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A Mathematical Model for Nanoparticles Transport within Two-phase Flow in Heterogeneous Porous media

Abstract : Transport of nanoparticles in porous media is a growing concern among scientific research and technological development, such as in the preservation of groundwater quality, pollution control and remediation, and enhancement of oil recovery. Indeed, recent advances in the later field suggested significant improvements in the recovered volumes by injecting hydrophobic nanoparticles which enhance or reverse the initial reservoir wettability favoring an increase in the relative permeability of the oil phase and the capillary pressure gap between phase pressures. A new mathematical model, based on previous work by Sbai and Azaroual [Adv. Water Resour. 34(1), 62-68, 2011] is developed which couples the incompressible two-phase fluid flow reservoir equations at the macroscopic level to equations of nanoparticles transport at a smaller, but still macroscopic, secondary scale. The latter accounts for pore scale processes of colloidal and hydrodynamic release from pore surfaces, deposition in pore surfaces and possibly clogging the pore throats. The mechanism of particles interphase transfer is accounted for based on the wettability of nanoparticles surfaces. Nanoparticles are divided among several classes based on their size and wettability properties. Each class is assumed to have a constant colloidal and hydrodynamic detachment rates taken as first-order kinetics, a constant surface deposition rate in pore walls of the same wettability according to filtration theory, and a constant mass capture rate at pore throats by blocking and bridging. For each nanoparticle class a mass convection-diffusion equation with a total rate of all related mechanisms is solved numerically with a finite volume method. Change of absolute permeability is correlated to porosity change resulting from mass distributions of flowing, surface, and pore-throat deposited nanoparticles. Relative permeability and capillary pressure functions are optionally allowed to be time- dependent as a function of the mass fraction of deposited nanoparticles of the same wettability. Many multi-dimensional applications of the presented model are given for performance evaluation. The newly developed model has many applications and opens interesting perspectives for environmental remediation, well injectivity design, re-engineered fluids injection, and CO2 sequestration in deep geological formations. Finally, a nested multiscale finite element method is applied to this problem where three hierarchical scales are considered for the resolution of the global pressure, fluid saturation, and nanoparticles transport equations. An important speedup is achieved by this procedure allowing for realistic engineering grade applications to be tackled efficiently.
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Soumis le : mercredi 23 novembre 2011 - 11:27:25
Dernière modification le : mardi 2 août 2022 - 16:15:15
Archivage à long terme le : : vendredi 24 février 2012 - 02:22:43


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  • HAL Id : hal-00643908, version 1



Mohammed Adil Sbai, Mohamed Azaroual. A Mathematical Model for Nanoparticles Transport within Two-phase Flow in Heterogeneous Porous media. Flows and mechanics in natural porous media from pore to field scale. Pore2Field, Nov 2011, Paris, France. ⟨hal-00643908⟩



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