Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 8th Sem 2180503 Process Modeling , Simulation And Optimization Previous Question Paper
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?VIII (NEW) EXAMINATION ? WINTER 2020
Subject Code: 2180503 Date: 28/01/2021
Subject Name: Process Modeling , Simulation & Optimization
Time: 02:00 PM TO 04:00 PM Total Marks: 56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Differentiate between deterministic and stochastic models.
03
(b) Describe any one chemical process simulator and its salient features.
04
(c) Develop the equations for the series of isothermal, variable holdup CSTRs. List all 07
the assumptions with their justifications.
Q.2 (a) Minimize f(x) = 42
2 subject to
03
1 + 52
21 + 32 - 6 = 0 using Lagrange
multipliers method.
(b) Determine the optimum L/D ratio for a cylindrical storage vessel. Compare it with 04
the thumb rule L/D = 3. List the necessary assumptions.
(c) What is Optimization? List the six general steps for the analysis and solution of 07
optimization problems.
Q.3 (a) Explain the uses of mathematical models.
03
(b) Compare different methods used for economic analyses.
04
(c) The analysis of labor costs involved in the fabrication of heat exchangers can be used 07
to predict the cost of a new exchanger of the same class. Let the cost be expressed as
a linear equation.
C = 1 + 2A + 3N
Where 1, 2, and 3 are constants, N = number of tubes, A = shell surface area.
Estimate the values of the constants 1, 2 and 3 from the data in following table.
Labor cost ($)
310 300 275 250 220 200 190 150 140 100
Area (A)
120 130 108 110 84
90
80
55
64
50
No. of tubes (N) 550 600 520 420 400 300 230 120 190 100
Q.4 (a) List various equations for the chemical kinetics used in process modeling.
03
(b) Describe in detail the principles of formulation of mathematical models.
04
(c) Discuss the optimization of a pipe diameter.
07
Q.5 (a) Minimize f = (x - 1)4 by Newton's method, starting at x0 = -1.5.
03
(b) Develop the model equations for a single component vaporizer
04
(c) Explain black-box model, white-box model, and gray model.
07
Q.6 (a) Mention the conditions to be satisfied for extremum of the function of a single 03
variable and find extremum for f(x) = x4.
(b) For the digraph given below:
04
i) develop a signal flow graph.
ii) find the streams that are to be teared (i.e. cut set) using any algorithm. Write the
important steps.
1
(c) Explain the fundamental laws of physics and chemistry with their application to 07
simple chemical systems.
Q.7 (a) Differentiate between equation oriented model and modular based model.
03
(b) A chemical process is represented by the following set of equations:
04
f1(x3, x4) = 0; f2(x5, x2) = 0; f3(x6) = 0;
f4(x6, x1) = 0; f5(x3, x2) = 0; f6(x4, x5, x1) = 0
Determine Associated incidence matrix, digraph of the process and associated
adjacency matrix.
(c) A refinery has two crude oils that have the yields shown in the following table. 07
Because of equipment and storage limitations, production of gasoline, kerosene, and
fuel oil must be limited as also shown in this table. There are no plant limitations on
the production of other products such as gas oils. The profit on processing crude #1
is $l.00/bbl and on crude #2 it is $0.70/bbl. Find the approximate optimum daily feed
rates of the two crudes to this plant via a graphical method.
Volume % Yields
Maximum allowable Product
Crude #1
Crude #2
rate (bbl/day)
Gasoline
70
31
6,000
Kerosene
6
9
2,400
Fuel oil
24
60
12,000
Q.8 (a) A cylindrical container is designed to hold 20 m3 of liquid. The material for the top 03
and bottom costs $10 per m2 and material for the sides costs $8 per m2. Find the
radius (r) of the base and height (h) of the most economical container.
(b) Derive the model equations for two heated tanks.
04
(c) Classify the methods to solve unconstrained multivariable problems.
07
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This post was last modified on 04 March 2021