The Physical Meaning of the Koval Factor

Abstract

When originally developed, the Koval theory was meant to interpret the core-scale production of oil by a miscible displacement by solvent injection. An essential parameter in the theory is the Koval factor, K_V, which combines both the viscosity contrast effect (E) and the heterogeneity effect (H_K) as K_V = E H_K. The Koval method has done an excellent job of interpreting oil recovery; however, the physical origin of this simple model is not clear. To address the physical significance of these factors, this paper explains a novel approach to derive the Koval factor using petrophysical data and vertical equilibrium theory. The study examines core data from 112 vertical production wells from fields located in the United States and Algeria. The heterogeneity factor is estimated from the flow- and storage-capacity relations, according to the Koval theory. Then, using fractional flow theory and assuming vertical equilibrium, we derive a mathematical expression that conveys the physical interpretation of the Koval factor. The results indicate that the physical explanation of the Koval factor is that of a product of the mobility ratio and the heterogeneity of the reservoir. The Koval factor simplifies computations of oil recovery by transforming the original reservoir to one with uniform layers, in vertical equilibrium, and piston-like displacement within each using only the flow and storage capacities. The physical interpretation of the Koval factor could offer new insights to examine previous results obtained from the theory itself.