The Resistivity of a Fluid-Filled Porous Body

Abstract

Abstract A model of a porous body is presented in which the pore space consists of asystem of voids and interconnecting tubes. Relationships between porosity andresistivity formation factor are determined partly by calculation, partly byexperiment. Constriction effects characteristic of the model are shown to besufficient to account for high formation factors. It is shown that constrictionmay be combined with moderate amounts of tortuosity to give model pore systemsexhibiting to a first approximation porosity and resistivity properties similarto those of natural porous bodies. Introduction The relationship between the electric resistivity of a fluid-filled porousbody and the geometry of its pore space is so complex that the calculation ofthe resistivity of a natural porous rock is a practical impossibility. Both theresistivity of a body and its porosity are measurable quantities, however, andprevious successes at relating them have been reached by an empirical approach.Efforts at obtaining theoretically derived formulae relating them havegenerally been unsatisfactory. One of the reasons for this may lie in the puregeometry that has been assumed. The Tortuosity Concept A parameter called the formation factor is useful in discussing theresistivity of a fluid-filled porous body. This parameter is the ratio of theresistivity of a fluid saturated porous body to the resistivity of thesaturating fluid. Formation factors are often available from measurements oncores or from electric logs, and many attempts have been made to correlateformation factors and porosities of geological formations. Whenever asuccessful correlation is found, the engineer working with electrical logs hasa useful tool for the determination of porosities of pay sections. T.P. 3352