(445e) Application of Primal-Dual Iteration to the Solution of Process Network Synthesis Problems

The Infinite DimEnsionAl State-space (IDEAS) conceptual framework has been previously applied to various process synthesis problems, including reactor networks, reactive distillation networks, multicomponent mass exchange networks, membrane networks, power cycle synthesis, and distillation networks. The IDEAS framework possesses two unique characteristics: it considers all feasible networks and it leads to a convex (linear) optimization formulation.

The IDEAS framework decomposes process networks into two subnetworks: an operator (OP) subnetwork, where process technologies (unit operations) and / or their aggregate effects are represented, and a distribution (DN) subnetwork, where mixing, splitting, recycling, and bypassing operations occur. The OP and DN subnetworks have an infinite number of inlets and outlets, which gives rise to infinite dimensional solutions with a linear feasible region.

The infinite dimensional linear program formulated with the IDEAS framework usually can not be solved explicitly, but rather its solution can be approximated with a series of finite linear programs of increasing size, whose sequence of values converges to the infinite dimensional problem. The size of the finite problem is typically increased with uniform discretization to approximate the condition space of the process operator (space of intensive stream conditions: temperature, pressure, concentration, residence time, etc.), which brings along a significant increase in computational memory requirement.

In this work we submit a proof and algorithm that uses primal-dual iterations for the generation of finite programs with nonuniform discretization which result in reduced computational memory requirements for the finite approximation to the solution of the IDEAS problem and faster convergence.