Chen S L
Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA, USA.
Proc Math Phys Eng Sci. 2019 Jan;475(2221):20180658. doi: 10.1098/rspa.2018.0658. Epub 2019 Jan 23.
Hydraulic fracturing is the primary method of stimulation in unconventional reservoirs, playing a significant role in oil and gas production enhancement. A key issue for the analysis of hydraulic fracture initiation is to accurately determine the stress distributions in the vicinity of the borehole caused by the injection of pressurized fluids. This paper develops an exact, three-dimensional, poroelastic coupled analytical solution for such stress analysis of an arbitrarily inclined borehole subjected concurrently to a finite-length fluid discharge and stresses, using Fourier expansion theorem and the Laplace-Fourier integral transform technique. The complicated boundary conditions, which involve the mixed boundary values at the borehole surface and the coupling between the total radial stress and injection-induced pore pressure over the sectioned borehole interval, as well as the fully three-dimensional far field stresses, are addressed in a novel way and deliberately/elegantly decomposed into five fundamental, easier to handle modes. The rigour and definitive nature of the proposed analytical methodology facilitates fundamental understanding of the mechanism underlying the stress responses of the borehole and porous medium. It can be and is used here as a benchmark for the numerical solutions obtained from the finite-element analysis commercial program (ABAQUS).
水力压裂是非常规油藏增产的主要方法，在提高油气产量方面发挥着重要作用。水力裂缝起裂分析的一个关键问题是准确确定由注入加压流体引起的井眼附近的应力分布。本文利用傅里叶展开定理和拉普拉斯 - 傅里叶积分变换技术，针对同时承受有限长度流体排放和应力的任意倾斜井眼的此类应力分析，开发了一种精确的三维孔隙弹性耦合解析解。复杂的边界条件，包括井眼表面的混合边界值、分段井眼区间上总径向应力与注入引起的孔隙压力之间的耦合以及完全三维的远场应力，以一种新颖的方式得到处理，并被有意/巧妙地分解为五个基本的、更易于处理的模式。所提出的解析方法的严谨性和确定性有助于从根本上理解井眼和多孔介质应力响应的潜在机制。它可以并且在此用作从有限元分析商业程序（ABAQUS）获得的数值解的基准。
