An Algorithm for Generating Rock Fracture Patterns: Mathematical Analysis

A statistical, rule-based algorithm for generating fracture patterns similar to those observed in Limestone is presented. For each fracture set, initial seed points are randomly positioned within the modelled domain with the same density as the fractures observed in the field. An orientation is associated with each point by sampling from the distribution of orientations for the corresponding fracture set. Fractures are then allowed to grow from the seed points in both directions with this orientation until they meet other fractures whereupon they continue or terminate according to a fixed probability. A mathematical analysis of this method is presented for the case in which fractures within a set are assumed to be parallel. Approximations to the distribution of semi-trace lengths are derived which are shown to be in good agreement with simulation results. Fracture spacing distributions are also derived for this case.     

Fracture Length Estimation from Borehole Image Logs

We describe a method to estimate fracture length for circular fractures from borehole image logs. The relative frequency of fractures, which have complete circumference trace on image logs is related to fracture length. A simple functional relationship can be derived for the relative frequency of complete fracture traces in terms of average fracture inclination to borehole, borehole diameter and fracture length. This formulation however, tends to underestimate fracture length because a constant length is assumed. A more accurate length estimate can be obtained by assuming that fracture length is linearly correlated to fracture aperture or spacing. Cumulative frequency distribution of fracture aperture and spacing can be obtained from borehole image logs. The problem then transforms itself to finding the scaling factor between fracture length and aperture (or spacing) from the relative frequency of fractures with complete traces. The product of the scaling factor and average fracture spacing (or aperture) gives the average fracture length.     

Rock Quality Designation Model Formulation and Simulation for Correlated Fracture Intact Lengths

An important factor in the rock quality assessment analysis from discontinuity measurements along a scanline is the correlation of intact lengths. The autorun model and first order autorun coefficient are proposed as a method for objectively quantifying intact length correlation structure and discontinuity occurrences along any scanline. Necessary definitions for the methodology are presented on a quantitative basis such as the alternative intact length percentages and experimental autorun coefficient. An expression is proposed for the number of discontinuity occurrences along a scanline depending on the scanline length, alternate intact length percentages, and the autorun coefficient. Monte Carlo simulation technique is used with a suitable autorun model to verify this expression. A mathematical expression is derived for the expected Rock Quality Designation (RQD) value by taking into account the correlation of the intact lengths. Additional simulations show the validity of the new RQD expression. With the methodology proposed much less engineering experience and judgment are required in estimating the RQD value from scanline measurements. The application of the methodology has been presented for some field data.     

考虑压裂裂缝的煤层气藏井网井距确定方法

煤层气藏具有低渗透率特点, 这使得其在直井排采前须对产层进行压裂改造,而压裂裂缝参数对井距的确定影响很大,因此研究裂缝长度、导流能力与井距的关系具有实际意义。通过对比不同裂缝穿透比和导流能力下的煤层气产量与采出程度,探讨裂缝参数对煤层气产出的影响规律;并以煤层气开采15a采出程度达到50%时的井距作为评价指标,研究压裂效果与井距的关系。研究结果表明,裂缝越长,导流能力越大,井距就越大-尤其在渗透率较小时,裂缝参数对井距的影响更明显。因此,在确定煤层气藏井距时,由于人工裂缝影响,裂缝方向的井距可适当放大。以我国韩城矿区煤层气区块储层参数为例,在给定优化指标下,宜选择矩形井网(350m×300m),或菱形井网(对角线长度为700m×400m)。     

成矿环境空间结构的模糊建模

为了提高矿产预测的精度和可靠性, 必须分析和利用与矿床有关的空间结构信息.提出了一种用模糊集建立成矿环境空间结构模型的方法.成矿环境空间结构是地质变量在矿床周围的分布, 可用变量与空间点之间的模糊关系来描述.同一地区的同类矿床, 其空间结构具有一定相似性, 通过这种相似性的极大化可对结构模型进行优化.优化的结构模型是一种包含了方向和距离关系的特殊的空间关联规则集, 也是模糊推理矿产预测的推理规则库.通过模糊推理进行结构相似性的比较, 可对任意点上的找矿有利性进行预测.以云南东川地区铜矿预测的实例说明了该方法具有良好的应用效果.      

Detection of Cyclic Patterns Using Wavelets: An Example Study in the Ormskirk Sandstone, Irish Sea

This study shows how wavelet analysis can be used on well log and drill core data to identify cyclicity in sedimentary sequences. Three possible methods for determining wavelength were investigated: the Morlet wavelet, the Fourier transform, and the semivariogram. When applied to several hypothetical signals similar to those observed in petrophysical measurements in hydrocarbon reservoirs, all three methods could identify the presence of cyclicity. Only the wavelet scalogram, however, gave a clear indication of when the cyclic element was present and where frequency changes occurred in the signal. To illustrate the wavelet analysis, we processed well log and core data from a well in the Ormskirk Sandstone and determined the wavelet coefficients for each zone and the wavelengths of the strongest cyclicities. The cyclicities observed corresponded well with sedimentary features of the formation (e.g., channels and channel sets). Also, ratios of the cyclicity wavelengths corresponded with ratios of the Milankovitch precession, obliquity, and eccentricity periods. This result is in agreement with other investigators, who have proposed that Milankovitch-driven climate changes exercised an important control on Ormskirk Sandstone deposition.     

The Impact of Biased Sampling on the Estimation of the Semivariogram Within Fractured Media Containing Multiple Fracture Sets

Monte Carlo simulation was used to examine the error (statistical bias) introduced in estimating a sample semivariogram through application of oriented sampling patterns to variables which are correlated with fracture orientation. Sample semivariograms of the directional components of the water velocity were used to illustrate that oriented sampling schemes can provide biased data sets which result in error in the estimation of the semivariogram, particularly in the estimation of the sill (or variance). Three sampling patterns were used to analyze directional semivariograms of the components of the fluid velocity: sampling along lines parallel to the mean regional hydraulic gradient, sampling among lines perpendicular to the mean regional hydraulic gradient, and sampling along fracture segments. The first two sampling patterns were shown to introduce substantial error in the sills of the velocity variograms. It is argued that this error is due to the combination of unequal sampling of fractures with different orientations (i.e., sampling bias) and the systematic variation in the magnitude of the velocity components with orientation of the fracture. As a consequence, it is suggested that correction factors developed to correct fracture frequency statistics need to be extended to improve estimation of spatial moments of variables which are correlated with fracture orientation.     

克拉苏构造带盐下超深层断背斜裂缝带发育模式及预测方法

克拉苏构造带盐下超深层埋深大于6500 m的断背斜圈闭,白垩系砂岩储层内部裂缝普遍发育且分布复杂,对储层产能影响较大,目前仍然缺乏有效的裂缝发育模式指导裂缝带建模。本文通过钻、测井资料及物理模拟实验,分析了盐下断背斜内裂缝类型及空间分布规律:(1)盐下深层断背斜裂缝带可以分为"挤压剪切型、拱张型与调节型"三种成因类型,挤压剪切型裂缝带主要分布于断背斜翼部,受推覆作用而成,平面呈近EW走向或NW-SE走向。拱张型则主要发育于背斜核部,受控于断背斜拱张作用,平面近EW走向,调节型裂缝带则发育于断背斜的构造转换部位,呈近SN走向;(2)物理模拟实验证明拱张型裂缝带受褶皱褶曲度控制,剪切型、调节型裂缝带则受逆冲断层断距控制,根据断背斜拱升角及垂直断距变化可以预测裂缝带的平面分布;(3)地质资料和物理模拟实验证明"调节裂缝带"及"拱张裂缝带"张开程度最大,有利于改善超深层储层的储集性能,这类裂缝带的单井天然气产量较高。     

裂缝密度约束的离散裂缝网络建模方法与实现

如何高效地用多种类型资料(如地震、测井、岩芯等)所得到的裂缝信息对离散裂缝网络建模至关重要。为此本文提出一种裂缝密度约束的离散裂缝网络建模方法,将多种裂缝先验信息转换为裂缝密度,通过密度约束裂缝网络模型。方法对裂缝位置的确定方法进行改进,从编程的角度对二维和三维实现进行了分析,同时讨论了方法的适用性及参数设定。为验证方法效果,实例分析部分选用鄂尔多斯盆地延河剖面附近的一井区数据进行裂缝建模,并与实际生产资料进行比对,结果表明该方法所建立的裂缝模型与实际生产数据吻合。     

Scanline Method to Determine the Fractal Nature of 2-D Fracture Networks

A previous method proposed to measure the fractal dimension of pore spaces is adapted and modified for 2-D fracture networks. The method relies on scanning a 2-D fracture network through successive straight lines from top to bottom and measuring the distance between two fractures. The fractal dimension is then obtained using the log–log plot of the feature size and the number of features for this particular size at different magnifications. It is shown in this study that the method proposed to measure the fractal dimension of porous structures can be applicable to 2-D fracture networks with some modifications after testing it on synthetic and natural fracture patterns. The method is simplified to be useful for practical applications in the fractal analysis of fracture networks. The results reveal that, on the basis of the direction of scanning lines, different fractal behavior and dimensions can be obtained indicating that 2-D fracture networks possess multifractal character. This approach takes into account the effect of fracture orientation on the fractal behavior and anisotropic nature of fracture networks as well as the fracture density, length, and spatial distribution.     

气井水力压裂有效缝长评估及影响因素研究

为了准确确定气井压后有效缝长及其影响因素,提高川西须家河气藏水力压裂针对性,对于具备生产历史拟合条件的气井,利用数值模拟软件进行了生产历史拟合获得有效水力裂缝缝长,与采用净压力拟合方法获得的水力裂缝支撑缝长进行对比和拟合,获得了有效缝长和支撑缝长的关系式,计算了川西须家河储层单井压后有效缝长;采用灰色关联分析理论分析了各个参数对有效缝长的影响程度和对压裂设计的启示。结果表明：压后有效缝长与支撑缝长具有较强相关性(Le=00584 Lp1359 3),有效缝长明显比支撑缝长短;施工参数(特别是用液量)是影响须家河储层有效缝长的关键,而储层和隔层间应力差则是影响有效缝长的重要客观因素。该研究方法为水力压裂压后评估和提高压裂设计水平提供了较好的借鉴。     

利用方位角道集处理方法预测煤层裂隙

煤层瓦斯含量受多种因素影响,而煤层中的节理裂隙密集带则容易导致瓦斯聚积。在煤田地质勘探中,依据振幅随炮点和检波点入射角的变化可以预测裂隙的发育方向和发育密度。在对淮南地区张集西三煤矿的三维地震数据资料处理时,按不同的方位角增量抽取方位角道集,并对其方位角道集进行速度分析、NMO校正、叠加和偏移,得到6个方位偏移数据体。根据Malick等人的理论模型对其进行计算,获得d、A、B值,并据此预测裂缝发育方向与发育密度。将其预测成果与常规地震解释成果对比,发现两者之间非常吻合,可见利用方位角道集处理方法预测煤层裂隙具有可行性。     

Spatial analyses of groundwater levels using universal kriging

For water levels, generally a non-stationary variable, the technique of universal kriging is applied in preference to ordinary kriging as the interpolation method. Each set of data in every sector can fit different empirical semivariogram models since they have different spatial structures. These models can be classified as circular, spherical, tetraspherical, pentaspherical, exponential, gaussian, rational quadratic, hole effect, K-bessel, J-bessel and stable. This study aims to determine which of these empirical semivariogram models will be best matched with the experimental models obtained from groundwater-table values collected from Mustafakemalpasa left bank irrigation scheme in 2002. The model having the least error was selected by comparing the observed water-table values with the values predicted by empirical semivariogram models. It was determined that the rational quadratic empirical semivariogram model is the best fitted model for the studied irrigation area.     

Numerical Modelling of the Heterogeneous Rock Fracture Process Using Various Test Techniques

Summary A series of numerical tests including both rock mechanics and fracture mechanics tests are conducted by the rock and tool (R–T^2D) interaction code coupled with a heterogeneous masterial model to obtain the physical–mechanical properties and fracture toughness, as well as to simulate the crack initiation and propagation, and the fracture progressive process. The simulated results not only predict relatively accurate physical–mechanical parameters and fracture toughness, but also visually reproduce the fracture progressive process compared with the experimental and theoretical results. The detailed stress distribution and redistribution, crack nucleation and initiation, stable and unstable crack propagation, interaction and coalescence, and corresponding load–displacement curves can be proposed as benchmarks for experimental study and theoretical research on crack propagation. It is concluded that the heterogeneous material model is reasonable and the R–T^2D code is stable, repeatable and a valuable numerical tool for research on the rock fracture process.     

应用随裂缝倾角变化的孔隙模型改进储层饱和度计算

复杂的孔隙结构及多变的孔隙类型使得裂缝性储层成为测井评价的难点,通过假定不同孔隙类型间的导电方式来建立合理的孔隙模型,进而结合阿尔奇方程实现饱和度计算是目前裂缝性储层定量评价的主要方法和途径。在经典的双孔隙模型中求取岩石系统的总孔隙指数m时,未考虑裂缝与电流线的夹角变化带来的影响。通过在裂缝性储层中同时考虑裂缝曲折度、裂缝与电流线夹角双重因素,构建了改进双重孔隙模型,并结合电成像资料提供的倾角信息进行了实例处理。结果表明,改进模型的计算值与取心分析有着更好的一致性;若不考虑裂缝与电流线夹角等因素,将带来321%的相对误差。     

水压致裂煤层裂缝发育特点的研究

本文对煤岩基本力学性质、煤层水压致裂缝形成条件、裂缝形态以及裂缝开裂角方位等基本理论进行了研究与探讨，通过大量煤岩力学性质测试，证实了试验区目的层煤岩弹性模量低，泊松比较高，脆性大，易破碎，易压缩。文章还得出了目的层煤岩Ｍｏｈｒ断裂准则二次抛物线型包络线，煤层水压致裂裂缝形式判断，裂缝开裂角方位的计算公式以及有关结论。     

Quantification of Natural Fracture Surfaces Using Fractal Geometry

The purpose of this paper is to present an extensive evaluation of the methods to calculate the fractal dimension of natural fracture surfaces. Three methods; variogram analysis (VA), power spectral density (PSD), and roughness-length method (RMS) are applied to 2-D surface data (PSD) and 1-D profiles (VA and RMS) extracted from the surface data of 54 mm diameter crystallized limestone samples. Surface topography of the samples is quantified through a newly designed fully automated device. Before the application, self-affinity of the surface roughness and the applicability of these methods are validated using synthetically generated fractal surfaces. Fractal dimension values of the profiles are obtained as between 1 and 1.5 with a few exceptions. VA and RMS methods yield consistent fractal dimensions while the PSD values are lower than those of the other two methods. In terms of practical applicability, the VA is found more convenient than other two methods because there still exists shortcomings with the PSD and RMS methods due to difficulties in the mathematical analysis of the plots whose slopes are used in the computation of fractal dimension. However, it is observed that the data of limited size fracture surfaces are convenient for fractal analysis and the results are promising for further applications if the fracture surface size is restricted like cores recovered from deep boreholes.     

Characterization of the Structure of River-Bed Gravels Using Two-Dimensional Fractal Analysis

This paper is concerned with the application of fractal analysis to understand the structure of water-worked gravel-bed river surfaces. High resolution digital elevation models, acquired using digital photogrammetric methods, allowed the application of two-dimensional fractal methods. Previous gravel-bed river studies have been based upon sampled profiles and hence one-dimensional fractal characterisation. After basic testing that bed elevation increments are Gaussian, the paper uses two-dimensional variogram surfaces to derive directionally dependent estimates of fractal dimension. The results identify mixed fractal behavior with two characteristic fractal bands, one associated with the subgrain scale and one associated with the grain scale. The subgrain scale characteristics were isotropic and sensitive to decisions made during the data collection process. Thus, it was difficult to differentiate whether these characteristics were real facets of the surfaces studied. The second band was anisotropic and not sensitive to data collection issues. Fractal dimensions were greater in the downstream direction than in other directions suggesting that the effects of water working are to alter the level of surface organisation, by increasing surface irregularity and hence roughness. This is an important observation as it means that water-worked surfaces may have a distinct anisotropic signal, revealed when using a fractal type analysis.     

利用测井资料建立地层剪破裂模型

利用测井资料建立地层剪破裂模型是对现有张破裂的有效补充,有利于完善钻井、压裂等石油工程中的破裂机理。运用FMI（地层微电阻率扫描成像）测井资料能识别钻井诱导缝和剪破裂的方位、数量和密度。本文通过对地层剪破裂的理论研究和影响因素分析,利用内摩擦系数与矿物含量之间的非线性假设,建立了地层剪破裂的临界剪应力模型。研究发现,地层中的黏土矿物含量、内摩擦系数、内聚强度和应力大小是诱发剪破裂的重要因素。利用内摩擦系数（或内摩擦角）与泥质体积分数之间的统计回归模型简化了地层剪破裂模型,并增强了模型的适用性。实际资料表明,地层发生剪破裂时的临界剪应力与钻井诱导缝数量之间呈反比关系,理论研究与实际资料具有良好的一致性。     

阿拉尔断裂研究综述

根据前人对阿拉尔断裂的研究调研发现目前对阿拉尔断裂的几何学方面研究主要集中在走向、倾向、倾角和断距等方面,在断面的构造结构特征上研究欠缺,如断面的顶端构造特征,断面与两侧的岩层关系等。由于对阿拉尔断裂的研究方法和角度不同以及资料上的差异,得出的阿拉尔断裂演化的结论也有所差异,建议加强对断裂断面结构及影响断裂发育的动力因素方面的研究。