Thus, M.. represents the steady state material balances for all

components on all stages.

 The name of an indexed function is used to distinguish functions

of one function type from functions of another function type. Therefore,

material balance functions, designated "M," and energy balance functions,

designated "E," would belong to different function types. Similarly,

variables occurring in indexed functions are classed by "variable type."

For example, component liquid flow rate is of a different variable type

from component vapor flow rate. It should be noted that in modeling a

multi-unit process, material balance equations in a given unit contain

different function types from material balance equations in another

unit, even though the units are similar, e.g., distillation columns.

 It is convenient to make a distinction between the indices which

subscript a function type and those which subscript a variable type.

Consider equation 2-1. The indices "i" and "j" which subscript the

function type M are said to be function indices. Similarly, the indices

which subscript the variables 1, v, and f are said to be variable

indices.

 In order to structurally analyze a set of equations it is not

necessary to know the exact form of the equations. It is sufficient to

kno;: wh.ih variables occur in which equations. All existing algorithms

which perform structural analysis use only this information. This being

the cas, ai further simplification of the representation of indexed

euuations is made, with the ain of facilitating i2e structural analysis

of the equation set.

 The convention is adopted that function indices will be designated

by the letter "i." Thus, M. would become M,. ., the subscript on the
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