A fully-implicit upscaling method for accurate representation of the balance of viscous and capillary forces

In many cases, small-scale laboratory measurements of relative permeability and capillary pressure must be upscaled carefully to obtain large-scale. rock/fluid properties for accurate reservoir simulation. The simulation and upscaling, processes can be simplified if one or more of the viscous, capillary or gravity forces can be ignored. In particular, the scale-up process may sometimes be speeded up by assuming that the fluids are in a steady state. At small scales, gravity is often negligible and capillary pressure is very important. However, at intermediate flow rates, capillary and viscous effects may be of similar magnitude. In these cases, neither viscous nor capillary dominated steady state methods may be applicable. The viscous dominated method will underestimate trapping, which occurs in strongly water wet rocks, while the capillary dominated method provides an over-estimate. A new method is presented which can be used to obtain pseudos efficiently while accurately capturing the balance of forces. In this method, the steady-state water saturation distributions are determined directly, using a fully-implicit flow simulation for a range of values of the fractional flow of water. The effective permeabilities for oil and water are then calculated individually at each fractional flow level, and effective-relative permeability curves are generated as a function of average water saturation. While slower than methods where a single force is dominant, this method retains some of the advantages of these methods in terms of the simplicity of the solution. Also, pseudos are obtained faster than those obtained using the Kyte and Berry method. The new method is compared to that of Kyte and Berry and the results are analysed as a function of the accuracy and speed with which pseudos are obtained.