An assessment of steady-state scale-up for small-scale geological models

The calculation of pseudo-relative permeabilities can be speeded up conside rably by using steady-state methods. The capillary equilibrium limit may be assumed at small scales (30 cm or less), when the flood rate is low. At hi gh flow rates and larger distance scales, we may use a viscous-dominated st eady-state method which assumes constant fractional flow. Steady-state pseu dos may also be calculated at intermediate flow rates using fine-scale simu lations, and allowing the flood to come into equilibrium at different fract ional flow levels. The aim of this paper is to assess the accuracy of stead y-state scale-up for small-scale sedimentary structures. We have tested steady-state scale-up methods using a variety of small-scale geological models. The success of steady-state scale-up depends not only o n the flow rate, but also on the nature of the heterogeneity. If high perme ability zones are surrounded by low permeability ones (e.g. low permeabilit y laminae or bed boundaries), oil trapping may occur in a water-wet system. In this case pseudo-oil-relative permeabilities are very sensitive to flow rate, and care must be taken to upscale using the correct viscous/capillar y ratio. However, in permeability models, where phase trapping may not occu r (unconnected low permeability regions), the pseudos are similar, whatever the viscous/capillary ratio. The disadvantage of steady-state scale-up is that it cannot take account of numerical dispersion, in the manner in which dynamic methods can. However, we show examples of coarse-scale simulations with viscous-dominated steady -state pseudos which agree favourably with line-scale simulations. Provided there are sufficient grid blocks in the coarse-scale model, the smearing o f the flood front due to numerical effects is not serious.