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Dynamic modelling of substrate degradation in sequencing batch anaerobic reactors (SBAR)
Wat. Res. Vol. 27, No. I1, pp. 1619-1628, 1993 Printed in Great Britain. All rights reserved
0043-1354/93 $6.00+0.00 Copyright © 1993 Pergamon Press Ltd
D Y N A M I C M O D E L L I N G OF S U B S T R A T E D E G R A D A T I O N IN SEQUENCING BATCH ANAEROBIC REACTORS (SBAR) L. FERNANDES, K. J. KENNEDY* ~) a n d Z u o J u N NING Department of Civil Engineering, University of Ottawa, Ottawa, Ontario, Canada K I N 6N5
(First received October 1992; accepted in revised form March 1993) Abstraet--A dynamic model was developed for sequencing batch anaerobic reactors (SBARs) to describe substrate degradation under non-steady-state conditions. Assuming unionized volatile fatty acids were inhibitory, simulation results showed that product inhibition of methanogenesis and substrate degradation in the SBAR process can be expressed by modified Haldane or non-competitive inhibition functions, The proposed modified functions also reflect quite accurately the effect of large variations in reactor biomass concentration as a result of dilution during the fill stage. The determination of kinetic parameters and the verification of the model were made with different sets of experimental data. Simulated results from the model were in good agreement with experimental data under different operating strategies.
Key words--SBAR, modelling, anaerobic, inhibition
NOMENCLATURE
initial total COD concentration (g/l) Sp~o. = propionic acid concentration as C O D (g/l) S~.0 = influent propionic acid concentration as COD (g/l) Ss~ = sucrose concentration as COD (g/l) Ss~.0 = influent sucrose concentration as COD (g/l) SwA = volatile fatty acids concentration as COD (g/l) SVFA/ScoD = ratio of SvF^ to ScoD t = total reaction time (h) t r = fill time (h) tf.~tx = fill time considering mixing effect (h) tr = react time (h) VT = culture volume at the end of fill stage (1) v = culture volume (I) V0 = initial culture volume at the beginning of fill stage (1) X = biomass concentration (g/l) X0 = initial biomass concentration (g/l) Y = bacterial yield coefficient (g/g) ~/= COD removal efficiency SOLR = specific organic loading rate (g COD/g VSS d) SCOD, e =
b = bacterial decay coefficient (h-~) c = HS fraction in total COD HS = unionized volatile fatty acids concentration (g/l) k = maximum specific substrate uptake rate constant (h -l) K a = ionization constant K~ = product inhibition constant (g/l) K s = half velocity constant (g/l) K[ = apparent product inhibition constant (g/l) K~ = apparent half velocity constant (g/l) KM = maximum specific substrate uptake rate constant (h -~) Ki,u = product of K~ and culture volume (g) Ks,u = product of Ks and culture volume (g) M s = total mass of substrate in the reactor (g) Mx = total mass of biomass in the reactor (g) Q = influent flowrate in fill stage (l/h) R = rate of substrate uptake (g/1 h) RD,co o = rate of C O D degradation (g/l h) Ro,s~. = rate of sucrose uptake (g/l h) RD,ac/meth.= rate of acetic acid degradation to methane
INTRODUCTION
(g/lh)
RD.pro. = rate of propionic acid degradation (g/l h) R M = total substrate uptake rate in reactor (g/h) Rp,.c./p~o. = rate of acetic acid production from propionic acid (g/l h) Rp,ac./suc. = rate of acetic acid production from sucrose (g/1 h) Rp,hyd./pro" = rate of hydrogen-COD production from propionic acid (g/1 h) RP,hyd./s.c. = rate of hydrogen-COD production from sucrose (g/1 h) Rpmo./s,c. = rate ofpropionic acid production f~om sucrose (g/1 h) S ~ = acetic acid concentration as C O D (g/l) S~,0 = influent acetic acid concentration as COD (g/l) SCOD = total COD concentration (g/l) SCOD.Ù= total C O D concentration in influent (g/l)
A p p l i c a t i o n o f s e q u e n c i n g b a t c h r e a c t o r s ( S B R s ) in a e r o b i c a n d a n o x i c w a s t e w a t e r t r e a t m e n t processes h a s b e e n s t u d i e d extensively. T h e m a i n a d v a n t a g e s a s s o c i a t e d w i t h S B R s are: o p e r a t i o n a l flexibility, potential to select a specific m i c r o b i a l p o p u l a t i o n a n d p l u g flow kinetics ( W i l d e r e r et al., 1991; A r o r a et al., 1985; Irvine et al., 1977). H o w e v e r , r e s e a r c h o n the a p p l i c a t i o n o f S B R t e c h n o l o g y to a n a e r o b i c treatm e n t is very limited. T h e feasibility a n d flexibility o f sequencing batch anaerobic reactors (SBARs) was i n v e s t i g a t e d by K e n n e d y et al. (1991). T h e y f o u n d t h a t i n h i b i t i o n c a u s e d b y excessive f l u c t u a t i o n o f o r g a n i c l o a d i n g d u r i n g fill time severely affected t h e kinetic m e r i t s o f S B R s for a n a e r o b i c t r e a t m e n t .
*Author to whom all correspondence should be adressed,
However, modelling of SBARs has not been reported in t h e literature. 1619
1620
L. FERNANDESet al.
Mathematical models for aerobic SBRs are available in the literature, but these are not applicable to anaerobic conditions because of the different metabolic pathways involved in these two biological processes. In SBARs, carbon and electron flow involves three major groups of bacteria: fermentative, protonreducing acetogenic and methanogenic (aceticlastic and hydrogen-utilizing) bacteria. Each of these groups may suffer from various types of inhibition under unbalanced metabolic conditions. Inhibition factors in anaerobic reactors include pH, hydrogen concentration and intermediate products, mainly volatile fatty acids (VFAs). It is believed that the inhibition phenomenon occurring in SBAR can be described by a dynamic model, Andrews and Graef (1971) developed a dynamic model for a continuous flow anaerobic reactor (CSTR) which incorporated the Haldane-type inhibition function to describe product inhibition at different pH values. They also assumed that unionized VFAs were the growth limiting and inhibiting substrate to methane bacteria. Guiot (1991), Fukuzaki et al. (1990) and Kroeker (1978) have supported Andrews' hypothesis. Recently, a detailed model for a high-rate continuous flow anaerobic treatment system was developed by Costello et al. (1991a, b), based on the research result from Mosey (1982). In this model competitive and non-competitive inhibition functions were used to explain the inhibition of acetogenic and acid forming bacteria by acetic acid and total VFAs, respectively. However, inhibition of methanogenic bacteria by VFAs was not included when considering product inhibition. Smith and McCarty (1990) developed a non-steady-state model to predict organic substrate and product concentration, methane production and the response of
a shock-loaded CSTR digester. Nevertheless, significant differences were observed between experimental and simulated results, indicating that the metabolic processes under shock loading conditions involves complex oxidation/reduction reactions producing intermediate substances, that must be carefully determined. The operational mode of SBARs is very different from continuous flow reactors. Transient or nonsteady state conditions occur in the former system due to fluctuations of organic loading and biomass concentration during the fill stage. At present, few SBAR studies have been reported on and a predictive type model has yet to be proposed for this sytem. The objective of this paper is to present a dynamic model that considers product inhibition to describe soluble carbonaceous substrate degradation in SBARs. The proposed model will be calibrated and tested with the available experimental data. It is hoped that this model can offer a better understanding of the SBAR process and predict process behaviour at different operating strategies. MODEL DEVELOPMENT
A typical SBAR cycle consists of five stages: fill, react, settle, draw and idle. The variation of culture volume during one cycle is graphically shown in Fig. 1. Commonly, in continuous flow anaerobic reactors the main intermediates formed are acetic, propionic and butyric acids while other complex fatty acids such as valerate and caproate are produced in very low concentrations. For SBARs, related information on production of intermediates is scarce. Kennedy et al. (1991) observed that in a SBAR fed with sucrose t f - End of the fill time t r " End of the react time t s - End of the settle t ~ e
V(L)
t W" ti
V0
End of the w i t h d r a w time - End of the idle time
.....................................................................
t
4......
tr
}
|
i
t
i
ts
tw
TIME ( h o u r s ) Fig. 1. Variation of the culture volume in the reactor operating in SBR mode.
ti
"-
Modelling substrate degradation in SBAR and acetic acid the intermediates formed were still simple volatile fatty acids, mainly acetic and propionic acids, although intense fluctuation in substrate concentration existed in the fill stage. Therefore, in the modelling of the SBAR only volatile fatty acids were assumed to be the main intermediates. More detailed considerations can be derived from the results presented in this paper. The following assumptions were made in the development of the dynamic SBAR model: (l) Substrate biodegradation takes place in the fill and react stages only. Substrate utilization during settle, draw and idle stages is negligible, (2) The reactor is completely mixed during fill and react stages, (3) Biomass increase in one cycle is insignificant compared with the total amount of biomass in the reactor. (4) Reactor pH is controlled in an optimum range. No pH inhibition effect is expected, Mathematical description o f substrate degradation Based on mass balances, the variation of sucrose, propionic acid and acetic acid concentrations during fill and react stages in a SBAR can be expressed by
equation (1)-(3), respectively: Sucrose: d(Ss.c, dv Ssuc.o - Ro,suc.V dt v) = ~-~
(1)
Propionic acid: d(Spro,v) __ dv Spro 0 "~ Re.pro./suc.v -- R Dpro v dt dt " '
(2)
Acetic acid: d(Sac.V) dv dt =~-~ S~¢.0+ Rp,,¢./s.c.v + Rp,ac./proV--RD,ac./meth.V (3) where subscripts P and D represent "production" and "degradation", respectively. Substrate concentration is expressed as chemical oxygen demand (COD). For biomass, d(Xv__...~)= ( Y R - bX)v (4) dt From assumption (3), d(Xv)/dt = 0 and according to initial conditions (Fig. 1), X = X 0 and v = V0 at the beginning of the fill time, t = 0. Thus: Xv = X o Vo (5)
Since experimental data are usually expressed as total soluble COD and/or VFAs, equations (1)-(3) are further simplified. Using assumption (3), since, ScoÜ = Ss,¢. + Spro.+ S~c.
RD,suc----Rv,P'o./~"~. + Rv,"¢./sue"+ Ra.hyd'/suc" RD,pro..= Rp.ac./pro,+ Rp,hyd./pro"
1621
adding equations (I), (2) and (3) results in a general equation for fill and react stages as shown below: d(Scoo V) dv - = dt d-I SCOD'° -- (RD'ac'/meth" + Rp.hyd./suc"at- Rp.hyd.:pro.)V
(6)
Letting, RD.COo -= RD.ac./meth' + Rp, hyd./suc"+ Rp, hyd./pro
and since dv/dt = Q and dv/dt = 0 for the fill and react stages, respectively, equation (6) can be rewritten as: For fill sequence: dSco D --v = Q(ScoD. 0 --SCOD)- RD.cooV dt (0 ~< t ~< tf) (7a) For react sequence: dS¢°Ü
RDCOD
dt
'
(tf~< t ~< tr)
(7b)
Prior to solving equation (7), RD,CODmust be determined. In continuous reactors, the Monod equation is often used to describe the rate of substrate degradation, however it does not account for inhibition. In anaerobic digestion product inhibition has been frequently documented (Andrews and Graef, 1971; Costello et al., 1991a), although the proposed inhibitor and the form of inhibition function can vary. The Haldane-type inhibition function used by Andrews and Graef (1971) to describe the inhibition of both pH and VFAs to methanogenic bacteria in anaerobic digesters is: kX(HS) RD'c°° = Ks + HS + (HS)2/Ki
(8)
where, HS is unionized volatile fatty acids concentration determined at a fixed pH and substrate concentration by the following equation, [HS] =
[H +][SvFA] Kd
(9)
where K, is the ionization constant and SVFAthe total volatile acids concentration. Costello et al. (1991a) and Dinopoulou et al, (1988) used a non-competitive inhibition function to describe product inhibition for the acidogenic phase of anaerobic digestion in continuous reactors with total volatile acids as inhibitor [equation (10)]. Considering that neither the Haldane or non-competitive inhibition functions have been applied to SBARs, both inhibition functions are tested in this paper: RD,COD=
kX(HS) (Ks + HS)(I + HS/K~)
Existence of product inhibition in SBARs confirmed by Kennedy et al. (1991), and reported that VFA concentrations in SBARs between 2000 and 4000 mg/l, with as much as
(10) was they was 10%
L. FERNANDESet al.
1622
attributed to propionic acid. The concentration of VFAs inhibiting methane fermentation can vary greatly• Mawson et al. (1991) and Kroeker (1978) reported that VFAs between 1000 and 3000 rag/! may significantly retard the digestion operation, which is a clear indication that product inhibition is affecting the process. Equations (8) and (10) can be further simplified by
In the SBAR react stage, reaction conditions are identical to a batch process, the culture volume reaches its maximum, liT, which is constant and equal to V0 + Q × tr. Hence, equation (16), for the react stage becomes:
expressing HS in terms of COD, based on equation (9):
Comparing equation (14) and (17):
HS = cScoo
kM XScoo RD COD=
"
K~'M/ VT "~-Sc°D -~-S2OD/(Ki•M/ VT) (17)
(11)
k M= k
where
(18a)
Ks•M = K~ Vv
10-PH SVFA
c= - x -(12) Ka SCOD Substituting equation (11) into equation (8), results in:
kXScoD RD'COD= Ks/c + SCOD+ (ScoD)2/(gi/c)
(13)
Ki M = K~ Vv (18c) • Therefore, the rate equation for the react stage can keep its original form, equation (14). In the fill stage, the volume of mixed liquor and biomass concentration fluctuates. Thus, based on equation (16), the following equation can be developed:
where Ks/c and Ki/c are referred to as apparent Ks and Ki and designated as K~ and K~, respectively. Hence, equation (13) is rewritten as:
kXScoD RD'COD= K~ + Sco D + (ScoD)2/K~
(14)
At 35°C, the ionization constant (Ka) value is 1.73 × 10 -5 (Kroeker, 1978). Concomitantly, the values of K~ and K~ will be much larger than Ks and Ki at normal pH ranges in anaerobic reactors. In a similar manner as above, the non-competitive inhibition function [equation (10)] can be written as:
kXScoD Ro•coD -- (K~ + ScoD)(l + ScoD/K~)
(15)
Modification of Haldane and non-competitive inhibition functions in SBARs In SBARs, both biomass and substrate concentrations in the reactor change significantly during the fill stage. Dilution and variation in mixed liquor volume occurs because influent addition can double or triple the initial mixed liquor volume (Kennedy et al., 1991), and may invalidate direct application of the Haldane inhibition function to SBARs. In this study, the mass of biosolids and substrate is considered instead of their concentration to avoid the problem of volume variation, Assuming the volume of culture in the reactor is "v" at time t and total biomass is basically constant as it would be in a continuous or batch process, the Haldane function, based on mass terms, can be written in a general form as:
(18b)
kMXSco D Ro.coD =
(19)
Ks,M/V "~-SCOD~- S2OD/(Ki,M/V) where, v is a variable and v = V0 + Q × t. k M, Ks.M and Ki,M are constants. If the same set of kinetic constants is used in both fill and react stages, substituting equation (18) into (19), the modified rate equation for the SBAR fill stage is: RD COD-
"
kXScoo K~(VT/V) + ScoD + S~OD/[K~(VT/v)]
(20)
The modified non-competitive inhibition function for the fill stage, equation (21), can also be developed using the same procedures,
kXScoD
Ro,co o =
[K~(VT/v) + SC°D]{I + SC°D/[K[ (VT/V)]} (21) Both K~ and K~ in the fill stage are affected by variable volume (v) and attain their maximum values in the react stage, i.e. when v = VT. Similar findings were observed by Templeton et aL (1988). Their experimental work showed that K s decreased as the dilution rate increased, however, related biological pinciples were not discussed. Substituting equations (20) and (14) into (7), a dynamic model describing substrate degradation with Haldane-type inhibition for SBARs is developed. For fill stage, dScoD
d------~v=Q(ScoD,o--ScoD) kXSco Dv
R M= where
kMMxM~ KsM + M, + (Ms)2/Ki,M
(16)
' K,(VT/v)+ Scoo +(ScoD) 2/[Ki, (VT/V )]
•
(0 < I ~< tf)
(22a)
and for react stage,
R M = VRD,cOD Mx=vX Ms = VScoD
dScoD d------~ =
k XScoo K~ + ScoD +(ScoD)2/K[
(tf<~ t <~tr) (22b)
Modelling substrate degradation in SBAR
k and K'~ determination
A dynamic model for SBAR which includes a noncompetitive inhibition function can be obtained by substituting equations (15) and (21) into equation (7). For fill stage, dSco D --/)
dt
The UBF reactor showed high COD removal efficiency, ranging from an average of 93% of SOLR of 0.30g COD/g VSS d to an average of 91% at a SOLR of 0.86 g COD/g VSS d. Acetic acid was the main VFA in the reactor, acetic acid concentration was less than 50mg/I at low SOLR and about 250rag/1 at high SOLR. High COD removal efficiency and low VFAs indicated that no significant inhibition took place in the reactor under these operating conditions. Consequently, the values of k and K~ were determined from the continuous-flow reactor data and incorporated into the dynamic SBAR model to describe substrate degradation under different operating strategies. The k and K~ values incorporated in the present model were determined by curve fitting the experimental data. The values determined were k = 0.104 h-I and K~ = 3.9 g/l, respectively. It should Ix noted that the K~ value is quite large, yet it is in the same order of magnitude as the results from Ghosh and Klass (1978), who used similar substrate in their research. On the other hand, K~ is the apparent half velocity constant and K~ = K~/c. Assuming typical UBF reactor operating conditions are 35°C, pH 7.8 and K s = 1.73 x 10 -5, the value of c is 9.12 x 10 -4 at SVFA/ScoD= 1. Accordingly the half velocity constant, Ks, will be equal to 3.56 mg/l, which is close to the K~ of 1.99 rag/1 reported in Andrews' model.
= O(ScoD,0- SCOD)
kXScor, V [K,(VT/v)+ScoD]{I+Scoo/[K~(Vr/v)]} (0 ~< t ~< tr)
(23a)
and for react stage,
dSco_..._~o= dt
kXScoD
1623
(tf~< t ~< tf)
(K~ + ScoD)(l + Scoo/K~) (23b) DETERMINATION OF MODEL PARAMETERS
The model parameters to be determined are kinetic constants k, K~ and inhibition constant K~. Since limited experimental data on SBARs are available in the literature, one set of experimental data from Kennedy et al. (1991) was used to determine these parameters, while five other different data sets from the same research work were used for model verification and validation. Kennedy et al. (1991) used four laboratory-scale upflow sludge blanket anaerobic reactors (USBA) operated in sequencing batch mode at 35°C and fed a (50/50 w/v) sucrose/acetic acid substrate. Each reactor was operated at different organic loading rates by changing the fill/react sequence length, and maintaining the same influent concentration, 7 g COD/I. A continuous-flow upflow blanket filter reactor (UBF) with identical design configuration to the SBARs was used as the control. The control reactor was operated at the same temperature with the same feed compo-
Kt determination The same K i was used for modelling fill and react stages. The value of Ki was determined by non-linear regression using the rate equation for the react period [equation (22b)] and Ki = c * K~, resulting in:
sition and seeded with the same anaerobic granular sludge. The upflow blanket filter was operated at four different specific organic loading rates (SOLR), which were changed by stepwise increases of the flow rates, corresponding to SOLR applied to the SBARs. The pH in all reactors was in the range of 7.1-8.1, despite fluctuations in substrate concentration in SBARs during the fill cycle. Completely mixed conditions were set up by internal reactor recirculation. The SBARs' operating conditions are summarized in Table 1.
dSco o d-----~=
kXScoD K~ + Sco o + (ScoD)2/(Ki/c)
The experimental data for determination of Ki were based on experimental SBAR data with a fill/react of 2/10 (h). This data set was selected because a relatively constant SVFA/Scoo in the react stage existed in this operating mode so that the error caused by averaging SVFA/Scoo at different reaction times is minimized. The ratio of SVFA/ScoD was 0.88, the
Table 1. Operating parameters in the SBARS experiment Operating strategies Parameters Cycle length Reactor volume Feed volume Specific organic loading rate Operating mode Fill React Settle Draw Idle
Units
1
2
3
4
(h) (1) (I)
9 4.0 2.7
15 4.1 2.7
24 4.1 2.7
15 4.1 2.7
(gCOD/gVSS d)
0.86
(h) (h) (h) (h) (h)
I 5 2 1 0
(24)
0.48 2 10 2 1 0
0.30 3 18 2 1 0
5 24 4.1 2.7
6 24 4.1 2.7
0.48
0.30
0.30
4 8 2 I 0
7 14 2 I 0
14 7 2 1 0
L. FERNANDES et aL
1624
average pH in the reactor was 7.79, and Ka value at 35°C is known, hence c can be determined. Ki was determined with a non-linear data-fitting procedure based on least squares principle. From the regression analysis, K~ was found to be 0.36 mg/! for the Haldane function and 0.93 mg/l for the noncompetitive inhibition function. Corresponding K( values were 0.47 and 1.15 g/l, respectively.
Table3. pH and SVFA/ScoDvalues used for model implementation* Operating Fill stage React stage strategies fill/react(h) pH SVFA/S(7oD pH SwA/ScoD I/5 8.0t 0.67 7.8t 0.77 2/10 7.97 0.5 7.79 0.88 3/18 7.96 0.7 7.87 0.6 4/8 7.91 0.61 7.88 0.72 7/14 7.88 0.7 7.8t 0.35 14/7 7.81 0.68 7.76 0.58 *All values are averages of experimentaldata. ";'Estimatedvalues due to no correspondingdata.
MODEL VERIFICATION Model verification was conducted with experimental data obtained from five different SBAR operating strategies (Table 1), with the exception of a fill/react of 2/10 (h) which was used for Ki determination. The R u n g e - K u t t a method was employed to solve the proposed dynamic model as expressed by equations (22) and (23) since an analytical solution to these equations in the fill stage was not available. Model implementation was performed with G W - B A S I C software on an IBM personal computer. Specific to each operating strategy, the same kinetic parameters k, K~ and K~ (Table 2) were used in the simulation of all five operating strategies. For model verification the initial and process-control variables Vx, Vo, SCOD.0, SCOD.e, X0, K~, pH, tr and SwA/ScoD had the same values as those applied in the experimentai study. Of course, these state variables used were by no means restricted to those values, but could take any other design value at different assumed situations in the model simulation. A m o n g the tested state variables, Vx and V0 were constants; Ka, )to and SCOD.0 were considered as being constants for all reactors, their values were 1.73 x 10 -5 (at 35°C), 45 and 7 g/l, respectively. The fill time, if, was a prime control variable for a specific operating mode. The substrate concentration at the beginning of the SBAR cycle in the reactors (ScoD.D was set to 0.7 g/l based on average COD removal efficiency of 90%. From model calculations, it was observed that the value of SCOD.o had little effect on the simulation results (Table 5). Although the pH was controlled in the experimental work, values ranged from 7.1 to 8.1. The average pH values in the fill and react stages for each operating condition were individually and carefully considered in the model verification, since explicitly different features were shown during these two stages, and pH was found to be very sensitive to model simulation results. Table 3 presents average values of pH at different operating strategies,
It is apparent that substrate degradation in SBARs can be accounted for in more detail with equations (1)-(3) and, at the same time, the ratio SwA/Sco0 can be determined. However, it was felt that the model validity would be obscured since too many kinetic parameters need to be estimated from the literature for resolving these expressions. In order to test model validity, the SVFA/ScoD ratios were calculated from experimental data and results presented in Table 3. Although a complete-mixed state in the reactor was assumed in the model development [assumption (2)], in practice this is not the case. Simulation results showed that the model matched experimental data well in the react stage for any of the tested operating strategies. This is a good indication that the model kinetic parameters were determined with reasonable accuracy. However, model fitting results showed a different picture in the fill stage. Simulated results were higher than the measured experimental data for all operating strategies except for a fill/react of 14/7 (h). It was interesting to observe that the error between the simulated and experimental data became larger as the fill time, tr, decreased. Analysis of the experimental data suggested that the critical factor contributing to this error was non-ideal mixing. Insufficient mixing, which was achieved by liquid recirculation in the reactor, caused apparently poor substrate mixing and distribution in the reactor. These findings are illustrated in Fig. 2. In this
re~ 5 zo 8 4a-
[ /'"i / F /
.it"
........................ ..,.~ - ~ I 1 -
÷
/ / ~ /.// ~ i .~ ~t,,v = - ' ~ o [] a- ~ ÷ tf.Mxx ~ - ~ ' ~ -"--7-..° 1- f
Table 2. Model kinetic parameters Haldane-type Non-competitive Parameters function function k* (h i) 0.104 0.104 K~* (g/I) 3.9 3.9 Ki (mg/l) 0.36 0.93 *Valueswere obtained from the experimentaldata of the continuous flow reactor used as the control (Kennedyet al., 1991). +The valueswere determinedby non-linearregressionwith the data from SBAR operating mode fill/react of 2/10(h).
0 0
----~,,,~,i 2 4
6 a 1'o 1'2 14 TIME0aoun't Fig. 2. Non-ideal mixing phenomenon in data. Experimental results: I-1, run I; +, run 2. Simulated results for a non-competitive function model with operating strategy fill/react, 4/8 (h): - - - , substrate dilution action without biological degradation;----, substrate dilution and simuluted biological degradation with tf; , substrate dilution and simulated biological degradation with tf.Mtx.
Modelling substrate degradation in SBAR Table 4. COD results around controlled tr Operating styles COD* (g/I)/t (h)
fill/react (h) 1/5 2/10 3/18 4/8 7/14 14/7
tf-A/ 3.5 (0.5)? 0.85 (1.0) 2.92 (2.0) 2.58 (2.5) 2.46 (6.0) 2.68 (13.0)
tf 4.9 (1.0) 3.33 (2.5) 3.44 (3.0) 2.99 (3.5) 2.62 (7.0) 2.48 (14.0)
RESULTS AND DISCUSSION
lf+ At 5.15 (2.5) 3.36 (3.0) 3.68 (4.0) 3.34 (4.5) 3.18 (8.0) 2.57 (15.0)
*Average COD values based on experimental data. ?Numbers in parentheses indicate the sampling time from the beginning of the SBAR cycle,
situation, maximum Scoo did not occur at the end of the fill stage (/f) as expected, but at a time, tf + At. Table 4 lists original experimental data for substrate concentrations at tf, t f - 1 and tf + 1 h for the various operating strategies. It is evident that the poor substrate distribution phenomenon in the reactor operating at 14/7 was negligible in comparison to the other fill/react ratios tested, suggesting that in the reactor the influent flowrate was low and near ideal complete mixing can be expected. It can be concluded from the experimental results that non-ideal complete mixing was occurring in reactors with short fill time, while a nearly complete mixing can be expected where very long fill periods are incorporated, The proposed dynamic model does not include a term that reflects the degree of mixing in SBAR. In fact, a general solution for mixing schemes for the fill stage in SBAR is difficult because the phenomenon is largely dependent on particular experimental conditions. Analysis of the experimental data revealed that although different influent flowrates were involved, it took about 1 h after influent feeding was stopped for the substrate concentration at the sampling point to reach the maximum value at all tested operating modes except for the mode, 14/7 (h). This suggests that time delay was mainly determined by the recirculating rate and not by the influent flowrate. Since all recorded experimental data for substrate concentration were taken at the same sampling position, a realistic fill time should be selected based on the delayed mixing time rather than the controlled operating fill time for process modelling. Therefore, a modified fill time (tr,Mtx) as shown in equation (25) was used for model verification, tf, Mlx -~- tf + AtMtx
1625
(25)
w h e r e /f,MlX represents the virtual fill time as reflected at the sampling point and AtMl x is the difference
between controlled and virtual fill time which was found to be approx. 1 h as shown in Table 4. Consequently, tf.Mtx instead of tf was used in the model simulation. As shown in Fig. 2, for reactors operating at 4/8 (h) the model results with tr.M~X are in better agreement with the experimental data than model results using operating fill time, tf. Results for other operating strategies are discussed in the following section,
Based on the conditions stated above, the proposed dynamic model incorporating the modified Haldane and non-competitive functions were implemented for five different operating strategies. The simulated resuits from the model are presented in Figs 3-7. Considering the complexity of SBAR experimental conditions, it is seen that the proposed models predict t h e e x p e r i m e n t a l d a t a r e a s o n a b l y well. V e r y g o o d
matches between simulated results and experimental data were observed for operating strategies 4/8, 7/14 and 1/5 (h). Differences between the predicted and measured results can be linked to simplification of the model and possible experimental error. A major simplification in the present model development is the biodegradation of sucrose, propionic acid and acetic acid at fixed pH and temperature. Biodegradation was simulated simply as being the degradation of total COD in the digesters. This can lead to some error in the simulated results, because only unionized VFA, a fraction of total COD, acted as the usable substrate for methanogenic bacteria. As displayed in Fig. 4, experimental data showed a relatively fast biodegradation rate at the beginning of the react period while the rate decreased at the end of the react time significantly. This suggests that acetic acid was utilized first at a fast rate and then propionic acid was degraded at a slower rate by acetogenic and methanogenic bacteria. However, the simulated curve presented in Fig. 4 showed an approximately constant degradation rate rather than considering each of the substrates individually. With the exception of kinetic parameters, the state variables VT, V0, X0, Ka, ScoD.0, SCOD,e, tf, pH and SVF~,/ScoDin the model had to be defined according to experimental conditions or based on measured experimental values. An error in these parameters will also affect the simulation results. Therefore the sensitivity of these parameters was analysed to know the care that should be exercised in determining these parameters. Considering that, in practice, VT, V0, tf and temperature can be measured precisely, only So, X0, ScoD.e, pH and SVFA/Scor,were tested for sensitivity analysis. Among them, pH and SVFA/ScoDare a a ~ r ~ 4 ~ a a r
0
i
a
~
~ 5 a TL,,m0aom)
~
a
a
Fig. 3. Simulation ofSBAR for fill/react, l/5(h). Data: I-q, run I; +, run 2. Simulated results with the model: , with non-competitive function; - - , with Haldane-type function.
L. FERNANDESet al.
1626 7.
7-
g.
g.
5-
5-
3"
3"
2
2-
~
1"
r~
0
i3
9
ia Oaoum)
i5
l'e
1-
~,1
o
~
6
b 1'2 TIME (bourn)
l's
l'e
21
Fig. 4. Simulation of SBAR for fill/react, 3/18 (h). Data: I-q, run 1; +, run 2. Simulated results with the model: - - - , with non-competitive function; - - , with Haldane-type function,
Fig. 6. Simulation of SBAR for fill/react, 7/14 (h). Data: I-q, run 1; +, run 2. Simulated results with the model: - - - , with non-competitive function; - - , with Haldane-type function.
variables that were treated in this study as average
Haldane-type and non-competitive inhibition functions
constants. A simple approach was used for the sensitivity analysis: (1) possible maximum random errors in the examination of samples for each parameter were estimated from the literature (APHA, 1989), sampling error was not considered here; (2) the model was tested with the measured value of the parameter and the parameter value plus maximum random error, for each operating condition; and lastly ( 3 ) a comparison was made between the values obtained with and without considering the random error factor at reaction time t = t r, since maximum simulation error can be expected at this point, Sensitivity analysis results presented in Table 5 shows that the most sensitive parameters were Scoo,0 and pH and error increased as the time of the react sequence increased. Simulation results for fill/react mode, 1/5 (h), considering a 5% error in SCOD,0 is shown in Fig. 8. The simulation indicates that different fitting results can be produced as a result of a small error in SCOD.0measurement. The pH sensitivity is highlighted in Fig. 9, one can surprisingly find that only a small error, in the order of 0.1 pH units can significantly affect the model's simulation results, These observations strongly suggest that care must be exercised in determining Scoo.0 and pH for model implementation,
In this study, it was found that both Haldane-type and non-competitive inhibition functions can predict the SBAR performance fairly well. Simulation results were in good agreement with the experimental data for all the tested operating strategies as shown in Figs 3-7, with the exception of the fill/react of 14/7 (h). For an operating mode of 14/7, a better prediction was achieved with the non-competitive rather than by the Haldane-type function for the experimental data in the fill stage, while in the react stage, similar results can be obtained using both functions. The similarity between the two functions is shown in the following analysis. Rearranging the rate expression that includes the non-competitive inhibition function [equation (10)], gives: kX(HS) RD'c°° = Ks + HS + (HS)2/Ki + (Ks/Ki)(HS)
when Ks '~ Ki, the term (Ks/K~) • (HS) is negligible compared with the other terms in the denominator, and since HS is very small [equation (11)] at normal pH in an anaerobic digester, the non-competitive function will be same as the Haldane-type, which means that the latter can be considered as a more generalized inhibition function. In the present model
7'
7-
4"
8
,. °o
(26)
4-
,: i
~
.~ i
g b ~ g TiME (ho~)
g 1'o 1'1 t'2 13
Fig. 5. Simulation of SBAR for fill/react, 4/8 (h). Data: I-1, run 1; + , run 2. Simulated results with the model: , with non-competitive function; - - , with Ha]dane-type function,
°o
5
b
g i2 TIME (bo==)
is
l'e
21
Fig. 7. Simulation of SBAR for fill/react, 14/7 (h). Data: I-1, run 1; + , run 2. Simulated results with the model: , with non-competitive function; - - , with Ha]dane-type function.
Modelling substrate degradation in SBAR Table 5. Model parameters sensitivityanalysis Error caused by the deviation in model simulationat t? fill/react (h) Deviation in Parameters measurement 1/5 3/18 14/7 Scot),0 5% 5% 5.5% 8.8% Scoo.~ 7% 0.27% 0.35% 0.27% X0 I% 0.04% 0.2% 1.3% pH +0.1 0.56% 2.1% 13% SVFA/Sco D 8% 0.18% 0.77% 4.1% *The modelwith non-competitivefunctionis employed.
7 ~ e
~
5
simulation the value derived for K~ was 3.56 rag/l,
clearly, the condition Ks <~K~ was attained. It is not clear why the inhibition constant K~, determined in this study, has a smaller value than Ks. A possible explanation could be that methane bacteria in SBARs are more sensitive to responsible inhibitors, UVFAs. A point of interest is that both functions give similar results in the fill period when the fill times are shorter than 7 h. It is believed that there are two main processes occurring during the fill period: dilution and biological degradation. The former will play a dominant role for a relatively short fill time and it can minimize the error caused by omitting the item (KJK~) • HS. But the error will be more evident in the opposite situation, where a very long fill period is used, such as the fill/react mode 14/7 (h). In this paper, results from the model verification tend to suggest that the non-competitive function is better suited than the Haldane-type inhibition function to predict SBAR performance, SUMMARY A dynamic model for soluble carbonaceous substrate degradation in SBARs has been presented, g-
84
7.81
//
! a. ~
2' r~ 1" '~* 3
÷ ÷ ""
e
0
7.9t
".~,~*~7//*"
12
15
[ I
I
18
21
Fig. 9. Sensitivity analysis of pH for fill/react, 14/7, (h). Data: D, run 1; + run 2. Simulation with non-competitive function at different pH: Haldane-type and non-competitive inhibition functions were used in the model development. These inhibition functions were modified to describe the biodegradation in the fill stage of the SBAR, during which both biomass and substrate concentration in the mixed liquid fluctuate due to dilution action from influent wastewater. From the verification and the validation of the model, it was found that both inhibition functions can predict SBAR performance fairly well. Noncompetitive and Haldane-type functions lead to similar results when the operating fill time is short, less than 7 h. But, the non-competitive function fits the data better than the Haldane-type function, when the fill time is long (fill time of 14 h). Influent substrate concentration, SCOD.0, and pH were found to be the most sensitive process parameters in the model. Mixing conditions in the digester should also be considered when modelling SBARs. As a starting point for modelling SBARs, the model developed in this study is a simple and practical one. It is based on limited experimental data presently available, yet its validity has been confirmed by model verification. A more detailed model in which pH, individual VFAs and mixing state in the reactor are considered is being developed to better simulate SBAR performance.
REFERENCES
"V a-
SCOD.0 = 9.345 g/L
7"~ z~
pH = 7.71
/
0
while K~ values were 0.93 and 0.36mg/l for noncompetitive and Haldane-type functions, respectively. Andrews and Graef (1971) used a set of Ks and Ki values of 1.99 and 39.9 mg/l in his model. Fukuzaki et al. (1990) found the values of Ks and Ki for acetate-acclimatized sludge to be 0.024 and 276 mg/l, respectively. Both studies used the Haidane-type function to express inhibition and,
1627
~
O
~
/
/
v " v v g/L w~8.445
Andrews J. F. and Graef S. P. (1971) Dynamic modelling and simulation of the anaerobic digestion process. In Adv. Chem. Ser. 105, Anaerobic Biological Treatment Process.
8 s ~/// ~4 a
2
÷
F
1 o
~
~
~
4
5
e
~
a'lME(hours) Fig. 8. Scoo.o sensitivity analysis for fill/react, 1/5 (h). Data: 1--I, run I; +, run 2. Simulation with non-competitive function at different assumed COD feed concentrations: - Wit 27/11-=C
American Chemical Society, Washington, D.C. APHA (1989) Standard Methods for the Examination o] Water and Wastewater, 17th edition. American Public Health Association, New York. Arora M. L., Barth E. F. and Umphres M. B. (1985) Technology evaluation of sequencing batch reactors. J. Wat. Pollut. Control Fed. 57, 867-875. Costello D. J., Greenfield P. F. and Lee P. L. (1991a) Dynamic modelling of a single-stagehigh-rate anaerobic reactor--l. Model derivation. Wat. Res. 25, 847-858. Costello D. J., Greenfield P. F. and Lee P. L. (1991b) Dynamic modelling of a single-stage high-rate anaerobic reactor--II. Model verification. Wat. Res. 25, 859-871.
1628
L. FERNANDES et al.
Dinopoulou G., Sterritt R. M. and Lester J. N. (1988) Anaerobic acidogenesis of a complex wastewater: If. Kinetics of growth, inhibition, and product formation. Biotechnol. Bioengng 31, 969-978. Fukuzaki S., Nishio N. and Nagai S. (1990) Kinetics of the methanogenic fermentation of acetate. Appl. envir. Microbiol. 56, 3158-3163. Ghosh S. and Klass D. L. (1978) Two-phase anaerobic digestion. Prog. Biochem. 13, 15-23. Guiot S. R. (1991) Modelling of the upflow anaerobic sludge bed-filter system: a case with hysteresis. Wat. Res. 25, 251-262. Irvine R. L., Fox T. P. and Richter R. O. (1977) Investigation of fill and batch periods of sequencing batch biological reactors. Wat. Res. I1, 713-717. Kennedy K. J., Sanchez W. A., Hamoda M. F. and Droste R. L. (1991) Performance of anaerobic sludge blanket sequencing batch reactors. J. Wat. Pollut. Control Fed. 63, 75-83.
Kroeker E. J. (1978)Anaerobic treatment process stability. J. Wat. Pollut. Control Fed. 51, 718-727. Mawson A. J., Earle R. L. and Larsen V. F. (1991) Degradation of acetic and propionic acids in the methane fermentation. Wat. Res. 25, 1549-1554. Mosey F. E. (1982) Mathematical modelling of the anaerobic digestion process: regulatory mechanisms for the formation of short-chain volatile acids from glucose. War. Sci. Technol. 15, 209-232. Smith D. P. and McCarthy P. L. (1990) Factors governing methane fluctuations following shock loading of digesters. J. Wat. Pollut. Control Fed. 62, 58-64. Templeton L. L. and Leslie Grady C. P. Jr (1988) Effect of culture history on the determination of biodegradation kinetics by batch and fed-batch techniques. J. War. Pollut. Control Fed. 60, 651~58. Wilderer P. A., Rubio M. A. and Davids L. (1991) Impact of the addition of pure cultures on the performance of mixed culture reactors. Wat. Res. 25. 1307-1313.
0043-1354/93 $6.00+0.00 Copyright © 1993 Pergamon Press Ltd
D Y N A M I C M O D E L L I N G OF S U B S T R A T E D E G R A D A T I O N IN SEQUENCING BATCH ANAEROBIC REACTORS (SBAR) L. FERNANDES, K. J. KENNEDY* ~) a n d Z u o J u N NING Department of Civil Engineering, University of Ottawa, Ottawa, Ontario, Canada K I N 6N5
(First received October 1992; accepted in revised form March 1993) Abstraet--A dynamic model was developed for sequencing batch anaerobic reactors (SBARs) to describe substrate degradation under non-steady-state conditions. Assuming unionized volatile fatty acids were inhibitory, simulation results showed that product inhibition of methanogenesis and substrate degradation in the SBAR process can be expressed by modified Haldane or non-competitive inhibition functions, The proposed modified functions also reflect quite accurately the effect of large variations in reactor biomass concentration as a result of dilution during the fill stage. The determination of kinetic parameters and the verification of the model were made with different sets of experimental data. Simulated results from the model were in good agreement with experimental data under different operating strategies.
Key words--SBAR, modelling, anaerobic, inhibition
NOMENCLATURE
initial total COD concentration (g/l) Sp~o. = propionic acid concentration as C O D (g/l) S~.0 = influent propionic acid concentration as COD (g/l) Ss~ = sucrose concentration as COD (g/l) Ss~.0 = influent sucrose concentration as COD (g/l) SwA = volatile fatty acids concentration as COD (g/l) SVFA/ScoD = ratio of SvF^ to ScoD t = total reaction time (h) t r = fill time (h) tf.~tx = fill time considering mixing effect (h) tr = react time (h) VT = culture volume at the end of fill stage (1) v = culture volume (I) V0 = initial culture volume at the beginning of fill stage (1) X = biomass concentration (g/l) X0 = initial biomass concentration (g/l) Y = bacterial yield coefficient (g/g) ~/= COD removal efficiency SOLR = specific organic loading rate (g COD/g VSS d) SCOD, e =
b = bacterial decay coefficient (h-~) c = HS fraction in total COD HS = unionized volatile fatty acids concentration (g/l) k = maximum specific substrate uptake rate constant (h -l) K a = ionization constant K~ = product inhibition constant (g/l) K s = half velocity constant (g/l) K[ = apparent product inhibition constant (g/l) K~ = apparent half velocity constant (g/l) KM = maximum specific substrate uptake rate constant (h -~) Ki,u = product of K~ and culture volume (g) Ks,u = product of Ks and culture volume (g) M s = total mass of substrate in the reactor (g) Mx = total mass of biomass in the reactor (g) Q = influent flowrate in fill stage (l/h) R = rate of substrate uptake (g/1 h) RD,co o = rate of C O D degradation (g/l h) Ro,s~. = rate of sucrose uptake (g/l h) RD,ac/meth.= rate of acetic acid degradation to methane
INTRODUCTION
(g/lh)
RD.pro. = rate of propionic acid degradation (g/l h) R M = total substrate uptake rate in reactor (g/h) Rp,.c./p~o. = rate of acetic acid production from propionic acid (g/l h) Rp,ac./suc. = rate of acetic acid production from sucrose (g/1 h) Rp,hyd./pro" = rate of hydrogen-COD production from propionic acid (g/1 h) RP,hyd./s.c. = rate of hydrogen-COD production from sucrose (g/1 h) Rpmo./s,c. = rate ofpropionic acid production f~om sucrose (g/1 h) S ~ = acetic acid concentration as C O D (g/l) S~,0 = influent acetic acid concentration as COD (g/l) SCOD = total COD concentration (g/l) SCOD.Ù= total C O D concentration in influent (g/l)
A p p l i c a t i o n o f s e q u e n c i n g b a t c h r e a c t o r s ( S B R s ) in a e r o b i c a n d a n o x i c w a s t e w a t e r t r e a t m e n t processes h a s b e e n s t u d i e d extensively. T h e m a i n a d v a n t a g e s a s s o c i a t e d w i t h S B R s are: o p e r a t i o n a l flexibility, potential to select a specific m i c r o b i a l p o p u l a t i o n a n d p l u g flow kinetics ( W i l d e r e r et al., 1991; A r o r a et al., 1985; Irvine et al., 1977). H o w e v e r , r e s e a r c h o n the a p p l i c a t i o n o f S B R t e c h n o l o g y to a n a e r o b i c treatm e n t is very limited. T h e feasibility a n d flexibility o f sequencing batch anaerobic reactors (SBARs) was i n v e s t i g a t e d by K e n n e d y et al. (1991). T h e y f o u n d t h a t i n h i b i t i o n c a u s e d b y excessive f l u c t u a t i o n o f o r g a n i c l o a d i n g d u r i n g fill time severely affected t h e kinetic m e r i t s o f S B R s for a n a e r o b i c t r e a t m e n t .
*Author to whom all correspondence should be adressed,
However, modelling of SBARs has not been reported in t h e literature. 1619
1620
L. FERNANDESet al.
Mathematical models for aerobic SBRs are available in the literature, but these are not applicable to anaerobic conditions because of the different metabolic pathways involved in these two biological processes. In SBARs, carbon and electron flow involves three major groups of bacteria: fermentative, protonreducing acetogenic and methanogenic (aceticlastic and hydrogen-utilizing) bacteria. Each of these groups may suffer from various types of inhibition under unbalanced metabolic conditions. Inhibition factors in anaerobic reactors include pH, hydrogen concentration and intermediate products, mainly volatile fatty acids (VFAs). It is believed that the inhibition phenomenon occurring in SBAR can be described by a dynamic model, Andrews and Graef (1971) developed a dynamic model for a continuous flow anaerobic reactor (CSTR) which incorporated the Haldane-type inhibition function to describe product inhibition at different pH values. They also assumed that unionized VFAs were the growth limiting and inhibiting substrate to methane bacteria. Guiot (1991), Fukuzaki et al. (1990) and Kroeker (1978) have supported Andrews' hypothesis. Recently, a detailed model for a high-rate continuous flow anaerobic treatment system was developed by Costello et al. (1991a, b), based on the research result from Mosey (1982). In this model competitive and non-competitive inhibition functions were used to explain the inhibition of acetogenic and acid forming bacteria by acetic acid and total VFAs, respectively. However, inhibition of methanogenic bacteria by VFAs was not included when considering product inhibition. Smith and McCarty (1990) developed a non-steady-state model to predict organic substrate and product concentration, methane production and the response of
a shock-loaded CSTR digester. Nevertheless, significant differences were observed between experimental and simulated results, indicating that the metabolic processes under shock loading conditions involves complex oxidation/reduction reactions producing intermediate substances, that must be carefully determined. The operational mode of SBARs is very different from continuous flow reactors. Transient or nonsteady state conditions occur in the former system due to fluctuations of organic loading and biomass concentration during the fill stage. At present, few SBAR studies have been reported on and a predictive type model has yet to be proposed for this sytem. The objective of this paper is to present a dynamic model that considers product inhibition to describe soluble carbonaceous substrate degradation in SBARs. The proposed model will be calibrated and tested with the available experimental data. It is hoped that this model can offer a better understanding of the SBAR process and predict process behaviour at different operating strategies. MODEL DEVELOPMENT
A typical SBAR cycle consists of five stages: fill, react, settle, draw and idle. The variation of culture volume during one cycle is graphically shown in Fig. 1. Commonly, in continuous flow anaerobic reactors the main intermediates formed are acetic, propionic and butyric acids while other complex fatty acids such as valerate and caproate are produced in very low concentrations. For SBARs, related information on production of intermediates is scarce. Kennedy et al. (1991) observed that in a SBAR fed with sucrose t f - End of the fill time t r " End of the react time t s - End of the settle t ~ e
V(L)
t W" ti
V0
End of the w i t h d r a w time - End of the idle time
.....................................................................
t
4......
tr
}
|
i
t
i
ts
tw
TIME ( h o u r s ) Fig. 1. Variation of the culture volume in the reactor operating in SBR mode.
ti
"-
Modelling substrate degradation in SBAR and acetic acid the intermediates formed were still simple volatile fatty acids, mainly acetic and propionic acids, although intense fluctuation in substrate concentration existed in the fill stage. Therefore, in the modelling of the SBAR only volatile fatty acids were assumed to be the main intermediates. More detailed considerations can be derived from the results presented in this paper. The following assumptions were made in the development of the dynamic SBAR model: (l) Substrate biodegradation takes place in the fill and react stages only. Substrate utilization during settle, draw and idle stages is negligible, (2) The reactor is completely mixed during fill and react stages, (3) Biomass increase in one cycle is insignificant compared with the total amount of biomass in the reactor. (4) Reactor pH is controlled in an optimum range. No pH inhibition effect is expected, Mathematical description o f substrate degradation Based on mass balances, the variation of sucrose, propionic acid and acetic acid concentrations during fill and react stages in a SBAR can be expressed by
equation (1)-(3), respectively: Sucrose: d(Ss.c, dv Ssuc.o - Ro,suc.V dt v) = ~-~
(1)
Propionic acid: d(Spro,v) __ dv Spro 0 "~ Re.pro./suc.v -- R Dpro v dt dt " '
(2)
Acetic acid: d(Sac.V) dv dt =~-~ S~¢.0+ Rp,,¢./s.c.v + Rp,ac./proV--RD,ac./meth.V (3) where subscripts P and D represent "production" and "degradation", respectively. Substrate concentration is expressed as chemical oxygen demand (COD). For biomass, d(Xv__...~)= ( Y R - bX)v (4) dt From assumption (3), d(Xv)/dt = 0 and according to initial conditions (Fig. 1), X = X 0 and v = V0 at the beginning of the fill time, t = 0. Thus: Xv = X o Vo (5)
Since experimental data are usually expressed as total soluble COD and/or VFAs, equations (1)-(3) are further simplified. Using assumption (3), since, ScoÜ = Ss,¢. + Spro.+ S~c.
RD,suc----Rv,P'o./~"~. + Rv,"¢./sue"+ Ra.hyd'/suc" RD,pro..= Rp.ac./pro,+ Rp,hyd./pro"
1621
adding equations (I), (2) and (3) results in a general equation for fill and react stages as shown below: d(Scoo V) dv - = dt d-I SCOD'° -- (RD'ac'/meth" + Rp.hyd./suc"at- Rp.hyd.:pro.)V
(6)
Letting, RD.COo -= RD.ac./meth' + Rp, hyd./suc"+ Rp, hyd./pro
and since dv/dt = Q and dv/dt = 0 for the fill and react stages, respectively, equation (6) can be rewritten as: For fill sequence: dSco D --v = Q(ScoD. 0 --SCOD)- RD.cooV dt (0 ~< t ~< tf) (7a) For react sequence: dS¢°Ü
RDCOD
dt
'
(tf~< t ~< tr)
(7b)
Prior to solving equation (7), RD,CODmust be determined. In continuous reactors, the Monod equation is often used to describe the rate of substrate degradation, however it does not account for inhibition. In anaerobic digestion product inhibition has been frequently documented (Andrews and Graef, 1971; Costello et al., 1991a), although the proposed inhibitor and the form of inhibition function can vary. The Haldane-type inhibition function used by Andrews and Graef (1971) to describe the inhibition of both pH and VFAs to methanogenic bacteria in anaerobic digesters is: kX(HS) RD'c°° = Ks + HS + (HS)2/Ki
(8)
where, HS is unionized volatile fatty acids concentration determined at a fixed pH and substrate concentration by the following equation, [HS] =
[H +][SvFA] Kd
(9)
where K, is the ionization constant and SVFAthe total volatile acids concentration. Costello et al. (1991a) and Dinopoulou et al, (1988) used a non-competitive inhibition function to describe product inhibition for the acidogenic phase of anaerobic digestion in continuous reactors with total volatile acids as inhibitor [equation (10)]. Considering that neither the Haldane or non-competitive inhibition functions have been applied to SBARs, both inhibition functions are tested in this paper: RD,COD=
kX(HS) (Ks + HS)(I + HS/K~)
Existence of product inhibition in SBARs confirmed by Kennedy et al. (1991), and reported that VFA concentrations in SBARs between 2000 and 4000 mg/l, with as much as
(10) was they was 10%
L. FERNANDESet al.
1622
attributed to propionic acid. The concentration of VFAs inhibiting methane fermentation can vary greatly• Mawson et al. (1991) and Kroeker (1978) reported that VFAs between 1000 and 3000 rag/! may significantly retard the digestion operation, which is a clear indication that product inhibition is affecting the process. Equations (8) and (10) can be further simplified by
In the SBAR react stage, reaction conditions are identical to a batch process, the culture volume reaches its maximum, liT, which is constant and equal to V0 + Q × tr. Hence, equation (16), for the react stage becomes:
expressing HS in terms of COD, based on equation (9):
Comparing equation (14) and (17):
HS = cScoo
kM XScoo RD COD=
"
K~'M/ VT "~-Sc°D -~-S2OD/(Ki•M/ VT) (17)
(11)
k M= k
where
(18a)
Ks•M = K~ Vv
10-PH SVFA
c= - x -(12) Ka SCOD Substituting equation (11) into equation (8), results in:
kXScoD RD'COD= Ks/c + SCOD+ (ScoD)2/(gi/c)
(13)
Ki M = K~ Vv (18c) • Therefore, the rate equation for the react stage can keep its original form, equation (14). In the fill stage, the volume of mixed liquor and biomass concentration fluctuates. Thus, based on equation (16), the following equation can be developed:
where Ks/c and Ki/c are referred to as apparent Ks and Ki and designated as K~ and K~, respectively. Hence, equation (13) is rewritten as:
kXScoD RD'COD= K~ + Sco D + (ScoD)2/K~
(14)
At 35°C, the ionization constant (Ka) value is 1.73 × 10 -5 (Kroeker, 1978). Concomitantly, the values of K~ and K~ will be much larger than Ks and Ki at normal pH ranges in anaerobic reactors. In a similar manner as above, the non-competitive inhibition function [equation (10)] can be written as:
kXScoD Ro•coD -- (K~ + ScoD)(l + ScoD/K~)
(15)
Modification of Haldane and non-competitive inhibition functions in SBARs In SBARs, both biomass and substrate concentrations in the reactor change significantly during the fill stage. Dilution and variation in mixed liquor volume occurs because influent addition can double or triple the initial mixed liquor volume (Kennedy et al., 1991), and may invalidate direct application of the Haldane inhibition function to SBARs. In this study, the mass of biosolids and substrate is considered instead of their concentration to avoid the problem of volume variation, Assuming the volume of culture in the reactor is "v" at time t and total biomass is basically constant as it would be in a continuous or batch process, the Haldane function, based on mass terms, can be written in a general form as:
(18b)
kMXSco D Ro.coD =
(19)
Ks,M/V "~-SCOD~- S2OD/(Ki,M/V) where, v is a variable and v = V0 + Q × t. k M, Ks.M and Ki,M are constants. If the same set of kinetic constants is used in both fill and react stages, substituting equation (18) into (19), the modified rate equation for the SBAR fill stage is: RD COD-
"
kXScoo K~(VT/V) + ScoD + S~OD/[K~(VT/v)]
(20)
The modified non-competitive inhibition function for the fill stage, equation (21), can also be developed using the same procedures,
kXScoD
Ro,co o =
[K~(VT/v) + SC°D]{I + SC°D/[K[ (VT/V)]} (21) Both K~ and K~ in the fill stage are affected by variable volume (v) and attain their maximum values in the react stage, i.e. when v = VT. Similar findings were observed by Templeton et aL (1988). Their experimental work showed that K s decreased as the dilution rate increased, however, related biological pinciples were not discussed. Substituting equations (20) and (14) into (7), a dynamic model describing substrate degradation with Haldane-type inhibition for SBARs is developed. For fill stage, dScoD
d------~v=Q(ScoD,o--ScoD) kXSco Dv
R M= where
kMMxM~ KsM + M, + (Ms)2/Ki,M
(16)
' K,(VT/v)+ Scoo +(ScoD) 2/[Ki, (VT/V )]
•
(0 < I ~< tf)
(22a)
and for react stage,
R M = VRD,cOD Mx=vX Ms = VScoD
dScoD d------~ =
k XScoo K~ + ScoD +(ScoD)2/K[
(tf<~ t <~tr) (22b)
Modelling substrate degradation in SBAR
k and K'~ determination
A dynamic model for SBAR which includes a noncompetitive inhibition function can be obtained by substituting equations (15) and (21) into equation (7). For fill stage, dSco D --/)
dt
The UBF reactor showed high COD removal efficiency, ranging from an average of 93% of SOLR of 0.30g COD/g VSS d to an average of 91% at a SOLR of 0.86 g COD/g VSS d. Acetic acid was the main VFA in the reactor, acetic acid concentration was less than 50mg/I at low SOLR and about 250rag/1 at high SOLR. High COD removal efficiency and low VFAs indicated that no significant inhibition took place in the reactor under these operating conditions. Consequently, the values of k and K~ were determined from the continuous-flow reactor data and incorporated into the dynamic SBAR model to describe substrate degradation under different operating strategies. The k and K~ values incorporated in the present model were determined by curve fitting the experimental data. The values determined were k = 0.104 h-I and K~ = 3.9 g/l, respectively. It should Ix noted that the K~ value is quite large, yet it is in the same order of magnitude as the results from Ghosh and Klass (1978), who used similar substrate in their research. On the other hand, K~ is the apparent half velocity constant and K~ = K~/c. Assuming typical UBF reactor operating conditions are 35°C, pH 7.8 and K s = 1.73 x 10 -5, the value of c is 9.12 x 10 -4 at SVFA/ScoD= 1. Accordingly the half velocity constant, Ks, will be equal to 3.56 mg/l, which is close to the K~ of 1.99 rag/1 reported in Andrews' model.
= O(ScoD,0- SCOD)
kXScor, V [K,(VT/v)+ScoD]{I+Scoo/[K~(Vr/v)]} (0 ~< t ~< tr)
(23a)
and for react stage,
dSco_..._~o= dt
kXScoD
1623
(tf~< t ~< tf)
(K~ + ScoD)(l + Scoo/K~) (23b) DETERMINATION OF MODEL PARAMETERS
The model parameters to be determined are kinetic constants k, K~ and inhibition constant K~. Since limited experimental data on SBARs are available in the literature, one set of experimental data from Kennedy et al. (1991) was used to determine these parameters, while five other different data sets from the same research work were used for model verification and validation. Kennedy et al. (1991) used four laboratory-scale upflow sludge blanket anaerobic reactors (USBA) operated in sequencing batch mode at 35°C and fed a (50/50 w/v) sucrose/acetic acid substrate. Each reactor was operated at different organic loading rates by changing the fill/react sequence length, and maintaining the same influent concentration, 7 g COD/I. A continuous-flow upflow blanket filter reactor (UBF) with identical design configuration to the SBARs was used as the control. The control reactor was operated at the same temperature with the same feed compo-
Kt determination The same K i was used for modelling fill and react stages. The value of Ki was determined by non-linear regression using the rate equation for the react period [equation (22b)] and Ki = c * K~, resulting in:
sition and seeded with the same anaerobic granular sludge. The upflow blanket filter was operated at four different specific organic loading rates (SOLR), which were changed by stepwise increases of the flow rates, corresponding to SOLR applied to the SBARs. The pH in all reactors was in the range of 7.1-8.1, despite fluctuations in substrate concentration in SBARs during the fill cycle. Completely mixed conditions were set up by internal reactor recirculation. The SBARs' operating conditions are summarized in Table 1.
dSco o d-----~=
kXScoD K~ + Sco o + (ScoD)2/(Ki/c)
The experimental data for determination of Ki were based on experimental SBAR data with a fill/react of 2/10 (h). This data set was selected because a relatively constant SVFA/Scoo in the react stage existed in this operating mode so that the error caused by averaging SVFA/Scoo at different reaction times is minimized. The ratio of SVFA/ScoD was 0.88, the
Table 1. Operating parameters in the SBARS experiment Operating strategies Parameters Cycle length Reactor volume Feed volume Specific organic loading rate Operating mode Fill React Settle Draw Idle
Units
1
2
3
4
(h) (1) (I)
9 4.0 2.7
15 4.1 2.7
24 4.1 2.7
15 4.1 2.7
(gCOD/gVSS d)
0.86
(h) (h) (h) (h) (h)
I 5 2 1 0
(24)
0.48 2 10 2 1 0
0.30 3 18 2 1 0
5 24 4.1 2.7
6 24 4.1 2.7
0.48
0.30
0.30
4 8 2 I 0
7 14 2 I 0
14 7 2 1 0
L. FERNANDES et aL
1624
average pH in the reactor was 7.79, and Ka value at 35°C is known, hence c can be determined. Ki was determined with a non-linear data-fitting procedure based on least squares principle. From the regression analysis, K~ was found to be 0.36 mg/! for the Haldane function and 0.93 mg/l for the noncompetitive inhibition function. Corresponding K( values were 0.47 and 1.15 g/l, respectively.
Table3. pH and SVFA/ScoDvalues used for model implementation* Operating Fill stage React stage strategies fill/react(h) pH SVFA/S(7oD pH SwA/ScoD I/5 8.0t 0.67 7.8t 0.77 2/10 7.97 0.5 7.79 0.88 3/18 7.96 0.7 7.87 0.6 4/8 7.91 0.61 7.88 0.72 7/14 7.88 0.7 7.8t 0.35 14/7 7.81 0.68 7.76 0.58 *All values are averages of experimentaldata. ";'Estimatedvalues due to no correspondingdata.
MODEL VERIFICATION Model verification was conducted with experimental data obtained from five different SBAR operating strategies (Table 1), with the exception of a fill/react of 2/10 (h) which was used for Ki determination. The R u n g e - K u t t a method was employed to solve the proposed dynamic model as expressed by equations (22) and (23) since an analytical solution to these equations in the fill stage was not available. Model implementation was performed with G W - B A S I C software on an IBM personal computer. Specific to each operating strategy, the same kinetic parameters k, K~ and K~ (Table 2) were used in the simulation of all five operating strategies. For model verification the initial and process-control variables Vx, Vo, SCOD.0, SCOD.e, X0, K~, pH, tr and SwA/ScoD had the same values as those applied in the experimentai study. Of course, these state variables used were by no means restricted to those values, but could take any other design value at different assumed situations in the model simulation. A m o n g the tested state variables, Vx and V0 were constants; Ka, )to and SCOD.0 were considered as being constants for all reactors, their values were 1.73 x 10 -5 (at 35°C), 45 and 7 g/l, respectively. The fill time, if, was a prime control variable for a specific operating mode. The substrate concentration at the beginning of the SBAR cycle in the reactors (ScoD.D was set to 0.7 g/l based on average COD removal efficiency of 90%. From model calculations, it was observed that the value of SCOD.o had little effect on the simulation results (Table 5). Although the pH was controlled in the experimental work, values ranged from 7.1 to 8.1. The average pH values in the fill and react stages for each operating condition were individually and carefully considered in the model verification, since explicitly different features were shown during these two stages, and pH was found to be very sensitive to model simulation results. Table 3 presents average values of pH at different operating strategies,
It is apparent that substrate degradation in SBARs can be accounted for in more detail with equations (1)-(3) and, at the same time, the ratio SwA/Sco0 can be determined. However, it was felt that the model validity would be obscured since too many kinetic parameters need to be estimated from the literature for resolving these expressions. In order to test model validity, the SVFA/ScoD ratios were calculated from experimental data and results presented in Table 3. Although a complete-mixed state in the reactor was assumed in the model development [assumption (2)], in practice this is not the case. Simulation results showed that the model matched experimental data well in the react stage for any of the tested operating strategies. This is a good indication that the model kinetic parameters were determined with reasonable accuracy. However, model fitting results showed a different picture in the fill stage. Simulated results were higher than the measured experimental data for all operating strategies except for a fill/react of 14/7 (h). It was interesting to observe that the error between the simulated and experimental data became larger as the fill time, tr, decreased. Analysis of the experimental data suggested that the critical factor contributing to this error was non-ideal mixing. Insufficient mixing, which was achieved by liquid recirculation in the reactor, caused apparently poor substrate mixing and distribution in the reactor. These findings are illustrated in Fig. 2. In this
re~ 5 zo 8 4a-
[ /'"i / F /
.it"
........................ ..,.~ - ~ I 1 -
÷
/ / ~ /.// ~ i .~ ~t,,v = - ' ~ o [] a- ~ ÷ tf.Mxx ~ - ~ ' ~ -"--7-..° 1- f
Table 2. Model kinetic parameters Haldane-type Non-competitive Parameters function function k* (h i) 0.104 0.104 K~* (g/I) 3.9 3.9 Ki (mg/l) 0.36 0.93 *Valueswere obtained from the experimentaldata of the continuous flow reactor used as the control (Kennedyet al., 1991). +The valueswere determinedby non-linearregressionwith the data from SBAR operating mode fill/react of 2/10(h).
0 0
----~,,,~,i 2 4
6 a 1'o 1'2 14 TIME0aoun't Fig. 2. Non-ideal mixing phenomenon in data. Experimental results: I-1, run I; +, run 2. Simulated results for a non-competitive function model with operating strategy fill/react, 4/8 (h): - - - , substrate dilution action without biological degradation;----, substrate dilution and simuluted biological degradation with tf; , substrate dilution and simulated biological degradation with tf.Mtx.
Modelling substrate degradation in SBAR Table 4. COD results around controlled tr Operating styles COD* (g/I)/t (h)
fill/react (h) 1/5 2/10 3/18 4/8 7/14 14/7
tf-A/ 3.5 (0.5)? 0.85 (1.0) 2.92 (2.0) 2.58 (2.5) 2.46 (6.0) 2.68 (13.0)
tf 4.9 (1.0) 3.33 (2.5) 3.44 (3.0) 2.99 (3.5) 2.62 (7.0) 2.48 (14.0)
RESULTS AND DISCUSSION
lf+ At 5.15 (2.5) 3.36 (3.0) 3.68 (4.0) 3.34 (4.5) 3.18 (8.0) 2.57 (15.0)
*Average COD values based on experimental data. ?Numbers in parentheses indicate the sampling time from the beginning of the SBAR cycle,
situation, maximum Scoo did not occur at the end of the fill stage (/f) as expected, but at a time, tf + At. Table 4 lists original experimental data for substrate concentrations at tf, t f - 1 and tf + 1 h for the various operating strategies. It is evident that the poor substrate distribution phenomenon in the reactor operating at 14/7 was negligible in comparison to the other fill/react ratios tested, suggesting that in the reactor the influent flowrate was low and near ideal complete mixing can be expected. It can be concluded from the experimental results that non-ideal complete mixing was occurring in reactors with short fill time, while a nearly complete mixing can be expected where very long fill periods are incorporated, The proposed dynamic model does not include a term that reflects the degree of mixing in SBAR. In fact, a general solution for mixing schemes for the fill stage in SBAR is difficult because the phenomenon is largely dependent on particular experimental conditions. Analysis of the experimental data revealed that although different influent flowrates were involved, it took about 1 h after influent feeding was stopped for the substrate concentration at the sampling point to reach the maximum value at all tested operating modes except for the mode, 14/7 (h). This suggests that time delay was mainly determined by the recirculating rate and not by the influent flowrate. Since all recorded experimental data for substrate concentration were taken at the same sampling position, a realistic fill time should be selected based on the delayed mixing time rather than the controlled operating fill time for process modelling. Therefore, a modified fill time (tr,Mtx) as shown in equation (25) was used for model verification, tf, Mlx -~- tf + AtMtx
1625
(25)
w h e r e /f,MlX represents the virtual fill time as reflected at the sampling point and AtMl x is the difference
between controlled and virtual fill time which was found to be approx. 1 h as shown in Table 4. Consequently, tf.Mtx instead of tf was used in the model simulation. As shown in Fig. 2, for reactors operating at 4/8 (h) the model results with tr.M~X are in better agreement with the experimental data than model results using operating fill time, tf. Results for other operating strategies are discussed in the following section,
Based on the conditions stated above, the proposed dynamic model incorporating the modified Haldane and non-competitive functions were implemented for five different operating strategies. The simulated resuits from the model are presented in Figs 3-7. Considering the complexity of SBAR experimental conditions, it is seen that the proposed models predict t h e e x p e r i m e n t a l d a t a r e a s o n a b l y well. V e r y g o o d
matches between simulated results and experimental data were observed for operating strategies 4/8, 7/14 and 1/5 (h). Differences between the predicted and measured results can be linked to simplification of the model and possible experimental error. A major simplification in the present model development is the biodegradation of sucrose, propionic acid and acetic acid at fixed pH and temperature. Biodegradation was simulated simply as being the degradation of total COD in the digesters. This can lead to some error in the simulated results, because only unionized VFA, a fraction of total COD, acted as the usable substrate for methanogenic bacteria. As displayed in Fig. 4, experimental data showed a relatively fast biodegradation rate at the beginning of the react period while the rate decreased at the end of the react time significantly. This suggests that acetic acid was utilized first at a fast rate and then propionic acid was degraded at a slower rate by acetogenic and methanogenic bacteria. However, the simulated curve presented in Fig. 4 showed an approximately constant degradation rate rather than considering each of the substrates individually. With the exception of kinetic parameters, the state variables VT, V0, X0, Ka, ScoD.0, SCOD,e, tf, pH and SVF~,/ScoDin the model had to be defined according to experimental conditions or based on measured experimental values. An error in these parameters will also affect the simulation results. Therefore the sensitivity of these parameters was analysed to know the care that should be exercised in determining these parameters. Considering that, in practice, VT, V0, tf and temperature can be measured precisely, only So, X0, ScoD.e, pH and SVFA/Scor,were tested for sensitivity analysis. Among them, pH and SVFA/ScoDare a a ~ r ~ 4 ~ a a r
0
i
a
~
~ 5 a TL,,m0aom)
~
a
a
Fig. 3. Simulation ofSBAR for fill/react, l/5(h). Data: I-q, run I; +, run 2. Simulated results with the model: , with non-competitive function; - - , with Haldane-type function.
L. FERNANDESet al.
1626 7.
7-
g.
g.
5-
5-
3"
3"
2
2-
~
1"
r~
0
i3
9
ia Oaoum)
i5
l'e
1-
~,1
o
~
6
b 1'2 TIME (bourn)
l's
l'e
21
Fig. 4. Simulation of SBAR for fill/react, 3/18 (h). Data: I-q, run 1; +, run 2. Simulated results with the model: - - - , with non-competitive function; - - , with Haldane-type function,
Fig. 6. Simulation of SBAR for fill/react, 7/14 (h). Data: I-q, run 1; +, run 2. Simulated results with the model: - - - , with non-competitive function; - - , with Haldane-type function.
variables that were treated in this study as average
Haldane-type and non-competitive inhibition functions
constants. A simple approach was used for the sensitivity analysis: (1) possible maximum random errors in the examination of samples for each parameter were estimated from the literature (APHA, 1989), sampling error was not considered here; (2) the model was tested with the measured value of the parameter and the parameter value plus maximum random error, for each operating condition; and lastly ( 3 ) a comparison was made between the values obtained with and without considering the random error factor at reaction time t = t r, since maximum simulation error can be expected at this point, Sensitivity analysis results presented in Table 5 shows that the most sensitive parameters were Scoo,0 and pH and error increased as the time of the react sequence increased. Simulation results for fill/react mode, 1/5 (h), considering a 5% error in SCOD,0 is shown in Fig. 8. The simulation indicates that different fitting results can be produced as a result of a small error in SCOD.0measurement. The pH sensitivity is highlighted in Fig. 9, one can surprisingly find that only a small error, in the order of 0.1 pH units can significantly affect the model's simulation results, These observations strongly suggest that care must be exercised in determining Scoo.0 and pH for model implementation,
In this study, it was found that both Haldane-type and non-competitive inhibition functions can predict the SBAR performance fairly well. Simulation results were in good agreement with the experimental data for all the tested operating strategies as shown in Figs 3-7, with the exception of the fill/react of 14/7 (h). For an operating mode of 14/7, a better prediction was achieved with the non-competitive rather than by the Haldane-type function for the experimental data in the fill stage, while in the react stage, similar results can be obtained using both functions. The similarity between the two functions is shown in the following analysis. Rearranging the rate expression that includes the non-competitive inhibition function [equation (10)], gives: kX(HS) RD'c°° = Ks + HS + (HS)2/Ki + (Ks/Ki)(HS)
when Ks '~ Ki, the term (Ks/K~) • (HS) is negligible compared with the other terms in the denominator, and since HS is very small [equation (11)] at normal pH in an anaerobic digester, the non-competitive function will be same as the Haldane-type, which means that the latter can be considered as a more generalized inhibition function. In the present model
7'
7-
4"
8
,. °o
(26)
4-
,: i
~
.~ i
g b ~ g TiME (ho~)
g 1'o 1'1 t'2 13
Fig. 5. Simulation of SBAR for fill/react, 4/8 (h). Data: I-1, run 1; + , run 2. Simulated results with the model: , with non-competitive function; - - , with Ha]dane-type function,
°o
5
b
g i2 TIME (bo==)
is
l'e
21
Fig. 7. Simulation of SBAR for fill/react, 14/7 (h). Data: I-1, run 1; + , run 2. Simulated results with the model: , with non-competitive function; - - , with Ha]dane-type function.
Modelling substrate degradation in SBAR Table 5. Model parameters sensitivityanalysis Error caused by the deviation in model simulationat t? fill/react (h) Deviation in Parameters measurement 1/5 3/18 14/7 Scot),0 5% 5% 5.5% 8.8% Scoo.~ 7% 0.27% 0.35% 0.27% X0 I% 0.04% 0.2% 1.3% pH +0.1 0.56% 2.1% 13% SVFA/Sco D 8% 0.18% 0.77% 4.1% *The modelwith non-competitivefunctionis employed.
7 ~ e
~
5
simulation the value derived for K~ was 3.56 rag/l,
clearly, the condition Ks <~K~ was attained. It is not clear why the inhibition constant K~, determined in this study, has a smaller value than Ks. A possible explanation could be that methane bacteria in SBARs are more sensitive to responsible inhibitors, UVFAs. A point of interest is that both functions give similar results in the fill period when the fill times are shorter than 7 h. It is believed that there are two main processes occurring during the fill period: dilution and biological degradation. The former will play a dominant role for a relatively short fill time and it can minimize the error caused by omitting the item (KJK~) • HS. But the error will be more evident in the opposite situation, where a very long fill period is used, such as the fill/react mode 14/7 (h). In this paper, results from the model verification tend to suggest that the non-competitive function is better suited than the Haldane-type inhibition function to predict SBAR performance, SUMMARY A dynamic model for soluble carbonaceous substrate degradation in SBARs has been presented, g-
84
7.81
//
! a. ~
2' r~ 1" '~* 3
÷ ÷ ""
e
0
7.9t
".~,~*~7//*"
12
15
[ I
I
18
21
Fig. 9. Sensitivity analysis of pH for fill/react, 14/7, (h). Data: D, run 1; + run 2. Simulation with non-competitive function at different pH: Haldane-type and non-competitive inhibition functions were used in the model development. These inhibition functions were modified to describe the biodegradation in the fill stage of the SBAR, during which both biomass and substrate concentration in the mixed liquid fluctuate due to dilution action from influent wastewater. From the verification and the validation of the model, it was found that both inhibition functions can predict SBAR performance fairly well. Noncompetitive and Haldane-type functions lead to similar results when the operating fill time is short, less than 7 h. But, the non-competitive function fits the data better than the Haldane-type function, when the fill time is long (fill time of 14 h). Influent substrate concentration, SCOD.0, and pH were found to be the most sensitive process parameters in the model. Mixing conditions in the digester should also be considered when modelling SBARs. As a starting point for modelling SBARs, the model developed in this study is a simple and practical one. It is based on limited experimental data presently available, yet its validity has been confirmed by model verification. A more detailed model in which pH, individual VFAs and mixing state in the reactor are considered is being developed to better simulate SBAR performance.
REFERENCES
"V a-
SCOD.0 = 9.345 g/L
7"~ z~
pH = 7.71
/
0
while K~ values were 0.93 and 0.36mg/l for noncompetitive and Haldane-type functions, respectively. Andrews and Graef (1971) used a set of Ks and Ki values of 1.99 and 39.9 mg/l in his model. Fukuzaki et al. (1990) found the values of Ks and Ki for acetate-acclimatized sludge to be 0.024 and 276 mg/l, respectively. Both studies used the Haidane-type function to express inhibition and,
1627
~
O
~
/
/
v " v v g/L w~8.445
Andrews J. F. and Graef S. P. (1971) Dynamic modelling and simulation of the anaerobic digestion process. In Adv. Chem. Ser. 105, Anaerobic Biological Treatment Process.
8 s ~/// ~4 a
2
÷
F
1 o
~
~
~
4
5
e
~
a'lME(hours) Fig. 8. Scoo.o sensitivity analysis for fill/react, 1/5 (h). Data: 1--I, run I; +, run 2. Simulation with non-competitive function at different assumed COD feed concentrations: - Wit 27/11-=C
American Chemical Society, Washington, D.C. APHA (1989) Standard Methods for the Examination o] Water and Wastewater, 17th edition. American Public Health Association, New York. Arora M. L., Barth E. F. and Umphres M. B. (1985) Technology evaluation of sequencing batch reactors. J. Wat. Pollut. Control Fed. 57, 867-875. Costello D. J., Greenfield P. F. and Lee P. L. (1991a) Dynamic modelling of a single-stagehigh-rate anaerobic reactor--l. Model derivation. Wat. Res. 25, 847-858. Costello D. J., Greenfield P. F. and Lee P. L. (1991b) Dynamic modelling of a single-stage high-rate anaerobic reactor--II. Model verification. Wat. Res. 25, 859-871.
1628
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Kroeker E. J. (1978)Anaerobic treatment process stability. J. Wat. Pollut. Control Fed. 51, 718-727. Mawson A. J., Earle R. L. and Larsen V. F. (1991) Degradation of acetic and propionic acids in the methane fermentation. Wat. Res. 25, 1549-1554. Mosey F. E. (1982) Mathematical modelling of the anaerobic digestion process: regulatory mechanisms for the formation of short-chain volatile acids from glucose. War. Sci. Technol. 15, 209-232. Smith D. P. and McCarthy P. L. (1990) Factors governing methane fluctuations following shock loading of digesters. J. Wat. Pollut. Control Fed. 62, 58-64. Templeton L. L. and Leslie Grady C. P. Jr (1988) Effect of culture history on the determination of biodegradation kinetics by batch and fed-batch techniques. J. War. Pollut. Control Fed. 60, 651~58. Wilderer P. A., Rubio M. A. and Davids L. (1991) Impact of the addition of pure cultures on the performance of mixed culture reactors. Wat. Res. 25. 1307-1313.