The workflow promoted in this book is to populate facies in 3D and then to populate petrophysics by facies. The present section gives us the occasion to illustrate what might go wrong if the petrophysics is interpolated without a facies framework in place.

Let’s consider two wells with facies and VSH information (Figure 1). Well 1 shows 50m of Shale at the top followed by 30m of Sand, 20m of Shaly Sand and at last 10m of Sand. Well 2 is Sand all along except for 20m of Shaly Sand near the base of the reservoir. The Shaly Sand is interpreted as a continuous facies zone across the area while the Shale is believed to be of limited lateral extent. No data can tell where the Shale exactly stops between the two wells though. Each facies shows a specific range of VSH: the Sand is associated to VSH less than 30%, the Shaly Sand has VSH between 30% and 70% and the Shale is associated to VSH superior to 70%. We need to model the VSH and the facies in 3D while respecting our interpretation of the reservoir. Ideally, we need to be able to create multiple models showing different lateral extent of the Shale between the two wells. For an initial path, we would like a Shale ending approximately half-way between the two wells. To do the modeling, we have a 3D grid refined enough to capture these three facies’ spatial distribution.
We decide to test two different modeling approaches. On one hand, we model VSH in 3D with a geostatistical algorithm and then we apply the VSH cut-offs to assign a facies code everywhere (Figure 2). On the other hand, we follow what we have advocated since the beginning: we model the facies in 3D with a geostatistical algorithm and then we model the VSH by facies, also with a geostatistical approach (Figure 3). Which approach gives the more reasonable results?

Both models show the proper relationship between facies and VSH (we don’t have high values of VSH in the Sand for example). Both models also show the same lateral extent of the lower Shaly Sand zone. But the two models differ drastically in the upper part of the unit. When we model the facies first, we have what we expected: a sharp transition between Shale/Sand approximately half-way between the wells (Figure 3). We also know from experience that if we were to use a smaller variogram range for modeling the Shale, we will be able to “place” the limit Shale/Sand closer to well 1 or to well 2. We have an algorithm with which it will be easy to manage this uncertainty in multiple realizations. On the contrary, the other approach creates a lateral transition Shale/Shaly-Sand/Sand that we didn’t interpret to start with (Figure 2). Why is that?

VSH is a continuous property which can takes a continuous range of values between 0% and 100%. All interpolators of continuous properties (as far as we know) create by definition models which vary continuously across the 3D grid. In the upper part of the unit, VSH will necessarily change progressively from 80% in average in the Shale on well 1, to 70%, 60%, 50%, 40% and 30% to finish around 20% in average in the Sand of well 2. It is unavoidable. When facies are calculated based on the cut-offs, it creates this halo of Shaly-Sand not observed at the wells. If the well data were showing that Shale and Sand are never in direct contact but instead are always separated by a zone of Shaly Sand, and VSH smoothly transition from high values to low values, then seeing Shaly Sand and a smooth VSH transition between the wells would be reasonable. But that is not what the wells are showing. Well 1 shows that VSH changes without transition between high and low values (limit Shale/Sand), but also between low and average values (limit Sand/Shaly Sand). The smooth VSH model (Figure 2) and the forced succession Shale – Shaly Sand – Sand are not backed up by the well data.

Even for models which must ensure a specific lateral succession of facies, modeling facies first makes more sense as we have algorithms in our geostatistical toolbox which gives us a lot of control on the process (plurigaussian simulations). It would still be much more preferable than modeling the VSH first.
In conclusion, only model continuous properties such as VSH, porosity, SW or permeability within domains in which they smoothly vary. Those domains will often be based on the subdivision of each geological unit into different facies zones. So, model your facies first and then model the continuous properties by facies.