Modelling reactive distillation

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5213Fig. 25. The non-equilibrium cell model of Higler, Krishna and Taylor(1999a).over the cross-sectional area of the column can lead toloss of interfacial area. This is known to be one of themain reasons for inadequate performance of packed columns.To deal with this shortcoming of earlier models,Higler, Taylor and Krishna (1999c) and Higler,Krishna and Taylor (1999a,b) developed an NEQ cellmodel. The distinguishing feature of this model is thatstages are divided into a number of contacting cells, asshown in Fig. 25. These cells describe just a small sectionof the tray or packing, and by choosing an appropriateconnection pattern, one can very easily study the in#uenceof #ow patterns and maldistribution on the distillationprocess.Flow patterns on distillation trays are modelled bychoosing an appropriate number of cells in each #owdirection. A column of cells can model plug-#ow in thevapor phase, and multiple columns of cells can modelplug-#ow in the liquid-phase as depicted in Fig. 26.Backmixing may also be taken into account by using anappropriate number of cells. This may be derived fromcalculating an equivalent number of cells from eddydi!usion models. Flow patterns in packed columns areevaluated by means of a natural #ow model. The #owsare split up according to the ratio of the cell surface areasbetween the cells. Various #ow patterns may be approximatedusing di!erent #ow splitting policies.A schematic diagram of the unit cell for a vapor}liquid}porous catalyst system is shown in Fig. 27. Eachcell is modelled essentially using the NEQ model forheterogeneous systems described above. The bulk of bothvapor and liquid-phases is assumed to be completelymixed. Mass transfer resistances are located in "lms nearthe vapor/liquid and liquid/solid interfaces, and the Maxwell}Stefanequations are used for calculation of themass transfer rates through each "lm. Thermodynamicequilibrium is assumed only at the vapor}liquid interface.Mass transfer inside the porous catalyst may bedescribed with the dusty #uid model described above.The unit cell for homogeneous systems (and for heterogeneoussystems modelled as though they were homogeneous)is as depicted in Fig. 23. The equations for eachcell are essentially as given above.For RD, the staging in the liquid-phase could havea signi"cant in#uence on the reaction selectivity. This isemphasised in the study by Baur et al. (1999) of thein#uence of hardware design on the formation of theby-product DEG in the hydration column (sieve tray)shown in Fig. 24(a). Their simulation results are presentedin Fig. 28. For "ve mixing cells in both vapor andliquid-phases (which corresponds closely to plug-#owconditions for either phase), the formation of by-productDEG is reduced while the conversion to EG is increased.Removing the mass transfer resistances, i.e. assuming theEQ model, gives the best performance with respect toconversion and selectivity; see the point towards thebottom right of Fig. 28. Reaction selectivity can be in-#uenced by tray hardware design. Decreasing the weirheight from 80 mm (base case) to 50 mm decreasesformation of EG and increases by-product DEG formation.This reduction is due to a lowering in the interfacialarea with decreasing weir height. Increasing the weirheight from 80 to 100 mm leads to improved conversionand improved selectivity. High weir heights, and operationin the froth regime, are generally to be preferred inRD operations. Increasing the number of passes from1 to 2 increases by-product formation; see the top pointin Fig. 28. This is because the liquid load per weir lengthis reduced by 50%. This reduction in the liquid load leadsto a reduction in the clear liquid height and lowering inthe total interfacial area, which has a detrimental in#uenceon both the conversion and selectivity. It appearsthat the usual design rules for conventional distillationcolumn design cannot be carried over to RD columnsbecause, for a column of 1.7 m diameter the conventionaldesign philosophy would be to use two passes for theliquid #ow.5.5. Pseudo-homogeneous vs. heterogeneous NEQmodellingHigler, Krishna and Taylor (2000) used the dusty #uidequations to model di!usion and reaction in porouscatalysts in RD. The MTBE process (following thecon"guration of Jacobs and Krishna (1993) shown in