Statistical Scale-up: Concepts and Application to Reservoir Flow Simulation

Petrophysical measurements are used to construct reservoir models at a scale that are different from that at which they are measured. This disparity necessitates an adjustment or scale-up of the measured values before they are used. Scale-up is complicated by the properties being heterogeneously distributed in space and self- or autocorrelated. The autocorrelation means that the heterogeneity itself must be preserved during the scale up. We discuss scale up in the following two contexts. The first is the scaling of permeability and ultimate recovery efficiency as the size of a flow field increases. The second is the nature of adjustments to the model properties that are needed to better reconcile the observed behavior at different scales. We look at the effect of scale up procedures on the distribution and correlation structure of fluid velocities. Despite the long history of scaling up reservoir simulation models, we find relatively little literature on this type of scaling up.