饱和度对波在土层交界面的反射、透射系数的影响

把均匀流体概念引入Biot两相多孔介质动力理论中，用Biot的两相多孔介质模型模拟不完全饱和土层，给出SV波，P波从不完全饱和土层入射到弹性土层时，在土层交界面上反射，透射系数的表达式，结果表明与完全饱和相比，饱和度发生很小的变化就会对交界面上反射，透射系数产生很大的影响。今后应该重视饱和度变化对地震动力响应的影响。     

Simulation of less‐mobile porosity dynamics in contrasting sediment water interface porous media

Considering heterogeneity in porous media pore size and connectivity is essential to predicting reactive solute transport across interfaces. However, exchange with less‐mobile porosity is rarely considered in surface water/groundwater recharge studies. Previous research indicates that a combination of pore‐fluid sampling and geoelectrical measurements can be used to quantify less‐mobile porosity exchange dynamics using the time‐varying relation between fluid and bulk electrical conductivity. For this study, we use macro‐scale (10 s of cm) advection–dispersion solute transport models linked with electrical conduction in COMSOL Multiphysics to explore less‐mobile porosity dynamics in two different types of observed sediment water interface porous media. Modeled sediment textures contrast from strongly layered streambed deposits to poorly sorted lakebed sands and cobbles. During simulated ionic tracer perturbations, a lag between fluid and bulk electrical conductivity, and the resultant hysteresis, is observed for all simulations indicating differential loading of pore spaces with tracer. Less‐mobile exchange parameters are determined graphically from these tracer time series data without the need for inverse numerical model simulation. In both sediment types, effective less‐mobile porosity exchange parameters are variable in response to changes in flow direction and fluid flux. These observed flow‐dependent effects directly impact local less‐mobile residence times and associated contact time for biogeochemical reaction. The simulations indicate that for the sediment textures explored here, less‐mobile porosity exchange is dominated by variable rates of advection through the domain, rather than diffusion of solute, for typical low‐to‐moderate rate (approximately 3–40 cm/day) hyporheic fluid fluxes. Overall, our model‐based results show that less‐mobile porosity may be expected in a range of natural hyporheic sediments and that changes in flowpath orientation and magnitude will impact less‐mobile exchange parameters. These temporal dynamics can be assessed with the geoelectrical experimental tracer method applied at laboratory and field scales.     

The Dual-Domain Porosity Apparatus: Characterizing Dual Porosity at the Sediment/Water Interface

The characterization of pore-space connectivity in porous media at the sediment/water interface is critical in understanding contaminant transport and reactive biogeochemical processes in zones of groundwater and surface-water exchange. Previous in situ studies of dual-domain (i.e., mobile/less-mobile porosity) systems have been limited to solute tracer injections at scales of meters to hundreds of meters and subsequent numerical model parameterization using fluid concentration histories. Pairing fine-scale (e.g., sub-meter) geoelectrical measurements with fluid tracer data over time alleviates dependence on flowpath-scale experiments, enabling spatially targeted characterization of shallow sediment/water interface media where biogeochemical reactivity is often high. The Dual-Domain Porosity Apparatus is a field-tested device capable of variable rate-controlled downward flow experiments. The Dual-Domain Porosity Apparatus facilitates inference of dual-domain parameters, i.e., mobile/less-mobile exchange rate coefficient and the ratio of less mobile to mobile porosity. The Dual-Domain Porosity Apparatus experimental procedure uses water electrical conductivity as a conservative tracer of differential loading and flushing of pore spaces within the region of measurement. Variable injection rates permit the direct quantification of the flow-dependence of dual-domain parameters, which has been theorized for decades but remains challenging to assess using existing experimental methodologies.     

介观尺度孔隙流体流动作用对纵波传播特征的影响研究——以周期性层状孔隙介质为例

介观尺度孔隙流体流动是地震频段岩石表现出较强速度频散与衰减的主要作用.利用周期性层状孔隙介质模型,基于准静态孔弹性理论给出了模型中孔隙压力、孔隙流体相对运动速度以及固体骨架位移等物理量的数学解析表达式,同时利用Biot理论将其扩展至全频段条件下,克服了传统White模型中介质分界面处流体压力不连续的假设. 在此基础上对准静态与全频段下模型介质中孔隙压力、孔隙流体相对运动速度变化形式及其对弹性波传播特征的影响进行了讨论,为更有效理解介观尺度下流体流动耗散和频散机制提供物理依据.研究结果表明,低频条件下快纵波孔压在介质层内近于定值,慢纵波通过流体扩散改变总孔隙压力, 随频率的增加慢波所形成的流体扩散作用逐渐减弱致使介质中总孔压逐渐接近于快纵波孔压,在较高频率下孔压与应力的二次耦合作用使总孔压超过快纵波孔压.介质中孔隙流体相对运动速度与慢纵波形成的流体相对运动速度变化形式一致;随频率的增加孔隙流体逐渐从排水的弛豫状态过渡到非弛豫状态,其纵波速度-含水饱和度变化形式也从符合孔隙流体均匀分布模式过渡到斑块分布模式,同时介质在不同含水饱和度下的衰减峰值与慢纵波所形成的孔隙流体相对流动速度具有明显的相关性.     

Dependence of borehole shear‐horizontal‐wave seismoelectric response on soil textures

The phenomenon of acoustic waves inducing electric fields in porous media is called the seismoelectric effect. Earlier investigators proposed the usage of seismoelectric effect for well logging. Soil texture has a strong influence on the coupled wave fields during shallow surface explorations. In this article, we study the borehole pure shear‐horizontal wave and the coupling transverse‐electric field (acoustic–electrical coupling wave fields) in the partially saturated soil. Combined with related theories, we expand the formation parameters to partially saturated forms and discuss the influence of soil texture conditions on the seismoelectric wave fields. The results show that the elastic and electrical properties of porous media are sensitive to water saturation. The compositions of the acoustic and electric fields for different soil textures do not change, but the waveforms differ. We also use the secant integral method to simulate the interface‐converted electromagnetic waves. The results show that interface response strength is greatly influenced by soil texture. In addition, considering the sensitivity of the inducing electric field to fluid salinity, we also simulate the time‐domain waveforms of electric field for different pore fluid salinity levels. The results show that as the salinity increases, the electric field amplitude decreases monotonically. The above conclusions have certain significance for the application of borehole shear wave and its coupled electric fields for resource exploration, saturation assessment and groundwater pollution monitoring.     

含黏性流体孔隙介质分界面上反透射系数特征研究

地下岩石由岩石骨架和孔隙流体组成,通常流体含黏性.地震波在地下介质中传播时受岩石骨架和黏性流体的影响会呈现出复杂的变化.本文将流、固体位移和应力连续作为边界条件,推导出含黏性流体孔隙介质分界面上反透射系数方程;通过建立上层为饱油、下层为饱盐水的砂岩孔隙介质模型,开展反透射系数特征研究,分别分析不同频率、不同黏滞系数条件下,含黏性流体孔隙介质分界面上反透射系数随入射角的变化.研究表明,孔隙介质分界面上和等效介质分界面上的反透射系数分别随入射角的变化趋势基本一致,说明方程推导和数值计算的正确性;快纵波反透射系数受频率、流体黏性的影响较小,而快横波反透射系数在一定入射角范围内受频率、流体黏性的影响比较大;由于黏性孔隙流体的作用,慢纵波和慢横波的反透射系数受入射角、频率及流体黏性的影响都很大.     

On the shape of the non-steady interface intersecting discontinuities in permeability

The simplifying assumption is often made, that when two fluids (whether miscible or immiscible) occupy the void space of a porous medium, they are separated by a sharp interface. Examples are the phreatic surface (between air and water) and the interface between fresh and salt water in a coastal aquifer. The orientation of such a sharp interface as it crosses a surface of discontinuity between media of different permeabilities, and as it intersects an impervious boundary, is shown to depend not only on the fluid and porous media properties, but also on the direction and rate of motion of the interface. Thus, advancing and retreating interfaces intersect boundaries of discontinuity in permeability at different angles.     

A transport phase diagram for pore-level correlated porous media

Transport in porous media is often characterized by the advection–dispersion equation, with the dispersion coefficient as the most important parameter that links the hydrodynamics to the transport processes. Morphological properties of any porous medium, such as pore size distribution, network topology, and correlation length control transport. In this study we explore the impact of correlation length on transport regime using pore-network modelling. Earlier direct simulation studies of dispersion in carbonate and sandstone rocks showed larger dispersion compared to granular homogenous sandpacks. However, in these studies, isolation of the impact of correlation length on transport regime was not possible due to the fundamentally different pore morphologies and pore-size distributions. Against this limitation, we simulate advection–dispersion transport for a wide range of Péclet numbers in unstructured irregular networks with “different” correlation lengths but “identical” pore size distributions and pore morphologies. Our simulation results show an increase in the magnitudes of the estimated dispersion coefficients in correlated networks compared to uncorrelated ones in the advection-controlled regime. The range of the Péclet numbers which dictate mixed advection–diffusion regime considerably reduces in the correlated networks. The findings emphasize the critical role of correlation length which is depicted in a conceptual transport phase diagram and the importance of accounting for the micro-scale correlation lengths into predictive stochastic pore-scale modelling.     

A fractal model for streaming potential coefficient in porous media

Streaming potential is the result of coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz–Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge, the fractal geometry theory is not yet applied to analyse the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid?liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension, and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz–Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz–Smoluchowski equation, particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analysed.     

Pressure and shear stress caused by raindrop impact at the soil surface: Scaling laws depending on the water depth

Raindrop impact is an important process in soil erosion. Through its pressure and shear stress, raindrop impact causes a significant detachment of the soil material, making this material available for transport by sheet flow. Thanks to the accurate Navier–Stokes equations solver Gerris, we simulate the impact of a single raindrop of diameter D, at terminal velocity, on water layers of different thickness h: , , D, 2D, in order to study pressures and shear stresses involved in raindrop erosion. These complex numerical simulations help in understanding precisely the dynamics of the raindrop impact, quantifying in particular the pressure and the shear stress fields. A detailed analysis of these fields is performed and self‐similar structures are identified for the pressure and the shear stress on the soil surface. The evolution of these self‐similar structures are investigated as the aspect ratio h/D varies. We find that the pressure and the shear stress have a specific dependence on the ratio between the drop diameter and the water layer thickness, and that the scaling laws recently proposed in fluid mechanics are also applicable to raindrops, paving the road to obtain effective models of soil erosion by raindrops. In particular, we obtain a scaling law formula for the dependence of the maximum shear stress on the soil on the water depth, a quantity that is crucial for quantifying erosion materials. Copyright © 2016 John Wiley & Sons, Ltd.     

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

 A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against the plume scale.     

Stochastic modeling of the permeability of randomly generated porous media

Permeability of porous media in subsurface environments is subject to potentially large uncertainties due to the heterogeneity of natural systems. In this study, a first-order reliability method (FORM) is combined with a lattice Boltzmann method (LBM) to estimate the permeability of randomly generated porous media. The proposed procedure provides an increased ease of addressing complex pore structures by employing LBM to model fluid flow, while inheriting the computational efficiency from FORM. Macroscale-equivalent permeability can thus be estimated with significantly reduced computational efforts, while maintaining a connection to the complex microscale fluid dynamics within a pore structure environment. Implemented on several randomly generated porous media domains, the proposed method provides 13–120 times the efficiency compared to Monte Carlo methods.     

Estimation of water saturation dependence of dispersion in unsaturated porous media: experiments and modelling analysis

In the dispersion theory, a linear relationship has been verified between the coefficient of hydrodynamic dispersion and water velocity, both in saturated and in unsaturated porous media. But for unsaturated soils the variability of flow directions and microscopic velocities can be larger than in saturated soils because of the lower degree of water saturation. This leads to an increased dispersion. Therefore, relationships between water content and relative water velocity fluctuations and water content together with the coefficient of dispersivity in unsaturated porous media respectively have been investigated systematically by displacement experiments in glass beads and coarse-textured sandy soil columns. The breakthrough curves (BTCs) of chloride showed that an increase of solute mixing with a decrease of water content was caused by an increase of flow velocity fluctuations for different pathways. In order to explain the observed tailing effect in unsaturated flow, two mathematical models were used to fit theoretically derived nonlinear functions of water content dependent dispersivities for both porous media. The close agreement between the observed and computed results suggests that the theoretical model of hydrodynamic dispersion can be extended to transport in unsaturated porous media, providing that BTCs of the effluent water are used to estimate representative dispersivity parameters of soils.     

Direct numerical simulation of pore-scale flow in a bead pack: Comparison with magnetic resonance imaging observations

A significant body of current research is aimed at developing methods for numerical simulation of flow and transport in porous media that explicitly resolve complex pore and solid geometries, and at utilizing such models to study the relationships between fundamental pore-scale processes and macroscopic manifestations at larger (i.e., Darcy) scales. A number of different numerical methods for pore-scale simulation have been developed, and have been extensively tested and validated for simplified geometries. However, validation of pore-scale simulations of fluid velocity for complex, three-dimensional (3D) pore geometries that are representative of natural porous media is challenging due to our limited ability to measure pore-scale velocity in such systems. Recent advances in magnetic resonance imaging (MRI) offer the opportunity to measure not only the pore geometry, but also local fluid velocities under steady-state flow conditions in 3D and with high spatial resolution. In this paper, we present a 3D velocity field measured at sub-pore resolution (tens of micrometers) over a centimeter-scale 3D domain using MRI methods. We have utilized the measured pore geometry to perform 3D simulations of Navier–Stokes flow over the same domain using direct numerical simulation techniques. We present a comparison of the numerical simulation results with the measured velocity field. It is shown that the numerical results match the observed velocity patterns well overall except for a variance and small systematic scaling which can be attributed to the known experimental uncertainty in the MRI measurements. The comparisons presented here provide strong validation of the pore-scale simulation methods and new insights for interpretation of uncertainty in MRI measurements of pore-scale velocity. This study also provides a potential benchmark for future comparison of other pore-scale simulation methods. © 2012 Elsevier Science. All rights reserved.     

Stochastic analysis of immiscible displacement in porous media

The interface of two immiscible fluids flowing in porous media may behave in an unstable fashion. This instability is governed by the pore distribution, differential viscosity and interface tension between the two immiscible fluids. This study investigates the factors that control the interface instability at the wetting front. The development of the flow equation is based on the mass balance principle, with boundary conditions such as the velocity continuity and capillary pressure balance at the interface. By assuming that the two-phase fluids in porous media are saturated, a covariance function of the wetting front position is derived by stochastic theory. According to those results, the unstable interface between two immiscible fluids is governed by the fluid velocity and properties such as viscosity and density. The fluid properties that affect the interface instability are expressed as dimensionless parameters, mobility ratio, capillary number and Bond number. If the fluid flow is driven by gravitational force, whether the interface undergoes upward displacement or downward displacement, the variance of the unstable interface decreases with an increasing mobility ratio, increases with increasing capillary number, and decreases with increasing Bond number. For a circumstance in which fluid flow is horizontal, our results demonstrate that the capillary number does not influence the generation of the unstable interface.     

Laboratory Study of Air Sparging: Air Flow Visualization

Laboratory flow visualization experiments, using glass beads as the porous medium, were conducted to study air sparging, an innovative technology for subsurface contaminant remediation. The purpose of these experiments was to observe how air flows through saturated porous media and to obtain a basic understanding of air plume formation and medium heterogeneity effects. The experiments indicate that air flow occurring in discrete, stable channels is the most probable flow behavior in medium to fine grained water saturated porous media and that medium heterogeneity plays an important role in the development of air channels. Several simulated scales of heterogeneities, from pore to field, have been studied. The results suggest that air channel formation is sensitive to the various scales of heterogeneities. Site-specific hydrogeologic settings have to be carefully reviewed before air sparging is applied to remediate sites contaminated by volatile organic compounds.     

含两项不混合/单项黏性流体孔隙介质分界面上反透射系数特征研究

弹性孔隙介质分界面上的反透射系数特征,在岩性划分、流体识别、储层边界判识等方面有重要的应用.本文研究上层为含两项不混合黏性流体孔隙介质、下层为含单项黏性流体孔隙介质分界面上的反透射理论.首先根据两种孔隙介质分界面上的能量守恒得到边界条件,再将波函数、位移、应力与应变关系代入边界条件,推导出完全连通孔隙情况下,第一类纵波入射到孔隙介质分界面上的反透射系数方程.通过建立砂岩孔隙介质模型,分别分析不同孔隙流体类型、不同含油饱和度及不同入射角情况下,各类波的反透射系数特征.研究表明,第二、三类纵波反透射系数数值比第一类纵波小多个数量级,且两者对入射角的变化不敏感,但对孔隙流体性质、含油饱和度的变化较敏感,而横波反透射系数特征恰好与此相反;第一类纵波反透射系数特征比较复杂,入射角、孔隙流体的性质及含油饱和度的变化都对其产生影响.不同孔隙流体弹性物性的差异、孔隙介质中含油饱和度的变化及不同入射角引起垂向和切向应力分量的变化都会影响各类波的反透射系数特征,分析这些特征可以为研究储层含油气性提供理论基础.     

Extended Roof snap-off for a continuous nonwetting fluid and an example case for supercritical CO2

A dominant mechanism for residual trapping of a nonwetting fluid in porous media during imbibition is snap-off or the disconnection of a continuous stream of the nonwetting fluid when it passes through pore constrictions and when a criterion based on capillary pressure imbalance is met. While quasi-static criteria for Roof snap-off have been defined for pores based on the imbalance between capillary pressure across the front/tail meniscus and local capillary pressure at the pore throat, and expressed in terms of pore body to pore throat ratio for simplification, we extended the previous quasi-static snap-off criterion by considering the local capillary pressure imbalance between the pore body and the pore throat for both circular and noncircular pores when the wetting film exists. We then used the criterion to analyze results from computational fluid dynamics (CFD) simulations of multi-phase flow with supercritical CO₂ as the nonwetting fluid and water as the wetting fluid. The extended criterion successfully described most situations we modeled. Furthermore, we compared fluid interface shape for a noncircular 3D pore predicted by the minimum surface energy (MSE) theory against 3D CFD simulations. While the fluid interface shape at the pore throat for 3D simulation was consistent with the shape predicted by MSE theory, the shape could not be successfully predicted by the MSE theory at the upstream and downstream pore body. Moreover, film flow existed for the noncircular pore at the downstream pore body.     

Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids

The phenomenon of reflection and transmission of plane harmonic waves at the plane interface between two dissimilar poroelastic solids saturated with two immiscible viscous fluids is investigated. Both porous media are considered dissipative due to the presence of viscosity in pore‐fluids. Four attenuated (three dilatational and one shear) waves propagate in such a dissipative porous medium. A finite non‐dimensional parameter is used to define the effective connections between the surface‐pores of two media at their common interface. Another finite parameter represents the gas‐share in the saturation of pores. An attenuated wave in a dissipative medium is described through the specification of directions of propagation and maximum attenuation. A general representation of an attenuated wave is defined through its inhomogeneous propagation, i.e., different directions for propagation and attenuation. Incidence of an inhomogeneous wave is considered at the interface between two dissipative porous solids. This results in four reflected and four transmitted inhomogeneous waves. Expressions are derived for the partition of incident energy among the reflected and transmitted waves. Numerical examples are studied to determine the effects of saturating pore fluid, frequency, surface‐pore connections and wave inhomogeneity on the strengths of reflected and transmitted waves. Interaction energy due to the interference of different (inhomogeneous) waves is calculated in both the dissipative porous media to verify the conservation of incident energy.