A Novel Model for Oil–Water Stratified Flow in Horizontal Wells With a Curved Interface Based on Dynamic Contact Angle

During the process of oil production and transportation, oil–water two-phase flow is a common occurrence. Well completion optimization and production design are greatly affected by the prediction accuracy of two-phase flow characteristics. In this paper, a novel model is proposed to predict the influence of interface shape on stratified flow. Dynamic contact angle theory and minimum energy method are introduced to solve the momentum equations with a curved interface and dispersed phase holdup in the lower water layer or the upper oil layer, respectively. When the Eotvos number is lower than ten, the interface shape changes from a flat surface to a curved surface, and the flow area of the upper water layer and the lower oil layer will increase and decrease, respectively. Results show that the dynamic contact angle and pressure gradient are greatly affected by oil superficial velocity, oil viscosity, and pipe diameter. By comparing the prediction with available experiment results, the validity of the model is evaluated. Results show that the novel model has an overall good prediction performance for the pressure gradient, with an average percentage error of 13.12%. While the average percentage error of Liu's model and two-fluid model are 22.89% and 34.98%, respectively. The novel model is a unified model that could be used to solve the problem with a curved/flat interface. It will also promote the oil well production design and horizontal well completion optimization.