Solving Diffusion Time in Heterogeneous Microscale Rock Matrix by 3D Computations: Non-Fickian Dispersion Observed in Porous Media

摘要

Understanding and simulating the underlying microscopic physics of the rock matrix is very useful for determining macroscopic physical properties such as permeability. Matrix diffusion is an important transport parameter controlling the late-time behaviour of breakthrough curves (BTCs). We compute the memory function, implemented in the sink/source term of Mobile-immobile mass transfer by solving the matrix diffusion using a time diffusion random-walk approach. The diffusion is controlled by different parameters like the porosity, tortuosity, mobile-immobile interface and immobile domain cluster shapes. All these properties are investigated by X-ray microtomography that captures the main characteristics of matrix diffusion at three dimensions. We compare the memory function deduced from the field-scale tracer tests well with the computed memory function. Simulation results of the memory function appeared to be coherent with that measured from the tracer test for a large tortuosity value. Probably, the diffusion paths are longer, and they are controlled by the properties mentioned above. From a representative elementary volume of natural reservoirs studied here, we conclude that, microscale diffusion process in the immobile domain play a crucial role to better understand the non-Fickian dispersion measured from the tracer test.