Advancement in tray efficiency modeling through RTD chambers

Cross-flow trays are widely favored vapor-liquid contacting devices in the process industry. It is approximated that distillation columns consume 3% of the worldwide energy, while half of them are equipped with trays. An accurate quantification of column performance is a prerequisite prior to process optimization through external measures. Since a column is a cascade of trays with more or less same function, it is appropriate to consider the trays as a fundamental unit of the column, and thus focus on understanding of their operation and performance.
Flow and mixing patterns on these trays strongly affect their separation efficiency. Mathematical models have been formulated in the literature to relate these patterns with the tray efficiency. Recent advances in imaging and simulation techniques have revealed the biphasic non-idealities existing on the trays. The available efficiency models, recently reviewed by Vishwakarma et al.(1), however, usually consider flow conditions at the tray boundaries only, and assume uniform homogenous vapor load on the tray. Such efficiency assessment conveys the impression of trays as a black-box.
A significant improvement in tray efficiency modeling can be achieved by mathematically segmenting the tray into an arbitrary number of chambers amidst inlet and outlet. A new model built upon the available residence time distribution (RTD) approach(2) is proposed in the present work, where the tray efficiency is computed through contribution of the RTD efficiencies of the individual chambers. This segmentation further complements in studying the impacts of vapor maldistribution and flow path length on the tray efficiency, thereby signifying the advantage of this new model over the existing ones. The mathematical construction of the proposed model along with its theoretical validation and analyses through case studies will be highlighted in this work. The cases studies will further attempt to break the black-box convention of the trays.

(1) V. Vishwakarma, M. Schubert and U. Hampel. ‘Distillation tray efficiency modelling: a forgotten chapter’, Jahrestreffen der ProcessNet-Fachgruppe Fluidverfahrenstechnik, 16-17 March 2016, Garmisch-Partenkirchen (Germany).

(2) A. S. Foss, J. A. Gerster and R. L. Pigford. ‘Effect of liquid mixing on the performance of bubble trays’, AIChE Journal, 4(2):231-239, 1958.