CHAPTER 1

 INTRODUCTION



 The design or simulation of a chemical process requires finding

the solution to a large set of equations (many of them non-linear).

Oftentimes these equations represent either a physical recycling of

a process stream from one unit to another, or an interaction among

variables within a unit; both conditions force a simultaneous solution

of the equations. Since the equations are, in general, non-linear, an

iterative solution is necessary. Frequently convergence of the itera-

tive solution depends on the manner in which the solution is carried

out. Unless the engineer has special familiarity with the particular

set of equations he is trying to solve, he essentially must choose

blindly from among the possible methods apparent to him. An alternative

to this is to develop algorithms suitable for implementation on a

digital computer capable of analyzing the structural and numerical

properties of the set of equations with the aim oF finding a means of

solving the equations which is not only efficient, but also likely to

converge to the solution. The method chosen to solve a set of equations,

whether chosen by the engineer or analytical algorithms, is called the
"'solu-tion procedure."

 Two commonly employed types or solution procedures are tearing

procedures (such as Gauss-Seidel) and "iNewton" type procedures (such as

Newton-Raphson). Because of the cost (usually in computer time) of