Anastasia Glinskikh

Spontaneous potential (SP) logging remains a widely used method in well geophysics. However, its interpretation is often limited by simplified physical models and correction charts that do not fully account for the processes governing SP generation, particularly in shaly and heterogeneous formations. In this study, we develop a finite element-based algorithm for modeling SP responses in complex near-wellbore environments, with the aim of providing a more physically consistent framework for interpretation. The proposed algorithm is based on the numerical solution of the Poisson equation with electrochemical source terms, incorporating the cation transport number to describe diffusion–adsorption processes and allowing for smooth variations in formation resistivity, fluid properties, and shale content. The numerical implementation is validated against published analytical solutions, correction charts, and previous numerical studies, showing good agreement in both the shape and amplitude of modeled SP responses across a range of geological scenarios, including thin beds and invasion zones. Application to real data from a Southeast Asia gas field demonstrates that the approach provides reliable estimates of formation water salinity and the cation transport number, with results consistent with independent estimates. The proposed method offers a flexible tool for SP response modeling and may complement existing interpretation techniques, particularly when working with heterogeneous formations and limited legacy datasets.

An algorithm for the numerical simulation of spontaneous potential (SP) signals based on the finite element method is proposed. The SP signals are passively recorded electrical signals resulting from the physical and chemical processes of various nature occurring inside the well and adjacent formations. The proposed algorithm allows one to simulate the SP signals for the case of axial symmetry of the studied area and an electrochemical SP source. Using sigmoidal functions to describe the distribution of petrophysical parameters in the study area allows one to obtain an analytical expression for the density of the SP source. The correctness of the proposed algorithm is verified on a simplified three-layer model. The dependence of the obtained SP signals on the thickness of the permeable formation and on its salinity is demonstrated.

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.

(1) This article is devoted to the development of a theoretical and algorithmic basis for numerical modeling of the spontaneous potential method (SP) as applied to the study of sandy-argillaceous reservoirs. (2) In terms of coupled flows, we consider a physical–mathematical model of SP signals from an electrochemical source, with regards to the case of fluid-saturated shaly sandstone. (3) An algorithm for 2D finite-element modeling of SP signals was developed and implemented in software, along with its internal and external testing with analytical solutions. The numerical SP modeling was carried out, determining the dependences on the reservoir thickness and porosity, the amount of argillaceous material and the type of minerals. We performed a comparative analysis of the simulated and field SP data, using the results of laboratory core examinations taken from wells in a number of fields in the Latitudinal Ob Region of Western Siberia. (4) The results of the study may be used either for the development of the existing SP techniques, by providing them with a consistent computational model, or for the design of new experimental approaches.

(1) The article is devoted to the development of a theoretical and algorithmic basis for numerical modeling of the spontaneous potential method (SP) as applied to the study of sandy-argillaceous reservoirs. (2) In terms of coupled flows, we consider a physical-mathematical model of SP signals from an electrochemical source, with regard to the case of fluid-saturated shaly sandstone. (3) An algorithm for 2D finite-element modeling of SP signals was developed and implemented in software, along with its internal and external testing with analytical solutions. The numerical SP modeling was carried out, with determining the dependences on the reservoir thickness and porosity, the amount of argillaceous material and the type of minerals. We performed a comparative analysis of the simulated and field SP data, using the results of laboratory core examinations taken from wells in a number of fields in the Latitudinal Ob Region of Western Siberia. (4) The results of the study may be used either for the development of the existing SP techniques, by providing them with a consistent computational model, or for the design of new experimental approaches.