Multiscale Simulation of Thermal Flow in Porous Media
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In this thesis we develop a multiscale method that solves non-isothermal flow in porous media. A sequential formulation is established that decouples corresponding equations into three systems, one pertaining pressure, one pertaining temperature and one pertaining transport. The sequential method is then verified against a standard fully implicit method on two examples with varying degree of complexity on the permeability field. By adjusting a tolerance that decides the number of outer iterations in the sequential method, the method converges toward the fully implicit method. After the sequential method is verified, we use the sequential structure in the development of an accurate and efficient multiscale method for the pressure and temperature systems. This multiscale method is then vigorously tested against the sequential method on several examples with varying degrees of complex grids and permeability fields, as well as being verified for both single-phase and multiphase flow. The multiscale method can, by adjusting the parameters of the original sequential method, converge towards various fully implicit solutions, or give a reasonable approximation on the coarse scale. The experiments show that the multiscale method provides a flexible and stable solver that accurately solves the equations describing non-isothermal flow in porous media more efficiently than both the fully implicit method and the sequential method as long as heterogeneous permeabilities are used.