Non-equilibrium Stage Modeling

In recent years the evidence has been growing that distillation (and related) operations are better simulated with non-equilibrium (NEQ) models that take account of mass (and energy) transfer (and sometimes of fluid-flow patterns) in a manner that is more rigorous than is possible with the EQ stage models. 

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The variation of efficiencies is due to interaction phenomena caused by the simultaneous diffusional transport of several components. From a fundamental point of view one should therefore take these interaction phenomena explicitly into account in the description of the elementary processes (i.e. mass and heat transfer with chemical reaction). In literature this approach has been used within the non-equilibrium stage model (Sivasubramanian and Boston, 1990). Sawistowski (1983) and Sawistowski and Pilavakis (1979) have developed a model describing reactive distillation in a packed column. Their model incorporates a simple representation of the prevailing mass and heat transfer processes supplemented with a rate equation for chemical reaction, allowing chemical enhancement of mass transfer. They assumed elementary reaction kinetics, equal binary diffusion coefficients and equal molar latent heat of evaporation for each component. 

Krishnamurthy and Taylor [51] developed a so-called non-equilibrium stage model , the characteristics of which were the balance of mass and energy for each component in the two phases. These are coupled over the energy and mass flows in the boundary layers and are at equilibrium at the phase boundary. 

Schultes presented an absorption model for packed columns including simulations [81], while Eden [18] developed a non-equilibrium stage model describing the absorption of electrolytes in co-current and countercurrent scrubbers. The simultaneous view of phase and reaction equilibrium and the existence of solids in the liquid phase were emphasized in these reports. 

The reactive distillation processes which combine reaction and gas liquid separation are of increasing interest for scientific investigation and industrial application. Nowadays, simulation and design of multi component reactive distillation is carried out using the non equilibrium stage model (NEQ model) due to the limitation of conventional equilibrium stage efficiency calculations for equilibrium model (Lee Dudukovic (1998), Baur al. (2000), Taylor Krishna (1993), and Wesselingh (1997)). So, the NEQ model is developed by numerous authors. But there is a lack of experimental data in order to validate the model. Some input/output measurements are available but they provide little information about the behaviour inside the column. With this in mind, our paper is focus on the NEQ models and experimental validation. 

The design of absorbers (and strippers) typically involves a computer-assisted, Iray-by-tray. heat- and material-balance calculation to determine the required number of equilibrium stages, which arc then related to the required number of actual trays by an estimated tray efficiency. More recently, a non-equilibrium stage model has been developed for computer application which considers actual trays (or sections of packing) and performs a heat and material balance for each phase on each actual tray, based on mass and heat transfer rates on that tray. 

Figure 3.52. Model representation of a non-equilibrium staged extraction column.

At the prevailing high levels of dispersion normally encountered in such types of extraction columns, the behaviour of these essentially differential type contactors, however, can be represented by the use of a non-equilibrium stage-wise model. 

If a very fast reaction is considered, the reactive separation process can be satisfactorily described assuming reaction equilibrium. Here, a proper modeling approach is based on the non-reactive equilibrium stage model, extended by simultaneously... 

Two different approaches have evolved for the simulation and design of multicomponent distillation columns. The conventional approach is through the use of an equilibrium stage model together with methods for estimating the tray efficien -cy. An alternative approach, the nonequilibrium, rate-based model, applies rigorous multicomponent mass- and heat-transfer theory to distillation calculations. This non-... 

This chapter is concerned solely with the modeling of RD processes. The widely used equilibrium stage model is described first, followed by a discussion of the variety of non-equilibrium models needed to model these complicated processes. A perspective on the use of these models in RD process design concludes this chapter. 

For example, the standard synergetic approach [52-54] denies the possibility of any self-organization in a system with with two intermediate products if only the mono- and bimolecular reaction stages occur [49] it is known as the Hanusse, Tyson and Light theorem. We will question this conclusion, which in fact comes from the qualitative theory of non-linear differential equations where coefficients (reaction rates) are considered as constant values and show that these simplest reactions turn out to be complex enough to serve as a basic models for future studies of non-equilibrium processes, similar to the famous Ising model in statistical physics. Different kinds of auto-wave processes in the Lotka and Lotka-Volterra models which serve as the two simplest examples of chemical reactions will be analyzed in detail. We demonstrate the universal character of cooperative phenomena in the bimolecular reactions under study and show that it is reaction itself which produces all these effects. 

However this way could not give a self-consistent description between equilibrium and dynamical characteristics for elementary stages [80,89]. The lattice-gas model is the unique one that provides a self-consistent description of the equilibrium distribution of molecules as well as their dynamic behavior if the correlation effects are taken into account. Then the first correlator that provides such self-consistent description of elementary stages is a pair correlator 0j (r) (m — 2) in the quasi-chemical approximation. In the non-equilibrium conditions to calculate the unknown functions 6j (r) the kinetic Eq. (28) should be used. 

Most of the published literature on reactive distillation (RD) has been focussed mainly on aspects such as conceptual design with the aid of residue curve maps, steady-state multiplicity and bifurcations, and development of equilibrium (EQ) stage and rigorous non-equilibrium (NEQ) steady-state and dynamic models [1, 2]. Relatively little attention has been paid to hardware design. In this chapter the concepts underlying the selection of the appropriate hardware for RD columns are discussed. For RD column design, detailed information on hydrodynamics and mass transfer for the chosen hardware is required, but this information is often lacking. Modern tools such as computational fluid dynamics (CFD) can be invaluable aids in hydrodynamic and mass-transfer studies. 

The development and application of the equilibrium (EQ) stage model for conventional (i. e., non-reactive) distillation has been described in several textbooks [4]. Here we are concerned with the extension of this standard model to distillation accompanied by chemical reaction(s). 

To deal with this shortcoming of earlier non-equilibrium models, both steady state and dynamic NEQ cell models have been developed [12-15]. The distinguishing feature of this model is that stages are divided into a number of contacting cells, as shown in Fig. 9.6. These cells describe just a small section of the tray or packing. 

A schematic representation of the non equilibrium model (NEQ) is shown in Fig.l. This NEQ stage may represent a tray or section of packing. It is assumed that the bulk of both vapour and liquid phase are perfectly mixed and that the resistance to mass and heat transfer are located in two thin films at the liquid/vapour interface (film theory, Krishna Standard, 1976 Krishna, 1977). 

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