Python, analytics and inferential statistics in geoscience - use regression's prediction interval to discuss economic risk (an oil production example)
In this short article I would like to show one way to use statistical inference to discuss economic risk in Oil and Gas.
The data we will use comes from this paper: Many correlation coefficients, null hypotheses, and high value (Lee Hunt, CSEG Recorder, December 2013).
The target variable to be predicted, y, is oil production (measured in tens of barrels of oil per day) from a marine barrier sand for 21 wells. The independent variable, x, is gross pay in meters.
The prediction interval, as explained in detail in this article, is the interval defined around any predicted (forecasted) value of y, say y0, for a specific value of x, x0, such that there is a 95% probability that the real value of y in the population (not sampled) for the specific x0 is within this interval. The larger is the interval, the greater the uncertainty; but we can use this to help us constrain economic risk, for example of the production for the well to be drilled (the next y value in the population to be sampled), by giving us an interval in which the production of this future well will fall with a certain probability.
I used Statsmodels' Ordinary Least Square to perform the regression and also to calculate the prediction interval, and Matplotlib to display them in a single figure, shown below.
How do we use this figure then? Let's say we drilled the 21 wells; we're in an appraisal stage. We have a minimum economic production cutoff of 20 (bbl/d x10). With 21 wells the regression would suggest a minimum gross pay of 3.5 m to be above the cutoff value. But how likely is that? If we used the prediction interval, we could constrain the probability, but we'd have to pick a minimum gross pay of 12 m for the next well, which is equivalent to saying that there's a 95 % probability the production will be between 20 (our cutoff) and 56 (bbl/d x10).
Question: what would happen in an exploration setting, where we might have far less wells? Find out the answer to this question, and the full Python code to make your own plots in the Jupyter notebook on GitHub.
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About Matteo
Matteo Niccoli is a Geophysicist registered with APEGA, the Association of Professional Engineers and Geoscientists of Alberta. With 12 years of experience in the E&P business, he is currently a Senior Geophysicist with Birchcliff Energy in Calgary. He is an independent enterpreneur with MyCarta and Geoscience blogger / researcher. He is @my_carta on Twitter.