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

15

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: jackswsc@q.com

• 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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