a kinetic model for anaerobic digestion of biological sludge

A Kinetic Model for Anaerobic Digestion of Biological Sludge

Spyros G. Pavlostathis and James M. Gossett School of Civil and Environmental Engineering, Cornell University, lthaca, New York 14853

Accepted for publication November 25, 1985

The principal objective of this study was the development and evaluation of a comprehensive kinetic model capable of predicting digester performance when fed biological sludge. Preliminary conversion mechanisms such as cell death, lysis, and hydrolysis responsible for rendering viable biological sludge organisms to available substrate were studied in depth. The results of this study indicate that hydrolysis of the dead, particulate biomass-primarily consisting of protein-is the slowest step, and therefore kinetically controls the overall process of anaerobic digestion of biological sludge. A kinetic model was developed which could accurately describe digester performance and predict effluent quality.

INTRODUCTION

Previous studies’,* dealing with the anaerobic digestion of activated sludge (AS) have shown that kinetic models which assume that methanogenesis is the sole rate-limiting step are inapplicable in the case of biological sludges. Anaerobic degradation of AS requires that the potentially-degradable portion of viable AS organisms must first be converted to available substrate by preliminary conversion mechanisms such as cell death, lysis, and/or hydrolysis. It was shown2 that for solids retention times (@‘IG) values of practical interest, acidogenesis and methanogenesis are not process-controlling steps in digesters receiving biological sludges. The predominant degradable constituent in the effluents of such digesters is particulate protein, indicating that hydrolysis and/or other preliminary conversion mechanism(s) is (are) Limiting from the point of view of substrate availability.

Which of the postulated, preliminary-conversion mechanisms is most kinetically limiting can only be inferred from these previous investigations. Their direct study was not undertaken. Examination of continuous-flow anaerobic digestion data2 from digesters which were fed autoclaved sludge showed that a significant preliminary barrier remains, even after autoclaving. Since autoclaving induces cell death and lysis, these data suggest that the most kinetically limiting of

the possible preliminary conversion mechanisms may be hydrolysis and not cell death or lysis.

The purpose of this article is to examine directly the preliminary conversion step in detail, considering mechanisms such as cell death, lysis and hydrolysis, so as to evaluate their relative importance in the anaerobic digestion of biological sludges. This is done in the context of a conceptual model for biological sludge digestion, which is here presented and evaluated.

MODEL DEVELOPMENT

Conceptual Model of Biological Sludge Digestion

A conceptual representation of the processes involved in the anaerobic digestion of AS is shown in Figure 1. Gossett and Belser’ demonstrated that the biodegradable fraction of AS consists almost exclu- sively of the biodegradable portion of viable, activated sludge organisms. The biodegradable portion of viable AS cells may be thought of as comprising two substrate pools: one particulate and one soluble. Upon death, the cell membrane ruptures (i.e. lysis occurs), and part of the intracellular, soluble, degradable COD (i.e. soluble BOD) (presumably the lowest molecular weight components) is immediately released. Then, the remaining intracellular soluble BOD pool of a dead cell changes with time because of soluble BOD production via intraceliular hydrolysis (IH) and loss of soluble BOD due to diffusion. Much of the IH may be due to remaining, native intracellular enzymes, uncontrolled upon cell death. Contributions to IH from exoenzymes produced by the anaerobic microflora may also be sup- posed. The dead cell particulate BOD is additionally subject to extracellular hydrolysis (EH), presumed to be primarily induced by the active digester microorganisms. The extracellular soluble BOD pool is subject to decrease because of uptake by the digester microflora, especially by the acid-forming bacteria. From that point on the model follows the classical two-phase

Biotechnology and Bioengineering, Vol. XXVIII, Pp. 1519-1530 (1986) 0 1986 John Wiley & Sons, Inc. CCC 0006-3592/86/101519-12$04.00

EXTRACELLULAR

ACIW~ESIS

M * . co,

k,

Figure 1. Conceptual model for anaerobic digestion of biological solids (I.H. is intracellular hydrolysis; E.H. is extracellular hydrolysis; kd is the death rate coefficient; kh, and kh, are the intra- and extracellular hydrolysis rate coefficients; k , is the soluble BOD diffusion rate coefficient; and y is the cell soluble BOD immediately released, fraction of total BOD).

Dum/LysIs

anaerobic digestion scheme: acidogenesis and methanogenesis.

Validation of the above-outlined model requires the direct estimation of all constants and parameters involved. Due to the complexity of the system, difficul- ties are encountered in developing analytical techniques to accomplish this without simplification. For example, note that the conceptual model equates death and lysis. From the point of view of substrate availability, cell lysis is more important than death. How- ever, lysis is difficult to assay, compared with the quan- tification of death. Certainly, all cells which lyse are dead. 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 measure cell lysis rate, but they were not successful, as is discussed in a later section. On the other hand, it is believed that once the cell is dead, the permeability barrier provided by the plasma membrane is rapidly destroyed, and most of the soluble cell contents (presumably the lowest molecular weight components) leak out.3 Thus, from the point of view of substrate availability, we assume here that there is practically no lag between death and lysis. Hence, we refer to both as a singular death/lysis mechanism.

Upon cell death/lysis a good portion of the intracellular soluble BOD is believed to be released almost immediately. The remaining intracellular soluble BOD- originally present in the viable cell and also produced via intracellular hydrolysis of particulate BOD following cell death-must diffuse out of the dead cell if the

oRocyys ,

k h

cell membrane, although ruptured, still provides a barrier. Whether or not the damaged membrane provides a significant barrier to release depends on the relative size of the membrane perforations compared with the size of the material leaking out. Evidence is presented in a later section which suggests that diffusion from within 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 may be collectively referred to as “hydrolysis.” Accord- ingly, the conceptual model presented in Figure 1 can be simplified as is shown in Figure 2.

SUBSTRATE REQUIRING HYDROLYSIS

Equations

The following assumptions and premises were considered in the derivation of model equations: 1) all variables are expressed on a COD unit basis; in fact, all except microorganism concentrations are expressed as degradable COD; 2) the inherent, net biodegradable fraction (fd) of viable AS organisms and anaerobic microflora is the same; 3) we do not differentiate between cell death and lysis, but we assume that lysis occurs soon after death; 4) upon death/lysis, all soluble intracellular material is released as “soluble” substrate, and it is taken as a constant fraction of the total cell degradable COD (i.e., diffusion of soluble material out of the damaged cell is rapid-this assumption is jus- tified later); and 5 ) facultative AS bacteria which may ultimately survive are not considered as part of the acid-phase, active biomass.

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

- -kdXfs r d = p - dXfs

dt

1520 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 28, OCTOBER 1986

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

The hydrolysis rate is assumed to be a first-order reaction with respect to the concentration of degradable particulate COD:

where F is the degradable, particulate (nonviable) COD concentration (g/L) and kh is the hydrolysis rate coefficient (day-'). In terms of the complex conceptual model (Fig. 1)-and given our assumption that there is no diffusional limitation for transport of solubilized material out of the damaged cell-then this kh is really the sum of intracellular and extracellular hydrolysis rate coefficients.

The microbial growth rate and substrate utilization rate for any particular group of digester bacteria are based on the Monod equation4:

d X YkSX r x = - - - ~ - bX

d t K , + S

kSX K , + S

-~ - d S dt r " = - -

(3)

(4)

where X is the active microorganism concentration (g/L); S is the substrate concentration (g/L); Y is the microbial growth yield coefficient (g biomass produced/g substrate utilized); k is the maximum specific substrate utilization rate (day- '); K , is the half-velocity coefficient (g/L); and b is the microorganism decay coefficient (day - I ) .

For the case of a completely mixed, continuous-flow reactor without recycle, at steady-state, the following mass balances can be derived (definitions of terms follow):

Mass Balance on Degradable Portion of Viable AS Microorganisms (fdXts)

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

Mass Balance on Nonviable Substrate Requiring Hydrolysis (F)

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

Mass Balance on Soluble Substrate for Acid Phase (9')

Q(SS - SA) + VkhF + VYfdk&fiS kASAXi

Kf + SA = 0 (7) -

Mass Balance on Degradable Portion of Active Acidogenic Biomass (fdX$)

erAX20 - X 3 YAkASAX$ + vfd[ K:' c SA - b A X t ] = 0 (8)

Mass Balance on Products

We may define (as did Eastman and Ferguson5) a quantity, P , which is the concentration of volatile acids formed by acidogenic bacteria, plus any influent volatile acids. Parameter P differs from the actual, observed concentration of volatile acids remaining, due to their consumption by methanogenic bacteria. Thus, P is the sum of observed volatile acids, plus methane formed, plus methanogenic biomass formed, all in COD units. The mass balance on P then becomes:

VkASAX2 - VYAkASAX2 Kf + SA Kf + SA Q(Po - PI +

where Q is the hydraulic flow rate (L/day); V is the reactor volume (L); X;p,S is the influent, viable AS biomass COD concentration (g/L); Fo is the influent degradable particulate (nonviable) COD concentration (g/L); y is the fraction of total degradable COD in X,"' released as "soluble" COD upon deathilysis; SS is the influent soluble substrate COD to the reactor (g/L); X i o is the influent active acidogenic microorganism concentration (g COD/L); Po is the influent product concentration (g COD/L); and fd is the net biodegradable fraction of active biomass. (Note that superscript AS refers to activated sludge and superscript A refers to the acid phase).

The last mass balance was derived based on the following reasoning: COD is conserved in an anaerobic digestion system and the utilized substrate COD is either incorporated into cellular material or converted to products for microbial energy. Therefore, the difference between the substrate utilized and the net cellular COD 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 retention time for systems without biomass recycle) ap-

PAVLOSTATHIS AND GOSSETT: ANAEROBIC DIGESTION OF SLUDGE 1521

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

which substituted into Equation (10) gives:

fAX$rjj - XCS) + (Fa - F ) + ( S t - SA) + xto - X:[1 + (1 -fd)Pf9] + (Po - P ) = 0 (IOa)

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

D COD,, f d

X$rjj =

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

Model Equations

The model equations are as follows:

-X:[1 + (1 - f d ) b A O ] (17)

In the last phase, i.e. methanogenesis, we make use of the Monod model for substrate and biomass concentrations (Note that superscript B refers to methanogenesis). Ignoring X:a,

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

bB is the decay coefficient for methanogens (day- I);

YB is the yield coefficient for methanogens (g biomass COD/g substrate COD utilized); kB is the maximum specific substrate utilization rate for methanogens (g

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

substrate COD/g biomass COD day-’); Xf is the total methanogenic biomass (g COD/L); (Sg)effec is the ef- fective influent volatile acid COD to the methane phase (g/L); and the rest of the symbols are as defined in previous sections.

The connection between the acid phase and methane phase of the present model is made via the product formed in the former phase, which is essentially the “influent” to the last phase, i.e., = P. Since the product equation includes a correction for acidogenic biomass produced in the system, the only correction of the processed COD for the digester performance 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 determine the kinetic constants involved. However, the biggest analytical difficulty faced in the present study, which was the inability to differentiate (and measure) AS biomass from the acidogenic and methanogenic biomass produced in the digester, made such a deter- mination impossible. To overcome these problems, a number of batch experiments were conducted, to independently provide important constants.

PROGRAM OF STUDY

Skeptics might note that there are sufficient kinetic parameters in the complex model depicted in Figure 2, such that one could-through “convenient” selec- tion of parameter values-fit almost any performance data! Legitimate evaluation of the model requires the independent measurement of parameters employed in it. However, it is not necessary to do this for all parameters-only the important ones. For example, it will later be shown through a sort of sensitivity analysis that the important, limiting steps are those relating to preliminary conversion of substrate to available, soluble form, and the later conversion of acetate and propionate to methane. Acidogenesis is relatively rapid. This is to be expected, based upon previous Thus, it makes little sense to do anything more than to expropriate kinetic parameters for acidogenesis from literature values. [The one exception was the yield coefficient for the acidogenic bacteria ( YA), which was measured, though with only modest s ~ c c e s s . ~ ]

Hence, many phases of study described in subsequent sections were undertaken with the purpose of independently measuring sludge and kinetic parameters of importance to the proposed model. Some ex- amples: the deathhysis rates of viable AS organisms in anaerobic environments were measured in continuous flow systems, using an oxygen uptake technique;


hydrolysis rates were inferred from solubilization studies employing batch-fed digesters which received differing amounts of active, anaerobic seed. Measure- ments of other important model parameter values (e.g., ultimate biodegradability of autoclaved and intact AS; half-velocity coefficients for acetate and propionate utilization) were presented previously.2 In a final analysis phase of study, the various independently measured parameter values were employed with the simplified version of the model depicted in Figure 2, allowing comparison of observed, continuous-flow digestion performances with model predictions. For this comparison, digester performance data presented elsewhere were employed.*

MATERIALS AND METHODS

Reactor configurations and modes of operation for the laboratory generation of activated sludge and its subsequent anaerobic digestion were described previously.2 The AS was produced in a 150-L fill-and-draw reactor fed with a soluble synthetic waste. The resulting sludge volatile suspended solids were thus en- tirely of biological origin. The digesters were con- structed from 2-L Pyrex bottles fitted with holes and rubber stoppers to allow for feeding, withdrawal of digested sludge, mixing of the digester contents (me- chanically), sampling of the mixed liquor and measurement of the gases. The digesters were fed on a once-per-hour basis via a timer, a series of solenoid valves and two metering pumps with variable-speed drives. Digested sludge was withdrawn once or twice a day via a sampling port.

Batch Digestion Experiments

A variation of the serum bottle technique outlined earlier2 was used to investigate the hydrolysis (actually solubilization) of AS in anaerobic environments. In this case, seed and media were transferred anaerobically to the serum bottles-already containing the substrate-separately in order to permit the use of various amounts of seed. Autoclaved AS solids were employed as substrate. Autoclaving was chosen as a cell disrup- tion technique.2 It was thought that autoclaved AS solids would represent cell particulate matter left after cell death and lysis and requiring further hydrolysis (see the Hydrolysis Rate Coefficient section). All bottles received the same amount of defined media (20 mL) and the same amount of substrate (15 mL from a stock suspension of ca. 20 g COD/L). The amounts of seed used were 0, 20, and 40 mL of digester mixed liquor receiving intact AS as feed. These samples are later referred to as Bo, B , , and B2, respectively. Twelve replicates were prepared; two were opened immediately after filling with media and/or seed (for assay of initial conditions and substrate measurements), and the

rest were opened one-by-one each time that a measurement was effected. The incubation time was one month and the room temperature was 35 * 1°C. The bottles were manually shaken twice per day.

On a predetermined schedule, the gas productions were measured in all replicates, and then one bottle from each group was opened and the following anal- yses were performed on its contents: pH, soluble COD, and volatile acids. The gas composition was also measured. The particulate substrate COD was accurately measured only at the beginning of the experiment. This is the difference between total and soluble COD of the composite sample (i.e., substrate + seed + media) after subtracting seed and media blanks.

The autoclaved AS “solids” fraction was prepared using the following technique: settled AS was autoclaved (121”C, 30 min), cooled, then centrifuged (104g for 1 h), and the centrate was wasted. The pellet was resuspended in distilled water and centrifuged again (lo4 g for 30 min). The last step was repeated one more time. Finally, the centrate was wasted and the pellet was suspended in distilled water, yielding the “solid” sample.

Cell Death/Lysis Rate(s)

An oxygen uptake rate (OUR) technique was used for estimation of the death rate constant (kd) of AS microorganisms fed to continuous flow digesters operated at different @IG. The decrease in OUR-measured in preaerated (30 min) digester mixed liquor under substrate saturation conditions (ca. 300 mg glucose/L)-with incubation time (i.e. digester retention time) was assumed to represent microbial death.

The use of this OUR technique for kd estimation is certainly questionable: The OUR is more a measure of biological activity, and activity and viability are not necessarily synonyms. It is conceivable that the OUR of a biological community may decrease without an equal decrease in viability (i.e., percent of viable organisms of the total). For example, in the case under discussion, facultative bacteria originally in the AS, now growing in an anaerobic environment, may not exert high OUR immediately upon reintroduction to the aerobic environment, although their viability may not have been decreased. Another concern about using the OUR technique with anaerobic media is the strictly chemical oxygen consumption that reduced substances may exert under aerobic conditions. In order to assay the significance of this source of oxygen consumption, ethanol (95%) was added to an aliquot of digester mixed liquor, left to stand for 15 min, then aerated for 15 min prior to measurement of OUR. The OUR was practically zero over 25 min of measurement. This led us to conclude that, although there is a chemical oxygen consumption exerted by various reduced substances in the digester mixed liquor, this rate is almost negli-

PAVLOSTATHIS AND GOSSElT: ANAEROBIC DIGESTION OF SLUDGE 1523

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

Other direct viability measurement techniques (e.g. plate counts) were judged inappropriate primarily because of the inability to completely disperse an activated sludge floc without killing the bacteria. Plate counts are appropriate for use where viable numbers range over orders of magnitude. However, their accuracy is too limited to be of use in our studies. Thus, despite its limitations, the OUR technique was selected for monitoring relative changes in AS viability.

Initially, we intended to distinguish death from lysis, and to separately determine death and lysis rates for AS organisms in anaerobic environments. As a mechanism for converting membrane-enclosed, potential substrate into available substrate, cell lysis is perhaps more important than cell death. Attempts were made to directly monitor cell lysis via ultraviolet (UV) absorbance (at 260 nm) of soluble material produced during batch anaerobic incubation of unseeded, intact AS samples. Unfortunately, the absorbance at 260 nm (corresponding to release of intracellular nucleic acid mate~-ial~. '~) was masked by absorbance at 275 nm, probably due to amino acid production via protein hydrolysis. ",'' The fast turnover rate of soluble materials released upon cell lysis also limits the utility of this technique.

Unsuccessful attempts were also made to distinguish death from lysis using microscopic differentiation of three categories of bacterial cells: viable, dead-intact, and dead-damaged. Fluorescein diacetate (FDA) and ethidium bromide (EB) stains were combined into a single a ~ s a y . ' ~ . ' ~ Results were negative, in that viable cells did not fluoresce when stained with FDA, and all cells, regardless of viability, stained positively with EB. The failure of the staining procedure might be due to the nature of the particular microorganisms present in our system. At the time, the dominant organism form appeared to be that of a well-dispersed tetrad resem- bling Micrococcus spp.

Because of the inability to separately measure death and cell lysis rates, and because a good body of evidence3 supports the notion of simultaneous cell death and lysis, the lysis rate is equated to the cell death rate in our model. Therefore, all limitations applied to our measurement of the death rate constant-estimated by use of the OUR technique-apply to its use as a combined deathhysis rate coefficient as well. For all practical purposes, this rate coefficient is hereafter called the death/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 30 min, followed by filtration through 0.45-pm membrane filters); dissolved oxygen (membrane electrode method, Sec. 421 F); and gas composition [gas chromatographic method, Sec. 511B, with a silica-gel column (50°C) in series with a molecular sieve column (25"C)I. Gas production measurements and volatile acids were assayed as described elsewhere.'

EVALUATION OF MODEL PARAMETERS

AS Organism Decay Coefficient (PSI The average decay coefficient applicable to the aero-

bic, activated sludge organisms (bAS) was measured using an OUR technique' under starvation conditions (i.e., the AS mixed liquor was aerated over 17 days without any exogenous substrate addition). A plot of the logarithmic (base e) OUR vs. time resulted in a straight line with a slope, bAS = 0.12 per day (R2 =

0.997). The bAS value is well within the range of decay coefficients found for mixed-culture aerobic systems: 0.10-0.20 per day.4

AS Viable Cell Degradable Fraction (f,)

Gossett and Belser' expropriated the following equation from Christensen and McCartyt6 as an expression for the AS biodegradability (D), when the AS is gen- erated from a soluble feed:

This equation can be solved for fd:

D(l + bASeS) fd = 1 + ( D b A S e S )

The applicable microorganism decay coefficient (bAS) was measured and found to be ca. 0.12 per day (see the previous section). The activated sludge reactor solids retention time (eS) was 10 days, and the ultimate AS biodegradability (D) ranged 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 it themselves. Gossett and Belser' found an fd value of 0.68 for a similar AS. A range offd from 0.65 to 0.80 is found in the literature (cited by Gossett and Belser'). The fd values estimated in the present study are well within this range. Henceforth, we employed our average value of fd = 0.73 which corresponds to the observed, average, ultimate AS biodegradability of 55.8%, based on gas data.2


Death/Lysis Rate Coefficient (&J

The kd was estimated by use of an OUR technique. The limitations of this technique were discussed in a previous section. For the case of a completely mixed, continuous-flow reactor without recycle, the surviving fraction of viable AS organisms-assuming a first- order death rate [eq. (])]-is given by eq. (23):

1 (23)

Assuming that there is a direct proportionality between X t S and OUR, eq. (23) becomes equivalent to:

- - - XtS x;; 1 + k d p

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

This technique was applied to the mixed liquors from the continuous-flow digesters receiving intact AS and the results are shown in Figure 3. The kd value was found to be equal to 2 per day by use of eq. (23a).

Cell Soluble BOD Pool and Diffusional Considerations

The conceptual model (Fig. 1) accounts for intracellular soluble BOD that is immediately released upon cell lysis, followed by continued release of additional intracellular solubilized material under possible diffusional limitations. However, in the simplified model (Fig. 2), it has been assumed that there is no significant, diffusional limitation. Two questions need to be ad- dressed: 1 ) how much of the intracellular soluble BOD is immediately released upon cell lysis and 2) is there any diffusional limitation that controls the rate of release of remaining soluble BOD or soluble BOD formed via intracellular hydrolysis?

Experimentally, it seems almost impossible to quan-

PREDtCTlON SHOWN FOR:

OUR,-^ rnpi-’min-’

k,-2 day-‘

E

5 0 2 j \ T

0 1w 0 2 4 6 8 1 0

SRT,Doys

Figure 3. Estimation of deathilysis rate coefficient (kd) for intact AS fed to continuous-flow digesters by use of oxygen uptake rate technique (bars indicate 95% confidence intervals).

tify both the intracellular soluble BOD and its rate of release under “natural” conditions, i.e., under conditions prevailing in a digester. In search of an estimation, we followed an indirect approach: it was assumed that autoclaved cells resemble dead, damaged cells that got that way “naturally,” and that the quantity of soluble matter eventually released from autoclaved cells held in a sterile environment is a good measure of the quantity of soluble matter in an intact cell that would be capable, eventually, of permeating a damaged membrane without requiring further hydrolysis. These are, admittedly, rather tenuous assumptions. However, microscopic examination of autoclaved cells shows them to be essentially identical to viable cells, with intact cell walls. Heat may, of course, damage the membrane far more than “normal” death/lysis, but the literature suggests that upon death, the life of a microbial membrane is relatively short.3 Heat may also alter the relative proportions of “particulate” and “soluble” materials within the cell, as well as the cellular chemical composition. But finding no other path available, the above assumptions were made of necessity.

Intact AS was placed in glass dilution bottles closed with heat-resistant screw-caps and autoclaved (121”C, 30 min). Following sterilization, the bottles were equi- librated to 35 t 1°C temperature by immersing them in a water bath. Finally, the bottles were placed in a controlled temperature room (35 ? 1°C). At time intervals, one bottle was opened and its soluble fraction was separated by centrifugationlfiltration. COD measurements and UV scans were taken of the autoclaved sludge soluble fractions. During ca. 5 days following sterilization, the UV scan showed no change, and nei- ther did the soluble COD. For example, immediately after sterilization, the soluble COD was 1180 mg/L, with a coefficient of variation (i.e. lOOS/2?l equal to 1%; the total intact (i.e., before autoclaving) AS COD was 4230 mg/L with 40 mg/L as soluble COD. This represents ca. 28% solubilization. Subsequent soluble COD measurements showed an average of 1200 mg/L with a coefficient of variation equal to 5%.

From the above results, along with knowledge of the intrinsic biodegradabilities of soluble and solid fractions (90.7 and 70. I%, respectively*), we conclude that the intracellular soluble BOD is equal to 30% of the total cell BOD, and that it is all immediately released upon cell lysis. Thus, the diffusion of soluble intracellular BOD was neglected, resulting in the simplified model (Fig. 2).

Hydrolysis Rate Coefficient (khl

The hydrolysis rate coefficient was estimated from batch studies in which autoclaved AS solids were in- oculated with differing amounts of an anaerobic culture. Autoclaved AS solids were employed as substrate

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

because elimination of the cell membrane barrier via autoclaving allows kh values to be easily inferred from observations of solubilization rate (after appropriate corrections detailed below). With use of intact AS as substrate, solubilization rate is influenced by both lysis and hydrolysis kinetics, necessitating the numerical solution of three simultaneous, differential equations in order to estimate kh.8

Use of batch reactors fed autoclaved AS solids requires acceptance of at least two assumptions: that the hydrolytic environment of a batch system can approx- imate that of a continuous-flow reactor, provided a relatively large volume fraction of inoculum is employed, and that the hydrolysis rate in an anaerobic system fed autoclaved AS solids is representative of the rate in a comparable system fed intact AS. This latter assumption really encompasses two others: that autoclaved solids resemble nonviable solids which result from more “natural” death/lysis processes, and that the thermal destruction of AS enzymes via the autoclaving process-with loss of one possibly-significant source of hydrolytic enzymes in AS fed digesters-does not adversely affect the estimation of kh.

The proposed digestion model (Fig. 2) assumes a simplistic, first-order dependence of hydrolysis rate upon nonviable, particulate BOD concentration [eq. (2)]. No explicit dependence on digester microorganism concentration is assumed. If production of hydrolytic exoenzymes by anaerobic microorganisms-andor enzymatic activity following production-are regulated processes, then resulting enzymatic activity might indeed be relatively independent of anaerobic microorganism concentration, influenced solely by perceived need (i.e., substrate and/or product concentrations). If hydrolytic activity is thus regulated, it can be argued that autoclaved AS is a better choice of substrate than intact AS for use in batch experiments.

Some batch experiments were performed using intact AS. Estimates of kh obtained using numerical solution techniques appear unrealistically high.8 It is thought that the pulse of AS enzymes released when intact AS is batch-fed to an anaerobic environment may elevate hydrolytic activity to artificial levels. In a continuous-flow system, on the other hand, the relatively slow steady influx of these AS enzymes may merely decrease the need of native anaerobic bacteria to produce exoenzymes in order to keep pace with the pressures of outflow and natural enzyme destruction/consumption. In essence, the natural regulatory mechanism may be capable of incorporating the intact AS contribution to enzymatic activity in continuous- flow systems, but is likely overwhelmed in batch-fed systems.

Despite obvious concerns, but considering all the above arguments, we decided to employ autoclaved AS solids as substrate in batch hydrolysis assays. The simplistic first-order form of the hydrolysis model was

tested by utilization of differing amounts of anaerobic seed in the studies.

A summary of the results from the batch studies with autoclaved AS solids is given in Table 1 . The data were corrected for methane production, microbial growth, and decay during batch anaerobic digestion, since these affect the particulate and soluble COD pools. In other words, new biomass produced at the expense of soluble COD had to be estimated and properly added to the solubilized COD pool. The correction was based on a COD conservation equation and the anaerobic digestion process was viewed as a two-phase process (i.e. acidogenesis and methanogenesis).2 Detailed data are given only for one sample (B , in Table 11). An apparent difference was observed in rate and extent of solubilization between the two samples incubated with different amounts of seed (Bl and B2), but only after ca. 4-5 days incubation. And, curiously, the B , systems then exhibited greater hydrolytic activity than did B2 systems. The samples incubated without any anaerobic seed (B,) showed solubilization almost from the beginning of the incubation period and after ca. 7.5 days incubation, methane was detected in the gaseous head space of these bottles, indicating active methanogenesis. Although these bottles were not deliber- ately seeded with anaerobic inoculum, contamination is assumed since preparation of substrate solids, media transfers, and other bottle preparations were effected in a nonsterile environment. However, given the large volumes of inoculum used in seeded systems, it is hard to imagine how contamination could have significantly influenced results for B1 and B2 samples.

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

0 0.5 1 1.5 2 2.5 3.5 4.5 5.5 7.5 8.5

12.5 13.5 18.5 22.5 24.5 30.5

2745 2650 2585 2440 2330 2320 2230 2155 2040

1830 1785

1395 1330

1370

-

-

-

3265 3055

2805

2620 2540 2490

2350

-

-

-

-

-

2020 1660

1350 1205

-

3265 2990

2735

2650 2550 2530

2480

-

-

-

-

- 2220 2040

1890 1790

-

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).


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 50 0.5 140 35 175 80 40 120 30 5 35 210 1.5 290 85 375 160 110 270 80 5 85 460 2.5 265 255 520 140 130 270 115 15 130 650 3.5 140 440 580 50 95 145 125 25 150 730 4.5 35 580 615 10 10 20 125 35 160 775 7.5 20 715 735 10 5 15 135 40 175 910

13.5 < 5 1020 1020 < 5b < 5 b - 165 60 225 1245 18.5 10 1335 1345 < 5 < 5 - 190 75 265 1610 24.5 < 5 1635 1635 < 5 1 5 - 205 80 285 1920 30.5 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 batch experiment was performed with autoclaved AS solids, with results virtually identical to the first experiment. The divergence in activities of B1 and B2 systems after the first 4-5 days of incubation remains unexplained.

Solubilization during the first few days of incubation was found to fit the assumed model of eq. (2) very well. Naturally, we decided to base kh estimates on these initial data, rationalizing that errors in all those “corrections” required to adjust observed solubilization in order to estimate “true” solubilization may be the ex- planation for anomalous results obtained as incubation proceeded. The corrections are less important near the beginning of incubation.

The Bl systems showed “ultimate” COD solubili- zations averaging 63.1% at 30 days incubation. This compares reasonably well with ultimate digestibilities of 69.5% earlier reported for autoclaved AS solids incubated for 85 days.2 Note that the data of Table I1 indicate that solubilization equates with degradability, since practically all soluble COD is converted to methane.

With 63.1% as an estimate of the total, ultimately solubilizable fraction of initially fed COD, the remaining solubilizable praticulate BOD (F) was estimated for both B , and B2 systems using cumulative solubilization vs. time data. Upon integration, eq. (2) gives:

(24)

where Fo is the maximum solubilizable particulate COD (g/L). Thus, the hydrolysis rate coefficient (kh) can be estimated-in the case of autoclaved sludge solids- from the slope value of the straight line obtained by plotting In (FIFO) vs. time.

Figure 4 shows how the kh was estimated for sample

B1 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 purposes, an average kh value of 0.15 day- I is proposed.

The observation that kh appears relatively independent of anaerobic microorganism concentration supports its omission from the hydrolysis model. The goodness of fit between eq. (2) and the initially obtained solubilization data supports the specific form (i.e. first- order assumption) of the model.

Questions remain concerning the extrapolation of kh values measured in batch systems to application in continuous-flow systems. Care was taken to ensure that abiotic parameters (e.g., pH, alkalinity, redox potential, etc.) in the serum bottle assays were close, if not identical, to values observed in the continuous- flow digesters also employed in this research. Biotic parameters, though, are difficult to quantify or control. Applicability of kh values so-obtained is evaluated in the next section.

AUTOCUMD SLUDGE SOLIDS (81

kh -0.16 day -’ I -1.5

0.0 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) evaluation for autoclaved

PAVLOSTATHIS AND GOSSElT: ANAEROBIC DIGESTION OF SLUDGE 1527

Table 111. (continuous-flow digestion).

Summary of model parameters with typical values used in this study

Values for

Parameter

Influent COD concentration [COD,, (g/L)J Ultimate digestibility [D (fraction)] Net biodegradable fraction of active biomass Ud) Cell soluble degradable COD immediately

released [ y (fraction of total degradable COD)] AS cell death rate coefficient [kd (day-')] Hydrolysis rate coefficient [ k , (day- ')I Decay coefficient for acid formers [bA (day-')] Yield coefficient for acid formers [ Y A (g COD

biomass/g COD utilized)] Maximum specific substrate utilization rate for

acid formers [kA (g COD utilized/g biomass COD day-')]

Half-velocity coefficient for acidogenesis

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

biomass/g COD utilized)] Maximum specific substrate utilization rate for

methanogens [kB (g COD utilized/g biomass COD day-')]

[K? (g COD/L)I

[K;' (g CODWI

Half-velocity coefficient for methanogenesis

Intact Autoclaved AS sludge

14.8 14.95 0.558 0.722 0.73 0.73 0.30 0.30

2.0 -

0. I5 0.15 0.10 0.10 0.20 0.20

8.0 8.0

0.045 0.045

0.015 0.015 0.057 0.057

6.2 6.2

0.045 0.125

MODEL PREDICTIONS OF DIGESTER PERFORMANCE

A summary of the model parameter values is given in Table I11 for both intact and autoclaved sludges. The values for parameters such asfd, y, kh, and kd were measured directly in this study and are discussed in previous sections of this article. Values for CODin and D were presented previously.2 Values for bA and YA were chosen based on results discussed elsewhere.* The values of kA and K$ were chosen to minimize the nonvolatile acid effluent degradable soluble COD based on continuous-flow digestion data which showed that this component is neglible.2 The biokinetic coefficients for methanogens were chosen from literature values" (for bB and YE) or by fitting of acetate and propionate data in this study' (for kB and K:).

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

An additional performance data point was obtained for digesters receiving intact AS. At the completion of the previously reported continuous-flow digestion studies,2 the feed rate was increased to the digester

operated at the lowest @ P I G , decreasing retention time to three days. Operation continued for 10 days, after which its level of performance was noted. This data point is included in Figure 6.

DISCUSSION

The model adequately predicts digester performance for intact sludge using the hydrolysis rate coefficient estimated by batch digestion of autoclaved sludge sol-

h

P + 0 20 3 L11 t-

8 10 n

AUTDCUMD SLUDGE 50

AUTDCUMD SLUDGE h

c3 -30 z P + 0 20 3 L11 t-

MODEL PREOlCnONS

k "-0.1 5 doy -' 8 10 n

MODEL PREOlCnONS

0-0.722

k "-0.1 5 doy -' I 2

Figure 5. Continuous-flow digester performance, model predictions for autoclaved sludge (bars indicate 95% confidence intervals on data).


0 2 4 6 8 1 0 1 2 SRT.Days

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

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

A sensitivity analysis was performed in order to quantify the effect of each parameter on the digester performance prediction. The results are shown in Ta- ble IV. The “base-line’’ values are the same values reported in Table 111. From these results, it is obvious that the ultimate digestibility has a major impact on digester performance predictions. Parameters such as fd, y, kd . kh, bA, YA, and YB have less impact on the model prediction. The rest of the parameters have almost negligible effect on the model predictions. The results of the sensitivity analysis support our experi- mental approach, which was to concentrate on independent measurement of important parameters, such as D and kh, while being satisfied with literature values for many others.

However, if erroneous interpretations are to be avoided, these results should be used with caution. All that is shown in Table IV is the percent change of the

Table IV. @‘IG = 8 days).

Sensitivity analysis of model parameters (Intact AS;

Percent change in predicted Base-line digester performance with parameter 10% increase in parameter

Parameter value“ value (%)

14.8 0.558 0.73 0.30 2.0 0.15 0.10 0.20 8.0 0.045 0.015 0.057 6.2 0.045

0.1 10.1 0.8 2.0 0.5 2.4 0.4

-1.5 0 0 0

- 0.5 0. I

-0.1

For parameter units, see Table 111

model prediction (at @‘IG = 8 days) for a 10% change in each parameter. Two points are noteworthy: all 14 parameters are interrelated, and therefore the percent change in model prediction around a “base-line’’ for a 10% change of one parameter depends on the level (value) of the other thirteen parameters, and all parameters are not expected to have equal uncertainties.

Based on the kd and kh values found in this study for intact AS, and on the results of the sensitivity analysis (Table IV), we can conclude that hydrolysis is a more kinetically limiting mechanism than death/lysis, with respect to conversion of viable AS organisms into available substrate. Of course, there is uncertainty as- sociated with the kd value (2 day-’) reported in this study due to the technique used to measure it. What should not be overlooked here is that no matter the exact value of kd, these data suggest that it is a large number compared with the kh value. Digester performance becomes a very insensitive function of kd.

Part of the influent viable AS biomass may adjust to the anaerobic environment (e.g., facultative AS bacteria) and become active acidogenic biomass. In this case, the acidogenic biomass is underestimated by the present model, and kd measurements might be in error. Presently, the above point cannot be either proved or disproved due to lack of accurate techniques for differentiation and estimation of acidogenic, methanogenic, and viable AS bacterial population densities. However, previous anaerobic digestion studies’s20 have shown that fastidious, nonmethanogenic, obligate anaerobic bacteria are present in numbers one or two orders of magnitude greater than facultative bacteria. On the other hand, most of the principal genera of AS bacteria recorded in taxonomic studies are found to be strict aerobes.21 Thus, the importance of AS facultative bacteria as active anaerobic digester acidogenic bacteria seems to be very minimal.

The superiority of the present model vis-a-vis models which consider methanogenesis ‘rate-limiting,” lies in the analytical prediction of the digester effluent characteristics. As was discussed previously,2 the O’Rourke model-formulated for raw primary sludge digestion and based largely on lipids degradation-ig- nores effluent particulate BOD of other waste components (e.g. protein) and assumes complete hydrolysis of the influent degradable COD for @IG higher than ca. 7 days. It works well for digestion of largely lipid waste. In the case of AS digestion, ca. 99% of the total effluent COD is particulate, showing that hydrolysis is not complete, even for 0PIG higher than 25 days. Particulate protein comprises between 80 and 90% of the total effluent degradable COD.

The present model represented by eqs. (131420) can easily be adapted to situations where the digester influent contains significant contributions of nonbiological, degradable sources, such as in the digestion of combined municipal primary and waste activated

PAVLOSTATHIS AND GOSSET: ANAEROBIC DIGESTION OF SLUDGE 1529

sludges. (Of course, the accuracy of the model in such cases has not been demonstrated.) In the simplest case where the applicable hydrolysis coefficient for the nonbiological BOD roughly equals that of the lysed, biological solids, all that is necessary is the addition of a finite Fo value to eq. (14). If the hydrolysis coefficients differ for biological and nonbiological solids, separate mathematical treatment of the two sludges is required down 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 composition may influence the half-velocity coefficient for methanogenesis (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 contributions from long-chain fatty acids.

In prediction of dynamic behavior the complex model presented 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 predictions suggest that death/lysis and acidogenesis mechanisms are sufficiently rapid that they may be neglected, at least for retention times of practical interest. Doing so results in essentially the model proposed by Gossett and Belser, * but where the preliminary conversion step of concern has been properly acknowledged as a hydrolysis step, rather than a death/lysis step.

CONCLUSIONS

Based on the results of this study, the following conclusions can be drawn. In the conversion of viable, biological solids to available substrate for the anaerobic microflora, mechanisms such as death, lysis and hydrolysis play an important role. Results suggest that hydrolysis of degradable, particulate, dead AS biomass is much slower than death or lysis. Therefore, hydrolysis appears to be the rate-controlling step in the case of anaerobic digestion of biological solids. As a result, ca. 99% of the degradable, effluent COD is particulate (mostly protein).

The death rate coefficient (kd)-estimated by use of an oxygen uptake rate technique-of viable AS biomass under anaerobic conditions (2 per day) is more than 16 times higher than the decay coefficient (bAS) under aerobic starvation conditions (0.12 per day).

An anaerobic digestion model for biological sludge was developed and evaluated. The four major steps in this model are: viable cell death/lysis; hydrolysis of particulate dead biomass; acidogenesis; and methan-

ogenesis. A sensitivity analysis of the parameters involved in this model showed that the most important parameter is the ultimate digestibility of the sludge, followed by other parameters such as those relating to hydrolysis and cell-soluble fraction. Overall, the model proved to be adequate for predicting the performance of a laboratory-scale digester receiving a biological solids feed. An extension of the model for use in cases of combined primary and waste-activated sludge appears feasible.

This research was supported by the U.S. Environmental Pro- tection Agency through Grant No. R 809500-01-0. This article has not been subjected to the Agency’s required peer and administrative review and, therefore, does not necessarily reflect the views of the Agency and no official endorsement should be inferred.

References

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a kinetic model for anaerobic digestion of biological sludge

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