Semi-Analytical Rate Relations for Oil and Gas Flow PETE 613 (2005A) Slide — 1 T.A. Blasingame,...

PETE 613(2005A)

Slide — 1Semi-Analytical Rate Relationsfor Oil and Gas Flow

T.A. Blasingame, Texas A&M U.Department of Petroleum Engineering

Texas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.2292 — [email protected]

Petroleum Engineering 613Natural Gas Engineering

Texas A&M University

Lecture 06:Semi-Analytical Rate Relations

for Oil and Gas Flow

PETE 613(2005A)


Rate Relations for Oil and Gas FlowHistorical Perspectives

"Backpressure" equation. Arps relations (exponential, hyperbolic, and harmonic).Derivation of Arps' exponential decline relation.Validation of Arps' hyperbolic decline relation.

Specialized Gas Flow Relations:Fetkovich Gas Flow Relation.Ansah-Buba-Knowles Gas Flow Relations.

Specialized Oil Flow Relations:Fetkovich Oil Flow Relation.

Inflow Performance Relations (IPR):Early work (for rationale).Oil IPR and Solution-Gas Drive IPR.Gas Condensate IPR.

PETE 613(2005A)


Gas Well Deliverability:The original well deliverability

relation was completely empiri-cal (derived from observations), and is given as:

This relationship is rigorous for low pressure gas reservoirs, (n=1 for laminar flow).

From: Back-Pressure Data on Natural-Gas Wells and Their Application to Production Practices — Rawlins and Schellhardt (USBM Monograph, 1935).

History: Deliverability/"Backpressure" Equation

nwfppCgq )( 22

PETE 613(2005A)


Diffusivity Equations for a "Dry Gas:" p2 Relations p2 Form — Full Formulation:

p2 Form — Approximation:

)()()][ln()( 2222

22 ptk

cpz

pp tg

g

)()( 222 ptk

cp tg

History: p2 Diffusivity Equations

PETE 613(2005A)


"Dry Gas" PVT Properties: (gz vs. p) Basis for the "pressure-squared" approximation (i.e., use of p2 variable). Concept: (gz) = constant, valid only for p<2000 psia.

History: Gas p2 Condition (gz vs. p, T=200 Deg F)

PETE 613(2005A)


"Dry Gas" PVT Properties: (gz vs. p) Concept: IF (gz) = constant, THEN p2-variable valid. (gz) constant for p<2000 psia. Even with numerical solutions, p2 formulation would not be appropriate.

dpzpp

pp

zp

gbasep

gpg

n

History: Gas p2 Condition (gz vs. p, T=200 Deg F)

PETE 613(2005A)


Arps' (Empirical) Rate Relations:Exponential decline case (conservative). Harmonic decline case (liberal).Hyperbolic decline case (everything in between).

Fetkovich (Radial Flow) Decline Type Curve:Exponential, hyperbolic, harmonic decline cases.

Derivation of the Arps' Exponential Rate Relation:Combination of liquid material balance and liquid pseudo-

steady-state flow equation solved for pwf constant.Useful for deriving auxiliary relations (cumulative production

functions, in particular).Derivation of the Arps' Hyperbolic Rate Relation:

Interesting exercise, limited practical value.

History: "Arps" Equations

PETE 613(2005A)


Flowrate-Time Relations: )exp( tDqq ii

bi

i

tbD

qq

/1)(1

)(1 tD

qq

i

i

Exponential: (b=0)

Hyperbolic: (0<b<1)

Harmonic: (b=1)

Cumulative Production-Time Relations:

)]exp([1 tDD

qN i

i

ip

])(1[1)(1

/11 bi

i

ip tbD

Db

qN

)ln(1 tDD

qN i

i

ip

Exponential: (b=0)

Hyperbolic: (0<b<1)

Harmonic: (b=1)

Arps Relations: Summary (1/2)

PETE 613(2005A)


Flowrate-Cumulative Production Relations:

Exponential: (b=0)

Hyperbolic: (0<b<1)

Harmonic: (b=1)

)()1(1

pbi

ib NNq

Dbq

p

i

ii N

q

Dqq exp

pNiDiqq

b

i

bi

p qDb

qNN

1

)1()(or

Plot of: q versus Np

Plot of: log(q) versus Np

Plot of: log(N-Np) versus log(q)

Arps Relations: Summary (2/2)

PETE 613(2005A)


Sewell Ranch Well No. 1 — Barnett Field (NorthTexas)

1.E+04

1.E+05

1.E+06

1.E+07

1.E+01 1.E+02 1.E+03 1.E+04

Gas Production Rate, MSCFD(G

-Gp

), M

SC

F

(G-Gp) Data Function

Exponential Model

Hyperbolic Model

Method is designed for hyperbolic decline case

a. Semilog "Rate-Time" Plot: Barnett Gas Field.

b. Cartesian "Rate-Cumulative" Plot: Barnett Gas Field (North Texas).

c. Log-Log "(G-Gp)-Rate" Plot: Barnett Gas Field (North Texas).

a.

b.

c.

pNiDiqq

b

i

bi

p qDb

qNN

1

)1()(

)exp( tDqq ii

bi

i

tbD

qq

/1)(1

bp

b

i

bi NNDb

qq

1

11

1

)()1(

(Exponential)

(Exponential)

(Hyperbolic)

(Hyperbolic)

(Hyperbolic)

Arps Relations: Example 1 (1/2)


0

200

400

600

800

1000

1200

1400

0 250,000 500,000 750,000 1,000,000 1,250,000 1,500,000

Cumulative Gas Production, MSCF

Gas

Pro

du

ctio

n R

ate,

MS

CF

D Cumulative Gas Production

Exponential Model

Hyperbolic Model


1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0 500 1000 1500 2000 2500 3000 3500 4000

Producing Time, days

Gas

Pro

du

ctio

n R

ate,

MS

CF

D

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Flo

win

g T

ub

ing

Pre

ssu

re,

psi

g

Gas FlowrateExponential Rate ModelHyperbolic Rate ModelWellbore Pressure

PETE 613(2005A)


)exp( tDqq ii bi

i

tbD

qq

/1)(1(Exponential) (Hyperbolic)


1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0 500 1000 1500 2000 2500 3000 3500 4000


Gas

Pro

du

ctio

n R

ate,

MS

CF

D

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Flo

win

g T

ub

ing

Pre

ssu

re,

psi

g



EUR Analysis: Barnett Field (North Texas (USA)) Semilog "Rate-Time" Plot: Barnett Gas Field. Note data scatter and apparent fit of hyperbolic function.

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a. Semilog "Rate-Time" Plot: SPE 84287 — East Texas Gas Well 1.

b. Cartesian "Rate-Cumulative" Plot: SPE 84287 — East Texas Gas Well 1.

c. Log-Log "(G-Gp)-Rate" Plot: SPE 84287 — East Texas Gas Well 1.

a.

b.

c.

pNiDiqq

b

i

bi

p qDb

qNN

1

)1()(

)exp( tDqq ii

bi

i

tbD

qq

/1)(1

bp

b

i

bi NNDb

qq

1

11

1

)()1(

(Exponential)

(Exponential)

(Hyperbolic)

(Hyperbolic)

(Hyperbolic)

Arps Relations: Example 2 (1/2)SPE 84287 — East TX Gas Well 1 (Low Permeability Gas)

1.E+02

1.E+03

1.E+04

1.E+05

0 50 100 150 200 250 300 350


Gas

Pro

du

ctio

n R

ate,

MS

CF

D

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

3000

Flo

win

g T

ub

ing

Pre

ssu

re,

psi

g


SPE 84287 — East TX Gas Well 1 (Low Permeability Gas)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 250,000 500,000 750,000 1,000,000 1,250,000 1,500,000

Cumulative Gas Production, MSCF

Gas

Pro

du

ctio

n R

ate,

MS

CF

D

Cumulative Gas Production

Exponential Model

Hyperbolic Model


1.E+04

1.E+05

1.E+06

1.E+07

1.E+01 1.E+02 1.E+03 1.E+04

Gas Production Rate, MSCFD(G

-Gp

), M

SC

F

(G-Gp) Data Function

Exponential Model

Hyperbolic Model

Method is designed for hyperbolic decline case

PETE 613(2005A)


)exp( tDqq ii bi

i

tbD

qq

/1)(1(Exponential) (Hyperbolic)


EUR Analysis: SPE 84278 Well 1 (East Texas (USA)) Combination "Rate-Time" and "Pressure-Time" plot. Note pressure buildup (used to check with PTA).


1.E+02

1.E+03

1.E+04

1.E+05

0 50 100 150 200 250 300 350


Gas

Pro

du

ctio

n R

ate,

MS

CF

D

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

Flo

win

g T

ub

ing

Pre

ssu

re,

psi

g


PETE 613(2005A)


Fetkovich "Empirical" Decline Type Curve: Log-log "type curve" for the Arps "decline curves" (Fetkovich, 1973). Initially designed as a graphical solution of the Arps' relations.

Fetkovich Decline Type Curve: Empirical

PETE 613(2005A)


From: SPE 04629 — Fetkovich (1973).

From: SPE 04629 — Fetkovich (1973).

"Analytical" Rate Decline Curves: Data from van Everdingen and

Hurst (1949), replotted as a rate decline plot (Fetkovich, 1973).

This looks promising — but this is going to be one really big "type curve."

What can we do? Try to collapse all of the trends to a single trend during boundary-dominated flow (Fetkovich, 1973).

"Analytical" stems are another name for transient flow behavior, which can yield estimates of reservoir flow properties.

Analytical Type Curves: Radial Flow

PETE 613(2005A)


Fetkovich "Analytical" Decline Type Curve: (constant pwf) Log-log "type curve" for transient flow behavior (Fetkovich, 1973). First "tie" between pressure transient and production data analysis.

Fetkovich Decline Type Curve: Analytical

PETE 613(2005A)


Fetkovich "Composite" Decline Type Curve: Assumes constant bottomhole pressure production. Radial flow in a finite radial reservoir system (single well).

Fetkovich Decline Type Curve: Composite

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Oil Material Balance Relation:

Oil Pseudosteady-State Flow Relation:

Steps:1. Differentiate both relations with respect to time.2. Assume pwf = constant (eliminates d(pwf)/dt term).3. Equate results, yields 1st order ordinary differential equation.4. Integrate.5. Exponentiate result.

oi

o

tpssoiii B

B

NcbDtDqq

11 exp

,

poi

o

ti N

B

B

Ncpp

1

s

r

ACekh

Bb

wA

oopsso 2,

14ln

21

141.2

opssowf qbpp ,

Derivation: Arps' Exponential Decline Case

PETE 613(2005A)


Validation: Arps' Hyperbolic Decline Case

a. Hyperbolic flowrate relations for the case of constant pressure production from a solution gas drive reservoir (Camacho and Raghavan (1989)).

b. Hyperbolic decline type curve with data simulation performance data superimpos-ed (Camacho and Raghavan (1989)).

(Details of derivation are omitted, see paper SPE 19009, Camacho and Raghavan (1989)).

PETE 613(2005A)


Specialized Gas Flow Relations

Fetkovich Gas Flow Relation (poor approximation):Rate-time.Characteristic behavior plot.

Results from Knowles-Ansah-Buba work:Rate-time.Rate-cumulative.

PETE 613(2005A)


Gas Material Balance Relation: (z=1 ! (ideal gas?))

Gas Pseudosteady-State Flow Relation: (Fetkovich)

Final Result: (Fetkovich)

1)( ipi

i zzGG

ppp

Fetkovich Gas Flow Relation: Poor Approximation

nwfppgCgq )( 22

0)(

122

)12(1

1

wfp

nn

tGgiq

n

giqgq

PETE 613(2005A)


Fetkovich "Analytical" Gas Decline Type Curve: (pwf = 0) Cheated (z=1) ... this is not a valid solution (Fetkovich, 1973). Good intentions ... wanted to develop a "simple" gas solution.

Fetkovich Decline Type Curve: Gas

PETE 613(2005A)


Knowles — Gas Rate-Time Relation

1

)exp(1

11

)exp(1

11

)1(

2

2

2

DdwDwD

wD

DdwDwD

wD

wD

wD

gi

ggDd

tpp

p

tpp

p

p

p

q

qq

t

Gzp

zp

qt

ii

wfwf

giDd

/

/1

22

ii

wfwfwD zp

zpp

/

/

"Knowles" rate-time relation for gas flow:Models decline of gas flowrate versus time.Better representation of rate-time behavior than the "Arps"

hyperbolic decline relations.

Assumptions:Volumetric, dry gas reservoir.pi < 6000 psia.Constant bottomhole flowing pressure.

PETE 613(2005A)


"Knowles" relations for gas flow:qg — Gp follows quadratic "rate-cumulative" relation.Approximation valid for pi<6000 psia.Assumes pwf = constant.

This work presents an analysis and interpretation se-quence for the estimation of reserves in a volumetric dry-gas reservoir. This is based on the "Knowles" rate-cumulative production relation for pseudosteady-state gas flow given as:

2

222

/

/1

/

/1

2 p

ii

wfwf

gip

ii

wfwf

gigig G

Gzp

zp

qG

Gzp

zp

qqq

Knowles-Buba — Gas Rate-Cumulative Relation

PETE 613(2005A)


Simplified Gas Flow: Validation of Knowles Eqs.

a. Simulated Performance Case: qg versus t (pi= 5000 psia, pwf=1000 psia, Gquad=4.20 BSCF).

qg vs. t and Gp vs. t: Base plots ― verify models by

Ansah, et. al Comparative trends of 0.9qgi , qgi

and 1.1qgi . Comparison applied to all analysis plots.

Very good match on both plots, accuracy verifies model.

b. Simulated Performance Case: Gp versus t (pi= 5000 psia, pwf=1000 psia, Gquad=4.20 BSCF).

PETE 613(2005A)


Simplified Gas Flow: Validation of Buba Eq.

"Knowles-Buba" relations for gas flow:Simulated performance case: qg-Gp (quadratic "rate-cumulative").pi= 5000 psia, pwf=1000 psia, Gquad=4.20 BSCF.Data function matches well with quadratic model function.

2

2

1p

ipigig G

G

DGDqq

Gzp

zp

qD

ii

wfwf

gii

2

/

/1

2

PETE 613(2005A)


Specialized Oil Flow Relations

Fetkovich Oil Flow Relation:Rate-time (Decline Type Curve Analysis).Deliverability (Isochronal Testing of Oil Wells).

PETE 613(2005A)


Oil Material Balance Relation: (p2 – formulation!)

Oil Pseudosteady-State Flow Relation: (Fetkovich)

Final Result: (Fetkovich)

pi

i NN

ppp

222 )(

)()(

Fetkovich Oil Flow Relation: (Approximation)

nwfpp

ipp

oiJoq )( 22

0)( 12

21

1

1

wfpn

tNoiqoiq

oq

PETE 613(2005A)


Fetkovich "Analytical" Oil Decline Type Curve: (pwf = 0) Cheated (pressure-squared material balance relation?) ... this is not a

valid solution (Fetkovich, 1973).

Fetkovich Decline Type Curve: Solution Gas Drive

PETE 613(2005A)


Oil "Backpressure" Relation: Fetkovich (1/2)

a. Deliverability ("backpressure") plot developed for Well 2/4-2X prior to matrix acidizing treatment. (Fetkovich [SPE 004529 (1973)]).

b. Deliverability ("backpressure") plot developed for Well 2/4-2X after matrix acidizing treatment. Note much higher flowrate performance and apparent non-linear (i.e., non-laminar) flow behavior (Fetkovich [SPE 004529 (1973)]).

PETE 613(2005A)


Oil "Backpressure" Relation: Fetkovich (2/2)

a. Comparison of simulated and predicted IPR behaviors for solution-gas-drive case (Vogel [SPE 001476 (1968)]).

b. Deliverability ("backpressure") plot developed using Vogel data. Proof of concept for "backpressure" flow relation (Fetkovich [SPE 004529 (1973)]).

PETE 613(2005A)


Inflow Performance Relations (IPR)

Early work (for rationale)Oil IPR and Solution-Gas Drive IPR

Vogel IPR work (for familiarity with approach)Other IPR work (for reference/orientation)

Gas Condensate IPR Fevang and Whitson work (for reference)

PETE 613(2005A)


History Lessons — Early Performance Relations

Early “Gas Deliverability Plot," note the straight-line trends for the data (circa 1935).

Early “Gas IPR Plot," note the quadratic relationship between wellhead pressure and flowrate (circa 1935).

Well deliverability analysis: (after Rawlins and Schellhardt) These plots represent the earliest attempts to quantify behavior and to

predict future performance.

PETE 613(2005A)


Gas Well Deliverability:The original well deliverability

relation was derived from observations:

The "inflow performance relation-ship" (or IPR) for this case is: (assuming n=1)

From: Back-Pressure Data on Natural-Gas Wells and Their Application to Production Practices — Rawlins and Schellhardt (USBM Monograph, 1935).

History Lessons — "Backpressure" Equation

)( 22wfppCgq

nwfppCgq )( 22

0)( )( 2 wfppCmax,gq

2

1

pwfp

max,gqgq

PETE 613(2005A)


History Lessons — IPR Developments/Correlations

Early "Inflow Plot," an attempt to correlate well rate and pres-sure behavior — and to esta-blish the maximum flowrate, (after Gilbert (1954)).

Inflow Performance Relationship (IPR): Correlate performance, estimate maximum flowrate. Individual phases require, separate correlations.

IPR "comparison" — liquid (oil), gas, and "two-phase" (solution gas-drive) cases presented to illustrate comparative behavior (after Vogel (1968)).

1

p

pqq wfmaxo,o

2 1

p

pqq wfmaxg,g

2 0.8 0.2 1

p

p

p

pqq wfwfmaxo,o

PETE 613(2005A)


Solution-Gas Drive Systems — Vogel IPR

IPR behavior is dependent on the depletion stage (i.e., the level of reservoir depletion). No single correlation of IPR behavior is possible.

Vogel IPR Correlation: Solution Gas-Drive Behavior Derived as a statistical correlation from simulation cases. No "theoretical" basis — Intuitive correlation (qo,max and pavg).

The Vogel IPR correlation and its variations are well establish-ed as the primary performance prediction relations for produc-tion engineering applications. The original correlation is de-rived from reservoir simulation.

2 0.8 0.2 1

p

p

p

pqq wfwfmaxo,o

Vogel Correlation: (Statistical)

PETE 613(2005A)


Solution-Gas Drive Systems — Other Approaches

Other IPR Correlations: Fetkovich: Derived assuming linear mobility-pressure relationship. Richardson, et al.: Empirical, generalized correlation.

2 ) (1 1

p

pν

p

pνq

q wfx

wfxmaxx,

x

Fetkovich IPR: (Semi-Empirical)n

maxo,o

pwfp

qq

2

1

Richardson, et al. IPR: (Empirical)

(x = phase (e.g., oil, gas, water))

PETE 613(2005A)


Solution-Gas Drive Systems— Other Approaches

Other IPR Correlations:Wiggins, et al.: Used a polynomial expansion of the mobility function in

order to yield a semi-rigorous IPR formulation.Coefficients (a1, a2…) are determined based on the mobility function

and its derivatives taken at the average reservoir pressure.

Wiggins, et al. IPR: (Semi-Rigorous)

... 13

3

2

21

p

pa

p

pa

p

paq

q wfwfwfmaxo,o

PETE 613(2005A)


Solution-Gas Drive Systems— Other Approaches

Other IPR Correlations: strong function of pressure and saturation. Semi-rigorous IPR formulation (derived for the solution-gas case) has

the same form of the Richardson, et al. IPR (which is empirical).

dpoBoμokp

basepnpokoBoμppop )(

Pseudopressure Formulation – Oil Phase

pbapfpoBoμ

ok 2)(

Mobility Function

2 ) (1 1

p

pν

p

pνq

q wfo

wfomaxo,

o

PETE 613(2005A)


Gas Condensate Systems — Pseudopressure

dpoBoμoksR

oBoμokp

wfpsw/rerkgq

3/4)ln( h

141.21

Three flow regions were characterized:

Region 1 — Main cause of productivity loss, oil and gas flow simultaneously.

Region 2 — Two phases coexist, but only gas is mobile.

Region 3 — single-phase gas.

Fevang and Whitson Correlation: Gas Condensate systems Pressure and saturation functions need to be know in advance —

GOR, PVT properties and relative permeabilities.

PETE 613(2005A)


Model-Based Performance Study:Radial, fully compositional, single well simulation modelParameters/functions used in simulation:

Reservoir Temperature: T = 230, 260, 300 Deg F Critical Oil Saturation: Soc = 0, 0.1, 0.3 Residual Gas Saturation: Sgr = 0, 0.15, 0.5 Relative Permeability: 7 sets of kro-krg data Fluid Samples: 4 synthetic cases, 2 field samples

Assumptions used in simulation: Interfacial tension effects are neglected Non-Darcy flow effects are neglected Capillary pressure effects are neglected Refined simulation grid in the near-well region Skin effect is neglected Gravity and composition gradients are neglected

Simulations begun at the dew point pressureCorrelation of gas and gas-condensate performance using Richardson

IPR model.

Gas Condensate IPR — Del Castillo 2003 (TAMU)

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Gas Condensate — IPR Trends (Condensate)

Condensate IPR Correlations (gas condensate reservoirs) All eight depletion stages regressed simultaneously. Excellent correlation — all stages.

Base IPR plot (condensate) — Case 16 (gas condensate sys-tem).

Dimensionless IPR plot (condensate) — Case 16 (gas condensate system)

IPR Curves - Condensate Production(Case16)

0

1000

2000

3000

4000

5000

6000

0 200 400 600 800

q o , STB/D

pw

f, p

sia

Np/N = 0.18%Np/N = 0.36%Np/N = 1.79%Np/N = 3.58%Np/N = 5.37%Np/N = 7.15%Np/N = 8.94%Np/N = 10.73%

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Legend

Normalized Oil Flowrate(Case16)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

p wf /p bar

qo/q

o,m

ax

Np/N = 0.18%Np/N = 0.36%Np/N = 1.79%Np/N = 3.58%Np/N = 5.37%Np/N = 7.15%Np/N = 8.94%Np/N = 10.73%IPR Model

Legend

PETE 613(2005A)


Gas IPR Correlations (gas condensate reservoirs) All eight depletion stages regressed simultaneously. Excellent correlation — even when there is a more pronounced curve

overlap (gas).

Base IPR plot (gas) — Case 16 (gas condensate system).

Dimensionless IPR plot (gas) — Case 16 (gas condensate system).

IPR Curves - Gas Production(Case16)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000

q g , MSCF/D

pw

f, p

sia

Gp/G = 0.09%Gp/G = 0.47%Gp/G = 0.95%Gp/G = 4.75%Gp/G = 9.5%Gp/G = 23.74%Gp/G = 47.48%Gp/G = 66.48%

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Legend

Normalized Gas Flowrate(Case16)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

p wf /p bar

qg/q

g,m

ax

Gp/G = 0.09%Gp/G = 0.47%Gp/G = 0.95%Gp/G = 4.75%Gp/G = 9.5%Gp/G = 23.74%Gp/G = 47.48%Gp/G = 66.48%IPR Model

Legend

Gas Condensate — IPR Trends (Gas)

PETE 613(2005A)



0

1000

2000

3000

4000

5000

6000

0 200 400 600 800

q o , STB/D

pw

f, p

sia


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Legend


0

1000

2000

3000

4000

5000

6000

0 100 200 300 400

q o , STB/D

pw

f, p

sia


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Legend

Condensate IPR Shape (gas condensate reservoirs) Remarkable difference in shape between a very rich gas condensate

system and a lean one.

Base IPR plot (condensate) — Case 16 (Very rich gas condensate system).

Base IPR plot (condensate) — Case 1 (Lean gas condensate system).

Gas Condensate — Difference in IPR Trends

PETE 613(2005A)


Condensate or gas IPR parameter (gas condensate reservoirs) Low o or g values — IPR more concave. Exact value of not crucial — similar curves for different o or g values.

Legend

Dimensional IPR curves

0

1000

2000

3000

4000

5000

6000

0 500 1000 1500 2000

Oil or Gas flowrate

pw

f, p

sia

= 0.15 = 0.18 = 0.29 = 0.49 = 0.55 = 0.68

Dimensionless IPR curves

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

p wf /p bar

qo

,g/q

o,g

,max

= 0.15 = 0.18 = 0.29 = 0.49 = 0.55 = 0.68

Legend

Dimensional IPR curves

0

1000

2000

3000

4000

5000

6000

0 500 1000 1500 2000

Oil or Gas flowrate

pw

f, p

sia

= 0.15 = 0.18 = 0.29 = 0.49 = 0.55 = 0.68

Legend

Dimensionless IPR curves

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

p wf /p bar

qo

,g/q

o,g

,max

= 0.15 = 0.18 = 0.29 = 0.49 = 0.55 = 0.68

o,go,go,go,go,go,g

o,go,go,go,go,go,g

Base IPR plot.Dimensionless IPR plot.

Gas Condensate — IPR Parameter (o or g )

2 ) (1 1

p

pν

p

pνq

q wfx

wfxmaxx,

x (x = phase (e.g., oil, gas, water))

PETE 613(2005A)


T.A. Blasingame, Texas A&M U.Department of Petroleum Engineering

Texas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.2292 — [email protected]

Petroleum Engineering 613Natural Gas Engineering

Texas A&M University

Lecture 06:Semi-Analytical Rate Relations

for Oil and Gas Flow(End of Lecture)

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Semi-Analytical Rate Relations for Oil and Gas Flow PETE 613 (2005A) Slide — 1 T.A. Blasingame,...

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