# Numerical method for calculating heat and mass transfer of two-phase fluid in fractured-porous reservoir

## Authors

• Yuliya O. Bobreneva Institute of Petrochemistry and Catalysis RAS
• Yury A. Poveshchenko Keldysh Institute of Applied Mathematics RAS
• Viktoriia O. Podryga Keldysh Institute of Applied Mathematics RAS; Moscow Automobile and Road Construction State Technical University (MADI)
• Sergey V. Polyakov Keldysh Institute of Applied Mathematics RAS; Institute of Petrochemistry and Catalysis RAS
• Ravil M. Uzyanbaev Institute of Petrochemistry and Catalysis RAS; Ufa State Petroleum Technical University (USPTU)
• Kamila F. Koledina Institute of Petrochemistry and Catalysis RAS; Ufa State Petroleum Technical University (USPTU)
• Pаrvin I. Rahimly Keldysh Institute of Applied Mathematics RAS

## Keywords:

two-phase fluid filtration, dual porosity model, fractured-pore type collector, piezoconductivity, temperature, matrix sweep

## Abstract

The work proposes an approach to numerical modeling based on splitting by physical processes for a non-isothermal problem of filtration in a fractured-porous medium. The task is complicated by the presence of a two-phase fluid and dual porosity of the reservoir. The system of equations defining the model is complex and is described by a system of strongly non-linear partial differential equations. The use of the splitting method according to physical processes makes it possible to simplify the solution algorithm while maintaining the equivalence to the conservative difference approximation of the original equations and ensuring the stability of the problem solution. In the numerical solution, the approximations of differential operators obtained in the framework of the finite difference method are used. The implementation of the numerical algorithm is based on the matrix sweep method. To test the method, a series of computational experiments were carried out. Calculations have shown that the developed methodology is correct and allows one to simulate the dynamic operating conditions of wells.

## Author Biographies

### Yuliya O. Bobreneva

Institute of Petrochemistry and Catalysis RAS
• Engineer

### Yury A. Poveshchenko

Keldysh Institute of Applied Mathematics RAS
• Professor, Leading Researcher

### Sergey V. Polyakov

Keldysh Institute of Applied Mathematics RAS
Institute of Petrochemistry and Catalysis RAS

### Ravil M. Uzyanbaev

Institute of Petrochemistry and Catalysis RAS
Ufa State Petroleum Technical University (USPTU)
• Senior Lecturer

### Kamila F. Koledina

Institute of Petrochemistry and Catalysis RAS
Ufa State Petroleum Technical University (USPTU)
• Associate Professor, Leading Researcher

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13-02-2024

## How to Cite

Бобренева Ю.О., Повещенко Ю.А., Подрыга В.О., Поляков С.В., Узянбаев Р.М., Коледина К.Ф., Рагимли П.И. Numerical Method for Calculating Heat and Mass Transfer of Two-Phase Fluid in Fractured-Porous Reservoir // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2024. 25. 33-46. doi 10.26089/NumMet.v25r104

## Section

Methods and algorithms of computational mathematics and their applications