Line source in a poroelastic layer bounded by an elastic space
Line source in a poroelastic layer bounded by an elastic space
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DOI：
10.1002/nag.2405
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发表时间：
2015-10
影响因子：
4
通讯作者：
J. Marck;A. Savitski;E. Detournay
中科院分区：
文献类型：
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作者：
J. Marck;A. Savitski;E. Detournay
本文导出了连续线源的基本解，即在无限大非渗透弹性层所包围的孔隙弹性层厚度上以恒定速度注入流体。这种理想化的问题在水文地质学和石油工程中都有应用，因为它可以用来评估通过直井在地下注入或取出流体所造成的力学扰动。解的构造利用了孔隙压力场的解耦，在这种特殊情况下，它是由无限长线源扩散方程的经典奇异解给出的。然后，通过求解具有与时间相关的孔压梯度成正比的体力场的弹性类问题来确定机械场。由于问题的对称性，弹性力学的Navier方程可归结为径向和垂直(轴向)位移分量的两个解耦偏微分方程组，并利用傅立叶变换和汉克尔变换进行双重求解。解决方案在小时间、中时间和大时间表现出不同的机制。当扩散半径与时间的平方根成正比，小于或相当于渗透层的厚度时，诱导变形被限制在与扩散半径具有相同量级的特征尺寸的区域内。在很大程度上，当扩散半径与渗透层厚度相比较大时，油藏中的变形速率基本上是固结(单轴)的。基于识别互补的内部域和外部域问题的演化特征的概念模型，证明了不同的解的机制。导出的解可以作为耦合油藏模拟器的一个有价值的基准。它还提供了对注水、储集层/盖层界面剪切以及生产井周围的应力重新分布等问题的见解。版权所有©2015 John Wiley&Sons，Ltd.
The fundamental solution of a continuous line source, injecting fluid at a constant rate over the thickness of a poroelastic reservoir bounded by infinite impermeable elastic layers, is derived in this paper. This idealized problem has applications in hydrogeology and in petroleum engineering, as it can be used to assess the mechanical perturbations caused by injection or withdrawal of fluid in the subsurface through a vertical well. Construction of the solution takes advantage of the uncoupling of the pore pressure field, which, in this particular case, is given by the classical singular solution of the diffusion equation for an infinite line source. The mechanical fields then are determined by solving an elasticity‐like problem with a body force field proportional to the time‐dependent pore pressure gradient. On account of the problem symmetries, the Navier equations of elasticity reduce to two uncoupled partial differential equations for the radial and vertical (axial) displacement components, which are solved by a twofold application of Fourier and Hankel transforms. The solution exhibits different regimes at small, intermediate, and large times. When the diffusion radius, proportional to the square root of time, is smaller than or comparable to the thickness of the permeable layer, the induced deformation is confined to a region with a characteristic dimension of the same order as the diffusion radius. At large time, when the diffusion radius is large compared with the permeable layer thickness, the deformation rate in the reservoir is essentially oedometric (uniaxial). The different regimes of solutions are justified with a conceptual model based on identifying the evolving characteristics of complementary interior and exterior domain problems. The derived solution can serve as a valuable benchmark for coupled reservoir simulators. It also provides insights in to such problems as waterflooding, shearing at reservoir/cap rock interfaces, and stress redistribution around producing wells. Copyright © 2015 John Wiley & Sons, Ltd.