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Summary

A finite-difference, equation-of-state (EOS), compositional simulator has been used to study CO₂ flooding. First, unstable first-contact-miscible (FCM) displacements were simulated with a fine mesh to investigate the transition from gravity override to viscous fingering. Next, a direct comparison was made for FCM and multiple-contact-miscible (MCM) displacements under the same conditions to investigate effects of phase behavior on the growth of viscous fingers. Then, the effects of gravity, physical dispersion, capillary pressure, phase behavior, and heterogeneity were combined and simulated for CO₂ flooding on a field scale with stochastic permeability fields.

Introduction

For many years, viscous fingering has been considered one of the dominant flow patterns for displacements at adverse mobility ratios and has been an active research topic both experimentally and theoretically. Most of the studies, however, have been conducted under simplified conditions. For example, Peaceman and Rachford,¹ Christie and Bond,² Araktingi and Orr,³ Ewing et al.,⁴ Christie,⁵ Christie et al.,⁶ and Waggoner et al.⁷ simulated viscous fingering for FCM displacements. Remarkably, none of these studies considered multiphase flow, which commonly occurs in MCM floods. One motivation for our studies was to determine the effect of multiphase flow on viscous fingering.

Many factors affect viscous finger growth. Fayers and Newley⁸ and Christie et al.⁹ showed that FCM displacements are dominated by viscous fingering only at low gravity number, N_g (defined as the ratio of gravity to viscous forces). At high N_g, displacements are dominated by gravity override. Fingering is defined as viscous instability. This distinction is important because fingering and gravity override do not scale the same and do not have the same remedies for improving oil recovery. Fingering disappears for mobility ratios 1, whereas gravity override disappears only when fluid densities are equal. Furthermore, water-alternating-gas (WAG) injection is commonly used to stabilize fingering in CO₂ flooding. Christie⁵ and Christie et al. ⁶ demonstrated that viscous fingering was reduced for miscible WAG displacements at optimal WAG ratios.

Most fingering studies have been limited to quasihomogeneous porous media with small permeability variations. In typical oil reservoirs, however, a larger heterogeneity with a 0.6 to 0.8 Dykstra-Parsons coefficient is typical. Araktingi and Orr³ and Waggoner et al.⁷ included heterogeneities of this magnitude in their studies. Araktingi and Orr applied a random-walk model to simulate unstable flow in statistically generated heterogeneous porous media. Their model was restricted to incompressible FCM fluids. Waggoner et al. used a finite-difference simulator to simulate unstable displacements and introduced the notion of constructing flow regime maps that we illustrate for MCM displacements below. Fayers et al. ¹⁰ investigated the effects of heterogeneity for lean gas, FCM, and surfactant displacements. However, only limited heterogeneity runs were made in their study.

The motivation of this study was to investigate the importance of viscous fingering in MCM flooding, in particular in CO₂ flooding. The phase behavior of CO₂ flooding is always more complicated than that of FCM displacements even when the pressure is far above the minimum miscibility pressure (MMP). The viscosity contrast between swept and unswept zones for CO ₂ flooding can be reduced because of extraction of hydrocarbon components from the oil phase to the CO₂-rich phase, or vice versa, and because relative permeabilities for multiphase flow lower the fluid mobilities compared with those for single-phase flow. Both factors will reduce the mobility ratio at the displacement front and thus stabilize the displacement. Another important factor is the permeability distribution. Displacements may channel when reservoirs have permeability fields of large correlation length.³ The distinction between viscous fingering and channeling is also important because they do not scale the same way and do not have the same effect on oil recovery or the same remedies. Channeling is caused by permeability variations; it will not occur in the presence of uniform permeability or random permeability fields but will occur at unit mobility ratio. These effects plus gravity, capillary pressure, and dispersion reduce the tendency for viscous fingering.

Because all these factors can exist for CO₂ flooding, one may wonder whether fingering is ever important for field applications of CO₂ flooding. If it is not, under what conditions is fingering important? What are the dominant flow patterns under field conditions?

We began with simulating unstable FCM displacements to investigate the conditions under which viscous fingering is the dominant flow pattern when gravity effects are included. In addition, simulations were made to investigate possible 3D effects on these unstable displacements. Then, the effects of phase behavior on viscous fingering were studied by comparing FCM displacements with CO₂ flooding. Quasihomogeneous reservoirs were used in these initial simulations. The complexity of the simulated conditions was further increased in the final study when reservoir heterogeneity was included in addition to gravity and physical dispersion. The effects of heterogeneity, gravity, capillary pressure, and dispersion on the flow patterns were investigated for field-scale CO₂ flooding.

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