Transient Solution for the Energy Balance in Porous Media Considering Viscous Dissipation and Expansion/Compression Effects Using Integral Transforms

Abstract

Monitoring of downhole flowing temperatures in oil wells is gaining attention in the recent years due to the possibility of exploring these data for reservoir characterization and determination of inflow profiles along the well completions, leading to an increased interest in the development of solutions for the equations governing the thermal behavior of a reservoir. In this work, it is proposed to use the generalized integral transform technique (GITT) to provide solutions for the energy balance equation, considering the thermal effects related to fluid flow. A formal and general solution for the energy balance in the porous media is presented and validated. It is presented the application of the proposed solution to one-dimensional and two-dimensional problems in the Cartesian coordinate system. The two-dimensional problem, which considers heat transfer to the surrounding impermeable formations, is tackled by a single domain formulation. The mathematical approach taken in these solutions is rigorous, valid for all flow regimes (transient, late-transient and pseudo-steady-state/steady-state) and for any orthogonal coordinate system, presenting the possibility of achieving differentiable and stable solutions with controlled accuracy. The solution comprises an important contribution to support the application of temperature data to reservoir engineering problems.