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.

The accuracy of predicting waterflooding performance is crucial in determining the scale of investment for oilfield development. However, existing common waterflooding prediction models often relies on assumptions that may not apply universally or lack theoretical derivation through statistical analysis. This has led to unsatisfactory prediction accuracy and multiple potential solutions. To address these limitations, it is proposed to incorporate the oil/water relative permeability ratio model into the derivation process of waterflooding prediction models. Initially, an evaluation of prevalent oil/water relative permeability ratio models is conducted, along with an analysis of their primary constraints. Additionally, the applicability of the analytical relative permeability model is thoroughly examined. Building upon the analytical relative permeability model and a modified Welge equation, a new waterflooding model is formulated, encompassing all pertinent physical coefficients. Notably, this model aligns seamlessly with the commonly used Arps’ decline curve, while extending its applicability to a broader range of conditions. Moreover, it can be simplified to generate typical water drive curves under suitable circumstances. The semi-log relationship between oil/water relative permeability ratio and water saturation is further simplified into a linear relationship or a multi-term formula. Compared with the traditional waterflooding model, the new model proposed in this research has a wider application range and can be applied to oilfield at high water cut. At the same time, the new model clarifies the coefficient of waterflooding curve A and the physical meaning of parameter 7.5 in Tong’s chart method for the first time. The new model proposed in this research further enriches the connotation of waterflooding theory and has certain application significance.

Reservoir rock type (RRT) classification is commonly used for the fine characterization of strongly heterogeneous reservoirs. Many research focused on proposing different RRT methods, while few studies focused on the relationship between micropore structure and macroscopic seepage law of fluid transporting through different types of formation. Considering the different diagenesis degrees of rock types in different sedimentary facies, the quadrant unit method and FZI method were applied to classify and evaluate the strongly heterogeneous reservoirs. The corresponding capillary pressure curves and relative permeability curves for different rock types could be obtained. A set of theoretical models that could describe the macroscopic seepage law are proposed, and numerical simulation case studies were carried out to explore the superimposed seepage law in reservoirs under different degrees of heterogeneity. Results show that water cut rises faster in poor-property RRT formation than in good-property RRT formation, with a lower recovery factor under the same conditions. The water cut rising rate increases firstly and then decreases with water cut and recovery degree increasing. The poorer the rock property is, the earlier and higher the peak value of water cut rising rate is. Also, based on numerical simulation case studies, the superimposed seepage law is close to that in the poor-property formation as the heterogeneity degree strengthens. The newly proposed method not only could provide a reference for rock type classification based on micropore structure but also could expound the influence of micropore structure on the change law of macroscopic water cut and elaborates the macroscopic change law after the superposition of different types of reservoirs. The conventional normalization of relative permeability curves is only applicable to relatively homogeneous reservoirs and not applicable to strongly heterogeneous reservoirs, especially when the permeability variation is higher than 0.7. The newly proposed approach is capable of analyzing the effect of micropore structure on macroscopic seepage law and improving the prediction accuracy of the production profile.