394
Ind. Eng. Chem. Process Des. Dev. 1982, 21, 394-395
diameter glass sphere which should contribute to large electrostatic effects. Acknowledgment The authors wish to acknowledge the National Science Foundation for support for carrying out this study. Nomenclature CDs = drag coefficient, single particle D = tube diameter D, = diameter of sphere having same volume of the particle E, = electric field Fd = drag force F = gravitational force $ = frictional force F, = electrostatic force f = particle friction factor (= solid friction factor g = gravitational constant L = tube length = mass of particle = total pressure drop (AP/L),lectrie= pressure drop due to eletrostatics Re, = Reynolds number of particle t = time
at
U, = superficial gas velocity
Ut = terminal velocity of particle U = particle velocity $ = fluid velocity W,= solid flow rate Greek Letters c
= voidage
p = fluid viscosity pp = particle density
pf =
fluid density
Literature Cited Insmute of Gas Technology, Department of Energy Contract FE 2286-32, Chicago, IL, Oct 1978. King, P. W. 2nd Intematknal Conference on Pneumatic Transport of sdids in Pipes, Britlsh Hydraulic Research Association, Gulidford, England, Sept 1973 p D2-9. Peters, L. K. R.D. Mssertatbn, University of Pittsburgh, Pittsburgh, PA, 1971. Shimizu, A.; Echigo, R.; Hasegawa, S.;Hishida, M. I n t . J . MuMphase Flow 1978, 4 , 53. Volirath, R. E. Fhp. Rev. 1932, 42, 298. 'fang, W. C. J . POW& Bulk sdM6 Technol. 1977, 1 , 89.
Received for review August 15, 1980 Revised manuscript received September 24, 1981 Accepted February 12, 1982
Diffusion Coefficient of Trona in Water Gurmukh D. Mehta' and Satkh C. Jaln' I n t 8 r T e ~ h n o k g y / ~ OCorporation, k~ Warrenton, Virginia 22 186
Laboratory experiments were conducted to measure the diffusion coefficient of trona in water. The diffusion coefficient of trona from saturated solution in water was measured to be 1.167 X cm2/s with a standard deviation of 6.2% at 25 O C .
Introduction Trona is a naturally occurring chemical, commonly known as sodium sesquicarbonate (Na2C03.NaHC03. 2H20). The world's largest deposit of trona, containing an estimated amount of 17 billion tons, is in Green River, WY (Kirk-Othmer, 1964). This salt is mainly used in the manufacture of soda ash, i.e., sodium carbonate. Because of the abundant supply of nearly pure trona in the United States,this solute is potentially a very attractive candidate for use in a salt-stratified nonconvecting solar pond (Tabor, 1963; Nielsen, 1980; Mehta, 1979). While there are ample data on mining of trona and of solid trona in equilibrium with Na2C03-NaHC03 solution, very little, if any, information is available on the chemical stability of trona or solution of trona solution or solution of trona and soda ash in various proportions without any solid phase. Consequently, a laboratory investigation was conducted to determine the solubility, saturation density, and chemical stability of trona solution and 3:2 molar mixture of Na2C03 and NaHC03 in water and to estimate the
* Science Applications, Inc., 1710 Goodridge Drive, McLean, VA 22102. Amoco Production Company, 4502 East 41st Street, Tulsa, OK 74102. 0196-4305/82/1121-0394$01.25/0
diffusion coefficient of trona in water. The objective of thisnote is to present the reaulta of the diffusion coefficient of trona from saturated trona solution in water at room temperature. Experimental Section The diffusion coefficient of trona from saturated trona solution in water at 25 OC was determined by employing a relative method. This method is described in detail elsewhere (Shoemaker et al., 1979). This method is both rapid and inexpensive and was first used by Schulze (1914) and later by Wall et al. (1952, 1953a,b). In this method a porous, unglazed porcelain disk (frit) filled with saturated trona solution was suspended in a large bath of distilled water. The disk used was 7.5 em in diameter and 0.4 cm thick, made of a microporous filter of grade 10 porosity, and was supplied by Selas Corporation of America, Philadelphia, PA. It has an external geometric volume of about 29 cm3 and dry weight of 36 g. This disk held about 12 cm3, of liquid, and ita porosity was such that the trona ions had completely diffused into the water in a reasonable time. The frit was suspended in the bath by a wire from one end of an analytical balance, and the progress of diffusion was followed by recording the apparent weight of the frit with time. For an estimation of the average 0 1982 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982 395 -1.5
log W , = -aDt
-1.75
-2.0
3 -2.25
-2.5
0
20
€4
40
80
100
120
140
160
TIME It), MIN
Figure 1. Determination of diffusion coefficient of saturated trona solution in water at 25 O C .
-1.75
-2.0
-2.25
-2.5
-2.75
I 0
20
40
60
80
100
TIME It), MIN
Figure 2. Determination o f apparatus constant for diffusion experiment.
diffusion coefficient, the density of the solution is assumed as a linear function of concentration in the form d(C) = 4 0 ) + KC (1) where d(0) = solvent density, g/cm3, d(C) = density of solution at concentration C, g/cm3, and K = constant. The diffusion coefficient is calculated by using the following equation from Shoemaker et al. (1979)
+ log BLAK(C1 - C,)(8/a2)
(2)
where W , = W(t)- W(m), W ( t )= apparent weight of the frit at time t, W(m)= apparent weight of the frit after equilibrium has been reached, C1 = initial concentration in the frit at time t = 0, Co = concentration in the bath, which is assumed to be constant, A = effective cross-sectional area of the disk, 2L = effective thickness of the porous disk, D = diffusion coefficient of trona, and a = apparatus constant, characteristic of the frit used. Thus, as is evident from eq 2, the plot of log W , against t will give a straight line of slope (-d). This plot is shown in Figure 1. The apparatus constant a was then determined by repeating the same experiment with a salt of known diffusion coefficient, which was a 1.5 M solution of KCl. Figure 2 shows the straight line used in calculation of apparatus constant a. The value of the average diffusion coefficient for trona in water at 25 "C was estimated to be 1.167 X IO-5 cmz/s with a standard deviation of 6.2%. This is approximately 60% of that for a 1.5 M KC1 solution and about 80% of that for a 1.0 M NaCl solution at 25 "C. Thus, €or the same concentration gradient, the diffusion solute flux in a trona unsaturated solar pond will be about 80% of that for a sodium chloride solar pond. Acknowledgment This work was funded by the U.S.Department of Energy under Contract No. DE-AC04-79CS12142. The authors are grateful to one of the reviewers in pointing out an error in estimating the correct value of the diffusion coefficient. Literature Cited Klrk-Othmer "Encyclopedia of Chemical Technology"; Interscience: New York. 1964; Vol. 18. p 460. Mehta, 0. D. "Salt Stratified Solar Ponds"; Proceedings of the United Nations Institute for Training and Research Conference on LongTenn Energy ReSOWCBS, MOntrSel, Canada. NOv-Dec 1979. Niebn. C. E. "NpnconvectkrgSail &adlent Solar Ponds"; Proceedings of the NonConvecting Solar Pond Workshop, Mdean, VA, July 1980. Schulze, 0. Z . phvs. Chem. 1914, 89, 168. Shoemaker, D. P.; Garland, C. W.; Stelnfeld, J. J. "Experiments in Physical Chemlstry", 3rd ed.; McGraw-Hill: New York, 1979, Chapter VI. pp 203-212. Tabor, H. Sol. Energy 1963, I , 189. Wail, F. T.; Grleger, P. F.; Chllders, C. W. J . Am. Chem. Soc.1952, 74, 3562. Wall, F. T.; Grleger, P. F.; Childers, C. W. J . Am. Chem. Soc. 1953r, 75, 3550. Wall, F. T.; Grieger, P. F.; Chllders, C. W. J . Am. Chem. Soc. 1953b, 75, 6340.
Received for review N o v e m b e r 17,1980 Revised manuscript received September 6 , 1981 Accepted January 7,1982
