Fractal analysis of 2-D fracture networks of geothermal reservoirs in south-western Turkey

Natural fracture patterns of producing geothermal formations in south-western Turkey are mapped at different scales. The fractal dimensions of different fracture network properties, such as spatial distribution, density, connectivity, orientation, and length are measured by different methods. Analysis of the natural fracture patterns from giga to microscales identifies the descending behavior of box-counting fractal dimension with respect to the scale. It is observed that the fracture networks represent scale-invariant properties, but fractal dimensions might notably differ when the mass dimension is measured applying different methods. Anisotropic nature of fracture networks is also included in the fractal analysis.     

Spatial Distribution,Scaling and Self-similar Behavior of Fracture Arrays in the Los Planes Fault,Baja California Sur,Mexico

We present a case of detailed analysis of fracture arrays spanning four orders of magnitude in length; all of them measured at a single natural site by acquiring images at progressively larger scales. There is a high dispersion of cumulative-length exponents, box dimensions and fracture densities. However, the fractal analysis supports the fractal nature of fracture arrays. Our data indicate the existence of an upper limit for the density parameters, as similarly reported by other authors. We prove that box dimension is in inverse relation with fracture concentration and in direct relation with fracture density. These relations are also observed in our data and additionally there is an upper limit for the box dimensions. We interpret the dispersion in our results as more fundamental than methodological problems. It represents a truncation in the complete evolution of the fracture systems because in natural cases strain initiates overprinting of previous fracture arrays. Considering that larger fractures accommodate strain more efficiently than small fractures, the generation of small fractures is inhibited in the presence of pre-existing larger fractures. Maximum values of fracture density prevent accommodating an excess of strain in a single or restricted range of scales; we claim this condition produces migration of fracturing to larger scales originating fracture scaling.     

Comparing connected structures in ensemble of random fields

Very different connectivity patterns may arise from using different simulation methods or sets of parameters, and therefore different flow properties. This paper proposes a systematic method to compare ensemble of categorical simulations from a static connectivity point of view. The differences of static connectivity cannot always be distinguished using two point statistics. In addition, multiple-point histograms only provide a statistical comparison of patterns regardless of the connectivity. Thus, we propose to characterize the static connectivity from a set of 12 indicators based on the connected components of the realizations. Some indicators describe the spatial repartition of the connected components, others their global shape or their topology through the component skeletons. We also gather all the indicators into dissimilarity values to easily compare hundreds of realizations. Heat maps and multidimensional scaling then facilitate the dissimilarity analysis. The application to a synthetic case highlights the impact of the grid size on the connectivity and the indicators. Such impact disappears when comparing samples of the realizations with the same sizes. The method is then able to rank realizations from a referring model based on their static connectivity. This application also gives rise to more practical advices. The multidimensional scaling appears as a powerful visualization tool, but it also induces dissimilarity misrepresentations: it should always be interpreted cautiously with a look at the point position confidence. The heat map displays the real dissimilarities and is more appropriate for a detailed analysis. The comparison with a multiple-point histogram method shows the benefit of the connected components: the large-scale connectivity seems better characterized by our indicators, especially the skeleton indicators.     

甘肃北山花岗岩裂隙几何学特征研究及岩石质量初探

文中以甘肃北山花岗岩中发育的构造裂隙(主要指节理)为研究对象,通过野外裂隙调查,应用传统的概率统计方法与分形几何学理论,利用Mapinfo,ArcGIS平台进行裂隙几何学参数(方位、长度、密度等)的统计、计算和裂隙网络的空间结构分析,研究花岗岩岩体中裂隙的几何学特征。并以此为基础,对甘肃北山花岗岩岩体质量优劣进行初步评价。结果表明:在10～200cm范围内,裂隙网络是分形的;5个测点裂隙网络的分维值分别是1.636,1.548,1.596,1.724,1.604。分维数D不仅能刻画岩体中结构面发育的数量,而且能反映结构面在岩体中分布的均匀程度和交切方式。因此,可以表征岩体的质量优劣,对岩体质量进行分级。按照分维所划分的岩体质量分级,北山花岗岩属于裂隙较发育、岩体质量等级一般的岩体     

Volcanic vents rooted on extension fractures and their geodynamic implications in the Ethiopian Rift

Most of the extension fractures located in the Ethiopian rift are related to rift dynamics, and they have consistently similar orientations for hundreds of kilometers. The orientation of extension fracture gives the local extension direction which is perpendicular to its horns (end segments of an extension fracture). We have established clear geometrical relationships between tectonics and volcanism in the Main Ethiopian Rift by interpreting high-resolution images obtained from Landsat-TM and SPOT satellites and by quantitatively analyzing the geometry of extension fractures, elongated vents and linear volcanic clusters. Applying the relationships obtained, we show that extension fractures in the rift served as channels for magma rising to the surface, and that extension fractures underlie most of the elongated volcanic vents and linear volcanic clusters. The geometry of extension fractures beneath volcanic edifices can be deduced from the shape of elongated vents and pattern of linear volcanic clusters rooted on them. Utilizing the orientations of extension fractures directly observed and those inferred from elongated volcanic vents and linear clusters, we found that the extension direction of the Main Ethiopian Rift is northwest–southeast and that the direction has been rotated clockwise for about 20° in the time interval 2.83 to 0.023 Ma. The Recent axis of rift opening is oriented N40° and located closer to the southeastern escarpment giving an asymmetric geometry to the Main Ethiopian Rift (MER).     

Numerical evaluation of the effect of fracture network connectivity in naturally fractured shale based on FSD model

In this paper, the effect of pre-existing discrete fracture network (DFN) connectivity on hydraulic fracturing is numerically investigated in a rock mass subjected to in-situ stress. The simulation results show that DFN connectivity has a significant influence on the hydraulic fracture (HF) & DFN interaction and hydraulic fracturing effectiveness, which can be characterized by the total interaction area, stimulated DFN length, stimulated HF length, leak-off ratio, and stimulated total length. In addition, even at the same fluid injection rate, simulation models exhibit different responses that are strongly affected by the DFN connectivity. At a low injection rate, total interaction area decreases with increasing DFN connectivity; at a high injection rate, total interaction area increases with the increase of DFN connectivity. However, for any injection rate, the stimulated DFN length increases and stimulated HF length decreases with the increase of connectivity. Generally, this work shows that the DFN connectivity plays a crucial role in the interaction between hydraulic fractures, the pre-existing natural fractures and hydraulic fracturing effectiveness; in return, these three factors affect treating pressure, created microseismicity and corresponding stimulated volume. This work strongly relates to the production technology and the evaluation of hydraulic fracturing effectiveness. It is helpful for the optimization of hydraulic fracturing simulations in naturally fractured formations.     

Laboratory measurement of hydrodynamic saline dispersion within a micro-fracture network induced in granite

We report the first measurements of hydrodynamic dispersion in a microfractured granite using a combination of novel techniques. A fracture network was induced in a cylindrical plug of Ailsa Craig micro-granite by thermal stressing, to produce an isotropic network of fractures with an average aperture of  0.3 μm, a density of approximately 4 × 10⁴ fractures/mm³ and a permeability of 5.5 × 10^− 17 m². After saturating the cores with 0.01 M NaCl solution a step in the concentration profile to 1 M was advected into the plug at flow rates of 0.07 to 2.13 cm³ h^− 1. The longitudinal electrical impedance of the plug was measured continuously as the solute front advected through its length until the plug was saturated with the concentrated electrolyte. Analysis of the impedance versus time relationships allows the derivation of the longitudinal dispersion coefficient, D_L, and hydrodynamic retardation, R_H. The Peclet number–dispersion relationship for the micro-fracture network is very similar to that predicted for other, radically different, fracture networks. Thus dispersion may be more dependent on fracture connectivity and length than fracture density and display a relationship similar to that shown by particle beds and clastic sandstones. The high retardation values observed (2.2–4.9) reflect flow behaviour within a fracture network with a proportion of ‘blind’ sections, and demonstrates how such networks can slow the advance of conservative solute components.     

Surficial fractures in the Navajo sandstone,south-western USA: the roles of thermal cycles,rainstorms, granular disintegration,and iterative cracking

Deep (> 5 m) sheeting fractures in the Navajo sandstone are evident at numerous sites in southern Utah and derive from tectonic stresses. Strong diurnal thermal cycles are, however, the likely triggers for shallow (< 0.3 m) sheeting fractures. Data from subsurface thermal sensors reveal that large temperature differences between sensors at 2 and 15 cm depth on clear summer afternoons are as great as those that trigger sheeting fractures in exposed California granite. Extensive polygonal patterns in the Navajo sandstone are composed of surface-perpendicular fractures and were produced by contractile stresses. Numerous studies have shown that porewater diminishes the tensile strength of sandstone. Based on our thermal records, we propose that cooling during monsoonal rainstorms triggers polygonal fracturing of temporarily weakened rock. On steep outcrops, polygonal patterns are rectilinear and orthogonal, with T-vertices. Lower-angle slopes host hexagonal patterns (defined by the dominance of Y-vertices). Intermediate patterns with rectangles and hexagons of similar scale are common. We posit that outcropping fractures are advancing downward by iterative steps, and that hexagons on sandstone surfaces (like prismatic columns of basalt) have evolved from ancestral orthogonal polygons of similar scale. In lava flows, fractures elongate intermittently as they follow a steep thermal gradient (the source of stress) as it rapidly moves through the rock mass. In our model, a steep, surficial thermal gradient descends through unfractured sandstone, but at the slow pace of granular disintegration. Through time, as the friable rock on stable slopes erodes, iterative cracking advances into new space. Hexagonal patterns form as new fractures, imperfectly guided by the older ones, propagate in new directions, and vertices drift into a configuration that minimizes the ratio of fracture length to polygon area. © 2020 John Wiley & Sons, Ltd.     

基于叠前方位振幅的大港—埕海地区奥陶系风化壳裂缝储层的叠前预测

P波通过裂缝地层传播时,其响应会随着地面观测方位的变化而变化,表现出明显的方位各向异性.这种随方位变化的裂缝响应信息(如振幅等)广泛存在于叠前方位一偏移距二维空间域中,检测此域中的裂缝响应,通过椭圆拟合的方法识别各向异性的存在,进而计算裂缝的方向——椭圆长轴的方向,和裂缝密度——椭圆长轴与短轴的比.本文研究出了一种基于常规叠前地震反射振幅来检测裂缝的三维叠前裂缝储层预测方法.它采用面元组合的方法扩大方位角和偏移距范围;采用多级数据控制技术获取所需的信息;采用稳妥的技术步骤来预测.通过大港油田实际工区的应用,结果表明本文研究出的方法技术应用效果好、精度高、经济实用.     

Experimental and theoretical investigations of drainage in horizontal rough-walled fractures with different correlation structures

Experiments on the immiscible displacement of water by air were performed in two horizontal artificial open rough-walled fractures with different correlation structures. The aperture field of the first fracture has a Gaussian variogram with a finite correlation length, while that of the second one has a power-law variogram, for which no finite correlation length can be assigned. We simulated the displacement process using an invasion percolation model, which takes the in-plane curvature of the interface between water and air into account. The correlation structure of the aperture field has no effect on the irregularity of the shape of the air clusters. However, the correlation structure in combination with the in-plane curvature influences the density of the air clusters and thus has an impact on characteristic properties of the flow. We analyze the model parameters and properties with respect to the fracture properties. The stochastic average of the air clusters for models with different curvature numbers and fields with different correlation lengths is then calculated in order to analyze their influence on continuum approach models.     

Geologic heterogeneity recognition using discrete wavelet transformation for subsurface flow solute transport simulations

Subsurface flow and solute transport simulations are performed using different scenarios of permeability fields generated from the sequential Gaussian simulation method (SGS), the multiple-point FILTERSIM algorithm and a new multiple-point wavelet-based simulation method (SWS). The SWS method is a multiple-point pattern-based simulation method which uses discrete wavelet transformation for the representation of geologic heterogeneity. For pattern-based simulation, patterns are generated by scanning a training image with a spatial template. The pattern classifications were performed after reducing the dimension of patterns by wavelet decomposition at the suitable scale and by taking only scaling components of wavelet decomposed patterns. The simulation is performed in a sequential manner by finding the best-matched class corresponding to the conditioning data and by randomly sampling a pattern from the best-matched class. The developed method is compared with two other multi-point simulation algorithms, FLTERSIM and SIMPAT. The comparative results revealed that the proposed method is computationally faster than the other two methods while the simulation maps are comparable. Numerical simulations of two flow problems are performed using SGS, SWS and FILTERSIM realizations. The numerical results show a superiority of the SWS method over SGS and FILTERSIM in terms of reproduction of the reference images main features, and agreement with flow and transport results obtained on reference images.     

成像测井解释模式在基岩油气藏裂缝性储层的应用研究

基岩油气藏裂缝性储层具有复杂的储集空间和储层非均质性,为了实现对基岩油气藏储层的精细评价,以地层微电阻率扫描成像测井和井周声波成像测井资料为核心,通过岩心资料标定,结合录井、常规测井、试油、地质等实际资料,系统建立了基岩油气藏变质岩储层的成像测井解释模式.根据成像测井模式的识别实现了对基岩油气藏特征的认识、准确的裂缝分析和现今地应力场分析.分析结果表明,研究区基底变质岩地层中基本以基岩内幕油气藏为主;裂缝以中高角度缝、网状裂缝为主,其主要走向与井旁断层走向大致平行,属纵裂缝;裂缝主要发育在东西两侧靠近断层、近源的构造陡坡上;现今最大水平主应力方向主要呈NE-SW和NEE-SWW.成像测井解释结果与地质情况吻合较好.     

Influence of source region properties on scaling relations forM<0 events

Excavation induced seismic events with moment magnitudesM<0 are examined in an attempt to determine the role geology, excavation geometry, and stress have on scaling relations. Correlations are established based on accurate measurements of excavation geometry and methodology, stress regime, rock mass structure, local tectonics, and seismic locations. Scaling relations incorporated seismic moments and source radii obtained by spectral analysis, accounting for source, propagation, and site effects, and using Madariaga's dynamic circular fault model. Observations suggest that the interaction of stresses with pre-existing fractures, fracture complexity and depth of events are the main factors influencing source characteristics and scaling behaviour. Self-similar relationships were found for events at similar depths or for weakly structured rock masses with reduced clamping stresses, whereas a non-similar behaviour was found for events with increasing depth or for heavily fractured zones under stress confinement. Additionally, the scaling behaviour for combined data sets tended to mask the non-similar trends. Overall, depth and fracture complexity, initially thought as second order effects, appear to significantly influence source characteristics of seismic events withM<0 and consequently favour a non-similar earthquake generation process.     

Coding random self-similar river networks and calculating geometric distances: 1. General methodology / Codage de réseaux hydrographiques auto-similaires aléatoires et calcul de distances géométriques: 1. Méthodologie générale

Abstract

This study proposes a preliminary method for coding random self-similar river networks as a series of numbers, and investigates the corresponding algorithm that calculates the geometric distances from the code series. The coding method, generating random self-similar patterns with various probabilities of particular pattern links, and transferring the pattern into numerical code series, is proposed, based on the wide range of stochastic characteristics of natural patterns. The heredity of self-similarity and the connecting relationships inside the generated pattern are discussed. Finally, the algorithm to calculate the geometric distances of the generated pattern are developed.     

Fracture patterns at lava–ice contacts on Kokostick Butte, OR, and Mazama Ridge, Mount Rainier, WA: Implications for flow emplacement and cooling histories

Cooling lava commonly develop polygonal joints that form equant hexagonal columns. Such fractures are formed by thermal contraction resulting in an isotropic tensional stress regime. However, certain linear cooling fracture patterns observed at some lava–ice contacts do not appear to fit the model for formation of cooling fractures and columns because of their preferred orientations. These fracture types include sheet-like (ladder-like rectangular fracture pattern), intermediate (pseudo-aligned individual column-bounding fractures), and pseudopillow (straight to arcuate fractures with perpendicular secondary fractures caused by water infiltration) fractures that form the edges of multiple columns along a single linear fracture. Despite the relatively common occurrence of these types of fractures at lava–ice contacts, their significance and mode of formation have not been fully explored. This study investigates the stress regimes responsible for producing these unique fractures and their significance for interpreting cooling histories at lava–ice contacts.Data was collected at Kokostick Butte dacite flow at South Sister, OR, and Mazama Ridge andesite flow at Mount Rainier, WA. Both of these lava flows have been interpreted as being emplaced into contact with ice and linear fracture types have been observed on their ice-contacted margins. Two different mechanisms are proposed for the formation of linear fracture networks. One possible mechanism for the formation of linear fracture patterns is marginal bulging. Melting of confining ice walls will create voids into which flowing lava can deform resulting in margin-parallel tension causing margin-perpendicular fractures. If viewed from the ice-wall, these fractures would be steeply dipping, linear fractures. Another possible mechanism for the formation of linear fracture types is gravitational settling. Pure shear during compression and settling can result in a tensional environment with similar consequences as marginal inflation. In addition to this, horizontally propagating cooling fractures will be directly influenced by viscous strain caused by the settling of the flow. This would cause preferential opening of fractures horizontally, resulting in vertically oriented fractures.It is important to note that the proposed model for the formation of linear fractures is dependent on contact with and confinement by glacial ice. The influence of flow or movement on cooling fracture patterns has not been extensively discussed in previous modeling of cooling fractures. Rapid cooling of lava by the interaction with water and ice will increase the ability to the capture and preserve perturbations in the stress regime.     

逾渗与岩石破裂的计算机模拟研究

用计算机模拟方法研究了岩石破裂的逾渗模型，给出了在微裂隙随机分布情况下破裂集团的分布图象、破裂集团的大小分布规律、总破裂集团数、集团平均大小、ｂ值、逾渗分维Ｄ及临界情形。所得结果与其他模型和实验基本一致，表明通渗模型是描述岩石破裂扩展演化过程的一种较合适的模型。还发现了岩石破裂过程存在的两个转折点，深入研究这两个转折点附近岩石的宏观性质，可为探索地震孕育演化过程的前兆性质提供依据。     

Hydraulic tomography for detecting fracture zone connectivity

Fracture zones and their connectivity in geologic media are of great importance to ground water resources management as well as ground water contamination prevention and remediation. In this paper, we applied a recently developed hydraulic tomography (HT) technique and an analysis algorithm (sequential successive linear estimator) to synthetic fractured media. The application aims to explore the potential utility of the technique and the algorithm for characterizing fracture zone distribution and their connectivity. Results of this investigation showed that using HT with a limited number of wells, the fracture zone distribution and its connectivity (general pattern) can be mapped satisfactorily although estimated hydraulic property fields are smooth. As the number of wells and monitoring ports increases, the fracture zone distribution and connectivity become vivid and the estimated hydraulic properties approach true values. We hope that the success of this application may promote the development and application of the new generations of technology (i.e., hydraulic, tracer, pneumatic tomographic surveys) for mapping fractures and other features in geologic media.     

A study on relation between acoustic emission and characteristic displacement field on the sample with multi en echelon structures——The theoretic and experimental explorations of strain gap

Introduction ZHOU, et al (1994) collected and investigated periods of level deformation data from 1954 to 1992, and gained sequence of a picture per year (or several years) that vividly showed the varia-tion of the deformation field of Tangshan earthquake source area around the Tangshan diamond block which was 21.3. They indicated that the Tangshan earthquake source area showed de-formation gap and the hard solid characteristic of relative stabilization or relative closedown. In the investig…     

Topographic characteristics of laboratory induced shear fractures

The topography of laboratory induced shear fracture surfaces of Westerly granite was studied. Three types of fracture surfaces were examined: (1) a fresh fracture from the shear failure of an intact sample under polyaxial loading (₂ = 40 MPa > ₃ = 15 MPa); (2) a shear fracture subjected to frictional sliding of 100 m under polyaxial loading; (3) a shear fracture subjected to frictional sliding of 800 m under conventional triaxial loading (₁ > ₂ = ₃ = 40 MPa). Both sliding distances are within the range of the grain size of Westerly granite. The results are represented by a power spectral method.Similar to the power spectra from natural rock surfaces, the power spectra of the induced shear fracture surfaces fall off about 2 orders of magnitude per decade increase in spatial frequency. No corner frequency exists in the power spectra over a spatial frequency range from that corresponding to the profile length to the Nyquist frequency. A slope break in the power spectrum was identified, however. It separates a steeper low frequency segment from a less steep high frequency segment. The spatial frequency at the slope break corresponds to a wavelength of several hundred microns which is on the scale of the microcracking and contact breaking on the fractures. Upon re-examining power spectra of natural fault traces and fault surfaces obtained in previous studies, we noted similar slope breaks. We suggest that this slope break may have significant implications in the scaling problem. Both the induced fracture surfaces and natural faults exhibit topographic characteristics different from those of sawcut surfaces, which have been widely used in laboratory rock friction experiments. In the present study, we observed that even a small amount of sliding (less than a grain size) already results in significant mismatches between the paired sliding surfaces in the direction normal to sliding.