The Cause and Devilish Effect of Heterogeneity
- Let's look at heterogeneity in permeability of the naturally fractured reservoir. We can look at permeability heterogeneity based on the Flow Capacity Index, or FCI. The Flow Capacity Index is a tool that gets used several ways of characterization of naturally fractured reservoirs. But I'm just going to use it, here, I'm only going to discuss its use in assessing heterogeneity in the reservoir. So, what Flow Capacity Index is, it's just the ratio of kh from a well measured in a pressure transient test to kh determined from the matrix over the same interval. h, being the interval in the well, is the same in the numerator and denominator, and k, being permeability, can be the same or different. It is essentially well performance observed divided by well performance predicted. Now, as I mentioned, h is the interval in the well, and it's the same in the numerator and denominator. So we can cancel the h out of this equation, and we get permeability in the well divided by permeability in the matrix. So you can see that's a very useful thing to know. We now know, in a sense, whether any particular well has been uplifted, its permeability is greater than expected from the matrix alone, and we see this for any value of FCI that is substantially greater than a value of one. Wells that significantly over-perform, or have FCIs very much greater than one, are suggestive, at least, of fracture-controlled production. So we can look at this in a cross-plot, in which we plot kh of the well, measured in the well test on the y-axis, versus kh of the matrix, our predicted kh, on the x-axis. I should say one more thing about kh, and that is, kh is a standard measure that is made during pressure transient testing of a well. And that's the reason we always start off with kh in the numerator position. We don't have a direct measure of permeability in general. The kh of the matrix is usually determined from porosity-permeability transform in the well, and so that's the basis for our prediction. So if we look at the plot here, it's a log-log plot, and you see a red line with a slope of one. That represents wells with an FCI of one, where the prediction from the matrix is equal to the flow that's tested in the well. And there's a window, in this case, the window is a factor of four, that surrounds that red line. My statement with regard to that window is that, the points that fall within the window there represent wells that perform approximately according to our matrix-based prediction. There's always some uncertainty and variability in that determination of FCI, so we rarely get points that fall directly on the FCI equals one line. So any in that window are considered dominated by their matrix property. But you see the points that represent over-performing wells, each point being an individual well, the over-performing wells fall up in this yellow zone. These are the points that are significantly greater than the predicted matrix permeability. So, let's just take a look here for a moment. Here's a point right in the center of the plot with a circle around it, and it's within the gray zone just right at the margin. You see it's offset from the FCI equals one line by about a factor of four. So its permeability is four times that of FCI equals one. Yeah, not very interesting in terms of fracture contribution to permeability. A factor of four is pretty small. But if we look at some other points, such as this point on the left side in the center of the plot, here the point is offset from the FCI equals one line by quite a bit. In fact, by a factor of 200. So the permeability here for this well is 200 times greater than the permeability predicted based on its matrix properties. That's telling us that particular well almost certainly has natural fractures in it. But, by the way, this set of data, the wells that are represented by the points on this plot all come from a single naturally fractured reservoir. And I know from other data that fractures are a big concern in this reservoir. Most studies of fractured reservoirs involve looking at multiple sources of data, and in this case we have image logs for many of these wells, and therefore I know that open fractures are a significant feature of the reservoir. And that's why I'm able, when I see this significant uplift in permeability, to suggest almost with certainty that it's fractures that are the cause of that high permeability. Now, coming back to heterogeneity. What we see is the green points in this field of over-performing wells are not very uniform in their values. Their range of enhancement permeability relative to the matrix permeability varies considerably, so that the blue point here is enhanced by a factor of 200, but some other points are enhanced by a factor of significantly less, maybe only 50. Others are getting up to a factor of over 1,000 times higher permeability than the matrix. It's that well-to-well high variability in permeability that leads to heterogeneity in productivity here, so that every well that we drill has a substantially different performance. So we see wide variation in FCI across the reservoir, and that's indicative of the heterogeneity of the reservoir.