equations would either be solved for component liquid or vapor flow

rates, not some liquid and some vapor flow rates. Similarly the flow

rates solved for would always be those leaving the tray over which the

material balance is being made. These are exactly the type of restric-

tions which are being made on the FVIM and index outputs. In addition,

because the outputs are made with small matrices (FVIM's and IDM's)

existing algorithms can be used for the most part, which avoids the

necessity of including in a computer program package, such as GENDER,

separate routines for output set assigning indexed and non-indexed

equations. Finally, by assigning the outputs to the small sub-matrices

much effort is saved when compared to output set assigning the full

incidence matrix.


2.6 Acceleration of Variables

 A possible consequence of defining variable indices with a range

is a phenomenon called "acceleration of variables." Acceleration of

variables is said to occur when the number of variable indices in a

problem increases faster than the number of function indices as the

range on a function index is increased. Acceleration of variables

occurs at the lowest level of decomposition, i.e., on function indices

and their associated variable indices. It is, of course, possible to

have the number of variables in an entire problem increase faster than

the number of equations and have no acceleration of variables. Accel-

eration of variables is actually a possible result of the manner in

which the indices are defined. To illustrate, consider the following

function index and variable index: