Interplay of Phase Behavior and Numerical Dispersion in Finite-Difference Compositional Simulation

Abstract

Compositional simulation of multicontact miscible (or nearmiscible) gas injection problems is typically performed by use of numerical finite-difference (FD) schemes. Such simulations are intrinsically affected by numerical dispersion.* In this paper, we propose a method to assess the sensitivity of a particular displacement calculation to the effects of numerical dispersion for systems with realistic multicomponent fluid descriptions. We use two simple ternary systems to illustrate how dispersion and convection interact to determine displacement composition paths and to define a "dispersive distance." We show how the dispersive distance relates to displacement performance with a detailed analysis of grid size effects on the recovery predictions for 1D displacements of a CH 4 -C 4 -C 10 system by pure N 2 and mixtures of N 2 and CH 4 . We then show that the sensitivity of multicomponent compositional simulations also correlates well with the dispersive distance. We demonstrate that quantitative difference between oil recovery predicted by coarse-grid numerical simulations, and values obtained from analytical solutions to the conservation equations, can be estimated well from calculating the distance between the dilution line and the composition path predicted by the method of characteristics. Finally, we apply the assessment of sensitivity to 2D displacements in a heterogeneous porous medium to demonstrate the interplay of phase behavior, adverse mobility, heterogeneity, and numerical dispersion.

A segregated flow scheme to control numerical dispersion for multi-component flow simulations

“…In other words, the use of coarser grids while underpredicting recoveries in 1D, could overpredict recoveries in multi-dimensions. Jessen et al [15] reported consistent findings. In 2D areal displacements, the coarser grids predicted higher recoveries despite the lower recoveries observed in 1D.…”

“…In 2D areal displacements, the coarser grids predicted higher recoveries despite the lower recoveries observed in 1D. Numerical dispersion leads to an improved sweep due to the suppression of preferential flow paths [15]. In summary, due to the interplay between numerical dispersion effects, which determine local displacement efficiencies, and viscous and gravity forces, which determine sweep efficiencies, the need to use fine grids to reasonably predict recoveries of miscible gas injection is problem dependent.…”

“…Augmented-water simulations still use a black oil model but the coupling between the solute concentration and the fractional flow exacerbates numerical dispersion effects. Similarly, in compositional simulations, the coupling between components concentration and the phase behavior renders some problems more sensitive to numerical dispersion [14,15]. Examples of such problems include miscible and near miscible gas injection as well as surfactant flooding [16].…”

“…For 1D displacements, it has been established that higher levels of dispersion hinder the development of miscibility and hence underpredict the displacement efficiency [1,15,[18][19][20]. For this reason, the use of coarse grids (with correspondingly significant numerical dispersion) in addition to underpredicting recoveries could also overpredict the optimum enrichment (the gas enrichment level above which insignificant incremental recoveries are realized) [18].…”

“…In a flash calculation, an increment of solvent which is injected in a gridblock will be fully mixed-despite the size of a gridblock-so that a uniform composition is obtained [35]. Hence, in the second timestep, a fraction of that solvent may be allowed to flow into the neighboring cell through numerical dispersion, even if this over-estimates the transport speed of the component [15].…”