Columns equilibrium stage model

Availability of large digital computers has made possible rigorous solutions of equilibrium-stage models for multicomponent, multistage distillation-type columns to an exactness limited only by the accuracy of the phase equilibrium and enthalpy data utilized. Time and cost requirements for obtaining such solutions are very low compared with the cost of manual solutions. Methods are available that can accurately solve almost any type of distillation-type problem quickly and efficiently. The material presented here covers, in some... 

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. 

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 methods based on the equilibrium stage model have existed for over 30 years and refinements continue, but serious development of nonequilibrium models has begun only recently. These methods are an alternative means to the stage model for predicting column performance. They are expected to make inroads, especially for systems for which stage efficiency prediction is very difficult, such as reactive distillation, chemical absorption, and three-phase distillation. However, their progress into systems where efficiency prediction is well-established is likely to be slower. Their complexity due to the restriction to... 

Chemical engineers have been solving distillation problems by using the equilibrium-stage model since 1893 when Sorel outlined the concept to describe the distillation of alcohol. Since that time, it has been used to model a wide variety of distillation-like processes, including simple distillation (single-feed, two-product columns), complex distillation (multiple-feed, multiple-product columns), extractive and azeotropic distillation, petroleum distillation, absorption, liquid-liquid extraction, stripping, and supercritical extraction. 

Solving the NEQ Model Equations In general, a nonequilibrium model of a column has many more equations than does an equivalent equilibrium-stage model. Nevertheless, we use may essentially the same computational approaches to solve the nonequilibrium model equations simultaneous convergence (Krishnamurthy and Taylor, op. cit.) and continuation methods [Powers et al., Comput Chem. Engng., 12, 1229 (1988)]. Convergence of a nonequilibrium model is likely to be slower than that of the equilibrium model because of the greater... 

In this particular case the converged composition and temperature profiles have the same shape as those obtained with the equilibrium-stage model (with specified efficiency) and, therefore, are not shown. The reason for the similarity is that, as noted above, this is basically a binary separation of very similar compounds. The important point here is that, unlike the equilibrium-stage model simulations, the nonequilibrium model predicted how the column would perform no parameters were adjusted to provide a better jit to the plant data. That is not to say, of course, that NEQ models cannot be used to fit plant data. In principle, the mass-transfer coefficients and interfacial area (or parameters in the equations used to estimate them) can be tuned to help the model better fit plant data. 

Even at steady state, efficiencies vary from component to component and with position in a column. Thus, if the column is not at steady state, then efficiencies also must vary with time as a result of changes to flow rates and composition inside the column. Thus, equilibrium-stage models with efficiencies should not be used to model the dynamic behavior of distillation and absorption columns. Nonequilibrium models for studying column dynamics are described hy, e.g., Kooijman and Taylor [AlChE 41, 1852 (1995)], Baur et al. [Chem. 

The equilibrium stage model reported by Zhang et al. [7], which accounts for the influence of fluid flow rate on fee column efficiency, has been used for the optimization simulations. 

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 efficiency. This approach is discussed in Chapter 13. An alternative approach based on direct use of matrix models of multicomponent mass transfer is developed in Chapter 14. This nonequilibrium stage model is also applicable, with only minor modification, to gas absorption and liquid-liquid extraction and to operations in trayed or packed columns. 

In fact, through use of matrix models of mass transfer in multicomponent systems (as opposed to effective diffusivity methods) it is possible to develop methods for estimating point and tray efficiencies in multicomponent systems that, when combined with an equilibrium stage model, overcome some of the limitations of conventional design methods. The purpose of this chapter is to develop these methods. We look briefly at ways of solving the set of equations that model an entire distillation column and close with a review of experimental and simulation studies that have been carried out with a view to testing multicomponent efficiency models. 

The next task is to set up the equations that model a complete distillation column. As noted in the introduction to this chapter, simulation of multicomponent distillation operations usually is carried out using the equilibrium stage model introduced below. 

The column solution methods described in this chapter are based on an equilibrium stage model. Normally, the vapor and liquid leaving a tray are not at equilibrium due to imperfect mixing or insufficient residence time on the tray. Tray efficiencies, discussed in Chapter 14, are parameters that relate actual performance to equilibrium stage performance. By replacing the equilibrium relationship in the model with an equation based on the Murphree tray efficiency, the actual column performance can be calculated. The accuracy of the model obviously depends on the reliability of the tray efficiencies used in the calculations. 

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