constants.

PROGRAMOF STUDY

Skeptics might note that there are sufficient kineticparameters in the complex model depicted in Figure2 , such that one could-through “conv enien t” selec-tion of parameter values-fit almost any performancedat a Legitimate evaluation of the model requires theindependent measurement of parameters employed init. However, it is not necessary to do this for all pa-rameters-only the important ones. For example, itwill later be shown through a sort of sensitivity analysisthat th e important, limiting st eps are th ose relating t opreliminary conversion of substrate to available, sol-uble form, and the later conversion of aceta te and pro-pionate to methane. Acidogenesis is relatively rapid.This is to be expec ted, based upon previousThus, it makes little sense to do anything more thanto expropriate kinetic parameters for acidogenesis from

literature values. [The one exception was the yieldcoefficient fo r th e acidogenic bacteria ( YA ) ,which wasmeasured, though with only modest s ~ c c e s s . ~ ]

Hence, many phases of study described in subse-quent sections were undertaken with the purpose ofindependently measuring sludge and kinetic parame-ters of importance to the proposed model. Some ex-amples: the deathhysis rates of viable AS organismsin anaerobic environments were measured in contin-uous flow systems, using an oxygen uptake technique;

1522 BIOTECHNOLOGY AND BIOENGINEERING,VOL.28, OCTOBER 1986


5/12

hydrolysis ra tes we re inferred from solubilization stud-ies employing batch-fed dige sters which received dif-fer ing amounts of act ive, anaerobic seed. Measure-men ts of other importan t model parame ter values (e.g.,ultimate biodegradability of autoclaved and intact AS;half-velocity coefficients for acetate and propionateutilization) were presented prev iously.2 na final anal-ysis phase of study, the various independently mea-sured parameter values were employed with the sim-

plified version of the mode l depicted in F igure 2, allowingcomparison of observed, continuous-flow digestionperformances with model predictions.For this com-parison, digester performance data presented else-where were employed.*

MATERIALS AND METHODS

Reactor configurations and modes of operation forthe laboratory generation of activated sludge and itssubsequent anaerobic digestion were described pre-viously.2 Th e AS w as pro duce d in a 150-L fill-and-drawreactor fed with a soluble synthetic waste. The re-sulting sludge volatile su spended solids were thus en-tirely of biological origin. The digesters were con-structed from 2-L Pyrex bottles fit ted with holes andrubber stoppers to allow for feeding, withdrawal ofdigested sludge, mixing of the digester conten ts (me-chanically), sampling of the m ixed liquor and m ea-surement of the gases . The digesters were fed onaonce-per-hour basis via a t imer, a series of solenoidvalves and two metering pumps with variable-speeddrives. Digested sludge was w ithdrawn once o r twicea day via a sampling port.

Batch Digestion ExperimentsA variation of the serum bottle technique outlined

earlier2wa s used to investigate the hydrolysis (actuallysolubilization) of AS in anaerob ic environm ents. In thiscase, seed and media were transferred anaerobicallyto the seru m bottles-already containing the sub-strate-separately in orde r to permit the use of variousamountsof seed. AutoclavedA S solids were employ edas substrate . Autoclaving was ch osen asa cell disrup-tion tech nique.2 It wa s thought that autoclav edASsolids would represen t cell particulate matter left aftercell death and lysis and requiring further hydrolysis

(see the Hydr olysis Rate Coefficient s ection). All bot-tles received the same amount of defined media (20mL ) and the same am ount of substrate (15m L f rom astock suspensionof ca. 20 g COD/L). T he am ounts ofseed used were 0, 20, and 40 mL of digester mixedliquor receiving intactAS as feed . These samples a relater referred to asBo, B , ,and B2, espectively. T welvereplicates were prepared; two were opened immedi-ately after filling with media and/or seed (for assay ofinitial conditions and s ubstra te measurem ents), and the

rest were opened one-by-one each time thata mea-surement was effected. The incubationtime was onemonth and the room temperature was35 * 1°C. Thebottles were manually shaken twice per day.

O n a predetermined schedule, the gas productionswere measured in all replicates, and then one bottlefrom each group was opened and the following anal-yses were performed on its contents: pH , soluble COD ,and volatile acids. The g as composition was also mea-

sured. The par t iculate substrate COD was accuratelymeas ured only a t the beginningof the experiment . Thisis the difference between total and soluble C OD of thecomposite sample (i .e. , substrate + seed media)after subtrac ting seed and media blanks.

The autoclaved AS “sol ids” fract ion was preparedusing the following technique: settled AS was auto-claved (121”C,30 min), cooled, then centrifuged (104gfor 1 h) , and the centrate was wasted. Th e pellet wasresuspended in distilled water and centrifuged again( l o4g for 30 min). Th e last step was repeated o ne moretime. Finally, the centrate was wasted and the pelletwas suspended in distilled water, yielding the “solid”sample.

Cell Death/Lys is Rate s )

An oxygen uptake rate (OUR ) technique was usedfor es t imat ion of the death rate constant(kd) of ASmicroorganisms fed to continuous flow digesters op-erated at different @ I G . Th e decre ase in OUR-mea-sured in preaerated (30 min) digester mixed liquor un-der substrate saturation conditions (ca. 300 mgglucose/L)-with incubation time (i.e. dige ster reten -tion time) was assumed to represent microbial death.

The use of this OU R technique forkd estimation iscertainly questionable: The OUR is more a measureof biological activity, and activity an d viability a re notnecessarily synony ms. It is conceivable that the OU Rof a biological community may decrease without anequal decrease in viability (i.e., percent of viable or-ganisms of the total). F or exam ple, in the case und erdiscussion, facultative bacteria originally in the AS,now growing in an anaerobic environment, may notexert high OUR immediately upon reintroduction tothe ae robic environm ent, although the ir viability maynot have been decreased. Another conce rn about usingthe OU R technique with anaerobic media is the strictly

chemical oxygen consumption that reduced subs tance smay exert under aerobic condit ions. In order to ass aythe significance of this so urce of oxyge n consum ption,ethanol (95%) was add ed to a n aliquot of digester mixedliquor, left to sta nd for 15 min, the n aer ated fo r 15 minprior to measurement of OUR . TheOUR was practi-cally zero ov er 25 min of meas urem ent. This ledus t oconclude that, although there is a chemical oxygenconsum ption exerted by various reduce d substancesin the digester mixed liquor, this rate is almost negli-

PAVLOSTATHIS AND G OSSE lT: ANAEROBIC DIGESTION OF SLUDGE 1523


6/12

gible over the time that the OUR of a sample is mea-sured (usually 20 min).

Other direct viability measurement techniques (e.g.plate counts) were judged inappropriate primarily be-cause of the inability to completely disperse an acti-vated sludge floc without killing the bacteria. Platecounts are appropriate for use where viable numbersrange over orders of magnitude. However, their ac-curacy is too limited to be of use in our studies. Thu s,

despite its limitations, th e OUR techn ique was selectedfor monitoring relative changes in AS viability.

Initially, we intended to distinguish death from lysis,and to separately determine death and lysis rates forAS organisms in anaerobi c environments. A s a mech-anism for converting membrane-enclosed, potentialsubstrate into available substra te, cell lysis is perhapsmore important than cell death. Attempts were madeto directly monitor cell lysis via ultraviolet (UV) ab-sorbance (at 260 nm) of soluble material produced dur-ing batch anaerobic incubation of unseeded, intact A Ssamples. Unfortunately, the absorbance at 260 nm(corresponding to release of intracellular nucleic acidmate~- ia l~ . '~ )as masked by absorbance at 275 nm,probably d ue to amino acid production via protein hy-drolysis. ,'' The fast turnover ra te of soluble materialsreleased upon cell lysis also limits the utility of thistechnique.

Unsuccessful att empts were also made to distinguishdeath from lysis using microscopic differentiation ofthree categories of bacterial cells: viable, dead-intact,and dead-damaged. Fluorescein diacetate (FDA) andethidium bromide (EB) stains were combined into asingle a ~ s a y . ' ~ . ' ~esults were negative, in that viablecells did not fluoresce when stained with FDA, and allcells, regardless of viability, stained positively withEB. The failure of the staining procedure might be dueto the nature of the particular microorganisms presentin our system. At t he time, the dominant organism formappeared to be that of a well-dispersed tetrad resem-bling Micrococcusspp.

Because of the inability to separately measure deathand cell lysis rates, and because a good body of evidence3supports the notion of simultaneous cell death and lysis,the lysis rate is equated to the cell death rate in ourmodel. Therefore, all limitations applied to our mea-suremen t of the dea th rate constant-estimated by useof the OUR technique-apply to its use as a combined

deathhysis rate coefficient as well. For all practicalpurposes, this rate coefficient is hereafter called thedeath/lysis rate coefficient.

Analytical Methods

The following parameters were assayed in accord-ance with procedures outlined in Standard MethodsIs:pH (Sec. 423); chemical oxygen demand (COD) (di-

chromate reflux method, Sec. 508A, with "soluble"COD measured on samples centrifuged at lo4 g for 30min, followed by filtration through 0.45-pm membranefilters); dissolved oxygen (membrane electrode method,Sec. 421 F); and gas composition [gas chromatographicmethod, Sec. 511B, with a silica-gel column (50°C) inseries with a molecular sieve column (25"C)I. Gas pro-duction measurements and volatile acids were assayedas descri bed elsewhere.'

EVALUATION OF MODEL PARAMETERS

AS Organism Decay Coeffici ent PSI

The average decay coefficient applicable to the aero-bic, activated sludge organisms (bAS)was measuredusing an OUR technique' under starvation conditions(i.e., the AS mixed liquor was aerated over 17 dayswithout any exogenous substrate addition). A plot ofthe logarithmic (base e) OUR vs. time resulted in astraight line with a slope, bAS = 0.12 per day ( R 2 =0.997). The bAS alue is well within t he range of decaycoefficients found for mixed-culture aerobic systems:0.10-0.20 per day.4

AS Viable Cell Degradable Fractio n (f,)

Gossett and Belser' expropriated the following equa-tion from Christensen and McC artyt6 as an expressionfor the AS biodegradability D), when the AS is gen-erated from a soluble feed:

This equation can be solved for d:

D l + bASeSfd = 1 D b A S e S )

The applicable microorganism decay coefficient (bAS)was measured and found to be ca. 0.12 per day (seethe previous section). The activ ated sludge reacto r sol-ids retention time (eS)as 10 days, and the ultimateAS biodegradability D) anged from 51 -7 to 61 S .'Substituting these values into eq. (22), the calculated

fd range is 0.70-0.78. Christensen and McCarty16 sug-gested a value of 0.8, but did not actually measure itthemselves. Gossett and Belser' found an fd value of0.68 for a similar AS. A range offd from 0.65 to 0.80is found in the literature (cited by Gosset t and Belser').The fd values estimated in the present study are wellwithin this range. Henceforth, we employed our av-erage value of fd = 0.73 which corresponds to theobserved, average, ultimate AS biodegradability of55.8%, based o n gas data.2

1524 BIOTECHNOLOGY AN D BIOENGINEERING, VOL. 28, OCTOBER 1986


7/12

Death/Lysis Rate Coefficient (&J

T h e kd was est imated by use of an O UR technique.Th e limitations of this technique were discussed in aprevious sect ion. For the c ase ofa completely mixed,continuous-flow r eacto r without recycle, th e survivingfrac tion of viable AS organisms-assuming a first-orde r death rate [eq. (])]-is given by eq. (23):

1(23)

Assuming that there is a direct proportionality betweenX t Sand O UR , eq. (23) becomes equivalent to:

tS

x 1 + k d p

where (OUR), and O UR are the oxygen uptake ratesof the digester influent and mixed liquor, respectively(mg O2 L I min- ] ) .

This technique w as applied to th e mixed liquors fromthe continuous-flow digesters receiving intact AS a ndthe results are shown in Figure 3. Thekd value was

found to be e qual to 2 per day by use of eq. (23a).

Cell Solub le BOD Pool and Diff usio nalConsiderations

The conceptual model (Fig. 1) accounts for intra-cellular soluble BO D that is imm ediately released uponcell lysis, followed by continued release of additionalintracellular solubilized material under possible diffu-sional limitations. However, in the simplified model(Fig. 2), it has been a ssum ed that there is no significant,diffusional l imitation. Two questions need to be ad-dressed: 1 ) how m uch of the intracellular soluble BO Dis immediately released upon cell lysis and 2) is thereany diffusional limitation that controls the rate of re-lease of remaining soluble B OD o r soluble BO D formedvia intracellular hydrolysis?

Experim entally, i t seems almost impossible to quan-

PREDtCTlON SHOWN FOR:

OUR,-^ rnpi-’min-’k,-2 day-‘

E

5 2 j \ T1 w2 4 6 8 1 0

SRT,Doys

Figure 3. Estimation of deathilysis rate coefficient ( k d )for intactA S fed to continuous-flow digesters by use of oxygen uptake ratetechnique (bars indicate 95% confidence intervals).

tify both the intracellular soluble BOD and its rate ofrelease under “natural” conditions,i.e., under con-ditions prevailing in a digester. In search of an esti-mation, we followed a n indirect app roac h: it wasas-sumed that autoclavedcells resemble dead , damagedcells that got that way “naturally,” and that the quan-tity of soluble matter eventually released from auto-claved cells held in a sterile environment isa goodmea sure of the quantity of soluble m atter in an in tact

cell that would be capable, eve ntually, of permeatinga damaged membrane without requiring further hy-drolysis. These are, admittedly, rather tenuous as-sumptions. How ever , microscopic exam ination of au-toclaved cells sh ow s them to be essentially identicalto viable cells, with intact cell walls. Heat may, ofcourse, damage the m embrane far more than “normal”death/lysis, but the li terature suggests that upon d eath,the life of a microbial membrane is relatively short.3Heat may also alter the relative proportions of “par-ticulate” a nd “soluble” materials within the cell,aswell as the cellular chemical composition. But findingno other path available , the abo ve assumptions weremade of necessity.

Intact AS was placed in glass dilution bottles closedwith heat-resistant screw- caps and autoc laved (121”C,30 min). Following sterilization, th e bottles w ere equi-librated to 35 1°C tempe rature by immersing themin a water bath. Finally, the bottles were placed in acontrolled temperature room (35 ? 1°C). At time in-tervals, one bottle w as opened and its soluble fractionwas separated by centrifugationlfiltration. COD mea-surem ents and UV s cans were taken of the autoclavedsludge soluble fractions. During ca.5 days followingsterilization, the U V scan show ed no change , and nei-ther did the soluble COD. For example, immediatelyafter sterilization, the soluble COD was 1180 mg/L,with a coefficient of variation (i.e. lOOS/2?l equal to1 ; the total intact (i.e., b efore autoclaving) AS C ODwas 4230 mg/L with 40 mg/L as soluble COD. Thisrepresen ts ca . 28 solubilization. Sub sequ ent solubleCO D m easurements showed an average of 1200 mg/Lwith a coefficient of variation equal to5%.

From the abo ve results, along with knowledge of theintrinsic biodegradabilities of soluble and solid frac-tions (90.7 and 70. I , respectively*), we conclude thatthe intracellular soluble BOD is equal to30 of thetotal cell BOD, and that it is all immediately released

upon cell lysis. Thus, the diffusion of soluble intra-cellular BO D was neglected, resu lting in the simplifiedmodel (Fig. 2).

Hydrolysis Rate Coefficient (khl

The hydrolysis rate coefficient was estimated frombatch studies in which autoclave d AS solids were in-oculated with differing amounts of an anaerobic cul-ture. Autoclaved AS solids were employed as substrate

PAVLOSTATHIS AND G O S S E T : ANAEROBIC DIGESTION OF SLUDGE 1525


8/12

because elimination of the cell membrane barrier viaautoclaving allows kh values to be easily inferred fromobservations of solubilization rate (after appropriatecorrec tions detailed below). With use of intact AS assubst rate, solubilization rate is influenced by bot h lysisand hydrolysis kinetics, necessitating the numericalsolution of three simultaneous, differential equationsin order to estimate kh.8

Use of batch reacto rs fed autoclaved AS solids re-

quires acceptance of at least two assumptions: that thehydrolytic environment of a batch system can approx-imate that of a continuous-flow reactor, provided arelatively large volume fraction of inoculum is em-ployed, and that the hydrolysis rate in an anaerobicsystem fed autoclav ed AS solids is representativ e ofthe rate in a comparable system fed intact AS. Thislatter assumption really encompasses two others: thatautoclaved solids resemble nonviable solids which re-sult from more “natural” death/lysis processes, andthat the thermal destruction of AS enzymes via theautoclaving process-with loss of one possibly-signif-icant source of hydrolytic enzymes in AS fed diges-ters-does not adversely affect the estimation of kh.

The proposed digestion model (Fig. 2) assumes asimplistic, first-order dependence of hydrolysis rateupon nonviable, particulate BOD concentration [eq.(2)]. No explicit dependence on digester microorgan-ism concent ration is assumed. If production of hydro-lytic exoenzymes by anaerobic microorganisms-andorenzymatic activity following production-are regu-lated processes, then resulting enzymatic activity mightindeed be relatively independent of anaerobic microor-ganism concentration, influenced solely by perceivedneed (i.e., subst rate and/or product concentrations). Ifhydrolytic activity is thus regulated, it can be arguedthat autocl aved AS is a better choice of substrate thanintact AS for use in batch experiments.

Some batch experiments were performed using in-tact AS. Estimates of kh obtained using numerical so-lution techniques appear unrealistically high.8 It isthought that the pulse of A S enzymes released whenintact AS is batch-fed to an anaerobic environmentmay elevate hydrolytic activity to artificial levels. Ina continuous-flow system, o n th e ot her hand, the rel-atively slow steady influx of these AS enzymes maymerely decrease the need of native anaerobic bacteriato produce exoenzymes in order to keep pace with the

pressures of outflow and natural enzyme destruc-tion/consumption. In essence, the natural regulatorymechanism may be capa ble of incorporating the intactAS contribut ion to e nzymatic activity in continuous-flow systems, but is likely overwhelmed in batch-fedsystems.

Despite obvious concerns, but considering all theabove arguments, we decided to employ autoclavedAS solids as substrate in batch hydrolysis assays. Thesimplistic first-order form of the hydrolysis model was

tested by utilization of differing amounts of anaerobicseed in the studies.

A summary of the results from the batch st udies withautoclaved AS solids is given in Table 1 The data werecorrected for methane producti on, microbial growth,and decay during batch anaerobic digestion, since theseaffect the particulate and soluble COD pools. In otherwords, new biomass produced at the expense of sol-uble COD had to be estimated and properly added to

the solubilized COD pool. The correction was basedon a COD conservation equation and the anaerobicdigestion process was viewed as a two-phase process(i.e. acidogenesis and methanogenesis).2 Detailed dataare given only for one sample B , in Table 11). Anapparent difference was observed in rate and ext ent ofsolubilization between the two samples incubated withdifferent amounts of seed (Bl and B 2 ) ,but only afterca. 4-5 days incubation. And, curiously, the B , sys-tems then exhibited greater hydrolytic activity thandid B 2 systems. The samples incubated without anyanaerobic seed B,) showed solubilization al most fromthe beginning of the incubation period and after ca . 7.5days incubation, methane was detected in the gaseou shead space of these bottles, indicating active meth-anogenesis. Although these bottles were not deliber-ately seeded with anaerobic inoculum, contaminationis assumed since preparation of substra te solids, mediatransfers, and oth er bottle preparations were effectedin a nonsterile environment. However, given the largevolumes of inoculum used in seeded sy stems, it is hardto imagine how contamination could have significantlyinfluenced results for B 1 nd B2 samples.

Table I. Influent particulate COD remaining during batch anaerobicdigestion of autoclaved sludge “solid” samples (mg/L).

00.511.522.53.54.55.5

7.58.512.513.518.522.524.530.5

274526502585244023302320223021552040

18301785

13951330

1370

32653055

2805

262025402490

2350

20201660

13501205

32652990

2735

265025502530

2480

22202040

18901790

a Values corrected for inoculum contribution.Subscripts indicate relative amounts of anaerobic seed used:

Bo = 0%; B , = 22.2%; and B , = 44.4% (v/v).

1526 BIOTECHNOLOGY AND BIOENGINEERING, VOL.28, OCTOBER 1986


9/12

Table 11.in mg CODIL; seed-blank values subtracted).

Incubation Sum of soluble Volatile acids Biomass formed“

Measured and calculated parameters for autoclaved sludge solids sample B , during batch anaerobic digestion (all parameters

time Measured Cumulative and cumulative Corrected(days ) soluble COD methane COD methane COD Acetic propionic sum Xi? xb Sum “soluble” COD‘

0 50 0 50 15 15 30 0 0 0 500.5 140 35 175 80 40 120 30 5 35 2101.5 290 85 375 160 110 270 80 5 85 4602.5 265 255 520 140 130 270 115 15 130 650

3.5 140 440 580 50 95 145 125 25 150 7304.5 35 580 615 10 10 20 125 35 160 7757.5 20 715 735 10 5 15 135 40 175 910

13.5 < 5 1020 1020 < 5b < b 165 60 225 124518.5 10 1335 1345 < 5 < 5 190 75 265 161024.5 < 5 1635 1635 < 5 1 5 205 80 285 192030.5 10 1740 1750 < 5 < 5 230 80 310 2060

a Xi? and XB, are total acidogenic and methanogenic biomasses formed respectively (see ref. 2 for details).

a Sum of measured soluble COD, cumulative methane COD and total biomass formed.The lower detection limit of individual volatile acids was ca. 5 mg/L.

A second ba tch experiment was performed with au-

toclaved A S solids, with results virtually identical tothe first experime nt. Th e divergenc e in activities ofB1and B2 syste ms afte r the first 4-5 da ys of incubationremains unexplained.

Solubilization during the first few da ys of incubationwas fou nd to fit the assum ed m odel of eq. (2) very well.Naturally, we decided to base kh est imates on theseinitial data, rationalizing thaterrors in all those “cor-rections” required to adjust obs erved solubilization inorde r to estimate “tru e” solubilization may be the ex-planation for an oma lous results obtained a s incubationproceeded. Th e correct ions are less important near thebeginning of incubation.

T h e B l system s showe d “ultimate” CO D solubili-zations averaging 63.1 at 30 days incubation. Thiscompares reasonably well with ultimate digestibilitiesof 69.5% earlier rep orted for autoclavedA S solids in-cubated for 85 days.2 Note that the d ata of Table I1indicate that solubilization equa tes with degradability,since practically all soluble COD is converted tomethane.

With 63.1 as an estimate of the total, ultimatelysolubilizable frac tion of initially fed CO D, th e remain-ing solubilizable praticulate BOD F) as est imatedfor both B , and B2 system s using cu mu lative solubili-zation vs. t ime data. Upon integration, eq. (2) gives:

(24)

where Fo is the maximum solubilizable particulate COD(g/L). Th us, the hydrolysis rate coefficient( k h )can beestimated-in the cas e of auto clave d sludge solids-from the slope value of the straight l ine obtained byplotting In (FIFO) s. t ime.

Figure 4 show s how thekh was est imated for sample

B 1 via eq. (24). A kh value of 0.16 day-’ was obtained.

Likewise, the B2 sample data gave kh = 0 .14 day- ’R2 = 0.92). For all practical purpose s, an ave ragekh

value of 0.15 day- I is proposed.Th e observat ion thatkh appe ars relatively indepen-

dent of anaerobic microorganism concentration sup-ports i ts omission from the hydrolysis model. Thegoodnes s of fit between eq. (2) and the initially ob tainedsolubilization d ata supp orts th e specific fo rm (i.e. first-orde r assum ption) of the model.

Questions remain con cerning the extrap olation ofkhvalues measured in batch systems to application incontinuous-flow systems. Care was taken to ensurethat abiotic param eters (e.g., pH , alkalinity, re dox po-tential, e tc.) in the serum bottle assa ys we re close, ifnot identical, to values observed in the continuous-flow digesters also employed in this research. Bioticpara me ters, though, a re difficult to quantifyor control.Applicability of kh values so-obtained is evaluated inthe next section.

AUTOCUMD SLUDGE SOLIDS(81

kh 0.16 day -’ I

1.50.0 0.5 1.0 1.5 2.0 2 5 3.0

TIME.Days

Figure 4.sludge solids (batch experiment, sample B , ) .

Hydrolysis rate coefficient ( kh ) valuation for autoclaved

PAVLOSTATHIS AND GOSSElT: ANAEROBIC DIGESTION OF SLUDGE 1527


10/12

Table 111.(continuous-flow digestion).

Summ ary of model parameters with typical values used in this study

Values for

Parameter

Influent CO D concentration [COD,,(g/L)JUltimate digestibility[ fraction)]Net biodegradable fraction of active biomassUd)Cell soluble degradable COD immediately

released [ y (fraction of total degradable CO D)]AS cell death rate coefficient[kd (day- ' ) ]Hydrolysis rate coefficient[ k , (da y- ' )IDecay coefficient for acid formers[ b A day- ' ) ]Yield coefficient for acid formers[ YA g COD

biomass/g CO D util ized)]Maximum specific substra te uti lization rate fo r

ac id formers [ kA(g COD utilized/g biomassC OD d ay - ' ) ]

Half-velocity coefficient for acidogenesis

Decay coefficient for methanogens[bB day- ' ) ]Yield coefficient for m ethanogens[ YB( g COD

biomass/g CO D util ized)]Maximum specific substra te util ization rate for

methanogens [kB g COD utilized/g biomassC OD d ay - ' ) ]

[K? (g COD/L)I

[K;' (g C O D W I

Half-velocity coefficient for methanogenesis

Intact AutoclavedA S sludge

14.8 14.950.558 0.7220.73 0.730.30 0.30

2.0

0. I5 0.150 10 0 10

0.20 0.20

8.0 8.0

0.045 0.045

0.015 0.0150.057 0.057

6.2 6.2

0.045 0.125

MODEL PREDICTIONS OF DIGESTERPERFORMANCE

A summary of the model parameter values is givenin Table I11 for both intact and autoclaved sludges. Thevalues for parameters such asfd, y, kh, and kd weremeasured directly in this study and are discussed inprevious section s of this article. Values for CODin ndD were presented previously.2 Values for bA and YAwere chosen based on results discussed elsewhere.*The values of kAand K$ were chosen to minimize thenonvolatile acid effluent degradable soluble COD basedon continuous-flow digestion data which showed thatthis component is neglible.2 The biokinetic coefficientsfor methanogens were chosen from literature values"(for bB and YE)or by fitting of acetate and propionatedata in this study' (for kB and K:).

Based on the above-presented parameter values,digester performance predictions were obtained. Forautoclaved AS (Fig. 5 ) , eqs. (13)-(20) were employed,with X$$ = 0; Po = 0.26 g COD/L (i.e ., influent mea-sured volatile acid COD); S = y D COD,, Po; andFo = 1 y)D CODin. For intact AS (Fig. 6), eqs.(12)-(20) were employed , with S = Fo = Po = 0. Thefit of the mode1 is quite good.

An additional performance data point was obtainedfor digest ers receiving intact AS. At the completion ofthe previously reported continuous-flow digestionstudies,2 the feed rate was increased to the digester

operated at the lowest @ P I G , decreasing retention timeto three days. Operation continued for 10 days, afterwhich its level of performance was noted. This datapoint is included in Figure 6.

DISCUSSION

The model adequately predicts digester performancefor intact sludge using the hydrolysis rate coefficientestimated by batch digestion of autoc laved sludge sol-

P 20L11

8 10n

AUTDCUMD SLUDGE50

AUTDCUMD SLUDGE

c330

z

P 20L11

MODEL PREOlCnONS

k -0.1 5 doy -'

8 10n

MODEL PREOlCnONS

0-0.722

k -0.1 5 doy -'

2

Figure 5. Continuous-flow digester performance, model predic-tions for autoclaved sludge (bars indicate95 confidence intervalson data) .

1528 BIOTECHNOLOGYAND BIOENGINEERING,VOL. 28, OCTOBER 1986


11/12

2 4 6 8 1 0 1 2SRT.Days

Figure 6 . Continuous-flow digester performance, model predic-tions for intact AS (bars indicate 95% confidence intervals on data).

ids, together with the ultimate digestibility data andother parameter values presented in Table 111.

A sensitivity analysis was performed in order toquantify the effect of each parameter on the digesterperformance predict ion. The resul ts are shown in Ta-ble IV. The “base-line’’ values are the same values

reported in Tab le 111. Fro m thes e results, it is obviousthat the ultimate digestibility has a major impact ondigester performance predict ions. Parameters such as

fd, y, k d . kh, bA, YA ,and YBhave less impact on themodel prediction. Th e rest of the param eters have al-most negligible effect on the model predictions. Theresults of the sensitivity analysis support ou r experi-mental approac h, which was to concen trate on inde-pendent measurem ent of important parameters , suchas D and kh, while being satisfied with liter ature valuesfor many others.

However, i f erroneous interpretat ions are to beavoided, the se results should be used with caution. All

that is shown in Table IV is the percen t change of the

Table IV.@ = 8 days).

Sensit ivity analysis of model parameters (Intact AS ;

Percent change in predictedBase-line digester perform ance withparameter 10% increase in parameter

Parameter value“ value( )

14.80.5580.730.302.00.150.100.208.00.0450.0150.0576.20.045

0.110.10.82.00.52.40.4

-1.50000.50.

-0.1

For parameter units, see Table111

model prediction (at @‘G = 8 days) for a 10% changein each param eter. Tw o points are noteworthy: all14parameters are interrelated, and therefore the percentchange in model prediction arounda “base-line’’ fora 10 change of one parameter dependson the level(value) of the other thirteen parameters, and all pa-rame ters are not e xpected to have equal uncertainties.

Based on the kd and kh values found in this studyfor intact A S , and o n the resu lts of the sensitivity ana l-

ysis (Table IV), we c an conclude that hydrolysis isamore kinetically limiting mechanism than death/lysis,with respect to convers ion of viableAS organisms intoavailable substr ate. Of course, there is uncertainty as-sociated with the kd value (2 day-’) reported in thiss tudy due to the technique used to m easure i t . Whatshould not be overlooked here is thatno matter theexact value of kd , these da ta suggest that i t is a largenumber compared with thekh value. Digester perform-ance becomes a very insensitive function ofk d

Part of the influent viableAS biomass may adjust tothe anaerobic environment (e.g., facultativeA S bac-teria) and become active acidogenic biomass. In thiscase, the acidogenic biomass is underes timated by thepresent m odel, andkd mea surem ents might be in error.Present ly, the above point cannot be ei ther proved ordisproved due t o lack of accura te techniques for dif-ferentiation and estimation of acidogenic, methano-genic, and viable AS bacterial population densities.How ever, previous a naerobic digestion studies’s20 haveshown that fastidious, nonmetha nogenic, obligate an-aerobic bacter ia are present in numbers one or twoorde rs of m agnitude gre ater than f acultative bacteria.On the oth er hand , mos t of the principal genera ofASbacter ia recorded in taxonom ic s tudies are found to bestrict aerobe s.21Thu s, the impo rtance of AS facultativebacteria as active anaerob ic digester acidogenic bac-teria seems to b e very minimal.

Th e superiority of the present model vis-a-vis mod-els which conside r methanogen esis ‘rate-limiting,”lies in the analytical prediction of the digester efflu-ent characteristics.As was discussed previously,2 theO’R ourk e model-formulated for raw primary sludgedigestion and base d largely o n lipids degradation-ig-nores effluent particulate BOD of other waste com-ponents (e.g. protein) and assumes complete hydrol-ysis of the influent degradable CO D for@ I G higherthan ca. 7 days. It works well for digestion of largely

lipid waste. In the case of AS digestion, ca. 99% ofthe total effluent CO D is particulate, showing that hy-drolysis is not com plete, even for0PIG higher than 25days. Particulate protein comprises between80 and90% of the total effluent degradable COD .

The present model represented by eq s.(131420) caneasily be adapted to situations where the digester in-fluent contains significant contributionsof nonbiolog-ical, degradable sources, such as in the digestion ofcombined municipal primary and waste activated

PAVLOSTATHIS AN D GO SS ET : ANAEROBIC DIGESTIONOF SLUDGE 1529


12/12

sludges. (Of course , the accuracy of the model in suchcases has not b een demonstrated.) In the simplest casewhere th e applicable hydrolysis coefficient for the non-biological BOD roughly equals that of the lysed, bio-logical solids, all that is necessary is the addition of afinite Fo value to eq. (14). If the hydrolysis coefficientsdiffer for biological and nonbiological solids, sep aratemathematical treatment of the two sludges is requireddown to the point of soluble COD production. From

that point onward , the presented model may be used,regardless of the soluble COD source. Additionally,however, it should be noted that the feed compositionmay influence the half-velocity coefficient for meth-anogenesis (K:); if significant lipid material is present,use of a greatly increased value of K: may be in order,to properly reflect the expected high effluent contri-butions from long-chain fatty acids.

In prediction of dynamic behavior the complex modelpresented in this article is perhaps necessary. How-ever, for many practical applications, it may be un-warranted. If desired, the model may be simplified,based on results presented here. Model predictionssuggest that death/lysis and acidogenesis mechanismsare sufficiently rapid that they may be neglected, atleast for retention times of practical interest. Doing soresults in essentially the model proposed by Gossettand Belser, but where the preliminary conversion stepof concern has been properly acknowledged as a hy-drolysis ste p, rather than a death/lysis step.

CONCLUSIONS

Based on the results of this stud y, the following con-clusions can be drawn. In the conversion of viable,

biological solids to available subs trate for the anaer-obic microflora, mechanisms such as death , lysis andhydrolysis play an important role. Results suggest thathydrolysis of degradab le, particulate, dead AS biomassis much slower than death or lysis. Therefore, hy-drolysis appe ars to be the rate-controlling step in thecase of anaerobic digestion of biological solids. As aresult, ca. 99 of the degradable, effluent COD is par-ticulate (mostly protein).

The death rate coefficient (kd)-estimated by use ofan oxygen uptake rate technique-of viable A S bio-mass under anaerobic conditions (2 per day) is morethan 16 times higher than the decay coefficient (bAS)

under aerobic starvation conditions (0.12 per day).An anaerob ic digestion model for biological sludgewas developed and eval uated . The four major steps inthis model are: viable cell death/lysis; hydrolysis ofparticulate dead biomass; acidogenesis; and methan-

ogenesis. A sensitivity analysis of the parameters in-volved in this model showed that the most importantparameter is the ultimate digestibility of the sludge,followed by other parameters such as those relating tohydrolysis and cell-soluble fraction. Overall, t he modelproved to be adequate for predicting the performanceof a laboratory-scale digester receiving a biological sol-ids feed. An extension of the model for use in casesof combined primary and waste-activated sludge ap-

pears feasible.This research was supported by the U.S . Environmental Pro-tection Agency through GrantNo. R 809500-01-0. This articlehas not been subjected to the Agency’s required peer andadministrative review and, therefore, does not necessarilyreflect the views of the Agency and no official endorsementshould be inferred.

References

I J. M. Gossett and R. L. Belser, J . Environ. Eng. Div. ASCE,108, 1101 (1982).

2. S. G. Pavlostathis, “ A Kinetic Model for Anaerobic Digestionof W aste Activated Sludge,” Ph.D. thesis, Cornell University,I thaca , NY, 1985.

3. T. D. Brock, Biology of Microorganisms, 3rd. ed. (Prentice-Hall, Englewood Cliffs, NJ, 1979).

4. A. W. Law rence and P. L. McCarty, J . Sanit. Eng. Div. ASC E,96, 757 (1970).

5. J. A. E as tman and J. F. Ferguson, J . Water Pol lu t . ControlFed. , 53, 352 (1981).

6 . P. L. McCarty, Int. J Air W ater Pollut. ,9, 621 (1965).7. S. Ghosh , Biotechnol. Bioeng. Sym p..11 301 (1981).8. S. G. Pavlostathis and J. M. Gossett , unpublished.9. J . R. Pos tga te and J. R. Hunter, J . Gen. Microbiol. ,29, 233

10. R. A. Laddaga and R. A. MacLeod,Can . J . Microbiol. ,28,414

11. K. M. Sorrells, R. A. Cowman, and H. E. Swaisgood, J . Bac-

12. K. Ohmiya and Y . Sato , Agric . Biolog. C h e m . ,42, 7 (1978).13. J . L . Jarnagin and D. W . Luchs inger,Stain Technol., 55 , 253

14. J . T. Kvach and J. R. Veras, Int. J. Leprosy, 50, 183 (1982).15. American Public Health Association,Standard Methods for the

Examination of Water and Wastewater, 15th ed., (AmericanPublic Health Association, Washington, DC,1980).

16. D. R. Christensen and P. L. McCarty,J Water Pollut. ControlFed. , 147, 2652 (1975).

17. J . T. O’Rourke , “Kinetics of Anaerobic Treatment at ReducedTemperatures,” Ph.D. thesis, Stanford University, Stanford,C A , 1968.

18. D . F. Toerien, M. L. Sieber t , and W. H. J. Hattingh, WaterR e s . , 1, 497 (1967).

19. P. G. Thiel, D. F. Toerien, W . H. J. Hattingh, J. P. Kotze , andM. L. Siebert , Water Res . , 2, 391 (1968).20. R . A. Mah and C. Sussman,Appl. Microbiol. ,16, 358 (1968).21. E. B. Pike, “Aerobic Bacteria,” inEcological Aspectsof Used-

Water Treatment C. R. C urds and H. A. Hawkes , Eds . (Aca-demic , London, 1975), Vol. 1.

( 1962).

(1982).

teriol. , 112, 474 (1972).

( 1980).

1530 BIOTECHNOLOGY AND BIOENGINEERING,VOL. 28, OCTOBER 1986

pavlostathis, gossett - 1986 - a kinetic model for anaerobic digestion of biological...

Documents