Continuous-time random-walk model of transport in variably saturated heterogeneous porous media

Zoia, Andrea; Néel, Marie-Christine; Cortis, A.

doi:10.1103/physreve.81.031104

Cited by 29 publications

(24 citation statements)

References 54 publications

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“…Remarkably, none of the widely used approaches, such as dead‐end pore model (Coats & Smith, ), the mobile‐immobile (MIM) model (van Genuchten & Wierenga, ), and the multirate mass transfer model (MRMT; Haggerty & Gorelick, ), incorporates the multiphase fluid flow in the model, at least in a physically consistent manner. Continuous‐time random walk (CTRW) models (Dentz & Berkowitz, ) have been used to simulate coupled steady state unsaturated flow (the Richards equation) and transport (Cortis & Berkowitz, ; Zoia et al, ). The relation between the probability distributions for waiting‐time and displacement of the random walker for the mobile and immobile phases is defined as time‐dependent exponential or power‐law decay functions.…”

Section: Introductionmentioning

confidence: 99%

Saturation Dependence of Non‐Fickian Transport in Porous Media

Hasan

Niasar

Karadimitriou

et al. 2019

Water Resources Research

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In two-phase flow through porous media, the percolating pathways can be hydrodynamically split into the flowing and stagnant regions. The highly variable velocity field in the pore space filled by the carrier fluid leads to significant differences in the transport time scales in the two regions that cannot be explained by the Fickian (Gaussian) advection-dispersion equation. In contrast with the Darcy-scale studies, up to now, relatively limited pore-scale studies have been devoted to the characterization of transport properties in two-phase flow. In this paper, we report on the results of computer simulation of advection-dispersion transport in steady state two-phase flow through porous media using a pore network model, employed as an upscaling tool. The simulation results are upscaled to directly estimate the Darcy-scale transport coefficients and properties, namely, stagnant saturation, the mass transfer coefficient between the flowing and stagnant regions, and the longitudinal dispersion in the flowing regions. The mobile-immobile model, one of the most commonly used models for simulating non-Fickian transport in porous media, is used to estimate the transport properties using the inverse modeling of effluent concentration profiles. The disagreement between the directly estimated parameters and those obtained by the mobile-immobile-based inverse modeling implies fundamental shortcomings of the latter for describing transport in two-phase flow. The simulation results indicate that the relative permeabilities may be used to obtain accurate estimates of the stagnant saturation, which link two-phase Darcy's law and transport.Plain Language Summary Solute transport in two-phase flow through porous media is an important topic for many industrial and natural processes such as nutrient transport in partially saturated soils in agriculture, transport of chemicals in oil reservoirs for enhanced oil recovery, or in soil remediation. Modeling multiphase flow and transport in different applications is essential to improve the design and operational condition. Hence, the predictive capabilities of such models need to be improved. To evaluate the assumptions embedded in one of the most commonly used theories, referred to as the mobile-immobile theory, we have performed pore-scale simulations of these physical processes. By upscaling the simulation results, we directly estimated the transport properties and compared them with the inverse modeling results using the mobile-immobile theory. There is a significant discrepancy between the directly and indirectly estimated results that imply the potential shortcomings in the mobile-immobile theory. Moreover, it has been discussed that potentially the two-phase relative permeability data can be used as a proxy to estimate the stagnant (immobile) saturation that will link two-phase Darcy theory with the transport models. Key Points:• The steady state simulation resultsshow that the stagnant saturation strongly depends on the fluids topology rather than Peclet number • The preliminar...

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Section: Introductionmentioning

confidence: 99%

Saturation Dependence of Non‐Fickian Transport in Porous Media

Hasan

Niasar

Karadimitriou

et al. 2019

Water Resources Research

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“…Nevertheless, during the last two decades, fractional calculus has attracted the attention of many researchers and it has been successfully applied in various areas like computational biology [21] or economy [9]. In particular, the first and well-established application of fractional operators was in the physical context of anomalous diffusion, see [34,35] for example. Let us mention [23] proving that fractional equations is a complementary tool in the description of anomalous transport processes.…”

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confidence: 99%

Existence of a weak solution for fractional Euler–Lagrange equations

Bourdin

2013

Journal of Mathematical Analysis and Applications

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“…Since φ(0, ·) = Id R d and Q is solution of (EL α h ), taking s = 0 in (27) leads to (26). From this last result, we conclude that the discrete fractional Euler-Lagrange equation (EL α h ) allows to preserve the fractional Noether's Theorem 2 at the discrete level.…”

Section: 2mentioning

confidence: 75%

“…Fractional calculus is the emerging mathematical field dealing with the generalization of the derivative to any real order. During the last two decades, it has been successfully applied to problems in economics [9], computational biology [20] and several fields in Physics [5,6,16,26]. We refer to [17,23,25] for a general theory and to [19] for more details concerning the recent history of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%