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Posted By: sunil Member Level: Diamond Posted Date: 02 Jul 2008
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2007 Jawaharlal Nehru Technological University Chemical engineering IV B.Tech II Semester Regular Examinations, Apr/May 2007 OPTIMIZATION OF CHEMICAL PROCESS Question paper
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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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