1 Summary

In this project, I worked in cooperation with Avatar Energy’s R & D lab in South Burlington, specificallyCSO Guy Roberts, engineer Brian Pinand, and lab technician Samantha Csapilla, to develop a mathemat-ical modeling framework for methanogenesis in anaerobic digesters. The motivation was to provide theAvatar team with an inexpensive way to optimize the operation of their digesters, and specifically to analyzestart-up protocols for new feedstocks. Crucially, the model needed to be both theoretically consistent andexperimentally informed, to achieve realistic results with a simpler model than has been previously possible.This will inspire more confidence in their clients, and allow for faster and safer digester start-up, which willlead to shorter break-even times.

The current status of this (ongoing) work is that the modeling framework is complete, and an initial modelhas been developed to the point where we are ready to incorporate the lab data. Once this has been accom-plished, experiments will be performed to test the model’s ability to suggest start-up feeding schedules andamounts, based on feedstock, to grow the methanogen population as quickly as possible without crashing itthrough over-acidification (and resulting growth inhibition).

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2 Introduction

In this section we first introduce the project objectives and community partner with which the project wasdone, Avatar Energy. We then give some background information on the process of anaerobic digestion, andlay out the plan of action timeline as it was originally conceived, with notes about how that timeline changedover the course of the project.

In the sections that follow, we’ll outline the methodology for model development, including some back-ground on previous modeling approaches and specific strategies for incorporating experimental data into themodel, in Section 3, then describe the resulting model as it currently stands, including descriptive modelequations and example model output, in Section 4, and conclude the report in Section 5 by laying out thebenefits garnered by Avatar through this work, and the planned future directions in which it will be taken.

2.1 Objectives

The main objective of this project is to develop amodeling framework for anaerobic digestion using ex-perimental data to represent hydrolysis, acidogene-sis and acetogenesis, and a mathematical model ofmethanogenesis only. The motivation for this de-sign is to avoid unrealistic assumptions about themore complex, less understood processes driving thefirst stages of digestion. Furthermore, restricting themodeling component to methanogenesis reduces thedimension of the model state space, and parameterspace, and will thus reduce uncertainty, (and allowfor more accurate measurement of that uncertainty).Armed with a simple model, Avatar will be able topredict gas output for various feedstocks without thenecessity of full-scale lab tests, other than to verifythe output for potentially promising new fuel sources.Examples of feedstocks with potential that could beanalyzed using the model appear in Figure 1. Figure 1: Mean biogas yields for various substrates

An important application for this model will be in the planning of digester start-up protocol, which isinherently feedstock dependent, and very important for the economic success of Avatar. The wonderful bugsthat perform the final stage of digestion to produce methane (more on this in the Background section) arevery sensitive to pH; they hate acidic environments, which is very sad for them since the food that theyneed to grow is an acid! The model we develop here will help to determine starting feedstock quantities,feeding schedules and amounts, in order to maximize the growth of the methanogen population, withoutover-acidifying their environment, (and thus inhibiting their growth).

2.2 Background

2.2.1 Community partner

This project was undertaken in partnership with Avatar Energy: “A renewable energy company dedicatedto increasing profitability and sustainability of agriculture, capturing renewable energy, and protecting theenvironment.” – Avatar website. Avatar was founded in 2005, and has developed the first scalable, modu-lar anaerobic digester, aimed primarily at the midsize farm market. The company has offices in Californiaand Nevada, but research and development happen mainly in the South Burlington, Vermont lab, and withcommercial units on Vermont farms.

Figure 2 shows a commercial-scale Avatar digester in operation at the Pike farm in Stowe, Vermont, andFigure 3 shows a valuable co-product of the digestion process, sanitary animal bedding, resulting from theseparation of the fibrous solids of the digested manure.

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Figure 2: A commercial-scale Avatar digester operating in Vermont, processing approximately half of themanure for a 100-head dairy farm. Manure enters on the far end of the hull after being warmed and stirred,is digested slowly as it travels through the hull, and exits (at the right of the photo) to be separated intoliquid (used for fertilizer), and valuable pathogen-free fibrous solids that can be used for animal bedding. Aschematic of the separator, and photo of some bedding are shown in Figure 3.

Figure 3: (Left) Schematic of the separator (found on the door to the actual separator), and the valuablepathogen-free bedding comprised of the fibrous solids resulting from separation (right).

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2.2.2 Anaerobic digestion

Anaerobic digestion occurs in four stages (simplified here for presentation): (1) bacterial hydrolysis, wherebyinsoluble organic polymers (e. g. carbohydrates) are broken down into sugars; (2) acidification, during whichother bacteria convert the sugars into organic acids, with some other outputs such as CO2 and hydrogen;(3) acetogenesis, during which these same (and other) bacteria then convert much of the organic acids intoacetic acid; and finally (4) methanogenesis, whereby anaerobic archaea convert the acetic acid into methane,and some more CO2. A flow chart indicating some of the pathways described above appears in the left panelof Figure 4, and a pretty picture of some of the methanogens that perform the last stage (and are of mostinterest to us here), appears in the right panel.

Figure 4: (Left) A flow chart indicating digestion pathways, and some methanogens that perform the finalstage (right). Both taken from the presentation delivered to our class by Guy Roberts from Avatar.

2.3 Plan of action

The timeline of the project extends over 6 weeks, ending April 12. In addition to Guy Roberts, the ChiefScientific Officer of Avatar, I will also work with company engineer, Brian Pinand, and lab technician,Samantha Csapilla. We’ll have weekly Thursday morning meetings at the R and D lab in South Burlington,starting on March 7th. Planned activities are outlined in the sections below. In addition to the listedactivities, I’ll be working on this report throughout.

2.3.1 Week 1, March 4-8

The primary goal of week 1 will be to familiarize myself with the components of the Anaerobic DigesterModel 1 (ADM1), the industry standard in modeling anaerobic digestion. To do this, I’ll be reading a texton the model provided by Avatar, as well as discussing its components with Guy and Brian. By the end ofthis week, the aim is to know exactly what data inputs we’ll need from experiments to represent the firststages of digestions so that we can: (1) begin running experiments to produce that data (work with Sam);and (2) start coding the model, which will be partly based on ADM1 (the methanogenesis component), andpartly specialized to Avatar, (to take direct data input, and test predicted gas output against experimentalresults).

2.3.2 Weeks 2 and 3, March 11-22

As Sam is running experiments (which should be 4 to 5-day assays) to produce necessary model inputs forvarious feedstocks (manure, and food, maybe broken up into breakfast/lunch/dinner for the other students’project), I’ll be continuing to code the model. The goal for the end of this 2-week period is to have a completemodel that we can test/debug. All three of the Avatar contingent will be involved: Sam for the experiments,

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Brian for assistance in porting the ADM1 methanogenesis design into our model, and Guy to help verifythat the model is behaving properly.

2.3.3 Weeks 4 and 5, March 25 - April 5

In these two weeks we hope to perform as many experiments as possible. The exact design has not yetbeen determined, but it will probably go something like this: (1) take experimental values for all of thesalient quantities resulting from the first stages of digestion for various feedstocks (and maybe varioussizes/geometries of digester) and plug them into the model; (2) record predicted gas output (both volumeand relative concentrations of methane and CO2) as a function of time; (3) compare predicted results to thosemeasured in the lab; (4) measure predictive accuracy of the model using appropriate metrics; (5) quantifyuncertainty, potentially including sensitivity of results to model parameters. Again, all Avatar folks will beinvolved.

2.3.4 Week 6, April 8-12

In the final week of the project, we’ll finish up any experiments that need finishing and compile results. ThenI’ll finish the project report, including a recommendation for future work necessary to improve the model,and any notes on potential weakness or pitfalls that I can foresee.

3 Methodology

In this section, we’ll outline the methodology for model development, including some background on previousmodeling approaches, and specific strategies for incorporating experimental data into the model.

3.1 Anaerobic Digester Model 1 (ADM1)

The IWA modeling task force developed a very complicated model of the entire anaerobic digestion processseveral years ago. In the modeling framework we develop in the next section, we reduce the ADM1 equationsshown on the next page in Figure 5 to only three, one of which comes from the third to last column in thebottom panel of that figure, and two of which come from experimental data.

3.2 Modeling framework

Table 1: Volatile organic acid concentrations usedto determine acetic acid concentration growth curvesfor incorporation into the model.

The three dynamic variables in our modelingframework will be: (1) acetic acid production, A;(2) methanogen population M , expressed in terms ofacetic acid demand; and (3) pH. The first and third ofthese will be determined a priori with experimentaldata in the following ways.

To determine acetic acid production for a particu-lar feedstock, we assume a logistic form and performvolatile organic acid (VOA) assays on a seeded di-gester with inhibition of methanogenesis. An exam-ple of such an assay appears to the left in Table 1.These data can be used to fit the limiting concentra-tion L, and growth rate µ in the assumed logistic formfor any particular feedstock. Toy examples appear inthe left panel of Figure 6. These curves can than beused to represent the driving force of acetic acid pro-duction in a digester, including a feeding schedule, bysuperposition of logistics with different temporal off-sets, resulting in overall acetic acid production witha shape that appears in the right panel of Figure 6.

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Figure 5: Equations for ADM1

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time (hrs)

[HO

Ac

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µ=0.8, L=0.1

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[HO

Ac

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Figure 6: (Left) Toy examples of logistic fits for experimental VOA data, and (right) a superpositionof logistics with temporal offset determined by feeding schedule, to represent acetic acid production in aregularly fed plug-flow digester.

We also use experimental data to determine the dynamics of pH in our model framework. To do this, weassume that acetic acid is the main driver trying to force the pH downward (acidify the digester), but thatthere is inherent buffering capacity in the system. For starters, we assume this buffering capacity comesfrom the solids inside the digester. So, to inform the model using experimental data, we perform titrationsof a suitably diluted sample of digester solids. This provides the theoretically informed, but experimentallydetermined buffering capacity curve shown as the green line in Figure 7. Higher values mean more resistanceto change in pH.

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HOAc alone

HOAc with solids

Figure 7: Experimentally determined buffering capacity curve (green), shown with the acetic acid bufferingcapacity curve (blue) for reference.

Finally, the population dynamics of the methanogens come directly from the ADM1 equations, witheventual appropriate parameter fitting for the context of a plug flow digester using units of VOA demandinstead of BOD (biological oxygen demand). In the next section we give the equations that arise fromthe combination of theoretical and experimentally informed dynamics, in descriptive form (for illustrativepurposes, but lacking in detail for proprietary reasons).

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4 Results - Avatar Methanogenesis Model (AMM)

In this section we detail the model as it currently stands. First the equations in descriptive form:

dA

dt= production from superimposed logistics − uptake of acetic acid by methanogens

dM

dt= yield rate ∗ uptake of acetic acid by methanogens ∗ pH inhibition − death of methanogens

dpH

dt=

quantity proportional to acetic acid production

buffering capacity at current pH

A plot of a 15-day model simulation appears in Figure 8

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Figure 8: A plot of model output for a 15-day simulation. The red vertical axis on the right applies tothe red line only, which is the pH. The left vertical axis indicates both acetic acid concentration (blue) andacetic acid demand (green) of the methanogens, which is proportional to the population size.

5 Conclusions

5.1 Benefits to community partner

Avatar now has the beginnings of a simple model to assist in many important R & D tasks for the company.First and foremost, the AMM will allow for optimization of digester start-up protocol for new feedstocks.New digesters can be started as swiftly as possible, without overwhelming the delicate growing population ofmethanogens. This will make Avatar more attractive to clients, who want to be up and running as quicklyas possible, but with minimal risk of costly start-up crashes that typically require labor to clean and restartthe digester. Furthermore, the fact that the model is based on experimental data from the laboratory willinspire more confidence (on the part of Avatar researchers as well as clients) in its predictions, both in thisstart-up optimization as well as whatever other tasks to which it might be put in the future.

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5.2 Future directions

The immediate next step in this work, which we’re starting right away, is to finish tuning the model withexperimental data from the lab. After that, we’ll be ready to do experiments with several feedstocks,inoculants, digester sizes, etc., to test the performance of the model. If all goes well, we hope to have muchof this experimentation done this summer, so that trial runs in real installations can be performed... veryexciting!

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