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A further study on Welge equation

Buckley–Leverett theory and Welge equation is one of the most widely used methods for predicting fluid transport in porous media. However, the average water saturation in Welge equation is a function of both water saturation and water cut, which is inconvenient to be used. While the linear relationship (the slope is 2/3) of the average water saturation and outlet water saturation proposed by Зфрос provides a simple method the oil–water viscosity ratio greatly limits the application. In this paper, based on the analytical relative permeability model and Welge equation, a new average water saturation equation with a variable (the outlet water saturation) was derived and applied in some cases under different relative permeability parameters and oil–water viscosity. Moreover, a simplified equation was proposed through certain data regression. Thus, the coefficient calculation method of the linear function was introduced based on the actual production data. Results showed a nonlinear relationship between the average water saturation and outlet water saturation, which is mainly related to water and oil relative permeability, and oil–water viscosity ratio. For the outlet water saturation higher than frontal saturation, the equation can be simplified to a linear function, which is the derivation of Зфрос equation. However, it is a function of both relative permeability and oil–water viscosity ratio instead of a constant slope of 2/3. In view of the fact that oil–water viscosity is mostly bigger than 10 in most reservoirs, the new model is an important supplement to Buckley–Leverett theory and Welge equation.