A FILM MODEL ANALYSIS OF NON-EQUIMOLAR DISTILLATION OF MULTICOMPONENT MIXTURES zyxwvutsrqponmlkjihgfed RAJAMANI KRISHNAt Department of Chemical Engmeermg, Umverslty of Manchester Institute of Science and Technology, Sackvdle Street, Manchester M60 lQD, England Abstract-Ddferences m the molar heats of vaporlzatlons of component species m a multlcomponent mixture lead to non-equrmolar mass transfers dunng dlstdlatlon separations The interphase mass transfer process IS analysed usmg a film model and a procedure developed for calculatmg multlcomponent transfer coefficients and transfer rates from mformation on binary transport coefficients and partial molar enthalples of the constituent species m either flmd phase It IS shown wtth the aid of a numencal example that the commonly made assumption of eqmmolar transfer durmg distdlatlon may Iead to significant errors m the calculation of constituent species transfers INTRODUCTION The zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA two-film resistance model 1s widely used for calculating the transfer efficlencles for dlstlllatlon operations[l-31 For a tray column the first step m the calculation of the overall column efficiency 1s the determmatlon of the pomt efficiency For binary se- parations ZOp,,, the point vapour efficiency, ISusually reIated to the overall number of vapour phase transfer umts KY-Q by Zp,, = 1 - exp (-NY21,,) (1) The overall number of vapour phase transfer units N.T??&,, IS calculated from the partial numbers of transfer umts m the vapour and hquld phases usmg the addltlvlty of resistances formula For packed column dlstlllatlon design the transfer efficiency LS reflected m the overall height of a transfer unit XT% _,, calculable from the mdlvldual heights of transfer umts for the vapour and liquid phases by use of the relation [3] The addltivlty of resistances formulae (2) and (3) above are derived from the formula for addltlon of mass transfer coefficients xi; = XY-’ + rnXX ’ (4) Stnctly speakmg eqns (2)-(4) are valid only for bmary systems under condltlons of low mass transfer rates As discussed by Bird, Stewart and Llghtfoot[4] the effect of finite to high transfer rates on binary systems IS to alter the composltlon profiles m the dlffuslon zone and thus tPresent address Department EE, KomnkhJke/Shell-Labora- tormm, Amsterdam, Badhulsweg 3, Postbus 3003, Amsterdam- Noord, The Netherlands alter the values of the mass transfer coefficients themselves The analysts of the effect of fimte mass transfer rates on the transport behavlour of multlcom- ponent systems has been carried out by Stewart [5,6] and others [7,8] Tradltlonally rn the mass transfer analysis of dlstlllatlon processes, the assumption of equlmolar transfer Nr = 2 iq = 0 a=1 IS made, vahdatmg the relations (2) and (3), at least for bmary systems The basis of the assumption (5) 1s that the molar heats of vaporlzatlons of many chemical species have values close to one another For the mixture ethanol-water, for example, the molar heats of vaponza- tlon differ by about 5% In general case an energy balance at the interface between the vapour and hquld phases must be consldered m addltlon to the mass balance relations Sigmficantly different molar latent heats would lead to net condensation or evaporation and the con- sequent timte transfer rates would alter the mass transfer coefficients and invalidate equations (2)-(4) The slmul- taneous heat and mass transfer process dunng dlstlllatlon of binary mixtures has been consldered by many authors[9-161 but a proper treatment for multlcomponent mixtures does not seem to have been carried out Multlcomponent systems show many transport charac- terlstlcs not possible for slmpl5 two component systems, dIffusIonal Interacttons m multlcomponent systems can give rise to osmotic dlffuslon, diffusion barrier and reverse dlffuslon as discussed in detail by Toor[l7] It IS the purpose of this paper to consider a local film model analysis of non-equlmolar mass transfer process durmg multlcomponent dlstlllatlon Proper account 1s taken m the analysis of the posslblhty of dlffuslonal mteractlons between the transferring species Such dlffuslonal mteractlons become slgmficant m systems made up of species with widely different molecular sizes and nature, 1 e non-ideal systems For such systems one may expect the molar latent heats to also be slgmficantly different and therefore it may be antkclpated that for systems showing large non-ldeahtles both multlcomponent dlffuslonal interacttons and effects due to non-eqmmoiar transfer 1197