Key characteristics of three-phase oil relative permeability formulations for improved oil recovery predictions

Significant three-phase regions can occur in a range of reservoir development strategies and oil relative permeability may then critically affect ultimate oil recovery. Unfortunately, three-phase oil relative permeabilities are not generally well characterized. In this paper we focus on theoretical methods of estimating three-phase oil relative permeabilities, as typically applied in reservoir simulation. In the absence of good physical models, we propose applying a mathematical filter to the many existing methods before fitting to measured data. First, the key characteristics of methods for predicting three-phase oil relative permeabilities are discussed, including choice of variables, behaviour at low oil saturations and three-phase residual oil saturations. Second, a numerical comparison of both predicted oil relative permeabilities and predicted incremental oil recoveries for immiscible WAG over waterflood is presented. None of the four most commonly used formulations assessed passed the mathematical filter successfully. Shortcomings were found in both of Stone's commonly used formulations for estimating expected recoveries. A wide range of incremental oil recoveries for immiscible WAG was found from choosing different formulations or different three-phase residual oil saturations. Some recommendations for best practice have been made.