Use of Border Regions for Improved Permeability Upscaling

A procedure for the improved calculation of upscaled grid block permeability tensors on Cartesian grids is described and applied. The method entails the use of a border region of fine-scale cells surrounding the coarse block for which the upscaled permeability is to be computed. The implementation allows for the use of full-tensor permeability fields on the fine and coarse scales. Either periodic or pressure–no flow boundary conditions are imposed over the extended local domain (target block plus border regions) though averaged quantities, used to compute the upscaled permeability tensor, are computed only over the target block region. Flow and transport results using this procedure are compared to those from standard methods for different types of geological and simulation models. Improvement using the new approach is consistently observed for the cases considered, though the degree of improvement varies for different models and flow quantities.     

Flow Simulations To Evaluate Upscaling of Permeability

We study upscaling of the permeability for porous media flow on a grid with one million blocks. The purpose is to illustrate how flow simulations can be used to evaluate upscaling methods.     

四川盆地广安地区上三叠统须家河组四段低孔渗砂岩成岩相类型划分及半定量评价

成岩相是在一定沉积和成岩环境下经历了一定成岩演化阶段的产物,包括岩石颗粒、胶结物、组构和孔洞缝特征及其演化的综合面貌。成岩相的研究已成为低孔渗砂岩当前勘探阶段的研究重点。将广安地区须家河组四段划分为五种成岩相类型:粗中粒砂岩火山岩屑较强溶蚀低孔特低渗成岩相、火山岩屑弱溶蚀—强压实特低孔超低渗成岩相、中细粒砂岩压实致密相、中粗粒岩屑石英砂岩硅质胶结致密相以及方解石胶结致密相,并建立了不同类型成岩相的测井曲线特征。在单井成岩相分析基础上,通过编制成岩相的厚度百分含量等值线图、厚度等值线图、成岩相平面分布图等对成岩相进行了半定量化评价。     

潮流量推算方法及其误差的初步分析

通过误差比较,对代表潮平均法、代表潮连时序法、潮汐要素法等潮流量推算方法的应用进行评价,提出潮流量推算的方法建议。     

三轴应力下不同粒径破碎砂岩渗透特性试验

地下工程中破碎岩体往往处于三向应力状态,此类岩体具有孔隙率大、渗透性高等特点,在地应力与高水头作用下易发生渗流失稳破坏,诱发突水灾害。为研究三轴应力下破碎砂岩的渗透特性,运用自主研发的破碎岩石三轴渗流试验系统,采用稳态渗透法进行5种粒径破碎砂岩的渗流试验,得到了三轴应力下破碎砂岩渗透特性变化规律,推导了有效应力与渗流速度之间的关系。试验结果表明：三轴应力下破碎砂岩的有效应力与渗流速度呈线性关系,且轴向位移越大时,随有效应力的增加渗流速度减小的幅度越小;三轴应力下5种粒径破碎砂岩的孔压梯度与渗流速度服从Forchheimer关系,两者之间的相关系数达0.95以上;轴向位移恒定时,随着围压的增大,破碎砂岩渗透率k减小,非Darcy流β因子增大,各级轴向位移下,破碎砂岩的渗透率与围压之间呈指数函数关系;随着孔隙率的减小,5种粒径的破碎砂岩渗透率呈减小趋势,非Darcy流β因子整体增大,且渗透率量级为10-14～10-11 m2,非Darcy流β因子的量级为106～1012 m-1。     

Permeability tensors for sedimentary structures

Accurate modeling of fluid flow through sedimentary units is of great importance in assessing the performance of both hydrocarbon reservoirs and aquifers. Most sedimentary rocks display structure from the mm or cm scale upwards. Flow simulation should therefore begin with grid blocks of this size in order to calculate effective permeabilities for larger structures. In this paper, we investigate several flow models for sandstones, and examine their impact on the calculation of effective permeability for single phase flow. Crossflow arises in some structures, in which case it may be necessary to use a tensor representation of the effective permeability. We establish conditions under which tensors are required, e.g., in crossbedded structures with a high bedding angle, high permeability contrast, and laminae of comparable thickness. Cases where the off-diagonal terms can be neglected, such as in symmetrical systems, are also illustrated. We indicate how the method of calculating tensor permeabilities may be extended to model multiphase flow in sedimentary structures.     

Effective Permeability Estimation for 2-D Fractal Permeability Fields

Hurst exponents (H) of the distribution of permeability at micro (pore) scale were measured as close to 0.1 for sandstone and limestone samples. Based on these observations and previously reported H values for field scale permeability distribution ranging between 0.6 and 0.9, square permeability fields at different scales varying between 1 and 100 ft were generated for the H values of 0.1, 0.5, and 0.9. The study also considered different permeability fields and number of grids ranging from 10 to 500 md and from 8 × 8 to 64 × 64, respectively. The effective permeability of fractally distributed 2-D fields was calculated using different averaging techniques and compared to the actual (equivalent) permeability obtained through numerical simulation. The geometric mean and power averaging techniques as well as the perturbation theory yielded the most reasonable agreement between the actual and calculated effective permeabilities. The accuracy of these techniques increases with increasing average model permeability. It was also observed that as the H decreases, the permeability values obtained were higher than the actual values. Two extreme values of the number of grids (8 × 8 and 64 × 64) yielded the highest error percentages. Thus, the optimum number of grids was found to be 16 × 16 and 32 × 32 depending on the average permeability of the model. The exponent of the power law model was correlated to the fractal dimension of the permeability field for 8 × 8 and 64 × 64 grids. While a good correlation exists for 8 × 8 number of grids, no correlation was obtained for 64 × 64. Hence, an alternate model was proposed for 8 × 8 grids but for grid numbers higher than 32 × 32, no technique was found suitable for averaging of the fractal permeability fields.     

苏德尔特油田低渗透凝灰质砂岩成岩作用及储层质量差异性演化

海拉尔盆地贝尔凹陷苏德尔特油田兴安岭油层为典型的富火山物质的低渗致密砂岩储层。利用岩心观察、薄片鉴定、扫描电镜分析、压汞测试分析等方法,对兴安岭油层储层成岩作用及其控制下的储层质量演化过程进行了系统研究。结果表明,储层目前主要处于中成岩A期,整体经历了压实作用-早期方解石胶结作用/方沸石胶结作用-方沸石溶解/长石溶解作用/高岭石胶结作用/硅质胶结作用-晚期方解石胶结作用。兴安岭油层储层可以划分出强压实成岩相（I）、弱压实-方解石中强胶结成岩相（II）、中等压实-方沸石/长石强溶解成岩相（III）、中等压实-方沸石/长石中强溶解-高岭石强烈充填成岩相（IV）4种类型的成岩相。压实作用和早期方解石胶结作用导致储层孔隙度和渗透率降低,方沸石和长石的溶解作用有效提高储层孔隙度和渗透率,高岭石的沉淀作用导致储层渗透率大大降低。成岩相I和成岩相II储层质量最差,孔隙度和渗透率均较低,为典型的特低孔特低渗致密储层;成岩相III储层质量最好,具有较高的孔隙度和渗透率,为中孔-中低渗储层;成岩相IV储层质量中等,具有较高的孔隙度,但渗透率较低,为中孔（特）低渗储层。     

Numerical estimation of REV and permeability tensor for fractured rock masses by composite element method

The Monte Carlo method is used to generate parent stochastic discrete fracture network, from which a series of fractured rock samples of different sizes and orientations are extracted. The fracture network combined with a regular grid forms composite element mesh of the fractured rock sample, in which each composite element is composed of sub‐elements incised by fracture segments. The composite element method (CEM) for the seepage is implemented to obtain the nodal hydraulic potential as well as the seepage flow rates through the fractured rock samples. The application of CEM enables a large quantity of stochastic tests for the fractured rock samples because the pre‐process is facilitated greatly. By changing the sizes and orientations of the samples, the analysis of the seepage characteristics is realized to evaluate the variation of the permeability components, the existence of the permeability tensor and the representative element volume. The feasibility and effectiveness are illustrated in a numerical example. Copyright © 2008 John Wiley & Sons, Ltd.     

镇泾油田低渗透油藏岩石渗透率应力敏感性研究

对镇泾油田低渗透油藏岩石进行了渗透率应力敏感性实验研究,并对其进行了应力敏感性评价。实验是在一定围压下,通过降低和增加内压的方式完成的,共进行了2个围压下的变内压实验。实验结果和应力敏感性评价结果表明,镇泾油田低渗透油藏不存在渗透率强应力敏感性,在原始地层压力条件下,衰竭式开发对地层的渗透率几乎没有影响,注水开发对地层的渗透率会有一定程度的改善。同时,通过对有效应力定律方程的研究,得出渗透率有效应力系数为常数且值很小,这从机理上解释了镇泾油田低渗透油藏岩石的渗透率对应力不敏感的原因。     

利用不对称的地下水位潮汐波动确定滨海含水层参数

在滨海地区,地下水水位受潮汐波动影响较大,使得传统的抽水试验、水位回复试验等方法确定含水层参数存在困难且花费较大。通过对广西北海市滨海含水层地下水位动态资料进行分析,发现其上升段和下降段是不对称的。基于海岸带承压含水层正弦潮汐波的传播理论,提出了确定含水层参数的分段法,并与振幅衰减法和滞后时间法进行对比,各种方法求出的储水系数与导水系数之比(S/T)很接近,说明分段法是有效的。对于北海市滨海含水层,上升段求出的S/T值比下降段要大,其成因机理还有待进一步分析。     

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.     

基于粒度控制的复杂储层渗透性建模方法

岩石颗粒大小反映了沉积岩结构的主要特征,是岩石岩性的主要评价指标,同时也是影响沉积物渗透性的主要因素。沉积环境在纵向上表现出来的差异性,使得粒序控制下的地层渗透性在纵向上也表现出非均质性。为了精细地描述由于粒度大小造成的渗透率的非均质性,本文首先结合岩心粒度分析资料,分析了研究区粒度大小对物性影响的规律,利用自然伽马、中子、密度、声波曲线,通过测井地质分析提取敏感参数,建立了粒度计算模型;然后以粒度为指标,建立了不同粒度大小条件下的渗透率计算模型。通过现场资料的处理及其与岩心资料的对比,认为这种渗透率建模方法能够较好地反映沉积物粒度对岩石渗透性的控制作用,能够更加精确地描述复杂岩性地层渗透率的非均质性特征,从而可为地质开发研究提供更为准确的渗透率剖面。     

鄂尔多斯盆地南部上古生界低孔低渗砂岩储层成岩作用特征研究

对鄂尔多斯盆地南部山西组二段—下石盒子组八段储层砂岩的岩石学特征、孔隙类型与物性特征、胶结物种类及成岩作用特点的详细研究表明:山西组二段—下石盒子组八段砂岩的主要孔隙类型大部分是与胶结物和泥质杂基有关的微孔隙,也是造成研究区砂岩储层低孔低渗的内在原因之一。砂岩主要的成岩作用包括机械压实作用、胶结作用、溶蚀溶解作用。压实作用是成岩早期导致砂岩储层质量变差的主要原因之一;胶结作用包括硅质胶结、钙质胶结和粘土矿物胶结,硅质胶结对储层物性的贡献大于其他胶结类型,方解石是造成储层物性降低的主要胶结物;煤系地层埋藏后提供的酸性孔隙流体造成早期长石和方解石的溶蚀溶解,形成次生孔隙,对早期储层物性起到了一定的改善作用,但由于后期强烈的方解石胶结作用而消失殆尽。     

Strain fields and mechanical response of a highly to medium fissured bentonite clay

This article presents the developments of an ongoing research aimed at modelling the influence of fissuring on the behaviour of clays. In particular, it recalls the main results of an extensive laboratory investigation on a fissured bentonite clay from the south of Italy and presents the data of a new investigation on the evolution with shearing of the strain fields developing within the clay, resulting from Digital Image Correlation (DIC). Element test results are analysed in the framework of continuum mechanics and linked to the clay fissuring features, once characterised using the Fissuring IDentity (F‐ID) chart. This article compares the bentonite behaviour with that of other fissured clays of different F‐IDs, highlighting the common behavioural features. Thereafter, the soil response at the macro level is related to the DIC‐derived strain fields evolving within the clay with loading. For this purpose, DIC was successfully used to investigate the deformation processes active in the fissured clay and the sources of the localisation phenomena. DIC is shown to provide indications of the extent to which highly to medium fissured clays element test results can be of use to model the clay behaviour according to continuum mechanics. Copyright © 2012 John Wiley & Sons, Ltd.     

非常低延展性裂隙岩体REV存在性研究

裂隙岩体渗流问题一直是水文地质与工程地质的前沿课题之一,等效多孔介质模型是裂隙岩体渗流研究和工程应用的主要方法,此方法的重点在于裂隙岩体渗流模型即典型单元体(REV)的确定。本文采用作者自行开发的离散元软件FractureToKarst,根据国际岩石力学协会对岩石的分类,讨论了非常低延展性裂隙岩体典型单元体(REV)的存在性及大小,并给出确定其存在性的一般方法。通过研究可知,非常低延展性裂隙岩体REV存在的条件就是裂隙平均间距在0.2m以下,即极密间距、很密间距和密间距裂隙岩体存在REV。裂隙平均间距大于0.2 m,即中等间距、宽间距、很宽间距和极宽间距裂隙岩体不存在REV。     

基于三维裂隙网络的裂隙岩体表征单元体研究

岩体表征单元体（REV）的研究一直是岩土工程中的重要问题。裂隙岩体REV是其内部复杂结构在尺寸效应上的体现,归因于岩体内裂隙系统的随机性。在三维网络模型的基础上通过计算体积节理数建立了确定岩体REV的方法。这种方法考虑了岩体内裂隙的三维空间密度的特征,采用体积节理数这一参数的收敛状况确定岩体REV的大小。建立了实际岩体的模拟裂隙系统,用一定大小的立方体来分割裂隙系统,统计不同立方体内的体积节理数,并将均值作为最终裂隙岩体的参数。将此参数作为裂隙岩体的属性,通过判别其收敛状况获得了岩体REV的尺寸。考虑了岩体不连续面的特征,建立了REV的分析模型,得出工程岩体的REV的尺寸是裂隙平均迹长的4倍的结论。     

裂缝性储集层岩芯裂缝统计分析

在系统介绍岩芯裂缝基本参数统计的基础上,给出岩芯裂缝空间分布规律的表示方法,并概括了裂缝孔隙度和渗透率的估算方法,提出有效孔隙度、渗透率和单井控制的有效裂缝体积可作为裂缝性储集层等级划分和裂缝综合评价的依据.     

裂隙岩体三维柔度张量的数值试验方法

在裂隙岩体二维柔度张量数值试验的基础上,建立了裂隙岩体三维柔度张量及其表征单元体积（REV）尺度研究的简化数值试验方法。首先根据岩体裂隙的统计参数及分布规律,运用蒙特卡罗方法在研究域内获得与实际岩体裂隙同分布的三维随机裂隙网络,提取位于不同方位的岩体试件,运用二维柔度张量的数值试验方法求出各个平面方向上的二维柔度张量,然后根据二维与三维柔度张量的拓扑关系,用数学方法求解裂隙岩体的三维柔度张量。对于含3组正交全贯通裂隙的岩体,通过数值试验获得的柔度张量与理论解相比,其主对角线上各参数的误差在5%以内,表明该数值试验方法较为可靠。最后将此方法运用到小湾水电站工程中,确定左岸坝区裂隙岩体的应力REV为11 m×11 m×11 m,并获得该区域裂隙岩体的三维柔度张量。     

Permeability determination of porous media using large‐scale finite elements and iterative solver

The problem of finite element simulation of incompressible fluid flow in porous medium is considered. The porous medium is characterized by the X‐ray microtomography technique in three dimensions. The finite calculus‐based stabilization technique is reviewed to implement the equal order finite element interpolation functions for both velocity and pressure. A noble preconditioner, the nodal block diagonal preconditioner, is considered whose performance is thoroughly investigated. Combining this preconditioner with a standard iterative solver during the computational homogenization procedure, it is possible to carry out the large‐scale fluid flow simulation for estimating permeability of the porous medium with reasonable accuracy and reliability. Copyright © 2013 John Wiley & Sons, Ltd.