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Journal of Porous Media
Импакт фактор: 1.49 5-летний Импакт фактор: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN Печать: 1091-028X
ISSN Онлайн: 1934-0508

Выпуски:
Том 22, 2019 Том 21, 2018 Том 20, 2017 Том 19, 2016 Том 18, 2015 Том 17, 2014 Том 16, 2013 Том 15, 2012 Том 14, 2011 Том 13, 2010 Том 12, 2009 Том 11, 2008 Том 10, 2007 Том 9, 2006 Том 8, 2005 Том 7, 2004 Том 6, 2003 Том 5, 2002 Том 4, 2001 Том 3, 2000 Том 2, 1999 Том 1, 1998

Journal of Porous Media

DOI: 10.1615/JPorMedia.v5.i1.50
8 pages

Evaluation of Steady Flow Through a Six-Lobe Sand Cartridge Filter by the Boundary Perturbation Method

H. R. Patel
Department of Chemical Engineering, The University of Akron, Akron, Ohio 44325-3906
S. I. Hariharan
Department of Mathematical Sciences, The University of Akron, Akron, Ohio, U.S.A.; and ICOMP, NASA Lewis Research Center, Cleveland, Ohio, U.S.A.
G. G. Chase
Department of Chemical Engineering, Microscale Physiochemical Engineering Center, The University of Akron, Akron, Ohio 44325-3906

Краткое описание

Consolidated sand cartridge filters are used in the oil industry to filter particles from produced water before pumping the water back into the ground for secondary oil recovery. The sand filter is essentially an annulus, but its outer surface is structured into a six-lobed curved geometry that gives it larger surface area for filtration. The larger surface area increases the life of the filter, but the geometry is more difficult to evaluate than the simple cylindrical geometry. The problem addressed in this article is to determine the steady-state pressure profile for radial flow of water through the filter. This pressure profile can then be used to determine the velocity profiles through the filter, and finally determine the flow rate that can be achieved through the filter. For porous media with uniform isotropic permeability, Darcy's law (Darcy, 1856) is used to describe the pressure-velocity relationship. The six-lobed geometry forms a boundary condition that does not coincide with a level surface in cylindrical coordinates. This is not only a basic flow problem of addressing the needs of filtration industry, oil industry, or chemical engineering, but it is also of mathematical interest. The boundary perturbation method (Van Dyke, 1975; Georgescu, 1995) is not widely used to solve partial differential equations, even though the method is well illustrated. The application of the method to model the irregular geometry of the six-lobed cartridge filter is new. When the boundary perturbation method is used to solve a partial differential equation, the resulting solution can be described in a series form. The first term of the solution corresponds to the simple cylindrical annular geometry. The subsequent terms converge to describe the solution for the six-lobed geometry. A third order solution, beyond the annular solution, is sufficiently accurate for calculating the pressure profile, for typical filter designs. The results show that for a given pressure drop, the six-lobed design provides greater flow rates than would be obtained for cylindrical filters of similar size.


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