# 2.4 Kriging & simulation - dense dataset

The datasets and the variograms introduced in the previous section were used as input for kriging and simulation. The dense dataset is used in this section, while the limited dataset is used in the next section. Figure 2 shows the conceptual model from which the dense dataset was extracted. The limited dataset is a subset of the large one. The area represents a set of fluvial channels which flow from the North to the South along the azimuth 150 degrees. Naturally, in a real study, the truth is not known. Here, we are assuming that the well data and the geological context lead the geologist to see it is a fluvial system and the dipmeter data helped identifying the main azimuth of 150 degrees. Kriging was applied first with different variograms (Figure 3, Figure 4 and Figure 5) before simulation was run using the most elongated ellipse (Figure 6 and Figure 7).

Kriging was first done using an isotropic variogram (Figure 3), even if the variogram analyzer showed that this variogram has too short a range in the azimuth 150 (Figure 1A). After all, with such a dense dataset, why shall we worry about the preferred orientation of the facies distribution? The data will take care of everything for us with some simple interpolation! The result is good overall and the sand facies does align along North-South geobodies, which might be interpreted as large channels. These channels are, nevertheless, wider than the input ones we know the dataset is coming from.

Then, kriging is done using a variogram model matching the experimental variogram (Figure 1B). One might argue that the plateau for the azimuth 150 is lower than the plateau at azimuth 60. In a real study, this would be investigated further. The resulting model (Figure 4) is closer to what we expected. The sand geobodies are more continuous along the azimuth 150 than in the first model. As our variogram is fitting to the experimental points, we could stop here.
The geologist insisted though that he expected the channels to be even more continuous than they are now. He asked us to see if we could find a way to make it happen. After some testing, we decided to run kriging with a highly anisotropic variogram (Figure 1C). Of course, this variogram no longer matches the experimental variogram in the azimuth 150 - our new range is much too large. The kriging results pleased the geologist though (Figure 5) as the channels are now much better defined than before, as can be seen in the rectangle area labelled 2 noted in Figure 2, Figure 3, Figure 4 and Figure 5. In the meantime though, we start creating channel geobodies where none should exist (rectangle labelled 1, same pictures). Also, we still can’t get some channels right (rectangle labelled 3, same pictures). This channel was not sampled well enough by our wells for kriging to be able to track it.

In a real project, it would make sense to carry forward at least the two anisotropic variograms as it is impossible to know which one is the most reasonable one. The shape, dimensions and orientations of the variograms is a major source of uncertainty. In many reservoir modeling projects though, studying the variogram uncertainty is not done. Instead, modelers tend to pick one variogram – here the highly anisotropic one for example – and they run numerous simulation models with it. Figure 6 and Figure 7 are examples of two such simulation realizations. Each realization respects the input data, the input facies proportion and the input variogram. But each does it by distributing the sand and shale slightly differently.

Realizations defined by simulation have considerable value as together they build a range of possible rock distributions for the reservoir. This range can then be used to run sensitivity analysis while doing well planning or reserve computations for example. Ideally, modelers should first spend time understanding the uncertainty hidden in the variograms but also in the proportions they are using. In a second step, they can use simulation to generate multiple realizations in which these different key sources of uncertainty are taken into account.

At last, modelers should not limit themselves in matching the data strictly. It often makes sense to adjust our data analyses in light of the extra information provided to them by their team. General geological knowledge must be used to transform data into information.