(491d) Iteratively Refined Distillation Line Methods

Traditional distillation line methods for synthesis and design generate trajectories by starting at both product ends of a column and integrating toward the feed stage. When the rectifying and stripping trajectories intersect, the column design is considered feasible; when they do not, the design is infeasible. Unfortunately, even when trajectories intersect, the component mass balances around the feed stage are not closed and, for equilibrium stage models, conditions of phase equilibrium are also not satisfied. That is, the liquid composition at the end of the stripping trajectory is usually not in equilibrium with the vapor composition calculated from the rectifying trajectory.

Recently, Lucia et al. (2008) have proposed a bottom up (or equivalently top down) approach to design using a distillation line methodology in which a stripping line trajectory is generated from a specified bottoms product, a switch is made at the feed stage, and then the rectifying line trajectory is generated by continuing the integration to the distillate product. For any rectifying trajectory that lands within a given open ball around the specified distillate product, the design is considered feasible. Otherwise, the design is infeasible. The bottom up approach has the advantage of exactly satisfying all component mass balances and equilibrium conditions at the feed stage. However, there is generally a mismatch in the overall component mass balances for the column.

To resolve overall component mass balance errors in the bottom up distillation line methodology, we propose two simple iterative refinement schemes based on direct and accelerated direct substitution that have the additional advantage of being able to find feasible designs even when the given column product specifications are infeasible. Many examples are presented, including mixtures with as many as six components and phase equilibrium models ranging from constant relative volatility to those that model azeotropy. Numerical results clearly show that the proposed iterative refinement schemes can easily find feasible distillation designs. Geometric illustrations are used to highlight key points.