Simulation of Continuous Stirred Tank Reactors (CSTR’s) Using Orthogonal Functions

Abstract

Over the centuries, several numerical methods have been developed to approximate the solution of mathematical problems that are difficult to be solved by analytical methods. These numerical techniques succeeded in attaining a solution that is close enough to the exact solution with minimum errors and maximum stability. However, there may be the development of several other numerical methods which can be robust and efficient than the existing methods.My proposed research work is about the application of one such method-Orthogonal functions. Orthogonal functions can be broadly classified in to three families; namely, the piecewise constant, polynomial, and sine-cosine family. Walsh function and block pulse function belong to the piecewise constant family. So far orthogonal functions have been used in the optimal control, solving integro-differential equations, trajectory problems and so on. However, orthogonal functions have not been applied to chemical systems and processes. Hence my work is emphasised on simulating reactors using orthogonal functions; mainly block pulse functions and triangular functions. The continuous stirring tank reactors (CSTR’s) are widely used in the chemical industries. Hence the reactions in a CSTR are modelled by a set of differential equations which are discretised to a set of algebraic equations by orthogonal functions. Block-pulse functions have been used to obtain the dynamics of concentration and temperature of the continuous stirring tank reactors (CSTR’s). Further a recurrence relationship developed using block-pulse functions and triangular functions have been used in solving linear and non-linear system of differential equations. The major importance of orthogonal functions lies in its application to optimal control to systems. A recursive algorithm developed using block pulse functions has been applied to a linear control problem to determine the states and optimality criterion