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.

Simulation of Surfactant Oil Recovery Processes and the Role of Phase Behaviour Parameters

“…In three-phase systems (water-oil-microemulsion), the treatment is relatively straightforward and simulators use the same approach: aqueous and oleous phases are considered pure, and the composition of the microemulsion is assumed to be constant and function only of salinity and temperature. Due to these factors, the simulation of three-phase systems in fields with high salinity or thermal gradients may cause numerical issues (e.g., appearance of spurious oscillations, numerical instabilities), rendering the method ineffective [9,11]. In contrast, in two-phase systems, the components' volume concentrations in the phases respond to a more complex model.…”

“…Simulation of multiphase and multicomponent flow in porous media requires solving a number of coupled, highly non-linear equations dealing with temporal and spatial derivatives of pressure and mass concentrations. It is adopted in this model a second-order accuracy discretization scheme, along with a Total Variation Diminishing (TVD) flux limiter, which reduces the occurrence of numerical diffusion and dispersion mechanisms [11]. The compositional flow is a suitable approach to study the different cEOR techniques, which can be described as the mass transfer of a number of components (e.g., polymers, surfactants, salts, etc.)…”

“…The numerical simulator presented in this paper is based on previous ones developed also for EOR flooding [38,53]. The 2D model was validated against academic and commercial simulators in a previous paper, discussing also its order of convergence ( Figure 2) [9,11]. Since this model it is an extension of a previous one, it is considered that the validation process previously done is valid for this model [54][55][56].…”

“…In this model a complete second-order explicit discretization scheme is employed based on flux limiting techniques. This increases the numerical accuracy of the simulator and decreases the influence of numerical phenomena on the results [11,25,[57][58][59]. Thus, the discretized mass conservation equation is,…”

“…The objective in this paper is to present the numerical simulation of surfactant EOR flooding. Thus, a novel numerical simulator is presented to analyze tertiary recovery processes in a 2D oilfield [9][10][11], simulating a two-phase, four-component flow.…”