(183b) Separation Efficiency Estimation without Mass Transfer Coefficients: a New Approach for Structured Packed Columns
Corrugated sheet structured packings are well known for their high separation efficiency at relatively low pressure drop (Kurz et al., 1991; Brunazzi and Paglianti, 1997). A considerable disadvantage of these packings is their high cost per unit volume as compared to high-efficiency random packings and trays. Hence, an accurate design of process units equipped with corrugated sheet structured packings is very important for the investment costs minimization. Such a design cannot be realized without sound and predictive process models.
Although structured packings were expected to be more amenable to rigorous modeling than conven-tional random packings, there is still a lack of truly predictive models for the estimation of their hydrau-lic and mass transfer characteristics. The reason is insufficient understanding of fundamental hydraulic and mass transfer phenomena which can be attributed to the high complexity of the multiphase flow structure encountered in the majority of separation operations and to a limited computational power. As a consequence, the modeling of the transport phenomena in structured packings has been accom-plished with a big portion of empiricism.
It is well known that separation performance of structured packings largely depends on their geometric and surface characteristics. In the most advanced geometry-based models reported in the literature, the mass transfer coefficients based on empirically obtained correlations explicitly include the major geometric characteristics of the packings (e.g. channel dimensions, corrugation inclination angle) to-gether with the operating conditions and system physical properties (see, e.g., Olujic et al., 2000). These coefficients are then used in the framework of the rate-based approach, most often with the film theory (Taylor and Krishna, 1993). However, this theory, once developed for binary mass transfer in non-reactive systems, is now used for much more complicated processes. This requires additional as-sumptions which are frequently in conflict with the physical backgrounds. As a consequence, the straightforward application of the film theory for complex problems, e.g. reactive separations in multi-component mixtures, may become difficult.
In this work, we suggest another modeling approach to the design of structured packed columns based on rigorous equations of fluid dynamics. This approach rests on analogies between the trans-port phenomena under complex multiphase flow conditions dominating most of industrial separations and phenomena encountered in geometrically simpler flow patterns (e.g. planar films, spherical drops, circular jets, etc.). The actual hydrodynamics in structured packings cannot be described by the partial differential equations of fluid dynamics directly. However, when replaced by an appropriate combina-tion of geometrically simpler flow patterns, such a description becomes possible.
The developed physical model of a structured packing is based on its simplified geometric representa-tion and incorporates major experimentally observed hydrodynamic effects. It consists of a bundle of identical channels with the diameter defined via the hydraulic diameter of the actual (triangular) flow channels and with their total number derived from the packing geometric specific area. Some channels are wetted by the liquid according to the packing surface wettability characteristics, whereas the gas phase is spread over all channels. In line with experimental observations (see, e.g., Stoter, 1993; Shetty and Cerro, 1997; Valluri et al., 2005), the liquid is assumed to flow over the inner surface of these channels in form of laminar films, with the rest of the channel volume occupied by a counter-current gas flow. To reproduce the observed large-scale mixing effects in the both fluid phases (Zogg, 1972; Petre et al., 2003), the gas and liquid flows are presumed to be ideally mixed at regular inter-vals. The interval length for each phase represents the packing specific model parameter and is de-rived directly from the corrugation geometry and the packing layer dimensions (Shilkin and Kenig, 2005). Additionally, the gas phase turbulence is directly incorporated into the model in order to ac-count for the small-scale mixing effects caused by the friction at open channel sides and mainly re-sponsible for the pressure drop in structured packings.
The transport phenomena in the physical model described above are governed by the partial differen-tial fluid dynamics equations. As a result, the use of empirical transport coefficients required in tradi-tional modeling methods is avoided. The mathematical model comprises a set of convection-diffusion and heat conduction equations as well as the Navier-Stokes equations written for each phase sepa-rately. These equations are supplemented by the conjugate boundary conditions at the phase inter-face.
A numerical solution of the mathematical model yields velocity profiles as well as temperature and composition fields in all the channels. These values are used to determine the average temperature and composition profiles over the packing height.
The developed model is verified using total reflux distillation data available in the literature. The ex-periments are conducted in columns equipped with structured packings of different type, with both bi-nary and ternary test mixtures, covering a broad range of operating conditions. Additionally, simula-tions with the traditional film model are performed to compare accuracy and application range of the both modeling approaches.
It is demonstrated that the accuracy of the film model strongly depends on process operating condi-tions and applied correlations for the transport coefficients. On the contrary, the model based on the hydrodynamic analogy approach has a stable performance over a broad range of investigated operat-ing conditions. The proposed approach demonstrates an excellent agreement with experimental data and can be recommended for design, revamp and optimization of structured packed distillation col-umns.
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