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Crystallization of n-octacosane by the rapid expansion of supercritical solutions
......... CRYSTAL GROWTH
ELSEVIER
Journal of Crystal Growth 155 (1995) 112-119
Crystallization of n-octacosane by the rapid expansion of supercritical solutions Gregory J. Griscik, Ronald W. Rousseau, Amyn S. Teja * School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, USA
Received 30 September 1994; manuscript received in final form 10 March 1995
Abstract Crystals of a model wax (n-octacosane) were produced by the rapid expansion of supercritical solutions (RESS) containing n-octacosane and carbon dioxide. Pre-expansion temperatures and pressures were varied to study their effects on crystal morphology. Four distinct types of particles were observed, including regular hexagonal crystals and irregular fused particles. Particle size decreased and the particle size distribution narrowed with an increase in pre-expansion temperature. On the other hand, changes in pre-expansion pressure showed no significant influence on particle size.
I. Introduction Changing temperatures and pressures may cause waxes to crystallize from crude oil and natural gas streams, and therefore affect the operation of processing equipment. If these waxes can be made to crystallize in a structure that is less likely to plug, or if the waxes can be prevented from coming out of solution altogether, then a potentially serious problem can be mitigated. Wax deposition from natural gases generally occurs under conditions at which the natural gas is in a supercritical state; therefore, it is important to know the solubility and crystalline behavior of waxes in supercritical fluids. The solubility of a s o h t e in a supercritical solvent is strongly dependent on the pressure and
* Corresponding author. Fax: + 1 404 894 2866.
temperature of the system, and generally increases dramatically near the critical point of the solvent [1,2]. This dramatic change in solubility has been exploited to produce particles in a process known as RESS (rapid expansion of supercritical solutions) [3], in which a solute with a low vapor pressure is dissolved in a supercritical fluid and then expanded rapidly through an orifice or nozzle [4]. Expansion produces conditions far from equilibrium and the solute experiences very high supersaturations, resulting in a large number of nuclei being formed in a very short time (estimated to be of the order of microseconds or less) [5]. A number of RESS variables dictate the morphology of the particles resulting from the expansion. These variables range from the pressure and temperature of the supercritical solution before expansion, to the pressure and temperature of the environment into which the solution is ex-
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G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
panded. The concentration of the solution before expansion, as well as the nozzle geometry and diameter, also play a role in the expansion process [5]. On the other hand, the physical properties of the solute do not directly affect the expansion properties of the system, since the solute is typically at a low concentration and the solution has bulk physical properties very close to those of the solvent [6]. In the present work, we have studied the particle habit of a model wax (n-octacosane) upon expansion from a supercritical solvent (carbon dioxide). Carbon dioxide was chosen as the solvent because it is an important component of natural gas. The solute, n-octacosane, was chosen because it represents a typical paraffin wax and solubility data for this wax + carbon dioxide system are available in the literature and have also been measured in our laboratory [20,21]. There have been no reported studies of the crystallization of waxes from supercritical solutions. However, the structure of n-alkanes obtained by crystallization from a melt has been examined by a number of researchers [7-10]. They have found that alkanes crystallize in different lattice forms depending on carbon number and on the presence of impurities. The morphology of octacosane (n-C28) and dotriacontane (nC32) crystals grown from liquid hexane solutions has been studied by Liu and Bennema [7]. They investigated the effect of concentration and growth temperature (near the roughening temperature) on crystal morphology. In all cases, whether crystals were grown above or below the roughening temperature, the overall shape remained plate-like and only the side faces were affected by changes in crystallization conditions. These studies provide some indication of the morphology of particles that could be obtained in the RESS expansion.
2. Experimental procedure A schematic of the equipment used in this work is shown in Fig. 1. Liquid carbon dioxide was drawn by means of a dip tube from a cylinder (A) and then piped into a battery of piston pumps
I
i
RESS
IJ Fig. 1. Experimental apparatus.
(B) (a Milton Roy miniPump and an Eldex Laboratories Model AA-100-S pump). The pumps were operated in parallel and used to pressurize the carbon dioxide into a reservoir (C) consisting of 1/4 inch o.d. × 1/16 inch i.d. stainless steel tubing. The gas flow was then directed to a frontpressure regulator (D) (Tescom 26-1023-44) and also to a back-pressure regulator (E) (Tescom 26-1722-24). The back-pressure regulator was used to prevent the reservoir from exceeding a predetermined pressure. A purge valve (I) was installed directly behind the front pressure regulator in order to facilitate depressurization of the system. From the front-pressure regulator (D), the carbon dioxide was channeled through two columns (G) immersed in a water bath. The bath was heated and controlled by a circulator/heater (F) (Lauda Model T-I). The high-pressure columns were each about 200 mm in length and packed with alternating layers of n-octacosane and 3 mm glass beads. The supercritical solution from the columns was then directed to valve (H). This valve controlled the flow of carbon dioxide by either allowing the fluid to flow through the columns or past them via a bypass line. Valve (H) was maintained at a constant temperature by heating tape controlled with an Omega temperature controller (Omega CN9000A). The line from the valve to the nozzle was wrapped with heating tape and fiberglass insulation. A thermocouple placed directly before the nozzle allowed the monitoring of solution temperature just before expansion. Heating tape was placed around the nozzle itself, and the temperature in this device was monitored by a thermocouple and a controller (Omega CN9000A) which maintained the
114
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
temperature within _+ I°C. The (pre-expansion) pressure of the system was measured at a point between the valve (H) and the nozzle by a computer-interfaced digital pressure gauge (Heise 901A). The pressure gauge was interfaced with a 386DX personal computer that collected pressure data throughout the operation. The n-octacosane particles suspended in the carbon dioxide jet emanating from the expansion nozzle were collected directly on scanning electron microscope (SEM) sample stubs. Each stub was positioned so that its face was perpendicular to the axis of the carbon dioxide/n-octacosane spray coming from the nozzle. A piece of double-sided SEM tape was placed on the surface for the collection of n-octacosane particles. The RESS parameters of interest are as follows: (1) n-octacosane concentration in supercritical carbon dioxide, (2) pre-expansion temperature, (3) pre-expansion pressure, (4) post-expansion temperature, (5) post-expansion pressure, (6) nozzle type and configuration, and (7) collection procedure. Only RESS conditions 2 and 3 were varied in the present work. The post-expansion temperature was ~ 295 K, the post-expansion pressure ~ 1 atm, and the nozzle configuration was that of a fused silica capillary tube with an inside diameter of 50 /~m and a length of 10 mm. The SEM sample stub was 15 cm from the tip of the nozzle, and the RESS jet was discharged over the sample stub for 20 min. An n-Octacosane mole fraction of ~ 2.5 x 10 -4 was used for each of the pre-expansion pressures. The pre-expansion pressure was determined by calculating the average of the pressure measurements recorded by the computer during each 20 min sampling period. The measured pressure fluctuations were in the range +0.41 bar, which is slightly greater than the measurement error of the pressure gauge, + 0.29 bar. n-Octacosane solubilities in carbon dioxide were calculated at a temperature of 314.8 K and at each of the three pre-expansion pressures used in this work (173.9, 195.7, and 221.6 bar). The solubilities were estimated by the method described in the appendix and the results are given in Table 1. Two aspects of n-octacosane particle morphol-
Table 1 Calculated n-octacosane solubility in supercritical carbon dioxide at 314.8 K Pressure Mole fraction (bar) (×10 4) 173.9 195.7 221.6
2.37 2.47 2.53
ogy were studied. For each sample, particle size and shape were examined and characterized. Particle size was measured directly from the SEM samples that had been sputter coated with gold. For a given particle, the longest dimension and the perpendicular dimension (usually the shortest length) were averaged and defined to be the equivalent diameter of the given particle. All the particle diameters for a specific sample were averaged and a standard deviation computed.
3. R e s u l t s a n d d i s c u s s i o n
Fig. 2 shows that a marked change in particle size occurred in going from pre-expansion temperatures in the range 323 to 373 K (two-phase expansions) to pre-expansion temperatures in the range 413 to 523 K (one-phase expansions). The term two-phase expansion refers to the fact that the path of the expansion of the supercritical carbon dioxide goes through a two-phase (liquid-vapor) region before ending in the vapor phase. One-phase expansion means the carbon 3O 25
20
E
15
u
:E
s 0 313
I
I
I
I
363
4t3
463
513
Pre-Expansion T (K)
Fig. 2. Variation of the mean particle diameter with pre-expansion temperature. ( • ) 173.9bar, ( • ) 195.7 bar, ( • ) 221.6 bar.
G.J. Griscik et aL /Journal of Crystal Growth 155 (1995).112-119 3O
115
dioxide goes directly from the supercritical state to vapor phase. The particles produced with pre-expansion pressures between 323 to 373 K were larger (up to 25 /~m) than those produced at pre-expansion temperatures between 413 and 523 K (5-10/xm). Also, the particles produced in the lower temper-
ature range showed a greater variation in size (Fig. 3). Examination of the photographs revealed the formation of four different types of particles. At the lower pre-expansion temperatures (323 to 373 K), the particles appeared to be a fused mass. A second type of particle was found at pre-expansion temperatures of 413 and 423 K. These particles had sharp and well-defined edges, and the particle size distribution varied less than that at lower temperatures. A third type of particle was produced at pre-expansion temperatures of 433 and 443 K. These particles appeared spherical in shape and were made of densely packed subparticles. A pre-expansion temperature of 523 K produced a fourth type of particles. These particles were spherical in shape but did not appear to be made of any subparticles. Most of the SEM pictures showed the first particle type consisting of masses of subparticles fused together. These particles were produced at pre-expansion temperatures between 323 and 373
Fig. 4. n-octacosane particles produced from carbon dioxide at pre-expansion conditions of T = 373 K, P = 221.6 bar.
Fig. 5. n-octacosane particles produced from carbon dioxide at pre-expansion conditions of T = 423 K, P = 195.7 bar.
°
•
10
~=
¢I a.
0
L1 i i ~ i
313
363
lltl
Ji::;
413
i,,:;:,,,
463
513
Pre-Expansion T (K) Fig. 3. Mean particle diameterwith standard deviationsat a pre-expansion pressure of 173.9bar.
116
G.J. Griscik et aL /Journal of Crystal Growth 155 (1995) 112 119
size was also uniform, especially compared to the size diversity of the samples produced at pre-expansion temperatures between 323 to 373 K. Fig. 8 shows an example of the particles produced at the highest pre-expansion temperature (523 K). These particles were spherical in overall shape and similar in size and shape to particles produced at pre-expansion temperatures of 433 and 443 K. However, the particles produced at 523 K do not appear to be made of any well defined subparticles. The mechanism for particle formation is difficult to determine due to the short time in which the process takes place. Therefore, only an initial hypothesis can be proposed based on solving the mass, energy, and momentum equations for carbon dioxide expanding through a nozzle, combined with the solubility calculations outlined in Appendix A. Our calculations suggest that at pre-expansion temperatures lower than 373 K, nucleation occurs in the nozzle. Moreover, the expanding fluid enters the two-phase region after Fig. 6. n-octacosane particles produced from carbon dioxide at pre-expansion conditions of T = 443 K, P = 195.7 bar. K, which are low enough for two-phase expansion of the carbon dioxide. Fig. 4 shows these fused particles at a pre-expansion temperature of 373 K and pre-expansion pressures of 221.6 bar. Fig. 5 shows a representative picture of samples that were produced with pre-expansion temperatures of 413 and 423 K. A transition to the third type of particle morphology can be seen. For the most part, the particles and constituent subparticles had sharp and well-defined edges. The particles were generally oblong, and showed less variation from particle to particle than in the other types. Figs. 6 and 7 show examples of particles produced at pre-expansion temperatures of 433 and 443 K. The particles are all spherical and composed of densely packed, well-defined subparticles. The subparticles have distinct facets with one face usually being dominant. The plate-like and faceted shape of the subparticles look similar to the crystals of n-octacosane produced from n-hexane by Liu and Bennema [7]. The particle
Fig. 7. n-octacosane particles produced from carbon dioxide at pre-expansion conditions of T = 443 K, P = 221.6 bar.
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
Fig. 8. n-octacosaneparticles produced from carbon dioxide
at pre-expansion conditionsof T = 523 K, P = 221.6 bar. it exits the nozzle. Thus, nuclei are in contact with the supersaturated solution in the nozzle and experience a rapid growth period at high supersaturation. The final particle shape, flat and without distinct side faces, parallels the crystals produced in the work by Liu and Bennema [7] that were grown at high supersaturations that caused roughening of the crystal edge faces. The abrupt expansion from the exit of the nozzle effectively ends the growth phase by crystallizing the remaining solute out of solution. For particles produced at pre-expansion temperatures of 413 K and above, nucleation occurs outside the nozzle and, little or no growth occurs because the solute becomes insoluble relatively quickly. Some coalescence of the nuclei occurs in the expansion jet, so that the overall particles appear to be composed of subparticles. The subparticles are plate-like and also have distinct faceted edges, which would point to only a brief period of growth (growth at high supersaturations
117
causes roughening of the edge faces). The particles produced at a pre-expansion temperature of 523 K are not composed of the plate-like subparticles. The reason for this could be that the solute is forced out of solution at a temperature above its melting point (since the pre-expansion temperature is high) and the molten droplet then solidifies as the jet continues to expand and cool. Since supersaturation occurs more rapidly in these cases and there is little time for growth, these particles are smaller than those produced at pre-expansion temperatures of 373 K and below. Finally, the increased particle size distribution of the particles produced at the lower pre-expansion temperatures could be due to the fact that these particles nucleate inside the nozzle, where there is a velocity profile. This velocity profile leads to different elution times for different particles depending on the location of the particle in the velocity profile. The particles that remain in the nozzle for a longer period of time have more contact with the expanding supersaturated solution, and thus experience a longer growth period. Particles which nucleate outside the nozzle do not experience this growth period and thus have a narrower size distribution.
4. Conclusions
The effects of pre-expansion temperature and pre-expansion pressure were experimentally studied on particles of n-octacosane formed from carbon dioxide by the RESS process. Both particle size and shape were dependent on pre-expansion temperature, whereas pre-expansion pressures did not show any significant effects. These dependences have also been reported by others [11,12]. Particles produced at pre-expansion temperatures between 323 and 373 K were larger, had a wider size distribution, and possessed a distinct shape. Particles produced at or above 413 K were smaller, had a narrower size distribution, and exhibited different overall particle shapes. Fluid expansion calculations and solubility calculations suggest that nucleation occurs in different parts of the expansion process, depending on the pre-expansion temperature. The larger, fused
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
118
particles were produced when nucleation and growth occurred primarily in the nozzle. On the other hand, smaller particles composed of distinct faceted subparticles were produced when nucleation was believed to occur past the exit of the nozzle. Future work will be focused on the expansion calculations in order to test this hypothesis.
Acknowledgement We acknowledge the Exxon Foundation for partial financial support of this work.
Appendix A The n-octacosane solubility in carbon dioxide could not be measured using the apparatus constructed in this study. As a result, the solubility had to be interpolated to the conditions of interest using literature values of n-octacosane-carbon dioxide solubilities. An equation of state approach was chosen for this purpose because it also allows for solubility prediction outside the range of known solubility data. n-octacosane solubilities were calculated using the following equation from thermodynamics [13]: Y2 = Psub2 exp
RT
/(b2P'
(A.1)
where Yz is the solubility of n-octacosane in carbon dioxide at a pressure P, and temperature T. R is the gas constant, V2s the molar volume of n-octacosane, p~ub the sublimation pressure of n-octacosane, and ~2 the fugacity coefficient of n-octacosane in carbon dioxide at P and T. Eq. (A.1) was obtained from the thermodynamic condition of equality of fugacities of the two phases in equilibrium [13]. It assumes that none of the carbon dioxide dissolves into the solid n-octacosane; that V2s is independent of pressure; and that p~ub is lOW SO that gas phase imperfections for pure n-octacosane at the sublimation pressure can be neglected. The temperature T and the pressure P were defined by the conditions under which the n-oc-
tacosane was saturated in the supercritical carbon dioxide. The molar volume of solid n-octacosane V2s was determined from the density given by the manufacturer. Since density change with respect to pressure in the solid phase is negligible, the density of n-octacosane at ambient conditions was used in the calculations. The sublimation pressure of n-octacosane was obtained from correlations reported by Moradinia and Teja [14]. The final variable needed for the solubility calculation is the fugacity coefficient for n-octacosane in the dense gas phase. This was calculated by using a modified Patel-Teja equation of state [15]. The Patel-Teja equation of state was chosen to correlate the pure component solubility data because it is simple and works well for long chain hydrocarbons. The equation is given by RT P= V-b
a[T] - V(V+b) +c(V-b)
'
(A.2)
where a[T], b, and c are the equation of state constants. The equation of state constants for carbon dioxide were obtained by fitting temperature versus vapor pressure, saturated liquid density, and saturated vapor density data. All of the carbon dioxide data were obtained from Angus et al. [16]. Data for n-octacosane are not as readily available. Therefore, the equation of state constants were fit to temperature versus vapor pressure and estimated saturated liquid density data. Estimated values were also used for the critical temperature and critical pressure. Vapor pressure data for n-octacosane was obtained from TRC Tables [17], and the saturated liquid density was estimated from the modified Rackett technique [18]. The critical temperature and critical pressure for n-octacosane were estimated by a carbon number correlation of Teja et al. [19]. In order to estimate the fugacity coefficient, a mixing rule is needed for the n-octacosanecarbon dioxide system. The van der Waals mixing rules with one adjustable binary interaction parameter [15] were used in the calculations. The single binary interaction parameter in the mixture model was optimized using the experimental data of McHugh et al. [20] and Smith et al. [21].
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
Solubility data were not available at the temperature used in this work. Therefore, an interaction p a r a m e t e r was fit to solubility data at the two isotherms closest in t e m p e r a t u r e to the temperature of interest. The required interaction parameter was then obtained by interpolation.
References [1] J.B. Hannay and J. Hogarth, Proc. Roy. Soc. (London) 29 (1879) 324. [2] J.B. Hannay and J. Hogarth, Proc. Roy. Soc. (London) 30 (1880) 178. [3] D.W. Matson, R.C. Petersen and R.D. Smith, Adv. Ceram. 21 (1987) 109. [4] D.W. Matson, R.C. Petersen and R.D. Smith, J. Am. Chem. Soc. 108 (1986) 2100. [5] D.W. Matson, K.A. Norton and R.D. Smith, Chemtech 19 (1989) 480. [6] R.D. Smith, J.L. Fulton, R.C. Petersen, A.J. Kopriva and B.W. Wright, Anal. Chem. 58 (1986) 2057. [7] X.Y. Liu and P. Bennema, J. Appl. Cryst. 26 (1993) 229. [8] P. Bennema and X.Y. Liu, J. Crystal Growth 121 (1992) 679. [9] A.R. Gerson and J.N. Sherwood, J. Crystal Growth 99 (1990) 145.
119
[10] M.G. Broadhurst, J. Res. Natl. Bur. Std. (US) 66 A (1962) 241. [11] D.W. Matson and R.D. Smith, Symp. on Processing, Morphology, Fabrication and Engineering Properties of New Materials, AIChE Meeting, Houston, Texas (1987). [12] R.S. Mohamed, P.G. Debenedetti and R.K. Prud'homme, AIChE J. 35 (1989) 325. [13] J.M. Prausnitz, R.N. Lichtenthaler and E.G. Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed. (Prentice-Hall, Englewood Cliffs, New York, 1986). [14] I. Moradinia and A.S. Teja, Fluid Phase Equilibria 28 (1986) 199. [15] N.C. Patel and A.S. Teja, Chem. Eng. Sci. 37 (1982) 463. [16] S. Angus, B. Armstrong and K.M. Reuck, IUPAC International Thermodynamic Tables of the Fluid Carbon Dioxide (IUPAC Project Center, London, UK, 1973). [17] Thermodynamic Research Center, Thermodynamic Tables. Hydrocarbons (Texas A & M University, College Station, Texas, 1972) k-1030. [18] C.F. Spencer and R.P. Danner, J. Chem. Eng. Data 18 (1973) 230. [19] A. Teja, R. Lee, D. Rosenthal and M. Anselme, Fluid Phase Equilibria 56 (1990) 153. [20] M.A. McHugh, A.J. Seckner and T.J. Yogan, Ind. Eng. Chem. Fund. 23 (1984) 493. [21] V.S. Smith, P.O. Campbell, V. Vandana and A.S. Teja, Intern. J. Thermophys. (1994), submitted.
ELSEVIER
Journal of Crystal Growth 155 (1995) 112-119
Crystallization of n-octacosane by the rapid expansion of supercritical solutions Gregory J. Griscik, Ronald W. Rousseau, Amyn S. Teja * School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, USA
Received 30 September 1994; manuscript received in final form 10 March 1995
Abstract Crystals of a model wax (n-octacosane) were produced by the rapid expansion of supercritical solutions (RESS) containing n-octacosane and carbon dioxide. Pre-expansion temperatures and pressures were varied to study their effects on crystal morphology. Four distinct types of particles were observed, including regular hexagonal crystals and irregular fused particles. Particle size decreased and the particle size distribution narrowed with an increase in pre-expansion temperature. On the other hand, changes in pre-expansion pressure showed no significant influence on particle size.
I. Introduction Changing temperatures and pressures may cause waxes to crystallize from crude oil and natural gas streams, and therefore affect the operation of processing equipment. If these waxes can be made to crystallize in a structure that is less likely to plug, or if the waxes can be prevented from coming out of solution altogether, then a potentially serious problem can be mitigated. Wax deposition from natural gases generally occurs under conditions at which the natural gas is in a supercritical state; therefore, it is important to know the solubility and crystalline behavior of waxes in supercritical fluids. The solubility of a s o h t e in a supercritical solvent is strongly dependent on the pressure and
* Corresponding author. Fax: + 1 404 894 2866.
temperature of the system, and generally increases dramatically near the critical point of the solvent [1,2]. This dramatic change in solubility has been exploited to produce particles in a process known as RESS (rapid expansion of supercritical solutions) [3], in which a solute with a low vapor pressure is dissolved in a supercritical fluid and then expanded rapidly through an orifice or nozzle [4]. Expansion produces conditions far from equilibrium and the solute experiences very high supersaturations, resulting in a large number of nuclei being formed in a very short time (estimated to be of the order of microseconds or less) [5]. A number of RESS variables dictate the morphology of the particles resulting from the expansion. These variables range from the pressure and temperature of the supercritical solution before expansion, to the pressure and temperature of the environment into which the solution is ex-
0022-0248/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-0248(95)00197-2
113
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
panded. The concentration of the solution before expansion, as well as the nozzle geometry and diameter, also play a role in the expansion process [5]. On the other hand, the physical properties of the solute do not directly affect the expansion properties of the system, since the solute is typically at a low concentration and the solution has bulk physical properties very close to those of the solvent [6]. In the present work, we have studied the particle habit of a model wax (n-octacosane) upon expansion from a supercritical solvent (carbon dioxide). Carbon dioxide was chosen as the solvent because it is an important component of natural gas. The solute, n-octacosane, was chosen because it represents a typical paraffin wax and solubility data for this wax + carbon dioxide system are available in the literature and have also been measured in our laboratory [20,21]. There have been no reported studies of the crystallization of waxes from supercritical solutions. However, the structure of n-alkanes obtained by crystallization from a melt has been examined by a number of researchers [7-10]. They have found that alkanes crystallize in different lattice forms depending on carbon number and on the presence of impurities. The morphology of octacosane (n-C28) and dotriacontane (nC32) crystals grown from liquid hexane solutions has been studied by Liu and Bennema [7]. They investigated the effect of concentration and growth temperature (near the roughening temperature) on crystal morphology. In all cases, whether crystals were grown above or below the roughening temperature, the overall shape remained plate-like and only the side faces were affected by changes in crystallization conditions. These studies provide some indication of the morphology of particles that could be obtained in the RESS expansion.
2. Experimental procedure A schematic of the equipment used in this work is shown in Fig. 1. Liquid carbon dioxide was drawn by means of a dip tube from a cylinder (A) and then piped into a battery of piston pumps
I
i
RESS
IJ Fig. 1. Experimental apparatus.
(B) (a Milton Roy miniPump and an Eldex Laboratories Model AA-100-S pump). The pumps were operated in parallel and used to pressurize the carbon dioxide into a reservoir (C) consisting of 1/4 inch o.d. × 1/16 inch i.d. stainless steel tubing. The gas flow was then directed to a frontpressure regulator (D) (Tescom 26-1023-44) and also to a back-pressure regulator (E) (Tescom 26-1722-24). The back-pressure regulator was used to prevent the reservoir from exceeding a predetermined pressure. A purge valve (I) was installed directly behind the front pressure regulator in order to facilitate depressurization of the system. From the front-pressure regulator (D), the carbon dioxide was channeled through two columns (G) immersed in a water bath. The bath was heated and controlled by a circulator/heater (F) (Lauda Model T-I). The high-pressure columns were each about 200 mm in length and packed with alternating layers of n-octacosane and 3 mm glass beads. The supercritical solution from the columns was then directed to valve (H). This valve controlled the flow of carbon dioxide by either allowing the fluid to flow through the columns or past them via a bypass line. Valve (H) was maintained at a constant temperature by heating tape controlled with an Omega temperature controller (Omega CN9000A). The line from the valve to the nozzle was wrapped with heating tape and fiberglass insulation. A thermocouple placed directly before the nozzle allowed the monitoring of solution temperature just before expansion. Heating tape was placed around the nozzle itself, and the temperature in this device was monitored by a thermocouple and a controller (Omega CN9000A) which maintained the
114
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
temperature within _+ I°C. The (pre-expansion) pressure of the system was measured at a point between the valve (H) and the nozzle by a computer-interfaced digital pressure gauge (Heise 901A). The pressure gauge was interfaced with a 386DX personal computer that collected pressure data throughout the operation. The n-octacosane particles suspended in the carbon dioxide jet emanating from the expansion nozzle were collected directly on scanning electron microscope (SEM) sample stubs. Each stub was positioned so that its face was perpendicular to the axis of the carbon dioxide/n-octacosane spray coming from the nozzle. A piece of double-sided SEM tape was placed on the surface for the collection of n-octacosane particles. The RESS parameters of interest are as follows: (1) n-octacosane concentration in supercritical carbon dioxide, (2) pre-expansion temperature, (3) pre-expansion pressure, (4) post-expansion temperature, (5) post-expansion pressure, (6) nozzle type and configuration, and (7) collection procedure. Only RESS conditions 2 and 3 were varied in the present work. The post-expansion temperature was ~ 295 K, the post-expansion pressure ~ 1 atm, and the nozzle configuration was that of a fused silica capillary tube with an inside diameter of 50 /~m and a length of 10 mm. The SEM sample stub was 15 cm from the tip of the nozzle, and the RESS jet was discharged over the sample stub for 20 min. An n-Octacosane mole fraction of ~ 2.5 x 10 -4 was used for each of the pre-expansion pressures. The pre-expansion pressure was determined by calculating the average of the pressure measurements recorded by the computer during each 20 min sampling period. The measured pressure fluctuations were in the range +0.41 bar, which is slightly greater than the measurement error of the pressure gauge, + 0.29 bar. n-Octacosane solubilities in carbon dioxide were calculated at a temperature of 314.8 K and at each of the three pre-expansion pressures used in this work (173.9, 195.7, and 221.6 bar). The solubilities were estimated by the method described in the appendix and the results are given in Table 1. Two aspects of n-octacosane particle morphol-
Table 1 Calculated n-octacosane solubility in supercritical carbon dioxide at 314.8 K Pressure Mole fraction (bar) (×10 4) 173.9 195.7 221.6
2.37 2.47 2.53
ogy were studied. For each sample, particle size and shape were examined and characterized. Particle size was measured directly from the SEM samples that had been sputter coated with gold. For a given particle, the longest dimension and the perpendicular dimension (usually the shortest length) were averaged and defined to be the equivalent diameter of the given particle. All the particle diameters for a specific sample were averaged and a standard deviation computed.
3. R e s u l t s a n d d i s c u s s i o n
Fig. 2 shows that a marked change in particle size occurred in going from pre-expansion temperatures in the range 323 to 373 K (two-phase expansions) to pre-expansion temperatures in the range 413 to 523 K (one-phase expansions). The term two-phase expansion refers to the fact that the path of the expansion of the supercritical carbon dioxide goes through a two-phase (liquid-vapor) region before ending in the vapor phase. One-phase expansion means the carbon 3O 25
20
E
15
u
:E
s 0 313
I
I
I
I
363
4t3
463
513
Pre-Expansion T (K)
Fig. 2. Variation of the mean particle diameter with pre-expansion temperature. ( • ) 173.9bar, ( • ) 195.7 bar, ( • ) 221.6 bar.
G.J. Griscik et aL /Journal of Crystal Growth 155 (1995).112-119 3O
115
dioxide goes directly from the supercritical state to vapor phase. The particles produced with pre-expansion pressures between 323 to 373 K were larger (up to 25 /~m) than those produced at pre-expansion temperatures between 413 and 523 K (5-10/xm). Also, the particles produced in the lower temper-
ature range showed a greater variation in size (Fig. 3). Examination of the photographs revealed the formation of four different types of particles. At the lower pre-expansion temperatures (323 to 373 K), the particles appeared to be a fused mass. A second type of particle was found at pre-expansion temperatures of 413 and 423 K. These particles had sharp and well-defined edges, and the particle size distribution varied less than that at lower temperatures. A third type of particle was produced at pre-expansion temperatures of 433 and 443 K. These particles appeared spherical in shape and were made of densely packed subparticles. A pre-expansion temperature of 523 K produced a fourth type of particles. These particles were spherical in shape but did not appear to be made of any subparticles. Most of the SEM pictures showed the first particle type consisting of masses of subparticles fused together. These particles were produced at pre-expansion temperatures between 323 and 373
Fig. 4. n-octacosane particles produced from carbon dioxide at pre-expansion conditions of T = 373 K, P = 221.6 bar.
Fig. 5. n-octacosane particles produced from carbon dioxide at pre-expansion conditions of T = 423 K, P = 195.7 bar.
°
•
10
~=
¢I a.
0
L1 i i ~ i
313
363
lltl
Ji::;
413
i,,:;:,,,
463
513
Pre-Expansion T (K) Fig. 3. Mean particle diameterwith standard deviationsat a pre-expansion pressure of 173.9bar.
116
G.J. Griscik et aL /Journal of Crystal Growth 155 (1995) 112 119
size was also uniform, especially compared to the size diversity of the samples produced at pre-expansion temperatures between 323 to 373 K. Fig. 8 shows an example of the particles produced at the highest pre-expansion temperature (523 K). These particles were spherical in overall shape and similar in size and shape to particles produced at pre-expansion temperatures of 433 and 443 K. However, the particles produced at 523 K do not appear to be made of any well defined subparticles. The mechanism for particle formation is difficult to determine due to the short time in which the process takes place. Therefore, only an initial hypothesis can be proposed based on solving the mass, energy, and momentum equations for carbon dioxide expanding through a nozzle, combined with the solubility calculations outlined in Appendix A. Our calculations suggest that at pre-expansion temperatures lower than 373 K, nucleation occurs in the nozzle. Moreover, the expanding fluid enters the two-phase region after Fig. 6. n-octacosane particles produced from carbon dioxide at pre-expansion conditions of T = 443 K, P = 195.7 bar. K, which are low enough for two-phase expansion of the carbon dioxide. Fig. 4 shows these fused particles at a pre-expansion temperature of 373 K and pre-expansion pressures of 221.6 bar. Fig. 5 shows a representative picture of samples that were produced with pre-expansion temperatures of 413 and 423 K. A transition to the third type of particle morphology can be seen. For the most part, the particles and constituent subparticles had sharp and well-defined edges. The particles were generally oblong, and showed less variation from particle to particle than in the other types. Figs. 6 and 7 show examples of particles produced at pre-expansion temperatures of 433 and 443 K. The particles are all spherical and composed of densely packed, well-defined subparticles. The subparticles have distinct facets with one face usually being dominant. The plate-like and faceted shape of the subparticles look similar to the crystals of n-octacosane produced from n-hexane by Liu and Bennema [7]. The particle
Fig. 7. n-octacosane particles produced from carbon dioxide at pre-expansion conditions of T = 443 K, P = 221.6 bar.
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
Fig. 8. n-octacosaneparticles produced from carbon dioxide
at pre-expansion conditionsof T = 523 K, P = 221.6 bar. it exits the nozzle. Thus, nuclei are in contact with the supersaturated solution in the nozzle and experience a rapid growth period at high supersaturation. The final particle shape, flat and without distinct side faces, parallels the crystals produced in the work by Liu and Bennema [7] that were grown at high supersaturations that caused roughening of the crystal edge faces. The abrupt expansion from the exit of the nozzle effectively ends the growth phase by crystallizing the remaining solute out of solution. For particles produced at pre-expansion temperatures of 413 K and above, nucleation occurs outside the nozzle and, little or no growth occurs because the solute becomes insoluble relatively quickly. Some coalescence of the nuclei occurs in the expansion jet, so that the overall particles appear to be composed of subparticles. The subparticles are plate-like and also have distinct faceted edges, which would point to only a brief period of growth (growth at high supersaturations
117
causes roughening of the edge faces). The particles produced at a pre-expansion temperature of 523 K are not composed of the plate-like subparticles. The reason for this could be that the solute is forced out of solution at a temperature above its melting point (since the pre-expansion temperature is high) and the molten droplet then solidifies as the jet continues to expand and cool. Since supersaturation occurs more rapidly in these cases and there is little time for growth, these particles are smaller than those produced at pre-expansion temperatures of 373 K and below. Finally, the increased particle size distribution of the particles produced at the lower pre-expansion temperatures could be due to the fact that these particles nucleate inside the nozzle, where there is a velocity profile. This velocity profile leads to different elution times for different particles depending on the location of the particle in the velocity profile. The particles that remain in the nozzle for a longer period of time have more contact with the expanding supersaturated solution, and thus experience a longer growth period. Particles which nucleate outside the nozzle do not experience this growth period and thus have a narrower size distribution.
4. Conclusions
The effects of pre-expansion temperature and pre-expansion pressure were experimentally studied on particles of n-octacosane formed from carbon dioxide by the RESS process. Both particle size and shape were dependent on pre-expansion temperature, whereas pre-expansion pressures did not show any significant effects. These dependences have also been reported by others [11,12]. Particles produced at pre-expansion temperatures between 323 and 373 K were larger, had a wider size distribution, and possessed a distinct shape. Particles produced at or above 413 K were smaller, had a narrower size distribution, and exhibited different overall particle shapes. Fluid expansion calculations and solubility calculations suggest that nucleation occurs in different parts of the expansion process, depending on the pre-expansion temperature. The larger, fused
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
118
particles were produced when nucleation and growth occurred primarily in the nozzle. On the other hand, smaller particles composed of distinct faceted subparticles were produced when nucleation was believed to occur past the exit of the nozzle. Future work will be focused on the expansion calculations in order to test this hypothesis.
Acknowledgement We acknowledge the Exxon Foundation for partial financial support of this work.
Appendix A The n-octacosane solubility in carbon dioxide could not be measured using the apparatus constructed in this study. As a result, the solubility had to be interpolated to the conditions of interest using literature values of n-octacosane-carbon dioxide solubilities. An equation of state approach was chosen for this purpose because it also allows for solubility prediction outside the range of known solubility data. n-octacosane solubilities were calculated using the following equation from thermodynamics [13]: Y2 = Psub2 exp
RT
/(b2P'
(A.1)
where Yz is the solubility of n-octacosane in carbon dioxide at a pressure P, and temperature T. R is the gas constant, V2s the molar volume of n-octacosane, p~ub the sublimation pressure of n-octacosane, and ~2 the fugacity coefficient of n-octacosane in carbon dioxide at P and T. Eq. (A.1) was obtained from the thermodynamic condition of equality of fugacities of the two phases in equilibrium [13]. It assumes that none of the carbon dioxide dissolves into the solid n-octacosane; that V2s is independent of pressure; and that p~ub is lOW SO that gas phase imperfections for pure n-octacosane at the sublimation pressure can be neglected. The temperature T and the pressure P were defined by the conditions under which the n-oc-
tacosane was saturated in the supercritical carbon dioxide. The molar volume of solid n-octacosane V2s was determined from the density given by the manufacturer. Since density change with respect to pressure in the solid phase is negligible, the density of n-octacosane at ambient conditions was used in the calculations. The sublimation pressure of n-octacosane was obtained from correlations reported by Moradinia and Teja [14]. The final variable needed for the solubility calculation is the fugacity coefficient for n-octacosane in the dense gas phase. This was calculated by using a modified Patel-Teja equation of state [15]. The Patel-Teja equation of state was chosen to correlate the pure component solubility data because it is simple and works well for long chain hydrocarbons. The equation is given by RT P= V-b
a[T] - V(V+b) +c(V-b)
'
(A.2)
where a[T], b, and c are the equation of state constants. The equation of state constants for carbon dioxide were obtained by fitting temperature versus vapor pressure, saturated liquid density, and saturated vapor density data. All of the carbon dioxide data were obtained from Angus et al. [16]. Data for n-octacosane are not as readily available. Therefore, the equation of state constants were fit to temperature versus vapor pressure and estimated saturated liquid density data. Estimated values were also used for the critical temperature and critical pressure. Vapor pressure data for n-octacosane was obtained from TRC Tables [17], and the saturated liquid density was estimated from the modified Rackett technique [18]. The critical temperature and critical pressure for n-octacosane were estimated by a carbon number correlation of Teja et al. [19]. In order to estimate the fugacity coefficient, a mixing rule is needed for the n-octacosanecarbon dioxide system. The van der Waals mixing rules with one adjustable binary interaction parameter [15] were used in the calculations. The single binary interaction parameter in the mixture model was optimized using the experimental data of McHugh et al. [20] and Smith et al. [21].
G.J. Griscik et al. /Journal of Crystal Growth 155 (1995) 112-119
Solubility data were not available at the temperature used in this work. Therefore, an interaction p a r a m e t e r was fit to solubility data at the two isotherms closest in t e m p e r a t u r e to the temperature of interest. The required interaction parameter was then obtained by interpolation.
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[10] M.G. Broadhurst, J. Res. Natl. Bur. Std. (US) 66 A (1962) 241. [11] D.W. Matson and R.D. Smith, Symp. on Processing, Morphology, Fabrication and Engineering Properties of New Materials, AIChE Meeting, Houston, Texas (1987). [12] R.S. Mohamed, P.G. Debenedetti and R.K. Prud'homme, AIChE J. 35 (1989) 325. [13] J.M. Prausnitz, R.N. Lichtenthaler and E.G. Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed. (Prentice-Hall, Englewood Cliffs, New York, 1986). [14] I. Moradinia and A.S. Teja, Fluid Phase Equilibria 28 (1986) 199. [15] N.C. Patel and A.S. Teja, Chem. Eng. Sci. 37 (1982) 463. [16] S. Angus, B. Armstrong and K.M. Reuck, IUPAC International Thermodynamic Tables of the Fluid Carbon Dioxide (IUPAC Project Center, London, UK, 1973). [17] Thermodynamic Research Center, Thermodynamic Tables. Hydrocarbons (Texas A & M University, College Station, Texas, 1972) k-1030. [18] C.F. Spencer and R.P. Danner, J. Chem. Eng. Data 18 (1973) 230. [19] A. Teja, R. Lee, D. Rosenthal and M. Anselme, Fluid Phase Equilibria 56 (1990) 153. [20] M.A. McHugh, A.J. Seckner and T.J. Yogan, Ind. Eng. Chem. Fund. 23 (1984) 493. [21] V.S. Smith, P.O. Campbell, V. Vandana and A.S. Teja, Intern. J. Thermophys. (1994), submitted.