This paper presents a new method for scaling up multi-phase flow properties which properly accounts for boundary conditions on the upscaled cell. Scale-up works by allowing us to omit the simulation of a complete finely-gridded model, but requires us to either make assumptions about the proper boundary conditions for the isolated blocks being scaled up or to determine them in some other way. To date, all scale up methods have made assumptions about fine-scale boundary conditions.
The paper describes how to use the concept of injection tubes (which are hypothetical streamtubes connecting the injection wellbore to all of the inlet-face fine gridblocks of the isolated blocks being scaled up) to determine the appropriate boundary conditions. The use of injection tubes enables us to capture the fine-scale flow behavior of a finely-gridded model at the inlet face of the isolated blocks as if the complete finely-gridded model was simulated. We describe how to scale up a whole 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 almost perfectly reproduced the average performance of the finely-gridded model. To date, we have confirmed that the method is applicable not only to viscous dominated flow but also to flow affected by gravity for reasonable viscous to gravity ratios.