Permeability in fractured carbonate reservoirs is very heterogeneous due to fracturing at different scales superimposed on inherent textures from deposition and diagenesis. Observations of fractures in core and outcrop indicate that flow in open fractures in carbonate rock tends to be channelled rather than through fissures. Most of the flow takes place along a few dominating channels in the fracture plane, whereas most of the fracture plane is not effective for fluid flow. The formation of flow channels is caused by a combination of mechanical and, in particular, diagenetic processes. Single extension fractures occur as partly open or vuggy fractures, and their hydraulic properties are controlled by dissolution and cementation. Single shear fractures are typically open at local steps in the fault plane controlled by shearing along irregular fracture surfaces. Fault damage zones tend to be concentrated at fault tips, intersections, pull-aparts and overlap zones that represent areas of dilation. These damage zones represent elongated features in three dimensions with a high fracture density that will result in channelled flow at reservoir scales. The effect of channelled flow should be taken into account during evaluation of fractured carbonate reservoirs and when building dynamic flow models.

Steady-state upscaling techniques are attractive because they are quick and simple to implement; unlike dynamic methods, there is no need for fine grid simulation and the upscaled properties are not case dependant. They are based on the assumption that either capillary forces (capillary equilibrium limit, CL) or viscous forces (viscous limit, VL) dominate flow. However, the reservoir conditions for which these assumptions are valid have not been clearly defined. It is generally supposed that the CL method is valid at ‘low’ flow rates over ‘small’ lengthscales, while the VL method is valid at ‘high’ flow rates over ‘large’ lengthscales. These qualitative criteria are difficult to properly apply and can be easily violated, yielding significant errors in predicted reservoir performance. We have identified a comprehensive suite of dimensionless groups which can be used to define the validity of steady-state methods. The groups account for the effect of heterogeneity, as well as the other parameters which control the balance between capillary and viscous forces. Numerical simulations have been used to identify the range of values for these groups over which steady-state methods are valid. Our results yield a practical set of quantitative criteria which can be used to determine the validity of steady-state upscaling methods for a wide range of geological models. They capture the effects of capillary trapping and are valid regardless of fluid mobility, wettability or end-point saturation. We test our criteria against three realistic models of small-to intermediate-scale geological heterogeneity. We find that the criteria do a good job of predicting the range of validity for each method, and are conservative in all cases, suggesting that if they are met then steady-state upscaling techniques can be applied with confidence, and may still be valid for slightly less restrictive conditions. However, in the models investigated, we find that the validity of the CL method is restricted to very low flow rates which are unlikely to be encountered in most production scenarios. This is because the CL method overestimates the amount of capillary trapping. In general, VL upscaling is valid over a much more reasonable range of reservoir flow rates. Introduction Steady-state multi-phase upscaling has become increasingly popular because it is fast, robust and computationally cheap (e.g [1–8]). Unlike their dynamic counterparts, steady-state techniques do not need a full fine-grid simulation prior to generating the pseudo (upscaled) rock properties. However, steady-state upscaling is limited to areas in the reservoir where either capillary (capillary limit, CL) or viscous (viscous limit, VL) forces dominate flow. Using steady-state upscaling methods outside their validity range can yield significant errors in predicted recovery (e.g. [6]).

We present new dimensionless criteria to determine the validity of steadystate upscaling techniques in the limit that capillary (capillary limit, CL) or viscous (viscous limit, VL) forces dominate flow in a simple, layered geological system. We begin by identifying a suit of dimensionless groups which characterize the balance of capillary and viscous forces, then use numerical experiments to determine empirically the threshold values of these dimensionless groups for which each upscaling method is valid. Our criteria capture the effects of capillary trapping and are valid regardless of fluid mobility, wettability, or end-point saturation. They can be used to determine the reservoir conditions for which each upscaling method is valid. Previous studies have used a single dimensionless number to characterize the balance of forces, so have failed to properly identify the range of validity. We apply our new criteria to explain cases when the upscaling methods have been observed to do unexpectedly well or poorly. We also demonstrate that the CL method can be valid for a wider range of reservoir conditions than previously thought, particularly in mixed-and oil-wet systems where capillary trapping is minimal.

Summary Steady-state upscaling techniques are attractive because they are quick and simple to implement; unlike dynamic methods, there is no need for fine-grid simulation, and the upscaled properties are not case dependent. They are based on the assumption that either capillary forces (capillary equilibrium limit, CL) or viscous forces (viscous limit, VL) dominate flow. However, the reservoir conditions for which these assumptions are valid have not been clearly defined. It is generally supposed that the CL method is valid at "low" flow rates over "small" lengthscales, while the VL method is valid at "high" flow rates over "large" lengthscales. These qualitative criteria are difficult to properly apply and can be easily violated, yielding significant errors in predicted reservoir performance. We have identified a comprehensive suite of dimensionless groups which can be used to define the validity of steady-state methods. The groups account for the effect of heterogeneity, as well as the other parameters which control the balance between capillary and viscous forces. Numerical simulations have been used to identify the range of values for these groups over which steady-state methods are valid. Our results yield a practical set of quantitative criteria which can be used to determine the validity of steady-state upscaling methods for a wide range of geological models. They capture the effects of capillary trapping and are valid regardless of fluid mobility, wettability, or endpoint saturation. We test our criteria against three realistic models of small- to intermediate-scale geological heterogeneity. We find that the criteria do a good job of predicting the range of validity for each method, and are conservative in all cases, suggesting that if they are met, then steady-state upscaling techniques can be applied with confidence and may still be valid for slightly less restrictive conditions. However, in the models investigated, we find that the validity of the CL method is restricted to very low flow rates, which are unlikely to be encountered in most production scenarios. This is because the CL method overestimates the amount of capillary trapping. In general, VL upscaling is valid over a much more reasonable range of reservoir flow rates.

Summary Carbonate fractured reservoirs introduce a tremendous challenge to the upscaling of both single- and multiphase flow. The complexity comes from both heterogeneous matrix and fracture systems in which the separation of scales is very difficult. The mathematical upscaling techniques, derived from representative elementary volume (REV), must therefore be replaced by a more realistic geology-based approach. In the case of multiphase flow, an evaluation of the main forces acting during oil recovery must also be performed. A matrix-sector model from a highly heterogeneous carbonate reservoir is linked to different fracture realizations in dual-continuum simulations. An integrated iterative workflow between the geology-based static modeling and the dynamic simulations is used to investigate the effect of fracture heterogeneity on multiphase fluid flow. Heterogeneities at various scales (i.e., diffuse fractures and subseismic faults) are considered. The diffuse-fracture model is built on the basis of facies and porosity from the matrix model together with core data, image-log data, and data from outcrop-analogs. Because of poor seismic data, the subseismic-fault model is mainly conceptual and is based on the analysis of outcrop-analog data. Fluid-flow simulations are run for both single-phase and multiphase flow and gas and water injections. A better understanding of fractured-reservoirs behavior is achieved by incorporating realistic fracture heterogeneity into the geological model and analyzing the dynamic impact of fractures at various scales. In the case of diffuse fractures, the heterogeneity effect can be captured in the upscaled model. The subseismic faults, however, must be explicitly represented, unless the sigma (shape) factor is included in the upscaling process. A local grid-refinement approach is applied to demonstrate explicit fractures in large-scale simulation grids. This study provides guidelines on how to effectively scale up a heterogeneous fracture model and still capture the heterogeneous flow behavior.