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Gas Hydrate Modeling

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

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

  3. Outline • Purpose of model • Model overview • Generation – some detail • Dependency • A statistician’s perspective

  4. Methane in Ice Courtesy USGS

  5. Location of Hydrates US BOEM

  6. Where are They? USGS

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

  8. US Bureau of Ocean & Energy Management Assessment

  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

  10. 1995 USGS AssessmentSize-Frequency Model Size Frequency

  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

  12. Hydrate Volume By Cell, Gulf of Mexico

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

  14. Input Data for Each Cell(GOM 200,000 cells, 2.32 km2 each) • Location • Water depth • Sediment thickness • Crustal age (Pleistocene to Oligocene) • Fraction sand • Presence of bottom surface reflector • Total organic carbon

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

  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

  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

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

  19. Catchment Basins (Gulf of Mexico)

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

  21. Generation Components

  22. Atlantic TOC

  23. Total Organic Carbon Sites - GOM

  24. GOM TOC

  25. Pacific

  26. Pacific TOC

  27. GOM Asymptotic Conversion Efficiency Weibull fit

  28. Geothermal Gradient Gulf of Mexico

  29. GOM Geothermal Gradient C0/km of depth Truncated normal fit

  30. Geothermal Gradient (GTG) Pacific Well Sites

  31. Water Bottom Temp Model

  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

  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

  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

  35. Maximum Initial Production Grams/cubic meter/million years x 106

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

  37. Arrhenius’ Law (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) Modified from Milkov and Sassen (2001)

  39. Volume • Let X1 = charge (g) at RTP • Let X2 = (X1 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 X3 = X2/fvf (cu m) at RTP, where fvf is the formation volume factor • Let Y = container size (cu m) at RTP = NetHSZ (m) x 30482 (m2) x Saturation • Then if X3 > Y then Vol = Y, else Vol = X3 • Vol <= Vol x fvf

  40. BOEM 2008, Gulf of Mexico

  41. Gulf of Mexico (2008 results)

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

  43. Model Construction • 2nd 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

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

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

  46. A Statistician’s Concerns • Uncertainty • Input data • Model components • Propagation of error • Consistence with knowledge • Bias • Statistical • Sampling • Measurement error

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

  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

  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

  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