Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

Immiscible water-alternating-gas (WAG) flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency. Nevertheless, considering the complicated phase behavior and various multiphase flow characteristics, gas tends to break through early in production wells in heterogeneous formations because of overriding, fingering, and channeling, which may result in unfavorable recovery performance. On the basis of phase behavior studies, minimum miscibility pressure measurements, and immiscible WAG coreflood experiments, the cubic B-spline model (CBM) was employed to describe the three-phase relative permeability curve. Using the Levenberg–Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially, optimization of production performance including pressure drop, water cut, and the cumulative gas–oil ratio was performed. A novel numerical inversion method was established for estimation of the water–oil–gas relative permeability curve during the immiscible WAG process. Based on the quantitative characterization of major recovery mechanisms, the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment. The proposed method is reliable and can meet engineering requirements. It provides a basic calculation theory for implicit estimation of oil–water–gas relative permeability curve.