CIPC 2008-109 - Petroleum Engineering - Texas A&M University
CIPC 2008-109 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls
*Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 +1.979.845.2292 — [email protected] CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 1/19
D. Ilk, Texas A&M U. J.A. Rushing, Anadarko Petroleum Corp. and T.A. Blasingame,* Texas A&M U.
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 2/19
Presentation Outline zRationale For This Work zNew Rate Equation: ■ Power Law form for Decline Constant ■ Power Law Exponential Rate Model zField Examples: ■ Case 1 — West Virginia Gas Well ■ Case 2 — East Texas (US) Gas Well zClosure: ■ Summary ■ Recommendations
Rationale For This Work ●Definitions:
■ Loss Ratio:
1 q ≡− D dq/dt ■ Derivative of Loss Ratio: d ⎡1⎤ d ⎡ q ⎤ b≡ ⎢ ⎥≡− ⎢ ⎥ dt ⎣ D ⎦ dt ⎣ dq/dt ⎦ ■ Hyperbolic Rate Relation: qi q= [1 + bDi t ](1 / b )
⎡ dq ⎤ ⎢or D ≡ − ⎥ dQ ⎦ ⎣
⎡ d ⎡ 1 ⎤⎤ ⎢or b ≡ q ⎥ ⎢ ⎥ dQ ⎣ D ⎦ ⎦ ⎣
■ Hyperbolic relation mis-applied to transient data. ■ What is the "characteristic behavior" of the D and b-parameters — evaluate continuously using data. CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 3/19
●Cause and Effect:
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 4/19
Rationale For This Work
New Rate Equation
n ˆ = qˆi exp[− Di t ] CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 5/19
●Observed Behavior of Decline Parameter: 1 dq −B D≡− ≈ At q dt ●Solving for Flowrate: A ( 1 − B ) q = qˆi exp[− t ] (1 − B)
(1/5)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 6/19
Example 1: SPE 13169 (W. Virginia Well A)
(2/5)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 7/19
Example 1: SPE 13169 (W. Virginia Well A)
(3/5)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 8/19
Example 1: SPE 13169 (W. Virginia Well A)
a. "Log-log Plot" — Specialized hyperbolic "rate-cumulative" type curve (qg/qgi vs. 1(Gp/G)).
(4/5)
b."Cartesian Plot" — Specialized hyperbolic "rate-cumulative" type curve (qg/qgi vs Gp/G).
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 9/19
Example 1: SPE 13169 (W. Virginia Well A)
(5/5)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 10/19
Example 1: SPE 13169 (W. Virginia Well A)
(1/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 11/19
Example 2: SPE 84287 (E. Texas Gas Well)
(2/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 12/19
Example 2: SPE 84287 (E. Texas Gas Well)
(3/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 13/19
Example 2: SPE 84287 (E. Texas Gas Well)
(4/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 14/19
Example 2: SPE 84287 (E. Texas Gas Well)
a. "Log-log Plot" — Specialized hyperbolic "rate-cumulative" type curve (qg/qgi vs. 1(Gp/G)).
(5/6)
b."Cartesian Plot" — Specialized hyperbolic "rate-cumulative" type curve (qg/qgi vs Gp/G).
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 15/19
Example 2: SPE 84287 (E. Texas Gas Well)
(6/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 16/19
Example 2: SPE 84287 (E. Texas Gas Well)
Summary:
●The hyperbolic D and b-parameters are can be
characterized using production data. The ratecumulative formulation should be somewhat better than the rate-time formulations (at least in our experience). ●The new rate relation is given as:
n ˆ ˆ q = qi exp[− Di t ]
●The hyperbolic D and b-parameters are given in terms of the new rate relation as:
1 (1 − n) −n t b≡ n Dˆ i
Note that the D and b-parameters are both given as power law functions — as would be expected.
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 17/19
n−1 ˆ D ≡ Di n t
Recommendations:
●The power law observation of the D-parameter (in
time) must be investigated further. This behavior appears to be universal. ●Plots of the D and b-parameters should be used as part of production data diagnostics. ●(suggestion) A "super-hyperbolic" could be constructed using the basis condition for the hyperbolic relation; i.e.,
⎡ q ⎤ d ⎢ ⎥ perhaps of the form c ≡ − [b] dt ⎣ dq/dt ⎦
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 18/19
d b≡− dt
CIPC 2008-109 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls
End of Presentation *Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 +1.979.845.2292 — [email protected] CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 19/19
D. Ilk, Texas A&M U. J.A. Rushing, Anadarko Petroleum Corp. and T.A. Blasingame,* Texas A&M U.
*Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 +1.979.845.2292 — [email protected] CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 1/19
D. Ilk, Texas A&M U. J.A. Rushing, Anadarko Petroleum Corp. and T.A. Blasingame,* Texas A&M U.
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 2/19
Presentation Outline zRationale For This Work zNew Rate Equation: ■ Power Law form for Decline Constant ■ Power Law Exponential Rate Model zField Examples: ■ Case 1 — West Virginia Gas Well ■ Case 2 — East Texas (US) Gas Well zClosure: ■ Summary ■ Recommendations
Rationale For This Work ●Definitions:
■ Loss Ratio:
1 q ≡− D dq/dt ■ Derivative of Loss Ratio: d ⎡1⎤ d ⎡ q ⎤ b≡ ⎢ ⎥≡− ⎢ ⎥ dt ⎣ D ⎦ dt ⎣ dq/dt ⎦ ■ Hyperbolic Rate Relation: qi q= [1 + bDi t ](1 / b )
⎡ dq ⎤ ⎢or D ≡ − ⎥ dQ ⎦ ⎣
⎡ d ⎡ 1 ⎤⎤ ⎢or b ≡ q ⎥ ⎢ ⎥ dQ ⎣ D ⎦ ⎦ ⎣
■ Hyperbolic relation mis-applied to transient data. ■ What is the "characteristic behavior" of the D and b-parameters — evaluate continuously using data. CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 3/19
●Cause and Effect:
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 4/19
Rationale For This Work
New Rate Equation
n ˆ = qˆi exp[− Di t ] CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 5/19
●Observed Behavior of Decline Parameter: 1 dq −B D≡− ≈ At q dt ●Solving for Flowrate: A ( 1 − B ) q = qˆi exp[− t ] (1 − B)
(1/5)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 6/19
Example 1: SPE 13169 (W. Virginia Well A)
(2/5)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 7/19
Example 1: SPE 13169 (W. Virginia Well A)
(3/5)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 8/19
Example 1: SPE 13169 (W. Virginia Well A)
a. "Log-log Plot" — Specialized hyperbolic "rate-cumulative" type curve (qg/qgi vs. 1(Gp/G)).
(4/5)
b."Cartesian Plot" — Specialized hyperbolic "rate-cumulative" type curve (qg/qgi vs Gp/G).
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 9/19
Example 1: SPE 13169 (W. Virginia Well A)
(5/5)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 10/19
Example 1: SPE 13169 (W. Virginia Well A)
(1/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 11/19
Example 2: SPE 84287 (E. Texas Gas Well)
(2/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 12/19
Example 2: SPE 84287 (E. Texas Gas Well)
(3/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 13/19
Example 2: SPE 84287 (E. Texas Gas Well)
(4/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 14/19
Example 2: SPE 84287 (E. Texas Gas Well)
a. "Log-log Plot" — Specialized hyperbolic "rate-cumulative" type curve (qg/qgi vs. 1(Gp/G)).
(5/6)
b."Cartesian Plot" — Specialized hyperbolic "rate-cumulative" type curve (qg/qgi vs Gp/G).
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 15/19
Example 2: SPE 84287 (E. Texas Gas Well)
(6/6)
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 16/19
Example 2: SPE 84287 (E. Texas Gas Well)
Summary:
●The hyperbolic D and b-parameters are can be
characterized using production data. The ratecumulative formulation should be somewhat better than the rate-time formulations (at least in our experience). ●The new rate relation is given as:
n ˆ ˆ q = qi exp[− Di t ]
●The hyperbolic D and b-parameters are given in terms of the new rate relation as:
1 (1 − n) −n t b≡ n Dˆ i
Note that the D and b-parameters are both given as power law functions — as would be expected.
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 17/19
n−1 ˆ D ≡ Di n t
Recommendations:
●The power law observation of the D-parameter (in
time) must be investigated further. This behavior appears to be universal. ●Plots of the D and b-parameters should be used as part of production data diagnostics. ●(suggestion) A "super-hyperbolic" could be constructed using the basis condition for the hyperbolic relation; i.e.,
⎡ q ⎤ d ⎢ ⎥ perhaps of the form c ≡ − [b] dt ⎣ dq/dt ⎦
CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 18/19
d b≡− dt
CIPC 2008-109 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls
End of Presentation *Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 +1.979.845.2292 — [email protected] CIPC/SPE Gas Technology Symposium 2008 Joint Conference — Calgary, AB (Canada) — 17–19 June 2008 Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls (Ilk/Rushing/Blasingame) T.A. Blasingame — Texas A&M University (19 June 2008)
Slide — 19/19
D. Ilk, Texas A&M U. J.A. Rushing, Anadarko Petroleum Corp. and T.A. Blasingame,* Texas A&M U.
