The in situ stress states associated with core discing estimated by analysis of principal tensile stress

Core discing occurs due to tensile stress induced by boring within or below a core stub when the minimum principal stress is nearly in the same direction as the core axis. To determine the effects of the core length on the magnitude and direction of tensile principal stress, a finite element analysis was carried out for an HQ core of different lengths for 77 in situ stress conditions. According to the minimum value and the mean inclination relative to the core axis for ‘the maximum semi-axial tensile stresses’, 30 in situ stress conditions were identified as being stress conditions under which core discing is likely to occur, and conditions necessary for in situ stress were proposed. The critical tensile stress, which is the tensile stress that can produce a tensile fracture that propagates throughout a cross-section, was analyzed for these stress conditions and a new criterion for core discing, which can be applied to a core of any length, was proposed. The stress conditions estimated by the criterion were consistent with previous experimental results for a long core and for thin discs. According to the criterion, the relationship between the core length and the in situ stress necessary for core discing was examined. Our analysis showed that the stress field can be divided into three regions and that core discing of short length mostly occurs at great depth. The average relationship between the core length and the disc thickness was determined by assuming that the position of a fracture is given by the mean position of ‘the maximum semi-axial tensile stresses’. Our theoretical estimates reproduced previous experimental results regarding the effects of stress magnitude on the thickness of the disc. Thus, the present proposed criterion can be used to estimate the stress condition for core discing with a given disc thickness.     

In situ rock stress determinations in deep boreholes at the Underground Research Laboratory

Deep in situ rock stress determinations are typically conducted using hydraulic fracturing in an existing borehole or by applying specialized overcoring techniques that require the installation of a strain-monitoring instrument in a central pilot borehole that is subsequently overcored. The unusually high horizontal to vertical stress ratio at depth in Canada's Underground Research Laboratory (URL) results in problems in the application of either of these methods. At 420-m depth, the rock in the URL is massive granite with virtually no fractures. The maximum principal stress is approximately 60 MPa and is sub-horizontal. The minimum principal stress is only 11 MPa, resulting in a horizontal to vertical stress ratio of almost 6 to 1. In these conditions, hydraulic fracturing is unable to produce axial fractures in sub-vertical boreholes or is unable to fracture the rock at all. Overcoring methods requiring a pilot hole are not feasible because of persistent core discing. To resolve these problems, AECL has applied a remote data logger/signal conditioner to the design of a Deep Doorstopper Gauge System (DDGS) for use to 1000-m depth. The DDGS is much less susceptible to core discing than most other overcoring methods because it does not require a pilot hole. This paper describes the operating principle of the DDGS and the results of field testing at the URL, as well as issues related to its use and the interpretation of results.     

Effects of poisson's ratio and core stub length on bottomhole stress concentrations

Core disk fractures are produced by the concentration of in situ stresses at the wellbore bottomhole cavity. In order to better understand core disking, these stress concentrations were calculated using detailed three-dimensional finite element modeling of a bottomhole geometry with a variety of core stub lengths. Biaxial compression applied perpendicular to the wellbore axis induces high tension at the root of the core stub. This tension is reduced when a uniaxial compression directed parallel to the wellbore axis is applied. A state of incipient core disking consequently depends on the relative magnitudes of these in situ stresses. Hypothetical incipient failure curves derived from the modeling are in good agreement with early experimental results, and indicate that the core disks produced under a combined state of vertical and uniform horizontal farfield stresses result from tensile fracture. A Mohr-Coulomb shear mechanism cannot explain the experimental observations. The magnitude of the stress concentrations depend strongly on Poisson's ratio and the stress concentrations are higher in materials with small Poisson's ratios. The length of the core stub influences the magnitudes of the concentrated stresses with tensions increasing to a maximum for normalized core stub lengths of 0.25. Additional hypothetical failure curves for differing core stub lengths suggest that core disk thickness can aid in the estimation of in situ stress magnitudes.     

A strain-softening numerical model of core discing and damage

There has been a debate in the rock mechanics community regarding the mechanisms causing what is known as core discing. This phenomenon occurs when diamond drill cores are retrieved from rock masses in which high in situ stresses relative to rock strength are present. The interest in that phenomenon is to use it to estimate the in situ stresses from the shape and frequency of the failures along the core axis. In the present paper we argue that discing is only an indicator of high stresses, and that estimating in situ stresses from fracture observations is much too inaccurate.As most of the literature found on the subject has tackled the problem using elastic numerical models, it is shown that the stress distribution in the core being formed obtained from such models does not exist once failure has been reached. Numerical analyses using Flac^2D with an elasto-plastic cohesion softening friction hardening model show that for a given stress state, discing or core damage may involve tensile failure, a combination of shear and tensile failure, or only shear failure, depending on the stress state and ratio of tensile to shear strength of the rock. The numerical model used is validated by replicating core discing observed under controlled laboratory conditions. Parametric analyses involving changes in mesh density, deformability parameters, dilatancy, drill bit pressure, drilling fluid pressure and applied stress states are also performed. Finally, it is shown that drilling-induced core discing or damage store important residual stresses in the core which may explain why recovered core samples tend to show a deterioration of their mechanical properties with time.     

Strength criterion for rocks under compressive-tensile stresses and its application

Estimating in-situ stress with hydraulic borehole fracturing involves tensile strength of rock. Several strength criteria with three parameters result in tensile strengths with great differences, although they may describe the relation between strength of rock and confining pressure with low misfits. The exponential criterion provides acceptable magnitudes of tensile strengths for granites and over-estimates that for other rocks, but the criterion with tension cut-off is applicable to all rocks. The breakdown pressure will be lower than the shut-in pressure during hydraulic borehole fracturing, when the maximum horizontal principal stress is 2 times larger than the minor one; and it is not the peak value in the first cycle, but the point where the slope of pressure-time curve begins to decline.     

Damage in a rock core caused by induced tensile stress and its relation to differential strain curve analysis

A finite element analysis was carried out to analyze the distribution of tensile stress within and below a long HQ core stub for 77 in situ stress conditions. The maximum tensile stress experienced by the core along the axis during boring under in situ stress was accumulated in an equal-area stereonet for a central part of the cross-section. The maximum tensile stress accumulated for a central area of less than about 60% of the total cross-sectional area was concentrated in a certain direction, which was nearly the same direction as the minimum principal stress for all of the stress conditions, except those in which the minimum principal stress (σ₃) was equal to the intermediate principal stress (σ₂). When σ₂=σ₃, the direction of the cumulative maximum tensile stress lay approximately in the plane of σ₂=σ₃, which is perpendicular to the maximum principal stress. Based on the assumption that a penny-shaped crack is produced normal to the maximum tensile stress in proportion to the magnitude of such stress, the crack density in the core was analyzed by calculating strain under hydrostatic pressure as in differential strain curve analysis (DSCA). The maximum principal crack density in the central part of the core was much greater than the intermediate and minimum principal crack densities, excluding special cases in which σ₂=σ₃. The direction of the maximum crack density was similar to that of the accumulated maximum tensile stress. Thus, the direction of the maximum crack density obtained by DSCA predicts the direction of the minimum principal stress rather than that of the maximum principal stress, if the distribution of pre-existing microcracks before stress relief is isotropic and if additional microcracks are produced only by tensile stress during boring under in situ stress. To verify this, crack parameters were measured by DSCA for two cores of quartz-diorite, which were taken by overcoring when the hemispherical-ended borehole technique was used to measure in situ stress. The directions of the maximum crack parameters measured by DSCA were nearly the same as that of the minimum principal stress for one of the cores. For the other core, for which the magnitudes of the intermediate and minimum principal stresses were close to each other and, accordingly, the direction of the minimum principal stress was uncertain, the direction of the maximum crack density estimated by damage analysis under the assumption that σ₂=σ₃ coincided with the directions of the maximum crack parameters measured by DSCA.     

新疆某高放废物预选处置库区地应力测量研究

 为了获得预选处置库区现今地应力的赋存特征,在该区花岗岩体内的4个深钻孔中采用水压致裂方法进行地应力测量。基于钻孔岩芯编录结果,在0～700 m深度范围内,成功取得地应力量值和最大水平主应力方向数据。依据获取的地应力实测资料,结合拜尔利定律和断层摩擦库伦准则,对预选区的地应力状态及断层活动性进行分析。结果表明：(1) 3个主应力随深度呈现出较好的线性关系;(2) 测试深度范围内,水平应力普遍高于垂向应力,预选区构造应力占主导地位,且随深度的增加逐渐减弱,岩体北部的水平力作用强于中部及南部,南部最弱;(3) 最大水平应力优势方位为NEE,与区域构造应力场方向基本吻合,自青藏高原内部及边缘到东天山地区,现今最大主应力的作用方向表现为由NE～NEE的变化规律;(4) 预选区地应力量值未达到断层摩擦滑动临界值,断层活动性较弱;(5) 研究成果为处置库的开挖设计和稳定性评价提供科学的指导,实测资料填补了该区域地应力数据的空白,为我国西部地区地应力场分布规律研究提供重要参考资料。     

在地应力测量中准确求解最大、最小水平应力问题 的探讨

目前,在地应力测量和应用中,人们常常用近于水平的两个主应力或其在水平面上的投影来代替或估计最大和最小水平应力,这在一般情况下误差不大,但是当应力结构比较特殊时这种代替或近似将带来较大的误差,甚至给工程实践带来危害。以投影近似为例按 3 种三维应力状态分别讨论了方位误差随应力形因子 <> R 与主应力轴倾角的变化和量值误差随 <> R 、主应力轴倾角和最大、最小主应力量值之差的变化。并用原地应力测量资料求得了方位和量值误差。理论分析和实例都证明了用近于水平的两个主应力的投影代替两个水平应力的误差可能很大。建议在研究与水平应力相关的问题或与水平方向相关的物理参量时采用本文的计算方法求出准确值。     

Uncertainty in the maximum principal stress estimated from hydraulic fracturing measurements due to the presence of the induced fracture

The classical theory for hydraulic fracturing stress measurements assumes an ideal case with a linear elastic, homogenous, and isotropic medium; and a fracture that reopens distinctly when the minimum tangential borehole stress is exceeded. The induced fracture disturbs this ideal picture in several aspects, which are important for the evaluation of the maximum horizontal principal stress using the fracture reopening pressure. This disturbance can be attributed to the fracture normal stiffness and the initial hydraulic fracture permeability. In this paper, the hydraulic fracturing reopening test is studied by coupled hydromechanical modeling that takes into account an induced fracture that is incompletely closed. The result shows that with realistic equipment compliance, the apparent fracture reopening evaluated from the well-pressure is close to the magnitude of the minimum horizontal principal stress with little or no correlation to the maximum horizontal principal stress. This observation suggests that the determination of maximum principal stress by hydraulic fracturing using the reopening pressure is very uncertain.     

水压致裂过程的三维数值模拟研究

基于RFPA数值分析方法和并行计算技术,建立了反映岩石细观损伤演化过程的三维渗流–应力–损伤耦合模型。对具有120万单元的方形岩石材料模型,进行了4组不同应力状态下水压致裂过程的三维大规模科学计算分析。计算结果分析表明：起裂压力与失稳压力并不重合,起始裂纹均为张性,裂纹扩展形式、表面平整度、走向、扩展失稳过程以及裂纹的空间分布形态受应力状态影响。当竖直方向为最大主应力方向时裂纹呈空间竖片分布,当水平应力差较大时裂纹表面形态平整,失稳到来较快;当竖直方向为最小主应力方向时裂纹的空间分布呈水平片状;不等的主应力情况下裂纹总是分布在最小主应力面内;当三向主应力相等时,裂纹起裂位置和扩展方向具有竞争趋势,空间分布不具规律,裂缝分支较多。数值模拟结果与物理实验结果有着较好的吻合,该研究对水压致裂工程设计有一定参考价值。     

Constraining the stress tensor in the Visund field, Norwegian North Sea: Application to wellbore stability and sand production

In this study we examine drilling-induced tensile wellbore failures in five exploration wells in the Visund oil field in the northern North Sea. We use observations of drilling-induced wellbore failures as well as density, pore pressure, and leak-off test measurements to estimate the magnitudes and orientations of all three principal stresses. Each well yields a very consistent azimuth of the maximum horizontal stress (100°±10°), both with depth and laterally across the field. Stress orientations are constrained at depths as shallow as 2500 m and as deep as 5300 m in these wells. We show that the magnitudes of the three principal stresses (S_v, S_hmin, and S_Hmax) are also consistent with depth and reflect a strike-slip to reverse faulting stress regime. The magnitude of the maximum horizontal stress is shown to be significantly higher than the vertical and minimum horizontal stresses (e.g. S_v=55 MPa, S_hmin=53 MPa, and S_Hmax=71.5 MPa at 2.8 km depth). Data from earthquake focal plane mechanisms (Lindholm et al., 1995, Proceedings of the Workshop on Rock Stresses in the North Sea, Trondheim, Norway [1]) show similar stress orientations and relative magnitudes and thus indicate a stress field that is relatively consistent throughout the thickness of the brittle crust.We illustrate how knowledge of the full stress tensor allows one to place bounds on in situ rock strength and determine optimally stable trajectories for wellbore stability and sand production during drilling, after the completion of drilling, and as pore pressure is reduced during oil and gas production.     

Determination of stress orientation and magnitude in deep wells

In this paper, we review a suite of techniques for determination of in situ stress orientation and magnitude in deep wells and boreholes. As these techniques can be utilized in both vertical and highly deviated wells, they have had extensive application in the petroleum industry where knowledge of stress orientation and magnitude at depth is important for addressing a wide range of problems. The techniques we have developed for estimation of the maximum horizontal principal stress, S_Hmax, make extensive use of observations of non-catastrophic failures of the wellbore wall—both compressive failures (breakouts) and tensile failures (drilling-induced tensile fractures) as well as the stress perturbations associated with slip on faults cutting through the wellbore. The widespread use of wellbore imaging in the petroleum industry has been a critical development that makes utilization of these techniques possible. In addition to reviewing the theoretical basis for these techniques, we present case studies derived from oil and gas fields in different parts of the world. These case studies document the facts that the techniques described here yield (i) consistent stress orientations and magnitudes over appreciable depth ranges within and between wells in a given field (thus indicating that the techniques are independent of formation properties), (ii) stress magnitudes that are consistent with absolute and relative stress magnitudes predicted by Anderson and Coulomb faulting theories, (iii) stress orientations and relative magnitudes that are consistent with regional stress indicators and tectonics observed with other techniques at much larger scales and (iv) sufficiently well-constrained estimates of the full stress tensor that are useful in application to engineering problems such as wellbore stability.     

岩芯成饼单元安全度三维数值试验及地应力反馈分析

岩芯饼化是深部及高应力地质环境特有的现象,通过岩芯饼化来推测地应力有重要的理论和工程意义。首先模拟不同应力对岩芯饼化厚度的影响,并综合三维弹性数值模拟和带拉伸的莫尔-库仑强度准则,提出岩芯饼化"潜在破坏面"单元安全度的计算方法,研究不同地应力对岩芯潜在破坏面的影响。模拟结果表明,在水平应力一定的条件下,随着竖向地应力的变化,竖直岩芯潜在破坏面单元安全度、剪切破坏和拉伸破坏模式都发生变化。单元安全度方法能够直观显示岩芯潜在破坏面安全度的分布,并量化地反映地应力与岩芯破坏模式之间的对应关系。采用单元安全度方法,对美国Williston盆地Bakken页岩储层的前期勘测地应力和观测岩芯分析,取得相一致的计算结果,说明利用该方法分析与识别地应力是可行的。     

Stress field determination from local stress measurements by numerical modelling

A back analysis using a three-dimensional (3D) boundary element method (BEM) is used to calculate the far-field stress state from local stresses measured in situ. The far-field stresses are decomposed into tectonic and gravitational components and account for the influence of localized faulting and topography. Therefore, the far-field stresses are taken to consist of a constant term, a term that varies linearly with depth, and a hyperbolic term, with one of the principal stresses being vertical. A BEM for inhomogeneous bodies is introduced to calculate elastic gravitational stresses, which is necessary for determination of the far-field stresses.An application to the stress field determination for the Mizunami underground research laboratory (MIU) is carried out. Based upon the local stresses generally measured by conventional hydraulic fracturing (HF), the unknown stress state at MIU is estimated and compared with the measurements carried out recently by the improved HF method with flow rate measurements at the position of straddle packer. After calculating the far-field stress state by BEM back analysis, 3D-finite difference methods (FDM) forward analysis was carried to calculate the in situ stresses at certain locations. The 3D FDM results roughly coincide with the measured results.     

南水北调西线工程区地应力测量及地应力场特征分析

基于对南水北调西线一期工程场区现场水压致裂地应力测试工作,得出如下初步结论:(1)各线路孔中最大水平主应力值最高约为25 MPa,最大水平主应力方向均为NNE或NEE;(2)各坝址孔中最大水平主应力值最高约为17 MPa,最大水平主应力方向受局部地形地势影响变化较大,但大多数孔方向仍为NNE或NEE;(3)在试验深度范围内,线路孔侧压系数随着钻孔深度的增加逐渐减小;当测试深度在200 m以下时,侧压系数值基本维持在2左右;(4)各测孔侧压系数均大于1,表明工程场区地应力以构造应力为主导;(5)在测试深度范围内,各测孔的最大、最小水平主应力随岩层深度的增加均有增大趋势;(6)回归分析结果表明线路孔的最大水平主应力值随深度呈现良好的线性关系;(7)由于隧洞洞室埋深较深,且穿越高应力区,存在中等强度岩爆或流变的可能性。     

Drilling-induced tensile wall-fractures: implications for determination of in-situ stress orientation and magnitude

Detailed investigation of failure of the borehole wall in two scientific drilling projects, the German KTB (Kontinentales Tiefbohrprogramm der Bundesrepublik Deutschland) and the European geothermal research project at Soultz-sous-Forêts, France, has lead to new insight in the phenomena of tensile fractures induced in the wellbore wall during drilling. Comparison of the orientation of the fractures with the orientation of the horizontal principal stress known from breakout and hydraulic fracturing analysis demonstrates that these fractures are reliable indicators of the orientation of the maximum horizontal principal stress S_H. A model for the initiation of the fractures is presented which points out the important influences of (a) the tectonic stress state, (b) increased mud pressures during drilling operation and (c) thermal stresses induced by circulation of relatively cold drilling mud. Analysis of drilling-induced fractures in the GPK1 borehole at Soultz-sous-Forêts (where the magnitude of S_H is known from hydraulic fracturing experiments) demonstrates the validity of this model for the initiation of the fractures. Further, a new method is proposed to estimate the magnitude of S_H from the occurrence of drilling-induced fractures and knowledge of thermally induced stress and pumping pressure during drilling. The method is successfully applied to both KTB boreholes. An independent method to estimate the magnitude of S_H based on the analytical calculation of the stress intensity factor for drilling-induced fractures taking into consideration both, increased mud pressure and thermal stress, is also presented. Application of this method confirms the results derived with the analysis described above. Additionally, the evaluation of the orientation of the fractures with respect to the wellbore axis indicates that over major depth sections of the investigated wells the vertical stress is a principal stress.     

Orientation and magnitude of in situ stress to 6.5 km depth in the Baltic Shield

Understanding the state of stress in the earth is important for a broad range of engineering and geological problems. To obtain the state of stress in boreholes where conditions are such that conventional stress measurement techniques are impossible, we have used recent developments in the analysis of compressive and tensile wellbore failure in an integrated stress measurement strategy, involving also direct measurement of the least principal stress. The analysis is carried out in the two deep boreholes in the Siljan Ring area of the Baltic Shield. The Gravberg-1 borehole reached 6779 m true vertical depth (TVD) in the Siljan region, central Sweden, and the Stenberg-1 borehole, drilled 10 km to the south of Gravberg-1, was completed at 6529 m TVD. Analysis of vertical, drilling-induced tensile fractures in the nondeviating part of the Gravberg-1 well indicated that one principal stress is vertical and thus could be calculated from density estimates. Borehole breakouts and tensile fractures indicated that the average direction of the maximum horizontal stress, S_H, is N72°W±7° in Gravberg-1 and N53°W±9° in the Stenberg-1 well. The direction of S_H is on average very stable in both wells. Lower bound limits on the magnitude of the minimum horizontal stress, S_h, in the Gravberg-1 well were obtained from controlled and uncontrolled hydraulic fracturing and formation integrity tests. At 5 km depth in the Gravberg-1 borehole the minimum horizontal stress is approximately two-thirds of the vertical stress. We estimated the magnitude of the maximum horizontal stress in Gravberg-1 on the basis of drilling-induced tensile fractures identified in the borehole. S_H was estimated by calculating the stress at the borehole wall necessary to cause tensile failure of the formation, incorporating our lower bound S_h estimates, corrections for the cooling of the wellbore by drilling fluids and differential fluid pressures. Our results indicate a strike-slip faulting regime in the Siljan area and that the state of stress is in frictional equilibrium with a coefficient of friction in the range 0.5 to 0.6.     

晋城矿区地应力场研究及应用

 随着矿井开采深度与强度的不断增加,地应力对围岩变形与破坏的影响更加突出,在煤矿矿区进行地应力测量,并分析地应力场分布特征具有重要意义。在晋城矿区,采用小孔径水压致裂地应力测量装置,进行10个煤矿、62个测点的二维与三维地应力测量。实测数据表明：晋城矿区原岩应力以水平应力为主,构造应力占绝对优势,属于典型的构造应力场类型;地应力值属于中等水平;矿区东部与西部水平主应力方向变化较大,主要原因是受晋获褶断带的影响。基于实测数据,绘制晋城矿区地应力分布图;采用回归方法分析地应力随埋藏深度的变化规律;论述水平主应力与垂直主应力的比值同埋藏深度的关系,并与霍克–布朗包线进行比较。选择典型矿井,将地应力测量结果应用于巷道布置与支护设计,根据地应力场分布特征提出合理的巷道轴线布置方向,并在井下应用中得到验证。井下地应力测量为晋城矿区提供了可靠的基础数据,对指导矿区井田开拓、巷道布置与支护设计、采煤方法的选择等工程实践具有重要参考价值。     

横观各向同性地层水平井井壁拟三维应力场计算模型

 针对横观各向同性地层,基于各向异性材料力学理论,运用应力叠加原理和坐标变换方法,考虑井筒流体压力、最大水平主应力、最小水平主应力和上覆岩层压力作用,推导横观各向同性地层中,水平井沿任意方向钻进时井壁应力场的拟三维解析解。进而分析了页岩和砂岩水平井井壁上任意岩石质点3个主应力的分布规律,分析表明,与地层力学性质各向同性条件相比,力学性质各向异性时,井壁上任意岩石质点的第一主应力 没有改变,而第二主应力 和第三主应力 发生了改变,岩石力学性质各向异性度越大,主应力 和 改变越大,岩石力学性质高各向异性度增加了井壁可能发生张性破裂的点数。研究成果可为横观各向同性地层水平井水力裂缝起裂以及井壁稳定性分析提供参考。     

基于不同岩石抗拉强度值确定最大水平主应力的对比分析

水压致裂原地应力测量系统的柔性对最大水平主应力的结果会产生很大的影响,提高最大水平主应力的测量精度对各种地下等工程设计都具有重要意义。通过进行直接拉伸试验、“垫条加载”和“角锥荷载”形式的圆盘劈裂实验、弯曲拉伸实验获得岩石抗拉强度,结合实测破坏压力、孔隙压力数据及相关理论计算出最大水平主应力,并与利用经典水压致裂公式计算得到的最大水平主应力进行数据对比分析。结果表明:通过“角锥荷载”圆盘劈裂实验、直接拉伸试验、“垫条加载”圆盘劈裂实验、三点弯曲实验所获得的最大水平主应力均大于经典水压致裂公式计算得到的最大水平主应力,且偏差依次增大,由此也说明测试系统的柔性会导致利用经典公式计算的最大水平主应力偏小。4种实验中,通过“角锥荷载”圆盘劈裂实验所获得的数据较其他3种方法更接近经典公式计算得到的最大水平主应力,且偏差较小,可以作为估算最大水平主应力的一种替代方法。在未来的工作研究中,可以为避开系统柔性对实测最大水平主应力的影响、提高测量精度提供方法参考。