Single- and two-phase flow model in low-permeability reservoir

In petroleum development, low-permeability reservoir means having permeability of porous media lower than 50 micro-Darcy. The mathematical model of liquid flow in low-permeability reservoirs has been difficult to describe for a long time, and an ideal model has not been available until now because of the threshold pressure gradient. With the boundary adhesion layer model of a micro-channel as basis, a new liquid flow model was derived for low-permeability reservoirs in this study. The no-movement liquid layer close to the solid surface was defined as the boundary adhesion layer regarded as the negative slip length. Using the exponential function of the boundary stick layer to the pressure drop gradient, the formulae of the liquid velocity and flow rate of a round channel were derived. The liquid flows model in low permeability reservoirs was then obtained. Finally, the flow model was tested by examples, and applications to a low-permeability reservoir were demonstrated. The analysis results show that the new non-linear model of liquid flows exhibits clear physical definition, and can be easily used to describe liquid flows in low-permeability media.