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Aggregation of forecasts
Managing forecast portfolio uncertainty
It is often necessary to investigate the forecast uncertainty for a portfolio of fields or reservoirs to evaluate, for example, the risks and opportunities of an exploration portfolio, of a new business strategy, for an “urban planning” study or to evaluate uncertainty in the regional portfolio. A Portfolio could be any of the following:
- Multi-reservoir fields
- Cluster developments
- Gas contract pool
- Regional portfolio
- Global corporate forecast
It is important to understand whether the portfolio uncertainties are dependent or independent. Cases 1, 2 and 3 are often dependent with complex interactions of the parameters and strong inter-dependencies (both positive and negative correlations) and with common system constraints. In this case, a comprehensive Monte Carlo analysis of the system is recommended that includes all the complex system interactions. Aggregation tools are available in the industry to do this complex probabilistic aggregation after individual field forecasts have been generated; however, most IPSM tools have the ability to evaluate the system uncertainty for all assets concurrently and the latter approach would be preferred, but is sometimes considered too time-consuming.
If the uncertainties can be assumed to be largely independent, as in Cases 4 and 5 (regional and global portfolio of a company) , and also in some gas contract pools (Case 3) then the aggregation can be done with a simple Monte Carlo simulation or analytically as in the example below:
Company A has 3 assets: Two producing fields on decline and a green field under development. The fields are stochastically independent and probabilistic forecasts have been made for each of the three assets individually, resulting in expectation, P10 and P90 forecasts for each asset (Gallery 1 Asset 1,2,3 with their uncertainty range).
Gallery 1 Asset 1,2,3 with their uncertainty range.
Management would like to understand the uncertainty at the portfolio level.
The reservoir engineer does an analytical aggregation using the following algorithm:
This results in the uncertainty range represented in Gallery 2 (Expectation forecast for the portfolio and uncertainty range) for the company’s portfolio. This shows that the P90 of the portfolio is significantly higher than the arithmetic sum of the low cases.
Gallery 2 Expectation forecast for the portfolio and uncertainty range To validate the results, the reservoir engineer also compares the analytical aggregate with a Monte Carlo simulation as represented in Gallery 3 (Uncertainty range in cum. vs. time.). This shows that the P90 of the portfolio is significantly higher than the arithmetic sum of the low cases also in cum. QC with Monte Carlo simulation.
Gallery 3 Uncertainty range in cum. vs. time Simple analytical aggregation is considered adequate in this case.
The algorithm may be applied to yearly rates or yearly cumulatives. The results will be slightly different. The preferred approach depends on the question being addressed:
- If the question is
- what is the likelihood that the company drops below 100 kB/D during the next 5 years, then the aggregation should be carried out using rates.
- If the question is
- what is the likelihood that the company produces more than 500 MMBO in the next 10 years, then the aggregation should be carried out using cumulatives.
From the charts above, the answer to the first questions is: more than 10% and less than 50%, the answer to the second question is less than 10% and more than 0.1%.
Many Companies use P50 rather than mathematical expectation as their best-estimate forecast. In this case the P50 forecast should be adjusted as follows, before the algorithm is applied: μ ~ (3 • P50 + P10 + P90 ) /5.
Note that if the distribution is symmetric then the correction yields µ = P50 and no adjustment is necessary. If the distribution is moderately skewed, then the correction yields a very close approximation.
The resulting distribution is only an approximation (but this is not a problem because we have only an incomplete understanding of the input distributions), but it fulfils the following essential criteria:
- Exact if the input distributions are normal distribution
- Fully preserves the skew of the input distributions
The P90-P10 range of the aggregate forecast is significantly narrower than the arithmetic sum of the low and high cases. The more assets in a portfolio, the more the P10/P90 will converge towards the mean by the “law of large numbers” or “central limit theorem”. This is why companies carry a portfolio to spread their risk.
The analytical aggregation is exact if:
- The base forecasts are stochastically independent and
- The underlying distributions are normal distributions (an therefore symmetric),
- The underlying distributions are half normal distributions and the best estimate is the mean.
In most cases of moderate skew and moderate dependencies, it provides a good approximation and should always be used to calibrate more complex aggregation methods.
Portfolio aggregation approach
Note that the portfolio aggregation approach should only be used for business decisions and risk analysis and not for reserves estimate when a company is subject to SEC rules because the SEC states:
Regardless of whether the reserves were determined using deterministic or probabilistic methods, the reported reserves should be simple arithmetic sums of all estimates at the well, reservoir, property, field, or project level within each reserves category.
The 2007 PRMS recommends a similar approach when aggregating fields but allows probabilistic aggregation within a project where appropriate. It states the following in Section 4.2.1:
The aggregation methods utilized depends on the business purpose. It is recommended that for reporting purposes, assessment results should not incorporate statistical aggregation beyond the field, property, or project level. Results reporting beyond this level should use arithmetic summation by category but should caution that the aggregate Proved may be a very conservative estimate and aggregate 3P may be very optimistic depending on the number of items in the aggregate.
The PRMS application guide Chapter 6 gives more examples and also discusses how to manage the tension between technically correct aggregation and SEC compliant aggregation.
Well level aggregation
The PRMS application guide also discusses well-level aggregation, specifically when forecasts are made with DCA.
- Securities and exchange commission, 17 cfr parts 210, 211, 229, and 249, [release nos. 33-8995; 34-59192; fr-78; file no. S7-15-08], rin 3235-ak00 Modernization of oil and gas reporting, revisions and additions to the definition section in rule 4-10 of regulation s-x http://www.sec.gov/rules/final/2008/33-8995.pdf
- Society of Petroleum Engineers (SPE), American Association of Petroleum Geologists(AAPG), World Petroleum Council (WPC), and the Society of Petroleum Evaluation Engineers (SPEE) http://www.spe.org/industry/docs/Petroleum_Resources_Management_System_2007.pdf
- Guidelines for Application of the Petroleum Resources Management System November 2011 http://www.spe.org/industry/docs/PRMS_Guidelines_Nov2011.pdf
Noteworthy papers in OnePetro
Amudo, C., Walters, S., O'Reilly, D. I., Clough, M., Beinke, J. P., & Sawiris, R. S. (2011, January 1). Best Practices and Lessons Learned in the Construction and Maintenance of a Complex Gas Asset Integrated Production Model (IPM). Society of Petroleum Engineers. http://dx.doi.org/10.2118/146968-MS.
Kabdenov, S., Aitkazin, M., Macary, S., & Aitzhanov, A. (2014, January 19). IPM Tool for Strategic Decisions: Diverse Applications of IPM in the Supergiant Tengiz Field. International Petroleum Technology Conference. http://dx.doi.org/10.2523/17252-MS.
Tillero, E., Rincón, J., & Nuñez, H. (2014, May 21). An Innovative Workflow for Appropriate Selection of Subsurface-Surface Model Integration Scheme Based on Petroleum Production System Nature, User Needs, and Integrated Simulation Performance. Society of Petroleum Engineers. http://dx.doi.org/10.2118/169243-MS.
Torrado, R. R., Echeverria Ciaurri, D., Mello, U., & Embid, S. (2013, September 30). Fast Reservoir Performance Evaluation Under Uncertainty: Opening New Opportunities. Society of Petroleum Engineers. http://dx.doi.org/10.2118/166392-MS.