Simulation and optimization of three-phase distillation processes

The geometry of vapor-liquid (VL) and vapor-liquid-liquid (VLL) solutions to simulation and optimization problems for heterogeneous flash and distillation processes is studied. Particular emphasis is placed on the relationship between VL and VLL solutions to the same problem and any associated algorithmic implications. Solution curve approximations are used to build an accurate and inexpensive global picture of the various solutions to flash problems and, when needed, to aid the problem solving tasks. The essential solution geometry for homogeneous and heterogeneous solutions to three-phase distillations is captured using a projected 2-surface in R/sup 3/. Steep fronts, regular turning points and bifurcation points are shown in the homogeneous solution manifold. Paths from multiple homogeneous solutions to the heterogeneous solution to the same problem are also studied as well as the structure of various heterogeneous solution manifolds. The level sets of an objective function on a projected 2-surface in R/sup 3/ are used to study the optimization of heterogeneous distillations. Specific attention is focused on the existence of local optima and their effect on both active set and line searching strategies. 24 refs., 14 figs., 7 tabs.