Water Quality Dynamics as the Basis for Aquaculture System Design

Striped Bass and Other Morone Culture R.M. Harrell (Editor) 9 1997 Elsevier Science B.V. All rights reserved.

99

Chapter 4

Water Quality Dynam&s as the Basis for Aquaculture @stem Design David E. Brune 4.1 INTRODUCTION The primary task facing the fish culturist is to provide an optimal environment to insure maximum growth and reproduction of the aquatic animal of interest while minimizing stress effects. Tomasso, in Chapter 10 of this volume, lists water temperature, dissolved oxygen concentration, water hardness, pH, light levels, ammonia, nitrate, nitrite and suspended solids concentrations as the factors of greatest importance in affecting the culture of striped bass and its hybrids. The design of a successful aquaculture system is heavily dependent on our ability to make accurate predictions ofthe dynamics ofthese important water quality parameters as affected by operator controlled, fish stocking levels and feeding intensity. It is the intent of this paper to demonstrate that relatively simple chemical, physical and biological models can be used to make reasonable long-term predictions of the dynamics of the water quality parameters of importance in recirculating aquaculture systems, as well as, fish culture ponds. The approach used to design a particular aquaculture system generally falls into one of three catagories. First, there is the cookbook approach; this is used for aquaculture system designs in those cases where the behavior of the system is poorly quantified, or so complex, that the system behavior cannot be predicted well enough to insure success of any deviation from past designs. An example of this type of system is the complex technique of pond fertilization, followed sequentially by algal culture, zooplankton culture, and fish rearing which is typical of the current methodology for striped bass fingerling production. The second type of approach is the use of semi-empirical models. In this approach a sufficient data base exists to allow for reasonable predictions of system performance based on correlations between fish production and water quality parameters. Typical of this approach are the models used for prediction of pond dissolved oxygen by Boyd (1979, 1991) and others (Busch et al., 1974) in pond catfish production. The third approach is sometimes referred to as the mechanistic approach. In this latter case, a mass and energy balance is used to represent the nutrient and energy flux in an aquaculture system. This approach is most successfully applied to the design of intensive recirculating aquaculture systems, and is beginning to be used for pond aquaculture systems (Smith 1988; Piedrahita 1991; Brune 1994). This chapter will offer an application of a mixture of these three techniques. A simplified mechanistic representation of an aquaculture system will be used to predict values for the controlling water quality parameters of dissolved oxygen, water pH, nitrogen concentration, and pond algal biomass concentration and rate of photosynthesis. The empirical approach is used to define "typical" field operating conditions and the limits to system performance. Finally, predictions of system behavior based on this field calibrated simplistic model is compared to past "cookbook" based system performance. 4.2 WATER REUSE SYSTEMS The primary design criterions and forcing functions for a water reuse system are fish oxygen consumption rate and the feeding rate. These rates are species and individual fish weight dependent, varying from 0.4 to 10% of body weight fed per day, and 0.5 to 4 g of oxygen per 100 g of body weight per day.

100

Specific values of feed rate and oxygen uptake are available from a number of sources (Piper et al., 1982; Andrews et al., 1975). Furthermore, important water quality parameters, such as CO2, pH, and ammonia levels can be tied to these forcing functions. Generally, 20-25% of feed nitrogen is removed by the fish (Brune and Gunther, 1981; Colt 1986), with typically 60% of feed nitrogen being returned to the culture system as ammonia, with the remaining 15-20% trapped in waste solids. If this waste is not removed rapidly from the system (< 1 day), the solids organic nitrogen will be returned to the aquatic environment as ammonia nitrogen. A useful rule of thumb for calculating the impact of respiration on system pH is to assume that one mole of carbon dioxide will be produced per mole of oxygen consumed (Colt, 1986). Release of ammonia nitrogen into the aquaculture system can further impacts the oxygen concentration and pH as a result of the bacterial process of nitrification. The theoretical balance (Wheaton et al., 1991) for this two step process is summarized as" _

NH 4" + 1.8302 + 1.98 HCO 3 (4.1) 0.021CSH702 N + 0.98NO 3 + 1.883CO 2 This process reduces the oxygen concentration through the process of ammonia oxidation. It affects the water pH by the destruction of alkalinity and production of CO_,. Field observations of the nitrification reactions suggest that 7.1 mg of alkalinity (as CaCO3) is neutralized per mg of NH4-N oxidized. In addition, 4.6 mg of 02 is consumed per mg of NH3 -N oxidized (US EPA, 1975). These forcing functions and relationships, combined with equations describing the rate of system oxygenation and carbonate equilibrium chemistry, can be used to predict system water quality dynamics at a desired fish loading and feeding rate in an aquaculture water reuse system. 4.3 POND AQUACULTURE SYSTEMS The primary driving force for a pond aquaculture system is the level of feed input. For the purpose of predicting system design capacity, the total oxygen demand imposed on the pond is assumed to equal the total ultimate oxygen demand (BODL) of the feed fed to the pond per day. A value of 0.65 mg of oxygen demand per mg of dry feed fed is a reasonable assumption for the purpose of design (Chieng et al., 1989). The addition of nitrogen and phosphorus to a natural water body (as fertilizer, fish food, or fish metabolites) drives the production of organic carbon fixation through the process of phytoplankton photosynthetic biomass production. The elemental composition of this biomass production can vary widely. This composition is often represented as a value referred to as the Redfield ratio (Redfield et al., 1963): 106CO 2 + 16NO 3- + HPO 4 + 122H20 § IgH* $ sunlight

(4.2)

C106 H263 O110 NI6 P1 + 13802 The forward process is referred to as photosynthesis, while the reverse represents the combined processes of respiration and algal cell mineralization. One would expect that since the forward reaction occurs only during the daylight hours and respiration occurs continuously, that a day/night polarization of both oxygen concentration and pH would occur. This is the well known observation of diurnal oxygen concentration

101

fluctuation and diumal pH cycling, resulting from daytime CO2 fixation, and oxygen production followed by nighttime CO2 production and oxygen uptake. The Redfield ratio suggests a algal composition of 35.8% carbon, 6.3% nitrogen and 0.87% phosphorus of algal dry weight. The Redfield ratio was determined from marine phytoplankton. Repeated measurements of freshwater algal biomass suggests slightly higher values of 45% carbon, 8% nitrogen and 1% phosphorus (Goldman, 1980). These latter values will be assumed to best represent the composition of freshwater pond phytoplankton for the purpose of all design calculations. These later values agree with the Redfield Ratio in suggesting an algal C/N ratio of 5.62/1. Furthermore, the Redfield equation suggests an oxygen production of 3.47 mg of O2 per mg of carbon fixed through photosynthesis. 4.3.1 Pond Primary Production Much has been written about the nutrients limiting primary production in freshwater ecosystems (Lehman et al., 1975). Many researchers suggest that phosphorus concentration controls the total algal biomass in most freshwater communities (Schindler, 1971). However, when attempting to predict the primary productivity of an aquaculture pond for design purposes, it is more practical and useful to base predicted rates of algal production on nitrogen loading. In most cases, the nitrogen content of the fish feed is well known, and feed phosphorus content is usually supplied at P/N ratios that are typically equal to, or greater than, the P/N ratio of the expected algal biomass. As a result, the sediment of most aquaculture ponds quickly becomes phosphorus rich, thereby ensuring adequate long-term phosphorus supply to support algal growth in the pond. On the other hand, excessive nitrogen applied to a pond will eventually migrate to the sediment where it will be lost through denitrification. Most importantly, predictions of algal biomass based on nitrogen addition from feeds with carbon, nitrogen, and phosphorus content similar to the C/N/P composition offish biomass correlate well with observations of pond algal biomass, as will be demonstrated in latter worked examples. Calculations of pond productivity, based on daily nitrogen loading rate, should be considered useful

averaged predictions. Day-to-day pond algal biomass can vary widely because of changes in short term nutrient availability, light levels, and zooplankton populations. However, the averaged values yield useful information in terms of predicting overall pond oxygenation requirements and fish carrying capacities. Algal growth rates as high as 2.0 doubling per day have been observed under laboratory and controlled field conditions (Shelef et al., 1973; Goldman and Ryther, 1975). Under such conditions sustained algal productivities in excess of 12 g carbon/m2-day have been observed. However, in the typical aquaculture pond, overall cell turnover is generally limited to maximum rates of 0.5 per day (i.e., a 2 day algal cell age) and a minimum of 0.1 per day (a 10 day algal cell age) with productivities ranging from 1 to 4 g carbon/m2-day (Brune, 1991; Schroeder et al., 1991). Typical values of cell age range from 5-10 days. Therefore in an aquaculture pond, the algal productivity will generally be controlled by availability of nitrogen mass loading up to the level that can sustain a fixation rate of 4 g carbon/m2-day. Typically, water quality parameters are measured and expressed in mg/liter, mmole/liter, or meq/liter, while most US aquaculturists use lbs/acre to describe pond fish carrying capacity and pond feed application rates. It is therefore useful to be able to convert from lb of feed fed to mg/liter of resulting nitrogen in the pond water, and for this reason these english/metric conversions will be incorporated into the rate expressions. Assuming that 75% of the nitrogen contained in the feed added to a pond will be incorporated into algal biomass, (i.e., no waste solids removal from the pond and 25% of fed nitrogen is incorporated into fish flesh) the daily algal fixation can be calculated by multiplying the feed application rate in lb/acre-day by the

102

percent protein contained in the feed and, further by multiplying by the 16% of the feed protein as nitrogen and finally, converting to units of g-N/m2-day: F

lb feed acre -day

p

r [.000134] = IN nitrogen loading g-N protein content m 2-d L percent feed

(4.4)

If the pond is assumed to average 1 meter in depth, then the rate of addition in g-N/m2-d is equivalent to mg-N/L, since 1 m 3 = 1000 liters. The carbon fixation rate can be calculated from the Redfield C/N ratio of 5.62/1: C

g -C m 2-day

= [N] [5.62]

(4.3)

4.3.2 Pond Oxygen Production Once the carbon fixation rate is established, the effect of oxygen production by the algal biomass can be calculated using the Redfield oxygen/carbon ratio of 3.47/1:

O 2

g-oxygen 2 m -day

= [C] [3.47]

(4.5)

In a one meter deep pond, g-oxygen/m2-day is equal to mg/L of 0 2. Total oxygen demand in a pond can also be tied to the feed rate. The ultimate biological oxygen demand of pelleted feeds of 0.65 mg O 2 per mg of feed can be taken to represent the combined fish oxygen demand as well as the pond oxygen demand due to uneaten food or excreted organic waste. The amount of gross oxygen production that results in a net oxygen gain in the pond depends on the average algal cell age. Any algal organic matter that is physically removed from the pond either directly or indirectly by incorporation into filter feeding zooplankton and/or fish, results in algal organic oxygen demand not exerted in the pond, and therefore, a net oxygen addition to the overall pond oxygen balance. As an example, if the pond is fixing a net 3 grn of carbon/m2-day, which is equivalent to 10.4 gm of oxygen/m 2-day with an average algal cell age of 5 days, then 20% of this production is being removed each day either by sedimentation to the pond bottom or incorporation into the pond food chain. Past observations of pond oxygen dynamics suggest that this relatively low rate of algal organic matter removal can be considered to be "lost" from the pond with regard to impact on oxygen dynamics. Therefore, this leads to the expectation of a net oxygen gain in the pond of(0.2) X (10.4 gm) or 2.1 gm oxygen/m2-day. This effect, if controllable, offers one of the greatest potentials to the pond aquaculturist to increase the carrying capacity of his pond. In ponds with unmanaged algal production, the long-term net oxygen yield varies between 10 and 20% of daily production (Brune et al., 1992; Schroeder et al., 1991). For simplicity, and as an added factor of safety in later calculations of pond oxygenation, these low levels of net pond oxygenation from unmanaged algal production will not be routinely included in pond oxygen balances.

103

4.3.3 Algal Standing Crop and Secchi Disk For the purpose of pond design and prediction of system performance, algal standing crop, best represented as total volatile suspended solids (TVSS) and pond total suspended solids (TSS) are the most difficult variables to predict in a aquaculture pond. Algal standing crop is a direct function of the average algal cell age and algal productivity. As indicated above, past observations suggest that this age typically ranges from 5 to 10 days depending on settling rates and zooplankton grazing rates (Brune et al., 1992). Average algal standing crop can be predicted by multiplying the daily carbon fixation rate by the average cell age: SC g-carbon

- [C] [01

(4.6)

where 0 varies from 5 to 10 days in a typical aquaculture pond. For design purposes, it is best to calculate the extremes of expected algal density as an estimation of the range of algal standing crop in the pond. The algal cell density as total volatile suspended (TVSS) solids is obtained by converting from g-carbon/m 2to mg/L of total volatile suspended solids using the ratio of 2.22 g of TVSS per g of carbon: (4.7) rVSS

mg

L

[SC] [2.22]

From the calculation of pond total volatile suspended solids, it is possible to predict average pond secchi disk (SDV in meters) from a correlation between total suspended solids and secchi disk (Almazan and Boyd, 1978) assuming that 100% of TSS is present as TVSS: TSS = 6.03 (SDV) -0"932

(4.8)

Drapcho (1993) later showed that at secchi disk readings of less than 0.5 meter, a more accurate representation of this relationship is: TSS = 11.65 + 297e(-$'22)(SDV)

(4.9)

In both equations 4.8 and 4.9, we are assuming the total volatile suspended solids is equal to total suspended solids as measured by the membrane filtration technique used by both Almazan and Boyd and later by Drapcho. In unmixed ponds this is usually a reasonable assumption, however, in extremely muddy ponds the ratio of TSS/TVSS may often times range as high as 2/1. This effect should be taken into consideration when attempting to predict algal biomass (TVSS) in muddy ponds from secchi disk readings which are correlated to total suspended solids (TSS).

104

4.4 DISSOLVED OXYGEN C O N C E N T R A T I O N 4.4.1 Equilibrium Gas Concentration At a given temperature and salinity, the concentration of oxygen that is soluble in water is a direct function of the partial pressure of gaseous oxygen in contact with the water: Cs

Po~ KH

=

(4.10)

This relationship, referred to as Henry's Law, expresses the equilibrium dissolved oxygen concentration (Cs) as a function of Henry's constant for oxygen (KH) and the contacting partial pressure of oxygen (Po2) . 4.4.2 Gas Transfer Rate If the water is not at equilibrium with regard to gas saturation, then there exists a driving force for oxygen to move into, or out of solution. This non-equilibrium driving force is quantitatively expressed as the oxygen deficit (D) or Cs-C where Cs is the equilibrium value given by Henry's Law and C is the actual solution concentration. The rate at which oxygen moves into solution is controlled by the oxygen transfer at the air water interface, schematically represented in Figure 4.1:

x GAS

PHASE ADVECTION

PC,AS

I I GAS FILM

LIQUID FILM

I

I

I

I

PHASE ADVECT,ON

WATER FILM

Cs

CONCENTRATION

Fig. 4.1. Representation of gas/liquid interfacial transfer. The rate of change of oxygen in the bulk water can be described as a function of the interracial surface area (A), the diffusitivity of the gas (D) in the liquid of interest (oxygen in water in this case), the stagnant water film thickness (X) (the water film is the slower, therefore, the rate controlling layer), and the volume of water under the influence of the aeration device (V). The relationship is then expressed as: dc

t i m e r a , e o , change

of oxygen concentration

=

105

Usually, precise values of A, V, X and D are not well known for a particular situation. For this reason, the effects of these parameters are lumped together into a single empirically determined rate constant referred to as the overall gas transfer coefficient (KLa) where: de - KLa (Cs - C) dt where;

(4.12)

KLa = rate of oxygenation, time-X C = system oxygen concentration, m_._gg L C

s

= oxygen saturation concentration, mg L

dc dt

-

rate of change of system oxygen concentration,

mg L -time

This relationship is a first order exponential, illustrated in Figure 4.2:

z o_

CO

t-<~ r~ z

Cs

z 0 z w o X 0

TIME

Fig. 4.2. Exponential time rate of change of oxygen concentration predicted by equation 4.12. A particular value of KLa, which is specific for a given set of conditions, can be used to describe the rate of transfer of oxygen into or out of solution, as shown above. In a system in which fish or other oxygen demand is present, the KLa can be determined by measuring the steady state oxygen deficit (D) and the fish respiration rate (R). This is illustrated in Figure 4.3. With the aeration device on, and the system at steady state, the oxygen concentration in the water remains constant, with the respiration rate (R) equal to the oxygen replacement rate (KL~D). If the aerator is turned off at time equal to tl, the oxygen concentration will begin to fall at a rate equal to R. When the aerator is switched back on, the oxygen concentration will return to C in an exponential fashion described by KLa(CsC) -R. The overall transfer rate (KLa) can be determined from this simple experiment by measuring the rate of respiration and dividing by the driving force or deficit at steady state;

106

KLa

(4.13)

=

Cs - C AERATION OFF

zl

AEFb~TION ON

_o ~_. z ,,, (.3 z o o

Cs (Cs-C)=D R=K

LA

D

z bJ o>x o

LA ( C s - C ) - R

to

i

i

t 1

t 2

,

TIME

Fig. 4.3. Dynamic response of oxygen concentration with simultaneous respiration and aeration.

A detailed presentation that describes how to obtain the KL~value from operating systems is given in Mueller and Boyle (1988). Example 4.1 Kt~ Determination A 1000 L tank containing 100 kg of fish with a known respiration of 1.5 kg of 02 per 100 kg of fish per day must be maintained at an oxygen concentration of 5.0 mg/L. What overall transfer coefficient is required? Solution:

Assuming that dry air is used to aerate this tank at a water temperature of 70~

and a

pressure of 1 ATM pressure, the tank equilibrium saturation value for oxygen can be calculated from Henry's Law directly or obtained from previously calculated tabulated values. The total oxygen demand is: 1.5 kg O~

100 k S fish

100 kg fish day

1 day 24 hr

= 0.01736

C s @ 70~

1 hr

1 min

60 min

60 sec

mg

L -sec

_ dc

dt

and 1 atm pressure = 8.5 m___gg L

106 mg 1000 L

kg

107

With C = 5.0 m~jL, and Cs = 8.5 m g ~ , and dc/dt = 0.01736 mg/L-sec, the K La can be determined: dc dt - KLa (Cs - C)

K~a =

= KLa

(

) mg 8.5 - 5.0 m__gg = 0.0173 L L -sec

0.01736 m8

L

L-sec

3.5 mg

= 0.005 sec -1

4.4.3 Manufacturers Oxygenation Capacity In the case of a small tank, the volume of water under the influence of the aeration device is well known. In a pond however, this volume, referred to as the volume of influence of the aerator, is often not well known. Different aerator designs can produce considerably different oxygen mass transfer rates because of the mixing pattern produced by the device. Manufacturers will frequently rate a particular aeration system with an aeration capacity number which is usually determined by calculating the overall oxygen transfer in clean water at an oxygen concentration of zero and water temperature of 20~ and an assumed, or measured volume of influence (V): No

/

manufacturers

/

oxygenation capacity]

(4.14)

= KLa (Cs2~ - 0 ) V

Example 4.2 OxygenationCapacity The manufacturer lists an aerator as being capable of supplying 4.0 kg of 02 per Kw- h (No) at standard test conditions of water temperature = 20~ What is the field oxygenation capacity (Nf) for fish culture conditions with Cmm= 5.0 mg/L, and Cs = 9.02 mg/L?

Solution: (solving by using ratios),

N O = 4.0

kg - (9.14 - 0)V ~ kw -h

therefore: V o = 0.437

Nf -" (8.0 - 5.0)Vf assuming Vo = Vf Nf = (3.0)(0.437) = 1.31

kg kw -h

This is the rate of oxygenation that can be expected to be supplied to the pond from the aeration device per Kw-h of energy supplied to the aerator, assuming an average pond oxygen concentration of 5.0 mg/L, and a solution oxygen concentration of 9.02 mg/L.

108

4.4.4 Surface Reaeration The rate at which oxygen transfer occurs across the surface of an open body of water has been quantified by Banks and Herrera (1977) as a function of water depth and wind speed:

(4.15) where; KLa = transfer coefficient, day l base e V = wind speed, km/h measured 10 meters above water surface H = water depth, meters This equation was developed from data taken from shallow lakes and assumes that the zone of influence, in this case the entire water depth, is well mixed.

Example 4.3 Surface Reaeration If the early morning (6 AM) dissolved oxygen in a pond is 3.0 mg/L and saturation is 8.0 mg/L, what will the oxygen concentration in the pond be at noon assuming there is no respiration or photosynthesis in the pond?

Solution: Assuming the pond is 1 meter deep and the average wind speed = 9.65 km/h (6 mph) KLa = (1 meter) [(0.384(9.65) '/: - 0.088(9.65) + 0.0029(9.65)2)] KLa = (1)[( 1.193 - 0.849 + .27)] KL, = 0.614 day ~ Converting this value to a per hour rate: 0.614

day

day

24h

= 0.0256h-1

A table can be prepared to estimate the time dependent oxygen concentration by repeatedly solving equation 4.12 for small (1 h in this case) time steps (see Table 4.1). By noon, the oxygen concentration will have increased to 3.72 mg/L as a result of wind reaeration at a constant wind velocity of 9.65 km/h. This value (1.44 mg/L over 12 hrs) compares favorably with the observed values from Schroeder (1987) of 1.69 mg/L oxygen gain over a 12 hour period following a 50% an observed saturation oxygen concentration at dusk.

109

4.5 C A R B O N A T E E Q U I L I B R I U M AND P H One of the most important properties of water is its weak tendency to disassociate into its ionic components: H 2 0 -~- H +

OH-

(4.16)

The ratio of the ionic products to the concentration of water is expressed as the equilibrium constant for water (Kw): Kw = [H+][OH-] [H20]

_= 1 X 10 -~4 @ 25~

(4.17)

Table 4.1. Stepwise solution to reaeration equation. At

Time 6 AM

C

dc/dt = Kea(Cs - C) At

3.0 mg/L

1 hr

(0.0256 hr~)(8.0- 3.000)(1 h r ) = 0.128 mg/L 7 AM

3.000 + 0.128 - 3.128

1 hr

(0.0256)(8.0- 3.128)= 0.125 8 AM

3.128 + 0.125 = 3.253

1 hr

(0.0256)(8.0 - 3.253) = 0.122 9 AM

3.253 + 0.122 = 3.375

1 hr

(0.0256)(8.0- 3.375) = 0.118 10AM

3.375+0.118=3.493

1 hr

(0.0256)(8.0- 3.493)= 0.115 11 AM

3.493 + 0.115 = 3.608

1 hr

(0.0256)(8.0- 3.608) = 0.112 12 Noon

3.608 + 0.112 = 3.720

By convention, the concentration of water [H20] is set equal to 1, and the ion product ([I-F][OH]) in water is seen to vary over 14 orders of magnitude. For convenience, this concentration spectrum is defined as the water pH, where pH is expressed as: pH =

1 = -log [H +] log [H ~]

(4.18)

110

In most natural waters, the factor that exerts the greatest influence on pH is the concentration of inorganic carbon in the water. The presence of approximately 360 ppm CO2 in the atmosphere, and calcium and magnesium carbonate in most rocks and soils, insures that inorganic carbon is present to interact with water pH. Atmosphere CO2 dissolves in water to produce carbonic acid according to: [H2CO 3] H20 + CO 2 ~- H2 CO 3

[CO2]

= KCO'

(4.19)

Carbonic acid undergoes two additional equilibrium reactions:

[HI[HCO3-] H 2 CO 3 * H" + H CO a-

= K~

(4.20)

[H2CO 3]

HCO; ~ H § + CO;

In "][co~:] [nco~-]

= K2

(4.21)

The end result is that the total inorganic carbon present in water at any time is the sum of the three forms:

C T = [H2CO31 + [HCO3- ] + [CO/]

(4.22)

The total carbon in solution is also related, through the principle of charge balance, to the titratable negative charges (or anions) in solution. A commonly used indication of the total titratable negative charge in solution is called the alkalinity (alk)of the water expressed in either equivalents or milliequivalent per liter (meq/L); [Alk] = C r(tzl + 2tz2) + [OH-] - [H+]

(4.23)

In equation 4.23 0~1and cz2represent the fraction of the total carbon present as (HCO-~ and (CO,respectively: [H2CO3 ] = Crtz ~

(4.24)

[HCO3- ] = C r cz~

(4.25)

[CO3-] = C r tz2

(4.26)

where: tz0 + 0~1 "1-

0~ 2 " -

1

(4.27)

These ionization fractions are a function of the solution pH, temperature, solution ionic strength, and equilibrium constants Kco, K I, and K 2 and can be calculated as der~crib~d in Appendix A, Figure A-2. Other anions such as boron 2(B(OH)T ), ammonium, (NH~), phosphate (PO4-3), or silicate (S iO4-) can affect

III

this relationship; However, in most fresh waters, these concentrations are low relative to the inorganic carbon concentration and can be ignored. For the striped bass culturist, the practical importance of these relationships is summarized in the graphical representation of Equations 4.18 - 4.22 in Figure 1, Appendix A. This figure from Stumm and Morgan 198 l, illustrates that the pH of most natural water can be quantitatively predicted from knowledge of the solution alkalinity and total inorganic carbon content. For example, if a water is at pH - 8.0 with an alkalinity = 2 meq/L (2 meq/L alkalinity = 100 mg/L as CaCO3), then as Figure 1 shows, the water would be expected to have an inorganic carbon content of approximately 2.1 mmole/L. If, as a result of algal photosynthesis, 1 mmole/L of inorganic carbon is taken up and fixed as organic carbon, then the resulting short-term pH can be predicted by tracing a horizontal line from the previous point of intersection in Figure 1 to 1.1 mmole/L of total carbon, yielding a solution pH of 10.35. It should be noted that eventually this pH will again fall as atmospheric CO2 moves back into the solution to return the water CO2(aq) concentration back to equilibrium as predicted by Henry's Law (at atmosphere CO levels the equilibrium pH at 2.0 meq/L alkalinity is approximately 8.3). If both the rate of algal carbon fixation and the K La(C O 2) in a pond or recirculating aquaculture system is known, then the time rate of change of the water pH can be quantitatively predicted. 4.6 PREDICTION OF AQUACULTURE POND PERFORMANCE AND WATER QUALITY The best way to test the validity of the equations and assumptions proposed in this chapter is to evaluate them by comparing the predicted performance of a typical pond to field experience. Because more published pond experience is available for catfish, the examples will be adjusted to account for typical catfish feeding rates, feed nitrogen content, and water temperatures. Three examples are considered; the case of maximum carrying capacity without active aeration, the case of nightly routine aeration with a 1 horsepower per acre aerator (3500 lb/acre carrying capacity), and finally the case of maximum observed feeding capacity of 100 lb/acre fed in routinely aerated catfish ponds.

Example 4.4 Surface Reaeration Limited Fish Carrying Capacity Calculate the fish carrying capacity in an unaerated pond, in upstate South Carolina with an average wind speed of 6 mph (9.65 km/h) assuming an average dissolved oxygen concentration in the pond of 5 mg/L, and a water temperature of 28~ with 1.5% of fish body weight being fed per day with a 35% protein feed.

Solution:

Surface reaeration can be predicted using from the

KLavalue of 0.614 day-~ previously

obtained in example 4.3 and assuming an average acceptable oxygen concentration in the pond of 5.0 mg/L. Pond dissolved oxygen saturation at 28~ is 7.75 mg/L: dc _ (0.614/day_l) (7.75 - 5 . 0 ) = 1.68 rng dt L -day

The pond feed rate is based on the assumption of 0.65 mg 02 demand per mg of feed fed to the pond, which is 1 meter deep:

112

1.68

mgO 2

gO 2

- 1.68

L -day

in a 1 meter deep pond

m 2-day

therefore; 1 $; feed

1.68 g 02 m 2 day

1.0 wet feed wt 0.90 dry feed

0.65 g 02

=

25.6

4048 m 2

1 lb

I acre

454 g

lb feed acre -day

This feeding rate can then be used to predict an algal standing crop and secchi disk using equations 4.3-4.9: First the pond nitrogen loading rate is calculated from equation 4.3" 25.6 lb feed acre

[35% protein] [.000134] = 0.120 mg N L -day

The algal carbon fixation rate is then obtained from equation 4.4: mg N ] g-carbon 0.120 L ' d a y ] [5.62] = 0.674 m2-day

Photosynthetic oxygen production is obtained from equation 4.5:

0.674 g-carbon m 2 -day

[3.47] = 2.34

g 02

m 2-day

The algal standing crop is then predicted from equation 4.6: 0.675 g-carbon m 2-day

[5] = 3.37 g-carbon m

2

0.675 g_-carbo_.....,n [10] = 6.75 g-carbon 2 m 2-day m

typical minimum

typical maximum

113

These values can be converted to algal volatile suspended solids using equation 4.7: 3.37 g_-c_arbo_.___n [2.2] = 7.4 mg TSS L m 2-day

typical minimum

6.75 g_-carbon [2.2] = 14.85 mg TSS L m 2-day

typical maximum

The pond secchi disk value can be predicted using equations 4.8 and 4.9:

0.932 = 0.80 m maximum

14.85 - 11.65 297

= 0.55 m minimum

-8.22

As a "best guess," it is reasonable to assume an average cell age for the algal biomass of 7.5 days (13.3% algal biomass loss each day). This gives an algal standing crop of 11.1 mg/L and a secchi disk of 0.52 m. Actual observed secchi disk readings in ponds receiving from 10 to 70 lb/acre-day of feed (Data from Tucker et al., 1979) correlate well with predicted secchi disk values obtained using this technique (Figure 4.4). The fish carrying capacity and projected pond oxygen concentration can be calculated assuming an average feeding rate of 1.5% of body weight per day, at the end of the season. 25.6 lb feed acre day

100 lb fish day 1.5 lb feed

= 1707 lb fish acre

If 13.3% of the algal biomass is lost each day by being "stored" in the pond food chain (and therefore does not respire away the oxygen produced by fixation), then this suggests that of the 2.34 mg O2/L-day of photosynthetic oxygen production 13.3% or a net addition of 0.31 mg/L or 0.31 g O2/m2-day will be added to the pond. This small addition of 0.31 g O2/m2-day to the pond from algal harvest would suggest an increase in pond carrying capacity of(1.68 mg + 0.31 mg O2)/1.68 or a 1.18 increase, resulting in a prediction of 30.3 Ib of feed and 2014 lb of fish carrying capacity. In a typical pond, in which the algal cultures are unmanaged, it is likely that the actual oxygen yield from algal harvest could vary from lows of 5% per day to highs of 30% per day. To be conservative, this gain in carrying capacity is disregarded in the calculations presented in Figure 4.4.

114

10.0 _

0.9 5 0.8

2

~

i

0.7-

9

.5

~= o . 6 x_

.2

p 9

0.5 ~ -T-

0.4

P

_

o 0

3

2

9

p

9

0.3

9

0.2 -

o.iL

,,

0

L

0

10

20

30 FEED

40 RATE

50 (Ib/ocre

i

'

60

70 per

80

90

1 O0

doy)

Fig. 4.4. Observed vs. predicted secchi disk at various feeding rates. (1 = 4,942 fish/HA, 2 = 10,003 fish/HA, 3 = 20,385 fish/HA, p = predicted value from equations 4.3 - 4.9. Data from Tucker et al. 1979. )

Example 4.5

Aeration Requirements for 3500 Ib/acre Fish Carrying Capacity.

Calculate the supplemental aeration needed to support 3,500 lb/acre of catfish. Use a feed rate of 1.5% of fish body weight per day with 35% protein feed with a pond water temperature of 28~

Solution." The rate of nitrogen loading to the pond is based on a feeding rate 1.5% of fish body weight per day or 52.5 lb/acre-day. Using equation 4.3, this feeding rate yields;

52.5

lb [35% protein] [.000134] = 0.246 acre -day

g-N m

2-day

115

Algal production, standing crop and secchi disk are calculated from equations 4.4, 4.6 and 4.9:

0.246 m2_----~~ay ] g - N [5.62] = 1.38 g-carbOnm2_day

1.38 g-carbon m 2-day

average standing crop @ 0=7.5 days

[7.5] = I0.35 g-carb~ m2

r

10.35 g-carb~

[2.2] = /22.77 mg TSS

L

m 2

1n[22.77 - 11.65 297 -8.22

L

= [0.399 m]

average TSS @ 0=7.5 days

average predicted secchi disk

The photosynthetic oxygen production of the pond is calculated from equation 4.5:

I

1.38 g-carbon m 2-day

[3.47] = 4.79

g-O 2 m 2-day

or 4.79

mg 0 2 L

If the pond is aerated in such a manner to insure an average dissolved oxygen of 5.0 mg/L, then the predicted ADO of 4.79 mg/L suggests a maximum pond oxygen concentration of 7.39 mg/L and a minimum value of 2.60 mg/L. The aeration requirement in excess of the 1.68 g Ojm2-day supplied by surface reaeration (example 6.4) is calculated from the BODL loading to the pond from the feed: 52.5 lb feed

454 gm

acre

0.65 g 02

4048 m 2

g feed

= 3.83 acre-day

g

0 2

m 2-day

116

This oxygen requirement from external aeration (reduced by the 1.68 g 02/m2-day from wind driven re-aeration) corresponds to:

3.83 - 1.68 = 2.15

g 02 m 2-day

or

19.2

lb

0 2

acre-day

A one horsepower per acre aerator running 12 hours per night is typically capable of supplying 1-2 lb ofO 2/hp-h-acre or 12-24 lb O ~cre-day. This corresponds to field observations that 3500 Ib/acre represents a carrying capacity that will require routine nightly aeration at maximum oxygen demand. Conversely, ifa 2.0 mg/L dissolved oxygen concentration is defined as the lowest acceptable average concentration in the pond then the wind driven interfacial oxygen transfer can be recalculated from equation 4.12 as" de - (0.614 day-l)(7.75 - 2.0) = 3.53 g-oxygen m 2-day

This oxygenation rate can be converted to a pond feeding rate in the same manner as calculated in Example 4.4: 3.53 g O a

1 ~; feed

1.0 wet feed

4048 m 2

I lb

m 2 day

0.65 g 02

0.9 dry feed

1 acre

454

= 53.8

lb feed acre -day

This value corresponds to almost exactly the feeding rate observed by Cole and Boyd (1986) as the maximum feeding rate tolerated in unaerated ponds (Figure 4.5).

Example 4.6

M a x i m u m Observed Pond Fish Carrying Capacity.

The maximum sustained carrying capacity of ponds is observed to be in the range of 100 lb/acre-day of feed application. Calculate the fish carrying capacity, oxygenation requirements and expected secchi disk reading for a pond at this limit.

Solution:

Fish carrying capacity is calculated from 1.5% of body weight fed per day: 100 lb feed

1O0 lb fish

acre-day

1.5 lb feed

= 6666

lb fish acre

117

Algal productivity and standing crop is predicted from equations 4.3, 4.4, 4.6, 4.7 and 4.9: ] 100 lb feed [35% protein] [.000134] = 0.469 .....g-N . acre -day m 2-day

J

F [5.62] = [2.64 g.-c_arbo.__.._n m 2-day

0.469 g - N m 2-day

2.64 g-carbon m 2-day

[

F [7.5 days] = ~19.80 g-e_arbo_..._n m 2-day L

19.77 g -carbon m2

average standing crop

[2.2] = [43.56 mg TSS]L averageTss

F

In [43.49 - 11.65 L"" "297 -8.22

= [0.27 m] average predicted secchi disk

Pond oxygen production is predicted from equation 4.5"

2.64 g-carbon m _2 -day

or

r [3.471 = [9.16 g._o_xyge_...__.n m 2_day [

9.16 m_._gg in a 1 meter deep pond L

Pond oxygen demand is calculated from feed application:

100 lb feed

0.9 g dry feed

454

acre

0.65 g

0 2 g 0 2 =

6.56

m 2-day acre-day

1.0 g wet feed

lb

4048 m 2

g-feed

118

Pond oxygenation requirement, assuming an average DO of 5.0 mgjL, is calculated by subtracting file wind driven aeration (1.68 g O2/m2-day) from the pond oxygen demand: g 02 :

4 , ,

m 2-day

m 2-da

or 43.5

lb 0 2

oxygenation requirement

acre -day

This corresponds to an active supplemental aeration of 1.81 lb O:/hp-h for a 2 hp/acre aerator running 12 hours every night at maximum carrying capacity. It is interesting to note that the carbon fixation rate of 2.64 g C/m2-day under these conditions is approaching the limit observed in "unmanaged" algal culture ponds. This suggests that the observed 100 lb/acre feed limit may be due to the inability of the pond algal crop to process added nitrogen at rates exceeding this value. Furthermore, if at this carbon fixation rate 20% of the algal photosynthesis is "lost" to the pond each day as is frequently observed in these systems, and if this 20% per day (corresponding to an average algal cell age of 5 days) is stored in biomass, which is ultimately removed from the pond, then 20% of the 9.16 g OJm 2day production will be available to aerate the pond. This amount of photosynthetic aeration would reduce pond supplemental aeration to 27.2 lb OJacre-day. This explains why on certain days the pond may appear to need

SO0

.--

0

i

Z 0 ,/

//

! -

/ / / i

I

i

i 2OO f

o@"-

coy)

Fig. 4.5. Field determined aeration requirements vs. feeding rate to maintain a minimum pond dissolved oxygen of 2.0 mg/L (from Cole and Boyd 1986).

119

less aeration than on others. If the algal cell age could be reduced to 1.83 days (53.3% of algal photosynthetic oxygen returned to the pond) by active removal of algal biomass production through the use of filter feeders or physical chemical removal, the supplemental aeration could be reduced to zero as the net algal oxygen production of (9.16) (.533) = 4.88 g O2/m2-day would offset net pond oxygen demand.

Example 4.7 Prediction of Pond pH and Effect of Liming. Predict the pond pH in example 4.5 with 3,500 lb/acre of fish carrying capacity. Assume that the pond has a water alkalinity of 50 mg/L as CaCO> What effect will increasing pond alkalinity to 100 mg/L (as CaCO3) with lime addition have on pond pH?

Solution:

The carbon fixation rate was calculated previously as 1.38 g-carbon/m2-day or 1.38 mg/L-day. The carbon addition rate to the pond is based on the feed addition and is calculated assuming that 85% of added feed carbon is respired into the water: The total carbon released to the pond is calculated from the feed addition rate:

52.5 lb ,,

acre-day

0.9 lb dry feed

0.85 lb carbon released

0.5 lb carbon

1.0 lb added feed

1.0 lb carbon added

Ib dry feed

454 g 1.0 lb

or 2.25

1 acre

4048 m 2

mgC L -day

,,,

= 2.25 g-carbon m Z_day

in a 1 meter deep pond

It is reasonable to assume that pond respiration is constant while photosynthetic carbon fixation occurs only during the daylight hours, therefore, a diumal carbon balance can be constructed:

120

Carbon Balance

Day

Night

Fixation

- 1.38 rag C L

0

Feed/fish respiration

+ 1.125 mg C L

+ 1.125 mg C L

Algal Decomposition

+0.69 mg C L

+0.69 rag C L

TOTAL

+0.435 mg C L

+ 1.815 mg C L

The average net carbon flux rate is out of the pond and occurs at the carbon loss rate of 2.25 mg/L-day. However, because daytime photosynthesis is refixing some of the excess CO2, the intensity of the carbon loss is 4.17 times greater at night than day. This carbon loss rate can be related to the total inorganic carbon concentration by using the gas transfer equations 4.12 and 4.14. The KL~for CO2 can be estimated from the KLa(O2) used in example 4.3 by adjusting for the molecular weight of carbon dioxide:

= [ mwt KL~(C~

32] [o.614 day-l]- 0.446 day-1

02 [rawt CO 2 KLa(O,) = - ~

The average daily pH is obtained by first calculating the total carbon gas transfer driving force from equation 4.12:

dCdt - ( 0 . 4 4 6 d a y - l ) ( A c O 2 ) = (0.435 rag_12 -carbon hrs

During the day

and dedt - (0.446 day -l ) (ACO2) =

1.815

rag-carbon) L"12~rs

During the night

or ACO 2 = 1.95 mg carbon/L A CO 2 = 8.14 mg carbon/L Therefore, the C O 2 transfer rate of 0.435 mg-carbon/L-12 hrs is calculated to occur at an average ACO2 of 1.95 mg-carbon/L or 1.95/12 = 0.1625 mmole/L of carbon. In the worst case, this CQ loss rate increases to 1.815 mg-carbon/L-12 h at night yielding a A C O 2 of 8.14 mg-carbon/L or 0.678 mmole/L of carbon.

121

The calculations required to predict pond pH can be very complex, and a trial and error solution is often required to determine exact values. However, approximate solutions can be obtained from Figure A- 1 in Appendix A. In water at equilibrium with atmospheric CO,, the C for total carbon (in mmole/L) in solution is approximately equal to the alkalinity (in meq/L). Furthermore, at the pH values typically encountered in aquaculture ponds, it is reasonable to assume that the driving force for CO2 gas transfer is C r or the total inorganic carbon concentration (Stumm and Morgan, 1981). Therefore, Figure A- 1 predicts an approximate equilibrium water pH of 8.0 at a water alkalinity of 50 mg/L a s CaCO 3 or 1.0 meq/L. The range of carbon flux rates calculated above suggest an equilibrium Cv of 0.678 mmole/L higher than equilibrium at night, and 0.1625 mmole/L higher than equilibrium at day. Figure one predicts pH's of 6.6, and 7.0, respectively at these CT values of 1.678 and 1.1625 mmole/L and 1.0 meq/L alkalinity. By increasing the alkalinity to 100 mg/L as CaCO3 (or 2 meq/L alkalinity) the effect is to suppress the pH variation from an approximate equilibrium value of 8.5 to a daytime pH of 7.5 and a nighttime pH of 6.8. This compares very well with Tucker's et al. (1979) field observations of average low pH of 6.8 at these feeding rates. However, Tucker also observed occasional daytime high pH's of 9.0. How can this be accounted for? The algal growth in a typical fish pond is often observed to behave in batchwise crashes and blooms. If this were to occur, the algal decomposition may not occur on an average daily basis as shown the carbon balance. In other words, during unbalanced periods of algal bloom, little or no algal decomposition might occur. This could lead to a net gain of carbon into the pond due to photosynthesis of as much as 0.255 mg carbon/L- 12 hrs or a rate of 0.51 mg/L-day (algal decomposition = 0, see carbon balance). This yields (from Equation 4.12) an inorganic carbon concentration 0.091 mmole/L less than equilibrium. Figure 1 Appendix A predicts a pH of 9.5 at this condition ofCr = (1.0 - 0.091) or 0.909 mmole/L and an alkalinity = 1.0 meq/L.

4.7

PREDICTION OF AQUACULTURE REUSE SYSTEM PERFORMANCE AND WATER QUALITY

The design capacity and water quality dynamics in a water reuse aquaculture system is based on the fish loading, feed rate, and fish oxygen demand. A mass balance is used to tie fish metabolism to system design and resultant water quality.

Example 4.8 Reuse System with Nitrification A 264 gal (1000 L) tank holds 0.24 kg/L of fish biomass (2.0 lb/gal). Fish are fed a 42% protein feed at 1.2% of body weight per day. The oxygen uptake rate of this fish biomass is 1 kg O 2/100 kg fish. Water temperature is 28~ If the exit dissolved oxygen must not fall below 5.0 mg/L and the total ammonia must not exceed 0.5 mg/L, what flow rate is required? What is the oxygen demand due to nitrification of the effluent in a nitrifying reactor? What amount of alkalinity must be supplied to the system to offset the alkalinity destruction of the nitrifying filter?

Solution."

The calculation of water flow rate is based on oxygen uptake rate"

1000 L

0.24 kg fish L

1 kg O~ 1O0 kg fish-day

= 2.40

kg

0 2

day

or

2,400,000

mg

0 2

day

122

Assuming that the water is reoxygenated to saturation (7.75 mg/L) on each pass through the system, the water flow is calculated from an oxygen mass balance:

2,400,000 m~ O~

L

day

= 872,727

7.75 - 5.0 mg 02 available

L day

This result is typical for most high density recirculating fish culture systems. Water recirculation for oxygen replacement leads to excessively high flows and pumping requirements. In this case, a flow amounting to 160 gpm (606 L/m) would be required, with a tank hydraulic detention time of only 1.65 minutes. To avoid this situation, oxygen is usually supplied directly to the tank and the water flow is controlled by the maximum allowable ammonia concentration in the tank. Given the maximum total ammonia concentration of 0.5 mg NH3-N, the ammonia limited flow is based on a nitrogen mass balance, assuming that 60% of nitrogen fed to the fish is released to the tank (Gunther et al., 1981):

1000 L

0.24 k~ fish

I

0.012 k~; feed

L

[ 0.9 kg dry. feed

kg fish

[

0.42 kg protein kg dry feed

kg wet feed

0.16 k~ TKN

60% NH~-N released

106 mg

kg protein

Kg TKN

kg

NH 3-N

= 104,509 mg

day

This ammonia nitrogen production rate is transformed into a water flow rate by dividing by the allowable maximum ammonia concentration:

104,509 mg NH~-N day

-- 209,018 0.5 mg NH3-N

L day

This reduces the system flow requirements by a factor of 4.2. The oxygen demand from a nitrification reactor converting the ammonia production into NO3- can be calculated using Equation 4.1"

104,509 m~, NH~-N

4.6 mg O,

day

mg NH3-N

= 480,741

mg 0 2

day

123

Therefore, the nitrification reactor will increase system oxygen demand by 20% over the fish oxygen requirement. In addition, equation 4.1 can be used to calculate the alkalinity destruction due to this nitrification demand:

104,509 mg NH3-N

7.1 mg alkalinity

day

mg NH3-N

= 742,013 ~mg as CaCO 3 L

This corresponds to an alkalinity destruction of [742,013/(1000)(50)] = 14.8 eq/day of alkalinity. If this alkalinity were supplied with NaHCO3 (sodium bicarbonate) this would amount to 2.74 lbs of NaHCO3 needed per day.

4.8 SUMMARY The underlying assumptions of using feed oxygen demand and feed nitrogen loading to a pond as a basis for prediction of pond water quality may, at first, seem foolishly simplistic. However, comparisons of predicted pond pH, pond oxygen levels, pond secchi disk readings, and pond oxygenation requirements are seen to compare favorably to actual field experiences. While these assumptions may be used to make reasonable predictions of the average behavior of these water quality and design parameters, they may not however, be accurate for day-to-day predictions. Pond sediment nutrient dynamics, algal carbon fixation, and surface reaeration can change radically on a day-to-day basis as a result of increases in wind velocity, cloudiness, and changes in zooplankton density. The equations can be adjusted to account for direct effects of wind on surface reaeration. Unfortunately, the effects of such meteorological events on sediment recycling of nutrients is not well quantified. Furthermore, cycling of zooplankton populations has yet to be predicted with any degree of confidence. Therefore, precise day-to-day behavior of these complex pond aquaculture systems will likely remain empirical for some time. However, the technique outlined here is very useful for predicting the averaged behavior of water quality in a pond under different feed loadings or fertilization intensities. These types of predictions are important in that they allow the fish farmer to determine the limits to which he can "push" his pond with respect to nitrogen assimilative capacity, and the resultant impact on water quality, particularly pond dissolved oxygen concentrations and pond aeration requirements. These effects will be the same regardless of whether the pond is growing catfish or stripped bass. Unfortunately, little field data is available from stripped bass pond production systems. For this reason we must turn to observations of catfish pond performance to confirm our predictions. Furthermore, these calculations allow fish farmers to explore the possibilities of increasing production by pond design modification. For example, the calculations and field observations show that the algal growth and oxygen production capacity in conventional fish ponds is currently under-utilized by a factor of 2 to 3. Designing a fish culture pond to take full advantage of the 6-12 g C/m-' day of photosynthetic capacity that is possible from managed algal cultures could theoretically increase fish production to 10,000-20,000 lb/acre year. Research is currently underway at Clemson University (Brune et al., 1995; Schwedler et al., 1994) in an effort to prove this level of predicted carrying capacity in the field, through the utilization of managed algal photosynthesis in aquaculture ponds.

124

References

Almazan, G. and Boyd, C.E. 1978. An evaluation of secchi disk visibility for estimating plankton density in fish ponds. Hydrobiologia, 61 (3): 205-208. Andrews, J.W. and Matsuda, Y. 1975. The influence of various culture conditions on the oxygen consumption of channel catfish. Transactions of the American Fisheries Society, 2: 322-327. Banks, R.B. and Herrera, F.F. 1977. Effect of wind and rain on surface reaeration. Journal of Environmental Engineering Division, ASCE, 103(EE3): 489-503. Boyd, C.E., 1991. Empirical modeling of phytoplankton growth and oxygen production in aquaculture ponds. Pages 363-395 in D.E. Brune and J.R. Tomasso, editors. Aquaculture and water quality. The World Aquaculture Society, Baton Rouge, LA. Boyd, C.E., 1985. Chemical budgets for channel catfish ponds. Transactions of the American Fisheries Society, 114: 291-298. Boyd, C.E., 1979. Water quality in warmwater fish ponds. Auburn University Agricultural Experiment Station, Auburn, AL. Brune, D.E., Drapcho, C.M. and Piedrahita, R.H., 1992. Pond oxygen dynamics; design and management strategies. Aquaculture 92 International Conference, American Society of Agricultural Engineers, Paper No. Aqua 92-101, Orlando, FL. Brune, D.E., Collier, J.A. and Schwedler, T.E., 1995. Nutrient recovery and reuse for water quality control in the partitioned aquaculture system. Proceedings of the Sustainable Aquaculture 95 Conference. Pages 57-68, Honolulu, HI. Brune, D.E. and Gunther, D.C., 1981. The design of a new high rate nitrification filter for aquaculture water reuse. Journal of the World Mariculture Society, 12: 20-32. Brune, D.E., 1991. Fed pond aquaculture. Aquaculture systems engineering, Proceedings of the World Aquaculture Society and American Society of Agricultural Engineers, Jointly sponsored session, ASAE Publication, 02-91. Pages 15-33. Busch, C.D., Flood, C.A., Jr., Koon, J.L. and Allison, R., 1977. Modeling catfish pond nighttime dissolved oxygen levels. Transactions of the American Society of Agricultural Engineers, 17:433-435. Chieng, C.A., Garcia, A. and Brune, D.E., 1989. Oxidation requirements of a formulated micropulverized feed. Journal of the World Aquaculture Society, 29: 24-29. Cole, B.A. and Boyd, C.E., 1986. Feeding rate, water quality, and channel catfish production in ponds. The Progressive Fish-Culturist, 48: 25-29. Colt, J., 1986. An introduction to water quality management in intensive aquaculture, Use of supplemental oxygen. Section 6, Pages 1-16/n H. Lorz, convener, Northwest Fish Culture Conference, Eugene, OR. Drapcho, C.M., 1993. Modeling of algal productivity and diel oxygen profiles in the partitioned aquaculture system, Ph.D. Dissertation, Department of Agricultural Engineering, Clemson University, Clemson, SC.

125

Goldman, J.C. and Ryther, J.H., 1975. Nutrient transformations in mass cultures of marine algae. Joumal of Environmental Engineering Division, ASCE, 101 (EE3): 351-364. Goldman, J.C. 1980. Physiological aspects in algal mass culture. Pages 345-359, in G. Shelef and C. J. Soeder, editor , Algal biomass, Elsevier Press, New York. Gunther, D.C., Brune, D.E. and Gall, G.A.E. 1981. Ammonia production and removal in a trout rearing facility, Transactions o f the American Society o f Agricultural Engineers, 24( 5): 1376-1380. Lehman, J.T., Botkin, D.B., Likens, G.E., 1975. The assumptions and rationales of a computer model ofphytoplankton. Population Dynamics, Limnology and Oceanography, 20: 343-364. Meyer, D.I. and Brune, D.E., 1982. Computer modeling of the diumal oxygen levels in a stillwater aquaculture pond. Aquacultural Engineering, 1" 245-263. Mueller, J.A., and Boyle, W.C., 1988. Oxygen transfer under process conditions, Journal Water Pollution Control Federation, 60 (3): 332-341. Piedrahita, R.H., 1991. Modeling water quality in aquaculture ecosystems. Pages 322-362 in D.E. Brune and J.R. Tomasso, editors. Aquaculture and water quality. World Aquaculture Society, Baton Rouge, LA. Piper, R.G., McElwain, I.B., Orme, L.E., McCraren, J.P., Fowler, L.G. and Leonard, J.R., 1982. Fish hatchery management. U.S. Department of Interior, Washington, DC. Redfield, A.C., Ketchum, B.H. and Richards, F.A., 1963. The influence of organisms on the composition of sea-water. Pages 26-77, in M.N. Hill, editor. The sea. volume 2. New York. Schindler, D.W., 1971. Carbon, nitrogen and phosphorus and eutrophication of freshwater lakes. Journal of Phycology, 7:321-329. Schroeder, G.L. 1987. Carbon and nitrogen budgets in manured fish ponds on Israel's coastal plain. Aquaculture, 62: 259-279. Schroeder, G.L., Alkon, A. and Laher, M., 1991. Nutrient flow in pond aquaculture systems, Pages 489-505 in D.E. Bnme, and J.R. Tomasso, Jr., editors, Aquaculture and water quality, World Aquaculture Society, Baton Rouge, LA. Schwedler, T.E., Brune, D.E. and Collier, J.A., 1994. Development and modeling of the partitioned aquaculture system. USDA funded project, Aquaculture Special Grants Program, Washington, DC. Shelef, G., Schwartz, M. and Schechter, H., 1973. Prediction of photosynthetic biomass production in accelerated algalbacterial wastewater treatment systems. Pages 181-189, in S.H. Jenkins, editor. Advances in water pollution research. Pergamon Press, Oxford, Great Britain. Smith, D.W. and Piedrahita, R.H., 1988. The relation between phytoplankton and dissolved oxygen in fish ponds. Aquaculture, 68: 249-265. Stumm, W. and Morgan, J.J., 1981. Aquatic chemistry, 2nd edition. John Wiley & Sons, New York. Tucker, L., Boyd, C.E. and McCoy, E.W., 1979. Effects of feeding rate on water quality production of channel catfish and economic returns. Transactions of the American Fisheries Society, 108: 389-396.

126

U.S. Environmental Protection Agency, 1975. Process Design Manual for Nitrogen Control. Washington, D.C. Wheaton, F. Hochheimer, J. and Kaiser, G.E., 1991. Fixed film nitrification filters for aquaculture. Pages 272-303/n D.E. Brune and J.R. Tomasso, Jr., editors, Aquaculture and water quality, World Aquaculture Society, Baton Rouge, LA.