748
Ind. Eng. Chem. Process ~ e s ~. e v 1. 9 ~ 52, 4 , 748-753
ficienta based on this recommendation are also included in Table I. The generalized correlation of Moysan et al. (1983) is recommended when optimal interaction coefficients are not available. Acknowledgment Financial support of this work was provided by the Department of Refining of the American Petroleum Institute. Nomenclature R = gas constant T = temperature T , = critical temperature P = pressure P, = critical pressure x. = mole fraction in the liquid phase y = mole fraction in the vapor phase o = acentric factor a = Soave's temperature dependence of the Redlich-Kwong attractive energy parameter a = Soave attractive energy parameter
b = Soave excluded volume parameter k , = binary interaction coefficient ti = critical parameter of ith component = (aiIn (ai In 2)1/2/bi fiL = fugacity of component i in liquid phase ti' = fugacity of component i in vapor phase & = fugacity coefficient of ith component Ki = K ratio of ith component = yi/xi Literature Cited Graboekl. M. S.; Daubert, T. E. Ind. Eng. Chem. Process Des. D e v . 1978a, 17, 443. (jraboski. M. S.; Daubert, T. E. Ind. Eng. Chem. Process Des. Dev. 1978b, 17, 448. Graboskl, M. S.; Daubert, T. E. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 300. Huron, M. J.; Vidal, J. Nuki Phase Equuib. 1979. 3 , 255. Moysan, J. M.; Huron, M. J.; Paradowski, H.; Vidal, J. Chem. Eng. Sci. 1983, 3 8 , 1085. Oelhich, L.; Plocker, U.; Prausnb. J. M.; Knapp, H. I n t . Chem. Eng. 1981, 2 1 , 1. Paunovic, R.; Jovanovlc, S.; MIhaJbv,A. NuMPhase Equilib. 1981, 6 , 141. Soave, G. Chem. Eng. Sci. 1972, 2 7 , 1197. Vidal, J. Chem. Eng. Sci. 1978, 3 3 , 787.
Received for review May 21, 1984 Accepted October 23, 1984
Flow Properties of Foam with and without Solid Particles Nan& N. Thodavadl and Robert Lemllch' Depattmnt of Chemical and Nuclear Engineering, Unhwshy of Cincinnati, Cincinnati, ohlo 45221
An aqueous foam, made with a cationic surfactant, was passed through horizontal pipes of various diameters at an apparent shear rate of 0.2 to 6.2 s-'. Variation h Sauter mean bubble diameter from 0.1 to 1 mm and variation in foam quality from 0.88 to 0.99 were without significant effect on the pressure drop. The presence of up to 35 wt % small coal or sand particles was also of no significant effect. In acrylic pipes the foam flowed with an essentially flat profk along a liquki film at the wall. In galvanized steel pipes the foam flowed pseudoplastically with no discernible slip. Results were analyzed by Mooney's classical formalism.
Introduction Although various regimes of two-phase flow have been studied rheologically over the years, that of foam passing through pipes with diameters greater than a few millimeters has been largely neglected. Among the comparatively few such experimental investigations of foam that have been reported are thme of Wenzel et al. (1967) at low shear rates in plexiglass, Wise (1951) at higher shear rates in commercial iron pipe, and Blauer et al. (1974) a t higher shear rates in metal tubing. Okpobiri and Ikoku (1983) and Sanghani and Ikoku (1983) employed annuli of aluminum and acrylic, while Grove et al. (1951) used an annulus of brass and glass but of only 1.59-mm clearance. This relative neglect has existed despite the growing applications of foam including mineral flotation, fire fighting, paper and textile finishing,petroleum production, and other uses (Lemlich, 1972; Biker", 1973, Okpobiri and Ikoku, 1983). Furthermore, researchers appear to be divided as to whether foam is better described as pseudoplastic or Bingham plastic. Experiments with channels and viscometers of narrow clearance are of limited help in this connection since the foam may not behave in them as a continuum unless the bubbles are extremely small.
Accordingly, the present work was undertaken to investigate experimentally the flow of aqueous foam, with and without solid particles, through horizontal commercial acrylic and galvanized steel pipes. Experimental Section Figure 1shows the apparatus. Prehumidified nitrogen gas was passed into the foam generator which consisted of a large modified inverted Erlenmeyer flask fitted with coarse sintered glass bubblers. The flask in turn was connected to the horizontal test section which was of pipe roughly 3 m in length. Four clear acrylic (Plexiglas, Rohm and Haas) pipes of 4.44, 2.49, 1.59, and 1.22 cm i.d. and two galvanized steel pipes of 5.33 and 2.67 cm i.d. were employed, in turn. The distance between adjacent pressure taps was 61 to 64 cm. The foam exiting from the test pipe was collected in a large plastic drum, broken with a spray of chemical foam breaker (DB-31, Dow Corning) diluted in tap water, and sewered. The cationic surfactant ethylhexadecyldimethylammonium bromide (EHDA, technical grade, Eastman Kodak) was used as the foaming agent. (Caution: EHDA is noxious. Inhalation and ingestion should be avoided.) It was dissolved in distilled water to make 0.1% solution
Q196-43Q5/85/1124-Q748$Q1.5Q/Q 0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 0
740
I
2,
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Tw Figure 1. Schematic of apparatus: (B) foam breaking drum; (C) chemical foam breaker diluted in tap water; (D) distribution flask; (F) foam generator; (H) humidifiers; (I) injection of dye; (L) liquid leveler; (M) gas flow meters; (N)nitrogen; (P)manometers; (R)trap; (S)surfactant solution; (W) wet bulb/dry bulb psychrometer; (Z) sewer.
and pumped into the overflow tank. The height of the tank was adjusted to obtain the desired liquid level in the foaming flask. The humidified nitrogen was then slowly passed through one or more of the bubblers. Temperature was 25 f 1"C. The foam was allowed to flow through the test section for at least 20 min in order to reach steadystate operation. Pressure drops were monitored. The foam was photographed (at the middle of the test section in the case of acrylic pipe which is transparent) in order to measure the bubble size distribution. Gas flow rates through the individual flow meters and through the main flow meter were also recorded. The wall velocity of the foam was measured by tracking a bubble along the wall and timing ita travel over a known distance. At the same time, the foam exiting the test section was collected for determination of foam quality (volumetric gas fraction). Finally, the velocity profile of the foam flow was measured by injecting a compatible tracer dye (congo red) through a specially designed multineedle syringe at various radial locations and timing the appearance of the pulses a t the exit of the pipe. Similar measurements were made for the runs with solid particles in the foam. For the calculation of foam quality, the solids volume was ignored as it was small compared to that of the liquid and gas. The solids content was measured by weighing oven-dried collapsed foam. The particles were of coal and sand, in turn. Pulverized Pittsburgh seam coal (Cincinnati Gas and Electric) was screened to three different sizes, viz., 80-115 mesh, 115-150 mesh, and finer than 150 mesh. The sand was floated pure silica (Fischer Scientific) in three different sizes, viz., 80-120 mesh, finer than 140 mesh, and approximately 240 mesh. A combined grand total of 664 runswere conducted with particle-free and particle-loaded foam. Further details are on file (Thondavadi, 1983). Results and Discussion The foam was photographed in all runs except those with coal particles. The thusly determined Sauter mean bubble diameter, d3,2,was found to range between approximately 0.1 and 1 mm. No effect of d3,2on the relationship between total volumetric flow rate of foam, Qt, and wall shear stress, T,, could be discerned. This is illustrated in Figure 2 for particle-free foam in acrylic pipe. T, was obtained in the customary manner as RAP/2L, where R is the internal radius of the pipe and AP is the pressure drop between pressure taps spaced a distance L
45
eb
75
B
(DYN/CM2)
Figure 2. Total flow rate v8. shear stresa at the wall for particle-free foam flowing through acrylic pipe of 4.44 cm i.d. for various grouped Sauter mean bubble diameters in millimeters as follows: (0)C0.25; 0.25 5 (A)
