gas hydrate modeling by jack schuenemeyer southwest statistical consulting, llc cortez, colorado usa...
TRANSCRIPT
Gas Hydrate Modelingby
Jack SchuenemeyerSouthwest Statistical Consulting, LLC
Cortez, Colorado USA
2012 International Association of Mathematical Geoscientists
Distinguished Lecturer
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Dallas Geophysical Society, March 22, 2012
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
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Outline
• Purpose of model
• Model overview
• Generation – some detail
• Dependency
• A statistician’s perspective3
Methane in Ice
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Courtesy USGS
Location of Hydrates
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US BOEM
Where are They?
6USGS
Interest in Hydrates
• Governments of:• USA• Japan• India• China• South Korea• Canada
• Major energy companies• Universities
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US Bureau of Ocean & Energy Management Assessment
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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
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1995 USGS AssessmentSize-Frequency Model
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0 2 4 6 8 10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Volume
Pro
ba
bili
ty d
en
sity
6 8 10 12 14
0.0
00
.05
0.1
00
.15
0.2
0
Number of prospects
Pro
ba
bili
ty d
en
sity
FrequencySize
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
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Hydrate Volume By Cell, Gulf of Mexico
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The Gas Hydrate Assessment Model
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Basin
Generate
All Cells in Basin
Charge
Under sat
HSZ
Concentration
Volume
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
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Sources of Data
• Hard Data– Drilling– Geophysical
• Published literature• Analogs• Expert judgment
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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
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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
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What This Statistician Worries About
• Representative data• Model structure• Expert judgment• Uncertainty interval
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Catchment Basins (Gulf of Mexico)
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Look At Models
• Generation• Hydrate Stability Zone (HSZ)• Volume
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Generation Components
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Atlantic TOC
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Total Organic Carbon Sites - GOM
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GOM TOC
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Pacific
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Pacific TOC
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GOM Asymptotic Conversion Efficiency
27Weibull fit
Geothermal Gradient Gulf of Mexico
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GOM Geothermal Gradient
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C0/km of depth
Truncated normal fit
Geothermal Gradient (GTG) Pacific Well Sites
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Water Bottom Temp Model
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0 500 1000 1500 2000
05
10
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Atlantic
Water Depth (m)
Te
mp
(d
eg
C)
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
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Crustal Age Thickness
(m) Duration
(my) Seafloor Pleistocene 2000 1.95 Pliocene 700 3.1 Upper Mio 1200 5.95 Middle Mio 350 7.25 Lower Mio 400 6.4Deepest Oligocene 500 5.35
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
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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
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Maximum Initial Production
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Grams/cubic meter/million years x 106
To Derive Max Initial Production
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From Price & Sowers, Proc NAS, 2004
Arrhenius’ Law
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Comparison of Arrhenius curves
-2.00E-01
0.00E+00
2.00E-01
4.00E-01
6.00E-01
8.00E-01
1.00E+00
1.20E+00
0 20 40 60 80 100
Temperature
rate
Mesa Function
Original Function
(Deg C)
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)
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( | ) [ ] [ ln( ) ]1000
HSZf HSZ WD GTG WBT HSZ WD
Modified from Milkov and Sassen (2001)
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
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BOEM 2008, Gulf of Mexico
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Gulf of Mexico (2008 results)
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Model Construction
• 1st stage– Published literature
• Review theory• Review models
– Historic data• Identify needs for additional data
– Identify experts
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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
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Model Construction
• 3rd stage– Run model– Debug model– Run model– Debug model– Run model– Debug model– DOCUMENT– Evaluate model
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Model Construction
• 3rd, 4th, 5th, … stages– Model results to subject matter experts– Use new data when possible– Revise model– DOCUMENT
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A Statistician’s Concerns
• Uncertainty– Input data– Model components– Propagation of error– Consistence with knowledge
• Bias– Statistical– Sampling– Measurement error
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More Concerns
• Use of analogs
• Expert judgment
• Dependency/correlation– Input – model components – aggregation
• Spatial correlation– Data/coverage
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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
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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
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Dependency Concerns
• Many past oil, gas and other resource assessments have assumed:
– Pairwise independence between assessment units (plays, cells, basins, etc.)
– Total (fractile) dependence
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
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Aggregation Results for Atlantic MarginExample Data for Illustration
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Assumption Min F95 F75 F50 Mean F25 F05 MaxIndependence 404 409 411 413 413 415 418 422
Basin correlation 157 235 310 383 414 477 707 1995Total dependence 0 16 87 220 411 494 1425 7738
Units (trillions of cubic meters)
Empirical distribution statistics
Independence – all cells independent
Basin correlation – all cells within basin are dependent
Total dependence – all cells dependent
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
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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
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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
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Thank you
• Questions – comments – suggestions
• Jack’s contact info: [email protected]
• Southwest Statistical Consulting LLC: www.swstatconsult.com
• Book: Statistics for Earth and Environmental Scientists by JH Schuenemeyer & LJ Drew www.earthstatbook.com
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