modelling of two-stage anaerobic digestion using the iwa anaerobic digestion model no. 1 (adm1)

ARTICLE IN PRESS

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doi:10.1016/j.w

�Correspond+49 351 463372

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(F. Blumensaat

Water Research 39 (2005) 171–183

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Modelling of two-stage anaerobic digestion using the IWAAnaerobic Digestion Model No. 1 (ADM1)

F. Blumensaata,�, J. Kellerb

aInstitute for Urban Water Management, Technische Universitat Dresden, D-01062 Dresden, GermanybAdvanced Wastewater Management Centre, University of Queensland, QLD 4072, Research Road, St.Lucia, Brisbane, Australia

Received 2 November 2003; received in revised form 4 May 2004; accepted 23 July 2004

Abstract

The aim of the study presented was to implement a process model to simulate the dynamic behaviour of a pilot-scale

process for anaerobic two-stage digestion of sewage sludge. The model implemented was initiated to support

experimental investigations of the anaerobic two-stage digestion process. The model concept implemented in the

simulation software package MATLABTM/Simulinks is a derivative of the IWA Anaerobic Digestion Model No.1

(ADM1) that has been developed by the IWA task group for mathematical modelling of anaerobic processes. In the

present study the original model concept has been adapted and applied to replicate a two-stage digestion process.

Testing procedures, including balance checks and ‘benchmarking’ tests were carried out to verify the accuracy of the

implementation. These combined measures ensured a faultless model implementation without numerical incon-

sistencies. Parameters for both, the thermophilic and the mesophilic process stage, have been estimated successfully

using data from lab-scale experiments described in literature. Due to the high number of parameters in the structured

model, it was necessary to develop a customised procedure that limited the range of parameters to be estimated. The

accuracy of the optimised parameter sets has been assessed against experimental data from pilot-scale experiments.

Under these conditions, the model predicted reasonably well the dynamic behaviour of a two-stage digestion process in

pilot scale.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Anaerobic two-stage digestion; Sewage sludge; Mathematical modelling; ADM1; Benchmarking; MATLAB/Simulink

1. Introduction

Primary and waste activated sludges are by-products of

municipal wastewater treatment. Prior to their re-use or

disposal, the sludges require further treatment to reduce

pathogen levels and organic content. Anaerobic diges-

e front matter r 2004 Elsevier Ltd. All rights reserve

atres.2004.07.024

ing author. Tel.: +49 351 46336908; fax:

04.

ess: [email protected]

).

tion, particularly the mesophilic single-stage process, is a

well established biological treatment process for the

degradation and stabilisation of municipal sewage sludge,

producing valuable methane gas. Changing standards for

the use and disposal of sewage sludge and the need to

reduce operational costs lead to an increased interest in

processes that treat sewage sludge more effectively. One

way to increase efficiency involves the physical separation

of the single-stage anaerobic digestion process into two

process stages, a thermophilic pre-treatment followed by

a mesophilic main treatment stage.

d.

www.elsevier.com/locate/watres

ARTICLE IN PRESSF. Blumensaat, J. Keller / Water Research 39 (2005) 171–183172

To improve the understanding of this particular

process configuration, a model concept was reviewed,

adapted for a thermophilic/mesophilic digestion process

and implemented into MATLAB/Simulink. The imple-

mentation has been tested, calibrated using lab-scale

data from literature (Siegrist et al., 2002), and finally

validated against data obtained from pilot-scale experi-

ments. The generation of this model implementation was

initiated to support a pilot-scale investigation of the

anaerobic two-stage digestion process for municipal

sewage sludge.

The model presented is based on the International

Water Association (IWA) Anaerobic Digestion Model

No. 1 (ADM1) published in the IWA Scientific and

Technical Report No.9 (STR), (Batstone et al., 2002).

To date, little experience exists in implementing the

ADM1 model concept or derivatives of it. Findings of

this study may contribute further information about

modelling and simulation work with this as yet new

model concept.

2. Theoretical background

2.1. Two-stage anaerobic digestion

The process of anaerobic degradation can be divided

into several reactor processes to optimise operational

conditions. The concept of splitting the conventional

process of anaerobic digestion into two different stages

is known as two-stage, or two-phase anaerobic diges-

tion. These two terms are frequently and equally used to

describe this particular process technology.

The anaerobic two-stage process investigated in this

study is a process that permits selection and enrichment

of different bacteria by independently controlling the

operating conditions in each digesting system. The

original naming ‘‘two-phase digestion’’ is based on

Pohland and Ghosh (1971), who first proposed to

separate the two main groups of microorganisms, acid-

forming bacteria and methanogenic archaea, physically

Feed Sludge

First Stage

Thermophilic Reactor

Biogas

Transfer Sludge

Fig. 1. General process scheme of the tw

into two reactors. Thus, optimal conditions for their

different growth kinetics are provided. The acid form-

ing, or acidogenic bacteria are favoured in the first stage,

producing volatile fatty acids (VFAs) such as acetate

from complex carbon sources. The VFAs are then

utilised by methanogenic archea in the second stage of

the process. A general process scheme of the two-stage

anaerobic process is shown in Fig. 1.

Numerous authors have demonstrated the advantages

of two-stage anaerobic digestion compared to conven-

tional single-stage systems, e.g. Cohen et al. (1979,

1980), Siegrist et al. (1993), Anderson et al. (1994) and

Oles et al. (1997).

On the other hand, few disadvantages such as high

investment costs and operational instability under

certain circumstances are known as drawbacks of the

two-stage process configuration. The benefits however

underline the significance of this particular digestion

technology and hence justify its application and the

development of a process model.

2.2. The ADM1 as basic model concept

The ADM1 is a structured, mathematical model based

on COD as a common base unit in wastewater

characterisation. It describes the anaerobic digestion

process in a continuous-flow stirred tank reactor.

Biochemical processes included in the ADM1 are:

�

o-s

disintegration of composites,

�
hydrolysis of particulate COD, such as carbohy-
drates, proteins and lipids,

�
six substrate degradation processes together with
their six specific biomass growth and decay processes.

The novel aspect, in comparison with other previously

developed anaerobic digestion models (Siegrist et al.,

1993; Vavilin et al., 1994; Angelidaki et al., 1999;

Batstone 2000), is the implementation of the disintegra-

tion step. Cellular solubilisation steps are divided into

disintegration and hydrolysis, of which the first is largely

a non-biological step that converts composite particulate

Digested Sludge

Second Stage

Mesophilic Reactor

Biogas

tage anaerobic digestion process.

ARTICLE IN PRESSF. Blumensaat, J. Keller / Water Research 39 (2005) 171–183 173

substrate to inerts, particulate carbohydrates, proteins

and lipids.

The subsequent phases, microbial-induced enzymatic

hydrolysis of particulates and the stepwise degradation

of the hydrolysed substrates, are represented according

to the generally accepted theory.

Decay processes are described producing inert and

degradable particulate organic matter (composites)

which again undergoes the disintegration step. The

physicochemical process of stripping the gaseous com-

pounds, hydrogen, methane and carbon dioxide, is

included to represent the production of biogas. The

pH calculation is based upon six additional physico-

chemical processes, describing the acid/base equilibria of

CO2/HCO3�, NH4

+/NH3, acetic acid/acetate, propionic

acid/propionate, butyric acid/butyrate and valeric acid/

valerate.

Thus, the reactor state is defined by 26 or 32 state

variables respectively, depending on the implementation

method. Dynamic states for cations and anions are

introduced to address the influence of positively and

negatively charged ions present in the system on the pH.

Using the same approach as in the ASM1 (Henze et al.,

1987), the entire system of dynamic state variables is

expressed in a rate equation matrix.

3. Material and methods

3.1. Model structure

The following section briefly summarises the funda-

mentals of the present model derived from the ADM1

model concept (Batstone et al., 2002).

Dynamic state variables: As a set of ordinary

differential equations (DE system), the model consists

of 32 dynamic state concentration variables and involves

19 biochemical rate processes, three gas–liquid transfer

processes and an additional six acid–base kinetic

processes. In order to characterise the acid–base

dissociation in aquatic systems, the dynamic states for

VFAs, inorganic carbon (IC) and inorganic nitrogen

(IN) are split into two components each.

Rate equation matrix: Table 1 shows the 32 state

variables structured in the modified process rate and

stoichiometric matrix for biochemical and acid/base

equilibria reactions. The original matrix provided in the

STR (Batstone et al., 2002) was modified as suggested by

including physicochemical reactions in order to describe

the effect of physicochemical states, such as pH, upon

the biochemical reactions.

Calculation of the derivatives: As proposed in the

original model concept, it is assumed that there is no

biomass accumulation and hence, the hydraulic reten-

tion time (HRT) equals the solids retention time (SRT).

The calculation of the state variables is shown in Eq. (1),

provided that the bulk volume in the reactor remains

constant.

dSliq;i

dt¼

qSin;i

V liq�

qSliq;i

V liqþ

X

j¼1�19

rjvi;j ; (1)

where the termP

j¼1�19rjvi;j is the sum of the specific

kinetic rates for process j, multiplied by the stoichio-

metric coefficient ni,j (see Table 1). Vliq is the liquid

reactor volume, q the flow into and out of the reactor,

Sin;i the input concentration of the soluble (or X in;i for

the particulate) components and Sliq;i the derivative of

the soluble (or Xi for the particulate) components.

Gas state variables: The integration of the gas state

variables into the system of dynamic state variables was

done to avoid the implementation of an additional gas

vessel, which would have complicated the entire model

structure. The three additional gas state variables were

calculated according to algebraic variables, the overall

gas flow and the gas transfer rate.

The biogas composition was described by the partial

pressures of methane, carbon dioxide and hydrogen as

well as the water vapour pressure.

Acid/Base equilibria: For the integration of the

acid–base rates, a different approach was used to the

one suggested in the STR (Batstone et al., 2002). The

acid–base rates are applied to the differential equations

for the VFAs and IC as follows

dSliq;i

dt¼

qSin;i

V liq�

qSliq;i

V liqþ rA=B;i; (2)

and

dSliq;i�

dt¼

qSin;i�

V liq�

qSliq;i�

V liqþ

X

j¼1�19

rjvi;j � rA=B;i; (3)

where i and i� stand for the free and ionic forms

respectively of organic acids and bicarbonate. On the

other hand, the acid–base equilibrium of inorganic

nitrogen is implemented differently. The biochemical

rate equation termP

j¼1�19rjvi;j is applied to ammonium

rather than to ammonia. The use of this configuration

was motivated by the perception that it is more

appropriate to apply the rate equation term to the

quantitatively dominant form of the split state variables,

rather than to the form which represents only a small

amount of the respective compound. It had been

assumed that this application causes the least numerical

problems. This assumption was proved right by

extensive testing, where the greatest accuracy was

achieved performing simulations with this particular

configuration.

Inhibition: Inhibition kinetics were comprehensively

reviewed by Batstone et al. (2002). To reduce the

complexity of the model it was suggested that only a

few inhibition mechanisms should be addressed. Follow-

ARTICLE IN PRESSTable1

Biochem

icalratecoefficients(n

i;j)andkineticrateequations(r

j)F. Blumensaat, J. Keller / Water Research 39 (2005) 171–183174


ing this recommendation, the inhibition forms were

applied as proposed in the STR (Batstone et al., 2002).

Processes excluded: In order to further reduce the

complexity of the model, a number of processes were

excluded. Processes being omitted from the model

concept are:

�
production of lactate from glucose fermentation,
�
sulphate reduction and sulphide inhibition,
�
nitrate reduction,
�
long chain fatty acid (LCFA) inhibition,
�
competitive uptake of H2 and CO2 between hydro-
genotrophic methanogenic archaea and homoaceto-

genic bacteria (significant in psychrophilic systems),

�
solids precipitation due to high alkalinity or other
chemical precipitation reactions.

The model presented aims to simulate sewage sludge

digestion at typical conditions. Based on this stipulation,

it is presumed that none of the above processes

significantly influence the modelled system.

3.2. Consistency checks

Balance checks for carbon and nitrogen were per-

formed using the stoichiometric coefficients and para-

meters suggested by Batstone et al. (2002). Discrepancies

were found in both balances, and modifications to the

carbon or nitrogen content of particular compounds

were made to eliminate or minimise those. Key

modifications made are outlined in the following section.

COD balance: COD balancing is implied in the rate

equation matrix. No fitted or calculated ‘‘product on

substrate yields’’ are necessary and hence no internal

balance was calculated.

Carbon balance: The rate coefficient for inorganic

carbon is expressed as balancing term (Eq. (4)), as

recommended in the STR (Batstone et al., 2002). The

term is originally applied to the uptake of sugars, amino

acids, propionate, acetate and hydrogen (biochemical

processes j=5, 6, 10, 11, 12) since in these cases

inorganic carbon is the carbon source for, or the

product of, anabolism and catabolism. Due to the

model implementation as ODE system with an expanded

number of state variables, the term was extended for

these additional state variables to give

v15;j ¼ �X

i¼1�13;16�30

Civi;j ; (4)

where Ci is the carbon content (kmol CkgCOD�1) of

the component i and n15,j is the inorganic carbon

stoichiometric coefficient for process j.

Furthermore, an inorganic carbon balance term

for decay processes was introduced. Initial carbon

balance checks revealed that the amount of inorganic

carbon released due to decay of biomass ‘‘is lost’’ in

the system. Assuming that decaying biomass remains

as particulate composites in the system, which is

then partially disintegrated into particulates and

subsequently hydrolysed into soluble substrate, the

carbon cycle must close. However, the carbon

content of biomass (Cbac=0.03125 kmol CkgCOD�1)

and the carbon content of the particulate composites

in the feed (CC=0.0279 kmolCkgCOD�1) differs

significantly. To resolve this discrepancy the following

term (Eq. (5)) was introduced to shift the

inorganic carbon released due to decay of biomass

to the dissolved inorganic carbon state

v15;j ¼ �X

i¼19;23�29

Civi;j : (5)

Nitrogen balance: As with the carbon balance, the

nitrogen balance calculated using the original para-

meters given in the ADM1 concept did not close. This

was again caused by a discrepancy between the nitrogen

content in the biomass and the composite material in the

feed. A balance term was used to close the nitrogen

balance (see Eq. (6)) which related the nitrogen ‘‘losses’’

to the inorganic nitrogen concentration.

The relationship balancing the difference of the

nitrogen content of biomass (Nbac=0.00625 kmol

NkgCOD�1) and the nitrogen content of particulate

composites (NC=0.002 kmolNkgCOD�1) reads as

follows:

v16;j ¼ �X

i¼19;23�29

Nivi;j ; (6)

where Ni is the nitrogen content (kmol NkgCOD�1) of

the component i and n16,j is the nitrogen stoichiometric

coefficient for the respective biochemical process j

(processes j=12–19).

3.3. Benchmarking

The implementation developed was compared with a

‘benchmark implementation’, an independently devel-

oped implementation of the same model concept in a

different simulation system. The aim of this testing

procedure was to prove the absence of numerical

discrepancies. The ‘benchmark implementation’ was

developed in AQUASIM 2.0, a different modelling

platform, by the taskgroup for model testing using the

parameter set in Batstone et al. (2002).

The ‘benchmark simulations’ were performed to

verify the implementation’s numerical accuracy, under

constant as well as under varying input conditions.

Operational conditions, reactor features, input data and

parameter sets used were precisely the same. Solving

algorithms applied in both simulation systems are

similar: ODE 15 s, a variable-step, variable-order solver

based on the numerical differentiation formulas, is used

in MATLAB/Simulink to simulate the implementation

ARTICLE IN PRESS

Integration ofdynamic equations

Initial estimation ofparameter set

Comparison withmeasured data

Manual adjustment of parameter set

Optimisedparameter set Optimal fit

Siegrist, 2002 [1] Lai, 2001 [18]

etc.Romli, 1993 Ramsey, 1997 [17]

ADM1 [2]

Lab-scale experiments

yes

no

Model Validation

ODE solver

Fig. 2. Estimation procedure to identify most sensitive parameters.

F. Blumensaat, J. Keller / Water Research 39 (2005) 171–183 177

generated in this study, whereas the solver used in

AQUASIM 2.0 (‘benchmark implementation’) is based

on a implicit variable-step, variable-order integration

technique known as GEAR’s method.

As a result, a complete verification of the computation

procedure and the model code was expected.

3.4. Parameter estimation

Initial parameter values used have been derived from

a variety of sources (Siegrist et al., 2002; Batstone, 2000;

Costello, 1989; Romli, 1993; Ramsey, 1997; Lai, 2001)

including the STR (Batstone et al., 2002), and other

adequate literature (Stumm and Morgan, 1996; Lide

2001). An iterative procedure (see Fig. 2) was applied to

optimise the a priori as most sensitive identified

parameters used in this model.

Stoichiometric coefficients implied in the rate equation

matrix have been taken from the STR without any

changes. Carbon and nitrogen contents of the system’s

components were recalculated after the implementation

of balance terms into the rate equation matrix in order

to close carbon and nitrogen balance.

Physicochemical parameters, such as equilibrium coef-

ficients and constants, were principally taken from the

STR except for a limited number of physico-chemical

coefficients found in Stumm and Morgan (1996).

Most of the kinetic parameters were considered fixed

since they are generally known to have limited

variability in anaerobic systems (Batstone, 2000). Many

kinetic parameters given in the STR (Batstone et al.,

2002) were reviewed and compared with values found in

related reports (Batstone, 2000; Costello, 1989; Romli,

1993; Ramsey, 1997). Values with a low sensitivity were

preferably taken from these studies without any changes

as this reduces the degrees of freedom and therefore, the

difficulty to estimate the comprehensive parameter set.

Within the given small-scale system, it was considered

reasonable to assign fixed values to physical parameters

such as kLa and total gas pressure in the headspace.

Thus, identical kLa values for all three gases and a

constant headspace gas pressure were assumed.

Ultimately, eight parameters were identified based on

the sensitivity analysis given in the STR (Batstone et al.,

2002) as having the greatest impact upon the model

outputs, and were estimated in comparison to experi-

ARTICLE IN PRESS

Table 2

Initial and estimated parameter values for the parameters that have been optimised manually including literature source of initial

parameter values

Parameter Name Initial value

(meso/thermo)

Estimated value

(meso/thermo)

Unit Source

kdis;35=55 Disintegration constant 0.5/1.0 1.0/0.5 d�1 Batstone et al., (2002)

km;ac Maximum uptake rate for

acetate utilisers

8/16 9/25 Kg

CODkgCOD�1 d�1Batstone et al., (2002)

km;pro Maximum uptake rate for

propionate utilisers

13/20 9/16 Kg

CODkgCOD�1 d�1Batstone et al., (2002)

kS;ac Half-saturation constant for

acetate utilisers

0.15/0.3 0.15/0.4 kg CODm�3 Batstone et al., (2002)

kS;pro Half-saturation constant for

propionate utilisers

0.1/0.3 0.2/0.4 kg CODm�3 Batstone et al., (2002)

kS;H2Half-saturation constant for

hydrogen utilisers

7� 10�6/

5� 10�57� 10�6/

1� 10�5kg CODm�3 Batstone et al., (2002)

kI;H2 ;pro Hydrogen inhibition

constant for propionate

utilisers

3.5� 10�6/

1� 10�53.5� 10�5/

7� 10�6kg COD Batstone et al., (2002)

kI;NH3Ammonia inhibition

constant for acetate utilisers

0.0018/0.011 0.0011/0.011 kmolm�3 Batstone et al., (2002)

F. Blumensaat, J. Keller / Water Research 39 (2005) 171–183178

mental lab-scale data. Data sets were provided by Siegrist

et al. (2002) who performed extensive trials using

single-stage and two-stage digesters in small-scale

(Vmesophil=28 l single-stage and Vthermophil=16 l/

Vmesophil=28 l two-stage respectively).

An iterative, heuristic method (illustrated in Fig. 2)

was applied to estimate the parameters for the thermo-

philic and mesophilic process stage manually. Original

and optimised values for the selected parameters are

given in Table 2.

3.5. Pilot-scale experiments

A set of data for the purpose of model validation was

generated during pilot-scale experiments (Advanced

Wastewater Management Centre and Gold Coast City

Council, 2001). The set-up of the two-stage digestion pilot

plant generally corresponds to the scheme outlined above.

Reactors were completely mixed and had an operating

volume of 160 l for the thermophilic and 800 l for the

mesophilic process stage, respectively. The pilot plant

facility was partially controlled and monitored through a

process logic controller (PLC) connected to a computer.

Temperatures were so kept constant (55 1C for the

thermophilic and 35 1C for mesophilic reactor); biogas

production and operating temperature were continuously

monitored and recorded. Sludge samples were taken

regularly to record quality parameter of sludge and

biogas (VSS, TSS, COD, SCOD, amino acids, acetate,

propionate, TKN, biogas composition, pH). The two-

stage system was semi-continuously fed with 40 l day�1 of

a mixture of primary and secondary sewage sludge from a

BNR (incl. nitrification/denitrification) treatment plant.

This corresponds to a HRT of 4 days for the thermophilic

and 20 days for the mesophilic reactor.

4. Results and discussion

4.1. Benchmarking

Correct benchmarking results were achieved using

steady-state data as well as varying input data, as

exemplary shown in Fig. 3. Both model implementa-

tions, the Simulink implementation and the ‘benchmark

implementation’, were initialised using output data from

steady-state simulations before simulating varying input.

The benchmark simulation with varying input was

performed to verify the model’s numerical accuracy

under dynamic conditions. Similarly to the constant

input simulations, the Simulink model outputs and the

outputs of the ‘benchmark implementation’ do not differ

significantly. The low mean relative error in an order of

magnitude of 0.01% indicates the numerical preciseness

in generating the output for both model implementa-

tions.

4.2. Model calibration

The model has been calibrated for a two-stage

thermophilic/mesophilic process configuration and mu-

nicipal sewage sludge with typical characteristics as

substrate input. Experimental results of Siegrist et al.

(2002) were used to assist the model calibration. Fig. 4

ARTICLE IN PRESS

Fig. 3. Benchmarking results for sugars, amino acids and LCFA including error plot for varying input.

0 10 20 30 40 50 600

0.02

0.04

0.06

0.08

[m3 d

- 1]

Time [days]

Biogas simulatedBiogas measured

0 10 20 30 40 50 600

20

40

60

80

[%]

Time [days]

Methane measuredMethane simulatedCarbon Dioxide simulatedCarbon Dioxide measuredHydrogen simulatedHydrogen measured

first load step second load step

Fig. 4. Biogas production and biogas composition in comparison with experimental data for the thermophilic stage of the two-stage

process after the parameter optimisation.


shows measured and simulated biogas production for

the thermophilic process stage applying the optimised

parameter set.

Both the biogas volume and composition was predicted

accurately for low (10 kg COD (m3d)�1 at HRT=4d)

and medium load (21 kg COD (m3d)�1 at HRT=2d)

ARTICLE IN PRESS

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

[kg

CO

D m

-3]

Time [days]

Propionate simulatedPropionate measured

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

1.2

1.4

[kg

CO

D m

-3]

Time [days]

Acetate simulatedAcetate measured

Fig. 5. VFA production in comparison with experimental data for the thermophilic stage of the two-stage process after the parameter

optimisation.

F. Blumensaat, J. Keller / Water Research 39 (2005) 171–183180

conditions. The model predicts the decline of the biogas

production as a response of the load increase, as well as

the adaptation of the system after the step changes.

However, at extremely high loading (HRT=1.33 d),

the accuracy of the model prediction decreased. It can be

seen that the model simulates an overload situation, the

biogas production decreases, and the methane propor-

tion in the biogas is reduced. Also, the total COD

removal decreases due to the accumulation of

hydrolysed COD (data are not shown). The VFA

production in the thermophilic reactor, particularly

acetate (lower chart of Fig. 5), also indicates the

difficulty to accurately predict the behaviour under high

loading conditions. It was complicated to further

optimise the parameter set, and a complete match of

simulated and experimental data for all loading condi-

tions could not be obtained. The lab-scale system on the

other hand, responds prompt with a drop in the biogas

production but eventually recovers despite the high

volumetric loading (31.5 kg COD (m3 d)�1).

Initial and estimated parameter values for the a priori

as most sensitive identified parameters are given in Table

2. Many parameters, principally those with low sensi-

tivity on model outputs, have been applied without any

optimisation. Hydrolysis constants for carbohydrates,

proteins and lipids are also among those parameters that

have not been optimised. Even though these parameters

are assumed to be highly sensitive for the degradation of

heterogeneous substrate, the influence is not as decisive

for homogenous substrate, such as the one that was

considered in this study (Batstone et al., 2002). Further

changes to hydrolysis constants or some other, not as

sensitive identified parameters may result in an im-

proved correspondence between model outputs and

experimental data.

4.3. Model validation

To assess the quality of the optimised parameter sets

and their applicability in process models, a validation

study was undertaken. The model outputs were com-

pared with measured data from a two-stage digestion

process in pilot scale. The process was simulated

applying the same implementation as described above

and without changing the previously optimised para-

meter set. The principle of the pilot-scale process is

equivalent to the process scheme that has been outlined

above.

Steady-state conditions were reached after a start-up

phase with rather unstable operation. After stable

functioning had been achieved and data could be seen

as representative the feed regime was changed from

constant to varying input to observe the dynamic

process behaviour.

The comparison of model outputs and experimental

data for the VFA production is exemplary shown in

ARTICLE IN PRESS

0

0.1

0.2

0.3

0.4

[m3 d

-1]

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

[m3 d

-1]

Time [days]

0 20 40 60 80 100 120 140

Time [days]



Fig. 7. Validation results with data from pilot-scale experiments for the biogas production in the thermophilic reactor (upper chart)

and the mesophilic reactor (lower chart).

0 50 100 150

0 50 100 150

0

200

400

600

800

1000

0

200

400

600

800

1000

[mg

l -1]

[mg

l -1]

[mg

l -1]

[mg

l -1]

Time [days]

0 50 100 150

Time [days]



Acetate simulatedAcetate measured

0

10

20

30

40

50

60

70

Time [days]

0 50 100 150

Time [days]

0

10

20

30

40

50

60Acetate simulatedAcetate measured

Fig. 6. Validation results with data from pilot-scale experiments for the VFA production in the thermophilic reactor (upper charts)

and the mesophilic reactor (lower charts).


Fig. 6. Particularly, the VFA production in the first

process stage (upper charts in Fig. 6) is well predicted by

the model though smoothed a little.

More detailed data for the mesophilic process stage

would reduce the influence of outliers and hence, give a

better idea of the curve’s fit. Nevertheless, it can be seen


that the concentration level of model outputs and

analytical data correspond well.

Some deviations in predicting the biogas production

and quality have been found (see Fig. 7). The differences

can be explained with the non-optimisation of several

parameters, for instance the application of identical and

non-optimised gas transfer coefficients. In fact, gas

transfer coefficients may differ in reality and the

dependence on the specific reactor configuration applied

has been neglected.

5. Conclusions

Several modifications to the original ADM1 model

concept were necessary to allow an application for the

pilot-scale digestion process.

Verification methods, such as consistency checks and

model benchmarking, have been applied to ensure a

completely verified and hence mathematically faultless

implementation of the ADM1 for a thermophilic/

mesophilic digestion process. It became clear that the

current understanding of modelling anaerobic digestion

processes is insufficient, reflected in the necessity to

implement balance terms (Eqs. (4), (5) and (6)). These

account for the inorganic carbon or nitrogen released

from biomass decay, and the implementation of these

‘add-ins’ evidently led to the minimisation of discre-

pancies in the carbon balance and to the closure in the

nitrogen balance. More fundamental research is re-

quired (a) to clarify the disposition of inorganic carbon

and nitrogen from decaying biomass, (b) to close the

carbon balance in the model concept completely and (c)

to verify the application of the implemented balance

terms. The implementation of additional balance terms

for other processes, such as the disintegration of

composite material and the hydrolysis of lipids, should

also be examined when applying the ADM1 in future

studies.

Even though the benchmarking process shed no

information on the ability of the model to predict the

performance of an anaerobic digester, it proved to be a

useful procedure to verify the numerical accuracy of the

model implementation.

In spite of the high-number biochemical parameters in

the model (37 for each process stage) it was possible to

obtain a good fit for most of the important process

parameters. Even though the curve fitting resulted in a

good agreement, principally, a parameter optimisation

for a structural model with such a high number of

parameters requires proof with data from several

dynamic experiments. This becomes evident in case the

model is further adapted, particularly for the parameters

that describe volatile acid production (hydrolysis con-

stants).

The validation results underline the good parameter

estimation and confirm the ability of the model to

adequately predict the behaviour of this particular

digestion process. However, a further assessment of

the model performance it is recommended. Additional

data representing a well-defined dynamic process beha-

viour should be used to confirm a dynamic model

validation. A further validation study is valuable to

show how the model is capable of simulating overload

situations or how the model predicts the degradation

process for different substrates under similar conditions.

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