4.6692016090 – the Most Important Number in Upstream E&P??

Huh??

One number??

Instead of numbers like 1200 BOPD or 6500# ftp or 15,000’ MD? Or even 200,000 gross acres under lease?

Probably a small percentage of those of you reading this know this number as Feigenbaum’s constant – a very important number in chaos theory.

Important because it implies that within what appears to be chaotic information there is a universal constant. And with a universal constant, there’s some hope of being able to find order, and maybe even predictability, within the non-linear enterprise that we know as upstream oil and gas exploration and development.

In doing some very light research I’ve found that chaos theory has been applied to understanding business organization, HR programs, stock price behaviors, and ecosystems. I’ll be willing to bet that some of the strongest players in E&P have applied it to reservoir behavior and exploration strategies, and maybe even development models.

And given that we’re living in an unconventional reservoir world maybe we should be thinking about the entire enterprise in an unconventional way.

## Initial Conditions Matter

One of the great stories in the development of chaos theories concerns Edward Lorenz (*Dartmouth College class of 1938*). He was at MIT and had done some very early programing in 1961 to attempt to predict weather outcomes. One day he started a new model and decided he wanted to look at a segment of the output in detail. So he re-ran the model using the numbers that his model had generated from the last calculation. Picking up where he left off, as it were. What he found shocked him.

Within a finite number of iterations the same model, the same inputs began to give him wildly varying results (assume the red is the initial run)!

**Image Source:** James Gleick (Chaos-Making a New Science, p17, Penguin Books)

How does this happen? The function didn’t change. But inputs were not exactly the same!

Lorenz had rounded his second iteration inputs from six significant digits to three. As a result, his model absolutely blew up.

This was termed the Butterfly Effect, and was popularized by the image of a butterfly suddenly flapping its wings in the Amazon, ultimately perturbing the atmosphere by just enough to create large changes in weather in North America. Message: small changes in initial conditions can have profound effects.

## Would this matter to E&P?

Well, think of modelling future corporate cash flow based on last month’s production numbers – and then finding that in the most current month those production numbers were corrected.

Or your petrophysics work relies on LAS curves that have porosity values that are one digit too low or too high.

Or your decline curve analysis is sampling at too gross a rate.

You would be forgiven for thinking that ALMOST right is equivalent to CERTAINLY wrong.

## Lorenz Attractors in E&P?

As Lorenz and other workers worked through their non-linear models they began to find that there would come a point where data periodicities would become chaotic, leading to a not-so-comforting conclusion that non-linear systems could never be understood.

But they persevered, and one of the things Lorenz found was this—the Lorenz Attractor

It tells us that in a chaotic time series system no three variables will ever generate the same point, but they will deliver values that are constrained and which approach predictability.

## So how amenable is E&P to chaos theory analysis?

Can it be analyzed and thought of in out-of-the box kinds of ways that will be illuminating?

Does it behave like an ecosystem with predator/prey relationships? If so, what constitutes food?

Do acreage acquisition strategies have “initiators” that can be abstracted into simple repeating models of behavior that can predict acreage buy areas or characterize the lessee universe?

How fractal is the distribution of fractures?

Can a simple fractal model of this:

predict this?

We’re curious about this so we’re going to initiate a series of unconventional looks at unconventional reservoirs. Simple out-of-the box arm waving that may yield some very useful insight.

So stay tuned! And chaotic….

## Your Turn

What do you think? Leave a comment below.

#### Mark Nibbelink

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Very intriguing subject. I worked for a bit with Chaos theory and I know there is a lot of interest – in different fields – in borrowing concepts from Chaos theory and apply it there. Unfortunately, there is still a lot of confusion between chaos and stochasticity, along with other misconceptions. At the end, finding the parameters and initial conditions for the nonlinear analytic systems, is more difficult than formulating the systems themselves. I hope more people jump on this discussion/subject and one day we see actual use of chaos theory in the Oil industry (and other industries as well).

Very intriguing subject. I worked for a bit with Chaos theory and I know there is a lot of interest – in different fields – in borrowing concepts from Chaos theory and apply it there. Unfortunately, there is still a lot of confusion between chaos and stochasticity, along with other misconceptions. At the end, finding the parameters and initial conditions for the nonlinear analytic systems, is more difficult than formulating the systems themselves. I hope more people jump on this discussion/subject and one day we see actual use of chaos theory in the Oil industry (and other industries as well).

Great topic! I recently (4 months ago) worked on a project dealing with the fractal dimension of time series data applied to stock prices as part of my Masters degree in applied math. I am certainly interested in the insights that you may pull from answering the question “How fractal is the distribution of fractures?” Also, I wonder if windowing the fractal dimension of the distribution of fractures (computing FD in square windows across your grid in the image above) would lead to different insights as opposed to only computing the overall fractal dimension? Looking forward to the next post!

Great topic! I recently (4 months ago) worked on a project dealing with the fractal dimension of time series data applied to stock prices as part of my Masters degree in applied math. I am certainly interested in the insights that you may pull from answering the question “How fractal is the distribution of fractures?” Also, I wonder if windowing the fractal dimension of the distribution of fractures (computing FD in square windows across your grid in the image above) would lead to different insights as opposed to only computing the overall fractal dimension? Looking forward to the next post!

I am just a Pup in terms of oil and gas, about 7 years as a Geoscience Technician. There is a definite need to rethink the process of how to predict what a lease or play will grow into. I’ve seen the randomness in the Appalachian Basin where you drill one $6 million dollar horizontal that barely produces and another company drills one 2 miles away and it produces 100 times more gas! Would the chaos theory really be able to identify why? I feel we need to define exactly what caused the difference in production. I would start with trying to correlate rock properties with the production and then compare that to a correlation of completion practices to production. This kind of analysis would really identify what is driving the randomness behind oil and gas wells.

I am just a Pup in terms of oil and gas, about 7 years as a Geoscience Technician. There is a definite need to rethink the process of how to predict what a lease or play will grow into. I’ve seen the randomness in the Appalachian Basin where you drill one $6 million dollar horizontal that barely produces and another company drills one 2 miles away and it produces 100 times more gas! Would the chaos theory really be able to identify why? I feel we need to define exactly what caused the difference in production. I would start with trying to correlate rock properties with the production and then compare that to a correlation of completion practices to production. This kind of analysis would really identify what is driving the randomness behind oil and gas wells.