Three-phase flow is present in many oil recovery processes of interest to the oil industry. It occurs in processes such as primary production below bubble point pressure in reservoirs with water drive, in gas or water alternating gas (WAG) injection into waterflooded reservoirs, in thermal oil recovery, and in surfactant flooding. Despite its common occurrence, our ability to reliably model three-phase flow using numerical simulation is questionable. This paper shows the importance of three-phase flow at typical oil field conditions. It also shows the uncertainties in the predictions of oil recovery due to the three-phase relative permeability model.
Numerical simulations of immiscible gas and WAG injection into a waterflooded one eighth of a five-spot were performed to determine the importance of the three-phase flow at conditions that are of interest to the oil industry. Consistent oil-water imbibition and oil-gas drainage relative permeability and capillary pressure were derived for this purpose, including a new form for imbibition capillary pressure.
Dimensionless scaling groups for three-dimensional three-phase flow in porous media were developed. The scaling groups were used to design simulations at various conditions of gravity, viscous and capillary force interactions. In addition, several simulations were made to determine the uncertainty of the results due to the model for three-phase relative permeabilities.
The results of this study show that there is a significant uncertainty associated with the selection of the three-phase relative permeability model for field scale simulations of gas and WAG injections. This uncertainty is translated into doubtful simulation results in terms of distribution of the fluids inside large volumes of the reservoir, total oil recovery, and fluids production rates. It is shown that additional oil recovery due to gas injection after a waterflood can be different by a factor of two depending on the model for three-phase relative permeability. It is also shown that the producing gas oil ratio (GOR) varies considerably depending on the model for three-phase relative permeability, while maintaining the same two-phase relative permeabilities. Accurate predictions of oil recovery in processes that exhibit three-phase flow need more rigorous models for three-phase relative permeability.
Large three-phase flow regions were present for most of the conditions simulated. The size of the three-phase flow regions ranged from 20% to 80% of the volume of the reservoir. The size of the three-phase flow region was a strong function of the kro model used. Thus, an argument asserting that only a small part of the reservoir is affected by the uncertainties in the three-phase relative permeability model is not supported by these results.