second derivative grows toward infinity in the limit of vanishing A.
X = meniscus height, nondimensional, x/ho u = surface tension of the liquid-air interface
Nomenclature a = capillary length of liquid, (2cr/pg)'
2,
mm
B1 = upper profile intercept, nondimensional, eq 18 Bz = lower profile intercept, nondimensional, eq 2 c = curvature of meniscus, eq 7, mm-I C = curvature of meniscus, nondimensional, eq 7a Ca = capillary number, u ( p / u ) g = acceleration of gravity h = meniscus thickness at any point, mm h, = characteristic thickness, ( p u / p g ) f ' 2 ,mm ho = film thickness, constant thickness region, mm H = meniscus thickness, nondimensional, h/a L = meniscus thickness, nondimensional, h/ho Ml = slope of upper profile, nondimensional, eq 18 M z = slope of lower profile, nondimensional. eq 2 p = pressure in liquid phase po = pressure in gas phase R = vertical distance down, nondimensional, zlho Re = Reynolds number, hcup/p TO = film thickness, nondimensional, ho(pg/pu)l 2, eq 1 u = belt velocity, mm/sec LI = liquid velocity parallel to the belt, mm/sec, eq 4 x = vertical coordinate upward from bath, meniscus height, mm X = meniscus height, nondimensional, x / a y = horizontal coordinate, distance from belt, mm z = vertical coordinate, downward, mm
Literature Cited Cox, B. G., J. FluidMech . 14, 81 (1962). Denson, C. D., General Electric Co., personal communications, 1969, 1970. Deryagin. D. V., Levi, L. M., "Film Coating Theory," Chapters 2 and 4, Focal Press, New York, N. Y., 1964. Dervaain. D. V.. Titivevskava, A. S..Dokl. Akad. Nauk S S S R . 50, 307 (i9i5). Groenveld, P., Chem. Eng. SC;.. 25, 33 (1970). Groenveld. P., Van Dortmond. R. A,. Chem. Eng. Sci.. 25, 1571 (1970). Landau, L. D.. Levich. V. G., Acta Physicochim. U R S S . 17, 42 (1942). Lee. C. . Y.., Ph.D. Dissertation. Drexel Universitv. PhiladelDhia. Pa.. 1974. Lee, C. Y.. Braccilli. J. J.. Tallmadae. J. A,. Annual AIChE Meetina. New York. N Y 1972 Lee, C Y , Tallmadge J A , 46 National Colloid Symposium, ACS, Amherst. Mass.. 1972a. Lee. C. Y.. Tallmadge. J. A , , AlChEJ.. 18, 858 (1972b). Lee, C. Y . , Tallmadge. J. A , , AlChEJ. 18, 1077 ( 1 9 7 2 ~ ) . Lee. C. Y., Tallmadge, J. A,, AlChEJ. 19,403 (1973a). Lee, C. Y., Tallmadge, J. A.. AlChEJ. 19, 865 (1973b). Lee, C. Y., Tallmadge, J. A . , AlChE J. 20,1079 (1974a) Lee, C. Y., Tallmadge, J. A , , lnd. Eng. Chem. Fundam., 13, 356 (1974b) Levich, V. G., "Physicochemical Hydrodynamics," Chapter 12, PrenticeHall, New York. N . Y., 1962. Miller. C., E. I. duPont Co., personal communication. 1974. Soroka, A. J.. Ph.D. Dissertation, Drexel University. Philadelphia, Pa., 1969. Soroka. A. J., Tallmadge, J. A,, A l C h E J . . 17, 505 (1971). Tallmadge. J. A., Chem. Eng. Sci.. 28, 311 (1973). Van Rossum. J. J . , Appl. Sci. Res.. A7, 121 (1958). White. D. A,. Tallmadge. J. A . , Chem Eng. Sci.. 20, 33 (1965).
Greek Letters = liquidviscosity = liquiddensity
Received for review N o v e m b e r 2, 1973 Accepted J u n e 14,1974
p p
EXPERIMENTAL TECHNIQUES
Multipurpose High-pressure Phase-Equilibrium Apparatus Edgar W. Slocum Engineering Technology Laboratory. E I du Ponf de Nernours & Company lnc , Wilmington, Delaware 19898
A glass equilibrium cell is described that permits direct observation of single- or multiple-phase systems at temperatures from - 5 0 to +250°C and pressures from full vacuum to 1000 psig. The apparatus has a wide field of application in the study of reactions, densities, vapor pressures, vapor-liquid equilibria, liquid-liquid equilibria, and critical phenomena.
Reliable phase-equilibrium data are constantly in demand for the design and operation of distillation equipment, absorbers, scrubbers, condensers, and reactors. Although many different types of apparatus have been used in such measurements (see Literature Cited), most are restricted to a specific type of measurement or to narrow ranges of temperature and pressure. This paper describes a new phase-equilibrium apparatus of broad utility, the heart of which is a glass-walled cell containing a magnetically driven impeller designed to continuously disperse a light phase into an underlying heavy phase. The cell vol126
Ind. Eng. Chem., Fundam., Vol. 14, No. 2, 1975
ume can be varied by mercury injection from an adjacent reservoir. The visibility afforded by the glass walls of the cell is useful in the detection of solid or liquid phases, dew and bubble points, critical points, and colored reaction products. This apparatus can be used to determine PVT data for gases or liquids, vapor pressures, equilibrium phase composition data for single or multicomponent systems, and vapor-liquid or liquid-liquid critical constants. It may also be used as a reactor. The associated equipment includes a constant-temperature bath equipped with heating and cooling coils to permit operation from ap-
Figure 2. Phase-equilibrium apparatus: ( A ) reference pressure source; (B) vacuum system; (C) vent; (D) pressure gauge; (E) sample charging cylinder; (F) right angle valve drive; ( G ) to panel; (H) packless valve; (J) mercury drain line; ( K ) constanttemperature bath; (L) mercury; (M) mercury reservoir; (N) equilibrium cell.
Figure 1. Equilibrium cell assembly. (A) hollow pivot cone; (B) O-ring; (C) Graphitar bearing; (D) magnet cover; ( E ) impeller shaft; ( F ) bearing support rod; (G) Pyrex pipe; (H) pivot cone; (J) socket head cap screws; ( K ) support and tie rod; (L) Belleville washer; ( M ) hex nut; ( N ) upper head; (0) magnets; (P) wavy washer; (9) magnet can; (R) impeller; (S) connecting hole in shaft; (T) Graphitar bearing; ( U ) bearing support; ( V ) lower head.
proximately -50 to +250”C. Pressures within the cell can be varied from full vacuum to 1000 psig, provided a suitable barricade or shield is used. If the pressure is restricted to 500 psig, the apparatus may be used to 325°C. Detailed Description A sectional view of the equilibrium cell is shown in Figure 1. The cylindrical cell wall G consists of a standard 2-in. i.d. by 6-in. long tempered Pyrex glass pipe nipple sold under the trade name Double Tough by the Corning Glass Works, Corning, N.Y. The pipe is clamped between spring-loaded metal end flanges N and V. The ends of the pipe are sealed by elastomeric or glass-filled Teflon TFE-fluorocarbon resin O-rings B having a nominal inside diameter of 2% in. and a cross-sectional diameter of 78 in. The O-rings are not self-actuated seals; rather they function as jammed gaskets. The O-ring grooves in the metal head are dimensioned to position a stretched O-ring under the groove tooled in the ends of the standard glass pipe. Groove depth is calculated so that when the O-rings completely fill the grooves in the heads and pipe. there is approximately 0.005 in. clearance between the glass and the metal on each end. The end flanges are spring-loaded with Inconel-X Belleville springs I,,mounted on the tie rods K, to maintain a pressure in the gasket higher than the vessel internal pressure. Agitation in the equilibrium cell is provided by an internally vaned metallic impeller R, mounted on a hollow shaft E. The shaft runs on pivot bearings A and H contacting Graphitar bearings C and T. The impeller is driven by the magnetic couple between external and internal driving magnets 0. The internal driven magnet is potted in epoxy inside a metallic nonmagnetic can Q. Vapor passes through the upper hollow pivot bearing and the hollow shaft and emerges into the throat of the impeller through a connecting hole S. A wavy washer P under the
upper Graphitar bearing allows for differential thermal expansion of the driven components. The relationship between the equilibrium cell and its auxiliary equipment is shown in Figure 2 . A mercury reservoir M , similar in construction to the equilibrium cell but without the impeller, is mounted adjacent to the equilibrium cell N in a glass constant-temperature bath K. Equilibrium cell volume and internal pressure are controlled by adjustment of inert-gas pressure over the mercury reservoir. Mercury height in both equilibrium cell and reservoir is measured with a cathetometer relative to a sharpened probe mounted in the constant-temperature bath to minimize error from dimensional changes occasioned by changing temperatures in the bath. For variable-volume experiments with a mercury piston the impeller (R in Figure 1) is positioned just below the canned magnet. The connecting hole in the shaft S may be brought into the correct position in the throat of the impeller by turning the shaft upside down. Both steady-state and low-lag knife-type intermittent electrical heaters are positioned in the bath. A cooling coil is also provided for rapid adjustment of bath temperature. Safety Considerations This equipment has been used in a wide range of experimental investigations for over 10 years, with only an occasional glass vessel failure. Experience has shown that the visibility afforded by this equipment is so valuable in laboratory investigations that the user is tempted to adapt the design, often without full realization of the factors involved in the safe use of tempered glass pipe a t high pressures. It is therefore important that a discussion of these factors be included here. The glass pipe in this design is rated by the manufacturer for use in pipeline systems a t 50 psig a t a maximum temperature of 232°C when the maximum “sudden” temperature differential between inside and outside pipe walls does not exceed 111°C. Utilization of the pipe a t pressures and temperatures above the manufacturer’s recommendation involves attention to several factors, discussed below. 1. Shielding. At an internal gas pressure of 1000 psig, hydraulic vessel failure can generate glass fragments of sufficient energy to cut the surface of mild steel plate. Enclosure of the glass cells in a glass constant-temperature bath filled with a hot heat-transfer fluid further increases the danger to personnel. Occasional failures of the glass vessels can be expected a t pressures from 750 to 1000 Ind. Eng. Chem., Fundam., Vol. 14, No. 2, 1975
127
psig. Failures a t lower pressures could occur because of defects in the glass or misassembly. It is therefore imperative that the apparatus be enclosed in a suitable shield or barricade. We have used a cubic shield 2 ft on each side constructed of 1/4-in.-thick mild steel plate with a partially opened back and 1-in.-thick 5-ply safety-glass window having a maximum span of 12 in. This shield can withstand hydraulic failure of a single vessel filled with nitrogen gas a t 2000 psig, provided the vessel is not closer than 8 in. to the safety-glass window. If the device is to be used to study reactive systems in which the energy release could be higher than that in hydraulic failure, a barricade with much greater internal volume and heavier walls and windows must be provided. The possibility of explosion of a mist generated by the blast, either from the contents of the equilibrium cell or from the heat-transfer fluid in the constant-temperature bath, must also be considered. All ignition sources should be excluded from the shielded area to minimize this possibility. The author on one occasion witnessed a severe explosion of silicone oil mist above its flash point, ignited by the hot filament of an unshielded electric light bulb inadvertently left near the glass constant-temperature bath. 2. Use of Tempered Glass Pipe. The 2-in. i.d. Corning Double Tough Pyrex glass pipe is supplied tempered throughout in lengths up to 18 in. Longer lengths are tempered only on their ends. Certain other shapes supplied by the vendor are not tempered, for example pipe caps in the form of a test tube. Experience has shown that annealed glass pipe is markedly less strong than tempered glass pipe. The use of lengths longer than 18 in. or of shapes that are annealed is therefore not recommended a t pressures above the manufacturer's rating. The failure of glass under tension is both time and stress dependent. Use of overpressures for pressure testing will shorten the life of the vessel. After 150 hr exposure a t the maximum 1000 psi pressure, the glass should probably be discarded. At room temperature vessel lives in our laboratory have ranged from a few minutes to many months a t pressures from 1200 to 1500 psig. We have no evidence that operation at temperatures up to 245°C reduces the life expectancy of the vessels. Gasket failure by extrusion, however, can occur a t elevated pressures. 3. End Flange Design. Corning Double Tough Pyrex glass pipe is intended by the manufacturer to be coupled with standard Corning connectors, which bear on the back face of the conical end bells of the pipe. This type of closure is quite suitable a t the manufacturer's rated pressure
128
Ind. Eng. Chem., Fundarn., Vol. 14, No. 2, 1975
but will not give an ultimate pipe strength as high as can be obtained by clamping between end flanges. In designing the end flanges we must consider several important factors. The possibility of stress in the vessel by eccentric tie-rod loading with long pipe lengths must be minimized. There is some variability in the root depth of the tooled groove on the ends of the pipe as supplied. Care must be taken in assembling the equilibrium cell to prevent metal-to-glass contact at any point. The glass must be cushioned on the deformable gaskets. Tempered glass contains a considerable amount of stored energy. Permitting metalto-glass contact on initial assembly of an equilibrium cell has on one occasion caused failure of the vessel, with consequent ejection of a spray of glass particles around the assembly area. The inner lip of the O-ring groove on each end flange should be recessed to positively preclude metal-to-glass contact a t that point, and a feeler gauge should be used around the circumference of the glass a t both ends during assembly to prevent metal-to-glass contact either through improper sizing of the O-ring grooves or from cocking of the heads on assembly. The Belleville springs, used to maintain sealing pressure, must be selected to provide sufficient thrust to overcome the pressure in the heads due to the system and to maintain a pressure in the gaskets higher than the internal pressure. Acknowledgments Credit is due to George W. Holtzlander of the Engineering Technology Laboratory of the Du Pont Company for developing the gas recirculation impeller design. I also benefitted greatly from discussions on the use of glass pipe a t elevated pressures with Gabriel DeCristofano of the Sentinel Glass Company and Edward K . Lofberg of the Coming Glass Works. Mr. Lofberg suggested the use of clamped end flanges to maximize operating pressures. Literature Cited Gibbs, R . E., Van Ness, H. C., Ind. Eng. Chem.. Fundarn.. 11, 410 (1972). Hala, E.. Pick. J.. Fried, V.. Vilin, O., "Vapour-Liquid Equilibrium," 2nd English ed, pp 280-350. Pergamon Press, New York, N.Y., 1967. Robinson, C. S..Gilliland, E R., "Elements of Fractional Distillation." 4th ed. pp 3-15, McGraw-Hill, New York, N.Y., 1950. Weissberger. A . . Ed.. "Technique of Organic Chemistry," Vol. 1, Part 1. 3rd ed. pp 387-522, Interscience. New York. N.Y., 1959.
Received f o r reuiezc July 25, 1973 Accepted December 24,1974
