1887

Abstract

Summary

One of the main difficulties when simulating nanoparticle transport in porous media is the lack of accurate field-scale parameters to properly estimate particle retention across large distances. Furthermore, current field models are, in general, not based on mathematically rigorous upscaling techniques, and empirical models are being fed by experimental data. This study proposes a rigorous and practical way to connect pore-scale phenomena with Darcy-scale models, providing accurate macro-scales results. In order to carefully resolve nanoparticle transport at the pore-scale, we develop numerical solver based on the open-source C++ library OpenFOAM, able to account for shear-induced detachment of nanoparticles from the walls in addition to usual isotherm attachment/detachment processes. We employ an integrated approach to generate random, user-oriented, and periodic porous structures with tunable porosity and connectivity. A periodic face-centered cubic geometry is employed for simulations over a broad range of Péclet and Damköhler numbers, and effective parameters valid at the macro-scale are obtained by mean of volume averaging in periodic cells, as well as breakthrough approximates to asymptotic behaviour. Coupling between these techniques leads to a comprehensive estimation of a first-order kinetic rate for nanoparticle retention and the maximum retention capacity based on breakthrough curves and asymptotic curves. We apply this upscaling process to real cases found in literature, to estimate the penetration radius of a typical stimulation operation settling. The profiles are compared against different spatial discretization in the radial direction and different dimensionless numbers to study their impact upon travel distances. The present workflow gives a new insight into some aspects of pore-scale boundary conditions that usually are hedged, such as the validity of some usual mathematical expressions or the correctness of pore-scale results representing larger scales. Finally, this study proposes a mathematical relationship between pore-scale parameters and some important macro-scale dimensionless numbers that can be used to estimate field-scale effective parameters for nanoparticle retention in well stimulation and Oil&Gas industry applications.

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/content/papers/10.3997/2214-4609.202035019
2020-09-14
2021-09-27
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