Torres, Leonardo de Gil; (1995) On some reduced order models for packed separation processes. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The use of packed-bed separation columns as a liquid-gas contact system in absorption and distillation has steadily increased in the chemical and process industries and with it the need for tools for their adequate design and control. The mathematical models for packed separation columns are known for their large dimensionality. This can pose a problem when one considers the design and/or optimisation of systems involving more than one column or a single large column. The use of reduced-order models came as an answer to this problem. Reduced-order models presented to date do not rigorously solve the mass transfer subproblem. Four generalised steady-state reduced-order models for separation processes in packed columns are developed and compared in this work. The models are based on the two film theory of mass transfer and the more rigorous of them have as a starting point one of the so called rate based methods. The mass and energy transfer rates across the vapour liquid interface are evaluated by means of different approximate solutions of the Maxwell-Stefan equations for steady-state, unidirectional mass transfer. The differential equations of the models are converted into algebraic equations through the application of the orthogonal collocation procedure on the spatial variable. The resulting system of algebraic equations is subsequently solved using a modification of the Powell hybrid method. Three case studies dealing with distillation columns are presented but the models are easily modified to work with other separation processes (e.g., absorption). The results of the simulations indicated a clear advantage when using more rigorous methods for the computation of the interphase mass transfer rates. Their inclusion in the reduced-order models improved the convergence characteristics of the solution with respect to the number of collocation points and also increased the robustness of the models in converging towards the solution. These improvements were obtained without increasing significantly the time spent in the simulations when compared with a model using an effective diffusivity approach in the evaluation of the mass transfer rates.

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