A transport phase diagram for pore-level correlated porous media

Water Resources Research

Karadimitriou

et al. 2019

Self Cite

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...

Section: Resultsmentioning

confidence: 87%

Section: Methodsologymentioning

confidence: 99%

Saturation Dependence of Non‐Fickian Transport in Porous Media

Hasan

Water Resources Research

Karadimitriou

et al. 2019

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“…To estimate the stagnant saturation at a given saturation topology, we above which the advective transport starts to be pronounced [3]. Thus, we 318 chose 0.1 as the threshold to differentiate the flowing and stagnant regions.…”

mentioning

confidence: 99%

Pore-scale insights into transport and mixing in steady-state two-phase flow in porous media

Aziz

International Journal of Multiphase Flow

Martínez-Ferrer

2018

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Hydrodynamic dispersion and mixing under two-phase flow can be found in many natural, industrial, and engineering processes such as the modified salinity water flooding (MSWF). In MSWF the injected water displaces the formation brine and will interact with the crude oil and rock to improve the oil recovery. We show throughout numerical simulations that access of the injection water to the available pore space is not homogeneous, even in homogeneous porous media, and it is controlled by the saturation topology and pore-scale velocity field.Under the steady-state two-phase flow in a homogeneous porous medium, the velocity field has a bimodal distribution. The bimodal distribution of pore-scale velocity dictates two different transport time scales spatially distributed over the stagnant and flowing regions at a given saturation topology. These distinctly different transport time scales lead to a non-Fickian transport, which cannot be captured using the conventional advection-dispersion equation.Using the volume-of-fluid method implemented in the OpenFOAM (ver. 4.0), we simulated pore-scale two-phase flow and the hydrodynamic transport at different saturations. We have investigated the impact of stagnant saturation and the tortuosity of flow pathways on the dispersion coefficient and the mass exchange rate -as the two major parameters controlling transport and mixing -under steady-state two-phase flow. At the Darcy scale, different theories such as the mobile-immobile (MIM) theory have been proposed to capture the non-Fickian transport and mixing in two-phase flow through porous media. Based on the simulation results, we assess the validity of the assumptions employed in MIM to define the stagnant saturation and mass exchange rate coefficient. The results of this research provide fresh insights into the potential impact of saturation topology on mixing between the modified salinity water and the formation brine under steady-state flow conditions, which has not been investigated and reported in the literature.Hydrodynamic dispersion and mixing in two-phase flow through porous 2 media are found in many natural, industrial, and engineering processes such 3 as contaminant transport in the vadose zone where the infiltrated water car-4 ries the contaminants and mixes with the resident water, while air has filled 5 some part of the pore space [37,4,23]. Another example is the modified-6 (or low-) salinity water flooding (MSWF) as one of the enhanced oil recovery 7 techniques, in which injection water with a tuned chemical composition is 8 injected into the reservoir filled originally with the formation brine and the 9 crude oil [31, 1,29,42]. The performance of MSWF depends on many pore-10 scale physio-chemical factors such as crude oil chemistry, formation brine and 11 injection water chemistry, temperature, and rock mineralogy, which have 12 been extensively studied [33, 2,25]. However, the larger-scale mechanical 13 factors such as transport and mixing of the modified-salinity water have not 14 been extensively studied. ...

“…Several comprehensive studies have emphasized the importance of accounting for the effects of spatial correlations of macroscopic‐level parameters such as permeability or hydraulic conductivity, flow channeling, and connectivity on transport coefficients and solute transport (e.g., Dentz et al, ; Knudby & Carrera, ; Knudby & Carrera, ; Renard & Allard, ; Vogel, ). However, to our best knowledge, only a limited number of studies have been specifically dedicated to understand the effect of pore‐level spatial correlation on macroscopic transport properties (see, e.g., Babaei & Joekar‐Niasar, ; Bernabé & Bruderer, ; Bruderer & Bernabé, ; Bruderer‐Weng et al, ; le Borgne et al, ; Liu & Mostaghimi, ; Makse et al, ). More recently, Babaei and Joekar‐Niasar () and Liu and Mostaghimi () incorporated pore‐scale correlated heterogeneity into pore network models and studied their impacts on macroscopic diffusivity and reaction rates, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…However, to our best knowledge, only a limited number of studies have been specifically dedicated to understand the effect of pore‐level spatial correlation on macroscopic transport properties (see, e.g., Babaei & Joekar‐Niasar, ; Bernabé & Bruderer, ; Bruderer & Bernabé, ; Bruderer‐Weng et al, ; le Borgne et al, ; Liu & Mostaghimi, ; Makse et al, ). More recently, Babaei and Joekar‐Niasar () and Liu and Mostaghimi () incorporated pore‐scale correlated heterogeneity into pore network models and studied their impacts on macroscopic diffusivity and reaction rates, respectively.…”

Section: Introductionmentioning

confidence: 99%

Effects of Pore‐Scale Heterogeneity on Macroscopic NAPL Dissolution Efficiency: A Two‐Scale Numerical Simulation Study

Aminnaji

Rabbani

Water Resources Research

et al. 2019

Self Cite

Interphase mass transfer or dissolution coefficient of nonaqueous phase liquids (NAPL) is an important parameter in predicting the transport of contaminant species in porous media. While the literature offers valuable insights into the dependence of this coefficient on different parameters at the continuum scale (e.g., contaminant saturation and Darcy velocity), effects of pore‐scale heterogeneity on macroscopic dissolution coefficient have received little attention. In this work a three‐dimensional pore‐scale model is developed to simulate interphase mass transfer over different synthetic pore network structures with various pore radii correlation lengths. The pore network modeling simulates dissolution of immobile NAPL into water (single phase) through diffusive throats for the water‐NAPL interface. The impacts of pore network spatially correlated heterogeneities, NAPL saturation/distribution, and aqueous phase velocity on NAPL mass transfer coefficient and water‐NAPL interfacial surface area are studied. These macroscopic properties are then employed in two‐dimensional continuum‐scale domains formed by concatenating 20 by 20 pore networks in x and y directions. The results highlight the impact of pore‐scale heterogeneity on the distribution of NAPL and subsequently on the dissolution rate (i.e., dissolution coefficient). An uncorrelated distribution of pore radii consistently leads to higher NAPL dissolution coefficient than spatially correlated heterogeneity. The results of continuum modeling show that NAPL dissolution rates are only different between domains formed by correlated and uncorrelated pore networks at very high flow rates and Darcy velocities. However, for typical values of Darcy velocity in groundwater systems, variation in mass transfer coefficient due to pore‐scale heterogeneity is minimal for efficient mass removal.