Stokes-Darcy耦合流动问题的交界面条件研究

On the interface boundary conditions for the Stokes-Darcy coupling problem

近年来,随着我国碳酸盐岩缝洞型油藏开发的不断深入,Stokes-Darcy耦合流动问题备受关注.由于两方程的微分阶次存在差异,为不同尺度上的流动描述,因此需在耦合交界面处引入合适的界面条件,属于典型的多尺度多物理场耦合问题.本文从微观孔隙尺度上的流动数学模型出发,基于体积平均法进行了尺度升级研究,以此为基础建立了一组新的交界面条件来耦合Stokes-Darcy方程.新界面条件的数学形式与经典的Beavers-Joseph速度滑移条件相类似,但引入了一个新参数来修正渗流速度,该参数不仅是孔隙度和渗透率的函数,而且与界面过渡区域的结构特征密切相关.与之前的研究相比,本文界面条件能更准确地表征出界面过渡区域对耦合流动的影响,与实验结果的吻合度也更好.

Recently, the Stokes-Darcy coupling flow problem has been taken much attention because of its importance in the fractured vuggy carbonate reservoirs. However, the descriptive equations for a free-flow region and a porous medium are different from each other due to the scale difference. Therefore, a suitable interface boundary conditions should be found to couple such two flows. To this end, a theoretical development is conducted based on the volume averaging up-scaling approach, which starts from the mathematical models on the micro pore-scale. After that, a novel set of interface conditions at the fluid-porous interface is developed. Such novel interface conditions are similar to the Beavers-Joseph conditions. However, a new coefficient has been introduced to modify the Darcy velocity. This coefficient is not only the function of the porosity and permeability of the porous medium, but also related to the structure characteristic of the interface transition zone. We have compared the theory with the experimental studies of Beavers-Joseph and our LDA experiment data. The results have shown that our new interface boundary conditions provide better agreement with the experimental data than the previous study.