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ABSTRACT
In low-permeability reservoirs, the average pore throat radius is small and the heterogeneity is severe, and the threshold pressure gradient exists obviously. Because of the pore throat radius sorting of porous media, the threshold pressure gradients of the pore throats with different radius are different, which leads to the asynchronism of the fluid participating in flow in the pore throats with different radius. The apparent permeability of the rock is a variable value before it reaches the average permeability of the rock, which makes low-velocity nonlinear porous flow come into being. The essence of nonlinear porous flow is the process of the fluid participating in porous flow gradually according to pore throat radius from large to small in pore throats with different radius under the combined action of threshold pressure gradient and pore throat radius sorting. This is an inevitable stage before the porous media reaches Darcy flow. The porous media keeps in nonlinear porous flow stage before all the pore throats participate in flowing. Based on the pore throat radius sorting of porous media, the nonlinear porous flow equation in low-permeability reservoirs was established using unequal-diameter parallel capillary bundle model with the capillary radius commonly in accordance with normal distribution. The equation can not only reveal low-velocity nonlinear porous flow mechanism but also describe the forming process of nonlinear porous flow. Furthermore, the equation is a general equation. Both Darcy’s law and the pseudo-Darcy equation with the threshold pressure gradient in low-permeability reservoirs are the particular cases.