A THEORETICAL INVESTIGATION ON THE FORMATION FACTOR/PERMEABILITY/POROSITY RELATIONSHIP USING A NETWORK MODEL*

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Abstract
The knowledge of hydraulic and electric properties of porous media and the relations between them is essential for the quantitative evaluation of electric well logs and the solution of other reservoir engineering problems. The state of the art in this field is not yet satisfying. Theories still show considerable discrepancies with practice due to oversimplified model approaches. Empirical relations are either too coarse, not fully determined, or valid under specific geological and geographical conditions only. This article deals with the development of a general theory of the electric and hydraulic resistance behavior of porous media on the basis of a very general statistical network model. A general solution of the relations between formation factor, permeability, and porosity is presented by means of a rigorous mathematical treatment of two limiting cases of such a network. The solution shows that the product of the formation factor and the permeability can be expressed in the expectation values and the variation coefficients of pore channel cross section and shape factor and by a network factor, that depends on the mesh texture of the network. This network factor is in the range zero to one. It is further shown that the path length increase enters both the electric and the hydraulic tortuosity by its square.