Znd. Eng. Chem. Res. 1988,27, 1551-1553 D3113-80, D3263-82, D2790-83, and D887-82. Ghanim, A. N. MSc. Thesis, University of Baghdad, Baghdad, Iraq, 1986. Moore, R. E.; Bischof, A.E.; Robins, J. D.; Bronneman, D. R. Met. Prop. Perform. 1972, 11(3),41. Pierce, W. C.; Haenisch, E. L.; Sawyer, D. T. Quantitative Analysis, 4th ed.; Wiley: New York, 1958. Quraishi, M. S.; Fahidy, T. Z. Can. J. Chem. Eng. 1981, 59, 563. Schmidt, N. 0.;Wiggins, L. F. Ind. Eng. Chem. 1954, 46, 867. Smith, C. F.; Nolan, T. J.; Crenshaw, P. L. JPT, J. Pet. Technol. 1968,20(11), 1249.
1551
'Present address: United Nations-ESCWA,
Baghdad, Iraq.
Numan A. Abdul-Latif,* Suham H. F. Al-Madfai,' Alaa N. Ghanim Department of Chemical Engineering University of Baghdad Baghdad, Iraq Received for review April 27, 1987 Revised manuscript received April 15, 1988 Accepted May 2, 1988
An Improved Equation for Predicting the Solubility of Vegetable Oils in Supercritical C 0 2 An improved equation of Chrastil's model was developed for predicting the solubility of vegetable oil (c, gram of oil/liter of COO)in compressed COz as a function of temperature (2') and density (p), which accounts for variations of the solute's heat of vaporization with temperature: c = exp(40.361 - 18708/T 2186840/P)p'0.724f 2.7. The equation was validated for absolute temperatures from 293 to 353 K and pressures between 150 and 880 a t m and adequately predicted solubilities under 100 g/L within the region suggested for commercial supercritical fluid extraction of food components.
+
Supercritical fluid extraction (SFE) has been proposed as a viable alternative to current extraction processes used by the vegetable oil industry. Carbon dioxide (CO,) is an ideal solvent for foods because it is (a) nontoxic, nonflammable, and nonexplosive; (b) available with high purity and a t low cost; (c) highly selective for some solutes, such as lipids, and (d) separable from the extracted solutes (Stahl et al., 1980; Friedrich, 1984). According to Rizvi et al. (1986a,b), a quantitative representation of the phase equilibria between the solute(s) and the solvent is required to evaluate optimal conditions for the extraction process. Rizvi et al. (1986a) have reviewed those attempts to relate the solubility of liquids and solids to the pressure and temperature of the supercritical fluid (SCF) based on chemical potentials, fugacities, and solubility parameters. Chrastil (1982) derived an equation relating the solubility directly to the density of the SCF, which predicted the solubility of several solutes in supercritical COz (SC-C02)over a range of pressures and temperatures. Major drawbacks of Chrastil's equation are that it is valid for solubilities under 100-200 g/L and for a restricted temperature range. This work presents an improved version of Chrastil's equation allowing the solubility of vegetable oils to be estimated in compressed COz. The equation has been tested with data from the literature.
Model and Methods Chrastil (1982) related the solubility of the solute (c, g/L) to the density ( p , g/mL) and the absolute temperature (T, K) of gas B by the following equation, based on a physicochemical model where one molecule of A associates with k molecules of B to form a solvatocomplex which is in equilibrium with the gas: ln
C
+
+
= 9 - hl ( [ l o o o M ~ ] ~ / [ Mk~h f ~ ] )
AH/RT
+ k In p
(1)
where MAand MB are the molecular weights, k is an association number, A H is the total reaction heat (heat of solvation plus heat of vaporization of the solute), and q is a constant. According to eq 1, a plot of In c versus In p for isothermal conditions should give a straight line with slope k and an intercept Z for p = 1 g/mL. This behavior was first ob0888-5885/88/2627-1551$01.50/0
served by Stahl et al. (1978) who measured the solubility of sugars, amino acids, and other polar compounds in SC-C02up to 1974 atm. Furthermore, if I values &e., the natural logarithm of the solubility c for p = 1 g/mL) for different isotherms are plotted against 1/T, a straight line with a slope m and an intercept b would be obtained, i.e.,
I =b
+ m/T
(2)
where b = q - ln ([lO0OhfBlk/[M~ + kMB])and m = AH/R. Hence, an empirical modification was introduced to eq 1to compensate for the variation of AHvapwith temperature:
I = b'+ m'/T
+- n ' / T 2
(3)
Local AH(T) values were evaluated as H = R d I / d ( l / T ) = R(m'+ 2n'/T). Constants of the model, i.e., b', k, m', and n', were estimated by a multivariable linear regression analysis for In c as a function of In p, 1/T, and 1/T2, using a software package for data analysis from SAS (Statistical Analysis System), in a IBM 4341 computer under CMS.
Data The improved equation was validated with data from Stahl et al. (1980) on the solubility of soybean oil a t 293 and 313 K between approximately 150 and 340 atm and of sunflower seed oil at 313 K between approximately 230 and 670 atm and with data from Friedrich (1984) on the solubility of soybean oil a t 313, 323,333, and 343 K from approximately 200 to 680 atm; cottonseed oil a t 313,323, 328,333,343, and 353 K from approximately 750 to 1020 atm; and corn oil a t 353 K and 264 atm. The density of the compressed solvent was evaluated by double-square interpolation in tables for the compressibility factor of C02 (2,dimensionless) as a function of the pressure (p, atm) and the reciprocal of the absolute temperature (T-l, K-l) (Pickering, 1928), as p
= 0.5362 [ p / Z ( p ,T-l)T ]
(4)
The solubility data of Stahl et al. (1980) (Figures 4 and 5 in the original reference), formerly expressed in milligrams of oil/nanoliter of COz (where 1L of COz = 1.8420 g of COz, or the weight of 1L of gas at 293 K and 1atm), 0 1988 American Chemical Society
1552 Ind. Eng. Chem. Res., Vol. 27, No. 8, 1988
Table I. Regression Analysis of the Improved Equation degrees of freedom
source of variation
sum of mean squares square F value Analysis of Variance 3 53.846 17.949 2369.9 0.008 47 0.356 50 54.202 parameter std t for H,: estimate error parameter = 0 Parameter Estimates 40.361 3.824 10.556 -18708 2448 -7.641 2 186 840 391 334 5.588 10.724 0.178 60.219
model error total variable intercept 1/T* 1/ T In P
prob. > F 0.0001 prob. > It1
3-
0.0001 0.0001 0.0001 0.0001
2i-
\ \
I
I
000278
I
I
000294
I
I
I
000313
I
~
000333
000357
l/T[K-’] A 360 340 320 300
I
1$
Figure 2. Estimated logarithm of the solubility of vegetable oil in COz compressed to 1 g/mL (I)as a function of the reciprocal temperature.
1-
0806r 04
-
0
0
,
07
I
08
09
10
11
P[glmll
Figure 1. Solubility of vegetable oils
in compressed COz as a function of solvent density ( p ) . Solid lines represent values predicted by eq 5.
A
(c)
were transformed to grams of oil/liter of C02 multiplied by p/1.8420. The solubility data of Friedrich (1984) (Table I in the original reference), formerly in weight percent, were also expressed as grams of oil/Liter of C02 multiplied by lop.
The new equation was further validated with data of de Filippi (1982) (Figure 2 in the original reference) at 293 and 328 K and data from Stahl et al. (1980) a t 293 K, for the pressure range between 125 and 500 atm.
Results and Discussion The fitted model derived was In c = 40.361 - 18708/T + 2186840/T2
+ 10.724 In p
(5)
r2 = 0.99
The statistical analysis of the regression equation is presented in Table I. The effect of T and p on c is statistically significant a t a confidence level of 0.0170,and b’, m‘,n’, and k are all significantly different from zero at the same confidence level. Data of log c versus p are plotted in Figure 1. Straight lines represent selected isotherms between 293 and 353 K as predicted by eq 5. As shown in Figure 1,there is good agreement between observed and predicted solubilities for values below 100 g of oil/L of C 0 2 and p under 880 atm. Predicted I values are plotted against 1 / T in Figure 2. In the experimental region under study, an almost linear relationship between I and 1/T exists, which represents
002
c
To 293°K 293OK 328OK
REFERENCE Slahl e ol (1980)
de Filippi de Filiwi
I
(1982 (1982)
I
1
I
300
400
500
P [atml Figure 3. Isothermal solubility curves for vegetable oils in compressed COz as a function of pressure for 293 and 328 K. Solid lines represent values predicted by eq 5.
a slight variation of AH with temperature. Calculated values for k and -AH were 10.724 and 7.512, respectively, and fitted in the range for many different solutes in SC-C02 (1.463-12.095 and 2.388-34.485 for k and -AH, respectively) as reported by Chrastil (1982). Isotherms of In c versus p for 293 and 328 K are presented in Figure 3. Data of de Filippi (1982) and Stahl et al. (1980) are adequately predicted by the model, particularly considering the scattering of the experimental data. In conclusion, eq 5 adequately represents the solubility of several vegetable oils in compressed C 0 2for temperatures between 293 and 353 K and pressures from approximately 150-200 t~ 680 atm for 353 K, 880 atm for 353 K, 750 atm for 343 K, and 880 atm for 333 K or less. Conditions under which this equation is valid coincide with the practical region for SFE of vegetable oils. Hubert and Vitzthum (1978) established the range between 308 and 353 K as the preferred one for the SFE with C02. According to de Filippi (1982), applications a t pressures higher than 265-473 atm should be rejected because of the high cost of processing equipment, but Friedrich (1984), based upon the improvements in solubility at temperatures of 328-333 K and pressures above 543 atm, recommended SC-C02 extraction of lipid-containing substrates under these conditions.
I n d . E n g . C h e m . R e s . 1988,27, 1553-1555
Acknowledgment The authors acknowledge financial support from the Direcci6n de InvestigaciGn, Universidad Cat6lica (DIUC), through Grant 36/85. Registry No. COz, 124-38-9.
Literature Cited Chrastil, J. "Solubility of Solids and Liquids in Supercritical Gases". J. Phys. Chem. 1982,86,3016-3021. de Filippi, R. P. "COPas a Solvent Application to Fats, Oils and Other Materials". Chem. Ind. (London) 1982, 385-394. Friedrich, J. P. "Supercritical COz extraction of lipids from lipidcontaining materials". U.S. Patent 4, 446, 923, 1984. Hubert, P.; Vitzthum, 0. G. "Fluid Extraction of Hops, Spices and Tobacco with Supercritical Gases". Angew. Chem., Int. Ed. Engl. 1978,17, 710-715. Pickering, S. F. "p-v-TRelations in the Gaseous State for Substances which are Gases at 0 "C and 1 atm". In international Critical Tables of Numerical Data, Physics, Chemistry and Technology, 1st ed.; Washburn, E. W., Ed.; McGraw-Hill: New York, 1928; VOl. 3, p 3. Rizvi, S. S. H.; Benado, A. L.; Zollweg, ,J. A,; Daniels, J. A. "Supercritical Fluid Extraction: Fundamental Principles and Modeling Methods". Food Technol. 19868,40(6), 55-65.
1553
Rizvi, S. S. H.; Daniels, J. A.; Benado, A. L.; Sollweg, J. A. "Supercritical Fluid Extraction: Operating Principles and Food Applications". Food Technol. 198613, 40(7), 57-64. Stahl, E.; Shilz, W.; Schutz, E.; Willing, E. "A Quick Method for the Microanalytical Evaluation of the Dissolving Power of Supercritical Gases". Angew. Chem., Int. Ed. Engl. 1978, 17, 731-738. Stahl, E.; Schutz, E.; Mangold, H. K. "Extraction of Seed Oils with Liquid and Supercritical Carbon Dioxide". J.Agric. Food Chem. 1980,28, 1153-1157.
Jose M. del Valle Department of Food Science University of Illinois a t Urbana-Champaign 3820 Agricultural Engineering Sciences Building 1304 W e s t Pennsylvania Avenue Urbana, Illinois 61801
Jose M. Aguilera* Department of Chemical Engineering Pontificia Universidad Catolica de Chile P.O. Box 61 77 Santiago, Chile Received f o r review November 19, 1987 Revised manuscript received April 18, 1988 Accepted April 30, 1988
A Simple Meter with Zero Pressure Drop for Gas Flows A simple and inexpensive meter with zero pressure drop for gas flows has been developed. A number of these meters have heen in continuous operation for several years. The working principle, as well as operating experience and design rules are presented in this paper. Measuring the rate of flow of a gas produced by microorganisms is a delicate task. Maintaining a gas-producing system a t a constant pressure is difficult because gas meters in general cause a pressure drop. The problem is further aggravated if the system hai3 to be kept a t atmospheric pressure; the need for atmospheric pressure may be called upon in order to prevent gas, from leaking out to the surroundings. The present paper describes the experience with a simple meter developed primarily for laboratory and pilotplant experiments; see Figure 1. The meter determines the on-line rate of flow with virtually zero pressure drop. The operation of the apparatus can be adjusted in such a way that the system pressure can be maintained on an arbitrary level. The pressure can be selected as negative, relative to the atmosphere, which enables the use of the gas meter as an inherent gas pump.
Description of the Flow Meter
A schematic diagram of the meter is shown in Figure 2. The meter consists of a gas cell and two valves at the inlet and outlet control, respectively, of the gas to be measured. The box is both an electronic control and recording unit. Figure 3 displays how the gas cell works. The gas enters the cell from the top and passes through the inner tube. As the gas enters the jacket, the liquid level sinks a t the same rate as gas is supplied. When the level of water in the jacket reaches the lower level electrode, the inlet valve closes and the outlet valve opens. Hence, the gas is passed out by means of an aspirator. At the same time, the water level increases in the jacket until it rieaches the upper electrode. Here, the control unit switches the valves again, and the cycle is repeated. 0S8S-5SS5/S8/2627-1553$01.50/0
In the present illustration, Le., Figure 3, the level of the water in the external beaker has been adjusted to the same level as the exit hole of the inner tube. Thus, the gas is maintained a t atmospheric pressure throughout the system. On the other hand, if the water level of the external communicating vessel is below the exit hole of the inner tube, the gas meter works as an inherent pump. Hereby a negative pressure is maintained in the flow meter. Similarly, the meter can be kept at an excess pressure by adjusting the level of the communicating vessel upward. The determination of the rate of flow is based on the number of cycles per time unit. Furthermore, the volume between the two level electrodes inside the jacket has to be known very accurately. The quickest and easiest way to determine this volume is to connect a syringe to the gas inlet and inject air until the valve closes. The accuracy of the meter is in this case determined by the accuracy of the syringe. The gas meter shown in Figure 2 has been equipped with a counter, which records a pulse for each cycle. The rate of flow can thus be obtained by manually reading the number of counts as a function of time. The control and recording unit can also be connected to a device such as a strip chart recorder or a desk top computer, which enables the time for each pulse to be registered.
Operating Experience Several meters have been tested on various types of equipment for biogas production from wastewaters and energy crops. One meter has been in continuous operation for over 2 years to measure gas production in an anaerobic fixed-film reactor. The rate of flow of gas varied up to 50 L/day (6 X m3/s) for this system. Figure 4 shows the record for continuous operation of the meter over a period 0 1988 American Chemical Society
