Mass Balances, Loading Mass Balances, Loading Rates,Rates,

and Fish Growth and Fish Growth

Michael B. Timmons Ph.D.Michael B. Timmons Ph.D.J.Thomas Clark Professor ofJ.Thomas Clark Professor of

Entrepreneurship & Personal EnterpriseEntrepreneurship & Personal Enterprise

Cornell UniversityCornell University

General Word EquationGeneral Word Equation

  

Transport Transport inin of "x" + of "x" + productionproduction of "x" of "x"

= transport = transport outout of "x" of "x"  

Control Volume ApproachControl Volume Approach

Treatment Device

C2

C1 P

C1 Q1

Qo

C1

Q1

CoQo

Control volume (look what crosses boundary)

In equation form…In equation form…

QQ11 C C22 + Q + Q

00 C C00 + P = Q + P = Q

00 C C11 + C + C

11 Q Q11

C0, C1 and C2: Concentrations of parameter X crossing the control volume, mg/LQ0: Flow rate passing through culture tank (discharge), m3/day (as kg/day)Q1: Water that is recirculated, kg/dayP: Production rate or consumption (negative)

Unit BalanceUnit Balance

(flow, Q) x (concentration, C)(flow, Q) x (concentration, C)

day

kg

kg

kg

day

kgCQ oxygen

water

oxygenwater 000,000,1

Mass Mass Transport=QTransport=Q x C x C

Qout

Qin

CO2

Example: Available OxygenExample: Available Oxygen

Qin x Cin = 100 gal/min x 9.89 mg/L

(make the units consistent)

= 5,390,445 mg/day x kg/106mg

= 5.39 kg/day of oxygen

dayL

mg

gal

LgalCQ inin

min144089.9785.3

min100

Selecting Tank ValuesSelecting Tank Values

YouYou must choose what you must choose what you want the tank water quality want the tank water quality

values to be set at !values to be set at !

Water Quality Design GuideWater Quality Design Guide

ParameterParameter TilapiaTilapia TroutTrout

Temperature, Temperature, FF 75 to 8575 to 85 50 to 6550 to 65

Oxygen, mg/LOxygen, mg/L 4 to 64 to 6 6 to 86 to 8

Oxygen, mm HgOxygen, mm Hg 9090 9090

COCO22, mg/L, mg/L 40 to 5040 to 50 20 to 3020 to 30

TSS, mg/LTSS, mg/L <80<80 <10<10

TAN, mg/LTAN, mg/L <3<3 <1<1

NHNH33-N, mg/L-N, mg/L <0.6<0.6 <0.02<0.02

Nitrite-N. mg/L Nitrite-N. mg/L <1<1 <0.1<0.1

Chloride, mg/LChloride, mg/L >200>200 >200>200

Calculate Available Oxygen for GrowthCalculate Available Oxygen for Growth

IN - OUT = AVAILABLE

QInCIn - QoutCtank = AVAILABLE

QInCIn - QoutCtank = 100 gal/min * (9.89 -5.00)mg/L (after unit balance)

= 2.67 kg/day O2

Balancing against the “P” termBalancing against the “P” term

Q CQ Cinin + P = Q C + P = Q Coutout

Q (CQ (Cinin – C – Coutout) = - P) = - P

Q (CQ (Coutout – C – Cinin) = + P) = + P

The Magical Treatment DeviceThe Magical Treatment Device for Anything! for Anything!

TreatmentDevice withEfficiency TCin Cout

QinQout

Concentration Leaving the deviceConcentration Leaving the device

T is the treatment efficiency Cbest is the absolute best result obtainable by a treatment system

)(100 inbestinout CCT

CC

Production TermsProduction Terms

PPoxygen oxygen (negative)(negative)

- - 0.25 kg consumed by fish

- - 0.12 kg by nitrifiers- - 0.13 heterotrophs

Total: = Total: = -- 0.50 kg per kg feed for system

PCO2 = 1.375 grams produced for each gram O2 consumed

(both fish and bacteria)

PTAN = F PC .092

PSolids, TSS = 0.25 kg feed fed (dry matter basis)

Loading RatesLoading Rates

L = 0.06 * Dfish / R

Loading capacity depends primarily on water quality, fish size and species

Loxygen = [144 * ΔO2] / [ 250 * F%]

Allowable loading (kg of fish per Lpm of flow) due to oxygen constraints

Allowable Loading vs Feeding rate % BWAllowable Loading vs Feeding rate % BW

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0 2 4 6 8 10 12 14

Delta DO

Lo

adin

g, k

g/lp

m

1%

2%

3%

4%

Cumulative Oxygen Consumption (COC)Cumulative Oxygen Consumption (COC)

Limit the allowable carrying capacity due to degradation in accumulated

ammonia or carbon dioxide or suspended solids

10 mg/L of oxygen consumed will produce:

• 1.4 mg/L of ammonia,

• 14 mg/L of carbon dioxide

• 10 to 20 mg/L of suspended solids

"Rule of Thumb"

Loss of Water = Loss of FishLoss of Flow = Loss of Fish

How do you lose fish?How do you lose fish?

Loss of water flowLoss of water flow

Lack of OxygenLack of Oxygen

"Rule of Thumb"

Cool water: 1 mg/L TANWarm Water: 2-3 mg/L TAN

How do you lose fish?How do you lose fish?

AmmoniaAmmonia

The apparent toxicity of ammonia is extremely variable and depends

on more than the mean or maximum concentration of ammonia

Ammonia productionAmmonia production

PPTANTAN = F x PC x .092 / (t= 1 day) = F x PC x .092 / (t= 1 day)

0.092 = .16 x .80 x .80 x .900.092 = .16 x .80 x .80 x .90

16% (protein is 16% nitrogen)16% (protein is 16% nitrogen)

80% nitrogen is assimilated80% nitrogen is assimilated

80% assimilated nitrogen is excreted80% assimilated nitrogen is excreted

90% of nitrogen excreted as TAN + 10% an urea90% of nitrogen excreted as TAN + 10% an urea

all TAN is excreted during time period “t”all TAN is excreted during time period “t”non assimilated nitrogen in feces is removed quicklynon assimilated nitrogen in feces is removed quickly

(no additional mineralization of nitrogenous compounds)(no additional mineralization of nitrogenous compounds)

"Rule of Thumb"

TAN production is about 3% of the feeding rate.

"Rule of Thumb"

1.375 grams of CO2 for each gram of O2 consumed.

How do you lose fish?How do you lose fish?

Carbon Dioxide, COCarbon Dioxide, CO2 2 ==

1.375 * O1.375 * O22 consumed consumed

"Rule of Thumb"

1 kg feed produces 8 liters of liquid waste!

How do you lose fish?How do you lose fish?

Suspended SolidsSuspended Solids

TSS = 0.25 kg feed fed (dry matter basis)

"Rule of Thumb"1 kg TAN produces 1 kg NO3

How do you lose fish?How do you lose fish?

NitrateNitrate

?

Fish GrowthFish Growth

Trout Tilapia Perch

Tbase 32 65 50

TUbase 28 15 25

Tmax 72 85 75

base

base

TU

TT

month

InchesGrowth

Weight = function( length)Weight = function( length)

CFCFtrouttrout = 400 = 400

CFCFtilapiatilapia = 760 = 760

CFCFperchperch = 490 = 490

Condition Factor and Fish WeightCondition Factor and Fish Weight

6

3

10inches

ibs

LCFWt

Calculate weight gain for 7 inch to an 8 inch tilapiaCalculate weight gain for 7 inch to an 8 inch tilapia

Wt(7”) = 760*(7)Wt(7”) = 760*(7)33/10/106 6 = 0.26 lb= 0.26 lb

Wt(8”) = 760*(8)Wt(8”) = 760*(8)33/10/106 6 = 0.39 lb= 0.39 lb

Feed/month = FG * WtFeed/month = FG * Wtnewnew- Wt- Wtoldold

=FG*(0.39-0.26)=FG*(0.39-0.26)

= FG*0.13 lb/fish= FG*0.13 lb/fish(FG’s are 0.9 to 2.0)(FG’s are 0.9 to 2.0)

Calculate Max Daily Feed Rate for 10,000 Calculate Max Daily Feed Rate for 10,000 tilapia at 80tilapia at 80ººF & CF = 760 & Wt = 2.00 lbF & CF = 760 & Wt = 2.00 lb

L = (10L = (1066*2.00/760)*2.00/760)1/3 1/3 13.8113.81

Growth = (80-65)/15 = 1.00”/month = 0.033”/dayGrowth = (80-65)/15 = 1.00”/month = 0.033”/day

WtWtday-1day-1 = 760(13.81-0.033) = 760(13.81-0.033)33/760 = 1.99 lb/760 = 1.99 lb

WtWtChangeChange /fish = 0.014 lb/fish /fish = 0.014 lb/fish

Tank Feed/day = 10,000fish x 0.014 lbTank Feed/day = 10,000fish x 0.014 lbgaingain/fish/fish

= FG*140 lb feed/day= FG*140 lb feed/day

Refer to Book Chapter 4 that has a complete Refer to Book Chapter 4 that has a complete design example worked out.design example worked out.

Example: Example:

Example: Required Flow Rate Design Problem

Calculate the required design flow rate for a 100% recirculating flow for a design fish feeding rate of 100 kg feed/day @ 38% protein. Calculate the required flow rate for each water quality parameter and then identify the controlling parameter.

Remember, once you calculate the required flows for each water Remember, once you calculate the required flows for each water quality control parameter, you OPERATE the tank at the quality control parameter, you OPERATE the tank at the maximum calculated flow rate. Usually oxygen is the controlling maximum calculated flow rate. Usually oxygen is the controlling flow rate. You can decrease the oxygen water flow rate by flow rate. You can decrease the oxygen water flow rate by enriching the oxygen concentration in the “device”.enriching the oxygen concentration in the “device”.

Required Flow RatesRequired Flow RatesWater Quality Parameter Required Flow rate (gpm)

TSS 612

TAN 916*

Oxygen 738

Carbon Dioxide 338

Other Considerations:Other Considerations:

The biofilter will have some required The biofilter will have some required hydraulic loading factor which may be hydraulic loading factor which may be the controlling flow ratethe controlling flow rate

Try to match flow rates among Try to match flow rates among different devicesdifferent devices

don’t forget COdon’t forget CO22 control control ammonia control is rarely the ammonia control is rarely the

controlling factorcontrolling factor

COCO22 CONTROL OPTIONS CONTROL OPTIONS

Packed Tower StrippingPacked Tower Stripping Sodium Hydroxide AdditionSodium Hydroxide Addition Water ExchangeWater Exchange In-tank Surface AerationIn-tank Surface Aeration Side-stream Surface AerationSide-stream Surface Aeration In-tank Diffused AerationIn-tank Diffused Aeration Side-stream Diffused Side-stream Diffused

AerationAeration

MODEL FACILITYMODEL FACILITY

Environment

Culture Tanks

VentilationCO2

CO2

Stripper

Moisture