On computation of strain‐dependent permeability of rocks and rock‐like porous media

Determination of transport properties of geomaterials is an important issue in many fields of engineering analysis and design. For example, in petroleum engineering, in situ permeability of an oil reservoir may be crucial in establishing its viability for exploitation, whilst prevention of leakage from underground storage facilities for oil and gas, nuclear waste as well as viability of CO₂ sequestration projects crucially depends on its long‐term values. Permeability is indirectly related to the porosity, pore‐size distribution and pore architecture of the porous media. These parameters evolve when a strain field is imposed. Physical measurement of permeability under a strain field in laboratory conditions is difficult, expensive and prone to a number of uncertainties. In the past, pore network models have been used to compute permeability of materials under stress/strain‐free conditions. In this paper, we propose an enhanced pore network model to compute permeability of rocks and rock‐like porous media under a stress/strain field. Data of pore‐size distribution obtained from mercury intrusion porosimetry are used to compute permeability of rock samples from various unspecified oilfields in the world. It is shown that the two permeabilities can be predicted from the model with sufficient accuracy. A hypothesis for change in porosity, pore‐size distribution and pore architecture as a result of imposed mechanical strains is then proposed. Based on this, permeability is computed again for one of the rock samples under uniaxial and triaxial compressive and tensile strain fields. It is shown that depending on the state of strain field imposed, permeability evolves in an anisotropic manner. Permeability under tensile strain field increases dramatically compared with the reduction that takes place under compressive strain field of the same magnitude. Copyright © 2014 John Wiley & Sons, Ltd.     

珊瑚砂三维孔隙微观特性研究

孔隙是多孔介质内渗流的发生场所,与介质渗透性存在必然的联系。珊瑚砂因其特殊的物质来源和形成过程,较陆源砂具有截然不同的孔隙特性。通过一系列微观研究手段,从本质上揭示了珊瑚砂特殊孔隙性质的原因。研究发现,从孔隙形状、孔喉尺寸和整体连通性3个角度描述孔隙性质较为合理。其中,孔隙形状用形状因子度量,孔喉尺寸包括孔隙半径和喉道半径,珊瑚砂多孔介质整体连通性利用配位数进行描述。而影响孔隙形状、孔喉尺寸和整体连通性的主导因素包括颗粒形状和颗粒表面粗糙度两方面。其中颗粒形状主要影响孔隙形状、喉道尺寸、孔喉尺寸离散性和介质内部连通性的均匀分布情况。颗粒表面粗糙度主要影响孔隙形状、孔隙形状离散性、孔隙尺寸和介质整体连通性。     

孔隙介质的渗透特性初探

孔隙的存在是岩土类介质材料结构的本质特征,它不但改变了岩土体的力学特性,而且严重影响着岩土体的渗透特性。大多数经典的渗流理论中,多孔介质模型都假定孔隙率和渗透系数是与时间无关的材料常数。实际上由于淘涮、侵蚀、冲刷等原因,它们是随时间和坐标变化的,同时又与孔隙中的压力、流速等因素有关。基于孔隙率和损伤变量之间的定量关系,从连续损伤力学的角度对多孔介质岩土材料的渗流力学特性进行了研究。首先,对传统的达西定律形式进行修正,提出了孔隙介质完备有效的达西定律（模型）;然后,对该模型中渗透参数的特性进行了讨论和分析,得出了一些有益的结论。     

基于数字岩心分形特征的渗透率预测方法

基于数字岩心技术,对岩心CT扫描图像进行处理,结合分形理论求取数字岩心的分形特征参数并通过构建数字岩心的等效分形介质模型对岩心渗透率进行预测。首先对两块砂岩岩心进行了微米CT扫描,提取岩心孔隙网络模型,分析岩心孔隙结构特征,结果表明岩心的孔喉半径分布与孔喉配位数分布对岩心渗透率有一定影响;其次利用MATLAB、Image J等软件对CT扫描得到的数字岩心及帝国理工学院网站公开的数字岩心进行处理,基于分形理论求取数字岩心分形维数、迂曲度、迂曲度分形维数和最大孔隙直径等参数;最后基于分形渗透率模型对岩心渗透率进行预测。结果表明：预测渗透率与岩心渗透率具有良好的相关性,相关系数大于0.97。因此,基于数字岩心技术,通过构建数字岩心等效分形介质模型,可以有效预测岩心渗透率。     

低渗孔隙型碳酸盐岩油藏储层特征及剩余油分布规律

为揭示低渗孔隙型碳酸盐岩油藏储层微观孔隙结构特征和水驱剩余油分布特征,以中东某孔隙型碳酸盐岩油藏为例,基于油藏物性测试、恒速压汞孔喉参数统计、CT扫描孔隙参数分析和水驱油流体微观分布特征等,得出孔隙型碳酸盐岩储层的微观孔隙、喉道发育特征及其影响下的剩余油分布规律;在此基础上,将孔隙型碳酸盐岩与砂岩储层研究结果进行对比,进一步明确了两类储层孔隙结构及剩余油分布特征差异。结果表明：与低渗砂岩储层相比,低渗碳酸盐岩储层呈现出"孔隙大而数量少""喉道数量多且类型全"的特征,并建立孔喉发育特征模型;由于孔隙型微观孔隙结构的影响,低渗碳酸盐岩储层大孔隙中的剩余油仍然是需要研究的对象,同时明确了剩余油挖潜开发方式建议。     

Model for large strain consolidation with compressible pore fluid

A numerical model, called CCPF1 (C onsolidation with C ompressible P ore F luid 1 ), is presented for one‐dimensional large strain consolidation of a saturated porous medium with compressible pore fluid. The algorithm includes all the capabilities of a previous large strain consolidation code, CS2, written for incompressible pore fluid. In addition, fluid density and fluid viscosity are functions of fluid pressure in CCPF1. Generalization of the numerical approach to accommodate these functions requires several modifications to the CS2 method, including phase relationships, intrinsic permeability, pore pressure, fluid potential, and mass flux. Inertial forces are neglected and isothermal conditions are assumed. The development of CCPF1 is first presented, followed by an example that illustrates the effects of pore fluid compressibility on the mechanics of consolidation of saturated porous media. Copyright © 2004 John Wiley & Sons, Ltd.     

一种适用于孔隙体积应变的有效应力方程

土力学奠基石Terzaghi有效应力原理被广泛应用于油藏孔隙和渗透率应力敏感研究中,然而其对于岩石孔隙体积应变的适用性存在争议。对颗粒不可压缩和颗粒可压缩的多孔介质分别进行了受力分析,推导了总体积、颗粒骨架、孔隙体积的有效应力表达式,与Biot、Skepmton有效应力方程对比,建立了适用于孔隙体积应变的新型有效应力方程,并进行了试验论证和应用举例。研究表明:在颗粒不可压缩多孔介质中,有效应力为超出平衡孔隙流压之外的颗粒间宏观等效应力;在颗粒可压缩变形多孔介质中,有效应力为其相同应变下的等效应力,有3种有效应力分别适用于总体积应变、颗粒体积应变、孔隙体积应变;新提出的孔隙体积有效应力方程与孔隙度、岩石总体积压缩系数、颗粒压缩系数、总应力和流压相关,4个理论计算式计算结果在3种多孔介质试验测试结果中的偏差均在5%以内;孔隙体积有效应力系数解决了如何定量增总应力来等效模拟储层降流压生产过程这一关键问题,3个压缩系数关系式理论计算准确方便。     

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。     

毛细管渗流模型在黄土渗透性中的应用探讨

黄土作为一种典型的多孔介质,多孔性是其重要特性之一。多孔性不仅影响着黄土的物理力学及化学特征,也严重影响着黄土的水理性质,特别是黄土的渗透特性。然而,作为多孔介质渗流理论的经典模型——毛细管模型,已经广泛应用于油气田开采、煤成气开采以及岩土工程等领域,但将多孔介质渗流理论模型引入表征黄土的多孔构造,这方面的资料尚欠缺。因此,本文以黄土的渗透性作为研究示例,在总结分析目前相对较为成功的多孔介质毛细管渗流模型的基础上,选取适于定量表征黄土渗透性的渗流模型,结合计算结果和渗透试验结果的对比,探讨将多孔介质毛细管渗流模型引入描述黄土渗透性这一方法的适用性。并提出孔隙的“香肠”构造（或称为“莲藕”构造）,为黄土的渗透性研究提供可借鉴的理论依据。     

Effective strength of saturated double porous media with a Drucker–Prager solid phase

This study aims at determining the macroscopic strength of porous materials having a Drucker–Prager solid phase at microscale and two populations of saturated pores with different pressures at both micro and meso scales. To this end, and taking account of the available results by Maghous et al. (2009), we first derive a closed‐form expression of approximate criterion for a dry porous medium whose matrix obeys to a general elliptic criterion. The methodology to formulate this criterion is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. The obtained results are then implemented in a two‐step homogenization procedure, which interestingly delivers analytical expression of the macroscopic criterion for dry double porous media whose solid phase at microscale obeys to a Drucker–Prager criterion. After a brief discussion of the results, we propose an extension to double porous saturated media, allowing therefore to quantify the simultaneous effects of the different pore pressures applied on each voids population. The results are discussed in terms of the existence or not of effective stresses. Finally, they are assessed by comparing them to recently available results. Copyright © 2013 John Wiley & Sons, Ltd.     

A dynamic two‐phase flow model for air sparging

Air sparging (AS) is an in situ soil/groundwater remediation technology, which involves the injection of pressurized air/oxygen through an air sparging well below the zone of contamination. Characterizing the mechanisms governing movement of air through saturated porous media is critical for the design of an effective cleanup treatment system. In this research, micromechanical investigation was performed to understand the physics of air migration and subsequent spatial distribution of air at pore scale during air sparging. The void space in the porous medium was first characterized by pore network consisting of connected pore bodies and bonds. The biconical abscissa asymmetric concentric bond was used to describe the connection between two adjacent pore bodies. Then a rule‐based dynamic two‐phase flow model was developed and applied to the pore network model. A forward integration of time was performed using the Euler scheme. For each time step, the effective viscosity of the fluid was calculated based on fractions of two phases in each bond, and capillary pressures across the menisci was considered to compute the pressure field. The developed dynamic model was used to study the rate‐dependent drainage during air sparging. The effect of the capillary number and geometrical properties of the network on the dynamic flow properties of two‐phase flow including residual saturation, spatial distribution of air and water, dynamic phase transitions, and relative permeability‐capillary pressure curves were systematically investigated. Results showed that all the above information for describing the air water two‐phase flow are not intrinsic properties of the porous medium but are affected by the two‐phase flow dynamics and spatial distribution of each phase, providing new insight to air sparging. Copyright © 2012 John Wiley & Sons, Ltd.     

低渗砂岩储层孔喉的分布特征及其差异性成因

应用筛析粒度、铸体薄片、图像孔隙、扫描电镜与高压压汞等方法,对苏北盆地沙埝地区E1f3和三塘湖盆地牛圈湖地区J2x两类不同低渗储层的孔喉类型和分布特征进行了分析对比,对其差异性成因进行了探讨。研究表明,E1f3储层孔隙类型主要为碳酸盐胶结物和长石溶孔,J2x储层主要为凝灰质和长石溶孔,前者溶蚀成因的粗大孔隙较多,而后者细小的晶间孔较多。E1f3储层喉道分布为溶蚀成因的粗单峰分布、压实或压实胶结混合成因的细单峰分布、管束状喉道的无峰分布,以及溶蚀成因与压实或压实胶结混合成因组成的双峰分布四类;J2x储层喉道为溶蚀成因的粗单峰分布、管束状喉道的细单峰分布,及管束状喉道与压实或压实胶结成因组成的双峰分布三类,未见溶蚀成因喉道与其他成因喉道组成的双峰分布。两区孔隙半径、喉道半径均随粒级变细呈减小趋势,平均孔隙半径也总是小于碎屑颗粒半径;在粒度相近的情况下,J2x储层孔隙、喉道半径均小于E1f3储层。E1f3储层较高的成分成熟度与结构成熟度和早期碳酸盐胶结作用使其在压实过程中保存了较大的原始粒间孔隙空间,且为后期溶蚀作用所扩大,牛圈湖地区J2x储层较高的塑性岩屑含量和同沉积期形成的凝灰质,使储层原始孔隙空间在压实过程中大量减少,后期溶蚀作用较弱。杂基对原始孔隙空间的充填程度及其与塑性岩屑共同造成的压实与溶蚀强度的差异,是造成两区目前孔隙结构差异的主要原因。     

鄂尔多斯盆地吴旗地区长6储层孔隙结构特征

孔隙结构研究是油藏精细描述、储层综合评价的重要内容,采用铸体薄片、扫描电镜、铸体图像分析、高压压汞和恒速压汞等多种技术手段,对鄂尔多斯盆地吴旗地区长6储层的孔隙结构进行了深入分析和研究.鄂尔多斯盆地吴旗地区长6储层具有高孔低渗的特征,储层以原生剩余粒间孔为主,长石、岩屑及早期碳酸盐胶结物的溶解是形成次生孔隙的主要原因.中孔和小孔是油气的主要储集空间,细喉和中喉则是长6的基本渗流通道.铸体薄片、孔喉图像分析表明,吴旗长6储层具有复杂的孔喉分布特征,不同微相孔喉分布及孔隙结构特征是造成油井产能差异的重要因素.     

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。      

Modelling mechanical behaviour of limestone under reservoir conditions

High porosity and low permeability limestone has presented pore collapse. As fluid is withdrawn from these reservoirs, the effective stresses acting on the rock increase. If the strength of the rock is overcome, pore collapse may occur, leading to irreversible compaction of porous media with permeability and porosity reduction. It impacts on fluid withdrawal. Most of reservoirs have been discovered in weak formations, which are susceptible to this phenomenon. This work presents a study on the mechanical behaviour of a porous limestone from a reservoir located in Campos Basin, offshore Brazil. An experimental program was undergone in order to define its elastic plastic behaviour. The tests reproduced the loading path conditions expected in a reservoir under production. Parameters of the cap model were fitted to these tests and numerical simulations were run. The numerical simulations presented a good agreement with the experimental tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Mechanical trapping of fine particles in a medium of mono‐sized randomly packed spheres

Mechanical trapping (or straining) of fine particles is a key mechanism in many filtration systems. For example, the performance of rapid sand filters depends in part on mechanical trapping of larger fine particles, while relying on adsorptive processes to trap very small fine particles and microbes. The ability to trap these particles is directly related to the construction of the packed bed used for filtration in this system. Thus, the ability to model the effect of the inner structure of the packed bed can lead to more efficient design for improved filtration. Because of its significant efficiency, gravitational sphere packing is employed in this work to simulate a bed of mono‐sized randomly packed spheres. The simulated bed provides a way to visualize the pore network and estimate the pore size distribution associated with the void space between particles. Furthermore, by subsequently introducing fine particles into the bed, we evaluate the mass‐rate of fine particles passing through and possibly saturating the packed bed. Results show that fine particles between 15% and 25% of the coarse particle size can be physically strained within the randomly packed bed. These results differ significantly from the results obtained assuming a periodically spaced bed. The technique therefore provides an efficient yet accurate alternative for understanding how fine particles pass through a coarse particulate medium. Copyright © 2014 John Wiley & Sons, Ltd.     

南堡地区碳酸盐岩储层孔隙结构特征及对物性的影响

利用数字图像分析法对南堡地区碳酸盐岩储层的孔隙结构参数进行定量求取,明确了不同类型孔隙的孔隙结构参数特征,分析了孔隙结构特征对储层物性的影响,并应用优选出的孔隙结构参数建立碳酸盐岩储层物性预测模型。结果表明:研究区内碳酸盐岩储层的储集空间以次生孔隙为主,为一套典型的孔隙型储层。应用孔隙结构参数可以较好的区分铸模孔、粒间孔、粒内孔和晶间孔等孔隙类型,其中铸模孔呈较低的平均等效直径与高的宽纵比,粒间孔以高等效直径25%为特征,粒内孔对应最低的比表面、最高的等效直径标准差,晶间孔比表面较高且宽纵比分布范围局限。等效直径、形状因子、球度和宽纵比等参数对储层物性的影响显著。分别针对孔隙度和渗透率,在提取的28项孔隙结构参数中优选出6种相关性高的参数,并应用多元线性回归方法分别进行拟合。验证结果显示拟合公式具有较高的可信度,且渗透率(R^2=0.916)优于孔隙度(R^2=0.778)。该方法可为研究区及其他地区的孔隙型碳酸盐岩储层评价研究提供参考。     

An expression for the permeability of anisotropic granular media

There are many expressions proposed for the permeability of isotropic media based on flow channel and pore size distribution concepts, but there are no such expressions for anisotropic media. In this paper an expression for the permeability of an anisotropic medium is proposed, which has been verified in the laboratory. The mechanism behind fluid flow through soil was investigated using microscopic computer simulations to propose an expression for macroscopic permeability. The soil was assumed to be a spatially periodic porous medium, and the Navier-Stokes equation was solved using the FEM with appropriate boundary conditions for several different arrangements of the porous medium. The basic variables influencing flow through soil at the microscopic level were identified as specific surface area, void ratio, particle shape, material heterogeneity and the arrangement of particles in a porous medium. A sensitivity analysis was carried out to obtain an expression for the permeability in terms of the above variables. The corresponding macroscopic variables for the above microscopic variables are average specific surface area, average void ratio, anisotropy, tortuosity due to material heterogeneity, and the arrangement of particles respectively. An expression for the directional permeability is proposed in terms of these variables for the most common occurrence of particles in a porous medium. For the verification of the proposed equation, the permeability values of a fine-grained sand were measured at different void ratios and were compared with those predicted by the proposed equation. The results show that the predicted permeability values from the proposed equation are very close to the measured values.