Global Bounds on Optimal Solutions for the Production of 2,3-Dimethylbutene-1

This paper is concerned with computer-aided optimal design of combined reaction−distillation processes. The production of solvent 2,3-dimethylbutene-1 by isomerization of 2,3-dimethylbutene-2 is considered as an innovative benchmark problem. Possible process candidates are a reactive distillation column, a reactor coupled to a nonreactive distillation column, or a reactive reboiler with a nonreactive distillation column on top. Suitable mathematical models of the different processes are formulated, and the reaction kinetics of the isomerization over an Amberlyst 15 catalyst is determined. Local mixed-integer nonlinear optimization indicates that reactive distillation has the lowest total annualized costs. However, because of the nonconvexity of the underlying optimization problem, better solutions for the other process candidates cannot be excluded with the local approach. Therefore, a new approach is presented which provides a global lower bound for the second best solution and therefore proves that reactive distillation is the best option. The new approach is based on some suitable polyhedral approximation of the underlying model equations leading to a mixed-integer linear optimization problem.