Mathematical and Computational Modeling of the Produced Water Re-Injection Process in Oil Reservoirs
Mathematical Modeling; Finite Element Method; Finite Volume Method; Particle Transport; Produced Water Re-Injection
Produced water reinjection is a process used in petroleum reservoirs, consisting of reinjecting the water produced during the extraction process. However, this technique can be affected by reactive phenomena, such as adsorption and mechanical retention, which reduce injectivity and impact oil production. Thus, this dissertation proposes a mathematical and computational model to accurately describe particle injection in porous media. The model is based on a system of partial differential equations governing the hydrodynamics and particle transport in the reservoir. The hydrodynamics are described by the total mass balance of fluid phases and the total Darcy's law, while particle transport follows an advective-dispersive-reactive regime, with its reactive nature modeled by ordinary differential equations. The computational formulation employs the dual mixed finite element method for hydrodynamics and the explicit Central-Upwind finite volume method for fluid phase movement. The discretization of particle transport is performed using a predictor-corrector algorithm, enabling the combined use of both methods. The developed simulator is validated through comparisons with analytical solutions, demonstrating high accuracy and stability. Finally, the model is applied to a more realistic scenario, considering a quarter of a \textit{five-spot} domain.