Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Decline-Curve Analysis for Gas Wells
At the end of this module, you will:●Be able to sketch the Arps exponential, hyperbolic, and harmonic decline relations.●Be able to state and derive the exponential rate decline relation (Eq. 9.2).●Be able to derive Eq. 9.10 (cumulative exponential) and explain its practical aspects.●Be able to state the form of the harmonic rate decline relation (Eq. 9.11). ●Be able to derive Eq. 9.16 (cumulative harmonic) and explain its practical aspects.●Be able to state the form of the hyperbolic rate decline relation (Eq. 9.1)●Be able to derive Eq. 9.21 (cumulative hyperbolic) and explain its practical aspects.●Be able to describe the concept of a "decline type curve".●Be able to sketch the Fetkovich "rate/time decline type curve" (i.e., Fig. 9.10).●Be able to explain the flow regimes seen on the Fetkovich decline type curve.●Be able to apply the dimensionless variables given by Eqs. 9.22-9.24.●Be able to state the procedure to apply the Fetkovich decline type curve.●Be able to demonstrate the solution of Example 9.2 (reproduce all details).●Be able to sketch the Carter "rate/time decline type curve" (i.e., Fig. 9.11).●Be able to explain the flow regimes seen on the Carter decline type curve.●Be able to state the procedure to apply the Carter decline type curve.●Be able to demonstrate the solution of Example 9.3 (reproduce all details).●Be able to explain the strengths/limitations of using "decline type curve" analysis.●Be familiar with "decline type curve" analysis without boundary-dominated flow.●Be familiar with "decline type curve" analysis for multi-well reservoirs.
From: Lee, W.J. and Wattenbarger, R.A.: Gas Reservoir Engineering, SPE (1996).
Slide — 1
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Decline-Curve Analysis for Gas WellsSummary of Arps Time-Rate and Time-Cumulative Relations
Exponential: (b=0)
Hyperbolic: (0<b<1)
Harmonic: (b=1)
Exponential: (b=0)
Hyperbolic: (0<b<1)
Harmonic: (b=1)
)exp( tDqq ii
bi
itbD
qq /1)(1
)(1 tDqqi
i
Time-Cumulative Production
)]exp([1 tDDqN ii
ip
])(1[1)(1
/11 bi
i
ip tbD
DbqN
)ln(1 tDDqN ii
ip
Time-Flowrate
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Slide — 2
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Arps Exponential Decline Relation
)exp( tDqq ii
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Flowrate
Constant"Decline"Parameter
InitialRate
Parameter
Time
Slide — 3
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Derivation of Arps Exponential Decline Relation
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.
oio
tpssoiii B
BNcb
DtDqq 11 exp,
poio
ti N
BB
Ncpp 1
s
r
ACekh
Bbqbpp
wAoo
pssoopssowf 2,,14ln
21 141.2
Derivation of the Exponential Rate Decline Relation
Slide — 4
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Derivation of Arps Exponential Decline Relation (SPE 98042)
From
:B
lasi
ngam
e, T
.A. a
nd R
ushi
ng, J
.A.:
"A P
rodu
ctio
n-B
ased
Met
hod
for D
irect
Est
imat
ion
of G
as-
in-P
lace
and
Res
erve
s,"
pape
r SPE
980
42 p
rese
nted
at t
he 2
005
SPE
East
ern
Reg
iona
l Mee
ting
held
in M
orga
ntow
n, W
.V.,
14–1
6 Se
ptem
ber 2
005.
Slide — 5
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Arps Hyperbolic Decline Relation
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Flowrate
Constant"Decline"Parameter
InitialRate
Parameter
Time
bi
itbD
qq /1)(1 Arps
"Hyperbolic"Parameter
Arps"Hyperbolic"
Parameter
Slide — 6
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
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 superimposed (Camacho and Raghavan (1989)).
(Details of derivation are omitted, see paper SPE 19009, Camacho and Raghavan (1989)).
Hyperbolic Decline — Orientation
Discussion: Arps' Hyperbolic Time-Rate Relation●Assumes decline parameter based on average mobility/compressibility.●Assumes hyperbolic parameter = f[d/dt(average mobility/compressibility)].
Slide — 7
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Derivation of Arps Hyperbolic Decline Relation (SPE 98042)
From
:B
lasi
ngam
e, T
.A. a
nd R
ushi
ng, J
.A.:
"A P
rodu
ctio
n-B
ased
Met
hod
for D
irect
Est
imat
ion
of G
as-
in-P
lace
and
Res
erve
s,"
pape
r SPE
980
42 p
rese
nted
at t
he 2
005
SPE
East
ern
Reg
iona
l Mee
ting
held
in M
orga
ntow
n, W
.V.,
14–1
6 Se
ptem
ber 2
005.
Slide — 8
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Derivation of Arps Hyperbolic Decline Relation (SPE 98042)
From
:B
lasi
ngam
e, T
.A. a
nd R
ushi
ng, J
.A.:
"A P
rodu
ctio
n-B
ased
Met
hod
for D
irect
Est
imat
ion
of G
as-
in-P
lace
and
Res
erve
s,"
pape
r SPE
980
42 p
rese
nted
at t
he 2
005
SPE
East
ern
Reg
iona
l Mee
ting
held
in M
orga
ntow
n, W
.V.,
14–1
6 Se
ptem
ber 2
005.
Slide — 9
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Arps Harmonic Decline Relation
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Constant"Decline"Parameter
InitialRate
Parameter
Time
)(1 tDq
qii
Flowrate
Slide — 10
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Decline-Curve Analysis for Gas WellsSummary of Arps Rate-Cumulative Relations
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Flowrate- Cumulative ProductionExponential: (b=0)
Hyperbolic: (0<b<1)
Harmonic: (b=1)
p
i
ii N
qDqq 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)
iibp
i DbqN
NN
qq)(1
1 )1(1 Plot of:
log(q/qi) versus log[1-(Np/N)]
Slide — 11
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Example 9.1 — Lee and Wattenbarger
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
1:1 Slope
1:3 Slope
Slide — 12
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Example 9.1 — Lee and Wattenbarger
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Exponential Trend
Slide — 13
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Example 9.1 — Lee and Wattenbarger
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Slide — 14
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Example 9.1 — Lee and Wattenbarger
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
1:1 Slope
Slide — 15
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Example 9.1 — Lee and Wattenbarger
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Harmonic Trend
Slide — 16
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Example 9.1 — Lee and Wattenbarger
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Exponential Trend
Slide — 17
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
(Production) Decline Type Curve Analysis
Slide — 18
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
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
Slide — 19
From
:Fe
tkov
ich,
M.J
. : "
Dec
line
Cur
ve A
naly
sis
Usi
ng T
ype
Cur
ves,
" JP
T(J
une
1980
) 106
5-77
.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
From: SPE 04629 — Fetkovich (1973).
From: SPE 04629 — Fetkovich (1973).
"Analytical" Rate Decline Curves: Data from van Everdingen and
Hurst (1949), re-plotted 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.
Van Everdingen-Hurst Type Curves — Radial Flow
Slide — 20
From
:Fe
tkov
ich,
M.J
. : "
Dec
line
Cur
ve A
naly
sis
Usi
ng T
ype
Cur
ves,
" JP
T(J
une
1980
) 106
5-77
.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
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 Transient Radial Flow Stems
Slide — 21
From
:Fe
tkov
ich,
M.J
. : "
Dec
line
Cur
ve A
naly
sis
Usi
ng T
ype
Cur
ves,
" JP
T(J
une
1980
) 106
5-77
.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Fetkovich "Composite" Decline Type Curve:●Assumes constant bottomhole pressure production.●Radial flow in a finite radial reservoir system (single well).
Fetkovich Decline Type Curve — Analytical and Empirical Stems
Slide — 22
From
:Fe
tkov
ich,
M.J
. : "
Dec
line
Cur
ve A
naly
sis
Usi
ng T
ype
Cur
ves,
" JP
T(J
une
1980
) 106
5-77
.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Fetkovich Example Match: SPE 04629 — (Fetkovich)●Lack of early time data is an omen of things to come.●Late time data follow an exponential trend (constant pwf).
Fetkovich Example Analysis — Decline Type Curve
Slide — 23
From
:Fe
tkov
ich,
M.J
. : "
Dec
line
Cur
ve A
naly
sis
Usi
ng T
ype
Cur
ves,
" JP
T(J
une
1980
) 106
5-77
.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
From: SPE 04629 — Fetkovich (1973).
From: SPE 04629 — Fetkovich (1973).
Discussion:●Assumptions:Constant bottomhole pressure. "Liquid" flow (not gas).
●"Empirical" Decline Type Curve: "Arps" empirical trends presented in
dimensionless "decline" format for "boundary-dominated flow behavior" (Fetkovich, 1973).
●"Analytical" Transient Type Curve:Collapses the transient flow trends
(dimensionless "decline" rates) into "stems" related to reservoir size and skin factor (Fetkovich, 1973).
●Comments (gas flow behavior): Fetkovich (and others) have noted
that most gas cases lie on or near the stems for 0.4<b<0.6.
No (direct) physical support for this "rule of thumb."
Fetkovich Decline Type Curves — General
Slide — 24
From
:Fe
tkov
ich,
M.J
. : "
Dec
line
Cur
ve A
naly
sis
Usi
ng T
ype
Cur
ves,
" JP
T(J
une
1980
) 106
5-77
.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Fetkovich "Composite" Decline Type Curve: b>1 Cases●b=1 is the constant rate case — no theory to support b>1 cases.●Rule: Transient flow — q concave UP, PSS flow — q concave DOWN.
Fetkovich Decline Type Curve — b>1
Slide — 25
From
:Fe
tkov
ich,
M.J
. : "
Dec
line
Cur
ve A
naly
sis
Usi
ng T
ype
Cur
ves,
" JP
T(J
une
1980
) 106
5-77
.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Type Curves for Gas Wells:Gas cases cannot be fully represented
using Arps' (hyperbolic) relations. However, the Arps' relations are often an acceptable approximation.
Constant pwf gas cases are dependent on the pwf/pi ratio (path-dependent non-linearity) — and cannot be extended to variable-rate, variable pressure drop.
Reconstruction of Fetkovich (SPE 04629 —1973) and Carter (SPE 12917 — 1985) type curves for the gas case (various pwf/pi).
(Zoom View) Reconstruction of Fetkovich (SPE 04629 — 1973) and Carter (SPE 12917 — 1985) type curves for the gas case (various pwf/pi).
Reconstruction of Fetkovich-Carter Type Curves
Slide — 26
From
:Fe
tkov
ich,
M.J
. : "
Dec
line
Cur
ve A
naly
sis
Usi
ng T
ype
Cur
ves,
" JP
T(J
une
1980
) 106
5-77
.C
arte
r, R
.D.:
"Typ
e C
urve
s fo
r Fin
ite R
adia
l and
Lin
ear G
as-F
low
Sys
tem
s: C
onst
ant-T
erm
inal
Pr
essu
re C
ase,
" SP
EI(O
ct. 1
985)
719
-28.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Fetkovich-Carter Decline Type Curve
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Slide — 27
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Example 9.1 — Lee and Wattenbarger
From
:Le
e, W
.J. a
nd W
atte
nbar
ger,
R.A
.: G
as R
eser
voir
Engi
neer
ing,
SPE
(199
6).
Slide — 28
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Modern Time-Rate Analysis
Slide — 29
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Work Path ― Analysis of Well Performance
Completions Production Reservoir Fluids Geomodel
Time-Rate
Time-Rate-
PressureReservoir
Model
Model: Time-RateBasis: Proxy model●Predictions●EUR●CorrelationsTime: Minutes/well
Model: Time-Rate-PressureBasis: Analytical/Numerical●Predictions●EUR/SRV●Estimate PropertiesTime: ~1 hour/well
Pres
sure
Time
Pres
sure
Time
Rat
es
Time
Rat
es
Time
Rat
es
Time
Model: Time-Rate-PressureBasis: Full Numerical●Predictions●EUR/SRV●Flow MechanismsTime: Days to weeks/well
Slide — 30
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Typical Flow Regimes in Unconventional Reservoir Systems
Required Model Parameters: ●Permeability (k)●Fracture half-length (xf)●Fracture conductivity (Fc)●Drainage area (A)●Skin factor (s)●Well length (Lw)●Number of fractures (nf)
Linear Flow:(fracture flow does not
interfere)
"SRV" Flow: ("depletion")(fracture flow does interfere)
"Post-SRV" Flow:("Compound Linear Flow")
Slide — 31
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
(Formation) Linear Flow — Theory
ktcBwfpipC
txfACq
hfxxfAt
xfAktcBwfpipq
DxftDp
1)( 128494.8
1 1
2 11)( 128494.8
1
Solution for a Single Fracture: (transient linear flow)
Additive Fractures: (transient linear flow)
+ + + → 1)(
1]...
[
tottot
,4,3,
2,1,tot
tACq
tAAA
AACq
xf
nxfxfxf
xfxf
Note:These solutions are only valid for transient linear flow [i.e., the case of non-interfering pressure distributions (due to the fractures)].
Slide — 32
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
(Formation) Linear Flow — Practice (Synthetic Example)
Formation Linear Flow●Log-log diagnostic plot: log[q(t)] versus log[t ] (slope = -1:2)●"qDb" (time-rate) plot: log[q(t)] log[D(t)] log[b(t)] versus log[t ]●"Traditional" plot: q(t) versus 1/SQRT[t ] (straight-line portion)●Extrapolation using a linear flow model will over-predict EUR…
Region ofover-
extrapolation…
Slide — 33
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Time-Rate Relations — Power Law Exponential Rate Model
Stretched Exponential: (SEM)— Observed Behavior of q(t):
— Differentiating to solve for D(t):
— Differentiating to solve for b(t):
Power-Law Exponential: (PLE)— Observed Behavior of D(t):
— Integrating to solve for q(t):
— Differentiating to solve for b(t):
ˆ)()(
1)( )1( nitDnD
dttdq
tqtD
] ˆ exp[ ˆ)( nii tDtDqtq
nn
i
i ttDDnnDntb
2)1( ] ˆ[
)1(ˆ)(
1)()(
1)( nntndttdq
tqtD
])/(exp[ ˆ)( ni tqtq
nntnntb
1)(
Discussion:●Models are the same when D∞ = 0.●The Power-Law Exponential model was derived from observations (Blasingame/Ilk).●The Stretched-Exponential model was taken from a statistics text (Valko).
Literature:●Kohlrausch (1854).●Phillips (1996).●Kisslinger (1993)●Decays in random, disordered,
chaotic, heterogeneous systems (e.g., relaxation, aftershock decay rates, etc.).
])/( exp[ˆ)( ni tqtq
Valkó (2009)
Jones (1942) and Arps (1945)
)1( 100
exp )(1
mtD
qtqm
oo
Slide — 34
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Time-Rate Relations — Power-Law Exponential Rate Relation
PLE Rate Relation:
Decline Function: D(t)
Hyperbolic Function: b(t)
nn
i
i ttDDn
nDn
tDdtdtb
2)1( ] ˆ[
)1(ˆ
)(1 )(
]ˆexp[ˆ)( nii tDtDqtq
)1(ˆ
1)(
nitDnD
dtdq
qtD
Ilk, D.: "Well Performance Analysis for Low to Ultra-Low Permeability Reservoir Systems," Ph.D. Dissertation, Texas A&M University, College Station, TX (Aug 2010).
Clean-up/ flowback effects
are not significant for
this case
Slide — 35
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U. Slide — 36
Introduction — Modern Time-Rate Relations
DCA Model Rate Relation
Power Law Exponential Model
Stretched Exponential Decline Model
Duong Model
Logistic Growth Model
Weibull Model
]ˆexp[ˆ)( nigi tDtDqtq
]]/[exp[ˆ)( ni tqtq
1at ,)1(1
exp)( 11
1
tqtmatqtq mm
ttMtq exp)(
1
2ˆ
1ˆ
)ˆ(
ˆˆ)(
n
n
ta
tnKatq
PLE: Derived by introducing terminal decline D∞ in D-parameter for matching BDF.SEDM: Linear superposition of simple exponential decays — analogous to PLE.Duong: Straight line behavior of q/Gp vs. Time (log-log) plot for linear/bilinear flow regime.LGM: Population growth models — modified form of hyperbolic logistic growth models.Weibull: Application of Weibull distribution for modeling time to failure.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Flow Regimes: (Barnett Shale Example)●Schematic illustrates flow regimes exhibited by time-rate-pressure data.●Duration/existence of flow regimes is DIFFERENT for each play.
EURLF (VERY OPTIMISTIC)
EURDep (CONSERVATIVE ???)
Pseudo-elliptical flow regime (flow from matrix to collection of fractures) might exist after fracture interference.
Slide — 37
Time-Rate Behavior — Flow Regimes for a Multi-Fracture Horizontal Well
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Calibration — Linear Flow (Gas Shales)Data taken from publicly available sources — Horizontal Shale (Dry) Gas Wells ONLY
Heckman, T.L., et al (2013): Best Practices for Reserves Estimation in Unconventional Reservoirs — Present and Future Considerations, Keynote presentation presented at the 2013 SPE Unconventional Resources Conference, The Woodlands, TX (USA), 10-12 April 2013.
Discussion:●START of "Linear Flow" (~3-6 months).●END of "Linear Flow" (~9-36 months).● "Linear Flow" is represented by b = 2.●EUR requires at least 20+ months (except Haynesville ~1 year; and Barnett ~3 years).
Slide — 38
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
Discussion:●START of "Linear Flow" (~3-6 months).●END of "Linear Flow" (~9-36 months).● "Linear Flow" is represented by linear trends on these plots.●Square root time plot used to show linear portion of trend (Gp(t) vs. SQRT(t) is most clear).
Data taken from publicly available sources — Horizontal Shale (Dry) Gas Wells ONLY
Heckman, T.L., et al (2013): Best Practices for Reserves Estimation in Unconventional Reservoirs — Present and Future Considerations, Keynote presentation presented at the 2013 SPE Unconventional Resources Conference, The Woodlands, TX (USA), 10-12 April 2013.
Calibration — Linear Flow (Gas Shales)
Slide — 39
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
Tom BLASINGAME | [email protected] | Texas A&M U.
(Sort of) "Big Data" Analysis ― Barnett Shale Example (Data prior to Mar 2013)
Slide — 40
Correlation of Gp,1Yr vs. Initial Gas Production (Barnett Shale horizontal gas wells).
Correlation of Gp,1Yr using Initial Gas Production and various completion parameters (Barnett Shale horizontal gas wells).
Histogram of Gp,1Yr (Barnett Shale horizontal gas wells).
Histogram of EUR30Yr (Barnett Shale horizontal gas wells).