Mathematical models for the analysis and forecasting of oil field development: a capacitive-resistive model without bottomhole pressure and a logarithmic model of well water breakthrough

I. V. Afanaskin^a, S. G. Volpin^b, A. V. Korolev^b, M. Yu. Ahapkin<sup>b

a</sup> Almetyevsk State Technological University, Petroleum Higher School, Almetyevsk, Russian Federation
^b Scientific Research Institute for System Analysis of the National Research Centre Kurchatov Institute, Moscow, Russian Federation

Abstract: We developed a modified Capacitance-Resistive Model (CRM) that does not require bottomhole pressure data. This semi-analytical model applies to waterflooding and elastic-water-drive reservoir development. Unlike traditional CRM formulations, our approach relies on cumulative production and injection volumes and incorporates inter-well interactions along with the effects of aquifers.We also introduced an empirical logarithmic model for water breakthrough, which relates water saturation to cumulative liquid production. The resulting equations enable the calculation of liquid flow rates and water breakthrough without bottomhole pressure, significantly broadening the model's applicability in fields with limited monitoring data.We tested the model on four production wells in a carbonate reservoir under elastic-water-drive conditions. Comparisons with the standard CRM model demonstrated acceptable accuracy in flow rate prediction without pressure input and high precision in modeling water breakthrough dynamics. This approach supports both development forecasting and real-time field analysis without relying on hard-toobtain parameters such as bottomhole pressure.

Keywords: mathematical models, oil field development forecasting, CRM model, water breakthrough model, elastic water drive.