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Vincent LEPEZ IFP School ASPO Meeting, May 26, 2003

Modelling of Remaining Reserves in a Mature Basin. Vincent LEPEZ IFP School ASPO Meeting, May 26, 2003. Introduction. The problem. For more than 30 years, the R/P ratio has been remaining quite stable: 30 to 40 years. Source: BP Statistical review.

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Vincent LEPEZ IFP School ASPO Meeting, May 26, 2003

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  1. Modelling of Remaining Reserves in a Mature Basin Vincent LEPEZ IFP School ASPO Meeting, May 26, 2003

  2. Introduction 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

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

  4. Statistical Process Hypotheses (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: Oil & Gas together. (quantities both converted in a common energy unit : Mboe) (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.

  5. Statistical Process Property of Stochastic invariance by scaling => Suggests a Lévy-Pareto distribution of field-sizes Fields’ sizes distribution (1) 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.

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

  7. Statistical Process Northern North sea data => The bigger the field the sooner its discovery Biased sampling (1) 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” ?

  8. Statistical Process Biased sampling (2) 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...

  9. Model Inclusion probability as a function of size (1) n1= 10 n2= 6 n3= 3 n4= 1 N1= 64 N2= 16 N3= 4 N4= 1 Observed populationn Poll world (observed) inclusion probability p =n/N p1= 0,156 p2= 0,375 p3= 0,75 p4= 1 Real world (unknown) Real populationN

  10. Model Prob 1,0 0,8 0,6 0,4 0,2 Size Inclusion probability as a function of size (2)

  11. Estimation Application(s) Viking Graben, Northern North Sea

  12. Application(s) Congo Delta

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

  14. Conclusion Some Remarks... (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: cannot be theoretically handled. =>Only intensive Monte-Carlo methods can provide ideas (3)World wide estimates: theidentification of petroleum systems may be very difficult. =>Experts in geology should be involved (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.

  15. Modelling of Remaining Reserves in a Mature Basin Vincent LEPEZ IFP School ASPO Meeting, May 26, 2003

  16. Enhancement of recovery factor Mb Years

  17. Reserves 500 450 400 350 300 Possible 3P = P10 250 200 2P = P50 Probable 150 1P = P90 100 50 Proved Time Better reservoir knowledge

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