MODELLING THE TEMPERATURE OF A COMPOST MICROREACTOR IN
ISOLATION
by
Mitchell Hawse
B.Sc., University of Northern British Columbia, 2016

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
IN
PHYSICS

UNIVERSITY OF NORTHERN BRITISH COLUMBIA
April 2020
© Mitchell Hawse, 2020

UNIVERSITY OF NORTHERN BRITISH COLUMBIA PARTIAL
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Title of Project/Thesis/Dissertation:

MODELLING THE TEMPERATURE OF A COMPOST MICROREACTOR IN ISOLATION

Author

Mitchell Hawse
April
Printed Name

Signature

Date 2020

Abstract
A mixture of waste-wood biomass and municipal biosolids waste was composted
in a plastic container inside of an insulated chamber. The mixture of biomass and
biosolids was approximately 50:50 and weighed 82.6 kg. The peak temperature of
the compost was 32.4◦C. The small scale of the compost system allowed the lower
limit of the compost decomposition rate to be studied. A model was successfully
developed to predict the core temperature of the compost using the ambient temperature in the insulated chamber. A literature review was conducted to determine
literature values for the overall convective and conductive heat transfer coefficient,
the dry mass fraction, and heat of combustion for both biomass and biosolids. The
model used an optimization algorithm to calculate the rate constant for the experimental setup. The calculated decomposition rate constant was 0.0525 Day−1 .

3

TABLE OF CONTENTS

Abstract

3

Table of Contents

4

List of Tables

5

List of Figures

6

List of Definitions

7

Acknowledgements

9

1

Introduction and Background
1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3
Compost Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10
10
11
11
11
13
15

2

Model Theory
2.1
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Numerical Algorithm . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Bounding Qloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17
17
21
21

3

Experimental Methods
3.1
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
Model Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4
Experimental Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24
24
27
28
31

4

Results and Discussion
4.1
Model Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2
Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3
Alternative Modelling Approaches . . . . . . . . . . . . . . . . . . .

33
33
35
36

4

4.3.1 Time Dependent Rate Constant, K . . . . . . . . . . . . . . . .
4.3.2 Two Bacteria Population Model . . . . . . . . . . . . . . . . . .
Computer Modelling Methodology . . . . . . . . . . . . . . . . . . .

37
38
40

Conclusion and Future Work
5.1
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2
Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41
41
42

A Calculations
A.1 Tsurf ≈ Tamb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Qloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46
46
48

4.4
5

5

LIST OF TABLES

2.1

Physical Parameters for Calculating ∆Tamb . . . . . . . . . . . . . . .

23

3.1

Physical Parameters for Modelling . . . . . . . . . . . . . . . . . . .

30

A.1

Physical Parameters for Calculating Qloss

49

6

. . . . . . . . . . . . . . .

LIST OF FIGURES

3.1

Diagram of experimental compost container showing thermocouple locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1

The measured temperature at the centre of the compost (-o-) along
with error bars, the predicted temperature based on the model (- -)
including error bars, the measured ambient temperature (.-) along
with error bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Residual values (o), measurement error (–) . . . . . . . . . . . . . .
Time dependent decomposition rate obtained from fitting model to
experimental data using handpicked values. . . . . . . . . . . . . . .
Two microorganism population fit (–) to experimental data (o) with
error bars, k1 = 0.0342, k2 = 0.3147 . . . . . . . . . . . . . . . . . . . .

4.2
4.3
4.4
A.1
A.2

Heat transfer diagram . . . . . . . . . . . . . . . . . . . . . . . . . . .
Insulated room diagram . . . . . . . . . . . . . . . . . . . . . . . . . .

7

25

35
36
38
39
47
48

LIST OF DEFINITIONS
The following definitions are provided to build a language with which to discuss the research and are defined by the author.

Municipal Biosolids or Biosolids − Organic matter obtained after human waste
has been treated at a waste water treatment facility.

Biomass − Shredded organic plant matter, usually from trees.

Compost − Any mixture of biological material that is decomposing by aerobic
processes.

Dry Matter − The part of a material that can be broken down by biological or
chemical processes, measured in kilograms of dry matter per kilogram of original
substance.

8

Acknowledgements
I would like to acknowledge the following parties for their help and support during the preparation of this thesis. The list of people I could thank is a long one, but
here I have chosen to mention a few of the most notable. First, to my supervisors,
Dr. Ian Hartley and Dr. Mark Shegelski, as well as the rest of my supervisory committee: thank you for your guidance, insight, and ultimately your time. You gave
me the skills and training that it takes to succeed while allowing me the freedom
to choose my own way. The impact of your contributions to this work, as well
as to my personal improvement, is something I will always value, thank-you. To
Dr. Matthew Reid, thank-you for answering question I had about programming
in Matlab, many hours of time spent debugging were prevented thanks to your
knowledge and experience with it. To Conan Veitch, thank-you for countless conversations that included good distractions, excellent advice, and good old fashion
pep talks. I would still be using Microsoft Word if not for you. To Gordon Everett
for making the entire project possible by coordinating with Silvis and allowing
me to obtain the biosolid material required to do my experiments, thank-you. To
Gavin Schlamp for helping with the “dirty work”, no amount of beer is worth
loaning out your truck and assisting someone to load biosolids into it...twice...yet
you did it for a 24 pack, thank-you. To my parents and family: your pride in, and
support of, my journey through university from my very first day until now, have
allowed me to stay the course, my sincerest appreciation and thanks. Finally, to my
wife Emily, and my children Ramona, and George: you are my biggest distractions
and my greatest support. The strength to see this through has all come from you,
you are everything to me, thank-you.

9

Chapter 1
Introduction and Background
1.1 Introduction
Composting has been used to dispose of organic waste for millennia and its usefulness as an agricultural aide is well known [1]. It is also known that composting
organic matter produces a significant amount of heat. Several studies have been
done wherein composting is used as an energy source [2] [3] [4]. By attempting
to use composting as an energy generating method for waste disposal, two issues
arise: (1) the temperature of the compost can rise too high causing the compost to
self-ignite [5]; and (2) the compost can become poorly aerated and, consequentially,
be quite odorous [6]. To take advantage of the energy released by compost while
minimizing the occurrence of these two issues, it is important to understand how
the physical properties of compost relate to the rate of decomposition and heat
generation. Mathematical models have been developed to predict the temperature
of compost and its dependence on physical parameters such as composition, moisture content, and dry matter content. Studies have also determined values for the
characteristics of compost systems such as the energy released per kilogram, the
degradation rate, and the fraction of dry matter for different compost materials.

10

Most of the studies done are either conducted on large-scale outdoor compost
piles or specialized sealed indoor compost reactors, both of which are not relevant
for small composting projects. One of the objectives of this work was to characterize smaller scale compost systems. The following sections present a broad
overview of composting theory followed by a model for predicting the temperature of municipal biosolid waste being composted in an isolated microreactor.

1.2 Background
1.2.1 Overview
In this section, relevant experimental research works, as well as mathematical
modeling approaches, are identified. The research cited introduces the type of
research being done with compost, the rationale for doing it, and the systems constructed to do the research. The questions that these studies answer, as well as
ones they do not, will be discussed. The key contributions made by these studies
that were relevant to this work have been highlighted throughout.

1.2.2 Background
As indicated earlier, composition, moisture content, and dry matter content are
parameters to consider when studying energy generation of a compost. Further to
these, air circulation, as well as microorganism type play a roll in energy generation. These are discussed in detail below.
A numerical model was used to predict the thermodynamics, kinetics, and energy use of composting systems [2]. The focus was not on extracting energy from
compost, but on how to obtain the highest quality compost for agricultural purposes, namely as a soil amendment. Compost intended for agriculture use needs

11

to be pasteurized, should be a homogeneous mixture, and should have a low internal temperature gradient while composting. These factors would be of concern for
a compost project designed for energy extraction as well since once the composting
has completed the remains will be of higher value if they meet these criteria.
Based on these criteria, higher quality compost was obtained when the temperature of the compost bed was regulated and kept consistent throughout the
pile [2]. This was achieved by recycling some of the air that had already been
blown through the sealed compost container back through it again. However,
there were a couple of drawbacks to the air recirculation process used: (1) it took
a substantial amount of energy to power the air recirculation system; and (2) after recirculating the air several times the air was sufficiently warmed such that it
was no longer able to remove heat from the pile. When this happened, the overall
temperature of the process increased, and the rate slowed.
The experimental apparatus built for this work was designed to only supply
minimal ambient air to the compost system without re-circulation. This was done
to maintain aerobic conditions in the compost without warming it.
In another study the cost associated with setting up and running a compost
heating system compared to leading competitors, namely geothermal and solar
power, was studied [4]. Compost heat was more expensive for water heating than
solar, and slightly more expensive for spatial heating than geothermal. However,
results showed that compost provided the most “reliable” heat when compared
with solar and geothermal for both spatial and water heating. The criteria for
reliability was that compost heat could be used for a larger portion of the year
compared to solar and geothermal [4]. The results for reliability were climate dependent and further work needed be done to completely characterize how ambient temperature affects the compost temperature. It was noted that because of
differences in seasonal temperatures, compost heat would only be able to be used
12

approximately 91% of the time for spatial heating and 70% of the time for hot water supply. For this reason, a boiler was required for backup spatial and water
heating. Based on these findings it would be desirable to be able to predict how
ambient temperature affects the compost temperature.
The effects of the presence of different types and amounts of bacteria on the
temperature of compost was studied [3]. The temperature of the compost was
measured at various stages. This data was then compared with a model for predicting compost temperature. The model took many variables into account including oxygen content, moisture content, porosity of the compost, and density of the
compost. From this study it is clear that understanding how the degradation rate
of compost varies over time with respect to variation in the bacteria population is
necessary for predicting the temperature of the compost.
Given the above discussion, the key topics to consider in this work were: (1)
how the ambient temperature and size of the reactor affect the temperature of compost, and (2) how the composition of the compost, as well as bacteria population
type, affect the degradation rate. Below are models that were developed to predict
the temperature of compost. Aspects of these models were used when developing
the model in this work.

1.2.3 Modelling
Testing of the thermal properties of compost made from municipal waste was investigated to quantify the heat energy released by composting biosolids [7]. The
municipal waste was classified as sorted “domestic waste”. The method used to
compost the biosolids was an insulated chamber along with a compressor to push
air through the compost pile. The pile was insulated in order to help determine the
heat released during the composting process. Two different quantities were measured to allow the amount of energy released to be calculated: (1) the total calorific
13

loss that occurred during composting, and (2) the amount of organic carbon loss
throughout the process. The study established a numerical value for the energy
released per kilogram of municipal waste composted of 900 kJ kg−1 , but noted that
the energy released per kilogram of compost varies substantially depending on the
material used. It was noted that follow up research needed to be done to characterize how cooling the municipal waste would affect the composting process and
how efficient extracting the heat would be. This work demonstrated that composting could be used to extract energy from waste, and that the amount of energy
available depended on the composition of the compost.
In order to model the temperature of compost made from municipal biosolids
it was necessary to know the energy available in municipal biosolids.
A study quantifying the particulate emissions from the combustion of municipal biosolids determined the heat of combustion for biosolids [8]. The biosolids
went through a treatment process involving de-watering and pulverization before
being co-fired with coal. Knowing both the heat of combustion for the coal, as well
as the energy output from the combustion, the heat of combustion for the biosolids
was determined. It’s value was approximately 6.6 MJ kg−1 .
Prediction of the temperature in a compost pile based on energy flow was done
on an industrial scale [9]. The model developed used mass transfer and solar exposure as sources of energy flow into the system, and considered conductive, convective, evaporative, and radiative losses as sources of energy flow out of the system.
The model was used to predict the temperature of the compost over a fifty-day
period while considering how varying the airflow rate affected the temperature of
the pile. It was shown that increasing the airflow rate reduced the temperature
of the compost. It is important to note that only loss terms depended on the airflow rate, and the decomposition rate was assumed to be constant, so there was
no mechanism for the temperature to increase with airflow. The rate constant used
14

was assumed to be the maximum value from published literature [10]. This model
therefore represents a compost system under optimal conditions with oxygen levels maintained at or above those required by the bacteria.
The physical parameters used in a model that optimized the efficiency of the
composting process were estimated [10]. The parameters studied were dry matter content, aeration, and ambient temperature. Their effects on the rate at which
degradation of compost occurred was observed. The study showed that the decomposition rate K was a function of the oxygen consumption and stated that its
value should be experimentally determined for the specific materials to be composted. The study then experimentally determined the reaction rate for a compost mixture made from chicken droppings and gave a theoretical value (K = 0.048
Day−1 ) for this setup [10].

1.3 Compost Theory
To understand the heating of compost, a discussion about the underlying mechanism is required. A description of the processes that occur during composting and
how they affect the temperature of the compost is presented below. This information was considered when the model in this work was developed.
In a compost system that is isolated1 from the environment, and where the
temperature does not go high enough for oxidization of cellulosic materials to occur [5], the only source of thermal energy is biological decomposition [9]. The
flora of microorganisms that provide decomposition is complex, as are the specific
metabolic processes used, but bacteria account for the majority of the decomposition (87% genus bacillus [11]). For the purpose of this work, it was assumed that the
heating due to microorganisms was caused by only bacteria, and that there was no
1 A system is isolated by having it insulated to minimize the effect of environmental temperature

changes

15

oxidation.
The rate of decomposition of compost would be impacted by this assumption.
Different types of microorganisms break down the various components of compost
(sugars, starches), and these processes occur at different rates [6] [7]. The overall
decomposition rate would be a function of these individual rates. The purpose
of this work was not to characterize the relative microorganism populations in
compost and doing so was beyond its scope.
In the model presented, a “best fit” rate constant was calculated for simplicity.
A discussion of how the model could be adapted to include more than one type of
decomposition is included in Chapter 4.
The general heating mechanism induced by bacteria is simple. Organic matter along with oxygen is consumed and broken down into smaller substituents.
Through this process energy is released and the mass of the compost is decreased.
The energy released heats the compost. There are two main phases to the heating of compost: (1) the mesophilic phase, and (2) the thermophilic phase. The
mesophilic phase is the first phase of compost decomposition and is characterized
by lower temperatures and the bacteria that thrive in them (mesophilic bacteria).
The temperature range of the mesophilic phase is from 10◦C to 40◦C [3]. The thermophilic phase is the second phase of composting where thermophilic bacteria
are responsible for the decomposition. The temperature ranges from 40◦C to 70◦C
during this phase. For municipal biosolids most of the decomposition happens
during the mesophilic phase [12], this justifies the assumption that no heating due
to oxidation occurred during the experiment conducted for this work.

16

Chapter 2
Model Theory
2.1 Theory
To characterize the compost heating for an isolated system, a mathematical model
was developed based on other accepted models, as described previously [7] [9]
[10]. The primary work used was [9], which modelled the temperature of the compost using

mcp

dT
= Qgain − Qloss = Qnet
dt

(2.1)

where Qgain and Qloss were terms quantifying energy flow in and out of the compost (kJ Day−1 ).
The model assumed a mass transfer mechanism for the energy generated by
the compost mixture given by:

Qdecomp = Hc

dm
dt

(2.2)

where Hc is the heat of combustion of 1 kg of compost [10]. The mass transfer

17

equation was given by:
dm
= −K(m − me )
dt

(2.3)

where m is the dry mass (kg) of compost, K is the degradation rate of the compost (Day−1 ) which is typically measured experimentally, and me is the equilibrium mass of the compost; defined to be the mass of compost that remains after a
substantial amount of time having been composted (6mo-1yr.).
To solve Equation 2.3, hold K constant, separate variables, and integrate to
yield;

ln

m(t ) − me
mi − me

= −Kt .

(2.4)

Solving for m(t’), and combining with Equations 2.3 and 2.2 gives
Qdecomp = −Hc K(mi − me )e−Kt

(2.5)

where mi is the initial dry mass of the compost. The negative sign before Hc indicates that energy was released by the mass transfer. This energy that is released by
the mass transfer goes into the compost, and therefore
Qgen = −Qdecomp .

(2.6)

where Qgen is the energy flow into the compost do the decomposition. In the
model, all of the energy flow terms were positive and the sign in front of the term
was used to show that it either added to, or subtracted from, the net energy going
into the compost.
Since the experimental design incorporated an insulated chamber, Qgen was the
only term that contributed to an increase in the net energy, whereas in other models
18

there were terms accounting for heating of the compost by the sun. Therefore,

Qgain = Qgen

(2.7)

and all that remained to fully characterize Equation 2.1 was to determine the form
of Qloss .
In previous works Qloss involved losses from different sources, including, evaporative, convective, conductive, and radiative [9]. Since this study was conducted
in an insulated chamber, a simplified approach was taken. Typically, in other experimental setups, evaporation was the largest contributor to energy loss in compost at 70% followed by convective loss (20%) and then radiative loss (10%) [13].
The evaporative loss was large because of the high temperature achieved during
composting. In the case of [9], a peak temperature of 71◦C was observed. In this
study the peak temperature was 32.5◦C. Since evaporative loss scaled as eT , the
evaporative losses in the setup studied herein were much less than typical [14].
Radiative losses were considered to be negligible since they occur at the edge
of the compost, and the temperature modelled in this work was that of the core.
It is common practice to assume that conductive and convective losses dominate
when considering the heat loss from the core of a compost pile to the surface [9].
As a result of these simplifications, Qloss had the form;

Qloss = Qcon = UA(Tc − Tsurf )

(2.8)

where U was the overall convective and conductive heat transfer coefficient, A was
the surface area of the compost vessel, Tc was the temperature at the centre of the
compost, and Tsurf was the temperature of the outer edge of the compost just inside the compost vessel (see figure 3.1) [15].

19

Since Tsurf was not measured experimentally an important assumption in the
model was that
Tsurf ≈ Tamb ,

(2.9)

where Tamb was the ambient temperature of the room. This was a reasonable assumption because the thickness of the container was small compared to the distance from the centre of the compost, where the temperature probe was, to the
edge of the compost. A more rigorous argument and calculation can be found in
Appendix A.
Combining Equations 2.5, 2.6, 2.7, and 2.8 with Equation 2.1 gave;
Qnet,n−1 = Hc K(m − me )e−Kt − UA(Tc,n − Tamb,n−1 ).

(2.10)

Qnet needed to be calculated for each day that the temperature was to be modelled for. The index n was added in Equation 2.10 to represent the nth day. To
compare the model to experimental data, the temperature for the nth day was calculated using:
Tc,n = Tc,n−1 + ∆Tc,n−1

(2.11)

Qnet,n−1
∆t.
mcp

(2.12)

where,
∆Tc,n−1 =

Equation 2.12, and Equation 2.11 were combined to give:

Tc,n = Tc,n−1 +

Qnet,n−1
∆t,
mcp

(2.13)

and along with Equation 2.10 were solved through an iterative process in MATLAB® .
This process was performed as outlined below.

20

2.1.1 Numerical Algorithm
The following iterative process was used to calculate the temperature for each of
the first 9 days after composting began. In order to calculate Tc,n (Equation 2.13)
both Tc,n−1 and Qnet,n−1 were required. The subtlety was in calculating Qnet,n−1 .
Qnet,n−1 depends on Tc,n ; the quantity that was sought. This was a result of conductive losses scaling with the temperature of the compost pile. The more the
temperature increased on day n-1 (∆Tc,n−1 ) the more the conductive loss would
have been during the same day (see Equation 2.8). The net difference between
these two effects determined the change in temperature on day n-1 (∆Tc,n−1 ), and
thereby the temperature the next day (Tc,n ).
This issue was solved by choosing an initial temperature for Tc,n in Equation
2.10 that was lower than the anticipated final value of Tc,n to be calculated using
Equation 2.12. Qnet,n−1 was then calculated using the chosen initial value for Tc,n
and the result was used to calculate Tc,n (Equation 2.13). The value obtained for
Tc,n (Equation 2.13) was inevitably larger than the initially chosen value used in
Equation 2.10. If the difference was larger than 0.1◦C the Tc,n value used in Equation 2.10 was increased by 0.1◦C and Tc,n (Equation 2.13) was re-calculated. This
process was repeated until both of the Tc,n values were within 0.1◦C.
Once the iterative process was done, the final Tc,n was calculated. This process was repeated for all 9 temperature predictions (n = 1 - 9). Note: Tc,o was the
measured temperature of the compost at the outset of data collection.

2.2 Bounding Qloss
In the model presented it was assumed that the only source of energy heating the
compost and its environment was Qgen . It was for this reason that the experiment
was conducted in an insulated room. A consequence of insulating the system was
21

that most of the energy released by the compost (Qloss ) would be retained in the
room and increase the ambient temperature of the room. However, the insulated
room was not a perfect calorimeter. The floor of the room was made of concrete
which would have acted like a heat sink, removing some of Qloss from the system.
By determining the net energy flow into the room the expected increase in ambient temperature could be calculated. This provided a method to bound Qloss and
ensure that the model was not over or under accounting for the energy lost from
the compost.
An estimate of the energy flowing out of the room (Qout ) through the floor was
calculated (see Appendix A). The rate was determined to be:
Qout = 39.2W .

(2.14)

On average, energy left the compost at a rate of:
Qloss = 46.3W .

(2.15)

This resulted in a net energy flow into the room of:
Qnet = Qloss − Qout = 7.1W ,

(2.16)

the equivalent of 613 kJ heating the air over the course of a day. The expected
change in ambient temperature due to this energy released by the compost would
be given by
∆Tamb =

Qnet
∆t.
m cp

(2.17)

The terms m’ and cp are, respectively, weighted mass and specific heat terms
that take into account the different materials that were heated by the energy leaving the compost. Materials that needed to be included were the air in the room, the
22

walls of the compost container, and the concrete floor. Including those materials in
Equation 2.17 resulted in:

∆Tamb =

Qnet
∆t.
Vair ρair cp,air + ρcon dcon A + mplastic cp,plastic

(2.18)

Using the values from the Table 2.1 in Equation 2.18 gives.

∆Tamb = 2.1◦C.

(2.19)

During the experiment the ambient temperature increased from 13.6◦C to 17.5◦C,
an average increase of approximately 0.5◦C per day. Although the expected temperature change was higher than the measured temperature change it should be
noted that the choice for the thickness of concrete that was assumed to be heated
was only 1 cm. This value was chosen somewhat arbitrarily. In reality much more
of the concrete would likely have been heated as Qout flowed through it. The fact
that the temperature changes were on the same order verifies that the assumptions
made in the model relating to how energy leaves the system, were valid.

Parameter
cp,air
cp,con
cp,plastic
ρair
ρcon

Physical Values
Value [16]
Parameter
−1
−1
1 kJ kg K
A
0.75 kJ kg−1 K−1
dcon
2.25 kJ kg−1 K−1
mplastic
−3
1.225 kg m
Vair
2400 kg m−3

Value
10 m2

0.01 m
10 kg
25 m3

Table 2.1: Physical Parameters for Calculating ∆Tamb

23

Chapter 3
Experimental Methods
This chapter is a description of the experimental systems and methods used to
obtain the data for this work. The first section describes the components of the
experimental setup. Then the methodology used to collect the data with the experimental apparatus is explained.

3.1 Experimental Setup
Compost container:
A high-density polyethylene container was used to hold the compost mixture. The
top of the container was cut-off and therefore open to the air. The container was 87
cm tall, had a diameter of 59 cm, and a wall thickness of 2.2 mm.

Heat exchange system:
The heat exchange system consisted of a 25 m, 0.64 cm diameter copper pipe, a
volume flow meter, and a garden hose. The garden hose was connected to a standard water line faucet on the one end and a volume flow meter on the other. The
copper pipe was attached to the downstream side of the volume flow meter. The
copper pipe was bent into a coil the width of the barrel (4 loops) and placed inside
24

Figure 3.1: Diagram of experimental compost container showing thermocouple
locations

25

the container. Note: the heat exchange system was not running while data was
collected for this work.

Air Supply:
The experimental design of the oxygen supply system consisted of an air compressor, air hose, a piece of steel pipe, an air gun, and a Wi-Fi controlled timer power
outlet. The air compressor was connected to the Wi-Fi timer power outlet which
was plugged into a regular (110 V, 15 A) outlet. This Wi-Fi timer power outlet was
used to set how long the compressor would run. The air compressor had a hose
attached to it and the air gun was attached to the other end of the hose to discharge
the air from the compressor. The air gun was connected to the pipe which was inserted into the compost mixture. The air gun had a trigger which was taped in the
fully depressed configuration so that when the compressor turned on air immediately started going through the pipe into the compost.

Compost:
The compost mixture was made by mixing biomass and biosolids 1:1 by volume.
One shovel full of biomass was placed in the barrel and then one shovel full of
biosolids was placed inside the barrel. This process was repeated until the barrel
was a third full. At that point a layer of dry grass clippings and leaves was added.
This entire process was repeated twice more. This produced 3 combined layers of
composite+clippings+leaves in the container.

Data Loggers:
The temperatures were measured using SmartReader 6 data loggers. Two thermocouples were used, each capable of taking three different measurements simultaneously. The thermocouples were used in tandem, each as redundancy for the
26

other. The three temperature locations (see Fig 3.1) were on the copper coil (not
shown) just downstream of the volumetric flow meter, in the centre of the compost
pile a third of the way down, and on the copper coil immediately after if came out
of the compost pile. Tsurf in Fig 3.1 was not measured.
A secondary temperature probe was used to access the accuracy of the temperature reading of the thermocouple in the centre of the pile. This was done because
the accuracy of the true temperature readings of the thermocouples was in question [17] (See Section 3.4 for a more in-depth discussion about the temperature
measurement error). The secondary probe was a Rain Bird temperature probe.
This temperature probe was checked periodically and compared with the reading
from the thermocouple in the centre of the compost. It was found the actual temperature as per the Rain Bird temperature probe was on average about 3◦C higher
than the temperature measured by the thermocouples.

The System:
The whole apparatus was kept inside a large insulated commercial freezer. The
approximate dimensions were 2.5 m x 4 m x 2.5 m. The freezer was not running
for the duration of the experiment.

3.2 Data Collection
After the experiment was set up as described above the data-loggers were started,
taking one measurement every minute. At the same time, the air supply system
was set to supply air to the system for one minute every hour. The system was
left to run for 24 hours at a time, once a day the door to the insulated room was
opened, the secondary temperature probe was checked, and the data loggers were
backed up. This process was repeated from July 22nd until July 31st.

27

3.3 Model Parameter Values
Values for all parameters besides the rate constant were taken from the literature
or calculated using literature values. This was done so that the rate constant (K)
could be calculated by fitting the model to the data. Having all other parameters
fixed strengthened the model. Extensive research was done in order to determine
physically realistic values that accurately reflected the physical setup used to collect the data in this work. Following are descriptions of the processes applied to
determine the parameter values used.

Mass Ratio of Biosolids and Biomass
The compost mixture was made using equal volumes of biosolids and biomass.
Determination of parameters such as, the specific heat, dry matter content (β),
and heat of combustion required knowing the individual masses of biosolids and
biomass. To obtain the respective masses from the total mass of compost, the density of one substance was required. Using the average literature density of biomass
(ρBM = 336 kg m−3 (288-384 kg m−3 ) [18]) the mass of the biomass was determined
by:
V
mBM = ρBM .
2

(3.1)

where V was the volume of the compost container. The mass of the biosolids was
calculated by:
mMBS = mT OT − ρBM

V
2

(3.2)

Equilibrium Mass and β
The equilibrium mass of a material is defined as the mass remaining after a long
period of time spent composting (on the order of a year). This mass does not break
down with further composting [10]. β is the ratio of this equilibrium mass (me )

28

and the initial mass of compost given by:

β=

me
.
mo

(3.3)

The value of β depends on the material being composted. For biomass it is
0.36 [10] and for biosolids it is 0.865 [10]. Taking a weighted average of these values based on the relative masses of biosolids and biomass resulted in a value of β
= 0.711.

Specific Heat Capacity of Compost
The specific heat of the compost was calculated using literature values for the heat
capacity of biosolids (2.98 kJ kg−1 K−1 [19]) and waste wood (2.30 kJ kg−1 K−1 [20])
and then taking a weighted average based on the mass fractions for biosolids and
biomass. The resulting heat capacity was 2.77 kJ kg−1 K−1 .

Heat of Combustion
The heat of combustion for biosolids varies substantially in the literature due to
varying compositions of the biosolids [7]. The value used in this work was 6.6 MJ
kg−1 because it was experimentally determined for municipal sewage sludge that
had undergone a similar treatment process as the biosolids used in this work [8].
The value for the heat of combustion of wood is better known. The standard literature value of 21.0 MJ kg−1 was used [18]. The weighted average value used was
10.7 MJ kg−1 .

Convective and Conductive Heat Loss Coefficient The literature value for the
thermal conductivity (k) coefficient ranged from 0.26 - 0.43 W/mK for compost [7].

29

The convective and conductive heat loss coefficient (U) is related to (k) by:

U=

kc
r

(3.4)

where r is the distance from the centre of the compost pile to the edge of the compost container [15]. The resulting range of values for (U) was 79-130 kJ m−2 K−1
Day−1 . The wide range in values is due in part to the dependence of the thermal
conductivity on moisture content. The thermal conductivity of compost increases
linearly with moisture content [21]. The moisture content of the compost used in
this work was 60% and was just in the predicting range (20% - 65%) of the study
cited.

Summary of Physical Parameter Values

Parameter
β
ρBM

cp
Hc
U

Physical Values
Literature Values
Parameter
0.711
K
−3
336 kg m
mBM
2.77 kJ kg−1 K−1
mMBS
10.7 MJ
mT OT
−2
−1
−1
130 kJ m K Day
r
V

Experimental Values
0.0525 Day−1
25.2 kg
57.4 kg
82.6 kg
0.286 m
0.15 m3

Table 3.1: Physical Parameters for Modelling

30

3.4 Experimental Error
As in all experimental systems error was introduced during the data collection
process. There were three dominant sources of error affecting the results: (1) The
thermocouples that were used have a measurement error; (2) the system studied
was not a perfectly isolated; and (3) the exact density of the biomass was unknown.
These sources of error are discussed in more detail below.

Thermocouple error:
The thermocouples used have an associated error in measurement of:
TCouple,Error = 4.05◦C.

(3.5)

However, the thermistor built into the thermocouple system has an error of only:
TT hermister,Error = 0.7◦C.

(3.6)

The thermistor error bound the error in measurement of the temperature since
relative temperature data was used in this study.
There were concerns that the thermocouples used might give erroneous results
since they were old and may have been damaged from a previous study [17]. For
this reason two different thermocouples were used in order to corroborate the results. A more in-depth description of the error associated with the thermocouples
can be found elsewhere [17], p. 99.

The System:
The room that contained the compost, although well insulated, was not a perfect
calorimeter. Loss of energy from the system due to conduction through the walls

31

and concrete floor would have occurred. Additionally, the door to the chamber
was opened approximately once every 24 hrs to backup the temperature measurements from dataloggers. This let some of the air inside the freezer escape and
would have caused some unaccounted energy loss from the system. These losses
would have contributed to the ambient temperature in the chamber not increasing
as much as expected.

Biomass Density error:
The composition of the biomass was not homogeneous. The smallest pieces were
comparable to sawdust and the largest were small branches. The species of tree
that the biomass was composed of was also unknown (and possibly varied). This
made the uncertainty in the value for the density of the biomass large and required
an average literature value for the density of biomass to be used. The range in
density was used to find an upper and lower bound for the model predictions.
The high, average, and low values of biomass density were each used to calculate
a different set of values of each parameter discussed in the preceding section. The
modelling algorithm was then run with these three different sets of values. Results
for the three runs were plotted in Fig 4.1.

32

Chapter 4
Results and Discussion
The results of this study are illustrated in Figure 4.1 and Figure 4.2. Figure 4.1
shows the temperature predicted by the model compared to the measured temperature, along with the ambient temperature, and the error in ambient, predicted,
and measured temperatures. Figure 4.2 shows the residuals of the model predictions.
In this chapter the first two sections discuss the model predictions and residuals individually, this is followed by a section describing alternative modelling
approaches that were considered. A section discussing the computer modelling
methodology concludes the chapter.

4.1 Model Predictions
The results in Figure 4.1 show that the model agrees with the experimental data,
within error, 9 out of 10 days. The temperature on Day 2 is outside the prediction
of the model. The model used the experimental ambient temperature and literature values to predict the temperature of biomass and biosolids compost. Upon
inspection of the ambient temperature it was observed that after Day 1 it increases
monotonically. Given that the predicted temperature of the compost depended
33

on the ambient temperature, it was intriguing that the predicted temperature has
the same trend (oscillating up and down) as the experimental temperature after
Day 6 despite the ambient temperature continuously increasing. This was an encouraging sign that the model used the correct form of loss terms. The loss terms
become dominant later in experimental time as a result of the exponential in Qgen
becoming small as t increases.
The temperature on Day 2 being outside the model’s predictive power was not
unexpected. Two of the assumptions in the model contributed to this result: (1)
the decomposition rate was assumed to be constant; and (2) only one type of bacterial decomposition was assumed to occur. The decomposition rate of the compost would vary with bacteria population which varies with time, but the model
used an optimized average decomposition rate constant. The decomposition rate
constant, as determined by fitting the model to the data, was influenced strongly
by the lower temperatures that occur later in time. The composting conditions at
this time were less optimal, and consequently the decomposition rate was lower
than it would be when decomposition first started. Additionally, the decomposition rate depends on the substrate being consumed by the microorganisms. The
easily digestible substances decompose earlier and a greater rate [7].

34

Figure 4.1: The measured temperature at the centre of the compost (-o-) along with
error bars, the predicted temperature based on the model (- -) including error bars,
the measured ambient temperature (.-) along with error bars

4.2 Residuals
Initially the residual plot in Figure 4.2 seems to present an issue; the distribution
of the residuals appears heteroscedastic. However, upon further inspection this
was not a concern. The sizes of the individual residuals (average of 1.86◦C) are on
the order of the error in measurement (average 1.6◦C). A plot of the measurement
errors added in quadrature alongside the residuals (Figure 4.2) shows that only
two of the residuals are outside the error band, and of those two, only one is more
than 0.5◦C outside the error band. Conclusions cannot be drawn from residuals
that are on the order of the error.

35

Figure 4.2: Residual values (o), measurement error (–)

4.3 Alternative Modelling Approaches
Considering the simplicity of the model, the fit to experimental data is quite good.
This section characterizes how the different assumptions incorporated in the model
affected the results. There were two primary assumptions that simplified the model
substantially.
The first was that the decomposition rate was constant in time. This assumption was used for three reasons: (1) it simplified the computer algorithm, (2) it
strengthened the model by reducing the number of free parameters, and (3) it is
consistent with the assumption in [9].
The second assumption was that only one type of microorganism population

36

contributes to the decomposition rate. Again, this assumption reduced the number of free parameters in the model, and simplified the computer algorithm. The
following sections show how these assumption affected the model results.

4.3.1 Time Dependent Rate Constant, K
As discussed the decomposition rate was assumed to be constant for this work.
Having a time-dependent rate constant is an intuitive next step and work was done
to determine its form [10]. However, the time-dependent form of the decomposition rate determined was for composting in the temperature range 35-60◦C. The
experimental temperatures in this work were not in that range, and therefore unable to be modelled with the time-dependent decomposition rate developed. Determining a time-dependent rate constant for the appropriate temperature range
was beyond the scope of this work. To understand the impact of a time-dependent
decomposition rate without having to determine it’s form an alternate approach
was used.
Values for the decomposition rate at different points in time were chosen so that
the model temperature was within 0.1◦C of the experimental temperature. A plot
of decomposition rate versus time was then generated (see Figure 4.3). From the
figure it is clear that the form of K mirrors that of the experimental temperature.
More explicitly, the model is sensitive to the decomposition rate. This was expected
since: (1) K was the only parameter in the model; (2) the model was very simple;
and (3) K is responsible for much of the physical character of the system.

37

Figure 4.3: Time dependent decomposition rate obtained from fitting model to
experimental data using handpicked values.

4.3.2 Two Bacteria Population Model
In Section 1.4 a discussion about how the microorganisms in compost cause it to
heat up is given. A brief discussion of the types of microorganisms that contribute
to the heating was presented. The argument was made that determining the individual components of a multi-microorganism population rate constant was beyond the scope of this work. This section presents an example of how including
multiple microorganism populations impact the model results. It was modelled by
having a second energy generation term of the form in Equation 2.5 with a different decomposition rate. The modified version of the model was then run through
38

the same algorithm discussed in Chapter 2.

Figure 4.4: Two microorganism population fit (–) to experimental data (o) with
error bars, k1 = 0.0342, k2 = 0.3147

Fig 4.4 shows the result of including another bacteria population. The peak
temperature on day 2 is much closer to being in the range of the model. In general
the predicted temperature was closer to the experimental temperature than for the
original “one population” model presented in this work. It should be noted that
this approach was not rigorous and was done for demonstration purposes. The
implications of the results are therefore limited, but do serve to show the potential
of a two population model were one to be developed.

39

4.4 Computer Modelling Methodology
Initially Microsoft Excel® was used to analyze the data and generate the model
results. Excel® was chosen because the author was experienced with it and it allowed the author to very quickly reproduce an approximation of the model in [9].
Excel also had the advantage that the data and calculations could all be displayed
visually. This allowed for easy debugging of the early versions of the model. These
early versions of the models were very useful for interpreting model predictions
and troubleshooting, but had limited success at reproducing the experimental results. Some of the assumptions used to simplify the model to the point it could be
modelled in Excel were too restrictive. The models developed in Excel used average values for the daily temperature increases needed to calculate the amount of
energy lost throughout that same day. A better approach was to use the iterative
algorithm discussed in Section 2.1.1 to determine the predicted temperature each
day and use this more accurate value to calculate the energy loss. An iterative process like the one employed could have been done using Excel but would have been
much more difficult. This ultimately resulted in the author using MATLAB® for
the remainder of the modelling done. The technique developed to approximate the
convective and conductive losses in the model, using the iterative algorithm, is itself a useful result of this work. All results presented in this chapter were obtained
using MATLAB® .

40

Chapter 5
Conclusion and Future Work
5.1 Conclusion
The model satisfactorily predicts the temperature of the compost for 90% of the
data using only literature values for the materials composted and the ambient
temperature in the isolated system. This was an objective identified in the introduction of this work. Additionally the decomposition rate constant for municipal
biosolids and wood waste compost was determined. The value of the constant was
K = 0.0525 Day−1 , and this value is consistent with the literature for compost made
from similar materials including animal waste [6] [10].
The only data point that is not within the range of error values was Day 2,
and the difference between the predicted and experimental temperature was large
(2.7◦C). This indicated that the model was missing a significant contribution to
the energy into the system at this time. The mostly likely cause for this underaccounting of energy into the system was the assumption that the decomposition
rate of the compost was constant.

41

5.2 Future work
Chapter 1 of this work pointed out several topics worth investigating and two of
them were investigated herein. The first was the determination of the decomposition rate for biosmass and biosolids compost, and the second was the correlation
between the ambient temperature and the temperature of the compost. In this section the topics that were not addressed in this work, but that are the logical next
step are discussed.
Sections 4.3.1 and 4.3.2 briefly discuss the benefits of considering a time dependent decomposition rate, and a two bacteria population model respectively. Both
of these topics are worth investigating further in the future.
A third topic that was highlighted in the introduction of this work, but not focused on after that, is the size of the compost pile. The temperature of the compost
studied never went above 35◦C. This is not typical, and often not desired. Higher
temperatures are usually maintained in order to “pasteurize” the compost. However, in very niche settings, limiting the compost to lower temperatures could be
of interest. Further work to characterize how the size (mass) of the compost pile
affects the decomposition rate and the maximum obtainable temperature would
be beneficial.

42

Bibliography
[1] M. Smith, D. Friend, and H. Johnson, “History of Composting - Composting
for the Homeowner,” University of Illinois Extension, May 2018. [online]
http://web.extension.illinois.edu/homecompost/history.cfm.
[2] K. Ekinci, H. M. Keener, and D. Akbolat, “Effects of feedstock, airflow rate,
and recirculation ratio on performance of composting systems with air recirculation,” Bioresource Technology, vol. 97, pp. 922–932, May 2006.
[3] I. Biaobrzewski, M. Mik-Krajnik, J. Dach, M. Markowski, W. Czekaa, and
K. Guchowska, “Model of the sewage sludge-straw composting process integrating different heat generation capacities of mesophilic and thermophilic
microorganisms,” Waste Management, vol. 43, pp. 72–83, Sept. 2015.
[4] G. Irvine, E. R. Lamont, and B. Antizar-Ladislao, “Energy from Waste: Reuse
of Compost Heat as a Source of Renewable Energy,” International Journal of
Chemical Engineering, vol. 2010, pp. 1–10, June 2010.
[5] T. Luangwilai, S. D. Watt, S. Fu, H. S. Sidhu, and M. I. Nelson, “Modelling the
effects of ambient temperature variation on self-heating process of compost
piles,” in Chemeca 2019: Chemical Engineering Megatrends and Elements,
pp. 84–96, Engineers Australia, 2019. Publisher: Engineers Australia.

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[6] M. C. Gutirrez, J. A. Siles, J. Diz, A. F. Chica, and M. A. Martn, “Modelling of
composting process of different organic waste at pilot scale: Biodegradability
and odor emissions,” Waste Management, vol. 59, pp. 48–58, Jan. 2017.
[7] E. Klejment and M. Rosiski, “Testing of thermal properties of compost from
municipal waste with a view to using it as a renewable, low temperature heat
source,” Bioresource Technology, vol. 99, no. 18, pp. 8850 – 8855, 2008.
[8] W. S. Seames, A. Fernandez, and J. O. L. Wendt, “A Study of Fine Particulate Emissions from Combustion of Treated Pulverized Municipal Sewage
Sludge,” Environmental Science & Technology, vol. 36, pp. 2772–2776, June
2002.
[9] El-Sayed G Khater, Adel H Bahnasawy, Samir A Ali, “Mathematical
Model of Compost Pile Temperature Prediction,” Environmental Analytical
Toxicology, vol. 4, pp. 1–7, Sept. 2014.
[10] H.M. Keener, “Optimizing the Efficiency of the Composting Process,”
in Science and Engineering of Composting:

Design Environmental,

Microbiological, and Utilization Aspects, pp. 59–68, Worthington, Ohio: Renaissance Publications, 1993.
[11] P. F. Strom, “Identification of Thermophilic Bacteria in Solid-Waste Compostingt,” Applied and Environmental Microbiology, vol. 50, pp. 906–913, 1985.
[12] N. O. Moraga, F. Corvaln, M. Escudey, A. Arias, and C. E. Zambra, “Unsteady 2D coupled heat and mass transfer in porous media with biological and chemical heat generations,” International Journal of Heat and Mass
Transfer, vol. 52, pp. 5841–5848, Dec. 2009.

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[13] R. Robinzon, E. Kimmel, and Y. Avnimelech, “Energy and Mass Balances of
Windrow Composting System,” Transactions of the ASAE, vol. 43, pp. 1253–
1259, August 2000.
[14] A. de Guardia, C. Petiot, J. C. Benoist, and C. Druilhe, “Characterization and
modelling of the heat transfers in a pilot-scale reactor during composting under forced aeration,” Waste Management, vol. 32, pp. 1091–1105, June 2012.
[15] R. T. Haug, The Practical Handbook of Compost Engineering. Boca Raton,
FL: Lewis Publishers, 1st ed., 1993.
[16] “Air - Density, Specific Weight and Thermal Expansion Coefficient at
Varying Temperature and Constant Pressures,” Engineering ToolBox, 2003.
[online] https://www.engineeringtoolbox.com/air-density-specific-weightd 600.html.
[17] Gigliotti, Dino A., “Modelling Heat Transfer in the Conditioning Process Used
in Plywood Manufacturing,” Master’s thesis, UNBC, Prince George, B.C.,
April 2008.
[18] R. Nelson and W. D. Dobie, J., Conversion Factors for the Forest Products
Industry in Western Canada. Vancouver, B.C.: Forintek, 1st ed., 1985.
[19] C. Liu, “Pathogen Inactivation in Biosolids with Lime and Fly Ash Addition,”
Master’s thesis, UM, Winnipeg, M.B., February 2000.
[20] “Thermtest Materials Database - Thermal Properties,” Thermtest Inc., 2019.
[online] https://thermtest.com/materials-database.
[21] J. Van Ginkel, Physical and biochemical processes in composting material.
PhD thesis, Agricultural University Wageningen, Wageningen, NL, 1996.

45

Appendix A
Calculations
A.1 Tsurf ≈ Tamb
An important assumption in the model is that;
Tsurf ≈ Tamb .

(A.1)

The calculation verifying the validity of this assumption is a familiar heat transfer
problem. First using;
Q=

kA(T1 − T2 )
∆x

(A.2)

where Q is the heat flow, k is the thermal conductivity of a material, A is the area
though which the energy flows, and ∆x is the distance the energy flows.
Referring to Figure A.1 and knowing that heat flow through the compost is the
same as the heat flow through the compost vessel yields;
kp (Tsurf − Tamb )
kc (Tc − Tsurf )
=
r
d

46

(A.3)

Figure A.1: Heat transfer diagram

47

or

kc d
kp r Tc + Tamb
Tsurf =
1 + kkcpdr

(A.4)

using the values from Table A.1 yields;
kc d
≈ 0.0066
kp r

(A.5)

Tsurf ≈ Tamb + 0.0066Tc .

(A.6)

and therefore;

Equation A.6 shows that even for a relatively large Tc the original approximation
in Equation A.1 is good.

A.2 Qloss

Figure A.2: Insulated room diagram

48

A rough calculation was done to bound the energy leaving the system through the
concrete floor. The energy flow is give by:

Qout =

Tinside − Toutside
Rtot

(A.7)

where Tinside is Tamb , Toutside is Tground , and Rtot is the total thermal resistance
between the two temperature locations. Here

Rtot =

1
hsoil A

+

x
kconcrete A

+

1
hair A

.

(A.8)

combining these last two equations gives

Qout =

Tamb − Tearth
.
x
1
hsoil A + kconcrete A + hair A
1

(A.9)

using values from Fig A.2 [16] [20], Table 3.1 and the average value of Tamb (15.4◦C)
results in
Qout = 39.2W

(A.10)

Summary of Physical Parameters

Parameter
hair
hsoil
kc
kp

Physical Values
Literature Values
Parameter
5 W m−2 K−1
d
−2
−1
2.88 W m K
r
−1
−1
0.43 W m K
x
0.5 W m−1 K−1

Experimental Values
0.0022 m
0.286 m
0.15 m

Table A.1: Physical Parameters for Calculating Qloss

49

Office of Graduate Programs

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Result of Oral Examination
Masters Degree
Candidate Name: Mitchell Hawse
Candidate for the Degree: Master of Science in Physics
Date of Oral Examination: April 22, 2020

Chair: Dr. Andrea Gorrell

This form needs to be returned to the Office of Graduate Programs immediately after the Oral Examination is finished.

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April 30, 2020
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The committee found the thesis overall to be very concise, with committee members mentioning work was excellent, the defense was
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Date: April 22, 2020

Signature: ________________________________

Revised August 2017

THESIS APPROVAL
Name:

Mitchell Hawse

Degree:

Master of Science in Physics

Title:

MODELLING THE TEMPERATURE OF A COMPOST
MICROREACTOR IN ISOLATION

Chair of Defence:

_______________________________________________
Dr. Andrea Gorrell
University of Northern British Columbia

Examining Committee:
________________________________________________
Supervisor: Dr. Ian Hartley
University of Northern British Columbia

________________________________________________
Co-Supervisor: Dr. Mark Shegelski
University of Northern British Columbia

________________________________________________
Committee Member: Dr. Mark Reid
University of Northern British Columbia

________________________________________________
Committee Member: Mr. Maik Gehloff MASc
University of Northern British Columbia
________________________________________________
External Examiner: Dr. Ronald Thring
University of Northern British Columbia

Date Approved:

April 22, 2020

Angela Seguin
From:
Sent:
To:
Subject:

Mark Shegelski
Wednesday, April 29, 2020 10:34 AM
Angela Seguin
Re: Required: Signature on Approval Page

Hi Angela,
Please consider this email as my approval for Mitchell's thesis.
Thanks,
Mark Shegelski
From: Angela Seguin
Sent: Wednesday, April 29, 2020 9:12 AM
To: Ian Hartley; Mark Shegelski; Ron Thring; Matt Reid
Subject: Required: Signature on Approval Page
Please sign the attached approval page for Mitchell Hawse, or return this email stating your approval.
Angela

1

Angela Seguin
From:
Sent:
To:
Subject:

Ron Thring
Wednesday, April 29, 2020 9:47 AM
Angela Seguin
RE: Required: Signature on Approval Page

Hello Angela:
I approve.
Cheers,
Ron
From: Angela Seguin
Sent: Wednesday, April 29, 2020 9:12 AM
To: Ian Hartley ; Mark Shegelski ; Ron Thring ; Matt Reid
Subject: Required: Signature on Approval Page
Please sign the attached approval page for Mitchell Hawse, or return this email stating your approval.
Angela

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