GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VII(NEW) EXAMINATION - SUMMER 2019
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Subject Code: 2180503 Date: 17/05/2019Subject Name: Process Modeling, Simulation & Optimization
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 (a) List out the important model building steps for a process. 03
(b) List out various professional simulator and explain features of any one in detail. 04
(c) Explain scope and hierarchy of optimization. 07
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Q.2 (a) Compare lumped parameter model and distributed parameter model. 03
(b) Write a note on the transport equations used for modeling. 04
(c) A box with a square base and open top is to hold 1000 cm3. Find the dimensions that require the least material (assume uniform thickness of material) to construct the box. 07
OR
(c) What are the applications of optimization in chemical process and plants? Explain any one in detail with example. 07
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Q.3 (a) Explain the meaning of following terms for optimization: feasible solution, feasible region and optimum solution. 03
(b) Explain any one tearing algorithm with all the necessary steps. 04
(c) What is Hessian matrix? Write down its application in optimization. 07
Determine whether the following function is convex or concave:
f(x) = 4x12 + 3x22 + 5x32 + 6x1x2 + x1x3 - 2x2x3 + 15
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OR
Q.3 (a) Determine the optimum L/D ratio for a cylinder storage vessel. Also list the necessary assumptions. 03
(b) Differentiate between steady state and dynamic simulation. 04
(c) Minimize f(x) = x4 - x + 1 using Newton’s method for a starting point of x=0.6 (Show 3 iterations, use four decimal point accuracy). 07
Q.4 (a) Differentiate sequential modular approach and simultaneous modular approach. 03
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(b) A chemical process is represented by following set of equations: 04
f1(x2, x4) = 0;
f2(x5, x2) = 0;
f3(x6) = 0;
f4(x6, x1) = 0;
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f5(x3, x2) = 0;f6(x4, x5, x1) = 0;
Determine associated matrix and the diagraph of the process.
(c) Develop the equations for the series of isothermal, variable holdup CSTRs. List all the assumptions with their justifications. 07
OR
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Q.4 (a) Explain the term partitioning and tearing with respect to process simulation. 03
(b) Develop a signal flow graph for the diagraph given below: 04
(c) Explain: black-box model, white box model, gray model. 07
Q.5 (a) Minimize the quadratic function f(x) = x2 - x by Secant method. Use the range of -3 to +3. 03
(b) Explain the application of optimization in fitting vapor-liquid equilibrium data. 04
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(c) Find the maximum of following function using Lagrangian multipliers; y = 10x12 - 4x1x2 + 3x22 + 5x1; subject to
x1 + 2x2 < 3
x1 - x3 > 2
x1 = 1
OR
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Q.5 (a) List out various region elimination methods for optimization. Also explain limitations of region elimination methods. 03
(b) Discuss the optimization of pipe diameter. 04
(c) Minimize following function using Simplex method: 07
Z = 3x1 + 5x2 subject to
2x1 < 12;
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3x1 + 2x2 < 18;x1, x2 = 0
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