Lithology-controlled stress variations: A case study of ...
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Scope of Work Lithology-controlled stress variations: A case study of hydraulic fracturing in the Woodford Shale, Oklahoma Xiaodong Ma 1 (6085564958; [email protected]) and Mark D. Zoback 1 (6504683871; [email protected]), 1 Department of Geophysics, Stanford University, Stanford, CA 94305 Geomechanical Setup What causes the in situ stress magnitude to vary so much along the horizontal wells, even within the same WDFD forma:on ?? Δσ = S V − S h min uniform lateral strain boundary facies 3 S hmin,1 S hmin,2 S hmin,3 S v Stress relaxaSon factor Logging data along the central vertical well for the WDFD formation. According to the signature of clay (and kerogen) content, the WDFD formation can be coarsely divided into three lithofacies (WDFD -1, 2, 3). This constitutes the vertical heterogeneity of the EDFD shale. Ma, X. and Zoback, M. (2017), Lithologycontrolled stress variaSons and padscale faults: a case study of hydraulic fracturing in the Woodford shale, Oklahoma, Geophysics 82(6): 110, doi:10.1190/GEO20170044.1 Ma, X. and Zoback, M. (in review), Lithologycontrolled stress variaSons in the Woodford Shale, Oklahoma: modeling and their effect on hydraulic fracturing. submi\ed to Journal of Petroleum Science and Engineering. References From creep funcSon to relaxaSon funcSon (via Laplace transformaSon) 1 B ≈ E Reciprocal of Creep compliance, 1/B Young’s Modulus, E N Mississippi Limestone Woodford Shale play, Oklahoma MSSP (Well A, C) and WDFD (Well B, D) Sone and Zoback (2014, IJRMMS) Framework of Viscoplastic Deformation and Stress Relaxation Empirical relaSonship between E and n The inherent lithological heterogeneity inside shale reservoir induces variaSons in the in situ stress states and mechanical properSes along the well lengths. The knowledge of the in situ stress requires the integraSon of various informaSon, such as geophysical logs, geology and well trajectory, and rock rheology. We believe the applicaSon of viscoplasSc stress relaxaSon can potenSally contribute to the predicSon of S hmin along the horizontals to intelligently place hydraulic fractures and esSmate hydraulic fracture verScal propagaSons. Concluding Remarks A geomechanical case study was conducted to investigate the stress variations along two sub-parallel horizontal wells in the Woodford shale (WDFD) in central Oklahoma. The minimum horizontal stress (S hmin ), indicated by the Instantaneous Shut-In Pressure (ISIP) of each frac stage, was found to vary dramatically along both wells and appears to significantly affect the success of hydraulic fracturing (HF). The variations of compliant components (clay and kerogen) along the length of two horizontal wells were due to small variations in the trajectories of the horizontals wells and the penetration of three thin, but compositionally distinct WDFD lithofacies. We found S hmin systematically varied with the abundance of clay and kerogen, and we attributed the contrast of S hmin between lithofacies to the varying degrees of viscoplastic stress relaxation characteristic of each lithofacies over geologic time. The modeling shows the difference between S V and S hmin diminishes as the compliant component content increases, and the modeled variations of S hmin along both horizontal wells were in reasonable agreement with the ISIP measurements. We believe the application of viscoplastic stress relaxation can facilitate understanding of the stress variations with lithology and potentially contribute to the prediction of S hmin along the horizontals to improve HF effectiveness. We utilize a viscoplastic model complemented with laboratory empirical relationships to quantify the relaxation of stress difference (S V – S hmin ), assuming a reasonable lateral deformation produced by constant strain rate over geologic time. Sone and Zoback (2014, JPSE) creep compliance = ε creep Δσ Barne\ Haynesville Eagle Ford Creep compliance σ 1 σ 2 = σ 3 Laboratory creep experiments (constant differenKal stress, Kme dependent axial deformaKon) Empirical rela:onship between longterm creep parameter and the transient, elas:c parameter Et () = 1 B ⋅ t − n σ t () = ! ε ⋅ 1 B ⋅ t − n 0 ∫ dt = ! ε ⋅ 1 B ⋅ 1 − n ( ) ⋅ t 1 − n = ε 0 ⋅ E ⋅ t − n 1 − n Jt () = B ⋅ t n Accumulated stress difference over relaxa:on under constant strain rate
Transcript of Lithology-controlled stress variations: A case study of ...
Scope of Work
Lithology-controlled stress variations: A case study of hydraulic fracturing in the Woodford Shale, Oklahoma Xiaodong Ma1 (608-‐556-‐4958; [email protected]) and Mark D. Zoback1 (650-‐468-‐3871; [email protected]), 1Department of Geophysics, Stanford University, Stanford, CA 94305
Geomechanical Setup
What causes the in situ stress magnitude to vary so much along the horizontal wells, even within the same WDFD forma:on ??
Δσ = SV − Shmin
uniform lateral strain
boundary
facies 3
Shmin,1
Shmin,2
Shmin,3
Sv
Stress re
laxaSo
n factor
Logging data along the central vertical well for the WDFD formation. According to the signature of clay (and kerogen) content, the WDFD formation can be coarsely divided into three lithofacies (WDFD -1, 2, 3). This constitutes the vertical heterogeneity of the EDFD shale.
Ma, X. and Zoback, M. (2017), Lithology-‐controlled stress variaSons and pad-‐scale faults: a case study of hydraulic fracturing in the Woodford shale, Oklahoma, Geophysics 82(6): 1-‐10, doi:10.1190/GEO2017-‐0044.1 Ma, X. and Zoback, M. (in review), Lithology-‐controlled stress variaSons in the Woodford Shale, Oklahoma: modeling and their effect on hydraulic fracturing. submi\ed to Journal of Petroleum Science and Engineering.
References
From creep funcSon to relaxaSon funcSon (via Laplace transformaSon)
!!1B≈ E
Reciprocal of Creep compliance, 1/B
Youn
g’s M
odulus, E
N
³
³
³
³ ³³ ³³
³
³ ³
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³
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KANSAS
Norman
OklahomaCity
Enid
Stillwater
PoncaCity
98° W
97° W
37° N
36° N
50 km
SHmax Orientation Method: ³ Borehole Image Logs³ Shear-wave Anisotropy³ World Stress Map Quality:³ A ³ B ³ C
Earthquakes since 2009 (Mw):2.50 - 2.802.81 - 3.303.31 - 3.803.81 - 5.60
OKLAHOMA
Mississippi Limestone -‐ Woodford Shale play, Oklahoma MSSP (Well A, C) and WDFD (Well B, D)
Sone and Zoback (2014, IJRMMS)
Framework of Viscoplastic Deformation and Stress Relaxation
Empirical relaSonship between E and n
The inherent lithological heterogeneity inside shale reservoir induces variaSons in the in situ stress states and mechanical properSes along the well lengths. The knowledge of the in situ stress requires the integraSon of various informaSon, such as geophysical logs, geology and well trajectory, and rock rheology. We believe the applicaSon of viscoplasSc stress relaxaSon can potenSally contribute to the predicSon of Shmin along the horizontals to intelligently place hydraulic fractures and esSmate hydraulic fracture verScal propagaSons.
Concluding Remarks
A geomechanical case study was conducted to investigate the stress variations along two sub-parallel horizontal wells in the Woodford shale (WDFD) in central Oklahoma. The minimum horizontal stress (Shmin), indicated by the Instantaneous Shut-In Pressure (ISIP) of each frac stage, was found to vary dramatically along both wells and appears to significantly affect the success of hydraulic fracturing (HF). The variations of compliant components (clay and kerogen) along the length of two horizontal wells were due to small variations in the trajectories of the horizontals wells and the penetration of three thin, but compositionally distinct WDFD lithofacies. We found Shmin systematically varied with the abundance of clay and kerogen, and we attributed the contrast of Shmin between lithofacies to the varying degrees of viscoplastic stress relaxation characteristic of each lithofacies over geologic time.
The modeling shows the difference between SV and Shmin diminishes as the compliant component content increases, and the modeled variations of Shmin along both horizontal wells were in reasonable agreement with the ISIP measurements. We believe the application of viscoplastic stress relaxation can facilitate understanding of the stress variations with lithology and potentially contribute to the prediction of Shmin along the horizontals to improve HF effectiveness.
We utilize a viscoplastic model complemented with laboratory empirical relationships to quantify the relaxation of stress difference (SV – Shmin), assuming a reasonable lateral deformation produced by constant strain rate over geologic time.
Sone and Zoback (2014, JPSE)
!!creep!compliance!=
εcreepΔσ
Barne\ Haynesville Eagle Ford
Creep compliance
σ1
σ2 = σ3 Laboratory creep experiments
(constant differenKal stress, Kme-‐dependent axial deformaKon)
Empirical rela:onship
between long-‐term creep parameter and the transient, elas:c parameter
!!E t( ) = 1B ⋅t −n
σ t( ) = !ε ⋅ 1B⋅ t−n
0∫ dt = !ε ⋅ 1
B ⋅ 1− n( ) ⋅ t1−n
= ε0 ⋅E ⋅ t−n
1− n
!J t( ) = B ⋅t n
Accumulated stress difference over relaxa:on under constant strain rate
