饱和多孔介质化学-热-弹性模型及应用

本文基于热局部非平衡(LTNE)条件和加权平均温度概念，并假设孔隙流体由溶质和溶剂两组元组成，对页岩（饱和多孔介质），推导给出了一种LTNE条件下的化学-热-弹性模型，同时讨论了耦合方程组的解耦求解问题．作为模型的应用，考虑无限大平面含一圆形孔的情况，研究了冷/热对流以及溶质摩尔分数突变边界条件下圆孔附近的孔隙压力和化-热应力问题，用Laplace变换得到了平面轴对称情况下有关力学变量的表达式．数值分析了圆孔边界上冷/热对流的Biot数和溶质摩尔分数改变量对圆孔附近孔隙压力和化-热应力的影响．结果表明：在Biot数为中等值(1~5)范围内，LTNE效应是非常明显的；化学作用对孔隙压力和固相应力的影响不可忽视．

A Chemo-Thermo-Poroelasticity Model for Saturated Poroelastic Media and Its Application

Based on the weighted average of the fluid and solid temperatures in the constitutive relations of chemo-thermo-mechanical responses and the variations of solute and solvent contents, this paper presents a local thermal non-equilibrium (LTNE) chemo-thermo-poroelasticity model for a porous medium (shale) saturated with a chemically active fluid, in which the pore fluid is modeled as a two-species constituent comprised of the solute and the solvent. When the displacement field is irrotational in an infinite medium, the decoupled problem, the pore pressure and the variations of solute mole fraction are decoupled from the displacements in the governing equations of the displacements and pore pressure and solute mole fraction variation, is also discussed. Subsequently, this model is applied to study the pore pressure and stresses around a hole in an infinite porous medium subjected to the actions of a chemically active fluid and convective cooling / heating on the hole boundary. This problem is simplified as an axisymmetric plane strain problem in an infinite plane with a borehole, the pore pressure and stresses around a borehole are obtained by using Laplace transform. The effects of LTNE and chemical action on the pore pressure and chemo-thermal stresses around the borehole are examined, the results show that the LTNE effects become more pronounced when the convective heat transfer boundary conditions with moderate Biot numbers are considered, and the chemical action in the analysis of pore pressure and stresses is not negligible.