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At least 19 records

Slip effects associated with Knudsen transport phenomena in porous media

Porous media used in phase separators and thermomechanical pumps have been the subject of characterization efforts based on the Darcy permeability of laminar continuum flow. The latter is not always observed at low speed, in particular at permeabilities below 10 to the -9th/squared cm. The present experimental and theoretical studies address questions of slip effects associated with long mean free paths of gas flow at room temperature. Data obtained are in good agreement, within data uncertainty, with a simplified asymptotic Knudsen equation proposed for porous plugs on the basis of Knudsen's classical flow equation for long mean free paths.

Frederking, T. H. K.↗

A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

Most porous media, such as geomaterials and biomaterials are highly heterogeneous in nature, and they contain large variations of microscopic pore structures, such as pore sizes, pore distribution, and pore shapes. The oscillation of microscopic structures is a substantial challenge in theoretical characterization and is usually ignored in continuous modeling. However, mechanical behavior of porous media such as deformation and failure, are essentially impacted by the microscopic heterogeneity which needs to be considered in modeling a porous media. Here, this research proposes a numerical modeling framework with a capability to investigate the effect of microscopic heterogeneity on the macroscopic fracture behavior in porous media by using a numerical homogenization technique, combined with the phase-field fracture modeling method. This numerical modeling strategy computes a homogenized elasticity tensor based on microscopic heterogeneous pore structures heterogenous porous domain by solving boundary value problems at microscopic domain. The strain energy and subsequent propagation of macroscopic fractures will be updated using homogenized stiffness information. Using this numerical scheme, the microscopic pore structure’s impact on the fracture behavior through the homogenized elastic tensor will be taken into account. This multiscale technique is benchmarked against classical problems. Finally, the results highlight the importance of the underlying pore structure and reveal that both fracture strength and propagation path can be influenced by the microscopic heterogeneity.

36 MATERIALS SCIENCE↗

Hydrate is a Nonwetting Phase in Porous Media

In porous media containing gas hydrate, the hydrate morphology impacts the flow behavior of the fluid phases. We hypothesize that hydrate emplaces itself as a nonwetting phase and use this idea to describe relative permeability of water in a hydrate/water system. We perform steady-state relative permeability measurements in hydrate-bearing samples with a range of hydrate saturation. We measure and compare water relative permeability in the presence of gas and in the presence of hydrate and find that the water relative permeability is the same in both cases. This suggests that (1) relative permeability for hydrate systems can be obtained without performing difficult experiments on hydrate bearing sediments, (2) flow properties are porous-media dependent, and (3) models that assume a fixed pore or tube geometry are inadequate.

58 GEOSCIENCES↗

Comprehensive study of the interactions between the critical dimensionless numbers associated with multiphase flow in 3D porous media

Multiphase flow in porous media is of signifcant interest in many engineering applications, such as geologic carbon sequestration, enhanced oil recovery, and groundwater contamination and remediation. In order to advance the fundamental understanding of multiphase flow in complex three-dimensional (3D) porous media, the interactions between the critical dimensionless numbers, including the contact angle, viscosity ratio, and capillary (Ca) number, were explored using X-ray micro-computed tomography (micro-CT) scanning and lattice Boltzmann (LB) modeling. In this study, the 3D pore structure information was extracted from micro-CT images and then used as interior boundary conditions of flow modeling in a pore-scale LB simulator to simulate multiphase flow within the pore space. A Berea sandstone sample was scanned and then two-phase flow LB simulations were performed based on the micro-CT images. The LB-simulated water/CO 2 distributions agreed well with the micro-CT scanned images. Simulation findings showed that a decreasing contact angle causes a decrease in wetting-fluid relative permeability and an increase in non-wetting fluid relative permeability. A rising Ca number increases both wetting and non-wetting fluid relative permeabilities. An increasing viscosity ratio (the ratio of non-wetting fluid viscosity to wetting fluid viscosity) facilitates the increase of non-wetting fluid relative permeability and mitigates the reduction of wetting fluid relative permeability, when the contact angle decreases continuously. The primary novel finding of this study is that the viscosity ratio affects the rate of change of the relative permeability curves for both phases when the contact angle changes continuously. To date, we believe it is the first time that comprehensive interactions between these dimensionless numbers are demonstrated in a sandstone sample based on real 3D structures. We also investigated the role of the changes of flow direction and sample location on relative permeability curves. Simulation results showed that the change in non-wetting fluid relative permeability was larger when the flow direction was switched from vertical to horizontal, which indicated that there was stronger anisotropy in larger pore networks that were primarily occupied by the non-wetting fluid.

42 ENGINEERING↗

Solute mixing regulates heterogeneity of mineral precipitation in porous media

Here, synchrotron X-ray microtomography was used to track the spatiotemporal evolution of mineral precipitation and the consequent alteration of the pore structure. Column experiments were conducted by injecting CaCl 2 and NaHCO 3 solutions into granular porous media either as a premixed supersaturated solution (external mixing) or as separate solutions that mixed within the specimen (internal mixing). The two mixing modes produced distinct mineral growth patterns. While internal mixing promoted transverse heterogeneity with precipitation at the mixing zone, external mixing favored relatively homogeneous precipitation along the flow direction. The impact of precipitation on pore water flow and permeability was assessed via 3-D flow simulations, which indicated anisotropic permeability evolution for both mixing modes. Under both mixing modes, precipitation decreased the median pore size and increased the skewness of the pore size distribution. Such similar pore-scale evolution patterns suggest that the clogging of individual pores depends primarily on local supersaturation state and pore geometry.

42 ENGINEERING↗

Enhanced delivery of engineered Fe-Mn binary oxides in heterogeneous porous media for efficient arsenic stabilization

Heterogeneity in sediment and aquifer is universal, resulting in preferential flows of injected materials in the high permeability regions and forming flow by-passed zones in the low permeability regions during in-situ subsurface remediation. This adverse effect can considerably delay the completion of remedial operations and significantly increase the cost. Column experiments were designed and conducted to study the transport of starch- and starch-xanthan gum modified Fe-Mn binary oxide particles (SFM and SXFM) in saturated heterogeneous porous media and to reveal the particles’ arsenic (As) stabilization performance. Fine-in-Coarse (FIC) and Coarse-in-Fine (CIF) patterns of heterogeneous packings were set up in the columns. Testing results demonstrated that starch-xanthan gum dual treatment on Fe-Mn binary oxides successfully improved the particles’ migration capability in heterogeneous porous media and their distribution uniformity attributed to the profound shear thinning behavior of xanthan gum solution. The addition of xanthan gum to the system increased the viscosity and shear thinning property of SXFM suspension, making it a better candidate for delivery. Both SFM and SXFM stabilized As in heterogeneously packed sediment collected from a contaminated site, with SXFM showing better stabilization performance than SFM. The stabilization effects of SXFM were 90.7-97.0%, compared to 82.0-95.2% of SFM.

Yan, Xiulan↗

Chapman–Enskog Analyses on the Gray Lattice Boltzmann Equation Method for Fluid Flow in Porous Media

The gray lattice Boltzmann equation (GLBE) method has recently been used to simulate fluid flow in porous media. It employs a partial bounce-back of populations (through a fractional coefficient θ, which represents the fraction of populations being reflected by the solid phase) in the evolution equation to account for the linear drag of the medium. Several particular GLBE schemes have been proposed in the literature and these schemes are very easy to implement; but there exists uncertainty about the need for redefining the macroscopic velocity as there has been no systematic analysis to recover the Brinkman equation from the various GLBE schemes. Rigorous Chapman–Enskog analyses are carried out to show that the momentum equation recovered from these schemes can satisfy Brinkman equation to second order in ϵ only if θ=O(ϵ) in which ϵ is the ratio of the lattice spacing to the characteristic length of physical dimension. The need for redefining macroscopic velocity is shown to be scheme-dependent. When a body force is encountered such as the gravitational force or that caused by a pressure gradient, different forms of forcing redefinitions are required for each GLBE scheme.

42 ENGINEERING↗

Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

Abstract Multiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

Yang, Hyung Jun↗

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.

02 PETROLEUM↗