Formation factor and tortuosity of homogeneous porous media |
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Authors: | Ravi Suman Douglas Ruth |
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Institution: | (1) Department of Mechanical and Industrial Engineering, University of Manitoba, R3T 2N2 Winnipeg, MB, Canada |
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Abstract: | In this paper, volume averaging in porous media is applied to the microscopic electric charge conservation equation (differential form of Ohm's law) and an expression is derived for the formation factor of a homogeneous porous medium saturated with an electrically conductive fluid. This expression consists of two terms; the first term involves the integral of the current density over the fluid volume and the second term involves the integral of the electric potential over the solid-fluid interface. The physical meaning of the two terms is discussed with the help of three idealized porous media. The results for these media indicate a definite relation between the second term and tortuosity. These results also demonstrate the simplistic nature of the classical definition of the tortuosity as a ratio of geometric lengths. An exact relation between the formation factor and tortuosity is presented. It is shown that the assumed equivalence of the electrical and hydraulic tortuosities is not valid. The general application of the expression for the formation factor is discussed briefly. |
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Keywords: | Ohm's law formation factor volume averaging REV network theory idealized porous media tortuosity |
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