GENERAL INTEGRAL EQUATIONS OF STOKES FLOW THROUGH THE RANDOM STRUCTURE POROUS MEDIA

2015 ◽  
Vol 13 (5) ◽  
pp. 375-392 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Porous Media ◽  
Integral Equations ◽  
Stokes Flow ◽  
Random Structure ◽  
General Integral ◽  
Flow Through

Transport processes in periodic porous media

1995 ◽  
Vol 299 ◽  
pp. 1-15 ◽  
Author(s):  
R. B. Saeger ◽  
L. E. Scriven ◽  
H. T. Davis
Keyword(s):  
Porous Media ◽  
Stokes Equation ◽  
Stokes Flow ◽  
Scaling Law ◽  
Equation System ◽  
Transport Processes ◽  
Formation Factor ◽  
Flow Through ◽  
Elliptic Grid Generation ◽  
The Stokes Equation

The Stokes equation system and Ohm's law were solved numerically for fluid in periodic bicontinuous porous media of simple cubic (SC), body-centred cubic (BCC) and face-centred cubic (FCC) symmetry. The Stokes equation system was also solved for fluid in porous media of SC arrays of disjoint spheres. The equations were solved by Galerkin's method with finite element basis functions and with elliptic grid generation. The Darcy permeability k computed for flow through SC arrays of spheres is in excellent agreement with predictions made by other authors. Prominent recirculation patterns are found for Stokes flow in bicontinuous porous media. The results of the analysis of Stokes flow and Ohmic conduction through bicontinuous porous media were used to test the permeability scaling law proposed by Johnson, Koplik & Schwartz (1986), which introduces a length parameter Λ to relate Darcy permeability k and the formation factor F. As reported in our earlier work on the SC bicontinuous porous media, the scaling law holds approximately for the BCC and FCC families except when the porespace becomes nearly spherical pores connected by small orifice-like passages. We also found that, except when the porespace was connected by the small orifice-like passages, the permeability versus porosity curve of the bicontinuous media agrees very well with that of arrays of disjoint and fused spheres of the same crystallographic symmetry.

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