Simulation of the Semicontinuous Supercritical Antisolvent

Ind. Eng. Chem. Res. 2000, 39, 1487-1496

1487

Simulation of the Semicontinuous Supercritical Antisolvent Recrystallization Process Michele Lora,† Alberto Bertucco,*,† and Ireneo Kikic‡ Istituto di Impianti Chimici, Universita` di Padova, via Marzolo 9, 35131 Padova, Italy, and DICAMP, Universita` di Trieste, piazzale Europa 1, 34127 Trieste, Italy

A model is developed for simulating semicontinuous supercritical antisolvent recrystallization processes. Thermodynamics, hydrodynamics, and mass-transfer issues are addressed. The model makes it possible to calculate the composition and flow-rate profiles of the vapor and liquid phases and the amount of the solid product along the precipitator. The effect of the operating variables is discussed. With reference to a CO2-toluene-naphthalene-phenanthrene system, it is shown that the dissolution of the antisolvent in the liquid phase is usually faster than the evaporation of the solvent, that the two solutes may behave in completely different ways at the same process conditions (for example, phenanthrene can be easily precipitated, while for naphthalene a higher gas-to-liquid flow-rate ratio is needed, to force solvent evaporation), and that under proper operating conditions it is possible to selectively precipitate phenanthrene from a phenanthrene + naphthalene solution. Introduction The use of supercritical fluids as media for fine particle formation is finding widespread applications, above all in the pharmaceutical and fine chemical industries. Among others the most attractive technique seems to be the recrystallization with a supercritical fluid antisolvent (SAS). SAS is based on the fact that fluids in a dense gas state are usually soluble in organic solvents and in their solutions with the solutes to be crystallized. The dissolution of the gaseous antisolvent causes a remarkable volumetric expansion of the solution, lowers the solvent power of the mixed solvent, and forces the solute to precipitate. This technique has been the subject of a number of studies from various researchers, as can be seen in the proceedings of the last conferences about supercritical fluid technology (Sendai, Japan, 1997; Nice, France, 1998; Nottingham, England, 1999; see Reverchon1 for a recent review). The technique has been successfully applied to many different materials (biocompatible polymers, drugs, explosives, catalysts, and superconductors; see again ref 1). Both batch and semicontinuous modes of operation are used. In the batch case2 the organic solution containing the solid to be precipitated is loaded into the precipitation vessel; then, the vessel pressure is increased by feeding the supercritical fluid, and the solution is progressively expanded until the mixed solvent is no longer able to keep the heavy component solubilized. This mode of operation is simple to perform, but it is difficult to reach a uniform antisolvent composition in the expanded liquid and so a uniform supersaturation and precipitation rate. In addition, the system cannot be operated at a constant specified pressure, because it undergoes all pressure levels from ambient to the final value. All of these facts lead to a wider diameter distribution curve. * To whom correspondence should be addressed. Tel.: +39 049 8275457. Fax: +39 049 8275461. E-mail: bebo@ polochi.cheg.unipd.it. † Universita ` di Padova. ‡ Universita ` di Trieste.

To improve the productivity and to better control the operating conditions, the same antisolvent effect has been proposed and implemented in a number of semicontinuous devices,3-6 where both the liquid solution and the supercritical solvent are continuously fed at constant flow rates to the precipitation vessel. When a SAS process is performed in this way, the vessel has to be previously loaded with the antisolvent up to the selected pressure. The solution is fed through a nozzle, to obtain the maximum dispersion of the liquid in the gas phase and to maximize the interfacial area. Depending on the operating conditions, either two or three phases may be present in the vessel. After the desired amount of product is obtained, the solution feed is stopped but the flow of antisolvent is maintained to obtain solvent-free solid particles. Necessarily, the product recovery is always a batch step. Even if a large amount of experimental work has been performed, only little has been done to simulate these processes. For the batch case the authors have developed a model7 able to calculate the composition profile of the liquid phase at increasing pressure and to predict the precipitation pressure of the solute. The model is based on the hypothesis that the phases in the precipitator are time by time at equilibrium, so that hydrodynamics and mass-transfer problems are neglected. The same model can be used also to check if fractional crystallization is possible. On the other hand, few references can be found in the literature about the modeling of the semicontinuous process.8,9 This work is aimed to develop a model able to quantify the effect of operating variables on the semicontinuous SAS process. Flow rates and phase composition profiles along the precipitator are calculated, and it is shown that under proper operating conditions fractional crystallization is feasible and can be achieved easily also in a semicontinuous mode. Solvent Selection and Effect of Operating Pressure and Temperature It is useful to discuss some points about the effect of operating temperature and pressure and about the

10.1021/ie990685f CCC: $19.00 © 2000 American Chemical Society Published on Web 04/12/2000

1488

Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000

Figure 1. Phase behavior of the system CO2-toluene at different temperatures.

choice of the most suitable solvent for a given application. This part is developed before the discussion of the model, because in a continuous process, temperature and pressure are constant and their effect can (and should) be evaluated a priori. The qualitative discussion on the choice of the solvent will be complemented with some simulation results in the following sections. In this section (except where otherwise indicated) we refer simply to the system solvent-antisolvent: similar considerations hold also when the solute is added; it is more immediate to develop them with reference to binary systems. It is important to note that temperature and pressure affect above all equilibrium conditions, while their effect is less pronounced on hydrodynamics and mass-transfer coefficients. For example, in Figure 1 vapor-liquid (VL) equilibrium calculations for the system CO2-toluene at different temperatures are presented. Calculations are performed with the Peng-Robinson equation of state and one binary interaction parameter, whose value is available in the literature.10 We note that, at a given temperature and pressure, (a) the bubble-point lines provide a measure of the amount of CO2 soluble in toluene (antisolvent effect) and (b) the dew-point lines give an indication of how much toluene is soluble in gaseous CO2 (evaporation effect). When the temperature is increased, a higher pressure is needed to obtain the same concentration of CO2 in the liquid phase, so that the antisolvent effect is lower at increasing temperature. On the other hand, a higher temperature leads to higher solubility of the solvent in the gas phase, i.e., to a stronger evaporation effect. Operating temperature and pressure have to be selected accordingly: in particular, if the temperature is increased, the final washing process to extract the solvent from solid product is shorter; on the other hand, a higher pressure is needed for the antisolvent effect to be high enough to obtain the desired precipitation. It is also possible to increase the pressure up to the mixture critical point and over. In this case the two components are fully miscible, no interface is formed, and mass transfer is faster. On the other hand, the pressure required can be too high, also because the presence of the third component (the solute) shifts the mixture critical point to higher pressures. Another point is the solvent selection. Given that the antisolvent is CO2 (as usual for the applications we are referring to), the solvent has to dissolve the solute of interest to a significant extent and to be miscible enough

with CO2. With reference to the classification of Scott and van Konynenburg,11 the better case is that the system solvent-antisolvent is of type I, i.e., with a continuous mixture critical locus and without liquidliquid immiscibility. Instead, the occurrence of a type III or type IV phase behavior should be avoided if possible. In particular, type III is characterized by the presence of a L-L-V equilibrium and by two mixture critical points, a L-L one and a L-V one. If the L-L miscibility gap is narrow enough, this behavior can still allow a high antisolvent effect and the process can be carried out as well. Type IV systems exhibit again L-L-V equilibrium and a V-L critical point. However, both branches of the L-L equilibrium rise steeply with increasing pressure, and the maximum amount of antisolvent that can be solubilized in the liquid phase is low. So, if the system CO2-solvent is of type IV, the process is not likely to be performed. When a solute is added to the system, the miscibility gaps become larger (that is, the antisolvent effect gets smaller) because of the addition of a component which interacts better with the solvent rather than with CO2. The most popular organic solvents (benzene, toluene, ethyl acetate, acetone, and ethanol) show with CO2 a type I phase behavior; types III and IV occur when the solvent is largely different in size from CO2 (for example, CO2-squalane and CO2-hexadecane are type IV systems). If the selection is among different type I solvents, the solubility of CO2 in them is similar, and it is enough to vary pressure within a narrow range to obtain similar antisolvent effects. In this case the choice can be done with regard to the volatility of the solvent: to decrease the precipitated solute washing time, the most volatile solvent has to be chosen. Development of the Model A simple model has been built up, according to which the precipitation vessel is divided axially in elements of infinitesimal height dh, where the axial coordinate h is the independent variable. The hydrodynamics and mass-transfer equations are written as differential equations with reference to such an element. The flow rates, compositions, drop velocities, and drop diameters are supposed to be constant within each element. Starting from the top of the precipitator, the system is integrated numerically along with h. Only steady-state calculations have been performed. The model has been primarily developed with reference to the binary system solvent-antisolvent to study hydrodynamics and mass transfer. When a third (and a fourth) heavy component is added in small amounts, hydrodynamics and mass-transfer properties of the system are supposed not to be modified. Thermodynamic relations are used to calculate whether the liquid phase becomes saturated in each solute, thus allowing precipitation to occur. Another important assumption is that the system is isothermal. It is well-known that thermal effects might be relevant in SAS processes; however, in this initial modeling effort, it seems reasonable to make the approximation of constant temperature. In the following paragraphs, the equations of the model are developed. First the thermodynamics of binary, ternary, and quaternary systems is addressed. Then the hydrodynamic study is presented, and equations are developed for calculating drop velocity and interchange area profiles along the precipitator. Finally,

Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000 1489

mass-transfer coefficients, flux equations, and material balances are put together to allow the calculation of flow rate and composition profiles along the precipitator. Thermodynamics. In the binary system solventantisolvent, the equilibrium composition of the two phases is unique: the system has 2 degrees of freedom, which are fulfilled when temperature and pressure are set. The equilibrium compositions are calculated once by means of the Peng-Robinson equation of state (PR EOS) with classical mixing rules and used throughout the simulation. When a third or fourth component is added, the equilibrium composition at the V-L interface is calculated by imposing the solid (S)-L-V equilibrium condition. To calculate when the liquid bulk becomes saturated in solute, at every step the fugacity of the solute in the liquid is compared to that of the pure solid solute at the same temperature and pressure. For the pure solid solute fugacity, an approach developed by Kikic et al.13 is used. It applies the PR EOS to calculate the fugacity of the solute at a pure liquid reference state and its heat of fusion and melting temperature to bridge the gap to the real solid state. Note that each solute is supposed to precipitate as a pure substance, and the formation of a solid solution is not considered.7,12 It is assumed that saturation is reached when the fugacity of the solute in the liquid phase becomes higher than that of the solid solute. A certain amount of supersaturation is actually needed to obtain precipitation, but here we suppose that precipitation occurs at equilibrium conditions, i.e., when the fugacities of the solute in the liquid become equal to that in the solid phase. From this point onward the mole fraction of the solute in the liquid phase is no longer given by a mass balance, but it is calculated from the isofugacity equation; the solute mass balance allows one to evaluate the amount of precipitated solute. Hydrodynamics. The aim of the various injection devices proposed in the SAS literature is always to obtain a uniform dispersion of small liquid droplets into the continuous gas phase and to increase the interface area and mass-transfer rate. When a liquid is forced through a nozzle, at the nozzle exit it forms a continuous cylindrical jet with a diameter equal to that of the nozzle. Once out of the nozzle, the jet is subject to cohesive and disruptive forces, essentially of three kinds:14 (a) the cohesive force is given by the surface tension that keeps the liquid phase together (drops, or jets as in this case), minimizing the surface per unit volume; (b) the friction between the jet and the surrounding gas is the first disruptive force, which is a function of the relative velocity between the two phases; (c) the turbulence of the jet itself is the second disruptive force. If the fluid motion in the nozzle is turbulent, radial velocity components are different from zero. Once the jet is out of the nozzle, these radial components are no longer contrasted by the nozzle walls and prevail rapidly over surface tension forces, leading again to jet breakup. The relative strength of these three forces causes different jet breakup mechanisms. When friction and turbulence are small, the so-called Rayleigh jet breakup occurs: it is caused by the interaction of surface tension forces with disturbances in the liquid; in this regime drops are larger than the nozzle diameter. When friction and/or turbulence become progressively larger, the so-called continuous length (defined as the distance

from the injection at which break-up occurs) decreases; the drops are irregular in diameter, but they become progressively smaller. At a certain point friction and turbulence are so large that break-up in very fine droplets occurs immediately out of the nozzle: this is the so-called atomization. Other factors are able to push the system to the atomization break-up mode. If the ratio between the nozzle length and diameter is low, turbulence is favored, because the liquid flow through the nozzle does not have enough time to evolve and stabilize. In fact, very short nozzles are usually used in order to decrease the pressure drop. Another factor increasing the turbulence is nozzle roughness. Also the role of pressure in the spray chamber is important, because of the effect on the gas viscosity: there is experimental evidence14 that the continuous length decreases significantly if the jet is injected in a high-pressure gas. Finally, different solvents (with different viscosity and surface tension) can behave in a completely different way also with the same spraying device. To improve atomization, a low-viscosity and low surface tension solvent has to be used. Unfortunately, no correlations accounting for all of these factors are available for the estimation of the highpressure continuous length and average drop diameters after break-up. Necessarily, the model has to be simplified: in particular, drops are claimed to form right at the nozzle exit, and their diameter is supposed to be equal to the nozzle diameter. Once formed, every drop evolves on its own and is not affected by the presence of other surrounding drops (drop coalescence is not allowed). Such an assumption overestimates the interface area near the nozzle exit (because in the real situation jet break-up has not occurred yet) and underestimates it when the distance is larger than the continuous length (because the real jet has broken down into droplets smaller than the nozzle diameter). This second effect seems to be dominant, but it is partially compensated by the fact that in the real case droplets are very close to one another (i.e., they partially coalesce), which surely reduces mass-transfer rates with respect to the case of independent drops. With reference to the element of height dh, a drop of liquid undergoes three forces: its weight, the buoyancy, and the viscous friction. The following relation is obtained from the momentum equation written for a single drop:

dν FL - FG g 18µG ) dh FL v F d 2

(1)

L

where FL and FG are the densities of the liquid and gas phases, d is the drop diameter, v is the drop velocity, and µG is the viscosity of the gas phase. Gas density and viscosity are calculated by assuming that the gas is pure CO2 and are kept constant along the precipitator. For density the Bender equation of state is used, while the viscosity is calculated with the Lucas method.15 The density of the liquid phase varies with composition and is updated at each step by the Peng-Robinson equation of state with a Peneloux volume shift. The differential eq 1 can be solved numerically to build the velocity profile of a drop along the precipitator. The number of drops dn in the infinitesimal element dh is given by

dn )

L 6 dh FLv πd3

(2)

1490


where L is the liquid molar flow rate. At steady state the drop number rate (number per second) entering the precipitation vessel is constant; therefore

6L0 6L ) constant ) 3 πFLd πFL0d03

(3)

where 0 refers to the inlet section. From eqs 2 and 3 the variation of the drop number with height can be derived:

6L0 1 dn ) dh πF d 3 ν L0 0

(4)

with ν varying according to eq 1. The volume of a single drop, V, is given by the ratio between the volumetric flow rate of the liquid and the drop number rate, defined by eq 3: 3

V)

L πFL0d0 FL 6L0

(5)

This volume corresponds to the following drop diameter:

d)

( ) L FL0 L0 FL

1/3

d0

(6)

The area for mass transfer (dA) in the element dh is given by the surface area of a drop times the number of drops within dh:

dA dn ) πd2 dh dh

(7)

Equations 1, 6, and 7 allows the calculation of drop velocity, drop diameter, and interface area, which are the relevant hydrodynamic parameters involved in mass-transfer equations. Mass Transfer. Both the flux of the antisolvent from the gas to the liquid phase and that of the solvent in the opposite direction are considered. Note that, because the solubilities of the solutes in the gas phase are negligible at the conditions used in SAS processes, their fluxes from the liquid to the gas phase are not accounted for, and the mass-transfer equations for the binary system solvent-antisolvent do not need to be modified when one or more solutes are added. The following conditions on each component liquid- and gas-phase fluxes are imposed:

N1L ) x/1(N1L + N2L) - kL(x/1 - x1) ) y/1(N1G + N2G) - kG(y1 - y/1) ) N1G (8) N2L ) x/2(N1L + N2L) + kL(x2 - x/2) ) y/2(N1G + N2G) + kG(y/2 - y2) ) N2G (9) where 1 indicates the antisolvent and 2 the solvent, N is the flux, x and y are the liquid- and gas-phase compositions, respectively, the asterisk refers to equilibrium (interface) conditions, and kL and kG are the mass-transfer coefficients in the liquid and gas phases. These equations account for mass-transfer resistances in both the gas and liquid phases; any independent set

of two of them can be coupled with the material balance to simulate the process. To calculate the mass-transfer coefficient in the gas, it is necessary to model the hydrodynamics of the system. Liquid droplets (dispersed phase) flow within a dense gas (continuous phase); in addition, the slip velocity between the liquid and gas is large, causing the influence of convection on mass transfer to be important. This problem has been extensively studied (even though at lower pressures) by Hughmark.16,17 Because no reliable models for evaluating mass-transfer from drops at high pressure are available, the Hughmark equation was applied to calculate mass transfer coefficients in the continuous phase:

Sh ) 2 + 0.0187Re0.779Sc0.546(dg0.333DG-0.667)0.116 (10) where Sh, Re, and Sc are the Sherwood, Reynolds, and Schmidt numbers, respectively, d is the drop diameter, DG is the diffusion coefficient of the solvent in the gas phase. The dimensionless groups are calculated by using molecular properties (viscosity and density) of the gas phase and hydrodynamic properties (velocity and diameter) of the drop: these are evaluated at each step through the hydrodynamics equations (1-7). In the following simulations, three different solvents will be considered: acetone, toluene, and dimethyl sulfoxide (DMSO). To calculate the diffusion coefficients of acetone and toluene in the gas phase (supposed to be pure CO2), an interpolation of available literature data18-22 has been performed. No data were available for DMSO in dense CO2; we assumed the diffusion coefficient of DMSO was equal to that of acetone, because of the similarity of the two molecules. The mass-transfer coefficient in the liquid phase is given again by eq 10. As a first-step assumption, convective motions and circulation within small droplets can be neglected,23 so that mass transfer in the drop is driven only by molecular diffusion (Rel ) 0). Because Sh ) 2, eq 10 reduces to

kL )

2FLDL d

(11)

where DL is the diffusion coefficient of the antisolvent in the liquid phase. Because the composition of the liquid phase varies from zero to 0.8-0.95 (CO2 mole fraction), it is not possible to use for DL the value at infinite dilution of CO2 in the solvent, and a composition dependence is needed. The Vignes24 method for diffusion in binary mixtures of normal organic solvents states that the diffusion coefficient of a component in a mixture of both depends on mixture composition and varies with the activity coefficient. When this approach is applied to our system, it predicts large negative variations in the diffusion coefficient as more and more CO2 is added. Such a behavior is inconsistent with the only available data of composition-dependent diffusion coefficients for CO2 (the system is CO2-heptane25). A slight decrease in the diffusion coefficient, which was much smaller than that calculated with the Vignes approach, is observed in this case. So, the diffusion coefficients in the liquid phase have been calculated by averaging the two limiting values (i.e., infinite-dilution values) according to the Vignes equation again:

Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000 1491 0 DL ) (D CO )xsolv(D 0solv)xCO2 2

(12)

Note that all simulations were performed at conditions enough below the critical point of the mixture solvent-antisolvent so that the Vignes equation can be reasonably applied. To calculate the infinite-dilution diffusion coefficient 0 , literature correlations of of CO2 in toluene, D CO 2 experimental data were used,26 while for acetone and DMSO, the Wilke-Chang equation15 was applied. The diffusion coefficient of each solvent in liquid CO2, D 0solv, is calculated from that in gaseous CO2 with the following equation, derived from the Stokes-Einstein equation:

DCO2scµCO2sc ) DCO2liqµCO2liq

(13)

where µ indicates viscosity. Note that if the operating temperature is higher than the CO2 critical temperature, CO2 does not exist as a liquid. The viscosity of CO2 in the hypothetical state of overheated liquid is calculated with a literature correlation.15 Note that again the presence of solutes in the liquid phase is neglected, because no data for CO2 diffusion in solute-solvent mixtures are available. The flux equations are coupled to the following mass balances, referring to the element dh:

dL ) -dG

(14)

d(Lx1) ) N1 dA

(15)

d(L(1 - x1)) ) N2 dA

(16)

-d(G(1 - y1)) ) N2 dA

(17)

where L and G are the liquid and gas flow rates, respectively. In this way the liquid and gas flow rates and the composition of the phases can be calculated. When one or more solutes are present, mass balance equations need to be written for each one of them. Before the solution becomes saturated, all of the solute is in the liquid phase, and its mass balance is given by

d(Lxi) ) 0

(18)

When saturation is reached, it is assumed that precipitation occurs; then, the solute mole fraction in the liquid is given by the thermodynamic equilibrium equation. The mass balance allows one to calculate the amount of precipitated solute in each element:

d(Lx/i ) ) dPrci

(19)

where Prci is the amount of each precipitated solute. It is important to notice that the limits of the presently proposed approach are due essentially to the thermodynamic model. When dealing with heavy compounds such as polymers, it is nonsense to use a cubic equation of state, because it is not possible to evaluate meaningful model parameters in this case. On the other hand, if a suitable equation of state, able to provide the thermodynamic properties needed is adopted, the same model structure can be retained to carry out simulations. Work is in progress with respect to that.27 Results Also in this section binary systems are considered first. Ternary system calculations are performed to show

Figure 2. (a) Mole fraction of antisolvent (CO2) in the liquid phase as a function of the distance from the injection at different values of R (d0 ) 0.005 cm; v0 ) 300 cm/s; R ) 9.6, 23.9, and 47.8). (b) Composition of the liquid phase as a function of the residence time at different values of R (d0 ) 0.005 cm; v0 ) 300 cm/s; R ) 9.6, 23.9, and 47.8).

the different sensitivity of various solutes to the operating parameters. Quaternary simulations are aimed to show that complete separation between two solutes (naphthalene and phenanthrene) from a solution of both in toluene is predicted by the model if suitable operating conditions are adopted. The systems selected have been considered as meaningful examples because they can be treated accurately by the PR EOS, and experimental data are available in the literature for the evaluation of interaction parameters. Binary Systems. Calculations are performed for the system CO2-toluene at T ) 315.15 K and P ) 83.4 bar, which means equilibrium values of CO2 mole fractions of 0.911 in the liquid phase and 0.990 in the gas phase. The influence of the gas-to-liquid flow-rate ratio on a weight basis (R), initial drop velocity (v0), and initial drop diameter (d0) is considered. The composition of the liquid phase as a function of H (distance from the injection nozzle) at different values of R is reported in Figure 2a. It is clear that, under the conditions considered, saturation is reached early in the precipitator (after 2-3 cm) and that it is insensitive to R. Instead, the liquid flow rate (Figure 3a) changes considerably with R. At the beginning a steep increase is observed, because of fast dissolution of CO2. Evaporation becomes evident only after saturation has been almost reached, and the amount of evaporated liquid depends strongly on R: it can be negligible (at low R) or total (at high R). If the liquid evaporates completely, only one phase is present in the lower part of the precipitator. In such a case it can be concluded that

1492


Figure 3. (a) Liquid-phase flow rate as a function of the distance from the injection at different values of R (d0 ) 0.005 cm; v0 ) 300 cm/s; R ) 9.6, 23.9, and 47.8). (b) Liquid-phase flow rate as a function of the residence time at different values of R (d0 ) 0.005 cm; v0 ) 300 cm/s; R ) 9.6, 23.9, and 47.8).

liquid saturation (antisolvent effect) is much faster than evaporation and that solute precipitation is expected to be caused by the antisolvent effect rather than the evaporation effect. If the former is not enough to obtain precipitation and also the contribution of solvent evaporation is needed, precipitation is expected to be slower, with important consequences on the product morphology. The composition of the liquid phase against the residence time of the drops in the precipitator is plotted in Figure 2b. It is worth noting that the saturation time is really short (50-100 ms); this is expected to cause high supersaturation and nucleation rates. The liquid flow rate against the residence time τ, defined as

τ)

∫0Hdh v

(20)

is reported in Figure 3b. The plot is similar in shape to that of Figure 3a, but the initial parts of the curves of the two figures show opposite convexity. This is caused by the large decrease of drop velocity. At the beginning the drop is fast, so the H diagram is “expanded” with respect to the residence time diagram; after a short time (and a short distance) the drops have almost reached the final constant speed, and the two diagrams become similar. The effect of the initial drop velocity is presented in Figure 4a,b. When the liquid flow rate is reported as a function of H, an increasing drop velocity expands the curves toward higher values of H, but when L is plotted against the residence time, which is the true independ-

Figure 4. (a) Liquid-phase flow rate as a function of the distance from the injection at different values of the initial drop velocity (d0 ) 0.005 cm; R ) 23.9; v0 ) 100, 300, and 500 cm/s). (b) Liquidphase flow rate as a function of the residence time at different values of the initial drop velocity (d0 ) 0.005 cm; R ) 23.9; v0 ) 100, 300, and 500 cm/s).

ent variable for the process considered, no effect of the initial velocity is evidenced. Indeed the initial drop velocity slightly influences the mass-transfer rates by enhancing the gas-phase mass-transfer coefficient. However, this effect is small too, because of the fast speed decrease along the precipitator. The dependence on the initial drop diameter is presented in Figure 5a,b. In this case the liquid-phase composition profiles vary if represented both against H and against the residence time. An increase in the initial drop diameter at a constant liquid flow rate causes an interface area decrease, that is, a slower mass-transfer rate. This effect is more evident when the CO2 mole fraction is plotted against H. Finally the behavior of three different solvents is compared in Figures 6a,b. The calculations are performed at the same conditions of temperature and pressure; the values of the corresponding equilibrium composition, calculated with the PR EOS, are reported in Table 1. Both dissolution of CO2 in the solvent and solvent evaporation are progressively increased going from DMSO to acetone. Because the mass-transfer coefficients are almost equal for all of these solvents, the difference is caused by an increase in the driving force (due to the different solubility of CO2 in the solvents). The competition between solvent evaporation and CO2 dissolution rates causes the different shapes of the curves in Figure 6a,b. Note that for DMSO evaporation is almost negligible (the flow-rate curve remains flat at its maximum value), while it is not for toluene and acetone. Note also that, at the examined


Figure 5. (a) Composition of the liquid phase as a function of the distance from the injection at different values of the initial drop diameter (R ) 23.9; v0 ) 300 cm/s; d0 ) 0.005, 0.0075, and 0.01 cm). (b) Composition of the liquid phase as a function of the residence time at different values of the initial drop diameter (R ) 23.9; v0 ) 300 cm/s; d0 ) 0.005, 0.0075, and 0.01 cm).

value of the flow-rate ratio, a liquid phase is always present in the precipitator. Ternary Systems. Ternary calculations are performed for the systems CO2-toluene-phenanthrene and CO2-toluene-naphthalene, because reliable S-L-V equilibrium data are available for these systems,12 and they can be accurately modeled13 with the PR EOS. The addition of a solute is assumed to have a small effect on both the hydrodynamics and the mass-transfer rates: for example, some changes of the diffusion coefficients in the liquid phase are expected, because of the presence of a different molecule in solution, but because of the lack of experimental data and the relatively low solute concentrations, we have neglected this contribution. On the other hand, as discussed in the Thermodynamics subsection, the phase equilibrium of the system changes dramatically. The presence of a solute almost immiscible with CO2 leads to solution supersaturation and solute precipitation when enough CO2 has diffused into the liquid phase. In this section we analyze the behavior of two different solutes and the effect of operating parameters on the amount of solid product obtained. The different behaviors of naphthalene and phenanthrene are compared in Figure 7a,b. The amount of precipitated phenanthrene is only slightly affected by the flow-rate ratio, because the antisolvent effect is strong enough to trigger precipitation, and solvent evaporation is not relevant to it. On the other hand, naphthalene is more soluble in the liquid phase, and the antisolvent effect may not be strong enough for

Figure 6. (a) Composition of the liquid phase as a function of the distance from the injection with CO2 as the antisolvent and different organic solvents (R ) 23.9; v0 ) 300 cm/s; d0 ) 0.0075 cm). (b) Liquid-phase flow rate as a function of the distance from the injection with CO2 as the antisolvent and different organic solvents (R ) 23.9; v0 ) 300 cm/s; d0 ) 0.0075 cm). Table 1. Equilibrium Compositions for Different CO2-Solvent Systems at T ) 315.15 K and P ) 83.4 bar solvent

xCO2

yCO2

acetone toluene DMSO

0.960 0.911 0.716

0.984 0.990 0.999

precipitation to occur.7 Only if a large amount of solvent is evaporated can the precipitation be obtained: for naphthalene it is strongly dependent on the flow-rate ratio and can occur only if R is large enough. The composition profiles of the liquid phase at different initial solute mole fractions are represented in Figure 8a,b; these profiles can be represented either as a function of the mole fraction of CO2 in the liquid, as in Figure 8a, or along with the vessel height, as in Figure 8b. In both cases also the S-L equilibrium curve is shown (in bold), calculated at the value of the CO2 mole fraction in the liquid at the corresponding height. It is evident that phenanthrene precipitation always occurs, even if the initial solution is far away from saturation. When the initial solution becomes more diluted, saturation is reached at a larger h. For naphthalene, instead, it is necessary to start with an almost saturated solution to obtain precipitation; if this is not the case (a mole fraction of naphthalene less than 0.3), the equilibrium line is never crossed; i.e., precipitation cannot be achieved. This representation (with operating lines and equilibrium lines) is similar to the one proposed by the authors for the SAS batch process.7 Quaternary Systems. Quaternary calculations are performed on the system CO2-toluene-naphthalene-

1494


Figure 7. (a) System CO2-toluene-phenanthrene: percent amount of precipitated phenanthrene as a function of the distance from the injection at different values of R (T ) 315.15 K; P ) 80 bar; x0phen ) 0.18; d0 ) 0.0075 cm; v0 ) 300 cm/s; R ) 8.2, 20.5, and 41). (b) System CO2-toluene-naphthalene: percent amount of precipitated naphthalene as a function of the distance from the injection at different values of R (T ) 315.15 K; P ) 83.4 bar; x0napht ) 0.4; d0 ) 0.0075 cm; v0 ) 300 cm/s; R ) 8.3, 20.7, and 41.4).

Figure 8. (a) System CO2-toluene-phenanthrene: phenanthrene mole fraction in the liquid phase as a function of the mole fraction of CO2 in the liquid phase (T ) 315.15 K; P ) 80 bar; x0phen ) 0.05, 0.1, 0.15, and 0.2; d0 ) 0.0075 cm; v0 ) 300 cm/s; R ) 6.6). (b) System CO2-toluene-naphthalene: naphthalene mole fraction in the liquid phase as a function of the distance from the injection (T ) 315.15 K; P ) 83.4 bar; x0napht ) 0.2, 0.3, 0.35, and 0.4; d0 ) 0.0075 cm; v0 ) 300 cm/s; R ) 21.4).

phenanthrene, at T ) 300.15 K and P ) 64.2 bar. Simulations at higher temperatures have not been done, because from equilibrium calculations a L-L equilibrium is expected to occur.7 Accordingly, a solute-rich liquid phase is at equilibrium with an antisolvent-rich liquid phase, thus leading to a sudden decrease in the antisolvent effect. The aim is to explore the possibility of separating the two solutes by means of a semicontinuous SAS process. In the foregoing section the antisolvent effect was shown to be higher for phenanthrene than for naphthalene. This fact can be exploited to reach separation and to precipitate pure phenanthrene. Simulations have been performed to analyze the effect of R and of the liquid-phase composition. At the operating pressure and temperature, the evaporation effect is small, because the gas at equilibrium is almost pure CO2, so changing R leaves the behavior of the system essentially unchanged. Thus, the precipitation of a solute is a matter of true antisolvent effect rather than evaporation effect. The initial solution composition plays a key role in obtaining separation. Many simulations have been performed, analyzing the whole spectrum of solute mole fractions from zero to saturation concentration. Phenanthrene precipitation is predicted in any case, even if the starting solution is almost saturated in naphthalene and diluted in phenanthrene; on the other hand, a critical

value of concentration needs to be exceeded in order to obtain naphthalene precipitation. As a consequence, pure naphthalene can never be precipitated (because whatever the ratio is between naphthalene and phenanthrene in the initial solution, the second one will always precipitate), while it is possible to precipitate pure phenanthrene (given that the naphthalene concentration in the initial solution is under a certain limit). The maximum amounts of phenanthrene and naphthalene in the initial solution allowing the precipitation of pure phenanthrene are presented in Figure 9. Note that when the initial naphthalene mole fraction is lower than 0.2, naphthalene never precipitates and pure phenanthrene can always be obtained. The addition of more phenanthrene to a solution with a fixed amount of naphthalene pushes also naphthalene to precipitation, because the solvent availability is less for both. The addition of more naphthalene to a solution with a fixed amount of phenanthrene pushes obviously also naphthalene to precipitation. The percent of precipitated solutes as a function of the distance from the inlet nozzle is presented in Figure 10. The starting concentration is close to saturation values for both phenanthrene and naphthalene: in this case, precipitation of both solutes is obtained, even if the percent amount of precipitated phenanthrene (with respect to the global amount in the solution) is greater. In another simulation the starting solution was diluted


Figure 9. Solutes precipitation as a function of the initial solution composition.

different ways. Phenanthrene is easily precipitated by the antisolvent effect, and the process is driven essentially by CO2 dissolution in the liquid phase. For naphthalene the antisolvent effect needs to be coupled to evaporation, which occurs much more slowly and is a function of the flow-rate ratio. According to quaternary calculations, phenanthrene can be selectively precipitated if the initial solution is within a certain composition range (see Table 2). Interesting is the fact that pure phenanthrene can be precipitated even from a solution with 28 mol % of naphthalene and only 3 mol % of phenanthrene. The proposed approach is useful for the simulation of SAS processes if a thermodynamic model suitable to represent phase equilibria of the system of interest is available. Acknowledgment The authors acknowledge M.U.R.S.T. (Ministero dell’Universita` e della Ricerca Scientifica e Tecnologica) for financial support (ex-40%). Literature Cited

Figure 10. System CO2-toluene-naphthalene-phenanthrene: percent amount of precipitated solute as a function of the distance from injection (T ) 300.15 K; P ) 64.2 bar; x0napht ) 0.32; x0phen ) 0.22; d0 ) 0.0075 cm; v0 ) 300 cm/s; R ) 20).

in phenanthrene (mole fraction 0.03) and more concentrated in naphthalene (mole fraction 0.28); in this case pure phenanthrene was predicted to precipitate, and about 65% of its initial amount could be recovered as a pure solid. If the initial solution is more concentrated in phenanthrene (with the mole fraction of naphthalene being constant), the yield in terms of pure phenanthrene becomes still higher. Conclusions Thermodynamics, hydrodynamics, and mass-transfer phenomena have been modeled in order to simulate a semicontinuous antisolvent recrystallization process. Two main phenomena occur in the precipitator: the dissolution of the antisolvent (CO2) in the liquid phase and the evaporation of the solvent from the liquid to the dense gas phase. With reference to a CO2-toluenenaphthalene-phenanthrene system, it was shown that the first one is much faster, leading to a fast saturation of the liquid phase, independent of the flow-rate ratio. The evaporation process is slower and is a strong function of the flow-rate ratio. The initial drop velocity affects the profiles when they are plotted against the distance from the injection, but its effect is negligible when the residence time is chosen as the independent variable. A change in the initial drop diameter affects both profiles, by modifying the interface area, that is, the mass-transfer rates. From ternary system simulations it was found that the two heavy solutes considered behave in completely

(1) Reverchon, E. Supercritical Antisolvent Precipitation of Micro- and Nano-Particles. J. Supercrit. Fluids 1999, 15, 1. (2) Gallagher, P. M.; Coffey, M. P.; Krukonis, V. J.; Klasutis, N. Gas Antisolvent Recrystallization: New Process to Recrystallize Compounds Insoluble in SCF. In Supercritical Fluid Science and Technology; Johnston, K. P., Penninger, J. M. L., Eds.; ACS Symposium Series 406; American Chemical Society: Washington, DC, 1988; Chapter 22. (3) Yeo, S.-D.; Lim, G.-B.; Debenedetti, P. G.; Bernstein, H. Formation of Microparticulate Protein Powders Using a Supercritical Fluid Antisolvent. Biotechnol. Bioeng. 1993, 41, 341. (4) Dixon, D. J.; Johnston, K. P.; Bodmeier, R. A. Polymeric Materials Formed by Precipitation with a Compressed Fluid Antisolvent. AIChE J. 1993, 39, 127. (5) Jaarmo, S.; Rantakyla¨, M.; Aaltonen, O. Particle Tailoring with Supercritical Fluids: Production of Amorphous Pharmaceutical Particles. Proceedings of the 4th International Symposium on Supercritical Fluids, Sendai, Japan, 1997. (6) Mawson, S.; Kanakia, S.; Johnston, K. P. Coaxial Nozzle for Control of Particle Morphology in Precipitation with a Compressed Fluid Antisolvent. J. Appl. Polym. Sci. 1997, 64, 2105. (7) Bertucco, A.; Lora, M.; Kikic, I. Fractional Crystallization by a Supercritical Antisolvent Technique: Theory and Experiments. AIChE J. 1998, 44, 2149. (8) Kikic, I.; Lora, M.; Bertucco, A. Thermodynamics and Mass Transfer for the Simulation of Recrystallization Processes with a Supercritical Antisolvent. Proceedings of the 4th Italian Conference on Supercritical Fluids and Their Applications, Capri, Italy, 1997. (9) Rantakyla, M.; Ja¨ntti, M.; Jaarmo, S.; Aaltonen, O. Modeling Droplet-Gas Interaction and Particle Formation in Gas AntiSolvent System (GAS). Proceedings of the 5th Meeting on Supercritical FluidssMaterials and Natural Products Processing, Nice, France, 1998. (10) Ng, H.-J.; Robinson, D. B. Equilibrium Phase Properties of the Toluene-Carbon Dioxide System. J. Chem. Eng. Data 1978, 23, 325. (11) Scott, R. L.; van Konynenburg, P. B. Static Properties of Solutions: van der Waals and Related Models for Hydrocarbon Mixtures. Discuss. Faraday Soc. 1970, 49, 87. (12) Dixon, D.; Johnston, K. P. Molecular Thermodynamics of Solubilities in Gas-Antisolvent Crystallization. AIChE J. 1991, 37, 1441. (13) Kikic, I.; Lora, M.; Bertucco, A. A Thermodynamic Analysis of Three-Phase Equilibria in Binary and Ternary Systems for Application in RESS, SAS and PGSS. Ind. Eng. Chem. Res. 1997, 36, 5508.

1496


(14) Lefebvre, A. H. Atomization and Sprays; Taylor & Francis: London, 1989. (15) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases and liquids, 4th ed.; McGraw-Hill Book Company: Singapore, 1988. (16) Hughmark, G. A. Liquid-Liquid Spray Column Drop Size, Holdup, and Continuous Phase Mass Transfer. Ind. Eng. Chem. Fundam. 1967, 6, 408. (17) Hughmark, G. A. Holdup and Mass Transfer in Bubble Columns. Ind. Eng. Chem. Fundam. 1967, 6, 219. (18) Swaid, I.; Schneider, G. M. Determination of Binary Diffusion Coefficients of Benzene and Some Alkylbenzenes in Supercritical CO2 between 308 and 328 K in the Pressure Range 80 to 160 bar with Supercritical Fluid Chromatography (SFC). Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 969. (19) Suarez, J. J.; Bueno, J. L.; Medina, I. Determination of Binary Diffusion Coefficients of Benzene and Derivatives in Supercritical Carbon Dioxide. Chem. Eng. Sci. 1993, 48, 2419. (20) Bueno, J. L.; Suarez, J. J.; Dizy, J.; Medina, I. Infinite Dilution Diffusion Coefficients: Benzene Derivatives as Solutes in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1993, 38, 344. (21) Sassiat, P. R.; Mourier, P.; Caude, M. H.; Rosset, R. H. Measurement of Diffusion Coefficients in Supercritical Carbon

Dioxide and Correlation with the Equation of Wilke and Chang. Anal. Chem. 1987, 59, 1164. (22) Nishiumi, H.; Fujita, M.; Agou, K. Diffusion of Acetone in Supercritical Carbon Dioxide. Fluid Phase Equilib. 1996, 117, 356. (23) Bennett, C. O.; Myers, J. E. Momentum, Heat and Mass Transfer; McGraw-Hill Book Company: New York, 1982. (24) Vignes, A. Diffusion in Binary Solutions. Ind. Eng. Chem. Fundam. 1966, 5, 189. (25) Saad, H.; Gulari, E. Diffusion of Carbon Dioxide in Heptane. J. Phys. Chem. 1984, 88, 136. (26) Snijder, E. D.; te Riele, M. J. M.; Versteeg, G. F.; van Swaaij, W. P. M. Diffusion Coefficients of CO, CO2, N2O, and N2 in Ethanol and Toluene. J. Chem. Eng. Data 1995, 40, 37. (27) Favari, F.; Bertucco, A.; Elvassore, N.; Fermeglia, M. Multiphase Multicomponent Equilibria for Mixtures Containing Polymers by the Perturbation Theory. Chem. Eng. Sci. 1999, accepted for publication.

Received for review September 13, 1999 Revised manuscript received February 15, 2000 Accepted February 25, 2000 IE990685F

Simulation of the Semicontinuous Supercritical Antisolvent

Recommend Documents