Gujarat Technological UniversitySummer 2026 examination

GTU 2180503 Process Modeling, Simulation & Optimization Summer 2026 Question Paper & PDF

B.E. · Chemical Engineering · Semester 8 · Subject code 2180503
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 10:30 AM – 1:00 PM
Questions
5 with internal choice
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Q.1

14 Marks
(a)
3 marks
Explain the uses of mathematical models.
(b)
4 marks

Describe briefly the fundamental laws used in mathematical models of chemical engineering systems.

(c)
7 marks
Derive the mathematical model for a non-isothermal Continuous Stirred Tank Reactor
(CSTR) where a first-order exothermic reaction A → B occurs. State all assumptions
clearly.

Q.2

14 Marks
(a)
3 marks
Explain the term 'partitioning' with respect to process simulation.
(b)
4 marks
Explain the sequential modular approach for simulation and state its main advantages.
(c)
7 marks

A process is represented by the following set of equations: 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 the associated matrix and the diagraph for the process.

(c)
7 marks

Explain any one tearing algorithm with all the necessary steps. Apply it to a suitable example of a cyclic process flow diagram.

Q.3

14 Marks
(a)
3 marks

Define the following terms for optimization: feasible solution, feasible region, and optimum solution.

(b)
4 marks

Determine the convexity or concavity for the following function: f(x1,x2) = 2x12−3x1x2+2x22 .

(c)
7 marks

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.

(a)
3 marks
List the essential features of an optimization problem.
(b)
4 marks

Find the extremum of the function f(x)=x3−6x2+11x+6 and determine if it is a local maximum or minimum.

(c)
7 marks

A poster is to contain 300 cm² 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.

Q.4

14 Marks
(a)
3 marks
Explain the algorithm of the Secant method used for one-dimensional optimization.
(b)
4 marks
Explain the difference between 'black-box', 'white-box', and 'gray-box' models.
(c)
7 marks

Minimize f(x)=x4−x+1 using Newton's method. Take an initial guess of x0=1.0. Show at least 3 iterations.

(a)
3 marks

Explain the algorithm of the Golden Section search method for one-dimensional optimization.

(b)
4 marks

Compare and contrast lumped parameter models and distributed parameter models with suitable examples.

(c)
7 marks

The following data have been collected for the model y=αxβ. Estimate the values of the constants α and β using the method of least squares. x10 20 30 40 50 y1.0 1.26 1.86 3.31 7.08

Q.5

14 Marks
(a)
3 marks
Differentiate between deterministic and stochastic models.
(b)
4 marks

What is linear programming? State the standard form of a linear programming problem.

(c)
7 marks

List out multivariable analytical methods for optimization problems with restricted variables equality constraints and explain any one of them with example.

(a)
3 marks
Compare linear and non-linear models, providing one example of each.
(b)
4 marks
Explain the Simplex algorithm for solving linear programming problems.
(c)
7 marks

Develop the mathematical model for an ideal binary distillation column. List all assumptions clearly.

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About this paper

Official Gujarat Technological University (GTU) examination paper for Process Modeling, Simulation & Optimization (Summer 2026, B.E. · Chemical Engineering, Sem 8). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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