A New Nonlinear Model of Liquid Flows in Low Permeability Reservoirs

In the petroleum development engineering, the low permeability reservoir is that the permeabili- ty of porous media is lower than 50 micro-Darcy. Because of the existence of the threshold pres- sure gradient (TPG), the mathematical model of liquid flow in low permeability media is difficult to describe this kind of flow. Until then there is not an ideal model, although there are several models used to fields of well testing analysis and petroleum numerical simulations. Based on force between liquid and surface solid, and the negative slip boundary model of a micro-channel, a new liquid flow model was derived for low permeability reservoirs in this paper. First we defined the no-movement liquid layer close to the solid surface as the boundary stick layer which is regarded as the negative slip length, and used the inverse proportion of the height of the boundary stick layer to the pressure drop gradient, thus the formulae of liquid velocity and the flow rate of a round channel were derived; Then the model of liquid flows in low permeability reservoirs was gotten, based on the capillaries model; Finally the flow models were tested by examples and showed how to get the TPG of the low permeability reservoirs. The results show that there is no TPG on the whole of the low permeability reservoirs, but in small local pressure gradient, the ef- fects of boundary layer can be seen. Compared different power fittings on the experimental data, the first power exponential function fitting is relatively accurate.