Published 12 issues per year
ISSN Print: 1091-028X
ISSN Online: 1934-0508
Indexed in
DUAL SCALES OF PERMEABILITY IN REGULARLY STRUCTURED PACKED BEDS OF SPHERES
ABSTRACT
Dual scales of permeability are encountered in many situations, and one such instance is in water treatment where packed beds of permeable spheres are essential. For design purposes, it is necessary to know the relationship between the rate of fluid flow and the corresponding pressure drop in the packed beds. By the use of numerical simulation, a comprehensive investigation of the pressure drop in different geometric bed configurations and different degrees of sphere permeability was performed. Three ordered packings were considered (simple cubic, body-centered cubic, and face-centered cubic) and were studied over a range of Reynolds numbers between 0.01 and 150. A convenient dimensionless parameter ζ, for sphere permeability, was varied from 0.0001 to 0.01, where larger values of ζ represent higher permeability. In addition, results for nonpermeable spheres were obtained for comparison. Multiple pressure drop correlations for the different operating parameters are presented along with displays of flow visualization to enhance the understanding of the fluid mechanics occurring in the beds. The present numerical results are compared with well-established existing experimental-based correlations for nonpermeable spheres, and excellent agreement was found for the applicable cases.
-
Aichlmayr, H.T. and Kulacki, F.A., The Effective Thermal Conductivity of Saturated Porous Media, Adv. Heat Transf, vol. 39, pp. 377-460, 2006.
-
Allen, K.G., Von Backstrom, T.W., and Kroger, D.G., Packed Bed Pressure Drop Dependence on Particle Shape, Size Distribution, Packing Arrangement and Roughness, Powder Technol., vol. 246, pp. 590-600, 2013.
-
Atmakidis, T. and Kenig, E.Y., CFD-Based Analysis of the Wall Effect on the Pressure Drop in Packed Beds with Moderate Tube/Particle Diameter Ratios in the Laminar Flow Regime, Chem. Eng. J., vol. 155, no. 1, pp. 404^10,2009.
-
Bagci, O., Dukhan, N., and Ozdemir, M., Flow Regimes in Packed Beds of Spheres from Pre-Darcy to Turbulent, Transp. Porous Media, vol. 104, no. 3, pp. 501-520, 2014.
-
Beavers, G.S., Sparrow, E.M., and Rodenz, D.E., Influence of Bed Size on the Flow Characteristics and Porosity of Randomly Packed Beds of Spheres, J. Appl. Mech, vol. 40, pp. 655-660, 1973.
-
Blazejewski, R. and Murat-Blazejewska, S., Resistance to Creeping Flow and Permeability of Stacked Spheres, J. Porous Media, vol. 17, pp. 731-740, 2014.
-
Bradford, S.A. and Kim, H., Implications of Cation Exchange on Clay Release and Colloid-Facilitated Transport in Porous Media, J. Environ. Qual., vol. 39, no. 6, pp. 2040-2046,2010.
-
Brauer, H., Grundlagen der Einphasen-und Mehrphasenstromungen, vol. 2, Sauerlander, 1971.
-
Brinkman, H.C., A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles, Appl. Sci. Res, vol. 1, no. 1,pp. 27-34, 1949.
-
Choi, E.S., Cheema, T., and Islam, M.R., A New Dual-Porosity/Dual-Permeability Model with Non-Darcian Flow through Fractures, J. Petrol. Sci. Eng., vol. 17, no. 3, pp. 331-344,1997.
-
Cronin, M.B., Flemings, P.B., and Bhandari, A.R., Dual-Permeability Microstratigraphy in the Barnett Shale, J. Petrol. Sci. Eng., vol. 142, pp. 119-128,2016.
-
Darcy, H., Les Fontaines Publiques de la Ville de Dijon, Dalmont: Paris, 1856a.
-
Darcy, H., Determination des lois d'ecoulement del'eau a Travers le Sable, Paris, 1856b.
-
Ding, Q.L., Ju, F., Song, S.B., Yu, B.Y., and Ma, D., An Experimental Study of Fractured Sandstone Permeability after High-Temperature Treatment under Different Confining Pressures, J. Nat. Gas Sci. Eng., vol. 34, pp. 55-63, 2016.
-
Dixon, A.G., Nijemeisland, M., and Stitt, E.H., Systematic Mesh Development for 3D CFD Simulation of Fixed Beds: Contact Points Study, Comput. Chem. Eng., vol. 48, pp. 135-153, 2013.
-
Dupuis, G., Bouillot, J., Zaitoun, A., Caremi, G., and Burrafato, G., Combined Water/Sand Control Polymer Treatments in Offshore Gas Wells, SPEEOR Conf. at Oil and Gas West Asia, Society of Petroleum Engineers, 2016.
-
Eppinger, T., Seidler, K., and Kraume, M., DEM-CFD Simulations of Fixed Bed Reactors with Small Tube to Particle Diameter Ratios, Chem. Eng. J, vol. 166, no. 1, pp. 324-331, 2011.
-
Ergun, S. and Orning, A.A., Fluid Flow through Randomly Packed Columns and Fluidized Beds, Ind. Eng. Chem, vol. 41, no. 6, pp. 1179-1184,1949.
-
Ergun, S., Fluid Flow through Packed Columns, Chem. Eng. Prog, vol. 48, pp. 89-94, 1952.
-
Evseev, A.R., Visual Study of Turbulent Filtration in Porous Media, J. Porous Media, vol. 20, pp. 549-557, 2017.
-
Gerke, H.H. and Kohne, J.M., Dual-Permeability Modeling of Preferential Bromide Leaching from a Tile-Drained Glacial Till Agricultural Field, J. Hydrol., vol. 289, no. 1, pp. 239-257,2004.
-
Gibilaro, L.G., Di Felice, R., Waldram, S.P., and Foscolo, P.U., Generalized Friction Factor and Drag Coefficient Correlations for Fluid-Particle Interactions, Chem. Eng. Sci., vol. 40, no. 10, pp. 1817-1823, 1985.
-
Gunjal, P.R., Ranade, V.V., and Chaudhari, R.V., Computational Study of a Single-Phase Flow in Packed Beds of Spheres, AIChE J, vol. 51, no. 2, pp. 365-378, 2005.
-
Hill, R.J., Koch, D.L., and Ladd, A.J., Moderate-Reynolds-Number Flows in Ordered and Random Arrays of Spheres, J. Fluid Mech., vol. 448, pp. 243-278, 2001.
-
Henning, J., Broholm, M.M., and Bjerg, P.L., Role of Diffusion in Chemical Oxidation of PCE in a Dual Permeability System, Environ. Sci. Technol., vol. 41, no. 24, pp. 8426-8432, 2007.
-
Kohne, J.M., Mohanty, B.P., Simunek, J., and Gerke, H.H., Numerical Evaluation of a Second Order Water Transfer Term for Variably Saturated Dual-Permeability Models, Water Resour. Res., vol. 40, no. 7, W07409,2004.
-
Kohne, S., Lennartz, B., Kohne, J.M., and Simunek, J., Bromide Transport at a Tile-Drained Field Site: Experiment, and One- and Two-Dimensional Equilibrium and Non-Equilibrium Numerical Modeling, J. Hydrol, vol. 321, no. 1, pp. 390-408, 2006.
-
Larsbo, M., Roulier, S., Stenemo, F., Kasteel, R., and Jarvis, N., An Improved Dual-Permeability Model of Water Flow and Solute Transport in the Vadose Zone, Vadose Zone J, vol. 4, no. 2, pp. 398-406, 2005.
-
Liu, L., Xue, Q., Wan, Y., and Tian, Y., Evaluation of Dual Permeability of Gas Flow in Municipal Solid Waste: Experiment and Modeling, Environ. Prog. Sustain., vol. 35, no. 1, pp. 41-47, 2016.
-
Macdonald, I.F., El-Sayed, M.S., Mow, K., and Dullien, F.A.L., Flow through Porous Media-The Ergun Equation Revisited, Ind. Eng. Chem. Fund, vol. 18, no. 3, pp. 199-208, 1979.
-
Martin, J.J., McCabe, W.L., and Monrad, C.C., Pressure Drop through Stacked Spheres: Effect of Orientation, Chem. Eng. Progress, vol. 47, pp. 91-94, 1951.
-
Montillet, A., Akkari, E., and Comiti, J., About a Correlating Equation for Predicting Pressure Drops through Packed Beds of Spheres in a Large Range of Reynolds Numbers, Chem. Eng. Process, vol. 46, no. 4, pp. 329-333,2007.
-
Nijemeisland, M. and Dixon, A.G., Comparison of CFD Simulations to Experiment for Convective Heat Transfer in a Gas-Solid Fixed Bed, Chem. Eng. J, vol. 82, no. 1, pp. 231-246, 2001.
-
Patankar, S.V., Liu, C.H., and Sparrow, E.M., Fully Developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area, ASMEJ. Heat Transf., vol. 99, no. 2, pp. 180-186,1977.
-
Pillai, K.M. and Advani, S.G., Numerical and Analytical Study to Estimate the Effect of Two Length Scales upon the Permeability of a Fibrous Porous Medium, Transp. Porous Media, vol. 21, no. 1, pp. 1-17, 1995.
-
Renken, K.J., and Poulikakos, D., Experiment and Analysis of Forced Convective Heat Transport in a Packed Bed of Spheres, Int. J. Heat Mass Transf, vol. 31, no. 7, pp. 1399-1408, 1988.
-
Riefler, N., Heiland, M., Rabiger, N., and Fritsching, U., Pressure Loss and Wall Shear Stress in Flow through Confined Sphere Packings, Chem. Eng. Sci., vol. 69, no. 1, pp. 129-137,2012.
-
Rose, H.E., On the Resistance Coefficient-Reynolds Number Relationship for Fluid Flow through a Bed of Granular Material, P. I.Mech. Eng., vol. 153, no. 1, pp. 154-168,1945.
-
Rumble, J.R. ed., CRC Handbook of Chemistry and Physics, 98th ed. (Internet Version), Boca Raton, FL: CRC Press/Taylor and Francis, 2018.
-
Schure, M.R., Maier, R.S., Kroll, D.M., and Davis, H.T., Simulation of Ordered Packed Beds in Chromatography, J. Chromatogr. A, vol. 1031, no. 1, pp. 79-86,2004.
-
Singh, R. and Olson, M.S., Transverse Chemotactic Migration of Bacteria from High to Low Permeability Regions in a Dual Permeability Microfluidic Device, Environ. Sci. Technol., vol. 46, no. 6, pp. 3188-3195,2012.
-
Song, Y.S., Chung, K., Kang, T.J., and Youn, J.R., Prediction of Permeability Tensor for Three Dimensional Circular Braided Preform by Applying a Finite Volume Method to a Unit Cell, Compos. Sci. Technol., vol. 64, no. 10, pp. 1629-1636, 2004.
-
Susskind, H. and Becker, W., Pressure Drop in Geometrically Ordered Packed Beds of Spheres, AIChE J, vol. 13, no. 6, pp. 1155-1159, 1967.
-
Tallmadge, J.A., Packed Bed Pressure Drop-An Extension to Higher Reynolds Numbers, AIChE J, vol. 16, no. 6, pp. 1092-1093, 1970.
-
Thararoop, P., Karpyn, Z.T., and Ertekin, T., Development of a Multi-Mechanistic, Dual-Porosity, Dual-Permeability, Numerical Flow Model for Coalbed Methane Reservoirs, J. Nat. Gas Sci. Eng., vol. 8, pp. 121-131,2012.
-
Thoenes, D. and Kramers, H., Mass Transfer from Spheres in Various Regular Packings to a Flowing Fluid, Chem. Eng. Sci, vol. 8, nos. 3-4, pp. 271-283, 1958.
-
Verma, V.K. and Dixit, P.K., Flow Past a Porous Sphere of Radially Varying Permeability Embedded in Another Porous Medium, Spec. Topics Rev. Porous Media: Int. J, vol. 8, no. 3, pp. 231-243, 2017.
-
Wan, T., Evaluate EOR Potential in Fractured Shale Oil Reservoirs by Cyclic Gas Injection, Unconventional Resources Technology Conf, 2013.
-
Wang, X.D., Zhou, Y.F., and Luo, W.J., A Study on Transient Fluid Flow of Horizontal Wells in Dual-Permeability Media, J. Hydrodyn., Ser. B, vol. 22, no. 1, pp. 44-50, 2010.
-
Yang, J., Wang, Q., Zeng, M., and Nakayama, A., Computational Study of Forced Convective Heat Transfer in Structured Packed Beds with Spherical or Ellipsoidal Particles, Chem. Eng. Sci, vol. 65, no. 2, pp. 726-738, 2010.
-
Awad Mohamed M., Bejan Adrian, Dhir Vijay K., Goldstein Richard J., Haji-Sheikh Abdolhossein, Howell John R., Jaluria Yogesh, Lloyd John R., Patankar Suhas V., Simon Terrence W., Tamma Kumar K., Viskanta Raymond, In Memoriam: Professor Ephraim Maurice Sparrow, Journal of Heat Transfer, 142, 4, 2020. Crossref