Process Modelling, Simulation and Optimization — Summer 2022

List out the important model building steps for a process.

Write the various equations of motion for process modeling.

Explain the six steps for solving optimization problems. List the general obstacles to solve optimization problems.

Explain the uses of mathematical models.

Minimize f(x) = 4X 2 +5X 2 subject to 2X +3X −6 = 0 using Lagrange Multipliers method.

Explain black-box model, white-box model, and gray model.

What is linear Programming Problem? State the linear programming in standard form and write down its application in chemical industries.

Differentiate between deterministic and stochastic models.

List various equations for the chemical kinetics used in process modeling.

What are the necessity and sufficiency conditions for the optimization problems? Give examples of Optimization applied to Chemical Industries.

Maximize f(x) = 1−8x +2x2 − 10 x3 + 1 x4 + 4 x5 − 1 x6 By Newton's method (two iterations will suffice). Start at x = -2. Hint: f′(x) = (1+x)2(2−x)3

Compare linear model and non linear model.

Explain partitioning and tearing with example.

Show the advantages and disadvantages of Newton’s Method.

Abox with a square base and open top is design to hold 1000 cm3 of material. Find the dimensions that require the least material (assume uniform thickness of material) to construct box.

Consider the vapourizer sketched in the figure.1 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 Qto 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.

List out essential features of optimization

List the applications of optimization in chemical engineering.

Write down various professional simulation packages and explain features of any one shortly.

Develop the model equations for a single component vaporizer.

Explain Simplex algorithm for linear programming.

Maximize following function using Simplex method; f = x +3x12 subject to −x +x +x = 1123 x +x +x = 2124 x ≥ 0 where i= 1,2,3,4 i where x ,x ,x x are slack variables. 1 2 3,

Derive the model equations for two heated tanks.

Determine convexity or concavity for the following function, f(x) = 2X 2 −3X X +2X

Discuss the optimization recovery of waste Heat.