Heat Transfer in the Formation Invaded by Drilling Fluid Losses from a Geothermal Well

Abstract

An analysis of fluid and heat transport in a region of the formation around a geothermal well that is invaded by drilling fluid is presented. The formation is considered as a fractured porous medium, where the liquid-phase flows through a rigid, impermeable solid-phase. 2D volume-averaged governing equations are used to describe flow of an incompressible fluid through an isotropic porous medium which is assumed to follow Darcy´s law. The thermal model is a based on volume-averaged mass, energy and momentum balances which consider the porous medium as an effective medium. A one-equation thermal transport model is derived from the averaged transport equations of the individual phases and the application of the principle of local thermal equilibrium. The total thermal effective thermal conductivity tensor is evaluated through available correlations in the literature. Finite differences and the ADI algorithm are used to solve the resulting mathematical model. Application to 3x3m portion of a geothermal reservoir around a geothermal well,, indicates that fluid velocities in the formation are on the order of 10-5 m/s, implying creeping flow. The temperature distribution indicates a predominant effect of heat convection at short times while diffusion dominates at longer times.