The influence of relative permeability functions on the oil and water production

In this paper we analyse the influence of relative permeability functions on the production of oil and water from an oil reservoir.The analysis presented is of practical significance for injection well treatments with polymer gels.First we formulate a test-case with relative permeabilities depending linearly on saturation for which a semi-explicit solution is found.The results from this test-case agree perfectly well with results obtained from a numerical method based on a Finite Volume approach with a higher order discretisation.This numerical method is used for more general shapes of the relative permeability functions of oil and water.First we analyse the Corey-shape relative permeability and subsequently we use more general forms.It is concluded that the shape of the relative permeability function plays an important role in the production of water and oil.