Fluid Mechanics of Distillation Trays (I): Depth-Averaged Theory and One-Dimensional Flows

Abstract

Rigorous design of a distillation column requires a better fundamental understanding of the fluid mechanics of bubble formation and global flows on trays than that currently available. To progress beyond the empirical-or correlation-based state of understanding that currently exists, a theoretical and computational framework is described here that is based on reducing the governing set of three-dimensional conservation equations to a two-dimensional set by averaging them across the depth of the fluid film flowing across the tray. In contrast to related previous works, realistic boundary conditions to the flow problem are provided in this paper by solving simultaneously for the flow on the tray and its inlet and outlet downcomers. In this first of a series of papers, attention is focused on situations in which the flow is invariant in the direction perpendicular to the main flow direction. By means of such a set of one-dimensional, depth-averaged equations, predictions are made in several interesting and practically important situations in which the flow is either steady or time dependent.