Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 8th Sem New 2180503 Process Modeling Simulation And Optimization Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180503 Date: 29/11/2018
Subject Name: Process Modeling, Simulation & Optimization
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Describe in detail the principles of formulation of mathematical models. 03
(b) Explain the fundamental laws of physics and chemistry with their applications
to simple chemical systems.
04
(c) Consider a batch reactor in which the following first-order consecutive reactions
are carried out.
Reactant A is charged into the vessel. Steam is fed into the jacket to bring the
reaction mass up to a desired temperature. Then cooling water must be added to
the jacket to remove the exothermic heat of reaction and to make the reactor
temperature follow the prescribed temperature-time curve. This temperature
profile is fed into the temperature controller as a set-point signal. Derive the
temperature profiles for the process and metal wall for the batch reactor
described above.
07
Q.2 (a) Write the various equations of motion for process modeling. 03
(b) List the various professional simulators and equation solver software. 04
(c) Consider the vapourizer
sketched in the figure.
Liquefied petroleum gas (LPG) is fed into a pressurized tank to hold the liquid
level in the tank. We will assume that LPG is a pure component: propane. The
liquid in the tank is assumed perfectly mixed. Heat is added at a rate Q to hold
the desired pressure in the tank by vapourizing the liquid at a rate Wv (mass per
time). Heat losses and the mass of the tank walls are assumed negligible. Gas is
drawn off the top of the tank at a volumetric flow rate Fv. Fv is the forcing
function or load disturbance. Derive the model equations for the system for
steady state model and liquid and vapour dynamics model.
07
OR
(c) List the structural components of general purpose sequential modular program. 07
Q.3 (a) Find the values of x and z (both > 0) that maximize the function:
U = -x
2
+ 10x + xz ? z
2
+ 8z + 2
03
k k
12
A B C ? ? ? ? ? ?
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180503 Date: 29/11/2018
Subject Name: Process Modeling, Simulation & Optimization
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Describe in detail the principles of formulation of mathematical models. 03
(b) Explain the fundamental laws of physics and chemistry with their applications
to simple chemical systems.
04
(c) Consider a batch reactor in which the following first-order consecutive reactions
are carried out.
Reactant A is charged into the vessel. Steam is fed into the jacket to bring the
reaction mass up to a desired temperature. Then cooling water must be added to
the jacket to remove the exothermic heat of reaction and to make the reactor
temperature follow the prescribed temperature-time curve. This temperature
profile is fed into the temperature controller as a set-point signal. Derive the
temperature profiles for the process and metal wall for the batch reactor
described above.
07
Q.2 (a) Write the various equations of motion for process modeling. 03
(b) List the various professional simulators and equation solver software. 04
(c) Consider the vapourizer
sketched in the figure.
Liquefied petroleum gas (LPG) is fed into a pressurized tank to hold the liquid
level in the tank. We will assume that LPG is a pure component: propane. The
liquid in the tank is assumed perfectly mixed. Heat is added at a rate Q to hold
the desired pressure in the tank by vapourizing the liquid at a rate Wv (mass per
time). Heat losses and the mass of the tank walls are assumed negligible. Gas is
drawn off the top of the tank at a volumetric flow rate Fv. Fv is the forcing
function or load disturbance. Derive the model equations for the system for
steady state model and liquid and vapour dynamics model.
07
OR
(c) List the structural components of general purpose sequential modular program. 07
Q.3 (a) Find the values of x and z (both > 0) that maximize the function:
U = -x
2
+ 10x + xz ? z
2
+ 8z + 2
03
k k
12
A B C ? ? ? ? ? ?
2
(b) A poster is to contain 300 cm
2
of printed matter with margins of 6 cm at the top
and bottom and 4 cm at each side. Find the overall dimensions that minimize the
total area of the poster.
04
(c)
An irreversible, exothermic reaction is carried out in a single
perfectly mixed CSTR as
shown in figure.
The reaction is nth-order in reactant A and has a heat of reaction ?? (Btu/lbmol
of A reacted). Negligible heat losses and constant densities are assumed. To
remove the heat of reaction, a cooling jacket surrounds the reactor. Cooling
water is added to the jacket at a volumetric flow rate FJ, and with an inlet
temperature of TJo. The volume of water in the jacket VJ is constant. The mass
of the metal walls is assumed negligible so the thermal inertia of the metal need
not be considered. Derive the model equations with the assumption of a perfectly
mixed cooling jacket.
07
OR
Q.3 (a) State objective functions in terms of the adjustable variable for chemical reactor. 03
(b) A box with a square base and open top is to hold 1000 cm
3
. Find the dimensions
that require the least material (assume uniform thickness of material) to
construct the box.
04
(c) What is a linear programming problem? State the linear programming in
standard form and write down its application in chemical industries.
07
Q.4 (a) Minimize the quadratic function: f(x) = x
2
? x using quasi-newton method. 03
(b) Explain random search and grid search method for unconstrained multivariable
optimization.
04
(c) Discuss feature of basic tearing Algorithm. 07
OR
Q.4 (a) Classify the methods to solve unconstrained multivariable problems. 03
(b) The total annual cost of operating a pump and motor (C) in a particular piece
of equipment is a function of the size (horsepower) of the motor (X),
?? = 500 + ?? +
4500
??
Find the motor size that minimizes the total annual cost. Use Newton?s method
from the starting point of Xo = 10. Does the solution converge? Solve the
equation analytically and determine actual solution.
04
(c) Discuss the optimizing recovery of waste heat with suitable figure and
equations.
07
Q.5 (a) Determine convexity or concavity for the following functions.
f(x) = 4?? 1
2
+ 6?? 1
?? 2
+ 3?? 2
2
+ 5?? 3
2
+ ?? 1
?? 3
- 3?? 1
- 2?? 2
+ 15
03
(b) Explain the application of optimization in fitting vapour-liquid equilibrium data. 04
(c) The analysis of labor costs involved in the fabrication of heat exchangers can be
used to predict the cost of a new exchanger of the same class. Let the cost be
expressed as a linear equation.
07
k
AB ? ? ?
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180503 Date: 29/11/2018
Subject Name: Process Modeling, Simulation & Optimization
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Describe in detail the principles of formulation of mathematical models. 03
(b) Explain the fundamental laws of physics and chemistry with their applications
to simple chemical systems.
04
(c) Consider a batch reactor in which the following first-order consecutive reactions
are carried out.
Reactant A is charged into the vessel. Steam is fed into the jacket to bring the
reaction mass up to a desired temperature. Then cooling water must be added to
the jacket to remove the exothermic heat of reaction and to make the reactor
temperature follow the prescribed temperature-time curve. This temperature
profile is fed into the temperature controller as a set-point signal. Derive the
temperature profiles for the process and metal wall for the batch reactor
described above.
07
Q.2 (a) Write the various equations of motion for process modeling. 03
(b) List the various professional simulators and equation solver software. 04
(c) Consider the vapourizer
sketched in the figure.
Liquefied petroleum gas (LPG) is fed into a pressurized tank to hold the liquid
level in the tank. We will assume that LPG is a pure component: propane. The
liquid in the tank is assumed perfectly mixed. Heat is added at a rate Q to hold
the desired pressure in the tank by vapourizing the liquid at a rate Wv (mass per
time). Heat losses and the mass of the tank walls are assumed negligible. Gas is
drawn off the top of the tank at a volumetric flow rate Fv. Fv is the forcing
function or load disturbance. Derive the model equations for the system for
steady state model and liquid and vapour dynamics model.
07
OR
(c) List the structural components of general purpose sequential modular program. 07
Q.3 (a) Find the values of x and z (both > 0) that maximize the function:
U = -x
2
+ 10x + xz ? z
2
+ 8z + 2
03
k k
12
A B C ? ? ? ? ? ?
2
(b) A poster is to contain 300 cm
2
of printed matter with margins of 6 cm at the top
and bottom and 4 cm at each side. Find the overall dimensions that minimize the
total area of the poster.
04
(c)
An irreversible, exothermic reaction is carried out in a single
perfectly mixed CSTR as
shown in figure.
The reaction is nth-order in reactant A and has a heat of reaction ?? (Btu/lbmol
of A reacted). Negligible heat losses and constant densities are assumed. To
remove the heat of reaction, a cooling jacket surrounds the reactor. Cooling
water is added to the jacket at a volumetric flow rate FJ, and with an inlet
temperature of TJo. The volume of water in the jacket VJ is constant. The mass
of the metal walls is assumed negligible so the thermal inertia of the metal need
not be considered. Derive the model equations with the assumption of a perfectly
mixed cooling jacket.
07
OR
Q.3 (a) State objective functions in terms of the adjustable variable for chemical reactor. 03
(b) A box with a square base and open top is to hold 1000 cm
3
. Find the dimensions
that require the least material (assume uniform thickness of material) to
construct the box.
04
(c) What is a linear programming problem? State the linear programming in
standard form and write down its application in chemical industries.
07
Q.4 (a) Minimize the quadratic function: f(x) = x
2
? x using quasi-newton method. 03
(b) Explain random search and grid search method for unconstrained multivariable
optimization.
04
(c) Discuss feature of basic tearing Algorithm. 07
OR
Q.4 (a) Classify the methods to solve unconstrained multivariable problems. 03
(b) The total annual cost of operating a pump and motor (C) in a particular piece
of equipment is a function of the size (horsepower) of the motor (X),
?? = 500 + ?? +
4500
??
Find the motor size that minimizes the total annual cost. Use Newton?s method
from the starting point of Xo = 10. Does the solution converge? Solve the
equation analytically and determine actual solution.
04
(c) Discuss the optimizing recovery of waste heat with suitable figure and
equations.
07
Q.5 (a) Determine convexity or concavity for the following functions.
f(x) = 4?? 1
2
+ 6?? 1
?? 2
+ 3?? 2
2
+ 5?? 3
2
+ ?? 1
?? 3
- 3?? 1
- 2?? 2
+ 15
03
(b) Explain the application of optimization in fitting vapour-liquid equilibrium data. 04
(c) The analysis of labor costs involved in the fabrication of heat exchangers can be
used to predict the cost of a new exchanger of the same class. Let the cost be
expressed as a linear equation.
07
k
AB ? ? ?
3
?? = ?? 0
+ ?? 1
?? + ?? 2
??
Where ?0, ?1, and ?2 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), m
2
120 130 108 110 84 90 80 55 64 50
Number of
tubes (N)
550 600 520 420 400 300 230 120 190 100
OR
Q.5 (a) Explain black box model. 03
(b) Minimize f(x) = ?? 4
? ?? + 1 using Newton?s method. Take starting point = 0.64 04
(c) Solve the following non-linear function with constraints using Lagrange
multiplier method.
Minimize: f(x, y) = ????
?1
?? ?2
, Subject to: g(x,y) = ?? 2
+ ?? 2
= ?? 2
07
*************
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This post was last modified on 20 February 2020