favored by the availability and relative cheapness of phenol as compared to the solvents of choice for the liquid-liquid ex. traction process studied by Hood and Davison. The removal of the chemicals used, to concentrations far below toxicity levels. follo\vs standard engineering practice. The points recommending this process include a lowenergy requirement estimated at about 250,000 B.t.u. per 1000 gallons of salt-depleted product and operation at room temperature with avoidance of scaling and corrosion. The chief disadvantage is a high initial capital investment. The total cost. conservativelv estimated by the procedure of the U. S. Office of Saline TVater (a), of producing 10,000,000 gallons of potable ivater per dav from sea water, amounts to 59 to 77 cents per thousand gallons and includes both direct and fixed costs This is within the cost projection of 60 to 100 cents per thousand gallons of the Office of Saline Water (2) for methods under extensive development, and is subject to the same possibilities of reduction Ivith development
literature Cited
R.?Isbell, A. F., Smith, I$’. H., Wood, D. IV., ”Development of Solvent Demineralization of Saline rl;ater,” U. S. Dept. Interior, Office of Saline Iliater, R & D Progr. Rept. 5 5 (September 1961). (2) Gillam, W. S.,McCutchan, J. W., Science 134, 1041 (1961). (3) Hood, D. W., Davison, R. R., Adoun. Chem. Ser.. No. 28, 40 (1960). (4) Hood, D. W..Davison, R. R., “Development of Solvent Demineralization of Saline Water,” U. S. Dept. Interior, Office of Saline IVater, R & D Progr. Rept. 35 (February 19601. (5) Orbnite Division, California Chemical Co., San Francisco, Calif., “Oronite Phenol, U.S.P.,” 1955. (6) U. S. Dept. Interior, Office of Saline Water, “New Process for Production of Fresh Water from Sea LVater.*’R & D Progr. Rept. 47 (June 1961). (7) Zbid., “Saline Water Conversion by Direct Freezing with Butane,” No. 40 (July 1960). (8) Zbid., “Standardized Procedure for Estimating Costs of Saline Water Conversion” (March 1956). (1) Davidson, R.
RECEIVED for review February 26, 1962 ACCEPTED June 18, 1962
CORRESPONDENCE CRITICAL EVALUATION OF BOUNDARY CONDITIONS FOR TUBULAR FLOW REACTORS SIR: Liang-Tseng Fan and Yong-Kee Ahn’s evaluation [“Critical Evaluation of Boundary Conditions for Tubular DESIGNDEVELOP. Flow Reactors.” IND.ENG.CHEM.PROCESS 1, 190 (1962)l of boundary conditions is a clear demonstration of the superiority of Danckwerts’ conditions. They concluded that the other commonly used boundary restrictions result in “iinreasonable” conversions. Their solutions and plots make possible some further interesting comparisons and observations. First, the boundary conditions identified as I1 and I11 result in violations of a fundamental over-all material balance. This is readily apparent from the authors’ Figure 1. An over-all material balance may be written (in the authors’ nomenclature) as Over-all conversion = over-all reaction rate
This integral is simply the area under a curve of Figure 1. Inspection shows that for cases I1 and 111, y (1) increases with increasing area-i.e.. decreasing M - c o n t r a r y to Equation A. whereas y (1) and the area are in proper relationship for case I. A physical interpretation of the family of curves for either case I1 or case I11 is not possible: The plots indicate that higher concentration driving forces result in lower conversions. It can further be shown that if the condition common to both I and 11. given by either ? b or 8b as dr(l)/dq = 0 at 7 = 1, i q applied. then Equation ?a gives the only other condition consistent \vith both the differential material balance of Equation 6 and the over-all balance of Equation A. Substituting y from Equation 6 into Equation A results in
S o w , if & ( l ) ’dq = 0, Equation B gives the necessary second boundary condition as d
9 = 2.44 [?(Of)
- 11
which is identical to Equation ?a. On the other hand, substitution of both Equations 8a and 8b into Equation B results in
Comparison of Equation D with Equation A shows that the over-all material balance is in error by the term 1/2M [&(Of)/ d q ] for the case I1 conditions. A similar treatment for case I11 results in
Thus, the error is proportional to the integral on the right and is positive because d2y/dq2 is always positive. Perhaps the most interesting observation is that the use of the condition given by Equation 8a is actually an application of 7a, but with an important difference. With the aid of a dimensionless variable r = C/C(O+)> it can be shown that all the solutions presented for case I1 in terms of y = C/C, are in fact solutions of case I for r-that is, yII(q) = r l ( q ) = y,(q)/yI(O+). Division of y ( q ) from Equation 15 by y (0-k) from Equation 14 results in a quantity identical to y (7) from Equation 20, thus proving this hypothesis. Multiplication of each of the case I1 plots by the ratio y,(O+) superimposes the curves on the case I curves. This is not true where M = 0, because these solutions were not obtained from these equations. No such simple translation is possible for case 111, because this is fundamentally a different solution wherein the gradient a t the outlet is maintained at a nonzero value.
Maurice G. Lorenz
ESSO Research and Engineering Co. Linden, N . J . 88
I & E C P R O C E S S DESIGN A N D DEVELOPMENT
