A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media

被引:0
作者
Wang, Ping [1 ]
Liu, Wenchao [2 ]
Ding, Wei [1 ]
Kong, Xiangwen [1 ]
Fan, Hailiang [3 ]
机构
[1] PetroChina Res Inst Petr Explorat & Dev, Beijing, Peoples R China
[2] Univ Sci & Technol Beijing, Sch Civil & Resource Engn, Beijing, Peoples R China
[3] China ZhenHuaOil Co Ltd, Beijing, Peoples R China
关键词
exact analytical solution; threshold pressure gradient; heterogeneity; Darcian flow; low-velocity non-Darcian flow; moving boundary; THRESHOLD PRESSURE-GRADIENT; LOW-PERMEABILITY RESERVOIR; ONE-DIMENSIONAL CONSOLIDATION; DEPTH PROFILE CONTROL; HORIZONTAL WELL; GAS-RESERVOIRS; STEFAN PROBLEM; BINGHAM FLUID; FRACTAL MODEL; DARCYS-LAW;
D O I
10.3389/fenrg.2022.941605
中图分类号
TE [石油、天然气工业]; TK [能源与动力工程];
学科分类号
0807 ; 0820 ;
摘要
In consideration of vertical formation heterogeneity, a basic nonlinear model of 1D commingled preferential Darcian flow and non-Darcian flow with the threshold pressure gradient (TPG) in a dual-layered formation is presented. Non-Darcian flow in consideration of the TPG happens in the low-permeability tight layer, and the Darcian kinematic equation holds in the other high-permeability layer. The similarity transformation method is applied to analytically solve the model. Moreover, the existence and uniqueness of the analytical solution are proved strictly. Through analytical solution results, some significant conclusions are obtained. The existence of the TPG in the low-permeability tight layer can intensify the preferential Darcian flow in the high-permeability layer, and the intensity of the preferential Darcian flow is very sensitive to the dimensionless layer thickness ratio. The effect of the layer permeability ratio and layer elastic storage ratio on the production sub-rate is more sensitive than that of the layer thickness ratio. In addition, it is strictly demonstrated that moving boundary conditions caused by the TPG should be incorporated into 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 for solving non-Darcian seepage flow problems in engineering by numerical simulation validation and physical experiment design. Furthermore, they are very helpful for better understanding the preferential flow behavior through the high-permeability paths (such as fractures) in the water flooding development of heterogeneous low-permeability reservoirs; then, the efficient profile control technology can be further developed to improve oil recovery.
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页数:19
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