verification of a thermal model for affordable solar assisted biogas digesters in cold climates
TRANSCRIPT
Verification of a Thermal Model for Affordable
Solar-Assisted Biogas Digesters in Cold Climates
by
Vergil C. Weatherford
B.S.E, Duke University, 2005
A project submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Civil Engineering
2010
This project entitled:Verification of a Thermal Model for Affordable
Solar-Assisted Biogas Digesters in Cold Climateswritten by Vergil C. Weatherford
has been approved for the Department of Civil Engineering
Prof. Z. John Zhai
Prof. Michael Brandemuehl
Jaime Martı Herrero
Date
The final copy of this project has been examined by the signatories, and we find that both thecontent and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.
iii
Weatherford, Vergil C. (M.S., Building Systems)
Verification of a Thermal Model for Affordable
Solar-Assisted Biogas Digesters in Cold Climates
Project directed by Prof. Z. John Zhai
Energy sources are scarce in the chilly, high mountains of the developing world. Solar-assisted
biogas digesters have recently been adapted to this climate providing an alternative cooking fuel for
some rural families, but little is known about the thermal performance of these digesters. Internal
slurry temperature is one of the important design factors in biodigesters. In this work, an existing
one-dimensional thermal computer simulation model is adapted in order model an experimental
biodigester in Cusco, Peru and is shown to predict thermal performance reasonably well. A set
of design recommendations for small-scale, cold-climate digesters is presented based on parametric
runs of the model considering multiple design parameters.
iv
Acknowledgements
I would like to thank my advisor John Zhai and my committee members Mike Brandemuehl
and Jaime Martı Herrero for their guidance in this project. Jaime’s gracious invitation to Bolivia
allowed me to visit a number of GTZ’s biodigesters, and to participate in a technician training
workshop, both of which were valuable experiences. Also, my involvement in this project would
not have been possible without the initial invitation and coordination of Davide Poggio, who also
completed his graduate research in Cusco and continues to be involved with the research efforts
there. I would also like to thank professors Ivet Ferrer of the Polytechnic University of Spain (UPC)
and Arcadio Calderon of the National University of San Antonio Abad of Cuzco (UNSAAC), for
providing the financial resources and work space at the K’ayra agricultural campus in Cusco. Of
course, without the work of Thibault Perrigault in developing the model originally, this verification
the need for this work would not exist. I would like to also thank James Duncan for giving me an
introduction to anaerobic digestion and biogas, and Pete Haas, Steve Crowe, and Jose Ordonez of
the Appropriate Infrastructure Development Group in Guatemala for giving me the opportunity
to design, build, and fix anaerobic digesters during my internship there, which inspired me to focus
my graduate research on biogas in the developing world.
Here at at the University of Colorado, I would like to express my gratitude to the Engineering
Excellence Fund for providing the initial funding for the Pyranometer. Also, Lars Kalnajs and Sam
Dorsi provided indispensible help with the anemometer and pyranometer data acquisition systems.
I would also like to acknowledge Samuel LeBlanc and the Skywatch meteorological station crew for
help with the calibration of the pyranometer. Thanks also to those who have helped in other direct
and indirect ways, but whom I have not the space to mention.
v
Contents
Chapter
1 Introduction 1
1.1 The big picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The role of biofuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Anaerobic digestion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Challenges for small-scale biogas technology . . . . . . . . . . . . . . . . . . . . . . . 4
2 Literature Review 5
2.1 Tubular polyethylene biodigesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Effect of temperature on biogas production . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Solar-assisted digesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Active solar digesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 Passive solar digesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Non solar-assisted thermal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Description of the Perrigault Thermal Model 16
3.1 Model assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Energy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Radiative heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
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3.4.1 Radiative heat transfer to the sky . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4.2 Radiative heat transfer between model elements . . . . . . . . . . . . . . . . 22
3.4.3 Absorbed solar radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Convective heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5.1 Convective heat transfer to ambient air . . . . . . . . . . . . . . . . . . . . . 23
3.5.2 Convective heat transfer within the greenhouse . . . . . . . . . . . . . . . . . 24
3.5.3 Convective heat transfer within the digester headspace . . . . . . . . . . . . . 25
3.6 Conductive heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6.1 Soil temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6.2 Conductive heat transfer from the slurry to the ground . . . . . . . . . . . . 26
3.7 Mass flow heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.8 Solution algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.9 Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Field Campaign/Data Collection 28
4.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.1 Test digesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.2 Gas storage and combustion testing . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Test equipment/sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.1 HOBOr UA-002-64 pendant temperature and light loggers . . . . . . . . . . 31
4.2.2 EKOr MS-602 pyranometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.3 Davis anemometer and wind vane . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.4 Wind vane counter circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2.5 HOBOr U12-006 4 channel data logger . . . . . . . . . . . . . . . . . . . . . 35
4.2.6 HOBOr U12-013 temp/RH/2 external data logger . . . . . . . . . . . . . . . 36
4.2.7 Weatherproof housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
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4.4 Preliminary data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4.1 Weighting of internal digester temperatures . . . . . . . . . . . . . . . . . . . 42
4.4.2 Estimation of direct and diffuse radiation components . . . . . . . . . . . . . 42
5 Model Verification and Parametric Analysis 44
5.1 Modifications to the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2 Model adjustment/calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2.1 Comparison: single pitch vs. double pitch . . . . . . . . . . . . . . . . . . . . 46
5.2.2 Substitution of meteorology data . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2.3 Correction of wind data and thermal lag . . . . . . . . . . . . . . . . . . . . . 47
5.2.4 Comparison of ambient temperature . . . . . . . . . . . . . . . . . . . . . . . 48
5.2.5 Examination of material property assumptions . . . . . . . . . . . . . . . . . 49
5.2.6 Adjustment of insulation to calibrate model . . . . . . . . . . . . . . . . . . . 50
5.3 Heat Transfer Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.4 Parametric studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4.1 Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4.2 Cover transmissivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.4.3 Tube material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.4.4 Parametric Studies: Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.4.5 Parametric Studies: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 59
6 Conclusions 60
6.1 Factors influencing solar-assisted digester performance . . . . . . . . . . . . . . . . . 60
6.2 Future work: experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.3 Future work: models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.4 General design recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.5 Closing summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
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Bibliography 64
Appendix
A Reference 67
A.1 Equipment specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
ix
Tables
Table
3.1 Nomenclature for discussion of the Perrigault model . . . . . . . . . . . . . . . . . . 18
A.1 Specifications for the UA-002-64 waterproof pendant loggers . . . . . . . . . . . . . . 69
A.2 Specifications for the EKO MS-602 Pyranometer used in this study . . . . . . . . . . 69
A.3 Specifications for the HOBO U12-002 data logger . . . . . . . . . . . . . . . . . . . . 70
x
Figures
Figure
1.1 The “Energy Ladder” and the biogas shortcut . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Chinese fixed-dome digester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Indian KVIC-style floating dome digester . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 General schematic of a tubular plug-flow digester . . . . . . . . . . . . . . . . . . . . 6
2.4 Growth rate of methanogens for different temperature regimes . . . . . . . . . . . . 8
2.5 Fixed-dome type biogas plant with integrated solar collectors . . . . . . . . . . . . . 10
2.6 Fixed-dome type biogas plant modeled by axaopoulos . . . . . . . . . . . . . . . . . 11
2.7 Greenhouse structure over an 80 m3 floating dome style digester in Masoodpur, India 12
2.8 Elements included in Sodha’s 1-D thermal model from the Sodha greenhouse digester 13
2.9 A cross-sectional view of Gupta’s experimental greenhouse with thermal mass . . . . 15
2.10 Below-ground digester and heat transfer components for the Wu/Bibeu model . . . . 15
3.1 General cross-section of the digester simulated in the Perrigault thermal model . . . 16
3.2 Energy balance for the greenhouse cover . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Energy balance for greenhouse air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Energy balance for Wall 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Energy balance for Wall 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.6 Energy balance for the gas holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.7 Energy balance for the gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
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3.8 Energy balance for the slurry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.9 General cross-section modeled in the original, shed roof 1-d thermal model . . . . . . 27
4.1 Nine sampling ports in the side of digester 4 at K’ayra . . . . . . . . . . . . . . . . . 29
4.2 Interior view of one of the test digesters . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 Entrance to the Digester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.4 HOBOr Temperature/Light Intensity Pendant Logger . . . . . . . . . . . . . . . . . 31
4.5 EKOr MS-602 Pyranometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.6 Pyranometer calibration curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.7 Modified calibration curve with erroneous data removed . . . . . . . . . . . . . . . . 33
4.8 Anemometer and pyranometer mounted on a post near the digester . . . . . . . . . . 34
4.9 The completed frequency to voltage circuit . . . . . . . . . . . . . . . . . . . . . . . 35
4.10 Calibration curve for the wind vane counter circuit . . . . . . . . . . . . . . . . . . . 35
4.11 Wind Rose plot of direction and intensity of wind . . . . . . . . . . . . . . . . . . . . 36
4.12 HOBOr U12-006 4-Channel data logger . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.13 Plot of the HOBOr’s external instrument voltage excitation . . . . . . . . . . . . . . 37
4.14 Signal processing circuitry mounted inside the logger box . . . . . . . . . . . . . . . 37
4.15 Penetrations in the side of the logger box . . . . . . . . . . . . . . . . . . . . . . . . 37
4.16 Sensor locations within the digester - end view . . . . . . . . . . . . . . . . . . . . . 38
4.17 Sensor locations within the digester - side view . . . . . . . . . . . . . . . . . . . . . 38
4.18 Plot of ambient air temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.19 Plot of wind speed at 1.8m off the ground near digester . . . . . . . . . . . . . . . . 39
4.20 Total Horizontal Solar Radiation at the site . . . . . . . . . . . . . . . . . . . . . . . 39
4.21 Plot of all 9 internal pendant temperature sensors . . . . . . . . . . . . . . . . . . . 40
4.22 Average temperatures for top three, middle three, and bottom three sensors . . . . . 40
4.23 Temperature of the greenhouse air during the study period . . . . . . . . . . . . . . 40
4.24 Temperature of the gas in the headspace (gas holder) during the study period . . . . 40
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4.25 Temperature of the soil 5 cm below the surface and 70 cm below the surface . . . . . 41
4.26 Temperatures inside and outside the straw insulation at 35 cm depth . . . . . . . . . 41
4.27 Interior and exterior surface temperatures of the Southeast adobe wall . . . . . . . . 41
4.28 9-point weighted average of the digester slurry temperature . . . . . . . . . . . . . . 41
4.29 Weighting areas for the 3 sensor heights . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.30 Direct, diffuse, and total horizontal radiation . . . . . . . . . . . . . . . . . . . . . . 43
5.1 Surface reference for view factor calculations . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Comparison of single pitch vs. double pitched roof on digester, 30 degree slope . . . 46
5.3 Plot of modeled slurry temperature and weighted average of experimental data . . . 47
5.4 8760 hourly plot of wind speed used in first model run . . . . . . . . . . . . . . . . . 48
5.5 Normalized 8760 hourly plot of wind speed used in subsequent model runs . . . . . . 48
5.6 Plot of onsite measured ambient temperature with data from Cusco airport . . . . . 49
5.7 Modeled slurry temperature and experimental results with updated weather file . . . 50
5.8 Modeled and experimental results with revised straw thermal conductivity . . . . . . 51
5.9 Modeled and experimental results calibrated using the thickness of straw insulation . 51
5.10 Annual average heat transfer at every surface for the shed-roof digester . . . . . . . 52
5.11 Annual average heat transfer at every surface for the gable roof digester . . . . . . . 52
5.12 Plot of average modeled temperature increase with parameterized insulation . . . . . 53
5.13 Plot of average modeled temperature increase with parameterized cover transmittance 54
5.14 Average modeled temperature increase comparing three common tube materials . . . 55
5.15 Diagram showing the concept of thermal lag associated with massive walls . . . . . . 56
5.16 Model modification to incorporate wall resistance . . . . . . . . . . . . . . . . . . . . 57
5.17 Average modeled temperature increase with parameterized wall thickness before
changes to model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.18 Average modeled temperature increase with parameterized wall thickness before
changes to model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
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5.19 Average modeled temperature increase with parameterized digester orientation . . . 59
A.1 Circuit diagram for the frequency to voltage counter . . . . . . . . . . . . . . . . . . 67
A.2 Circuit design for the pyranometer signal amplifier . . . . . . . . . . . . . . . . . . . 68
Chapter 1
Introduction
I have no doubt that it is possible to give a newdirection to technological development, a directionthat shall lead it back to the real needs of man,and that also means: to the actual size of man.Man is small, and, therefore, small is beautiful.
E. F. Schumacher - Small is Beautiful
In 1957, Admiral Hyman G. Rickover spoke in front of an assembly of scientists in St. Paul,
Minnesota. The main thrust of his speech was that, because of fossil fuels, the modern middle-class
U.S. American posesses greater personal energy wealth than did most ancient kings[35]. His line
of reasoning can be summarized in brief, updated with today’s figures: Given that a human can
expend roughly 35 watts of energy continuously while working and that the annual per-capita energy
consumption in the US in 2008 was around 100 million Watt-hours, an average U.S. American has
an equivalent of 330 slaves waiting on them around the clock[11]. It is undeniable then, that the
extraction and utilization of fossil fuels by human beings has fundamentally changed both our
lifestyles and ourinteraction with the rest of the natural environment. Coal, oil, and natural gas
have given humans an unprecedented ability to grow food, travel, manufacture goods, and recreate.
It has also contributed to a drastic alteration in the chemistry of our planet’s air and water which
may cause the planet’s ecosystems hardships as they adapt to the changing climate[5].
1.1 The big picture
While some human inhabitants of this planet are living comfortably as a result of the extrac-
tion of fossil fuels, others are struggling to simply exist. In the absence of a cheap, high-grade fuel,
a great physical effort is required to fulfill even the most basic necessities such as gathering fuel for
2
cooking, hauling water, and transporting goods to market. According to the International Energy
Agency, 2.4 billion people on this planet rely on traditional biomass (wood, agricultural waste, and
dung) for cooking and heating[22]. Not only does this signify a large number of humans foraging for
fuel every day (thus diminishing the world’s forests), but also a massive health problem: typically
biomass is burned inefficiently in primitive cook stoves. A significant number of respiratory illnesses
arise in people exposed to poor indoor air-quality caused by the smoke and particulate matter from
cooking fires[49]. There is a great need for small-scale, clean energy sources to help close the gap
between the world’s energy wealthy and its energy impoverished.
1.2 The role of biofuels
The problem of the energy wealth gap is exacerbated by the fact that the majority of the
energy resources in use at this time are not renewable. The benefit humans are receiving from fossil
fuels today will only last as long as the the sources themselves which is, unequivocably speaking,
a finite period of time. As the world’s population grows, so does demand for energy. This puts
greater pressure on finite stores of fossil fuels and new sources of energy will be required in order
to meet the growing demand. Biofuels have been viewed as a way to sustainably harvest the sun’s
energy through biochemical conversion, which can help alleviate our reliance on non-renable soruces
of energy. However, biofuels have also been criticized because the feed stocks are often in direct
competition with food-growing agriculture, which can cause disruptions in global food supply. One
biofuel that is not generally a contributor this problem is biogas produced by Anaerobic Digestion
(AD) of organic material. Anaerobic digestion of is most often employed in dealing with excess
organic wastes rather than digesting fresh feedstocks. Furthermore, one of its main byproducts is
an effective fertilizer used in agriculture agriculture[24].
1.3 Anaerobic digestion
Anaerobic Digestion is the biological process by which organic materials–such as agricultural
or food wastes–are decomposed into biogas and stable humus material (fertilizer). The process
3
is carried out by a population of anaerobic microorganisms which work sequentially in a number
of connected stages to complete the conversion process. The work of designing anaerobic biogas
digesters, or Biodigesters, involves providing a suitable environment that is free of oxygen and
a balanced diet of appropriate organic material for the microorganisms to digest. The anaerobic
digestion process happens in 4 stages: Hydrolysis, Acetogenesis, Acidogenesis, and Methanogenesis.
A separate population of anaerobes is responsible for each step of the process[24].
Anaerobic digestion has a number of benefits. It provides energy in the form of gas which is
mostly methane. It creates a highly effective fertilizer which, when spread on crops can increase
yield greatly. It reduces the demand for biomass fuels when used to fulfill cooking needs in the
developing world. It reduces foul odors better than other forms of agricultural waste management,
and it reduces nutrient polution by lowering the both the Biological Oxygen Demand (BOD) and
Chemical Oxygen Demand (COD) of the waste effluent[28]. For further information on the science,
benefits, and societal issues of small-scale anaerobic digestion, the reader is referred to the vast
body of articles and books on this subject, such as The Biogas Handbook by David House[21].
1.4 Motivation
The divide between “developed” nations and “underdeveloped” nations is most simply de-
scribed by a wealth–or lack–of energy. During his famous remarks in 1957, admiral Rickover went
on to discuss the lack of energy signifying a missed opportunity to accumulate knowledge, develop
technology, and afford leisure because of the great amount of time devoted to basic subsistence.
Anaerobic digestion technology is a direct way to increase the energy leverage of the small farmer.
Figure 1.1 shows how, with the help of biogas, farmers can move quickly up the “energy ladder”
to cleaner indoor air quality and a better standard of living. By using the gas to fuel generators
adapted for biogas, they can even make electricity.
However, these benefits can only be realized with a small investment by farmers living in
tropical climates. Those who live in colder climates and higher altitudes cannot take advantage of
the same type of digesters, as the slurry must operate above a certain minimum temperature in
4
Figure 1.1: Energy ladder showing the shortcut biogas can provide to a cleaner, high-grade energysource [9]
order to be effective. Thus, the design must be adapted to colder climates. A full review of the
work done in this area is found in chapter 2. The study outlined in this paper aims to support
the adoption of biogas technology to cold climates and making it available to a wider range of the
world’s population by improving the thermal performance of these digesters.
1.5 Challenges for small-scale biogas technology
While there are still a large number of technical improvements that can be made to small-
scale biodigesters, one major obstacle to its widespread adoption is an array of complicating social
factors. Biogas programs have been introduced in many countries around the world by governments
and NGOs, but these programs have been met with mixed success. It is not uncommon to see the
long-term rate of successful (utilized) installations in a biogas program be under 50%. Factors
which influence the successful adoption of the technology include economics, availability of other
fuels, cultural norms and cooking habits, and end-user education and training. Although they are
beyond the scope of this work, these social factors are just as important as the technological factors
to the design of a successful biogas program and the reader is referred to the book Running a Biogas
Programme: A Handbook by David Fulford for a more thorough discussion of these issues[14].
Chapter 2
Literature Review
Perhaps our greatest distinction as a species isour capacity, unique among animals, to makecounter-evolutionary choices.
Jared Diamond
Although the phenomenon of anaerobic digestion has been described by humans dating as far
back as 2000-3000 years ago, its utilization as a means for generating a fuel and fertilizer is much
more recent. The first biodigesters are said to have been built in the 1800s, and their development
has continued through the present. Domestic biogas plants, or plants built for the household scale,
came about in the early 20th century primarily in China and India. The predominant design
constructed in China has been the underground, fixed-dome digester in which gas accumulates and
is stored at naturally-generated pressure in a sealed dome above the slurry (see figure 2.1). In
India the predominant design has been the floating dome digester, in which the gas holder is a
rigid, air-tight drum which floats up and down in the slurry pit with the build-up and release of
gas pressure. In both cases, the high cost of construction is often a barrier especially to poorer
farmers[14]. Only in the past 30 years has a more affordable design emerged, making it a more
feasible solution for the poor: the plug-flow, polyethylene tubular biodigester.
2.1 Tubular polyethylene biodigesters
Tubular polyethylene biodigesters emerged in the early 1980s. They were introduced in the
developing world as a potential solution to the organic waste and cooking fuel problems faced in
rural communities. They are easily constructed out of basic and affordable materials, and only
require the addition of water and manure to operate. The first low-cost tubular digester was the
6
Figure 2.1: Chinese fixed-dome digester [13] Figure 2.2: Indian floating dome digester [13]
Figure 2.3: General schematic of a tubular plug-flow digester
7
“red mud PVC” digester, so called because it is made from a polyvinylchloride compound that
exists as a reddish slurry byproduct of the aluminum industry[33].
The technology has been improved upon and adapted to many different geographical regions
based on available resources and variation in agricultural and cultural practices. Preston improved
and simplified the design in Ethiopia (Preston Unpublished), and Botero adapted the design to
the materials and construction techniques of Columbia[7]. Later, Bui Xuan An improved the
design in Vietnam by sourcing ultra low-cost polyethylene-bag material, reducing the material
costs even further[1]. Tubular polyethylene biodigesters have been promoted in a number of other
countries including Tanzania, Vietnam, Cambodia, China, Costa Rica, Ecuador, Argentina, Chile,
and Mexico.[37][39][44].
Improvements to the initial design have largely been usability improvements, with the basic
design staying intact. However, these polyethylene tubular digesters were exclusively built for use
in tropical climates. Due to the nature of the microbial processes that take place during anaerobic
digestion, a certain minimum temperature is required for reasonable digestion efficiency. In 2003,
Martı Herrero first adapted Botero’s design to cold climates in the altiplano of Bolivia by adding
a simple shed-roof adobe greenhouse structure over the digester[29]. Poggio, in Peru, proposed
adding a solar water heating system to the Martı Herrero design, by storing water in a 4-inch PVC
tube running the length of the digester under a modified version of the greenhouse[32].
2.2 Effect of temperature on biogas production
According to Meynell, biogas production becomes insignificant below 15 C[30]. Gunnerson
and Stuckey introduced a model to describe the volumetric methane yield in m3 gas per kg volatile
solid (VS), which was then improved upon by Safley and Westerman [16] [38]:
B = Q ·B0
(1− K
(µmΘ)− 1 +K
)(2.1)
8
Where B0 is the maximum biodegradability at infinite retention time (m3 CH4/kg VS), Q is the
organic loading rate (kg VS/m3), Θ is the Hydraulic Retention Time (HRT) of the solids, K is the
maximum utilization coefficient (dimensionless), and µm is the maximum growth rate of microbes
(day−1). The growth rate of the microbes, µm can be described by the Arrhenius equation [27]:
µm = A · e−Ea/RT (2.2)
Where µm is the process rate (t−1), A is the frequency factor (t−1), Ea is the apparent
activation energy (J/mol), and R is the gas constant (8.31 × 105 J/mol · K). It is apparent
from equation 2.2 that as the temperature increases, the growth rate increases and (from equation
2.1) the gas production also increases. According to Sweeten et Al., the population growth of
Figure 2.4: Growth rate of methanogens for different temperature regimes [47]
the micro-organisms in an anaerobic digester can be seen to fall into two distinct temperature
regimes, namely the mesophilic (27C−43C) and the thermophilic (45C−65C). There exists a
third regime in which growth occurs called psychrophilic, but growth is significantly protracted[43].
Figure 2.4 shows the three major regimes and relative growth rates. In addition to the minimum
temperature requirement, another prerequisite for optimum methane production is the stability
of the digester temperature to within a 5C band during operation[8]. If the temperature of
the particular climate is low (below 15 C average temperature), an outside source of heat is
9
required to meet the temperature requirements of the process. From a technological and economical
perspective, the mesophilic temperature requirements are easier to meet for domestic biodigesters
than the thermophilic range. While the temperature requirements can be met through a variety
of heat sources, solar heating can provide a simple, low-cost solution particularly suited to the
developing world.
2.3 Solar-assisted digesters
There has been extensive research done on solar-assisted digesters since the early 1980s. It
appears a natural solution to use a low-grade, low-cost form of heat (solar radiation) in order to
facilitate the production of a high-grade form of energy (biogas). Although much of the work
has been theoretical (through the development of mathematical thermal models) there are also a
number of studies citing experimental verification of these models. The work can be divided into
two categories: active and passive solar heating.
2.3.1 Active solar digesters
Active solar includes any systems that require external energy inputs to run (pumps, fans,
etc.). While these systems tend to cost more, they can also be more effective at reaching and
maintaining temperature goals due to their more controllable nature. In 1980, Hills and Stephens
described a system for heating the influent to an insulated dairy-manure digester via a solar collec-
tor, with an electric heating element to provide supplemental heat[20]. In 1986, Gupta, Rai, and
Tiwari developed a transient model for the solar heating of an underground, fixed-dome digester.
They determined that in order to keep the temperature within the desired temperature range at
night, a thick layer of insulation should be built around the digester. Figure 2.5 shows their modeled
system[18]. In 1988 Tiwari, Sharma, and Gupta described a similar thermal model, adapted for
a floating-dome digester. In the same year, Ali Beba simulated a new large-scale (100m3) hybrid
solar-biogas system, and determined payback to be 6 to 8 years depending on the solar resource
and fuel prices[6].
10
Figure 2.5: Fixed-dome type biogas plant integrated with solar collectors [18]
More recently, in Greece, Axaopoulos et Al. simulated the thermal performance (in TRNSYS)
and validated with experimental results an in-ground, plug-flow biodigester with a single-slope roof
consisting of solar hot water panels. They found that slurry temperature was influenced greatly
by feeding rate and feedstock temperature, while the temperature of the air in the gas holder was
influenced largely by the ambient temperature. Their simulation agreed with experimental results
very well[4].
A similar model was developed for a different geometrical configuration in 2004 by El-Mashad
et. Al. using Matlab and Simulink software. Thermal heat-recovery from the effluent and waste-
heat utilization from the pumping equipment and a structurally-integrated solar hot water array
were considered, and found to improve the digester performance by about 4 to 6 C on average[12].
In a 2009 masters thesis, Buysman developed a model for an affordable solar heating system
for a household scale fixed-dome digester in which the heat from the above-ground panel is pumped
in tubes to the underground digester. Results were simulated for a number of different climates[9].
11
Figure 2.6: Fixed-dome type biogas plant modeled by axaopoulos showing 1, manure; 2, enclosedbiogas; 3, solar collector; 4, plastic cover; 5, heat exchanger; 6, pump; 7, ground.[4]
2.3.2 Passive solar digesters
In order to overcome the disadvantages of active solar systems (high cost and complicated
construction), a number of researchers have proposed and built or modeled passive solar heating
systems. Passive solar heating systems generally involve taking advantage of solar gains without
the input of exterior sources of energy like fans or pumps. The most common approach to passive
heating of digesters consists of adding a greenhouse structure over the digester to capture and store
the sun’s heat.
2.3.2.1 Greenhouse
In 1985, Dayal, Singh, Bansal, and Ram proposed a number of different passive solar methods
for heating a floating dome digester including a greenhouse, night insulation, shallow solar pond
(SSP), and an SSP with a greenhouse. They developed a simple, 1-D mathematical model in order
to compare digester temperature with the 4 improvements. They found that the greenhouse coupled
with an SSP brought the best performance[10]. The greenhouse model was further improved in
1988 by Kumar et Al. to include more complex heat transfer mechanisms[25]. Sodha Conducted an
12
experimental validation of the Kumar model and found reasonable agreement between experimental
and simulated temperatures. In 2008 Kumar and Bai revisted the question of solar greenhouses
and presented a field study in which an above-ground plastic tank biodigester was covered with
a solar greenhouse and monitored for temperature. The temperature was higher than a standard
underground Deenabandhu model digester which was used for comparison[26]. The concept of
Figure 2.7: Greenhouse structure over an 80 m3 floating dome style digester in Masoodpur, India[41]
building a greenhouse for aiding in the heating of tubular polyethylene digesters was first introduced
by Jaime Martı Herrero as early as 2003. In order to keep costs down and improve thermal storage,
the greenhouse was built out of adobe bricks and the digester lined with straw as insulation [29].
In 2007, Poggio added to this design a simple structure for pre-heating mixing water by suspending
a large PVC pipe inside the greenhouse filled with water to capture heat. The addition of a faucet
at the inlet end of the digester allows the pre-heated water to empy into the mixing box during
loading[32].
2.3.2.2 Other passive solar heating methods
Although greenhouses have been extensively studied as a means for heating biodigesters, a
number of other passive solar techniques exist in the literature. In 1979, Reddy et. Al described
13
Figure 2.8: Elements included in Sodha’s 1-D thermal model from the Sodha greenhouse digester[41]
a shallow solar pond used to heat a KVIC floating dome biodigester[34]. A decade later, Subra-
manyam adapted the design for a different kind of digester[42]. Tiwari and Chandra added both
a blackened surface and night insulation to the KVIC style fixed-dome design, building on the
original shallow solar pond design in a 3-way hybrid. They presented a thermal model to describe
this system[45]. In 1989 Sodha introduced a similar design concept of a low greenhouse cover for
a fixed-dome digester, with the roof of the digester under the greenhouse blackened to improve
absorption. In this instance, an experimental model was built and its temperatures monitored with
good agreement with the model[40]. In separate work that year, Jayashankar found the optimum
area for blackening and double-glazing over a fixed-dome biogas plant to maximize the temperature
increase[23].
2.4 Non solar-assisted thermal models
A large number of the solar-assisted biodigester papers cited above develop mathematical
thermal models to aid in the analysis of the design of biodigesters. A few other papers are worth
mentioning on the subject of thermal modeling, particularly those which describe thermal models
of heated biodigesters, or greenhouses with thermal masses.
14
In 2002 Gupta and Tiwari developed and validated a computer model to predict tempera-
tures inside a simple polyethylene-covered greenhouse with a single, known quantity of liquid in a
drum as thermal mass. They found that their model predicted the experimental results with fair
accuracy[17]. In 2005, Gebremedhin et Al. developed a 1-D thermal model for determining the
heating requirements for plug-flow digesters built below grade, partially below grade, and entirely
above grade. Validation of the model was carried out using data from two dairy-manure digesters.
Agreement was fair, with error less than 20% for all months of the year[15].
Wu and Bibeu developed a 3-D model also describing a plug-flow digester, particularly for
use in cold climates. The model developed is flexible, with multiple geometries considered. Using
the same data as Gebremedhin, the authors found better agreement with the experimental data via
the 3-D model. They also conducted a comparison of various geometries for digesters, and found
that, as predicted, the cylindrical digester design had lower heat loss than did shapes that were
rectangular, rectangular with arched top, or cylindrical with conical bottom[48].
15
Figure 2.9: A cross-sectional view of Gupta’s experimental greenhouse with thermal mass (a) duringsunshine hours, (b) during off-sunshine hours [17]
Figure 2.10: Below-ground digester and heat transfer components for the Wu/Bibeu model [48]
Chapter 3
Description of the Perrigault Thermal Model
Waste equals food.
William McDonough - Cradle to Cradle
A 1-dimensional thermal model of a solar-assisted polyethylene tube digester was developed
by Thibault Perrigualt in early 2010. The model was written entirely in Matlab (a numeric com-
puting language) and it calculates 8760 hourly values in a year for temperatures of the elements of
the digester. Below follows a simplified description of the model summarized from Perrigualt. This
is a rudimentary summary, and is included only to provide context. For a more thorough discussion
of the model physics, assumptions, and sources, the reader is referred to the original work[31].
Figure 3.1: General cross-section of the digester simulated in the Perrigault thermal model
17
3.1 Model assumptions
The Perrigault model makes following assumptions in order to simplify the system’s physics:
(1) Each element of the system is represented by a single temperature (1-D). Stratification in
the fluids and thermal gradation in the solids is neglected.
(2) Thermal mass effects are neglected for the greenhouse cover, the air inside the greenhouse,
the gas holder (the bubble formed by the top of the polyethylene tube), and the biogas.
(3) The gas layer inside the gas holder is assumed to be a rectangular prism whos height is
calculated based on the volume of a totally inflated gas holder.
(4) Solar radiation reflected inside the system is neglected.
(5) Internal heat generation due to exothermic microbial activity are negligible.
(6) Properties of the feeding mixture added to the system are assumed to be equivalent to the
properties of the slurry with the exception of temperature.
(7) Heat loss through the small end-walls is neglected as well as losses out the entrance and
exit tubes.
(8) The soil is assumed to have uniform properties (specific heat, thermal conductivity, and
density) throughout the depth.
(9) Soil temperature is assumed to vary sinusoidally from grade level to a calculated depth and
assumed constant thereafter.
(10) Heat losses from evaporation inside the digester and the mass flow rate of the gas are
neglected.
(11) It is assumed that digester does not affect the soil temperature.
18
3.2 Nomenclature
Major Terms
T Temperature
S Solar insolation (cumulative radiation)
I Solar irradiance (instantaneous radiation)
Qr Radiative heat (gain or loss)
Qc Convective heat (gain or loss)
Qcd Conductive heat (gain or loss)
m Mass (gain or loss)
Cp Specific heat
A Area
F Radiative view factor
U Velocity
∝ Thermal diffusivity
τ Transmissivity
η Emissivity
α Absorptivity
σ Stephan-Boltzmann Constant
Subscripts
gc Greenhouse cover
ga Greenhouse air
gh Gas holder
g Gas
w1 Wall 1
w2 Wall 2
gr Ground (soil)
s Slurry
sky Sky
amb Ambient air
ext Exterior
int Interior
Table 3.1: Nomenclature for discussion of the Perrigault model
19
3.3 Energy balance
Energy balances for each element of the digester are shown below:
For the greenhouse cover:
Figure 3.2: Energy balance for the greenhouse cover, as shown in equation 3.1
0 = Sgc +Qr,w1−gc +Qr,w2−gc +Qr,gh−gc +Qr,gh−gc +Qwind,gc +Qc,ga−gc (3.1)
For the interior of the greenhouse:
Figure 3.3: Energy balance for greenhouse air, as shown in equation 3.2
20
0 = Qc,gc−ga +Qc,w1−ga +Qc,w2−ga +Qc,gh−ga (3.2)
For wall 1 (the shorter of the two long walls if the wall heights are unequal):
Figure 3.4: Energy balance for Wall 1, as shown in equation 3.3
mw1Cp,w1∂Tw1∂t
= Sw1 +Qr,w1−sky +Qr,gc−w1 +Qr,w2−w1 +Qr,gh−w1 +Qc,w1−ga +Qwind,w1 (3.3)
For wall 2:
Figure 3.5: Energy balance for Wall 2, as shown in equation 3.4
mw2Cp,w2∂Tw2∂t
= Sw2 +Qr,w2−sky +Qr,gc−w2 +Qr,w1−w2 +Qr,gh−w2 +Qc,w2−ga +Qwind,w2 (3.4)
21
For the gas holder:
Figure 3.6: Energy balance for the gas holder, as shown in equation 3.5
0 = Sgh +Qc,gh−g +Qc,gh−ga +Qr,gh−w1 +Qr,gh−w2 +Qr,gh−s +Qr,gh−gc (3.5)
For the gas in the headspace above the slurry:
Figure 3.7: Energy balance for the gas, as shown in equation 3.6
Tg =(Tgh + Ts)
2(3.6)
22
For the slurry:
Figure 3.8: Energy balance for the slurry, as shown in equation 3.7
msCp,s∂Ts∂t
= Ss +Qc,s−g +Qr,gh−s +Qcd,s−gr +Qmanure (3.7)
3.4 Radiative heat transfer
3.4.1 Radiative heat transfer to the sky
The sky is modeled as a black body at the temperature equivalent to
Tsky = 0.0552T 1.5amb (3.8)
With heat transfer from digester element i to the sky being
Qr,i−sky = σFiεiAi(Ti + Tsky)(T2i + T 2
sky)(Ti − Tsky) (3.9)
Having view-factor Fi = (1 + cos(βi))/2 for i ∈ gc, w1, w2.
3.4.2 Radiative heat transfer between model elements
The radiation heat transfer from one element of the system to another is expressed as
Qr,i−j = σAi(T 2j + T 2
i )(Tj + Ti)
(1−εj)Ai
εjAj+ 1
Fi−j+ (1−εi)
εi
(Ti − Tj) (3.10)
With (i, j) ∈ gc, w1, w1, gh2 or (i, j) ∈ s, gh2. Fi−j is the view factor from i to j.
23
3.4.3 Absorbed solar radiation
The solar radiation heat flux absorbed by the greenhouse cover is given by
Sgc = αgc·Agc · Igc,T (3.11)
And the solar radiation heat flux absorbed by each wall is
Sw1 = αw1 ·Aw1 · (Iw1,ext,T + τc · Fw1 · Iw1,int,T ) (3.12)
and
Sw2 = αw2 ·Aw2 · (Iw2,ext,T + τc · Fw2 · Iw2,int,T ) (3.13)
Where the ext subscript is used for the wall side in contact with ambient air, and the int subscript
for the wall side in contact with ambient air. The solar radiation heat flux absorbed by the gas
holder is:
Sgh = τc · αgh · Fgh ·Agh · Igh,T (3.14)
Fw1, Fw2, and Fgh are shading factors. The shading factor represents the percentage of solar radi-
ation directly striking the surface of the element. These are dependent on latitude and elevation.
3.5 Convective heat transfer
3.5.1 Convective heat transfer to ambient air
The convective heat transfer between an element of the greenhouse (cover and walls) and the
ambient air is expressed as
Qwind,i = hwind,iAi(Ti − Tamb) (3.15)
where i ∈ gc, w1, w2 For simplicity, the digester is treated as a flat plate and the convective heat
transfer coefficient of air (hwind) is calculated from the from the Nusselt number
NuL =hwindL
kair=
0.664Re12Pr
13 Re < 2× 105
0.037Re45Pr
13 Re > 3× 106
(3.16)
Re =UwindL
vair=ρair · UwindL
µair(3.17)
24
3.5.2 Convective heat transfer within the greenhouse
The air inside the greenhouse gains and loses heat by free convection along the two walls,
the greenhouse cover and the gas holder. The Nusselt number in those cases depends only on
heat transfer area orientation (in this study: horizontal, vertical and tilted) and the fluid / solid
temperature difference.
Qc,i−ga = hc,i−gaAi(Ti − Tga) (3.18)
Where i ∈ gc, w1, w2, gh. All convective heat transfer coefficient calculations are based on the
Nusselt and Rayleigh Number calculations
hc,i−ga = NuL ·kgaL
(3.19)
and
RaL =gβga(Ti − Tga)L3
αgavga(3.20)
For vertical plates, the characteristic length (Ls) is the plate height, and the Nusselt number is
NuL =hwindkair
=
0.68 + (0.67Ra
14L)/
(1 + (0.492/Pr)
916
) 49
RaL ≤ 109(0.825 + (0.387Ra
16L)/
(1 + (0.492/Pr)
916
) 827
)2
RaL > 109
(3.21)
For horizontal plates, the characteristic length (Ls) is the ratio between the plate area and perime-
ter. For the upper surface of hot plate or the lower surface of cold plate, the Nusselt Number is
expressed as:
NuL =hwindkair
=
0.54Ra14L 104 ≤ RaL ≤ 107
0.15Ra13L 107 ≤ RaL ≤ 1011
(3.22)
while for the lower surface of hot plate or the upper surface of cold plate:
NuL = 0.27Ra14L 105 ≤ RaL ≤ 1010 (3.23)
For plates inclined at angle θ from the vertical where 0 ≤ θ ≤ 60 and which are either the lower
surface of a hot plate or the upper surface of a cold plate, the calculations are the same as for a
vertical plate except that the Rayleigh number is calculated using g = g cos(θ). The characteristic
25
length is equal to the plate width. In all other cases the vertical plate calculations are used for
θ ≤ 60 and and the horizontal plate calculations for θ > 60.
3.5.3 Convective heat transfer within the digester headspace
The biogas contained in the gas holder can gain or lose heat by convection from the gas
holder and the slurry. To calculate the heat transfer, the gas holder is approximated as a horizontal
rectangular cavity with upper and lower plates at different temperatures (gas holder and slurry,
respectively) while the remaining surfaces are assumed to be insulated from the surroundings.
Qc,s−gh = hc,s−ghAi(Ts − Tgh) (3.24)
RaL = gβg(Ts − Tgh)L3
αgvg(3.25)
The characteristic length is the average height of the gas in the gasholder. For Ts > Tgh, the Nusselt
number is expressed
NuL =
h = kmL = 1 RaL ≤ 5× 104
0.06913Pr0.074m 3× 105 < RaL
(3.26)
3.6 Conductive heat transfer
3.6.1 Soil temperature
The soil temperature profile is modeled as
Tgr(z, t) = Tgr,av +A0e− z
d sin
[2π
365(t− t0)−
z
d− π
2
](3.27)
where Tgr(z, t) is the soil temperature at time t (days) and depth z (meters), Tgr,av is the average
soil temperature (C), A0 is the annual amplitude of the surface soil temperature (C), d is the is
the damping depth (m) of annual fluctuation expressed as d =√
2 ∝ ·3600 · 2ω , with ω = 2π/365,
∝= kρCp
and t0 equal to the time lag (days) from an arbitrary starting date to the occurrence of
the minimum temperature in a year.
26
3.6.2 Conductive heat transfer from the slurry to the ground
Conduction between the slurry and the ground is expressed as:
Qcd,s−gr =1(∑ k
δ
)As−gr(Ts − Tgr)
(3.28)
One ground temperature is considered for the digester base and another ground temperature is
considered for the digester sides, equal to the squared mean temperature between the surface and
the digester base using equation 3.27.
3.7 Mass flow heat transfer
Energy required to heat influent manure at Ts,in, to reach the required operating temperature
inside the digester is calculated as
Qmanure = mmanureCp,s (Ts,in − Ts) (3.29)
The model accounts for a regular digester feeding regime as a part of the inputs.
3.8 Solution algorithm
In order to solve the equations of the elements with thermal mass, finite differences are
substituted for the partial derivatives as
∂Ti∂t
=Ti(t+ ∆t)− Ti(t)
∆t=Tn+1i − Tnp i
∆t(3.30)
Where i ∈ s, w1, w2,∆t = 1 hour, and n is a given hour. The basic solution algorithm runs
iteratively as follows.
(1) Input all required information (digester dimensions, materials properties, weather condi-
tions, etc.)
(2) Assume values for Ts, Tw1, Tw2 for time n = 1
(3) Iterate to get Tgc, Tgh, Tga, Tg at time n = 1 using equations: 3.1, 3.2, 3.5, and 3.6
27
(4) Calculate Ts, Tw1, Tw2 for time n+ 1 using equations 3.3, 3.4, 3.7.
(5) Repeat this procedure from step 3.
The model is first run for 365 days in order to get approximate initial conditions for the digester
elements, and then another full 365 days to calculate the final temperature values in the digester.
3.9 Modifications
The original Perrigualt model was designed for use with a single-pitched roof (as shown in
figure 3.9), rather than a 2-pitch roof. Single-pitch roofs are a common configuration for these types
of digesters, particularly in Bolivia as described in Mart Herrero’s biodigester design guide[19]. In
collaboration with the author of the model, changes were made to the code in order to incorporate
the effects of having the 2-pitch roof instead of a single-pitch roof. Heat transfer between the
two covers was neglected for simplicity, but all other effects were calculated. A more in-depth
description of the changes to the model are found in chapter 5
Figure 3.9: General cross-section modeled in the original, single-sloped 1-d thermal model. Cour-tesy: Thibault Perrigualt
Chapter 4
Field Campaign/Data Collection
Put your faith in the two inches of humus thatwill build under the trees every thousand years.
Wendell Berry
- Manifesto: The Mad Farmer Liberation Front
During February and March of 2010, a 7 week field campaign was conducted in the highlands
of Peru and Bolivia to collect thermal data on digesters both in the field and in a laboratory
in Cusco, Peru. Most of the research took place at the K’ayra satellite agronomy and animal
husbandry campus of the Universidad Nacional San Antonio Abad del Cusco (UNSAAC). The
research on small-scale biodigesters there is done in association with GREDCH research group
from the Polytechnic University of Catalunia (UPC) in Spain. A research facility for testing this
technology was set up within the vermiculture and soil science compound at K’ayra over the span
of the last 5 years.
In addition to the laboratory work, a number of side trips were conducted to visit biodigesters
in the field, including 10 days in Bolivia and an overnight trip to the small mountain town of
Yanaoca, Peru. Although some temperature data was collected at 2 field sites, the majority of
the visits were for survey purposes only. The 30+ biodigester visits were conducted primarily to
note differences in construction techniques and materials in order to better inform the assumptions
and inputs to the thermal model. It was also a qualitative view of some of the technical and
societal difficulties in having complete and successful integration of biogas technology on rural
farms. However, only findings related to the verification of the thermal model are included here.
29
Figure 4.1: Nine sampling ports in the side of digester 4 at K’ayra
4.1 Facilities
Located about a 30 minutes outside of Cusco, the K’ayra campus of UNSAAC supports
approximately 500 students in the Agronomy and Animal Husbandry programs. The facilities
include classrooms, laboratories, barns, greenhouses, and crop fields. The majority of the students
are undergraduates, though there are a number of graduate-level students conducting research as
well.
4.1.1 Test digesters
The biodigester research facility at K’ayra has four full-scale test digesters, each with a
capacity of 2.5 cubic meters of liquid volume. They are located inside a large walled compound
which contains the compost, soils and vermiculture center. The digesters are each constructed of a
long, polyethylene tube bag set in a hand-dug trench lined with straw for insulation. A low-walled
adobe structure has been built over each digester, and covered with “agrofilm”, a common material
used in constructing greenhouses. The digesters are lined up side by side, for ease of access while
loading and mixing slurry in the inlet box. The outlet boxes of each of the digesters are plumbed
30
Figure 4.2: Interior view of one of the test di-gesters
Figure 4.3: Typical entrance and mixing box forthe digesters
to a canal which carries the liquid fertilizer effluent to a common holding tank where it is allowed
to settle, and is then applied to crops. One of the digesters was constructed with 9 ports in the
side for taking samples and temperature measurements (see figure 4.1). There is an in-line gas flow
meter for each of the four digesters that measure the rate of gas production of each digester which
has been used to measure the influence of different feedstocks on gas production.
4.1.2 Gas storage and combustion testing
After passing through the gas flow meters, the biogas produced by the test digesters is piped
into a 1 m3 flexible storage bag which is stored in a loft in the “kitchen” (burner testing laboratory).
Dispensing pressure is provided by a metal floating dome reservoir (similar to the dome in figure
2.2). Combustion and burner efficiency testing takes place at a station which is outfitted with two
burner ports for attaching the testing stoves. This facility was not used in the present study aside
from cooking the occasional lunch of boiled corn and potatoes.
4.2 Test equipment/sensors
As the main goal of the field campaign was to verify the existing thermal model (which pre-
dicts the temperature of the components of the digester), the majority of the equipment purchased
for this study was for collecting temperature data in and around the digester, although measure-
31
ments of wind and solar radiation were also necessary. Although some limited thermal experiments
had been done by researchers at K’ayra during a previous field campaign, they cited a lack of
equipment as a major obstacle. The following sections outline the equipment used in this study, all
of which was purchased in the U.S. and transported to Peru with the exception of the PCE T-395
4-channel thermocouple logger, which was graciously loaned by the GREDCH researcher team.
4.2.1 HOBOr UA-002-64 pendant temperature and light loggers
16 HOBOr brand pendant loggers were purchased for this project. Each logger has two
channels: light intensity, and temperature. The pendants are small and waterproof, and maintain
their hermetic seal when launching and reading out data, because data is transmitted through the
transluscent wall of the pendant to the docking station via infrared signal. The loggers each have
64 kilobytes of memory, which translates into approximately 28,000 samples. These loggers were
used for a number of different purposes including sampling air temperatures, surface temperature
of the walls, and slurry temperature (inside the digesters). For full specifications on these loggers,
see table A.1.
Figure 4.4: HOBOr Temperature/Light Inten-sity Pendant Logger
Figure 4.5: EKOr MS-602 Pyranometer used forsampling total horizontal radiation
32
4.2.2 EKOr MS-602 pyranometer
The pyranometer used in this study was originally purchased with a grant from the Engineer-
ing Excellence Fund (EEF) at CU Boulder, for a separate research project in Guatemala regarding
affordable solar hot water collectors. As that research project had concluded, the pyranometer was
employed in this study (see figure 4.5. The EKOr MS-602 is rated as a “Second Class” pyranome-
ter according to the ISO 9060 standards, though for the purposes of this research, it is of sufficient
accuracy and precision. Table A.2 in appendix A outlines the full specifications of the MS 602
Pyranometer.
4.2.2.1 Amplification circuit
Because the signal of the pyranometer is too weak for the standard range of most data
loggers (the pyranometer outputs a signal of 7 mV at 1000 W/m2), a circuit was built to amplify
the signal. The circuit is based around the INA122 instrumentation amplifier chip, a precision
op-amp used for sensitive applications like data acquisition. Gain can be adjusted by selection of
the external resistor. Figure A.2 in appendix A shows the circuit diagram including RC filters to
smooth the signal. This circuit was mounted inside the waterproof logger box described in section
4.2.7 and used in conjunction with the HOBOr 4-channel logger to collect the raw voltages. The
gain-adjusting resistor was selected at 974 Ohms for a calculated gain of 203. However, a simple
calibration test was carried out once the circuit was complete in which small signal voltages were
applied to the amplifier. The resulting output was 218.8 times the input, which means the circuit
actually amplifies the signal to produce an output of roughly 1.5 V at 1000 W/m2. This is well
within the 0-2.5 V range of the HOBOr U12-006 data logger described in section 4.2.5.
4.2.2.2 Calibration
In order to verify the accuracy of the pyranometer, amplification circuit, and data logger
setup, a simple post-mission calibration was carried out against a Kipp & Zonen CMP-3 second class
pyranometer at CU Boulder’s on-campus Skywatch meterology station (http://skywatch.colorado.edu/).
33
The EKOr MS-602 pyranometer was set up on a level surface approximately 2 feet away from the
Skywatch station’s pyranometer. Data was collected on 10 second intervals over a span of 5 days,
then linearly interpolated so that the timestamps of the MS-602 data matched those of the Sky-
watch system. Plotting the raw voltage outputs of the MS-602 pyranometer against those of the
Kipp & Zonen CMP-3 pyranometer yielded the plot shown in figure 4.6. Upon inspection, the
radiation values are seen to deviate from linear in lower ranges of the instruments. It was deter-
mined (by inspecting the ratios of the two signals over the time series) that these erroneous points
occurred every morning very near sunrise, and probably represent uneven shading from far away
buildings due to the horizontal spacing difference in the instruments. As the relevant data for this
study occurs in the higher range of the instrument, a second plot was made in which the data below
265 W/m2 and 0.4 Volts was discarded in order to filter out the experimental error and to develop
a more appropriate linear fit to the data.
Figure 4.6: Raw Voltages of MS-602 plottedagainst Skywatch’s Kipp & Zonen CMP-3
Figure 4.7: Modified calibration curve with erro-neous data removed
From the pyranometer’s calibration cerficate and the gain setting on the instrumentation
amplifier, the linear response of the system was calculated to be 642 W/m2 per Volt. By fitting a
line to the data (and forcing it through the origin), the linear response was calculated to be 652
W/m2 per Volt (as shown in figure 4.7). The linear response is reasonably close (within 1.7%), and
verifies that the equipment is functioning and its signal is amplified correctly.
34
4.2.3 Davis anemometer and wind vane
Figure 4.8: Anemometer and pyranometer mounted on a post near the digester
For collecting wind speed and direction, a Davis standard cup anemometer was mounted on
a post 1.8 meters off the ground near the biodigesters to get a representative sample of windspeed
in the area. The anemometer circuitry consists of a small, stationary reed switch and a rotating
magnet which closes a circuit once every rotation of the cups. Because of the high cost of the OEM
counting and data logging equipment, it was decided that the a simple electronic circuit be built
that converts a signal of electrical pulses into an analogue voltage. This circuit is based on an
LM2907 frequency to voltage converter chip, along with some simple RC filters to clean the output
signal. Figure 4.9 shows the completed circuit, and figure 4.10 shows a simple calibration curve
relating output voltage to frequency. Refer to figure A.1 in appendix A for the circuit diagram.
The anemometer is factory calibrated such that the rotation (in revolutions per second) is
approximately equal to the wind velocity in m/s. In other words, a rotation speed of 1 Hz is
equivalent to a wind velocity of 1.006 m/s. The sampling interval for all meterology during this
study was 30 seconds. While this is not ideal for capturing the instantaneous variability of wind
speed, since the data is averaged over one hour it should be suitable for the purposes of this study.
Figure 4.11 shows a wind rose plot of the data collected during this study.
35
4.2.4 Wind vane counter circuit
Figure 4.9: The completed frequency to voltagecircuit
Figure 4.10: Calibration curve for the wind vanecounter circuit
The wind vane is integrated with the Davis Anemometer and consists of a variable resistance
potentiometer which turns as the wind shifts direction, keeping the vane pointed into the wind.
The HOBOr U12-006 sends out a reference 2.5V pulse to all channels just before sampling a data
point. The variable resistor in the wind vane will return a voltage proportional to the direction the
wind is blowing. A simple circuit was built which takes advantage of the 2.5 volt excitation current
put out by the U12-006 HOBOr logger to run a current through the resistor just before recording
a sample (see figure 4.13). A simple onsite calibration of the vane with a needle compass allows a
particular voltage to be associated with a compass heading.
4.2.5 HOBOr U12-006 4 channel data logger
This 12-bit logger has 64 kilobytes of memory and has 4 inputs, which can record a 0-2.5V
analog input. Complete specs are shown in table A.3 in appendix . For this study, only 3 channels
were used: one for the wind vane (wind direction), one for the cup anemometer (wind speed), and
one for the pyranometer (solar radiation). The pyranometer amplification circuit required a power
supply, so the onboard HOBOr excitation voltage was wired into the circuit. To save battery, the
logger applies a 2.5V from a short time before to a short time after taking each measurement (see
36
Figure 4.11: Wind Rose plot of direction and intensity of wind during the study period with digesterorientation overlayed
figure 4.13). The logger was housed in the weatherproof box, along with the circuitry and power
supply for the anemometer/wind vane. See section 4.2.7 for a description of the housing.
4.2.6 HOBOr U12-013 temp/RH/2 external data logger
This logger was used for collecting ambient temperature and relative humidity, and soil
temperature (using external probes) at 70cm below the surface, and at 5 cm below the surface.
Aside from the differences in channels, the characteristics are very similar to those of the U12-006
logger.
4.2.7 Weatherproof housing
In order to house the signal-processing electronics and data loggers and keep them out of
the elements, a protective box was fashioned out of a watertight camera case. The circuitry for
37
Figure 4.12: HOBOr U12-006 4-Channel datalogger
Figure 4.13: External instrument voltage exci-tation plot (grey band represents the period forwhich a measurement is taken)
the pyranometer, anemometer, and wind vane were all housed inside, as well as a 9 volt battery
pack. Penetrations through the side (shown in figure 4.15) were made as waterproof as possible.
On site, the box was secured inside another lockable box to ensure the temperature of the circuitry
remained fairly steady.
Figure 4.14: Signal processing circuitry mountedinside the logger box
Figure 4.15: Penetrations in the side of the loggerbox
4.3 Experimental setup
The goal of this verification experiment and the fundamental objective of the field campaign
was to capture both the local ambient climatological conditions and, simultaneously, a represen-
tative sample of temperatures within the digester to ascertain the thermal performance of the
digester over time. First, the climatological data is input into the existing 1-dimensional model,
38
and model outputs are then compared with the experimental results to determine the effectiveness
of the model.
In order to capture the temperatures inside the digester, the HOBOr pendant loggers (which
are buoyant) were tied at specific lengths along 3 strings, each weighted at the bottom and tied to
a central cord. Then, in a method quite like inserting a three masted ship into a bottle, the strings
of sensors were pushed into the digester with a semi-rigid length of PVC tubing. Once inside the
digesters, the 3 strings floated upright in the slurry, collecting temperatures for the bottom, middle
and surface. Figure 4.16 shows the locations of the temperature loggers during the study period
and cross-sectional digester dimensions. Figure 4.17 shows a side view of the placement of the
pendant loggers laterally inside the digester.
Figure 4.16: Dimensions of the digester cross section and approximate locations of the temperaturesensors during the study
Figure 4.17: Approximate locations of the pendant temperature sensors ine slurry during the study
39
4.4 Preliminary data
The following plots show the data as it was collected on site during a study period of 5 days,
averaged on an hourly interval.
Figure 4.18: Plot of ambient air temperature
Figure 4.19: Plot of wind speed at 1.8m off theground near digester
Figure 4.20: Total Horizontal Solar Radiation atthe site
40
Figure 4.21: Plot of all 9 internal pendanttemperature sensors corresponding to figure 4.17
Figure 4.22: Average temperatures for top three,middle three, and bottom three sensors in figure4.21
Figure 4.23: Temperature of the greenhouse airduring the study period
Figure 4.24: Temperature of the gas in theheadspace (gas holder) during the study period
41
Figure 4.25: Temperature of the soil 5 cm belowthe surface and 70 cm below the surface duringthe study (logger malfunction beginning March24)
Figure 4.26: Temperature at digester wall insideand outside the straw insulation at 35 cm depth,halfway between the entrance and the exit
Figure 4.27: Interior and exterior surface tem-peratures of the Southeast adobe wall during thestudy period
Figure 4.28: 9-point weighted average of the di-gester slurry temperature, with the temperature35 cm below the surface of the digester, on theinside of the insulation as point of comparison
42
4.4.1 Weighting of internal digester temperatures
Rather than averaging the 9 internal digester temperatures by a simple arithmetic mean, a
weighting system was developed to give greater influence to the sensors in the middle of the fluid
as shown in figure 4.29. This is because the top and bottom sensors are very near surfaces at which
heat transfer happens with another medium, and are thus influenced by those other media. The
calculated area weighting percentages are: 11.4% for the bottom, 69.2% for the middle, and 19.4%
for the top.
Figure 4.29: Weighting areas for the 3 sensor heights
4.4.2 Estimation of direct and diffuse radiation components
The insolation data captured by the EKOr MS-602 pyranometer used in this study is a
record of the total global radiation falling on a horizontal surface. The Perrigault model requires
diffuse and beam components in order to calculate the radiation incident on the surfaces of the
digester. Several models have been presented which approximate direct and beam components of
the global radiation from total horizontal radiation. Recently, a number of different models for
determining beam and diffuse components were evaluated [46]. The authors found that for hourly
values, the models that account for dynamics (sun angle) and persistence yielded the best results.
Hence, the Boland-Ridley-Lauret (BRL) model was chosen for calculating the diffuse fraction of
the solar radiation for this study. According to the BRL model, the diffuse fraction, kd, is defined
by equation 4.1.[36]
43
kd =1
1 + e−5.38+6.63kt+0.006AST−0.007αs+1.75Kt+131ψ(4.1)
Where:
kt is the hourly clearness index
AST is the apparent solar time, in decimal hours
αs is the solar elevation angle, in degrees
Kt is the daily clearness index
ψ is the persistence factor, defined as an average of the lag and lead of the clearness index:
ψ =
kt+1+kt−1
2 sunrise < t < sunset
kt+1 sunrise
kt−1 sunset
(4.2)
The diffuse fraction, kd was calculated from the insolation data collected in the field. Solar elevation
angle, total hourly and daily extraterrestrial radiation (used for calculating clearness indices), and
AST were all calculated using the University of Oregon’s Solar Radiation Monitoring Laboratory’s
online calculator. Direct (or beam) radiation was calculated simply by subtracting the diffuse
radiation from the total. Figure 4.30 shows a plot of the direct, diffuse, and total global radiation.
Figure 4.30: Direct, diffuse, and total horizontal radiation during the 5 day study period
Chapter 5
Model Verification and Parametric Analysis
The longer I live the greater is my respect formanure in all its forms.
Elizabeth von Arnim
The primary benefit of having a thermal model of affordable polyethylene tube digesters is
to aid in making decisions for their design and construction. To that end, the following chapter
describes the verification of a 1-Dimensional thermal model.
5.1 Modifications to the model
The original Perrigault model was coded and commented in Spanish. As a first step for
understanding the model, it was translated into English line by line. This allowed for a detailed
view of the model assumptions, and operating procedure.
Next, as a full annual simulation took 5 hours to run, some changes were made to the code
to optimize it for speed. A number of unnecessary loops were had been nested in the calculation of
solar radiation incident on each element of the digester; a little re-arrangement of the code allowed
for a reduction in the number of calculations by roughly 80 million. Furthermore, as the view
factors and incident solar radiation calculations take place on every run, by calculating them once
and saving the data for cases in which geometry and weather conditions did not change, run time
was reduced to one minute per simuluation. As the original model considers a digester with a
single-pitched roof, the code was modified with the help of the original author to include double-
pitched roofs, similar to the ones being built in the Peruvian altiplano. The process for accounting
for a double-pitched roof was primarily a theoretical exercise, and the fundamental energy balance
45
Figure 5.1: Surface reference for view factor calculations
equations were not changed. First, the roof was split into two different sections and view factors to
the other digester elements were calculated for each. These factors were then summed to get the
total view factor from the cover to each element. For instance: referring to figure 5.1, the updated
view factor from the cover (2 and 3) to wall 1 is simply
F23−1 = F2−1 + F3−1 (5.1)
Although the original author solved equations for determining view factors from fundamental ge-
ometric cases, the complications of changing these equations to include the second pitch would
have been time prohibitive, so a Matlab function called ViewFactor was used (written by Nicolas
Lauzier), which calculates view factors for any two planes.
Incident solar radiation was modified so as to be calculated individually for each pitch, and
then summed to get the total incident solar radiation for the cover. Convection and radiation were
treated the same as before (as the fundamental angles do not change), with simple modifications
to alter the area used in the calculations. The only major assumption made when making these
changes was to neglect heat transfer between the two covers.
46
5.2 Model adjustment/calibration
5.2.1 Comparison: single pitch vs. double pitch
Using the statistical-year meteorology data from the original model but the geometry for the
actual experimental digester, a comparison was made between the single-pitch and double-pitch
roof configurations, for an arbitrary period in the month of March (similar to the time period
of this study, for comparison). The gabled roof (double pitch) was about 2 degrees warmer on
average than did the the shed roof (single pitch). This is because the main axis of the digester runs
roughly Northeast/Southwest, and thus having a high wall on one side shades the digester for a
large portion of the day.
Figure 5.2: Comparison of single pitch vs. double pitched roof on digester, 30 degree slope
5.2.2 Substitution of meteorology data
Because the model requires a full-year simulation to run, the original data file with Cusco
Meteonorm data was kept, and the data collected on site was inserted into the file in the proper
location. This includes ambient temperatures from March 5 to March 30, and wind speed and
47
solar radiation from March 13 to March 30. As shown from figure 5.3, the predicted temperatures
are much higher than actual temperatures, and are seen to be climbing steadily from the point at
which the on-site meteorology was inserted into the weather file. Further investigation into this
issue is outlined below.
Figure 5.3: Plot of modeled slurry temperature and weighted average of experimental data
5.2.3 Correction of wind data and thermal lag
In order to determine the cause of this instability, the weather data was inspected. The
first discovery was that the original model used monthly averaged wind speeds for the local Cusco
airport at 10 meters of height. In other words, during times outside the study period, the model
uses very high wind-speeds in its simulation of the forced convection on the outside of the digester.
Once the study period begins, wind speed values are much lower, and thus convective losses are
less and the modeled slurry temperature floats upwards towards some higher temperature regime.
To remedy this problem, the monthly average values were normalized to experimental data using
the month of March. The ratio of the average wind speed at the Cusco Airport to the average wind
speed at the K’ayra research station during march was roughly 16. Figures 5.4 and 5.5 show the
48
original and corrected annual hourly wind data.
Figure 5.4: 8760 hourly plot of wind speed usedin first model run
Figure 5.5: Normalized 8760 hourly plot of windspeed used in subsequent model runs
5.2.4 Comparison of ambient temperature
An examination of the ambient temperatures collected on site showed that maximum tem-
peratures were consistently quite high for normal temperatures in this climate. While this can
sometimes be explained by an anomalously hot experimental period, a comparison with ambient
temperatures from the Cusco airport (just 7 km away) during the study period showed that the
ambient temperatures collected onsite were more than 5 to 10 C warmer than at the airport.
Due to a shortage of loggers, the ambient temperature measurement was taken as the internal
temperature channel from the HOBO U12-013 data logger, which was also employed for taking
soil measurements. Because of this, the logger was placed low to the ground, near the inlet box to
the digester where it received radiation from a number of surfaces that were in the direct sunlight
in the afternoons. As a point of comparison, the Senamhi high and low temperatures (Senamhi
stands for “Servicio Nacional De Meteorologia E Hidrologia Del Peru”, of which the Cusco data
is collected at the K’ayra campus) were plotted along with the onsite and Cusco airport ambient
temperatures. Although the ambient temperature data from the Cusco airport is not of the best
49
Figure 5.6: Plot of onsite measured ambient temperature with ambient temperature observationsfrom the Cusco airport during 5 day study period
quality, it is likely more accurate than the temperatures collected onsite, judging by the Senamhi
high and low recorded temperatures. Because of this, temperature data from the Cusco airport
was substituted in the weather data file for the onsite measured data for subsequent runs.
After making the above changes to the weather file, the model was run once more, this time
apparently reaching some stability (rather than continually increasing during the study period),
albeit at still higher than expected values. Figure 5.7 shows the results.
5.2.5 Examination of material property assumptions
With modeled results still higher than experimental values, the listed material properties and
sources for these values were reviewed. Although the majority of the values appeared reasonable,
the thermal conductivity of the straw seemed low. As the model’s original creator could not locate
a value for the thermal conductivity of straw, he selected a value of 0.065W/m −K, which is on
the order of typical building insulation (fiberglass batt or cellulose). In reality, however, the straw
is compacted a great deal from the weight of the slurry in the trench. According to Apte et. Al,
50
Figure 5.7: Plot of modeled slurry temperature and weighted average of experimental data withupdated weather file
the thermal conductivity of compacted straw bales is 0.32W/m−K, or a factor of 5 greater than
the thermal conductivity originally used[2]. Figure 5.8 shows the model results as compared to the
observed values once thermal conductivity of the straw has been updated to the value found in the
literature. Now the experimental and modeled data are much closer to one another.
5.2.6 Adjustment of insulation to calibrate model
In order to compare the results more closely, the model was calibrated using a parametric
run on the thickness of straw insulation, to match the 5-day averages as closely as possible. By
increasing the straw insulation thickness by 10% over the intially chosen values, a close match
was found, as shown in figure 5.9. Although the model seems to have a higher capacitance (lower
magnitude temperature swings and slower reaction time) than the experimental setup, it generally
follows the daily and nightly diurnal swings, and is within a similar order of magnitude variance.
Unfortunately, the data acquired for the biodigester doesn’t cover a wide enough range of weather
variability to make this a robust calibration. This was due mainly to time and budget constraints
51
Figure 5.8: Plot of modeled slurry temperature and weighted average of experimental data withupdated weather file and revised straw thermal conductivity
Figure 5.9: Plot of modeled slurry temperature and weighted average of experimental data aftercalibrating using the thickness of straw insulation
for the field campaign. However, the model’s usefulness does not necessarily lie in precise prediction
of results, but rather in the general characterization of the influence of different design factors. In
52
the next section, some of these design factors are explored.
5.3 Heat Transfer Diagrams
In order to more fully understand the thermal heat transfer processes in play in this system,
the following two diagrams were made based on the model outputs showing the average heat transfer
occuring at each boundary of the digester with the ambient environment.
Figure 5.10: Annual average heat transfer with the ambient environment at every surface for theshed-roof digester (for the study digester in Cusco)
Figure 5.11: Annual average heat transfer with the ambient environment at every surface for thegable roof digester (for the study digester in Cusco)
53
5.4 Parametric studies
The following parametric runs are based solely upon the digester tested in Cusco, Peru. This
means they may only be valid for the Cusco climate and for this particular configuration of digester.
However, the results should be suggestive of the relative influence of various design parameters for
cold climate solar-assisted digesters built with similar materials.
5.4.1 Insulation
The design parameter which perhaps most greatly influences average slurry temperatures is
the thickness of insulation along the bottom and sides of the trench. For this parameterization, it
is assumed that the insulation material is compact straw, and that it is the same thickness both
in the bottom and along the sides of the digester. Figure 5.12 shows the effects that changing the
amount of straw insulation has on annual average temperature.
Figure 5.12: Plot of average modeled temperature increase (over average ambient temperature)with parameterized insulation
54
5.4.2 Cover transmissivity
One significant downfall of using an inexpensive material such as agrofilm for the green-
house cover is that the sun’s rays can degrade the material, decreasing the transmissivity. On
visual inspection, the covers on the test digesters that had been sitting in the sun for over a year
appeared significantly cloudier than the digester with new agrofilm plastic. This degradation of
visual transmittance certainly affects the performance of the digester, as more sunlight is reflected
and absorbed by the cover rather than allowing it to pass through. While new agrofilm has a visual
transmittance of 0.65, a significantly degraded material could have transmittance as low as 0.55 or
0.5. Figure 5.13 shows the effect that changing the visual transmittance of the cover has on average
temperature rise above the ambient (as compared to the T=0.65 case).
Figure 5.13: Plot of average modeled temperature increase (over average ambient temperature)with parameterized cover transmittance normalized to the transmittance of new agrofilm (0.65)
5.4.3 Tube material
There are several materials from which the tubular bags (containing the slurry and gas) can
be made. They vary in price as well as in durability, and also have different material properties
55
such as thickness, transmissivity, and absorptivity. The experimental digester in Cusco was made
of “Geomembrane,” which is a thicker black material specially welded for the purpose of building
this test digester. Although it will likely last much longer than polyethylene or Agrofilm, it is also
much more expensive. Figure 5.14 shows the relative temperature rise over ambient temperatures
that is acheivable using each material. As expected, the clear agrofilm performs the best, because
it allows sunlight to penetrate directly to the surface of the slurry. The geomembrane performs
second best because it is black, and there for highly absorptive. The LDPE plastic is fairly opaque,
but doesn’t absorb nearly as much radiation as the geomembrane, and so it is reasonable to expect
that it will not perform as well.
Figure 5.14: Bar chart of average modeled temperature increase (over average ambient temperature)comparing three common tube materials
56
5.4.4 Parametric Studies: Limitations
There are a number of limitations to the Perrigault thermal model, which reduce its effective-
ness for determining certain optimal design characteristics. First, the model is one-dimensional,
which means that each element is modeled as a single temperature. For the thermally massive
elements in which conduction plays a large role in heat transfer (slurry, walls, and ground), this
is an over-simplification. In reality, there are dynamic temperature gradients through these ele-
ments that affect the overall performance of the model. For instance, adobe walls should produce
a thermal lag as the wall heats up on one side and then slowly moves through the wall. This
should produce a phase shift similar the one shown in figure 5.15 (the cement block is analogous
to adobe–both are thermally massive).
Figure 5.15: Diagram showing the concept of thermal lag associated with thermally massive walls[3]
57
In order to improve the model’s ability to capture the system’s thermal mass effects, an
attempt was made to improve the way it calculates conduction through the walls. Rather than
rebuilding the model with multiple temperature nodes in the walls, (which would involve a signif-
icant restructuring of the code), thermal resistance values for the adobe walls were incorporated
into the internal and external convective heat transfer coefficients, which are already calculated by
the model. The thermal resistance of the wall was divided into two parts as in figure 5.16, and half
of the resistance was incorporated into the internal convective heat transfer coefficient (hconv,int)
and half was incorporated into the external convective heat transfer coefficient (hconv,ext) using
equations 5.2 and 5.3.
hint =1
Rcond,int + 1hconv,int
(5.2)
hext =1
Rcond,ext + 1hconv,ext
(5.3)
Where Rcond = kadobeL .
Figure 5.16: Model modification to incorporate wall resistance
58
Unfortunately, this solution does not seem to affect model results significantly. Figures 5.17
and 5.18 show a parameterization of adobe wall thickness both before and after the changes to
thermal resistance in the wall was made.
Figure 5.17: Plot of average modeled tempera-ture increase (over average ambient temperature)with parameterized adobe wall thickness beforechanges to wall thermal resistance in the model
Figure 5.18: Plot of average modeled temperatureincrease (over average ambient temperature) withparameterized adobe wall thickness after changesto wall thermal resistance in the model
One would expect to see some positive contribution to digester performance as wall thickness
is increased to a certain point, then dropping off as the thermal lag of the wall becomes too great
and the mass’s dampening effects overpower its beneficial lag. If the model was improved to include
even just two nodes (interior and exterior), it is likely that the benefits of the thermal mass effects
of the walls could be seen in the model results.
Another instance where the simplicity of the model was unable to capture more complex
physics was in the parameterization of azimuth. Figure 5.19 shows that there are advantages to
orienting the digester in a particular direction based on best annual performance. The undulation
in each of the plotted points represent the effects that typical daily weather patterns can have an
impact on overall performance. It is also easy to see that the single-pitched roof performs more
poorly when it is facing towards the west, because its high back wall shades the rest of the digester
during the sunny morning period (rain showers typically come during the afternoons during the
59
wet season). However, one would expect that the single-pitch roof would have a higher optimal
performance than the double-pitched roof simply because of solar access. The issue here is that,
because the model does not correctly deal with thermal mass issues, the single-pitched roof performs
more poorly since it has a greater amount of surface area (because of the higher back wall) than
the two-pitch roof digester where both walls are the size of the shorter front wall. In reality, this
wouldn’t necessarily be a detriment to performance, but the model simply interprets greater surface
area as greater potential for heat loss without accounting for the benefits of thermal lagging.
Figure 5.19: Plot of average modeled temperature increase (over average ambient temperature)with parameterized digester orientation for single pitch and double-pitch roofs
5.4.5 Parametric Studies: Conclusions
The parametric analysis of biodigester design characteristics using a simplified thermal model
has certain limitations. Relative comparisons of the effects of non-massive elements of the digester
(such as the cover material, insulation, and tube material) yield reasonable results, and give some
insight into solving some design questions. However, in order to determine optimal geometries for
more complicated aspects of the digester such as thermal mass and storage, a more advanced heat
transfer model is needed. Recommendations for future work in this area are included in the next
chapter.
Chapter 6
Conclusions
We will not change the world merely because wecan generate biogas. Rather, we face the moredifficult problem of generating hope, peace, justice– and even, outworn as the word may be, love.
David House - The Biogas Handbook
In this study, the thermal performance of solar assisted biogas digesters for cold climates
was explored through the verification of an existing thermal model and by subsequent parameter-
izations of different design criteria. It is shown that, while it doesn’t produce results with a high
degree of accuracy, a 1-dimensional thermal model can predict diurnal termperature fluctuations in
slurry temperatures and overall temperature of the slurry within reasonable magnitude of temper-
ature swings. Most importantly, however, different design characteristics can be modeled so that
recommendations for design and construction can be made.
6.1 Factors influencing solar-assisted digester performance
The following factors are shown to have an effect on the annual average slurry temperature
within a digester
• Orientation - Depending on the climate and the roof design, it is possible that the optimum
orientation is a value other than due south (or due north, if in the southerm hemisphere)
• Insulation thickness - The thicker the insulation, the better the thermal performance of the
digester
61
• Visible transmittance of the cover - As transmittance degrades with exposure to the sun’s
UV rays, the overall temperature of the digester can decrease by up to 2 C depending on
the degree of degradation.
• Tube material - the best material from a thermal performance standpoint is a clear one,
so that the sun’s radiation can directly penetrate to the slurry. Heavy, dark materials also
perform well. Thin, opaque materials (like blue LDPE plastic) perform the most poorly.
6.2 Future work: experimentation
Although the model was seen to predict digester temperatures within a short time-period
with some accuracy, the true ability of the model to predict digester temperatures across a wide
range of climatic and ambient temperature conditions is unknown. To more fully understand the
system, further experiments should be done in different climates, and over broader ranges of time
to encompass greater variability in weather conditions.
6.3 Future work: models
The model developed by Thibault Perrigault is a good first step in advancing the understand-
ing of the thermal performance of these simple digesters. It has proven useful in predicting with
some accuracy the digester slurry temperatures in a given climate as well as the relative impact
of different design parameters. However, it has its limitations. Assuming a single temperature for
each element of the model does not capture some of the more complex physical phenomena occuring
within the digester. For instance, the walls have a temperature gradient from the inside (warmer)
to the outside (cooler). This gradient is not considered in the model, but it certainly effects the
results. Also, there is stratification of the temperatures within the slurry and the greenhouse air
that is not captured in this model. Furthermore, the slurry should be modeled as a multi-phasic
substance, as the solid particles tend to settle to the bottom of the digester near the exit, and have
different thermal properties from the rest of the slurry.
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Another aspect of the model that could stand improvement is in its configurability. Due to
its simple nature, the model can only be configured to simulate two very basic tubular digester
geometries. However, there are many other greenhouse digester designs that exist, and it would be
helpful to be able to compare performance of those different designs as well.
The following recommendations are given for future work in thermal modeling for small-scale,
solar-assisted plug flow digesters for cold climates. Future modelling efforts should:
• take into account 3-dimensional thermal effects, including entrance and exit effects and
sidewall shading.
• address slurry and greenhouse temperature stratification.
• include the ability to model more complex geometries.
Although this model was intended solely for the purpose of academic research, it is conceivable
that other stakeholders might be interested in using this model as well. In order to improve the
usability and make the model accessible to a wider audience, it should:
• interface easily with a global weather database to allow the model to be run for a number
of different climates
• include a wide array of construction materials and material properties to choose from
• include a graphical user interface
• incorporate some basic biogas output modeling based on anticipated organic material,
loading rate, temperature, etc.
6.4 General design recommendations
Based on the results of the model parameterizations and from observations during the field
work, the following recommendations can be made to improve the design of this type of digester:
• include drainage especially to protect organic insulation material
63
• develop a method to prevent insulation from compacting
• change cover material as the visual transmittance fades, and before it develops holes which
can let in water
• when replacing covers, do not simply add another cover or keep the second for protection.
As the transmissivity decreases, so does digester performance
• For North-South axis digesters, a gable roof (two pitch) will give the best performance. For
East-West axis digesters, a shed roof (single pitch) will give the best performance.
6.5 Closing summary
While Rickover’s point that fossil fuels are providing modern human beings with unprece-
dented energy wealth remains very poignant, technologies such as small-scale anaerobic digesters
have promise to be able to provide an energy alternative for the world’s rural poor. As this tech-
nology improves and becomes more affordable, greater numbers of farmers in colder climates can
take advantage of this renewable, clean-burning fuel source. While there is still much improvement
needed in both the social and technological aspects of biodigesters, one can take comfort in the
fact that there are currently many NGOs, governments, academics, and biogas-tinkerers all over
the world working to improve this technology.
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Appendix A
Reference
Figure A.1: Circuit diagram for the frequency to voltage counter
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Figure A.2: Circuit design for the pyranometer signal amplifier
69
A.1 Equipment specifications
Measurement rangeTemperature: −20 to 70C(−4 to 158F )Light: 0 to 320,000 lux (0 to 30,000 lumens/ft2)
AccuracyTemperature: ±0.47C at 25C(±0.85F at 77F )Light intensity: Designed for measurement of relative light levels
Resolution Temperature: 0.10C at 25C(0.18F at 77F )
Drift Less than 0.1C/year (0.2F/year)
Response timeAirflow of 2 m/s (4.4 mph): 10 minutes, typical to 90%Water: 5 minutes, typical to 90%
Time accuracy ± 1 minute per month at 25C(77F )
Operating rangeIn water/ice: −20 to 50C(−4 to 122F )In air: −20 to 70C(−4 to 158F )
Water depth rating 30m from −20 to 20C(100ft from −4 to 68F )
Battery life 1 year typical use
Memory UA-002-64: 64Kbytes (approximately 28K samples)
Materials Polypropylene case; stainless steel screws; Buna-N o-ring
Weight 18 g (0.6 oz)
Dimensions 58 x 33 x 23 mm (2.3 x 1.3 x 0.9 inches)
Table A.1: Specifications for the UA-002-64 waterproof pendant loggers
Specifications MS-602 / MS-601F
ISO 9060 classification Second class
Response time 95% 17 (sec)
Zero offset - Thermal radiation (200 W/m2) + 10 W/m2
Zero offset - Temperature change (5 K/hr) ± 6 W/m2
Non-stability (change/year) -1.70%
Non-linearity (at 1000 W/m2) ± 1.5%
Directional response (at 1000 W/mW/m2) ± 25 W/m2
Spectral selectivity ( 0.35− 1.5µm ) -1.10%
Temp. response (for 50C band) < ± 2%
Tilt response (at 1000 W/m2) < ± 2.0%
Sensitivity (mV/kW/m2) 7.12
Impedance (Ω) 20 to 140
Operating temperature (C) -40 to +80
Cable length 10 m
Wavelength range (more than 50% of transmittance) 305 to 2800 nm
Table A.2: Specifications for the EKO MS-602 Pyranometer used in this study
70
Measurement range External input channels: 0 to 2.5 DC Volts
Accuracy±2mV ± 2.5% of absolute reading±2mV ± 1% of reading for logger-powered sensors
Resolution 0.6 mV
Time accuracy ± 1 minute per month at 25C(77F )
Operating range −20 to 70C(−4 to 158F )
Humidity range 0 to 95% RH, non-condensing
Battery life 1 year typical use
Memory 64Kbytes (approximately 43,000 12-bit measurements)
Weight 46 g (1.6 oz)
Dimensions 58 x 74 x 22 mm (2.3 x 2.9 x 0.9 inches)
Table A.3: Specifications for the HOBO U12-002 data logger