Fluid Saturation Evaluation
In his treatise on electricity and magnetism, Maxwell (1873) published an equation that described the conductivity of an electrolyte that contained nonconducting spheres as: . . . Ψ = co/cw = 2Φ/(3-Φ) . . . where the “meaning” of Ψ (psi) has been most commonly interpreted as some expression of tortuosity, Co and Cw are the conductivity of the medium and the electrolyte, respectively, and Φ is the proportion of the medium that is occupied by the electrolyte. Since that time, considerable efforts have been devoted to elucidation of the electrical properties of porous materials, particularly with the advent of the first resistivity log in 1927, which founded an entire industry focused on estimating fluid saturations in hydrocarbon reservoirs from downhole measurements. To some degree, spirited discussions in the literature reflect two schools of thought, one that considers the role of the resistive framework from a primarily empirical point of view, and the other that models the conductive fluid phase in terms of electrical efficiency. Clearly, the two concepts are intertwined because resistivity is the reciprocal of conductivity and the pore network is the complement of the rock framework. If the solid part of the rock is nonconductive, then the ability of a rock to conduct electricity is controlled by the conductive phase in the pore space, which should make the case for equations to be formulated from classical physical theory. This approach is typically developed using electrical flow through capillary tubes as a starting point. Unfortunately, the topological transformation of a capillary tube model to a satisfactory representation of a real pore network is a formidable challenge, so that mathematical solutions may not be acceptable, even though they are grounded in basic physics. The most successful model along these lines has been proposed by Herrick and Kennedy (1994), who maintain that while the Archie equation is a useful parametric function, it has no physical basis. Some of their conclusions are reviewed at the end of this chapter.