CHAPTER THREE CHARACTERIZING APULSED LIMESTONE BED …
Transcript of CHAPTER THREE CHARACTERIZING APULSED LIMESTONE BED …
CHAPTER THREE
CHARACTERIZING A PULSED LIMESTONE BED REACTOR TO TREAT
IDGH ACIDITY WATER
Abstract
Acid wastewaters are usually treated by one or more of several methods
including addition of lime and basic solutions to meet pH requirements for discharge.
The use of limestone as the acid neutralizing agent can reduce operating costs in
comparison to most other methods. However, limestone use is currently restricted to
sites with low acidities, due to the low solubility of limestone and problems associated
with the development of a metal hydroxide coating on the limestone particles that
further reduces solubility. A method invented by Watten (1999) that increases
solubility of limestone by using a fluidized (pulsed) bed system with a carbon dioxide
pretreatment step was investigated.
Four carbon dioxide pressures (34.5, 69.0, 137.9 and 206.8 kPa), three influent
flow rates (3.8, 6.8 and 9.8 Lpm), and three influent temperatures (12, 17 and 22°C)
were tested using a prototype pulsed bed reactor system. Performance characteristics
were used to develop a mathematical model to predict performance. Hydraulic
retention time and applied carbon dioxide pressure were the only significant variables
found in the regression models.
Increased hydraulic retention time of the acid water in the reactor increased
eflluent alkalinity from 300 mgIL as CaC03 to 500 mgIL when the hydraulic retention
time was increased from 0.8 min to 1.1 min at 34.4 kPa carbon dioxide pressure at
12°C. Temperature did not significantly affect the effluent alkalinity over the range of
temperatures investigated.
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The pulsed bed reactor system consumed 98% (on average) of the raw
limestone by weight with the remaining 2% being transported through the reactor
system without dissolving. The average bed expansion ratios were 134%, 179%, and
224% ~t superficial velocities of 0.8 cm/s, 1.5 cm/s and 2.1 cm/s, respectively. Bed
expansion increased over time as limestone was consumed indicating a change in
particle size distribution.
Regression models to predict eflluent alkalinity were developed from the data.
Introduction
AMD Problem
Acid mine drainage (AMD) contributes significantly to acid waters in mining areas.
AMD is generated when wetted sulfide minerals are exposed to the atmosphere,
thereby producing sulfuric acid. The acid in tum dissolves aluminum, manganese,
zinc, and copper from the soil with which the AMD waters come in contact.
Therefore AMD drainage is not only highly acidic, but may contain high levels of
metallic ions. Treatment of AMD could be achieved by adding alkaline material, such
as sodium hydroxide or potassium hydroxide, followed by clarification to remove
insoluble metal hydroxide products. However, these materials are both caustic and
relatively expensive and this limits their widespread application due to these safety
and cost issues and thus they are rarely used.
Limestone is a desirable treatment agent, because of its relatively low cost and
its relative neutral pH product. Limestone reacts with acid to form bicarbonate:
CaC03 + It" = Ca2+ + HC03- (1)
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Currently, limestone use is constrained due to its slow dissolution rate and
problems associated with development of metal hydroxide coatings on the surface of
the limestone particles (referred to as armoring; Evangelou, 1995). The armoring
results in decreased dissolution.
Pearson (1975) described the kinetic chemical reactions associated with using
limestone to neutralize acid waste and found that the concentrations of hydrogen ion
and carbon dioxide are the controlling factor in the limestone dissolution rate. Santoro
(1987) described the surface precipitation of metal ions in a limestone treatment bed
and found the rate of precipitation is related to the rate of limestone dissolution and
hydroxide precipitation.
Pulsed limestone bed (PLB) Process
The USGS has recently patented the pulsed limestone bed (PLB) process
(Watten, 1999) to mitigate AMD water. The PLB process is designed to enhance
solubility of limestone and to circumvent problems associated with alternative
methods that incur high reagent costs, produce large sludge volumes, or are subject to
over treatment and large handling requirements. The PLB treatment method is also
highly efficient, since it can treat AMD water to an acceptable pH level within several
minutes as opposed to several hours or days as is the case when using a limestone
channel.
The PLB method is comprised of the following three steps:
• charging the AMD water with carbon dioxide,
• intermittently fluidizing and expanding the bed m one-minute
cycles for four minutes,
• displacing the limestone treated AMD water with untreated charged
effiuent.
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The PLB process is based in part on the reaction of carbon dioxide with water
and limestone to form calcium bicarbonate:
CaC03 + CO2+ H20 = Ca2++ 2HC03- (2)
Pressured carbon dioxide supplied in the system accelerates the dissolution of
limestone while also contributing to a higher level of alkalinity. The excess alkalinity
allows for a sidestream treatment and hence a potentially large reduction in the size of
the reactor given the ability of HC03- to react with acids:
HC03- + W = CO2+ H20 (3)
Fluidized Bed
The PLB is designed using fluidized bed principles (Summerfelt, 1993). The
fluidized bed is an effective process to increase the contact surface area of granule
particles with a fluid medium that requires some type of water treatment. The
relationship between superficial velocity, bed expansion and pressure drop have been
described by Summerfelt (1993). The performance of the fluidized bed is affected by
the physical properties of the granular media (diameter, density, bed porosity) and
fluid physical chemistry properties e.g., density, viscosity (Weber, 1972).
The expansion ratio is defined as fluidized bed height divided by settled bed
height as a percentage. The expansion ratio of a fluidized bed will be directly related
to the particle size and particle size distribution (uniformity coefficient) of the media
used in the bed. Changes in expansion characteristics of a PLB system between
recharging of limestone, refilling the reactor vessels with raw limestone, would be
indicative that the physical characteristics of the bed are changing, e.g. small particles
are being dissolved leavinc behind an increased percentage of larger particles. Such
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effects would have an impact on the rate of recharging and whether or not limestone
should be partially removed and replaced between charges with an entirely new
quantity of limestone. The effects of particle size on PLB system performance may
also indicate that the limestone material may require pretreatment to some specific
size range of particles or achieving some specific uniformity coefficient for the
limestone charging material. Mathematical modeling of the PLB process and in
particular the fluidization characteristics requires an accurate characterization of the
particle size distribution as a time dependent variable. Particle size would impact the
scouring and abrasion properties of the limestone particles and could therefore be
important in future modeling efforts to describe the PLB treatment process for AMD
waters.
Carbonate Chemistry
Carbon dioxide (C02) concentrations in water can be controlled by the applied
C02 pressure. Source CO2 can be obtained from commercial suppliers, a carbon
dioxide generator or by capturing and then recycling the off-gases from the PLB
effluent or a combination of above. The solubility of carbon dioxide is related to the
C02 conversion from the gas phase to the liquid phase. C02 equilibrium will be
established between liquid and gaseous phases if sufficient time is allowed. The
equilibrium concentration for C02 is usually modeled using Henry's law:
P=H·Ca(4)
where
P = gas concentration in the gas phase, atm
H, = Henry's constant, atm
C = gas concentration in the liquid phase, mole/mole
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The calcium carbonate (limestone) that dissolves in an acid solution is the
result of a series of kinetic reaction processes. The kinetics involve the hydrogen ions
that are transported from the bulk fluid to the particle surface, the chemical reaction on
the surface and the resulting products that return to the bulk solution (plummer, 1978).
The specific kinetic parameters that affect the PLB process are: applied C02 pressure,
temperature, hydraulic retention time and limestone bed height. These were the
parameters investigated in the present study. Changes in particle size distribution of
the limestone were not measured during the experiments.
Temperature Effects
Chemical reaction rates and solubilities of some particulates generally increase with
increasing temperature (Weber, 1972). The equilibrium of the chemical reaction is
determined by the Gibb's Free energy. The solubility of CO2 in water (expressed as
mole fraction of C02 in liquid phase) drops from 0.000287 to 0.000212 as temperature
rises from ro-c to 20°C at C02 partial pressure of 30 kPa (Lide, 1998). However,
such relationships as mentioned are at equilibrium conditions only. The rapid
exchange of the fluidized reactor would preclude any equilibrium to occur during
short retention times as used in their application.
Hydraulic retention time Effects
Since the change in chemistry of a particular water property e.g., viscosity, will
be affected by the length of time in the process, hence, hydraulic retention time is a
parameter considered in most mechanisms. The hydraulic retention time affects on
effiuent alkalinity was discussed (Sverdrup, 1985).
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Objectives
The objective of this study was to determine the operational characteristics of a
PLB process as affected by temperature, hydraulic retention time, applied carbon
dioxide pressure, and limestone bed height as indicated by effluent alkalinity,
limestone utilization and bed expansion ratio. A regression model was developed to
predict the effluent alkalinity performance for this particular PLB system.
Materials and Methods
PLB System
A PLB reactor unit was constructed by Watten (1999) as shown in Figure 3.1.
The unit was capable of handling AMD water flow rates up to 15 L/min. The major
components of the system consisted of four 10 em diameter x 203 cm tall pressure
vessels, a centrifugal pump, a packed tower carbonator, and a timer-relay control
system that was used to direct the system's 3-way electric ball valves. Each vessel was
filled or charged with 8.2 kg of granular limestone (D60 of 0.60 mm particle size). The
particle distribution of the limestone material used is shown in Figure 3.2.
In operation, during a four-minute treatment cycle, two of the four limestone
beds (columns 1 and 2) receive recycle water sequentially in one minute increments
from the carbonator under pressure to maintain high carbon dioxide concentrations.
Columns 1 and 2 are maintained at higher than atmospheric pressure as a result of the
carbon dioxide being supplied from a compressed C02 pressure tank. The high CO2
gas pressure in the limestone columns serves to accelerate limestone dissolution
(Equation 2). A specific system pressure was established by adjusting the pressure
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tank regulator valve to achieve the desired vessel pressure. A carbonator (see Figure
3.1) links columns 1 and 2 and the C02 pressure tank. The carbon dioxide feed rate
was measured by a mass flow meter (model GFM-37, Aalborg Company, Orangeburg,
New York). While columns 1 and 2 are in the treatment phase of a cycle, columns 3
and 4 are isolated from the carbonator by the control system and vented to the
atmosphere. Degassing occurs in columns 3 and 4 as the treated water is displaced by
incoming acid water applied as in column 1 and 2 sequentially in one minute
increments. The water supplied to all columns is introduced at a rate that fluidizes the
limestone bed. Beds contract when water flow is interrupted during a one minute
settling phase. Upon completion of a four-minute cycle, column 1 and 2 (treatment
cycle) are switched to the discharge cycle, and at the same time, column 3 and 4 are
switched to the treatment cycle. The four-minute cycle then is repeated providing a
constant discharge from the treatment unit. Effluent samples used to measure
alkalinity and pH were taken during one of the 4-minute cycles from the discharging
treatment pair of columns.
The applied pressure of the carbon dioxide and influent flow temperature were
fixed for each set of tests. A summary of the influent characteristics and treatment
conditions employed are shown in Table 3.1. Three different flow rates (3.8, 6.8 and
9.8 Lpm), which in turn control hydraulic retention time (HRT), were employed
during a set of tests for a specific temperature and applied CO2 pressure. The
sequence of flow rates evaluated were always conducted in the same order, lowest
flow rate, medium flow rate, and then highest flow rate. This sequence was followed
to minimize the potential of washing out limestone media from the reactor vessels.
Each sequence was conducted three times at each specific temperature and CO2
pressure condition. After a specific temperature and applied CO2 pressure and the
three flow rates were evaluated, i.e. 3 tests with an individual flow rate being a test,
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the system was turned off for at least two hours and then this same set of conditions
for temperature and C02 pressure was repeated with each of the three flow rates two
more times. The two hour period between a series of 3 tests was so that complete
settling of the bed would result to allow reasonably accurate measurements of the
amount of limestone material left in the columns. The series of tests can be
considered a 3x3x3 replicated experiment that provided replicate combinations of
operating conditions.
Limestone Characteristic and Charging
The limestone used was supplied by Con-Lime Inc., in Bellefonte, PA. The
particle size (D60) was 0.60 mm. The distribution of particle size was obtained by
plotting in logarithmic scale a cumulative percent passing versus sieve opening size in
microns (Sibrell, 2001). The uniformity coefficient (D60!D1O) for this material was
3.0.
Each vessel was initially charged with 8.2 kg of granular limestone. After each
series of three replicated tests (low, medium and high flow rates) at a specific
condition of temperature and applied C02 pressure, the remaining limestone from each
vessel was removed and replaced with a new charge of 8.2 kg of limestone. The
limestone bed was then rinsed with well water at a 8.3 Lpm flow rate for 90 minutes,
allowed to settle for at least two hours, and then measured for its initial bed height.
The flow rate of8,3 Lpm was used during the rinsing process to remove dust and other
small particles that could clog the system during test runs; although the 8.3 Lpm is not
the same as the maximum flow rate used (9.8 Lpm), the 8.3 Lpm was practically the
highest flow rate that could be used during the rinsing process that would not flush out
excessive material and 90 minutes were used for the rinsing period.
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------------------------------------------------: .........•••····
..nt
"="="="="="="='~........
..II..
t_::5l.~f7Dd:..
II
••Column 2 Column 4
IC~--6..CarbonatorII
I·~ ....•I···•···.j
Column 1 Column 3
~ .
I····'4----------------------------------tI! •••••••••••• ••••••••••••••••••••••~.
~C3-WayBallCvcle
,Influent
••••••••••. =::~
Gate Valve Check Valve Pwnp Recharge Cycle Treatment
Figure 3.1. Schematic of flows through the AMD water treatment system using a
pulsed limestone bed (PLB) fluidized reactor system.
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Table 3.1. Pressures tested at each of three temperatures.
Temperature eC) Pressure (kPa)
12 34.5
69.0
137.9
206.8
17 34.5
206.8
22 34.5
206.8
Each unique set of conditions was replicated three times at each of three flow rates
(3.79; 6.82; 9.84 Lpm).
1000
800
600
e 500:=QS 400!oil...•
00~ 300-Cj...•-••~
=-c 200
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D60=O.60mm
100
o 20 40 10060 80
Cumulative % Passing
Figure 3.2. Limestone particle size distribution (particle size in log scale).
Water............._..........• Cooling
System~ •.........•.........._.
AcidWaterFlow
Acid WaterStorage Tank1,890 Liter
CO2Tank
.........._ .............•
WellWaterFlow
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EfiluentDischarge
.......................•
EfiluentDischarge
Figure 3.3. Schematic plot of the acid water circulation system.
PLB Process
WaterHeatingSystem
'-- ---I ~
CO2Charge
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Inflow Temperature Control
The influent water flow was taken from a ground water source at the Leetown
Science Center, Kearneysville WV. The typical composition of this groundwater was
pH 7 ± 0.1, alkalinity 280 mg/L as CaC03 and temperature 12 ± O.SoC. The
temperature of the inflow water was controlled by a heat exchanger that used ground
water as the cool water heat sink. At elevated test temperatures (17°C and 22°C), the
inflow water was circulated first to an insulated storage tank and then heated using an
adjustable electric resistance heater. A schematic of the operating system is shown in
Figure 3.3. The desired temperature was maintained within O.SoCby using both the
heat exchanger and heater.
Simulated AMD
In order to simulate AMD water with a pH of 2.5, 900 ml of concentrated
sulfuric acid (Fisher Scientific Brand, A-300) was added to 1890 liters of spring water
in an insulated tank. The resulting acidity was analyzed using standard methods
(APHA 1995) to be 450 ± 50 mg/L as CaC03 (air stripped). From here on, the
influent water will be referred to as acidic water. Metal ions in AMD water were not
included in the acid water.
Hydraulic Retention Time (Flow Rate) Control
Each of the three flow rates produced a specific hydraulic retention time
(HR.T). The HR.T was calculated as the volume of the expanded limestone less the
volume occupied by the limestone particles not including any porosity volume divided
by the influent flow rate, i.e. only the solid volume of the limestone is subtracted from
the vessel volume. The HR.Tcould be determined as:
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h ·A-h ·A·(l-e)HRT= e s
1000·Q (5)
where
HRT = hydraulic retention time, min
he = expanded bed height, em
A = cross sectional area of the vessel, cm2
h, = static bed height, em
c = porosity of limestone bed at static bed height
Q = flow rate, Lpm
1000 = unit conversion factor of cnr' to liters
At each specific flow rate, several measurements of flow and time were taken
to ensure that the desired flow rate was being maintained during each run.
Chemistry Analysis: Acidity, pH, Alkalinity
The influent acidity was measured both as an air stripped and a non-air
stripped condition. The pH and alkalinity measurements were done immediately after
taking an effluent sample during one of the four-minute cycles. The effiuent sample
was treated in one of four ways before pH and alkalinity were measured:
1) filtered using glass MicroFibre Filters (Whatman 934-AH, pore size 1.5 urn)
and then vigorously air stripped (bubbling air into the 500 ml sample for 7
minutes to strip C02 from the sample at minimum CO2 concentration in the
solution), referred to as FA,
2) neither filtered nor air stripped, referred to as NFNA.
3) filtered but non-air stripped, referred to as FNA and
4) non-filtered but air stripped, referred to as NFA
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Acidity and alkalinity were measured by titration using standard methods
(American Public Health Association, APHA, 1995). The pH was measured
electrochemically using a pH meter (Accumet, Model 50) and probe (ORION,
PerpHecT ROSS) with temperature compensation. The pH meter was calibrated
against standard solutions every three days.
Alkalinity and acidity in a carbonate system can be defined as
Alk = [HC03"]+ 2[C032-]+ [Olf] - [W]
Acy = [HC03"]+ 2[H2C03*] + [W] - [Olf]
(6)
(7)
Where
Alk = alkalinity, eq/L
Acy = acidity, eq!L
[H2CO/], [HC03-], [COlO], [Olf] , [W] = concentration of H2C03', HC03", C032",
orr, W respectively (M)
[H2C03*] = [C02(aq)]+ [H2C03]
Theoretically, stripping CO2from effluent will not affect alkalinity at all since
C02 does not contribute to alkalinity as shown in Equation 6. Stripping CO2will only
affect pH (pH rises as excess C02 stripped out) since CO2is contributed as weak acid.
The reason excess C02 is stripped from the effluent is to increase pH to an acceptable
range near pH 7 in order to meet discharge standards. During the stripping process, it
is likely that some Ca2+ will begin to precipitate as pH rises and therein decreases
solubility of Ca2+. Similarly, since CO2 affects acidity (see Equation 7), the stripping
of C02 from the effluent samples would theoretically decrease its acidity.
Filtering limestone particles from the effluent is necessary to obtain an
accurate measurement of alkalinity. This is because an acid titration process was used
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to determine alkalinity, and if not removed, the limestone particles will continue to
dissolve in presence of an acid, which releases bicarbonate until all the limestone
particles in the solution are consumed.
Since effluent alkalinity is reported in a variety of manners, the effluent
samples were post-treated with the four combinations of filtered or not filtered and/or
air stripped or not stripped so that others could compare their results to the results
reported in this research. Also, results from commercial field work are often reported
based upon a sample post treatment being stripped but not filtered.
An alternative method to measure alkalinity is to measure the calcium ion
(Ca2j directly in the eftluent:
CaC03 = Ca2+ + CO{ (8)
By measuring Ca2+ concentration ([Ca2+], mole/L, M) in the eftluent, alkalinity
in the solution could be calculated, since for every mole of limestone dissolved, two
equivalents of alkalinity are generated in the carbonate system. Unfortunately, Ca2+
measurement was not performed on site while doing experiments because of the lack
of analytical equipment.
Bed Height Measurement
The limestone bed heights were measured as an unexpanded height, hs, for
tracking limestone usage and at an expanded height, he, to determine hydraulic
retention time (see Equation 5). The h, value was measured at the beginning of
each individual flow test (the bed height is at the lowest level) after a settling time
of either approximately l-minute (when a succeeding flow rate test was conducted
after a l-minute settling time) or after over-night (after a series of tests were
performed, the PLB system was shut off and then re-started the next day; this
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condition would only be true for the lowest flow rate tests since the lowest flow,
rate test was always conducted first in the series.).
Limestone Usage
The effectiveness of limestone dissolution from a specific test was established
by comparing effiuent samples that were air stripped, filtered and not filtered. The
quantity of limestone removed by the filter was used as an indicator of the amount of
limestone that was being hydraulically flushed from the reactor vessels. The
limestone usage ratio was defined as follows:. A/k +Acy
LImestone Usage = at na (9)A/kanf + ACYna
where
A/kat = effiuent alkalinity in air stripped and filtered sample, mg/L as CaC03
A/kanf = effluent alkalinity in air stripped and non-filtered sample, mg/L as CaC03
Acy na = influent acidity, mg/L as CaC03
Limestone used in PLB system was not only for generating alkalinity
(Equation 2) but also used for neutralizing influent acid water (Equation 1). The
amount of limestone dissolved (Ca21 is equal to the acidity of influent that was
neutralized (Acidna) plus the alkalinity generated and measured in the effiuent (Alkar).
Hence,
(10)
where
[Ca2+] = calcium concentration, expressed as mg/L as CaC03
Equation 10 is the numerator of Equation 9. Again, calcium ([Ca2+]) was not
measured in the experiment. However, alkalinity and acidity were measured.
Furthermore, there is some fraction of the limestone particles that have not dissolved
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and are flushed from the system, which need to be accounted for to determine
limestone usage. The mass of limestone particles that was flushed from the system as
solid particles could have been measured directly if samples were filtered and oven
dried, which is a very time intensive process. Alternatively, an indirect and faster
method was used by measuring effluent alkalinity that had not been post filtered
(Alkanf),and also calculating the total amount of limestone (including undissolved
limestone) used ([CaC03 used]) from the following equation:
[CaC03 used] = ACYna+ Alkanr (11)
where
[CaC03 used] = limestone concentration, mg/L as CaC03
The limestone usage was calculated usmg the limestone mass dissolved
(Equation 10) and limestone used (Equation 11) and substituting these values into
Equation 9. This value characterizes the neutralization efficiency of the overall PLB
process.
Predictive Models and Statistical Analysis
Predictive models of effluent alkalinity were developed using multiple
regression analysis. The four models correspond to the four post treatments for the
effluent alkalinity: air stripped and filtered (at), non-air stripped and filtered (nat), air
stripped and non-filtered (ant), and non-air stripped and non-filtered (nant). Each of
the models used the same primary experimental variables: carbon dioxide applied
pressure, hydraulic retention time, influent temperature and limestone bed initial
height. The regression analysis also included the interaction terms and the higher
order terms (squared and cubic terms) for each of the primary variables. Individual
independent variables were eliminated one at a time starting with the least significant
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terms and then repeating the regression. This process was repeated until all variables
remaining were significant at a P value < 0.05. This analysis was performed using
Minitab software (Minitab Inc. on 1829 Pine Hall Road, State College, PA 16801).
Results
CO2 Pressure Effects
The effluent alkalinities were greatly affected by the applied carbon dioxide
pressure since higher dissolution of limestone. The results of alkalinity (Alkanr)
related to the applied C02 pressure are shown on Figure 3.4. Alkalinities increased
with increasing C02 pressure (P<0.05) because of increased dissolution of limestone.
Limestone Bed Height Effect
Eflluent alkalinity was positively related to the bed height. The relationship of
bed height and eflluent alkalinity (Alkanr)for different flow rates and applied C02
pressure is shown on Figure 3.6.
Hydraulic Hydraulic retention time Effect On Efflnent Alkalinity
The hydraulic retention time positively affected the eflluent alkalinity
(P<O.05). As the hydraulic retention time increased, the influent water remains in
longer contact with the limestone allowing the limestone to release more bicarbonate
(alkalinity). The relation between hydraulic retention time and effluent alkalinity is
shown on Figure 3.7.
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Limestone Bed Expansion Ratio
The average of the bed expansion ratios are 134%, 179% and 224% as the
superficial velocity of fluidized bed increased from 0.8 cm/s, 1.5 cm/s and 2.1 cm/s
respectively. The bed height of the limestone had a small but significant effect on the
measured expansion ratio. After consuming limestone during the process, the overall
bed height dropped but the expansion ratio increased (P<0.05). The relationship
between bed height and bed expansion ratio at different flow rates is shown on Figure
3.8.
Temperature Effects
There was no significant relationship found between temperature and effluent
alkalinity. This is attributed to the rapid exchange of acidic water through the PLB
system, i.e. low HR.T values and there was a very limited range in the HR.T values
investigated. A broader range ofHRT and/or temperature may show a different result,
particularly if the HR.T was increased so that equilibrium might be achieved. Typical
results of effluent alkalinity (Alkanr) versus temperature at different flow rates for two
applied CO2 pressures are shown on Figure 3.5.
Regression Models
The models for effluent alkalinity were all of the same form:
y = co + al X, + a2 X2
where
y = A1kaf,Alk nanfs Alk nafor Alk anf
Alk af = effluent alkalinity, mg/L as CaC03, that is air stripped and filtered
Alknanr= effiuent alkalinity, mg/L as CaC03, that is non-air stripped and non-filtered
Alknaf= effiuent alkalinity, mg/L as CaC03, that is non-air stripped and filtered
(12)
~e 600:?t<
1200
1000
800
400
200
96
-----------------~
• Iii~!II;
!II
••• •
.3.8 Lpm
.6.8 LpmA 9.8 Lpm
0+----.,...-----.,.----.,.----..,.-------1o 50 100 150 200 250
Applied COz pressure (kPa)
Figure 3.4. A relationship between applied C02 pressure and the effluent alkalinity
(inlet temperature, 12°C; air stripped treatment).
1200
900
600
300
0
- 900~Ob8-- 600~<
300
0
900
600
300
97
• •• '. •• "i
~A-4 -..
• 206.8 kPa
!3.8LPm I A 34.5 kPa
• •• •• .,•A6'*+ •••••• ••• •••
16.8LPm I
• l ••• •••• 4 • •19.8Lpm I
o8 18 23 2813
Influent Temperature ("C)
Figure 3.5. Effect of temperature on eflluent alkalinity at each of3 flow rates and 2
pressures.
600 • ••• •• •300 •• * * •••
0I 34.5kPa I
-~
900S--.t> 600
~
.-=.--=.::t: 300-<1137.9kPa
0
1200
98
900
.... __ .I·3.8 Lpm• 6.8 L~:=~~~~~I
900
A
600 ••.. ....•.••• •
3001206.8kPa
050 55 60 65 70 75
Bed Height (em)
Figure 3.6. Effect of initial bed height on effluent alkalinity at each of3 flow rates and
3 operating pressures.
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1200 .....---------- ~
800.-..0U~U'"~ 600~S:=-e x
400
1000
200
.68.95 kPa; 12C .34.47 kPa; 12C .137.9 kPa;12C X 206.84 kPa; 12C
:t: 34.47 kPa; 22C • 206.84 kPa; 22C + 34.47 kPa; HC - 206.84 kPa; 17C
0--.+-----....----....----....-----.------.-------<0.60 0.70 0.90 1.000.80 1.10 1.20
Retention time (min)
Figure 3.7. Effect of hydraulic retention time on eft1uent alkalinity at 8 unique
conditions of temperature and pressure.
f-' 200--e.•..~= ISOe.-~=~Q.,
~ 100
300
•+.•• ...~
•
250
•-
SO
...........:••• •. .. - ....•• • ••••
• 3.8 Lpm• 6.8Lpm.• 9.8 Lpm
100
O+----.....,----.------,-------i40 SO 60 70
Bed Height (em)80
Figure 3.8. Effect of settled bed height on bed expansion achieved (limestone bed
expansion ratio) at each of these water flow rates.
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Table 3.2. Coefficients for the alkalinity regression equations.
Regression a.o Ul U2 R2
(coefficient) (C02 applied (hydraulic
pressure) retention time)
Alk sf -755. 2.32 1138 0.797
Alk nanf -864 2.53 1262 0.824
Alknaf -756 2.40 1141 0.832
Alkanf -836 2.43 1240 0.825
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1200 .
200
1000
~ 800 •~ •A~ •-< 600 •=oS..,..,f~41 400~
o -!£----,-----,-----r------,.---..,.------i
o 200 400 600 800 1000 1200Ob8elVed AIk. (mgIL)
Figure 3.9. The goodness of fit for the regression model of air stripped and non-
filtered alkalinity versus observed values (n=80).
103
Alkanf= eflluent alkalinity, mg/L as CaC03, that is air stripped and non-filtered
X, = C02 applied pressure (kPa)
X2 = Hydraulic retention time (minute)
00 = constant
a1 = coefficient of Xl
(12= coefficient of'X,
The coefficients of 00, aI, a2, and the R2 of different regression models are
listed in Table 3.2. The coefficients in Table 3.2 each had a p-value ofless than 0.05.
The goodness of fit for the regression Alkammodel is shown in Figure 3.9. All models
were similar in terms of their goodness offit.
Discussion
The PLB process for acid water remediation performed well usmg this
prototype reactor. The C02 pressure and HRT are important parameters affecting
alkalinity performance. If the PLB is used to treat real AMD, the accuracy of the
predictive models is uncertain. The models developed in this research were based
upon acidic waters that had no additional ions present that could cause armoring when
treated, e.g. ferric ions. The armoring effect could dramatically affect the performance
of a PLB system, depending upon how often the limestone particles are exchanged
with new media and the concentration of these other metal ions. Further research is
needed to develop corrective adjustments to the models presented in this paper to
account for such armoring effects. Also, the economic impact and feasibility of
recycling C02 captured in the treated effluent treated water requires investigation.
The limestone bed height did not significantly impact effluent alkalinity, which
was a bit surprising. The measurement of bed height was subject to some
experimental error. Over a sequence of tests, the bed height might be reduced by
104
approximately 20 mm of a total initial height of 400 to 500 mm and then was replaced
with new limestone material. Measuring the height of the bed between sequential tests
was compromised, since complete settling would not occur for many hours, e.g. the
limestone bed might settle approximately 10 mm overnight compared to the
measurement obtained after 1 minute of settling, hence, the measurements of bed
height were suspected to have potential errors. Inferences made about bed height or
using bed height measurements to quantify alkalinity change should be made with
some caution.
Temperature also did not significantly impact effluent alkalinity. This could
be attributed to both a fairly narrow range of temperatures used and that the short
HRT's used in the experiments did not allow sufficient time for chemical equilibrium
to occur. The temperature range evaluated is considered appropriate for the conditions
that will be encountered when employing a PLB system. Also, temperature may affect
chemical reaction rates, viscosity of the fluid, limestone dissolving rate and gas
transfer rate etc. However, the kinetics of the PLB system still needs more research to
be understand the relationships.
Air Stripping Post-treatment
Some of the C02 in the system was released immediately from the water after
the vessels were opened to the atmosphere during the start of the discharge cycle. The
samples referred to as air-stripped were only partially stripped of CO2 because the
atmosphere contains 10.3.5 atms of C02. The non-air stripped effiuent would have
some uncertain amount of C02 dissolved in the effluent due to the opening of the
vessel and collecting the samples will result in some stripping of the sample of CO2.
Since C02 is not a component of alkalinity (acid neutralizing capacity), the alkalinity
are identical for both air-stripped and non-air stripped effluent. The pH rises after air
105
stripping because when CO2 is present, it acts as a weak acid. In our case pH typically
raised to a pH>8.0. Generally, the pH of the effiuent without air stripping after pulsed
bed treatment rose from pH 2.5 to pH 6.3 (±O.2). In this pH range (pH 6.1 - 6.5),
H2C03 (includes C~ aq) and HC03 - dominate the aqueous system. Since there is
substantial carbon dioxide in the water and caused the pH lower than 7.0, such waters
will generally not suitable for wastewater discharge. After air stripping, the effiuents
were between pH 7.6 to pH 8.2, where HC03- dominates the carbonate species; such
eftluents would meet most wastewater discharge standards.
Limestone Usage Ratio
The limestone usage ratio describes the percentage of limestone that has been
used to restore alkalinity and the total limestone used. It is important to know the
amount of limestone that is used in the treatment process for design purposes. For the
tests conducted, 98% of the limestone that left the reactor vessel could be accounted
for by a change in alkalinity. Thus, only 2% of the limestone was leaving the system
as un-dissolved particulate, which clearly indicates the PLB is an efficient process to
dissolve limestone for restoring alkalinity.
Tests on Limestone Bed Expansion Ratio
The bed expansion ratio is negatively correlated with the limestone bed height
at a fixed flow rate (Figure 3.8). At the high flow rate (9.8 Lpm), the slope is higher
than it is for the low flow rate (3.8 Lpm). As previously discussed, our hypothesis is
that the small particles disappear first and the remaining particles become smaller and
smoother. Both of these characteristics would result in the bed expansion ratio
increasing. The fact that the slopes for the different flow rates shown in Figure 3.8
reduce as flow rate reduces could be related to a number of factors that are beyond the
106
scope of this study. However, the fact that the expansion ratio did increase as the
limestone was consumed, does support the hypothesis that the particle size distribution
is going to a smaller overall size. The coarse particles may be more readily polished
in the vigorous flow and the particles may break apart as the collision energy and
frequency are significant. This may explain why the expansion ratio increase is more
significant in high flow than in low flow rate conditions. It is of some practical
relevance to know the expansion ratio for the PLB reactor vessels, since it is important
to prevent limestone particles from being carried out of the vessel due to over
expansion or to subject components in the upper reaches of the reactor vessel to
abrasion. Finally, accurate modeling of the fluidization process could be important in
predicting scouring and armoring effects related to the fluid dynamic behavior of the
limestone particles.
Emuent Alkalinity Predictive Model
The regression models presented in this paper accurately predict the treatment
effects of using a PLB reactor to recondition AMD waters. There are positive
relationships between effiuent alkalinity and PLB values of applied carbon dioxide
pressure and hydraulic retention time. The air stripped but non-filtered effluent
alkalinity, Alkanf,is used as our major predictive model, since it is similar to the
procedures used in commercial field work (air stripped and non-filtered).
All the models were of the same linear form. No primary variables that were
in higher forms (squared, cubic, and interactive terms) were statistically superior in
predicting the dependent variables. More sophisticated models can be developed in
the future, but would minimally require that the range of data be expanded beyond
what was tested in this research.
107
Commercial Application
Finally, the PLB process appears to offer major reductions in the time required
to treat AMD waters. For example, in the laboratory experiments a complete
treatment cycle required only a total of eight minutes; similar cycle times would
characterize commercial applications since the process is a fluidized bed. The
quantity of AMD waters treated on a continuous basis becomes solely dependent upon
the size of the reactor vessels. In comparison to most current treatment processes
taking days or weeks to achieve treatment, the PLB could afford substantial savings in
time and operating expense.
The PLB offers an efficient and fast acid water remediation technology,
because of its ability to achieve high limestone usage ratios (98%) and to raise pH's up
to 8 from 2.5 in minutes, as opposed to days and weeks with conventional limestone
treatment systems. Effiuent characteristics using the PLB system can be adjusted by
changing one of only two operating parameters: applied CO2 pressure or hydraulic
retention time.
108
Symbols in this chapter
a.o = constant
al = coefficient of Xl
a2 = coefficient of X2
A = cross sectional area of the vessel, cm2
Alk = alkalinity (eq/L)
Acy = acidity (eq/L)
Alkaf= effiuent alkalinity that is air stripped and filtered (mgIL as CaC03)
Alknanf= effiuent alkalinity that is non-air stripped and non-filtered (mgIL as CaC03)
Alknaf= effluent alkalinity that is non-air stripped and filtered (mgIL as CaC03)
Alkanr = effiuent alkalinity that is air stripped and non-filtered (mgIL as CaC03)
C = gas concentration in the liquid phase, mole/mole
[R2C03 *], [RC03 "], [CO/oJ, [Off], [W] = concentration of H2C03 ', HC03", CO/",
Off, W respectively (M)
[R2C03 *] = [C02(aq)] + [H2C03]
H,= Henry's constant, atm
he = expanded bed height, em
h, = static bed height, em
MI = heat absorbed in the evaporation of 1 mol of gas from solution, kilocalorie /
kmol (kcal / kmol), for Carbon dioxide, MI = 2070
J = empirical constant, for Carbon dioxide, J = 6.73
P = gas concentration in the gas phase, atm
Q = flow rate, Lpm
R = gas constant, 1.987 kcal / kmol
T = temperature, K
V = volume of bulk fluid (crrr')
109
X, = regression symbol of applied CO2 Pressure in Equation 12. (kPa)
X2 = regression symbol of applied hydraulic retention time in Equation 12. (minute)
e = porosity of limestone bed at static bed height
Acknowledgements
We wish to acknowledge the assistance of Tom Jackson and Rachel Sears of
the Leetown Science Center in equipment assembly and adjustment.
110
References
American Water Works Association., 1990. Water Quality and Treatment, Fourth
Edition. McGraw-Hill, Inc., NY.
APHA., 1995. Standard Methods for the Examination oj Water and Wastewater, Iflh
edition. Washington, D.C.: American Public Health Association. Washington, D.C.
Colt, 1., 1984. Computation of Dissolved Gas Concentrations in Water as Functions of
Temperature, Salinity, and Pressure. American Fisheries Society Special Publication
No. 14.
Evangelou, V.P. 1995. Pyrite Oxidation and Its Control. Boca Raton,: CRC Press. FL
Dean, 1. A. ed. 1979. Lange's Handbook of Chemistry, Twelfth Edition. McGraW-Hill,
Inc., NY.
Lide D.R. 1998. CRC Handbook of Chemistry and Physics. Boca Raton, CRC Press,
NY.
Pearson, F. H. and McDonnell, A. 1. 1975. Use of Crushed Limestone to Neutralize
Acid Wastes. Journal oj The Environmental Engineering Division. vol. 101, No. EEL
Plummer, L.N., and Wigley T. M. L. 1976. The dissolution of calcite in CO2-saturated
solutions at 25QC and 1 atmosphere total pressure: Geochim. Et Cosmochim. Acta. 40:
191-202.
III
Plummer, L.N., Wigley T. M. L., and Parkhurst D. L. 1978. The kinetics of calcite
Dissolution in CO2-Water System at 5 °c to 60 °c and 0.0 to 1.0 Atm C02. Amer.
Jour. of Science 278:179-216.
Russo S. and Silver M. 2000. Introductory Chemistry: A Conceptual Focus. Addison
Wesley Longman, Inc., NY.
Santoro L., Volpicelli G. and Caprio V. 1987. Limestone neutralization of acid
waters in the presence of surface precipitates. Wat. Res. 21: 641-647.
Sibrell, P. L., Watten B. 1., Friedrich A. E., and Vinci, B. 1. 2001. ARD Remediation
with Limestone in a CO2Pressurized Reactor. In ICARD 2000 Proceedings From the
Fifth International Conference on Acid Rock Drainage, vol. II. Society for Mining
Metallurgy and Exploration, Inc.
Summerfelt, S. T., and Cleasby, 1. L. 1993. Hydraulics in Fluidized-Bed Biological
Reactors. In Techniques For Modern Aquaculture, ed. 1. K. Wang. Aquaculture
Engineering Group of American Society of Agricultural Engineering. St. Joseph, MI.
Sverdrup, H. U. 1985. Calcite Dissolution Kinetics and Lake Neutralization. Doctoral
Dissertation for the Department of Chemical Engineering, Lund Institute of
Technology, Sweden.
112
Watten, B. 1. 1999. Process and Apparatus for Carbon Dioxide Pretreatment and
Accelerated Limestone Dissolution for Treatment of Acidified Water. Washington,
D.C.: U.S. Department of Commerce, U.S. Patent No. 5,914,046.
Weber, W. 1. 1972. Physicochemical Process for Water Quality Control. John Wiley
& Sons, Inc.. Canada.
CHAPTER FOUR
THERMAL ANALYSIS MODEL OF ZERO WATER EXCHANGE INDOOR
SHRIMP FARMING SYSTEMS
Abstract
A mathematical model is introduced to quantify heat and mass transfer fluxes
associated with an indoor shrimp farm. A heat and mass balance is presented for a
generalized mathematical model and the calculating procedures are described. A
method is introduced based upon a ratio of thermal capacity of the air mass to other
heat absorbing materials to limit the thermal gain of the air mass. This ratio term is
referred to as the HCR variable and is dependent upon the air exchange rate for the
enclosure and the thermal properties and mass of materials within the enclosure. The
HCR model is used to simulate the heating demands for targeted indoor air and water
temperature for an entire year. The HCR model can be used to predict the
supplemental heating needs or ventilation requirements to maintain some set of
targeted conditions for inside air and water temperatures. Validations of model
predictions are compared with data from the Waddell Mariculture Center, Charleston,
South Carolina and from the Gulf Coast Research Laboratory, Ocean Springs,
Mississippi. The HCR model predicted air and water temperature for these regions
located in medium latitude (e.g. SC, M.S.) (p-value = 0.90 with Paired t-test on
measured and simulated air temperature in SC).
Keywords: Enclosed water recirculation system, shrimp, heat mass balance,
mathematical model
113
114
1.0 Introduction
In the year 2000, the U.S. spent $4.6 billion to pay for imported shrimp,
Atlantic salmon, and tilapia, Of this total, $3.8 billion was for shrimp. To put this in
perspective, the cost of these three aquacultural products in 2000 were equal in value
to the combined exports of the U.S. broiler and hog industries (US Department of
Agriculture, LDP-AQS-14, Oct 14, 2001). The total trade deficit related to seafood
trade is $6.2 billion (US Department of Commerce). In 2000, consumption of shrimp
increased from 3.0 to 3.2 lb per capita (National Marine Fisheries). Shrimp
production accounts for 1/3 of the total economic value of all seafood. The US
aquaculture industry generates about one billion dollars each year, with 70% of this
being from catfish production (NMFS, 2000a).
Marine aquaculture in the US currently produces about one third of the
aquaculture products, but growth remains constrained for a variety of reasons, with
environmental concerns and permitting processes being dominant. This constraint
naturally raises the advantages of recirculating aquaculture system (RAS) technology,
as RAS can eliminate any negative environmental impact from the farming operation.
RAS also conserves water, eliminates escapement of cultured animals, and is basically
site independent. The recycling nature of RAS also permits culture of marine or
freshwater species and allows the farms to be located primarily to the benefit of
market proximity as opposed to being sited based upon the availability of natural
resources such as high volume water or open ocean sites.
For marine aquaculture to increase production, more coastal sites must be
found or alternate production systems must he adapted such as RAS. Appropriate
sites are those located in protected areas with abundant access to unpolluted water.
However, these same type sites are also used for other high-profile activities such as
recreational fishing, wildlife protection, and aesthetic enjoyment. Alaska has
115
completely eliminated the use of any of its coastal shoreline for aquaculture in order to
protect their native salmon populations and the associated industries that they support.
More and more, other communities and states are following this example. In attempts
to circumvent these restrictions, there is considerable interest in developing what is
referred to as "off-shore" sites, which are within the 3 to 200 miles offshore zone
controlled by the US government. This is a difficult environment however and, ,
aquaculture in such areas will be subjected to higher capitalization and operating costs,
which makes the production of commodity type seafood all but impossible. The
practical alternative to these problems is the development of "in-shore" or land based
marine aquaculture systems.
1.1 Closed-Low-Cost (CLC) System for In-land Shrimp Production
The Belize-style shrimp farm (Browdy et al, 2001; McIntosh 2001) is based
upon creating a heterotrophic bacteria colony that provides both food to the shrimp
and protection from disease causing bacteria. The Belize system is dependent upon
maintaining the water column in a high mixing state or in wastewater engineering
terms, a mixed reactor vessel. The mixing is provided by supplying high levels of
aeration, using low pressure blowers. The aeration energy is from 10 to 15 kW per
acre of pond surface area. There has been initial success with the Belize design and
management as demonstrated in Belize. After more than 15 crops and 1 million kg of
shrimp being farmed through the Belize intensive pond system, the survivability from
the post larval stage (8-10 day PL's) through harvest has been greater than 80%.
Hatchery survival from hatch 10 days (pL-l 0) is 65 to 70%. Growth from post larvals
(pL's) to harvest animals of 15 to18 grams (market size; 25 to 30 count per pound) is
accomplished in approximately 115 days. Note this rapid turnover in crops: 115 days.
A shrimp crop is being grown to harvest and removed three times per year. Compare
116
this to sturgeon production and caviar that takes at least 5 years before the first cash
flow is realized. The biological risk is much reduced in shrimp and becomes more
comparable to broiler production (45 days between crops) than to a tree farm that is
more comparable to sturgeon caviar production. Rapid turnover of crops is a key
advantage to shrimp farming.
The Gulf Coast Laboratory-GeL (University of Southern Mississippi) has
demonstrated similar success in zero-exchange shrimp production systems (Ogle,
1998; Samocha, 2002). The GeL systems have been built and operated within
greenhouse buildings, providing information and experience on how to successfully
adapt the outdoor Belize system into an indoor system for other moderate or cold
climates. The features of the Gulf Coast Laboratory system and Belize outdoor
system can be combined into a Closed-Low-Cost (CLC) Belize system or a CLC
shrimp system by enclosing the rearing system within a closed canopy or building
becoming an indoor aquaculture farm. The CLC system provides rearing environments
and aerial environments that are controllable and removes the variations of a natural
environment. By covering the Belize-style system, two major advantages are attained:
1. evaporation is controlled that permits tropical water temperatures to be
maintained with minimal heating requirements during the winter
season
2. vectors for disease transfer are further minimized, eliminating the
major cause of poor economic performance in conventional shrimp
ponds
Using a cover on the CLC design will permit evaporation and associated heat
losses to be controlled. Using a covered rearing space will also permit control of light
spectrums and day length and this capability will provide additional potential for
improving the economic performance of shrimp farming, e.g. growth of both the
117
shrimp and the biotic community are affected by light spectrum. Since the CLC
design will incorporate a high level of aeration, the aeration energy will be absorbed
by the water column and this amount of energy input should be sufficient to greatly
reduce the need for supplemental heating, even when placing an CLC shrimp farm in a
moderate climate, such as Shepherdstown WV.
Additionally, locating CLC shrimp farms in northern climates will further
isolate these farms from disease transfer and will result in the farms being close to the
most attractive markets, e.g. Washington DC, Philadelphia, New York City, and
Atlanta.
The CLC design lacks information related to the expected operating costs of
such a system. The CLC design is or can be as simple as a greenhouse, depending
upon the type of covering material used for the building structure. Regardless of cover
type, important thermal environment variables for such a system will include many
psychrometric parameters, with dry-bulb temperature, wet-bulb temperature, dew-
point temperature, water vapor pressure, relative humidity being considered among the
most important (Albright, 1997). Temperature is one of the most important
parameters that affect growth performance of animals especially for cold-blood
species like fish and shrimp. The growth rate, survival rate, metabolism rate and
activity performance are highly related to the ~emperatureof surrounding environment.
Controlling moisture (humidity) in an acceptable range is also necessary in
buildings that raise animals especially for aquaculture where the surface area of
exposed waterways can be a significant percentage of the floor space. These large
exposed water surfaces can exert a large impact on the moisture balance within the
closed air space. Too much moisture in the building may cause structural
deterioration of the building materials and cause bacterial, algae and fungus growth on
the walls. Even worse, moisture migration may permit disease organisms to migrate.
118
Overly dry conditions in the building air will force higher evaporation rates which
requires additional water to be supplied and additional heating demands for the heat ofevaporation.
A mathematical model of the thermal balance would allow simulation prior to
construction and operation so that the economic costs of maintaining specific
environments and associated animal performance could be predicted. It is necessary
to consider management parameters such as inside air temperature, humidity and
water temperature as to their impact on the operating costs of such a system and how
these parameters can be managed to promote optimal economic return to the farming
enterprise. Timmons et at (2002) described the principles of a thermal balance in
enclosed aquaculture building. Thermal flow includes the heat transfer and
interactions between animals, equipment and environment conditions. A properly
constructed and verified mathematical model will contribute to an overall
understanding and quantification of the effects outdoor temperature and humidity,
indoor temperature and humidity, and water temperature etc on overall system
performance.
By carefully quantifying the different heat flows and sinks for the various
thermal loads for a particular building, the indoor air and water temperature can be
predicted and the required thermal energy inputs to achieve some pre-determined
target for water and or air temperature. Animal performance can be predicted
knowing a specific thermal environment.
Once a building or thermal envelope is established, ventilation and
supplemental heating/cooling are essentially the only management components that
can be used to control indoor air temperature and humidity. How these management
variables are controlled has direct impact on the costs to maintain a specific
environment. Increasing ventilation rates or air change rate (ACR) in the summer is
119
used to minimize temperature rise in the building air space and decreasing ventilation
in wintertime will decrease the heating demands but will concurrently increase
humidity. Therefore, optimizing ventilation control must satisfy both constraints on
humidity and temperature control.
The objective of this research was to develop a mathematical model based
upon fundamental heat and mass transfer principles that can predict the thermal
performance of an indoor aquaculture farm. This mathematical model will be referred
to as the HCR Model, with HCR being an acronym for heat capacity ratio.
2.0 Materials and Methods
The HCR model is based on a general heat and mass transfer balance for
thermal flows as described previously by Timmons et al. (2002) and the thermal flow
diagram is shown on Figure 4.1. The thermal balances of the HCR model contain
outdoor temperature and moisture simulations; heat gained or lost within the farm
building and water tank for mass and heat balance.
The time step used to simulate building response can impact the ability of the
model to predict time dependent response. This is particularly true when the building
is subjected to diurnal variations in temperature and solar flux. The HCR model uses
a one-hour time step simulation for all mathematical calculations of heat or mass flux,
e.g. the quantity of air mass that would enter the building during a time step is air flow
rate for one hour. The temperature difference due to thermal balance calculation is
added to the next time step (e.g. the following hour). The time step calculation could
also be used in tracking temperature changes.
120
Figure 4.1. General Heat Balance on an Enclosed Ventilated Air Space (Adapted from
Cayuga Aqua Ventures)
121
The control volume for the building is separated into two compartments: 1) building
air space and 2) water tank and floor. Each space has its own thermal boundary layers
for calculating thermal fluxes. Thermal transfer across each boundary for each
compartment and from one compartment to another is defined by classical heat
transfer equations for conduction and/or convection. Thermal fluxes include solar
radiation and supplemental heat to maintain water and air at some minimum target
values. Radiation fluxes from the building and interior surfaces back to the outside
environment are neglected. The HCR model uses a series of mathematical models
from the literature for the forcing functions: 1. daily and hourly outdoor temperatures,
humidity ratio, and solar radiation (Steenhuis, 1984; Gates, 1988; ASHRAE, 2001). 2.
sunrise and sunset time (Hsieh, 1986).
2.1 The HCR Concept
Heat capacity (HC) is the term to define the required energy that is used for
raising a particular material by 1°C. Heat capacity is defined as mass of the material
times its specific heat
HC=m x Cp (1)
where
m = mass of object, kg
C, = specific heat of object, kl/kg'K
For example, 10 m x 10 m of floor and 10 em depth, with specific heat of soil
1.2 kJ/kgOJ<and bulk density 1500 kg/nr'. Hence the heat capacity of soil is 18000
kJrK. Another example of air in 10m x 10m x3 m air space, with specific heat of air
1.008 kl/kg'K and specific volume of air 0.8 m3/kg. The heat capacity of air is 378
kJ/°K. This is a good indicator to know where the heat storage dominated in the
122
enclosed system. Heat Capacity Ratio (HCR) is defined to compare the relative ability
of a particular material to adsorb or release energy in the same boundary layer
(compartment). The HCR value is also developed as a ratio that compares all the
materials within the same compartment, thus the relative comparison:
HCR! = HC! / LHC (2)
where
HCR! = heat capacity ratio of object 1
HC! = heat capacity of object 1
IRC = sum of the heat capacity in the same compartment
Heat capacity ratio (HCR) is developed in the HCR model as a method by
which excess thermal energy in building air envelope (boundary layer) is allowed to
be partially absorbed by the air mass within the enclosed air space. The HeR term
defines how to mathematically account for excess heat energy in air compartment
once some defined allowance has been reached for air to absorb thermal energy. This
limit is established based upon practical considerations for an enclosed building whose
floor is covered by a significant percentage by a water tank or raceway. In other
words, the HCR model might not prove to be appropriate for a traditional animal
rearing enclosed space where very little if any of the floor space is occupied by a
water volume.
From the previous example for a specified amount of soil and air in the same
compartment, the HCR for the air term is defined as 378 (the HC of the air) divided by
18000 (the HC of the soil) or 0.021 (2.1%). This means that up to 2.1% of the excess
heat in air compartment can maximally be permitted to be absorbed into air and 97.9%
of excess heat can maximally be absorbed into ground soil. Even though physical
principles should define the mass and heat transfer for the system energy flows, it is
123
difficult to predict absolute changes in air temperature because air has such a low heat
capacity or low specific heat, resulting in potentially large changes in temperature
from a relatively small absorption of thermal energy. Conversely other high heat
capacity materials such as water, bricks, floor or woods, will change much less in
temperature while absorbing relatively large quantities of thermal energy. The HCR
model proposes to use a ratio of thermal capacitance to address the effects of excess
heat within air space for more accurate predictions of thermal flows and resulting air
temperatures.
Many of the thermal fluxes in the HCR model are based upon empirical values,
e.g. material thermal resistance R, solar radiation transmissivity, convection
coefficient for heat transfer and so forth. How applicable specific values for each of
these parameters are might be to the physical situation of interest is always open to
question. While almost all of these parameters will have accepted values, they are
often described as some range of acceptable values. The impact on the thermal balance
can be large when assigning specific thermal properties to particular components of\
the thermal balance from this mentioned acceptable range of values, and particularly
as to their potential impact on low thermal capacitance materials such as air.
In greenhouse environment modeling, one mathematical approach IS to
carefully measure the percentage solar radiation that was used in air heating and
calculate the associated air temperature change (Albright, 1997). Since solar radiation
characteristics for a given day are highly variable (Mobley, 1994) and also solar
energy transmissivity will change according to different wave lengths of light, careful
characterization of the solar radiation data is needed if the objective of its usage is
accurate prediction of inside air temperatures where a transparent covering surface is
used. The HCR model is developed to reasonably account for excess thermal energy
in air compartment over a reasonable range for indoor enclosed aquaculture farms
124
where the inside water temperature is of primary importance. If air temperature were
the major focus of a model, then more attention may be necessary to the effects of and
characteristics of the solar thermal load.
For example, the air temperature increment (or decrease) in an hour by theory,
LlTair,is .LlTair= Qexcess,building/ [m X Cp, air] (3)
And the HCR model of air temperature increment is shown below.LlTair= Qexcess,buildingx HCRair / [m x Cp, air] (4)
where
Qexcess, building= excess heat In air compartment, kl/hr (or energy/time)
(Equation 23)
HCRur = heat capacity ratio of the air
Qexcess,building= excess heat in building air space.m = mass flow of air (kg/hr)
Cp, air= specific heat of air, kJlKg OK
Excessheat in air compartment (Qexcess,building)is define as total energy goes into the air
compartment subtract energy goes out from the air compartment (Equation 23). The
Qexcess,buildingdoes not include excess heat stored in water since two compartments (air
and water) are defined in HCR model and each compartment has its own thermal
balance (boundary layer).
The inherent assumption in the HCR model is that utility gained in predictive
accuracy by increasing the complexity of the thermal model is not justified,
particularly if the HCR model can be shown to provide acceptable results between
comparisons of real and model predicted data. The HCR model assumes all thermal
sinks are accounted for in either the floor, or the air within the building air
125
compartment (envelop of boundary layer). The interactive effects of other building
structural components such as beams and plastic and wall insulation are ignored
because of their relatively small thermal mass compared to the floor. And the specific
heat of soil is assumed 1.20 kJ/Kg°K.
The HCR model only accounts for the excess energy in air compartment being
absorbed by the air and the floor, thus only a fraction of the thermal excess energy
goes into the air and the remaining energy is assigned to the floor. This is because the
water temperature change is already assigned by thermal balance, but floor, beams and
plastic etc are not included in the air space envelope nor are they accounted for in the
HCR model. We use the HCR approach to limit the rise or fall in temperature to
reflect this.
2.2 Daily Outdoor Temperature and Solar Radiation Model
Outdoor environmental conditions are controlled by nature and are
independent of indoor environmental conditions. The daily outdoor temperature and
solar radiation are calculated as follows (Steenhuis, 1984; Gates, 1988):Uday= [(Umax -Umin)/2x(1+Phi)+Umin (5)
where
Ulay = weather variable of the day (temperature or solar radiation)
Umax = maximum monthly average value for particular weather variable
Umin = minimum monthly average value for particular weather variable
Phi = sin((date - A.) x 1t 1180)
date = Julian day of a year
1t = 3.141592 ...
A = 83 for solar radiation and 100 for temperature
126
The simulated daily outdoor temperature and solar radiation of Waddell
Mariculture Center, Charleston, South Carolina are shown on Figure 4.2 and Figure
4.3.
2.3 Hourly Outdoor Temperature Model
The hourly outdoor temperature could be calculated as (ASHRAE, 2001a):
To,hour ::::TfDBX,day - T,.ange,day x PR (6)
where
To,hour= hourly outdoor temperature
Tmax,day= maximum temperature of the day (at 3:00 PM) = Tday+ 6 °C
Tday= average temperature of the day (calculated from equation 1)
Trange,day= temperature range of a day (daily swing) = 12 °C
PR = percentage range, hourly basis (Table 4.1)
2.4 Hourly Solar Radiation in Day Time Model
The hourly solar radiation could be calculated as:SRdaySRhou = ---~---
r hour _ of _ daytime(7)
where
SRttour= hourly solar radiation, Wh/m2-hr
S~y = daily solar radiation, Wh/m2 -day (calculated from Equation 1)
Assume no solar radiation on night time
.u".si15.00
•..
127
30.00
25.00
..................................................••···••··••• .•••••••.. u •••••.••••••••••••••••.•••••••••••..••.• ...................................................... ·················1
20.00
10.00
5.00
0.00 +----.,-----,.....----,.-------,-----,.-----r-----,-~o 50 100 350ISO 200
JuJianDay
250 300
Figure 4.2. Simulated outdoor daily average temperature of Waddell Mariculture
Center, located on Charleston, South Carolina.
128
450 --------------------------------------------------------------------------------------------------------------------------------------------------------------------.·--1
400
100
350
'i:' 300"'i'~~ 250=~~ 200..oSr1l 150
0+----,------,------,------,-----,-----,-----,----:o
50
50 100 150 200JuIlanDay
250 300 350
Figure 4.3. Simulated solar radiation of Waddell Mariculture Center, located on
Charleston, South Carolina.
129
Table 4.1. Percentage range (PR) on hourly outdoor temperature calculation (Equation
6) (ASHRAE, 2001, F29.16)
Hour I PR,% Hour I PR, %
1 87 13 11
2 92 14 3
3 96 15 0
4 99 16 3
5 100 17 10
6 98 18 21
7 93 19 34
8 84 20 47
9 71 21 58
10 56 22 68
11 39 23 76
12 23 24 82
130
2.5 Sunrise and Sunset Time Model
The determination of sunrise and sunset time is described in Hsieh (1986):
Sunset Timestd = 720 - 4 ( Longstd - Longloca1)- equation of time + 1/15 x
arccos(-tan Lat x tan delta) x 60 (8)
Sunrise Timestd ;::;720 - 4 ( Longstd - Longlocal) - equation of time - 1/15 x
arccos( -tan Lat x tan delta) x 60 (9)
where
Sunset Timestd = sunset time of standard time zone, minutes
Sunrise TimeStd= sunset time of standard time zone, minutes
LongStd= Longitude of the standard time zone, in degree, West = +, East = -
For EST = 75, CST = 90, MST ;::;105, PST;::; 120, AST = 150
Longloca1= Longitude of local spot, in degree, West = +, East = -equation of time = 9.87 x sin 2B -7.53 x cos B - 1.5 x sin B, in minutes (9.1)
(9.2)B ;::;360/364 (n-8l)
n > day of the year (Julian Day)
delta = solar declination, in degrees
And delta could be determind as
delta = 23.45 x sin [360/365 x (284 + n)] (9.3)
The simulated sunrise and sunset time of South Carolina is shown on Figure
4.4. The results are within 4 to 12 minutes different from the observed data from
National Oceanic and Atmospheric Administration (NOAA).
131
20
18
16
'..':l 14Qe~.~E-< 12~~oSU
10
8
6
40
.................._._-_._ -._ .. _ ····························1
I
50 100 150 200 250 300 350Julian day
Figure 4.4. Simulated sunrise and sunset time of South Carolina.
132
2.6 Outdoor Humidity Model
Humidity ratio is related to water vapor pressure and temperature. The equations for
these mathematical relations can be found in ASHRA, 2001 Fundamentals.
The saturated vapor pressure is determined as (ASHRAE, 2001b):
es = exp(c1 IT +CZ +c3T +c4Tz +cST3 +c6T
4 +c7ln T), for T<=273.15 K (0 °C) (10)
es = exp(cg IT +c9 + clOT+clITz +c12T3 +C13ln T), for T>273.15 K (0 °C) (11)
where
es = saturated vapor pressure, Pa
T = temperature, K
ci = -5.6745359 £+03
C2 = 6.3925247 £+00
C3 == -9.6778430 £·03
C4:; 6.2215701 E-07
Cs :; 2.0747825 £-09
C6 = -9.4840240 £·13
C7 = 4.1635019 £+00
cs = -5.8002206 £+03
C9 = 1.3914993 £+00
CIO = -4.8640239 £·02
Cll = 4.1764768 £-05
Cl2 = -1.4452093 £-08
Cn = 6.5459673 £+00
133
The ourdoor humidity ratio could be determined from the following equations
(ASHRAE, 2001c):
W.-, =[(2501+2.831·T )·Ws* -1006·(T -T )]/outdoor outdoor,wetbutb . outdoor.drybulb outdoor,wetbulb
[2501 +1.805· Toutdoor,drybulb - 4.186· I;,utdoor,wetbul.)]
(12)
where
Woutdoor= outdoor humidity ratio, kg water / kg dry air
Toutdoor,wetbulb= outdoor wet-bulb temperature, °C
Toutdoor,drybulb= outdoor dry-bulb temperature, °C
Ws * = saturated humidity ratio at wet-bulb temperature, kg water/kg airw.s* =0.62198.es* /(101325-es*) (13)
Where
es* = saturated vapor pressure at wet-bulb temperature, PaRHoutdoor= 101325· Woutdoor/ [es,outdoor. (0.62198 + Woutdoor)] (14)
Where
RHoutdoor= outdoor relative humidity, %
es, outdoor= outdoor saturated vapor pressure, Pa
Outdoor wet-bulb could be calculated from dry ..bulb temperature. Assuming at
5:00 AM of a day, Toutdoor,wetbulb= Toutdoor,drybulb= Tdewpoint1
Toutdoor,wetbulb= Toutdoor,dIybulb@5am+3(Toutdoor,dIybulb- Toutdoor,dIybulb@5AM) (15)
The simulated outdoor humidity ratio is shown on Figure 4.5 and the
magnifying scale of hourly outdoor humidity ratio on period of July 16th to July 17th of
South Carolina is shown on Figure 4.6.
.•..."; 0.012~~~ 0.01~~: 0.008~~.c 0.006:sa= 0.004
0.016
134
......._- -.- ············.·······u .
0.014
0.002
O+------,------.,------r------,,-----,.---~----,-~o 50 100 300150 200 250
JuIianDay
Figure 4.5. Simulated Outdoor Humidity Ratio of a year of South Carolina.
350
0.0145
0.0144
;;':t 0.0143
]os~ 0.0142
~,g~ 0.0141
~:a.~ 0.014::t:
0.0139
135
........................................................ ~ \
• • •• •• •
• ••• •••• ••• •• • • •. :
.:t
• ••• ••• •••••• • •••••••0.0138 +---,---r----,,----,.-----,-----,----,-----,---.,------.-,
197 197.2 197.4 197.6 197.8 198 198.2 198.4 198.6 198.8 199
Julian Day
Figure 4.6. Simulated hourly outdoor humidity ratio of SC from July 16th to July 17.
The peak appears on 3:00 PM of a day.
136
2.7 Thermal Model
The conductive heat transfer could be determined as:A
Qconductive = R' AT (16)
where
Qconductive = conductive heat transfer (W)
A = area of the surface (m2)
R = thermal resistance (m2.KIW)
A T = temperature difference (K or °C)
The conductive heat transfer includes heat transfer from inside to outside the
building space through walls, ceiling and floor, QwaJl, building and Qceiling building, Qf1oor,
building respectively. Also, it includes heat transfer from water tank: to indoor
environment through wall and floor of the tank:, Qwall, tank and Qf100r, tank.
The conductive heat transfer from indoor to outdoor through floor could be
modeled as (Timmons, 1986)Qfloor, building = H· Pbuilding • (Tindoor - Toutdoor) (17)
where
Qf100r, building = conductive heat transfer from indoor to outdoor through floor, W
H = 0.93 or 1.38 w/k-m for insulated or un-insulated environment,
Pbuilding = building outside perimeter, m
The conductive heat transfer from water tank: in the building to the indoor
environment was also modeled as
(18)
where
Qfloor, tank = conductive heat transfer from water tank: to indoor through floor, W
137
H:;::: O.93w/k-m for insulated condition
Ptank. :;:::tank outside perimeter, m
The convective heat transfer of the air could be determined as:.Q . <m-e ·(T -T )convective P , air indoor outdoor (19)
where
Qconvective :;:::convective heat transfer (kJ)•m :;:::air flow rate (kg/hr)
Cp, air :;:::specific heat of air (kJ/kg °C)
A general heat balance on an enclosed air space is depicted as shown in Figure
4.1. (Adapted from Timmons et aI., 2002)
For steady state conditions, the gains of heat must balance the heat losses, or in
equation form:
Qs + Qsolar + Qheater + Qm + Qvi = Qevap + Qwall + Q floor + Qvo
where
(20)
Qs:;::: sensible heat production offish (kJ/hr or Whlhr)
Qsolar :;:::solar heat gain (kJ/hr or WhIhr)
Qheater:;::: sensible heat added by space heaters (kJ/hr or Whlhr)
Qm :;:::sensible heat added by motors and lights (kJ/hr or Whlhr)
Qvi :;:::sensible heat ventilated into air space (kJ/hr or Whlhr)
Qevap :;:::rate of sensible heat converted to latent heat via evaporation (kJ/hr or Whlhr)
QwaU :;:::sensible heat conducted from the space through walls and ceiling (kJ/hr or
Whlhr)
Qfloor :;:::sensible heat lost through the floor (kJ/hr or Wh/hr)
Qvo:;::: sensible heat ventilated out of air space (kJ/hr or Whlhr)
138
2.8 Building Thermal Model
In steady state, heat input and output to the building air space (Qinput,buildingand
Qoutput,building)could be depicted as
Qinput,buiIding :::: QSOIar,building + Qcooduction,tank + QCOOVecI:ioo,tank + Qheater,air + Qrnotor&light (21)
Qoutput, building :::: Q wall, building + Qlloor, building + Qcei1ing, building + Q infiltration + Qevaporation (22)
where
Qinput,building= heat input to the building air space (kl/hr or Whlhr)
Qoutput,building= heat output from the building air space (kJlhr or WhIhr)
Qsolar,building= solar heat into the building space (kl/hr or Wh/hr)
Qconduction,tank =: conductive heat from the water tank (kl/hr or Whlhr)
Qconvection,tank = convective heat from the water tank (kl/hr or Whlhr)
QWall,building= heat transfer through wall of the building (kJlhr or Wh/hr)
Qfloor,building= heat transfer through floor of the building (kl/hr or WhIhr)
Qceiling,building= heat transfer through ceiling of the building (kl/hr or WhIhr)
Qinfiltration= heat transfer through the ventilation (kJlhr or WhIhr)
Qheater,air= sensible heat added by space air heaters (kl/hr or Whlhr)
Qmotor&light= sensible heat added by motors and lights (kl/hr or WhIhr)
Qevaporation= heat transfer for water evaporation (kl/hr or Whlhr)
The excess heat of the building space (Qexcess,building)is:
Qexcess, building :::: Qinput, building - Qoutput, building
The solar energy in the building space can be described as:
(23)
Qaolar,building = AHSR . Ac.iling • ST - AHSR . ST . A.,.otu • SRoba (24)
where
AHSR = average hourly solar radiation (Wh/m2-hr)
Aceiling= surface area of the building ceiling (m')
ST = solar transparency to the ceiling (%)(e.g. 900,/0 in the model)
139
Awater= surface area of the free water (uncovered surface'(m')
SRabs= Solar Radiation absorbance of water (%)( e.g. 20% in the model)
The conductive heat from the water tank is described as:
Q - 4ankwoll rt: T )oonductioe; tanIc - R . I .L tanIc ~ indoor
tanlcwall(25)
where
AtawewaIl= area of the wall of tank (m2)
R.tankwaIl= thermal resistance of the tank wall (m2•0KlW)
Ttank= temperature of the tank water eK)
Tindoor= air temperature of the indoor environment eK)
The convective heat from the water tank is described as:
(26)
where
hi = convection coefficient (W/m2 OK)
From ASHRAE 200ld for single glazing still air condition, the hi values are
grven as:
hi;:; 7, summer time, ~T = 30 "1<
hi = 3.5, winter time, as ~T = 9"1<
Note that hi is positively related to temperature difference. Convection coefficients for
~T between 9 -30 "1< were linearly interpolated and for AT values outside of the noted
range, the hi value was assigned the lower or higher value of the convection
coefficient.
The conducting heat from the wall of the building is described as:
(28)
140
where
Abuilding, wall = area of the wall of building (nr')
~uilding, wall = thermal resistance of the building wall (m2 0KlW)
The conducting heat from the ceiling of the building is described as:
Qceiling, building = Aooilding, ceiling 1~i1ding, ceiling x (T indoor - Toutdoor) (29)
where
Abuilding, ceiling = area of the ceiling of building (m2)
~uilding, ceiling = thermal resistance of the ceiling of building (m2.KIW)
The infiltration heat loss could be determined as:.Qinfiltration = m x Cp, air x (T indoor - Toutdoor).m = Vbuilding,net X ACR 1 'Oair
(30a)
(30b)where•m = air flow rate (kglhr)
Vbuilding,net = net building space volume (air space), m3
ACR = air change rate (volume/hr)
'Oair = specific volume of air (nr'/kg)
For more accurate value of specific volume of air, regression based upon the
temperature from 273.15 K to 363.15 K from ASHRAE (200 1e), and found the
relation
'Oair = 0.0028 x T - 0.002
with R2 (coefficient of determination) = 1.00
(31)
where T in OK
The evaporation heat could be described as:
Qevaporation = Pev X 2444.44 x 1000/3600 (32)
where
141
Qevaporation= evaporation heat needed (Whlhr)
Pev= water evaporation rate (kg-water/hr)
2444.44 (kJ/kg-water) = evaporation heat of water
1000::;: unit conversion, lkJ = 1000 J
3600 = unit conversion, 1 J = 1/3600 Wh
The HCR model calculates the change in indoor air temperature (ATindoor)at
current time as shown below: .ATindoor= Qexcess,buildingX HCRur / [m X Cp,air] (33)
where
HCRair = heat capacity ratio of the air
2.10 Indoor Temperature
In the HCR model, the indoor air temperature at time "t" (Tindoor,t) was
assigned as follows based upon inside outside temperature conditions from the
previous time step, t-I:
Tindoor,t = Toutdoor,t + ATindoor,t-1
Tindoor,t = Tmix,t + ATindoor,t.l
if ACR2: 1
ifACR<1
(34)
(35)
where
Tindoor,t = indoor temperature at time step t, °C
Tindoor,t-l= indoor temperature at previous time step, t-l, °C
Toudoor,t = outdoor temperature at time step t, °C
ATindoor,t-I = indoor air temperature difference at previous time step, t-l, °c (Equation
33)
Tmix,t = mix temperature of indoor and outdoor air at time step t, °C
And Tmix,t could be determined as follows when ACR<I:
142
Tmix,t = Tindoor,t-l x (l-ACR) + Toutdoor,t x ACR (36)
2.11 Water Tank Thermal Model
In steady state, heat input and output to the water tank: volume (Qinput,tank.and
Qoutput,tank.)could be depicted as
Qinput,tank.= Qsolar,tank.+ Qsensible,shrimp+ Qheaer,tank.
Qoutput,tank.= Qwall,tank.+ Qfloor,tank.+ QconvectioD,tank.+ Qrefill
where
Qinput,tank.= heat input to the tank: space, Wh/hr
Qoutput,tank.= heat output from the tank: space to the air space, Whlhr
Qsolar,tank.= solar heat into the tank: space, Wh/hr
Qsensible,shrimp= sensible heat from shrimp or animals, Wh/hr
Qheater,tank.= heat from the heater to the water tank, Whlhr
QWall,tank.= heat transfer through wall of the tank: to the air space, Whlhr
Qfloor,tank.= heat transfer through floor of the tank: to the slab, Whlhr
Qconvection,tank.= convective heat from the tank: water to air space, Whlhr
Qrefill= heat transfer for refilled water, Whlhr
(37)
(38)
The excess heat of the tank: volume can be described as:
Qexcess,tank.= Qinput,tank.- Qoutput,tank.
The solar heat to the tank: could be described as:
Qsolar,tank.= AHSR x STxAwater x SRabs (40)
The sensible heat from the animal (shrimp) could be determined as:
(39)
Qsensible,shrimp= TSW x SH (41)
where
TSW = total shrimp weight in the tank: (kg)
143
SH = sensible heat of shrimp (assume 0.6461 Wh/kg-hr)
The conducting heat from the wall of tank is determined as:
QWall,tank = Awall,tank / Rwal~tank x (T tank - Tindoor)
where
Rwal~tank = thermal resistance of the tank wall (m2.KIW)
The heat needed for the refilled water could be determined as:
Qrefill= PevX Cp, waterX (Ttank - Tref1ll)x 1000/3600
where
Cp, water=specific heat of water = 4.18 (kJ/kg water)
Trefill= temperature of refilled water
The water temperature increment (Of decrease), ~ Twater,by the heat flow is:
~ Twater= Qexcess,tank / [mwaterx c,air] (44)
where
mwater= mass of water (kg)
Cp, water= specific heat of water, 4.18 kJ/kg
(42)
(43)
2.12 Tank Water Temperature (time step calculation)
Water temperature is an important character that should be considered since
water directly controls metabolism and growth performance for ectothermic animals
such as fish or shrimp.. The water temperature is calculated as follows for time t:
Twater,t = Twater,t-I + ~Twater,t-l
where
Twater,t = tank water temperature at time step t (<>.Kor °C)
Twater,t-I = tank water temperature at previous time step, t-I (<>.Kor °C)
~Twater,t-I = water temperature increment at previous time step, t-I (<>.Kor °C)
(45)
(Equation 44)
144
2.13 Tank Water Evaporation
Evaporation Rate
From Schwab (1980), evaporation of water from water surface was depicted
as:
E = C (e, - ed)
where
E = the rate of evaporation (in/day)
es = saturated water vapor pressure at the temperature of the water surface (in-Hg)
ed = the actual vapor pressure of the air (in-Hg)
C = constant, relative to wind velocity above the water
And
(46)
ed=esxRH
where
RH = relative humidity, dimensionless
The C value in Eq. 46 is given by Rohwer (1931) as:
C == 0.44 + 0.118 w
where
w = wind velocity (mph)
The wind velocity depends on ACR in HCR model. The higher ACR, the
higher the wind speed. The wind speed within the building space is calculated as:
(46.1)
(46.2)
w = ACR x Vbuilding / AWall normal
where
V building = volume of building space
AWall ,normal = Cross section area of wall normal to wind direction
(47)
By converting units to the SI units, Eq. 46 could be determined as:
145
E = (0.44 + 0.0733375 w) x 7.50062 x 10-6x [es,tank- es,indoorx RHindoor] (48)
where
E = the rate of evaporation (m/day)
w = wind velocity (kph)
es,tank= saturated water vapor pressure at the temperature of the water surface (Pa)
es,indoor= saturated water vapor pressure at the temperature of indoor environment (pa)
Water evaporation rate per hour (Pev) is then determined as:
Pev= 1/24 x Ex Awaterx pw (49)
where
Pev= water evaporation rate (kg-water/hr)
Awater= free water surface area (m2)
pw= density of water (kg/nr') ~ 1000 kg/m"
The evaporation is also constrained by the air reaching the saturated vapor
pressure (RH= 100%) as the maximum evaporation occurred. In other words, there is
no evaporation if the indoor relative humidity reaches 100%.
2.14 Indoor Humidity Model
The indoor humidity ratio is needed at each time step to perform the mass
balance calculations related to evaporation. Humidity ratio is calculated as follows
and is also dependent upon ACR values:
Windoor,t = Woutdoor,t + Pev/ (ACR x Vbuilding,net/ l)air)
Windoor,t = Wmix,t + Pev/ (1 x Vbuilding,net/ l)air)
if ACR2: 1
ifACR < 1
(50)
(51)
where
Windoor,t = indoor humidity ratio at time step t, kg water / kg air
Windoor,t-l = indoor humidity ratio at pervious time step, t-l, kg water / kg air
146
Woutdoor,t = outdoor humidity ratio at time step t, kg water / kg air
Vbuilding,net= net building space volume (air space), m'
Uair= specific volume of air, m3/kg ::::::0.80 at room temperature
The specific volume of the air, 'Uair,can be calculated as a function of
temperature as follows for more accurate determinations as was done in this paper:
'Uair= 0.0028 x Tindoor- 0.002 (52)
where
Tindoorin K
Wmix,t = mix humidity ratio of indoor and outdoor air at time step t as ACR <1
Wmix,t = Windoor,t-I x (I-ACR) + Woutdoor,t x ACR (53)
Indoor relative humidity is calculated as follows:
RHindoor= 101325 x Windoor/ (e, indoorx (0.62198 + Windoor» (54)
where
RHindoor= indoor relative humidity
es,indoor= indoor saturated vapor pressure, Pa
Since indoor relative humidity affects the water evaporation and the water
evaporation then increases the air humidity ratio or relative humidity and this process
has an inherent limit of 100% RH, it is necessary to iterate so that the limit of indoor
relative humidity is not exceeded. This was reflected by reducing the water mass
transfer for a given time step so that the humidity content of the air did not exceed
100% RH. No other adjustments were made other than limiting the amount of water
evaporated.
147
2.15 Air Change Rate Control (time step calculation)
The air change rate (ACR) as controlled by the ventilation system can greatly
affect the indoor temperature and humidity and is either for moisture balance and
thermal balance. It is necessary to have some managing principle to control the indoor
environment by variable ACR to adjust heating demand and moisture control for a
year instead of using a fixed value for ACR. Generally, increasing ACR will decrease
the indoor humidity and decrease indoor temperature. Hence, the heating cost rises up
for moisture control purposes.
The HCR model uses a minimum ventilation rate of 0.03 ACR and the
maximum ventilation rate is set to 60 volume/hr. A 60 ACR value is a typical
maximum value for commercial farm production systems.
Air change rate is managed to control temperature and moisture with one or the
other becoming the constraining value.
mmoisture= Pev / ( Windoor- Woutdoor)
minfilt= Vnet,buildingx ACR I Uair
mtemp= QtotalI [Cpoairx ( Tindoor- Toutdoor)]
where
mmoisture= air mass flow rate for moisture control, kg air I hr
minfilt= air mass flow rate for infiltration, kg air / hr
mtemp= additional air mass flow rate for temperature control, kg air I hr
mmax= air mass flow rate for ventilation need. It's the max value among mmoisture,
(55)
(56)
(57)
minfiltand minfilt+ ffitemp
Hence, the air change rate needed for next time step on air quality control is
ACR = mmaxx Uair/ Vnet,building (58)
The programmed ACR is basically controlled by the indoor environmental
conditions (e.g. indoor air temperature and humidity). The programming process is
148
basically the same as described by Timmons (1986). In the HCR model, the indoor
temperature set point is set to 10 °C; the indoor relatively humidity is set to 80% and
water temperature is set to 20 °C for sample calculation. The flow of programmed
codes is described below:
1. If T outdoor2: T indoor,design
1.1 IfRHindoor > RHindoor,design1
1.1.1. ACRi+1 = ACRi + 1
1.2 IfRHindoor ~ RHindoor,design1
1.2.1. ACRi+1 = ACRi
2. If Toutdoor< Tindoor,design
2.1 If /).W > /).W design
2.1. 1. If (T indoor- Toutdoor)< (T indoor- T outdoor)designand
RHindoor> RHindoor,design1
2.1.1.1 ACRi+l = ACRi + 1
2.1.2. If (T indoor- T outdoor)> (T indoor- Toutdoor)designand
RHindoor< RHindoor,design1
2.1.2.1.ACRi+l = ACRI - 1
2.1.3. If (Tindoor- Toutdoor)2: (Tindoor- Toutdoor)designand
RHindoor2: RHindoor,design1 or
If (T indoor- Toutdoor):5 (T indoor- Toutdoor)designand
RHindoor~ RHindoor,design1
2.1.3.1. ACRi+l = ACRi
2.2. If /).W s /).W design
2.2.1. If (Tindoor- Toutdoor)< (Tindoor- Toutdoor)deslgnand
149
RHindoor > RHindoor, design 2
2.1.1.1 ACRi+1 = ACRi + 1
2.2.2. If (T indoor - T outdoor) > (T indoor - TOUtdoor)design and
RHindoor < RHindoor, design 2
2.2.2.1.AC~+1 = ACRi - 1
2.2.3. If (Tindoor - Toutdoor) 2: (Tindoor - Toutdoor)design and
RHindoor 2: RHindoor, design 2 or
If (T indoor - Toutdoor) :S(T indoor - T outdoor)design and
RHindoor :S RHindoor, design 2
2.1.3.1. ACRi+l = AC~
where
T indoor = indoor temperature
T indoor, design = designed set-point of the indoor temperature, lowest temperature that
should be maintained of the indoor
T outdoor = outdoor temperature
T indoor - Toutdoor = temperature difference between indoor and outdoor
(T indoor - T outdoor)design = set-point of temperature difference between indoor and
outdoor, ( 3°C)
W indoor - Woutdoor = L\W = humidity ratio difference between indoor and outdoor
L\Wdesign;:::: designed set-point of humidity ratio difference between indoor and outdoor,
user defined (0.009 kg water / kg air)
RHindoor = indoor relative humidity
RHindoor, design 1 = set-point 1 of indoor humidity, (e.g. 80%), user defined value
RHindoor, design 2 = set-point 2 of indoor humidity in spring and fall season,(95%), user
defined value
150
ACRj = air change rate at time sep i
AC~+1 = air change rate at time sep i+1
2.16 Calculation FlowDiagram
The calculation sequence used for the thermal balance in the HCR model using
an hour time step is shown in Figure 4.7.
2.17 Source of Validation Data
The HCR model was validated by a comparison with data obtained from two
operating shrimp farms: the Waddell Mariculture Center, located on Charleston,
South Carolina and the Latitude is North 32.82° and Longitude is West 79.97°and the
Gulf Coast Research Laboratory, Ocean Springs MS, Latitude is North 30.42° and
Longitude is West 88.92°
The Waddell building was 41 x 9.1 x 3.7 m and the raceway in the building
was 36.6 x 7.3 x 0.8 m. Water is added to offset the evaporation losses and the
temperature of the refilled water is 22°C. The building is constructed of steel frame,
end walls framed with treated lumber plywood sheeting (Thermal resistance value, R-
value,.is 0.2 K m2/w). The cover was a double layer of clear polyethylene (R-value is
0.1 K m2/w), transmissivity assumed of 90%. The indoor raceway was an at-grade
trench with the walls of the raceway made from rigid board polystyrene insulation (5
em thick, R-value of 1.2 K m2/w) covered with an HDPE liner
Ventilation was provided by 2 fans each providing 566 m3 air/min (20,000 a?/min) exchange capacity for temperature and humidity control. Single stage
thermostats controlled each fan. During the spring period (verification data taken at
this time), thermostats were set to prevent ventilation unless the daily inspection of the
151
greenhouse indicated that the space was becoming exceedingly hot. Direct interviews
with the operators indicated that on the dates used for data verification with the HCR
model, there was no mechanical ventilation employed as the water temperatures were
still trying to be increased. The greenhouse had only one door and was considered to
be very tight from an infiltration perspective and assume the ACR is 0.03 volumelhr.
The measured outdoor temperature, indoor temperature and raceway water
temperature of South Carolina from April 1 to April 2 are shown on Figure 4.8. The
outdoor temperature is used in the model to predict the indoor temperature and
raceway temperature for validation.
The Gulf Coast Research building was to x 3 x 2 m with an interior raceway
measuring 7.32 x 1.83 x 0.46 m. The building was constructed of steel frame without
wall coverings, i.e. a shade and rain cover only. The cover was clear polyethylene (R-
value is 0.1 K m2/w), transmissivity assumed of 90%. The indoor raceway used a
black liner; sides and floor were insulated using expanded polystyrene (5 em thick, R-
value of 1.2 K m2/w)
Ventilation was caused by wind and natural convection. In the model, an ACR
of 60 volumelhr was assumed to simulate natural ventilation.
The outdoor temperature was collected from two weather stations, New
Orleans, LA and Mobile AL from July 10th, to July nth, 2002, and average the
temperature data as outdoor temperature used in the model, since no data was
available on site to predict raceway temperature for validation. The collected outdoor
temperature (data from weather stations) and water temperature of Mississippi from
July 10thto July n" is shown on Figure 4.9.
152
Step 1: Calculating Outdoor Environmental Conditions:r----~..Solar Radiation (5,7,8,9)
Outdoor temperature (5,6)Outdoor Humidity (10,11,12,13,14,15)
ConductionConvection
Solar RadiationHumidity Solar Radiation
Step 2: Calculate Building Thermal:Heat Input (21): Solar Load (24), Tank Conduction(18,25), Tank Convection (26), Heater Load, Othersupplement (assume zero)Heat Output (22): Outdoor Conduction (17,28,29),Infiltration (30), Evaporation (32)Heat Excess (23) = Heat Input (21) - Heat Output(22)Air Temperature Increment (33)Indoor Air Temperature (Time Step Calculation, 34,35)~ ~ ~
ConductionConvection Evaporation
,. "Step 3: Calculate Water Tank Thermal:Heat Input (36): Solar Load (39), Sensible Heat of Shrimp (assumezero), Heater LoadHeat Output (37): Conduction (41,42), Convection (43), RefilledWater (46)Heat Excess (38) = Heat Input (36) - Heat Output (37)Water Temperature Increment (47)Water Temnerature (Time Sten Calculation. 48)
Step 5: ProgramACR (Time StepCalculation,optional by user)
Step 4: Iteration of Indoor Humidity (56,52,53),Evaporation (51) to get optimized values due tocooperated calculating parameters
Step 5: Output Data Needed:Indoor Temperature, Water Temperature, Humidity .... etc.
I
Recalculate Next Time Step.
Figure 4.7. Hourly basis calculation diagram of HCR model. Equation number in
quotes.
G' 30.00 I--.•...•.•~."-' ~~--t.a~ 25.00
5E- 20.00
153
50.00 ......................................................................................................................................................................................
45.00
40.00
35.00
15.00
10.00
5.00
-+- Outdoor T
--IOOoorT__ WaterT
o 4 8 12 16 20 o 4 8 12 16 20
Hour
Figure 4.8. Hourly data of measured outdoor temperature, indoor temperature and
raceway temperature of South Carolina shrimp farm from April 1 to April 2, 2002.
154
40
35
30
G' 25"-'e,g 20••..,Q"S..,
15Eo<
10
5
00
-.- Oudoor T---WaterT
4 8 12 16 20 o 4 8 12 16 20How-
Figure 4.9. Hourly data of measured outdoor temperature, water temperature of
Mississippi from July 10th to July 11th, 2002.
155
2.17 HCR Characteristics and Other Conditions Assumed for Simulation
1. Daily temperature difference (daily swing) is set to 12°C through out the year.
2. ACR = 0.03 for simulating S.C April 1st to April 2nd, 2002 as well insulated
structure and no active ventilation, only infiltration.
3. Ground soil depth involved in HCR calculation of air is set to 10 cm. Ground
materials were assumed to be a mixture pebbles, concrete, sand or soil etc.
around 10 em on top soil-layer; a specific heat of 1.2 kl/kg-K and bulk density
1500 kg/m" was assumed.
4. Solar transmissivity through clear roof is assumed as 90% of solar radiation.
5. Solar absorption of water converted into sensible heat is assumed to be 20% of
solar radiation that passes through the clear roof From Mobley, 1994,
radiance transfer equation
Ed(Z) = Ed x e-az
where
Ed(Z) = certain wave length of light measured under water depth Z.
Ed = certain wave length of light measured on top of water surface
Z = water depth, m
a = spectral absorption coefficient, mol
The value of a is 2.07 for 800 nm wave length radiance; 0.017 I for 400
(59)
nm radiance and 0.0145 for 450 nm radiance etc. under pure clear sea water
condition (Mobley, 1994). After using Equation 59 and using the measured
water depth for the SC data of 0.8 In, Ed (Z) = 0.19 Ed, 0.98 Ed, 0.99 Ed as
156
wave length is 800nm, 400nm and 450nm respectively. That means from 81%
to 1% of radiance is either absorbed or scattered by pure sea water. In a
shrimp farm, the water contents are much more complicated than pure sea
water. There may be much more scattering or absorbing than sea water.
Radiation may be absorbed by particles (e.g. feces, food, microbes, algae..)
instead of pure water molecules, hence, only certain portion of solar radiation
will actually absorbed by water molecular. The absorptivity could be
measured by specific thermal and quantum detector, but it still depend on
water contents and is changeable all the time whenever the environment
condition changes. The solar radiation entering the air space may not fully
tum into sensible heat to heat the water. Furthermore, distribution of
wavelength of light is dependent upon weather conditions and atmosphere
content. Jerlov (1976) indicated the majority distribution radiation by
wavelengths is between 400 nm to 550 nm in air. The absorption of thermal
solar energy was assumed as 20% of the solar radiation flux being absorbed as
sensible heat to heat the water. A sensitivity analysis of this assumption is
performed and discussed in the Discussion section.
6. Sensible heat of shrimp is assumed to be zero in the model since its relative
small heat (0.65 Wh/kg shrimp, or 1 BTU/lb shrimp) and low biomass
component compared to the thermal mass of water, e.g. 500 20 gram animals
per cubic meter is only 1% of the water mass.
157
3. Results
3.1 Hourly indoor and water temperature prediction of S.C from April 1st,
2002 to April 2nd, 2002.
The indoor and water temperature is predicted based upon the recorded
outdoor temperature, simulated solar radiation and simulated outdoor humidity ratio.
The ACR, soil depth, water absorptivity of solar radiation is fixed at 0.03 volume/hr,
0.1 m and 20% respectively for comparison with different ACR, soil depth and water
absorptivity of solar radiation individually. The indoor temperature prediction and
comparison of different ACR (0.01, 0.03, 0.3, 0.6, 0.9 volume/hr) is shown on Figure
4.10. The indoor temperature prediction and comparison of different soil depth (0.05,
0.1,0.2 m) is shown on Figure 4.11. The indoor and water temperature prediction and
comparison of different water absorptivity of solar radiation (20%, 50%, 80%) is
shown on Figure 4.12 and Figure 4.13 respectively. The best fit of predicting indoor
temperature is on fixed ACR at 0.03 volume/hr, soil depth at 0.1 m and water
absorptivity at 20%. The resulting p-value of paired t-test of measured versus
simulated indoor air temperature is 0.90.
3.2 Hourly indoor and water temperature prediction of MS from July 10th,
2002 to July n",2002
The water temperature is predicted based upon the recorded outdoor
temperature, simulated solar radiation and simulated outdoor humidity ratio. The
ACR is fixed at 60 volume/hr to simulate moderate natural wind flow since there is no
wall built. The water temperature prediction is shown on Figure 4.14 and the p-value
of paired t-test is 0.019.
158
50.00
45.00
40.00
35.00
£ 30.00f:f 25.00
!20.00 1~~~
15.00
5.00
-- T~ recorded--T~ACR=O.Ol
-- T~ACR = 0.03-- T~ACR = 0.3
-- T~ACR = 0.6
-- T~ACR = 0.9
10.00
o 4 8 12 16 20 o 4 8 12 16 20
HoW"
Figure 4.10. Indoor temperature prediction of SC from April l" to April 2nd, 2002.
and the comparison of different ACR effects on the model. Ti, recorded = recorded
(measured) data of indoor temperature. Ti, ACR = 0.01, 0.03, 0.3, 0.6, 0.9, are the
predicted indoor temperature basis upon different air change rate.
c_ 30.00e~e 25.008-5 20.00Eo-
159
50.00
45.00
40.00
35.00
15.00
10.00
-- Ti, recorded
-- TI, soil = 0.05 m
-- T~ soil = 0.10 m-- T~ soil = 0.20 m5.00
o 4 8 12 16 20 o 4 8 12 16 20
Hour
Figure 4.11. Indoor temperature prediction of SC from April 1st to April 2nd, 2002.
and the comparison of different soil depth effects on the model. Ti, recorded =
recorded (measured) data of indoor temperature. Ti, soil = 0.05,0.10,0.20 m, are the
predicted indoor temperature basis upon different soil depth.
160
50.00
45.00
35.00
40.00
G'"-' 30.00
~; 25.00
~E-o 20.00
15.00
5.00
-- T~ recorded--- T~ water solar absorb =20%__ T~water solar absorb = 50%
-.- TI,water solar absobr = 80%
10.00
o 4 8 12 16 20 o 4 8 12 16 20Hour
Figure 4.12. Indoor air temperature prediction of SC from April 1st to April 2nd , 2002.
and the comparison of different solar absorptivity of water effects on the model. Ti,
recorded = recorded (measured) data of indoor temperature. Ti, water solar absorb =
20%, 500.10, 80%, are the predicted indoor temperature basis upon different solar
absorptivity of water.
161
37.00 ......................................................................................................................................................................................... j
J
35.00
27.00
__ Tw, recorded
--- Tw, water solar absorb = 20%~ Tw, water solar absorb = 50%-.t.- Tw, water solar absobr = 80%
o 4 8 12 16 20 o 4 8 12 16 20
Hour
Figure 4.13. Water temperature prediction of SC from April l " to April 2nd, 2002.
and the comparison of different solar absorptivity of water effects on the model. Tw,
recorded = recorded (measured) data of water temperature. Tw, water solar absorb =20%, 50%, 80%, are the predicted water temperature basis upon different solar
absorptivity of water.
162
40
10-.- Tout, recorded
-- Tw, recorded-+- Tw, predicted
5
o 4 8 12 16 20 o 4 8 12 16 20HOW'
Figure 4.14. Water temperature prediction ofMS from July 10th to July n", 2002.
Tout, recorde~ = recorded (measured) data of outdoor temperature. Tw, predicted =
predicted water temperature. Tw, recorded = recorded (measured) data of water
temperature.
163
4. Discussion
4.1 HCR Model utilities
4.1.1. Yearly simulations
The HCR model could simulate natural occurred environment conditions by
setting ACR to 60 volumelhr and setting heater output to zero. The outdoor
temperature, indoor temperature and water temperature could also be simulated
according to thermal energy balance. Simulated temperature relations of SC are
shown on Figure 4.15. The average daily temperature of indoor is greater than
outdoor temperature due to thermal balance with water and water acts as an energy
source sink to heat the air when the water is warmer than the air.
The HCR model was used to simulate heating demand for maintaining indoor
air and water temperature above a certain set point, that means the temperature will be
greater than or equal to set point. For example, the results of maintaining indoor
temperature to 10 °c and water temperature to 20 "C of SC and set ACR = 5
volumelhr and the chart of heat needed is shown on Figure 4.16. Heat needs are high
during the winter time.
4.1.2 Simulating indoor and outdoor humidity ratio
The HCR model simulated humidity ratio changes during a year. For example,
setting indoor temperature to 10°C and water temperature to 20 °C of SC and set ACR
= 5 volume/he and the chart of humidity ratio is shown on Figure 4.17. Humidity ratio
goes higher as temperature goes higher. The indoor humidity ratio is higher than
outdoors' due to water evaporation load.
164
The HCR model was used to compare indoor temperature, water temperature,
indoor humidity and heat needed as affected by ACR changes and using the model to
allow ventilation rate changes to minimize heating demands for specific target values
of indoor temperature, water temperature, indoor humidity. The indoor temperature,
water temperature, indoor humidity and heat needed changed according to different
ACR (5, 30, and 60 volume/hr) on set point of indoor temperature at 10 °C and water
temperature at 20°C are shown on Figure 4.18, 4.19, 4.20 and 4.21 respectively. As
expected, as the ACR goes higher, indoor temperature, water temperature and
humidity ratio are lower and the heat needs are correspondingly higher. Of course, it
is better to operate ACR as low as possible to limit the cost of heating needs, but the
indoor humidity may exceed the desired condition and some times fungi may grow
and cause spreading of unwanted disease.
4.1.3 Simulating targeted indoor humidity and temperature control.
Since ACR plays an important role to control indoor temperature and
humidity, the HCR model can be used with a time-step dependent ACR value that is
changed due to indoor environmental condition needs. For example, the indoor
temperature is set to 10°C and relative humidity is set to 80% and a sample of the
program procedures as described on section 2.15 are used. The heat needs due to
programmed ACR and fixed ACR are compared and shown on Figure 4.22. The
optimized ACR is slightly larger than 5 volume/hr during the wintertime, but not as
low as 2 volume/hr that was believed to be the natural ventilation caused by wind in
typical farm buildings.
G 25.00-e.af 20.00
tEo<15.00
40.00
• Water Temp.-Indoor Temp.-------Outdoor Temp.
165
~•••••••••• _-_••• _.- •••••• - •••••••••••••••••• _••••••••••• _-_ ••••••••••••••••••••••••••••••••• __••• _-_ ••••••• ••••• ••••••• __n ••••••••••••••••••••••••••••••••••••••••• ---- ••••••••••••••• 1
50 100 ISO 200
35.00
30.00
10.00
5.00 '----0.00 +----,-----r----.----,..-----.-----..,-----..,---'
oJulian Day
250 300 350
Figure 4.15. Simulated daily average outdoor, indoor and water temperature of SC of a
year without any heat supplement.
1800
1600
1400
1200
~ 1000s~ 800
600
400
200
166
//I•I /
//I,
•• Total Heat needed
• Air Heat N eeded• Water Heat Needed
50 100o +-----,----' '-------..------"-,..-----,-------i
o 400150 200Julian Day
250 300 350
Figure 4.16. Simulated daily heat needs of SC in a year at set point of indoor
temperature = 10°C and water temperature = 20 °C and set ACR = 5 volume/hr.
167
0.02
O.oI8
............................................. ..................................................................................................................................j
FWil~-Wo0.016
;; 0.014!I.•.•.••-! 0.012~6 0.01,g&!.e- 0.008 1- -;;;
~ 0.006
0.004
0.002
0+-----,-----,------,r----,---,-----r---..,.--1o 50 100 150 200
JmanDay
250 300 350
Figure 4.17. Simulated daily indoor and outdoor humidity ratio of SC in a year at set
point of indoor temperature = 10°C and water temperature = 20 "C and set ACR = 5
volume/hr.
20.00
G''-'~E 15.008-
~
30.00 .... -. _ _ _ _ ", .. ···-1
-ACR=5-ACR=30
-ACR=60
10.00 __ :S:==:""""-
25.00
5.00
0.00 +------,------,----r------r----,----,-----,--.Jo 50 100 150 200 250 300 350
Julian Day
Figure 4.18. Comparison of indoor temperature due to ACR changes. The set point of
indoor temperature is 10°C and water temperature is 20 °c. At higher ACR, the
indoor temperature is lower.
168
35.00
30.00
25.00
c~ 20.00 -1--------l-o
2••t 15.00GI
E-
10.00
5.00
-ACR=5-ACR=30
-ACR=60
169
0.00 +-----,-----,.-----r-----r----,----~--~---'o 50 100 150 200 250 300 350
Figure 4.19. Comparison of water temperature due to ACR changes. The set point of
indoor temperature is 10°C and water temperature is 20 "C. At higher ACR, the water
Julian Day
temperature is lower.
i' 0.014~.:l:l:;! 0.012~~"" 0.01Q~oa~C 0.008
i0.006:J::
0.02
0.018
0.016
0.004 -+-----
0.002
170
-ACR=5
-ACR=30-ACR=60
O+----,---,----,----,----.--- __r-----,-.......J
o 50 100 150 200 250 300 350
Julian Day
Figure 4.20. Comparison of indoor humidity ratio due to ACR changes. The set point
of indoor temperature is 10°C and water temperature is 20 "C. At higher ACR, the
humidity ratio is lower.
171
7000
6000
5000
-ACR=5-ACR=30-ACR=60
:c'~ 4000
e.•.Ol 3000~
2000
1000
O+----.--~lo/l_--__r---_,_--__r--.ltlr!'::-...,._--__,r___'o 50 100 150 200 250 300 350
Julian Day
Figure 4.21. Comparison of heat needs due to ACR changes. The set point of indoor
temperature is 10 °C and water temperature is 20 °C. At higher ACR, the heat needs
are higher.
172
Comparison of Heat Needs of DifTerent ACR
------::1& ACR= 60
• ACR=30.ACR=5x Prograrrnrd ACR
7000
6000
5000
2000
1000
50 100
o +-----.---~ ••-_ ••••• ••••••••••II!::.-,------,---'
o 350150 200 250 300
Julian Day
Figure 4.22. Comparison of heat needs of programmed ACR and fixed ACR. The
optimized (programmed) ACR is slightly higher than 5 volume/hr.
173
4.2 The limitations of the ACR model
The HCR model is only appropriate for regions that the monthly outdoor
temperatures are greater than ° °C or the user must at least set the minimum allowable
inside temperature to be above freezing. No allowance is made for thermal effects due
to freezing.
The model may not work properly in regions close to the equator or the regions
in low latitude. From the work of simulating Mississippi, most of the time the water
temperature were higher than ambient temperature especially at noon (Figure 4.9). It
is different from moderate region that water temperature is within the temperature
swing of a day in summer time. The HCR model assumed the outdoor humidity
fluctuated due to dew-point temperature, dry bulb temperature and wet bulb
temperature changes and the modeled relative humidity is similar to data from weather
stations. It could be the measurement error of water temperature.
4.3 ACR smaller than 1 volumelhr
It is seldom to see a farm building with an ACR value of less than one
volume/hr, however such conditions can occur in well insulated and tight greenhouse
style buildings with minimum wind flow around them (Albright, 1997). The concept
of calculating indoor air temperature and humidity for ACR values less than 1
volume/hr condition is different from one where the ACR value is greater/equal than 1
volume/hr. For ACR's less than 1 volume/hr, the indoor air conditions (e.g.
temperature, humidity) are first mixed with outdoor air conditions to obtain a weighted
resulting temperature condition for the air and then the thermal fluxes are calculated as
previously described. Equation 34, 35 and Equation 50, 51 describe the different
calculation procedures used for these two different conditions where a plug flow
principle is used as ACR greater/equal than 1 volume/hr (Equation 34,35) while
complete mixing of the incoming air with the inside air volume remaining after the
174
incoming air has displaced a portion of the inside air (Equation 50, 51). Other than
this initial step, all other calculating sequences are the same.
4.4 Soil depth effects on air and water temperature using 80% solar adsorptionfor water
The solar radiation absorption by the water was assumed to be 20% for the HCR
model. Generally, much higher absorption values might be used, e.g. 80%. First, a
series of simulations were performed using the higher absorption value of 80% and an
ACR value of 0.6 (volumes per hour) and then changing the depth of the soil slab from
0.05-0.2 m, where the generalized HCR model used 0.1 m as the final selected value.
The effects on air and water temperature of SC at ACR=0.03 are shown on Figure
4.23, Figure 4.24 respectively. Also, for the model verification during the April 1-2
for SC, the ACR was assumed to be 0.03. This is a very low value compared to
ACR's that might be assumed to be more near 0.3 to 1.0 ACR for tight buildings.
Thus, a series of simulations were performed using an ACR of 0.6 and as before, a
solar absorption of 80%. These results are shown in Figures 4.25 and 4.26. As can be
seen, the thinner the soil slab, the higher the indoor temperature. The prediction of air
temperature was lower estimated by change solar adsorption to 80% of water (Figure
4.25). Alternative adjustment may applied by changing evaporation heat needed from
air to water and the results are shown on Figure 4.27 and Figure 4.28 of SC. The
depth of soil slab in this condition could not lower than 0.04 In, since the air
temperature begin to bounce in over 5 oC if soil slab lower than 0.04 m. The values
used for solar absorption and soil slab depth are thus dependent upon the goals for the
model in terms of what variables are of highest interest. Since, the main utility of the
HCR model is to predict aquatic animal performance, choosing parameters that give
the most accurate prediction for the water would be the preferred choice.
175
50.00 ................. __ __ _- __.__ ·········1
45.00
40.00
35.00
Q 30.00....se 25.00..•..e;: 20.00
15.00
10.00
5.00
0.000 4
--"Ii, recorded
-- TJ, soil= 0.05 m--"Ii, soil= 0.10 m--"Ii, soil = 0.20 m
8 12 16 20 o 4 8 12 16 20HOur
Figure 4.23. The effects of soil depth on indoor air temperature at 80% solar radiation
adsorbed by water of SC.
_ 25.00~u
~e 20.00IS.su•..
15.00
176
40.00 ···_.· ••••••••••• n •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• __••••••••••••••••••••••••••••••••• __•••••••••••••••••••••••••••••••••••••••••••••••••• __••••
-- Tw, recorded-4- Tw, soil= 0.05 m--Tw, soil=0.10m__ Tw, soil= 020 m
35.00 ~:::::::::==:I,I
30.00
10.00
5.00
o 8 16 202012 o 4 8 12 164Hour
Figure 4.24. The effects of soil depth on water temperature at 80% solar radiation
adsorbed by water of SC.
177
50.00 ...__ _- _---_ __ __ .__ __ _-_ ..--:
45.00
40.00
35.00
6'"-' 30.00e~ 25.00••t~ 20.00
15.00
10.00
5.00
0.00
0
-- T1, recorded-.- TI, soil = 0.05 m
--TI, soil=0.10m
-- T1, soil = 0.04 m
4 8 12 16 20 o 4 8 12 16 20
Hour
Figure 4.25. The effects of soil depth on indoor air temperature at 80% solar radiation
adsorbed by water and ACR = 0.6 ofSC.
Q 25.00
je 20.008-!•..
15.00
178
40.00 ................................................................................................................................................................................ :
-+- Tw,recorded-.-Tw, soil= 0.05 m---Tw, soil=0.10m
--- Tw, soil= 0.04 m
35.00
~::::::::::::=::::j30.00
10.00
5.00
o 8 2012 16 20 o 124 4 8 16
Figure 4.26. The effects of soil depth on water temperature at 80% solar radiation
adsorbed by water and ACR == 0.6 of SC.
179
50.00 •••••••••••••••••••••••••••••••••••••••••••••••••••••••• •••••••••• ••••••••••• u •••••••••••••••••• __••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• O __ ••••••• j
45.00
35.00
40.00
G"-' 30.00
ie 25.00~=-!20.00 , ••.
15.00-+- T~ recorded
-- T~ soil= 0.04 m-- T~ soil= 0.05 m-- T~ soil= 0.10 m5.00
10.00
o 4 8 12 16 20 oHour
4 8 12 16 20
Figure 4.27. The effects of soil depth on indoor air temperature at 80% solar radiation
adsorbed by water, evaporation heat from water and ACR = 0.6 of SC.
Q 25.00
je 20.001a..
Eo<15.00
180
40.00 ~."'---""""'-"""-""-"-'--""--' --- _- -..........................•...... __.n ..•................................................ _._ _.. _ ~
-- Tw, recorded-- Tw, soil=0.04 m__ Tw, soil=0.05 m
---Tw, soi=O.lOm
35.00
30.00
10.00
5.00
o 204 8 12 16 oHour
4 8 1612 20
Figure 4.28. The effects of soil depth on water temperature at 80% solar radiation
adsorbed by water, evaporation heat from water and ACR = 0.6 ofSC.
181
Symbols in this chapter
A = area of the surface (m2)
Abuilding,ceiling:;:;:area of the ceiling of building (m2)
~uilding,wall= area of the wall of building (rrr')
ACR = air change rate (volume/hr)
AHSR = average hourly solar radiation (Wh/m2 -hr)
Aceiling= surface area of the building ceiling (m2)
Awater= surface area of the free water (uncovered surfacejmr')
Atamc wall= area of the wall of tank (m2)
Awater= free water surface area (m2)
Awall,normal= Cross section area of wall normal to wind direction
a = spectral absorption coefficient, mol
B = 360/364 (n-81)
C = constant, relative to wind velocity above the water
C, = specific heat of object, kl/kg'K
Cp, air= specific heat of air, kJ/Kg Ol(
Cp, water=specific heat of water = 4.18 (kJlkg water)
Cp, water= specific heat of water, 4.18 kJlkg
Cl = -5.6745359 E+03
C2 = 6.3925247 E+OO
C3 = -9.6778430 E-03
C4 = 6.2215701 E-07
Cs = 2.0747825 E-09
C6 = -9.4840240 E-13
C7 = 4.1635019 E+OO
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cs =: -5.8002206 E+03
C9 =: 1.3914993 E+OO
CIO = -4.8640239 E-02
en =: 4.1764768 E-05
Cl2 = -1.4452093 E-08
Cl3 = 6.5459673 E+OO
delta = solar declination, in degrees
E = the rate of evaporation (in/day)
Ed = certain wave length of light measured on top of water surface
Ed(Z) = certain wave length of light measured under water depth Z.
es = saturated water vapor pressure at the temperature of the water surface (in-Hg)
ed = the actual vapor pressure of the air (in-Hg)
es,tank= saturated water vapor pressure at the temperature of the water surface (Fa)
es,indoor= indoor saturated vapor pressure, Pa
es = saturated vapor pressure, Pa
es,outdoor= outdoor saturated vapor pressure, Pa
H =: 0.93 or 1.38 w/k-m for insulated or un-insulated environment,
HCRl = heat capacity ratio of object 1
HCl = heat capacity of object 1
IHC = sum of the heat capacity in the same compartment, kJrK.
HCRair =: heat capacity ratio of the air
hi =: convection coefficient (W/m2 OK)
LongStd =: Longitude of the standard time zone, in degree
Longlocal= Longitude of local spot, in degree
m = mass of object, kg
mmoisture= air mass flow rate for moisture control, kg air / hr
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minfJlt= air mass flow rate for infiltration, kg air I hr,
mtemp= additional air mass flow rate for temperature control, kg air I hr
mrnax= air mass flow rate for ventilation need.
mwater= mass of water (kg)
m = mass flow of air (kg/hr)
n = day of the year (Julian Day)
Pbuilding= building outside perimeter, m
Ptank= tank outside perimeter, m
PR = percentage range, hourly basis
Pev= water evaporation rate (kg-water/hr)
Qexcess,building= excess heat in building air space, Wh/hr, kJ/hr
Qconductive= conductive heat transfer (W)
Qfloor,building= conductive heat transfer from indoor to outdoor through floor, W
Qconvective= convective heat transfer (kJ)
Qs = sensible heat production offish (kJ/h)
Qfloor,tank= conductive heat transfer from water tank to indoor through floor, W
Qsolar= solar heat gain (kJ/h)
Qheater= sensible heat added by space heaters (kJ/h)
Qrn= sensible heat added by motors and lights (kJ/h)
Qvi= sensible heat ventilated into air space (kJ/h)
Qevap= rate of sensible heat converted to latent heat via evaporation (kJ/h)
Qwa11= sensible heat conducted from the space through walls and ceiling (kJ/h)
Qfloor= sensible heat lost through the floor (kJ/s)
Qvo== sensible heat ventilated out of air space (kJ/h)
Qinput,building= heat input to the building air space
Qoutput,building= heat output from the building air space
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Qsolar, building = solar heat into the building space
Qconduction, tank = conductive heat from the water tank
Qconvection, tank = convective heat from the water tank
QwaU, building = heat transfer through wall of the building
Qfloor, building = heat transfer through floor of the building
Qceiling, building = heat transfer through ceiling of the building
Qinfiltration = heat transfer through the ventilation
Qheater, air = sensible heat added by space air heaters
Qmotor & light = sensible heat added by motors and lights
Qevaporation = heat transfer for water evaporation
Qinput, tank = heat input to the tank space, Wh/hr
Qoutput, tank = heat output from the tank space to the air space, Whlhr
Qsolar, tank = solar heat into the tank space, Wh/hr
Qsensible, shrimp = sensible heat from shrimp or animals, Wh/hr
Qheater, tank = heat from the heater to the water tank, WhJhr
QwaU, tank = heat transfer through wall of the tank to the air space, Wh/hr
Qfloor, tank = heat transfer through floor of the tank to the slab, Wh/hr
Qconvection, tank = convective heat from the tank water to air space, Whlhr
Qrefill = heat transfer for refilled water, Wh/hr
R = thermal resistance (m2•K!W)
Rwall, tank = thermal resistance of the tank wall (m2•0KlW)
RHindoor = indoor relative humidity
RHoutdoor = outdoor relative humidity, %
RtanIc wall = thermal resistance of the tank wall (m2•0KlW)
Rt,uilding, wall = thermal resistance of the building wall (m20K/W)
Rt,uilding, ceiling = thermal resistance of the ceiling of building (m2.K/W)
185
SH = sensible heat of shrimp
S~our == hourly solar radiation, Whlm2-hr
SRJay= daily solar radiation, Whlm2 -day
ST = solar transparency to the ceiling (%)
SRai,s= Solar Radiation absorbance of water (%)
Sunset TimeStd = sunset time of standard time zone minutes,
Sunrise Timestd = sunset time of standard time zone, minutes
T = temperature, K
To,hour= hourly outdoor temperature, °C, ~
Tmax,day= maximum temperature of the day
Tday= average temperature of the day
Trange,day= temperature range of a day (daily swing) = 12 °C
Toutdoor,wetbulb= outdoor wet-bulb temperature, °C
Toutdoor,drybulb= outdoor dry-bulb temperature, °C
Ttank= temperature of the tank water COK)
Tindoor= air temperature of the indoor environment COK)
Tindoor,t = indoor temperature at time step t, °C
Tindoor,t-l= indoor temperature at previous time step, t-l, °C
Toudoor,t = outdoor temperature at time step t, °C
Tmix,t= mix temperature of indoor and outdoor air at time step t, °C, if ACR<1
Twater,t = tank water temperature at time step t (~ or °C)
Twater,t-l = tank water temperature at previous time step, t-l ~ or °C)
Trefill= temperature of refilled water
TSW = total shrimp weight in the tank (kg)
Uday= weather variable of the day (temperature or solar radiation)
Umax= maximum monthly average value for particular weather variable
Umin= minimum monthly average value for particular weather variable
Vbuilding,net= net building space volume (air space), m3
Vbuilding= volume of building space
Windoor,t = indoor humidity ratio at time step t, kg water / kg air
Windoor,t-l :: indoor humidity ratio at pervious time step, t-1, kg water / kg air
Woutdoor,t :: outdoor humidity ratio at time step t, kg water / kg air
Woutdoor:: outdoor humidity ratio, kg water / kg dry air
Ws* :: saturated humidity ratio at wet-bulb temperature, kg water/kg air
Wmix, t :: mix humidity ratio of indoor and outdoor air at time step t as ACR<l
w = wind velocity ,mph, kph
vr> wind velocity (kph)
Z :: water depth, m
~ T = temperature difference (K or °C)
~Tindoor,t-l :: indoor air temperature difference at previous time step, t-1, °C
~Twater, t-l = water temperature increment at previous time step, t-l ('I< or °C)
pw :: density of water (kg/m")
Vair :: specific volume of air (m3/kg)
1t=3.141592 ...
A. = 83 for solar radiation and 100 for temperature
Acknowledgement
Thanks C.R Weirich for data supply.
186
187
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