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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