Sequential upscaling method

This paper presents a new method for scaling up multiphase flow properties which properly accounts for boundary conditions on the upscaled cell. The scale-up proposed does not require the simulation of a complete finely-gridded model, instead it calls for assumptions allowing the calculation of the boundary conditions related to each block being scaled up. To upscale a coarse block, we have to assume or determine the proper boundary conditions for that coarse block. To date, most scale-up methods have been based on the assumption of steady-state flow associated with uniform fractional flows over all the boundaries of the coarse block. However, such an assumption is not strictly valid when we consider heterogeneities. The concept of injection tubes is introduced: these are hypothetical streamtubes connecting the injection wellbore to all inlet faces of the fine grid cells constituting the block to be scaled up. Injection tubes allow the capturing of the fine-scale flow behavior of a finely-gridded model at the inlet face of the coarse block without having to simulate that fine grid. We describe how to scale up an entire finely-gridded model sequentially using injection tubes to determine the boundary conditions for two-phase flow. This new scale-up method is able to capture almost exactly the fine-scale two-phase flow behavior, such as saturation distributions, inside each isolated coarse-grid domain. Further, the resultant scaled-up relative permeabilities reproduce accurately the spatially-averaged performance of the finely-gridded model throughout the simulation period. The method has been shown to be applicable not only to viscous-dominated flow but also to flow affected by gravity for reasonable viscous-to-gravity ratios.