Water Alternating Gas (WAG) injection is one of the most successful enhanced oil recovery approaches. Properly accounting for the hysteretic effects of relative permeabilities is a critical issue encountered in numerical simulations of WAG at the mesoscale. proposed a sigmoid-based model for three-phase oil relative permeability, incorporating key physical effects taking place at the pore scale. The model can then be jointly used with the model, accounting for gas relative permeability hysteresis, to develop a formulation for three-phase relative permeability suitable for reservoir simulation.

In this study we illustrate the impact of this joint formulation on a field scale setting through a suite of numerical simulations of WAG injection targeting a reservoir model inspired to real life cases. The analysis is performed by embedding the illustrated relative permeability models in the black oil model implemented in the Matlab Reservoir Simulation Toolbox ( ). We assume non-hysteretic behavior for water relative permeability under water-wet conditions and characterize it upon relying on corresponding laboratory-scale data. As a baseline, the results are compared against a scenario in the absence of three-phase relative permeability hysteresis.

The computational domain is heterogeneous, the spatial distributions of porosity and absolute permeability varying across the ranges of [0.02 – 0.3] and [0.1 – 2600 mD], respectively. The model is set at equilibrium conditions, production being driven by three peripheral injectors and five up-dip producers. A given flow rate is assigned to each injector and a target value of liquid production rate is imposed at the producing wells. The numerically evaluated production rates constitute our target state variables. The schedule of the injectors is set to achieve a preliminary waterflooding phase followed by a WAG injection scheme. The latter is implemented by periodically switching the injected phase between water and gas for two injectors, the third injector continuously injecting water. The numerical simulations are performed through a fully implicit discretization of the equations governing the system dynamics. To minimize computational costs, we employ an algebraic multi-grid method and resort to a multi-processor high performance clustered computer system. Our results suggest that hysteretic effects are important across significant portions of the studied reservoir system. Field production responses are associated with a simultaneous increase of ultimate oil recovery and a corresponding decline of the gas-oil ratio when hysteretic effects are included in the simulations.


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