CP504: Simulation-type Assignment 03 (Dec 2012)
- worth a maximum of 25% marks allocated for CP504, and a bonus of 15%
Important notes on gaining marks:
1. Assignment shall be carried out under the supervision of Prof. R. Shanthini, and discussion sessions
on the assignments are mandatory.
2. Answer script should be complete with the required plots and programmes.
3. Answer script should be submitted on or before the deadline agreed upon.
4. Critical analysis of the results is required to earn maximum marks.
5. Marks earned will be divided by the number of near identical answer scripts submitted (assuming
copying has taken place).
Q1. Rate equations describing the cells (yeast), substrate (glucose), and product in the ethanol
fermentation batch process are given as follows:
dX
 rX  X
dt
dS
r
 rS   X
dt
YX / S
r
dP
 rP  X
dt
YX / P
where X, S and P are the concentrations of cells, substrate and product in the batch reactor
(g/L), rX , rS and rP are the respective reaction rates of X, S and P (g/L.h), YX/S is 0.06 g
cells produced / g substrate consumed, YX/P is 0.16 g cells produced / g product formed, 
is the specific cell growth rate (g/L.h), and t is time (h).
a) Derive the equations given above starting from the mass balances.
b) Simulate the given system at 0.005 h time step, and plot X, S and P as function of time
starting with the initial concentrations of 0.1 g/L cell and 100 g/L substrate in the
reactor. Assume no product initially in the reactor. Use the Monod model for  given
below:

m S
KS  S
where m = 0.24 h-1 and K S = 1.6 g/L
c) Repeat part (b) by replacing the Monod model with the product inhibition model given
below:
  S 
P
   m 1  
Pm 
 K S  S 
n
where m = 0.24 h-1, K S = 1.6 g/L, Pm = 100 g/L and n = 2
(Pm is the maximum product concentration beyond which no cell growth takes place.)
d) Comment on your solutions comparing the different models used.
Please turn over
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Q2. Rate equations describing the cells (X), substrate (S), and product (P) in a continuous stirred
tank fermenter (CSTF) operated at unsteady state are given as follows:
dX
 rX  DX ;
dt
r
dS
  X  D( Sin  S ) ;
dt
YX / S
dP
 rP  DP
dt
where X, S and P are the concentrations of cells, substrate and product in the CSTF (g/L),
rX and rP are the respective reaction rates of X and P (g/L.h), YX/S is 0.4 g cell produced / g
substrate consumed, D is the dilution rate (0.202 per h), Sin is the substrate concentration in
the feed (20 g/L), and t is time (h).
a) Derive the equations given above starting from the mass balances.
b) Simulate the given system to find out the steady state values of X, S and P starting with
different set of initial concentrations of X and S. Assume no product initially in the
reactor.
Additional data:
Rate of cell growth is given by rX   X , where  is the specific cell growth rate
(g/L.h) described by the following model substrate and product inhibition model:


S
P
1  
2 
Pm 
 K S  S  K I S 
  m 
where m (= 0.48 h-1) is the maximum specific cell growth rate, K S (= 1.2 g/L) is the
saturation constant, K I (= 0.04545 L/g) and Pm (= 50 g/L, which is the maximum
product concentration beyond which no cell growth takes place) are the inhibition
constants.
Rate of product formation is given by rP   rX   X , where  = 2.2 g product
formed / g of cell produced and  = 0.2 per hr.
c) Verify that the system has a non-trivial steady state solution given by X = 6 g/L, S = 5
g/L and P = 19.14 g/L for a large range of initial concentrations of X and S.
d) Comment on your solutions.
Reference for Q1: Problem 6.4 in Lee JM. 1992. Biochemical Engineering, Prentice-Hall.
Reference for Q2: Problem 5.16 in Jana, A.K. 2008. Chemical Process Modelling and
Computer Simulation. Prentice-Hall of India (Pvt) Ltd.
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