Multicomponent Mass Transfer Krishna

[Etta Lesniak]

Asimple non-equilibrium modeling approach is proposed to simulate multicomponent distillation process in packed columns. The real behavior of the column is simply considered by the evaluation of interphase mass transfer rate based on the overall mass transfer coefficient. Two distinct methods are used to calculate this overall coefficient including the effective mass transfer coefficient method and the packing efficiency method. The modelling procedure consists of an iterative segment-wise algorithm implemented in a MATLAB home-code. For verification, the obtained composition profiles from a structured and a random packed column are compared with reported experimental data. Comparisons show that the packing efficiency-based model could acceptably predict the experimental profiles with an average relative deviation of 18% and 25% for structured and random packed columns, respectively. This confirms that our simple non-equilibrium approach is a reliable and robust model for the performance evaluation of packed columns.

The Maxwell-Stefan (M-S) equations [Maxwell (1866), Stefan (1871)] describe the process of diffusion, where diffusive fluxes, Ji, of species through a plane, across which no net transfer of moles occurs, depend on all (n-1) independent driving forces in a mixture of n species. Their predictions, in particular that a species need not diffuse in the direction of its own driving force, have been confirmed by reliable experimental studies, e.g., Duncan & Toor (1962). A recent text describing their formulation, development and applications is Taylor and Krishna (1993) who quote them as,

In ideal mixtures at constant temperature and pressure, the left hand side simplifies toorfor one space dimension. Theik diffusivities are then the widely available binary diffusivities,ik. Further simplification for a binary gives Fick's Law. Equation (1) has been used to describe many processes, notably Distillation and Condensation. For a film model of interfacial transport, Krishna & Standart (1977) show an exact solution. The M-S equations are often written in matrix form, explicit in diffusive flux. Here braces and square brackets denote (n-1) column and square matrices, respectively, and normal matrix products are implied,

The second term in Equation (2) is the generalized form of Fick's Law and the composition dependence of the diffusion coefficients [D] is clear through the stated relationship with the M-S equations. Equation (2) is the origin of the Linearized Theory approach of Toor (1964) and Stewart & Prober (1964), which can be applied generally to film, surface renewal and boundary layer models of mass transfer. It also shows the dependence on activity coefficient, γ, in nonideal mixtures. Theik then become composition dependent, but may in some cases be estimated from binary diffusivities,, at infinite dilution, Taylor & Krishna (1993). The Maxwell-Stefan equations are the correct description of multicomponent mass transfer and their usage is steadily broadening as experimental evidence supporting their better applicability mounts.

The ChemSep Consortium has been created to provide for the furtherdevelopment of the ChemSep nonequilibrium model. Benefits of membership include:Access to the Cape-Open version that allows ChemSep to function with any Cape-Open compliant flowsheet simulation program, with more components and stages,The opportunity to use ChemSep throughout the member organizationAccess to new models as soon as they become available,Provide input into the research and development activities carried out by the consortium.Access to DIPPR 801 physical properties libraries in ChemSep readable format if sponsors have a license to the DIPPR materialsOne of the consortium's goal is to improve nonequilibrium models in general and theChemSep package in particular. Currently we are developing further the modelsidentified below:A model for three phase distillation,Advanced models for better description of fluid flow effects in packed and tray columns,Fundamentally sound mass transfer and hydrodynamic performance models,Models for reactive distillation,Unsteady state nonequilibrium models.These developments are described in more detail below. For more information on theChemSep consortium (including membership fees) please contact professorRoss Taylor atta...@clarkson.edu.Current members include:

Three-phase distillation remains relatively poorly understood comparedto conventional distillation operations involving just a single liquidphase. Simulation methods currently in use for 3-phase systems employthe equilibrium stage model, although the accuracy of availablethermodynamic models in predicting the highly non-ideal Vapor - Liquid- Liquid (VLL) equilibrium of these systems leaves something to bedesired. It is important to be able to correctly predict the locationof the stages where a second liquid phase can form (to determine theappropriate location for a sidestream decanter, for example). Thelimited experimental data available suggests that efficiencies are lowand highly variable with between 25% and 50% being not uncommon.Clearly, a model based on the assumption of equilibrium on every stagecannot hope to be able to predict column performance.

The material balances for a three phase system must allow for masstransfer to or from both of the other two phases. In addition, themodel contains up to six sets of mass transfer rate equations. Threesets of equilibrium equations, one for each possible interface, must beincluded in the model. Estimating mass transfer coefficients andinterfacial areas for three-phase systems is more difficult since thereare no published correlations; hence theoretical approaches arenecessary and are described in the references.

An issue that is not adequately addressed by most models is that ofvapour and liquid flow. Liquid flow patterns have a particularly stronginfluence on the performance of the column. ChemSep includes adispersion model to better describe liquid flows in columns. Cellmodels also have been developed in which stages are divided into anumber of contacting cells. Each cell describes a small section of thetray or packing, and by choosing an appropriate set of cellconnections, one can very easily study the influence of flow patternson the distillation process. A column of cells can model plug flow inthe vapour phase, and multiple columns of cells can model plug flow inthe liquid phase as depicted in the figure. Backmixing also may betaken into account. Flow patterns in packed columns (e.g.maldistribution) may be studied by means of a cell model.The objective of this phase of our work is to incorporate these modelsinto Cape-Open ChemSep.

Alternatively, ChemSepH.A. Kooijman, R. Taylor, Modelling Mass Transfer in MulticomponentDistillation, Chem. Eng. J., Vol. 57, No. 2 (1995), pp. 177-188. A. P. Higler, R. Krishna, and R. Taylor, A Nonequilibrium Cell Modelfor Packed Distillation Columns G The Influence of Maldistribution Ind.Eng. Chem. Res, 38, 3988-3999, 1999.Fundamentally sound mass transfer and hydrodynamic performance modelsThough ChemSep already comes with many mass transfer and hydrodynamicmodels, the need for more fundamentally sound models still remains. Mostmodels were derived empirically via directly fitting tray efficiencies ongeometry parameters and flowrates.As a result these models depend directly on the vapour flow or the tray weirheight instead on those parameters that actually determine the mass transfer,such as bubble diameters which determine the bubble rise velocity and bubbleinterfacial area.Implicitely, the bubble diameter and velocity are functions of the vapour flowand weir height, but then with more interrelated dependencies on the traygeometry, physical properties, and flow rates than as used in the "1st generation"type of mass transfer correlations.Consequently these correlations are limited in their applicability and a largenumber of them is needed to model all the different kinds of separations.Furthermore, new enhanced capacity mass transfer internals now on the marketoperate differently and require new performance models.The ChemSep consortium develops more fundamental "2nd generation" models fromfirst principles and tries to fit the parameters on available distillation andabsorption test data to obtain a generic kind of model.

Such new models are implemented in the ChemSep Model Developer whichallows the user to add any new kind of internal or model.The layout parameters of new internals can consist of switches, multiple choiceselections, or internals dimensions.The GUI can handle the entry for all.The program code for the new model or internal is compiled with the free OpenWatcomcompilers and then is linked dynamically to ChemSep.With the build in debug option the code can be tested and validated.The result is a new model or internal that can be used by any user after sharinga dynamic link library (DLL).DLL's enable the encapsulation of proprietary model information while still allowingothers to use the model.It also allows the in-house development of only those parts that are really neededwhile reusing the generic framework of a robust column simulator.This all can be done with minimal programming efforts to keep the focus on describingthe performance of the separation device itself.

The design and operation issues for reactive distillation processes aremore complicated than those of either conventional reactors orconventional distillation columns. The presence of chemical reactionswithin the column leads to complex interactions between vapor-liquidequilibrium, vapor-liquid mass transfer, intra-catalyst diffusion andchemical kinetics. For such systems the chemical reaction influencesthe efficiencies to such an extent that the concept loses its meaning.

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