Available online at www.sciencedirect.com
Bioresource Technology 99 (2008) 882–888
Prediction of methane yield at optimum pH for anaerobic digestionof organic fraction of municipal solid waste
Cun-fang Liu a, Xing-zhong Yuan a,*, Guang-ming Zeng a, Wen-wei Li a, Jing Li b
a College of Environmental Science and Engineering, Hunan University, Changsha, Hunan 410082, Chinab Department of Environmental Science and Engineering, Tsinghua University, Beijing 100084, China
Received 4 October 2006; received in revised form 11 January 2007; accepted 12 January 2007Available online 21 March 2007
Abstract
A concept of methane yield at optimum pH was advanced and subsequently a mathematical model that simulates the optimal pH of abatch process for anaerobic digestion of organic fraction of municipal solid waste (MSW) was developed and validated. The model wasdeveloped on the basis of the microbial growth kinetics and was divided into three processes: hydrolysis of substrates by hydrolytic bac-teria, consumption of soluble substrate by acidogenic bacteria, and finally consumption of acetate and methane generated by methano-genic bacteria. Material balance and liquid phase equilibrium chemistry were used in this study. A series of experiments were conductedto validate the model. The model simulation results agreed reasonably with experimental data in different temperatures and total solid(TS) concentrations under uncontrolled pH. A computer circulation program was used to predict the optimal pH in different conditions.Experiments in different temperatures and TS were run under optimal pH which predicted by the model. The model was succeeded inincreasing the methane production and the cumulative methane production had an average increment about 35% in optimal pH of dif-ferent temperatures and TS.� 2007 Elsevier Ltd. All rights reserved.
Keywords: Anaerobic process; Methane yield at optimum pH; Mathematical model; Municipal solid waste; Anaerobic batch reactor
1. Introduction
Anaerobic digestion is a natural process in which bacte-ria existing in oxygen-free environments decomposeorganic matter (Keshtkar et al., 2001). This has been pro-ven as a sound technology for treatment of the organicfraction of municipal solid waste (MSW) which could gen-erate renewable energy in the form of methane (Baere,2000; Parawira et al., 2004).
Since the establishment of the first dynamic model foranaerobic process by Andrews (1969), mathematical mod-els of anaerobic digestion process have been developedexpeditiously with the ever-deepening understanding andwidening application of anaerobic treatment. However,
0960-8524/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.biortech.2007.01.013
* Corresponding author. Tel.: +86 731 8823413; fax: +86 731 8823701.E-mail address: [email protected] (X.-z. Yuan).
almost all these models are process description modelsand the influence of pH on the digestion process was notsufficiently considered. In Masse and Droste’s (2000) modelwhich simulated anaerobic digestion of swine manuresludge, the effects of pH variation on microbial kineticswere neglected. The studies of Keshtkar et al. (2001) andSiegrist et al. (2002) involved pH inhibition in the anaero-bic digestion of cattle manure and sewage sludge, respec-tively, yet the pH was a factor other than a protagonistand the optimization of pH–methane yield relationshipswas not involved. The methane production efficiency isthe most important evaluation yardstick in anaerobicdigestion, there are several factors affecting methane pro-duction efficiency such as pH, temperature, type and qual-ity of substrate, mixing etc. (Molnar and Bartha, 1989),and the value of pH is the pivotal factor. Although it hasbeen proven that the optimal range of pH to obtain maxi-mal biogas yield in anaerobic digestion is 6.5–7.5, the range
C.-f. Liu et al. / Bioresource Technology 99 (2008) 882–888 883
is relative wide in the plant scale and the optimal value ofpH varies with substrate and digestion technique.
In 2002, the ADM1 model was developed by the IWATask Group for Mathematical Modeling of AnaerobicDigestion Processes. The model reflects the major processesthat are involved in the conversion of complex organicsubstrates into methane and carbon dioxide and inertbyproducts. In this model, all microbial mediated substrateconversion processes are subject to inhibition by extremesof pH. And an empirical correlation is employed as aprocess rate multiplier to reflect the effects of extreme pH(IWA, 2002). However, the ADM1 model employs a largenumber of constants and coefficients. Given the model com-plexity it was impossible to calibrate the model parameterswith any of the data sets that were available (Parker, 2005).
The objective of this study was to develop a mathemat-ical model which can describe the relationship between thepH and methane production for anaerobic digestion oforganic fraction of municipal solid waste (MSW) in a batchprocess. A computer circulation program was used forobtaining the optimal pH and a maximal cumulative CH4
production at this optimal pH. Therefore, the maximalrecover energy of MSW can be obtained by using optimiza-tion control of pH.
2. Mathematical model
2.1. Model description
The process optimization mathematical model presentedhere is based on models developed by Moletta et al. (1986),Kiely et al. (1996) and Keshtkar et al. (2001). This modelincludes three processes: hydrolysis of substrates by hydro-lytic bacteria, consumption of soluble substrate by acido-genic bacteria, and finally consumption of acetate andmethane generation by methanogenic bacteria. This modelis described as a set of algebraic equations that have beenformulated based on mass balances for substrates, prod-ucts and microbial components, and physico-chemicalequilibrium relationships among ionized/unionized species.Harper and Pohland (1986) and Mosey (1983) indicatedthe dissolved hydrogen concentration in the digester con-trols the course of substrate utilization. A digester that isfunctioning well has a very low dissolved hydrogen concen-tration, so the influence of hydrogen concentration indigester is not considered in this model. Bacterial cell massis represented by the empirical molecular formulaC5H7O2N. The growth of anaerobic microorganisms isexpressed by Monod-type kinetics, the consumption ofsubstrates and acids as well as the biomass decay isdescribed by first-order reactions.
2.2. Model development
2.2.1. Hydrolysis kineticsComplicated biodegradable organic substrate is hydro-
lyzed by hydrolytic bacteria and converted to soluble sub-
strate in hydrolysis process. The variation of concentrationof complicated biodegradable organic substrates with timecan be expressed by
dSh
dt¼ � lhX h
Y h
ð1Þ
where Xh is hydrolytic biomass (g/L); lh, the specificgrowth rate of hydrolytic bacteria (d�1); Sh, glucose equiv-alent concentration of complicated biodegradable organicsubstrates (g/L); Yh, the degradation coefficient of Sh
(g(Xh)/g(Sh)). The hydrolytic biomass with time is
dX h
dt¼ lhX h � KdhX h ð2Þ
where Kdh is the death rate of hydrolytic bacteria (d�1).Suppose the inhibition factors have no influence on thehydrolytic bacteria basically (Vavilin et al., 1996). The spe-cific growth rate of hydrolytic bacteria can be expresses asfollows:
lh ¼lhmaxSh
Ksh þ Sh
ð3Þ
where lhmax is the maximum specific growth rate of hydro-lytic bacteria (d�1); Ksh, the half-velocity constant forhydrolytic bacteria growth (g/L).
2.2.2. Acidification kinetics
In acidification process, the soluble substrate is metabo-lized by acid-producing bacteria to provide carbon dioxideand organic acids. Then the long chain organic acids areconverted into acetates by acidogenic bacteria (Nophara-tana et al., 2003). The variation of concentration of solublesubstrates with time is
dSa
dt¼ lhX h
Y vh
� laX a
Y a
ð4Þ
where Xa is the acidogenic biomass (g/L); la, the specificgrowth rate of acidogenic bacteria (d�1); Sa, glucose equiv-alent concentration of soluble substrates (g/L); Ya, the deg-radation coefficient of Sa (g(Xh)/g(Sa)); Yvh, the yieldcoefficient for Sa (g(Xa)/g(Sa)). The variation of acidogenicbiomass with time is
dX a
dt¼ laX a � KdaX a ð5Þ
where Kda is the death rate of acidogenic bacteria (d�1).The unionized acetate will influence acidogenic bacteriawhich are sensitive to pH. So the growth of acidogenic bac-teria is obeyed by modified Monod-type kinetics as follows:
la ¼lamax
1þ Ksa
Saþ Au
K ia
ð6Þ
where lamax is the maximum specific growth rate of acido-genic bacteria (d�1); Ksa, the half-velocity constant for aci-dogenic bacteria growth (g/L); Au, the concentration ofunionized acetate (g/L); Kia, the inhibition coefficient ofunionized acetate (g/L).
884 C.-f. Liu et al. / Bioresource Technology 99 (2008) 882–888
2.2.3. Methanogenesis kinetics
There are two major bacteria generating methane inmethanogenic process: aceticlastic methane bacteria andhydrogen utilizing methane bacteria. Aceticlastic methanebacteria metabolize acetate to methane and carbon diox-ide. Hydrogen utilizing bacteria consume carbon dioxidewith hydrogen to methane. Because it is very difficult toseparate the two kinds of bacteria for counting in theexperiment, the two bacteria are consolidated as methano-genic bacteria in this model. The variation of concentrationof acetate with time is
dAdt¼ laX a
Y va
� lmX m
Y m
ð7Þ
where Xm is methanogenic biomass (g/L); la, the specificgrowth rate of methanogenic bacteria (d�1); A, the totalacetate concentration (g/L); Ym, the degradation coefficientof A (g(Xm)/g(A)); Yva, the yield coefficient for A (g(Xa)/g(A)). According to ionization balance:
A ¼ Au þAc� ð8Þ
where Ac� is ionized acetate concentration (g/L); Au, un-ionized acetate concentration (g/L).
Au ¼Ac�1 �Hþ
Ka
ð9Þ
where H+ is the hydrogen ion concentration (g/L); Ka, thedissociation constant for acetate (1.728 · 10�5). The varia-tion of methanogenic biomass with time is
dX m
dt¼ lmX m � KdmX m ð10Þ
where Kdm is the death rate of methanogenic bacteria (d�1).The methanogenic bacteria is not only influenced by union-ized acetate but also by unionized ammonia (Mata-Alva-rez, 1987), so the growth of methanogenic bacteria isrepresented by modified Monod-type kinetics with twoinhibition factors as follows:
lm ¼lmmax
1þ Ksm
Auþ Au
K ixmþ NH3ðuÞ
K iam
ð11Þ
Table 1Kinetic parameters used in the model
Parameterunit
lhmax
(d�1)Ksh
(g/L)Kdh
(d�1)Yh (g(Xh)/g(Sh))
lamax
(d�1)
Value 0.03 10 0.05 0.2 0.4h 0.069 0.069 0.069 0.069
Ksm
(g/L)Kdm
(d�1)Yva (g(Xa)/g(A))
Ym (g(Xm)/g(A))
Kixm
(g/L)
Value 0.003 0.016 2.65 0.08 0.04h 0.10 0.069
Parameters of lhmax, Ksh, Kdh, Yh determined from Sun and Ke (1992); paramet al. (1996); parameters of Ksa, Kda, Yvh, Kia, Kixm, Vmmax, Y NH3
, YN, Km, Kim
Siegrist et al. (2002).
where lmmax is the maximum specific growth rate of meth-anogenic bacteria (d�1); Ksm, the half-velocity constant formethanogenic bacteria growth (g/L); Kixm, the inhibitioncoefficient of unionized acetate (g/L); NH3(u), the concen-tration of unionized ammonia (g/L); Kiam, the inhibitioncoefficient of unionized ammonia (g/L).
By Keshtkar et al. (2001), ammonia nitrogen is gener-ated in hydrolysis process and consumed in the whole pro-cess by all anaerobic microorganisms. The variation ofconcentration of ammonia nitrogen with time is written as
dNH3
dt¼ lhX hY NH3
� ðlh � Kdh þ la � Kda þ lm
� KdmÞ � Y N ð12Þ
where NH3 is the total ammonia concentration (g/L); Y NH3,
the yield coefficient for ammonia nitrogen (g(NH3)/g(Xh));YN, consumption coefficient for ammonia nitrogen(g(NH3)/g(Xi)(i is h, a, m)). When li � Kdi 6 0, the valueof YN is zero.
NH3 ¼ NH3ðuÞ þNHþ4 ð13Þ
NHþ4 ¼NH3ðuÞ �Hþ
KN �MNH3
ð14Þ
where MNH3is the mole weight of NH3 (17 g/mol); NHþ4 ,
the concentration of ionized ammonia (g/L); KN, the disso-ciation constant for ammonia (5.3 · 10�10). The variationof methane yield with time as expressed by Moletta et al.(1986) is
dCH4
dt¼ V mmaxX m
Au
Au þ Km
� �K im
K im þ Au
� �ð15Þ
where Vmmax is the maximal yield rate of methane (in vol-ume at 0 �C and 1 atm pressure) per gram of methanogenicbacteria per day (L/g d); Km, saturation constant of meth-ane yield (g/L); Kim, inhibition constant of acetate onmethane yield (g/L). According to the equations hereinbe-fore, the expression of relationship between pH and meth-ane yield is
Ksa
(g/L)Kda
(d�1)Yvh (g(Xh)/g(Sa))
Ya (g(Xa)/g(Sa))
Kia
(g/L)lmmax
(d�1)
0.26 0.06 0.22 0.188 0.02 0.60.035 0.055 0.069
Kiam
(g/L)Vmmax
(L/g d)
Y NH3(g(NH3)/
g(Xh))YN (g(NH3)/g(Xi))
Km
(g/L)Kim
(g/L)
0.12 0.7 0.183 0.15 0.0208 0.0590.061 0.086 0.086
eters of lamax, Ya, Yva, Ym, Ksm, Kiam, Kdm, lmmax determined from Kielydetermined from Moletta et al. (1986); parameters of h determined from
C.-f. Liu et al. / Bioresource Technology 99 (2008) 882–888 885
dCH4
dt¼ V mmaxX m
Ac�1 � 10�pH
Ac�1 � 10�pH þ KaKm
� �
� K imKa
K imKa þAc�1 � 10�pH
� �ð16Þ
The influence of the temperature on the kinetic expres-sions is assumed to be exponential F ðT Þ ¼ ehðT�T 0Þ. Allthe kinetic coefficients can be calculated on the basis ofthe mesophilic values at 25 �C.
2.3. Model calculation
Eqs. (1)–(16) were solved numerically by using thefourth order Runga–Kutta method. The time step chosenwas 0.01 days, as the smaller the time step, the closer theapproximate solution is to the actual one. Initial valuesfor pH, acetic acid and total solid concentration were thoseobserved on day 1 of the experiment. The values of param-eters are shown in Table 1. A computer circulation pro-gram was used for simulating the optimal pH.
3. Experiments
For the pre-treatment of the materials and the experi-ments refer to Rao and Singh’s (2004) method.
3.1. Materials and pre-treatment
The materials are the mixture of organic fraction ofMSW and excess activated sludge (inoculums), organicfraction of MSW consists of stover and food waste fromvegetable markets and household. The wastes were sortedand shredded, then mixed several times in laboratory.Twenty samples were analyzed for moisture content, totalsolids, total volatile solids, VFA and chemical oxygendemand. The chemical composition of the materials wasanalyzed using standard analysis methods (Wei, 2002).The mean chemical composition of the materials is givenin Table 2.
3.2. Experimental procedure
Two groups of comparative experiments of anaerobicdigestion of organic fraction of MSW in ABR were con-ducted on the base of the model before-mentioned.
Table 2Inoculums and MSW characteristics
Parameter Value
pH 7.0Total VFA as acetic acid (mg/L) 85.5Total chemical oxygen demand (mg/L) 2783Moisture (wt%) 85Total solids (wt%) 15Total volatile solids (wt% in total solids) 83.4C/N ratio 26.4
wt indicates weight fraction.
The experiments in mesophilic (35 ± 2 �C) and thermo-philic (55 ± 2 �C) temperature were conducted to verify thevalidity of the model under different temperatures. Twobioreactors each ran under uncontrolled pH and optimalpH, respectively with equal working volumes (2 L) andtotal solid concentrations (50 g/L) but differenttemperature.
The other group of experiments in different TS was con-ducted to verify the validity of model under different TS.Three bioreactors each ran under uncontrolled pH andoptimal pH, respectively with equal working volumes(10 L), but different TS concentrations. According to Raoand Singh (2004) the TS concentrations were picked as45 g/L, 70 g/L and 95 g/L, respectively. All the six reactorswere run under mesophilic temperature (35 ± 2 �C).
Glass bottles with bottom sampling outlet were used asbioreactors. The bottles were closed by rubber stoppersequipped with two glass tubes for gas removal and foradjusting the pH, respectively. The tube for adjusting thepH was dipped inside the slurry to avoid gas loss. The tem-perature of the slurry was controlled by water-heatingwhich had an accuracy ±0.5 �C and was measured by athermometer of range 0–80 �C with an accuracy ±0.2 �C.
The substrate was mixed with tap water to make slurryhave different TS concentration. The TS concentration wasexpressed as the weight of solids/total volume of solids pluswater assuming that the density of solid is approximatelyequal to the density of water. All the bioreactors were fedwith organic fraction of MSW, tap water and excess acti-vated sludge (inoculums). All the experiments were runningfor 30 days, liquid samples were drawn from each reactorperiodically and analyzed for pH and VFA. The pH wasmeasured daily and VFA was measured every two days.The gas production was measured at a fixed time everyday by using water displacement method. All the gas vol-umes were measured at an average temperature of 25 �Cand corrected to 0 �C and 1 atm pressure. The substratewas mixed once every day when the gas was measured, tomaintain intimate contact between the microorganismsand the substrate. Gas samples were collected by gas sam-pling injectors. The biogas composition (CH4 + CO2) wasdetermined using a Gas Chromatograph (Agilent 6890NGC).
4. Results and discussion
4.1. Model validation
The experimental data in uncontrolled pH were used tovalidate this model.
The profile of pH and VFA (mg/L) of the digestion atdifferent temperatures and TS concentrations are shownin Figs. 1 and 2, respectively. Because the buffer systemof the digestion such as CO2�
3 =HCO�3 , NHþ4 =NH3 �H2Odid not form in the first few days, a decrease in pH wasobserved due to the generation of VFA. And in the med-ium-term of the experiments the buffer system was stable
0
1
2
3
4
5
6
7
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
t(d)
pH
0
2000
4000
6000
8000
10000
12000
14000
16000
VFA
(mg/
l)
mesophilic digestion thermophilic digestion
Fig. 1. Profile of pH and VFA concentration in different temperatures.
0
1
2
3
4
5
6
7
8
1 3 5 9 11 13 15 17 19 21 23 25 27 29
t(d)
pH
0
1000
2000
3000
4000
5000
6000
7000
8000
VFA
(mg/
l)
45g/l 70g/l 90g/l
7
Fig. 2. Profile of pH and VFA concentration at different TSconcentrations.
Fig. 3. Comparison between experimental and prediction of cumulativemethane production in mesophilic and thermophilic digestion.
886 C.-f. Liu et al. / Bioresource Technology 99 (2008) 882–888
so the pH changed a little though the concentration ofVFA was higher. The initial pH drop and high volatilefatty acids concentration show that the substrate containssome easily biodegradable constituents. However, inFig. 1, the pH was dropped at the 13 d of the mesophilicdigestion because the VFA rose rapidly from 4000 mg/Lto 14000 mg/L. A little NaHCO3 was put in the mesophilicsystem to enhance the buffer capacity. Few days later thevalue of pH ascended subsequently the VFA fell.
According to the experimental value of pH, the cumula-tive methane production of the digestion could be pre-dicted by this model. The comparison betweenexperimental and prediction cumulative methane produc-tion in mesophilic and thermophilic temperature are illus-trated in Fig. 3. As can be seen from the figures, themodel could predict the trends of cumulative methane pro-duction approximately even the unsteady phase of the mes-ophilic digestion owing to the fluctuation of pH. However,
there are some deviations observed between the experimen-tal and model results. The model is underestimating theprediction for the first 15 days of the experiments and over-estimating in the later days. These deviations may becaused by the following reasons:
1. The reactor is assumed to be in a completely mixed statein the model, which is, in fact, hard to achieve.
2. The model assumed that the degradation rate of organicsolid was invariable, in reality, the rate is varied all thetime: in the first phase, the easily biodegradable solidswere plenteous, the degradation rate was faster thanassumed; and in later days, the easily biodegradable sol-ids were consumed so the degradation rate was less thanassumed.
3. In the experiments the density of solid is assumedapproximately equal to the density of water.
4. The values of kinetic parameters of this model weredetermined from different references.
The cumulative methane production at different TS con-centrations was also predicted and compared with experi-mental data. The comparison results were similar withthe results at different temperatures. Through the simula-tion results, it is obvious that when the total solid concen-tration was low (TS = 45 g/L), the predicted cumulativemethane productions closely followed the experimentaltrends. However, the deviations between the experimentaland the model results augmented when the TS concentra-tion increased. The deviation value reaches the maximumin simulations when the TS concentration is 95 g/L espe-cially at the first 10 days. This can be explained by the sub-strate inhibition change caused by the increase of TSconcentration while the basal Monod equation could notdescribe the hydrolytic process of anaerobic digestion ofthe MSW absolutely precisely.
The comparison between experimental and modelresults suggests that the model is basically valid in predict-
Fig. 5. Comparison between experimental and prediction of cumulativemethane production at optimal pH in different temperatures.
Fig. 6. Comparison between experimental and prediction of cumulativemethane production in optimal pH at different TS concentrations.
C.-f. Liu et al. / Bioresource Technology 99 (2008) 882–888 887
ing cumulative methane productions, and the optimal valueof pH in different conditions could be calculated fartherthrough this model.
4.2. Model simulation
The optimal values of pH of the experiments before-mentioned are simulated by using the computer circulationprogram of the optimization model. The parameters in thismodel are the same of experiments aforementioned. Thesimulated optimal values of pH at different temperaturesare shown in Fig. 4. It has been observed that the optimalvalues of pH are 7.10, 7.21 under mesophilic and thermo-philic temperature, respectively. In the same way, the opti-mal values of pH are 7.20, 7.21 and 7.19 under TS of 45 g/L, 70 g/L and 95 g/L, respectively at mesophilis tempera-ture. Although the optimal pH was little difference in differ-ent TS, it is essential to predict the optimal pH for eachconcrete experimental condition in practical operation,especially in plant-scale operation. In addition, throughthe optimal prediction, the minimum NaHCO3 was neededwhile the maximal CH4 was obtained; therefore, the maxi-mal economic benefit was achieved. The pH is a function ofVFA concentration, biocarbonate concentration, alkalinityof the system and fraction of CO2 in digester gas, so thepivotal factor to adjust the pH as a constant value is adjust-ing the relationship between the VFA and biocarbonateconcentration. Because the concentration of VFA variedwith the type and quality of substrate and it is hard to con-trol, consequently the further study would be the control-ling of the additional quantity of NaHCO3.
The experiments in different temperatures and TS wererun under optimal pH which had been predicted by themodel. The comparison between the model simulationresults and the experimental data for the volume of meth-ane production in optimal pH are shown in Figs. 5 and6. The cumulative methane production was increasedabout 35% in optimal pH. It indicated that the effect wasdistinct to control the pH under an optimal value. The sim-
Fig. 4. Simulated optimal values of pH at different temperatures.
ulation results followed the experimental trends well at thefirst 20 days but over-predicted the methane production inthe final 10 days. It might be due to the character hypoth-esis of experimental materials. The model assumed that thedegradation rate of organic solid was invariable, in reality,the organic solid in the final period of digestion was almostcellulose and hemicellulose, and they were degraded slowlyby bacteria. Hence the experimental data of the cumulativemethane production in the final 10 days was basicallyunchanged while the predicted result was increased as usualand deviations were made between the prediction andexperimental methane production. Furthermore, the pHin experiments was controlled by manual adjusting onceeach day owing to the limitation of operation condition,so when the pH fluctuated and some errors were made.
5. Conclusions
This paper represents a process optimization model ofpH–methane yield of an ABR system for digestion of
888 C.-f. Liu et al. / Bioresource Technology 99 (2008) 882–888
organic fraction of MSW. Through this model, the optimalpH at different temperatures and initial TS concentrationscan be obtained by using a computer circulation program.Furthermore, the maximal methane production can be pre-dicted in the optimal pH. Therefore a maximal generationrate of methane can be obtained and a great efficiency ofanaerobic digestion can be achieved in the operation ofanaerobic digestion of MSW. However, this paper onlyresearched on the relation between the pH and cumulativemethane production. The factors on the value of pH suchas the concentration of VFA, HCO�3 , NHþ4 and further-more the controlling of the additional quantity of NaHCO3
would be studied in future.
Acknowledgements
This research was financially supported by the NationalNatural Science Foundation of China (No. 50678062), theNational Basic Research Program of China(2005CB724203), and Chinese National Natural Founda-tion for Distinguished Young Scholars Project (No.50225926).
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