Ind. Eng. Chem. Res. 1998, 37, 1991-1997
1991
Development of an Apparatus for Mass-Transfer Studies in Supercritical Fluids John T. Baker and Mark A. Trebble* Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4
A gravimetric analysis apparatus to measure the mass-transfer rates of solid solutes into supercritical solvents has been designed, built, and tested. The heart of the apparatus is a miniature thin film strain gauge load cell which measures the mass of a solid suspended in a flowing fluid continuously over the duration of the experiment. From knowledge of the geometry of the solute pellet, the mass flux at the surface interface is determined directly. In this work, mass flux data was collected for the dissolution of naphthalene into supercritical carbon dioxide at 35 and 55 °C and at pressures ranging from 8359 to 12 000 kPa. From the data, binary diffusion coefficients were calculated and compared with published values to verify the methodology. As the calculated values fall within the range of the published diffusion coefficients, the apparatus can be considered to have been verified successfully and is fully operational. Introduction The industrial use of supercritical fluid (SCF) extraction has been increasing rapidly in recent years. In addition to potential energy savings, supercritical extraction provides higher selectivity and purity. The solvents are typically nontoxic and nonvolatile and do not pose the environmental hazard of the chemical solvents (chlorinated hydrocarbons) which they replace. It is generally understood that the supercritical state enhances the dissolution of solid particles. This is due to higher diffusivities, with lower density and viscosity as compared to liquid solvents (McHugh and Krukonis, 1994). The result is more rapid extraction and phase separation. However, before a system is designed to take full advantage of the solvating powers of supercritical fluids, the quantitative knowledge of underlying fundamentals and the ability to predict them is of utmost importance. Previous work focused on measuring the equilibrium solubilities of hydrocarbons with supercritical solvents, but this is insufficient as it ignores the effects of masstransfer resistances in flowing systems. These resistances often dominate in extraction and equilibrium is rarely achieved. To effectively model the system and to properly design and size equipment, better understanding of rate mechanisms is required. By studying the effects of mass transfer in the laboratory, it is possible to simulate the solvent recovery process with a good deal of accuracy. Liong, Wells, and Foster found that little work has been published on the mass-transfer properties of supercritical fluids as the more traditional methods of measuring transport properties do not work well at SCF pressures and temperatures (Liong et al., 1991). In this work, an experimental apparatus has been built, enabling the direct measurement of the mass transfer from a solid hydrocarbon sphere into a flowing supercritical solvent. Focus is on the design, construction, and testing of an apparatus capable of measuring * To whom correspondence should be addressed. Phone: (403) 220 4823. Fax: (403) 284 4852.
the mass flux of solute into supercritical solvents continuously over the duration of an experiment. Apparatus Figure 1 is a process flow diagram of the experimental apparatus. The solvent is pumped at a given rate into a coil where it is heated above its critical temperature before entering the extractor and contacting the solute. The extractor effluent passes through an on-line densimeter and then through a cold trap to precipitate the solute and finally is depressured through a pressure control valve and vented. Instrumentation outputs are sent directly to a PC-driven data acquisition system where data are recorded. The heart of the apparatus is a cantilever beam load cell used to measure the mass of the solute real-time. It is mounted inside a Ruska model 2329-800 ThroughWindow PVT cell chosen to be the extraction vessel as it allowed for observation of the sphere throughout the duration of the experiment. To mitigate entrance and exit effects, an inlet distributor fabricated from interlaced mesh screens and a 25-mm bed of 3-mm diameter glass beads were installed at the inlet and outlet nozzles, respectively, as shown in Figure 2. The Ruska cell, along with the preheater coil and the densimeter, were placed within a laboratory convection oven capable of controlling the temperature to (0.1 °C. A Ruska model 2248 proportioning pump was provided as the means of both pressurizing and accurately metering the solvent into the apparatus. One of the attractive features of supercritical extraction is the ease of separating the extracted solute from the solvent. However, this does imply that plugging in the effluent piping is a potential problem. The majority of researchers address this problem by first reducing the pressure through a heated pressure-reducing micrometering valve and then collecting the solute in a solvent bath. Instead, we chose to precipitate the solvent at constant pressure by reducing the temperature in a cold trap. The trap consists of four 20-cm diameter coils fabricated from a 3.6-m aluminum tubing string. It is designed to precipitate the solute to coat
S0888-5885(97)00169-3 CCC: $15.00 © 1998 American Chemical Society Published on Web 03/31/1998
1992 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
Figure 1. Process flow diagram of experimental apparatus.
several stages. A micrometer needle valve was placed in series upstream of the Research control valve model XA1-5A fitted with P5 trim and an electric actuator. The feedback control loop was tuned to control the system pressure to within 1% of setpoint with a minimum of oscillation. Spherical pellets were prepared from crushed solute purchased from the Aldrich Chemical Co., guaranteed to be 99% pure laboratory grade. Spheres were cast by first heating the mold and melting the solute in the laboratory oven. Using a syringe, liquid solute was injected into the mold through the sprue hole. A 1-mm diameter alloy hook was then inserted through the sprue hole into the molten solute. As the solute solidified, it contracted, yielding a cavity in the center. To alleviate this problem, additional liquid was injected into the sphere throughout the solidification process. The sphere was then polished lightly and the excess material at the sprue removed. It was weighed on a Mettler analytical balance against a statistical average of previous spheres which had been bisected to ensure there were no voids present. Figure 2. Sectional view of Ruska cell.
the inside wall of the coil. The larger diameter tubing was utilized to reduce the velocity and to prevent plugging. A demister constructed of a packed section of glass wool was incorporated in the outlet to prevent entrainment into the downstream tubing and valves. Sizing calculations indicated a control valve with a coefficient (CV) of < 0.0001 would be required to achieve pressure control for this low-flow, high-pressure-drop system. The alternative was to drop the pressure over
Calibration Calibration of the load cell consisted of hanging dead weights from the cantilever beam and recording the output voltage on the data acquisition system. To check for hysteresis, the procedure was repeated in descending order. From the data, a calibration curve was plotted and a proportionality constant was fitted using least squares regression. The load cell was found able to discern a 5-mg weight change.
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1993
Figure 3. Dynamic weight of suspended naphthalene sphere and carbon dioxide solvent (T ) 35 °C and P ) 8359 kPa).
Figure 4. Dynamic weight of suspended naphthalene sphere and carbon dioxide solvent (T ) 35 °C and P ) 10 000 kPa).
The Rosemount pressure transmitter was calibrated using a dead weight tester. Calibration was performed in the range 3500-14 000 kPa, with one measurement open to atmospheric pressure. Corrections were made for gravity, differential height, barometric pressure, etc., resulting in accuracy greater than 0.5%. The calibration data was regressed using a cubic equation which then directly converted the voltage to pressure within the data acquisition system. Calibration of the thermocouples was performed by immersing them in close contact with a Fisher 902963 mercury thermometer accurate to 0.1 °C in a heating bath.
Results The binary system of supercritical CO2 and naphthalene was chosen to verify the apparatus since there is a wealth of previously published data for the system in question. Figures 3-5 are typical plots of dynamic load (converted to mass) of the suspended sphere at several solvent flow rates. The data were then curve-fitted to eliminate the fluctuations due to noise on the signal and to enable the calculation of an analytical derivative (dM/dt) used subsequently in the flux determination. The form of these equations is tabulated in Table 1. It is important to recognize that the equations only
1994 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
Figure 5. Dynamic weight of suspended naphthalene sphere and carbon dioxide solvent (T ) 55 °C and P ) 12 000 kPa). Table 1. Regressed Equations operating conditions (P and T) 8359 kPa, 35 °C 10000 kPa, 35 °C
12000 kPa, 55 °C
fluid velocity (cm/s)
Reynolds number
equation
avg error (%)
std. dev. (%)
skew (%)
0.002 17 0.004 39 0.006 96 0.001 42 0.004 42 0.018 01 0.029 11 0.042 21 0.003 22 0.006 38 0.012 77
4.7-5.5 8.3-10.0 12.2-17.2 2.2-2.5 7.2-9.0 21.8-35.2 26.4-58.4 41.3-87.3 5.9-7.6 7.5-13.8 9.8-26.4
M ) -8.361e-10t3 + 2.3132e-6t2 - 2.6013e-3t + 3.0536 M ) -1.5977e-11t3 + 1.0317e-7t2 - 5.054e-4t + 1.8354 M ) -1.0513e-10t3 + 5.351e-7t2 - 1.2455e-3t + 2.6861 M ) -4.4247e-10t3 + 1.9039e-6t2 - 2.6461e-3t + 3.694 M ) -5.2075e-11t3 + 2.1985e-7t2 - 9.102e-4t + 2.7092 M ) 4.8931e-10t3 - 8.0542e-7t2 - 1.2568e-3t + 2.2145 M ) 4.6577e-10t3 - 1.1421e-6t2 - 8.6255-4t + 2.8205 M ) 4.8605e-10t3 - 1.0861e-6t2 - 1.1245e-3t + 2.9605 M ) -1.9997e-10t3 + 9.4214e-7t2 - 1.666e-3t + 3.0124 M ) -1.2183-10t3 + 5.3481e-7t2 - 1.4145e-3t + 2.482 M ) 1.2458-10t3 - 4.836e-7t2 - 6.3682e-4t + 2.5301
-0.05 -0.14 -0.098 -0.026 -0.003 -0.025 +0.32 -0.032 -0.023 -0.195 -0.56
(2.18 (3.9 (3.44 (1.78 (1.02 (2.76 (2.97 (2.21 (1.98 (1.71 (3.74
-0.01 +0.265 -0.8 -0.285 +0.119 -0.605 -0.322 +0.488 +0.44 +0.58 +0.395
represent the data over the range fitted and therefore extrapolation would be inappropriate. Determination of Flux Mass flux (j) is defined as the amount of material removed (g) in a given time interval (s) through a known surface area (cm2). Therefore, at the phase boundary it is the change in mass (dM/dt) over the surface area (A). Substitution of the relationship between the geometry and mass of a sphere yields
dM ( dt ) j) 3M (4π) ( ) F 1/3
2/3
(1)
The mass flux for two experiments conducted at a velocity of 0.004 42 cm/s, equivalent to a Reynolds number of 9, are shown in Figure 6. These mass flux data match the predictions of Readey and Cooper (1966) who suggested that “the rate of dissolution initially decreases with time and later increases with time”. This can be explained as the result of two competing effects. Initially, the change in the driving force, that is the concentration gradient, dominates since the concentra-
tion of the solute in solution is rapidly increasing. Later, when the solvent concentration approaches its steady state, the decreasing surface area of the shrinking sphere causes the flux to increase, tending toward infinity. Repeatability and Error Analysis Statistical analysis of the flux values found that at a given 1/xd value, there was an average absolute deviation from the calculated mean of 10.4% with a maximum single deviation of 19% for the runs taken at a fluid velocity of 0.004 42 cm/s. At the velocity of 0.018 cm/s, the average deviation decreased to 6.1% with a maximum value of 10.3%. For the highest obtainable flow rate of 0.0422 cm/s, it had dropped substantially to 3.8% and 8%, respectively. The trend indicates that the precision of the apparatus increases with higher flow rates. Evaluating any error in calculating the diameter involves examining how the mass of the solute is determined. The error in the load cell was resolved to be (5 mg during calibration. Buoyancy calculations required the density of the solute and solvent. The former was calculated by means of a DIPPR correlation and compared favorably to the value given in the CRC
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1995
Figure 6. Mass flux comparison (T ) 35 °C, P ) 10 000 kPa, and v ) 0.004 42 cm/s).
Handbook (1991). Errors in experimental pressure and temperature will affect the solvent density. Statistical analysis found the uncertainty in this apparatus to be (117 kPa and (0.5 °C, respectively, resulting in a 1% variance in the supercritical solvent density. The net effect on the diameter would be an uncertainty of less than 0.2 mm. An uncertainty of (0.2 mm translates into a 2.7% error in the surface area for a 15-mm sphere, but a 4.1% error in a 10-mm sphere. The impact on the flux is also 2.7% and 4.2%, respectively. There are two inherent assumptions in determining the surface area from the mass. First, the interfacial area is that of a smooth sphere. Surface roughness can affect the boundary layer as well as the surface area. However, for spheres cast in the manner outlined, there is little porosity and the assumption is quite valid. The second assumption is that the solute remains spherical throughout dissolution. Spheres were subsequently removed at the completion of each experiment, measurements taken, and the results of standard sphericity calculated:
φs )
6Vp dpAp
Table 2. Parameter Range for Steinberger-Treybal Correlation parameter
Treybal correlation
this work
1-30 000 1.1e7-94.5e7 2.01-8.13
1-90 18.9e7-56.4e7 2.22-5.56
Re (Gr × Sc) D/d
Flux can be expressed in terms of the mass-transfer coefficient (k):
j ) k(∆C) ) k(CR0 - Cb)
where the concentration at the interface CR0 is taken to be the saturated value (Cs) and the bulk concentration (Cb) is estimated as described subsequently. The Sherwood number is the mass-transfer coefficient in a dimensionless form. It expresses the ratio of the overall mass transfer to the mass transfer due to diffusion. For a sphere,
Sh )
(2)
yielded a value of 0.96, indicating that the surface area at the completion of the experiment was about 4% higher than that predicted from the mass. A sensitivity analysis was subsequently performed on the calculated flux values. This consisted of varying each parameter in eq 1 by (5% to evaluate its effect. The sensitivity analysis has shown that there is a oneto-one relationship between the change in the flux to a change in the derivative (dM/dt), but that any error in mass affects the flux by only half this value. Any experimental error in these values was significantly less that this 5% perturbation. Validation The apparatus was verified by modeling the masstransfer data collected, calculating diffusion coefficients, and comparing them to published values for CO2naphthalene in the literature.
(3)
kd DAB
(4)
Upon substitution, eq 3 becomes
j)
ShDAB (Cs - Cb) d
(5)
The Steinberger and Treybal (1960) Sherwood correlation
Sh ) 2 + 0.569(Gr × Sc)1/4 + 0.347(Re × Sc)0.62
(6)
was chosen as an appropriate model as it had been developed for mass transfer from soluble spheres into both liquid and gas solvents flowing in a similar geometrical configuration. Table 2 outlines the conditions over which the correlation is valid. Since the parameters for this study were within the range, use of the correlation should express the mass transfer within the 3-20% average deviation quoted by the authors.
1996 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
Figure 7. Comparison of diffusion coefficients.
Combining eq 5 with the Sherwood number correlation
j)
[
(
)
DAB (981)d3∆F 2 + 0.569 d µDAB
1/4
(( )) ]
10 000 kPa, 35 °C
1/2 0.62
(Cs - Cb) (7)
A Newton-Raphson procedure was employed to solve this nonlinear equation. The solvent density (F) was obtained from the NIST Thermophysical Properties of Pure Fluids Database. The work of Tsekhanskaya et al. (1966), who measured the molar volumes of saturated and unsaturated solutions, was used to calculate ∆F. Likewise viscosity (µ) was obtained from the work of Lamb et al. (1989). To calculate the bulk concentration (defined as the “mixing cup” average concentration) in the vicinity of the sphere, one performs a mass balance on the extractor:
1 dM ∂C ) CinQ˙ in + - CoutQ˙ out ∂t V dt
(8)
Knowing the amount of solute which has dissolved and that which has been removed from the vessel, one can deduce that amount which remains in solution. Integration of eq 8 with respect to time yields this concentration for any given time (t):
∫0tC(t)out dt
1 Cb ) [Mt - M0] - Q˙ out V
operating conditions (P and T) 8359 kPa, 35 °C
+
µ 0.347 Re FDAB
Table 3. Sample Values of Bulk Fluid Concentration
(9)
where Cin ) 0. The concentration of the effluent was determined from the measured density of the binary mixture. However, naphthalene in carbon dioxide has large negative excess volumes even at these low solubilities (Lim et al., 1989); therefore, an equation of state was deemed necessary. The Peng-Robinson (1976) cubic equation of state, with a volume translation to match the density of pure CO2, was chosen. The binary interaction parameter (kij) was tuned to provide a best fit to the published data of Tsekhanskaya et al. (1966) for unsaturated solutions of naphthalene in carbon
12 000 kPa, 55 °C
fluid velocity (cm/s)
CBulk (g/cm3)
0.004 39 0.006 96 0.004 42 0.018 01 0.003 22 0.006 38 0.012 77
0.0126 0.0116 0.0105 0.000 16 0.0146 0.0098 0.0063
dioxide. To test its proficiency, points not used in optimizing the kij were evaluated. This method is able to calculate the mole fraction of naphthalene to within 15% of the correct value. Table 3 summarizes some of the computed bulk concentration values calculated in this manner that were later applied to calculate diffusion coefficients in this work. Figure 7 confirms that these diffusion coefficients fall within the range of those published by other researchers. Taking into account errors in the flux measurement, determining the bulk concentration, modeling, etc., the estimated uncertainty in these diffusion coefficients is approximately (20%. The values tend to be higher than those reported using the chromatography technique and other gravimetric analyses, but lower than that obtained by Lee and Holder (1995) who applied a tortuosity value to their optimized effective diffusivities to arrive at a molecular diffusivity. Conclusions It has been demonstrated that the new apparatus is capable of measuring the dissolution of the solid solute into the solvent over its range of operability. From this measurement, the mass flux at the interface is determined directly given the inherent assumption of sphericity. A high-pressure syringe sampling device has since been fitted to the apparatus to facilitate the withdrawal of 1-cm3 samples from the extractor for injection into a chromatograph. This will enable direct measurement of the bulk concentration. The apparatus has been shown to generate reliable mass-flux data for the high-pressure systems for which it was designed. Real-time mass fluxes have been
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1997
measured directly for the dissolution of naphthalene into carbon dioxide. This flux data will undoubtably be valuable for future mass-transfer modeling. Acknowledgment This work was funded by a Natural Sciences and Engineering Research Council (NSERC) strategic grant. Nomenclature A ) area (cm2) C ) concentration (g/cm3) d ) diameter (cm) DAB ) binary diffusion coefficient (cm2/s) dM/dt ) change in mass (g/s) g ) acceleration due to gravity (981 cm/s2) Gr ) Grashof number, gFd3(∆F)/µ2 (dimensionless) j ) mass flux (g/cm2 s) k ) mass-transfer coefficient (cm/s) M ) mass (g) P ) pressure (kPa) Pr ) Prandtl number, Cpµ/k (dimensionless) Q ) volumetric flow rate (cm3/s) r ) radial distance (cm) Re ) Reynolds number, Fdv/µ (dimensionless) Sc ) Schmidt number, µ/(FDAB) (dimensionless) Sh ) Sherwood number (kd)/DAB (dimensionless) T ) temperature (°C) t ) time (s) v ) superficial velocity (cm/s) V ) volume (cm3) Greek Letters F ) density (g/cm3) µ ) viscosity (g/cm s) ∆F ) density difference (g/cm3) φs ) sphericity (dimensionless) Subscripts b ) bulk solution p ) pellet R0 ) sphere radius s ) saturated solution t ) time t 0 ) time 0 (initial condition)
Literature Cited Chemical Rubber Company. CRC Handbook of Chemistry and Physics: 72nd Edition; Lide, D. R., Ed.; CRC Press: Ann Arbor, 1991. Daubert, T. E.; Danner, R. P.; Sibul, H. M.; Stebbins, C. C. DIPPR® Data Compilation of Pure Compound Properties, Version 9.0 Database 11, Gaithersburg, MD, 1994. Knaff, G.; Schlu¨nder, E. U. Diffusion Coefficients of Naphthalene and Caffeine in Supercritical Carbon Dioxide. Chem. Eng. Process. 1987b, 21, 101-105. Lamb, D. M.; Adamy, S. T.; Woo, K. W.; Jonas, J. Transport and Relaxation of Naphthalene in Supercritical Fluids. J. Phys. Chem. 1989, 93 (12), 5002-5005. Lee, C. H.; Holder, G. D. Use of Supercritical Fluid Chromatography for Obtaining Mass Transfer Coefficients in Fluid-Solid Systems at Supercritical Conditions. Ind. Eng. Chem. Res. 1995, 34, 906-914. Lim, G. B.; Holder, G. D.; Shah, Y. T. Solid-Fluid Mass Transfer in a Packed Bed Under Supercritical Conditions. Supercritical Fluid Science and Technology; ACS Symposium Series 406; American Chemical Society: Washington, DC, 1989; Chapter 24. Lim, G. B.; Holder, G. D.; Shah, Y. T. Mass Transfer in Gas-Solid Systems at Supercritical Conditions. J. Supercrit. Fluids 1990, 3 (4), 186-197. Liong, K. K.; Wells, P. A.; Foster, N. R. Diffusion in Supercritical Fluids. J. Supercrit. Fluids 1991, 4 (2), 91-108. McHugh, M. A.; Krukonis, Val. J. Supercritical Fluid Extraction Principles and Practice, 2nd ed.; Butterworth-Heinemann: Boston, 1994. NIST Thermophysical Properties of Pure Fluids Database, Version 3.1, National Institute of Standards and Technology: Gaithersburg, MD, 1992. Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15 (1), 59-64. Readey, D. W.; Cooper, A. R. Molecular Diffusion With a Moving Boundary and Spherical Geometry. Chem. Eng. Sci. 1966, 21, 917-922. Steinberger, R. L.; Treybal, R. E. Mass Transfer from a Solid Soluble Sphere to a Flowing Liquid Stream. AIChE J. 1960, 6 (2) (June), 227-232. Tsekhanskaya, Y. V.; Iomtev, M. B. Diffusion Of Naphthalene in Compressed Ethylene and Carbon Dioxide. Russ. J. Phys. Chem. 1964, 38 (4) (April), 485-487. Tsekhanskaya, Y. V.; Roginskaya, N. G.; Mushkina, E. V. Volume Changes in Naphthalene Solutions in Compressed Carbon Dioxide. Russ. J. Phys. Chem. 1966, 40 (9) (September), 11521166.
Received for review February 24, 1997 Revised manuscript received January 6, 1998 Accepted January 14, 1998 IE970169U
