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Posted By: A santhosh Member Level: Diamond Posted Date: 29 Sep 2008
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2006 Jawaharlal Nehru Technological University Chemical engineering IV B.Tech. II Semester Regular Examinations, April/May -2006,OPTIMIZATION OF CHEMICAL PROCESS Question paper
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Code No: RR420805 Set No. 2
IV B.Tech II Semester Regular Examinations, Apr/May 2006
OPTIMIZATION OF CHEMICAL PROCESS
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. The total cost ( dollars per year) for pipe line installation/operation for an incom-
pressible fluid can be expressed by:
C = C1D1.5.L + C2mp/?
where C1is the installed cost of the pipe per foot length computed on an annual ba-
sis (C1D1.5is expressed in dollars per year per foot length),
C2 is based on $ 0.05 /
kWh, 365 days/year and 60 per cent pump efficiency.; D is the diameter to be opti-
mized; L is the length of the pipe line = 100 miles; m is the mass flow rate = 200,000
lb/h; p = 2?v2L/(Dgc) f = pressure drop in psi;?is the density = 60 lb/ft3; v is
the velocity = ( 4m) / (?pD2);f = friction factor = (0.046 m0.2)/(DoptandvoptCopt.)µ
is the viscosity = 1 cP.
(a) Find general expressions for DoptvoptandCopt.
(b) ForC1 = 0.3 ( D expressed in inches for installed cost), calculate Doptandvopt
for the following values ofµand?.
µ= 0.2, 1and10cP?= 50, 60and80lb/ft3
[16]
2. Discuss the important factors involved in optimizing profitability. [16]
3. Consider the following objective functions: is it convex ? use eigen values in the
analysis f(x) = 2x2
1+2x1x2+1.5x2
2+7x1+8x2+24 [16]
4. Describe in detail the basic concepts involved in linear programming? [16]
5. (a) How are capacity and economy affected in multiple effect evaporators? What
is the effect of boiling point elevation on capacity? Why are multiple effects
often economical?
(b) Write about the procedure for determining the optimum number of effects in
a multiple effect evaporator. [8+8]
6. (a) Discuss about the classification of optimization problems for steady state dis-
tillation.
(b) describe how the nonlinear regression technique(least squares) can be used to
fit vapor-liquid equilibrium data. Use van Laar model with two adjustable
parameters to correlate the VLE data. [8+8]
7. The cost function C representing the annual costs of a pipe line transporting a fluid
is given by
C = C1D1.3L + 0.142(C0/?)m2.8µ0.2?-2.0D-4.8L
where the cost coefficients are considered as C0= Rs. 0.59 and C1= Rs. 5.7. The
mass flow rate of fluid m = 25 kg/s, density?= 1000kg/m3,µ= 1.08x10-3N/sm2,
the pumping efficiency ?= 0.60 and the pipe length L= 10 m. Find the optimal
pipe diameter Dopt [16]
8. The dynamic model of a continuous flow biological chemostat is given by
. e = ?k2c - De
. c = k1s (e - c) - (k2 + k3)c - Dc
.s = k1s (e - c) + (k3c + D(so - s)
where e, c and s are biomass, metabolic and substrate concentrations in gmol/lit,
respectively. The values of rate constantsk1, k2andk3are 0.9 lit/mol.h,, 0.7h-1and
0.0, respectively. The limiting feed substrate concentration so =10.0 mol/lit and the
parameter ? = 0.09.The dilution rate D is an independent variable. The objective
is to maximize the steady state production of biomass given by f = De. Obtain the
steady solution of the system for
0 D 0.6
and plot the responses of e, c, s and
f as a function of D. Find the value of D that provides maximum of f.
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