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Renewable Energy 71 (2014) 701e714

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Renewable Energy

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Review

A review of simple to scientific models for anaerobic digestion

Nicoletta Kythreotou a, *, Georgios Florides b, Savvas A. Tassou a

a School of Engineering and Design, Brunel University, Uxbridge, Middlesex, UB8 3PH, UKb Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, 31 Arch. Kyprianou, P. O. Box, 50329,3603 Limassol, Cyprus

a r t i c l e i n f o

Article history:Received 8 February 2013Accepted 25 May 2014Available online

keywords:Anaerobic digestionModellingBiogas productionSimple calculators

* Corresponding author. Tel.: þ357 22437807; fax:E-mail address: nikoletta.kythreotou@brunel.ac.uk

http://dx.doi.org/10.1016/j.renene.2014.05.0550960-1481/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

To fully model the anaerobic digestion process, biological and physico-chemical background, the kineticsof bacterial growth, substrate degradation and product formation have to be taken into account. Thepresented approaches differ depending on the requirements and the developer of the model. Importantparameters affecting the process such as temperature, which can cause great inaccuracy, are rarelyincluded in the models. Simple calculators are also available that estimate the applicability of the processto a specific farm and provide information to a farmer or a decision maker. Six simple calculators arepresented in this study: AD decision support software, Anaerobic Digestion Economic Assessment Tool,BEAT2, BioGC, FarmWare and GasTheo. The simpler calculators mainly use the relation that exists be-tween volatile solids and biogas production. A tested case of 100 dairy cows and 50 sows was applied tothe simple calculators to compare the results.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Anaerobic digestion is a natural process that takes place in areaswhere free oxygen is not available and has been utilised by humansfor the treatment of waste from themid-1800s. Anaerobic digestionhas become more popular in the recent years, mainly due to itsability to generate energy from waste.

The technology is also considered as one of the most importantmitigation options for the greenhouse gases emissions (GHG) fromfarming. Alternative technologies to anaerobic digestion emit un-controlled GHG to the atmosphere: (a) the lagoons emit methaneand carbon dioxide if anaerobic conditions are developed in largedepths or carbon dioxide from the upper layers of the lagoon, (b)aerobic treatment causes the emission of considerable amounts ofcarbon dioxide due to the large amounts of energy required foraeration and/or mixing. On the other hand, anaerobic digestion is aclosed, airtight system, and one of the end products of the processis a gas mixture of methane and carbon dioxide known as biogas.

The typical ratio of methane to carbon dioxide in biogas whenoptimum conditions occur is 60:40. In cases that biogas is of suf-ficient quality and quantity, it is combusted to generate electricityor heat or both. This prohibits methane to be released to the

þ357 22344556.(N. Kythreotou).

atmosphere, and instead, carbon dioxide is emitted from thecombustion process. Therefore, smaller amounts of greenhousegases are emitted to the atmosphere by anaerobic digestion. This, inaddition to the privilege of producing energy, makes anaerobicdigestion preferable by farmers.

The main sources of greenhouse gases in a farm are entericfermentation and manure management. The gases emitted fromanimal farming are predominately methane (CH4) and nitrous ox-ide (N2O). These gases have a larger impact on the greenhousephenomenon compared to carbon dioxide since the molecules cantrap more heat energy within them; i.e. they have higher globalwarming potential (GWP) than carbon dioxide [51]. The interna-tionally accepted GWP for methane is 21 and for nitrous oxide 310[51].

Governments have also recognised the importance of anaerobicdigestion, and there are many countries that provide financial in-centives for farmers to proceed with the installation of anaerobicsystems. This is because (a) energy from anaerobic digestion isconsidered biomass energy and therefore a form of renewableenergy and (b) anaerobic digestion reduces greenhouse gasesemissions frommanure management and is therefore an importantmitigation measure.

Mathematical modelling of the anaerobic digestion process wasmotivated by the need for efficient operation of anaerobic systemsin the early 70's [31]. The scientific models on anaerobic digestionhave been developing for almost 40 years. Some use the kinetics of

Abbreviations

D flow per reactor volumedS/dt change of substrate concentration over change in time(dS/dt)c rate of product synthesis(dS/dt)e rate of maintenance and growth energy generation(dS/dt)r reaction rate(dS/dt)x rate of new cell material synthesisdX/dt change of cell concentration over timeEa activation energyGHG Greenhouse gasesGs gas productionGWP global warming potentialI inhibitor concentrationk rate constantkd death ratekmax maximum rate constantKi inhibition constant; the substrate concentration,

where bacteria growth is reduced to 50% of themaximum specific growth rate due to substrateinhibition

Ks Monod-constant; the substrate concentration at 50% ofthe maximum specific growth rate (mmax/2)

L Powell constant for diffusion and permeabilityMEV methane energy valueP product concentrationP* critical inhibitor concentration; where growth stopsR molar gas constantS substrate concentrationS0 initial substrate concentrationSi inhibitor concentrationS* critical inhibitor concentration; where growth stopsX concentrationYx yield coefficientYp1 yield coefficient of products, which result from

primary energy metabolismYp2 yield coefficient of products formed at side reactions or

following interactions of direct metabolic productsYs yield coefficient calculated stoichiometricallym specific growth ratemmax maximum specific growth rate

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714702

the growth of microorganisms to predict the behaviour of thesystem, whereas others depend purely on the chemical reactionsthat take place.

The recent interest in anaerobic digestion however, has givenrise to several publicly available simple software applications inaddition to the scientific models. These applications have beendeveloped to assist farmers assess (i) whether anaerobic digestionis financially viable for their farm (ii) the reduction of greenhousegases emissions that can be accomplished from the application ofanaerobic digestion at their farm and (iii) the energy that can beproduced through anaerobic digestion of their waste. Most of theavailable applications are for people with limited scientificknowledge on anaerobic digestion and biogas production and aresimple web-based calculators.

The aim of this paper is to present a review of scientific modelsavailable for anaerobic digestion and some simple software appli-cations that can be used in cases that the available information isnot sufficient to apply the detailed scientific models.

2. Scientific models simulating anaerobic digestion

Due to the complexity of the process, each model is developedfor a different purpose. As a result, there is currently a variety ofmodels that vary according to the purpose that they were designedfor. Among them, are comparatively simple models developedexclusively for calculating the maximum biogas rate, which willtheoretically be produced during digestion. Others calculate thebiogas rate taking into consideration degradation or digestion ratesof different components of the biomass.

Due to the limitation of many models to present the dynamicnature of the digestion, complex models have been developed toinclude the kinetics of the growth of microorganisms. The activityof microorganisms and consequently the biogas production ratecan thus be investigated for a variety of substrates rates of deathrate and washout of microorganisms via different mechanisms.

Several models are designed for a specific substrate or a smallnumber of substrates, and are therefore not applicable to other

types of substrate. Nevertheless, most of the available models allowfor the calculation of biogas and methane production rate. Todesign biogas plants and to evaluate the efficiency of such plantsboth parameters are very important. Additionally, some models arevery specialised and aim exclusively at the assessment of an effect,for example the evaluation of the influence of mixing on biogasproduction.

2.1. Theoretical biogas yield

The potential biogas yield of the anaerobic digestion of aparticular type of waste and the gas composition can be deter-mined by the chemical composition of a feedstock. Simple ways tocalculate the biogas production are the models developed by Refs.[23,21,11,54,5]. These models are based on data for basic elementsor components of organic matter and result only in estimates of theproduction of methane and carbon dioxide. These models are timeindependent, therefore the necessary retention time of thewaste inthe digester cannot be estimated.

According to Refs. [23]; methane and carbon dioxide yield canbe calculated with an uncertainty of about 5% using relation (1),given that the chemical composition of organic matter is known.However, relation (1) does not take into consideration the degra-dation of organic matter for the bacteria metabolism (i.e. synthesisof cell mass and energy for growth and maintenance). According tothis relationship, the methane fraction of fully degraded glucose is50% since C6H12O6 / 3CH4 þ 3CO2.

CaHbOcþ�a�b

4� c2

�H2O/

�a2þb8� c4

�CH4þ

�a2�b8þc4

�CO2

(1)

Ref. [21] modified relation (1), to include nitrogen and sulphurin the composition of organic matter. This enabled the fraction ofammonia and hydrogen sulphur in the produced biogas to beestimated according to relation (2).

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714 703

CaHbOcNdSe þ�a� b

4� c2þ 3$d

4þ e2

�H2O� �

/a2þ b8� c4� 3$d

8� e4

CH4

þ�a2� b8þ c4þ 3$d

8þ e4

�CO2 þ d NH3 þ e H2S

(2)

Ref. [11] proposed a specific biogas forming potential andmethane content for carbohydrates, fats and proteins. Specifically,Baserga proposes that carbohydrates can yield 790 l biogas per kgorganics of which 50% is CH4, fats can yield 1250 l biogas per kgorganics, with 68% CH4, and proteins can yield 700 l biogas per kgorganics, with 71% CH4.

Ref. [54] further developed the model of Ref. [11] to include adigestion rate that is depended on the type of substrate, assumingthat the degradation of organic matter is similar to the entericfermentation in a cow. Digestion rates for a large number of animalfeed depending on nutrient fractions were therefore measuredempirically and then used for the prediction of the gas yield andmethane fraction.

Ref. [5] developed a methane energy value model for differentenergy crops, to estimate the specific methane yield from thenutrient composition of each energy crop. Maize, cereals and grass(energy crops) were analysed for their nutrient composition priorto the digestion. During the performed anaerobic batch experi-ments, data on methane energy values was collected. The methaneenergy value model was then developed by carrying out a multi-functional analysis of full regression models, which estimatesmethane yield from the nutrient composition of energy crops inmono fermentation via regression models. The methane energyvalue model investigates and considers the impact of the content ofcrude protein (XP), crude fat (XL), crude fibre (XF), N-free extracts(XX) on the methane formation (MEV, methane energy value) withEq (3).

MEV ¼ x1$XPþ x2$XL þ x3$XFþ x4$XX (3)

where MEV is the methane energy value in 1NCH4/kg VS, XP thecrude protein content in % dry matter, XL the crude fat content in %drymatter, XF the crude fibre content in % drymatter and XX the N-free extracts content in % dry matter. x1, x2, x3 and x4 are the co-efficients of regression that were determined through the batchexperiments.

Fig. 1. Phases of growth of a bacteria cultu

2.2. Models with reaction kinetics

For the investigation of the kinetics of anaerobic digestion, thegrowth of microorganisms, the degradation of substrate and theformation of products have to be considered [37]. Processes can bedistinguished into continuous and discontinuous according to thesupply of substrate. In continuous processes, substrate continu-ously flows in and out of the system, resulting to a process withconstant substrate flow and gas production (steady-state process).Therefore, growth requirements for microorganisms are constantover time. The kinetics of bacterial growth, control the process ofdegradation and strongly depend on the medium and the growthrequirements. Discontinuous (batch) processes are fed only once.Consequently, substrate degradation and gas production changeover the retention time, whereby growth requirements for micro-organisms change permanently. The substrate balance of acontinuous or a discontinuous process can be expressed as:

dS=dt ¼ D$S0 � D$Sþ ðdS=dtÞraccumulation input output reaction (4)

where dS/dt is the accumulation rate (change of substrate con-centration over change in time), D is the dilution rate (flow perreactor volume, in 1/h), S the substrate concentration, S0 the initialsubstrate concentration and (dS/dt)r the reaction rate.

2.2.1. Growth kinetics

2.2.1.1. Growth of bacteria. As all living organisms, the life cycle ofbacteria is characterised by various phases of growth. Fig. 1 showsthe bacterial growth phases of cultures during batch anaerobicdigestion, as this was studied by Ref. [66]. Bacterial cultures gothrough phases with notable active cell growth or death, and astationary phase, due to changing concentrations of nutrients andinhibitors. This continuous adaption causes the occurrence of smalltime lags in cases where discontinuous processes take place, whichcorrespond to measurable deviations of kinetic parameters [95].Therefore, kinetic parameters describing the growth of bacteriaduring discontinuous processes cannot be applied to continuousprocesses.

The exact shape of the growth curve (Fig. 1) depends on factorssuch as ambient conditions, type and concentration of substrate,bacteria type, physiological conditions of the inoculum and initialconcentration of bacteria. The contact of bacteria cultures to a newsubstrate can lead to deceleration of growth, duration of whichdepends on the characteristics of the culture. If the new medium is

re and the respective growth rate [8].

Fig. 2. Specific growth rate depending on substrate concentration according to Monod[66].

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714704

similar to the medium already in use, the lag phase is small enoughthat can be neglected [66].

The real growth takes place primarily during the exponentialphase, where the rate of bacterial growth is constant. The acceler-ation phase is the transition between lag phase and exponentialphase, during which the growth rate increases. In most cases theacceleration phase can be neglected since the growth rate of theexponential phase changes only if nutrients are exhausted, toxicmetabolic products are accumulated or the pH value changes due tosubstrate degradation [66]. These effects will cause the start of theretardation phase, during which the growth rate decreases until thezero value is reached. During the stationary phase, the number ofcells remains constant, but several cell activities continue, (e.g.energy consumption due to metabolism or biosynthetic processes).Retardation and stationary phase are usually short and thereforequite often hardly observable. If the conditions of the medium orthe growth conditions are not changed, the microorganisms diewith a death rate kd (in 1/h). Even though the phase of decline alsobehaves exponentially, the rate is smaller than the one of theexponential phase. Dead biomass is assumed to decay into carbo-hydrates and protein and can be used as new substrate [9]. Thisprocess is called disintegration. The balance of bacteria cells can beexpressed by Eq. (5):

dX=dt ¼ D$X0� D$Xþ m$Xþ kd$Xaccumulation input output growth death (5)

with the cell concentration X (in g/l), the dilution rate D (in 1/h)and the specific growth rate m (in 1/h). The bacterial growth (m,X)depends on the specific growth rate (m). The specific growth ratecannot be infinite due to the limited availability of nutrients (sub-strate concentration S in g/l) and other ambient conditions such asinhibitors (inhibitor concentration I in g/l), pH value and temper-ature T, as shown in Eq. (6).

m ¼ mðS; I;pH; TÞ; ms∞ (6)

The limitation of the specific growth rate depending on nutri-ents and other requirements was described in several modelspublished in the last decades Refs. [28,59,66,70,91].

2.2.1.2. Models for the bacterial growth. The basis for modelling thekinetics of bacterial growth was derived by Michaelis and Mentenin 1913. Their model, describes how the enzyme activity dependson the substrate concentration. This relation can be related tobacterial growth, because the microbial growth is also an autocat-alytic reaction [95].

In 1949 Monod recognised the non-linear relation betweenspecific growth rate and limited substrate concentration, when heinvestigated the growth of bacteria cultures and the parallelism tothe MichaeliseMenten theory. For bacterial growth, Monod pro-posed that the specific growth rate is inversely proportional tosubstrate concentration; i.e. the specific growth rate increases fastat low substrate concentrations and slowly at high substrate con-centration, until a saturation of bacteria is reached (Fig. 2) ac-cording to Eq. (7):

m ¼ mmax$S

Ks þ S(7)

This limit is the maximum specific growth rate mmax. TheMonod-constant Ks is the substrate concentration at 50% of themaximum specific growth rate (mmax/2).

Specific growth rate is limited by the substrate concentration.The relation of bacteria to the limiting substrate is expressed by Ks

[66]. The specific growth rate is approximately linear when S < Ks.

Ks is always greater than zero, therefore S/(S þ Ks) is always lessthan 1 and consequently the specific growth rate is less than mmax.Unlike the enzyme activity described by Refs. [62]; m(S) does notstart at zero, due to the degradation of substrate by bacteria for theproduction of maintenance energy. Thus, the growth cannot startuntil S reaches a certain value [34]. If the substrate is not thelimiting factor due to a high enough concentration, the maximumspecific growth rate can be reached. According to Ref. [39]; themaximum specific growth rate is unique for every bacteria culture.

The Monod model applied for pure cultures and simple sub-strates has very high accuracy [27]. However, the model is suitablefor homogenous cultures but not for heterogeneous cultures orcomplex substrates (Ref. [88]). Ref. [73] concluded that the Monodkinetic cannot be used to describe the degradation of municipalwastes as a complex substrate. Furthermore, the lag phase is notincluded in the Monod model.

The Monod model is a bacterial growth model frequently usedfor biogas production. Users include Ref. [19] for batch processesRef. [22], for batch, steady-state and dynamic processes Ref. [69],for steady-state and dynamic processes, and Ref. [30] and Ref. [82]for dynamic processes. The bacterial growth model of Contois isapplied for batch processes (e.g. Ref. [97] and for steady-stateprocesses (e.g. Refs. [24e26,57] used their own model for steady-state processes, whereas Ref. [43] used the same model for batchprocesses.

Refs. [68] upgraded the model of Monod with a parameter n(usually n > 1) to integrate effects of adoption of microorganisms tostationary processes by mutation (Eq. (8)). For n ¼ 1 the specificgrowth rate becomes equal to the Monod model.

m ¼ mmax$Sn

Ks þ Sn(8)

For the calculation of the specific growth rate [27] also took intoaccount cell concentration in addition to the substrate dependency(Eq. (9)). Even though the lag phase is neglected, effects of inhibi-tion and of inoculum are directly included due to the pre-mentioned components [35]. According to Beba and Atalay how-ever [16], this model yields good results both for discontinuous andcontinuous processes, but its capability to model dynamic pro-cesses, is strongly limited.

m ¼ mmax$S

Kc$X þ S¼ mmax$

1Kc$XS þ 1

(9)

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714 705

Ref. [75] also included diffusion and permeation of substrate inaddition to reaction kinetics through the cell wall with two addi-tional parameters K and L (Eq. (10)). K describes the kinetics ofgrowth due to enzyme activity and the parameter L the diffusionand permeability.

m ¼ mmax$ðK þ Lþ SÞ

2$L$

"1�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 4$L$S

ðK þ Lþ SÞ2s #

(10)

Ref. [25] modified a model of Ref. [27]; to include the cell con-centration via the relation between substrate concentration andinitial substrate concentration Si (Eq. (11)). The integration of in-hibition by substrate or products is limited and as a result, noprediction of process failures due to inhibition of microorganisms ispossible. However, process failures due to washout effects can bepredicted [46].

m ¼ mmax$S=Si

K þ ð1�KÞ$SSi

(11)

The modified Monod model by Ref. [17] considers decelerationduring the lag phase by introducing an exponential part of themathematical model, with t for time and T for lag time (Eq. (12)).

m ¼ mmax$S

Ks þ S$½1� expð�t=TÞ� (12)

In the model of Ref. [63]; the specific growth rate also dependson the gas production Gs (Eq. (13)). The parameter n is 1.5 and in-dicates a higher substrate concentration, because mixed bacteriacultures need a higher substrate transport compared to purecultures.

m ¼ mmax$Sn

Sn$ð1þ Kb$GS$SnÞ(13)

Fig. 3 shows a comparison of the specific growth rate dependingon substrate concentration as calculatedwith a few of the discussedmodels.

Biological processes with short and long retention times ordegradation of complex substrates, are difficult to be described byusing these models, which have only one set of kinetic parameters.Therefore, the “first-order” models were developed, such as themodel of Ref. [76]; where the degradation of biodegradable sub-strate only depends on a constant k (dS/dt ¼ �k$S). These modelsare easy to handle but their accuracy is limited to confined re-quirements and they cannot be used for the prediction of optimumconditions for maximum biological activity or process failures [44].

Fig. 3. Specific growth rate depending on substrate concentration according to themodels of Monod [66], [68], [75], [37].

First-order kinetics were used in models of [9,12,22,55,81] for thehydrolytic step, whereas Ref. [80] used the first-order kinetics forall the steps of the process.

2.2.1.3. Influence of inhibitors on bacterial growth. Bacterial growthcan be inhibited by certain substrate and product concentrations asdescribed in the previous section. Inhibition paths of substrate andproduct inhibition are based on very similar effects and are closelyconnected especially for mixed bacteria cultures [37].

When substrate concentration increases, a maximum specificgrowth rate will be reached at a certain concentration, abovewhich a decrease of the specific growth rate takes place. Accordingto Ref. [32]; this is caused by a high osmotic pressure of the me-dium or a specific toxicity of the substrate. A reduction of themetabolic activity of a cell can lead to the following consequences:modified chemical potential of substrates, intermediates, orproducts, altered permeability of cells, changed activity of one ormore enzymes, dissociation of one or more enzymes or metabolicaggregates, affected enzyme synthesis by interaction with thegenome or the transcription process, or affected functional activityof the cell.

The effect of substrate inhibition on microbial growth has beentaken into consideration by a number of developed approaches. Ref.[4] developed the model by an empirical correlation, with simu-lated data of substrate inhibition agreeing well with empirical datafrom laboratory experiments (Eq. (14)).

m ¼ mmax$S

Ks þ S$expð�S=KiÞ (14)

The model of Ref. [93] was derived from enzyme kinetics withan integrated allosteric effect with b as reaction rate. The model ofRef. [41] is also derived from enzyme kinetics and is equivalent tothe one by Webb for b ¼ 0. Eq. (15) and (16) shows the models ofWebb and Haldane respectively.

m ¼ mmax$S

ðSþ KsÞ$ð1þ S=KiÞ¼ mmax$

SSþ Ks

$Ki

Sþ Ki(15)

m ¼ mmax$S$ð1þ b$S=KiÞ�Sþ Ks þ S2

�Ki� (16)

Ref. [96] generalised the approach of Ref. [41]; so that oneenzyme can accumulate several enzyme complexes (Eq. (17)). Interms of bacterial growth this means that n inhibitors are able toinfluence the specific growth rate.

m ¼ mmax$S

Ks þ S$

"1þPn

i¼1 ðS=KiÞi# (17)

According to the model of Ref. [40]; the specific growth ratedecreases almost linearly at high concentrations of the substrateinhibitor (Eq. (18)).

m ¼ mmax$1

Sþ Ki(18)

The model of Ref. [6] is also based on Ref. [41] but for enzymeinhibition at high substrate concentrations. When a maximumtolerable substrate concentration is exceeded, the specific growthrate decreases; therefore, an inhibition term is added to the modelof Ref. [66]. The inhibition constant Ki is the substrate concentra-tion, where bacteria growth is reduced to 50% of the maximumspecific growth rate due to substrate inhibition. Therefore, Ki is

Fig. 4. Methane production depending on undissociated hydrogen sulphur [60].

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714706

considerably higher than the Monod constant, Ks, which is thesubstrate concentration at 50% of the maximum specific growthrate (mmax/2). Ref. [47] further modified the model of Ref. [6] toinclude a second inhibitor. Eqs. (19) and (20) show the modelsproposed by Refs. [6] and [47] respectively.

m ¼ mmax$S

Sþ Ks þ S2Ki

¼ mmax$1

1þ KsS þ S

Ki

(19)

m ¼ mmax$S

Sþ Ks þ S2�Ki;1 þ S$I

�Ki;2

(20)

m ¼ mmax$

�1� S

S*

�n

$S

Sþ Ks$ð1� S=S*Þm (21)

The selection of a model that is appropriate for simulation of thewhole process of biogas production depends on the required ac-curacy, availability of the required data and constraints of theprocess. The models of Ref. [6] and of Ref. [41] were used in thiscontext; i.e. to simulate the whole process of biogas production[9,45,64].

The effects of product inhibition are similar to those of substrateinhibition. Therefore, somemodels such as Ref. [4] and Ref. [42] canbe used for both types of inhibition. Some of the available modelsfor product inhibition are listed in Table 1.

Some models for anaerobic digestion also take into consider-ation hydrogen inhibition, e.g. Refs. [12,55,81] and [90]. Addition-ally, H2S (undissociated hydrogen sulphur) influences the ionicequilibrium and thus the pH value [60]. Fig. 4 shows the stand-ardised methane production depending on the concentration ofundissociated hydrogen sulphur according to Ref. [60].

Table 1Models for bacterial growth including the effect of substrate inhibition.

Author Model

[50]

m ¼ mmax$S

Ks þ S$

Kp

Kp þ P(22)

Holzberg et al. [48]m ¼ mmax � K1$ðP � K2Þ (23)

Aiba et al. [4]

m ¼ mmax$S

Ks þ S$expð�K$PÞ (24)

Bazua and Wilke [15]

m ¼ SKs þ S

$

mmax;P¼0 � a$P

b� P

!(25)

Ghose and Tyagi [38]

m ¼ mmax$

�1� P

P*

�$

SSþ Ks þ S2

�Ki

(26)

Moser [68] and Bergter [17]

m ¼ mmax$Sn

Ks þ Sn$

Kp

Kp þ Pm(27)

Dagley and Hinshelwood [29]

m ¼ SKs þ S

$ð1� K$PÞ (28)

Han and Levenspiel [42]

m ¼ mmax$

�1� P

P*

�n

$S

Sþ Ks$ð1� P=P*Þm (29)

Furthermore, biogas production is very sensitive to the presenceof oxygen. Even a short-time presence of oxygen molecule can stopthe degradation process [60]. The inhibition by oxygen is notconsidered in any of the presented models in this paper.

2.2.1.4. Influence of pH on bacterial growth. The pH value has astrong impact on the degradation process (Fig. 5) and can be inte-grated directly into a mathematical model [8,55]. Modelsdescribing the influence of the pH value on bacterial growth arepresented in Table 2.

In most cases the pH is included in models via the ionic equi-librium. At a pH of 7 most acetic acid is dissociated in biogasdigestion. According to [60]; methane-forming bacteria can onlyuse un-dissociated acetic acid, therefore dissociation has to beconsidered for nutrients such as acetic acid and for inhibitors suchas acetic and propionic acids, long chain fatty acids (LCFA), H2, NH3or H2S. The influence of the pH value on NH3, H2S and CO2 is shownin Fig. 6. Furthermore, some components can buffer the pH value,whereby the pH value is not changing immediately. This effect iscalled alkalinity. The most important buffer systems are the CO2/CO3

� and the NH3/NH4þ system. The concentration of Hþ ions can be

calculated from the ionic balance [60]:

OH� þ Ac� þHCO�3 þ 2CO2�

3 þ HS� þ 2S2� þ H2PO�4

þ 2HPO2�4 þ 3PO3�

4 ¼ NHþ4 þHþ þ Z

(30)

Fig. 5. Maximum specific growth rate depending on substrate concentration fordifferent pH values [7].

Table 2Models describing the influence of the pH value on bacterial growth [18,83].

Model

m ¼ Ko þ K1$pHþ K2$pH2 (33)

m ¼ mþ mmax�1þ OH��KH

�$�1þ OH��KOH

� (34)

mmaxðpHÞ ¼mmax

1þ K1�Hþ þ K2$Hþ (35)

m ¼ mmax$KH

KH þ Hþ (36)

m ¼ mmax$KOH

KOH þ OH� (37)

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714 707

In Eq. (30) Z is the sum of further anion in the medium such aschloride, phosphate or sulphide, and of further cations such ascalcium, sodium or magnesium. From the ionic equilibrium the pHvalue can be determined by:

pH ¼ �log10�Hþ

(31)

The integration of the pH value or the ionic equilibrium intomodels describing bacterial growth is described very clearly byRef. [60]. Using the model of [50]; the specific growth rate wasderived as follows:

m ¼ mmax$HAc

KHAc þ HAc$

KHPr

HPr þ KHPr$

KH2S

H2Sþ KH2S$

KNH3

NH3 þ KNH3

(32)

Some of the models that include the ionic equilibrium are[7,9,55] and [81].

2.2.1.5. Influence of temperature on bacterial growth. As it hasalready been discussed, temperature is one of the most importantparameters for bacterial growth. Even though the integration oftemperature dependencies is poor for most models, in cases that itis considered, the Arrhenius equation is used [17,67]:

k ¼ kmax$exp�� EaR$T

�(38)

with the rate constant k, the temperature T and the molar gasconstant R. The activation energy Ea and the maximum rate con-stant kmax have to be determined empirically.

Fig. 6. Fraction of dissociated and undissociated ammonia, hydrogen sulphur andcarbon dioxide depending on the pH value [60].

This equation has been applied to various parameters, such as tothe specific growth rate [81], the maximum specific growth rate[8,43], the saturation constant, the hydrolysis rate, the death rate,the inhibition constants [81], the yield coefficient for substrate tobiomass [37], the dissociation constant, the Henry-constant and theself-ionisation of water [8]. Most of these approaches are ques-tionable from a theoretical point of view, since the Arrhenius law isnot valid for the specific parameters. However, for an empiricaldescription, the temperature dependence implied by Arrheniusmay be adapted.

Refs. [17] and [83] have adapted the Arrhenius law to the re-quirements of anaerobic digestion processes and proposed thefollowing relationship:

mmaxðTÞ ¼ k1$exp�� E1R$T

�� k2$exp

�� E2R$T

�(39)

where the first part describes the common increase of the reactionrate due to temperature. The second part with typically higheractivation energy, describes the fast decrease of the reaction rateabove a certain temperature limit (rate of inactivation). Fig. 7 showsan example for the resulting temperature dependence of themaximum growth rate.

Ref. [44] described the temperature dependence of themaximum specific growth rate between 20 and 60 �C with a simplelinear. Using data for activated sludge to empirically determine theparameters of the relation [61], considered an exponentialapproach for the reaction rate between 5 and 35 �C, where atemperature increase of 10 K doubled the reaction rate.Ref. [18] published further approaches to describe the temperaturedependence.

2.2.1.6. Influence of gaseliquid equilibrium on bacterial growth.The most common approach in modeling is to assume that liquidand gas are in equilibrium. The partial pressure of the volatilecomponents of the system, i.e. CO2, H2, H2S and NH3, is determinedby Henry's Law [8], specifying that: At a constant temperature, theamount of a given gas that dissolves in a given type and volume ofliquid is directly proportional to the partial pressure of that gas inequilibrium with that liquid. Concerning solubility, CO2 is mostlyconsidered, while on the contrary, CH4 in most cases is neglected[37].

Based on the above, the gaseliquid equilibrium has an influenceon the composition of biogas and on the ionic equilibrium, andtherefore on the nutrient and inhibitor concentration. Gaseliquidequilibrium has been considered in the models of [7,8,12] and [81].

Fig. 7. Maximum specific growth rate depending on temperature [83].

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714708

2.2.2. Kinetics of substrate degradationBacterial growth can be modeled using the appropriate re-

lationships for growth kinetics and including inhibition by sub-strate and product concentrations, pH value, ionic equilibrium,gaseliquid equilibrium and temperature. The result is the specificgrowth rate, which depends on the growth requirements andmedium. The substrate degradation (dS/dt)r that is based on thespecific growth rate, can be thus calculated to complete the sub-strate balance expressed by Eq. (5), because microorganisms needsubstrate:

(a) to synthesise new cell material (dS/dt)x,(b) to produce products such as exoenzymes, acetic acid or

methane (dS/dt)c, and(c) to supply required maintenance and growth energy (dS/dt)e.

The whole degradation of substrate is then considered equal tothe sum of these three terms:

�dSdt

�r¼�dSdt

�xþ�dSdt

�eþ�dSdt

�c

(40)

In the example of the conversion of acetic acid to biogas byMethanosarcina barkeri [92], approximately 95% of the acetic acid isconverted to biogas, 3% to cell material and the remaining 2% of thesubstrate is needed for energy supply. The conversion requiringmost energy is biogas production at the end of the process.

For the synthesis of new cell material, microorganisms have todegrade substrate [37]. This can be described stoichiometrically.Ref. [64] used the relation shown below for acid-forming bacteria:

C6H12O6 þ 1:2 NH3/1:2 C5H7NO2 þ 3:6 H2 O (41)

According to this relation, 1.2 mol acid-forming bacteria areformed by 1 mol of glucose. Considering the molar mass of glucoseand biomass and assuming that the empirical formula C5H7NO2,represents 92% of the dry biomass, the yield coefficient of glucose toacid-forming bacteria, Yx, is 0.82 g/g.

Representative molecular structures for biomass areC75H105O30N15P [58] or C5H9O3N [69]. The chemical constitution ofthe formed biomass is not constant and varies with bacteria group,growth phase and utilised substrate. The substrate degradation dueto biomass formation (dS/dt)x depends on the change of cell con-centration over time dX/dt and can be expressed with Eq. (42)Ref. [37]:

�dSdt

�x¼ � 1

Yx$dXdt

¼ �m$XYx

(42)

Bacteria need energy for the synthesis of cell ingredients, whichare degraded continuously, or for osmotic activities to sustain theconcentration gradient between cell interior and exterior [83]. Theenergy demand of a living organism can be divided into growth

Fig. 8. Substrate degradation, bacteria growth and product formation at different fermentaticoncentration [36].

energy and maintenance energy. The required energy is providedby the substrate. However, the substrate limiting the growth is notnecessarily the same as the substrate limiting the energy supply[86]. According to [64]; the substrate degradation for energy supplycan be represented as Eq. (43).

�dSdt

�e¼ Ksx$X$mþ Kmx$X$

SKs þ S

(43)

The first part on the right side is the substrate degradation forgrowth energy supply and the second part on the right side is thesubstrate degradation for maintenance energy supply.

The substrate degradation due to product formation can bedetermined by Eq. (44), where Ys is the yield coefficient, calculatedstoichiometrically.

�dSdt

�c¼ 1

Ys$

�dPdt

�p

(44)

Ref. [90]; specified the representative molecular composition ofproteins (C16H30O8N4, 404 g/mol), lipids (C47H96O9, 804 g/mol) andcarbohydrates (C6H12O6, 180 g/mol), and used these molecularcompositions, to provide substrate degradation for the hydrolysisstep. Further stoichiometrical approaches and applications can befound in models by Refs. [9,22,45,64,69,81] or very detailed at [55].

2.2.3. Kinetics of product formationEven though the end product of the process is biogas, a number

of intermediates are also very important products. The kinetics ofproduct formation can be calculated using the kinetics of substratedegradation and of bacterial growth. Ref. [36] investigatedfermentation processes and classified products into three types asshown in Fig. 8.

Type I: products, which result from primary energy metabolism.The products are formed at the same time as substrate is degraded;an example is the fermentation of alcohol.

dPdt

¼ Yp1$m$X ¼ Yp1$dXdt

(45)

Type II: products, which result from energy metabolism indi-rectly. The products are formed at side reactions or following in-teractions of direct metabolic products; an example is thefermentation of glucose to lactic acid [37]. Therefore, the productformation is delayed and two maxima appear in substrate degra-dation and bacterial growth.

dPdt

¼ Yp1$m$X þ Yp2$X ¼ Yp1$dXdt

þ Yp2$X (46)

Type III: products, which obviously do not result from energymetabolism. Production of complex molecules (biosynthesis), such

on types, where X is the concentration, S the substrate concentration and P the product

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714 709

as the formation of antibiotics. Energy metabolism is practicallycomplete while the complex product accumulates.

dPdt

¼ Yp2$X (47)

For the modelling of biogas production, Type I is primarily usedRefs. [7,22,30] and [84] are such examples.

2.3. IWA anaerobic digestion model no 1 (ADM1)

Recognising the need for a generalised anaerobic digestionmodel that would overcome the limitations of previously devel-oped models, the International Water Association (IWA) estab-lished in 1997 the Anaerobic Digestion Modelling Task Group. Theidentified limitations were over-specificity and inability to be morewidely applied [98]. The model was published in 2002 [13] and isstructured with disintegration and hydrolysis, acidogenesis, ace-togenesis and methanogenesis steps.

According to the ADM1 technical report [13] the developedmodel, includes multiple steps describing biochemical and physi-cochemical processes. Conventional process variables like concen-tration of volatile organic acids and ammonium, sludge pH, and gasflow rates were used as model outputs. Specificities and/or pecu-liarities for certain processes were not considered in the model, tomake it more generic and usable.

ADM1model comprises of complex reaction kinetics and a largenumber of simultaneous and sequential reactions, primarily clas-sified as either biochemical or physicochemical. Extra-cellular en-zymes are assumed to catalyse biochemical reactions involvingbiologically-available organic substrates. All extra-cellular ADM1biochemical reactions are assumed to follow empirically-based 1st-order rate law kinetics, and all intra-cellular ADM1 biochemicalreactions are assumed to follow Monod-type substrate uptake ki-netics (section 2.2.1.1). Substrate uptake reaction rates are consid-ered proportional to the biomass growth rate and biomassconcentration [13].

The model takes into consideration pH inhibition, through H2and free ammonia inhibition for acetogenic and aceticlastic meth-anogenic bacterial groups, respectively. Growth limitation, wheninorganic nitrogen in the form of ammonia or ammonium becomeslimited, is also taken into consideration via secondary Monod up-take kinetic equations. Physicochemical reactions are assumed tobe controlled by processes involving gaseliquid transfer and ionassociation/dissociation.

The ADM1 model has been widely applied and validated insimulating the anaerobic digestion of several organic wastes likeolive mill solid wastes [53], sludge from wastewater treatmentplants [20] and sewage sludge [79].

Even though complex models like ADM1 are well suited forprocess simulation, they are substantially limited for process

Table 3Simple calculators for anaerobic digestion applications.

Title Developer, reference

Anaerobic digestion decision support software Poliafico, M. (supervisedMEng Thesis. Departmenof Technology. Ireland. [7

Biomass Environmental Assessment Tool AEA Energy and EnvironAgency. UK. [1]

BioGC WFG Schw€abisch for theGasTheo_Win32_1.1 Schlattmann, M., 2008. G

of biomass, available fromThe Anaerobic Digestion Economic Assessment Tool Redman, G., 2010. A deta

to UK farming and wasteFarmWare U.S. Environment Protect

control and optimisation application [85]. Moreover, in large-scalesdigesters, it is difficult to encounter ideal mixing, and the actualcomplex flow behaviour is very different to constant-volume,completely-mixed system assumed by ADM1 [98].

The complexity of ADM1 leads to the need for many input pa-rameters, ultimately resulting in a large number of stoichiometricand kinetic equations, for which parameter identification andmanipulation can prove difficult.

3. Simple calculators

Due to the fact that the models presented in the previous sec-tion, demand considerably large amount of specialised data, theyare not accessible to farmers and other stakeholders with limitedscientific knowledge on the issue of anaerobic digestion. Given thelarge activity however in the recent years on the use of anaerobicdigestion for treatment of waste, production of energy and reduc-tion of greenhouse gases emissions, simple calculators have beendeveloped to provide the necessary information, without any needto get involved extensively in the science of anaerobic digestion.

Most of the available calculators have been developed on thebasis of very simple methodologies. In most cases, the end productsof such calculators are the amount of energy and biogas that can beproduced from the digestion of a certain waste stream. A verycommon output in several cases is also a financial analysis, whereasthere are also examples that calculate the reduction in greenhousegases emissions and estimate the environmental impacts. A list ofthe calculators that are described in the following section is given inTable 3.

3.1. Anaerobic digestion decision support software

This tool was developed in 2007 for the Environmental Protec-tion Agency of Ireland, with the purpose to assess the biogas pro-duction from animal wastes that is produced in Ireland, and isavailable for download from the Ireland Environmental ProtectionAgency website [74]. The tool consists of (a) an energy potentialmodel to estimate the biogas production from a specific number ofanimals, (b) an economic model to evaluate costs and incomesassociated to biogas plants and (c) a location model to identifyvaluable areas for the development of biogas projects according tothe number of installations in an area. The tool has been developedin Microsoft excel. The user can proceed in the various stages of themodel by changing excel sheets and excel workbooks. The esti-mation of abattoir waste, economic cost analysis model, livestockpopulation according to area and potential analysis model, are eachin a separated excel sheet. For the purpose of this paper, the dis-cussion will be concentrated on the economic cost analysis andpotential analysis model.

by J. D. Murphy) 2007. Anaerobic Digestion: Decision Support Software.t of Civil, Structural and Environmental Engineering. Cork Institute4]ment, North Energy Associates. 2008. Developed for DEFRA and the Environment

project Biogas Regions [94]asTheo e A program to calculate theoretical gas yields from anaerobic digestionwww.schlattmann.de/download/gastheo.php [78]

iled economic assessment of anaerobic digestion technology and its suitabilitysystems. The Andersons Centre for DECC and NNFCC [77]ion Agency, 2010 [89]

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714710

3.1.1. Potential analysis modelAll the coefficients used and calculations made are accessible to

the user, by unlocking the sheet. The essential input to the model isthe animal population of cattle and pigs according to animal age.The developer gives an option of time period for which the esti-mation of energy will be made. Then a corrective factor based onthe time period entered that takes into account (a) loss of feedstockdue to operational conditions, and (b) energy loss from the time ofwaste is produced to the time is digested anaerobically. 0.9 is usedas default, which corresponds to a loss of 10% and is based on thefindings of Irish [33,65,56] ; and [14]. The fourth step is the esti-mation of slurry, where the user can change the waste generationcoefficients. The waste generation is estimated according to the ageof the animals and is based on estimations of the developers usingspecific data from farms in Ireland. In case the user has data onannual waste production, one can start from inputting the amountof waste to the model at stage 5.

The conclusion of the developerwas that 1 tonof cattle slurry canproduce about 21 Nm3 of biogas, 1 ton of pig slurry about 24 Nm3 ofbiogas and 1 ton of animal carcasses about 168 Nm3 of biogas.

The calculations on biogas production are based on annualproduction of volatile solids concentration. The default total solidsconcentration of the model are 8.5% for cattle and 8% for pigs, whilethe default volatile solids concentration is 85% for cattle and 75% forpigs. The source of this information is [33,71]; and local data. Thenext stage is the estimation of biogas production, where the co-efficients used are 0.3 Nm3 biogas/kg volatile solids loaded forcattle and 0.4 Nm3 biogas/kg volatile solids loaded for pigs. Thecoefficients are based on a literature review of the developer. Thespecific weight of waste is assumed to be 1 t/m3.

The next sheets are for the estimation of biogas from carcassesof cattle, pigs and sheep. The default average mass per animal is324 kg for cattle, 77.5 kg for pigs and 20.3 kg per sheep, and the datais according to the central statistics office of Ireland. The total solidsused are 25% and volatile solids 90% for all animal species. For allanimal species, methane production per kg volatile solids input tothe anaerobic digester is 0.75 Nm3.

3.1.2. Economic cost analysis modelThe main data source for the costs analysis is for Denmark, and

the parameters used for the calculations are: Gas Yield in m3/m3 ofbiomass and m3/m3 of digester, Investments, Investments per unit

Table 4Technologies, feedstocks and key outputs of the Biomass Environmental Assessment Too

Technologies Feedstocks

Dedicated biomass plants for Straw Used with dedTypical furniture waste

electricity production MDF wastecombined heat and power (CHP) Chipboard waste

High biomass refusederived fuel

heat (industrial and domestic boilers)

Glycerine Used both witplants and co-Co-firing in existing plant Short rotation coppice

MiscanthusAnaerobic digestion Forestry residueson farm (heat, electricity and CHP) ‘clean’ wood waste

Imported wood chips/pellets Used with co-centralized (heat and CHP) Olive cake

Palm kernel expellerLiquid biofuels Cereal milling residues Used for anaebioethanolbiodiesel

Pig and dairy slurry

Food waste Used for liquidOSRWaste oilWheatSugar beat

of biomass, Investments per unit of gas yield, Operating Costs,Operating Costs per unit of biomass and Operating Costs per unit ofdigester. Using the information available for capital costs, runningcosts and biogas production, equations are formed relating thethree parameters to the total amount of biomass treated annually.The default inflation used is 3.5% and upgrading costs are alsoincluded. Incomes assume sale of methane and digestate withmarket prices of 0.98 V/m3 of methane and 15 V/m3 of digestate.Grants and loans are also taken into account, and so are the ex-ternalities for agriculture, industry and environment. In particular,improved fertilizer value (NPK) at 0.73 V/t, handling of liquidmanure at 0.2 V/t and reduced obnoxious smells at 0.67 V/t areconsidered for agricultural externalities, saving related to wastetreatment at 16.17V/t for industrial externalities and GHG emissionreduction at 3.01 V/t and value of reduced N-eutrophication ofground water at 0.39 V/t for environmental externalities. Thedefault plant lifetime of 20 years and interest rate of 8% are used forthe calculations.

3.2. Biomass environmental assessment tool

The Biomass Environmental Assessment Tool or “BEAT” wasdeveloped by AEA Energy and Environment, North Energy Associ-ates for DEFRA and the Environment Agency of the UK in 2008.Version 2.1 of the tool, “BEAT2”, is available at the DEFRA website.The toolhas beendevelopedwithMicrosoft access, and also requiresMicrosoft excel and word to be available. This tool covers all bio-energy technologies and is not only for anaerobic digestion. Ac-cording to the developers, the aim of this tool is to provide the userwith a means for assessing the potential benefits as well as associ-ated environmental impacts of bioenergy technologies. Technolo-gies, feedstocks and key outputs of the tool, are summarised inTable 4. According to the user guide (AEA Energy and [2]), an on-siteinstallation can be 0.2e2 MW thermal capacitance installedwhereas the centralised (or off-site) installation can be 4e40 MW.

The tool starts with an option for the user whether to open anexisting “scheme” or create a new one. It then requests the tech-nology to be used (dropdown menu) and asks for up to four feed-stocks types. In the case the user does not want to change thedefault parameters, the tool then goes directly to the results wheredetails are given on the key outputs listed in Table 4. In the alternate

l v.2.1. (BEAT2) [1].

Key outputs

icated biomass plants GHG emissions and savings

Primary energy useLand takeTransport impacts (number of deliveries to plant)

h dedicated biomassfiring in existing plant Qualitative assessment of other potential

environmental impacts (e.g. noise, visual,impacts on air, water, soil) from both feedstockproduction and conversion pant

firing in existing plant

robic digestion Estimate of production costs and support mechanisms,and estimate of costs of supportmechanisms per t CO2 saved

production of biofuels

Table 5Variables that can be altered by user and given range for theoretical estimation ofbiogas production [78].

Variable Value and range of change

Dry solids content 0e100% dry matterFree fibres 0e1000 g/kg Total solids

0e100% VQCH

Free Proteins 0e1000 g/kg total solids0e100% VQPR

Free Fats 0e1000 g/kg total solids0e100% VQLI

Removable free nitrogen 0-1000 g/kg total solids0-100% VQNFE

Carbohydrates Proteins Fatsl Nitrogen/kg total solids 630e950 550e850 900e1500% methane 40e60 55e85 55e85

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714 711

case, in which the user wants to customise the parameters, theoption is given to choose the parameters to be changed.

Biogas production is based on destruction of volatile solidscalculated according to the default parameters. The model alsoprovides the option to use a centralised system instead of an on-farm installation. The user may also view the excel sheet wherethe calculations take place.

The total capital cost of digester and connected system are basedon capacity (tones). For the estimations, a residence time of 21 daysand active volume of 75% are assumed. Available financial supportschemes are according to the existing supportmechanism in the UKat the time of publication of the model. The estimations are basedon 30% capital grant and a feed in tariff of 4.56 £/MWh electricityproduced, among others. Moreover, a discount rate of 3.5% is usedas a default value. Data concerning greenhouse gases emissions isaccording to the IPCC third assessment report [52] and countryspecific data reported in the user manual (AEA Energy and [2]).

The model does not require the user to enter animal populationoramountofwaste involumeormass. Theonly input required, is thecomposition of the feedstock in terms of ratio. The main parameter,on which the model is based, is the required energy output of theproposed plant and the characteristics of the feedstock.

3.3. BioGC

BioGC is a software develop by WFG Schw€abisch Hall in 2009 inthe framework of a project funded by the Intelligent energyeEu-rope program (WFG Schw€abisch [94]). The title of the project is“Promotion of biogas and its market development through localand regional partnerships” or “Biogas Regions” (acronym). Thebiogas calculator is available in eight European countries (the lan-guages of the participants to the project). It contains informationfor 88 substrates whose characteristics can be modified and savedby the user.

The user also has the option of adding other substrates that arenot included in the program. Most of the activity data onwhich thecalculations are based is in mass of substrate (tones). Some types ofsubstrate have to be entered in units of area (hectares). Additionalparameters that have to be entered by the user are hydraulicretention time and type and efficiency of the combined heat andpower (CHP) engine.

The final result of the calculator is a one page summary of in-formation regarding digester size and storage demand, energyproduction, investment costs, gas utilization, energy sales and in-come. The results can be exported to Microsoft excel.

3.4. GasTheo

GasTheo is a simple software in German, developed by MarcusSchlattmann in 2008 [78]. The software is freely available on theinternet. Its development is based on the use of Qt4 libraries, andrequires Microsoft Windows to run. “Qt” is a cross-platformapplication framework that is widely used for developing applica-tion software with a graphical user interface [87]. The user canchange the parameters listed in Table 5 and see the impact on thebiogas production. The estimation of the biogas production is basedon the methodology proposed by the German Agency for Renew-able [3]. The results are volume of biogas (l), volume of methane (l)per kg total solids and per kg dry solids, percent content of drysolids and percent content of methane.

3.5. The anaerobic digestion economic assessment tool

The tool was developed by G. Redman in 2010 for the NNFCCBiocentre, with funding from the Department of Energy and

Climate Change [77]. The tool has been developed in Microsoftexcel, and is part of a biogas toolbox designed to assist the ADdeveloper to assess viability and optimisation of different options.Default and suggested values are provided at most stages of thetool, which can be overwritten with specific data. Default valuesassume wet, mesophilic, continuous flow but other technologiescan be used by changing the retention period and output data.Estimations of biogas production are based on dry matter content.

The default values used for the tool for livestock breeding, arebased on the results of a project funded by the EU6th frameworkprogram, Renewable energy from crops and agrowastes (CROPGEN)[10]. The user also has the option of adding energy crops, otherfeedstocks such as vegetable wastes and old bread, or other feed-stock. The tool estimates a minimum digester capacity based on theretention period entered by the user. Default retention time is 60days.

The sheets with the financial information and calculations, es-timate the fertilizer value of the digestate and the land required forspreading, revenues from the sale of electricity or heat produced bythe biogas, estimation of capital and capital payment, and over-heads costs. The financial information is summarised in an overallfinancial summary sheet and an annual financial sheet.

The revenues are based on the assumption that there are11.2 kWh/m3 methane and with default methane content of 60%this corresponds to 6.72 kWh/m3 biogas. Energy losses are bydefault 10% and efficiency of CHP is 33% for electricity and 42% forthermal. Using the above default values the result is 2 kW/m3

biogas electrical energy and 2.51 kW/m3 thermal energy. Addi-tional options are given for the grants of electrical output.

Capital investment uses a “write off” period of 20 years forbuildings and infrastructure and 10 years for the machinery capitalas default. Default base rate is 2.5% and over base is 5%, whereas90% of the initial capital is funded by the bank with a 10 yearsfinance term.

Overhead costs include labour costs, maintenance, depreciationof the buildings and equipment, insurance, transport, licenses andother fees. Machinery maintenance for anaerobic digester isassumed to be 2% as default value and for CHP, £0.01/kWh.

The summary sheets provide graphic illustrations of the results.

3.6. FarmWare

The tool FarmWare has been developed in the framework of theU.S. Environmental Protection Agency's AgSTAR Program, which is avoluntary outreach and educational program promoting the re-covery and use of methane from animal waste. The latest version ofthe tool (3.5) was released in December 2010 (U.S. [33]). FarmWareis a tool designed to identify the potential benefits of integrating

Table 6Comparison of simple calculators.

Model Biogas production Energy production GHG emission reductions Financial assessment Environmental impacts

AD decision support software ✓ ✓ ✓

Anaerobic digestion economic assessment tool ✓ ✓ ✓

BEAT2 ✓ ✓ ✓ ✓ ✓

BioGC ✓ ✓ ✓

FarmWare ✓ ✓ ✓ ✓ ✓

GasTheo ✓

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714712

anaerobic digestion into existing or planned dairy or pig manuremanagement systems. The tool requires Microsoft Windows to runand allows the user to change the default values of the program.

Required fields by the tool include information concerning thelocation of the farm so as to withdraw climatic information fromthe software database. Climatic information and in particular,precipitation, evaporation, and temperature, are used to calculatemethane production and to set size parameters for waste man-agement systems. Moreover, precipitation information is used toestimate the impact on the runoff from an extreme storm event.

The available options for farm types are: dairy, swine farrow-to-finish, farrow-to-wean, nursery, farrow-to-wean plus nursery andgrow-finish. It provides options for the number of hours spend ateach housing area according to animal type, the technology wasteis collected from the barn (flush or scrub) and according to thewaste collection technology, an anaerobic digestion technology isautomatically proposed. Available anaerobic technologies arecomplete mix, plug-flow and anaerobic lagoon. The option is madeaccording to the total solids content: 0.5e3% for covered lagoons,3e10% for complete mix digesters and 11e13% for plug-flow di-gesters. An option for a separator is also available. The user also hasto define a system that is already installed or could be installedinstead of an anaerobic digester for waste management. Defaultmanure excretion rates are defined by the U.S. Department ofAgriculture, Natural Resources conservation service (NRCS) [72].This information can be changed by the user to farm specific data.The user also has the option to change the default design param-eters of all the technologies available in the program. Biogas pro-duction from anaerobic digestion is based on the methodologyproposed by Chen and Hashimoto as presented in kinetics ofmethane fermentation (1978).

3.7. Comparison of the simple calculators

Even though a number of other models are available for theestimation of the parameters considered, the particular modelshave been presented because, they are investigating similar issueswith similar approach starting from the number of animals and theamount of waste generated. All of the described calculators provideestimates for biogas production, whereas all with the exception ofGasTheo provide estimates for energy production and financial

Table 7Estimation of biogas production by the application of the models for a farm of 100 dairy

Model Biogas production Comments

AD decision support software 54,444 Nm3/y 2505 t waste/yAnaerobic digestion economic

assessment tool50,592 m3/y Using 2400 t/y da

BEAT2 Mass ratio Anaerobic digestioBioGC 86,048.34 m3/y 2650 t/y waste, 60FarmWare 116,844 m3/y Cattle: Free-stall s

storage or treatmePigs: pull plug/pitwith no solid trea

assessment. BEAT2 and FarmWare are the only calculators that alsoassess environmental impacts and reduction of greenhouse gasesemissions. A comparison of the models for all applications is pre-sented in Table 6.

To evaluate the performance of the six simple models, we testedthem for the production of biogas for a farm of 100 dairy cows and50 sows, without changing the default parameters. The results arepresented in Table 7. As shown, the estimation was not possible forGasTheo and BEAT2, since they did not accept the input of numberof animals. The outcome from the remaining four models rangesfrom 50,592 m3/y estimated by "Anaerobic Digestion EconomicAssessment Tool" to 116,844 m3/y estimated by FarmWare.

4. Discussion and conclusions

This review presents the various models that have been devel-oped to describe Anaerobic Digestion (AD) processes so as to un-derstand the process and optimise the design and operation ofanaerobic digesters. The relatively simple and implementable rate-limitingmodels were first highlighted. However, their diversity andcustomised development for applications involving specific sub-strates and conditions, limited their widespread implementation. Itwas found that the identification of rate-limiting steps and theintermediate fermentation products at different digester conditionsis crucial but difficult for AD processes involving complexsubstrates.

ADM1 represents the currently most comprehensive model ofthe AD process which serves as a basis for future development ofkinetics models. Nevertheless, its complex model structure stillwelcomes improvements, such as interactions between anaerobicmicroorganisms. The complexity of ADM1 however, leads to theneed for many input parameters, which can prove difficult.

That is the reason that simpler calculators have also beenstudied. Simpler calculators mainly use the relation that existsbetween volatile solids and biogas production. There are caseshowever, where the calculator is a simplified version of a specificmodel. Nevertheless, the aim of these calculators is not to simulatethe process of anaerobic digestion, but to estimate the applicabilityof the process to a specific farm and to provide information to afarmer or a decision maker.

cows and 50 saws.

iry waste and 100 t/y pig waste

n on farm producing electricity and heat, 50% dairy manure, 50% pig manuredays hydraulic retention time

crape barn, complete mix digester, with storage tank and no separate solidntrecharge barn, combined storage and treatment lagoon, completely mix digestertment

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714 713

The application of a model is an important step in the assess-ment of the feasibility of the plant, since solid data needs to beavailable proving the efficiency of such plant for the investor toproceed. The available models have a wide range of applicationsand are based on a wide range of aims. Moreover, they have greatvariation in complexity: from simple calculators just estimatingbiogas production based on the number of animals, to detailedmodels simulating every stage of anaerobic digestion, with exten-sive databases of information required to be applied. However, dueto the great complexity associated with the interferences betweenphysico-chemical and biological processes, the cases where highlydetailed models are applicable to different substrates and condi-tions are limited.

References

[1] AEA Energy and Environment and North Energy Associates. Biomass envi-ronmental assessment tool [Developed for DEFRA and the EnvironmentAgency. UK]; 2008.

[2] AEA Energy and Environment and North Energy Associates. BEAT2 (Biomassenvironmental assessment tool) v.2.1 e user guide. Issue number 4. [Devel-oped for DEFRA and the Environment Agency. UK]; 2010.

[3] Agency for Renewable Resources. Notes on the production and utilization ofbiogas [Handreichung Biogasgewinnung und-nutzung]. Gülzow, Germany:Fachagentur Nachwachsende Rohstoffe; 2005 [in German].

[4] Aiba S, Shoda M, Nagatani M. Kinetics of product inhibition in alcoholfermentation. Biotechnol Bioeng 1968;10(6):845e64.

[5] Amon T, Amon B, Kryvoruchko V, Machmüller A, Hopfner-Sixt K, Bodiroza V,et al. Methane production trough anaerobic digestion of various energy cropsgrown in sustainable crop rotations. Bioresour Technol 2007;98(17):3204e12.

[6] Andrews JF. A mathematical model for the continuous culture of microor-ganisms utilizing inhibitory substrates. Biotechnol Bioeng 1968;10:707e23.

[7] Andrews JF, Graef SP. Dynamic modeling and simulation of the anaerobicdigestion process. Anaerobic Biological Treatment Processes, Adv. Chem. Ser.105. Washington, D.C: American Chemical Society; 1971.

[8] Angelidaki I, Ellegaard L, Ahring BK. A mathematical model for dynamicsimulation of anaerobic digestion of complex substrates: focusing onammonia inhibition. Biotechnol Bioeng 1993;42:159e66.

[9] Angelidaki I, Ellegaard L, Ahring BK. A comprehensive model of anaerobicbioconversion of complex substrates to biogas. Biotechnol Bioeng 1999;63:363e72.

[10]] Banks C. Renewable energy from crops and agrowastes (CROPGEN). Projectno. SES6-CT-2004e502824. Duration 39 months. Research project funded bythe EU's 6th Framework programme. Project coordinator: School of Civilengineering and the environment, University of Southampton; 2007.

[11] Baserga U. Landwirtschaftliche Co-Verg€arungs-Biogasanlagen. FAT-BerichteNr. 512, Eidg. Forschungsanstalt für Agrarwirtschaft und Landtechnik,T€anikon, Schweiz (Agricultural co-fermentation, biogas plans. FAT-report no.512, Swiss Federal Research Station for Agricultural Economics and Agricul-tural Technology); 1998.

[12] Batstone DJ, Keller J, Angelidaki I, Kalyuzhnyi SV, Pavlostathis SG, Rozzi A,Sanders WT, Siegrist H, Vavilin VA. The IWA anaerobic digestion model No 1(ADM1). Water Sci Technol 2002;45(10):65e73.

[13] Batstone DJ, Keller J, Angelidaki I, Kalyuzhnyi SV, Pavlostathis SG, Rozzi A,et al. Anaerobic digestion model No. 1. London, UK: International Water As-sociation (IWA) Publishing; 2002. ISBN: 1-900222-78-7.

[14] Batzias FA, Sidiras DK, Spyrou EK. Evaluating livestock manures for biogasproduction: a GIS based Method. Renew Energy 2005;30:1161e76.

[15] Bazua CD, Wilke CR. Ethanol effects on the kinetics of a continuous fermen-tation with Saccharomyces cerevisiae. Biotechnol Bioeng 1977:105e18. SympNo. 7.

[16] Beba A, Atalay FS. Mathematical models for methane production in batchFermenters. Biomass 1986;11(3):173e84.

[17] Bergter F. Wachstum von Mikroorganismen: Experimente und Modelle. 2.Jena: Auflage, VEB Gustav Fischer Verlag; 1983 [Growth of microorganisms:experiments and models. Second Edition].

[18] Birjukow WW, Kantere WM. Optimising periodical processes of microbio-logical synthesis (russ.). Moskau: Nauka; 1985.

[19] Biswas J, Chowdhury R, Bhattacharya P. Kinetic studies of biogas generationusing municipal waste as feed stock. Enzyme Microb Technol 2006;38:493e503.

[20] Blumensaat F, Keller J. Modelling of two-stage anaerobic digestion using theIWA Anaerobic Digestion Model No. 1 (ADM1). Water Res 2005;39:171e83.

[21] Boyle WC. Energy recovery from sanitary landfills. In: Schlegel HG, Barnea J,editors. Microbial energy conversion. Oxford: Pergamon Press; 1977.pp. 119e38.

[22] Bryers JD. Structured modeling of the anaerobic digestion of biomass partic-ulates. Biotechnol Bioeng 1985;27:638e49.

[23] Buswell AM, Mueller HF. Mechanism of methane fermentation. J Ind EngChem 1952;44(3):550e2.

[24] Chen YR. Kinetic analysis of anaerobic digestion of pig manure and its designimplications. Agr Wastes 1983;8:65e81.

[25] Chen YR, Hashimoto AG. Kinetics of methane fermentation. Biotechn Bioeng1978:269e82. Symp No. 8.

[26] Chen YR, Varel VH, Hashimoto AG. Effect of temperature on methanefermentation kinetics of beef-cattle manure. Biotechnol Bioeng 1980:325e39.Symp. No. 10.

[27] Contois DE. Kinetics of bacterial growth: relationship between populationdensity and specific growth rate of continuous cultures. J Gen Microbiol1959;21:40e50.

[28] Coveney FM, Wetzel GR. Effects of nutrients on specific growth rate of bac-terioplankton in oligotrophic lake water cultures. Appl Environ Microbiol1992;58(1):150e6.

[29] Dagley S, Hinshelwood CN. Physicochemical Aspects of bacterial growth. PartI. Dependence of growth of Bacterium Lactis aerogenes on concentration ofmedium. J Chem Soc 1938:1930e6.

[30] Denac M, Miguel A, Dunn IJ. Modeling dynamic experiments on the anaerobicdegradation of molasses wastewater. Biotechnol Bioeng 1988;31:1e10.

[31] Donoso-Bravo A, Mailier J, Martin C, Rodríguez J, Aceves-Lara CA, VandeWouwer A. Model selection, identification and validation in anaerobicdigestion: a review. Water Res 2011;45:5347e64.

[32] Edwards VH. The influence of high substrate concentrations on microbialkinetics. Biotechnol Bioeng 1970;12(5):679e712.

[33] Environmental Protection Agency. Anaerobic digestion: benefits for wastemanagement, agriculture, Energy and the environment. discussion paper.Ireland; 2005.

[34] Fencl Z. Theoretical analysis of continuous culture systems. In: Malek I,Fencl Z, editors. Theoretical and methodological basis of continuous culture ofmicroorganisms. New York: Academic Press; 1966.

[35] Fujimoto Y. Kinetics of microbial growth and substrate consumption. J TheorBiol 1963;5:171e91.

[36] Gaden EL. Fermentation process kinetics. J Biochem Microbiol Tech Eng1959;1(4):413e29.

[37] Gerber M, Span R. An analysis of available mathematical models for anaerobicdigestion of organic Substances for production of biogas. In: International GasUnion Research Conference. Paris 2008; 2008.

[38] Ghose TK, Tyagi RD. Rapid ethanol fermentation of cellulose hydrolysate. II.product and substrate inhibition and optimization of fermentor design. Bio-technol Bioeng 1979;21(8):1401e20.

[39] Grady Jr CPL, Harlow LJ, Riesing RR. Effects of the growth rate and Influentsubstrate concentration on Effluent quality from Chemostats containingbacteria in pure and mixed culture. Biotechnol Bioeng 1972;14:391e410.

[40] Grant DJW. Kinetic aspects of the growth of klebsiella aerogenes with somebenzenoid carbon sources. J Gen Microbiol 1967;46:213e24.

[41] Haldane JBS. Enzymes. London: Logmans; 1930.[42] Han K, Levenspiel O. Extended Monod kinetics for substrate, product, and cell

inhibition. Biotechnol Bioeng 1988;32(4):430e7.[43] Hashimoto AG. Methane from cattle waste: effects of temperature, hydraulic

retention time, and influent substrate concentration on kinetic parameter.Biotechnol Bioeng 1982;24:2039e52.

[44] Hashimoto AG, Varel VH, Chen YR. Ultimate methane yield from beef cattlemanure: effect of temperature, constitute, antibiotics and manure age. AgrWastes 1981;3:241e56.

[45] Hill DT. A comprehensive dynamic model for animal waste methanogenesis.Trans ASAE 1982:1374e80.

[46] Hill DT. Simplified Monod kinetics of methane fermentation of animal wastes.Agr Wastes 1983;5:1e16.

[47] Hill DT, Barth CL. A dynamic model for simulation of animal waste digestion.J Water Pollut Control Fed 1977;10:2129e43.

[48] Holzberg I, Finn RK, Steinkraus KH. A kinetic study of the alcoholic fermen-tation of grape juice. Biotechnol Bioeng 1967;9:413e27.

[49] Ierusalimski ND. Bottle-necks in metabolism as growth rate controlling factor.In: Powell EO, Evans CGT, Strange RE, Tempest DW, editors. Microbial phys-iology and continuous culture. 3rd International symposium, Salisbury. Lon-don: H.M.S.O.; 1967. pp. 23e33.

[50] IPCC. Climate change 1995, the science of climate change: summary for pol-icymakers and technical summary of the working group I report; 1995.

[51] IPCC. Climate change 2001: synthesis report. A contribution of workinggroups I, II and III to the third assessment report of the intergovernmentalpanel on climate change. In: Watson RT, The Core Writing Team, editors.Cambridge, United Kingdom and New York, NY, USA: Cambridge UniversityPress; 2001. p. 398.

[52] Kalfas H, Skiadas IV, Gavala HN, Stamatelatou K, Lyberatos G. Application ofADM1 for the simulation of anaerobic digestion of olive pulp under meso-philic and thermophilic conditions. Water Sci Technol 2006;54(4):149e56.

[53] Keymer U, Schilcher A. Biogasanlagen: Berechnung der Gasausbeute vonkosubstraten. bayrische landesanstalt für landwirtschaft [Biogas plants:calculation of the gas yield of co-substrates, Bavarian State Institute forAgriculture]; 2003.

[54] Knobel A, Lewis A. A mathematical model of a high sulphate wastewateranaerobic treatment system. Water Res 2002;36:257e65.

[55] Krich K, Augenstein D, Batmale JP, Benemann J, Rutledge B, Salour D. Bio-methane from dairy waste e a sourcebook for the production and use ofrenewable natural gas in California. Prepared for Western United Dairymen.Funded part through USDA Rural Dev; 2005.

N. Kythreotou et al. / Renewable Energy 71 (2014) 701e714714

[56] Lo KV, Carson WM, Jeffers K. A computer-aided design program for biogasproduction from animal manure. In: Proceedings of the International Sym-posium on Livestock Wastes. St. Joseph: ASAE; 1981. pp. 133e5.

[57] Loehr RC. Agricultural waste management e problems, processes, and ap-proaches. New York, London: Academic Press; 1974.

[58] Mankad T, Bungay HR. Model for microbial growth with more than onelimiting nutrient. J Biotechnol 1988;7(2):161e6.

[59] M€arkl H, Friedmann H. Biogasproduktion (biogas production). In:Antranikian G, editor. Angewandte mikrobiologie (applied microbiology).Berlin, Heidelberg: Springer Verlag; 2006.

[60] McKinney RE. Mathematics of complete-mixing activated sludge. J Sanit EngDiv 1962;88:87e113.

[61] Michaelis L, Menten M. Die kinetik der invertinwirkung. Biochem Zg 1913;49:333e69.

[62] Mitsd€orffer R. Charakteristika der zweistufigen thermophilen/mesophilenSchlammfaulung unter Berücksichtigung kinetischer Ans€atze. Berichte ausWassergüte- und Abfallwirtschaft, Technische Universit€at München, No. 109(Characteristics of the two-stage thermophilic/mesophilic sludge digestion,taking into account kinetic approaches; 1991. Reports of Water Quality andWaste Management, Technical University of Munich, no. 109).

[63] Moletta R, Verrier D, Albagnac G. Dynamic modelling of anaerobic digestion.Water Res 1986;20(4):427e34.

[64] Møller HB, Sommer SG, Ahring BK. Methane Productivity of manure, Strawand solid fractions of manure. Biomass Bioenergy 2004;26:485e95.

[65] Monod J. The growth of bacterial cultures. Ann Rev Microbiol 1949;3:371e94.[66] Moser A. Bioprozesstechnik: berechnungsgrundlagen der reaktionstechnik

biokatalytischer prozesse [Bioprocess engineering: basic calculation of reac-tion engineering of biocatalytic processes]. Wien, New York: Springer Verlag;1981.

[67] Moser H. The dynamics of bacterial populations maintained in the che-mostat. Washington, D.C: Carnegie Institute of Washington; 1958. Publi-cation 614.

[68] Mosey FE. Mathematical modelling of the anaerobic digestion process: reg-ulatory mechanisms for the formation of short-chain volatile acids fromglucose. Water Sci Technol 1983;15:209e32.

[69] Mu Y, Yu HQ, Wang G. A kinetic approach to anaerobic hydrogen-producingprocess. Water Res 2007;41(5):1152e60.

[70] Murphy JD. The benefits of integrated treatment of waste for the productionof energy. Ph.D. Thesis. National University of Ireland, University College ofCork; 2003.

[71] Natural Resource Conservation Service. Animal waste management fieldhandbook. Washington DC: U.S. Department of Agriculture; 2008.

[72] Pfeffer JT. Temperature effects on anaerobic fermentation of Domestic Refuse.Biotechnol Bioeng 1974;16:771e87.

[73] Poliafico M. Anaerobic digestion: decision support software. MEng. Thesis.Ireland: Department of Civil, Structural and Environmental Engineering. CorkInstitute of technology; 2007.

[74] Powell EO. The growth rate of microorganisms as a function of substrateconcentration. In: Powell EO, Evans CGT, Strange RE, Tempest DW, editors.Microbial physiology and continuous culture. 3rd International Symposium,Salisbury. London: H.M.S.O; 1967. pp. 34e56.

[75] Rao MS, Singh SP. Bioenergy conversion studies of organic fraction of MSW:kinetic studies and gas yield-organic loading relationships for process opti-misation. Bioresour Technol 2004;95(2):173e85.

[76] Redman G. A detailed economic assessment of anaerobic digestion technologyand its suitability to UK farming and waste systems [The Andersons Centre forDECC and NNFCC]; 2010.

[77] Schlattmann M. GasTheo e a program to calculate theoretical gas yields fromanaerobic digestion of biomass. Available from: www.schlattmann.de/download/gastheo.php; 2008 [accessed 20.06.11].

[78] Shang Y, Johnson BR, Sieger R. Application of the IWA anaerobic digestionmodel (ADM1) for simulating full-scale anaerobic sewage sludge digestion.Water Sci Technol 2005;52:487e92.

[79] Shin HS, Song YC. A model for evaluation of anaerobic degradation charac-teristics of organic waste: focusing on kinetics, rate-limiting step. EnvironTechnol 1995;16:775e84.

[80] Siegrist H, Vogt D, Garcia-Heras JL, Gujer W. Mathematical model for meso-and thermophilic anaerobic sewage sludge digestion. Environ Sci Technol2002;36:1113e23.

[81] Simeonov IS, Momchev V, Grancharov D. Dynamic modeling of mesophilicanaerobic digestion of animal waste. Water Res 1996;30(5):1087e94.

[82] Sinclair CG, Kristiansen B. Fermentationsprozesse e Kinetik und Modelling(Fermentation process e kinetics and modelling). Berlin: Springer-Verlag;1993.

[83] Sinechal XJ, Installe MJ, Nyns EJ. Differentiation between acetate and highervolatile acids in the modeling of the anaerobic biomethanation process. Bio-technol Lett 1979;1(8):309e14.

[84] Stamatelatou K, Syrou L, Kravaris C, Lyberatos G. An invariant manifoldapproach for CSTR model reduction in the presence of multi-step biochemicalreaction schemes. Application to anaerobic digestion. Chem Eng J 2009;150:462e75.

[85] Stouthamer AH. Yield studies in microorganisms. In: Cook JG, editor. Patternsof progress. Durham: Meadowfield Press; 1976.

[86] Summerfield M. Advanced qt programming: creating great software withCþþ and qt 4. 1st ed. Addison-Wesley; 2010. p. 550.

[87] te Boekhorst RH, Ogilvie JR, Pos J. An overview of current simulation modelsfor anaerobic digesters. Livestock waste: a renewable resource. ASAE 1981;2:105e8.

[88] U.S. Environment Protection Agency. FarmWare user's manual: a guide toFarmWare Version 3.5. Appendix C AgSTAR Handb Man Dev biogas Syst A. TCommer farms United States. EPA-430-B-97e015; 2010.

[89] Vavilin VA, Vasiliev VB, Ponomarev AV, Rytow SV. Simulation model 'Methane'as a tool for Effective biogas production during anaerobic conversion ofcomplex organic matter. Bioresour Technol 1994;48:1e8.

[90] Vrede T. Elemental composition (C:N:P) and growth rates of bacteria andRhodomonas grazed by Daphnia. J Plankton Res 1998;20(3):455e70.

[91] Wandrey C, Aivasidis A. Continuous anaerobic digestion with Methanosarcinabarkeri. Ann N Y Acad Sci 1983;413:489e500.

[92] Webb JL. Enzyme and metabolic inhibitors. New York: Academic Press; 1963.[93] WFG Schw€abisch Hall. Promotion of biogas and its market development

through local and regional partnerships (Biogas Regions). Deliverable no. 4.Project funded by Intelligent energy e Europe program. Contract no. EIE/07/225/S12.467622. Duration 36. Information accessed through, www.biogasregions.org; 2009 [accessed 21.06.11].

[94] Wolf KH. Kinetik in der Bioverfahrenstechnik (Kinetics in biotechnology).Hamburg: Behr; 1991.

[95] Yano T, Nakahara T, Kamiyama S, Yamada K. Kinetic studies on microbialactivities in concentrated solutions. Part I. effect of excess sugars on oxygenuptake rate of a cell free respiratory system. Agric Biol Chem 1966;30(1):42e8.

[96] Yilmaz AH, Atalay FS. Modeling of the anaerobic decomposition of solidwastes. Energy Sources 2003;25(11):1063e72.

[97] Yu L, Wensel PC, Ma J, Chen S. Mathematical modeling in anaerobic digestion(AD). J Bioremed Biodeg 2013;2013:S4.