One might expect reserves and PV10 estimates to be intuitive and easy for investors to understand. After all, these are the measures endorsed by the SEC (with “Standardized Measure” in place of “PV10”) and international securities regulators to help investors understand what they’re getting themselves into. But the unfortunate reality is that these figures were designed for accuracy and internal consistency, not intuitiveness and simplicity. The SEC decided to put investors through a maze that might leave them seeing the world upside down and backwards in hopes that the gains of greater precision would more than offset the pains of lost clarity. In our experience, this has not been the case. More than once we have seen investors make decisions they came to regret after exiting the reserves reporting maze with an upside down and backwards perspective.

Deterministic vs Probabilistic Reserves Estimates

To start us off, we need to recognize that there are two overarching ways to estimate reserves: Deterministic and Probabilistic. The deterministic method is the older and more popular of the two. The probabilistic approach is the new kid on the block: less popular but an up-and-comer. Academics hail the probabilistic approach as the “enlightened” approach destined to overthrow the outdated deterministic methods.

Despite the ongoing debate, these two methods are closely related, such that understanding one helps in understanding of the other. Consequently, we’ll take a look at both methods before diving into the specific applications that can help investors.

Deterministic

Despite the academic rhetoric, deterministic methods are not necessarily inferior to probabilistic methods. Much depends on the context. Deterministic methods use the best-guess estimate for each input that goes into the reserves estimation formula being used. The formula itself can vary depending on the stage of development and what data is available. Wells with lots of production history will use Arp’s formula. Wells that haven’t been tested will use the volumetric formula. And wells with shut-in pressure tests may use material balance formulas. In any one of these cases, the estimated reserves will be called a “deterministic” estimate so long as one value for each input is fed into the equation.

This approach can still be used to produce estimates with varying levels of certainty, such as 1P (proved), 2P (proved + probable), and 3P (proved + probable + possible) reserves. But even here, we use just one value for each input in each scenario. To get the conservative (or “proved”) estimate of total reserves, a single conservative estimate is made for each of the inputs, which then go into the equation (whether Arp’s, volumetric, or material balance) and produce the conservative estimate. This same process is repeated for the “best” estimate (“proved” + “probable”) and the optimistic estimate (“proved” + “probable” + “possible”) as shown in Figure 1.

Deterministic vs Probabilistic Reserves Estimates

To start us off, we need to recognize that there are two overarching ways to estimate reserves: Deterministic and Probabilistic. The deterministic method is the older and more popular of the two. The probabilistic approach is the new kid on the block: less popular but an up-and-comer. Academics hail the probabilistic approach as the “enlightened” approach destined to overthrow the outdated deterministic methods.

Despite the ongoing debate, these two methods are closely related, such that understanding one helps in understanding of the other. Consequently, we’ll take a look at both methods before diving into the specific applications that can help investors.

Deterministic

Despite the academic rhetoric, deterministic methods are not necessarily inferior to probabilistic methods. Much depends on the context. Deterministic methods use the best-guess estimate for each input that goes into the reserves estimation formula being used. The formula itself can vary depending on the stage of development and what data is available. Wells with lots of production history will use Arp’s formula. Wells that haven’t been tested will use the volumetric formula. And wells with shut-in pressure tests may use material balance formulas. In any one of these cases, the estimated reserves will be called a “deterministic” estimate so long as one value for each input is fed into the equation.

This approach can still be used to produce estimates with varying levels of certainty, such as 1P (proved), 2P (proved + probable), and 3P (proved + probable + possible) reserves. But even here, we use just one value for each input in each scenario. To get the conservative (or “proved”) estimate of total reserves, a single conservative estimate is made for each of the inputs, which then go into the equation (whether Arp’s, volumetric, or material balance) and produce the conservative estimate. This same process is repeated for the “best” estimate (“proved” + “probable”) and the optimistic estimate (“proved” + “probable” + “possible”) as shown in Figure 1.

Those who oppose this method do so because the level of certainty assigned to each estimate tends to be more subjective than the level of uncertainty that can be established using probabilistic methods. An engineer can say, “I feel a high degree of confidence that the average porosity is going to be 6 percent or more,” but we can’t say numerically what a “high degree of confidence” means. Is it a 90% confidence estimate or an 89.99% confidence estimate? We just don’t know. And while the engineer could say, “When I say ‘a high degree of confidence’ I mean a 90 percent confidence level,” without probabilistic methods, we just don’t have any kind of numerical framework to help us explain why this is a 90% confidence level and not 89% or 91%--or if we wanted the 91% estimate, what that would be. As we’ll see, probabilistic methods impose this kind of numerical framework on the uncertainty assessment such that we can move easily from one estimate to another.

Probabilistic

Probabilistic estimates are calculated by assigning a probability distribution to each input that goes into the equation. Suppose, for instance, that a reservoir engineer comes up with a high, middle, and low estimate for porosity, and that there’s also empirical data showing that porosity tends to be normally distributed. The engineer can then come up with a “best fit” distribution with parameters that allow it to hit these low, middle, and high estimates while satisfying the basic requirements of a normal distribution. If the engineer can’t reconcile these estimates with the empirically determined distribution, it tells the engineer that there is a logical inconsistency between the estimates and broader set of empirical data--thus new estimates or a new distribution are required. Once a distribution has been selected for each input, a Monte Carlo simulation (or a similar type of simulation) where the calculation is performed thousands of time (called “trials”) with a single “sample” plucked from each input distribution for each sample. The result of all these “trials” is a distribution of possible outcomes for the amount of reserves we can expect. From this, the engineer can then come up with an estimate of reserves for any confidence level, whether 10%, 90%, or 97.8152%. Figure 2 shows this general process.

Probabilistic

Probabilistic estimates are calculated by assigning a probability distribution to each input that goes into the equation. Suppose, for instance, that a reservoir engineer comes up with a high, middle, and low estimate for porosity, and that there’s also empirical data showing that porosity tends to be normally distributed. The engineer can then come up with a “best fit” distribution with parameters that allow it to hit these low, middle, and high estimates while satisfying the basic requirements of a normal distribution. If the engineer can’t reconcile these estimates with the empirically determined distribution, it tells the engineer that there is a logical inconsistency between the estimates and broader set of empirical data--thus new estimates or a new distribution are required. Once a distribution has been selected for each input, a Monte Carlo simulation (or a similar type of simulation) where the calculation is performed thousands of time (called “trials”) with a single “sample” plucked from each input distribution for each sample. The result of all these “trials” is a distribution of possible outcomes for the amount of reserves we can expect. From this, the engineer can then come up with an estimate of reserves for any confidence level, whether 10%, 90%, or 97.8152%. Figure 2 shows this general process.

Bringing It All Back Together

As we said earlier, while there are clear advantages to using probabilistic methods, most of the publicly traded E&P companies use deterministic methods for reporting purposes. Most likely, this is to avoid shareholder lawsuits. Since these companies don’t know how historical precedents would be applied to probabilistic estimates, they would rather keep using deterministic methods instead of opening themselves up to becoming a “test case” on these issues. In other words, nobody wants to be the guinea pig.

Nonetheless, there are reasons to suspect that the “conservative”, “best”, and “optimistic” reserve estimates produced by deterministic calculations will increasingly converge to the P10, P50, and P90 estimates produced by probabilistic estimates.

First, due to the benefits of using probabilistic methods, the companies themselves are increasingly choosing to use probabilistic methods for their own internal purposes. Exxon Mobile, for example, uses probabilistic methods to guide its internal exploration programs, while continuing to use deterministic methods for reporting.

There are also concerted efforts coming from the Society of Petroleum Engineers (SPE) and academia to move increasingly towards probabilistic methods. And through the influence of these groups, the regulatory agencies are also starting to move in that direction. Before the 2008/2009 SEC’s rules modernization, deterministic methods were clearly favored, while probabilistic methods were not even mentioned--some felt that probabilistic methods were even being actively discouraged by the SEC. Now, after the modernization, probabilistic methods have been explicitly added as an acceptable way to compute reserves. The trend appears to continually be moving in this direction.

Who Cares? (Our favorite question)

For starters, probabilistic methods provide a powerful framework for seeing how reserve estimates with different confidence levels (“proved”, “probable”, and “possible”) are connected. Add to this that the fact that many factors appear to be moving deterministic estimates towards convergence with probabilistic methods, and it seems quite clear that there is much to gain for E&P investors by improving their understanding of how probabilistic methods work and how to interpret their results--thereby identifying opportunities and avoiding pitfalls along the way.

In Part 2, we will dive into this issue: How to understand probabilistic reserves estimates. Stay tuned.

As we said earlier, while there are clear advantages to using probabilistic methods, most of the publicly traded E&P companies use deterministic methods for reporting purposes. Most likely, this is to avoid shareholder lawsuits. Since these companies don’t know how historical precedents would be applied to probabilistic estimates, they would rather keep using deterministic methods instead of opening themselves up to becoming a “test case” on these issues. In other words, nobody wants to be the guinea pig.

Nonetheless, there are reasons to suspect that the “conservative”, “best”, and “optimistic” reserve estimates produced by deterministic calculations will increasingly converge to the P10, P50, and P90 estimates produced by probabilistic estimates.

First, due to the benefits of using probabilistic methods, the companies themselves are increasingly choosing to use probabilistic methods for their own internal purposes. Exxon Mobile, for example, uses probabilistic methods to guide its internal exploration programs, while continuing to use deterministic methods for reporting.

There are also concerted efforts coming from the Society of Petroleum Engineers (SPE) and academia to move increasingly towards probabilistic methods. And through the influence of these groups, the regulatory agencies are also starting to move in that direction. Before the 2008/2009 SEC’s rules modernization, deterministic methods were clearly favored, while probabilistic methods were not even mentioned--some felt that probabilistic methods were even being actively discouraged by the SEC. Now, after the modernization, probabilistic methods have been explicitly added as an acceptable way to compute reserves. The trend appears to continually be moving in this direction.

Who Cares? (Our favorite question)

For starters, probabilistic methods provide a powerful framework for seeing how reserve estimates with different confidence levels (“proved”, “probable”, and “possible”) are connected. Add to this that the fact that many factors appear to be moving deterministic estimates towards convergence with probabilistic methods, and it seems quite clear that there is much to gain for E&P investors by improving their understanding of how probabilistic methods work and how to interpret their results--thereby identifying opportunities and avoiding pitfalls along the way.

In Part 2, we will dive into this issue: How to understand probabilistic reserves estimates. Stay tuned.