Compartmental modeling of high purity air separation columns

Abstract

High purity distillation columns are critical unit operations in cryogenic air separation plants. The development of nonlinear control technology is motivated by the need to frequently change production rates in response to time varying utility costs. Detailed column models based on stage-by-stage balance equations are too complex to be incorporated directly into optimization-based strategies such as nonlinear model predictive control. In this paper, we develop reduced order dynamic models for the upper column of a cryogenic air separation plant by applying time scale arguments to a detailed stage-by-stage model that includes mass and energy balances and accounts for non-ideal vapor–liquid equilibrium. The column is divided into compartments according to the locations of liquid distributors and feed and withdrawal streams. The differential equations describing each compartment are placed in singularly perturbed form through the application of a physically based coordinate transformation. Application of singular perturbation theory yields a differential–algebraic equation model with significantly fewer differential variables than the original stage-by-stage model. A rigorous column simulator constructed using Aspen Dynamics (Aspen Technology) is used to access the tradeoff between reduced order model complexity and accuracy as the number of compartments is varied.