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Posted By: santosh kumar kanugula Member Level: Gold Posted Date: 29 Jun 2008
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2007 Jawaharlal Nehru Technological University B.Tech Chemical engineering OPTIMIZATION OF CHEMICAL PROCESS Question paper
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Code No: RR420805 Set No. 3
IV B.Tech II Semester Regular Examinations, Apr/May 2007
OPTIMIZATION OF CHEMICAL PROCESS
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. Briefly describe the important examples of the applications of optimization. [16]
2. Describe and discuss the relative merits and limitations of the common models for
electro-static precipitator. [16]
3. For f(x) = 3x2
1+2x1x2+1.5x2
2 find the equation for the principal axes and determined
a transformation x = Vz such that f = a11z2
1+a22z2
2 thus eliminating the interaction
term. [16]
4. Describe in detail the basic concepts involved in linear programming? [16]
5. Draw the schematic diagram of a power system for the recovery of waste heat from
a boiler. Ignoring mechanical friction and heat leaks, obtain an expression for
the optimum value of the working fluid temperature TH, at which the sum of the
operating costs and surface area costs would be minimum. [16]
6. (a) Describe the classification of optimization problems for steady state distilla-
tion.
(b) Formulate the equality constraints for optimal design and operation of a con-
ventional staged distillation column with the help of a neat schematic diagram
[8+8]
7. The annual costs of transporting a fluid through a pipe line depends on the di-
ameter of the of the pipe line. The objective function for the annual costs C is a
sum of annualized investment charges Cinvand pump operating costs Cop , which
are expressed as
Cinv= C1D0.3L
Cop= C0mDp/??
where C0 and C1 are cost coecients, m and r are mass flow rate and density of
fluid, h is pump eciency and L is the length of pipe line. The objective function
C includes four variables the pipe diameter D, the velocity v, the pressure drop p
and the friction factor f. Three of these variables have the following correlations:
p = 2f?v2L/D
m = (?QD2/4)v
f = (0.046ยต0.2)/(D0.2v0.2r0.2)
Formulate the objective function by eliminating p, v and f, and obtain an expres-
sion for the optimal pipe diameter D considering it as the independent variable.
[16]
1 of 2
Code No: RR420805 Set No. 3
8. Find the maximum of the following linear programming problem representing a
thermal cracker by graphical method.
The objective function :
f = 2.84x1-0.22x2-3.33x3+1.09x4+9.39x5+9.51x6
wherex1= fresh ethane feed, x2= fresh propane feed, x3 = gas oil feed, x4 = DNG
feed, x5 = ethane recycle and x6 = propane recycle.
The objective is subjected to the following constraints:
1.1x1+0.9x2+0.9x3+1.0x4+1.1x5+0.9x6 200, 000
0.5x1+0.35x2+0.25x3+0.25x4+0.5x5+0.35x6 100, 000
0.01x1+0.15x2+0.15x3+0.18x4+0.01x5+0.15x6 20, 000
0.4x1+0.06x2+0.04x3+0.05x4-0.6x5+0.06x6= 0
0.1x2+0.041x3+0.01x4-0.9x6= 0
xi 0 [16]
? ? ? ? ?
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