Mathematical Model for Oil Recovery Prediction of Polymer Microsphere Conformance Control Based on the Stream Tube Method

Oil recovery is an essential parameter for reservoir development performance evaluation, but there is no specific research on the theoretical oil recovery prediction model of polymer microspheres (PMs)’ conformance control. This research aims to establish an oil recovery prediction model that depends on the definition of oil recovery based on stream tube theory. PMs’ enhanced oil recovery mechanism is to plug the pore throat to expand the swept area. The assumption that the stream tube between injection and production wells is trapezoidal is proposed. Based on this premise, the area sweep efficiency equation suitable for the rhombus inverse nine-spot well pattern is established based on the stream tube theory. The vertical sweep efficiency equation is optimized by introducing the equivalent mobility ratio. Additionally, the model’s adaptability and validity are studied. The analysis results show that oil recovery decreases with increasing injection rate, injection concentration, and PMs size but increases with the increasing injection period. The theoretical oil recovery is 1.37%, and the actual oil recovery of the field application is 1.22%, with an error of 0.15%. This model has good consistency with the actual physical process of the field application. The oil recovery prediction model can provide oil recovery and optimize PMs’ conformance control injection scheme. This study fills the gap in the mathematical model for oil recovery prediction of PMs’ conformance control.