stage in a distillation column.
 NC
 LM. 0 = x..-l 3-2
 j=-1
where: LM = Function Type

 i = Stage number

 j = Component number

 NC = Number of components

 x.. = Liquid mole fraction of component j on stage i

The function type, LM, has one index. The only variable type is x,

which has two indices. By the restrictions stated above, there is no

possible output set assignment. There are two possible solutions to

this problem. The first is to rearrange algebraically the equations in

an attempt to eliminate the problem. The second is to assign, from the

other variable types in the problem, a different variable type, with the

correct number of indices, as an "implicit output." This variable would

have to be connected to the function through the other function types

(which means that through algebraic substitutions the implicit output

could be made to appear in the function, although this is not done).

A technique such as Newton-Raphson is then employed to converge the

implicit output.

3.3.2 Variable Type Decisions

 In the example problem the variable type z was a decision variable

 type. The only restriction on the choice of decision variable types is

 that they be made so as not to reduce the number of variables below the

 number of equations. If the FVIM outputs are chosen before the

 decisions there can be no problem. If, however, any decision variable

 types are to be chosen before the FVIM outputs are assigned care must be