Batch Distillation: The Forward and Inverse Problems

There are two basic theoretical and computational problems associated with batch distillation. The forward or direct problem consists on generating the distillation curve of a given mixture. This is an old problem, but new results are presented here to relate mathematical properties of the distillation curve with the physicochemical properties of the molecular species present in the mixture. The inverse problem consists of, given a distillation curve, finding a surrogate mixture that would accurately represent experimental data. There is more than one solution to the reverse problem because there are theoretically an infinite number of mixtures that will present very similar experimental distillation curves. The method developed in this paper requires the same number of molecular species in the surrogate mixture as the points of the distillation curve that will be matched precisely. The choice of exact points to match on the distillation curve allows to conform a square system of equations where the number of equations is equal to the number of unknowns. Other points of the distillation curve are satisfied within a prescribed small error tolerance. A surrogate mixture for gasoline was developed as an example.