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Issues with Permeability, Relative Permeability, and Capillary Pressure Architecture and Upscaling to Accurately Model Performance of Thin, Heterogeneous, Shallow-Shelf Carbonate Reservoirs in Kansas
Alan P. Byrnes and Saibal Bhattacharya
Kansas Geological Survey, Lawrence, KS
It is well recognized that accurate reservoir simulation and management requires a quantitative model of the spatial distribution of reservoir storage and flow properties and an understanding of the nature of reservoir heterogeneity at many scales. Within the thin (1.5-10 m thick), heterogeneous, shallow-shelf carbonates of the US Midcontinent, basic petrophysical properties (e.g., porosity, absolute permeability, capillary pressure, residual oil saturation, resistivity, and relative permeability) vary significantly horizontally, vertically, and with scale. In addition, many of these reservoirs produce from structures of less than 10-20m, and therefore exhibit variable initial saturations and relative permeability properties by virtue of being located at different heights (above Free water level) in the capillary (pressure) transition zone. Rather than being simpler to model because of their small size, simulation model sensitivity to property architecture is increased in these reservoirs challenging characterization and simulation methodology and illustrating issues often less apparent in larger reservoirs. Understanding these issues is critical to successful reservoir management as reservoirs mature and enhanced recovery methods are planned and implemented. Characterization and simulation of reservoirs from two major Kansas formations provide examples of the influence of petrophysical architecture, end-point saturations, and upscaling on predicted performance, and the errors in performance prediction that can result from using upscaled models as opposed to fine-scale architecture. Results from this study also illustrate how the input of properties measured at one scale into flow simulations models performed at another scale result in diverging reservoir performance prediction leading to potentially incorrect reservoir management.
In Kansas, Mississippian-age dolomite and limestone mudstones to moldic packstones were deposited in a shallow-shelf to gentle sloping ramp setting. Post-depositional regional uplift, subaerial exposure and differential erosion resulted in variable preservation and relief, dissolution of some bioclastic grains, and diagenetic overprinting of the original depositional fabric. Reservoir properties are well correlated with lithofacies with porosity (2-20%) and permeability (0.001-200 md) generally increasing from mudstones to packstones (Fig 1).
During the Pennsylvanian, changing sea level and episodic local processes led to accumulation, and local reworking and redeposition of multicycle elongate stacked, shingled, and cross-cutting oolite sand bars (0.5-10 m thick). Subsequent subaerial exposure and meteoric water percolation led to microporous cementation around the aragonite ooids and frequently dissolution of the ooids to form oomoldic grainstones. Reservoir characterization at several sites indicates that productive intervals as thin as 2-3 m thick can comprise up to three stacked, shallowing-upward cycles contained within a single higher-order shallowing-upward sequence accompanied by vertically increasing porosity and permeability ranging from <0.001 md at the base to >200 md at the top (Fig. 2).
Errors in Original Oil in Place Estimation
Capillary pressure and relative permeability change with lithofacies and with porosity and permeability for each lithofacies. Structural closures of 10-20 m place a major portion of these reservoirs in the transition zone (Fig. 3). Because saturations change markedly with depth the number of layers in a model can strongly influence grid cell water saturations calculated using capillary pressure curves in simulation studies. Even when uniform layer properties are assumed to exist in a reservoir, Figure 4 indicates that significant errors can exist for initial saturation estimates when less than 8 layers are used to build the reservoir model. Total error in OOIP estimation is a function of the capillary pressure curves and the portion of the reservoir in the transition zone, and can reach up to 20%. Error within the oil zone alone can be greater than that for the entire transition interval (below the oil-water contact but above the free water level where water saturation is 100%).
Errors in Relative Permeability and Fluid Recovery Volumes
Frequently only a few relative permeability (Kr) curves are utilized to simulate a field, however, Kr relations change with facies and with absolute permeability (Fig. 5). Typical shifts include increasing “irreducible” and critical water saturation (Swi, Swc) with decreasing permeability and potential changes of residual oil saturation to waterflood (Sorw) with changing permeability. Use of too few Kr curves that are not coupled to capillary pressure relations can result in incorrect flow calculations. For example, a low permeability rock with high Swc (e.g. 50%) which is assigned a high permeability Kr curve would be incorrectly predicted to be flowing water and no oil when it should only be flowing oil.
Rapidly changing water saturations with depth result in different initial saturations and relative permeability behavior. Land (1971) formulated the relationship between initial non-wetting phase saturation and residual non-wetting saturation. For the carbonate rocks studied here, Sorw increases with increasing initial oil saturation, Soi, for a given rock type due to emplacement of oil in fine pores where trapping is increased. Analysis shows that the Land trapping coefficient, C, increases with increasing porosity resulting in less trapping with increasing porosity (Fig. 6). This relationship, coupled with the increasing Swi with decreasing porosity and permeability results in a systematic change in Sorw with porosity/permeability and Soi (Fig. 7). With Soi changing continuously with depth in the transition zone, and it being one of the end-points for Kr curves, proper modeling of Kr in the transition zone requires a family of Kr curves to reflect changes in Kr with changing Soi (Fig. 8).
Comparison of simulation results from models that utilize Kr curves incorporating a changing Soi and Sorw within the transition zone with those that utilize Kr curves with a constant Soi (typical Kr with Soi=1-Swi) and Sorw shows that both oil and water recovery are greater from the transition zone when Kr curves include a variable Soi & Sorw (Fig. 9). Oil recovery is higher because Sorw is lower and water recovery is higher because Sw increases as oil-water contact is neared. Further, analysis shows that fluid recovery increases when an increasing number of layers are used to model the same reservoir.
Exploring how various scaling issues and incorporation of consistent reservoir properties in the construction of a reservoir model influence predicted flow performance reveals the relative merits of utilizing a fine-scaled model in these thin, heterogeneous carbonate reservoir systems. The results presented here for transition zones can be scaled to other systems as a function of its respective family of capillary pressure curves.
Figure 1. Basic petrophysical trends for Mississippian carbonates in Kansas.
Figure 2. Typical properties of Lansing-Kansas City oomoldic limestones in central Kansas as represented by properties in the Colliver lease, Hall-Gurney field.
Figure 3. Capillary pressure curves for Lansing-Kansas City and Mississippian rocks in Kansas showing that reservoirs with less than 45 feet of closure and hydrocarbon column height are dominated by properties in the transition zone.
Figure 4. Vertical scaling of model influences water saturations calculated using capillary pressure relations. Models with less than 8 layers can exhibit significant saturation error
Figure 5. Example of imbibition oil-water Kr curves showing shift with change in absolute permeability.
Figure 6. Illustration of Land relations and change in trapping C with permeability.
Figure 7. Relationship between Sorw and Soi for different porosity carbonates.
Figure 8. Family of Kr curves that are required to model flow in transition zone due to changing Kr with absolute K and changing Soi with position in transition zone. Each absolute permeability rock requires a unique set of Kr curves.
Figure 9. Simulation predicted recovery for a 30 md Mississippian rock comparing recoveries predicted for constant Soi, Sorw (Soc) models and variable Soi, Sorw (Sov) models and for different numbers of layers. Color figure illustrates the improved recovery in the lowermost transition zone with variable Kr curves. Increasing the number of layers increases predicted recovery.