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Transcript of 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)
Slide — 2Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 3Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 4Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 5Semi-Analytical Rate Relationsfor Oil and Gas Flow
"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)
Slide — 6Semi-Analytical Rate Relationsfor Oil and Gas Flow
"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)
Slide — 7Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 8Semi-Analytical Rate Relationsfor Oil and Gas Flow
Flowrate-Time Relations: )exp( tDqq ii
bi
i
tbD
/1)(1
)(1 tD
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)
Slide — 9Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 10Semi-Analytical Rate Relationsfor Oil and Gas Flow
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
/1)(1
bp
b
i
bi NNDb
1
11
1
)()1(
(Exponential)
(Exponential)
(Hyperbolic)
(Hyperbolic)
(Hyperbolic)
Arps Relations: Example 1 (1/2)
Sewell Ranch Well No. 1 — Barnett Field (NorthTexas)
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
Sewell Ranch Well No. 1 — Barnett Field (NorthTexas)
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)
Slide — 11Semi-Analytical Rate Relationsfor Oil and Gas Flow
)exp( tDqq ii bi
i
tbD
/1)(1(Exponential) (Hyperbolic)
Sewell Ranch Well No. 1 — Barnett Field (NorthTexas)
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
Arps Relations: Example 1 (2/2)
EUR Analysis: Barnett Field (North Texas (USA)) Semilog "Rate-Time" Plot: Barnett Gas Field. Note data scatter and apparent fit of hyperbolic function.
PETE 613(2005A)
Slide — 12Semi-Analytical Rate Relationsfor Oil and Gas Flow
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
/1)(1
bp
b
i
bi NNDb
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
Producing Time, days
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
Gas FlowrateExponential Rate ModelHyperbolic Rate ModelWellbore Pressure
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
SPE 84287 — East TX Gas Well 1 (Low Permeability Gas)
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)
Slide — 13Semi-Analytical Rate Relationsfor Oil and Gas Flow
)exp( tDqq ii bi
i
tbD
/1)(1(Exponential) (Hyperbolic)
Arps Relations: Example 2 (2/2)
EUR Analysis: SPE 84278 Well 1 (East Texas (USA)) Combination "Rate-Time" and "Pressure-Time" plot. Note pressure buildup (used to check with PTA).
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
Producing Time, days
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
Gas FlowrateExponential Rate ModelHyperbolic Rate ModelWellbore Pressure
PETE 613(2005A)
Slide — 14Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 15Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 16Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 17Semi-Analytical Rate Relationsfor Oil and Gas Flow
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
PETE 613(2005A)
Slide — 18Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 19Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 20Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 21Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 22Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 23Semi-Analytical Rate Relationsfor Oil and Gas Flow
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
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)
Slide — 24Semi-Analytical Rate Relationsfor Oil and Gas Flow
"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)
Slide — 25Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 26Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 27Semi-Analytical Rate Relationsfor Oil and Gas Flow
Specialized Oil Flow Relations
Fetkovich Oil Flow Relation:Rate-time (Decline Type Curve Analysis).Deliverability (Isochronal Testing of Oil Wells).
PETE 613(2005A)
Slide — 28Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 29Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 30Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 31Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 32Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 33Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 34Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 35Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 36Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 37Semi-Analytical Rate Relationsfor Oil and Gas Flow
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
2
1
Richardson, et al. IPR: (Empirical)
(x = phase (e.g., oil, gas, water))
PETE 613(2005A)
Slide — 38Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 39Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 40Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 41Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
PETE 613(2005A)
Slide — 42Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 43Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 44Semi-Analytical Rate Relationsfor Oil and Gas Flow
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
IPR Curves - Condensate Production(Case1)
0
1000
2000
3000
4000
5000
6000
0 100 200 300 400
q o , STB/D
pw
f, p
sia
Np/N = 0.43%Np/N = 0.86%Np/N = 4.29%Np/N = 8.59%Np/N = 12.88%Np/N = 17.17%Np/N = 21.46%Np/N = 25.76%
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)
Slide — 45Semi-Analytical Rate Relationsfor Oil and Gas Flow
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)
Slide — 46Semi-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(End of Lecture)