Analytical Model for Fluid Flow Coupling With Heat Transfer Integrating Heat Conduction and Convection in Radial System

Abstract

Enormous heavy oil resources has been found in western Canada. But some factors especially high viscosity limit their development. Thermal recovery methods which injecting heat into the reservoir or in-situ combustion, have been widely used to enhance heavy oil recovery. The viscosity of the crude oil has been lowered by raising the temperature of the reservoir, so temperature and pressure profiles are important factors for making operations and development plans in thermal recovery process. Understanding how heat transfer influences the fluids flow is the key knowledge for us to make the right decisions. In this study, a novel heat transfer model in radial system, integrating both conduction and convection, has been developed to describe the heat transfer in the heating reservoir. In this temperature domain model, heat injection rate keeps constant and dimensionless variables are defined to reduce the model to the dimensionless form. Variable transformation and Laplace transformation are performed to derive the analytical solution in Laplace space. By using Stehfest inverse algorithm, the solution in Laplace space can be converted to dimensionless analytical solution in real time space. With an analytical solution of temperature domain, fluid flow in the reservoir can be generated by dividing the whole reservoir into numbers of sub-sections. Pseudo-time is introduced to solve the changing viscosity and makes the analytical model can be solved. Dimensionless variables are also defined and the pressure are solved in Laplace space. Sequentially coupling method is applied to use the temperature profiles in pressure domain. The final dimensionless analytical solutions are obtained by Stehfest inverse algorithm. Numerical simulations by COMSOL Multiphysics are conducted to validate the analytical solutions of the models. Satisfactory agreements of the results are achieved between analytical solutions and numerical simulation results. Sensitivity analysis are also conducted to analyze the influence factors of heat transfer and fluid flow. Heat injection rate, heat capacity of fluids and rock, permeability are important parameters for heat