TWO-PASS STRATEGIES FOR SPARSE MATRIX COMPUTATIONS IN CHEMICAL PROCESS FLOWSHEETING PROBLEMS

The usual approach for solving chemical engineering process flowsheeting problems involves organizing the computation into modules, which then are solved sequentially. There are two major problems that seriously affect the efficiency of the sequential modular approach, namely the handling of design specifications and the presence of multiply nested iteration loops. These problems are particularly severe for processes with large and complex recycle stream structures. Because of the current effort to conserve material and energy, modern processes are likely to contain such complex structure. Therefore, the development of an alternate approach would appear particularly timely.; In principle these problems can be overcome by eliminating the computational modules and performing the calculations on the equation and variable level. An approach that employs this strategy is to simultaneously linearize all the equations and iterate on all the variables. The reason the simultaneous-linearization has not been considered in the past is that the large sparse linear set of equations that results was thought to be too unwieldly to solve on the computer.; Although current general sparse matrix techniques can solve problems with one or two thousand variables, it is felt that practical process flowsheeting problems will require solution of tens of thousands of variables. These techniques, however, fail to identify and exploit to the fullest extent the naturally occurring structure exhibited by process flowsheeting equation sets.; This work proposes employing a two-pass solution approach that is specifically designed to exploit this naturally occurring structure. The first pass reorders the equation set into a desirable form and the second pass numerically solves the equations. A number of methods are proposed for each of these passes and compared with currently available techniques. Although this work can only be considered as an initial effort in expanding the size of problem that can be solved, it is felt the proposed methods will allow solution of chemical flowsheeting problems of nearly ten thousand equations.