Effects of Biomass in Recirculating Aquaculture Water Heating and
Cooling Systems
by
Devin Murray
Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING
Major Subject: Mechanical Engineering
Approved:
_________________________________________
Prof. Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
December, 2014
© Copyright 2014
by
Devin Murray
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
LIST OF SYMBOLS ....................................................................................................... vii
LIST OF KEYWORDS .................................................................................................... ix
ACKNOWLEDGMENT ................................................................................................... x
ABSTRACT ..................................................................................................................... xi
1. Introduction.................................................................................................................. 1
1.1
State of the Aquaculture Industry ...................................................................... 1
1.2
Types of Aquaculture ......................................................................................... 3
2. Theory and Methodology ............................................................................................ 7
2.1
Theoretical System ............................................................................................. 8
2.2
Analytical Method .............................................................................................. 9
2.2.1
Definition of System Parameters ......................................................... 11
2.2.2
General Assumptions ........................................................................... 12
2.2.3
Heat Transfer Through Side Walls ...................................................... 12
2.2.4
Free Convective Heat Transfer from Surface ...................................... 13
2.2.5
Radiation Heat Transfer from Surface ................................................. 14
2.3
Baseline Heat Loads ......................................................................................... 14
2.4
Introduction of Biomass ................................................................................... 15
2.4.1
Modeling Biomass Resistance ............................................................. 16
2.4.2
Resistance Estimate.............................................................................. 16
2.4.3
Resistance Calculation ......................................................................... 18
2.4.4
Resistance Calculation - Convection ................................................... 19
2.4.5
Resistance Calculation - Conduction ................................................... 20
2.4.6
Resistance Calculation - Consolidation ............................................... 20
2.4.7
Final Resistance ................................................................................... 21
iii
3. Results and Discussion .............................................................................................. 22
4. Conclusion ................................................................................................................. 25
5. References.................................................................................................................. 26
Appendix A - Calculations .............................................................................................. 27
iv
LIST OF TABLES
Table 1: Thermal Properties of Seafood [7] ...................................................................... 7
Table 2: Thermophysical Properties [7] & [8] ................................................................ 11
Table 3: Raceway Aquaculture System Properties .......................................................... 12
Table 4: Concentration of Tilapia in Raceway ................................................................ 16
Table 5: Number of Tilapia in the Aquaculture System .................................................. 19
v
LIST OF FIGURES
Figure 1: Aquaculture Production of Tilapia in Millions of Tons [4] ............................... 2
Figure 2: Raceway Style Tank for Recirculating Aquaculture System [3] ....................... 4
Figure 3: Density of Fish in Raceway Style Tank [3] ....................................................... 5
Figure 4: Grid Coil Heat Exchanger [6] ............................................................................ 5
Figure 5: Raceway Dimensions ......................................................................................... 8
Figure 6: Heat Transfer Between Raceway and Surroundings .......................................... 9
Figure 7: Heat Transfer Diagram – Without Biomass ..................................................... 10
Figure 8: Heat Transfer Diagram – With Biomass .......................................................... 11
Figure 9: Simplified Heat Transfer Diagram – Baseline System .................................... 15
Figure 10: Simplified Heat Transfer Diagram – Biomass System .................................. 15
Figure 11: Tilapia Model ................................................................................................. 16
Figure 12: Introduction of Nile tilapia biomass ............................................................... 19
Figure 13: Simplified Heat Transfer Diagram – Water and Tilapia ................................ 21
Figure 14: Required Heat Load vs Tilapia Concentration ............................................... 22
Figure 15: Required Heat Load Reduction vs Tilapia Concentration ............................. 22
Figure 16: Estimated, Calculated, & Averaged Thermal Resistance .............................. 23
vi
LIST OF SYMBOLS
Symbol
Description
Unit
Tw1
Upper bound water temperature
K
Tw2
Lower bound water temperature
K
T∞
Ambient air temperature
K
vw
Velocity of water flow
m/s
dt
Diameter of tilapia
m
rt
Radius of tilapia
m
lt
Length of tilapia
m
tw
Thickness of cement wall
m
Aw
Area of walls
m2
Asurf
Surface area of raceway
m2
Pa
Air pressure
Pa
Vw
Volume of System
m3
ρw
Density of water (32° C)
kg / m3
ρa
Density of air (10° C)
kg / m3
kw
Thermal conductivity of water (32° C)
W/m×K
ka
Thermal conductivity of air
W/m×K
kc
Thermal conductivity of cement
W/m×K
kt
Thermal conductivity of tilapia (Avg)
W/m×K
Cpw
Specific heat of water (32° C)
kJ / kg × K
Ca
Specific heat of air (10° C)
kJ / kg × K
Cpt
Specific heat of tilapia (Avg)
kJ / kg × K
Cpb
Specific heat of water and tilapia biomass weight averaged
kJ / kg × K
νw
Kinematic viscosity of water (32° C)
m2 / s
νa
Kinematic viscosity of air (10° C)
m2 / s

Viscosity of water (32° C)
Pa × s

Viscosity of air (10° C)
Pa × s
αCp
Ratio of tilapia specific heat to fresh water specific heat
-
αk
Ratio of tilapia conductance to fresh water conductance
-
vii
tw
Time to cool water only system
hrs
Re
Reynolds Number
-
Nu
Nusselt Number
-
Ra
Raliegh Number
-
Pr
Prandtl Number
-
Dh
Hydraulic Diameter of Raceway
m
qwall
Heat transfer through side walls of raceway
W
qfconv
Heat transfer from water surface due to free convection
W
qrad
Heat transfer from water surface due to radiation
W
qbase
Total heat transfer out of water only baseline system
W
Rbase
Thermal resistance of water only baseline system
W/K
Rest
Thermal resistance estimate including water and tilapia
W/K
Rtcond
Thermal resistance through a single tilapia body
W/K
Rtconv
Thermal resistance at the tilapia to water interface
W/K
Rfish
Thermal resistance of all tilapia in the raceway
W/K
Rcalc
Thermal resistance calculation including water and tilapia
W/K
Ravg
Thermal resistance average of Rest and Rcalc
W/K
viii
LIST OF KEYWORDS
Key Word
Description
Aquaculture
Fish farming
Ectotherm
Cold blooded animal
FCR
Feed conversion ratio
Oreochromis
niloticus
Recirculating
system
Nile tilapia species of fish
Aquaculture system which mechanical circulates and treats water
Biomass
Mass of living tissue in a system
Conduction
Mechanism of heat transfer through solids
Convection
Mechanism of heat transfer through liquids and gases
Radiation
Thermal resistance
Mechanism of heat transfer from a warm body to cooler surroundings
through electromagnetic waves
Material or system property which represents the resistance to heat
flow
ix
ACKNOWLEDGMENT
I would like to thank my friends Jared Feist and Christopher Stubbs for accompanying
me in the pursuit of my graduate degree in engineering as well as my family for their
continuous encouragement. I would also like to extend thanks to my wonderful girlfriend
for her unwavering support. A special debt of gratitude is also due to Dr. Ernesto
Gutierrez-Miravete for his understanding and guidance throughout the completion of this
project.
x
ABSTRACT
High capacity water heating and cooling mechanical systems are typically employed in
large scale recirculating aquaculture systems, specifically in regions where the product
species may be subject to sub-optimal growth rates at the extremes of ambient
temperature. To optimize the heating and cooling loads required to keep water
temperatures in a desired range, an analytical model of a recirculating raceway is
constructed and then used to account for the inclusion of the product species biomass.
The aquaculture system studied accounts for conduction, forced and free convection, as
well as radiative heat transfer mechanisms between the raceway and the ambient
surroundings as well as convective and conductive heat transfer through the product
species biomass. Several different concentrations of biomass are analyzed to provide
bounding assumptions as to the extent to which biomass may affect water heating and
cooling loads. An overall reduction in the heat capacity required to maintain system
temperature is calculated for each case studied. This reduction is a comparison of the
baseline heating load required to maintain the temperature of the control body of fresh
water against the heating load required to maintain the temperature of the system when
accounting for varying levels of biomass. The aquaculture system studied models
biomass based on the properties of oreochromis niloticus or Nile tilapia and varies
concentration of the fish from 10 to 30% of the total system mass. It is shown that heat
load reductions ranging from 2.5 to 4.7% percent respectively can be obtained for tilapia
when accounting for the biomass of the product species in the aquaculture system. A
general approximation is proposed which relates the specific heats and concentrations of
the product species farmed and the fresh water in a recirculating aquaculture facility to
the heating or cooling load reduction which may be obtained over a baseline water only
system.
xi
1. Introduction
1.1 State of the Aquaculture Industry
Aquaculture, or fish farming, has been practiced by mankind in its various forms for
thousands of years [1]. Similar to terrestrial farming, aquaculture implies some sort of
intervention in the rearing process of the farmed animal such as regular stocking,
breeding, feeding, and protection from predators, to enhance production. In the United
States, the emergence of aquaculture can be traced back to the mid-19th century;
however it was not until the 1960s that rapid expansion in both production and variety of
animal species farmed took hold [2]. In the ensuing years, per capita consumption of
protein derived from some type of aquatic life form has continued to increase in the
United States reflecting similar rates in the worldwide consumption of fish.
To meet this ever rising demand for aquatic sources of protein, producers have begun to
increasingly turn towards aquaculture. Traditional fishing in the world’s oceans and
other large bodies of water is becoming seen as a resource that has been tapped to its
maximum sustainable limit. This is due to overfishing, pollution, and habitat destruction
which have led to significant loss in fish populations and natural diversity [1]. On the
other hand, aquaculture provides a sustainable and controllable means of producing fish
to meet the demands of an ever growing population. The initial investment and
continued maintenance of aquaculture facilities present the main obstacles which must
first be overcome to take advantage of the benefits over traditional fishing practices.
As stated above, current aquaculture practices began in the 1960s in which significant
biological and engineering expertise began to enter the field to optimize production. At
its heart, aquaculture is inherently a more energy efficient enterprise than farming of
land based animals. First, fish are ectotherms (cold blooded) and do not expend energy
maintaining body heat. Secondly, fish are neutrally buoyant in their environment and
therefore do not have to expend energy to support their bodies. Lastly, fish exist in a
three dimensional environment which greatly increases final yield on a per acre basis
[2]. For these reasons, the feed conversion ratio (FCR) of fish, which is the ratio of an
1
animal’s efficiency in converting feed mass into a usable protein output, is much greater
than that of traditionally farmed animals like cattle and pigs, and is similar to that of
poultry [3]. This allows aquatic farmers to expend more energy in maintaining the
optimum environment for their product animal while still remaining competitive in the
open market. Figure 1 below illustrates the recent growth of the aquaculture industry
with respect to Oreochromis niloticus, or Nile tilapia, which is one of the most
commonly farmed species of fish.
Figure 1: Aquaculture Production of Tilapia in Millions of Tons [4]
In the creation of the artificial habitats for the product animal, both biological sciences
and mechanical engineering practices come into play. Chemically, the water must be
free of toxins, pH balanced, and most importantly properly oxygenated to ensure the
survival of the product. Mechanically, the temperature and flow of the water must be
properly controlled to ensure an environment for optimal health and growth is
maintained. The mechanical aspect of controlling the water temperature for Nile tilapia
production will be further explored in the later sections of this report.
2
1.2 Types of Aquaculture
Modern aquaculture facilities for tilapia generally fall into one of four categories [5]. In
each category, the most important aspect of the water management system is to ensure
that clean and properly oxygenated water is provided to the product animal to ensure
survival. Of secondary, but also of very high importance is the control of water
temperature. Water must be controlled in the proper band of allowable temperatures to
ensure the following: survival of the product animal, rapid growth, and spawning. As
previously noted, all common commercially grown aquaculture products are ectotherms.
Therefore, these animals must rely on their environment to control body temperature,
with heat transfer taking place through gills and the body walls of the fish. The proper
water temperature encourages a high metabolic rate in the product animal which leads to
fast and efficient growth. Specific water temperatures are also required to allow animals
to spawn; however spawning is typically performed in smaller tanks and pens separate
from the main bodies of water used to grow-out fish to maturity. This provides
aquaculture farmers increased control over the spawning process.
The most common and least labor intensive, form of aquaculture is a pond water
production system. Nile tilapia are freshwater fish and therefore may be raised in inland
ponds fed by rainwater, streams and other larger lakes. These ponds may be natural or
man-made but must ultimately be large enough to induce a naturally occurring
ecosystem in which to sustain tilapia production. Harvest of fish is generally performed
by dragging large nets through the water.
Another common method of aquaculture production is cage culture, in which cages
made of netting are used to constrain the tilapia. Typically, these cages are placed in
much larger bodies of water than those that would be used in a pond water production
system and therefore the farmer has little control over the quality of the water in which
his fish grow. This can lead to sub-optimal growth conditions as well as exposure to any
toxins or pollutants that may be present in the ambient environment.
3
Flow-through raceway production systems are used in areas where an abundance of
fresh water flow is available, such as near large rivers of springs. These set ups usually
divert water from its source to allow for a continuous flow of new water through an open
trough which contains provisions to constrain the tilapia. Depending on the available rate
of water volume flowing through the raceway, the system may or may not need to be
mechanically supplemented to provide proper aeration for the density of tilapia
contained in the system.
The final category of aquaculture system, and the subject of this study, is a recirculating
system. These systems are used where water is not naturally available in significant
volume to use a flow through model or in regions where the ambient climate is not
suitable to permit year-round production of a particular species of fish. Recirculating
aquaculture systems may utilize earthen ponds, concrete tanks or some style of manmade raceway as the fish habitat. The most advanced re-circulating systems may be
located in large greenhouses or other climate controlled indoor facilities to aid in
mediation of ambient weather conditions and temperatures. Water treatment in
recirculating systems must include mechanical aeration to add dissolved oxygen,
mechanical filtration to remove large particulate, biological filters to enhance
nitrification and mechanical heating and cooling capacity to control water temperature
[5]. Figure 2 below shows raceway style tanks used in a recirculating aquaculture facility
while Figure 3 shows the high density of fish achievable in such a system.
Figure 2: Raceway Style Tank for Recirculating Aquaculture System [3]
4
Figure 3: Density of Fish in Raceway Style Tank [3]
In recirculating aquaculture systems, water heating and cooling capacity is often
generated through use of grid coil heat exchangers immersed directly in the tanks or
raceways which are used to grow-out fish to full maturity. A separate loop of
temperature maintained water is passed through these heat exchangers and is used to
maintain the overall temperature of the fish habitat. The quantity and size of the heat
exchangers present in the raceway or tank controls the maximum heating or cooling
capacity that can be delivered to the aquaculture system. Figure 4 shows a standard grid
coil heat exchanger.
Figure 4: Grid Coil Heat Exchanger [6]
5
Standard engineering practices for sizing the maximum heating or cooling loads required
to maintain optimal temperature in a recirculating aquaculture system involve
identifying the worst case ambient temperatures to which the system will be exposed,
identifying the optimal temperature band for fish growth, and calculating the expected
heat transfer into or out of the system based on the thermal resistance of the physical
system, the ambient temperature extremes, and the optimal temperatures. These
calculations are generally performed using the thermophysical properties of water only
to quantify heat loss or gain of the system through the mechanisms of conduction,
convection, and radiation.
The use of water properties alone in the sizing of heat loads for an aquaculture system
introduces an inherent conservatism in the capacity of the mechanical system designed
for maintaining water temperature. Identification of, and in appropriate cases elimination
of this conservatism may allow future recirculating aquaculture facilities to be optimally
and more cost effectively designed for the actual heat loads required by the system.
6
2. Theory and Methodology
This project explores the postulate that biomass should be accounted for when
performing required heat load calculations for recirculating aquaculture water heating
and cooling systems. The basis for this postulate is the addition of conductive and
convective heat transfer mechanisms that must occur within and at the boundary of the
biomass inside of the body of water. Table 1 below shows the thermal properties
(including conductivity and specific heat) of several species that are commonly grown in
aquaculture farms:
Table 1: Thermal Properties of Seafood [7]
Review of the information included in Table 1 shows that the conductivity of all
common species of animals grown in aquaculture farms is less than that of fresh water
(0.616 W/m·K [8]). The result of this natural phenomenon is that the heat transfer out of
a body of water containing a particular concentration of fish should face a higher
resistance than heat transfer out of a system containing only fresh water, even when
accounting for mainly convective heat transfer through the body of water. Therefore, the
potential for optimization of heating or cooling loads required to maintain a specific
water temperature exists and is likely dependent upon the percentage of biomass in the
system.
7
2.1 Theoretical System
To test the postulate proposed in this report, a control system is proposed with
parameters which attempt to adequately represent current commercial recirculating
aquaculture practices. To accomplish this end, a raceway style recirculating aquaculture
system was used to simulate a body of fresh water used to grow the Nile tilapia species
of fish. The raceway model used is a rectangular pool with cement walls in which the
length is many times greater than the width and the depth of water is kept to a minimum.
This design is optimal for indoor recirculating aquaculture facilities as the geometry of
the pool provides a natural river-like flow pattern from one end of the raceway to the
other to reduce eddy currents and aid in ensuring continued water replacement and
particulate removal. The total volume of water that fills the raceway must be cycled
through filter, aeration, and across temperature control systems at least once per day to
ensure sufficient water quality and temperature is maintained to allow for optimal
growth conditions of the aquaculture product. Figure 5 below shows the overall
geometry of the raceway used in this study:
Figure 5: Raceway Dimensions
The system represents a large section of a raceway pool; however it does not include the
ends of the raceway. This is done to simplify analysis by removing the need to consider
end effects of water discharge and return. These effects complicate analysis but do not
8
provide significant added value to the investigation at hand as the net result on the
heating or cooling loads would be the same for either a large body of water or one that
contains a concentration of biomass.
As stated earlier, this system is used to simulate the growth of Nile tilapia. The optimal
temperature for growth of tilapia is between 28 and 32°C, with growth declining greatly
as temperature decreases. Temperatures 10°C and below are considered lethal [5]. The
theoretical system therefore exists in an ambient environment of 283.15 K (10°C) with
initial water temperature of 305.15 K (32°C). Replacement of the entire volume of water
occurs once per day resulting in a steady current in the water from end to the other.
2.2 Analytical Method
This study uses the model proposed above to analyze the heat transfer phenomena in the
recirculating raceway. Figure 6 below shows the heat transfer mechanisms of
conduction, forced convection, free convection and radiation that are considered
between the raceway system and the ambient environment:
Figure 6: Heat Transfer Between Raceway and Surroundings
Forced convection occurs at the water to wall interface and heat transfer continues via
conduction through the wall. Free convective and radiative heat transfer occurs at the
water surface and transfers heat to the ambient surroundings. The mechanisms shown
9
pictorially in Figure 6 are equivalent to the standard engineering practices for sizing the
maximum heating load of a system. Evaluating heat loads in this manner treats the
volume of water as a single lumped mass with all heat transfer occurring only at the
boundary of the system. Figure 7 below shows the heat transfer diagram of a
recirculating raceway aquaculture system without considering biomass. As can be seen,
three parallel paths for heat transfer out of the system exist and the body of water is a
single lumped mass with temperature Tw.
Figure 7: Heat Transfer Diagram – Without Biomass
The treatment of the volume of water as a single lumped mass would be accurate for a
system consisting entirely of water. However, the introduction of fish into the system
adds a second ‘layer’ of heat transfer which must occur for energy initially in the
biomass to exit the system. Considering the conduction which must occur through the
body of the fish and the convection that must occur at the surface of the fish to water
interface therefore presents additional thermal resistance to the flow of thermal energy
out of the baseline system. Figure 8 below shows the heat transfer diagram which will be
used to simulate the effects of biomass in an aquaculture system.
10
Figure 8: Heat Transfer Diagram – With Biomass
This diagram represents the path of energy flow from the interior of a fish into the
ambient surroundings. Heat flow is considered to occur in parallel for the individual
representative fish masses. The temperature gradient through the body of water is
ignored for both systems and water temperature is treated as a bulk property.
2.2.1
Definition of System Parameters
The following thermophysical properties of water, air, and Nile tilapia are used in all
thermal resistance estimates and calculations performed in this study:
Table 2: Thermophysical Properties [7] & [8]
Variable
ρw
ρw
ρf
kw
ka
kc
kt
Cpw
Cpt
w
a
Description
Density of water (32° C)
Density of air (10° C)
Density of water (32° C)
Thermal conductivity of water (32° C)
Thermal conductivity of air
Thermal conductivity of cement
Thermal conductivity of tilapia (Avg)
Specific heat of water (32° C)
Specific heat of tilapia (Avg)
Viscosity of water (32° C)
Viscosity of air (10° C)
11
Value
996.025
1.1614
996.025
0.616
0.496
0.720
0.4961
4.181
3.513
8264 x 10-7
185 x 10-7
Unit
kg / m3
kg / m3
kg / m3
W/mK
W/mK
W/mK
W/mK
kJ / kg  K
kJ / kg  K
Pa  s
Pa  s
Table 3 below details the properties of the recirculating raceway aquaculture system
which are assumed for this study:
Table 3: Raceway Aquaculture System Properties
Variable
Tw1
Tw2
T∞
vw
rt
tw
Aw
Asurf
Vw
2.2.2
Description
Upper bound water temperature
Lower bound water temperature
Ambient air temperature
Velocity of water flow
Radius of tilapia
Thickness of cement wall
Area of walls
Surface area of raceway
Volume of System
Value
305.15
301.15
283.15
0.0126
0.08
.010
200
1000
1000
Unit
K
K
K
m/s
m
m
m2
m2
m3
General Assumptions
The proposed model uses the following major assumptions; additional assumptions are
made for specific calculations and are explained in the applicable section:
1. The bulk temperature of the body of water and biomass is considered constant
and does not vary along the length of the raceway. This is due to the use of
immersed grid coil heat exchangers throughout the length of the raceway which
provide a steady input of thermal energy into the system.
2. Temperature gradients in the water are negligible. Water temperature is a bulk
property of the system. This is due to the system being modeled as a steady state.
3. Temperature gradients in the biomass are negligible. Biomass temperature is a
bulk property of the system. This is due to the system being modeled as a steady
state.
2.2.3
Heat Transfer Through Side Walls
To quantify the heat transfer through the cement side walls of the raceway aquaculture
system, conductive and forced convective heat transfer mechanisms are considered. Heat
transfer due to conduction is simply based off of linear heat conductance theory shown
in Equation 1. Thermal resistance due to conduction is calculated by Equation 2.
𝒒𝒄𝒐𝒏𝒅 = 𝒌𝒄 × 𝑨𝒘
12
𝑻∞ −𝑻𝒘
𝒕𝒘
[1]
𝑹=𝒌
𝒕𝒘
𝒄 ∙𝑨𝒘
[2]
Forced convection at the water to wall boundary is calculated based off a Nusselt
number approximation for turbulent flow over a flat surface. The flow was determined to
be turbulent based on a calculated of a Reynolds number of 50620. This calculation
accounts for the raceway style flow by use of a hydraulic diameter calculated by
Equation 3.
𝑫𝑯 =
𝟒𝒂𝒃
𝟐𝒂+𝒃
[3]
The Nusselt number approximation used in this study is provided in Equation 4.
𝑵𝒖 = 𝟎. 𝟎𝟐𝟗𝟔 ∙ 𝑹𝒆𝟎.𝟖 ∙ 𝑷𝒓𝟎.𝟑𝟑
[4]
A coefficient of heat transfer is determined based on the calculated Nusselt number and
the thermophysical properties of water. Thermal resistance due to convection is
determined though use of Equation 5.
𝑹=𝒉
𝟏
𝒘 ∙𝑨𝒘
[5]
The thermal resistance of both conduction and convection are combined to find the total
heat transfer out of the system through the side wall, qwall, at the ambient temperatures
given in Table 3. All detailed calculations can be found in Appendix A.
𝑞𝑤𝑎𝑙𝑙 = 28,000 𝑊
2.2.4
Free Convective Heat Transfer from Surface
Heat transfer from the surface of the water in the raceway aquaculture system into the
ambient air is calculated based on the Nusselt number approximation shown in Equation
6 for free convection from a horizontal surface.
𝑵𝒖 = 𝟎. 𝟏𝟓 ∙ 𝑹𝒂𝟎.𝟑𝟑
[6]
The result of this approximation is used to determine the coefficient of heat transfer for
free convection. Equation 5 is again used to determine the resistance to free convective
heat transfer from the surface of the water to the air. The total heat transfer out of the
13
system due to free convection, qfconv, is then calculated. All detailed calculations can be
found in Appendix A.
𝑞𝑓𝑐𝑜𝑛𝑣 = 111,000 𝑊
2.2.5
Radiation Heat Transfer from Surface
A conservative value of radiation heat transfer from the surface of the water in the
raceway aquaculture system to the surrounding environment is calculated by assuming a
high emissivity of water and no irradiative energy reflected back into the water. The total
heat transfer out of the system due to radiation is qrad. All detailed calculations can be
found in Appendix A.
𝑞𝑟𝑎𝑑 = 125,000 𝑊
2.3 Baseline Heat Loads
The baseline system consisting of fresh water only is subject to all three heat transfer
mechanisms discussed in the previous sections. Combining all methods results in the
total sustained heat loss out of the raceway aquaculture system, qbase, and provides the
baseline required heat load needed to maintain constant temperature in a water only
system.
𝑞𝑏𝑎𝑠𝑒 = 265,000 𝑊
This value represents the result of following traditional aquaculture engineering
practices for sizing the maximum required heating load to maintain temperature in a
recirculating aquaculture system. To provide a basis for later calculations, a total system
resistance to heat transfer, thermal resistance Rbase, is calculated using Equation 7.
𝑹𝒃𝒂𝒔𝒆 =
(𝑻𝒘𝟏 −𝑻𝒊𝒏𝒇 )
[7]
𝒒𝒃𝒂𝒔𝒆
𝑅𝑏𝑎𝑠𝑒 = 0.00008302
𝐾
𝑊
Figure 9 below represents the simplified heat transfer diagram for the water only
baseline system and is a combination of all three parallel heat transfer paths in Figure 7.
14
Figure 9: Simplified Heat Transfer Diagram – Baseline System
2.4 Introduction of Biomass
When biomass is introduced into the fixed volume aquaculture system, water volume is
removed and replaced with fish biomass which is a solid and also consists of different
thermophysical properties than the water. The result of the added biomass is that
additional heat transfer mechanisms between the body of water and the fish biomass are
introduced which are not present in the baseline system. A simplified heat transfer
diagram for the flow of heat through the added biomass and out of the raceway
aquaculture system is shown below in Figure 10. This simplified diagram combines all
parallel paths of heat transfer from individual fish into a single thermal resistance, Rfish.
Figure 10: Simplified Heat Transfer Diagram – Biomass System
To account for the thermal resistance of the fish biomass an appropriate model of the
individual fish introduced to the system is constructed and the concentration of the fish
mass is determined. The model used in this study for tilapia is representative of a
medium sized adult male fish which can average 1 kg (2.2 lbs.) in weight. The tilapia is
modeled as a cylinder with diameter of 0.16 m and length of 0.20 m [10]. The
thermophysical properties of the cylinder are those defined in Table 2. The mass density
of Nile tilapia is assumed to be identical to that of water due to neutral buoyancy.
15
Figure 11: Tilapia Model
In a raceway style aquaculture system, common concentrations of tilapia range from
160-185 kg/m3 [11]. Introducing tilapia as modeled above to the raceway system at this
prescribed concentration results in approximately 20% of the system as biomass. To
provide additional insight into the effects of biomass on the thermal transfer within the
aquaculture system, five separate cases both above and below the average concentration
are considered. The concentrations studied are defined in Table 4 below:
Table 4: Concentration of Tilapia in Raceway
Case 1 Case 2 Case 3 Case 4 Case 5
10%
15%
20%
25%
30%
2.4.1
Modeling Biomass Resistance
Two methods are used to determine the increase in thermal resistance in the raceway
system due to the inclusion of biomass. First, a general estimate is made based on the
thermophysical properties of the fresh water, fish biomass and the overall time to cool
the system. Second, a more detailed investigation of the increase to thermal resistance of
the system due to biomass is pursued through calculation of the convective and
conductive heat transfer mechanisms occurring at the surface of and internal to the fish.
2.4.2
Resistance Estimate
To estimate the increase in the thermal resistance of the system due to inclusion of fish
biomass the lumped heat capacitance formula for cooling of a heated body is used. This
formula is shown in Equation 8 below:
16
𝑻𝒘𝟏 −𝑻𝒊𝒏𝒇
𝒕 = 𝝆𝒘 ∙ 𝑽𝒘 ∙ 𝑪𝒑 ∙ 𝑹𝒃𝒂𝒔𝒆 ∙ 𝒍𝒏 (𝑻
𝒘𝟐 −𝑻𝒊𝒏𝒇
)
[8]
This equation is first used to find the time required to cool the baseline water only
system from an initial temperature of 305.15 K (32°C) to 301.15 K (28°C) with an
ambient outside temperature of 283.15 K (10°C) and the overall thermal resistance of the
system of Rbase. The calculated time to cool, tw, represents the duration of time that must
pass in the ambient conditions for the baseline water only system to cool 4 K.
𝑡𝑤 = 19.271 ℎ𝑟𝑠
Using this calculated time and making the assumption that the time required to cool a
system with biomass is very similar to that of a water only system, a rough estimate of
the increased thermal resistance of the system when including biomass is determined. A
weight averaged specific heat, Cpb, accounting for the concentration of tilapia in the
system is calculated by use of Equation 9 and is substituted for the specific heat of water.
𝑪𝒑𝒃 = (𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑾𝒂𝒕𝒆𝒓 ∙ 𝑪𝒑𝒘 ) + (𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑩𝒊𝒐𝒎𝒂𝒔𝒔 ∙ 𝑪𝒑𝒕 ) [9]
Equation 8 is then rearranged to solve for the resistance estimate, Rest, of the new system
as shown in Equation 10.
𝒕𝒘
𝑹𝒆𝒔𝒕 =
𝑻𝟏 −𝑻𝒊𝒏𝒇
)
𝑻𝟐 −𝑻𝒊𝒏𝒇
[10]
𝝆∙𝑽∙𝑪𝒑𝒃 ∙𝒍𝒏(
It is noted that this estimate does not directly calculate thermal resistance due to
convective heat transfer at the surface of the fish or conductive heat transfer through the
volume of fish mass that has been introduced into the system; however it does allow for
a rough approximation of the effect of these heat transfer mechanisms. The estimate
assumes that the decrease in the specific heat of the system due to the addition of the fish
biomass (Cpb) is directly offset by the increased thermal resistance due to convective and
conductive heat transfer through the biomass. This basis of this estimate is considered
valid by a comparison of the ratios of the specific heat and thermal conductivity for Nile
tilapia and water as shown below:
𝛼𝐶𝑝 =
𝐶𝑝𝑡
= 0.84
𝐶𝑝𝑤
17
𝛼𝑘 =
𝑘𝑡
= 0.80
𝑘𝑤
The ratio of specific heats, αCp, indicates the effect on the energy required to change the
temperature of the system with biomass. Since the ratio is less than 1, the time to cool
the new system should decrease given a constant heat loss qbase as less energy loss is
required to cool the system. The ratio of thermal conductance, αk, indicates the effect on
the thermal resistance on the system with biomass. Since this ratio is less than 1, the
resistance to change in temperature in the new system should increase as it indicates
energy conducts more easily through water than tilapia biomass. Since the ratio of
specific heats is closer to 1 than the ratio of conductance (e.g. the tilapia thermophysical
property is more similar to that of water), the effect of biomass on the thermal resistance
of the system should be greater than the effect of biomass on the energy required to
change the temperature of the system. This initial estimate is used to provide a reference
point from which to begin a more detailed analysis of the theoretical system.
2.4.3
Resistance Calculation
To introduce biomass into the recirculating aquaculture system, individual Nile tilapia
are considered which weigh 1 kg and are modeled as cylinders with radius, rt = 0.08 m
and length lt = 0.2 m. For this calculation, water temperature is again treated as a bulk
property due to steady state conditions. Making this assumption allows the dispersal
pattern of the biomass in the system to be random as no temperature profile is considered
throughout the water mass. The assumption does not impact calculations on the
increased thermal resistance of an aquaculture system with biomass as the temperature
profile through the water mass is also ignored in baseline calculations. Figure 12 below
shows a cross-sectional view of the system with the introduction of biomass:
18
Figure 12: Introduction of Nile tilapia biomass
A second important assumption in the modeling of biomass in the aquaculture system is
the neglecting of end effects of heat transfer through the tilapia. All heat transfer
calculations are performed as a 2D cross-section of the system and then applied to the
entire length of the raceway. To this end, tilapia mass is modeled into the system in 100
m long cylinders of radius rt with each cylinder representing 500 individual fish. Table 5
below shows the total number of fish approximated for each case studied and the number
of representative cylinder present in a given cross-section of the raceway:
Table 5: Number of Tilapia in the Aquaculture System
Case 1
Individual Fish
Representative Cylinders (Nt)
2.4.4
Case 2
Case 3
Case 4
99,500 149,000
199,000
248,500 298,000
199
298
398
497
Case 5
598
Resistance Calculation - Convection
To calculate the increase in thermal resistance due to convective heat transfer from the
fish biomass into the surrounding water, the number of fish in the system is determined
based on the biomass concentration in each specific case. A convective heat transfer
coefficient is then calculated based on the system characteristics and the total surface
area of the fish modeled for each different scenario. Thermal resistance due to
convection is determined by Equation 5. All detailed calculations can be found in
Appendix A.
19
2.4.5
Resistance Calculation - Conduction
The thermal resistance due to conductive heat transfer through the fish biomass is
calculated by use of the fish radius, rt, thermal conductivity, kt an assumed inner
diameter of the fish rt1.
𝑹𝒕𝒄𝒐𝒏𝒅 =
𝒓
𝒍𝒏( 𝒕 )
𝒓𝒕𝟏
[11]
𝟐∙𝝅∙𝟏𝟎𝟎𝒎∙𝒌𝒕
The constant rt1 is chosen to allow for the majority of the fish mass to be accounted for
in the thermal resistance due to conduction through the fish body. Similar to the body of
water, the temperature distribution in the fish is ignored and considered to be a bulk
property due to steady state conditions. All detailed calculations can be found in
Appendix A.
2.4.6
Resistance Calculation - Consolidation
As shown in Figure 8, the thermal resistance of the system due to fish biomass is a
network of parallel conductive and convective heat transfer paths occurring through the
individual fish, into the body of water and finally out into the ambient environment. The
following equation is used to calculate the thermal resistance of all parallel paths of heat
transfer that originate within the tilapia biomass:
𝑹𝒇𝒊𝒔𝒉 =
𝟏
(
𝟏
𝑹𝒕𝒄𝒐𝒏𝒗 +𝑹𝒕𝒄𝒐𝒏𝒅
)∙𝑵𝒕
+ 𝑹𝒃𝒂𝒔𝒆
[12]
The variable Nt is the number of tilapia found in a cross section of the system at any
given point along the raceway. A final calculation is performed as part of the resistance
calculation to combine the parallel paths of heat transfer that occur out of the water only
and the heat transfer which originates in the biomass and also passes through the water.
Figure 13 below shows the simplified heat transfer diagram:
20
Figure 13: Simplified Heat Transfer Diagram – Water and Tilapia
These paths of heat transfer are averaged based on the weight concentration of fish in the
system to accurately represent the impact of each thermal resistance path on the system
as a whole. Equation 13 provides the formula used to average the system resistance
based on weight concentrations.
𝑹𝒄𝒂𝒍𝒄 =
𝟏
(
𝟏
𝑹𝒃𝒂𝒔𝒆
2.4.7
∙𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑾𝒂𝒕𝒆𝒓)+(
𝟏
𝑹𝒇𝒊𝒔𝒉
[13]
∙𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑩𝒊𝒐𝒎𝒂𝒔𝒔)
Final Resistance
To reduce the impact of assumptions made in both the thermal resistance estimate and
the thermal resistance calculation, the results of each method are averaged for each case
study. This average thermal resistance is used to compute the new total heat transfer out
of the system for the various levels of biomass concentration. All detailed calculations
can be found in Appendix A.
21
3. Results and Discussion
The thermal resistances determined in this report result in a reduction to heat loads
required to maintain system temperature versus the baseline water only calculation. As
expected, the reduction in overall heat loads positively correlates to the percentage of
biomass in the system. Figure 14 and Figure 15 below summarize the effects of the
thermal resistances calculated as part of this study on required heat loads.
Required Heat Load to Maintain
Temperature
Heat Load (W)
270000
265000
260000
255000
250000
245000
0%
10%
15%
20%
25%
30%
Tilapia Concentration
Figure 14: Required Heat Load vs Tilapia Concentration
Heat Load Reduction
Required Heat Load Reduction
5.0%
4.5%
4.0%
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
0%
10%
15%
20%
25%
Tilapia Concentration
Figure 15: Required Heat Load Reduction vs Tilapia Concentration
22
30%
The basis for the heat load reduction is the increased thermal resistance of the system as
a whole due to the inclusion of biomass in heat transfer calculations. The estimated,
calculated, and average thermal resistances calculated in this study are shown in Figure
16.
Estimated, Calculated & Average Thermal
Resistance
0.00009200
Thermal Resistance (K/W)
0.00009000
0.00008800
0.00008600
Calculated Resistance
0.00008400
Estimated Resistance
Averaged Resistance
0.00008200
0.00008000
1%
4%
7%
10%
13%
16%
19%
22%
25%
28%
31%
34%
37%
40%
43%
46%
49%
0.00007800
Tilapia Concentration
Figure 16: Estimated, Calculated, & Averaged Thermal Resistance
The above figure shows reasonable agreement between the estimated and calculated
thermal resistances. As methods for determining both the estimated and calculated
thermal resistance of biomass in the system did not overlap, this indicates increased
confidence in the calculation methods described in the preceding sections.
It is also clear in Figure 16 that the relationship of the tilapia concentration to thermal
resistance differs for the estimated and calculated methods. The estimated thermal
resistance shows a clear positive linear correlation between increase in tilapia
concentration and increase in thermal resistance. This type of correlation for the
estimated thermal resistance is expected due to the assumptions made and method of
linear change of specific heat used in the estimation. However, the calculated thermal
23
resistance of the system shows a clearly different relationship. The initial increase in
tilapia concentration (from 1% to 15%) results in an increase in thermal resistance at a
rate much higher than the estimated method. However, the calculated thermal resistance
quickly levels off after biomass concentration levels hit 15% with only gradual increase
in thermal resistance for increasing tilapia concentration. This effect is due to the
conductive and convective heat transfer considered for each individual tilapia occurring
in parallel. As a basic principle of thermal resistance circuits, the more pathways that
exist in parallel in a given system (the number of tilapia increase), the greater the
decrease in overall thermal resistance. This results in a leveling off of the calculated
thermal resistance. Review of calculations does show that the thermal resistance
calculated for all tilapia actually does decrease as more fish are added into the system.
This decrease is offset due to the fact that resistance through the tilapia is still always
greater than the baseline resistance due to water only, and therefore the total calculated
resistance of the system continues to increase with higher levels of biomass
concentration.
It is also noted that the calculated method results in a greater thermal resistance of the
system for tilapia concentrations less than 30% of total system mass, while the estimated
method begins to result in a greater thermal resistance of the system for concentrations
above 30%. A sensitivity analysis on the effect of fish size on thermal resistance reveals
that the intersection point for the two methods varies. When a fish model of half of the
mass (0.5 kg) is used at the same overall biomass concentration levels, the intersection
point drops to approximately 15% before the estimated method for resistance calculation
becomes greater. This is important as it shows a dependence of increased thermal
resistance on not only the concentration of biomass in a system but on the physical
characteristics of the biomass itself.
24
4. Conclusion
This study constructs an analytical model of a recirculating aquaculture system and
determines the effect of varying levels of biomass on the heat transfer out of the system.
The model is a raceway aquaculture system used to grow Nile tilapia with an ambient
temperature differential of 22°C between the system and ambient environment. Five
different levels of biomass were modeled into the system and their effect on the overall
thermal resistance to heat flow out of the aquaculture system was determined. The
thermal resistance due to biomass was first estimated and then calculated in an attempt
to control the influence of individual assumptions made in each method.
It was determined that biomass does have a measurable, albeit low percentage, impact on
overall heat loads required to maintain temperature in a given aquaculture system.
Thermal resistance increases as more fish are added to the raceway, however the level of
increase is contingent not only upon the total concentration of biomass in the system but
also upon the size of the individual fish the system. For the specific system studied, 1 kg
Nile tilapia ranging from 10 to 30% of total system mass, heat load reductions ranging
from 2.5 to 4.7% percent can be obtained when accounting for the biomass of the
product species in the aquaculture system.
To convert the results of this study for practical applications, the following
approximation is proposed for reducing the size of heat loads required to maintain
temperature in a recirculating aquaculture system of larger fish (mass 1 kg or greater):
𝑹𝒆𝒅𝒖𝒄𝒕𝒊𝒐𝒏 𝒊𝒏 𝑯𝒆𝒂𝒕𝒊𝒏𝒈 𝒐𝒓 𝑪𝒐𝒐𝒍𝒊𝒏𝒈 𝑪𝒂𝒑𝒂𝒄𝒊𝒕𝒚 = 𝟏 −
(𝑷𝒃 × 𝑪𝒑𝒃 ) + (𝑷𝒘 × 𝑪𝒑𝒘 )
𝑪𝒑𝒘
For this approximation, Pb is the percentage of biomass in the system and Cpb is the
specific heat of the biomass. Cpw and Pw are the specific heat and percentage of water
and the system respectively. This approximation is considered valid for fish of 1 kg in
weight and for biomass concentration levels up to 30%. Further study may be pursued to
provide bounding constraints for validity for this approximation for other sizes of fish.
25
5. References
[1]
Kathryn White, Brendan O’Neil, and Zdravka Tzankova, At a Crossroads: Will
Aquaculture Fulfill the Promise of the Blue Revolution? Copyright © 2004
[2]
LaDon Swann, A Basic Overview of Aquaculture History, Water Quality, Types
of Aquaculture, Production Methods, August 1992
[3]
Raise Fish Around the Globe, startsomegood.com/fisharoundtheglobe, Site
visited November 9, 2014
[4]
Food and Agriculture Organization of the United Nations, faostat.fao.org,
Copyright © 2013
[5]
Claude E. Boyd, Farm-Level Issues in Aquaculture Certification: Tilapia
[6]
Empire State Plating Products, filterpumpeast.com/Process_Technology_Page,
Site visited November 9, 2014
[7]
[8]
Measurement of Thermal Properties of Seafood; Radharkishnan, Sudhahrini;
Thesis Virginia Polytechnic Institute and State University June 26, 1997
Transport Phenomena in Multiphase Systems; A. Faghri and Y. Zhang;
Copyright © 2006; Elsevier Inc. – Appendix B, Page 980, Table B.48
[9]
Fundamentals of Heat and Mass Transfer; F. Incropera, D. Dewitt, T. Bergman,
A. Lavine; Copyright © 2007; John Wiley & Sons Inc.
[10]
Tilapia: Life History and Biology, thefishsite.com/articles/58/tilapia-life-historyand-biology,Copyright © 2000, site visited November 16, 2014
[11]
Cultured Aquatic Species Information Programme, Oreochromis niloticus
(Linnaeus, 1758), Food and Agriculture Organization of the United Nations,
fao.org/fishery/culturedspecies/Oreochromis_niloticus/en, Copyright © 2014,
site visited November 16, 2014
26
Appendix A - Calculations
27