Anaerobic Digestion Models: a Comparative Study

Anaerobic Digestion Models: a Comparative Study ⋆ Elena Ficara ∗ Sonia Hassam ∗ Andrea Allegrini ∗ Alberto Leva ∗ Francesca Malpei ∗ Gianni Ferretti ∗ ∗

Politecnico di Milano, 20133 Milan, Piazza Leonardo da Vinci 32, Italy (e-mail: [email protected]).

Abstract: Based on the adoption of object-oriented modelling and simulation tools, in this paper a comparison between the ADM1 and the AMOCO models is investigated, mainly in order to assess the performance of AMOCO for control design. The ADM1 model has been calibrated with reference to the degradation of waste activated sludge, based on literature data, and assumed as reference model. Then, in order to compare the outputs of the two models, some variables of ADM1 have been lumped to match the relevant aggregated AMOCO variables. Since AMOCO failed in predicting the steady state values relevant to the inorganic carbon species and alkalinity, a new version of it has been developed, accounting for the dynamics of the inorganic nitrogen concentration. Steady-state and dynamic simulations based on this new version showed an improvement with reference to simulations obtained with ADM1. Keywords: Models, Model approximation, Object modelling techniques, Plants, Waste treatment. 1. INTRODUCTION Modelling of the anaerobic digestion process is of fundamental importance not only to design wastewater treatment and biogas power plants, but also to study the sensitivity of the plant behavior to operational parameters, to monitor and control performance, and to assess the feasibility of the use of new substrates, with varying characteristics, biodegradability, and operational conditions. In the literature, many models have been proposed for specific applications or fermenters, fed with a very specific substrate, which can be roughly grouped into three main categories. The simplest ones Graef and Andrews (1974) are single-step models involving a single bacterial population, with a limited description of inhibition effects. Models of intermediate complexity Bernard et al. (2001) consider a higher number of processes and bacterial populations, as well as a more accurate description of inhibition factors. Finally, complex models Batstone et al. (2002); Stemann et al. (2005) account for a large number of processes and specific bacterial populations, along with an in-depth description of the inhibition effects and of relevant chemical equilibria. The best known and the most sophisticated model, able to describe the anaerobic degradation of various substrates (even if designed considering activated sludge as substrate), is the Anaerobic Digestion Model no. 1 (ADM1) Batstone et al. (2002), developed by the IWA Task Group for Mathematical Modelling and later modified by several authors Blumensaat and Keller (2005); Gal et al. (2009) to improve accuracy and robustness, and to fit other specific applications. While being very detailed, ADM1 can ⋆ This work has been performed within the project “La Fabbrica della Bioenergia”.

be hardly used for design and control purposes. A large number of parameters (about a hundred) depending on the specific substrate need to be estimated, which is particularly difficult in complex plant operations and also because of the scarce data available in the literature. This has motivated research on simpler models, focused for example on a few number of processes or specifically designed for particular substrates. Among them, the most important is AMOCO Bernard et al. (2001), which reaches a good compromise between simplicity and accuracy. AMOCO has been developed mainly as a tool to monitor and control the anaerobic digestion process rather than for accurate numerical simulation. In this paper, a comparison between ADM1 and AMOCO is investigated, mainly in order to assess the performance of AMOCO as a control design tool. First, ADM1 has been calibrated with reference to the degradation of waste activated sludge, considering data reported in Rosen et al. (2006), and assumed as the reference model. Then, in order to compare the outputs of the two models, some variables of ADM1 have been lumped to match the relevant aggregated AMOCO variables. The parameters of AMOCO have been then calibrated by assuming the steady-state ouputs of ADM1 as a reference. Since the values of the concentrations of the two biomass families considered in AMOCO, not measurable in normal operations, were available from ADM1 simulations, a different (and simpler) identification procedure has been followed with respect to the one proposed in Bernard et al. (2001). AMOCO however failed in predicting the steady state values relevant to the inorganic carbon species and alkalinity. The reason for this failure has been detected in the lack of description of the balance of the inorganic nitrogen species. Consequently, a new version of AMOCO has been developed, accounting for the dynamics of the inorganic nitrogen con-

Table 1. l C1 = Ssu l C3 = Sf a l C5 = Sbu l C7 = Sac l C9 = SCH4 l C11 = SIN l C13 l C15 l C17 l C19

= = = =

Xc Xpr Xsu Xf a

l C21 = Xpro l C23 = XH2 l C25 = Scat

ADM1 liquid flow connector concentrations.

Sugars Long chain fatty acids Butyric acid Acetic acid Dissolved methane Total inorganic nitrogen Composite Proteins Sugars degraders Long chain fatty acid degraders Propionate degraders Hydrogen degraders Cations

Table 2. g C1 g C3

l C2 = Saa l C4 = Sva

Amino acids Valeric acid

l C6 = Spro l C8 = SH2 l C10 = SIC

Propionic acid Dissolved hydrogen Total inorganic carbon

l C12 = Si

Soluble inerts

l C14 l C16 l C18 l C20

l C22 = Xac

Carbohydrates Lipids Aminoacid degraders Valerate and butyrate degraders Acetate degraders

l C24 = Xi

Particulate inerts

l C26 = San

Anions

= = = =

Xch Xli Xaa XC4

ADM1 gas flow connector concentrations.

= SCO2 = SH2

g

Carbon dioxide Hydrogen

C2 = SCH4

Methane

centration. Steady-state and dynamic simulations based on this new model version showed an improvement with reference to simulation obtained with ADM1. 2. THE ADM1 MODEL In a physical modelling approach the connection scheme of the anaerobic digester model can be sketched as in Fig. 1, having two connectors for the liquid inflow and outflow and one connector for the gas outflow. The variables of the liquid inflow or outflow connector are the volumetric flow rate q (m3 d−1 ), the concentrations of the soluble and particulate species {Cil } and the temperature T (K), while the variables of the gas outflow connector are gas volumetric flow rate qg (m3N d−1 ), the concentrations of the gas species {Cig } and the temperature Tg (K). The concentrations {Cil } are described in Table 2, and are all expressed in (kgCOD m−3 ), except for concentrations of total inorganic carbon SIC , total inorganic nitrogen SIN , cations Scat and anions San , which are expressed in (kmol m−3 ), while the concentrations {Cig } are described in Table 2, and are all expressed in (kgCOD m−3 ) apart from C1g = SCO2 , expressed in (kmol m−3 ). {C

q in { C il } i n T in

M

A D

q T

o d e l

g i

g

}

g

q out { C il } o u t T out

Fig. 1. Connection scheme of the anaerobic digester model. The liquid volume in the digester and the temperature must be controlled by acting on suitable control variables. However, in this work the focus is on the biochemical process, so a single stage CSTR (Continuous Stirred-Tank Reactor) with a constant volume and temperature and no biomass retention is considered. This means that the temperature T = Top is actually a parameter as well as the the liquid volume Vl , while tHR being the hydraulic retention time (days). The pH of the influent and the organic loading rate rOL (kgCOD m−3 d−1 ) can be considered as

Table 3.

ADM1 dissociated acids and free ammonia concentrations.

l C27 = Svam l C29 = Sprom l C31 = SHCO3

Table 4. 1 3 5 7 9 11 13 15 17 19

l C28 = Sbum l C30 = Sacm l C32 = SN H3

Valerate Propionate Bicarbonate

Butyrate Acetate Free ammonia

ADM1 biochemical processes.

Disintegration Hydrolysis of proteins Uptake of sugars Uptake of LCFA Uptake of butyrate Uptake of acetate Decay of Xsu Decay of Xf a Decay of Xpro Decay of XH2

2 4 6 8 10 12 14 16 18

Hydrolysis of carbohydrates Hydrolysis of lipids Uptake of aminoacids Uptake of valerate Uptake of propionate Uptake of hydrogen Decay of Xaa Decay of XC4 Decay of Xac

parameters, since they are computed from the properties of the influent. The organic matter undergoes a series of subsequent degradation steps taking place simultaneously. All the biochemical processes can be roughly grouped into four steps: the disintegration/hydrolysis of the composite material, leading to sugars, amino acids and long-chain fatty acids (LCFA) formation; the acidogenesis, leading to volatile fatty acids (VFAs, including acetic, butirric, propionic and valeric acid) formation; the acetogenesis, leading to acetic acid and hydrogen formation; and finally the methanization. Along with the anaerobic biodegradation, a series of physico-chemical conversion processes are involved. These are not biologically mediated and encompass ion association/dissociation and gas-liquid transfer. In particular, the chemical equilibria and pH, determined by ion association/dissociation, are of great importance because they have a strong influence on the biodegradation. In this work, the ADM1 version proposed in Blumensaat and Keller (2005); Rosen et al. (2006) is considered, which allows a more complete description of the anaerobic digestion than the original ADM1 Batstone et al. (2002). The model consists of a DAE system of 35 differential and 1 algebraic equation; 29 state variables are actually the concentrations in the liquid outflow connector and in the gas connector and are listed in Table 1 and 2, the other 6 are given by the concentrations of ionized VFAs (kgCOD m−3 ), bicarbonate (kmolC m−3 ) and free ammonia (kmolN m−3 ) and are reported in Table 3. The algebraic variable is the hydrogen ion concentration SH (kmolN m−3 ). The differential equations are given by the mass balances of the dynamic (state) variables, and involve 19 biochemical processes, listed in Table 4, 3 gas-liquid transfer processes and 6 additional acid-base processes. Starting from the soluble and particulate matter (the time unit is d) we have dCil dt


X qin i = 1, . . . , 24 l Ci,in − Cil + ρj υi,j , i 6= 10, 11 Vl 19

=

(1)

j=1

where ρj (kgCOD m−3 d−1 ) is the kinetic rate for process j and υi,j is the stoichiometric coefficient of the component i involved in the process j. In turn, these latter quantities are usually grouped in a Petersen matrix, where columns are related to the state variables and rows are related to the processes, while an extra column contains the kinetic equation corresponding to each process. In order to close

the inorganic carbon and nitrogen balances, additional terms were introduced in the original Petersen matrix as suggested in Blumensaat and Keller (2005) and then developed in the literature by several authors. These terms explicit the uptakes and releases in every process and affects the differential equations relevant to SIC and SIN l l (C10 and C11 ), thus l dC10

dt

=




qin l l + C11,in − C11 Vl

19 X

′ ρj υ11,j

=

Vl

Ci,in − Ci

,

(3)

(4)

while the dynamics of the dissociated acid and free ammonia are given by dCil dt

= −ρA,i ,

i = 27, . . . , 32

(5)

where ρA,i (kgCOD m−3 d−1 ) is the acid-base kinetic rate relevant to component Cil Rosen et al. (2006). The dynamic equations for the gas phase are dCig dt

=−

qg g Vl C + ρT,i , Vg i Vg

i = 1, 2, 3

(6)

where Vg (m3 ) is the total gas volume inside the reactor and ρT,i (kgCOD m−3 d−1 ) is the gas transfer rate relevant to component Cig Rosen et al. (2006). The only algebraic equation, defining the charge balance Sacm Sprom Sbum Scat + SNH4 − SHCO3 − − − 64 112 160 Kw Svam − San + Sh − =0 − 208 Sh

(7)

where SN H4 = SIN − SN H3 is the concentration of ammonium and KW (kmol2 L−2 ) is the dissociation constant of water, determines the molar concentration of hydrogen ion SH , which in turn determines the pH = − log10 SH , which affects the dissociation of VFAs and ammonia. Two other main straightforward modifications were introduced. Firstly, in order to have a single variable describing the neutralization capacity of the solution inside the reactor, its alkalinity was calculated by A = Scat − San + SIN

(8)

Secondly, to derive the pH of the influent substrate, the charge balance in (7) was calculated with reference to the influent composition. Finally, the biogas output flowrate qg can be computed as qg = kp (pg − patm )

pg patm

(10)

3. THE AMOCO MODEL

j=1

i = 25, 26

RTg RTg + SCH4 + SCO2 RTg + pH2 O 16 64

R being the gas constant.

′ ′ where υ10,j and υ11,j account respectively for the carbon and nitrogen content of the components and ρT,10 is the g gas transfer rate relevant to component C10 . For the sake of brevity the Petersen matrix is not reported here, the reader is deferred to Blumensaat and Keller (2005) or Allegrini (2010). Anions and cations dynamics is simply defined by the dilution effect of the reactor, since they are non reactive species, yielding
dCil qin l l

dt

p g = SH 2

(2)

j=1

l dC11

dt


X ′ qin l l + ρj υ10,j − ρT,10 C10,in − C10 Vl 19

=

where kp (m3N bar−1 d−1 ) is the outflow coefficient, pg (bar) is the biogas pressure and patm (bar) is the atmospheric pressure. In turn, the biogas pressure is given by the sum of the partial pressures of hydrogen, methane, carbon dioxide and water, thus

(9)

In the literature several anaerobic digestion models are reported which are much simpler than ADM1. Among them, the most important is AMOCO Bernard et al. (2001), developed to support monitoring and control system design for anaerobic digestion processes, rather than as a tool for numerical simulation of the process behaviour, and mainly focused on the description of the anaerobic digestion of soluble substrates or with a negligible particulate content. In contrast to ADM1, AMOCO has not been largely applied in the research field, probably because of its limited range of applicability. Only two bacterial populations are considered (instead of the seven considered by ADM1), in particular acidogenic and methanogenic, while the hydrolysis and acetogenic phases are no longer considered explicitly. In the first step, the acidogenic bacteria X1 (gVS L−1 ) consume the organic substrate S1 (gCOD L−1 ) and produce CO2 (mmol L−1 ) and volatile fatty acids S2 (mmol L−1 ). The population of methanogenic bacteria X2 (gVS L−1 ) uses, in the second step, the VFAs as substrate for growth and produces CO2 and methane (the gaseous species). The model is thus defined by 6 differential equations: 2 for the mass-balances of the bacterial populations X1 and X2 , 2 for the organic substrate S1 and the VFAs S2 and, finally, 2 for alkalinity Z and inorganic carbon C. This provides dS1 S1 qin = (S1,in − S1 ) − k1 µ1,max X1 dt VL S1 + KS1 S1 dS2 qin = (S2,in − S2 ) + k2 µ1,max X1 dt VL S1 + KS1 S2 − k3 µ2,max X2 S2 + KS2 + S22 /KI2 S1 dX1 qin =− X1 + µ1,max X1 dt VL S1 + KS1 dX2 qin S2 =− X2 + µ2,max X2 dt VL S2 + KS2 + S22 /KI2 qin dZ = (Zin − Z) dt VL dC qin S1 = (Cin − C) + k4 µ1,max X1 dt VL S1 + KS1 S2 + k5 µ2,max X2 − r C S2 + KS2 + S22 /KI2 ϕ = C + S2 − Z + K H P T k6 S2 + µ2,max X2 kLa S2 + KS2 + S22 /KI2

(11)

(12) (13) (14) (15)

(16)

(17)

rC = kLa (C + S2 − Z) − kLa

ϕ−

p

rCH4 = k6 µ2,max

ϕ2 − 4KH PT (C + S2 − Z) 2

S2 X2 S2 + KS2 + S22 /KI2

(18) (19)

where ki , (i = 1, . . . , 6) are stoichiometric coefficients, µi,max , (i = 1, 2) (d−1 ) are the maximum specific growth rates, KS1 (gVS L−1 ) and KS2 (mmol L−1 ) are the halfsaturation constants, KI2 (mmol L−1 ) is the inibition constant, KH is Henry’s constant for CO2 (mmol L−1 atm−1 ), PT = 1 (atm) is the atmospheric pressure, kLa (d−1 ) is the liquid-gas transfer coefficient, rC (mmol L−1 d−1 ) is the carbon dioxide production rate and rCH4 (mmol L−1 d−1 ) is the methane production rate. The inorganic carbon is assumed mainly composed of dissolved carbon dioxide CO2 (mmol L−1 ) and bicarbonate B (mmol L−1 ), neglecting the amount of carbonate in the normal operating conditions, while the total alkalinity Z is defined as the sum of dissociated acids in the liquid phase (bicarbonate and VFAs, assumed as completely dissociated in the pH range of interest). Of course, AMOCO introduces a number of simplifications with respect to ADM1. The influent substrate is considered to be already fully hydrolised, no particulate compound is therefore taken into account. Inert fractions (Xi and Si ) are not considered because the model does not consider non biodegradable fractions. The nitrogen balance is not taken into account nor it is included in the computation of the alkalinity. The pH calculation is based on the inorganic carbon equilibrium only and it has no influence in any process: it is just a rough estimation of the pH based on the bicarbonate chemical equilibrium only, Finally, relevant inhibition effects are neglected, such as excess of free ammonia or H2 inside the reactor. 4. MODEL TUNING ADM1 requires a detailed substrate definition but, on the other hand, the parameters monitored during the full-scale process are limited (just a few online) and, usually, they are macro-parameters describing aggregated information. Substrate characterization methods have been studied Zaher et al. (2003); Kleerebezem and Van Loosdrecht (2006); Huete et al. (2006) but, in general, the complete characterization of the substrate for ADM1 must be dealt with case by case. The work by Rosen and Jeppsson Rosen et al. (2006) reported an example of waste activated sludge characterization used for steady-state simulation. According to the authors, the input values may not be completely realistic for all variables but they have been chosen such that every input is active (i.e. non-zero) and able to excite all internal modes of ADM1. For this reason it was also chosen to be the benchmark substrate in this work. All parameters of ADM1 were therefore set to the values suggested in Rosen et al. (2006). A major issue in the comparison between the outputs of the two models is related to the need of lumping several variables of ADM1 into single variables of AMOCO. Omitting details for space reasons, and denoting with the tilde the equivalent AMOCO variable obtained by lumping ADM1 variables, the conversion formulas can be summarized as

˜ 2 = (Xac + XH )/1.55 X 2 ˜ = 1000 (Sva /208 + Sbu /160 Z + Spro /112 + Sac /64 + SHCO3 )

(25)

q˜c = 1000 ρT,10

(26)

q˜CH4 = 1000 ρT,9 /64

(27)

The AMOCO parameters can be estimated based on steady state measurements in different operating conditions Bernard et al. (2001), replaced in our case by steady state values obtained from ADM1, fed with the benchmark substrate Rosen et al. (2006) at varying hydraulic retention time. However, the simple linear least-square regression proposed in Bernard et al. (2001) failed at high tHR due to the absence of a decay term in the growth rate of the biomasses. A first modification of AMOCO has been therefore introduced, by adding a decay term for both biomasses, estimated as the 10% of the maximum bacterial growth rates µ1,max and µ2,max as   qin S1 dX1 =− X1 + µ1,max − k d X1 dt VL S1 + KS1 dX2 qin =− X2 dt VL



+

µ2,max

S2 − kd S2 + KS2 + S22 /KI2

(28)



X2

(29)

where kd is a decay constant. As a consequence, the linearity of the regression used for parameters tuning was lost, while linear least-squares regression was still applied to the estimation of the yield coefficients (ki , i = 1, . . . , 6). Anyway, the steady state values computed by AMOCO with the newly identified parameters were different from those computed by ADM1. Indeed, the steady-state concentrations of substrates and biomasses where sufficiently closed to the equivalent ADM1 values, whereas all variables concerning inorganic carbon (C, B, Z, CO2 , qc ) assumed much more different values. Note that also in Bernard et al. (2001), comparing the modelling results with experimental data, a bias was observed in total inorganic carbon C and alkalinity Z, and it was ascribed to the uncertainty in measurements of influent alkalinity. In this work, to improve the description of the total inorganic carbon inside the fermenter, a modification of AMOCO is proposed and described in the next section. 5. AMOCO MODIFICATION ACCOUNTING FOR THE ROLE OF NITROGEN As a consequence of having neglected the nitrogen species, AMOCO considers alkalinity Z as non-reactive and, consequently, its dynamics is just described by the dilution effect of the reactor (15). On the contrary, in ADM1 alkalinity is given by eq. (8) and its dynamics reflects the sum of the dynamics of the alkalinity constituents: bicarbonates, VFAs, hydroxide ions and, above all, free ammonia. In fact, from eqs. (7) and (8) one obtains (30)

(20)

S˜2 = 1000 (Sva /208 + Sbu /160 + Spro /112 + Sac /64) (21) ˜ 1 = (Xsu + Xaa + Xf a + XC + Xpro )/1.55 X 4

(24)

˜ = 1000 Sic C

A = Scat − San + SIN S˜1 = Ssu + Saa + Sf a + Xc + Xch + Xpr + Xli

(23)

(22)

so that if the inorganic nitrogen is neglected alkalinity is given by the difference between cations and anions concentrations in the solution only, which are actually

dN qin S1 = (Nin − N ) + [k1 NS1 − Nbac ] µ1,max X1 dt VL S1 + KS1 S2 − Nbac µ2,max X2 S2 + KS2 + S22 /KI2

/X

1 .2

X

X

2

1

/X

2

0

1

0

1 .4

1 .2

1

0 .8 0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

0 .8

3 5 0

0

1 .5 4

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

5 0

1 0 0

1 5 0 2 0 0 T im e ( d a y s )

2 5 0

3 0 0

3 5 0

/S

1 1

2

/S

0

5 0

2

6

0

2

S

S

2

1 0

0 .5 0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

0

3 5 0 1 .8

1 .4

1 .6

4

1 .6

0

/rC

H

1 .4 0

H

4

rc /rc

1 .2

1 .2

1 1

0 .8 0

5 0

1 0 0

1 5 0 2 0 0 T im e ( d a y s )

2 5 0

3 0 0

0 .8

3 5 0

0

Fig. 2. Responses of X1 /X10 a) X2 /X20 b) S1 /S10 c) S2 /S20 0 d) qCH4 /qCH e) qc /qc0 f) to 50% perturbations to 4 S1,IN . Solid line: ADM1 model, dotted line: AMOCO model, dashed line: AMOCO N model. 1 .6

1 .6

1 .4

1 .4

S1 dZ = D(Zin − Z) + [k1 NS1 − Nbac ] µ1,max X1 dt S1 + KS1 S2 − Nbac µ2,max X2 S2 + KS2 + S22 /KI2 (32)

The model thus maintains the same number of state variables of the original version, eq. (31) may be considered just to evaluate the dynamics of the variable N , if of interest. 6. COMPARISON BETWEEN ADM1 AND AMOCO 6.1 Steady-state analysis After the ADM1 variables lumping procedure and the parameter identification, steady-state computations were run. Details are omitted for space reasons; suffice to say that both models closely predict the behaviour of the organic substrate, the biomass concentrations , the pH, and the methane flow rate, with percentage differences always below 15%, while the performance of both AMOCO models with respect to the inorganic species is far less satisfactory, owing to the simplifications adopted in the description of the complex CO2 -producing fermentation processes.

1 .2

1

1

0 .8

0 .8 0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

1 .2

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

0

5 0

1 0 0

1 5 0 2 0 0 T im e ( d a y s )

2 5 0

3 0 0

3 5 0

/C O

1 .1

2

1 .2

C O

C /C

0

2

1 .3

1 .4 0

1 .6

1

1

0 .8 0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

0 .9

3 5 0

1 .1

1 .4

1 .0 5 0

1 .6

0

1 .2

p H /p H

N /N

The new state variable N should be added to the original state variable Z to determine a new value of alkalinity Z ′ , to replace Z in eqs. (17) and (18). However, by summing eqs. (15) and (31) while still denoting with Z the alkalinity, AMOCO may be simply modified, in order to account for the contribution of the nitrogen species, by substituting eq. (15) with

1 .2

B /B

0

0

(31)

where NS1 is represented by the nitrogen content of substrate S1 dependent on its protein content, which would be released into the reactor liquor during the acidogenic process; Nbac is the nitrogen content in the biomass, respectively uptaken from or released into the reactor liquor during biomass growth or decay.

+ kd Nbac µ1,max X1 + kd Nbac µ2,max X2

1 .6

1 .4

1

Z /Z

+ kd Nbac µ1,max X1 + kd Nbac µ2,max X2

1 .6

rC

non-reactive species in ADM1. Neglecting the contribution of the nitrogen species and, in particular, their interaction with the bicarbonate equilibrium, has also a direct consequence on the calculation of the concentrations of inorganic carbon species. In fact, a large amount of bicarbonate (HCO3− ) is required as counter-anion of ammonium (N H4+ ) released upon organic protein hydrolisis, to form ammonium bicarbonate (N H4 HCO3 ). AMOCO was therefore modified by adding a new state variable N accounting for the inorganic nitrogen, this of course entails the introduction of new parameters describing the nitrogen content of the organic substrate S1 and of the biomasses, hence

1

1 0 .9 5

0 .8 0

5 0

1 0 0

1 5 0 2 0 0 T im e ( d a y s )

2 5 0

3 0 0

3 5 0

0 .9

Fig. 3. Responses of Z/Z 0 a) B/B 0 b) C/C 0 c) CO2 /CO20 d) N/N 0 e) pH/pH0 f) to 50% perturbations to S1,IN . Solid line: ADM1 model, dotted line: AMOCO model, dashed line: AMOCO N model. 6.2 Dynamic simulation results More than in the steady state, we are interested in the prediction of the dynamic response by the simplified AMOCO models. Therefore, dynamic simulations of the digester response to a 50% step increase followed by an equivalent step decrease in the influent S1 concentration were performed with all models. For comparison purposes, the dynamic value of each state variable was referred to its steady state one, thus computing a percentage variation Y /Y 0 , where Y 0 is the steady-state value of variable Y . This was meant to make it easier to compare dynamic responses of variables having different, sometime remarkably, steady state values. Results are plotted in Figs. (2) and (3). For all models, biomasses concentration (X1 and X2 ) dynamics shows the typical response of first order systems, coherently with the fact that unlimited growth of microorganisms is described by a first order reaction. Slightly faster responses are simulated by the two AMOCO models, indicating that the calibration process has slightly overestimated the growth rate of these two lumped biomass populations. Growing faster, those biomasses also reach a slightly higher asymptotic concentration. More relevant differences can be observed when considering the S1 and S2 dynamics. As for S1 , the ADM1 response is again that one of a first order system, since X1 includes particulate components whose hydrolysis to soluble organic matter is de-

scribed by ADM1 as a first order reaction. On the contrary, this first order process is missing in both AMOCO versions, since the model was originally proposed to describe the anaerobic degradation of soluble organic compounds, as those taking place in UASB (Upflow Anaerobic Sludge Blanked) reactors. In AMOCO, S1 is used as the growth substrate for X1 , therefore it initially increases in response to the step increase in its influent concentration and is later reduced thanks to the increased X1 concentration. Generally speaking, the S1 concentration in both AMOCO models follows the typical response of a soluble substrate degraded biologically inside a CSTR. As for S2 , a major difference can be observed between AMOCO models and ADM1. This is related to the free ammonia inhibition on the growth of methanogens (the most relevant X2 biomass) that is taken into account in ADM1, but that is neglected in the AMOCO ones. Being methanogens growth inhibited, ADM1 predicts both a slower increase in X2 , and an increase in its substrate S2 . Due to the commented difference in the methanogenic process, the methane production dynamics is accordingly different, with less methane produced according to ADM1. When considering inorganic components, differences are observed between the original AMOCO and the modified one, the major one concerning the alkalinity dynamics. AMOCO N correctly predicts the alkalinity dynamic response, while the original AMOCO does not consider alkalinity as a reactive species. As a consequence, dynamic response for all inorganic carbon species are better predicted by AMOCO N, although time constants for AMOCO N are overestimated, possibly because of the already commented difficulty in estimating the CO2 release by the acidogenic process. Having improved the description of the alkalinity behaviour, also pH predictions are remarkably improved. Finally, the ammonium dynamics is sufficiently well predicted by the AMOCO N process, with a slightly faster release, that also causes the higher steady state nitrogen concentration. 7. CONCLUSIONS The simple AMOCO process, originally proposed to describe the anaerobic degradation of soluble organic matter, was applied to describe the anaerobic degradation of the more complex substrate that is waste activated sludge, taking place in a CSTR. Its applicability to this case study was checked by using ADM1 (Anaerobic Digestion Model n. 1) that is, at present, the most comprehensive model for the description of anaerobic digestion. To do that, a lumping procedure to compare the many ADM1 variables to the few AMOCO ones was proposed. Then, the AMOCO parameters were calibrated according to synthetic data series obtained by ADM1 simulations. Results show that, despite the much simpler model structure, AMOCO was able to well predict steady state values of biomasses and methane production rates, while being less performing in predicting the inorganic carbon species and pH values. Its dynamic response to a step modification in the influent concentration highlighted the major limits of this model. First, it does not include a first order hydrolysis step, that has a relevant impact in the simulation of the AMOCO S1 variable. Moreover, it does not consider the inhibition effects that some operative conditions may cause on the degradation process, such as the free ammonia inhibition on methanogens growth. Finally, due to simplifications in

the description of the physico-chemical processes, such as the hypothesis of a non reactive alkalinity, the inorganic species were also poorly predicted. As a first attempt to improve the AMOCO performance, the release of ammonium during the first degradation step was implemented, leading to a remarkable improvement in the simulation of the inorganic species. To further improve the AMOCO performance and applicability to complex substrates, one further first order hydrolysis step should be included, which requires the implementation of one more state variable.Also, the ammonia inhibition term may be added, as well as the effect of the process pH on the methanogenic process in order to couple the behaviour of the inorganic species to that one of the biological system. These modifications are expected to improve the model performance without loosing its simple structure. REFERENCES Allegrini, A. (2010). Anaerobic Digestion Modelling: a Comparison between ADM1 and AMOCO. Master’s thesis, Politecnico di Milano. Batstone, D.J., Keller, J., Angelidaki, I., Kalyuzhnyi, S.V., Pavlostathis, S.G., Rozzi, A., Sanders, W.T.M., Siegrist, H., and Vavilin, V.A. (2002). The IWA Anaerobic Digestion Model No. 1 (ADM1). Water Science and Technology, 45(10), 65–73. Bernard, O., Hadj-Sadok, Z., Dochain, D., Genovesi, A., and Steyer, J. (2001). Dynamical model development and parameter identification for an anaerobic wastewater treatment process. Biotechnology and Bioengineering, 75(4), 424–438. Blumensaat, F. and Keller, J. (2005). Modelling of twostage anaerobic digestion using the IWA Anaerobic Digestion Model No. 1 (ADM1). Water Research, 39(1), 171–83. Gal, A., Benabdallah, T., Astals, S., and Mata-Alvarez, J. (2009). Modified version of adm1 model for agro-waste application. Bioresource Technology, 100(11), 2783– 2790. Graef, S.P. and Andrews, J.F. (1974). Stability and control of anaerobic digestion. Journal of the Water Pollution Control Federation, 46(4), 666–683. Huete, E., de Gracia, M., Ayesa, E., and Garcia-Heras, J.L. (2006). ADM1-based methodology for the characterisation of the influent sludge in anaerobic reactors. Water Science and Technology, 54(4), 157–166. Kleerebezem, R. and Van Loosdrecht, M. (2006). Waste characterization for implementation in ADM1. Water Science and Technology, 54(4), 167–74. Rosen, C., Vrecko, D., Gernaey, K., Pons, M., and Jeppsson, U. (2006). Implementing ADM1 for plant-wide benchmark simulations in Matlab/Simulink. Water Science and Technology, 54(4), 11–19. Stemann, S.W., Ristow, N.E., Wentzel, M.C., and Ekama, G.A. (2005). A steady state model for anaerobic digestion of sewage sludges. Water SA, 31(4), 511–528. Zaher, U., Rodrguez, J., Franco, A., and Vanrolleghem, P.A. (2003). Application of the IWA ADM1 model to simulate anaerobic digester dynamics using a concise set of practical measurements. In Proceedings IWA Conference on Environmental Biotechnology, Advancement on Water and Wastewater Applications in the Tropics, 12. Kuala Lumpur, Malaysia.