Process Modeling, Simulation & Optimization — Summer 2021

List the applications of optimization in chemical engineering.

Describe the major obstacles in solving optimization problems.

Write the general procedure to solve optimization problems.

Determine whether the function is convex or concave: f = 2x 2 + 2x x + 1.5x 2 + 7x + 8x + 24

Determine and classify the types of extreme points of the function: f = x 3 + x 3 + 2x 2 + 4x 2 + 6.

Explain the steps for finding the optimum L/Dratio for a pressurized cylindrical storage vessel. List all the variables and the important assumptions.

Fit the following set of data to the equation y = aebx, a & b being constants. x 2.3 3.1 4.0 4.9 5.9 7.2 y 33 39.1 50.3 67.2 85.6 125

Explain the importance of degree of freedom in model building.

List the fundamental laws used in chemical system modeling.

Explain mathematical modelling of ideal binary distillation column.

Develop a model for a series of isothermal, variable hold-up CSTRs in which a first order reaction A → Bis taking place. State the assumptions clearly.

Differentiate between: i. Deterministic and stochastic process ii. Black box model, grey box model and white box model with proper example.

Explain Random search method and its significance.

Explain the Lagrange multiplier method and the Kuhn Tucker condition.

Solve the following Linear Programming Problem. Maximize Z = 6x + 8x12 subject to: 5x + 10x ≤ 60,12 4x + 4x ≤ 4012 x , x ≥

Minimize the quadratic function: f(x) = x2 – x using quasi-newton method.

Minimize the function f = 4x 2 + x 2 - 2x x using Newton’s method. Take starting point [1, 1].

Minimize f(x) = 4x 2 + 5x 2 subject to 2x + 3x = 6 using Lagrange multiplier method.

Explain (i) digraph and (ii) signal flow graph, with diagram.

Differentiate between modular approach and equation solving approach in simulation.

Explain any one tearing algorithm with all the necessary steps.

Write a short note on decomposition of networks.

Differentiate between sequential modular approach and simultaneous modular approach in simulation.

List the process simulators used in chemical engineering. Discuss the salient features of process simulators.