About Darcy's law in non-Galilean frame

This paper is aimed towards investigating the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium (e.g. a porous medium placed in a centrifuge basket). The filtration law is obtained by upscaling the flow equations at the pore scale. The upscaling technique is the homogenization method of multiple scale expansions which rigorously gives the macroscopic behaviour and the effective properties without any prerequisite on the form of the macroscopic equations. The derived filtration law is similar to Darcy's law, but the tensor of permeability presents the following remarkable properties: it depends upon the angular velocity of the porous matrix, it verifies Hall–Onsager's relationship and it is a non-symmetric tensor. We thus deduce that, under rotation, an isotropic porous medium leads to a non-isotropic effective permeability. In this paper, we present the results of numerical simulations of the flow through rotating porous media. This allows us to highlight the deviations of the flow due to Coriolis effects at both the microscopic scale (i.e. the pore scale), and the macroscopic scale (i.e. the sample scale). The above results confirm that for an isotropic medium, phenomenological laws already proposed in the literature fails at reproducing three-dimensional Coriolis effects in all types of pores geometry. We show that Coriolis effects may lead to significant variations of the permeability measured during centrifuge tests when the inverse Ekman number Ek⁻¹ is 𝒪(1). These variations are estimated to be less than 5% if Ek⁻¹<0.2, which is the case of classical geotechnical centrifuge tests. We finally conclude by showing that available experimental data from tests carried out in centrifuges are not sufficient to determining the effective tensor of permeability of rotating porous media. Copyright © 2004 John Wiley & Sons, Ltd.     

Pore to pore validation of pore network modelling against micromodel experiment results

Pore network modelling (PNM) has been widely used to study the multiphase flow and transport in porous media. Although a number of recent papers discussed the PNM validation on core-scale parameters such as permeability, relative permeability and capillary pressure; quantitative predictive potential of PNM on pore by pore basis has rarely been studied. The aim of this paper is to present a direct comparison between PNM simulations and corresponding micro-model experiments at the same scale and the same geometry. A number of well-defined and constrained two-phase flow in porous medium experimental scenarios were utilized to validate the physics solving part in PNM (filling rules, capillary and viscous pressure). This work validates that a dynamic pore network flow solver can predict two-phase flow displacements for these experiments for drainage situations at both pore and plug scales. A glass-etched micro-model is used to quantify the accuracy of a dynamic PNM solver on pore and core levels. Two-phase drainage micro fluidic experiments at different flow conditions are performed on micro-models. PNM simulations are performed on the same pattern and flow conditions as used in micro-model experiments. The two-phase distribution extracted from experiment images is registered onto rsults of PNM simulations for direct pore to pore comparison. Pore-scale matching level is found at around 75 % for all three test cases. The matching level of core-scale parameters such as S _{w c} and oil-phase permeability varies from case to case; the relative error to micro-model experiment measurements varies from 15 to 60 %. Possible reasons leading to discrepancies on core-scale parameters are discussed: missing considerations during validation of the combination of uncertainty in both simulator input parameters and experiments are seen as the principal factors.     

Numerical modeling of strongly coupled microscale multiphase flow and solid deformation

When fluid flows in porous media under subsurface conditions, significant deformation can occur. Such deformation is dependent on structural and phase characteristics. In this paper, we investigate the effect of multiphase flow on the deformation of porous media at the pore scale by implementing a strongly coupled partitioned solver discretized with finite volume (FV) technique. Specifically, the role of capillary forces on grain deformation in porous media is investigated. The fluid and solid subdomains are meshed using unstructured independent grids. The model is applied for solving multiphase coupled equations and is capable of capturing pore scale physics during primary drainage by solving the Navier-Stokes equation and advecting fluid indicator function using volume of fluid (VOF) while the fluid is interacting with a nonlinear elastic solid matrix. The convergence of the coupled solver is accelerated by Aitken underrelaxation. We also reproduce geomechanical stress conditions, at the pore scale, by applying uniaxial stress on the solid while simultaneously solving the multiphase fluid-solid interaction problem to investigate the effect of external stress on fluid occupancy, velocity-field distribution, and relative permeability. We observe that the solid matrix exhibits elasto-capillary behavior during the drainage sequence. Relative permeability endpoints are shifted on the basis of the external stress exerted.     

广州饱和软土固结过程微孔隙变化的试验分析

软土的孔隙特征及其变化规律对软土的压缩性和渗透性有重大的影响,软土孔隙特征随荷载变化规律的试验研究为揭示软土排水固结过程与变形规律,建立基于孔隙压缩规律和渗流机制的排水固结模型提供有力依据。利用美国全自动压汞仪,对不同压力下固结的广州番禺淤泥土样的孔隙及其尺度分布进行测试,根据测试结果对土样孔隙尺度分布特征及其随固结压力的变化规律给出了定量分析。试验结果表明：淤泥土中介于0.4～2.5 μm范围的颗粒间及团粒内的小孔隙所占比例最大,而大于10 μm的大孔隙和小于30 nm的超微孔隙所占比例均很小;较大的孔隙更易于被压缩而湮灭或被分裂成微小孔隙;固结压力将显著改变淤泥土的孔隙尺度及其分布特征,以致改变土体的压缩性和渗透性。在固结前期( 200 kPa)孔隙尺度较大,压缩系数和渗透系数较大并随固结压力增加而快速减小;在固结后期( 200 kPa)孔隙尺度小,压缩系数和渗透系数小,且随固结压力增加的变化趋于平缓。     

Computations of Absolute Permeability on Micro-CT Images

We apply an accurate numerical scheme to solve for Stokes flow directly on binarized three-dimensional rock images, such as those obtained by micro-CT imaging. The method imposes no-flow conditions exactly at the solid boundaries and employs an algebraic multigrid method to solve for the resultant set of linear equations. We compute the permeability of a range of consolidated and unconsolidated porous rocks; the results are comparable with those obtained using the lattice Boltzmann method and agree with experimental measurements on larger core samples. We show that the Kozeny–Carman equation can over-estimate permeability by a factor of 10 or more, particularly for the more heterogeneous systems studied. We study the existence and size of the representative elementary volume (REV) at lamina scale. We demonstrate that the REV for permeability is larger than for static properties—porosity and specific surface area—since it needs to account for the tortuosity and connectedness of the flow paths. For the carbonate samples, the REV appeared to be larger than the image size. We also study the anisotropy of permeability at the pore scale. We show that the permeability of sandpacks varies by less than 10 % in different directions. For sandstones, permeability changes by 25 % on average. However, the anisotropy of permeability in carbonates can be up to 50 %, indicating the existence of connected pores in one direction which are not connected in another.     

多尺度多孔介质有效气体输运参数的分形特征

非常规油气资源的孔隙结构及其连通性非常复杂,其孔隙尺度从毫米到纳米跨越多个量级.多孔介质中气体的输运过程不仅依赖于介质的多尺度微观结构特征,还依赖于气体的相关属性.气体在多尺度多孔介质中的输运过程包括无滑流、滑脱流和过渡流,涉及分子扩散和努森扩散等多种机制,因此很难用唯一的连续介质理论来描述气体的输运特征.大量的数据表明真实多孔介质中的内部孔隙具有分形标度特征,因此采用分形几何表征多尺度多孔介质的孔隙结构,引入孔隙分形维数和迂曲度分形维数定量表征多孔介质的微结构和弯曲流道,建立多尺度多孔介质气体输运过程的细观模型;推导了多尺度多孔介质中气体的有效渗透率和有效扩散系数,并讨论了多尺度多孔介质微结构参数和气体属性对于气体等效输运特性的定量影响.该研究不仅可以丰富渗流理论,且有利于深入理解非常规油气藏的产出机制.      

基于流动单元的砂砾岩储层渗透率测井精细评价

随着南海西部海域的勘探与开发,越来越多的砂砾岩油气藏被发现。但由于研究区域砂砾岩储层孔隙结构复杂,因此,孔隙度基本相同的储层之间渗透率差别很大,并且低渗砂砾岩储层的油水层测井响应特征不明显。针对于此,本文深入分析砂砾岩储层的孔隙结构特征及其对储集层电性的影响,总结不同沉积环境条件下渗透率的分布特征及影响因素。从宏观上看:受近物源的控制,快速堆积的碎屑杂基充填孔隙,储层渗透率表现为低渗特征;由于溶蚀作用改善了孔隙,远物源孔隙连通性较好,渗透率表现为中高渗特征;而压实作用较为强烈的储层则表现为特低渗特征。从微观上看,岩石平均孔喉半径是渗透率的重要内在控制因素。依据不同的沉积环境及孔隙结构特征,采用流动单元分析法,将砂砾岩储层细分为三大类,从而建立了三大类砂砾岩储层渗透率测井解释模型;并采用最能表征储层储集性能的补偿密度、补偿中子、泥质体积分数、地层流动带指数进行模糊聚类分析,得到Fisher线性判别模型。结果显示,流动单元法所建渗透率模型最终预测渗透率相对误差基本保持在50%以内,比传统孔渗模型方法精度更高,在研究区域更具有适用性和准确性。     

碳酸盐岩储层参数对微观渗流的影响

针对碳酸盐岩油藏孔隙大小的双峰分布特征,首先利用计算机模拟建立了描述不同孔隙特征的大孔隙网络模型和微孔隙网络模型,在此基础上提出一种耦合算法构建出的同时描述大孔隙和微孔隙特征的碳酸盐岩双孔隙网络模型;然后,基于侵入-逾渗理论,模拟双孔隙网络模型中油水两相流体的一次驱替和二次吸吮过程,并建立了毛细管压力和相对渗透率的求解模型;最后,通过调整双孔隙网络结构参数,模拟水湿油藏条件下碳酸盐岩储层参数对相对渗透率曲线的影响. 结果表明,随着微孔隙比例因子和平均配位数的增加,油相相对渗透率曲线升高;随着双孔隙半径比的增加,油相和水相相对渗透率曲线下降,这对碳酸盐岩油藏渗流机理研究有着重要的指导意义.      

Numerical Calculation of Equivalent Cell Permeability Tensors for General Quadrilateral Control Volumes

A new method for upscaling fine scale permeability fields to general quadrilateral-shaped coarse cells is presented. The procedure, referred to as the conforming scale up method, applies a triangle-based finite element technique, capable of accurately resolving both the coarse cell geometry and the subgrid heterogeneity, to the solution of the local fine scale problem. An appropriate averaging of this solution provides the equivalent permeability tensor for the coarse scale quadrilateral cell. The general level of accuracy of the technique is demonstrated through application to a number of flow problems. The real strength of the conforming scale up method is demonstrated when the method is applied in conjunction with a flow-based gridding technique. In this case, the approach is shown to provide results that are significantly more accurate than those obtained using standard techniques.     

Homogenization of a Darcy–Stokes system modeling vuggy porous media

We derive a macroscopic model for single-phase, incompressible, viscous fluid flow in a porous medium with small cavities called vugs. We model the vuggy medium on the microscopic scale using Stokes equations within the vugular inclusions, Darcy's law within the porous rock, and a Beavers–Joseph–Saffman boundary condition on the interface between the two regions. We assume periodicity of the medium and obtain uniform energy estimates independent of the period. Through a two-scale homogenization limit as the period tends to zero, we obtain a macroscopic Darcy's law governing the medium on larger scales. We also develop some needed generalizations of the two-scale convergence theory needed for our bimodal medium, including a two-scale convergence result on the Darcy–Stokes interface. The macroscopic Darcy permeability is computable from the solution of a cell problem. An analytic solution to this problem in a simple geometry suggests that: (1) flow along vug channels is primarily Poiseuille with a small perturbation related to the Beavers–Joseph slip, and (2) flow that alternates from vug to matrix behaves as if the vugs have infinite permeability.     

Computer simulation studies of Crystallization under confinement conditions

Crystallization under confinement conditions is a very important process in geochemistry and geophysics. Computer simulations of fluids in nanometer scale pore spaces can provide a unique microscopic insight into the structure, dynamics and forces arising from the crystallization process. We discuss in this paper molecular dynamics computer simulations of crystallization in pores of nanometer dimensions. The crystallization pressure due to the freezing of a model of Argon in a nanopore is computed using molecular dynamics simulations. We also investigate the influence of pore geometry in determining the dynamics of confined fluids, as well as mass separation in binary mixtures. It turns out that the pore geometry reveals itself as an important variable, leading to 1) new mechanisms for fast diffusion in confined spaces, and 2) accumulation of solute in specific regions inside the pore.     

基于分形理论探究砂岩最小孔隙半径的最优区间

渗透率是评价多孔介质导水性能的主要参数,是导水介质微观孔隙结构在宏观上的表现特征。通过扫描电镜实验和图像处理技术,统计出砂岩微观孔隙几何参数,并结合分形理论探究了砂岩微观孔隙结构对渗透率的影响。同时,以实测渗透率为约束条件,确定了对渗流起作用的最小孔隙半径r_min区间,该区间可作为渗透率预测时最小孔隙半径r_min的最优取值区间,并获取了与之对应的孔隙半径累积百分数区间。结果表明:砂岩最小孔隙半径r_min的取值对渗透率影响较大,随着砂岩最小孔隙半径r_min取值的增大,其渗透率先急剧下降,后渐渐地趋于稳定,并伴有上升趋势。在致密砂岩中,理论渗透率与实测渗透率相等时,对应的最小孔隙半径r_min落在孔隙半径累积百分数为15%~25%内,该孔隙半径累积百分数区间对应的孔隙半径区间可作为计算砂岩理论渗透率时最小孔隙半径r_min的最优取值区间,并且随着砂岩渗透率的增大,最小孔隙半径r_min对应下的孔隙半径累积百分数逐渐增加。      

基于热力学模型的煤孔隙结构分形表征

煤的孔隙结构复杂,难以用传统的欧氏几何理论描述其复杂性,而分形理论可定量表征孔隙结构的复杂程度。通过对渭北煤田韩城矿区10个煤样进行的压汞实验,采用热力学分形模型,获得了煤的渗流孔的分形维数,定量表征了煤的孔隙特征,并探讨了分形维数与渗透率的关系。研究表明:对于同等变质程度的煤来说,煤中吸附孔越多,孔隙分形维数越大;煤孔隙分形维数与渗透性呈负相关关系。由此可见,煤的渗流孔分形维数可作为煤储层渗透性评价的定量指标之一。      

Spontaneous imbibition and wettability characteristics of Powder River Basin coal

The wettability of coal is studied at scales that range from the microscopic to the core. While contact-angle measurements define wettability at microscopic (pore) and core scales, relative permeability curves define wettability and multiphase flow properties at core and reservoir scales. The microscopic wettability is evaluated based on the Frumkin–Derjaguin equation. Estimates for contact angles are made versus aqueous-phase pH. The calculations suggest a trend that goes through a maximum at a pH around 4. Contact angles become small at low and high pH suggesting an alteration of coal wettability with pH. Water imbibition studies indicate that the core-scale wetness has similar trends as those predicted for the pore scale. Contact angle goes through a maximum at a pH of around 7 and is low in highly acidic and basic solutions. X-ray computed tomography (CT) scanning based imbibition studies also provide a method of understanding multiphase flow in coal systems. Estimates for relative permeability of air–water flow in coal are obtained and reported. The results are encouraging as these are the first steps towards developing relative permeability curves for coal-methane and carbon-dioxide systems. These systems are important with regards to both CO₂ sequestration as well as enhanced methane production.     

Consolidation around a heat source buried deep in a porous thermoelastic medium with anisotropic flow properties

A solution is derived for the heat flow and consolidation which occur when a heat source is buried deep in a porous thermoelastic soil having anisotropic flow properties. This solution is used to examine the pore pressure generation and dissipation near both point and cylindrical heat sources. An increase in temperature will tend to generate an increase in excess pore pressure. However, the pore water will tend to flow from regions of high excess pore pressure to regions of low excess pore pressure, and so consolidation will occur, and temperature-generated excess pore pressures will tend to dissipate. Many natural soils exhibit horizontal layering and so have a higher horizontal than vertical permeability. It is shown that in soils the excess pore pressure generated by a heat source is significantly less than that in an isotropic soil having an equal vertical permeability.     

孔隙尺度多孔介质流体流动与溶质运移高性能模拟

深入探究孔隙尺度下的流体流动特性和溶质运移规律对石油开采、农田养分管理、地下水污染修复有着重要意义。以人工构建的多孔介质结构和同步辐射X射线显微CT扫描的土壤团聚体(分辨率3.7μm)为研究对象,在空间节点数多达64 000 000的情况下,基于格子Boltzmann模型和GPU并行技术计算得到多孔介质流体运动和溶质运移过程的关键参数,并据此探究多孔介质空间异质性对水力学特性的影响。通过对3组不同结构的多孔介质比较发现,结构复杂程度最高的土壤样品和不规则堆叠的圆球结构的渗透率在100 mD(即10^-13m^2)量级,远低于规则堆叠的圆球结构(>20 000 mD);土壤的迂曲度为1.40~1.60,明显高于规则堆叠的圆球结构。研究结果表明,渗透率大的样品具有较小的迂曲度,这与结构的空间异质性有较强的关系;土壤的渗透率和迂曲度呈现各向异性;在水力梯度一定的前提下,渗透率较大的样品,纵向弥散系数也较大;同时,结构的异质性也会影响溶质的穿透曲线。本研究提出的模拟方法可在土壤结构中进行高效的水流运动和溶质运移模拟,可用于土壤多孔介质在孔隙尺度下的水力学特性研究。     

孔隙尺度多孔介质流体流动与溶质运移高性能模拟

深入探究孔隙尺度下的流体流动特性和溶质运移规律对石油开采、农田养分管理、地下水污染修复有着重要意义。以人工构建的多孔介质结构和同步辐射X射线显微CT扫描的土壤团聚体（分辨率3.7 μm）为研究对象，在空间节点数多达64 000 000的情况下，基于格子Boltzmann模型和GPU并行技术计算得到多孔介质流体运动和溶质运移过程的关键参数，并据此探究多孔介质空间异质性对水力学特性的影响。通过对3组不同结构的多孔介质比较发现，结构复杂程度最高的土壤样品和不规则堆叠的圆球结构的渗透率在100 mD（即10^-13m²）量级，远低于规则堆叠的圆球结构（>20 000 mD）；土壤的迂曲度为1.40~1.60，明显高于规则堆叠的圆球结构。研究结果表明，渗透率大的样品具有较小的迂曲度，这与结构的空间异质性有较强的关系；土壤的渗透率和迂曲度呈现各向异性；在水力梯度一定的前提下，渗透率较大的样品，纵向弥散系数也较大；同时，结构的异质性也会影响溶质的穿透曲线。本研究提出的模拟方法可在土壤结构中进行高效的水流运动和溶质运移模拟，可用于土壤多孔介质在孔隙尺度下的水力学特性研究。     

A level-set corrector to an adaptive multiscale permeability prediction

We consider the inverse problem of permeability estimation for two-phase porous-media flow. The novel approach is based on regularization by zonation, where the geometry and size of the regions are chosen adaptively during the optimization procedure. To achieve this, we have utilized level-set functions to represent the permeability. The available data are sparsely distributed in space; hence, it is reasonable to confine the estimation to coarse-scale structures. The level-set approach is able to alter the boundaries between regions of different permeability without strict restrictions on their shape; however, when the data are sparse, a reasonable initial guess for the permeability is required. For this task, we use adaptive multiscale permeability estimation, which has the potential of identifying main permeability variations. These are described by a piecewise constant function, where the constant values are attained on rectangular zones. In the current work, we develop a level-set corrector strategy, assuming adaptive multiscale permeability estimation as a predictor.     

准噶尔盆地莫西庄地区侏罗系三工河组二段储层特征

利用多种方法对准噶尔盆地莫西庄地区侏罗系三工河组二段储层特征进行了分析。结果表明,其成分成熟度较低、结构成熟度较高,孔隙度主要属特低孔-中孔,渗透率属超低渗-中渗。当孔隙度大于10%时,储层的含油性受渗透率控制。主要孔隙类型为原生粒间孔、溶蚀-改造粒间孔和粒内溶孔,孔隙类别以特大孔为主,而喉道类别以微细喉为主。成岩作用类型主要为机械压实作用、胶结作用、溶蚀和交代作用,成岩阶段处于晚成岩期A亚期,成岩演化过程中,机械压实作用、胶结作用导致储层孔隙度减小约24.5%,同时因溶蚀作用使孔隙度增大约4.5%。     

柴达木盆地东部石炭系致密灰岩孔渗特征

碳酸盐岩储层孔隙系统复杂。对空隙结构特征、渗流机理的研究直接影响到油气资源的勘探和开采。本研究选取了柴达木盆地东部地区ZK5-2钻井中石炭系的5块致密灰岩样品,通过XRD、XRF技术对灰岩的矿物成分、化学成分进行定量测试;利用氦气双室法与孔径分布实验（包括压汞法、氮气吸附法、二氧化碳吸附法）确定灰岩的孔隙度与空隙的孔径分布;用CH4、N2、CO2、He四种气体进行渗流实验确定灰岩的表观渗透率。研究结果表明:致密灰岩的表观渗透率与其孔隙度没有明显的关系。表观渗透率由达西流、滑脱流与扩散流三部分组成,表观渗透率大小按CH4、N2、CO2、He的顺序依次增加,其中He所测得的表观渗透率明显高于其他三种气体。滑脱流对表观渗透率的贡献受到分子平均自由程与孔径的双重控制,当气体分子平均自由程与岩石内集中出现的孔径接近时,在这些相近孔径的孔隙中会出现明显滑脱现象,此时滑脱流将对表观渗透率产生较大的贡献。分子平均自由程较大的气体在致密灰岩中主要以扩散的形式运移。岩石孔径小于分子平均自由程的孔隙所占比例越大,扩散流对表观渗透率的贡献度越高。