Colloidal Transport in Locally Periodic Evolving Porous Media---An Upscaling Exercise

Muntean, Adrian; Nikolopoulos, Christos

doi:10.1137/17m1161531

Cited by 16 publications

(22 citation statements)

References 37 publications

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“…One of the major difficulties associated with its derivation is the fact that log-jamming is a process which intrinsically depends on pore-scale physics. Therefore, a comprehensive model would have to be derived from the analysis of the conservation equations at the pore-scale, and then upscaled in order to obtain the reaction rate as a function coupled to the pore-scale physics [17,18,19]. To derive a rigorous upscaled model for two-phase flow, including the transport of particles, is outside the scope of this work.…”

Section: Log-jamming and Particle Releasementioning

confidence: 99%

Transport of Polymer Particles in Oil–Water Flow in Porous Media: Enhancing Oil Recovery

et al. 2018

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We study a heuristic, core-scale model for the transport of polymer particles in a two phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when polymers are injected after the initial waterflood. The recovery mechanism is believed to be microscopic diversion of the flow, where injected particles can accumulate in narrow pore throats and clog it, in a process known as a log-jamming effect. The blockage of the narrow pore channels lead to a microscopic diversion of the water flow, causing a redistribution of the local pressure, which again can lead to the mobilization of trapped oil, enhancing its recovery. Our objective herein is to develop a core-scale model that is consistent with the observed production profiles. We show that previously obtained experimental results can be qualitatively explained by a simple two-phase flow model with an additional transport equation

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Section: Log-jamming and Particle Releasementioning

confidence: 99%

Transport of Polymer Particles in Oil–Water Flow in Porous Media: Enhancing Oil Recovery

et al. 2018

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“…|Ω| denotes the porosity density of the medium. For more details regarding the cell problem and the effective diffusivity, we refer to [21] where they are established via homogenization.…”

Section: Problem Statement and Solution Strategymentioning

confidence: 99%

“…While equation ( 1) is purely macroscopic, the computation of the effective permeability D i (u i ) is done on the micro-scale therefore leading to the two-scale nature of our problem. This system is a compact and abstract reformulation of a two-scale model for colloidal transport derived in [21] via asymptotic homogenization (more details are given in Section 2). Structurally similar (two-scale model with geometrical changes) models were investigated in, e.g., [11,25].…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario

Edén¹,

Nikolopoulos²,

Muntean³

2021

Preprint

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We study the weak solvability of a quasilinear reaction-diffusion system nonlinearly coupled with an linear elliptic system posed in a domain with distributed microscopic balls in 2D. The size of these balls are governed by an ODE with direct feedback on the overall problem. The system describes the diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of the problem relies on a suitable application of Schauder's fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.

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“…In similar situations, the effective diffusion coefficient degenerates. We refer the reader to [25] for a setting that accounts for local clogging of the pores. Instead, we will see that localization/trapping of concentration is in principle possible, as our simulations indicate.…”

Section: Background Motivationmentioning

confidence: 99%

Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure

et al. 2020

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We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift. Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving the upscaled model equations as well as the effective transport coefficients for suitable scalings in terms of both the inherent thickness at the strip and the typical length scales of the microscopic heterogeneities. Aiming at computable scenarios, we consider that the heterogeneity of the strip is made of an array of periodically arranged impenetrable solid rectangles and identify two scaling regimes what concerns the small asymptotics parameter for the upscaling procedure: the characteristic size of the microstructure is either significantly smaller than the thickness of the thin obstacle or it is of the same order of magnitude. We scale up the diffusion–polynomial drift model and list computable formulas for the effective diffusion and drift tensorial coefficients for both scaling regimes. Our upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We illustrate numerically the concentration profile of the chemical species passing through the upscaled strip in the finite thickness regime and point out that trapping of concentration inside the strip is likely to occur in at least two conceptually different transport situations: (i) full diffusion/dispersion matrix and nonlinear horizontal drift, and (ii) diagonal diffusion matrix and oblique nonlinear drift.

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Colloidal Transport in Locally Periodic Evolving Porous Media---An Upscaling Exercise

Cited by 16 publications

References 37 publications

Transport of Polymer Particles in Oil–Water Flow in Porous Media: Enhancing Oil Recovery

Transport of Polymer Particles in Oil–Water Flow in Porous Media: Enhancing Oil Recovery

A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario

Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure

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