Modelagem matemática e computacional do processo de reinjeção de água produzida em reservatórios de petróleo

Abstract

Produced water reinjection is a process used in oil reservoirs, consisting of reinjecting the water produced during oil production. However, this technique can be a!ected by reactive phenomena such as adsorption and mechanical retention. These phenomena may cause formation damage, leading to injectivity loss and, consequently, negatively impacting oil production curves. Given this, it is essential to develop mathematical and computational models that accurately describe the processes governing particle injection in porous media. In this context, the mathematical modeling developed in this dissertation aims to derive a system of partial di!erential equations that govern the hydrodynamics and particle transport in an oil reservoir. The hydrodynamics are governed by the total mass balance of the fluid phases, along with the total Darcy’s law, while particle transport is described by the advective-dispersive-reactive transport equation. The reactive nature of particle transport is modeled using kinetic laws expressed through ordinary di!erential equations. Regarding computational modeling, the hydrodynamics are discretized using the dual mixed finite element method, while the movement of the fluid phases is approximated using the explicit Central-Upwind finite volume method. For the discretization of the particle transport equation, we employ a predictor-corrector algorithm, which, due to the nature of the di!usive term, allows the equation to be numerically solved using the two aforementioned methods. The implemented computational simulator was validated against analytical solutions to assess its accuracy. The obtained numerical results demonstrate that the simulator can accurately and stably quantify the produced water reinjection process in oil reservoirs. Finally, the computational model is applied to a more realistic scenario, considering a quarter of a five-spot domain.