A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media - Wang, Ping; Liu, Wenchao; Ding, Wei; Kong, Xiangwen; Fan, Hailiang (Frontiers in Energy Research, 2022)
In consideration of vertical formation heterogeneity, a basic nonlinear model of 1D commingled preferential Darcian flow and non-Darcian flow with threshold pressure gradient (TPG) in dual-layered formation is presented. Non-Darcian flow in consideration of TPG happens in low-permeability tight layer; and Darcian kinematic equation holds in the other high-permeability layer. The similarity transformation method is applied to analytically solve the model. Moreover, existence and uniqueness of the exact analytical solution are proved strictly. Through the analytical solution results, some significant conclusions are obtained. Specially, the existence of TPG in the low-permeability tight layer can intensify preferential Darcian flow in the high-permeability layer. And intensity of the preferential Darcian flow in the high-permeability layer is very sensitive to the dimensionless layer thickness ratio. Effect of layer permeability ratio and layer elastic storage ratio on production sub-rate is more sensitive than that of layer thickness ratio. In addition, it is strictly demonstrated moving boundary conditions caused by TPG should be incorporated in the model. When the moving boundary is neglected, the preferential Darcian flow in the high-permeability layer will be exaggerated. Eventually, solid theoretical foundations are provided here, which are very significant in some fields such as numerical simulation validation and physical experiment design for solving non-Darcian seepage flow problems in engineering. What’s more, they are very helpful for better understanding the preferential flow behavior through the high-permeability paths (such as fractures) in the development of heterogeneous low-permeability reservoirs by water flooding so as to further develop efficient profile control technology to improve oil recovery.