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 introduces 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 oversimplified assumptions such as 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 adopted: these are hypo-thetical 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 the full 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 provide a coarsely gridded model which can reproduce the spatially-averaged performance of the finely-gridded model reasonably accurately. 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.


Great attention has been paid to the development of a process for upscaling multiphase flow properties. Modern reservoir simulation practice requires us to scale-up a detailed geological model to a more coarsely gridded model. Of particular interest is an upscaling process which works on a local domain (a coarse block) isolated from an entire detailed model.

The use of an isolated block in an upscaling process requires the appropriate boundary conditions of a coarse block being scaled up. This is because phase flow rates and pressures along the boundaries of the corresponding local domain are subject to spatial and temporal changes in an entire finely gridded model. Further, upscaled relative permeabilities have been shown to be flow-path dependent 5,7. Thus, the determination of the bound-ary conditions of an upscaled cell is the central difficulty in upscaling multiphase flow properties 18.

In the literature, there are two major approaches in averaging flow properties 5: dynamic-pseudos approaches and effective-properties approaches. In addition to these approaches, there exists a multistep upscaling process.

Dynamic-pseudos approaches 11,14,6 cannot synthesize the boundary conditions of an isolated block since dynamic-pseudos approaches are primarily developed to generate pseudofunctions based on the simulation results of an entire portion or a representative portion of a finely gridded model. On the other hand, effective-properties approaches work on an isolated block basis, but most of the exiting effective-properties approaches are limited to extreme flow regimes such as a viscous limit or a capillary limit. When the flow is in an intermediate regime, effective-properties approaches require us to conduct flow simulations over a local domain 10,1,13. however, it is questionable that the boundary conditions of an upscaled cell is properly considered in such effective-properties approaches. Similarly, we pointed out that the existing multistep upscaling processes 8,12,9 lacked in properly considering the flow-path de-pendence of multiphase flow properties 7,15.

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