Heat Transfer Upscaling in Geothermal Reservoirs
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In this thesis we implement a numerical model of heat transfer in geothermal reservoirs. We use existing pressure and flow transport solvers as a starting point to investigate discretization techniques for a convection-conduction temperature equation. Then we develop and analyse two different heat transfer solvers: explicit and implicit, that have different accuracy and convergence requirements. For the convective part of the energy equation the upwind scheme is implemented and the two-point flux approximation is used to discretize the conductive term. Usually heat transfer simulations require large computational time due to high resolution on a fine scale. For efficient computation we investigate flow-based upgridding techniques, which were used before for fluid transport in porous media. However upgridding and upscaling can lead to less accurate results due to much loss of details in a discrete model. We compare solutions on different types of grids such as Cartesian grid and flow-based grids that are generated according to various indicators like permeability, velocity, time-of-flight and thermal conductivity. In this work we simulate an initial- boundary value problem with a heat flow through boundaries and try to investigate, which coarse grid leads to the most accurate results when solving the energy equation.