CHAPTER 2

 INDEXED EQUATIONS



 In order to discuss indexed equations a terminology must first be

developed. This is especially true of the indices themselves since no

existing terminology seems well suited to them. This is done in the

next section of this chapter. Also, because it is desirable to have

algorithms which efficiently derive solution procedures it was necessary

to restrict both the types of equations allowed and the types of

solution procedures which can result. Since it has been the aim to

treat equations describing physical systems, those equations are among

those allowed. The remainder of the chapter is devoted to further means

of representing the equations and to a discussion of the restrictions

imposed on the problems.


2.1 Conventions Used in Describing Indexed Equations

 The set of material balance equations described dhove might be

written as:

 M 1 +v .-1 .-v .-f. = 0 2-1
 3i I1 ij i-,] i+l 1,j ij
where i = stage number

 i = component number

 M = name of function type, i.e., Material balance

 ., = liquid flow rate of component j leaving stage i

 v. = vapor flow rate of component j leaving stage i

 f.. = feed flow rate of component j entering stage i.
 1i7