Basin Modeling and Decision Analysis with Bayesian Networks

1. SCRF - Multidisciplinary Close collaborations with other research programs BPSM SCRF Stanford Center for Reservoir Forecasting Basin and Petroleum System Modeling

2. Basin Modeling and Decision Analysis SCRF - Multidisciplinary

3. SCRF - Multidisciplinary • Basin modeling inputs to decision analyses • using Bayesian networks • collaboration with Eidsvik, Martinelli (NTNU) • 2010

4. Basin Modeling and Decision Analysis Building Bayesian networks from basin modeling scenarios for improved geological decision making Martinelli, Tviberg, Eidsvik, Sinding-Larsen & Mukerji In press Petroleum Geosciences (2013)

5. Summary • Integration between quantitative BPSM methodologies and decision analysis; quantify uncertainties, and how uncertainty affect decisions • Use of BPSM multiple runs to train probabilistic decision tool (Bayesian network) • Provide inputs for aiding Value of Information (VOI) based decision techniques with BPSM.

6. Basin Modeling and Decision Analysis Building Bayesian networks from basin modeling scenarios for improved geological decision making

7. Bayesian Networks Bayesian networks (or Influence diagrams) are mathematical tools allowing fast computations of conditional probabilities Used in decision analysis Prof. Ronald Howard , James Matheson, Prof. Shachter, Koller, developed, refined and popularized influence diagrams.

8. Bayesian Networks (BN) Bayesian belief networks are probabilistic models where a graph structure is used to represent a set of random variables and their conditional dependencies.

9. Network Models - Arrows Arrows represent relationships or influence between the nodes. A B A influences B means that knowing A would directly affect our belief or expectation about the value of B. It does not necessarily imply a causal relation, or a flow of data or money. Evidential dependence, not necessarily causal dependence.

10. B A C D Network Models • Network structure • -nodes representing variables • -links representing dependencies between nodes P(B) P(A) P(C|B) P(C|A) P(D|C) • Probability distribution of variables at each node • given the state of its parent node

11. Bayesian Networks - examples Representation of the relation between uncertainties and decisions Example of Influence Diagram Bhattacharjya & Mukerji, 2006

12. Expanding the Nodes Example of Influence Diagram Bhattacharjya & Mukerji, 2006

13. Full Network Model for Monitoring Example of Influence Diagram Bhattacharjya & Mukerji, 2006

14. Network Models Help to factorize large multivariate joint PDFs into more manageable smaller PDFs using the network to find conditional independencies PDF: probability distribution functions

15. Evaluating Network Models Network diagrams useful for representing decision problems. But not merely pictorial depictions Also computational tools to solve decision problems efficiently

16. Bayesian Networks in Decision Analysis • Representation of the relation between • uncertainties and decisions • as well as • computation of optimal decisions • impact of evidence • value of information (VOI)

17. Bayesian Networks in BPSM Decision Analysis Bayesian networks (BN) need to encode dependencies in a geological system - source rock, - reservoir rock, - trap

18. Conditioning the Network model • Important to note that for a Bayesian network model • to be effective the prior conditional probabilities should • be case specific: • based on the opinion of experts in that field

19. Bayesian Networks in BPSM Decision Analysis Van Wees et al., 2008 Martinelli et al., 2010 Rasheva & Bratvold, 2011 Source Source Source Martinelli et al., 2010 Source

20. Conditioning the Network model • Important to note that for a Bayesian network model • to be effective the prior conditional probabilities should • be case specific: • based on the opinion of experts in that field • from quantitative basin modeling runs based on data specific to that field

21. Source rock Reservoir rock Seal rock Overburden rock Trap Formation Generation-Migration- Accumulation Basin and Petroleum System Modeling Seal Reservoir Migration Path Source Four essential elements and two processes Essential Elements Processes Leslie B. Magoon, Wallace G. Dow, The Petroleum System, AAPG Memoir 60 23

22. Key Modeling Factors Burial History (deformation, compaction) Thermal History (heat flow, thermal conductivities) Source Rock Geochemistry ( chemical kinetics) Fluid Migration (multiphase Darcy flow, streamlines) 24

23. Basin Modeling Coupled, non-linear, PDEs with moving boundaries Numerical solution (finite elements) 25

24. Key outputs Burial history Thermal history Geochemical history Hydrocarbon flow and accumulations 26

25. Bayesian Networks in BPSM Decision Analysis How can we train the network using BPSM simulations? Constructing Bayesian networks to address decision problems requires key inputs from basin modeling simulations

26. Bayesian Networks and BPSM Decision Analysis How can we train the network using BPSM simulations? Synthetic example and workflow

27. Synthetic Basin Model Example – Base Case Plausible petroleum system scenario and boundary conditions, 55Ma ago to present 100 x 100 km 9 layers Source (Mlf) Source (Eek)

28. Synthetic Basin Model Example – Base Case Plausible petroleum system scenario and boundary conditions, 55Ma ago to present 100 x 100 km Reservoir (Mmd, top) Reservoir (Ou, bottom)

29. Synthetic Basin Model Example – Base Case Plausible petroleum system scenario and boundary conditions, 55Ma ago to present 100 x 100 km Traps: Anticline (East) Fault (West) 4 possible prospects: Top, East (TE) Bottom, East (BE) Top, West (TW) Bottom, West (BW) East West

30. Synthetic Basin Model – Base Case Accumulations

31. Synthetic Basin Model – Base Case Migration pathways Anticline (East) Fault (West)

32. Synthetic Basin Model – Uncertain factors Experimental design, full factorial design with 4 factors Porosity, Heat Flow, Fault 3 and TOC 2 x 3 x 2 x 2 = 24 total levels

33. Porosity – 2 compaction depth trends Depth (m) Porosity Porosity (low) (High)

34. Synthetic Basin Model – Uncertain factors Experimental design, full factorial design with 4 factors Porosity, Heat Flow, Fault 3 and TOC 2 x 3 x 2 x 2 = 24 total levels Responses: generation (size, oil, gas) accumulation (size, oil, gas)

35. Analyze Outputs - examples HC Generation Total (MMBOE) HF TOC porosity Fault3

36. Analyze Outputs - examples Generation Eek Oil (MMBOE) HF TOC porosity Fault3

37. Analyze Outputs - examples Generation Eek Gas (MMBOE) HF TOC porosity Fault3

38. Analyze Outputs - examples Accumulation Ou Gas (MMBOE) HF TOC porosity Fault3

39. Analyze Outputs - examples Pareto charts

40. Decision Model Building the Bayesian Network (BN) • Source nodes • Trap nodes • Reservoir nodes • Accumulation nodes

41. Building the Bayesian Network (BN) Source sub-network

42. Building the Bayesian Network (BN) Reservoir sub-network

43. Building the Bayesian Network (BN) Trap sub-network

44. Bayesian Network

45. Decision Model Training the Bayesian Network (BN) (Learning the network) Conditional Probability Tables (CPT) associated with nodes Obtained by clustering output responses generation (low, medium, high) accumulation (low, high) CPTs estimated by ratio of corresponding counts

46. Training the Bayesian Network (BN) Clustering outputs: Accumulation 2 levels Accumulation total Top Bottom Gas Oil Gas Oil

47. Decision Model Training the Bayesian Network (BN) (Learning the network) Conditional Probability Tables (CPT) associated with nodes Obtained by clustering output responses generation (low, medium, high) accumulation (low, high) CPTs estimated by ratio of corresponding counts

48. { } max Prior Value = Using BN in Value of Information (VOI) calculations VOI = Value with evidence – Prior value f: recovery factor C: cost Value with evidence = Network model evaluates evidence based updating of probabilities

49. Evaluating the Bayesian Network Evidence based update of probabilities P(BE oil) Evidence about TE oil

50. Evidence based update of probabilities P(BE oil) Probability density Volume oil (MMBOE)