1. Gas Hydrate Modeling by Jack Schuenemeyer Southwest Statistical Consulting, LLC Cortez, Colorado USA 2012 International Association of Mathematical Geoscientists Distinguished Lecturer 1 Dallas Geophysical Society, March 22, 2012

2. Thanks to: US Bureau of Ocean and Energy Management (BOEM) for financial support Matt Frye, BOEM project leader Tim Collett, US Geological Survey Gordon Kaufman, MIT, Professor Emeritus Ray Faith, MIT, retired Also – This is a work in progress – Opinions expressed are mine 2

3. Outline Purpose of model Model overview Generation – some detail Dependency A statisticians perspective 3

4. Methane in Ice 4 Courtesy USGS

5. Location of Hydrates 5 US BOEM

6. Where are They? 6 USGS

7. Interest in Hydrates Governments of: USA Japan India China South Korea Canada Major energy companies Universities 7

8. US Bureau of Ocean & Energy Management Assessment 8

9. Comparison: In-place Hydrates USGS, 1995 GOM 38,251 tcf BOEM, 2008 GOM 21,444 tcf BOEM, 2008 GOM sand only 6,717 tcf EIA 2011 US Natural gas consumption 24.1 tcf EIA 2011 US Natural gas production 25.1 tcf 9

10. 1995 USGS Assessment Size-Frequency Model 10 Frequency Size

11. BOEM Mass Balance Model Cell based model (square 3 to 4 km on a side) Estimates in-place gas hydrates Biogenic process (thermogenic omitted) Stochastic as opposed to scenario US Federal offshore Below 300 meters water depth 11

12. Hydrate Volume By Cell, Gulf of Mexico 12

13. The Gas Hydrate Assessment Model 13 Basin Generate All Cells in Basin Charge Under sat HSZ Concentration Volume

14. Input Data for Each Cell ( GOM 200,000 cells, 2.32 km 2 each) Location Water depth Sediment thickness Crustal age (Pleistocene to Oligocene) Fraction sand Presence of bottom surface reflector Total organic carbon 14

15. Sources of Data Hard Data – Drilling – Geophysical Published literature Analogs Expert judgment 15

16. Model Parameter Inputs Excel spreadsheet Specific distribution or regression – Water bottom temp model – Hydrate stability temperature – Phase stability equations – Shale porosity – Sand porosity – Saturation matrix pore volumes 16

17. Important Model Variables with a Stochastic Component Total Organic Carbon (TOC) Rock Eval (quality measure) Geothermal gradient (GTG) Migration efficiency Undersaturated zone thickness Sand permeability Sand and shale porosity Shallow sand and shale porosities Water bottom temperature Formation volume factor 17

18. What This Statistician Worries About Representative data Model structure Expert judgment Uncertainty interval 18

19. Catchment Basins (Gulf of Mexico) 19

20. Look At Models Generation Hydrate Stability Zone (HSZ) Volume 20

21. Generation Components 21

22. Atlantic TOC 22

23. Total Organic Carbon Sites - GOM 23

24. GOM TOC 24

25. Pacific 25

26. Pacific TOC 26

27. GOM Asymptotic Conversion Efficiency 27 Weibull fit

28. Geothermal Gradient Gulf of Mexico 28

29. GOM Geothermal Gradient 29 C 0 /km of depth Truncated normal fit

30. Geothermal Gradient (GTG) Pacific Well Sites 30

31. Water Bottom Temp Model 31

32. Temp/Perm/Porosity Compute midpoint thickness Top & bottom temp Midpt sand perm Midpt shale porosity Midpt shale perm Ave bulk rock perm (i,j); scaled by WB perm 32

33. Productivity Function Generation potential (in grams): – Total Organic Carbon x Asymptotic conversion efficiency x Sediment thickness x Cell area x Sediment density Incremental Generation from epoch i to j: – Total Organic Carbon x Age duration x Cell area x Intercept x Arrhenius integral / Geothermal gradient 33

34. Intercept is a Product of: Maximum initial production, Epoch thicknesses, Seafloor temperature (from model), Top and bottom temperatures between, epochs fn(thickness and geothermal gradient), Seafloor perm: function(sand/shale ratio), Sand & shale permeability 34

35. Maximum Initial Production 35 Grams/cubic meter/million years x 10 6

36. To Derive Max Initial Production 36 From Price & Sowers, Proc NAS, 2004

37. Arrhenius Law 37 (Deg C)

38. Estimate Hydrate Stability Zone (HSZ) HSZ is a zero of: where – GTG is geothermal gradient (degrees/km) – WBT is water bottom temperature; a function of water depth (WD) 38 Modified from Milkov and Sassen (2001)

39. Volume Let X 1 = charge (g) at RTP Let X 2 = (X 1 x 0.001396) cu m at STP, where 0.001396 = 22.4 liters/mole x (1/(16.0425 g/mole)) / (1000 liters/cu m) converts grams to cubic meters. Let X 3 = X 2 /fvf (cu m) at RTP, where fvf is the formation volume factor Let Y = container size (cu m) at RTP = NetHSZ (m) x 3048 2 (m 2 ) x Saturation Then if X 3 > Y then Vol = Y, else Vol = X 3 Vol <= Vol x fvf 39

40. BOEM 2008, Gulf of Mexico 40

41. Gulf of Mexico (2008 results) 41

42. Model Construction 1 st stage – Published literature Review theory Review models – Historic data Identify needs for additional data – Identify experts 42

43. Model Construction 2 nd stage – New data – Create flow diagram – Modify existing models – Develop new models – Decide on modeling approach, i.e., Monte Carlo, scenario, deterministic, etc. – Code model 43

44. Model Construction 3 rd stage – Run model – Debug model – Run model – Debug model – Run model – Debug model – DOCUMENT – Evaluate model 44

45. Model Construction 3 rd, 4 th, 5 th, … stages – Model results to subject matter experts – Use new data when possible – Revise model – DOCUMENT 45

46. A Statisticians Concerns Uncertainty – Input data – Model components – Propagation of error – Consistence with knowledge Bias – Statistical – Sampling – Measurement error 46

47. More Concerns Use of analogs Expert judgment Dependency/correlation – Input – model components – aggregation Spatial correlation – Data/coverage 47

48. More Concerns Hard data – Occasionally data rich – satellite – Usually data poor – drilling expensive – Historical data sometimes unknown quality – Often spatially clustered Soft data – expert opinion – Electing information – Analogs – Integrating hard and soft data 48

49. Partial Solutions Documentation – However … Evaluation – Results seem reasonable – not all scientific results seem reasonable at first – Consistent with measurements where hard data exists – Make available to public 49

50. 50 Dependency Concerns Many past oil, gas and other resource assessments have assumed: – Pairwise independence between assessment units (plays, cells, basins, etc.) – Total (fractile) dependence

51. Middle Ground on Dependency Develop a statistical model using geologic data to estimate correlations between neighboring cells, i.e., spatial extent of total organic carbon Use expert judgment based upon geology and analogy to specify associations Assume that cells are totally dependent within basins and independent between basins 51

52. Aggregation Results for Atlantic Margin Example Data for Illustration 52 Independence – all cells independent Basin correlation – all cells within basin are dependent Total dependence – all cells dependent

53. Implications Perception of resource base is different depending on level of assumed or inferred association Risk that a government or company is willing to assume differs 53

54. Consider One Variable - Total Organic Carbon (TOC) Suppose a TOC = 3 wt % is selected from a random draw, i th trial, i = 1, 1000 Assumption – Independence – only applies to one cell – Basin dependence – applies to all cells in basin – Total (fractile) dependence – applies to all cells 54

55. Conclusions Mass balance reasonable approach Easily upgradable Incorporates geology and biology Probabilistic Preliminary results seem reasonable Output serve as input to technically recoverable estimate Transparent Reasonable run time 55

56. Thank you Questions – comments – suggestions Jacks contact info: jackswsc@q.comjackswsc@q.com Southwest Statistical Consulting LLC: www.swstatconsult.com www.swstatconsult.com Book: Statistics for Earth and Environmental Scientists by JH Schuenemeyer & LJ Drew www.earthstatbook.com www.earthstatbook.com 56