A three-dimensional solution of hydraulic fracture width for wellbore strengthening applications

Determining the width of an induced hydraulic fracture is the first step for applying wellbore strengthening and hydraulic fracturing techniques. However, current 2-D analytical solutions obtained from the plane strain assumption may have large uncertainties when the fracture height is small. To solve this problem, a 3-D finite element method(FEM) is used to model wellbore strengthening and calculate the fracture width. Comparisons show that the 2-D plane strain solution is the asymptote of the 3-D FEM solution. Therefore, the 2-D solution may overestimate the fracture width. This indicates that the2-D solution may not be applicable in 3-D conditions. Based on the FEM modeling, a new 3-D semi-analytical solution for determining the fracture width is proposed, which accounts for the e ects of 3-D fracture dimensions, stress anisotropy and borehole inclination. Compared to the 2-D solution, this new 3-D semi-analytical solution predicts a smaller fracture width.This implies that the 2-D-based old design for wellbore strengthening may overestimate the fracture width, which can be reduced using the proposed 3-D solution. It also allows an easy way to calculate the fracture width in complex geometrical and geological conditions. This solution has been verified against 3-D finite element calculations for field applications.

Influence of fracture width on borehole radar response

Fracture is a common underground structure phenomenon,which can provide space and passage for the storage and migration of oil and gas.Borehole radar is a fast and high-resolution geophysical detection method,which has been widely used in engineering,exploration and other fields.This paper mainly uses theoretical analysis and numerical simulation to study the variation law of the characteristics of the received borehole radar signal with the variation of fracture width.The Ricker wavelet is used as the pulse signal of the borehole radar.The results show that the amplitude of the signal received by the borehole radar first increases,then decreases,and finally tends to be a stable value with the increase of fracture width.The results have guiding significance for the detection of underground fractures and the estimation of fracture width by borehole radar.

Theoretic expression of flow rate for a single fracture with linearly varying width

By means of reasonable assumption and mathematical derivation, a theoretic expression of flow rate for a single fracture with linearly varying width was obtained. The mathematical derivation was based on the cubic law and the new theoretic expression was an extention of traditional parallel plate model. This study may help to analyze seepage in fractured rock mass.

ANTI-PLANE FRACTURE ANALYSIS OF FUNCTIONALLY GRADIENT MATERIAL INFINITE STRIP WITH FINITE WIDTH

The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.

Experiments on acoustic measurement of fractured rocks and application of acoustic logging data to evaluation of fractures

Fractures in oil and gas reservoirs have been the topic of many studies and have attracted reservoir research all over the world. Because of the complexities of the fractures, it is difficult to use fractured reservoir core samples to investigate true underground conditions. Due to the diversity of the fracture parameters, the simulation and evaluation of fractured rock in the laboratory setting is also difficult. Previous researchers have typically used a single material, such as resin, to simulate fractures. There has been a great deal of simplifying of the materials and conditions, which has led to disappointing results in application. In the present study, sandstone core samples were selected and sectioned to simulate fractures, and the changes of the compressional and shear waves were measured with the gradual increasing of the fracture width. The effects of the simulated fracture width on the acoustic wave velocity and amplitude were analyzed. Two variables were defined： H represents the amplitude attenuation ratio of the compressional and shear wave, and x represents the transit time difference value of the shear wave and compressional wave divided by the transit time of the compressional wave. The effect of fracture width on these two physical quantities was then analyzed. Finally, the methods of quantitative evaluation for fracture width with H and x were obtained. The experimental results showed that the rock fractures linearly reduced the velocity of the shear and compressional waves. The effect of twin fractures on thecompressional velocity was almost equal to that of a single fracture which had the same fracture width as the sum of the twin fractures. At the same time, the existence of fractures led to acoustic wave amplitude attenuations, and the compressional wave attenuation was two times greater than that of the shear wave. In this paper, a method was proposed to calculate the fracture width with x and H, then this was applied to the array acoustic imaging logging data.The application examples showed that the calculated fracture width could be compared with fractures on the electric imaging logs. These rules were applied in the well logs to effectively evaluate the fractures, under the case of no image logs, which had significance to prospecting and development of oil and gas in fractured reservoirs.

New bolting structure of fractured roof based on the Bossinesq equations

Present support theories contain a number of shortcomings in the designation of fractured roof bolt parameters of rectangular or trapezoidal coal roadways.Roof fall accidents occur easily in this kind of roadway.Based on the Bossinesq equations and the Mohr strength theory,we propose a theory of an anchored cluster structure for fractured roofs and have investigated the formation of such an anchored cluster structure,its self stability mechanism and mechanical properties.The results show that an anchor and the surrounding fractured rock can form a string-like supporting structure,referred to as the structure of an anchored cluster for rational bolt parameters.Not only can the structure maintain its own stability,but as well undertake the load of the overlying strata.The designated support parameters,based on anchored cluster theory can overcome the shortcomings of other support theories applied to a fractured roof of rectangular roadways or could not be calculated.Our anchored cluster theory can provide a theoretical basis for the design of support for rectangular fractured roofs.Furthermore,the theory will help to reduce the probability of roof fall accidents caused by local fractured rock blocks,which can destroy a supporting structure.

A new laboratory method for evaluating formation damage in fractured carbonate reservoirs

Natural carbonate core samples with artificial fractures are often used to evaluate the damage of fractured carbonate formations in the laboratory. It is shown that the most frequent error for evaluation results directly from the random width characterized by the artificial fractures. To solve this problem, a series of simulated fractured core samples made of stainless steel with a given width of fracture were prepared. The relative error for the width of artificial fracture decreased to 1%. The width of natural and artificial fractures in carbonate reservoirs can be estimated by image log data. A series of tests for formation damage were conducted by using the stainless steel simulated core samples flushed with different drilling fluids, such as the sulfonate/polymer drill-in fluid and the solids-flee drill-in fluid with or without ideal packing bridging materials. Based on the experimental results using this kind of simulated cores, a novel approach to the damage control of fractured carbonate reservoirs was presented. The effective temporary plugging ring on the end face of the simulated core sample can be observed clearly. The experimental results also show that the stainless steel simulated cores made it possible to visualize the solids and filtrate invasion.

Experimental study on attenuation of Stoneley wave under different fracture factors

To quantitatively determine the effect of different factors such as fracture width,dip angle,extension and filling material on Stoneley wave amplitude decreasing,the shock tube experiment method was changed from fixing the sample and vertically moving the sensor in the borehole to fixing the sensors along the shock tube wall and vertically moving the sample without drilling the borehole in it.The measurement accuracy and the signal-to-noise ratio of the first Stoneley wave were improved by the time corrections and amplitude corrections of Stoneley wave signals.At the same time,21 sets of core models with different fracture parameters were processed for this measurement method by using full-diameter carbonate core,and relative amplitudes were defined to characterize Stoneley wave amplitude decreasing.The experimental results show that the relative amplitude of Stoneley wave exponentially decreases with increasing fracture width.The relative amplitude of Stoneley wave linearly decreases with increasing fracture dip angle.The relative amplitude of Stoneley wave exponentially decreases with increasing fracture extension.The relative amplitude of Stoneley wave decreases with increasing the permeability of filling material in the fracture.Under the above four conditions,the fracture width has the greatest effect on the decreasing of Stoneley wave amplitude,followed by the fracture extension and the permeability of filling material,and finally the fracture dip angle.

A novel model for the proppant equilibrium height in hydraulic fractures for slickwater treatments

The proppant equilibrium height is the basis of investigating proppant distributions in artificial fractures and has a great significant influence on hydraulic fracturing effect.There are two shortcomings of current research on proppant equilibrium heights,one of which is that the effect of fracture widths is neglected when calculating the settling velocity and another of which is that the settling bed height is a constant when building the settling bed height growth rate model.To fill those two shortcomings,this work provides a novel model for the proppant equilibrium height in hydraulic fractures for slickwater treatments.A comparison between the results obtained from the novel model and the published model and experimental results indicates that the proposed model is verified.From the sensitivity analysis,it is concluded that the proppant equilibrium height increases with an increasing proppant density.The proppant equilibrium height decreases with an increase in the slickwater injection rate and increases with an increase in the proppant injection rate.The increase in proppant diameter results in an increasing the friction factor,which makes proppant equilibrium heights decrease.Meanwhile,the increase in proppant sizes results in an increase in proppant settling rates,which makes the proppant equilibrium height increase.When the effect of the proppant diameter on settling rates is more significant than that on friction factors,the equilibrium height increases with an increasing proppant size.This work provides a research basis of proppant distributions during the hydraulic fracture.

Maximum twin shear stress factor criterion for sliding mode fracture initiation

Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is the maximum twin shear stress factor criterion. The authors studied a finite width plate with central slant crack, subject to a far field uniform uniaxial tensile or compressive stress.

热液成矿系统构造控矿理论

构造对成矿的控制是热液成矿系统的典型特征之一,系统剖析多重尺度控矿构造的几何学、运动学、动力学、流变学和热力学对认识矿床成因和预测找矿至关重要;而如何实现控矿构造格架、渗透性结构、成矿流体通道和矿化变形网络由静态到多尺度时-空四维动态的转变,查明流体通道和矿床增量生长过程与控制因素,揭示热液成矿系统的构造-流体耦合成矿机制和定位规律是亟待解决的关键科学难题。为此,我们在对已有相关成果系统梳理的基础上,提出了科学构建热液成矿系统构造控矿理论的基本要点与对应方法及应用范畴:(1)流体而非构造是构造控矿理论的中心,热液系统的流体流动与成矿作用受控于断裂带格架及其渗透性结构,其中渗透率是将流体流动与流体压力变化联系起来理解控矿构造的核心;(2)不同控矿构造组合的关键控制是构造差应力和流体压力的大小,而矿化类型的变化可能是由于构造应力场引起的容矿构造方位的不同和赋矿围岩之间的强度差异所致;(3)流体通道的生长始于超压流体储库上游围岩中孤立的微裂隙沿流体压力梯度最大的方向、随裂隙发育且相互连结而形成新的长裂隙,并最终连通形成断裂网络内的流体通道,矿床的增量生长发生在高流体通量的短爆发期,断层反复滑动驱动其内流体压力、流速和应力快速变化,当由此诱发的流体通道生长破坏了流体系统的动态平衡时,随之而来的流体快速降压就成为金属沉淀成矿的关键驱动因素;(4)以热液裂隙-脉系统野外地质观测和构造-蚀变-矿化网络三维填图为基础,通过宏观与微观各级控矿构造相结合、地质历史与构造应力分析相结合、局部与区域点-线-面相结合、浅部与深部相结合、时间与空间相结合、定性和定量相结合,对各种控矿因素开展多学科、多尺度、多层次、全方位综合研究,是应遵循的基本原则;(5)通过构造-蚀变-矿化网络填图,将蚀变-矿化体与控矿构造的类型、形态、规模、产状和间距等几何学特征联系起来,利用热液裂隙-脉系统和断裂网络拓扑学及矿体三维几何结构分析等定量方法查明控矿构造格架和渗透性结构并揭示矿化变形网络的连通性与成矿潜力;(6)合理构建地质模型,选取合适的热力学参数和动力学边界条件,利用HCh和COMSOL等方法,定量模拟成矿过程中的流体流动、热-质传递、应力变形和化学反应等的时-空变化,是揭示构造-流体耦合成矿机理和定位规律、预测矿化中心和确定找矿目标的有效途径。进而提出了构造控矿理论的研究流程:聚焦构造-流体耦合成矿机制和定位规律这一关键科学问题,选择热液裂隙-脉系统和构造-蚀变-矿化网络为重点研究对象;通过几何学描述、运动学判断、流变学分析、动力学解析和热力学综合,厘定控矿构造格架,定位矿化中心,示踪成矿流体通道和多种矿化样式的增量生长过程及其关键控制,揭示渗透性结构的时-空演变规律及构造再活化与成矿定位的成因关联,建立构造-流体耦合成矿模式,服务新一轮战略找矿突破。以胶东焦家金矿田为例,开展控矿构造理论研究和成矿预测应用实践,证实了其科学性和有效性。

老年女性髋部骨折与其RDW及N-MID OC/β-CTX比值的相关性

目的探讨红细胞分布宽度(RDW)、骨钙素N端中分子片段(N-MID OC)与I型胶原羧基末端肽β特殊序列(β-CTX)比值与老年女性髋部骨折风险的相关性。方法以2021年1月至2021年12月,于四川省骨科医院收治的733例年龄大于60岁女性患者为研究对象,其中髋部骨折组375例,未骨折组358例,收集两组患者临床基数资料。采用二元Logistic回归模型分析RDW及N-MID OC/β-CTX比值与老年女性髋部骨折的相关性。结果Logistic回归分析显示年龄、红细胞分布宽度变异系数(RDW-CV)、N-MID OC/β-CTX、钙(Ca)、磷(P)水平为老年女性髋部骨折的风险因素。将RDW-CV、N-MID OC/β-CTX值从小到大排序后等比例分3层,结果显示RDW-CV越高、N-MID OC/β-CTX比值越低,老年女性发生髋部骨折风险越高(P<0.05)。根据受试者工作特征(ROC)曲线,单独与联合检测两指标均可用于骨折的诊断,但联合检测两指标可提高诊断性能,联合检测的曲线下面积(AUC)为0.729,敏感度、特异性分别为60.53%、75.42%。结论RDW-CV及N-MID OC/β-CTX比值与老年女性髋部骨折风险相关。

运用CT三维重建技术测量骨质疏松性椎体压缩骨折与中青年创伤性胸腰椎骨折患者椎弓根宽度的临床价值

目的探讨运用CT三维重建技术测量骨质疏松性椎体压缩骨折(OVCF)与中青年创伤性胸腰椎(T_(11)-L_(5))骨折患者椎弓根宽度(PW)的临床价值。方法收集2020年10月—2022年10月我院收治的117例脊柱胸腰段骨折患者资料进行回顾性分析,将65例OVCF患者纳入A组,将52例中青年创伤性胸腰椎(T_(11)-L_(5))骨折患者纳入B组,均采用CT三维重建技术测量T_(11)-L_(5)各对应脊椎PW,比较两组各对应弓根两侧PW及不同性别间的差异,并计算PW<5 mm及<7 mm的百分比。结果A组对应脊椎左右侧PW比较差异无统计学意义(P>0.05)。A组T_(11)-L_(5)各对应脊椎的PW值小于B组(P<0.05)。两组T_(11)-L_(5)各对应脊椎的PW值男性大于女性(P<0.05),A组T_(11)-L_(3)各对应脊椎的男性和女性PW值小于B组(P<0.05),两组的L_(4)、L_(5)脊椎PW值比较差异无统计学意义(P>0.05)。A组共测量655个椎弓根,PW<5 mm者占椎弓根总数的7.48%,主要分布于T_(11)-L_(3)脊椎,<7 mm占比37.25%,T_(11)-L_(4)均有分布;B组共测量359个椎弓根,PW<5 mm者占椎弓根总数的1.67%,T_(12)-L_(2)分别均有分布,<7 mm患者占比13.09%,分布于T_(11)-L_(3)。A组PW<5 mm占比和7 mm占比高于B组(均P<0.05)。结论老年OVCF患者T_(11)-L_(3) PW小于中青年创伤性胸腰椎骨折患者,且女性小于男性,故临床应对胸腰椎骨折患者术前行CT三维重建检查,测量PW,以评估手术治疗的可行性,并降低并发症发生。

大采宽综采工作面导水裂隙带高度探究

为了探究永煤公司新桥煤矿深埋煤层大采宽工作面导水裂隙带高度发育特征,以典型的开采宽度330 m的某工作面为研究对象,建立了深埋煤层大采宽工作面三维工程地质概化预开采模型,采用FLAC3D数值模拟软件对采动覆岩导水裂隙带高度进行研究,发现这种大采宽工作面开采后应力集中程度明显增大。和经验公式类比获得了该工作面导水裂隙带高度取值范围,提出了现行规范中的相关计算公式预计结果明显偏小,已不适合这种地质及开采条件。最后,在其他条件不变仅改变采宽条件下,模拟了7种不同采宽开采后沿倾向和走向导水裂隙带高度发育特征,对比分析发现导水裂隙带高度随采宽增加呈非线性变化,两者之间具有很好的自然对数拟合关系,确定了增加幅度的采宽阈值及其变化特征。

红细胞体积分布宽度与老年髋部骨折病人预后的关系

目的 探讨红细胞体积分布宽度(RDW)与老年髋部骨折病人预后的关系。方法 登陆我院建立的老年髋部骨折数据库,纳入2014年1月至2021年3月收治的926例病人为研究对象,提取这些病人的临床资料和相关实验室检查结果。绘制RDW预测老年髋部骨折病人预后的ROC曲线,根据RDW的最佳截断值将病人分为高、低RDW组,并对比2组的基本临床资料。随访病人的生存情况,绘制并比较2组的Kaplan-Meier生存曲线。采用Cox比例风险模型分析影响老年髋部骨折病人预后的危险因素,并进行贫血及非贫血的分层分析。结果 RDW预测老年髋部骨折病人预后的最佳截断值为14.40%。926例病人中,低RDW组(RDW≤14.40%)661例,高RDW组(RDW>14.40%)265例,2组年龄、性别、骨折类型、输血比例、贫血比例、Charlson合并症指数(CCI)分级、伤后至入院时间、血红蛋白、白蛋白水平差异有统计学意义(P<0.05或P<0.01)。所有病人中位随访43.68个月,高RDW组30 d、6个月和1年死亡率均高于低RDW组(P<0.05或P<0.01)。多因素Cox回归分析显示,RDW>14.40%、高龄、男性、CCI≥1、保守治疗、低白蛋白是老年髋部骨折病人1年内死亡的独立危险因素(均P<0.05)。进一步对贫血进行分层分析发现:在非贫血病人中,RDW>14.40%与老年髋部骨折病人的1年死亡风险独立相关(HR=2.969,95%CI:1.478~5.963,P=0.002),而在贫血病人中,二者无相关性(P=0.259)。结论 RDW与非贫血老年髋部骨折病人的预后密切相关。

裂缝等效宽度的斯通利波检测实验及反演

为了破解裂缝地层识别与评价的难题,进行缩比例模型井声波测量物理实验,结合数值模拟分析不同裂缝宽度和条数下斯通利波特征,总结水平裂缝不同宽度及条数对斯通利波衰减的影响规律,提出裂缝等效宽度的概念,定量表征裂缝带对斯通利波幅度的影响,建立基于裂缝等效宽度的反演方法和流程。研究结果表明:随着裂缝等效宽度的增大,直达斯通利波幅度呈指数规律减小;在裂缝等效宽度保持不变的情况下,裂缝条数越多,直达斯通利波幅度越大;利用裂缝等效宽度能够实现裂缝带的定量表征。

碳酸盐岩酸压裂缝内净压力变化规律研究

酸化压裂是开发碳酸盐岩储层最常用的增产技术,而酸压裂缝内净压力是反映裂缝扩展特征、推断裂缝几何形态的重要参数。以水力压裂裂缝延伸机理为基础,基于酸岩反应理论,考虑酸岩反应导致的缝宽变化、CO_(2)气体膨胀、酸液滤失及岩石力学性质变化,结合PKN模型,建立酸压裂缝内的净压力计算模型并进行验证。研究分析酸压裂缝内净压力的影响因素及其规律,结果表明:距缝口距离越远,水力裂缝与酸压裂缝的缝宽均越小,酸液的溶蚀作用会使裂缝宽度增大。随着液体的滤失,离缝口越远液体越少,水力裂缝与酸压裂缝净压力逐渐减小,越靠近裂缝尖端净压力衰减越快。随着作用时间延长,酸压裂缝缝宽逐渐增大,前期随着大量CO_(2)生成,净压力迅速增大,随着酸液消耗与滤失增加,之后逐渐减小并趋于稳定。随着排量的增大,滤失增大,酸压裂缝缝宽及净压力均逐渐增大且增量越来越小。在黏度较小的情况下,滤失较大,净压力逐渐减小;在黏度较大的情况下,CO_(2)膨胀作用大于滤失作用,净压力逐渐增大。随着酸液浓度的增大,酸岩反应速率增大,反应生成CO_(2)增多,净压力逐渐增大。

基于斯通利波的反射源定位及裂缝宽度反演

裂缝的渗流能力影响井的产能,因此裂缝识别和描述成为油藏管理的重要方面。在声波测井中,低频反射斯通利波通常可为过井眼裂缝的定位和评价提供技术依据。为便捷有效地反演裂缝宽度,该文采用反射堆叠法对实际数据进行了反射源定位和反射系数计算,采用一维等效波数法研究了过井裂缝的理论反射系数,随后提出了基于反射斯通利波的裂缝识别和裂缝宽度反演方法,并将其用于现场实际资料。数值模拟结果表明,渗透性裂缝的反射系数随频率的增大呈下降趋势。反演结果表明,斯通利波反演裂缝宽度与电成像裂缝宽度在变化趋势上有很好的一致性,验证了斯通利波反演方法的有效性,为无电成像资料井段的裂缝参数提取提供了新方法。

一种PMSM位置伺服系统的动态建模与控制

本文根据永磁同步电机(PMSM)的基本电磁关系及其动态数学模型建立了位置伺服控制模型,按照闭环负反馈控制原理,设计了具有电流、速度、位置三闭环的位置控制系统。首先,根据PMSM矢量控制的特性,利用3S/2S和2S/2R的坐标变换理论,建立了位置伺服系统在同步坐标系下的动态数学模型,同时给出了按照转子磁场定向的位置控制策略和算法;其次,研究了基于空间矢量脉宽调制(SVPWM)的数字实现,并根据电机的数学模型,在MATLAB/Simulink环境中构建了三环模型,同时搭建了基于DSP实验样机。在仿真和实验中直轴、交轴以及速度和位置均采用PI控制,在控制参数的整定过程中,遵循先内环(电流环),后速度环,再位置环的增量调试原理,实现了同步电机的位置闭环控制;最后,对仿真结果和试验结果进行了对比分析,说明了模型的正确性和有效性。

富血小板纤维蛋白对拔牙术后角化龈宽度以及牙龈软组织增量的影响

目的:探究拔牙术后应用富血小板纤维蛋白(Platelet-rich fibrin,PRF)对患者角化龈宽度及牙龈软组织增量的影响。方法:选择2020年12月-2021年12月于笔者医院行拔牙术的90例患者为研究对象,采用随机数字表法分为对照组(45例)和观察组(45例)。拔牙后,对照组采用新鲜血凝块填充拔牙窝,观察组采用PRF凝胶填充。比较两组患者拔牙创术区黏膜愈合时间、术后3 d和7 d的愈合率、黏膜颜色分级、肿胀程度分级、视觉模拟评分(Visual analogue score,VAS);比较两组患者术前及术后6个月的角化龈宽度、牙龈软组织增量。随机行走模型评价PRF的应用对患者上述指标的影响。比较两组患者术后并发症发生情况。结果:术后,观察组黏膜愈合时间明显短于对照组(P<0.05);术后3 d和7 d,观察组的黏膜愈合率明显高于对照组,黏膜颜色分级、肿胀程度分级、VAS评分明显低于对照组(P<0.05);术后6个月,两组患者的角化龈宽度明显高于术前,牙龈软组织增量明显低于术前,且观察组角化龈宽度、牙龈软组织增量明显低于观察组(P<0.05)。随机行走模型结果显示,观察组术后VAS评分、角化龈宽度改善显著,观察组能够维持患者牙龈软组织增量的相对稳定。观察组术后并发症发生率明显低于对照组(P<0.05)。结论:拔牙术后应用PRF能够促进拔牙创术区黏膜的愈合,减轻患者术后疼痛,保持角化龈宽度及牙龈软组织增量。