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Posted By: sunil       Member Level: Diamond       Posted Date: 02 Jul 2008

2007 Jawaharlal Nehru Technological University Chemical engineering IV B.Tech II Semester Regular Examinations, Apr/May 2007 OPTIMIZATION OF CHEMICAL PROCESS Question paper



Course: B.Tech Chemical engineering   University: Jawaharlal Nehru Technological University




Code No: RR420805




Set No. 1



IV B.Tech II Semester Regular Examinations, Apr/May 2007
OPTIMIZATION OF CHEMICAL PROCESS
(Chemical Engineering)

Time: 3 hours


Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?

Max Marks: 80



1. For a two stage adiabatic compressor, where the gas is cooled to the inlet gas
temperature between stages, the theoretical work is given by :
W = {kp1V1/(k - 1)}[(p2/p1){(k-1)/k}-2 + (p3/p2){(k-1)/k}]

where k = CP/CV,1p1= inlet pressure,p2 = intermediate stage pressure,
p3= outlet pressure andV1 = inlet volume.
We have to optimize the intermediate pressurep2 so that the work is minimum.

Show that ifp1 = 1atm. andp3 = 4 atm, p2opt = 2 atm.


[16]


2. Describe two commonly used models of reactors along with their governing equa-

tions

3. Does the following sets of constraints form convex region ?
g1(x) = -(x12+x22) + 9 = 0
g2(x) =g2(x) = -x1-x2+1 = 0
4. Maximize y = x1+3x2-x3
subject to x1 + 2x2 + x3 = 4
2x1 + x2= 5
x1, x2, x3 = 0

[16]



[16]

using the simplex method ?nd the optimize optimum values of x1, x2, x3 and y
solve the problem by 1) guessing to obtain an initial basis 2) Using a phase I or

phase II method

[16]


5. Obtain an expression for the optimum temperature of the working ?uid to be used
in a power system for recovery of waste heat from a boiler. Draw a neat schematic

diagram of the power system.

[16]


6. (a) Discuss about the classi?cation of optimization problems for steady state dis-
tillation.
(b) describe how the nonlinear regression technique(least squares) can be used to
?t vapor-liquid equilibrium data. Use van Laar model with two adjustable

parameters to correlate the VLE data.
7. The cost function C representing the annual costs of a pipe line transporting a ?uid
is given by C = C1D1.3L + 0.142(C0/? )m2.8m0.2 ?-2.0D-4.8L
where the cost coe?cients are considered as C0= Rs.0.59andC1= Rs.5.7.The mass
?ow rate of ?uid m = 25 kg/s, density r = 1000kg/m3, m = 1.08x10-3N/sm2, the
pumping e?ciency ?= 0.60and the pipe length L= 10 m. The ?uid velocity is
correlated by v = 4m/(? Q D2) Find the optimal pipe diameter Doptand optimal

?uid velocity vopt.

[16]


8. The steady state monod chemostat model for substrate mass balance and cell mass
balance is described by the following equations : D(sf- s) -yx/sµmax(s+sxKs)= 0
hµKmaxs+Ss - Di x + Dxf= 0
where x and s are cell and substrate concentrations, respectively and D is the dilu-
tion rate. The parameter values are: maximum speci?c growth ratemax= 1.0h-1,
yield factor Yx/s= 0.5,substrate growth rate constant Ks= 0.2g/lit,substrate feed
concentration sf= 10.0g/litand initial cell concentration xf= 0. The objective is to
?nd the optimal value of D that provide maximum cell production Dx. Obtain the
steady state solution for x and s as a function of D, 0 = D = 1.0and ?nd the value

of D that provide maximum cell production Dx.






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