Rate-based approach

A more physically consistent way to describe a column stage is known as the rate-based approach [42, 65, 66]. This approach implies that actual rates of multicomponent mass and heat transfer and chemical reactions are taken into account directly. 

Mass transfer at the vapor-liquid interface can be described using different theoretical concepts [4, 42]. Most often, the film model [67] or the penetration/surface renewal model [63, 68] are used, whereas the model parameters are estimated via experimental correlations. In this respect the film model is advantageous, since there is a broad spectrum of correlations available in the literature, for all types of internals and systems. For the penetration/surface renewal model, such a choice is limited, and therefore, in this chapter we focus on the film model. 

In the film model (Fig. 10.2), it is assumed that all of the resistance to mass transfer is concentrated in thin films adjacent to the phase interface and that transfer occurs within these films by steady-state molecular diffusion alone. Outside the films, in the bulk fluid phases, the level of mixing is so high that there is no composition gradient at all. This means that in the film region we have one-dimensional diffusional transport normal to the interface. 

Multicomponent diffusion in the films can be rigorously described by the Maxwell-Stefan equations derived from the kinetic theory of gases [69]. The 

Maxwell-Stefan equations connect diffusion fluxes of the components with the gradients of their chemical potentiaL With some modification these equations take a generalized form in which they can be used for the description of real gases and liquids [42]  

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Sivasubramanian, M. S. and Boston, J. F., 1990, The heat and mass transfer rate-based approach for modelling multicomponent separation processes, in Computer Applications in Chemical Engineering, pp. 331-336. Elsevier, Amsterdam. 

Reactive absorption, reactive distillation, and reactive extraction occur in multicomponent multiphase fluid systems, and thus a single modeling framework for these processes is desirable. In this respect, different possible ways to build such a framework are discussed, and it is advocated that the rate-based approach provides the most rigorous and appropriate way. By this approach, direct consideration... 

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. 

Despite the recent rapid development of computer technology and numerical methods, the rate-based approach in its current realization still often requires a significant computational effort, with related numerical difficulties. This is one of the reasons the application of rate-based models to industrial tasks is rather limited. Therefore, further work is required in order to bridge this gap and provide chemical engineers with reliable, consistent, robust, and comfortable simulation tools for reactive separation processes. 

Seader JD. The rate-based approach for modeling staged separations. Chem Eng Prog 1989 85(10)4149. 

Recently, a combination of CFD and rate-based process simulation has been proposed as a way to link different scales. In the rate-based approach, the influence of the column internals on hydrodynamics and mass transfer is directly accounted via relevant hydrodynamic and mass transfer correlations. These correlations can be now obtained not only from real experiments, but also by application of CFD simulations, thus reducing the number of necessary hydrodynamic experiments. Such virtual experiments allow the optimization of column internals, even without really manufactured internals. 

Gorak, A., Wozny, G., and Jeromin, L., Industrial Application of the Rate-Based Approach for Multicomponent Distillation Simulation, Proceedings of the 4th World Congress in Chemical Engineering, Karlsruhe, Germany, 1991. 

Seader, J. D., Computer Modelling of Chemical Processes, AIChE Monograph Series, No. 15, 81 (1986). Seader, J. D., The Rate-Based Approach for Modeling Staged Separations, Chem. Eng. Progress,... 

A major assumption made in the column models of Chapters 3 through 13 was the equilibrium stage. Tray hydraulics provides additional information essential for applying mass transfer theories to evaluate the column performance with a rate-based approach. This analysis provides a basis for calculating the tray efficiency associated with an equilibrium stage. The topics of rate-based analysis and tray efficiency are also discussed in this chapter. 

Understand the difference between the equilibrium-efficiency approach and the rate-based approach to multicomponent distillation problems. 

Chemical equilibrium 4- rate-based approach medium complexity... 

Reaction kinetics rate-based approach high complexity... 

More detailed models (fourth model) also account for the transport properties of the components, leading to a rate-based approach. The resulting model shows a high complexity but also leads to good results in the comparison to calculated with experimental results (Noeres et al, 2002). 

This program is a result of the first European project and has not (yet) been commercialized. However there are programs on the market that do the job at least partly. In many cases the results of these programs and the results cited above will agree. Some of the major companies have in-house tools suitable for RD. It is an open question if a rate-based approach as in Designer is really necessary. There are many examples where RD can be simulated adequately with an equilibrium model for thermodynamics. 

An overview of possible modeling approaches for RD is shown in Fig. 10.1. A process model consists of submodels for mass transfer, reaction and hydrodynamics whose complexity and rigor vary within a broad range. For example, mass transfer between the vapor and the liquid phase can be described on the grounds of the most rigorous rate-based approach, with the Maxwell-Stefan diffusion equations, or it can be accounted for by the simple equilibrium-stage model assuming thermodynamic equilibrium between the two phases. 

The horizontal liquid flow pattern is very complicated due to the mixing by vapor, dispersion, and the round cross section of the column. On single-pass trays, the latter results in the flow path, which first expands and then contracts. A rigorous modeling of this flow pattern is very difficult, and usually the situation is simplified by assuming that the liquid flow is unidirectional and the major deviation from the plug flow is the turbulent mixing or eddy diffusion. In [80], two different models, the eddy-diffusion model and the mixed pool model were developed and tested in the context of the rate-based approach for RD trays. The details of these models can be found in [81]. 

In this section, four examples illustrating the application of the rate-based approach discussed above to the RD modeling are presented. The systems selected are methyl acetate synthesis, MTBE synthesis, ethyl acetate synthesis and transesterification of dimethyl carbonate. In the first example, dynamic process modeling is highlighted, whereas in three other examples, different aspects of steady-state modeling are discussed. 

In terms of the rate-based approach, the pecuHarities of the specific process applications and the different solution strategies are treated while discussing the case studies. A detailed general description covers mass and heat transfer, reaction kinetics including the reaction-mass-transfer coupling, as well as steady-state and dynamic modeling issues. 

For the methyl acetate synthesis, dynamic modeling effects are investigated, whereas for other systems, the focus is on different steady-state issues, for example the influence of liquid-liquid separation, operational conditions and different column internals (ethyl acetate) or selectivity effect (dimethyl carbonate transesterification). The comparison between the simulation and experimental data made for all RD case studies proves that the rate-based approach is capable of predicting correct process behavior, both steady state and dynamic. 

The reforming reactions can be reflected in a rate-based approach, under an equilibrium assumption, or they are disregarded in the model. With regard to... 

Therefore, in this work a more physically consistent way is used by which a direct account of process kinetics is realised. This approach to the description of a column stage is known as the rate-based approach and implies that actual rates of multicomponent mass transport, heat transport and chemical reactions are considered immediately in the equations governing the stage phenomena. Mass transfer at the vapour-liquid interface is described via the well known two-film model. Multicomponent diffusion in the fdms is covered by the Maxwell-Stefan equations (Hirschfelder et al., 1964). In the rate-based approach, the influence of the process hydrodynamics is taken into account by applying correlations for mass transfer coefficients, specific contact area, liquid hold-up and pressure drop. Chemical reactions are accounted for in the bulk phases and, if relevant, in the film regions as well. 

Eckert, E., Vanek, T., 1999, Application of the Rate-Based Approach to Three-Phase Distillation Columns. Ind. Eng. Computers Chem. Engng. 23, pp. 331 - 334. 

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. 

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