Ind. Eng. Chem. Fundam. 1982, 2 1 , 413-416 Amundson, N. R. “Mathematical Methods in Chemical Engineering, Matrices and their Applications”; Prentlce Hall: Englewood Cliffs, NJ, 1966. Arnold, K. R.; Toor, H. L. AIChE J. 1987, 13, 909. Bandrowski, J.; Kubaczka. A. Int. J. Heat Mass Transfer 1981, 2 4 , 147. Bird, R. B.; Stewart, W. E.;Lightfoot, E. N. ”Transport Phenomena”; Wiley: New York. 1960. Buffham, 8. A.; Kropholler, H. W. Conference On Line Computer Methods Relevant to Chemical Englneering, UnkrersRy of Nottingham, 1971. Burchard, J. K.; Toor, H. L. J. W y s . Chem. 1982,66, 2015. Catty, R.; Schrodt, T. I n d . Eng. Chem. Fundam. 1975, 14, 276. Cotrone, A.; deGlorgi, C. Ing. Chim. Ita/. 1971, 7 , 84. Cullinan. H. T. Ind. Eng. Chem. Fundam. 1885,4 , 133. Cussler, E. L. “Multicomponent Diffusion”; Elsevier: Amsterdam, 1976. Crank, J. “The Mathematics of Diffusion”, 2nd ed.; Ciarendon: Oxford, 1975. Dekncey, G. B. J. Phys. Chem. 1989, 73, 1591. Deiancey, G. B. Chem. Eng. Sci. 1972,2 7 , 555. Dekncey, 0. B. Chem. Eng. Sci. 1974,2 9 , 2307. Dekncey, G. B.; Chiang, S. H. Ind. Eng. Chem. Fundam. 197Oa, 9 , 138. Dekncey, G. B.; Chkng, S. H. Ind. Eng. Chem. Fundam. 197Ob, 9 , 344. Krishna. R. Chem. Eng. Sci. 1978,33, 765. Krishna, R.; Panchai. C. B.; Webb, D. R.; Coward, I . C. Lett. Heat Mass Transfer 1978,3 , 163. Krishna, R.; Standart, G. L. AIChE J. 1978,22, 383. Krishna, R.; Standart, G. L. Chem. Eng. Commun. 1979,3 , 201.
413
Smith, L. W.; Taylor, R. Ind. Eng. Chem. Fundam. 1982,in press. Standart, G. L.; Krishna, R. Lett. Heat Mass Transfer 1979,6 , 35. Stewart, W. E. AIChE J. 1973, 19, 398. Stewart, W. E.; Prober, R. Ind. Eng. Chem. Fundam. 1984,3 , 224. Taylor, R. Chem. Eng. Commun. 1981a, 10, 61. Taylor, R. Lett. Heat Mass Transfer 1981b,8 , 397. Taylor, R. Lett. Heat Mass Transfer 1981c,8 , 405. Taylor, R. Comput. Chem. Eng. 1982,6 , 69. Taylor, R.; Webb, D. R. Chem. Eng. Commun. 1980, 7 , 287. Taylor, R.; Webb, D. R. Comput. Chem. Eng. 1981, 5 , 61. Thambvnavaaam. R. K.: Winter, P.; Branch, S. W. Trans. I . Chem. E . 1980, 58,’27?. Toor, H. L. AIChE J. 1957,3 , 197. Toor, H. L. AIChE J. 1984, 10, 448, 460. Toor, H. L. Chem. Eng. Sci. 1985,20. 945. Toor, H. L.; Marchello, J. M. AIChEJ. 1958, 4 , 97. Webb, D. R.; Sardesai, R. G. Int. J. Multiphase Flow 1981, 7 , 507. Wilkinson, J. H. “The Algebraic Eigenvalue Problem”; Clarendon: Oxford, 1965.
Received for review July 13, 1981 Revised manuscript received May 13, 1982 Accepted July 28, 1982
Estimating Gaseous Diffusion Coefficients from Passive Dosimeter Sampling Rates, with Application to HF Michael S. Young and Jamie P. Monat* WaMen Division of Abcor, Inc., Wilmington, Massachusetts 0 1887
Knowledge of gaseous diffusion coefficients is important for many gas-phase mass-transfer operations. I n many instances, these diffusion coefficients are difficult to measure with simple techniques. I n this paper, it is shown that passive dosimeters may be used experimentally to determine diffusion coefficients for species that are efficiently sampled by this technique. Examples are presented, and the method is applied to the determination of the HF-inair diffusivity, a quantity for which no previous experimental data have been published.
Introduction Gaseous diffusion coefficients are important for the quantitative description of many gas-phase mass-transfer operations, among them gas chromatography, diffusion separations, and gas-phase catalysis. In one recent application, predictable molecular diffusion has been used for the quantitative sampling of work-place atmospheric pollutants. In this correspondence it is shown that good estimates of gaseous diffusivities can be obtained from experimentally determined sampling rates for such diffusion-controlled sampling devices. Because the calibration procedure employs a dynamic test atmosphere, refinements of the method described herein may be of use in determination of gaseous diffusion coefficients for materials that are too reactive for normal static or chromatographic measurements, or for such materials that show large variations of diffusivity with relative concentration of the diffusing species. Good diffusivity estimates may be obtainable for binary mixtures where one of the diffusing species exists for as short as a few seconds. One must exercise caution in the application of this technique, however; it is valid only for those species that are efficiently sampled by passive dosimetry, and blind application of it to species for which collection efficiency has not been validated may lead to erroneous conclusions. Theory A number of devices have been marketed in recent years in which the limiting resistance to mass transfer is con0196-4313/82/ 1021-0413$0 1.25/0
tained in a current-free air layer of fixed geometry located between the diffusion opening of the device and an efficient sorbent located within the device. Palmes and Gunnison (1973) and Tompkins and Goldsmith (1977) have described in detail this mass-transport to two similar types of diffusion samplers. They have shown that the sampling rate for a diffusion sampler is given by eq 1for 100% collection efficiency and ideal response. DAC, N = - L (1) where N = diffusive sampling rate (mol/s), A = crosssectional area of diffusion path (cm2),L = diffusion path length (cm), C , = ambient concentration of pollutant (mol/cm3),and D = diffusivity of pollutant in air (cm2/s). N is measured by chemical analysis subsequent to controlled exposure of the device to known test atmospheres. For the Gasbadge dosimeter, an experimental calibration factor (R)is generally used to account for such parameters as less than 100% collection efficiency and adsorptive losses internal to the device. Equation 1is thus modified DRAC, N=Ir
where R is the experimental calibration factor. It is clear from eq 2 that the product D X R can be determined in a controlled test atmosphere experiment in which A and L are known, C , is measured by independent sampling 0 1982 American Chemical Society
414
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Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982
TO GC GAS SAMPLING VALVE
S O L V E N T MIXTURE INTRODUCED BY
I
I
U
U
m-l
M I X I N G 2' EXPOSURE CHAMBER CHAMBERS
COMPRESSED AIR
Figure 1. Organic vapor exposure system.
means, and N is determined analytically. Experimental Section Gasbadge dosimeter sampling rates (N) were measured for 10 organic solvents, ammonia (NH,), and hydrogen fluoride (HF) in controlled test atmosphere exposure chamber runs. For all experiments the relative humidity was 50% and the temperature ranged from 23 to 38 OC. Equipment a n d Instrumentation Controlled exposures to known test atmospheres were conducted with the exposure system illustrated in Figure 1. Airflow was controlled with calibrated flowmeters (Fisher & Porter No. 10 A 1338N32AX (10 L/min)) to yield 20 L/min maximum flow. All manifold tubing was glass or PVC. Humidity was controlled by diverting part of the gas stream through water-filled gas dispersion bottles. The dry and saturated streams were then re-mixed to yield the desired humidity. The syringe injector (employed for organic exposures) was constructed in our lab and was driven by an adjustable speed motor (Harvard Apparatus). The injection port temperature was adjustable to facilitate rapid solvent evaporation. The test gas was subsequently cooled to room temperature with a condenser before entering the exposure chamber. The exposure chamber employed for organics and ammonia was made of polycarbonate and was 51 cm X 3.3 cm X 6.5 cm (i.dJ; it could house up to seven Gasbadge dosimeters. A similar exposure system was used for the H F experiments; it is described in detail elsewhere (Young and Monat, 1981). Manifold and exposure chambers were constructed of polypropylene to minimize adsorptive effects. Gas chromatography was carried out on a Perkin-Elmer Sigma I system (Perkin Elmer, Norwalk, CT) or on a Perkin-Elmer Model 3920 interfaced with the Sigma I data handling system. For all analyses, the carrier gas was nitrogen a t 30 cm3/min, and a flame ionization detector (FID)was used exclusively. Hydrogen and air flows to the FID were as suggested by the manufacturer for general operation. For samples containing tetrachloroethylene only, the in. analytical column was 0.91 m (3 ft) long X 3.2 mm 0.d.) stainless steel packed with 80/100 mesh Porapak Q. The oven temperature was 190 "C isothermal. All other analyses were accomplished with a 6.2 m (20 ft) X 3.2 mm in.) 0.d. stainless steel column packed with 10% SP-1000 liquid phase on 80/lOO mesh Supelcoport. For multicomponent mixtures, the oven was programmed from 80 to 190 OC a t 8'/min. Single component analysis was done at the appropriate isothermal temperature. Columns were obtained from Supelco, Bellafonte, PA.
Colorimetric measurements were made with a Brinkman Model PC-600 colorimeter equipped with a 2.0-cm path length fiberoptics probe. Fluoride analyses were carried out with a fluoride ion selective electrode (Orion Model 96-09 combination). The potential was measured with a digital pH-mV meter (Orion Model 701A). All reagents were ACS reagent grade or better. Procedures For all experiments, the relative humidity was set at 50 f 3%. To generate organic vapor test gas mixtures, liquid organic solvents were injected via the motor-driven syringe into the humid air stream in either a mixture of up to five components or individually. Five to seven organic vapor Gasbadge dosimeters (Abcor Development Corp., Wilmington, MA) were placed in the polycarbonate exposure chamber and exposed for approximately 6 h to the generated contaminant air stream at a flowrate of about 250 cm3/s. The exposure chamber's internal dimensions were modified with shims to yield a face velocity of about 40 cm/s past the dosimeters. During exposure runs, the chamber air was independently sampled to determine the true integrated concentration of contaminant(s) by collection of the organic vapors on carbon adsorption tubes (SKC Lot-107, NIOSH type). Flow was controlled using 30 gauge X 2.5 cm stainless steel syringe needles as critical orifices, to give an air flow rate of 0.5 to 1.0 cm3/s, depending on the individual needle. Generally three tubes were exposed per run,with a relative standard deviation of better than 3.0%. After exposure, all dosimeter and reference carbon tube samples were desorbed with 3.0 mL of carbon disulfide. After 30 min of agitation, 2.0 pL of each sample was injected into the gas chromatograph. NH3 test gas was generated in the same manner as the organics except that a calibrated cylinder of 1000 ppm of NH, in nitrogen (Matheson) was used for the NH, source instead of the syringe injector. Seven dosimeters were exposed per run in the NH, study. During exposure runs, the true integrated NH3 concentration was determined by collection of the NH3 in midget impingers containing 0.05 M sulfuric acid solution. Air flow was controlled with calibrated 1.0-L/min critical orifices (Millipore). The absorbed NH3 was determined by direct nesslerization and measurement of absorbance at a wavelength of 440 nm. Gasbadge dosimeter collection media were prepared as specified by Mazur et al. (1978) and were used with the organic vapor dosimeters. After exposure they were desorbed with 5.0 mL of distilled water which was subsequently filtered; the absorbed NH3 was determined in the
Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982 415
Table I
substance benzene .__. (Fuller et al., 1966) n-hexane (Lugg, 1968) chlorobenzene (Fuller et al., 1966) n-heptane (Fuller et al., 1966) styrene (Lugg, 1968) tetrachloroethene (Lugg, 1968) toluene (Fuller et al., 1966) l,l,l-trichloroethane G u m , 1968) trichloroethane ( L w , 1968) ammonia (Fuller et al., 1966) means
substance hydrogen fluoride
A. Materials with Published D o no. published Do( T) of est Do(T) assuming R = 0.857 in air obs measd R 0.0962 (298.2) 33 0.816 i: 0.026 0.0916 i 10% (RSD)6
concn anal range, methppm odb 0.8-3.0 GC
% dev,
est/measd -4.8
10-37
GC
10%
+ 7.1 + 8.8
13-61
GC
f
11%
-0.2
9-34
GC
0.0788 0.0741
t
11%
i
10%
+12.4 -7.0
15-259 29-322
GC GC
0.825 i: 0.024
0.0828
i
10%
-3.7
13-47
GC
0.028
0.0766
t
10%
-3.5
15-336
GC
0.0818 f 9%
-6.5
14-68
GC
0.237
-4.1
15-50
C
0.0732 (298.0)
33
0.918
i:
0.032
0.0784
f
10%
0.0740 (299.1)
21
0.932
f
0.028
0.0805
i:
0.0740 (303.2)a
33
0.855
f
0.033
0.0738
0.0701 (298.0) 0.0797 (298.0)
54 42
0.963 0.797
?I
0.039 0.022
0.0860 (299.1)
33
0.0794 (298.0)
28
0.827
0.0875 (298.0)
21
0.801 i 0.019
0.247 (295.1)
21
0.822
i
0.05
0.867
t
7.0%
i:
t
t
13%
-0.15
B. Material (HF) with No Published D, est D o (298), no. of measd assuming calcd D o (298) obs D o X R (298) R = 0.857 0.247 (FSG) 91 0.209 f 0.04 0.244 t 0.05 0.243 (WL-HBS)
t
7.0%
% dev est/calcd
concn range, ppm
anal methodb
-1.2 (FSG) +0.4 (WL-HBS)
0.1-350
ISE
a Value for diffusivity in nitrogen. Abbreviations: GC, gas chromatography ; C, colorimetry; ISE,ion-selective electrode; RSD, relative standard deviation; SD, standard deviation; FSG, Fuller, Schettler, and Giddings (see text); WLHBS, Wilke and Lee (see text).
same manner as for the impinger samples. For the HF studies, the HF source was a set of 30 cm permeation tubes (Metronics 19X-430). Three to five Gasbadge HF dosimeters were placed in the polypropylene exposure chamber and exposed for approximately 4 h to the contaminant air stream at a flowrate of about 500 cm3/s and a face velocity of about 50 cm/s past the dosimeters. During exposure runs, the true integrated concentration was determined by collection of HF in midget impingers containing 1.0 M sodium hydroxide solution. Flow was controlled as for NH3 collection. After exposure, the absorbed HF for both impinger and dosimeter samples was determined with the fluoride ion-selective electrode.
Results and Discussion Organics and NH3. Measurement of R Values. Results for the organics and ammonia are summarized in Table I. Unless otherwise noted, the mean is given for the central value and the standard deviation is given for the dispersion. The dosimeter sampling constant, R, was calculated from eq 2 for all materials having known diffusivities. It was shown that the response factor R was fairly consistent for the materials studied. Furthermore, R was similar for adsorptive collection (organics) and for collection by reactive absorption (ammonia). The average value for R was 0.857 f 7%. R values were calculated from measured sampling rates (N) assuming that N varies with temperature as does D (eq 3) (3) where Do = the pollutant diffusivity at 298 K and 1atm. The data for R suggest that for efficiently sampled materials, the R factor arises mostly from badge design or
experimental bias rather than from differences in the collection media or in the nature of the diffusing species. Experimental Estimates of Diffusivities. The diffusion coefficient of an efficiently sampled material ( R I 0.8) can be accurately estimated from an observed diffusive dosimeter sampling rate, but only if the dosimeter sampling constant R is accurately known for that species. There may be some species for which R cannot be accurately determined, or for which R is not constant with concentration; this method would therefore be inappropriate for such materials. It was shown above that, for the species studied, R was relatively constant. It should be expected then that good estimates of Do may be obtained from the measured sampling rates (N) for those materials assuming that R is constant and equal to 0.857. The values in column 5 of Table I are values of the respective diffusion coefficients as determined from sampling rates (N), using eq 2 and assuming R = 0.857. For the ten materials, the average bias and precision of the predicted diffusivities are -0.15% and &7.0%, respectively. Hydrogen Fluoride (HF). Measurement of D o X R Values. Recently the authors adapted the Gasbadge dosimeter design to the monitoring of hydrogen fluoride (HF) vapor (Young and Monat, in press). This design employs a highly efficient alkaline absorbent as the collection medium and yields linear response to ambient HF concentration between 0.075 and 330 mg/m3, with *lo% accuracy. The observed value for Do X R could not be compared with experimental data for the HF diffusion coefficient, for such data do not appear to exist. Calculated Values for HF Diffusivity. A number of formulas have been advanced over the years to estimate gaseous diffusion coefficients where experimental data are
416
Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982
unavailable. Of these the methods of Fuller et al. (1966) (FSG), and the Wilke-Lee modification of the method of Hirshfelder et al. (Wilke and Lee, 1955) (WL-HBS), have been shown to be accurate to better than f10% for prediction of binary diffusion coefficients for gas pairs composed of a polar and nonpolar component (Fuller et al., 1966). The HF diffusivity in air was therefore calculated from each formula. For the FSG method, the molecular diffusion volume of HF was estimated to be 12.2 cm3/mol. For the WL-HBS method, the HF-air molecular interaction energy and collision integral were estimated from critical properties of HF. All other parameters were used as given in the respective methods. The following values were thus calculated for trace level HF diffusivity, at 298 K, 1.0 atm pressure: (FSG), Do = 0.247 cm2/s; (WL-HBS): Do = 0.243 cmz/s. Most of the uncertainty in these calculated values arises from the lack of data on the molecular volume of HF. For both formulas, the value for HF was estimated from LeBas’ data for F. Theoretical uncertainty limits for the calculated values can be estimated from the following logic. The molecular volume of HF must be intermediate between the volumes of F and F2 A theoretical upper bound on Do was obtained from the FSG formula by substituting the LeBas volume of F for the molecular diffusion volume of HF. = 0.280 cm2/s. Similarly, a lower Doing so yielded DO,man bound was obtained by substituting the LeBas volume of Fz for the volume of HF; doing so yielded DO,min= 0.220 cm2/s. Thus, from strictly theoretical arguments, 0.220 cmz/s 5 DOaF 5 0.280 cm2/s. Experimental Estimate of HF Diffusivity. The diffusion coefficient Do for HF, was estimated from recent experimental data obtained in our laboratory. The product Do.R was measured to be 0.209 cm2/s f 0.04 for the H F Gasbadge dosimeter (Young and Monat, in press). A lower bound on Do was estimated by setting R , the calibration factor, equal to 1.0. This yielded DOFh= 0.209 cmz/s. An approximate upper bound was determined by setting R equal to the lowest value of R ever measured for an efficiently sampled species in our laboratory, viz. R = 0.801. Doing this yielded DO,max= 0.262 cmz/s. Thus, from strictly experimental arguments, 0.209 cmz/s 5 Do,,, 5
0.262 cm2/s. This range was further refined to obtain a best estimate of DO,HF. If it is assumed that the value R = 0.857 also holds for the HF Gasbadge dosimeter, then Do for HF can be more accurately estimated from the HF sampling rate. Since D0.R = 0.209 f 0.04 cmz/s (measured (Young and Monat, in press)), and R = 0.857 f 7.0%, then Do for HF at 298 K = 0.244 f 0.06 cm2/s. This estimate for the diffusivity of trace-level HF into air agrees well with the value predicted by both the FSG and WL-HBS formulas. This number must be considered only a good estimate and not an empirical constant, but due to the lack of published diffusion data for HF, this estimate may be significant in the prediction of HF diffusive behavior for concentrations at which HF shows strictly monomeric behavior.
Acknowledgment Some of the organic vapor data reported in this paper were obtained in a dosimeter calibration study, the results of which were presented by Gillespie et al. (1979). The organic vapor manifold and exposure system were designed and constructed by Mr. Ken Martin of the Harvard University School of Public Health.
Literature Cited Fuller, E. N.; Schettler, P. D.; Giddings, J. C. Ind. Eng. Chem. 1966, 58, 19-27. Gillespie, J.; Daniel, L.; Martin, K.; Young, M. 178th Natlonal Meeting of the American Chemical Society, Washington, DC Sept 13, 1979, Division of Chemical Health and Safety. Lugg, G. A. Anal. Chem. 1968, 4 0 , 1072. Mazur, J. F.; Bamberger, R. L.; Pcdolak, G. E.; Esposito, G. G. Am. Ind. Hyg.assoc. 1978, 3 9 , 749-753. Palmes, E. D.; Gunnison, A. F. Am. Ind. Hyg. Assoc. J. 1973, 3 4 , 78-81. Tompkins, F. C., Jr.; Goldsmith, R. L. Am. Ind. Hyg. Assoc. J . 1977, 38, 371-377. Wilke, C. R.; Lee, C. Y. Ind. Eng. Chem. 1955, 4 7 , 1253-1257. Young, M. S.; Monat, J. P. Am. Ind. Hyg. Assoc. J. in press, 1982.
Received f o r review August 10, 1982 Accepted August 12, 1982 We are grateful to the U S . Department of Energy for support of the hydrogen fluoride research under grant number DEFG05-79-EV10249.
