SCOPE AND HIERARCHY OF OPTIMIZATION:
Examples of applications of optimization, the essential features, procedure of optimization problems, obstacles to optimization. Classification of models, fitting functions to empirical data, the method of least squares, factorial experimental designs, fitting a model to data subject to constraints, Continuity of functions, unimodal versus Multi-model functions. Convex and Concave functions, Convex region, Necessary and sufficient conditions for an extremism of an unconstrained function one-dimensional search quadratic approximation.
NUMERICAL METHODS:
Function of one variable, scanning and bracketing procedures, Newton’s, QuasiNewton’s and Secant methods of uni-dimensional search, region elimination methods, polynomial approximation methods, multivariable optimization: Direct methods, random search, grid search, uni-variate search, simplex method, conjugate search directions, Powell’s method, indirect methods- first order, gradient method, conjugate method, indirect method- second order: Newton’s method forcing the Hessain matrix to be positive definite, movement in the search direction, termination, summary of Newton’s method.
OPTIMIZATION OF UNIT OPERATIONS:
Recovery of waste heat, STHE and DPHE (Pinch technology), optimal design of stages in distillation column. Optimal pipe diameter, optimal residence time for maximum yield in an ideal isothermal batch reactor, chemostat, optimization of thermal cracker using liner programming, Optimization of components in bioreactor- media, oxygen requirement, pH, temperature. L/D ratio, Flow rate optimization of fluids. Optimal speed of agitator, paddles.
Solution of General form of dynamic models, dimensionless models.
General form of linear systems of equations, nonlinear function. General state-space form. Solving homogeneous, linear ODEs with distinct and repeated Eigenvalues. Solving nonhomogeneous equation, equation with time varying parameters. Introduction to systems and modelling – discrete and continuous system - Limitations of simulation, areas of application - Monte Carlo Simulation. Discrete event simulation. Random number generation and their techniques - tests for random numbers Random variable generation
Analysis of simulation data -
Input modelling – verification and validation of simulation models – output analysis for a single model. Related to li near regression and generalization of linear regression technique. Stirred tank heaters: model equations, Isothermal continuous stirred tank chemical reactors, Biochemical reactors: model equations, linearization. Case studies
Course outcomes:
After studying this course, students will be able to:
Textbook/ Textbooks
1 Optimization of chemical processes T.F.Edgar and Himmelblau DM Mc-Graw. Hill. 2001
2 Process system analysis and control Coughanowr and Koppel McGraw-Hill publishing company 2009
REFERENCE BOOKS
1 Optimization for Engineering Design Kalyan Moy Deb PHI 2000
2 Applied mathematics in chemical engineering Mickley, Sherwood and REED McGraw-Hill publishing company 2006
3 Chemical process control: an introduction to theory and practice George Stephanopoulos Prentice-Hall of India Private Ltd. 1994