Terminology explained: What is the Monte Carlo method?
We are starting a new series of post today – Terminology explained: What is the Monte Carlo Method?
Let’s find the definition we can find in this IEEE paper: Introduction to Monte Carlo simulation
“Monte Carlo simulation is a type of simulation that relies on repeated random sampling and statistical analysis to compute the results. This method of simulation is very closely related to random experiments, experiments for which the specific result is not known in advance. In this context, Monte Carlo simulation can be considered as a methodical way of doing so-called what-if analysis. We will emphasis this view throughout this tutorial, as this is one of the easiest ways to grasp the basics of Monte Carlo simulation.”
The following section tries to explain what the Monte Carlo Method represents for someone working in the oil and gas industry.
Consider that you are an operator of a platform in the North Sea. Let’s imagine also that your platform will have a failure every year. This failure could occur during the summer or during the winter (let’s assume we only have these two periods). The time to repair this failure would be different for each season:
- For the summer season, it would take us 10 days (240 hours). For this repair time, we are assuming the external environmental conditions to be stable i.e. no high-waves, no high-winds.
- For the winter season, it would take us 15 days (360 hours). For this repair time, we are assuming a harsh external environmental condition – extremely low temperatures
In simple terms, we are saying that, during the summer season it takes us less time to repair the system. So, failures occurring during the winter are more critical.
Now consider that you are working on estimates of production for the next ten years using Maros as part of your business plan. This is a simple model and this is how it would look like:
What is a lifecycle when applying the Monte Carlo Method?
When the simulation kicks-off, Maros will estimate the first lifecycle. A lifecycle scenario is a chronological sequence of events which typify the behaviour of a system in real-time. In theory, Maros can create an infinite number of such scenarios for any given system, each one being unique, however sharing the commonality of being a feasible representation of how the system would behave in practice. By analysing groups of life-cycle scenarios, statistics can be extracted relating to the system’s performance.
So, a lifecycle is a feasible representation of how the system might behave.
Now imagine for the first lifecycle, Maros randomly failures only occurring during the summer:
Focusing on the 2018’s actual production:
This is our lucky estimate!
Now imagine for the second lifecycle, Maros randomly failures only occurring during the winter:
Focusing on the 2018’s actual production:
This is our bad luck estimate.
But, intuitively, we would expect to see part of the failures occurring during winter and part of the failures occurring during the summer throughout the 10 years simulation, right?
If “sum-up” lifecycle one with lifecycle two and take the average – that’s what we see – part of failures happening during the summer and part of the failures happening during the winter!
Perhaps the next lifecycle will have 6 failures during summer and 4 during winter and the next one will have 5 failures during summer and 5 during winter. This simulation goes on and on for as many lifecycles we would want to model.
If we run enough lifecycles we will the number of failures averaging to 5 during winter and 5 during summer as expected. Does this sound familiar? Yes! From the beloved statistical Central Limit Theorem which states:
“The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough.”
This is what we really want to achieve – the average behaviour where a certain number of events are occurring during the summer and another set of events occurring during the winter.
With this we can test many lifecycles and incorporate the simulation process into our decision-making process – as we know the average behaviour of the plant.
What is next? What else can the Monte Carlo Method take into account?
Well, we only ran 2 cycles. Now we need to run another 98 cycles:
It is important to note that we are using the exponential distribution which will give us this random occurrence we would expect. Other distributions will give you a different behaviour – e.g. you could potentially use Weibull distributions to simulate how systems are getting old).
Furthermore, our initial estimate is 10 failures – the simulation process might be generating more occurrences for each lifecycle. For instance, one lifecycle might have 11 failures and another 9 failures. This adds another level of complexity to the simulation – lifecycles now are variable in the number of failures which are fully dependent on the statistical distribution.
At the end of the simulation process on can generate the normal distribution stated by the Central Limit Theorem. The normal distribution describes all the lifecycle by its production efficiency – the actual production referred to the potential life.
The impact of events might differ from time to time. For example, the natural declining of production rates from wells producing crude oil will add another level of uncertainty to the performance calculation. We discussed this one at the Production availability.
Monte Carlo Method is a fundamental tool for the decision-making process in the oil and gas industry.