Liquid Mass Transfer at Very Low Reynolds Numbers in Packed Beds

Abstract

Mass transfer coefficients from packed beds of benzoic acid spheres to water and propylene glycol solutions were measured in the very low Reynolds number, Nr/, range of 0.0016 to 55. Studies using bed heights from l/i to 4 inches showed the mass transfer, J, to be affected only slightly. No effects on J were found on diluting the bed by a factor of 1 0 to 1 with inert spheres. Varying the Schmidt number, Nsc, from 950 to 70,600 had no effect on J when Nsc2/3 was used. Data obtained from internal samples gave the same J values as from outlet samples and showed that axial mixing effects were small. Gupta and Thodos experimentally found J to be inversely proportional to the void fraction and this was shown to be very similar to that derived by Pfeffer. Equations are proposed for liquids for the entire range of Nr/ from 0.0016 to 1500. nil ass transfer of fluids in packed beds of spherical particles * " * is encountered in many different processes at very low velocities in chromatography, ion exchange, combustion of fine particles, and petroleum reservoir engineering. Relatively few data on liquids are available covering the effects on J of wide variations of Schmidt number, A/, at very low Reynolds numbers, //, below 0.05, of variations of bed length, and of dilution of the bed with inert spheres.Williamson, Bazaire, and Geankoplis ( 16) obtained mass transfer coefficients for packed beds of benzoic acid spheres and water in the A// range of 0.05 to 55. They correlated the data of others (6, 11) using A"Sc°-5S instead of /2'3. Mc-Cune and Wilhelm (7 7) used modified spheres of 2-naphthol and water and obtained J values for a ,Ylie' rangie of 14 to 1440. Gaffney and Drew (6) studied mass transfer of modified spheres with liquids in a -Yr/ range of 0.4 to 765 using a wide range of A/.Pfeffer (12) derived a theoretical equation relating J to A// which holds for high Peclet numbers and low ,YR/ or mainly liquids. He also derived an expression for the effect of ( on J. Gupta and Thodos (8) experimentally determined J to be proportional to 1/e for gases in the high A"Re' region. They also correlated all the mass transfer data on gases for a ArRe' range of 12 to 2140. Bradshaw and Bennett (7) showed that the J value of liquids should be lower than the J of gases at low A// because of the higher Schmidt number of liquids.DeAcetis and Thodos (3), Bradshaw and Meyers (2), Bradshaw and Bennett (7), and McCune and Wilhelm (77) studied effects of bed height on J at high Reynolds numbers. De-Acetis and Thodos (3) also studied dilute beds-i.e., the effect of inert spheres mixed with the active spheres in a packed bed.In the present work mass transfer coefficients of benzoic acid spheres in water and propylene glycol solutions w'ere obtained in packed beds in the A'R/ region of 0.0016 to 55. The effects of bed height, dilute beds, and internal sampling were also studied. The data were correlated and equations presented. Experimental MethodsThe apparatus used and the experimental methods are very similar to those used by Williamson...

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“…As shown in Section 7, in VERSE-LC the film mass transfer coefficient is calculated from a correlation developed by Wilson and Geankoplis (1966). Particle porosity is available from the data presented in Section 5.…”

“…Numerous mass transfer correlations exist as discussed by Foo and Rice (1975). One of the correlations compared in Foo and Rice (1975) is one developed by Wilson and Geankoplis (1966) based on low Reynolds number data. Large variations between correlations exist; however, the sensitivity of VERSE-LC results to the film coefficient has typically been low.…”

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“…Eqs. (15) and (16) were then used to calculate bed voidage and particle porosity. The results are listed in Table 1.…”

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“…C p , solute concentration in the liquid phase inside the particle pores (volume fraction ε p ); R, particle average radius; k f , external mass transfer coefficient from (Wilson and Geankopolis, 1966) …”