When modeling facies, it is common to run multiple realizations with the indicator simulation algorithm. As explained in the previous paper, to understand the true range of uncertainty in a reservoir model, it is also useful to study the impact of using range of variograms as well as a range of global facies proportions. Uncertainty on the VPCs and facies proportion maps should also be considered.

The sand proportion map previously built (Figure 1) has two main sources of uncertainty. Firstly, we don’t know the exact lateral extent of the channel. This uncertainty can be modeled either as a set of separate scenarios (an optimistic and a pessimistic geometry where the channel is respectively as large or as narrow as possible), or as a continuous range of lateral extents from which multiple “values” are picked by statistical techniques. Secondly, geostatistical techniques to grid the maps themselves should be used instead of a deterministic spline approach.

Uncertainties in VPCs are usually found in K layers with too few well input data and in K layers not crossed by any well at all. The former case was mentioned in the previous section. It is equivalent to the problem of under-sampled distributions in classical statistical studies. Figure 2 gives an example of the latter case. Only the horizontal internal layers (the K layers) are represented. The top layer (dashed red) and the deepest layer (dashed green) are not crossed by the two wells. The VPC is undefined for these K layers. It is up to the geologist to assign facies proportion values there, by extrapolation of the valid VPC values found in the other K layers. In both of these cases, the fact that a guess has to be made for some K layers might justify to create several versions of the VPC, which will change only in these problematic layers.

For fields with many wells, it is possible to build several sets of local VPCs, by splitting the domain different block sizes. Each set of VPCs could be used as one scenario. For example, how does the modeled facies really vary between using the global VPC versus using VPCs computed by splitting the domain in blocks of 5 square kilometers or by splitting the domain in blocks of one square kilometer?

Lastly, one should keep in mind that changing the internal layering of the 3D grid will completely change the VPCs. If several 3D grid geometries are tested, then each one should have its own set of VPCs.