## Reservoir Dogs: Sequential vs. simultaneous modelling solutions

Hello, and welcome back to the Cognitive Whiteboard. My name is Jim Ross, and today we’re going to be talking about sequential versus simultaneous modelling solutions. In particular, how to avoid an ugly, confrontational standoff between the two – not unlike this iconic scene from Quentin Tarantino’s “Reservoir Dogs”.

When we’re modelling things in oil and gas, we have a lot of variables in play at any one time. And, broadly speaking, we have two ways that we can address this. We can look at a multi-variable regression, which will try and tweak all the variables simultaneously to minimise our error to observe data, or we can look at a set of sequential functions of each variable that tries to reduce the error as we go along. So which one should we use? I’m going to say both.

Mathematically speaking, [simultaneous solving] is the preferable solution. If we give it the same starting points and the same search algorithm, we will end up with the same solution. However, we know that physics and, in particular, geology, rarely works like that: rarely is everything happening at once, and quite often, we have different behaviours imprinting upon each other as we look at our different facets of our modelling. To illustrate this, I’m going to look at a simple mass balance-based example from earlier in my career. And it’s just a simple tank, so mass in, mass out, and how the pressures and saturations respond to that coming and going of fluid.

So, if we look at the reservoir pressure history, we’ll see that it has a gentle enough decline to start, there’s a sudden spike, and then it levels off a little bit before it completely drops off a cliff and the production starts to peter out. If we try and use this multi-variable, simultaneous solution on that, we’re not going to get a very good history match with this simple model. And that’s because we’re trying to match fundamentally different periods of behavior all at the same time. The answer is not to lump more complexity into the model, but it’s actually to take a step back and look at what’s happening across the history of this model, this actual field, with this sequential behavior. In this first period, really, all we’ve got here is fluid expansion, which will be dependent upon the value of the stock tank oil in place, and the aquifer drive. What’s the strength of the aquifer in this field? In the second period, if we actually look at the production history of the field, we can see that that’s the point at which water injection starts. So naturally, that’s going to have a little impact. But if we can nail down a value of the variables [in period 1], we can carry that forward into the second part. Once we’ve done that, and maybe tuned the transient aquifer response, we can then look at this third period. And it was thought that there was some sort of fracture event and they were then losing fluid to another tank and thus pressure in the field.

So what we can do is we can take each solution and move it forward to inform the next one. We can take the stock tank oil and aquifer strength determined here and carry that forward, where we can then tune the transient response of that aquifer. And we can then take all that forward and then look purely characterising that transmissibility, and typically that would be a transmissibility factor we come up with. In other words, we simplified the problem by looking at a simultaneous solution, but considering each period of time in turn, and applying some sequential thought to that. In other words, if we can successfully combine these approaches, the final result is more robust. And we can not only directly calculate our past behavior, but we can be confident that the future behavior will be predicted well by our model. The alternative is one of these self-defeating standoffs that were so common in “Reservoir Dogs” and not only are we not going to be able to reliably create past behavior, we’re going to have no hope of predicting the future behavior.

I hope that’s been helpful. I look forward to seeing you at the Cognitive Whiteboard again in the future, and I hope that’s soon. I’ll see you then.