Temperature Collocation Algorithm for Fast and Robust Distillation Design

Abstract

In this paper, we describe a new minimum bubble-point distance (MIDI) algorithm for assessing the feasibility of a desired distillation specification. The algorithm computes the rectifying and stripping temperature profiles by temperature collocation on finite elements with orthogonal polynomials. We discovered the beneficial use of a dimensionless equilibrium tray temperature as an independent variable. This novel choice is bounded between 0 and 1, improves the numerical quality of the design problem formulation, and is well-behaved even in the vicinity of pinch regions. It also employs the fixed points of column sections as collocation points. Adaptive-element boundary placement at saddle temperatures can effectively overcome problems with numerical instability near pinch regions. Extensions of our MIDI algorithm to the calculation of the minimum and maximum refluxes are also introduced. We show the application of this algorithm in the separation of quaternary mixtures and provide an outlook of the methodology for optimal column sequencing. Cases studies demonstrate the algorithm's robustness and reliability.