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The presentation highlights the difference between the uncertainty quantification and the capacity of prediction of a model. Model uncertainty is due to various factors such as the lack of precise data, the use of imprecise data or the impossibility to conceive with certainty a conceptual model. Some of the factors can be accounted for (known source of uncertainty) and therefore be captured in a model, leading to classical uncertainty quantification. Other factors cannot be accounted for (unknown source of uncertainty), therefore limiting the capacity of prediction of the model.

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- 1. 3D Model Uncertainty Model-derived uncertainties or uncertainty about models Renaud Meunier - November 2013
- 2. Geomodels • A 3D geomodel is a numerical representation of the reality • It is used to compute uncertainty on global parameters: - Volumes (OOIP) Production forecast • It is possible to compute statistics locally (e.g. cell by cell) • Questions: - What are the values of these statistics? Could they help to predict properties or forecast production? o At the global and local scales? 2
- 3. Geomodeling workflow Uncertainty is present at each step 3
- 4. Where is uncertainty coming from? • "We deal with one reservoir only, but our knowledge of it is such that several reservoir models are compatible with our priori knowledge and data" (Dubrule, Geo-statistics for Seismic Data Integration in Earth Models, 2003) • We have several solutions matching the data that we have - Not enough certain data (e.g. well logs) Uncertain or imprecise data (e.g. seismic) o A matter of scale • Consequence: - We cannot predict with exactitude the reality 4
- 5. Global vs local prediction • The 3 maps below are different • But their statistics are the same Nb Ech : 40000 Minimum: 0.10 Maximum: 35.00 Moyenne: 1.69 Ec-Type: 2.34 0.8 0.7 Fréquences 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 • Global uncertainty will be the same but local uncertainty will be different, e.g.: - volumes (global) new well location (local) 5
- 6. How is the uncertainty measured? • We can simulate by stochastically varying key parameters • For global uncertainty we can “cumulate” the uncertainty coming from each input parameters 100 90 P90 80 70 Frequencie s e.g. <OOIP>=<GRV>*<NtG>*<φ>*(1-<Sw>)/Bo 60 P50 50 40 30 20 P10 10 0 1.1e+008 1.1e+008 1.1e+008 1.2e+008 Volumes (m3) • This approach can be generalized to production data: - By simulating flow in the model with varying dynamic parameters o If too long, an approximation by experimental design can be used 6
- 7. Quality of uncertainty computation • We need to find a minimal uncertainty on variable parameters • The uncertainty level depends on the degree of heterogeneity of the variable - Link to the data sampling o o Number of observations (should increase with the heterogeneity) Position in space (better when uniformly sampled) • Assuming same variable and field (i.e. same heterogeneity) + uncertainty - uncertainty 7
- 8. Heterogeneity Examples Sylvinite beds in potash mines can be continuous over long distances Shoal in carbonate environment can be very heterogeneous (less than the typical reservoir cell size) Underwater photograph of a reef front off Discovery Bay, Jamaica. Water depth is ~7 meters. (Noel James, 1983; from AAPG Memoir 33) Courtesy Jeffrey Yarus and Richard Chambers Consequences: - More heterogeneous our system is less we can predict at the local scale - But the global scale prediction still holds as long as the statistics (i.e. PDF) are accurate 8
- 9. Global parameters uncertainty Knowing the histograms or PDF, global uncertainty quantification can be done by a MonteCarlo approach GRV N/G F Sw Random number generation GRV x N/G x F x (1-Sw) STOOIP = ----------------------------Bo Need to take into account correlation between variables to get the right amount of uncertainty 9
- 10. Radical errors • Incertitude are computed on a mathematical model - Geostatistical simulation (PDF + Variogram + Data (hard and soft)) [1] Geostatistical inversion ([1] + physical forward model) • However it is possible to get radical errors occurring if the model is not realist - e.g. Presence of a sub-seismic fault o o seal problem structural problem +- 10m below or above target • This type of error is not captured by uncertainty quantification - Could have a minimum impact on reserves but a strong one on local parameters (e.g. reservoir top, connection between blocks) 10
- 11. What can be done? • A model is not a measure of the reality - It is our numerical approximation of the reality • To minimize the error we need to integrate data of different natures and of different scales - Well logs, cores Seismic, Gravimetric, EM… Dynamic synthesis (basic reservoir engineering) o Generally not taken into account in static model building • The geomodel quality then depends on the amount of information (knowledge) that it incorporates. - Integrating inputs (knowledge) from various disciplines helps reducing the risk of radical errors. 11
- 12. Consistency with dynamic synthesis • Dynamic synthesis allows defining the hydraulic connection between wells and/or stratigraphic units • Geomodels are expected to reproduce these connections - If not, History Match will be very difficult 12
- 13. Consistency with dynamic synthesis • There is no geostatistical algorithm honoring connections - Connections can be managed only by workflows linking geostatistical and morphological tools • Connections can be checked by mean of connected bodies Connected wells 13
- 14. Consistency with dynamic synthesis • Solving wells connection inconsistencies: - Modify local Vertical Proportion Curves to allow the presence of connecting facies between the wells or at the contact between units Connecting facies in blue VPC @ well1 0% 20% 40% 60% 80% VPC between wells 0% 100% 20% 40% 60% 80% VPC @ well2 100% 100% 0% 1 1 2 2 3 4 5 6 6 7 7 7 8 8 8 9 9 9 10 10 100% 5 6 80% 4 5 60% 3 4 40% 2 3 20% 1 10 The null proportion of connecting The presence of connecting facies facies between wells cuts the between wells allows the hydraulic hydraulic connection connection 14
- 15. Conclusion (1) • Geomodels are representations of the reality not the reality itself • Uncertainty is due to lack of precise data (e.g. well control), imprecise data (e.g. seismic), impossibility to conceive with certainty a conceptual model • Model uncertainty can be accessed by stochastically varying the model parameters and generating equiprobable outcomes 15
- 16. Conclusion (2) • Even if uncertainty on a global parameter is low, the prediction capability at local scale may be poor - Low uncertainty on OOIP may be associated with poor properties distribution prediction at local scale in heterogeneous environments Difference between local and global uncertainty Conceptual uncertainty require a scenario based approach • Geomodel quality depends on the amount of information (knowledge) that it incorporates. - Integrating knowledge from various disciplines helps reducing the risk of radical errors 16

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