Distillation efficiency models

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. 

In view of the large influence of interaction effects found by Toor and Burchard (1960) it is a little surprising that there have been so few design calculations reported in the literature. More experience with these models is required before definitive conclusions can be made regarding the use of complicated efficiency models in sophisticated distillation codes. The whole issue of multicomponent mass transfer models in distillation column simulation is taken up again in Chapter 14. 

Fletcher, J. P., A Method for the Rigorous Calculation of Distillation Columns Using a Generalized Efficiency Model, The Institution of Chemical Engineers Symposium Series No. 104, Distillation and Absorption 1987, A437-A447 (1987). 

It is standard practice in the modeling of distillation columns to assume that the liquid is incompressible and perfectly mixed on the trays, and that the vapor and liquid have the same temperature on the tray (thermal equilibrium), whereas the phases could be considered nonequilibrium and some vapor-phase efficiency is sometimes adopted in such cases (e.g., Murphree efficiency). Beyond these possible variants, the basic distillation column model can be reduced to total... 

Distillation appHcations can be characterized by the type of materials separated, such as petroleum appHcations, gas separations, electrolyte separations, etc. These appHcations have specific characteristics in terms of the way or the correlations by which the physical properties are deterrnined or estimated the special configurations of the process equipment such as having side strippers, multiple product withdrawals, and internal pump arounds the presence of reactions or two Hquid phases etc. Various distillation programs can model these special characteristics of the appHcations to varying degrees and with more or less accuracy and efficiency. 

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... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

The rate-based model gave a distillate with 0.023 mol % ethylbenzene and 0.0003 mol % styrene, and a bottoms product with essentially no methanol and 0.008 mol % toluene. Miirphree tray efficiencies for toluene, styrene, and ethylbenzene varied somewhat from tray to tray, but were confined mainly between 86 and 93 percent. Methanol tray efficiencies varied widely, mainly from 19 to 105 percent, with high values in the rectifying section and low values in the stripping section. Temperature differences between vapor and liquid phases leaving a tray were not larger than 5 F. 

Based on an average tray efficiency of 90 percent for the hydrocarbons, the eqiiilibniim-based model calculations were made with 36 equilibrium stages. The results for the distillate and bottoms compositions, which were very close to those computed by the rate-based method, were a distillate with 0.018 mol % ethylbenzene and less than 0.0006 mol % styrene, and a bottoms product with only a trace of methanol and 0.006 mol % toluene. 

The method for estimating point efficiency, outhned here, is not the only approach available for sieve plates, and more mechanistic methods are under development. For example, Prado and Fair [Ind. Eng. Chem. Re.s., 29, 1031 (1990)] have proposed a method whereby bubbling and jetting are taken into account however the method has not been vahdated tor nonaqueous systems. Chen and Chuang [Ind. Eng. Chem. Re.s., 32, 701 (1993)] have proposed a more mechanistic model for predicting point efficiency, but it needs evaluation against a commercial scale distillation data bank. One can expect more development in this area of plate efficiency prediction. 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

Analysts must recognize the above sensitivity when identifying which measurements are required. For example, atypical use of plant data is to estimate the tray efficiency or HTU of a distillation tower. Certain tray compositions are more important than others in providing an estimate of the efficiency. Unfortunately, sensor placement or sample port location are usually not optimal and, consequently, available measurements are, all too often, of less than optimal use. Uncertainty in the resultant model is not minimized. 

Stirred tanks are modeled assuming that both phases are well mixed. Tray columns are usually modeled as well mixed on each tray so that the overall column is modeled as a series of two-phase, stirred tanks. (Distillation trays with tray efficiencies greater than 100% have some progressive flow within a tray.) When reaction is confined to a single, well-mixed phase, the flow regime for the other phase makes little difference but when the reacting phase approximates piston flow, the flow regime in the other phase must be considered. The important cases are where both phases approximate piston flow, either countercurrent or cocurrent. 

The highly interactive nature of the balance and equilibria equations for the distillation period are depicted in Fig. 3.66. An implicit, iterative algebraic loop is involved in the calculation of the boiling point temperature at each time interval. This involves guessing the temperature and calculating the sum of the partial pressures, or mole fractions. The condition required is that Zyi + yw = 1. The iterative loop for the bubble point calculation is represented by the five interconnected blocks in the lower right hand corner of Fig. 3.66. The model of Prenosil (1976) also included an efficiency term E for the steam heating, dependent on liquid depth L and bubble diameter D. 

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