The Cause and Devilish Effect of Heterogeneity
- Let's take a look at some examples of heterogeneity in productivity in naturally fractured reservoirs. And I'd like to begin by showing an example where we compare the heterogeneity in a conventional reservoir or many conventional reservoirs with some fractured reservoirs. This is work that was published back in 1995 by Dennis Beliveau. And the way he went about comparing or measuring heterogeneity was he defined a parameter he called a productivity improvement factor, or PIF. And you see in this slide it's a very simple equation in which PIF is equal to the rate in a new horizontal well compared to the rate, production rate in a neighboring vertical well. So it takes that ratio and has made a distribution of that ratio in conventional reservoirs. Now the upper graph here shows that distribution from 790 wells. And what we see is PIF reaches a peak at around two to four. And you can see the statistics there, the PIF rate has a mode of two, median of three, and a mean of four. And it tapers off, tapers off very substantially as it gets above about 12. There are only a few percent of wells left that have PIF greater than 12. Compare that, if you would, to the results from naturally fractured reservoirs which Beliveau has labeled fractured fields. 172 wells in this distribution. And what we see here is the basic statistics. The mode is about six, the median is nine, the mean is 12. And values greater than 12 occupy more than 40% of the total population of wells in this study. So it's not even so much the assymetry of the distribution that indicates heterogeneity, but really the wide range of flow rates that we see, and with PIFs ranging quite high, quite a bit above 20. That's a clear indication of the heterogeneity in naturally fractured fields. Let's compare now this same kind of productivity variability but in this case we'll just compare straight up a conventional reservoir to a naturally fractured reservoir. In both cases the distributions that you see here, the histograms, are showing productivity index which is a measure of flow rate divided by change in pressure. The units on this particular, on both of these plots, are tons per day per bar of pressure change. And in this case both fields are in the same basin and in rocks of roughly the same age. But yet we see that the field dominated by matrix flow has a much lower range of productivity index than what we see in the naturally fractured reservoir. So a much higher heterogeneity in well production in that far. If we look at another carbonate field, this one producing gas, again, a very similar picture to what we see in that carbonate that's producing oil. That is some very high performing wells ranging down to low performing wells with an extreme anisotrip. And finally here's a tight gas sandstone, and we see that same kind of behavior. A few very high producing wells, but lots of wells that don't produce very well. Sometimes we can think of this as an 80/20 distribution. By that I mean 80% of the production comes from roughly 20% of the wells. All of this, it's that wide range of well performance that is indicative of the heterogeneity. Now let's consider the performance challenges when working in a field with a highly anisotropic flow distribution associated with it. In other words, a field that's very heterogeneous. I show here a sketch of an asymmetric distribution and I've marked on here some straightforward statistical references, the mean, the median, and the mode. And let's consider that you've proposed a new well in the... Let's say this is a field that you're working on and you've proposed a new well to some partners. At a partners meeting one of the partners turns to you and asks, "What kind of performance do you expect "of that next well that you're proposing to drill?" What's your answer? Well, unfortunately the answer is the most likely performance of the next well you're going to drill is most likely going to be the same performance that is most common in the past. And that's going to be the mode of the distribution, the peak of the distribution curve shown here. The reason I say unfortunately it's because that's a rather low number. That may be the next well performance that you have to count on, but in fact the majority of your production is out here in the toe. This is the well that you want to drill, but if you don't know an awful lot about how the reservoir behaves and what the controls of heterogeneity are, generally we don't have a very good handle on that in fractured reservoirs, you're going to be drilling down here in the area of the mode. So this is in a distribution, a case where we may know the well performance distribution. What about in the case of an exploration plate that you go into, hmm? How many wells are needed to evaluate an NFR? The problem in an exploration is you don't know what the shape of that distribution curve is. If you're planning to drill a single well on that exploration plate the most likely outcome is going to be the mode of the distribution. The problem with that is the mode is such a pessimistic number. The more asymmetric the distribution is, IE the more heterogeneous the reservoir behavior is, the lower the mode is going to be relative to the expected value of the distribution. Now the expected value of the distribution is actually the basis on which we judge our performance of the field overall. So we want the expected value to be as high as possible of course, but drilling just one or two wells on an exploration plate is unlikely to discover what that expected value is. So how many wells do we need in order to judge an exploration plate? That's hard to know. In fact it's unknowable. The only thing that we can say with certainty is it's going to take more wells to judge the potential of a reservoir with a strongly asymmetric production distribution curve, IE it's going to take more wells to judge a heterogeneous reservoir than it will to judge the performance of a conventional less heterogeneous reservoir.