Rate-based approach for modeling

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. 

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

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,... 

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]. 

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. 

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

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. 

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. 

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. 

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. 

Ciric and Gu (1994) present a MINLP-based approach for the design of RD columns for systems where multiple reactions take place and/or where reactive equilibrium or thermal neutrality caimot be assured. This method is based on the combination of a rigorous tray-by-tray model and kinetic-rate-based expressions to give basic constraints of an optimization model that minimizes the total annual cost. The major variables are the number of trays in the column, the feed tray location, the temperature and composition profiles within the column, the reflux ratio, the internal flows within the column and the column diameter. 

Although the MDEA/piperazine process can be modelled in a very similar fashion to MDEA-only (Section 2.3) using the ElecNRTL physical property approach in Aspen Plus, the ions of piperazine and their electrolyte reactions in Eqs. (14)-(17) are not contained in the Aspen Properties database. Therefore, the electrolyte wizard cannot be used to add the equations and their components, and instead they must be added in manually. Once the components have been added, the electrolyte reactions can then be manually added in the Chemistry section (be sure to include it in the same chemistry specification which also includes the MDEA electrolyte reactions). Note that newer versions of Aspen Plus now include a simple example for using this setup in the Examples folder (select ElecNRTL Rate Based PZ+MDEA Model.bkp). It is usually easier to start with this file and modify it for your own purposes than it is to enter the data manually. 

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. 

It should be stated that the number of equations in this approach is very large, and specialized computer programs have been developed far their solution. Our objective here is very limited, namely to provide an idea of the basis of these equations. The basic set of equations in such rate based or nonequilibrium models of a distillation plate/ stage is sometimes referred to as the MERSHQ equations (Taylor et id., 2003), with each letter representing equations for a particular aspect of the problem for any plate n of the n-component system. 

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