Spe 59781 leo

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

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

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

Overview of PresentationOverview of Presentation

IntroductionIntroduction Previous MethodsPrevious Methods New ApproachNew Approach ResultsResults ConclusionsConclusions


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

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


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

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


• Elementary Reservoir-Aquifer GeometriesElementary Reservoir-Aquifer Geometries

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


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


Definition ofDefinition ofAquifer Influence Functions (AIF)Aquifer Influence Functions (AIF)

tFtppwei 1


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

AquiferAquifer

Gas Gas ReservoirReservoir


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

Coats Coats etet al.al.’s Exact Solution’s Exact Solution

1

0 1i

tbi

ieatatF


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


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

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


GGp maxp max

GGoptopt

Two Questions Arise About Two Questions Arise About Use of Gajdica’s TechniqueUse of Gajdica’s Technique


Is the technique presented by Gajdica valid at all?

Is the anomaly due to errors in some of his field data?


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

Absolute Error Function Has Absolute Error Function Has Sound Statistical MeaningSound Statistical Meaning


obs

ii

n

i obs

obscalN n

ppA

1

obs

ii

n

i

obscal ppA1

Methodology to Analyze Methodology to Analyze Performance Behavior Performance Behavior


Analyze the behavior of the Normalized Absolute Error, AN, instead of the Relative Error

Use synthetic data to isolate the nature of the problem.

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.

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


The AIF must be positive or zero The AIF must be positive or zero

0)( tF



0.0000

6.0000

0 30

t

F(t

)

t

0we


The AIF must increase or remain The AIF must increase or remain constant constant

0 tF



0.0000

6.0000

0 30

t

F(t

)

t

0we


The AIF must be concave The AIF must be concave downward or be a straight linedownward or be a straight line

0 tF

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


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


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


AANN,

psi

/po

int

, p

si/p

oin

t

OGIP, BscfOGIP, Bscf

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


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

Pressure Match When G<GPressure Match When G<Gactualactual


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


AANN Behavior for G<G Behavior for G<Gactualactual


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


For G>GFor G>Gactualactual


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

For G>GFor G>Gactualactual


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

0

50

100

150

200

250

300

350

02004006008001,0001,200

OGIP, BScf

Middle RegionMiddle Region(Volumetric Depletion Reservoir)(Volumetric Depletion Reservoir)


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)


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


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%


OGIPactual=700 Bscf

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


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)


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



IntroductionIntroduction Previous MethodsPrevious Methods NewNew ApproachApproach ResultsResults ConclusionsConclusions


Performance Data of Field “A”Performance Data of Field “A”


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

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

OGIP Determined with New OGIP Determined with New ApproachApproach


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



IntroductionIntroduction Previous MethodsPrevious Methods NewNew ApproachApproach ResultsResults ConclusionsConclusions


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..



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.



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.


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

Volumetric Gas ReservoirsVolumetric Gas Reservoirs

No Water EncroachmentNo Water Encroachment


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.

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

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


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)


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


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)


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

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)


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)


LimitationsLimitations


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

LimitationsLimitations


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

Spe 59781 leo

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