Abstract
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.
Highlights
The memory function computed from X-ray microtomography (XMT) images at three-dimensions provides a more accurate definition rather than the two-dimensional, as the simulations results, shows a longer residence time of particles in the immobile domain
We determine the memory function to characterize the diffusion in the matrix
The XMT technique appears to be a promising tool to capture the properties of the immobile domain at 3D and compute the memory function using the time domain random walk
Summary
Transport properties in porous media are probably the most important parameters in many geophysical and engineering situations, including pollutant migra-. Reference (Haggerty et al, 2000; Haggerty et al, 2001; Haggerty et al, 2004) reported a study on the transport in the rock matrix using the multiple rates of mass transfers for any complex structures (Gouze et al, 2008) reported a study to solve the transport using a 2-D microscale description of the matrix structure, precisely by computing the memory function in Mallorc limestones sample using the classical random walk particle tracking method (Salamon et al, 2006; Delay et al, 2005) These authors were inspired by the non-Fickian dispersion observed on tracer test BTCs. The idea is to link this observation from field scale, to microscale diffusion process within water immobile zones. We compare the computed memory function with those deduced from the field-scale tracer tests
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