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8/3/2019 Presentation 100710
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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