Chapter 2 - Steady-State Lumped Systems

Abstract

The study of stoichiometry and unit operations concerns with the application of steady-state macroscopic balances to chemical process problems. When considering small sub-systems of chemical plants, the number of describing relations is small and the development of a computational strategy is easy. The relations can be solved directly by partitioning the equations. As equation sets become coupled, the probability that an equation set can be partitioned decreases. When an equation set cannot be partitioned, an iterative scheme devised. This chapter discusses numerical methods for simultaneously solving sets of linear and nonlinear algebraic equations. It presents the mathematical notion of a matrix as a linear transformation as well as the computer techniques. It presents a number of methods for the solution of a single non-linear equation and sets of non-linear equations. It discusses the use of scientific software library routines. It presents algorithms for structuring sets of algebraic equations into simple computational strategies.