Validity of Steady-State Upscaling Techniques

Abstract

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.