Solving Microscale Heterogeneous Matrix Diffusion Based on Two and Three-Dimensional Computing Using X-Ray Tomography Image Data
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Abstract
Matrix diffusion is widely cited as a critical transport process controlling the arrival times of tracers in porous media. We determine the memory function implemented in the sink/source term of the transport equation, to characterize diffusion in microscale heterogeneous rock matrix. A lagrangian method in time domain is used to solve transport by diffusion in the matrix. The properties that control diffusion (i.e., mobile-immobile interface and immobile domain cluster shapes, porosity, and tortuosity) are investigated by X-ray microtomography, where the main characteristics of matrix diffusion are captured by 2-D and 3-D calculations. Results of the memory function appeared to be different. A priori, the diffusion paths in 3-D are longer than those observed in 2-D, and they are controlled by the properties mentioned above. Simulation results using three-dimensional computations provide more accurate definition of the memory function rather than the two-dimensional calculations, providing a deeper understanding of the late time behaviour of breakthrough curves (BTCs).
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