Numerical Modeling and Validation of a Novel 2D Compositional Flooding Simulator Using a Second-Order TVD Scheme

Abstract

The aim of this paper is to present the latter and develop a numerical simulator aimed at solving a 2D domain porous medium, using the compositional approach to simulate chemical flooding processes. The simulator consists in a two-phase, multicomponent system solved by the IMplicit in Pressure, Explicit in Concentration (IMPEC) approach, which can be operated under an iterative/non-iterative condition on each time-step. The discretization of the differential equations is done using a fully second order of accuracy, along with a Total Variation Diminishing (TVD) scheme with a flux limiter function. This allowed reducing the artificial diffusion and dispersion on the transport equation, improving the chemical species front tracking, decreasing the numerical influence on the recovery results. The new model was validated against both commercial and academic simulators and moreover, the robustness and stability were also tested, showing that the iterative IMPEC is fully stable, behaving as an implicit numerical scheme. The non-iterative IMPEC is conditionally stable, with a critical time-step above which numerical spurious oscillations begin to appear until the system numerically crashes. The results showed a good correspondence in different grid sizes, being largely affected by the time-step, with caused a decrease in the recovery efficiency in the iterative scheme, and the occurrence of numerical oscillations in the non-iterative one. Numerically speaking, the second-order scheme using a flux splitting TVD discretization proved to be a good approach for compositional reservoir simulation, decreasing the influence of numerical truncation errors on the results when compared to traditional, first-order linear schemes. Along with these studies, secondary recoveries in constant and random permeability fields are simulated before employing them in tertiary recovery processes.