spe 59781 leo
TRANSCRIPT
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Determining OGIP and Aquifer Performance Determining OGIP and Aquifer Performance With No Prior Knowledge With No Prior Knowledge
of Aquifer Properties and Geometryof Aquifer Properties and Geometry
Leonardo VegaLeonardo VegaTexas A&M UniversityTexas A&M University
Masters’ DivisionMasters’ Division
SPE International Student Paper ContestSPE International Student Paper Contest
October 5, 1999October 5, 1999
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New ApproachNew Approach
OGIPOGIP Aquifer PerformanceAquifer Performance
No Prior Knowledge of Aquifer Properties or Geometry are RequiredNo Prior Knowledge of Aquifer Properties or Geometry are Required
Only Production Performance DataOnly Production Performance Data
© Leonardo Vega© Leonardo Vega
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Previous methods require a lot of information about the aquifer
Previous methods require a homogeneous aquifer
New method is very practical Other methods are very idealistic
Advantages of New MethodAdvantages of New Method
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Overview of PresentationOverview of Presentation
IntroductionIntroduction Previous MethodsPrevious Methods New ApproachNew Approach ResultsResults ConclusionsConclusions
© Leonardo Vega© Leonardo Vega
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Overview of PresentationOverview of Presentation
IntroductionIntroduction Previous MethodsPrevious Methods New ApproachNew Approach ResultsResults ConclusionsConclusions
© Leonardo Vega© Leonardo Vega
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Material BalanceMaterial Balance
G
G
Z
p
Z
pp
i
i
1
gi
erw GB
WC1
0
pi/zi
0 Gp=G
p/Z
Gp
Depletion
Water drive
Strong
Moderate
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Performance of Water-Drive Gas Performance of Water-Drive Gas Reservoirs Is Rate-DependentReservoirs Is Rate-Dependent
0
100
200
300
400
500
600
Ga
s R
ate
, M
Ms
cf/
Da
y
2,500
2,700
2,900
3,100
3,300
3,500
3,700
0 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000G
pGp, MMscf
p/z
© Leonardo Vega© Leonardo Vega
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p
2
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
0 200 400 600 800 1,000 1,200 1,400 1,600 1,800Gp, Bscf
p/z
psi
a
p/Z Plot of Water-Drive Gas p/Z Plot of Water-Drive Gas Reservoir May Look LinearReservoir May Look Linear
OGIP
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Overview of PresentationOverview of Presentation
IntroductionIntroduction Previous MethodsPrevious Methods New ApproachNew Approach ResultsResults ConclusionsConclusions
© Leonardo Vega© Leonardo Vega
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In 1949, van Everdingen-Hurst In 1949, van Everdingen-Hurst Presented Solution to Diffusivity Presented Solution to Diffusivity
EquationEquation
Aquifer
Gas Reservoir
• Aquifer HomogeneityAquifer Homogeneity
© Leonardo Vega© Leonardo Vega
• Elementary Reservoir-Aquifer GeometriesElementary Reservoir-Aquifer Geometries
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In 1964-65 Havlena-Odeh In 1964-65 Havlena-Odeh presented Technique for Aquifer presented Technique for Aquifer
FittingFitting
F/Eg
(Bscf)
WeBw/Eg (Bscf)
Aquifer too small
Aquifer too large
Correct Match
45o
G
© Leonardo Vega© Leonardo Vega
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Technique of Havlena-Odeh Technique of Havlena-Odeh Lacks UniquenessLacks Uniqueness
F/Eg
(Bscf)
WeBw/Eg (Bscf)
Aquifer Description 2Aquifer Description 2
Aquifer Description 1Aquifer Description 1
GG11
GG22
© Leonardo Vega© Leonardo Vega
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Definition ofDefinition ofAquifer Influence Functions (AIF)Aquifer Influence Functions (AIF)
tFtppwei 1
© Leonardo Vega© Leonardo Vega
Pressure drop due to a unit water Pressure drop due to a unit water influx rate at the original GWCinflux rate at the original GWC like type curveslike type curves unique to each aquiferunique to each aquifer
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AquiferAquifer
Gas Gas ReservoirReservoir
© Leonardo Vega© Leonardo Vega
In 1964, Coats In 1964, Coats et al.et al. Presented an Presented an Aquifer ModelAquifer Model
Systems of Arbitrary Geometry and Systems of Arbitrary Geometry and HeterogeneityHeterogeneity
They Proposed The Use AIF They Proposed The Use AIF
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Coats Coats etet al.al.’s Exact Solution’s Exact Solution
1
0 1i
tbi
ieatatF
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In 1988, Gajdica Proposed New In 1988, Gajdica Proposed New MethodMethod
Calculated OGIP and aquifer performance from production performance data
Used linear programming technique Used 32 field data sets to validate
results
© Leonardo Vega© Leonardo Vega
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Gajdica’s TechniqueGajdica’s Technique
obskk
n
k
calobs
OGIP
ppR
1R e l a t i v e E r r o r a s a
f u n c t i o n o f O G I P
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
1 . 2
1 . 4
1 . 6
0 1 0 0 2 0 0 3 0 0
O G I P , B s c f
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Gajdica’s Technique Had Gajdica’s Technique Had Problems Problems
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12
OGIP, Bscf
Rel
ativ
e E
rror
, psi
/Bsc
f
© Leonardo Vega© Leonardo Vega
GGp maxp max
GGoptopt
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Two Questions Arise About Two Questions Arise About Use of Gajdica’s TechniqueUse of Gajdica’s Technique
© Leonardo Vega© Leonardo Vega
Is the technique presented by Gajdica valid at all?
Is the anomaly due to errors in some of his field data?
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© Leonardo Vega© Leonardo Vega
Is Gajdica’s Technique Valid Is Gajdica’s Technique Valid At All?At All?
The Relative Error Function Lacks any Statistical Meaning
obskk
n
k
calobs
OGIP
ppR
1
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Overview of PresentationOverview of Presentation
IntroductionIntroduction Previous MethodsPrevious Methods New ApproachNew Approach ResultsResults ConclusionsConclusions
© Leonardo Vega© Leonardo Vega
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Absolute Error Function Has Absolute Error Function Has Sound Statistical MeaningSound Statistical Meaning
© Leonardo Vega© Leonardo Vega
obs
ii
n
i obs
obscalN n
ppA
1
obs
ii
n
i
obscal ppA1
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Methodology to Analyze Methodology to Analyze Performance Behavior Performance Behavior
© Leonardo Vega© Leonardo Vega
Analyze the behavior of the Normalized Absolute Error, AN, instead of the Relative Error
Use synthetic data to isolate the nature of the problem.
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Procedure To Determine OGIP and Procedure To Determine OGIP and AIF AIF
Assume several values of OGIP. Optimize the AN . For each assumed OGIP, report the
optimized AN, and corresponding AIF.
Plot the optimized AN versus the assumed OGIP.
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AIF Must Meet Certain AIF Must Meet Certain Smoothness ConstraintsSmoothness Constraints
Aquifer Influence Function
0.0000
6.0000
0 30
t
F(t
)
t
0we
© Leonardo Vega© Leonardo Vega
The AIF must be positive or zero The AIF must be positive or zero
0)( tF
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AIF Must Meet Certain AIF Must Meet Certain Smoothness ConstraintsSmoothness Constraints
Aquifer Influence Function
0.0000
6.0000
0 30
t
F(t
)
t
0we
© Leonardo Vega© Leonardo Vega
The AIF must increase or remain The AIF must increase or remain constant constant
0 tF
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AIF Must Meet Certain AIF Must Meet Certain Smoothness ConstraintsSmoothness Constraints
Aquifer Influence Function
0.0000
6.0000
0 30
t
F(t
)
t
0we
© Leonardo Vega© Leonardo Vega
The AIF must be concave The AIF must be concave downward or be a straight linedownward or be a straight line
0 tF
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Reservoir Data Assumed to Reservoir Data Assumed to Generate Synthetic PerformanceGenerate Synthetic Performance
Gas Reservoir Properties and Volume
G, Bscf 700Pi, psia 7,500
Sw, fraction 0.23cw, psi-1 5.00E-6cf, psi-1 6.00E-6t, days 365
g, fraction 0.65
T, oF 200
© Leonardo Vega© Leonardo Vega
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Volumetric Reservoir Flow Rate and Volumetric Reservoir Flow Rate and p/Z Performancep/Z Performance
p
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
0 20,000 40,000 60,000 80,000 100,000Gp , MMscf
0
10
20
30
40
50
60
70
80
90
100
© Leonardo Vega© Leonardo Vega
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AAN N DisplayedDisplayed Typical Behavior In Typical Behavior In
Volumetric Depletion ReservoirsVolumetric Depletion Reservoirs
0
50
100
150
200
250
300
350
0 200 400 600 800 1,000 1,200
0-A: Lower Region
A-B: Middle Region
Larger than B: Upper Region
B
A
© Leonardo Vega© Leonardo Vega
AANN,
psi
/po
int
, p
si/p
oin
t
OGIP, BscfOGIP, Bscf
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eew w CalculatedCalculated from Material from Material
Balance EquationBalance Equation
VolumetricVolumetric DepletionDepletion ReservoirReservoir
ew, rb/day, as a function of time for various assumed values ofthe OGIP, Bscf, in a volumetric depletion reservoir (actualOGIP=700 Bscf)Time,days
G=680Bscf
G=698Bscf
G=700Bscf
G=710Bscf
G=800Bscf
0 0 0 0 0 0
1 153 15 0 -76 -764
2 309 30 0 -155 -1,549
3 633 60 0 -322 -3,187
4 991 90 0 -511 -5,019
For G<Gactual
ew>0
For G>Gactual
ew<0
© Leonardo Vega© Leonardo Vega
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For G<GFor G<Gactualactual
(Volumetric Depletion Reservoir)(Volumetric Depletion Reservoir)
0)( tF
0)( tF
0)( tF
11
jn
n
jwni ttFeppj
0.0000E+00
1.0000E-02
2.0000E-02
3.0000E-02
4.0000E-02
5.0000E-02
6.0000E-02
7.0000E-02
0 50 100 150 200
Time, days
F(t
), p
si/(r
b/d
ay) G=600 Bscf
G=500 Bscf
G=400 Bscf
G=300 Bscf
G=200 Bscf G=100 Bscf
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Pressure Match When G<GPressure Match When G<Gactualactual
(Volumetric Depletion Reservoir)(Volumetric Depletion Reservoir)
6 , 5 0 0
6 , 6 0 0
6 , 7 0 0
6 , 8 0 0
6 , 9 0 0
7 , 0 0 0
7 , 1 0 0
7 , 2 0 0
7 , 3 0 0
7 , 4 0 0
7 , 5 0 0
7 , 6 0 0
0 5 0 0 1 , 0 0 0 1 , 5 0 0 2 , 0 0 0
T i m e , d a y s
Pre
ss
ure
, p
sia
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
Ga
s r
ate
, M
Ms
cf
© Leonardo Vega© Leonardo Vega
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AANN Behavior for G<G Behavior for G<Gactualactual
(Volumetric Depletion Reservoir)(Volumetric Depletion Reservoir)
0
50
100
150
200
250
300
350
0 200 400 600 800 1,000 1,200
AANN, p
si/p
oin
t, p
si/p
oin
t
OGIP, BscfOGIP, Bscf
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For G>GFor G>Gactualactual
(Volumetric Depletion Reservoir)(Volumetric Depletion Reservoir)
0)( tF
0)( tF
0)( tF
11
jn
n
jwni ttFeppj
AIF
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.010
0 100 200 300 400 500 600
Time, days
F(t
)
F(t)=0
pcal=0
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For G>GFor G>Gactualactual
(Volumetric Depletion Reservoir)(Volumetric Depletion Reservoir)
Since pcal=0
obsi
n
i obs
obsN n
pA
1
.constAN
0
50
100
150
200
250
300
350
02004006008001,0001,200
OGIP, BScf
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0
50
100
150
200
250
300
350
02004006008001,0001,200
OGIP, BScf
Middle RegionMiddle Region(Volumetric Depletion Reservoir)(Volumetric Depletion Reservoir)
© Leonardo Vega© Leonardo Vega
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 200 400 600 800
O G IP, BScf
Zoomed View of Lower RegionZoomed View of Lower Region(Volumetric Depletion Reservoir)(Volumetric Depletion Reservoir)
© Leonardo Vega© Leonardo Vega
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Water-Drive Gas Reservoir Water-Drive Gas Reservoir Aquifer Data AssumedAquifer Data Assumed
Properties and dimensions of linear aquifer
k, md 200Cross-sectional area, ft2 2,000,000
w,cp 1
, fraction 0.2xe, ft 20,000
© Leonardo Vega© Leonardo Vega
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0
10
20
30
40
50
60
200 400 600 800 1,000
Gp, MMscf
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
Gas RateObserved Pressure
Water Drive Gas ReservoirWater Drive Gas Reservoirqqgg=50 MMscf/D=50 MMscf/D
OGIP overestimated by 39%
© Leonardo Vega© Leonardo Vega
OGIPactual=700 Bscf
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Behavior of ABehavior of ANN Water Drive Gas Reservoir ( qWater Drive Gas Reservoir ( qgg=50 MMscf/D)=50 MMscf/D)
0
200
400
600
800
1 ,000
1 ,200
0 2 00 400 600 8 00 1,000 1, 200 1,40 0 1 ,600
OGIP, BScf
© Leonardo Vega© Leonardo Vega
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0 .0
0 .5
1 .0
1 .5
2 .0
2 .5
3 .0
3 .5
4 .0
4 .5
5 .0
0 20 0 400 6 00 8 00 1,00 0
O GIP , B S cf
Zoomed View of AZoomed View of ANN Water Drive Gas Reservoir ( qWater Drive Gas Reservoir ( qgg=50 MMscf/D)=50 MMscf/D)
© Leonardo Vega© Leonardo Vega
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0.0E+00
1.0E-02
2.0E-02
3.0E-02
4.0E-02
5.0E-02
6.0E-02
0 100 200 300 400 500 600Time, days
Obtained The Same AIF For All Obtained The Same AIF For All Production SchedulesProduction Schedules
© Leonardo Vega© Leonardo Vega
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Overview of PresentationOverview of Presentation
IntroductionIntroduction Previous MethodsPrevious Methods NewNew ApproachApproach ResultsResults ConclusionsConclusions
© Leonardo Vega© Leonardo Vega
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Performance Data of Field “A”Performance Data of Field “A”
© Leonardo Vega© Leonardo Vega
Rate and Pressure Behavior as a function of Gp
0
10
20
30
40
50
60
70
80
90
100
5 10 15 20 25 30 35Gpa, BScf5,200
5,300
5,400
5,500
5,600
5,700
5,800
5,900
6,000
6,100
Gas RateObserved p/Z
qqgg, M
Msc
f, M
Msc
f p/Z
, psia
p/Z
, psia
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p/Z Techniquep/Z Technique
0
10
20
30
40
50
60
70
80
90
100
50 100 150 200 250 300Gpa, BScf
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
Gas Rate
Observed
qqgg,
MM
scf/
d,
MM
scf/
d p/Z
, psia
p/Z
, psia
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OGIP Determined with New OGIP Determined with New ApproachApproach
© Leonardo Vega© Leonardo Vega
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 100 200 300
AANN,
psi
/po
i nt
, p
si/ p
oi n
t
OGIP, BscfOGIP, Bscf
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Overview of PresentationOverview of Presentation
IntroductionIntroduction Previous MethodsPrevious Methods NewNew ApproachApproach ResultsResults ConclusionsConclusions
© Leonardo Vega© Leonardo Vega
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ConclusionsConclusions
Unlike the Unlike the p/zp/z plot, the shape of the plot, the shape of the AANN
permits the recognition of the reservoir drive permits the recognition of the reservoir drive mechanism.mechanism.
The The AANN allows the determination of theallows the determination of the OGIPOGIP
in a water-drive reservoir.in a water-drive reservoir.
No prior knowledge or assumptions about No prior knowledge or assumptions about the aquifer properties and geometry are the aquifer properties and geometry are requiredrequired..
© Leonardo Vega© Leonardo Vega
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ConclusionsConclusions
The optimum The optimum OGIPOGIP is located where the is located where the middle and the lower regions coincide. middle and the lower regions coincide.
The drive mechanism and the optimum The drive mechanism and the optimum OGIPOGIP can be easily recognized, even when few can be easily recognized, even when few production-pressure data are available.production-pressure data are available.
© Leonardo Vega© Leonardo Vega
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ConclusionsConclusions
Even though the risk of a non-unique Even though the risk of a non-unique solution exists, its occurrence has been solution exists, its occurrence has been diminished.diminished.
Unlike the Havlena-Odeh method, when used Unlike the Havlena-Odeh method, when used along with the the van Everdingen Hurst exact along with the the van Everdingen Hurst exact solution, this method does not need a solution, this method does not need a continuous re-evaluation of the aquifer. continuous re-evaluation of the aquifer.
© Leonardo Vega© Leonardo Vega
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Determining OGIP and Aquifer Performance Determining OGIP and Aquifer Performance With No Prior Knowledge With No Prior Knowledge
of Aquifer Properties and Geometryof Aquifer Properties and Geometry
Leonardo VegaLeonardo VegaTexas A&M UniversityTexas A&M University
Masters’ DivisionMasters’ Division
SPE International Student Paper ContestSPE International Student Paper Contest
October 5, 1999October 5, 1999
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Volumetric Gas ReservoirsVolumetric Gas Reservoirs
No Water EncroachmentNo Water Encroachment
© Leonardo Vega© Leonardo Vega
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How to Generate Synthetic DataHow to Generate Synthetic Data
Assume aquifer geometry. Assume k, , , ct, A, and xe in aquifer.
Assume reservoir properties T, g, cf, cw, G and pi..
Calculate z, Bg, Bw, and Vp.
Assume qg(t) and calculate Gp.
Calculate pD(tD) from exact solution of Diffusivity Equation.
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Calculate p(t) using the Superposition Principle.
Use t, p(t) and DGp(t) as input to the AIF program (Reservoir Performance Data).
How to Generate Synthetic DataHow to Generate Synthetic Data
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0
2 0
4 0
6 0
8 0
1 0 0
1 2 0
2 0 0 4 0 0 6 0 0 8 0 0 1 , 0 0 0
G p, Bs c f
0
1 ,0 0 0
2 ,0 0 0
3 ,0 0 0
4 ,0 0 0
5 ,0 0 0
6 ,0 0 0
7 ,0 0 0
8 ,0 0 0
G a s R a t e
O b s e r ve d p re s su re s
Water Drive Gas Reservoir Water Drive Gas Reservoir qqgg=100 MMscf/D=100 MMscf/D
© Leonardo Vega© Leonardo Vega
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0
500
1,000
1,500
2,000
2,500
0 500 1,000 1,500
O G IP , BScf
AANN Behavior Behavior Water Drive Gas Reservoir ( qWater Drive Gas Reservoir ( qgg=100 MMscf/D)=100 MMscf/D)
© Leonardo Vega© Leonardo Vega
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0
20
40
60
80
100
120
140
160
200 400 600 800 1,000
Gp, Bscf
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
Gas Rate
Observed pressures
Water Drive Gas Reservoir Water Drive Gas Reservoir qqgg=150 MMscf/D=150 MMscf/D
© Leonardo Vega© Leonardo Vega
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0
5 0 0
1 , 0 0 0
1 , 5 0 0
2 , 0 0 0
2 , 5 0 0
3 , 0 0 0
3 , 5 0 0
0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0
O G I P , B S c f
AANN Behavior Behavior Water Drive Gas Reservoir (qWater Drive Gas Reservoir (qgg=150 MMscf/D)=150 MMscf/D)
© Leonardo Vega© Leonardo Vega
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Water Drive Gas ReservoirWater Drive Gas ReservoirVariable Production RateVariable Production Rate
p /z = -6 .7 6 5 7 G p + 6 2 5 8 .6
R2 = 0 .9 9 9 3
0
2 0
4 0
6 0
8 0
1 0 0
1 2 0
2 0 0 4 0 0 6 0 0 8 0 0 1 ,0 0 0
G p , B S c f
0
1 ,0 0 0
2 ,0 0 0
3 ,0 0 0
4 ,0 0 0
5 ,0 0 0
6 ,0 0 0
7 ,0 0 0
G a s R a te
O b s e rve dp re s su re
OGIP overestimated by 32%© Leonardo Vega© Leonardo Vega
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0
2 0 0
4 0 0
6 0 0
8 0 0
1 ,0 0 0
1 ,2 0 0
1 ,4 0 0
0 2 0 0 4 0 0 6 0 0 8 0 0 1 ,0 0 0
O G IP , B S c f
AN,
ps
i/p
oin
t
AANN Behavior Behavior
Water Drive Gas Reservoir (Variable Production Rate)Water Drive Gas Reservoir (Variable Production Rate)
© Leonardo Vega© Leonardo Vega
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0
2
4
6
8
10
12
14
16
18
20
0 200 400 600 800 1,000
OGIP, BScf
AANN Behavior (Zoomed View) Behavior (Zoomed View) Water Drive Gas Reservoir Water Drive Gas Reservoir (Variable Production Rate)(Variable Production Rate)
© Leonardo Vega© Leonardo Vega
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LimitationsLimitations
© Leonardo Vega© Leonardo Vega
y = -7.8066x + 6245.3
R2 = 1
0
200
400
600
800
1,000
1,200
1,400
2004006008001,000
Gpa, BScf
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000Gas Rate
Observed
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LimitationsLimitations
© Leonardo Vega© Leonardo Vega
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
600 650 700 750 800 850 900 950OG IP, BScf