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.

75

76

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)

77

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.

78

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

79

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

80

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).

81

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

82

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,

83

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.

84

------------------------------------------------: .........•••····

..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.

85

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

86

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

87

EfiluentDischarge

.......................•

EfiluentDischarge

Figure 3.3. Schematic plot of the acid water circulation system.

PLB Process

WaterHeatingSystem

'-- ---I ~

CO2Charge

88

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:

89

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

90

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

91

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

92

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

93

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

94

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.

95

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.

99

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.

101

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

102

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

184

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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