Analysis of Vertical Permeability and Its Influence on CO2 EOR and Storage in a Carbonate Reservoir

The objective of this study is to improve understanding of the geostatistics of vertical (bed-normal) permeability (kz) and its influence on reservoir performance during CO2 enhanced oil recovery (EOR) and storage. kz is scrutinized far less often than horizontal permeability (kx, ky) in most geological and reservoir modeling. However, our work indicates that it is equally important to understand kz characteristics to better evaluate their influence on CO2 EOR and storage performance prediction. We conducted this study on about 9,000 whole-core triaxial permeability (kx, ky, kz) measurements from 42 wells in a San Andres carbonate reservoir. We analyzed kz data, including heterogeneity, correlation, and sample sufficiency measures. We analyzed wells with the largest and smallest fractions of points with kz > kmax = max(kx, ky), to explore geological factors that coincided with large kz. We quantified these geological effects through conditional probabilities on potential permeability barriers (e.g., stylolites). Every well had at least some whole-cores where kz > kmax. This is a statistically justifiable result; only where Prob(kz > kmax) is statistically different from 1/3 are core samples non-isotropic. In conventional core data interpretation, however, modelers usually assume kz is less than kmax. For the well with the smallest fraction (11%) of cores where kz > kmax, the cumulative distribution functions differ and coincides with the presence of stylolites. We found that kz is about twice as variable as kx in many wells. This makes kz more difficult to interpret because it was (and usually is) heavily undersampled. To understand the influence of kz heterogeneity on CO2 flow, we built a series of flow simulation models that captured these geostatistical characteristics of permeability, while considering kz realizations, flow regimes (e.g., buoyant flow), CO2 injection strategies, and reservoir heterogeneity. CO2 flow simulations showed that, for viscous flow, assuming variable kx similar to the reservoir along with a constant kz/kx = 0.1 yields a close (within 0.5%) cumulative oil production to the simulation case with both kx and kz as uncorrelated variables. However, for buoyant flow, oil production differs by 10% (at 2.0 hydrocarbon pore volume HCPV of CO2 injected) between the two cases. Such flows could occur for small CO2 injection rates and long injection times, in interwell regions, and/or with vertically permeable conduits. Our geostatistical characterization demonstrates the controls on kz in a carbonate reservoir and how to improve conventional interpretation practices. This study can help CO2 EOR and storage operators refine injection development programs, particularly for reservoirs where buoyant flow exists. More broadly, the findings potentially apply to other similar subsurface buoyancy-driven flow displacements, including hydrogen storage, geothermal production, and aquifer CO2 sequestration.

Nongeostrophic Baroclinic Instability over Sloping Bathymetry: Buoyant Flow Regime

Baroclinic instabilities are important processes that enhance mixing and dispersion in the ocean. The presence of sloping bathymetry and the nongeostrophic effect influence the formation and evolution of baroclinic instabilities in oceanic bottom boundary layers and in coastal waters. This study explores two nongeostrophic baroclinic instability theories adapted to the scenario with sloping bathymetry and investigates the mechanism of the instability suppression (reduction in growth rate) in the buoyant flow regime. Both the two-layer and continuously stratified models reveal that the suppression is related to a new parameter, slope-relative Burger number Sr ≡ (M2/f2)(α + αp), where M2 is the horizontal buoyancy gradient, α is the bathymetry slope, and αp is the isopycnal slope. In the layer model, the instability growth rate linearly decreases with increasing Sr {the bulk form Sr = [U0/(H0f)](α + αp)}. In the continuously stratified model, the instability suppression intensifies with increasing Sr when the regime shifts from quasigeostrophic to nongeostrophic. The adapted theories are intrinsically applicable to deep ocean bottom boundary layers and could be conditionally applied to coastal buoyancy-driven flow. The slope-relative Burger number is related to the Richardson number by Sr = δrRi−1, where the slope-relative parameter is δr = (α + αp)/αp. Since energetic fronts in coastal zones are often characterized by low Ri, that implies potentially higher values of Sr, which is why baroclinic instabilities may be suppressed in the energetic regions where they would otherwise be expected to be ubiquitous according to the quasigeostrophic theory.