A computational framework for immiscible three-phase flow in deformable porous media

Several soil decontamination processes and enhanced oil recovery techniques involve the co-existence of three immiscible fluids, such as water, a nonaqueous phase liquid and a gas. In this work, a computational framework based on the individual mass balance of each phase is developed, aimed at simulating three-phase flow in a deformable rock through the finite element method, without resorting to specific simplifications that are usually required by standard numerical schemes. Key ingredients of the model are: expression of the residual in terms of mass contents, consistent lumping of the storage terms in the residual and algorithmic (tangent) matrix, consistent integration rules, the use of a minimum relative permeability and a time marching scheme based on trapezoidal integration. Special convective boundary conditions are adopted for pressures to be consistent with the assumed rock wettability properties during co-current imbibition. The resulting numerical scheme can deal with arbitrary saturation and/or pressure boundary conditions. The model is tested by simulating gas injection tests, and both co- and counter-current water imbibition tests, in a deformable core. To assess the performance and robustness of the whole framework, sensitivity analyses are performed upon varying key constitutive, loading and numerical parameters.