Geometric parameters and REV of a crack network in soil

Cracks are common in natural and engineered soils and provide preferential pathways for water infiltration into the soil. Statistical properties of crack geometries are important inputs for analyzing preferential flows in discrete random crack networks. This paper reports the outcome of a field study conducted on a compacted, cracked soil ground at a steady moisture condition. The objectives of the field study were to investigate the crack patterns and probability distributions of the geometric parameters of cracks and to determine the representative elementary volume (REV) of the crack network. The desiccation cracks at the survey site formed an inter-connected columnar structure. The traces of the cracks on the soil surface formed a primary structure consisting of inter-connected crack polygons and a secondary structure comprising of isolated cracks. The locations and orientations of the desiccation cracks followed a uniform distribution, differing from the distribution of fracture sets often observed in fractured rocks. The lengths and apertures of the cracks followed a lognormal distribution as expected. The REV size for the cracked soil was found to be approximately five times the mean crack length, above which the variation in crack porosity in relation to domain size was negligible.     

Seepage simulation using pipe network flow model in a discrete element system

The pipe network flow model can simulate the seepage process with DEM conveniently because of its simple algorithm. However, whether it can recover the correct seepage process has not been verified. In this paper, the equation to update the fluid pressure is rebuilt according to the flow conservation. Through the steady seepage simulation, this algorithm is verified to be able to recover Darcy’s law, and the equation to calibrate the aperture according to macro permeability is derived. Furthermore, the modified algorithm is used to simulate the unsteady seepage process, and the results show good agreement with the analytical solutions.     

Secular change of permeability in the fracture zone near the Nojima fault estimated using strain changes due to water injection experiments

Water injection experiments were performed in 1997, 2000 and 2003 at the 1800 m borehole near the fracture zone of the 1995 Hyogo-ken Nanbu earthquake. During these experiments, a contraction of about 10^− 8–10^− 7 was observed with three-component strainmeters at a bottom of the 800 m borehole, 70 m southwest of the 1800 m borehole. We estimated hydraulic properties of the fracture zone near the Nojima fault by using the strain data to investigate a healing of the fault during the postseismic stage. We calculated pore pressure changes due to the water injection using Darcy's equation and obtained strain changes due to the pore pressure changes as elastic deformations of the crust. The calculated strain changes have a nearly agreement with the observed strain changes. Hydraulic conductivity in 1997, 2000 and 2003 was determined to be 0.9 ± 0.2 × 10^− 6, 0.8 ± 0.2 × 10^− 6 and 0.4 ± 0.1 × 10^− 6 m/s, respectively. The reduced hydraulic conductivities in 2000 and 2003 suggest that the fractures had been healing.     

随机与确定耦合的裂隙岩体结构面三维网络模拟

离散裂隙随机网络模型中结构面的分布特征仅代表其统计规律,并非地质成因、结构模式、构造形迹的客观反映,以致后续力学计算及渗流模拟结果可信度偏低。针对国家高放废物处置库甘肃北山预选区出露良好的花岗岩体,基于实测结构面统计规律、内在成生关系及水力联系,在前期纯随机模型关键部位修正特征参数,并融入人工辨识的确定结构模式而构建“随机-确定”耦合模型。图形和渗流模拟两种定量检验结果表明：耦合模型结构面数量更接近客观实际,模型准确度提升约48.8%;耦合模型渗流路径与流量较之前更显客观真实,模拟结果与试验数据的接近程度比随机模型大约1/3。另外,不同孔位渗流结果显示：相比于随机结构面,确定性结构面对区域渗流控制作用更加明显,在渗流模拟中扮演更为重要角色。此耦合模型有益于拓宽结构面网络模拟的发展方向。     

Summary of Numerical Models for Predicting Productivity of Shale Gas Horizontal Wells

Shale gas production has gradually achieved high and stable output, which makes it possible to make up for the shortage of oil and gas energy as an alternative energy source. Shale reservoir is compact, with well-developed nano-pore, and has the characteristics of adsorption and desorption, diffusion and slippage. At the same time, there are a large number of natural cracks, bedding and foliation. Hydraulic fractures expand irregularly after volume fracturing in horizontal wells. The whole system has multi-field coupling and cross-scale flow effects. Productivity prediction of shale gas is difficult and uncertain, which restricts the efficient development and evaluation of shale reservoirs. In this paper, the development status of productivity numerical models for shale gas horizontal wells is reviewed in consideration of the multi-scale transport characteristics of shale gas. These models include dual media capacity models, multiple media capacity models, and complex seam productivity models. It is considered that the dual medium and multi-media productivity models weaken the large permeable flow area and channel provided by the complex seam network system after shale reservoir lamination, and cannot comprehensively characterize the full-scale coupled transport characteristics of shale gas. The numerical model for productivity prediction of shale gas horizontal wells based on complex fracture network provides a multi-scale flow embedded fracture network system, which solves the problem of systematic flow without losing the ability to accurately characterize each scale flow. It is necessary to obtain the complex fracture network morphological characterization which conforms to reservoir geological characteristics, rock mechanical behavior and fluid-solid coupling mechanism. Fracture network characterization is the key to the productivity prediction of shale gas horizontal wells.     

X-ray CT and hydraulic evidence for a relationship between fracture conductivity and adjacent matrix porosity

Multi-phase flow in fractured rocks plays an important role in any hydrocarbon recovery process, be it for environmental remediation or natural oil and gas extraction. Fractures may form the primary production conduits, and the mass transport at the fracture interfaces with the matrix determines the effectiveness of extraction processes. This paper presents specific evidence for a relationship between fracture apertures and the porosity of the adjoining perpendicular layers in Berea sandstone samples. Measurements of fracture apertures were done with high-resolution Micro-Computed Tomography (MCT) with a voxel resolution of about 0.05 mm in three dimensions. Multi-phase fluid flow experiments were done using a medical CT scanner with a voxel resolution of about 1.00 × 0.25 × 0.25 mm. MCT evidence shows a correlation between aperture and the porosity of the intersected layers. The comparison was made by generating two-dimensional maps of matrix porosity and CT values adjacent to the fracture and of the corresponding fracture apertures. High-porosity layers are lined up with large fracture apertures. Multi-phase fluid experiments provided hydraulic evidence that the high-porosity layers have high permeability. Oil injection into a water-saturated sample was tracked by a sequence of transverse scans near the downstream tip of a fracture. The hydraulic evidence from the two-phase flow experiments also confirms high permeability in fracture strips adjacent to high-porosity and high-permeability layers. The reasons for the relationship between fracture aperture and the properties of the adjacent layers are not fully understood. Some explanation for the physical and hydraulic observations rests in the method of fracturing, fracture propagation, and the lithological characteristics of the rock.     

The use of topology in fracture network characterization

In two-dimensions, a fracture network consist of a system of branches and nodes that can be used to define both geometrical features, such as length and orientation, and the relationship between elements of the network – topology. Branch lengths are preferred to trace lengths as they can be uniquely defined, have less censoring and are more clustered around a mean value. Many important properties of networks are more related to topology than geometry.The proportions of isolated (I), abutting (Y) and crossing (X) nodes provide a basis for describing the topology that can be easily applied, even with limited access to the network as a whole. Node counting also provides an unbiased estimate of frequency and can be used in conjunction with fracture intensity to estimate the characteristic length and dimensionless intensity of the fractures. The nodes can be used to classify branches into three types – those with two I-nodes, one I-node and no I-nodes (or two connected nodes). The average number of connections per branch provides a measure of connectivity that is almost completely independent of the topology. We briefly discuss the extension of topological concepts to 3-dimensions.     

利用岩石结构面网络模拟计算岩体带宽连通率及岩体强度参数

岩体中存在的结构面对岩体的力学特性有很大的影响，研究岩体的强度参数，必须弄清结构面在岩体中的分布情况，了解结构面对岩体强度的影响程度。岩体结构面的研究起初是靠人工进行现场测量，不仅耗费人力物力，而且获取的数据代表性不强，还略显粗糙。在计算机应用飞速发展的背景下，利用计算机进行结构面网络模拟的方法浮出水面，并成为现在国内外研究结构面的主要方法之一。此方法在众多的科学研究以及工程建筑领域得到了应用，并在应用之中得到了不断的完善和发展，取得了一定的成果。文章在对计算机结构面网络模拟原理分析的基础上，主要讨论了利用结构面网络模拟计算岩体连通率和岩体强度的方法，其中着重研究了带宽投影法的原理及带宽连通率的计算过程，介绍了利用带宽连通率计算岩体强度参数的方法。利用西北某水电站实际研究中应用此方法的工程实例对成果做了评价，成果与实际情况大体相符。对结构面网络模拟方法做了综合评价：简单易行，省时省力，效果良好。     

Permeability evolution in fractured coal: The roles of fracture geometry and water-content

We report laboratory experiments that investigate the permeability evolution of an anthracite coal as a function of applied stress and pore pressure at room temperature as an analog to other coal types. Experiments are conducted on 2.5 cm diameter, 2.5-5 cm long cylindrical samples at confining stresses of 6 to 12 MPa. Permeability and sorption characteristics are measured by pulse transient methods, together with axial and volumetric strains for both inert (helium (He)) and strongly adsorbing (methane (CH₄) and carbon dioxide (CO₂)) gases. To explore the interaction of swelling and fracture geometry we measure the evolution of mechanical and transport characteristics for three separate geometries — sample A containing multiple small embedded fractures, sample B containing a single longitudinal through-going fracture and sample C containing a single radial through-going fracture. Experiments are conducted at constant total stress and with varied pore pressure — increases in pore pressure represent concomitant (but not necessarily equivalent) decreases in effective stress. For the samples with embedded fractures (A and C) the permeability first decreases with an increase in pressure (due to swelling and fracture constraint) and then increases near-linearly (due to the over-riding influence of effective stresses). Conversely, this turnaround in permeability from decreasing to increasing with increasing pore pressure is absent in the discretely fractured sample (B) — the influence of the constraint of the connecting fracture bridges in limiting fracture deformation is importantly absent as supported by theoretical considerations. Under water saturated conditions, the initial permeabilities to all gases are nearly two orders of magnitude lower than for dry coal and permeabilities increase with increasing pore pressure for all samples and at all gas pressures. We also find that the sorption capacities and swelling strains are significantly reduced for water saturated samples — maybe identifying the lack of swelling as the primary reason for the lack of permeability decrease. Finally, we report the weakening effects of gas sorption on the strength of coal samples by loading the cores to failure. Results surprisingly show that the strength of the intact coal (sample A) is smaller than that of the axially fractured coal (sample B) due to the extended duration of exposure to CH₄ and CO₂. Average post-failure particle size for the weakest intact sample (A) is found to be three times larger than that of the sample B, based on the sieve analyses from the samples after failure. We observe that fracture network geometry and saturation state exert important influences on the permeability evolution and strength of coal under in situ conditions.     

Subcritical compaction and yielding of granular quartz sand

Cylindrical samples of water-saturated, initially loose, St. Peter quartz sand were consolidated using triaxial deformation apparatus at room temperature, constant fluid pressure (12.5 MPa), and elevated confining pressures (up to 262.5 MPa). The samples were deformed along four loading paths: (1) hydrostatic stressing tests in which confining pressure was monotonically increased; (2) hydrostatic stress cycling similar to (1) except that effective pressure was periodically decreased to initial conditions; (3) triaxial deformation at constant effective pressure in which differential stress was applied after raising effective pressure to an elevated level; and (4) triaxial stress cycling similar to (3) except that the axial differential stress was periodically decreased to zero. Hydrostatic stressing at a constant rate results in a complex nonlinear consolidation response. At low pressures, large strains occur without significant acoustic emission (AE) activity. With increased pressure, the stress versus strain curve becomes quasi-linear with a corresponding nonlinear increase in AE rates. At elevated pressures, macroscopic yielding is marked by the onset of large strains, high AE rates, and significant grain failure. Stress cycling experiments show that measurable inelastic strain occurs at all stages of hydrostatic loading. The reload portions of stress cycles are characterized by a poro-elastic response and lower AE rates than during constant rate hydrostatic stressing. As the stress nears and exceeds the level that was applied during previous loading cycles, strain and AE rates increase in a manner consistent with yielding. Triaxial stressing cycles achieve greater consolidation and AE rates than hydrostatic loading at similar mean stress levels. By comparing our results with previously published studies, we construct a three-component model to describe elastic and inelastic compaction of granular sand. This model involves acoustically silent grain rearrangement that contributes significant inelastic strain at low pressures, poro-elastic (Hertzian) deformation at all pressures, and inelastic strain related to granular cracking and particle failure which increases in significance at greater pressures.     

Fault zone characteristics,fracture systems and permeability implications of Middle Triassic Muschelkalk in Southwest Germany

Fault zone structure and lithology affect permeability of Triassic Muschelkalk limestone-marl-alternations in Southwest Germany, a region characterized by a complex tectonic history. Field studies of eight fault zones provide insights into fracture system parameters (orientation, density, aperture, connectivity, vertical extension) within fault zone units (fault core, damage zone). Results show decreasing fracture lengths with distances to the fault cores in well-developed damage zones. Fracture connectivity at fracture tips is enhanced in proximity to the slip surfaces, particularly caused by shorter fractures. Different mechanical properties of limestone and marl layers obviously affect fracture propagation and thus fracture system connectivity and permeability. Fracture apertures are largest parallel and subparallel to fault zones and prominent regional structures (e.g., Upper Rhine Graben) leading to enhanced fracture-induced permeabilities. Mineralized fractures and mineralizations in fault cores indicate past fluid flow. Permeability is increased by the development of hydraulically active pathways across several beds (non-stratabound fractures) to a higher degree than by the formation of fractures interconnected at fracture tips. We conclude that there is an increase of interconnected fractures and fracture densities in proximity to the fault cores. This is particularly clear in more homogenous rocks. The results help to better understand permeability in Muschelkalk rocks.     

High resolution facies architecture and digital outcrop modeling of the Sandakan formation sandstone reservoir,Borneo:Implications for reservoir characterization and flow simulation

Advances in photogrammetry have eased the acquisition of high-resolution digital information from outcrops, enabling faster, non-destructive data capturing and improved reservoir modeling. Geocellular models for flow dynamics with in the virtual outcrop in siliciclastic deposits at different sets of sandstone facies architecture remain, however, a challenge. Digital maps of bedding, lithological contrast, spatial-temporal variations of bedding and permeability characteristics make it more easy to understand flow tortuosity in a particular architecture. An ability to precisely model these properties can improve reservoir characterization and flow modeling at different scales. Here we demonstrate the construction of realistic 2 D sandstone facies based models for a pragmatic simulation of flow dynamics using a combination of digital point clouds dataset acquired from LiDAR and field investigation of the Sandakan Formation, Sabah, Borneo.Additionally, we present methods for enhancing the accuracy of outcrop digital datasets for producing high resolution flow simulation. A well-exposed outcrop from the Sandakan Formation, Sabah, northwest Borneo having a lateral extent of 750 m was chosen in order to implement our research approach. Sandstone facies and its connectivity are well constrained by outcrop observations, data from air-permeability measurements, bilinear interpolation of permeability, grid construction and water vector analysis for flow dynamics.These proportions were then enumerated in terms of static digital outcrop model(DOM) and facies model based on sandstone facies bedding characteristics. Flow simulation of water vector analysis through each of the four sandstone facies types show persistent spatial correlation of permeability that align with either cross-bedded orientation or straight with more dispersion high quality sandstone(porosity 21.25%-41.2%and permeability 1265.20-5986.25 mD) and moderate quality sandstone(porosity 10.44%-28.75% and permeability 21.44-1023.33 mD). Whereas, in more heterolithic sandstone(wavy-to flaser-bedded and bioturbated sandstone), lateral variations in permeability show spatially non-correlated patterns over centimeters to tens of meters with mostly of low quality sandstone(porosity 3.4%-12.31% and permeability < 1 mD to 3.21 mD). These variations reflect the lateral juxtaposition in flow dynamics. It has also been resulted that the vertical connectivity and heterogeneities in terms of flow are mostly pragmatic due to the interconnected sandstone rather than the quality of sandstone.     

Hydromechanical properties and alteration of natural fracture surfaces in the Soultz granite (Bas-Rhin, France)

Natural fractures are characterized by rough surfaces and complex fluid flows. A large distribution of apertures (residual voids) within their walls and the presence of contact points (in situ normal loads) produce heterogeneous flows (channeling). The resulting permeabilities, porosities or fluid–rock exchange surfaces cannot be realistically modeled by parallel and smooth plate models. Four natural fractures are sampled at different depths and degrees of alteration in the Soultz sandstone and granite (EPS1 drillhole, Soultz-sous-Forêts, Bas-Rhin, France). The fracture surfaces are measured with mechanical profilometry and maps of asperity heights (XYZ). Resulting local apertures (XYe) are then calculated. A statistical study of the surface profiles (XZ) show that the fractures are more or less rough and tortuous according to the types of alteration. Altered samples are characterized by smoother surfaces of fractures. Such differences imply that (i) the average fracture aperture is not representative for the whole fracture and that (ii) the different local apertures should be integrated in hydraulic and mechanical models. A hydraulic model (finite difference calculations) of fluid flow, taking into account the elastic closure (Hertz contact theory) of fractures with depth, is used. Maps of contact points and relative local loads within the fracture planes are compared to flow maps. They show different channeling of fluid flows. Strongly altered fractures are characterized by homogeneous fluxes despite the presence of numerous contact zones during the closure of fracture. By contrast, fresh fractures develop, increasing fluid flow channels with depth.Fracture closure (increasing normal stress) does not systematically increase the channeling of fluid flow. There is evidence for a general smoothing out of the irregularities of the fracture walls due to precipitation of secondary minerals, indicating that the cubic law can be commonly valid, also at great crustal depth but this validity depends on the degree of fracture alteration. Mineralogical and geochemical observations, thus, should be taken into account to perform more accurate permeability calculations and models of fluid circulation in fracture networks.     

近直立煤储层裂隙系统及优势渗流通道特征研究

为系统研究近直立煤储层裂隙系统发育特征,利用新疆库拜煤田中部近直立煤储层地表出露良好和生产矿井煤储层裂隙便于观测的有利条件,采用地表高精度构造裂隙填图和矿井煤储层裂隙观测技术,结合实验室扫描电镜和偏光显微镜观测方法,研究了近直立煤储层宏观和微观裂隙系统的发育特征。研究发现该区层面裂隙和外生裂隙延伸长、宽度大,是煤层气运移的优势渗流通道。同时分析了不同埋深条件下地应力场状态,阐明了研究区3种优势渗流通道分布特征为:(1)670 m以浅,优势渗流方向为NNW、NNE向;(2)670 m左右,优势渗流方向为近EW、NNW和NNE向;(3)670 m以深,优势渗流方向为近EW向。解释了层面裂隙、外生裂隙、内生裂隙和微裂隙的形成原因,揭示了渗流通道的形成模式,为研究区煤层气的勘探开发提供了地质依据。     

结构面三维网络模拟在岩体质量评价中的应用

岩石质量指标RQD是反映工程岩体完整程度的定量参数,广泛用于水利水电、矿山、地下工程、交通工程等岩体稳定性评价,但是传统的RQD定义不能满足实际工程岩体各相异性要求。针对贵州黔中水利枢纽工程拱坝坝基岩体结构面特征,利用Monte-Carlo法在计算机上生成岩体节理三维网络图,建立了模拟计算不同阀值t的岩石质量指标RQDt的计算机模拟方法。该方法能较真实客观地描述岩石质量。     

Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: Method and application to the field data from Sellafield,UK

A numerical procedure to determine the equivalent permeability tensor of a fractured rock is presented, using a stochastic REV (Representative Elementary Volume) concept that uses multiple realizations of stochastic DFN (Discrete Fracture Network) models. Ten square DFN models are generated using the Monte Carlo simulations of the fracture system based on the data obtained from a site characterization program at Sellafield, Cumbria, UK. Smaller models with varying sizes of from 0.25 m×0.25 m to 10 m×10 m are extracted from the generated DFN models and are used as two-dimensional geometrical models for calculation of equivalent permeability tensor. The DFN models are also rotated in 30º intervals to evaluate the tensor characteristics of calculated directional permeability. Results show that the variance of the calculated permeability values decreases significantly as the side lengths of the DFN models increase, which justifies the existence of a REV. The REV side length found in this analysis is about 5 m and 8 m with 20% and 10% acceptable variations, respectively. The calculated directional permeability values at the REV size have tensor characteristic that is confirmed by a close approximation of an ellipse in a polar plot of the reciprocal of square roots of the directional permeability.

Modeling the 3D crack network and anisotropic permeability of saturated cracked soil

Cracks on a natural soil surface provide preferential pathways for water infiltration and contaminant solute transport. Before the mechanical property and permeability of cracked soil can be studied, a crack network model must first be established. Based on statistical analysis of crack geometry from field observations, a new method of representing a 3D crack network was developed. A horizontal plane of a crack network was derived using the Voronoi diagram. Each vertical crack was idealized as an inverted triangular prism. The 3D permeability tensor was determined by modeling the water flow through the crack network. A computer program was developed to generate a 3D crack network automatically and compute the permeability tensor of cracked soil at different depths. The model was verified by comparing the measured permeability and computed permeability of cracked soil. The results showed that the computed permeability was consistent with the measured permeability.