Managing Uncertainty: Robust Ranges Using Trends

Warming to his heretical theme, Luke is back to discuss using trend analysis to drive uncertainty in geostatistical models. 

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Hello, and welcome back to the Cognitive Whiteboard. My name's Luke, and wow, did that last video generate a lot of interest in the industry! What we did was we talked about how variograms and trend analysis can work hand in hand to try to investigate how your properties are being distributed in three dimensional space. Today I want to show you how we can use the trend analysis to drive the uncertainty in your models as well. In doing so, I think I'll officially be promoted from geostatistical heretic to apostate. But let's see how we go.

What I want to do today is really run you through how I used to go about doing geological uncertainty management and how I do it today. I started by thinking about shifting histograms. I think a lot of us do this. If we wanted to get a low case, what if the data was worse than what we observed, or a high case, we could shift it upwards in the other direction? I've done this many times before in the early parts of my career. It's not a particularly valid way of doing it in many examples. When you do just shift the histogram and fit to the same world data, you'll generate people's and dimples around your wells, which is undesirable. But if you shift the observed data as well by saying, "Well, the petrophysicist has some uncertainty in their observations," what we're really beginning to invoke is that the greatest degree of uncertainty associated with that is at the wells. And I think we can all agree that the greater degree of uncertainty is away from the wells. There are important uncertainties here, but we have bigger ones to deal with up front.

The other way of trying to manage our uncertainty is also in the structure in how we distribute that data. Different variogram models are useful for doing this. We can say fairly that the interpretation of a geological variogram, that experimental data that you get is - particularly in a horizontal direction - usually uncertain. We don't have enough information there to be confident on how that variogram structure should look, so it's fair to test different geological models and see what will happen. What's interesting is, of course, if you vary the histogram, you'll change STOIP with a similar recovery factor, just generally better or worse. Whereas if you change this, you'll vary the connectivity, but you won't really change the STOIP very much. And it's often difficult to link this variogram structure back to a conversation you can have at the outcrop.

So over my, I guess,  five or six years now, I've been focusing on addressing uncertainty by saying, "Actually, the sampling of our data - the biased, directional drilling that we've gone out and sought the good spots in the reservoir, typically - is really what we need to try to investigate." How much does that bias our understanding of what could exist away from the well control?

Got an example here, a top structure map of a field, a real field through here with five appraisal wells along the structure, and the question is: in these two other locations that are gonna get drilled, is it gonna be similar, different, better, worse? And how could we investigate the uncertainty of the outcome on those locations?

We could, for example, investigate: is the variation that we observe in this data set a function of depth primarily? Or perhaps it's a function of some depositional direction - in this case, the Y position, as a theory. We don't know at this stage which one it is, and depending on which one we do first, we end up with different correlations. In fact, you can see on this sequence after taking out the Y position, if I analyze the residual for depth, we end up with not two porosity units by 100 meters of burial, but only one porosity unit being reduced as a function of depth. So you can see, fundamentally, we're invoking a different relationship as a result of that burial.

What's really interesting is that these are highly uncertain interpretations, but they're valid ones. And they give us different answers, not just in terms of the absolute positions of those two wells, but actually for the entire model the answer is different. And this is very representative of your uncertainty in three dimensional space. This input histogram with that particular shape is more to do with the sampling of your wells in the particular locations that they were, whereas this trend model behind it is helping you understand is there any variation in three dimension space that's going on? So we can end up with very different plumbing and in-place structures by really investigating how these trends can go.

You can do all of this manually one after the other through these routines. Our product Hutton does it for you automatically. We run about 300 different paths through your data set to try to investigate how that could go, and we find it's a very powerful way of really developing robust but different geological interpretations to address your uncertainty in your reservoir. If you're interested, drop me an email: I'll let you know more about it. But for now, that's all from the Cognitive Whiteboard. Thank you very much.