Asymptotic Analysis of an Elasticity Equation for a Finger-Like Hydraulic Fracture

We derive a novel integral equation relating the fluid pressure in a finger-like hydraulic fracture to the fracture width. By means of an asymptotic analysis in the small height to length ratio limit we are able to establish the action of the integral operator for receiving points that lie within three distinct regions: (1) an outer expansion region in which the dimensionless pressure is shown to be equal to the dimensionless width plus a small correction term that involves the second derivative of the width, which accounts for the nonlocal effects of the integral operator. The leading order term in this expansion is the classic local elasticity equation in the PKN model that is widely used in the oil and gas industry; (2) an inner expansion region close to the fracture tip within which the action of the elastic integral operator is shown to be the same as that of a finite Hilbert transform associated with a state of plane strain. This result will enable pressure singularities and stress intensity factors to be incorporated into analytic models of these finger-like fractures in order to model the effect of material toughness; (3) an intermediate region within which the action of the Fredholm integral operator of the first kind is reduced to a second kind operator in which the integral term appears as a small perturbation which is associated with a convergent Neumann series. These results are important for deriving analytic models of finger-like hydraulic fractures that are consistent with linear elastic fracture mechanics. Submitted to Journal of Elasticity on February 5, 2007. Re-submitted with revisions on May 30, 2007.     

煤层底板原位综合测试及突水危险性评估

在实施井下钻孔水压致裂地应力测量的同时,评价岩层阻水性能,确定导升带高度,做到一孔多用。测试区实际观测表明,泥岩、粉砂岩、中砂岩、灰岩阻水性能由大到小,导升高度则由小变大,平均导升高度约32m; 地应力测量表明,该测试区原始地应力状态为SH＞Sv＞Sh,最大水平主应力方向NE至NEE。突水临界指数评价表明,-550m水平采煤工作面掘进时突水的可能性较大,应当采取防范措施。     

煤层压裂裂缝三维延伸模拟及产量预测研究

针对煤层气井的压裂特点和产出机理,综合应用流体力学、线弹性断裂力学、传热学、计算数学和软件工程等方面的知识,提出了煤层压裂裂缝三维延伸模型和产量动态预测模型,其中裂缝三维延伸模型考虑了煤层、上下遮挡层之间的地应力和岩石力学参数变化的影响,产量动态预测模型考虑了煤层气先解吸扩散后渗流入井的产出机理。在此基础上研制了煤层气井三维压裂优化设计软件,并通过实例计算验证了其实用性和可靠性。     

Optimization of thin film solid phase microextraction and data deconvolution methods for accurate characterization of organic compounds in produced water

The continued rise in the extraction of unconventional oil and gas across the globe poses many questions about how to manage these relatively new waste‐streams. Produced water, the primary waste by‐product, contains a diverse number of anthropogenic additives together with the numerous hydrocarbons extracted from the well. Due to potential environmental hazards, it is critical to characterize the chemical composition of this type of waste before proper disposal or remediation/reuse. In this work, a thin film solid phase microextraction approach was developed and optimized to characterize produced water. The thin film device consisted of hydrophilic‐lipophilic balance particles embedded in polydimethylsiloxane and immobilized on a carbon mesh surface. These devices were chosen to provide broad extraction coverage and high reusability. Various parameters were evaluated to ensure reproducible results while minimizing analyte loss. This optimized protocol, consisting of a 15 min extraction followed by a short (3 s) rinsing step, enabled the reproducible analysis of produced water without any sample pretreatment. Extraction efficiency was suitable for both produced water additives and hydrocarbons. The developed approach was able to tentatively identify a total of 201 compounds from produced water samples, by using one‐dimensional gas chromatography hyphenated to mass spectrometry and data deconvolution.     

Hydrophobic guar gum derivatives prepared by controlled grafting processes–Part II: rheological and degradation properties toward fracturing fluids applications

Introduction of polyalkoxyalkyleneamide grafts to guar gum produces new water soluble guar derivatives as described in an earlier publication. 10 In this paper, the rhelogical behavior of these products was explored in more detail at 25 and 65°C. In addition, the viscosity was measured at high temperatures (90 and 120°C) and pressure (150 psi) to partially simulate the down hole conditions of oil wells. Upon treatment with zirconium lactate, the cross‐linked hydrophobically‐modified CMG derivatives exhibited better high‐temperature stability and higher gel viscosities than the corresponding CMHPG derivatives. The cross‐linked gel viscosities indicate that gels will be capable of supporting a high proppant carrying capacity. To facilitate removal of the gels from the formation, the hydrophobically modified derivatives were treated with an enzyme breaker system which produced fragments capable of producing stable emulsions when extracted with toluene. Thus, the clean up process will be enhanced by emulsification of the gel fragments produced by the gel hydrolysis. The low viscosities of the linear derivatives, the rapid formation of high viscosity gels upon cross‐linking and generation of emulsifiers during the gel removal suggest that these new derivatives are good candidates for fracturing fluid applications. Copyright © 2007 John Wiley & Sons, Ltd.     

How to identify dislocations in molecular dynamics simulations?

Dislocations are of great importance in revealing the underlying mechanisms of deformed solid crystals.With the development of computational facilities and technologies,the observations of dislocations at atomic level through numerical simulations are permitted.Molecular dynamics(MD)simulation suggests itself as a powerful tool for understanding and visualizing the creation of dislocations as well as the evolution of crystal defects.However,the numerical results from the large-scale MD simulations are not very illuminating by themselves and there exist various techniques for analyzing dislocations and the deformed crystal structures.Thus,it is a big challenge for the beginners in this community to choose a proper method to start their investigations.In this review,we summarized and discussed up to twelve existing structure characterization methods in MD simulations of deformed crystal solids.A comprehensive comparison was made between the advantages and disadvantages of these typical techniques.We also examined some of the recent advances in the dynamics of dislocations related to the hydraulic fracturing.It was found that the dislocation emission has a significant effect on the propagation and bifurcation of the crack tip in the hydraulic fracturing.     

基于灰色关联法的水平井压裂参数优化研究

针对低渗透薄互砂岩油藏A油田C9区块水平井井区储层物性差、非均质性强、开发难度大等问题,为改善水平井井区开发效果、提高水平井单井产能,应用灰色关联法,结合数值模拟软件,分析影响压裂水平井产能的主要因素,开展水平井压裂参数优化研究,结果表明裂缝半长和裂缝间距是影响压裂水平井产能的主要因素,优选出水平井压裂方案:裂缝半长为150m,裂缝间距为40m,裂缝导流能力为50μm~2·cm;裂缝与水平段夹角为90°.应用灰色关联分析法明确水平井压裂效果的主控因素,为低渗透薄互砂岩油藏现场水平井压裂施工提供了思路和借鉴,具有一定的理论指导意义.     

Transboundary extraction of groundwater in the presence of hydraulic fracturing

We studied transboundary groundwater management problems in the presence of hydraulic fracturing. We found that the presence of risk suggests there should be caution when considering hydraulic fracturing. Our results from the cooperative solution show a decrease in hydraulic fracturing and increase in the steady state survival rate of groundwater. We also provide a Pigouvian type tax that could be imposed on natural gas developers.     

织构化柱塞对压裂泵密封副的摩擦学性能影响

采用精密机械雕刻技术在压裂泵柱塞试样表面雕刻微凹坑阵列表面织构,利用MDW-100型微机控制立式万能摩擦磨损试验机对具有不同尺寸形状的微凹坑柱塞-丁晴橡胶密封试样进行摩擦磨损试验,研究了织构化柱塞试件与丁晴橡胶摩擦副在流体动压润滑条件下的润滑特性.结果表明:压裂泵柱塞试件表面合理织构组合可以显著地提高柱塞密封系统摩擦副的润滑和减摩性能,其中面积比为5.86%、均匀分布的圆柱形与条形混合凹坑织构是较优的,其摩擦副的摩擦系数、温升及磨损量相对于无织构试件分别降低了80%、90%及79.3%,且表面磨痕也显著低于无织构及其他织构组合的柱塞密封摩擦副.     

页岩储层体积压裂的地应力变化研究

页岩储层属于致密超低渗透储层,需改造形成复杂缝网才有经济产能.体积压裂是页岩储层增产改造的主要措施,而地应力场特别是水平主应力差值是体积压裂的关键控制因素. 理论研究表明:(1)当初始两向水平主应力差较小时,容易形成缝网,反之不易产生缝网;(2)人工裂缝的形成能够改变地层初始应力场. 因此应在前人研究的基础上优化设计压裂方式,以克服和翻转初始水平主应力差值,产生体积缝网.基于此,建立了页岩气藏水平井体积压裂数值模型,模型中采用多孔介质流固耦合单元模拟页岩基质的行为,采用带有孔压的"cohesive"单元描述水力裂缝的性质,模型对"Texas Two-Step" 压裂方法进行了数值模拟,模拟结果得到了压裂过程中地层应力场的分布及其变化,模拟结果和解析公式计算结果吻合良好.模拟结果表明:(1)裂缝的产生减弱了地层应力场的各向异性;(2 对于低水平应力差页岩储层,采用"Texas Two-Step"压裂方法可以产生缝网. 对于采用"Texas Two-Step"压裂方法无法产生缝网的高应力差页岩储层,提出了三次应力"共振" 和四次应力"共振" 压裂方法并进行了数值模拟,模拟结果得到了压裂过程中页岩储层应力场的分布及其变化,得到了缝网形成的区域,模拟结果表明:(1)对于高应力差页岩储层,采用"Texas Two-Step" 压裂方法无法产生缝网;(2)对于高应力差页岩储层,三次应力"共振" 和四次应力"共振"压裂方法是有效的体积压裂缝网形成的方法.