Modeling of thermally driven longitudinal fractures along a vertical well

IF 7 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL
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Abstract

Fluid injection via a vertical well into a high-temperature formation may induce multiple longitudinal thermal fractures, which may eventually transition to two-wing fractures during fracture propagation, depending on horizontal stress ratio κ. In this study, we develop a plane strain model with radial heat conduction to investigate either two-wing fractures under highly anisotropic stresses κha1 or multiple fractures under isotropic stresses κ=1. The coupled dimensionless elasticity equation and criteria of fracture propagation (and arrest) are formulated, discretized, and solved iteratively (with two special algorithms). Two additional critical model parameters are dimensionless effective confining stress T and wellbore radius A. The multiple-fracture solution of dimensionless fracture length L, angular spacing D, and aperture consists of solutions for competitive propagation of fractures with arrests in the near-wellbore region and the subsequent stable propagation of fractures away from the wellbore. Both the multiple-fracture and two-wing-fracture solutions accurately capture the early-time transient and late-time power-law changes with dimensionless time τ, as verified numerically. The late-time fracture propagation follows scaling law L=fT,A,Dτ12T/2. These solutions and scaling laws can be used to well bound a general solution with 1<κ<κha as demonstrated numerically for a geothermal site, for which the maximum fracture length reaches 0.45, 2.71, and 16.42 m in 1, 100 and 10,000 days of cooling, respectively. The applicability of the assumptions used in the theoretical and numerical analysis is discussed.
垂直井热驱动纵向裂缝建模
通过垂直井向高温地层注入流体可能会诱发多条纵向热裂缝,在裂缝扩展过程中,根据水平应力比κ的不同,这些裂缝最终可能会转变为两翼裂缝。在本研究中,我们建立了一个具有径向热传导的平面应变模型,以研究高度各向异性应力κha≫1条件下的两翼断裂或各向同性应力κ=1条件下的多重断裂。对耦合的无量纲弹性方程和断裂扩展(和闭合)准则进行了表述、离散化和迭代求解(采用两种特殊算法)。另外两个关键的模型参数是无量纲有效约束应力 T 和井筒半径 A。无量纲裂缝长度 L、角间距 D 和孔径的多重裂缝解法包括在近井筒区域裂缝的竞争性传播和阻滞解法,以及随后远离井筒的裂缝稳定传播解法。经数值验证,多裂缝和双翼裂缝解决方案都准确捕捉到了无量纲时间τ的早期瞬态和晚期幂律变化。晚期断裂扩展遵循缩放定律 L=fT,A,Dτ1-2T/2。这些解法和缩放定律可以很好地约束一般解法,即 1<κ<κha,这在一个地热场地得到了数值验证,在冷却 1 天、100 天和 10,000 天后,最大断裂长度分别达到 0.45 米、2.71 米和 16.42 米。讨论了理论和数值分析中所用假设的适用性。
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来源期刊
CiteScore
14.00
自引率
5.60%
发文量
196
审稿时长
18 weeks
期刊介绍: The International Journal of Rock Mechanics and Mining Sciences focuses on original research, new developments, site measurements, and case studies within the fields of rock mechanics and rock engineering. Serving as an international platform, it showcases high-quality papers addressing rock mechanics and the application of its principles and techniques in mining and civil engineering projects situated on or within rock masses. These projects encompass a wide range, including slopes, open-pit mines, quarries, shafts, tunnels, caverns, underground mines, metro systems, dams, hydro-electric stations, geothermal energy, petroleum engineering, and radioactive waste disposal. The journal welcomes submissions on various topics, with particular interest in theoretical advancements, analytical and numerical methods, rock testing, site investigation, and case studies.
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