Approach to the determination of the heat transfer coefficient between rock and fluid mixture for modeling non-isothermal multiphase flow

Abstract

The paper presents an approach to calculation of the coefficient determining the rate of heat transfer between a fluid mixture in oil reservoir and a matrix-rock. This coefficient is necessary for further joint modeling of hydrodynamic and thermal processes that occur in the field reservoir during its development using, for example, thermal methods for enhanced oil recovery. To model the processes of a non-isothermal multiphase flow, an approach based on implicit pressure calculation using the finite element method and explicit calculation of phase saturations is used. The approach to determining the heat transfer coefficient is based on solving the thermal problem in an area corresponding to a channel of a porous medium and a part of the matrix-rock around it. In this case, a fluid mixture with a known temperature value, different from the initial temperature in the channel and matrix-rock, enters the channel at a given rate. A two-dimensional problem is solved in an axisymmetric formulation by the finite element method.Numerical experiments to determine the heat transfer coefficient were carried out on models for various values of the channel size, porosity, initial temperatures of the medium, temperature of the mixture entering the channel, thermal properties of the fluid mixture and rock. As a result of the study, it was found that the channel size and porosity have the most significant effect on the value of the heat transfer coefficient, since these characteristics determine the volume of the matrix-rock, which should “warm up / cool down” when the temperature of the fluid mixture in the channel changes. Also, the coefficient values obtained were quite large, since the heat exchange between the rock and the mixture in the channel occurs in minutes, which practically corresponds to instantaneous heat transfer when it comes to modeling field development processes, where time steps are days and months.