CHAPTER 7

 EXAMPLE PROBLEMS



 A frequent simulation problem in chemical engineering is to model

mathematically a distillation column. Often, a solution procedure which

converges for certain problems will fail for other problems. The source

of this inability to converge must be numerical, since the structures of

the problems are identical. The examples in this chapter are two

distillation problems with widely differing numerical properties. The

two problems will be analyzed by the algorithms in GENIE in an attempt

to find a convergent solution procedure for each. A detailed expla-

nation of the application of the algorithms to the first problem will

be given. Important differences in the analysis of the second problem

will be pointed out and discussed.


7.1 Distillation Model

 The choice of the equations used to describe a problem rill affect

the solution procedure generated for that problem. In the examples

here, however, the effect of the particular form of the equations is

secondary to the effect of the numbers involved in the problem. The

same modeling equations will be used for both problems in order to

evaluate better the numerical effect. The modelinii equations used are:

 VF. 0 = ..-V
 ]7 1] *ili

 M. = 0 = .+v.-. -v
 i7 -7 .J 7 -1,3 i- i,j J .