Numerical investigation of coupled anomalous diffusion and heat transfer during thermal displacement process in porous media under local thermal equilibrium

Heterogeneities are acknowledged to exist on many different length scales in geological media and outcrops, leading to a huge range of fluid velocities, porosities, and effective thermal conductivities. In this regard, existing continuum-based non-isothermal simulation models may not always be accurate for predicting transport behavior in highly heterogeneous reservoir rocks, or fractured rocks with fractal geometry. In the present study, the fractional calculus theory is adopted to simulate anomalous fluid and heat transport in porous media under non-isothermal flow conditions. The resulting coupled mathematical model is developed under the assumption of local thermal equilibrium (LTE) and is handled numerically by employing existing finite difference and finite volume numerical discretization methods. Numerical experiments performed indicate that transport behavior of the anomalous non-isothermal model differs significantly from the classical non-isothermal formulation which is based on Darcy flux and Fourier-flux constitutive relations. The simulation results indicate that the sub-diffusive regime leads to a higher pressure-drop through the porous media. In addition, the rate of heat propagation in the porous media is noted to be retarded when the order of fractional differentiation deviates from unity. This study demonstrates the use of fractional calculus as a tool to characterize complex transport behavior observed in heterogeneous porous media.