Columns nonequilibrium stage model

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 Section 13.5.1 we presented the data of Vogelpohl for the distillation of two ternary systems acetone-methanol-water and methanol-2-propanol-water in a bubble cap column. Krishnamurthy and Taylor (1985b) simulated these experiments using a nonequilibrium stage model similar to the one described above. The AIChE correlations were used to calculate the mass transfer coefficients. Thermodynamic properties were calculated with the models described by Prausnitz et al. (1980). 

Chapter 12 presents models of mass transfer on distillation trays. This material is used to develop procedures for the estimation of point and tray efficiencies in multicomponent distillation in Chapter 13. Chapter 14 uses the material of Chapter 12 in quite a different way in an alternative approach to the simulation and design of distillation and absorption columns that has been termed the nonequilibrium stage model. This model is applicable to liquid-liquid extraction with very little modification. Chapter 15 considers the design of mixed vapor condensers. 

Baur R., Taylor R. and Krishna R. (2001a). Dynamic behaviour of reactive distillation columns described by a nonequilibrium stage model. Chemical Engineering Science 56, 2085-2102. 2.9.1.2, 2.9.1.2, 2.9.3, 4.3... 

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... 

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 nonequilibrium stage in Figure 14.1 may represent either a single tray or a section of packing in a packed column. In the models described in this chapter the same equations are used to model both types of equipment and the only difference between these two simulation problems is that different expressions must be used for estimating the binary mass transfer coefficients and interfacial areas. 

For the purposes of simulating a packed column the packing was divided into a number of sections each of which is modeled as a nonequilibrium stage as discussed above. The C4 splitter was modeled using 150 nonequilibrium sections, an equilibrium reboiler and a total condenser. The bottom product rate in molar units and the reflux ratio were fixed at the values observed in the plant tests. Additional specifications included the component feed flows and the column pressures. 

Gorak et al. (1991) and Wozny et al. (1991) presented a brief description of their use of a nonequilibrium state model to simulate vacuum distillation of fatty alcohols in columns fitted with structured packing. They found that the compositions predicted by the nonequilibrium model were closer to the experimental data than were the results of an equilibrium stage-HETP calculation. 

The focus of the investigations is on the theoretical and experimental analysis of the three-phase distillation in a packed column. The project is aimed to the development of a model for the calculation of the three-phase distillation in a packed column. The conventional three-phase equilibrium stage model and a new nonequilibrium model have been developed. The explanation of the new nonequilibrium model and the validation of this nonequilibrium model represent the main topic in the lecture. 

The nonequilibrium-model equations for the stage in Fig. 13-56 are as follows in residual form, where i = component (i = 1 to C), j = stage number (j = 1 to N), and V = a stage in another column that supplies an interlink. 

The relaxation, inside-out, and bomotopy-continuation methods are extensions of whole or part of the first four methods in order to solve difficult systems or columns. The nonequilibrium models are rate- or transport phenomena-based methods that altogether do away with the ideal-stage concept and eliminate any use of efficiencies. They are best suited for columns where a theoretical stage is difficult to define and efficiencies are difficult to predict or apply. 

In nonequilibrium models, as in the other models, the subscript j is for the stage. In a trayed column, it is the actual tray. In a packed column, j is a section of packing. By convention, transfer is to be from the liquid to the vapor with the mass transfer rate to the vapor, Nf, taken as positive. 

Computer software for equilibrium-stage and nonequilibrium column models is available from a number of suppliers. Many other models have been implemented primarily for research purposes and are not available commercially. 

The actual process flow rates are important in nonequilibrium model simulations, whereas in most equilibrium stage simulations, a simulation with a feed flow rate of 1 unit is as meaningful as a simulation with a feed flow of 10, 100, or 573 units. In real columns the flow rates influence the mass transfer coefficients as well as the tray hydraulics. An inappropriate flow specification may mean the column will flood or, just as likely, dump all the liquid through the holes in the tray. Thus, it is important to ensure that the specified (or calculated) flows and tray or packing characteristics are consistent with the satisfactory operation of the column. 

There are many excellent texts that discuss the design of distillation columns using equilibrium stage calculations. Some of them were cited in Chapters 12-14. These texts provide a wealth of examples that could be used as the basis for a design using the nonequilibrium model described in Chapter 14. We adapt one such example below (Exercise 14.1) in order to indicate how this might be done. 

A number of simulations were carried out using the nonequilibrium model of ChemSep for different column configurations (number of equilibrium stages and feed stage location). Only the specifications and results of our final simulation are reported here.The problem specifications presented in Table 6.5 were entered via the ChemSep menu and the program was executed, converging in 15 iterations. 

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