Distillation Maxwell-Stefan approach

This appendix shows how the Aspen Plus simulator can be used to do detailed rate-based analysis of distillation using the Maxwell-Stefan approach outlined in Sections 15.7 and 16.8. Lab 10 should be done before this lab. NOTE If you have convergence problems, reinitialize and try running again. 

The Ki, values for each species i and the enthalpies used in the energy balance equations for any stage ra are obtained from conventional approaches used in multistage distillation analysis. However, the species flux is expressed in terms of the sum of a convective component and a diffusive component. The diffusive component is modeled using the Maxwell-Stefan approach (Section 3.1.5.1) for this complex multicomponent system in a matrix framework. For an illustrative introduction, see Sender and Henley (1998). 

The modeling of RD processes is illustrated with the heterogenously catalyzed synthesis of methyl acetate and MTBE. The complex character of reactive distillation processes requires a detailed mathematical description of the interaction of mass transfer and chemical reaction and the dynamic column behavior. The most detailed model is based on a rigorous dynamic rate-based approach that takes into account diffusional interactions via the Maxwell-Stefan equations and overall reaction kinetics for the determination of the total conversion. All major influences of the column internals and the periphery can be considered by this approach. 

Strictly speaking, Eqs. (13-69) and (13-70) are valid only for describing mass transfer in binary systems under conditions where the rates of mass transfer are low. Most industrial distillation and absorption processes, however, involve more than two different chemical species. The most fundamentally sound way to model mass transfer in multi-component systems is to use the Maxwell-Stefan (MS) approach (Taylor and Krishna, op. cit.). 

Figures 10.7 and 10.8 show the liquid-phase compositions for the reboiler and condenser as functions of time. After column start-up, the concentration of methanol decreases continuously whereas the distillate mole fraction of methyl acetate reaches about 90%. A comparison of the rate-based simulation using the Max-well-Stefan diffusion equations (Eq. (10.1)) and experimental results for the liquid-phase composition at the column top and in the reboiler demonstrates their satisfactory agreement. Figure 10.9 shows the simulation results obtained after an operation time of 10000 s with different modeling approaches the model including the Maxwell-Stefan diffusion description, the model with effective diffusion coefficients, and the equilibrium-stage model. Both the Maxwell-Stefan...

Solutions to Eq. 115-721 are considered in detail by Krishna and Wesselingh (1997). Taylor and Krishna (1993), and Wesselingh and Krishna (1990, 20001. The Maxwell-Stefan matrix approach to multicomponent mass transfer is used in the Aspen Plus simulator to solve distillation problems. Use of the simulator to obtain rate-based solutions of distillation problems is considered in Section 16.8 and in the appendix of Chapter 16. 

The introductory Section 3.1.2.5 in Chapter 3 identifies the negative chemical potential gradient as the driver of targeted separation, and the relevant species flux expression is developed in Section 3.1.3.2 (see Example 3.1.9 also). Section 3.1.4 introduces molecular diffusion and convection and basic mass-transfer coefficient based flux expressions essential to studies of distillation and other phase equilibrium based separation processes. Section 3.1-5.1 introduces the Maxwell-Stefan equations forming the basis of the rate based approach of analyzing distillation column operation. After these fundamental transport considerations (which are also valid for other phase equilibrium based separation processes), we encounter Section 3.3.1, where the equality of chemical potential of a species in all phases at equilibrium is illustrated as the thermodynamic basis for phase equilibrium (Le. = /z ). Direct treatment of distillation then begins in Section 3.3.7.1, where Raouit s law is introduced. It is followed by Section 3.4.1.1, where individual phase based mass-transfer coefficients are reiated to an overall mass-transfer coefficient based on either the vapor or liquid phase. 

To resolve such problems, rigorous mass-transfer theory has been applied to a distillation stage in combination with the required heat transfer models (Krishna and Standart, 1979 Taylor and Krishna, 1993). Based on such theories, numerical models have been developed wherein correlations of mass-transfer and heat-transfer coefficients for the distillation device, of packed or plate type, are incorporated (Krishnamurthy and Taylor, 1985 Taylor etoL, 1994). For multicomponent systems, Maxwell-Stefan formalism (Section 3.1.5.1) provided a structural framework for such models. Such theories are known as a rate based approach for modding distillation where equilibrium between phases is nonexistent except at the vapor-liquid interfeice. 

BanaL F. A., Abu Al-Rub, F., Jumah, R., and Al-Shannag, M. (1999a). Application of Stefan-Maxwell approach to azeotropic separation by membrane distillation. Chem. Eng. J. 73, 71. 

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