Dynamic downscaling and upscaling in high contrast systems
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2017, Society of Petroleum Engineers Traditional upscaling and downscaling methods are based upon steady state (SS) or pseudo steady state (PSS) concepts of flow, while flow simulation relies upon the calculation of pressure transients. In high contrast or low permeability systems the SS/PSS limit may not be reached during a simulation time step, introducing a potentially significant bias into an upscaling or downscaling calculation. We utilize an asymptotic pressure transient analysis to improve upon the resolution of these dynamic effects. The methodology is an application of the concepts of the diffusive time of flight and drainage volume to obtain source functions that capture both the transient and the long time limits of the flow patterns. Diffuse source (upstream) or sink (downstream) functions are introduced within each fine cell of a coarse cell pair with a specified total flow between them, computed at a characteristic time for pressure transients across the cells. The ratio of volume averaged flux and pressure gradient is used to obtain the effective transmissibility between the cell pair. The application of pressure transient concepts has allowed us to develop completely local upscaling and downscaling calculations. A characteristic time is determined for which the pressure transients cover the cell but for which the overall flow is still infinite acting, allowing a coarse cell flow characterization in terms of infinite acting linear flow. Unlike steady state upscaling calculations which explicitly impose flow on the boundaries of an upscaling region, and implicitly couple the local problem to a global flow field, these calculations are completely local. Similarly, where multiscale downscaling calculations may assume PSS flow to determine a fine scale local velocity, these assumptions may now be tested in terms of this characteristic time. This characteristic time may also be used to examine the impact of net / non-net cutoffs. The methodology is tested on SPE10 where we have permeabilities varying over 5 orders of magnitude making it high contrast in nature. The results demonstrate the utility of the local transient approach relative to steady state upscaling methods.
