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1.
The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. 相似文献
2.
Tao Chen Christoph Clauser Gabriele Marquart Karen Willbrand Thomas Hiller 《Hydrogeology Journal》2018,26(6):1903-1916
Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models. 相似文献
3.
Louis J. Durlofsky 《Mathematical Geology》2000,32(4):421-438
4.
多孔介质渗流是普遍的物理过程,涉及地下工程、地热开采、环境工程等各行各业,尤其是工程建设,常面临防渗问题。由于地质条件的复杂性,工程区域地层受到成岩、压实、风化、生物作用等各种影响,故渗流性质复杂,常需要对建设区域的渗流状况进行数值模拟,从而为工程的设计施工提供决策依据。数值仿真结果依赖于对地层介质关键参数的选取,但目前工程多将其视为均匀介质处理,对于介质的非均匀特性考虑较少。文章旨在研究非均质多孔介质渗透率空间分布与等效渗透率的关系。基于连续介质假定、达西定律以及非均匀多孔介质渗透率空间分布函数,建立一维到三维的达西渗流问题模型,通过求解偏微分方程和理论推导,得到基于渗透率空间分布函数的等效渗透率理论表达式,并与有限元计算的数值解进行对比分析,结果表明理论值和数值解误差很小,证明等效渗透率的表达式的合理性。利用该成果可通过多点局部渗透率的测定构建渗透率空间分布函数,从而对整体渗流区域的渗透性质进行快速计算和评估,从而简化异常复杂的工程地质模型以减少计算量需求,对于工程仿真的快速计算和结果评估有重要意义。 相似文献
5.
The paper is devoted to the upscaling method appropriate for single-phase flow in media with discontinuous permeability distribution.
The suggested algorithm is a modification of the iterative adaptive local–global upscaling developed by Chen and coauthors.
The key feature of this method is a consistency between local and coarse global calculated characteristics. In this work,
we apply a modified procedure to determine the boundary conditions used in the local fine-scale computation. To increase the
accuracy of these boundary conditions on each iteration, we involve an additional preliminary step based on the results of
coarse scale calculations from the previous iteration. Numerical tests show an essential improvement of the accuracy of upscaled
flow rates for most of the realizations of statistical permeability distribution. Although the developed method is universal,
its efficiency increases with increasing of permeability contrast. 相似文献
6.
7.
采用渗流力学理论并结合Monte Carlo方法描述岩体裂隙的随机分布,研究渗流模型的尺寸效应并确定表征单元体积（REV）,得到了3种开口度分布形式的等效渗透系数椭圆曲线,建立了等效渗透系数方向性的判别标准。离散裂隙网络（DFN）模型假定流体只在岩体裂隙内部流动,而不通过岩体本身渗流。基于二维离散元程序UDEC并进行二次开发,建立DFN模型,通过改变流体的流动方向,得到不同流动方向下岩体裂隙网络的等效渗透系数,并分析不同的开口度分布形式对岩体裂隙网络等效渗透系数方向性的影响。计算结果表明,表征单元体积存在的条件是等效渗透系数保持稳定且渗透椭圆比较光滑。等效渗透系数的方向性受开口度分布形式的影响很大：当开口度-长度关联分布时,等效渗透系数各向异性;当开口度对数正态分布时,等效渗透系数各向同性;当开口度恒定分布时,等效渗透系数的特性介于二者之间。变化系数（CV）是否大于5%是判定岩体裂隙网络渗透系数是否具有方向性的判别标准。 相似文献
8.
A numerical scheme for the computation of the permeability of complex microstructures is presented. As a darcean counterpart of the FFT‐based scheme in elasticity, the method is designed to be directly coupled with 3D imaging techniques of porous samples, without meshing or definition of an equivalent pore network. The method relies on the variational principle of Hashin and Shtrikman, which ensures a rigorous upper bound status to the estimated permeabilities and provides an energetically consistent rule for heterogeneous voxels comprising both the solid and fluid phases. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
9.
砂岩型铀矿矿层渗透系数普遍具有空间非均匀性,但受试验和分析手段制约,非均匀渗透系数难以准确刻画,导致地浸采铀过程预测出现偏差,限制了地浸采铀过程精细化管控。针对该问题提出一种矿层非均匀参数分布随机表征方法,在此基础上,开展水盐耦合数值随机模拟,揭示不同渗透系数空间分布条件下,群井抽注所引起的溶浸剂储层内部迁移过程和影响范围。在内蒙古某铀矿床应用结果显示：沿区域地下水流方向渗透系数增加,有利于注入溶浸剂疏散;相反,溶浸剂易出现聚集效应。利用水位监测数据对模型边界条件进行识别与验证后,在均质假设条件下溶浸剂扩散速率为210 m2/d,20 a开采周期波及范围为1.53 km2;考虑矿层非均质性和参数不确定性,预测溶浸剂扩散速率为191～228 m2/d,波及范围为1.47～1.74 km2。相比于均质假设,溶浸剂扩散速率和波及范围不确定性显著,分别为17.62%和17.65%。考虑渗透系数非均质性和不确定性,使得溶浸剂迁移转化行为预测结果更具代表性,可为合理制定地浸采铀方案提供更加可靠的依据。 相似文献
10.
This paper presents semi-analytical solutions to Fredlund and Hasan’s one-dimensional consolidation for unsaturated soils under symmetric semi-permeable drainage boundary conditions. Two variables are introduced to transform two coupled governing equations of pore-air and pore-water pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. Then, the pore-air and pore-water pressures, and soil settlement are obtained in the Laplace domain. Crump’s method is adopted to perform the inverse Laplace transform in order to obtain semi-analytical solutions in time domain. It is shown that the present solution is more applicable to various types of drainage boundary conditions, and in a good agreement with existing solutions from the literature. Furthermore, several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with traditional drainage boundary (single or double), and single-sided and double-sided semi-permeable drainage boundaries. Finally, it illustrates the changes in pore-air and pore-water pressures and soil settlement with time at different values of symmetric semi-permeable drainage boundary conditions parameters. In addition, parametric studies are conducted by the variations of pore-air and pore-water pressures at different ratios of air-water permeability coefficient and the depth. 相似文献
11.
Upscaling methods that need to solve local problems subject to boundary conditions are addressed in this article. We define
a new upscaling method based on optimization problems, which can take into account general boundary conditions applied to
local problems. The determination of upscaled permeability leads to minimizing the difference of dissipated energies (or averaged
velocity) at fine and large scale. Using optimal control techniques, we obtain an effective computing algorithm that allows
us to recover, with classical boundary conditions, the well-known results. The uniqueness issue is tackled for the optimization
problems introduced in our approach. We show that the method is stable with respect to G-convergence, a property that establishes
a link with homogenization theory, and finally, 2D numerical experiments are presented. 相似文献
12.
Theis模型、Dupuit模型等经典井流模型分析非均质含水层井流试验数据有一定的局限性,获取的参数不适合表征非均质含水层特性。而GRF模型可以获取含水层流动特性的数据。相比于Theis模型、Dupuit模型,GRF模型更能表征非均质含水层特性。以黄石东湖新村棋盘洲长江大桥的抽水试验数据为例,采用Theis模型和GRF模型计算含水层渗透系数,结合实际水文地质条件,对比分析不同方法计算的水文地质参数,并计算含水层水流维数和表观压力传导系数（Kf /Ssf）。结果表明:研究区含水层为细砂夹条带状黏土透镜体的非均质含水层,采用GRF模型计算结果更符合实际情况,渗透系数为 4.09×10?3cm/s;含水层水流维数为1.61,地下水为双线性流动状态,含水层对抽水试验的响应主要受黏土条带控制;观测井和抽水主井的Kf /Ssf呈非线性相关,进一步验证了含水层的非均质性。在非均质孔隙含水层中,应用多孔联合非稳定GRF井流试验方法不仅能确定水文地质参数,并且能丰富对含水层特性的认知。 相似文献
13.
We propose a methodology, called multilevel local–global (MLLG) upscaling, for generating accurate upscaled models of permeabilities
or transmissibilities for flow simulation on adapted grids in heterogeneous subsurface formations. The method generates an
initial adapted grid based on the given fine-scale reservoir heterogeneity and potential flow paths. It then applies local–global
(LG) upscaling for permeability or transmissibility [7], along with adaptivity, in an iterative manner. In each iteration of MLLG, the grid can be adapted where needed to reduce
flow solver and upscaling errors. The adaptivity is controlled with a flow-based indicator. The iterative process is continued
until consistency between the global solve on the adapted grid and the local solves is obtained. While each application of
LG upscaling is also an iterative process, this inner iteration generally takes only one or two iterations to converge. Furthermore,
the number of outer iterations is bounded above, and hence, the computational costs of this approach are low. We design a
new flow-based weighting of transmissibility values in LG upscaling that significantly improves the accuracy of LG and MLLG
over traditional local transmissibility calculations. For highly heterogeneous (e.g., channelized) systems, the integration
of grid adaptivity and LG upscaling is shown to consistently provide more accurate coarse-scale models for global flow, relative
to reference fine-scale results, than do existing upscaling techniques applied to uniform grids of similar densities. Another
attractive property of the integration of upscaling and adaptivity is that process dependency is strongly reduced, that is,
the approach computes accurate global flow results also for flows driven by boundary conditions different from the generic
boundary conditions used to compute the upscaled parameters. The method is demonstrated on Cartesian cell-based anisotropic
refinement (CCAR) grids, but it can be applied to other adaptation strategies for structured grids and extended to unstructured
grids. 相似文献
14.
采用颗粒离散单元法进行动力计算时,人工截断边界上需设置吸收边界条件,以防止波的反射。鉴于颗粒离散单元数值计算模型的人工边界上颗粒单元半径大小不一、边界面凸凹不平,在连续介质的黏性、黏弹性、自由场边界条件方程基础之上,推导出适用于离散介质的等效方程。在离散介质的黏性边界条件等效方程中引入微调系数,提出比值迭代法以快速确定其最优值,以实现对波的最佳吸收。采用二维颗粒离散单元计算软件PFC2D,分别建立黏性、黏弹性、自由场边界条件相关数值分析模型,探讨颗粒分布模式对黏性边界上颗粒单元半径、速度分布及比值迭代过程的影响;采用外源波动算例及经典Lamb问题算例验证黏弹性边界设置方法的正确性;通过隧洞算例检验提出的自由场边界条件设置方法的正确性。 相似文献
15.
Fluid flow during permeation grouting of fine sands with a microcement-based grout is studied by assuming that the heterogeneous medium composed of the initial granular skeleton, filtered cement and the interstitial fluid phase can be replaced by a continuous equivalent medium at the macroscopic level. Consequently, the method of Homogenization of Periodic Structures (HPS) is used to identify the effective permeability tensor evolution under the effect of cement filtration. The expression of the macroscopic permeability tensor derived through the HPS procedure is shown to depend on the permeating fluid viscosity and the geometrical arrangement of the sand grains and cement deposit within the microstructure. Numerical computations are made using various two-dimensional and three-dimensional microstructures, and the model results are confronted with grouting experiments performed on small scale columns in the laboratory. 相似文献
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17.
The impact of organic matter on the flow capacity of shale oil rocks is presumably significant, and the knowledge about the representative size is fundamental for the upscaling studies. The error of the experimentally determined permeability values is comparable with the contribution of kerogen to shale permeability, instead a 2D numerical model is employed to explore the normalised equivalent permeability and the representative elementary area (REA) of shale oil rocks in detail incorporating the effects of kerogen. The discussions on the normalised equivalent permeability and the REA are based on the statistical average and standard deviation from 1000 different runs, respectively. The inorganic permeability heterogeneity is introduced based on the assumption of a lognormal pore size distribution and the Monte Carlo sampling method. The effects of kerogen geometric characteristics are incorporated by putting forward several representative cases for comparison. The effects of the organic permeability contrast (ratio of permeability to the inorganic permeability with no heterogeneity), total organic carbon (TOC, volume fraction), inorganic permeability heterogeneity and kerogen geometric characteristics on the normalised equivalent permeability (ratio of the intrinsic equivalent permeability to inorganic permeability with no heterogeneity) and the REA are discussed comprehensively. This work can provide a better understanding of shale oil rocks at the micrometer scale. 相似文献
18.
在降雨入渗模拟中,现有研究无法准确实现复杂降雨条件下降雨边界在流量与压力两类边界之间的双向动态转换。基于饱和?非饱和渗流理论,将降雨补给流量与实际入渗流量的差值作为两类边界动态转换的判别条件,改进了单重渗透介质降雨边界动态转换控制方程,并进一步提出了双重渗透介质降雨边界处理方法及控制方程,在此基础上进行了数值试验及工程实例验证。结果表明：改进的降雨边界动态转换控制方程克服了传统降雨边界只能实现流量到压力边界单向转换的局限性,可准确实现流量边界与压力边界的双向动态实时转换;案例边坡的降雨入渗模拟结果说明了改进后降雨边界的正确性和工程适用性。 相似文献
19.
在相控约束条件下,利用熵权方法,考虑了砂层厚度、有效厚度、砂岩系数、有效厚度系数、分层系数、夹层频数、夹层分布密度、孔隙度、渗透率、渗透率变异系数、突进系数、级差、含油饱和度共13种反映储层非均质性的参数,定量计算储层非均质综合指数。该方法包括确定对象集合、指标因素集合、指标矩阵、归一化指标值、指标权重和计算综合指数等。熵权非均质综合指数算法可将数值有差异的属性参数对非均质指数的贡献进行弱化和强化,即去同存异;熵权非均质综合指数的大小能定量表征储层的非均质性。利用该方法在下寺湾油田柳洛峪区长8储层进行了应用,定量地刻画了储层的平面非均质性,取得了满意的效果。 相似文献
20.
Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method 
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下载免费PDF全文 In the numerical modeling of fluid flow in heterogeneous geological media, large material contrasts associated with complexly intersected material interfaces are challenging, not only related to mesh discretization but also for the accurate realization of the corresponding boundary constraints. To address these challenges, we developed a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method (NMM) and the Lagrange multiplier method (LMM) for modeling boundary constraints. The advantages of NMM include meshing efficiency with fixed mathematical grids (covers), the convenience of increasing the approximation precision, and the high integration precision provided by simplex integration. In this discontinuous approach, the elements intersected by material interfaces are divided into different elements and linked together using the LMM. We derive and compare different forms of LMMs and arrive at a new LMM that is efficient in terms of not requiring additional Lagrange multiplier topology, yet stringently derived by physical principles, and accurate in numerical performance. To demonstrate the accuracy and efficiency of the NMM with the developed LMM for boundary constraints, we simulate a number of verification and demonstration examples, involving a Dirichlet boundary condition and dense and intersected material interfaces. Last, we applied the developed model for modeling fluid flow in heterogeneous media with several material zones containing a fault and an opening. We show that the developed discontinuous approach is very suitable for modeling fluid flow in strongly heterogeneous media with good accuracy for large material contrasts, complex Dirichlet boundary conditions, or complexly intersected material interfaces. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献