Steady-State Upscaling: From Lamina-Scale to Full-Field Model

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Abstract
Summary: In recent years, the impact of small-scale permeability structure on hydrocarbon recovery has been demonstrated, and upscaling procedures, such as the geopseudo method, have been developed to scale-up from the lamina scale using the hierarchy of geological length scales. However, upscaling is very time consuming, so many engineers still input rock curves into large-scale simulations. In this study, we show how the process may be speeded up using steady-state methods for calculating the pseudofunctions. Two examples are used to demonstrate the method. The first is a three-stage scale-up of a water flood in a fluvio-aeolian model. Capillary equilibrium was assumed for the first two stages, and viscous-dominated steady state for the third stage. Two different wettability cases were examined—water-wet and intermediate-wet. The effect of using the small-scale pseudo relative permeabilities depends on both the nature of the heterogeneities and on the wettability. In this study the recovery was reduced when small-scale pseudos were included, especially in the water-wet case. The second case study involved gas injection into the oil leg of a tidal deltaic reservoir. Scale-up was performed in two stages: (a) from the lithofacies scale to the geological model, and (b) from the geological model to the full-field simulation model. The viscous-dominated steady-state method was used in both cases. The results showed that the effect of the fine-scale heterogeneities was of the same order as the effect of the coarse-scale heterogeneity, indicating that (even in a system where capillary pressure is negligible) the fine-scale structure can be important.
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