Perez-Rosales, Candelario; Inst. Mexicano Perez-Rosales, Candelario; Inst. Mexicano del Petroleo
Abstract
A theory on the relationship between formation resistivity factor and porosity is presented. This theory considers that, from the standpoint of the flow of electric current within a porous medium saturated with a conducting fluid, the pore space can be divided into flowing and stagnant regions. This assumption leads to a general expression, and formulas currently used in practice are special cases of this expression. The validity of the new expression is established by the use of data corresponding to sandstones and packings and suspensions of particles. For the case of natural rocks, the theory confirms particles. For the case of natural rocks, the theory confirms Archie's equation and gives an interpretation of the physical significance of the so-called cementation physical significance of the so-called cementation exponent
Introduction
The formation resistivity factor of a porous medium is a valuable concept in the area of formation evaluation. It has been denned as the ratio of the resistivity of the medium when completely saturated with a conducting fluid to the resistivity of the saturating fluid. In this paper, a theory on the relationship between formation paper, a theory on the relationship between formation resistivity factor and porosity is presented. The theory evolves from the assumption that, from the standpoint of the flow of electric current, the pore space can be divided into traps and channels. The former are regions of stagnation, whereas the latter are portions that participate actively in the flow of electric current. This assumption, in conjunction with some ideas developed originally by Maxwell, leads to some interesting results. Among other things, the theory indicates that, in the case of natural rocks, a consider-able portion of the pore space comprises traps, thus indicating that the internal geometry of rocks is extremely complex. Also, the theory confirms the validity of the Archie equation I and provides a plausible explanation of the physical provides a plausible explanation of the physical significance of the cementation exponent.Attempts have been made to find a general correlation between formation resistivity factor and porosity. Maxwell studied this problem from the theoretical point of view for the case of dispersed spherical particles. From his ideas, a relationship known as the Maxwell equation can be deduced. In a theoretical paper, Fricke generalized the Maxwell equation to apply to systems of dispersed oblate and prolate spheroids. On the other hand, Archie obtained an empirical formula bearing his name that is applicable to natural rocks. Following the ideas of Archie, other workers have obtained empirical correlations similar to that of Archie. Finally, Perez-Rosales, in an attempt to generalize the Maxwell Perez-Rosales, in an attempt to generalize the Maxwell equation, arrived at a formula which, in general, gives good results but fails at low porosity values. In this paper, this limitation is eliminated and a more general paper, this limitation is eliminated and a more general equation is obtained. It can be shown that the formulas currently used in practice are special cases of the equation proposed in this paper. To test the validity of the theory, experimental data corresponding to natural rocks and to packings and suspensions of particles are used.
Theory
Consider the following experiment. A nonconducting porous rock is saturated with a conducting fluid, and porous rock is saturated with a conducting fluid, and then an electric current is passed through the system. Does the whole pore space participate in the flow of electric current? Laboratory studies indicate that the pore walls are extremely irregular, which in turn indicates regions of stagnation called traps. As a consequence, the total porosity, can be divided into two parts: a flowing porosity, associated with the channels, and a porosity, associated with the channels, and a stagnant porosity, associated with the traps.
SPEJ
p. 531
Unsteady Stokes flow induced by a point source of electric current in a non-Darcy hemispherical porous medium