New approach for quantifying process feasibility: Convex and 1-D quasi-convex regions



Uncertainities in chemical plants come from numerous sources: internal like fluctuated values of reaction constants and physical properties or external such as quality and flow rates of feedstreams. Accounting for uncertainty in various stages of plant operations was identified as one of the most important problems in chemical plant design and operations. A new approach proposed describes process's feasible region and a new metric for evaluating process flexibility based on the convex hull that is inscribed within the feasible region and determines its volume based on Delaunay Triangulation. The two steps involved are: 1. a series of simple optimization problems are solved to determine points at the boundary of the feasible region; 2. given the set of points at the boundary of the feasible region, the convex hull inscribed within the feasible region is determined. This is achieved by implementing the Quickhull algorithm, an incremental procedure for evaluating the convex hull, and then by computing a Delaunay Triangulation to determine the volume of the convex hull providing a new metric for process flexibility. This approach not only provides another feasibility measure, but an accurate description of the feasible space of the process. It was applied to 1-D convex problems, and work is in progress to extend it to nonconvex systems.