Radial Pore Diffusion with Nonuniform Intraparticle Porosities
Publication: Journal of Environmental Engineering
Volume 130, Issue 10
Abstract
Effects of radially dependent intraparticle pore sizes on solute fate and transport are examined for batch systems with spherical particles using a recently developed numerical model. The model can accommodate multiple particles distributed in size, mass transfer resistance at particle boundaries, intraparticle reversible sorption kinetics, and first-order decays. Two applications are examined. In the first application, random or deterministic intraparticle porosities across a spherical particle are considered. In the second application, multiple particles distributed in sizes with particle size-dependent intraparticle porosities are studied. Results from these applications indicate that concentration profiles are largely determined by interplays between , , and that incorporate the effects of intraparticle pore structures. Steady-state concentration values in both applications are determined by the volume-averaged intraparticle porosities. These results could be useful for understanding solute tailing behavior in natural porous media and the design of synthetic sorbents for treatment of contaminated waters.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ball, W. P., Buehler, T. C., Harmon, T. C., MacKay, D. M., and Roberts, P. V. (1990). “Characterization of a sandy aquifer material at the grain scale.” J. Contam. Hydrol., 5(3), 253–295.
2.
Başağaoğlu, H., Ginn, T. R., McCoy, B. J., and Marino, M. A. (2000) “Linear driving force approximation to a radial diffusive model.” AIChE J., 46(10), 2097–2105.
3.
Başağaoğlu, H., McCoy, B. J., Ginn, T. R., Loge, F. L., and Dietrich, J. P. (2002). “A diffusion limited sorption kinetics model with polydispersed particles of distinct sizes and shapes.” Adv. Water Resour., 25(7), 755–772.
4.
Bear, J. ( 1988). Dynamics of fluids in porous media, Dover, Mineola, N.Y.
5.
Carta, G., and Bauer, J. S. (1990). “Analytical solution for chromatography with nonuniform sorbent particles.” AIChE J., 36(1), 147–150.
6.
Choy, K. K. H., Porter, J. F., and McKay, G. (2001). “A film-pore-surface diffusion model for the adsorption of acid dyes on activated carbon.” Adsorption, 7(4), 305–317.
7.
Chung, G-Y., McCoy, B. J., and Scow, K. M. (1993). “Criteria to assess when biodegradation is kinetically limited by intraparticle diffusion and sorption.” Biotechnol. Bioeng., 41(6), 625–632.
8.
Cooney, D. O., Adesenya, B. A., and Hines, A. L. (1983). “Effects of particle size distribution on adsorption kinetics in stirred batch systems.” Chem. Eng. Sci., 38(9), 1535–1541.
9.
Cunningham, J. A., Werth, J. C., Reinhard, M., and Roberts, P. V. (1997). “Effects of grain-scale mass transfer on the transport of volatile organics through sediments 1. Model development.” Water Resour. Res., 33(12), 2713–2726.
10.
Dietrich, J. P., Başağaoğlu, H., Loge, F. J., and Ginn, T. R. (2003). “Preliminary assessment of transport processes influencing the penetration of chlorine into wastewater particles and the subsequent inactivation of particle-associated organisms.” Water Resour., 37(1), 139–149.
11.
Dougharty, N. A. (1972). “Effect of adsorbent particle-size distribution in gas-solid chromatography.” AIChE J., 18(3), 657–659.
12.
Farrell, J., and Reinhard, M. (1994). “Desorption of hologenated organics from model solids, sediments, and soil under unsaturated conditions. 2. Kinetics.” Environ. Sci. Technol., 28(1), 63–72.
13.
Fong, K. F., and Mulkey, L. A. (1989). “Simulate of solute transport in aggregated media.” AIChE J., 35(4), 670–672.
14.
Gierke, J. S., Hutzler, N. J., and McKenzie, D. B. (1992). “Vapor transport in unsaturated soil columns: Implications for vapor extraction.” Water Resour. Res., 28(2), 323–335.
15.
Goto, M. and Hirose, T. (1993). “Approximate rate equation for intraparticle diffusion with or without reaction.” Chem. Eng. Sci., 48(10), 1912–1915.
16.
Goto, M., Smith, J. M., and McCoy, B. J. (1990). “Parabolic profile approximation (linear driving-force model) for chemical reactions.” Chem. Eng. Sci., 45(2), 443–448.
17.
Haggerty, R., and Gorelick, S. M. (1995). “Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity.” Water Resour. Res., 31(10), 2383–2400.
18.
Harmon, T. C., and Roberts, P. V. (1994). “Comparison of intraparticle sorption and desorption rates for a halogenated aquifer in a sandy aquifer material.” Environ. Sci. Technol., 28(9), 1650–1660.
20.
Karapanagioti, H. K., Gossard, C. M., Strevett, K. A., Kolar, R. L., and Sabatini, D. A. (2001). “Model coupling intraparticle diffusion/sorption, nonlinear sorption, and biodegradation process.” J. Contam. Hydrol., 48(1-2), 1–21.
21.
Lu., P. Lannutti, K., Klobes, P., and Meyer, K. (2000). “X-ray computed tomography and mercury porosimetry for evaluation of density evolution and porosity distribution.” J. Am. Ceram. Soc., 83(3), 518–522.
22.
Lua, A. C., and Guo, J. (2001). “Adsorption of sulfur dioxide on activated carbon from oil-palm waste,” J. Environ. Eng., 127(10), 895–901.
23.
Meyers, J. J., Crosser, O. K., and Liapis, A. I. (2001). “Pore network modeling of affinity chromatography: Determination of the dynamic profiles of the pore diffusivity of -Galactosidase and its effect on column performance as the loading of -Galactosidase onto Anti--Galactosidase varies with time.” J. Biochem. Biophys. Methods, 49(1-3), 123–139.
24.
Meyers, J. J., and Liapis A. I. (1998). “Network modeling of the intraparticle convection and diffusion of molecules in porous particles packed in a chromatographic column.” J. Chromatogr. A,827(2), 197–213.
25.
Mihelcic, J. R., and Luthy, R. G. (1991). “Sorption and microbial degradation of naphthalene in soil-water suspensions under denitrification conditions.” Environ. Sci. Technol., 25(1), 169–177.
26.
Ng, C.-O. and Mei, C. C. (1996). “Aggregate diffusion model applied to soil vapor extraction in unidirectional and radial flows.” Water Resour. Res., 32(5), 1289–1297.
27.
Ni, C.-C., and San, J.-Y. (2000). “Mass diffusion in a spherical microporous particle with thermal effect and gas-side mass transfer re-sistance.” Int. J. Heat Mass Transfer, 43(12), 2129–2139.
28.
Papadopoulos, K. D., and Bailey, R. V. (1986). “Reaction-diffusion in suspended particle with limited supply of reactant.” Ind. Eng. Chem. Fundam., 25(2), 303–305.
29.
Pedit, J. A., and Miller, C. T. (1995). “Heterogeneous sorption processes in subsurface systems. 2. Diffusion modeling approaches.” Environ. Sci. Technol., 29(7), 1766–1772.
37.
Pignatello, J. J., and Xing, B. (1996). “Mechanism of slow sorption of organic chemicals to natural particles.” Environ. Sci Technol.30(1), 1–11.
30.
Press, W., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. ( 1992). Numerical recipes in Fortran, the art of scientific computing, Cambridge University Press, New York.
31.
Rasmuson, A., and Neretnieks, I. (1980) “Transport processes and conversion in an isothermal fixed-bed catalytic reactor.” AIChE J., 26(4), 686–690.
32.
Reyes, S., and Jensen, K. F. (1985). “Estimation of effective transport coefficients in porous solids based on percolation concepts.” Chem. Eng. Sci., 40(9), 1723–1734.
33.
Werth, C. J. and Reinhard, M. (1997). “Effects of temperature on trichloroethylene desorption from silica gel and natural sediments, 1. Isotherms.” Environ. Sci. Technol., 31(3), 689–696.
34.
Yang, X-Y., and Al-Duri, B. (2001). “Application of branched pore diffusion model in the adsorption of reactive dyes on activated carbon.” Chem. Eng. J., 83(1), 15–23.
35.
Yiacoumi, S., and Tien, C. (1994). “A model of organic solute uptake from aqueous solutions by soils.” Water Resour. Res., 30(2), 571–580.
36.
Zheng, J., and Reed, J. S. (1992). “The different roles of forming and sintering on disinfection powder compacts.” Am. Ceram. Soc. Bull., 71(9), 1410–1416.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 130 • Issue 10 • October 2004
Pages: 1170 - 1179
Copyright
Copyright © 2004 ASCE.
History
Published online: Oct 1, 2004
Published in print: Oct 2004
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.