Development of physical and mathematical models of spontaneous polarization potentials for oil and gas well logging

Among a large number of geophysical well logging methods, the spontaneous potential (SP) logging is a most demanded one for studying geological sections, and is widely used in all drilled wells. This paper presents a brief review of the main studies on the enhancement of a theoretical model for the SP phenomenon, and on the creation of algorithms for numerical modeling of SP logging data. First of all, we discuss the studies that were conducted shortly after the discovery of the phenomenon and became fundamental in the field of SP method theory. Most of the first works were aimed at identifying the key factors that influence the shape and amplitude of SP signals. The research vector of these works contributed to the creation of interpretation charts, which are widely used even today. This review also analyses the main results of the more recent theoretical works aimed at developing a quantitative SP logging model that takes into account the petrophysical properties of the geological environment, and works related to numerical approaches for the modeling of well logging data. In addition, to demonstrate the effectiveness of modern computational methods, the paper presents an original algorithm based on the finite element method and utilizing a correct physical and mathematical model of the SP phenomenon. The proposed approach makes it possible to calculate SP signals in the intervals of clayed reservoirs, with consideration to their porosity, water saturation, as well as the type and content of clay minerals. Comparison of the SP modeling results and field logging data obtained from wells in Western Siberian fields shows a high quality of our theoretical model. The presented review of key works devoted to the theoretical description of the SP method, as well as modern numerical approaches for analysing SP logging curves in complex geological conditions, demonstrates the potential of the SP method for new areas of practical application.