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
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Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — 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
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
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Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
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
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Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
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
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Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
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
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Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
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
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.
Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
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
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Petroleum Engineering 613 — Natural Gas Engineering Lecture 8 — Decline-Curve Analysis for Gas Wells
(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
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
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
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
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
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