# CUMULATIVE PROBABILITY P90 P50 P10 PDF

SensorPx and Examples demonstrating probabilistic forecasting and optimization. Reserves Definitions. Bayes' Theorem and Markov Chain Theory. When there are significant uncertainties in our heterogeneous reservoir descriptions, as there almost always are, there is no such thing as a meaningful P10, P50, P90, or Px case description. There are only meaningful P10, P50, or Px results that must be determined from probabilistic analysis. Any valid question in reservoir modeling, regardless of the model used, must be asked to some number of cases, representing many combinations of the uncertainties, in order to obtain a probabilistic distribution of the answer.

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When working with Monte Carlo simulations, some parameters that show up quite a lot are the P10, P50 and P The large amount of data produced by statistical methods sometimes make it difficult to effectively use its results in the decision-making process.

An example of its use in the oil and gas industry is the estimation of potential lifecycle i. Sometimes, when running models with a large variation, analysts will engage simulations that go beyond lifecycles.

This number multiplied by the specified period required to simulate the asset performance i. The P10, P50 and P90 are useful parameters to understand how the numbers are distributed in a sample. Consider the following sample list of observations. There are several options to display this data. You could decide to group the observations within a certain range and create a frequency table i. This is calculated by counting the observations with a specific value and dividing by the total number of observations e.

With this distribution, there is no need to have access to all the data points in the sample to start the inference work. We can tell, by looking at the graph, that most observations are around This table is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

One will notice that you can start from either the lower observation values to higher observation values or the opposite. So, we must introduce two new concepts:. Again, this graph adds up the frequency of occurrence as the value of the observation decreases i. This is what is called the probability of exceedance.

As mentioned before, another option is taking the opposite view — adding frequency of observations that will not exceed a certain value of observation. You should also note that, for the same distribution, the P10 for the probability of exceedance is exactly the same as the P90 of the probability of non-exceedance.

Another useful notion refers to the first and last value of these distributions. The first value for the Probability of exceedance and the last value for the Probability of Non-exceedance will always be equal to the total for all observations, since all frequencies will already have been added to the previous total.

Again, this distribution can be extremely useful when dealing with large samples. The calculate value will depend on the type of distribution you have chosen to create. P50 is more likely to occur because it is closer to the mean.

For this sample of observations, our P50 would be 95 which is exactly the mean i. There is a reason for this which is explained later in this article. We can never be sure exactly this is an important word which is the core reason of why we use probabilistic approach how much crude oil is available for production in the reserves. However, we can have a good estimate another important word.

Geologists and Reservoir Engineers working for the oil and gas industry have developed numerous methods and tools to calculate the potential production and get estimates of production rates from oil and gas reservoirs to obtain a high economic recovery.

When the range of uncertainty is represented by a probability distribution, a low, best, and high estimate shall be provided such that:. When using the deterministic scenario method, typically there should also be low, best, and high estimates, where such estimates are based on qualitative assessments of relative uncertainty using consistent interpretation guidelines.

Under the deterministic incremental risk-based approach, quantities at each level of uncertainty are estimated discretely and separately see Category Definitions and Guidelines, section 2.

The text gives us indication of what curve we should be using — actually recovered will equal or exceed — it means we should be using the probability of exceedance curve. Translating all these terms, the amount thought to be in the reserves is generally estimated as three figures:.

So, we would refer to:. This argument says that the mean will incorporate both the higher and the lower observations which will smooth the differences when added together.

Comparing to the P10, which could potentially give estimates that are over-optimistic, and the P90, a conservative estimate which could potentially leave too much oil, both providing confusing future trends. It is a common misunderstanding that the P50 is a synonym of mean. This will be true is the probability distribution function for the observations were symmetrical.

In this case, the mode, mean and P50 would all be the same. For distributions where the values tend to be skewed, the mode, P50, and the mean begin to diverge. The argument for the mean works well for distributions that are symmetrical but if the distribution has a degree of skewness it might be better to reconsider and perhaps look at the P INC array, k. INC uses a slightly less accurate algorithm, but it works for any value of k between 0 and 1.

This should help looking at a specific percentile for a distribution — then vary the k and you should get you distribution. Good explanation, I liked the approach. I remember a lecturer on renewable assets mentioning that a 1-year P50 value for energy output was very much different from a year P Is a year P50 value the median cumulative energy produced over a year period and to get to an annual energy output estimate you would simply divide that number by 10?

Any insight into this issue would be very appreciated as I see quite some deals that just throw those numbers around and the results are quite different. Thanks, M. Yes, they will be very different.

Using the calculation describe in the blog post, we can easily work out the P50 for each year and for the 5 years. Now, performing the same calculation for the 5 years, the P50 will be This value doesnt even show in the first year. I hope this makes sense! This article is crystal clear. Thank you very much.

I have one question: I remember my statistics lecturer saying that the P50 was the same for 1rs, 5yr or 10yr.

I cant remember the conceptual explanation. Could you help? Thanks again John. It would nice to understand more the context of your question so we can help you answering! Have you got an example which we can discuss? Cheers Victor. I just wanna make sure of a certain concept; if we have a P90 of number of variables we cannot sum the P90s up to have a P90 estimate of another output which depends on the other variables; can we?

Hi Mostafa, not really… unless you know the distribution behind it to create a new parameter! Very nice explanaition. I had to explain that once for the project manager and the client and was hard to make them understand it.

Some people also make some confusion about the P10 related to cumulative probability of failure in time 10 Years, months, days.

Your email address will not be published. Digitalization and software solutions Plant. What are these parameters? Why are they so important? Bell curve. Probability of Exceedance. Probability of Non-Exceedance. Follow us on social media Facebook Twitter LinkedIn. This field is for validation purposes and should be left unchanged. Paul Francis says:. Nov 14, at pm.

Victor Borges says:. Michael says:. Aug 22, at am. Aug 22, at pm. JSF says:. Jun 20, at am. Qiang says:. Jun 19, at am. Mostafa says:. Mar 29, at pm. Apr 6, at pm. Jaywant Joshi says:. Feb 27, at am. Dec 22, at pm. Dec 23, at am. Eduardo Calixto says:. Dec 21, at am. Reply with your comment Cancel reply Your email address will not be published. Cookies This site uses cookies to give you the best possible experience.

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When a risk simulation is complete, you are left with three forecasts based on their percentile. Specifically, there will be a P10, P50, and P90 forecast. These forecasts are automatically exported to the Analysis Manager , where they can be viewed from other worksheets, such as forecast or decline worksheets. When a risk simulation is re-run, these forecasts update with the most recent results. The three lines that are visible on the rate vs time, and rate vs cum plots are the P10, P50, and P90 curves.

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## Terminology Explained: P10, P50 and P90

When working with Monte Carlo simulations, some parameters that show up quite a lot are the P10, P50 and P The large amount of data produced by statistical methods sometimes make it difficult to effectively use its results in the decision-making process. An example of its use in the oil and gas industry is the estimation of potential lifecycle i. Sometimes, when running models with a large variation, analysts will engage simulations that go beyond lifecycles.

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## Uncertainty range in production forecasting

You must log in to edit PetroWiki. Help with editing. Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. More information. The situation is more complex for a production forecast because the forecast is a timeline and not a scalar.

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