Global analysis of combined reaction distillation processes

Polyhedral relaxation is a powerful tool for determining global bounds on optimal solutions in chemical process synthesis. Combined reaction distillation processes are considered as a challenging application example. To reduce complexity of the resulting mixed integer linear optimization problems, model reduction by means of wave functions is proposed, and polyhedral relaxations of sigmoidal wave functions in two variables are derived. It is shown that these relaxations provide better approximation quality than approximating the composed functions individually. Further, the concave envelope of such functions is characterized and (nonlinear) convex underestimators are derived.The approximation results are employed in the computation of lower bounds on the vapor flow of a combined reaction distillation process with a metathesis reaction 2B⇋A+C2B⇋A+C. We restrict computations to a domain around a known local optimum, trading computation time for some of the globality. This still proves a bound on the vapor flow, but for restricted operating conditions of the column.