# Statistical Process IntroductionModelEstimationApplication(s)Conclusion Vincent LEPEZ IFP School ASPO Meeting, May 26, 2003 Modelling of Remaining Reserves.

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Statistical Process IntroductionModelEstimationApplication(s)Conclusion Vincent LEPEZ IFP School ASPO Meeting, May 26, 2003 Modelling of Remaining Reserves in a Mature Basin

Statistical Process IntroductionModelEstimationApplication(s)ConclusionIntroduction The problem For more than 30 years, the R/P ratio has been remaining quite stable: 30 to 40 years. Source: BP Statistical review => There must be self-reproduction of fossil fuel reserves

Statistical Process IntroductionModelEstimationApplication(s)ConclusionIntroduction Various means for reserves’ replacement Re-evaluation of known fields Better reservoir knowledge Enhancement of recovery factor Price of crude oil New discoveries Impact on hydrocarbon reserves Predictability + / – Probabilistically assessed+ Unpredictable + / – Highly volatile+ Probabilistically predictable ? Forecasting future new discoveries means: - evaluating how many fields remain to be discovered; - estimating their sizes... => statistical modelling of the exploration process

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Hypotheses (1)Geographical scale of study: (1) Geographical scale of study: the Mature Petroleum System. (warrants homogenous geological parameters such as source rock, hydrocarbon migration process and trapping) (2)Hydrocarbon considered: (2) Hydrocarbon considered: Oil & Gas together. (quantities both converted in a common energy unit : Mboe) (3) Figures of interest: (3) Figures of interest: Proved Reserves. (is the only definition of hydrocarbon reserves that makes economical sense) (4) Working context: - petroleum system geoscience knowledge stable; - technology knowledge stable; - economic context stable; - no geopolitical constraints.

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Fields’ sizes distribution (1) Statistical Process It is very well known that close to giant fields, it is likely to find big fields. close to big fields, it is likely to find medium size fields. close to medium size fields, it is likely to find small fields. Property of Stochastic invariance by scaling => Suggests a Lévy-Pareto distribution of field-sizes

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Fields’ sizes distribution (2) Statistical Process Rank in the order statistic Size (Mb) But rather has this shape ! => Suggests a tricky and biased sampling scheme Should be this shape if Lévy-Pareto...

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Biased sampling (1) Statistical Process Step 1: the sample of existing fields in the subsoil is modelled by a Lévy-Pareto sample. Step 2: the sample of discovered fields is a subsample of the last one. But how “subsampled” ? => The bigger the field the sooner its discovery Northern North sea data

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Biased sampling (2) Statistical Process The sample of already discovered fields is a size-biased subsample of those existing in the subsoil. ie. the bigger the field, the larger its probability of being discovered ! ie. the probability of being discovered is an increasing function of the size. => Let’s build a model...

Statistical Process IntroductionModelEstimationApplication(s)ConclusionModel Inclusion probability as a function of size (1) Poll world (observed) Real world (unknown) inclusion probability p = n / N Observed population n Real population N n 1 = 10n 2 = 6n 3 = 3n 4 = 1 N 1 = 64N 2 = 16N 3 = 4N 4 = 1 p 1 = 0,156 p 2 = 0,375 p 3 = 0,75 p 4 = 1

Statistical Process IntroductionModelEstimationApplication(s)ConclusionModel Inclusion probability as a function of size (2) Prob 0,2 0,4 0,6 0,8 1,0 Size

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Viking Graben, Northern North Sea Application(s)Estimation

Statistical Process IntroductionModelEstimationApplication(s)ConclusionApplication(s) Congo Delta

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Other possible applications Application(s) (1)Economic studies: (1) Economic studies: the world total amount of reserves is a key figure for all of our industry. (2)Energy planning: (2) Energy planning: the model could help forecasting hydrocarbon shortages in mature areas. (3)Company strategy: (3) Company strategy: if an area is proved to be close to exhausted, no need to spend M\$ ! (4)Backward analysis: (4) Backward analysis: the model can help to analyse past-exploration efficiency.

Statistical Process IntroductionModelEstimationApplication(s)ConclusionConclusion Some Remarks... (1)Reliability: (1) Reliability: no possible validation on real data as no region in the world is really exhausted. => Only simulation and non-contradiction backfitting (2)Confidence intervals: (2) Confidence intervals: cannot be theoretically handled. => Only intensive Monte-Carlo methods can provide ideas (3)World wide estimates: (3) World wide estimates: the identification of petroleum systems may be very difficult. => Experts in geology should be involved (4)For the future: (4) For the future: let’s sharpen and extend the model... => Take other key factors of reserves reproduction into account => Try to develop a production model associated with new fields.

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Vincent LEPEZ IFP School ASPO Meeting, May 26, 2003 Modelling of Remaining Reserves in a Mature Basin

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Enhancement of recovery factor Mb Years

Statistical Process IntroductionModelEstimationApplication(s)Conclusion Time Reserves 50 100 150 200 250 300 350 400 450 500 3P = P10 2P = P50 1P = P90 ProvedProbable Possible Better reservoir knowledge

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