CVEN 5534: Wastewater Treatment

Fall 2010

Assignment 4: Due Thursday, Oct. 14

1. A wastewater containing 250 mg/l soluble COD is to be treated in a CSTR so that the effluent COD is

less than 25 mg/l. The flow rate is 10,000 m3/day

Assuming Monod kinetics, steady-state operation of the CSTR and neglecting cell decay:

and

Where = max. specific cell growth rate = 2 d-1

S = soluble CODS concentration, mg/l

KS = half-saturation constant = 50 mg/l CODS

X = heterotrophic cell concentration, mg-CODX/l

Y = COD yield = 0.6 g-CODX/g-CODS

a. What is the minimum hydraulic residence time, , before washout occurs?

b. What reactor volume is required for 90% COD removal?

c. What is the effluent cell concentration?

d. Compare the volume of an ideal plug flow reactor required for the same level of COD removal and the

same kinetic model.

e. Plot S vs for the CSTR and PFR

2. Wastewater containing 300 g/m3 COD is to be treated for 85% COD removal. The reaction rate is

assumed to be first order with respect to COD concentration because the concentration of cells is

constant.

rS = -kS

where: rS = rate of COD consumption (g/m3/d), k = first-order reaction coefficient = 5 d-1, and SS = COD

concentration (g/m3)

a. Compare the required system volumes for

i. An ideal single tank CSTR

ii. An ideal plug flow reactor

iii. A CSTR cascade with 2 cells

iv. A CSTR cascade with 4 cells

b. How will the ratio of required volumes change for 99% removal?

Q = 10,000 m3/d

So = 250 mg/l CODS

Xo = 0

Q = 10,000 m3/d

S = 25 mg/l CODS

X

V

S

X

3. Consider a CSTR where cells are perfectly separated from the effluent and are wasted in a separate

smaller flow which allows them to accumulate in the CSTR to a higher concentration than a CSTR with

no enhanced cell retention.

Assuming Monod kinetics, now with decay,

rX = ( – b)X

and as in #1

and

Assume the same wastewater characteristics, effluent COD limit and kinetic parameters as in problem 1 and b =

0.1 d-1.

Also 2 parameters are now available to describe CSTR conditions:

Where is called the average solids residence time (SRT).

a. Write steady state mass balances on cells (X) and CODS (S) and solve to get formulas for

i. S as a function of the kinetic and CSTR parameters

ii. X as a function of kinetic and CSTR parameters

b. If the cell wasting flow rate, Qw = 300 m3/day what is the CSTR cell concentration and the required

CSTR volume?

c. Compare V and X to the values you got for the CSTR in problem 1.

Q = 10,000 m3/d

So = 250 mg/l CODS

Xo = 0

Q-Qw

S = 25 mg/l CODS

Xe = 0

V

S

X

Qw, S, X