考虑裂隙的多孔介质中对流扩散现象的仿真模拟

SPH simulation of convection diffusion process in fractured porous media

摘要:

为研究裂隙多孔介质中的对流扩散现象,采用光滑粒子流体动力学（SPH）方法从孔隙尺度下模拟了裂隙中孔隙水的流动过程,仿真实现了考虑裂隙时溶质穿透多孔介质的真实运移过程,并提出一种简化处理的两流区模型对穿透过程加以描述.计算中首先采用SPH方法求解纳维斯托克斯方程,建立能考虑复杂多孔颗粒边界的二维流场模型,并基于此模型进行了溶质穿透三种不同裂隙宽度的多孔介质的仿真实验.随着介质中裂隙宽度增大,裂隙区域流速与基质区域流速差增大,穿透曲线中早期穿透和拖尾现象越明显；采用两流区模型能够描述这一现象,但一般化的模型难以得到精确解,因此提出一种简化处理办法,并给出了该简化模型的解析解.结果表明,该简化模型能够很好地描述裂隙多孔介质中溶质的运移规律,并可反演得到裂隙流中对流扩散的相关参数.

Abstract:

To study the convection diffusion in fractured porous media, the Smooth Particle Hydrodynamics (SPH) method was applied to simulate the flow process of water at the pore scale level. The real migration process of solute penetrating fractured porous media was realized by simulation, and a simplified Two-Region Model was proposed to describe the penetrating process. In the calculation, the SPH method was first used to discretize the Navier-Stokes equation, and a two-dimensional hydrodynamic field model considering complex porous particle boundary was established. Based on the constructed model, simulation experiments of solute penetration of porous media with three different fracture widths were carried out. As the fracture width in the medium increased, the flow velocity difference between the fracture region and the matrix region increased, and the early penetration and tailing phenomenon became more obvious. The Two-Region Model could well describe this phenomenon, while the traditional convection diffusion equation could not, though it is difficult to obtain accurate analytical solutions from the generalized model. Therefore, a simplified method was proposed and its corresponding analytical solution was provided. Results show that the proposed model can fit to the breakthrough curves accurately in fractured porous media, and the parameters of convection dispersion can be obtained by inversion.