Mass balance andbiofiltration kinetics

Dr. J. P. Blancheton

IFREMER, France

Mass balance approach

Whatever the product and for any type of system:

Inlet + production = stock + outlet + consumptionOrStock = Inlet + production - outlet - consumption

- for fluxes of one single product (weight per time un it)

- in a well defined system (clear boundaries)

- coherent units (concentrations, volumes, flow rates, time)

- at steady state, no stock variation

May be used for anything in everyday life:

Available money on your bank account (stock) =Income (salary) + stock profit (banking interest if an y) – expenses(current family expenses) - (overdrawn)

- for fluxes of money (€ per time unit)

- in a well defined system (your bank account)

- coherent units (€, month)

- at steady state, no stock variation

Mass balance approach

0 + 0 = stock variation + 0 + consomption

Mass balance for nitrification kinetics

Single product: total ammonia- N (TAN)

Limits of the system

General model for bacterial growth kinetics k at th e C TAN concentration: k = k max (constant when no limitation) * C / (C + Cs) Cs: constant value of the first nutrient limiting t he kinetics to 0,5 k max

0 = Vol * Dc/Dt + Vol * KineticsFor instance: [m 3 * g(N) m -3 h-1] + [m 3 * g(N) m -3 h-1]

Kinetics proportional to Dc/Dt

water packing media

Biofilter

PumpTank

Mass balance / nitrification kinetics

Biofilter

PumpTank

Nitrification kinetics

t c Dc Dt Dc/Dt

0 ci

t1 c1 c1-ci t1 (c1-ci)/t1t2 c2 c2-c1 t2-t1 (c2-c1)/

(t2-t1)

…. ….

…. …. ….

Units: h g m -3 g m -3 h-1

C: TAN conc. g m -3

g TAN m -3 (packing) day -1

Nitrification kineticsDc/Dt:

May consider constant kinetics

Kinetics depends on [TAN]

Nitrification kinetics

Kinetics (Kb) = Kbmax * C / (C + Cs)

C: TAN conc. g m -3

Dc/Dt: g TAN m -3 (packing) day -1

Vmax

Cs

Vmax/2

g TAN oxidized packing m -3 hour -1 = 9.2 * C / (C + 0.65)

C: TAN conc. g m -3

Dc/Dt: g TAN m -3 (packing) hour -1

For seawater and packing media of (eq.) 600 m 2 m-3

Kbmax = 9.2 g m -3 packing media/ h and Cs = 0.65 g m -3

Nitrification kinetics

9.2 g m -3 h-1

0.65 g m -3

Packing and biofilter volumes

For seawater and packing media of (eq) 600 m 2 m-3

If packing media of (eq) S m 2 m-3, * (S / 600)

If fresh water, nitrification kinetics* 1.3

Temperature effect: Kb(t) = Kb(20°) exp (0.06 * (t – 20))

Biofilter volume = packing media volume * biofilter filling ratio (about 50% for moving bed)

Residence time > 4’ to 5’

q * C0

Rearing tank

Biofilter q * Ci

(Q + q) Ci

Q * Ce

Kp * Vp

Kb * Vb

Mass balance for biofilter sizing

Steady state means no stock variation

Mass balance rearing tank: Q * Ce + q * Co + Kp * Vp = (Q + q) Ci

Mass balance biofilter: Q * Ci = Kb * Vb + Q * CeAll expressed in TAN flux (i.e. g TAN h -1)

Mass balance for biofilter sizing

q * C0

Rearing tank

Biofilter q * Ci

(Q + q) Ci

Q * Ce

Kp * Vp

Kb * Vb

Mass balance for biofilter sizing

Q * Ce + q * Co + Kp * Vp = (Q + q) CiCe = ((Q + q) Ci - q * Co - Kp * Vp) / Q

Kb = 9.2 Ce / (Ce + 0.65) [g TAN m -3 h-1)

Q * Ci = Kb * Vb + Q * CeVb = Q (Ci-Ce) / Kb [m 3]

Tb = Vb / Q [h]

RAS design and biofilter size for a seabass pre-gro wing unit composed of 4 tanks de 125 m 3 in the same recirculation loop:

Water flow rate in the tanks between 500 and 4000 m 3h-1

Makeup water availability between 20 and 200 m 3h-1

TAN concentration in tanks < 2 mgl -1

Water temperature between 15° and 25°

Fish density 10 to 90 kg m -3

Application

m3h-1

m3

Minimum volume for residence time > 4’ in biofilter

Sharp decrease between 1 and 3 times the tank volum e per hourLimitation due to the minimum residence time in bio filter

m3

mgl -1

Limited effect of the makeup water flow rate

m3

°c

Necessary volume doubled between 25 and 15°

1500 m3h-1, 20 m3h-1, 20°Ci = 1 mg l -1

1500 m3h-1, 20 m3h-1, 20°Ci = 2 mg l -1

m3

m3

Conclusion biofilter sizing

Sharp decrease of the nitrification kinetics below a TAN concentration of +/- 2 mg l -1

Resulting in an unrealistic biofilter size for a t oo low [TAN] or too high feed load

Increasing the tank water flow rate allows to decre ase the packing volume until minimal water residence time in the bi ofilter (> +/- 5’ to avoid the risk of NO 2 production)

Increasing the makeup water flow rate has a moderat e impact on the biofilter size

Important effect of temperature on kinetics (+/- dou bled between 15°and 25°)

Rearing tank

Biofilter

Ci

Ce

2.85*P^-0.247*t^1.25*10 -3 [g h -1 kg -1]

4,6 * (Ci – Ce) [g l -1]

Mass balance for oxygen needs

O2 biofilter consumption = nitrifying bacteria+ non-nitrifying bacteria consumptions

Weight of 1 fish [kg] Temperature [°c]

Ci O2

Ce O2

250 to 450 g kg feed -1

Rearing tank

Biofilter

Ci

Ce

(2.85*P^-0.247*t^1.25*10 -3) * 1.4 [g h -1 kg -1]

4,6 * (Ci – Ce) * 1.4 [g l -1]

Mass balance for CO 2 production

About 1,4 g CO 2 produced by g O 2 consumed

Ci O2

Ce O2

Ci CO2

Ce CO2

Degassing system

Cx CO2?

Mass balance for biofilter sizing

q * C0

Rearing tank

Biofilter q * Ci

(Q + q) Ci

Q * Ce

Kp * Vp

Kb * Vb

q * C0

q * Ci

Mass balance for biofilter sizing

q * C0

Rearing tank

Biofilter q

Ci

Ce

Kp * Vp

Kb * Vb

CO2 degazing SS filtration

Q1