- So, so far we've looked at plots like the one that's shown here, as an indication of heterogeneity. The strong asymmetry and wide range of values in the productivity index in this particular reservoir. This is yet another naturally fractured reservoir. And what I'd like to consider here, that we haven't talked about yet, is the fact that there's a spatial component to the heterogeneity. And this is a very critical aspect of the story of heterogeneity in naturally fractured reservoirs. So, if I were to look at a map with this PI data plotted at the location of wells, I might generate a map that looks something like this. It's a bubble map here. What you're seeing is each bubble is centered on a well location, and the bubble area is proportional to the well productivity index. So, what we see is a line of high-performing wells near the center that has a trend from northwest to southeast. And we can ask why that is. What's going on in this group of wells? If that trend that we see there is controlled by fractures, well, then we can start asking, maybe there's a major fault that runs through the center of the reservoir here, and the high fracture density associated with that fault. Or maybe some tight folding with the related high fracture density. But at this point in my assessment, I may not know what's going on in that part of the field. And, indeed, whether the heterogeneity that we're seeing is controlled by fractures or not. Perhaps what we're seeing is a street channel, let's say, that's running through here, that has very high permeability in the channel, and hence results in high performing wells along that trend. Or maybe we have a phases change in some carbonate if it's a carbonate reservoir, and the phases change is associated with high porosity, high permeability along a given trend such as shown by this. Looking at this spatial distribution of high performing wells doesn't really tell me that we're looking at a naturally fractured reservoir. Could, but not necessarily. However, so far, I've been playing a trick on you and this map that we're looking at is actually not the correct map to go with this data set. The map that we're looking at is something that I fabricated. Now, let's look at the real data map that's associated with this asymmetric data set here. I've labeled it NFR, and what you see here is near-neighbor wells show strong production variability. That is, we can have a high performing well, such as the one located here, and it's surrounded almost completely by much lower performing wells in the same neighborhood. And that's true as we look throughout the reservoir. The high performing well seem to be at a well, all the wells, based on their production, seem to be rather randomly located. That's typical of naturally fractured reservoirs and speaks to the considerable high heterogeneity of the reservoir. What we're seeing here is low spatial correlation. And one strong implication of this low spatial correlation is that naturally fractured reservoirs don't, on the whole, lend themselves to modeling using standard geostatistical techniques. That is, variogram based techniques. And the reason is that when you use a variogram in geostatistics, what you're assuming is that you have spatial correlation. We lack the spatial correlation for the most part in NFRs, hence, geostatistics is not very useful to us. And the method we use for modeling, I'm not going to go into here, but I'll just say that fractured reservoirs present a challenge in terms of spatial modeling. So, let me end here. This particular module, we've looked at heterogeneity within the production behavior, for the most part, of naturally fractured reservoirs. In effect, we've looked at engineering data so far. Now, we will move on and talk about the cause of heterogeneity in productivity of naturally fractured reservoirs. And as we get involved in trying to understand the heterogeneity, we'll be looking more especially at the geological aspects of naturally fractured systems. So, indeed, this is where, as we continue in the modules, the story becomes much more interesting.