SIMULATION OF HEAT AND MASS TRANSFER OF A CO2 BINARY MIXTURE, IN THE MISCIBLE CONDITIONS OF A SUPERCRITICAL ANTISOLVENT PROCESS

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1 SIMULATION OF HEAT AND MASS TRANSFER OF A CO2 BINARY MIXTURE, IN THE MISCIBLE CONDITIONS OF A SUPERCRITICAL ANTISOLVENT PROCESS T. Fdli, A. Erriguile*, S. Lugier, P. Sur-Pternult Université de Bordeux, Lortoire TREFLE, site ENSCPB, 16 venue Pey-Berlnd, Pessc, Frnce ; erriguile@enscp.fr A coplete description of the Supercriticl Antisolvent Process requires the odelling of severl coplex physicl phenoen such s het nd ss trnsfer, hydrodynic, phse equiliri of ternry ixtures, nd nucletion /growth of the specie to e precipitted; oreover, the description should lso ccount for the iphsic cse, where the jet of orgnic solvent reks up s droplets. As first step, we focus on the siultion of ss nd het trnsfer of inry CO2-solvent ixture in iscile conditions, sed on the pioneer work developed y Werling nd Deenedetti. The syste is descried s spot of pure solvent iersed in pure cron dioxide, ut copred to Werling s work nd further pulictions, we explore conditions where the tepertures of the solvent nd the fluid re different; hence, our clcultions llow to tke into ccount the het trnsfer in the ixture. The evolution of the spot size is detiled for vrious conditions of pressure nd teperture, nd for two CO2-ixtures. INTRODUCTION Crystlliztion is key opertion in powder technology since chrcteristics of produced prticles will influence the teril finl properties, nd ore specificlly iovilility or stility when ctive phrceuticl ingredients re considered. Properties like prticle en size nd prticle size distriution re influenced y oth therodynic nd kinetic fctors, nd when precipittion is induced y the ddition of third specie, the tie nd spce scles t which the ixing occurs ecoe significnt. Literture provides nuerous exples of crystllistion induced y CO 2 ; lthough the effect of severl operting preters on the product chrcteristics is evidenced, contrdictory trends could e otined. Moreover, the potentil interctions etween preters nd the diversity of the processed systes render the interprettion quite difficult. Hence, nuericl pproch ecoes fundentl either to identify the controlling phenoen, either to optiize the process ccording to sustinility concepts. In this rticle, we focus on the description of het nd ss trnsfers tht occur when pseudo droplet of solvent is iersed in copressed ntisolvent in iscile conditions, in the i of investigting ore specificlly teperture effects. This work is sed on the theticl odel for ss trnsfer lredy proposed y Werling nd Deenedetti [1]. Elvssore et l. [2] further refined the Werling s pproch y tking in ccount the solute. The diffusion in the ternry is tken into ccount with the generlised Mxwell-Stefn equtions. In the first prt, the odelling of the het nd ss trnsfers in the inry ixture is presented. In second prt, the odel is pplied for two ixtures, i.e. toluene/cron dioxide

2 nd ethnol/cron dioxide. Siultions re chieved in isotherl conditions nd non isotherl conditions, i.e. when tepertures of solvent nd CO 2 re different. MODELING OF THE HEAT AND MASS TRANSFER IN THE BINARY MIXTURE The equtions re in ter of olr quntities nd the suscript denotes the cron dioxide nd the solvent. In the supercriticl regie, the solvent nd the ntisolvent re fully iscile so only one eqution is needed to descrie the ss trnsfer. We ssue tht the ediu is stgnnt so the convective flux cn e neglected. The ss trnsfer is only ffected y diffusion so the ss lnce eqution, ccording to the Fick s lw, reds to: ρx t + ( ρd x ) 0 where ρ represents the density of the inry ixture, x the ole frction of the cron dioxide nd D the diffusion coefficient of the solvent in the cron dioxide estited with the Wilke nd Chng correltion [3]. The viscosity of the ediu, required in the clcultion of the diffusion coefficient, is estited with the Stiel nd Thodos reltionship [4]. The ole frction of the solvent is directly deduced y the reltion: x 1 x The teperture field is otined y solving the conservtion eqution of energy. Assuing tht the viscous energy dissiption cn e neglected nd y considering tht there is no het source, the conservtion eqution of energy is written s follows: T ρ C p ( λ T) 3 t where C p nd λ re respectively the het cpcity nd the het conductivity of the ixture. We consider tht in the rnge of the investigtion, het cpcity nd therl conductivity for ech coponent re constnt t given pressure. So the het cpcity nd therl conductivity for the inry ixture is given y: C x C + x p λ x λ p + x λ C p In the supercriticl regie, cron dioxide is dense fluid which will lter the coposition nd the density of the droplet in highly non idel wy. The Peng Roinson eqution of stte ws chosen to clculte the fluid density ecuse of its ility to predict phse equiliri, its reltive ccurte density prediction t high pressures, nd its ese of ppliction. The Peng Roinson eqution is written s: P RT v 6 v ( v + ) + ( v ) where the ixture preters nd re given y the following ixing rules, with the nd preters function of the criticl properties of individul species:

3 i j 0.5 ( ii jj ) ( 1 k ) x ix j i ( ii + jj ) ( 1 l ) 2 x x i j The criticl properties nd the inry interction preters for cron dioxide, toluene nd ethnol used in this work re reported in the tle 1. 7 Pc (r) Tc (K) olr ss (g/ol) k l CO Ethnol Toluene Tle 1: Criticl properties nd the inry interction preters for cron dioxide (ntisolvent), toluene nd ethnol SIMULATION AND RESULTS The syste of equtions is solved in order to otin the concentrtion nd teperture fields over the doin. The siultion tool ws sed on the Coputtionl Fluid Dynic lirry Aquilon, developed t TREFLE lortory. Aquilon contins set of discretiztion schees, solvers nd odels tht were deeed interesting for siulting this kind of prole. The pproxitions of the conservtion equtions were sed on regulr sphericl grid nd finite volues. For concentrtion nd teperture, the tie discretiztion is chieved with n iplicit Euler schee of first order; the spce discretiztion for energy is second order centered schee, whilst for the ss trnsport, TVD schee is used (Totl Vrition Diinishing) since it is prticulrly well suited for diffusion proles. The liner syste is solved t ech tie step, n itertive i-conjugte grdient stilized BICG-St II [5] preconditionned under odified nd Incoplete LU ethod is used. Configurtion nd initil/oundry conditions re shown in figure 1. The grid consists in cells. The initil rdius of the solvent droplet is fixed to 50 μ nd the rdius of the ntisolvent doin to 500 μ. Figure 1: Configurtion, initil nd oundry conditions for the study

In supercriticl conditions, the question of defining the droplet rdius rises, ecuse of the coplete isciility of the species even if pseudo droplet exists s we cn rerk in figure 2 which represents the

As first step nd in order to tch Werling pproch, the droplet rdius ws defined y cutoff vlue of density which llowed for distinguish solvent-rich nd n ntisolvent-rich zones.

4 In supercriticl conditions, the question of defining the droplet rdius rises, ecuse of the coplete isciility of the species even if pseudo droplet exists s we cn rerk in figure 2 which represents the evolution of the density profiles of the inry ixture. As first step nd in order to tch Werling pproch, the droplet rdius ws defined y cutoff vlue of density which llowed for distinguish solvent-rich nd n ntisolvent-rich zones. More detils cn e found in the rticle [1]. The cutoff vlue of the density is defined y: where ρ ρ cutoff cutoff ρco 2 ρ ρ nd CO2 CO ( ρx ρco ) if ρ 2 solvent ρco2 ( ρco ρ ) 2 solvent if ρsolvent ρco2 ρ solvent re the pure densities of the cron dioxide nd the solvent nd ρ x is the xiu ss density ttined y the inry ixture which cn e significntly greter thn the pure coponent densities [6] s 0.1s 0.27s 0.285s ) 90 r ρ (kg/ 3 ) 0.005s 0.015s 0.025s 0.03s ) 360 r ρ (kg/ 3 ) Figure 2: Evolution of the density profiles of the ixture CO 2 /Toluene t 318K for two pressures. Blck circle represent the effective droplet rdius defined y the criteri of Deenedetti. Isotherl conditions In isotherl conditions, solvent nd ntisolvent regions hve the se teperture. The figure 3 nd 3 show the evolution of the droplet rdius in cse of toluene nd ethnol s solvents, for different pressures. The Toluene cse displys the se ehviour thn descried in Werling s pper, hence, vlidting our clcultions. Copred to toluene, ethnol lso undergoes n expnsion t low pressure, nd shrinking ehviour for pressure ove 14 MP. The droplet ehviour is governed y the density differences etween the solvent-rich nd the ntisolvent-rich doins. When the pure solvent density is significntly higher thn the ntisolvent one, the droplets swell (figure 2); this swelling is ore pronounced t lower pressures due to the lrgest differences in densities. On the other hnd, when the CO 2 density is greter thn the solvent one, droplets re shrinking (figure 2); t very high pressure, the droplet lifeties re very short.

5 110 r 135 r 90 r ) 75 r ) 295 r 320 r 360 r 140 r 350 r Figure 3: ) Evolution of toluene droplet rdius t 318K nd for different pressures. ) Evolution of ethnol droplet rdius t 300K nd for different pressures. Non-isotherl conditions Clcultions were now perfored in cse of non-isotherl conditions, where solvent nd ntisolvent regions hve different tepertures. Figures 4 nd 4 show the droplet evolution t 14 nd 35 MP in cse of ethnol, considering tht the solvent ( suscript) is wrer thn cron dioxide. T 0 300K T 0 360K ) T 0 300K ) T 0 360K T 0 T 0 300K T 0 T 0 300K Figure 4: ) Evolution of ethnol droplet rdius t 140 r nd for different initil tepertures. ) Evolution of ethnol droplet rdius t 350 r nd for different initil tepertures. The influence of the teperture difference is quite significnt. When the solvent teperture increse, the pure density of the solvent decreses nd consequently the difference etween the solvent-rich region nd the ntisolvent-rich region is greter; s result, in coherence with the pressure effect descried erlier, the increse of teperture increses the droplet lifeties. Extr nuericl experients re currently in progress to vlid this ssuption. CONCLUSION This work developed odel of het nd ss trnsfer etween droplet of solvent nd copressed ntisolvent in iscile conditions, in order to ephsize the role of density or teperture on the droplet lifetie. Results for isotherl conditions llows for coforting the nuericl schee since results closely tched the ehviour reported y Werling nd

6 Deenedetti. First results otined in non-isotherl conditions indicte tht teperture grdient cn provide n opportunity to tune the droplet lifetie, esides the pressure effect. Extr nuericl clcultions re currently in progress to enlight the role of the density difference on the expnsion/shrinking ehviour nd on the shrinking tie. REFERENCES : [1] Werling, J. O., Deenedetti, P. G., Nuericl odeling of ss trnsfer in the supercriticl ntisolvent process: iscile conditions, Journl of Supercriticl Fluids, Vol. 18, 2000, p 11. [2] Elvssore, N., Cozzi, F., Bertucco, A., Mss trnsport odeling in Gs Antisolvent Process, Ind. Eng. Che. Res., Vol. 43, 2004, p [3] R. Reid,, J. Prusnitz, B. Poling, The Properties of Gses & Liquids, 5 th ed. Mc Grw-Hill, [4] A. Bertucco, G. Vetter, High Pressures Process Technology: Fundentls nd Applictions, Industril Cheistry Lirry, Vol. 9, [5] I. Gustfsson, On first nd second order syetric fctoriztion ethods for the solution of elliptic difference equtions, Chlers University of Technology, [6] C.J. Chng, C.Y. Chen, H.C. Lin, Soluilities of cron dioxide nd nitrous oxide in cyclohexne, toluene nd N,N-diethylforide t elevted pressures, J Che. Eng. Dt, Vol. 40, 1995, p 850.

Ideal Gas behaviour: summary

Ideal Gas behaviour: summary Lecture 4 Rel Gses Idel Gs ehviour: sury We recll the conditions under which the idel gs eqution of stte Pn is vlid: olue of individul gs olecules is neglected No interctions (either ttrctive or repulsive)