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Process Biochemistry 46 (2011) 557–565

Contents lists available at ScienceDirect

Process Biochemistry

journa l homepage: www.e lsev ier .com/ locate /procbio

odelling the effect of the OLR and OFMSW particle size on the performances ofn anaerobic co-digestion reactor

. Espositoa, L. Frunzob, A. Panicoc,∗, F. Pirozzi c

Department of Mechanics, Structures and Environmental Engineering, University of Cassino, via Di Biasio 43, 03043 Cassino (FR), ItalyDepartment of Mathematics and Applications Renato Caccioppoli, University of Naples Federico II, Via Cintia, Monte S. Angelo, I-80126 Naples, ItalyDepartment of Hydraulic, Geotechnical and Environmental Engineering, University of Naples Federico II, via Claudio 21, 80125 Naples, Italy

r t i c l e i n f o

rticle history:eceived 20 January 2010eceived in revised form7 September 2010ccepted 20 October 2010

eywords:naerobico-digestionathematical modelling

a b s t r a c t

A dynamic mathematical model capable to predict the methane production in an anaerobic completelystirred tank reactor (CSTR), performing the co-digestion of the organic fraction of municipal solid waste(OFMSW) and sewage sludge, is used to assess the effect of the organic loading rate (OLR) and OFMSWparticle size on the reactor performances.

The model is based on the approach proposed by the IWA Anaerobic Digestion Model no. 1 (ADM1),which has been modified to take into account the peculiarities of a co-digestion process. The main dis-tinctiveness of the proposed model consists in considering two separate influent substrates (i.e. sewagesludge and OFMSW), which are modelled with different biodegradation kinetics. The sewage sludgedegradation is modelled according to the ADM1 while a surface based kinetics is used to simulate the

FMSW particle sizeLRewage sludge

OFMSW disintegration process, which depends on particle size distribution (PSD) of the solid waste to bedisintegrated. The methane production of a full scale municipal wastewater treatment plant (MWWTP)digester has been evaluated to assess the model capability to estimate the potential energy productionunder different process conditions. In particular, a sensitivity analysis on two key operational param-eters of the CSTR co-digestion process, i.e. OLR and OFMSW particle size, has been carried out. Thisanalysis shows the model suitability to assess the combined effect of such parameters on the digester

the p

performances, predicting

. Introduction

Anaerobic combined digestion (co-digestion) of the organicraction of municipal solid waste (OFMSW) with sewage sludgen the anaerobic digesters of municipal wastewater treatmentlants (MWWTPs) represents a valuable solution for the disposal ofrganic wastes and an interesting option for generating energy byrenewable source [1]. Indeed, anaerobic co-digestion of organicatter results in waste stabilization as well as in biogas production.

his gas usually contains more than 50% methane, and therefore itan be used as bio-fuel in power generation systems to produceeat and energy.

Since the amount of energy which can be obtained by organicastes depends on the efficiency of the co-digestion process, the

perational optimization of this process is strategically relevant [2].or this purpose, pilot-scale experiments offer a high level of suc-

∗ Corresponding author. Tel.: +39 081 7683434; fax: +39 081 5938344.E-mail addresses: giovanni.esposito@unicas.it (G. Esposito),

uigi.frunzo@unina.it (L. Frunzo), anpanico@unina.it (A. Panico),rancesco.pirozzi@unina.it (F. Pirozzi).

359-5113/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.oi:10.1016/j.procbio.2010.10.010

rocess failure occurrence.© 2010 Elsevier Ltd. All rights reserved.

cess, but they require a long time to be started up and reach steadystate conditions. Furthermore, anaerobic digestion is a fairly com-plex process and the experimental assessment of the effects of allinvolved variables on the process efficiency is time consuming andhardly possible.

Therefore, the use of mathematical models capable to predictthe process performance over a range of design and opera-tional conditions is definitely very useful. Several steady state aswell as dynamic models describing the anaerobic degradation oforganic matter have been proposed in the literature [3–8]. Theypresent a different level of complexity and are based on differ-ent assumptions and simplifications. In 2002 the InternationalWater Association (IWA) Task Group for Mathematical Modelling ofAnaerobic Digestion Processes developed a comprehensive math-ematical model known as ADM1 [9], which was based on theknowledge on modelling and simulation of anaerobic digestionsystems emerged over the previous years.

However this model neglects some processes involved in theanaerobic digestion such as sulphate reduction, acetate oxidation,homoacetogenesis, solids precipitation and inhibition due to sul-phide, nitrate, long chain fatty acid (LCFA), weak acid and base[10]. Some of the previous aspects have been studied and modelled

558 G. Esposito et al. / Process Bioche

Fm

a2Ctp

Atpispt

tCdta

2

2

birg[

taitbbbs

ig. 1. Schematic representation of conversion pathways in the mathematicalodel.

fterwards; for instance two ADM1 extensions were published in003, concerning respectively the sulphate reduction [11], and theaCO3 precipitation [12]. A further extension aimed at removinghe ADM1 discrepancies in both carbon and nitrogen balances wasublished in 2005 [13].

A mathematical model [14] has been recently proposed by theuthors to extend the ADM1 applicability to the anaerobic diges-

ion of organic solid wastes. This model aims at assessing theerformances of a sewage sludge and OFMSW co-digestion system

n terms of COD removal, and includes the simulation of the organicolid particles disintegration. This model has been upgraded in thisaper to predict the methane production potential and simulatehe pH inhibition effect due to the LCFAs production.

Model simulations are carried out to show the model suitabilityo predict the effect of the OFMSW particle size and OLR on theOD removal efficiency and methane production of a full-scale co-igestion CSTR with no sludge recycle, where the sludge retentionime is the same as the hydraulic retention time, and thus is notffected by the OLR.

. Mathematical model

.1. Mass balance equations, kinetics and stoichiometry

The proposed mathematical model is based on differential massalance equations for substrates, products and bacterial groups

nvolved in the co-digestion process and includes the biochemicaleactions of the substrate conversion and the kinetics of microbialrowth and decay [14]. The matrix notation proposed by the ADM19] is used to describe the model equations (Tables 1A and 1B).

Besides including the prediction of methane production poten-ial, the upgraded mathematical model presented in this paperlso includes the possibility to separate each product of the dis-ntegration process (i.e. carbohydrates, proteins and lipids) into

wo fractions, i.e. a readily biodegradable fraction and a slowlyiodegradable fraction (Fig. 1, Table 1A). This separation is achievedy introducing a higher hydrolysis rate constant for the readilyiodegradable fraction and a lower hydrolysis rate constant for thelowly biodegradable fraction (Table 1A).

mistry 46 (2011) 557–565

2.2. Disintegration process

The main distinctiveness of the proposed model if comparedto the ADM1 is the capability to consider two separate influentsubstrates, i.e. sewage sludge and OFMSW. The sewage sludgedegradation is modelled according to the ADM1 while the follow-ing surface based kinetic expression [15] is used to simulate thedisintegration of organic waste particles, which is a fundamentalstep when the substrate to be disintegrated is highly complex asthe OFMSW:

dM

dt= −KsbkA (1)

This equation has been reformulated in terms of concentrations(Eq. (4)), by including the following two parameters, a and a* [14],which characterize the disintegration process:

a = A

Vliq(2)

a∗ = A

M(3)

dC

dt= −Ksbk · a∗ · C (4)

Assuming that all organic solid particles have the same spheri-cal shape and initial size and they are progressively and uniformlydegraded in all directions from the outside towards the inside, theprevious Eq. (3) can be rewritten as follows:

a∗ =∑n

i=1Ai∑ni=1Mi

= nAi

nMi= n4�R2

nı4/3�R3= 3

ıR(5)

where R is the organic solid particles radius, assumed time depen-dent in according with the following expression proposed by [15]:

R = R0 − Ksbkt

ı(6)

2.3. Acid–base equilibria

In the previous version of the mathematical model [14]acid–base equilibria were also taken into account, and pH deter-mination was performed using mass balances, chemical equilibriaand electro-neutrality relationships, which resulted in a nine-orderpolynomial equation with [H+] as unknown.

The same approach has been applied in the actual version ofthe model but also LCFA have been included among the chemi-cal species taken into account. As LCFA have a very small numberof charged sites per COD [9], they affect marginally the pH andtherefore their contribute in pH calculation is usually neglected inanaerobic digestion models of substrates not rich in lipids [9,16,17].However, this contribute has been taken into account in the presentmodel as the high amount of LCFA produced by lipids hydrolysis,when substrates rich in lipids are considered, is capable to cause asignificant decrease of pH and lead the anaerobic digestion processto failure [18].

The addition of LCFA effect on the pH modelling implies amodification of the nine-order polynomial equation with [H+] asunknown, which turns into a ten-order polynomial equation.

2.4. Liquid-to-gas mass transfer

The first version of the proposed mathematical model [14] wasonly aimed at predicting the performances of a co-digestion sys-tem, without any focus on methane formation. The equations ofmethane production by methanogenic archea and liquid to gasmass transfer, needed to predict the energy production potential

G.Esposito

etal./Process

Biochemistry

46(2011)

557–565559

Table 1AMatrix of model equations, part1.

Process Component Rate �j[kgCOD m−3 d−1]

1 2 3 4 5 6 7 8 9 10 11 12Ssu Saa Sfa Sva Sbu Spro Sac Sh2 SCH4 SIC SIN SI

1 Disintegration of OFMSW fsI,Xc Ksbk·C·a*2 Disintegration of sludge Kdis Slu·XSlu

3 Hydrolysis of carbohydrates (readily) 1 Khyd ch S·Xch R

4 Hydrolysis of carbohydrates (slowly) 1 Khyd ch S·Xch S

5 Hydrolysis of proteins (readily) 1 Khyd pr R·Xpr R

6 Hydrolysis of proteins (slowly) 1 Khyd pr S·Xpr S

7 Hydrolysis of lipids (readily) 1 − ffa,li ffa,li Khyd li R·Xli R

8 Hydrolysis of lipids (slowly) 1 − ffa,li ffa,li Khyd li S·Xli S

9 Uptake of sugars −1 (1 − Ysu) fbu,su (1 − Ysu) fpra,su (1 − Ysu) fac,su (1 − Ysu) fh2,su −∑

i=1,9−11,28

Ci�i,9 −(Ysu)Nbac Km,su · SsuKs+Ssu

· Xsu · I1

10 Uptake of amino acids −1 (1 − Yaa) fva,aa (1 − Yaa) fbu,aa (1 − Yaa) fpro,aa (1 − Yaa) fac,aa (1 − Yaa) fh2,aa −∑

i=13−20,26

Ci�i,10 Naa − (Yaa)Nbac Km,aa · SaaKs+Saa

· Xaa · I1

11 Uptake of LCFA −1 (1 − Yfa)0.7 (1 − Yfa)0.3 −(Yfa)Nbac Km,fa · SfaKs+Sfa

· Xfa · I2

12 Uptake of valerate −1 (1 − YC4)0.54 (1 − YC4)0.31 (1 − YC4)0.15 −(YC4)Nbac Km,C4 · SvaKs+Sva

· XC4 · 11+Sbu/Sva

· I2

13 Uptake of butyrate −1 (1 − YC4)0.8 (1 − YC4)0.2 −(YC4)Nbac Km,C4 · SbuKs+Sbu

· XC4 · 11+Sva/Sbu

· I2

14 Uptake of propionate −1 (1 − Ypro)0.57 (1 − Ypro)0.43 −∑

i=13−20,26

Ci�i,14 −(Ypro)Nbac Km,pro · SproKs+Spro

· Xpro · I2

15 Uptake of acetate −1 (1 − Yac) −∑

i=13−20,26

Ci�i,15 −(Yac)Nbac Km,ac · SacKs+Sac

· Xac · I3

16 Uptake of hydrogen −1 (1 − Yh2) −∑

i=13−20,26

Ci�i,16 −(Yh2)Nbac Km,h2 · Sh2Ks+Sh2

· Xh2 · I1

17 Decay of Xsu −∑

i=13−20,26

Ci�i,17 −∑

i=13−20,26

Ni�i,17 Kdec,Xsu·Xsu

18 Decay of Xaa −∑

i=13−20,26

Ci�i,18 −∑

i=13−20,26

Ni�i,18 Kdec,Xaa·Xaa

19 Decay of Xfa −∑

i=13−20,26

Ci�i,19 −∑

i=13−20,26

Ni�i,19 Kdec,Xfa·Xfa

20 Decay of XC4 −∑

i=13−20,26

Ci�i,20 −∑

i=13−20,26

Ni�i,20 Kdec,Xc4·Xc4

21 Decay of Xpro −∑

i=13−20,26

Ci�i,21 −∑

i=13−20,26

Ni�i,21 Kdec,Xpro·Xpro

22 Decay of Xac −∑

i=13−20,26

Ci�i,22 −∑

i=13−20,26

Ni�i,22 Kdec,Xac·Xac

23 Decay of Xh2 −∑

i=13−20,26

Ci�i,23 −∑

i=13−20,26

Ni�i,23 Kdec,Xh2·Xh2

560G

.Espositoet

al./ProcessBiochem

istry46

(2011)557–565

Table 1BMatrix of model equation, part 2.

Process Component Rate �j[kgCOD m−3 d−1]

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

C XCh R XCh S XPr R XPr S XLi R XLi S XSu Xaa Xfa XC4 Xpro Xac Xh2 XI XShu

1 Disintegration of OFMSW −1 fCh,Xc·fr fCh,Xc·fs fPr,Xc·fr fPr,Xc·fs fLi,Xc·fr fLi,Xc·fs fXI ,Xc Ksbk·C·a*2 Disintegration of sludge fCh,Xslu·fr fCh,Xslu·fs fPr,Xslu·fr fPr,Xc·fs fLi,Xslu·fr fLi,Xslu·fs −1 Kdis Slu·XSlu

3 Hydrolysis of carbohydrates (readily) −1 Khyd ch R·Xch R

4 Hydrolysis of carbohydrates (slowly) −1 Khyd ch S·Xch S

5 Hydrolysis of proteins (readily) −1 Khyd pr R·Xpr R

6 Hydrolysis of proteins (slowly) −1 Khyd pr S·Xpr S

7 Hydrolysis of lipids (readily) −1 Khyd li R·Xli R

8 Hydrolysis of lipids (slowly) −1 Khyd li S·Xli S

9 Uptake of sugars Ysu Km,su · SsuKs+Ssu

· Xsu · I1

10 Uptake of amino acids Yaa Km,aa · SaaKs+Saa

· Xaa · I1

11 Uptake of LCFA Yfa Km,fa · SfaKs+Sfa

· Xfa · I2

12 Uptake of valerate YC4 Km,C4 · SvaKs+Sva

· XC4 · 11+Sva/Sbu

· I2

13 Uptake of butyrate YC4 Km,C4 · SbuKs+Sbu

· XC4 · 11+Sva/Sbu

· I2

14 Uptake of propionate Ypro Km,pro · SproKs+Spro

· Xpro · I2

15 Uptake of acetate Yac Km,ac · SacKs+Sac

· Xac · I

16 Uptake of hydrogen Yh2 Km,h2 · Sh2Ks+Sh2

· Xh2 · I1

17 Decay of Xsu 1 −1 Kdec,Xsu·Xsu

18 Decay of Xaa 1 −1 Kdec,Xaa·Xaa

19 Decay of Xfa 1 −1 Kdec,Xfa·Xfa

20 Decay of XC4 1 −1 Kdec,Xc4·Xc4

21 Decay of Xpro 1 −1 Kdec,Xpro·Xpro

22 Decay of Xac 1 −1 Kdec,Xac·Xac

23 Decay of Xh2 1 −1 Kdec,Xh2·Xh2

G. Esposito et al. / Process Biochemistry 46 (2011) 557–565 561

Table 2Operational parameters used for model simulations.

Parameter Unit Simulations Set 1 Simulations Set 2

Digester volume m3 12,000 12,000Influent sewage sludge flow rate m3 d−1 430 430Sewage sludge OLR kgCOD d−1 m−3 1.43 1.43Sewage sludge carbohydrates content % 20 20Sewage sludge proteins content % 20 20Sewage sludge lipids content % 25 25Sewage sludge inerts content % 35 35OFMSW OLR kgCOD d−1 m−3 1.43 0–2.86OFMSW carbohydrates content % 40 40OFMSW proteins content % 10 10OFMSW lipids content % 15 15OFMSW inerts content % 35 35

−3 −2 −3

ou

2

eima

pd

c

woaal

fM

3

3

adoska[ta

The lower COD degradation due to a higher particle radiusimplies a lower methane production rate (Fig. 2C) and a lowercumulative methane formation (Fig. 2B). This points out the lim-iting effect of the disintegration step on the methane production,

Table 3Hydrolysis kinetic constants [19].

Hydrolysis kinetic constant Value (d−1)

K 2.0

OFMSW particle initial radius Ma* m2 kg−1

Gas pressure in the digester headspace BarTemperature ◦C

f the system, have been included in the present upgraded model,sing the equations proposed in the ADM1 [9].

.5. Numerical integration

The model equations system is composed by 30 ordinary differ-ntial equations (ODEs) and 1 algebraic equation (AE). The 30 ODEsnclude 15 mass balance equations of suspended materials and 12

ass balance equations of dissolved materials which are expresseds follows:

dS

dt= q

Vliq(Sin − S) +

∑

j=1..N

�j�j (7)

The following 3 mass balance equations of the 3 gaseous com-onents taken into account (i.e. CO2, CH4, H2) are included toetermine the gas composition of the digester headspace:

d[S](g)

dt= Vliq

VgaskLa([S](l) − [S∗](l)) − Qout,g

Vgas[S](g) (8)

The only algebraic equation is the following and expresses theondition of electro-neutrality in the water:

[Cat+] + [H3O+] + [NH4+] = [OH−] + [Pr−] + [Bu−] + ...

+[Va−] + [Ac−] + [LCFA−] + [HCO3−] + [An−]

(9)

here the squared brackets symbolise the molar concentrationf the considered chemical species (i.e. cations, hydronium ion,mmonium ion, hydroxyl ion, propionate ion, butyrate ion, valer-te ion, acetate ion, ion coming from the acid dissociation of theong chain fatty acids, bicarbonate ion and anions).

Numerical integration of the 31 DAEs system has been per-ormed using the ODE 15 s multi-step solving algorithm of

ATLAB®.

. Results and discussion

.1. Parameter values used for the simulations

The mathematical model proposed in this paper has beenpplied to simulate the co-digestion process and methane pro-uction in a digester of a typical MWWTP with a working volumef 12,000 m3 and the hypothetical characteristics of the influentewage sludge and OFMSW reported in Table 2. Values of the

inetic and stoichiometric parameters as well as Henry’s constantsccording to the suggested parameter value for mesophilic solids9], a kinetic disintegration constant Ksbk according to [15] andhe hydrolysis kinetic constants reported in Table 3 have beendopted for all simulations. The LCFA dissociation constant kLCFA

2.5 × 10 –5.0 × 10 5.0 × 109.09 × 10−2–1.82 9.10 × 10−1

1.25 1.2535 35

in the acid base equilibria equations has been assumed equal to1 × 10−4.5 according to [20]. Fractions of 50% readily biodegrad-able and 50% slowly biodegradable substrate have been assumed.Values of 2.16 d−1and 3.84 d−1 [21] have been used for the kLa coef-ficients of the liquid-to-gas mass transfer of methane and hydrogen,respectively, whereas a value of 60 d−1 [22] has been applied for thecarbon dioxide kLa coefficient.

As the radius of the organic solid particles becomes smaller withtime following a linear law [15], each simulation has been carriedout assuming a* constant and equal to the value resulting by Eq.(5), with the organic solid particles radius, R, equal to the arith-metic mean between its initial value, R0, and the value calculatedby means of Eq. (6) in correspondence of the digester solid retentiontime (SRT).

The initial values of the state variables reported in Table 4 havebeen used.

3.2. Effect of the OFMSW particle size on the digesterperformances

Fig. 2 shows the results of model simulations (set 1, Table 2)performed to assess the effect of the OFMSW particle size on thedigester performances in terms of COD removal efficiency andmethane production. Different particle initial radius (R0) of theOFMSW in the range 2.5 × 10−3–5 × 10−2 m have been investigated,assuming a continuous addition of 17,200 kg COD d−1 of OFMSWinto the digester for 160 days (i.e. from day 20 to day 180).

An increase of the OFMSW particle size results in the increase ofthe COD fraction of the OFMSW added into the reactor that is notbiodegraded (Fig. 2A) and remains in the effluent. The effluent CODdue to sewage sludge is 3.35 kgCOD m−3. The latter is not includedin the effluent COD reported in Fig. 2A, which is only related to theOFMSW.

hyd ch R

Khyd ch S 0.5Khyd pr R 0.8Khyd pr S 0.25Khyd li R 0.7Khyd li S 0.1

562 G. Esposito et al. / Process Biochemistry 46 (2011) 557–565

Fig. 2. Effect of the OFMSW particle size on the effluent COD (A), methane cumulative formation (B), methane production rate (C) and pH (D).

Fig. 3. Effect of the OFMSW addition on the effluent COD (A), methane cumulative formation (B), methane production rate (C), pH (D), hydrogenotrophic methanogenicarchea (E) and acetoclastic methanogenic archea (F).

Fig. 4. Combined effect of the OFMSW particle size and OLR on the digestion performances in terms of COD removal efficiency (�).

G. Esposito et al. / Process Biochemistry 46 (2011) 557–565 563

Table 4Initial values of the state variables.

State variable Symbol Value Unit

Initial monosaccharides concentration Ssu0 0.4639 kgCOD m−3

Initial amino acids concentration Saa0 0.1694 kgCOD m−3

Initial long chain fatty acids concentration Sfa0 6.5310 kgCOD m−3

Initial valerate concentration Sva0 0.0941 kgCOD m−3

Initial butyrate concentration Sbu0 0.1330 kgCOD m−3

Initial Propionate concentration Spro0 0.5478 kgCOD m−3

Initial Acetate concentration Shac0 0.0589 kgCOD m−3

Initial hydrogen gas concentration (aqueous phase) SH20 1.5401e−005 kgCOD m−3

Initial methane gas concentration (aqueous phase) SCH40 0.2596 kgCOD m−3

Initial inorganic carbon concentration SIC0 0.0083 kmoleC m−3

Initial inorganic nitrogen concentration SIN0 0.0382 kmoleN m−3

Initial soluble inerts concentration SI0 3.7355 kgCOD m−3

Initial sludge concentration Xc0 3.3464 kgCOD m−3

Initial readily degradable carbohydrates concentration Xch re0 0.0654 kgCOD m−3

Initial readily degradable lipids concentration Xpr re0 0.1593 kgCOD m−3

Initial readily degradable proteins concentration Xli re0 0.2263 kgCOD m−3

Initial slowly degradable carbohydrates concentration Xch sl0 0.2486 kgCOD m−3

Initial slowly degradable proteins concentration Xpr sl0 0.4660 kgCOD m−3

Initial slowly degradable lipids concentration Xli sl0 1.2257 kgCOD m−3

Initial sugar degraders concentration Xsu0 0.4117 kgCOD m−3

Initial amino acids degraders concentration Xaa0 0.3166 kgCOD m−3

Initial LCFA degraders concentration Xfa0 1.4815e−005 kgCOD m−3

Initial valerate and butyrate degraders concentration Xc40 0.1277 kgCOD m−3

Initial propionate degraders concentration Xpro0 0.0491 kgCOD m−3

Initial acetate degraders concentration Xac0 0.2434 kgCOD m−3

Initial hydrogen degraders concentration XH20 0.1084 kgCOD m−3

Initial particulate inerts concentration XI0 9.3388 kgCOD m−3

Initial methane gas amount (cumulative) CH4 c0 0 kmoleInitial dioxide carbon amount (cumulative) CO2 c0 0 kmoleInitial hydrogen gas amount (cumulative) H2 c0 0 kmole

Xofms −3

CH4 gCO2 gH2 gp

iocipoq

(Htgap

3

tOtsfi1ta

mf3ai

Initial OFMSW concentrationInitial methane gas concentration (gaseous phase)Initial dioxide carbon concentration (gaseous phase)Initial hydrogen gas concentration (gaseous phase)

.e. on the whole biological process. In fact, a larger particle sizef the organic particles feeding the digester affects the overall pro-ess efficiency, due to the decrease of the disintegration rate, whichmplies a limited (i.e. only partial) transformation in carbohydrates,roteins and lipids of these particles and, thus, a lower availabilityf substrates for the subsequent biological processes. As a conse-uence, a lower methane production is achieved.

The OFMSW addition at day 20 also implies a sharp pH decreaseFig. 2D) due to higher acids production by acidogenic bacteria.owever these acids are degraded by acetogenic bacteria and when

he biological system reaches new steady-state conditions the pHoes up to 6.6 again. A pH increase occurs when the OFMSWddition is stopped, i.e. at day 180, due to the decrease of acidsroduction, but a pH of 6.6 is reached again around day 280.

.3. Effect of the OFMSW OLR on the digester performances

Further simulations (set 2, Table 2) have been carried outo investigate the effect on the methane production of theFMSW amount added into the sewage sludge digester. Con-

inuous OFMSW additions from day 20 to day 180 have beenimulated. The results show that increasing the OFMSW inputrom 0 to 34,400 kgCOD d−1 (i.e. increasing the total organic load-ng rate, OLR, due to both sewage sludge and OFMSW from.43 kgCOD m−3 d−1 to 4.29 kgCOD m−3 d−1) results in an impor-ant increase of the OFMSW that is not biodegraded in the digesternd thus remains in the effluent (Fig. 3A).

Fig. 3B and C shows the increase of the cumulative methane for-

ation and methane production rate, respectively, which derive

rom the above cited increase of the OFMSW input from 0 to4,400 kgCOD d−1. The pH decrease (Fig. 3D) due to the OFMSWddition at day 20 is higher when a higher OFMSW amount is addednto the reactor. However for all OLRs investigated in the range

w0 0 kgCOD mp 2.8949 kgCOD m−3

p 0.1945 kmoleC m−3

3.0832e−004 kgCOD m−3

1.43–4.29 kgCOD m−3 d−1 the biological system slowly reachesnew steady-state conditions and the pH goes up to 6.6 again.

Whereas when an overall OLR of 4.43 kgCOD m−3 d−1 is consid-ered, the pH drop is irreversible and results in the digester failure(Fig. 3D). The pH drop affects the microbial activity, resulting ina sharp decrease of the bacterial concentration in the digester.For instance, the acetoclastic and hydrogenotrophic methanogenicarchea are completely washed out from the digester around day100 (Fig. 3E) and day 105 (3F), confirming the digester failure.

Fig. 3E also shows an increase of the concentration of ace-toclastic methanogenic archea from 0.24 to 0.99 kgCOD m−3,which results from the increase of the OLR from 1.43 to4.29 kgCOD m−3 d−1. The percentage increase of this concentration(412.5%) of methanogenic archea is higher than the percentageincrease of the OLR (300%), confirming the potential of OFMSWaddition into the digester to maximize the methane production.

3.4. Definition of optimal OFMSW particle size and OLR conditions

Fig. 4 shows the results of a sensitivity analysis on the 2 oper-ational parameters taken into account in this study, i.e. OFMSWparticle size and OLR, aimed at assessing their combined effecton the digester performances and the occurrence of the digestionprocess failure.

The model simulations have been carried out with the samedigester volume and the same characteristics of the influent sewagesludge as reported in Table 2, but ranging the particle radiusand the OLR between 5.0 × 10−4 and 2.5 × 10−2 m and 1.43 and

9.14 kgCOD m−3 d−1, respectively. In particular, for each particleradius several simulations have been performed, increasing theOLR from 1.43 kgCOD m−3 d−1 (i.e. only sewage sludge feeding thereactor) to the OLR value provoking the digestion process failure,corresponding to a point of the dotted line which defines the failure

5 ioche

zOo

ttfitr

4

•

•

•

A

RPRiE

A

aaAA

C

CCCCCfffHHHI

64 G. Esposito et al. / Process B

one in Fig. 4. The COD removal efficiency (�), including both theFMSW and sewage sludge COD, was predicted for each simulation,btaining the isoefficiency curves in Fig. 4.

Fig. 4 shows that the higher is the particle size of the OFMSW,he higher is the OLR that induces the digester failure. This is due tohe slower disintegration and thus slower acidification occurringor higher OFMSW particle sizes. However such larger particlesmply the slow down of all the digestion processes, resulting inhe decrease of the overall digestion efficiencies in terms of CODemoval, as showed by the isoefficiency curves in Fig. 4.

. Conclusions

The mathematical model proposed is capable to assess the effectof the OFMSW particle size on the methane production rate andcumulative formation of a system performing an OFMSW andsewage sludge co-digestion process.The mathematical model can be used to assess the maximum OLRincrease due to OFMSW addition that an anaerobic digester cantolerate. In particular, it can be applied to optimize the OFMSWaddition into the anaerobic digesters of the MWWTPs. Model sim-ulations show as an OLR excess results in a pH drop and thus adigester failure.Model calibration is needed to use the proposed mathematicalmodel to predict the performances of a full-scale digester fedwith a specific OFMSW. If compared to standard first order kinet-ics where the disintegration kinetic constant depends both onthe nature and PSD of the organic substrate, the main advantageof this approach is that Ksbk only depends on the organic sub-strate nature as the PSD is taken into account by the coefficienta*. Therefore simple laboratory-scale experiments [23,24] carriedout on OFMSW samples of any PSD are sufficient to determine theproper Ksbk value.

cknowledgements

This research was supported by the Italian Ministry of theesearch and University in the framework of the National Researchroject Advanced Treatments for Organic Waste Reuse and Energyecovery funded in 2006 and the Research Project Energy Sav-

ng with Valorisation of the Secondary Energy Sources as Distributednergy Sources funded in 2007.

ppendix A.

volume specific area [L−1]* mass specific area [L2 M−1]

disintegration surface area [L2]i disintegration surface area of the organic solid particle i

[L2]= M/Vliq concentration of the complex organic substrate

(OFMSW) in the digester [M L−3]i content of carbon in component i [mole M−3]H4 c methane gas amount (cumulative) [M]H4 gp methane gas concentration (gaseous phase) [M L−3]O2 c dioxide carbon amount (cumulative) [M]O2 gp dioxide carbon concentration (gaseous phase) [M L−3]

r readily degradable fraction [dimensionless]s slowly degradable fraction [dimensionless]

substrate1,substrate2 stoichiometric parameter [dimensionless]

gas Henry’s constant for the specific gas [M−1 T2 L−2]2 c hydrogen gas amount (cumulative) [M]2 gp hydrogen gas concentration (gaseous phase) [M L−3]

inhibition function [dimensionless]

mistry 46 (2011) 557–565

kLa global transfer coefficient of the specific gas [T−1]kLCFA LCFAs dissociation constantKdec,biomass first order decay rate [T−1]Kdis Slu first order sludge disintegration rate [T−1]Khyd ch R carbohydrates hydrolysis kinetic constant (readily

degradable) [T−1]Khyd ch S carbohydrates hydrolysis kinetic constant (slowly

degradable) [T−1]Khyd li R lipids hydrolysis kinetic constant (readily degradable)

[T−1]Khyd li S lipids hydrolysis kinetic constant (slowly degradable)

[T−1]Khyd pr R proteins hydrolysis kinetic constant (readily degradable)

[T−1]Khyd pr S proteins hydrolysis kinetic constant (slowly degradable)

[T−1]Km,process Monod maximum specific uptake rate [T−1]Ksbk kinetic disintegration constant [M L−2 T−1]KS,process half saturation value [M L−3]M complex organic substrate mass [M]Mi mass of the organic solid particle i [M]n total number of organic solid particles [dimensionless]N total number of processes involved [dimensionless]Ni nitrogen content in component i [mole M−3]pgas partial pressure of the specific gas, calculated according

to the Dalton’s law [M T−2 L−1]q influent flowrate [L3 T−1]Qout,g total effluent gas flowrate from the digester [L3 T−1]R organic solid particles radius [L]R0 initial organic solid particles radius [L]S substrate concentration [M L−3][S](g) molar concentration of the specific gas in gaseous phase

[L−3][S](l) molar concentration of the specific gas in aqueous phase

[L−3][S](l),in molar concentration of the specific gas in the digester

influent [L−3][S*](l) molar concentration of the specific gas in the aqueous

bulk of the reactor at thermodynamic equilibrium [L−3]Saa amino acids concentration [M L−3]Sac total acetate concentration [M L−3]Sbu total butyrate concentration [M L−3]SCH4 methane gas concentration [M L−3]Sfa long chain fatty acids concentration [M L−3]Sh2 hydrogen gas concentration [M L−3]SI soluble inerts concentration [M L−3]SIC inorganic carbon concentration [L−3]Sin substrate concentration in the digester influent [M L−3]SIN inorganic nitrogen concentration [L−3]Spro total propionate concentration [M L−3]Ssu monosaccharides concentration [M L−3]Sva total valerate concentration [M L−3]t time [T]Vgas volume of the digester headspace [L3]Vli liquid working volume of the anaerobic digester [L3]Xaa amino acids degraders concentration [M L−3]Xac acetate degraders concentration [M L−3]XCh R readily degradable carbohydrates concentration [M L−3]XCh S slowly degradable carbohydrates concentration [M L−3]XC4 valerate and butyrate degraders concentration [M L−3]Xfa LCFA degraders concentration [M L−3]

Xh2 hydrogen degraders concentration [M L−3]XI particulate inerts concentration [M L−3]XLi R readily degradable lipids concentration [M L−3]XLi S slowly degradable lipids concentration [M L−3]

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pro propionate degraders concentration [M L−3]Pr R readily degradable proteins concentration [M L−3]Pr S slowly degradable proteins concentration [M L−3]Slu sludge concentration [M L−3]su sugar degraders concentration [M L−3]substrate yield of biomass on substrate [dimensionless]

complex organic substrate density [M L−3]COD removal efficiency, including both OFMSW andsewage sludge COD (inert fraction not considered)[dimensionless]

j biochemical rate coefficient for process j involving thespecific gas [M L−3 T−1]

j specific kinetic rate for process j involving the specific gas[L−3 T−1]

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