presentation 100710

8/3/2019 Presentation 100710

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We Have a Problem

Forecasting methods we use inconventional reservoirs may not work well in

Tight gasGas shalesUnconventional gas resources generally


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What Can We Do About It?Understand limitations of conventional

methodsSupport efforts to improveUnderstanding of basic physics controlling

stimulation outcomes, production mechanismsModeling methods based on correct physicsReservoir characterization (model parameters)

Until verified theoretical models available, usemost appropriate empirical models (e.g.,decline curves)


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Decline Curves: ApproachesMajor categories

Arps empirical model As originally proposedWith terminal exponential decline imposedWith a priori terminal b value imposed

Recent empirical models

Valk Stretched-exponential modelIlk et al. Augmented Stretched-exponential model

10

100

1000

10000

0 100 200 300 400 500 600

Time, months

R a

t e , S

T B / m o

ExponentialHyperbolicHarmonic


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Critique of Arps ModelRequires stabilized (not transient) flow for

validity

Transient flow likelyfor most, possibly all,life of well in ultra-low permeability reservoirs

Best-fit b values almost always >1 for recent gaswellsExtrapolation to economic limit with high b valueleads to unrealistically large reserves estimates

Reserves as rate 0 (time ) for b 1

)/1()1(1

bi

i t bDqq +

=

0

200

400

600

800

1000

1200

1400

1600

0 100 200 300 400 500 600

Time, months

C u m

P r o

d ,

M S T B

Exponential

HyperbolicHarmonic


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Arps: Keeping Reserves EstimatesReasonable

Common method: Use best-fit b untilpredetermined minimum decline rate reached;then impose exponential declineProblems

Any extrapolation with best-fit b unrealistic apparent best b decreases continually with time

Appropriate minimum decline rate based on

observed long-term behavior in appropriate analogy usually unavailable in resource playsLeaves too many degrees of freedom, inevitablyleads to subjective judgment


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Minimum Decline From Analogy?

qi 5000 STB/DayADR = 55%

qt 200 STB/DayADR = 15%

mADR = 10%

mADR = 7%mADR = 5%

Courtesy Ryder Scott Company


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Terminal b Improves Forecast

(Cheng et al., SPE 108176)

100

1,000

10,000

100,000

0 50 100 150 200 250 300

Time, months

G a s r a

t e ,

M S C F / m o

Actual datab=0.6, new method, error=-2.97%b=1, constraint b1, error=-47.18%b=2.65, best fit, error=36.50%


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Stretched-Exponential ( ) Decline ModelEmpirical model

Model parametersq i initial rate (e.g., mscf/month) taken as peak

rate, usually in second month of production characteristic time (e.g., months)n exponent (dimensionless)

AdvantagesConservative (finite EUR at zero rate, infinite time)Easily applied straight-line plot to estimate reserves(recovery potential plot)

=

n

i

t qq exp


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Example Recovery Potential Plot: All US Gas Wells Completed in2000-2004 Having At Least 5 Years Production History: 45,506Wells (n : 0.36 andq i : 3.34 tcf/mo)

5.0 1091.0 10101.5 10102.0 10102.5 10103.0 1010

0.5

0.6

0.7

0.8

0.9

1.0

Q

r p

Mean 40 yr EUR:1.14 bcf/well


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Defining differential equation of the model

Rate expression as function of time stretched exponential

Dimensionless rate expression (t Dand q D)

Dimensionless cumulativeproduction expression

Dimensionless EUR expression

Recovery potential calculatedfrom dimensionless rate

t qt n

dt dq

n

= -

=

nt

qt q -exp)( 0

( )n D D t q -exp=

( )= n D D t nnQ ,

11n

=n

EUR D1

n

=Dqn

n

rp ln,1

11

[ ]

inf

0

1

/

/

,

:

D D

t

D D D

i D

D

z

t a

Q EUR

dt qQ

qqq

t t

dt et z a

where

D

=

=

==

=

EURQ

rp

where

= 1


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SPE 109625Rushing-Blasingame Study: 42 Simulated Cases


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Base Case Stretched-Exponential Model(based on 5-yr production history)

Out[930]=

0 500 1000 15000

500

1000

1500

2000

days

Q ,

m m c

Stretched - exp model n:0.25, t :25.4 days qi:11.7 mmcf d

0 500 1000 1500

0.5

1.0

2.0

5.0

10.0

days

q ,

m m c f

d

Stretched- exp model n:0.25, t :25.4 days qi:11.7 mmcf d


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Base Case Arps Model(based on 5-yr production history) Just as good a fit

0 500 1000 15000

500

1000

1500

2000

days

Q ,

m m c

Arps model b:1.5, D:0.007 1 days qi:4.823 mmcf d

0 500 1000 1500

0.5

1.0

2.0

5.0

10.0

days

q ,

m m c f

d

Arps model b:1.5, D:0.007 1 days qi:4.823 mmcf d


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Comparison: 50 yr Forecasts Based on 5-Yr Prod History

0 10 20 30 40 500

1000

2000

3000

4000

5000

6000

yrs

Q , m

m c

Red: Arps b 1.5 , Blue: Stretched exp n 0.25

Conclusion:While the limited span of data can be describedequally well with the traditional and the new model,the extrapolation to 50 yrs yields different results(the new model being more conservative and nearerto the actual value known in this case.)


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Forecasting Ability of SE Model Much BetterYears of

HistoryMatched

Best Fit,

Arps b

Arps: Error

inRemainingReserves,

%

SE: Error in

RemainingReserves,

%

2 2.66 145 36.15 1.91 104 23.9

10 1.51 30.6 6.7325 1.20 7.9 0.2150 1.14 N/A N/A


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Statistics for 42 Rushing-Blasingame Cases

50 yr forecast based on production history available for various yearsStretched exponential model with fixed n = 0.25

Based on yr 2 5 10 20 50

Mean abs error %(Stand. abs err.%)

11.3(16.2) 6.0(7.4) 5.6(4.6) 3.1(2.1) 0(0.002)


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Field/Reservoir/Formation Group Analysis:

The Data-Driven Approach

Is it better to try to match individualwells accuratelyOr

Match groups of wells in given area andderive individual well performance

project from group-average parameters?


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Some Problems with Individual WellsChanges in technology during life of wellRestimulationReactions to changes in gas prices

Variations in field pressures Available slots

But, for statistically valid sampleChanges may average out over lives of individual wells


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Example: Member ofGroup (n =0.3)


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Evidence Indicates Data-Driven Approach

Preferable

Applied to gas wells completed in 2000-2004 and having at least 5 yearsproduction history examples:

Barnett ShaleCarthageHaynesville

All US


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Barnett Shale


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Carthage Field


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Haynesville


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SE Analysis of Groups

Group BarnettShale

Carthage Haynesville All US

wells in group 2,849 1,126 1,629 46,506Mean current

cumulative

0.63 bcf 0.63 bcf 1.15 bcf 0.79 bcf

Model-par n=0.16=0.019 mo

n=0.32=3.71 mo

n=0.36=2.6 mo

n=0.36=3.7 mo

Mean 40yrforecast

1.4 bcf 1.08 bcf 1.54 bcf 1.14 bcf


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ConclusionsForecasting in resource plays uncertain

Understanding of basic physicsincomplete

Ability to model hypothesized controlson production limited by incompletedata, difficulty in validating models due

to limited duration well historiesIdentifying and applying appropriateempirical models necessary


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Conclusions Arps empirical model inappropriate

Best fit b changes (decreases) continuouslywith timeFit of data at given time can be excellent,

at least as good as fit with SE modelHowever, best fit b values > 1 lead tounreasonably large reserves estimateswhen used for extrapolation


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ConclusionsStretched exponential model moreappropriate

Fits both transient, stabilized flow data withunchanged parameters ( n , )Reserves estimates bounded as rate 0Particularly appropriate for large groups of wells smoothes noise due to operationsdecisions, identifies characteristic formationparameters


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A Better Way to Forecast Production inUnconventional Gas Reservoirs

John LeeTexas A&M University

7 October 2010

presentation 100710

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