Modelling reactive distillation

5202 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229which adopts the assumption of physical equilibrium,ideal mixing, thermal equilibrium with a chemical reactioncon"ned to the liquid-phase. Column hydraulics isaccounted for through a pressure drop equation anddepartures from equilibrium can be modelled usinga Murphree-type e$ciency factor. Extensive numericalresults are provided. The authors state that their programcan be used to study unsteady and unstable columnoperations such as start-up, shutdown and abnormalhydraulic column behaviour. The package allows fora number of standard thermodynamic property packs aswell as user-supplied models. Scenna, Ruiz and Benz(1998) employ READYS to study the start-up of RDcolumns. They show that the start-up policy can havea strong in#uence on the ultimate steady-state behaviourby sending the column to an undesirable operating point.READYS and Aspen Plus were used by Perez-Cisneros,Schenk, Gani and Pilavachi (1996) and Perez-Cisneros et al. (1997b) who also discussed their ownsomewhat di!erent approach to the EQ model. Theirmodel uses chemical &elements' rather than the actualcomponents. The chemical elements are the moleculeparts that remain invariant during the reaction. Theactual molecules are formed from di!erent combinationsof elements. A bene"t of this approach is that the chemicaland physical equilibrium problem in the reactivemixture is identical to a strictly physical equilibriummodel. A comparison with the RD data of Suzuki et al.(1971) is provided and it is noted that these data aredi$cult to match unless the `"tteda activity coe$cientmodel is used.Gani, Jepsen and Perez-Cisneros (1998) describeda generalised reactive separation unit model. Theirs is anunsteady-state EQ stage model that can handle systemsboth with and without reactions and with more than two#uid phases. The methodology is quite unique in that it isbased on the element approach of Perez-Cisneros et al.(1997b). Several numerical examples cover a range ofsimulation problems. Pilavachi et al. (1997) use the sameapproach, but their paper does not dwell on the computationalmethods; rather its focus is on some of theparameters that are important in RD modelling. Forexample, they discuss the e!ect of thermodynamic modelsand their parameters on RD simulation.Abufares and Douglas (1995) use an EQ stage modelfor steady-state and dynamic modelling of an RD columnfor production of MTBE. The steady-state model isRADFRAC from Aspen Plus. The unsteady-state modelequations are solved using SpeedUp, a commercial dynamicprocess simulation program. The focus of thispaper is the transient response of the system.Alejski and Duprat (1996) described a dynamic modelfor modelling kinetically controlled RD processes. Themodel is based on the conventional assumptions of negligiblevapor-phase hold-up and perfect mixing of the twophases. Departures from phase equilibrium could be handledby speci"cation of a vaporisation e$ciency, andcorrections of the conversion due to imperfect mixing areaccounted for using a `conversion e$ciencya, the latterbeing calculated from an eddy di!usion model in terms ofthe Peclet number. The model is compared to data obtainedin a pilot-scale column for the esteri"cation ofethanol with acetic acid and sulphuric acid as homogeneouscatalyst. Column start-up and disturbances ofcontinuous operation were investigated. The dynamictemperature pro"les are in reasonable agreement withthe data, but the predicted dynamic concentration pro-"les are very di!erent from the observed pro"les. Alejskiand Duprat (1996) also recommend that tray hydraulicsbe accounted for in any dynamic model of RD.Schrans, de Wolf & Baur (1996) carried out dynamicsimulations, using SPEEDUP, of the MTBE synthesisprocess using essentially the Jacobs}Krishna columncon"guration shown in Fig. 20(a). Their simulationsshowed that increase in the iso-butene feed by 4% leadsto oscillatory behaviour. A further increase of iso-butenefeed by 5% causes a jump from the high-conversionsteady-state to the lower one. Hauan, Schrans and Lien(1997) also showed oscillatory behaviour and suggestedthat it is due to an internal recycle of MTBE in thereactive zone.Sneesby, TadeH , Datta & Smith (1997a) model the synthesisof ETBE using an EQ stage model that they solvewith SpeedUp. Simulation results are compared to resultsobtained with the commercial simulation programPro/II. Homotopy methods are used to investigate thee!ects of important design variables (feed composition,ethanol excess, pressure, number of equilibrium stages* reactive or non-reactive, reboiler duty and so on).A process design methodology is suggested. In a companionpaper Sneesby, TadeH , Datta and Smith (1997b) developa dynamic model of the same process using SpeedUp.Their dynamic model assumes that reaction equilibriumis attained on all stages, neglecting reaction kinetics. Theauthors recommend including control issues early in thedesign process. Subsequent papers from this group lookat multiple steady-states in RD (Sneesby, TadeH & Smith,1998c}e). Sneesby et al. (1998d) (as well as Bartlett andWahnscha!t (1998) using RADFRAC) report that thetransition from one steady-state to another can be preventedusing appropriate control strategies. Sneesby et al.(1998a) show that an increase in fractionation (by increasingre#ux ratios, or numbers of equilibrium stages)does not always lead to improved performance of RDcolumns. This is exactly opposite to the situation inconventional distillation.Espinosa, Martinez and Perez (1994) presented a simpli"eddynamic model for an RD column. Vapor holdups,heat losses to the environment and the heat ofreaction were neglected. In addition, equimolar over#owand physical and chemical equilibrium were assumed.The resulting equations were rewritten in terms of the