Goals of Reservoir Simulation 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. Absolute predictions require a statistically significant set of cases, but optimizations may require only a small number see SensorPx Example 3.

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Oilinplace Multiplythefrequency distributions togethertoobtaina frequencydistribution andthencreateacumulative frequency distribution. Fromthefrequency distribution wecanreadofftheP90,P50 andP10confidencelevels. In summary, to create an oil volume distribution: Step 1: create continuous frequency distributions for each input parameters rock volume, porosity, oil saturation. Step 2: multiple the input parameters together using a computer and create an oil in place continuous frequency distribution.

Step 3: take the oil in place continuous frequency distribution and create an oil in place continuous cumulative frequency distribution. Step 4: From the oil in place continuous cumulative frequency distribution read off the estimate sizes that correspond to the P90, P50 and P10 confidence levels.

So now that you understand frequency distributions, cumulative frequency distributions and how we use them to create volumetric estimates you should be able to answer a few questions: Question 1: What does P90 mean? Question 2: Is the P90 estimate or the P50 estimate more likely to occur? Answer: P50 is more likely to occur because the estimate is expected to occur more often than the P90 estimate in the frequency distribution.

Question 3: Whats the most important number P90, P50 or P10? Answer: P50 is the most important number because its the best estimate.

P90 and P10 just show the range in the uncertainty of the estimate. Question 4: Am I more confident in the P90 estimate or the P50 estimate? Answer: You are more confident in the P90 estimate. This doesnt mean that the P90 estimate has a higher chance of occurring, as explained above, all it means is that you have a higher confidence in that estimate being exceeded by the actual outcome. This can be a difficult concept to grasp.

An easier way to think about it may be to say Im confident that the actual outcome will be greater than my P90 estimate but overall I expect that the final outcome will be closest to my P50 estimate.

Question 5: Does everybody do frequency distribution or probabilistic calculations? Answer: No. Some people just multiply single values deterministic best estimates together to calculate a single output estimate, not a frequency distribution.

Question 5a: So how can you tell the confidence of that single output estimate? Answer: You cant, its a single best estimate. You just have to use it as it is calculated. Note that in the example above we only calculated the oil in place. We can go one step further and calculate the recoverable oil.

Recoverable oil equals oil in place multiplied by a recovery factor. For the recovery factor we can create a frequency distribution like all other input parameters. Multiplying the oil in place frequency distribution by the recovery factor frequency distribution we end up with a recoverable oil frequency distribution and then we can convert this to a cumulative frequency distribution and read off the P90, P50 and P10 estimates.

All the same concepts as discussed above apply. Question 6: How do you create frequency distributions for all the variables? Answer: You go to university for years and become a geophysicist, geologist, petrophysicist or reservoir engineer, you get a good job with an oil and gas company, you get trained over years, you gain a lot of experience and knowledge in earth sciences and the physics of oil and gas moving through rocks and then you get to work on interesting things like estimating recoverable oil and gas.

But seriously, that question is taking us outside the scope of this document as it involves knowledge, experience and the measurement and analysis of the data that make up each of the individual input parameters.

For further detailed reading investors should consult the Recoverable Hydrocarbon Guidelines on Cooper Energys website policies section. Related Interests.

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## Cumulative Probability P90 P50 P10_2

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. What about P10, P50 and P90? 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.

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## Terminology Explained: P10, P50 and P90

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## P50 (and P90, Mean, Expected and P10)

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