Karlstads universitet 651 88 Karlstad Tfn 054-700 10 00 Fax 054-700 14 60 Information@kau.se www.kau.se
Fakulteten för hälsa, natur- och teknikvetenskap Miljö- och energisystem
Mats Sonesson
Methane yields from anaerobic digestion of food waste
Variation of load, retention time and waste
composition in simulating methane yields, using the
“Anaerobic digestion model no.1” (ADM1)
Metan från rötning av matavfall
Variation av last, uppehållstid och sammansättning i matavfallet med användning av ”Anaerobic digestion Model no.1” (ADM1)
Examensarbete 30 hp
Civilingenjörsprogrammet i energi- och miljöteknik
Juni 2013
Handledare: Alina Haqgelqvist Examinator: Roger Renström
Everything flows, and nothing stays.
Heraclitus
Förord
Ett antal människor har hjälpt mig igenom denna min sista ansträngning mot en civilingenjörsexamen. Först och främst vill jag tacka min handledare på Karlstads Universitet, Alina Hagelqvist. Tack för att du så tidigt gav mig både idéer och vidare läsning, och stort tack för ditt fantastiska engagemang.
Tack också till Christer Gustavsson på Pöyry AB, som fick mig att räkna om-och räkna rätt.
Tack dessutom till Anette Wästlund på Karlstads Energi AB, som fick mig att inse att allt inte står i böckerna.
Jag vill också tacka Anna Hörberg på Jönköpings Energi AB för mätdata, samt Ulf Jepsson på Lunds universitet för tålmodig mailkorrespondens. Tack även till Jan Forsberg på Karlstads Universitet för hjälp med felsökning av min kod.
Sist men inte minst vill jag även tillägna några rader till min bror, och tillika miljövetare;
Mikael Sonesson. För att du aldrig håller med mig, men alltid tror på mig.
Detta examensarbete har redovisats muntligt för en i ämnet insatt publik. Arbetet har därefter diskuterats vid ett särskilt seminarium. Författaren av detta arbete har vid seminariet deltagit aktivt som opponent till ett annat examensarbete.
Nomenclature
Variable Description Unit
d time Days
VS Volatile solids Kg [food waste]
COD Chemical oxygen demand Kg [O2]
SRT Hydrological retention time d [days]
Ik Inhibition factor number k [1]
KI,n Inhibition constant for compound n. [kgCOD/m3] or [kmol/m3]
OLR Organic loading rate kgVS/(m3*d)
Sliq,i State component i in liquid phase
kgCOD/m3 or kmol/m3*
Sin,i Steady state inflow of state
component i.
kgCOD/m3 or kmol/m3*
Sacid-/+ Acid/base for specific acid/base kgCOD/m3 or kmol/m3*
Vliq Liquid reactor volume m3
Vgas Gas headspace in reactor m3
qliq Volumetric fluid inflow m3
qgas Volumetric gas outflow m3
Relative error Difference in % between measured and simulated value.
[1]
Pi Production/decay term in ADM1
biochemical matrix
[kgCOD/m3] or [kmol/m3]
Contents
1. Introduction ... 1
1.1 Aim and purpose ... 8
2. Literature review of the ADM1 model ... 9
2.1 Fitting simulations to data and inhibition extensions ... 9
2.2 Mathematical extensions and implementation alternatives ... 9
2.3 Ion and mass balance ... 10
2.4 Gas transfer mathematics ... 10
2.5 characterizing the waste ... 11
3. Method ... 12
3.1 Assumptions and system boundary ... 12
3.2 Mathematics ... 13
3.3 Implementation of the ADM1 as an ODE system ... 13
3.4 Gas transfer ... 14
3.5 Choice of inhibition extensions. ... 15
3.6 Waste characterization... 17
3.7 Ion balance ... 19
3.8 Calibration and validation ... 20
3.9 Simulation ... 27
4 .Results ... 28
4.1 Simulations results depending on OLR, SRT and waste composition. ... 28
4.2 Comparison with real CSTR food waste degrading reactor ... 36
5. Discussion ... 37
5.1 Uncertainties relating to calibration and usage of VFA extension. ... 37
5.2 Difference in results because of food waste composition ... 38
5.3 Accuracy of results ... 40
5.4 Future research ... 41
5.5 Implementation choices ... 41
6. Conclusions ... 43
7. References ... 44
Appendix. ... 47
Sammanfattning
Ökande samhälleliga behov av förnyelsebara energikällor gör metanproduktion från biogasanläggningar allt mer attraktivt och lönsamt.
Vid projektering av biogasanläggningar används ofta data från begränsade experiment då processen är långsam och utförligare försök kan inte motiveras ur ett kostnadsperspektiv. Det blir då svårt att ta hänsyn till hur faktorer som den ingående strömmens koncentration av avfall, uppehållstiden i reaktorn och avfallets sammansättning påverkar metanproduktionen.
Syftet med detta examensarbete är därför att använda, ”Anaerobic digestion model no.1”, en internationellt erkänd matematisk beskrivning av reaktionshastigheten för de 24 mest betydelsefulla biokemiska omvandlingarna i biogasreaktorn, för att undersöka hur variation av olika parametrar i modellen påverkar metanproduktionen i en biogasreaktor som matas med matavfall. Biogasreaktorn som undersöks håller mesofil temperatur (≈35⁰C)
Parallellt undersöks även om, och hur, man med relativt enkla metoder och empirisk mätdata från laboratorier kan kalibrera modellen för att få goda prediktioner från en fullskalig biogasprocess.
En modell har kodats i Matlab®, där tillägg har gjorts för att inkludera negativ påverkan på metanproduktionen från korta fettsyror.
Modellen visar en god överenstämmelse med laboratoriedata från litteratur, och produktionsdata från en fullskalig biogasanläggning i Jönköping, Sverige.
Resultaten visar även på en potential i att öka lasten till reaktorn och tillåta en kortare uppehållstid utan stora förluster i metanproduktion.
Detta samband kan ge en fingervisning om hur ekonomiska fördelar relaterade till minskad reaktorvolym kan nås. Sambandet behöver dock utredas ytterligare då modellen har kalibrerats för laster som inte används i industriella sammanhang.
Abstract
High demands for renewable energy sources are increasingly making methane gas from biogas facilities more interesting and profitable.
When designing biogas facilities, engineers often have a limited set of data to work with. It is often too expensive and time consuming to examine the behavior of the anaerobic processes depending on some key operational parameters, such as the organic loading rate the reactor retention time and the waste composition.
The purpose of this thesis is to use the “Anaerobic Digestion Model no.1”, a well- known mathematical description of the biogas process describing the 24 most important biochemical reactions in the anaerobic process, to investigate how different parameters in the model affect methane production. The focus of this thesis is methane production from food waste.
The thesis also aims to describe if, and how, researchers can use relatively simple methods and data from literature in calibrating the model and if such a calibration can correlate with production data from a large scale biogas facility, which digests food waste. The biogas reactors which are investigated operate under mesophilic temperatures (≈35⁰C).
A model was implemented in Matlab® code and a mathematical extension was also brought to the default model to take into account the detrimental effects on methane production from volatile fatty acids.
The model used correlates well with lab scale data. Steady state comparisons between the production data from a large scale food waste degrading reactor was also made, and model predictions were very close to those of the acquired values.
Results also show a potential in increasing the reactor load and allowing a shorter retention time without much loss in methane production. This may show that important cost reductions relating to reactor size can be achieved. This, however, needs to be investigated further since the model has been calibrated for loads that are unreasonably high for industrial applications.
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1. Introduction
With accelerating greenhouse gas emissions, biogas from anaerobic digestion is becoming a viable alternative to fossil fuels. Also, with directives from the European Union the possibility of landfill disposal of municipal solid organic waste have become increasingly slim (Mata-Alvarez et al, 2000). This is especially true for Sweden, where it is no longer allowed to put organic waste on landfills (Förordning av deponering av avfall, SFS 2001:512).
A solution to this energy and legislative problem can be destruction of solid organic waste through anaerobic degradation, where the waste is converted to biogas: a mixture of mainly carbon dioxide and methane gas. At present, there is a total of 36 000 anaerobic digesters in Europe, and more is to be expected with the increased legislative demands from the European Union (Mata-Alvarez, 2000).
Because of this growing need, increased efforts in reducing biogas plant design cost and optimizing process operation is crucial. One way of doing this can be through mathematical modeling of the anaerobic process. This is a fact that has been recognized by researchers for a long time. Between the years 1972 and 2006 there have been about 750 publications concerning mathematical modeling of anaerobic digestion (Batstone et al, 2006).
But evaluating the merits of every scientific model on anaerobic digestion available would be a daunting task. Therefore, in recognizing both the great potential benefits of a functional model and the need of a more widely accepted mathematical description of the anaerobic process, the international water association (IWA) formed a task group aiming at the creation of a mathematical model of anaerobic digestion (Batstone et al, 2002). Quoting Batstone et al (2002), the full aims of the so called “Anaerobic Digestion Model no.1” (ADM1) are:
Increased model application for full scale plant design, operation and optimization
Further development work on process optimization and control, aimed at direct implementation in full scale plants
Common basis for further development and validation studies to make outcomes more comparable and competitive
Assisting technology transfer from research to industry.
Many authors have since the release of the ADM1 model showed that it possesses good predictive capabilities for different configurations of anaerobic digestion processes (Wayne and Parker 2005; Blumensaat and Keller 2005). Also, when published, the intent of the ADM1 was to model steady state processes, it has however been shown that a dynamic loading regime is, in terms of varying masses of waste, is not a great difficulty for the model (Ozkan-Yucel and Gökcay, 2010).
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Papers using anaerobic digestion with the ADM1 model when co-digesting food waste with another substrate note that the model, at the very least, predicts the average trend of transient (variation with time) processes (Derbal et al, 2009). Other authors achieve a very close fit to data (Zaher et al, 2009a). Papers comparing ADM1 simulations with anaerobic digestion of food waste only has not been found for the purpose of this thesis.
It even seems, that though model prediction errors increase at more extreme loadings, the trends indicating process failure are predicted by the ADM1 model (Schoen et al, 2009;
Boubaker and Cheikh-Ridha 2008). Especially predictions for volatile fatty acids in the digester can be over predicted in steady state systems with small reactors and high volumetric flows if the default model is used, i.e. a model not adapted in any way to a specific waste (Wayne and Parker, 2005). In other words, model predictions of volatile fatty acids errors at a small sludge retention time (SRT); a variable that will be defined later in this thesis.
The ADM1 model describes the five main biochemical steps (steps involving biological enzymes) in an anaerobic digester. Starting with disintegration, followed by hydrolysis, followed by acidogenesis, acetogenesis and lastly methanogenesis. Seen in fig(1.1)
Fig (1.1). The disintegration and biochemical steps in the ADM1 model. Taken from Batstone et al (2002). Reprinted with permission (see references).
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As shown by fig (1.1), the anaerobic process modeled by the ADM1 is complicated, with many processes being interrelated. But in simple terms, the process can be described by the following steps (Batstone et al, 2002):
1. In the disintegration step, complex biomass molecules are broken down to lipids (i.e. fats), carbohydrates and proteins
2. In the hydrolysis, molecules of carbohydrates, lipids and proteins are broken down to long chain fatty acids (LCFAs) amino acids and sugars (MS, AA and LCFA in fig (1.1)).
3. In the acidogenesis, these LCFAs, amino acids and sugars are broken down to volatile fatty acids (VFAs). Namely propionate, valerate, butyrate and some acetate 4. These VFAs are then transformed into acetate in the acetogenesis
5. This acetate is finally transformed into methane gas and carbon dioxide, in the methanogenesis.
An important process omitted in the five steps above is the process where hydrogen and carbon dioxide is transformed to methane. Because of this process in the ADM1 model and a real anaerobic digester, biogas can contain more than 50% methane, typically about 55-65%
methane gas on a volume basis (Abassi et al, 2012).
All in- all, there are 26 different compounds taken into account by the ADM1 model
An important group of components in the ADM1 model are biomass (i.e. anaerobic bacteria groups). In the ADM1 model, there are 7 types of biomass that degrade 8 different components (long chain fatty acids, amino acids, sugars, valerate and butyrate, propionate, acetate and hydrogen). These biomass groups have different sensibilities to process disturbances. These disturbances are referred to as inhibition.
Inhibition occurs when the uptake of a compound and growth of biomass is decreased. This can lead to a less efficient process, with lower methane yields or lead to a complete process failure. The ADM1 model comes in its default setting with inhibition factors describing major inhibition processes, namely: ammonia inhibition, hydrogen inhibition, pH inhibition, competitive inhibition (competition between valerate and butyrate utilizers for valerate and butyrate) and secondary inhibition (competition for nitrogen between biomass groups), see Batstone et al (2002). The pH dependence of ammonia is also included. Since a rise in pH displaces the ammonia-ammonium balance towards ammonia, Hansen et al (1997). Ammonia inhibition is strongly linked to the composition of the waste. Excess nitrogen, for example from high protein contents, can be converted into ammonia and inhibit the process. This ammonia can be created provided that the biomass (anaerobic bacteria) cannot use nitrogen in their cellular metabolism because of lack of carbon. A carbon-nitrogen (C/N) mole relation of 20-25 is considered optimum. If lower, nitrogen will be released and converted to ammonia, if higher the anaerobic bacteria will find it hard to meet their protein requirements and biomass growth will be inhibited (Abassi et al, 2012).
The system described by the ADM1 model is shown in fig (1.2). It describes how a wide range of different compounds enters the digester, some are converted to gases (hydrogen,
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carbon dioxide and methane) and leaves the digester as gas, and other compounds leave the digester in the water phase. Fig (1.2) describes how the ADM1 models a single stage steady state reactor. There is a continuous ingoing flow, which is equal in volume to the outgoing flow. This continuous flow is composed of water (used as solvent), biomass and the waste.
For a functioning process, ingoing values for protein, carbohydrates and fats are much higher than the outgoing levels. Correspondingly, outgoing levels of VFAs are relatively low. The pH value is calculated using mainly values of released nitrogen (converted to ammonium) and VFA-acids (Batstone et al, 2002). High amounts of ammonium raise pH. High amounts of VFAs lower pH (Batstone et al, 2002). The model can also take into account metallic and non-metallic ions in the waste that alter the pH balance. PH calculations are important since stable methane productions is, often, achieved for pH values around 7.2-8 and optimal pH levels in the digester are often somewhere in between 6-7 (Abassi et al, 2012). Although separating the acidogenic process from the methanogenetic processes results in higher output since different biomass groups in the anaerobic process has different pH optimums (Bouallagi et al, 2004). Methanogen biomass, which converts acetate to methane, is more sensitive to lower pH levels than acidogenic biomass that converts long chain fatty acid, amino acids and sugars to VFAs (Batstone et al, 2002).
An important assumption in the ADM1 model is that the reactor is well stirred; there are no effects due to fluid motion in the digester.
Anaerobic digestion is highly temperature dependent, and for industrial applications, process temperature is mesophilic with an optimum at 35⁰C or termophilic with an optimum at 55⁰C.
Termophilic conditions yields a faster production rate, but can be more unstable (Abassi et al, 2012). Different temperatures can be taken into account by the ADM1 model, but it cannot model temperature variations in the digester. Temperatures in the reactor are considered to be the same in all parts of the digester. For food waste, methane production data relevant for this thesis is mostly available for mesophilic temperatures (Carlson and Uldal, 2009); (Zaman, 2010).
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Fig (1.2). The CSTR reactor described by the ADM1 model, from Batstone et al (2002). Reprinted with permission (se references)
Some compounds in the ADM1 system are defined in terms of kmole (inorganic nitrogen, inorganic carbon, cat and an ions). Most compounds of the ingoing flow in fig (1.2), such as protein, lipids and carbohydrates, are however defined by amounts of COD, chemical oxygen demand. COD describes the amount of mass, in oxygen, that is oxidized when a compound is oxidized using a strong chemical oxidant (Tchobanoglous et al, 2004). It is theoretically possible to measure the concentration of all 26 ingoing compounds modeled by the ADM1 model. But this would require a great deal of costly measurements and it is an interesting question if the ADM1 model can be used to predict methane potential from food waste using only literature data of a wide range of food wastes, where only protein carbohydrate and lipid measurements are given. If so, lab experiments would not need to be conducted to measure methane production for every type of food waste, but the ADM1 model could be used in assessing methane potential from many different food waste compositions. This would be important since the composition of food waste is very wide.
Some main reasons for this variation in food waste composition are listed by Zaman (2010):
Avoidance of meat due to vegetarian diets
Eating habits and diets
Religion
Household income
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A typical “assessment” of the methane potential from a specific waste is shown in fig (1.3).
Here a small sample of food waste has been confided in a finite (no inlets or outlets) volume with some anaerobic bacteria. These experiments are often referred to as “batch experiments”.
As can be seen in fig (1.3), the methane yields are time dependent, and in general terms follow a logarithmic function with high rise of yields initially. At some day number “d”, the methane produced will reach a theoretical maximum which can be easily calculated if the molecular composition of the waste is known (Bushweel and Neave, 1930).
Fig (1.3). General behavior of an anaerobic batch process. Data from Zaman (2010). Substrate is food waste.
So, the behavior of a general anaerobic process is well known. However, quantitative yields of methane depending on some key operation factors are not. One of these factors has already been discussed: food waste composition varies and assessing methane potentials from all possible food waste compositions would be impractical. But quantitative estimates of an established range of food waste composition from the ADM1 model can bring clarity to how much the waste composition impacts methane production.
Fig(1.3) also shows that increasing the time that the waste stays in the biogas reactor increases methane yields. Increasing this time in a full scale reactor (the retention time) means that the reactor volume needs to be increased. Literature suggests that 70-80% of process cost is related to reactor costs, while maintaining the process operation only makes up 20-30% of the costs associated with biogas production (Abassi et al, 2012).
Full scale anaerobic digesters are often operated as continuous stirred tank reactors (CSTR).
Here, it is a common assumption that volumetric inflow equals the volumetric outflow of
“slurry” (a mixture of anaerobic bacteria, biodegradable waste and water used as solvent).
0 2000 4000 6000 8000 10000 12000 14000
1 2 3 4 5 6 7 8 9 1011121314151617181920
mL methane
Days
Methane production
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In CSTR reactors, increasing volume means an increase of the solid and hydraulic retention time (SRT and HRT). These parameters describe the time that the waste, the water solvent and the anaerobic bacteria spend in the CSTR reactor. And in a CSTR reactor they are considered to be equal, and defined by eq (1.1), from Abassi et al (2012).
(1.1)
All other things of the anaerobic process considered equal. For a CSTR reactor, the time t on the x-axis of fig (1.3) can be considered to be the solid retention time of a single stage (one reactor only) CSTR reactor. When deciding the volume of a biogas reactor, engineers therefore face a problem where increases of reactor volume yields higher methane gas productions, but at the same time increases design costs.
In summary, a methodology where measurements of a specific type of food waste, or other wastes, can give accurate estimates on the relationship between the solid retention time and the methane yields should be of value for engineers when deciding the volume of future anaerobic facilities.
Another key parameter of interest is the organic loading rate, OLR, defined by eq (1.2), from Zaman (2010).
(1.2)
Where VS is the volatile solid content, which describes how much mass of a dry sample that is oxidized when combusted at temperatures approximating 550⁰C (Angelidaki and Sanders, 2004). The difference between OLR and SRT, is that the SRT described by eq(1.1) is only a measurement of the total ingoing and outgoing liquid volume in relation to reactor size, in terms of water, anaerobic bacteria and waste. The OLR is a measurement of ingoing amount of combustible waste, per day and volume of the reactor.
It is possible to have a short SRT (high volumetric flow in relation to reactor volume), but a high OLR, and vice versa.
OLR also relates to reactor volume. Increasing OLR means a smaller volume can be used.
The cheapest possible biogas reactor has a high OLR and small SRT, which corresponds to a high organic load and volumetric flow in relation to the reactor volume. However, higher loadings in a CSTR reactor can cause process failure or decreased methane yields, as shown by Boubaker and Cheick-Reidah (2008), Schoen et al (2009) and Banks et al (2008).
With the above in mind one can establish three areas of interest relating to the anaerobic process:
1. Methane yield from food waste depending on SRT 2. Methane yield from food waste depending on OLR
3. The composition of food waste and its impact on methane yields.
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From an experimental point of view, the problem with the above areas is that examining them in a CSTR reactor demand a large number of tests.
An accurate mathematical description of the anaerobic process, such as the ADM1, could be a solution to this problem. Incorporated into computer code, a large number of OLRs, SRTs and food waste compositions could be tested fast.
1.1 Aim and purpose
There are five purposes with this thesis
1. Reviewing literature to describe food waste composition, relevant for usage in the ADM1 model and describe food waste composition impact on ADM1 simulations.
2. Describe if and how an ADM1 model can be calibrated to lab scale data from batch experiments on food waste. And investigate if the calibrated model can predict production from a real CSTR reactor
3. Examine to what extent a calibrated ADM1 model can use food waste compositions from different literature sources and give probable predictions.
4. Reviewing literature to investigate which, if any, modifications to the default ADM1 model described by Batstone et al (2002) that should be implemented to make it effective in describing food waste anaerobic digestion
5. Using OLR and SRT as a measurement of reactor size to discuss cost reductions, in terms of smaller reactors, in relation to methane yield.
The aims of this thesis are:
1. Implementing the ADM1 model in Matlab®.
2. Adapting the default ADM1 model to anaerobic food waste degradation.
3. Calibrate the model to anaerobic food waste degradation, using lab scale data from batch trials.
4. Compare predictions of the calibrated model with real data from a large scale food waste degrading anaerobic reactor, operating at mesophilic conditions.
5. Use a wide range of OLRs, SRTs and different food waste compositions with the ADM1 model to relate these variables impact on the performance for a mesophilic CSTR reactor, degrading food waste.
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2. Literature review of the ADM1 model
The ADM1 model is arguably quite complex. To understand the method used in this thesis, it is necessary to have a general grasp of some key concepts in the model that create differences between ADM1 implementations used by researchers.
2.1 Fitting simulations to data and inhibition extensions
It is common practice for authors to implement changes in the default ADM1 model to achieve a closer fit to data. In the introduction chapter, findings from Wayne and Parker were discussed, showing that with its default constants, ADM1 predictions of VFA accumulation could error. The ADM1 model comes with a large set of constants, and recommended values for these constants are found in the ADM1 publication, by Batstone et al (2002). It is common practice among researchers to change the values of one or more of these constants to achieve a closer fit to data (Lee et al, 2009; Blumensaat and Keller 2005; Kerroum et al, 2010; Zaher et al, 2009a).
Adding inhibition terms is another common practice among authors, see for example Derbal et al (2009); Thamsiriroj et al (2011); Batstone et al,( 2006); Boubaker and Cheikh-Ridha (2008). Additional inhibition factors than those used in the default ADM1 publication can be taken into account with addition to the ADM1 model (Batstone et al, 2006).
A particular problem with the default pH inhibition function recommended in Batstone et al al (2002) is that it is discontinues and may cause numerical instabilities. Similar pH functions have therefore been devised for the ADM1 model which “mimics” the original function without these instabilities (Rosén et al, 2006).
2.2 Mathematical extensions and implementation alternatives
The ADM1 only utilizes so called first order kinetics, since all differential equations in the ADM1 model are first order equations (Tchobanoglous et al, 2004). And the ADM1 model can be implemented as either a system of differential equations (DE-implementation) with 35 state variables in total, i.e. variables described by separate differential equations. Or, the ADM1 model can be implemented using differential equations and algebraic equations (DAE- implementation), with 29 state variables in total. In both implementations some compounds are counted twice since they exist both in gas and liquid phase, or are divided into acid base pairs.
The idea behind the DAE implementation is that it removes stiffness from the implemented system. A system is stiff when the range of time constants is large (Rosén et al, 2006).In essence this means that some state variables change very rapidly, such as acid base pairs, while some change much more slowly, such as biomass. Stiff system demand special solvers to solve computationally, these solvers can be quite slow when transient (variation with time) loads are simulated (Rosén et al, 2006).
10 2.3 Ion and mass balance
Rosén et al (2006), along with other authors such as Blumensaat and Keller (2005) notices that the ADM1 default model is not mass balanced, for inorganic carbon and inorganic nitrogen. For some processes, the default model “creates” inorganic nitrogen and inorganic carbon. According to Rosén et al (2006), and the ADM1 model, the total quantity of nitrogen from 1 kg COD of composites (Xc) will completely decay to (be transformed to):
(2.2.1.1)
X are particulate state variables, and S soluble state variable, as in the ADM1 publication. But the nitrogen content of Xc (composites) is 0.002 [kmoleN/kgCOD] if the default values of the ADM1 publication are used, as they are in eq (2.2.1.1). So one easily notes, as Rosén et al (2006) have done, that for every kg COD of composites that disintegrates, 0,001 [mole/kgCOD] is “created”. A similar problem exists for inorganic carbon.
This is a problem that is recognized by one of the ADM1 authors, although the author states that the error created should be small for most cases. (Batstone et al, 2006).
In the DAE implementation of the ADM1 model, the acid base pair reactions are approximated by algebraic equations, and so are assumed to occur infinitely fast. In the DE implementation; acid base pair reactions are calculated using differential equations and so are assumed to be time dependent, although still very fast reactions relative to other reactions in the ADM1 model. Since calculations of ion disassociation differ depending on implementation, the ways of calculating pH differ. The main focus of the ADM1 publication of Batstone et al (2002) is on using the DAE implementation. Rosén and Jeppson (2006) have given pH calculations in the DE implementation of the ADM1 model additional attention.
In the ADM1 model, the ion balance can be expressed in two ways. Either, one can calculate the negatively charged particles and the positively charged particles in an acid base pair as separate state variables. This method is recommended by Batstone et al (2002).
Or, one can define the total amount of an acid base pair as a single state variable, and the amount of negatively charged particles as the other state variable. If one is interested in the amount of positively charged particles, these can be calculated as the difference between the total amount of particles in an acid base pair and the amount of negatively charged particles.
This definition is recommended by Rosén et al (2006).
2.4 Gas transfer mathematics
Gas transfer, in terms of flows of hydrogen gas, methane gas and carbon dioxide gas, can be calculated in two ways in the ADM1 model. The first method is the “default” method of the ADM1 publication, but it can cause computational instabilities and Rosén et al (2006) recommends the alternative method, where it is assumed that the gas flow is restricted through an orifice. This however causes a digester overpressure. Although correction terms have been
11 developed to mitigate this (Rosén et al, 2006).
Both ways use a constant, kLa, which is the mass transfer coefficient between the liquid and gas volumes. Values for kLa are not given in the default ADM1 model, and the ADM1 publication refers to Tchobanoglous et al (2004) who refers on to other authors. Also, since kLa values are reactor size dependent and calculated using diffusion rates, which may vary (Tchobanoglous et al, 2004), it is impossible to identify a true kLa value for a general anaerobic digester. Furthermore kla values used are seldom mentioned by authors. Rosén and Jepsson (2006) however use a kLa value of 200[d-1].
Smith and Stöckle (2010) have developed alternative methods for gas flow calculations in the ADM1 model have been investigated to address issues relating to computational instabilities and digester overpressure in ADM1 simulations.
2.5 characterizing the waste
In the introduction chapter, it was explained that the ADM1 model takes “input” values in terms of COD. However, COD measurements on solid heterogeneous substrates, such as food waste, are according to one of the ADM1 authors “always difficult and open to some uncertainty” (Angelidaki et al, 2009). Volatile solids content (VS) is much more common measurement (Raposo et al, 2011). Indeed, food waste composition relevant for this thesis are only given in terms of VS (Carlson and Uldal, 2009; Zaman, 2010; Jansen et al, 2004).
If literature data for food waste is to be used in ADM1 simulations, it is therefore necessary to transform measurements of VS to COD. A method for doing this is described by Angelidaki and Sanders (2004), using the stoichiometric relationships between completely oxidized waste molecules and the oxygen necessary for complete oxidation.
VS content directly relates to another common measurement for solid substrates, namely total solids (TS). The TS is defined as the mass remaining when a wet sample has been dried at a specific temperature (103-105⁰C) (Tchobanoglous et al, 2004). TS is the sum of VS and ash content (Tchobanoglous et al, 2004).
Food waste is mainly composed of protein, lipids and carbohydrates (Zaman 2010; Jansen et al, 2004; Carlson and Uldal 2009). In theory one could take into account many more compounds entering the digester in fig (1.2) and “translate” them to ADM1 input variables.
Methods have been developed to do so (Zaher et al, 2009b; Kleerebezem and Van Loosdrecht, 2006; Girault et al, 2012). Research in these methods are relevant since additional measurements of different ions in the digester (VFAs, cat and an ions, inorganic carbon, inorganic nitrogen) affect the pH and can possibly have a major effect on process operation.
As discussed earlier, the aim and purpose of this thesis is partially to examine how accurate results researchers can achieve without using these more time consuming and expensive methods. For the aim and purpose of this thesis, it is however important to have these methods in mind for discussions concerning accuracy of results, future research and simulation improvements.
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3. Method
3.1 Assumptions and system boundary
The ADM1 model only describes the processes in the CSTR reactor of a biogas facility. The process of interest in this thesis is described in fig (2.1.1) where a sketch for a full scale biogas plant is shown. As can be seen in fig (2.1.1), some processes are omitted in this thesis, such as shredding of the waste, dilution of the waste, hygenization of the waste (destruction of dangerous pathogens) and storage, processing and distribution of the biogas. The focus of this thesis lies in the performance of the biogas reactor (circled) depending on food waste characteristics, OLR and SRT. In this thesis, dilution is implicitly expressed in terms of SRT (retention time) and OLR (organic loading rate) and is not considered to be a “stand-alone”
variable.
Fig (2.1.1). Sketch for a biogas plant accepting 10 000 metric tons of food waste annually. Circle show the process of interest in this thesis: biogas reactor performance depending on OLR, SRT and food waste composition. Courtesy of Karlstad Energi AB.
There is also an assumption made relating to the anaerobic degradation of the waste. This thesis assumes that the ingoing protein, lipids and carbohydrate fractions are readily available for the biomass. The only compound that disintegrates in the reactor is decayed biomass. For food waste, this is a reasonable assumption (Batstone et al, 2002).
This thesis also assumes that SRT is equal to HRT.
Lastly, as noted methane production is temperature dependent with either mesophilic conditions or termophilic conditions used in industrial applications. This thesis models mesophilic conditions only.
13 3.2 Mathematics
In this thesis the DE-ADM1 implementation was coded in Matlab®.
The basic structure for the differential equations, 26 in total, describing biochemical reactions and concentrations for cat and anion concentrations in the ADM1 model is shown in eq (3.2.1).
(3.2.1)
In words, eq (3.2.1) describes that the change of component i in liquid phase depending on time equals inflow of i minus outflow of i, plus production of/or decay of i.
The interrelation between different components is described by the production/ decay variable Pi. Determination of Pi is done using a 19 row, 24 column matrix found in appendix (b), taken with modifications from Batstone et al (2002).
Pi=0 for i=25 and i=26, since differential equation number 25 and 26 describe cat and an ions, which do not participate in any biochemical reaction. They only affect pH.
The method for determining Pi for each compound and an example for calculating Pi for a specific compound is found in appendix (b). Suffice to say is that the real complexity of the model is found in the expressions for Pi. Inhibition and gas transfer mathematics used, that are not defined by the biochemical matrix in appendix (b) are found in appendix (c). The Matlab® code used to define the ADM1 system is found in appendix (f).
3.3 Implementation of the ADM1 as an ODE system
The ADM1 model was implemented purely on the basis of differential equations (DE- implementation).
Using only differential equations (DE-implementation) to describe the 35 state variables, the ADM1 model was coded and implemented in Matlab® and solved with the variable step size, Euler method solver ODE15s for stiff differential equation systems.
Changes were done to the original ADM1 model to correct the mass balance for inorganic nitrogen and carbon, according to Rosén et al (2006) and Rosén and Jepsson (2006). These changes affect the biochemical matrix, used for Pi calculations, found in appendix (b).
PH calculations (calculations for H3O+ ions) are done using the “pH solver” found in Rosén and Jepsson (2006), since Batstone et al (2002) are not very precise on how to calculate pH for the DE-implementation. See appendix(c) for details.
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Acid concentrations were expressed in terms as the total amount of an acid base pair and the negative amounts of a base in an acid base pair, as recommended by Rosén et al (2006). The differential equation for calculating the amount of negatively charged particles in an acid base pair is shown by eq (3.3.1).
⁄ ( ( ) ) (3.3.1)
Where Sacid-,i is the negatively charged acid pair for acid number i, Sh+ the amount of H3O+ ions [mole/m3] and Sacid, total the sum of acid base pair (unit varies). –Ka/b is the acid base reaction coefficient (set to 1010 [mole/day] for all acid base pairs), Ka,acid the acid base equilibrium coefficient [Mole].
The pH inhibition function recommended by Rosén et al (2006) was also used. This is the so called “Hill inhibition function” based on H3O+ concentrations, found in Rosén et al (2006). , see appendix (c).
3.4 Gas transfer
Generally, the three differential equations describing gas concentration coming out from the gas headspace (the volume in the anaerobic reactor occupied by gas) in terms of gas number i is described by eq (3.4.1)
(3.4.1)
Vliq is the liquid volume of the anaerobic reactor, Vgas the gas volume of the anaerobic digester (set to be a factor twenty less than the liquid volume). Sgas,i is the concentration of gas number i.
The ρT,i is the kinetic rate of gas transfer (“the speed of gas transfer”) between the liquid and gas phases in the anaerobic reactor. And is calculated for gas i using (3.4.2) from Batstone et al (2002)
(3.4.2)
Where Sliq,i is the liquid phase concentration of gas i. And “c” a conversion factor from kgCOD to kmole (c equals16 for hydrogen and 64 for methane). And pgas,i is the partial pressure of gas i, calculated assuming ideal gas behavior. KH describes the Henrys law coefficient for gas i. Values for KH and expressions for its temperature dependence are given in Batstone et al (2002) and found in appendix (c)
The kLa value was set to 200[d-1] and the kp value to 5*104 [m3/(bar*d] in accordance with Rosén and Jepsson (2006). Full gas transfer mathematics is given in appendix (c).
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The gas flow from the created gas in the digester was assumed to be channeled through an orifice and eq (3.4.3) was used. This is the alternative method of calculating gas flows in the ADM1 model, and the
term has been added to mitigate the simulated gas overpressure, in accordance with Rosén et al (2006).
(3.4.3).
Ptot is the sums of partial pressures for all gases in the digester and qgas the total gas flow. Ptot and qgas both include water vapor. An expression for water vapor partial pressure is given in Batstone et al (2002) and was used, it can be found in appendix (c) .Patm is the atmospheric pressure, set to1.1013. Gas pressures are in [bar].
Gas volumes for methane were calculated assuming ideal gas behavior and using eq (3.4.4), from Cengel and Turner (2004).
̇
(3.4.4)
̇ is gas flow of gas number i, for example methane
3.5 Choice of inhibition extensions.
It is explicitly stated by Batstone et al (2002) that three inhibition processes have been left out in the default ADM1:
VFA inhibition is explicitly not included in the default ADM1 model. Concentrations of VFAs affect pH levels which in turn cause pH inhibition.
VFA inhibition however seems to be an important process factor for food waste.
Studies conducted show that VFA inhibition is a major detrimental factor in process operation where organic household waste is used (Banks et al, 2008).
The mechanism of VFA inhibition seems to be that of a disrupted cellular homeostasis. This is especially true for lower pH levels (Batstone et al, 2002).
Earlier studies seem to have only partially digested food waste in reactors, mixed with another substrate (Derbal et al, 2008); (Zaher et al, 2009a). It is possible that this co- digestion in earlier studies have mitigated. And the addition of any VFA inhibition extension to the ADM1 model used in these studies has not been implemented.
However, using olive mill wastewater and olive mill solid waste as a substrate added an inhibition term of VFAs on methanogenetic biomass (acetate to methane converting biomass) and noted that: “without adding this inhibition term, the original ADM1 model could not predict the reactor failure at short HRT”. An inhibition term for VFAs was therefore added.
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LCFAs (long chain fatty acids) also cause inhibition, being created from high lipid concentrations, though exactly how and to what extent is not clear. Earlier studies indicated that high LCFA concentrations induced cellular death (lysis), but consensus seem to have shifted towards the notion that high LCFA concentrations only cause a lag phase in biogas production (Long et al, 2011). Also, a review over published articles concerning addition of lipids to anaerobic processes show that for semi continuous reactors, an optimum lipid content seems to be in the range between 35- 50% of total VS (Long et al, 2011). Data for fully continuous reactors were not available. But measurements done on food waste does not motivate any addition of LCFA inhibition to the ADM1 model Jansen et al, (2004); Carlson and Uldal (2009);
Zaman (2010). On the contrary; compared to the measurements done by these authors increasing lipid concentrations roughly twofold would seem to increase biogas production, bringing the LCFA concentration closer to an optimum. Long et al (2011) also discusses the possibility that continuous stirred tank reactors (CSTRs), which are investigated in this study, dilutes the LCFA concentration better than reactors with a plug flow characteristic, making CSTR processes more resilient to LCFA concentrations. Because of this, LCFA inhibition was omitted in the ADM1 model here implemented.
Sulfur inhibition has also been omitted in the default ADM1 model. Depending on sulfur content of the waste, complex mathematical extensions to the ADM1 model have been developed by Fedorovich et al, (2003), for a high sulfur content and less complex extensions (Batstone, 2006) for a lower sulfur content. There seem to have been quite a high demand for this extension from researchers, perhaps because sulfur emissions are related to odor issues (Batstone et al, 2006). But because of the rather high uncertainty in molecular composition of food waste, it was however hard to motivate an addition of sulfur inhibition which adds notable complexity to the model, even if the “easier” sulfur inhibition mathematics described by Batstone (2006) is used. Sulfur inhibition was therefore omitted
Mathematically, inhibition is incorporated in the ADM1 model by adding an inhibition factor to the production term in eq (3.5.1). Using:
(3.5.1)
Where In is a product of k inhibition factors, relevant to the production or decay of compound i.
(3.5.2)
Values of In range from 1 (no inhibition) to 0 (complete inhibition).
When coding and implementing the ADM1 model in Matlab®. The VFA inhibition extension used by Boubaker and Cheikh-Ridah (2008) was used, and is described in eq(3.5.3)
(3.5.3)
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Where Stvfa is the sum of all VFA concentrations modeled by the ADM1 model (valerate, butyrate, propionate and acetate). KITvfa is an inhibition constant. The default value for KITvfa
used by Boubaker and Cheikh-Ridah (2008) was 5.2.
ITVFA is the inhibition factor applied to P11,P10,P9,P7 and P22 in eq (3.5.4). Note that for high values of total volatile fatty acids, ITVFA becomes close to zero (complete inhibition from VFAs).
(3.5.4).
In in (3.5.4) are additional inhibition factors used. Refer to the mathematics section in appendix(c)
The use of the inhibition factor in (3.5.3) differs in this thesis with how it was used by used by Boubaker and Cheikh-Ridah (2008). When using eq (3.5.3) in accordance with Boubaker and Cheikh-Ridha (2008) it was often difficult to reach steady state values. In some cases pH levels decreases with about 0.001% for every day, making it difficult to predict if steady state values can be achieved or not for a specific load. It could take up to 3000 days or more (i.e.
simulation had to be done for this period) for some overloads to be predicted and simulations took a very long time. When using the ITVFA term in dynamic simulations for a finite period of time, as Boubaker and Cheikh-Ridah (2008) does, this is not an issue. But for this thesis, steady state values are central.
Boubaker and Cheikh-Ridah (2008) also applied eq (3.5.3) to the whole differential equation for inorganic nitrogen (i=11), this was not done here.
This lead to higher KI,TVFA values being used, since it was shown that the impact on pH levels are greater with the implementation of eq(3.5.3) used in this thesis.
3.6 Waste characterization.
Waste characterizations were compiled using data from Jansen et al (2004), Zaman (2010) and Carlson and Uldal, (2009). Together with varying OLRs and SRTs, the impact on waste characteristics on simulated methane production was examined using the implemented ADM1 model.
The data for food waste are given terms of VS content. It is therefore necessary to convert measurements in VS to COD to be used in ADM1 simulations. The method using stoichiometric relationships described by Angelidaki and Sanders (2004) in eq (3.6.1)-(3.6.4) was used.
In eq (3.6.1) a biological compound composed of carbon, hydrogen and oxygen is fully oxidized and converted to carbon dioxide and water. The biological compound is composed of n carbon atoms, a hydrogen atoms and b oxygen atoms. Using eq (3.6.1) fractions of carbon dioxide and water can be determined. And the ratio between VS and COD can be defined by eq (3.6.2)
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( ) (3.6.1)
( )
(3.6.2)
Equation (3.6.2) describes a mass ratio between COD and VS, so if the VS content and molecular formula is known, the COD can be calculated. The constants 32, 12, 16 represent the molar mass of one oxygen molecule (O2), one carbon atom (C) and one oxygen atom (O) respectively. It is possible to use an extended form of equation (3.6.1), to include nitrogen, but one must assume in which form nitrogen is oxidized. Angelidaki and Sanders (2004) states that nitrogen (N) should preferably stay in a reduced form. If so the COD/VS ratio for any waste that also contains nitrogen can be calculated using (3,6.3)-(3.6.4) (Angelidaki and Sanders, 2004).
(3.6.3) And for this case the COD-VS ratio becomes:
COD/VS= (3.6.4)
Molecular composition of proteins, carbohydrates and lipids were assumed to be the typical characteristics of these substrate components shown by Angelidaki and Sanders (2004).
COD/VS fractions for proteins, lipids and carbohydrate are also shown in table (3.6.1) and have also been taken from Angelidaki and Sanders (2004).
For COD/VS conversion, sugar was supposed to consist of sucrose with molecular formula C12H22O11. For this molecule the COD/VS factor was determined to 1.12 using eq (3.6.1) and (3.6.2), given by Angelidaki and Sanders (2004).
Table(3.6.1). Assumed substrate composition and COD/VS fractions. Data, with the exception of sugars, from Angelidaki and Sanders (2004).
Substrate type Composition COD/VS conversion factor [kg/kg]
Carbohydrate (C6H10O5)n 1.19
Protein C5H7NO2 1.42
Lipids C57H104O6 2.90
Sugars C12H22O11 1.12
An important note on waste characteristics is that there is no general consensus between authors on nomenclature. Exactly what a carbohydrate is may differ some between authors.
Jansen et al for example characterize the waste in terms of sugars, fibers and carbohydrates, Carlson and Uldal and Zaman (2010) characterizes the waste terms of carbohydrates.
Cellulose, hemi cellulose and lignin. Carlson and Uldal 2009 define any remaining VS that are not lipids or proteins as carbohydrates.
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Overall, differences in composition due to definitions were not considered to be an important issue, since the aim and purpose of this thesis is to use the ADM1 model in investigating food waste composition impact. Not to identify exact differences in the food waste.
Composition of food waste samples as measured by Zaman (2010); Carlson and Uldal (2009) and Jansen et al (2004) are shown in fig (3.6.1).
Fig (3.6.1). Volatile solids distribution as measured by authors.
Measurements of cellulose and hemi cellulose were used as carbohydrate input to the model.
Lignin was assumed to be an inert material (non-biodegradable).
Measured sugar was used as sugar input to the ADM1 model.
For differences in volatile solids content relative to wet mass, one can refer to the different authors. Answers in the result section are given in terms of L methane/ (gVS) .
3.7 Ion balance
Simulations for OLR=1 to 10 and SRT=1to 75 were done assuming 1) there are metallic cat and non-metallic anions in the food waste and 2) there are no ions in the food waste. The authors used for data for food waste characterization in this thesis does not measure metallic ion concentration so data from Zhang et al (2006), where American food waste was characterized in terms of ion content, was used. Metal compound in the waste was assumed to all have a +1 charge. NO3-N concentration was considered to an anion with a -1 charge.
The cat ion concentration was calculated to 0.00237 [mole/gVS].
Anion concentration was calculated to 6*10-6 [mole/gVS].
20 3.8 Calibration and validation
When a functioning model had been coded into Matlab®, the calibration process began. This is the process where the default model constants were changed to achieve a closer fit to data.
A summary over which constants were changed, and what values were used for these constants, can be found in appendix (a). Default constants not changed can be found in Batstone et al (2002). The same nomenclature is used.
Data was taken from Zaman (2010) who performed extensive anaerobic degradation trials on food waste. When the model had been calibrated against lab data, model predictions were tested against real data from a real mesophilic anaerobic digester, in the city of Jönköping, Sweden. Given uncertainty in the real data, the calibrated model seemed to well predict the behavior of the real CSTR reactor. No changes were made to the model that had been calibrated against lab scale data.
Fig (3.8.1) describes this process of (1) calibration, (2) validation and (3) usage of a calibrated and validated model to quantify the impact of different SRTs and OLRs
Fig (3.8.1). Calibration, validation and implementation process.
A problem with available lab data is that it is mostly available from batch experiments. Data here used are from Zaman (2010). Batch experiments are experiments where a sample of waste is sealed within a volume together with anaerobic bacteria, without any outflow or inflow. There is only one outflow of biogas. As seen in fig(3.8.2).
1.
Calibrate against lab
data
2.
Validate calibrated model against
data from mesophilic
CSTR
3.
Run model for a wide range
of SRT, OLR and different
waste
compositions
21
Fig (3.8.2). A simple representation of a batch reactor. There are no inlets or outlets. The waste and anaerobic bacteria are confided in a finite volume.
But the ADM1 model simulates a CSTR reactor, shown in fig (1.2). So, it must be understood that calibration was done using the following assumption:
“The amount of methane gas [LCH4/gVS] from a CSTR reactor at operating SRT=t is equal to the accumulated amount of biogas from a batch reactor at time t in LCH4/gVS.
If this assumption is completely valid, model predictions are to behave in relation to batch measurements as seen in fig (3.8.3).
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Fig (3.8.3). Describing how predictions in a batch experiment are to be correlated with predictions from steady state CSTR simulations in the ADM1 model.
For small t and SRT, this assumption cannot be valid. At a minimum SRT, the growth of anaerobic bacteria is less than SRT (Batstone et al, 2002), causing a “wash out” in the reactor.
But for longer SRTs, when outflow of bacteria is a less important factor, the assumption should work better.
A general description of the calibration process should be helpful not only in understanding the calibration process itself, but also helpful when calibrating the ADM1 model to other types of wastes. In general terms, the iterative calibration process is described in fig (3.8.4)
Fig (3.8.4). Calibration process implemented
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In step 2 of fig (3.8.4), two calibration “targets” are identified:
Process failure prediction at high OLRs.
Relative error less than or equal to 5%
The relative error is defined by eq (3.8.1)
| | (3.8.1)
Data used were from Zaman (2010).For all calibrations used in simulations, anions and cat ion concentrations were set to zero.
A novelty with a measurement done by Zaman (2010) is that the volume used is greater than usual (3.5 L). A standard volume used is often about 250mL (Carlson and Uldal, 2009). When using a greater volume, variances in the food waste are taken into account in a better way (Zaman, 2010). For the 3.5L volume trials, three sets of data points for two different trials are published by Zaman (2010). Data points for these trials can be shown in table (3.8.1). And the trials they are related to are represented by bold and white X in fig (3.8.5). As can be seen in figure (3.8.5), there is a rather large variance in methane production. Data relating to bold and white X were used when calibrating since exact data was available, and also since other trials do not seem to have been stable for 60 days.
Table (3.8.1). Values for raw data point given in fig (3.8.5). 1Assumed to be at t=57. OLR is 18.8[gVS/(L*d)].
Days Trial 1 [LCH4/gVS] Trial 2 [LCH4/gVS] Mean value
6 0.326 0.291 0.3085
20 0.4 0.379 0.3895
55 0.393 0.4111
60 0.429
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Fig (3.8.5). Batch experiments conducted on food waste. By Zaman (2010). Reprinted with permission.
A relative error, as described by eq (3.8.1), of 5% was considered acceptable for the simulations relative to the mean values of data points in table (3.8.1). The following mechanism was assumed and used when calibrating:
When using the ADM1 model; increasing the hydrolysis speed increases methane yield at lower periods of time (i.e. at t=6). Increasing the disintegration speed increases methane yield at longer periods of time (i.e. t≈60).
Similar assumptions, especially concerning the hydrolysis step being rate liming (i.e. defines the speed of anaerobic degradation), have been used by authors when calibrating parameters for the ADM1 model in particular (Girault et al, 2012) and first order kinetic systems in general (Batstone et al, 2009). Also, it was assumed that hydrolysis constants were at least a factor ten lower than in the default ADM1 model (Zaher et al, 2009a).
The idea behind changing the disintegration constant after long time to fit data is that biomass decay, and resulting biogas production from decayed biomass, is a much slower process.
Increases in methane production after a long time will be due to biomass decay.
When calibration had been done, a relative error of 2.5% (for six days), 1.5% (for 20 days) and 0.6% (57 days) was achieved. The mean values of table (3.8.1) were used. Simulation results and these data points can be seen in fig (3.8.6), along with values from a simulation using the default model. Fig (3.8.6) was also compared with fig (3.8.5). Overall, it seems as the calibrated model well predicts the anaerobic degradation of food waste used by Zaman (2010).
