Probabilistic Reserves! Here at Last?
- E.C. Capen (Vadcon)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- October 2001
- Document Type
- Journal Paper
- 387 - 394
- 2001. Society of Petroleum Engineers
- 5.7.4 Probabilistic Methods, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 5.7.3 Deterministic Methods, 4.3.4 Scale, 5.7 Reserves Evaluation, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 1.10 Drilling Equipment, 5.6.3 Deterministic Methods
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Recently, SPE and the World Petroleum Congresses (WPC) modified earlierdefinitions of reserves for the industry. Through much lobbying about improvingthe definitions, the committees generally clung to the past.
In truth, reserves have always been about probability because there hasalways been uncertainty as to proved, probable, and possible reserves. Thispaper proposes to dust off some of the mystery about how to deal with reservesprobabilistically and correct some common procedures that do not follow thelaws of probability and thus produce the wrong answer. For example, despite thereasonableness of the rule, it is illegal to add proved reserves from wells toget proved field or reservoir reserves. Every engineer who uses that methodshortchanges his client and misleads the investors.
Many believe that for the first time, the official reserves definitionsallow for the use of probabilistic reserves though they do not require thismethodology. Not true - reserves estimates have always been probabilistic,whether or not the definition recognized that fact. Words such as "reasonablycertain," "with high confidence," "more likely than not," and "possible" alllay tribute to the concept of probability. These words and phrases by designtake the place of numerical probabilities so that estimators would not actuallyhave to use the mathematics of probability and statistics. On the other hand,the use of the word "proved" suggests that to some, probability is not such abig deal. When remaining proved reserves can increase by factors of 10 or moreover several years, we must admit that the uncertainties associated withreserve estimates are not so trivial after all.
One particularly sticky problem in the past was how to combine well reservesestimates to get reservoir reserves or field reserves. People simply added themtogether as intuition would dictate. Incorrect.
The occurrence of five rare events (obtaining less than proved reserves fromfive wells, for example) is much more rare than any one of the contributingelements. So what starts out as reasonably certain becomes extremely certain.This latter phrase no longer fits the definition of proved. With this errorpromulgating throughout districts, regions, companies, and the world, we end upwith nonsensical numbers. Whatever methodology one uses, he must both start andend with something about which he feels reasonably certain. Probabilisticmethods provide easy solutions.
First, estimators must recognize that the Central Limit Theorem (CLT) worksover time in our industry. It ensures that the distribution of remainingreserves is always log-normal and provides for the estimation of probable andpossible reserves. Time to quit debating this issue. Second, having created alog-normal distribution for zones, wells, or whatever building-blocksestimators use, they can combine them into reservoirs, fields, and companyreserves. The mean of the sums is always the sum of the means. Most of thetime, the variance of the sum is the sum of the variances. The effort need notrequire the labor of Monte Carlo analyses. A spreadsheet analysis worksquickly.
What if leaving those antiquated deterministic methods behind wouldlegitimately add 25 to 50% to a company's proved reserves? Read on.
What Can You Expect in These Pages?
We first talk about what goes wrong with the old-style combining of reservesestimates. Then, we move on to how to combine correctly. We examine what acompany may gain in reported assets when using probabilistic methods. Finally,we look at some real reserves data.
Executives, pay attention. Proved reserves for a portfolio of fields turnout much larger than the simple sum of the proved reserves for each field. Thatmeans that by converting to probabilistic reserves, you will likely reportlarger reserves than you used to. Stockholders should wonder why you want tochange the numbers. You could confess that you have been in error all theprevious years, and you now wish to mend your ways by doing the calculationscorrectly.
How much more reserves will companies report? Later.
The old (and still valid) definition essentially defined proved reserves asthose that were "reasonably certain." This will not surprise the reader, butthe phrase "reasonably certain" is about as constrained as a trailer home in atornado. I make it a practice when discussing this topic with various groups toask what probability they attach to the phrase. They routinely give numbersbetween 98% and 55%. The secondary phrase "high degree of confidence" doesn'tseem to make much difference. I know an engineer who translates that to50%.
With the recent modification in definitions, SPE and WPC allow forprobabilistic treatment of reserves. In truth, companies could have always usedprobabilistic methods had they wanted to and known how. In fact, we can have noconsistent definition of "reasonably certain" without using probabilities.
Officials say that if you use probabilities, then proved must mean a 90%or greater probability that the quantities recovered will be equal to orlarger than your estimate. The slip here is 90% or greater. For consistency,proved ought to be 90% for everyone - skip the phrase "or greater." Can youimagine the exploration manager, the engineering manager, and the banker allagreeing on the same definition?
Legal and Illegal
One cannot add proved reserves for zones to get well proved reserves. Norcan one add well reserves to get field reserves. Mathematically incorrect.Leads to the wrong answer.
Say the probability distributions associated with wells Maxine and Gerryappear as in Fig. 1. Vertical dotted lines show the means of eachdistribution. We've arbitrarily assigned "proved reserves" to a spot on thedistributions so that there is a 90% chance of producing at least as much.Similarly, "possible reserves" lie at points so that we have only a 10% chanceof achieving that amount or more. The horizontal lines labeled "Var." representthe width or "spread" of the distributions, typically defined as the varianceor its square root, standard deviation.
Now, what can we do with these numbers without violating any laws? Look atfour common equations (subscripts refer to well names).
Var.M+Var.G=Var.M+G if M and G areindependent.
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