Modeling of thermophysical processes in an oil reservoir during heating in a stopped well

Objectives. An important and urgent task of the oil producing industry is the identification of patterns of thermophysical processes in reservoirs. One approach to improving the efficiency of oil recovery in conditions of hard-to-recover reserves involves thermal action on the reservoir. The construction of mathematical models for describing such processes to optimize production technologies is based on the formation of nonstationary heat flows in the reservoir when a stopped well is heated. The application of mathematical modeling methods considered in the work forms a basis for calculating the distribution dependencies of nonstationary fields of thermophysical characteristics in the reservoir when heating the well to its parameters and the properties of the environments.Methods. The work is based on heat- and mass-transfer theory along with mathematical physics, analytical and numerical methods, as well as algorithms, computer modeling approaches, and the development of applications using modern programming languages and their libraries.Results. A formation saturated with oil, water, and a steam–gas mixture is theoretically described. A closed system of heat and mass transfer equations is obtained taking into account diffusion-droplet and heat flows and phase transformations. A formulated mathematical statement of the model comprises an initial–boundary value problem for equations relating the temperature, saturation, and pressure of the components of the saturating fluid in the formation. Numerical algorithms for solving are developed and their software implementation carried out. An application developed for computer implementation of the model provides convenient visualization of the calculation results consisting of several components (modules). Numerical experiments were carried out using the developed software to study how various factors, such as the properties of the formation sketch and the saturating liquid phase and heater characteristics, affect the thermophysical processes in the formation. Conclusions. The developed model can be used to clearly describe nonstationary distributions of thermophysical characteristics formed by thermal and diffusion-droplet flows in the reservoir during heating of a shut-up well. The obtained results expand current understandings of the regularities of thermophysical processes and the properties of the saturating phase in the reservoir under thermal influence.