Analysis of seepage characters in fractal porous media

Abstract In this paper, the plane-radial and plane-parallel flows for Newtonian fluid in fractal porous media are analyzed. Based on the assumption that the porous medium consists of a bundle/set of tortuous streamlines/capillaries and on the fractal characteristics of pore size distribution in porous media, the expressions for porosity, flow rate, velocity and permeability for both radial and parallel flows are developed. The obtained expressions are the functions of tortuosity, fractal dimension, maximum and minimum pore diameters, and there are no empirical constant and every parameter has clear physical meaning in the expressions. The pressure distribution equations for plane-radial and plane-parallel flows in fractal porous media are also derived. The pressure and velocity distributions in plane-radial reservoirs are calculated and discussed.

[1]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[2]  R. Beier.  Pressure Transient Model of a Vertically Fractured Well in a Fractal Reservoir , 1994 .

[3]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[4]  J. P. D. Plessis,et al.  Analytical quantification of coefficients in the Ergun equation for fluid friction in a packed bed , 1994 .

[5]  Boming Yu,et al.  SOME FRACTAL CHARACTERS OF POROUS MEDIA , 2001 .

[6]  Boming Yu,et al.  A fractal permeability model for bi-dispersed porous media , 2002 .

[7]  Zhang Hong-qing,et al.  The flow problem of fluids flow in a fractal reservoir with double porosity , 2001 .

[8]  I. F. Macdonald,et al.  Flow through Porous Media-the Ergun Equation Revisited , 1979 .

[9]  Cheng-Hsien Wu,et al.  IN-PLANE PERMEABILITY MEASUREMENT AND ANALYSIS IN LIQUID COMPOSITE MOLDING , 1994 .

[10]  R. Hicks,et al.  Pressure Drop in Packed Beds of Spheres , 1970 .

[11]  Boming Yu,et al.  A resistance model for flow through porous media , 2008 .

[12]  Yun Mei-Juan,et al.  A Geometry Model for Tortuosity of Streamtubes in Porous Media with Spherical Particles , 2005 .

[13]  Howard N. Hall,et al.  Compressibility of Reservoir Rocks , 1953 .

[14]  Jacques Comiti,et al.  A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles , 1989 .

[15]  S. Ergun.  Fluid flow through packed columns , 1952 .

[16]  M. Sahimi.  Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing , 1993 .

[17]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[18]  Jinsui Wu,et al.  A fractal resistance model for flow through porous media , 2007 .

[19]  Tianshou Zhao,et al.  An experimental study of two phase flow and boiling heat transfer in bi-dispersed porous channels , 2000 .

[20]  Boming Yu,et al.  A fractal in‐plane permeability model for fabrics , 2002 .

[21]  Xiao-yan Li,et al.  Permeability of fractal aggregates. , 2001, Water research.

[22]  F. Dullien.  Porous Media: Fluid Transport and Pore Structure , 1979 .

[23]  Morton M. Denn,et al.  Process Fluid Mechanics , 1979 .

[24]  C. Karacan,et al.  A fractal model for predicting permeability around perforation tunnels using size distribution of fragmented grains , 2003 .

[25]  Thompson,et al.  Fractal sandstone pores: Implications for conductivity and pore formation. , 1985, Physical review letters.

[26]  Yu Bo-Ming,et al.  A Geometry Model for Tortuosity of Flow Path in Porous Media , 2004 .

[27]  Yanjun Liu,et al.  A FRACTAL MODEL FOR RELATIVE PERMEABILITY OF UNSATURATED POROUS MEDIA WITH CAPILLARY PRESSURE EFFECT , 2007 .

[28]  R. Pandey,et al.  Density profile and flow of driven gas in an open porous medium with a computer simulation , 2001 .

[29]  Bin Zhang,et al.  A FRACTAL ANALYSIS OF PERMEABILITY FOR POWER-LAW FLUIDS IN POROUS MEDIA , 2006 .

[30]  Boming Yu,et al.  Geometrical Models for Tortuosity of Streamlines in Three-Dimensional Porous Media , 2008 .

[31]  R. Carbonell,et al.  The hydrodynamics of trickling flow in packed beds. Part II: Experimental observations , 1986 .

[32]  Boming Yu,et al.  FRACTAL DIMENSIONS FOR MULTIPHASE FRACTAL MEDIA , 2006 .

[33]  P. Adler,et al.  Effective Medium Analysis of Random Lattices , 2000 .