Download GTU B.Tech 2020 Winter 8th Sem 2180503 Process Modeling , Simulation And Optimization Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER-VIII (NEW) EXAMINATION — WINTER 2020

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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.

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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 the assumptions with their justifications. [07]

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Q.2 (a) Minimize f(x) = 4x₁² +5x₂² subject to 2x₁ +3x₂ —6 =0 using Lagrange multipliers method. [03]
(b) Determine the optimum L/D ratio for a cylindrical storage vessel. Compare it with the thumb rule L/D = 3. List the necessary assumptions. [04]
(c) What is Optimization? List the six general steps for the analysis and solution of optimization problems. [07]

Q.3 (a) Explain the uses of mathematical models. [03]
(b) Compare different methods used for economic analyses. [04]

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(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.
C=f₁+f₂A+f₃N
Where f₁, f₂, and f₃ are constants, N= number of tubes, A = shell surface area.
Estimate the values of the constants f₁, f₂ and f₃ from the data in following table.

Labor cost ($)	310	3000	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

[07]

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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)² by Newton’s method, starting at x₀ = -1.5. [03]
(b) Develop the model equations for a single component vaporizer [04]

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(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 variable and find extremum for f(x) = x³. [03]
(b) For the digraph given below: [04]
1) develop a signal flow graph.
i1) find the streams that are to be teared (i.e. cut set) using any algorithm. Write the important steps.

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(c) Explain the fundamental laws of physics and chemistry with their application to simple chemical systems. [07]

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(x₅) = 0;

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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 $1.00/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.

Product	Volume % Yields Crude #1	Volume % Yields Crude #2	Maximum allowable 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 20π m³ of liquid. The material for the top 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. [03]

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(b) Derive the model equations for two heated tanks. [04]
(c) Classify the methods to solve unconstrained multivariable problems. [07]