As an important parameter of multiphase flow in porous media, relative permeability curve is often calculated by JBN method which ignores the capillary pressure. However, owing to the fine throat and the complex construct in extra low permeability reservoir, the capillary pressure is very significant. In addition, researches have shown that the flow in low permeability media doesn't follow the Darcy's law and there is threshold pressure gradient occurring in the percolation. Therefore, the traditional method is no longer available for the extra low permeability reservoirs and a new method is needed urgently to resolve this problem.

In this paper, the relative permeability of extra-low permeability core was calculated by three methods: JBN method, fractal model and modified JBN method. The fractal model was set up based on the capillary pressure curve and the fractal geometry theory. The modified JBN method taken into the effects of capillary pressure and threshold pressure gradient, and a semi-log fit function other than polynomial function was used to improve the accuracy.

The results show that, comparing with JBN method, the fractal model and the modified JBN method can predict the relative permeability more accurately. And the modified JBN method is the best. The water cut calculated by the new method matched the production data better than that calculated by JBN method.

The new method overcomes the limitations of previous researches. It can be used to calculate relative permeability for extra low permeability reservoirs more accurately and help to develop extra low permeability reservoirs more reasonably.

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