A Precise and Locally Conservative Mathematical and Computational Model for the Polymer Injection Process in Oil Reservoirs
Petroleum Reservoir Simulation, Polymer Injection, Hybrid Mixed Dual Method, Central-Upwind
Polymer injection (PEOR) consists of a promising alternative to enhance oil recovery in reservoirs. However, its performance can be hindered by phenomena such as adsorption and mechanical retention, which affect injectivity and, consequently, the efficiency of the recovery process. Therefore, to fully understand the dynamics of polymer injection, a robust, accurate, and comprehensive mathematical and computational model is required to precisely represent all complexities involved in the process dynamics. In this context, the computational model proposed in this thesis incorporates various phenomena associated with polymer injection, such as the influence of gravity, fluid pseudoplasticity, formation damage, and the dependence of relative permeability on concentration. The model’s hydrodynamics, describing the flow of the aqueous and oil phases in the porous medium, is governed by Darcy’s law and mass balance equations. Meanwhile, polymer transport is described by a transport equation in a advective-dispersive-reactive regime, with physicochemical adsorption modeled by the Langmuir isotherm and mechanical retention by a linear kinetic law. In the numerical model, based on the Implicit Pressure and Explicit Saturation and Concentration (IMPESC) algorithm, the set of equations is subdivided into two parts: the hydrodynamic system and the transport system. The discretization of the hydrodynamic problem employs a conservative and accurate method, the Hybrid Mixed Dual Finite Element Method (HMFEM), which uses the Raviart-Thomas basis to achieve greater accuracy in capturing velocity at the element centers. Polymer transport, in turn, is discretized using the Central-Upwind finite volume method, capable of accurately capturing shocks and rarefactions. The proposed computational model is validated through accuracy tests, comparing numerical and analytical solutions, and assessed in PEOR applications on a quarter fivespot domain, including the SELEPOL technique.