Abstract
Thermal stresses may be induced in a hot dry rock when a cold fluid is injected in the well. To study this problem, we look at the thermoelastic response of a hot rock that is suddenly cooled. The cooling is assumed to be either at a constant temperature or at a constant heat flux per unit depth. Our approach is to nondimensionalize the equations and perform a parametric study and look at the temperature distribution and the induced-thermal stresses. The results indicate that depending on the extent of cooling and the cooling time, thermal stresses can be induced. Numerical simulations on sandstone, with an initial uniform temperature of 473 K, are also carried out. The results show that if the cooling is due to the surface temperature maintained at 463 K (10 °C lower than the initial temperature of the hot rock), thermal stresses that are larger than the rock tensile strength could be induced. When the cooling is due to a constant surface heat flux, this temperature can be reached after about 777 days of cooling with a minimum value of a heat flux of −20 W/m.
Issue Section:
Jets, Wakes, and Impingement Cooling
References
1.
Vilarrasa
,
V.
, and
Laloui
,
L.
, 2016
, “
Impacts of Thermally Induced Stresses on Fracture Stability During Geological Storage of CO2
,” Eighth Trondheim Conference on CO2 Capture, Transport and Storage
,
R.
Aarlien
,
N. A.
Rokke
, and
H. F.
Svendsen
, eds., Vol.
86
, Trodheim, Norway, pp. 411
–419
.2.
Murphy
,
H. D.
, 1978
, “
Thermal Stress Cracking and the Enhancement of Heat Extraction From Fractured Geothermal Reservoirs
,” Proceedings of Geothermal Resources Council Meeting
, Hilo, HI, p. 19
.https://www.osti.gov/servlets/purl/67717243.
Finnie
,
I.
,
Cooper
,
G. A.
, and
Berlie
,
J.
, 1979
, “
Fracture Propagation in Rock by Transient Cooling
,” Int. J. Rock Mech. Min. Sci.
,
16
(1
), pp. 11
–21
.10.1016/0148-9062(79)90771-X4.
Irfan
,
M. A.
, and
Chapman
,
W.
, 2009
, “
Thermal Stresses in Radiant Tubes Due to Axial, Circumferential and Radial Temperature Distributions
,” Appl. Therm. Eng.
,
29
(10
), pp. 1913
–1920
.10.1016/j.applthermaleng.2008.08.0215.
Tarasovs
,
S.
, and
Ghassemi
,
A.
, 2011
, “
Propagation of a System of Cracks Under Thermal Stress
,” Proceedings of the 45th Rock Mechanics/Geomechanics Symposium
, San Francisco, CA, June 26–29.https://www.onepetro.org/conference-paper/ARMA-11-5586.
Tarasovs
,
S.
, and
Ghassemi
,
A.
, 2012
, “
On the Role of Thermal Stress in Reservoir Stimulation
,” Proceedings of 37th Workshop on Geothermal Reservoir Engineering
, Stanford, CA, Jan. 30–Feb. 1, p. 6
.https://www.researchgate.net/publication/267846418_On_the_role_of_thermal_stress_in_reservoir_stimulation7.
Ghassemi
,
A.
,
Tarasovs
,
A.
, and
Cheng
,
A. D.-H.
, 2005
, “
Integral Equation Solution of Heat Extraction Induced Thermal Stress in Enhanced Geothermal Reservoirs
,” Int. J. Numer. Anal. Methods Geomech.
,
29
(8
), pp. 829
–844
.10.1002/nag.4408.
Tao
,
Q.
, and
Ghassemi
,
A.
, 2010
, “
Poro-Thermoelastic Borehole Stress Analysis for Determination of the In Situ Stress and Rock Strength
,” Geothermics
,
39
(3
), pp. 250
–259
.10.1016/j.geothermics.2010.06.0049.
Tarasovs
,
S.
, and
Ghassemi
,
A.
, 2014
, “
Self-Similarity and Scaling of Thermal Shock Fractures
,” Phys. Rev. E
,
90
(1
), p. 012403
.10.1103/PhysRevE.90.01240310.
Ghassemi
,
A.
, and
Zhang
,
Q.
, 2004
, “
A Transient Fictitious Stress Boundary Element Method for Porothermoelastic Media
,” Eng. Anal. Boundary Elem.
,
28
(11
), pp. 1363
–1373
.10.1016/j.enganabound.2004.05.00311.
Enayatpour
,
S.
, and
Patzek
,
T.
, 2013
, “
Thermal Shock in Reservoir Rock Enhances the Hydraulic Fracturing of Gas Shales
,” Proceedings of the Unconventional Resources Technology Conference
, Denver, Colorado, Aug. 12–14, Paper No. URTEC-1620617-MS.10.1190/urtec2013-15312.
Kim
,
K.
,
Kemeny
,
J.
, and
Nickerson
,
M.
, 2014
, “
Effect of Rapid Thermal Cooling on Mechanical Rock Properties
,” Rock Mech. Rock Eng.
,
47
(6
), pp. 2005
–2019
.10.1007/s00603-013-0523-313.
Browning
,
J.
,
Meredith
,
P.
, and
Gudmundsson
,
A.
, 2016
, “
Cooling-Dominated Cracking in Thermally Stressed Volcanic Rocks
,” Geophys. Res. Lett.
,
43
(16
), pp. 8417
–8425
.10.1002/2016GL07053214.
Roy
,
P.
,
Morris
,
J. P.
,
Walsh
,
S. D. C.
,
Iyer
,
J.
, and
Carroll
,
S.
, 2018
, “
Effect of Thermal Stress on Wellbore Integrity During CO2 Injection
,” Int. J. Greenhouse Gas Control
,
77
, pp. 14
–26
.10.1016/j.ijggc.2018.07.01215.
Xu
,
H.
,
Peng
,
N.
,
Ma
,
T.
, and
Yang
,
B.
, 2018
, “
Investigation of Thermal Stress of Cement Sheath for Geothermal Wells During Fracturing
,” Energies
,
11
(10
), p. 2581
.10.3390/en1110258116.
Zhang
,
S. K.
,
Huang
,
Z. W.
,
Li
,
G. S.
,
Wu
,
X. G.
,
Peng
,
C.
, and
Zhang
,
W. P.
, 2018
, “
Numerical Analysis of Transient Conjugate Heat Transfer and Thermal Stress Distribution in Geothermal Drilling With High-Pressure Liquid Nitrogen Jet
,” Appl. Therm. Eng.
,
129
, pp. 1348
–1357
.10.1016/j.applthermaleng.2017.10.04217.
Wu
,
B. S.
,
Liu
,
T. L.
,
Zhang
,
X.
,
Wu
,
B. L.
,
Jeffrey
,
R. G.
, and
Bunger
,
A. P.
, 2018
, “
A Transient Analytical Model for Predicting Wellbore/Reservoir Temperature and Stresses During Drilling With Fluid Circulation
,” Energies
,
11
(1
), p. 42
.10.3390/en1101004218.
Ngo
,
D. T.
, and
Pellet
,
F. L.
, 2018
, “
Numerical Modeling of Thermally-Induced Fractures in a Large Rock Salt Mass
,” J. Rock Mech. Geotech. Eng.
,
10
(5
), pp. 844
–855
.10.1016/j.jrmge.2018.04.00819.
Zhang
,
S. K.
,
Huang
,
Z. W.
,
Zhang
,
H. Y.
,
Guo
,
Z. Q.
,
Wu
,
X. G.
,
Wang
,
T. Y.
,
Zhang
,
C. C.
, and
Xiong
,
C.
, 2018
, “
Experimental Study of Thermal-Crack Characteristics on Hot Dry Rock Impacted by Liquid Nitrogen Jet
,” Geothermics
,
76
, pp. 253
–260
.10.1016/j.geothermics.2018.08.00220.
Phuoc
,
T. X.
,
Massoudi
,
M.
,
Wang
,
P.
, and
McKoy
,
M. L.
, 2019
, “
Heat Losses Associated With the Upward Flow of Air, Water, CO2 in Geothermal Production Wells
,” Int. J. Heat Mass Transfer
,
132
, pp. 249
–258
.10.1016/j.ijheatmasstransfer.2018.11.16821.
Fung
,
Y. C.
, and
Tong
,
P.
, 2001
, Classical and Computational Solid Mechanics
,
World Scientific Publishing
, Hackensack, NJ
.22.
Boley
,
B. A.
, and
Weiner
,
J. H.
, 1997
, Theory of Thermal Stresses
,
Dover Publications
, New York
.23.
Parkus
,
H.
, 2012
, Thermoelasticity
,
Springer Science & Business Media
, New York
.24.
Suhubi
,
E. S.
, 1975
, “
Thermoelastic Solids
,” Continuum Physics
,
A. C.
Eringen
, ed., Vol.
2
,
Academic Press
, New York
, pp. 173
–281
.25.
Carlson
,
D. E.
, 1972
, “
Linear Thermoealsticity
,” Encyclopedia of Physics
,
Springer-Verlag
, New York
, Vol. VIa/2
, pp. 297
–345
.26.
Schon
,
J. H.
, 1996
, Physical Properties of Rocks
,
Elsevier Science Inc
.,
New York
.27.
Hua
,
W.
,
Dong
,
S. M.
,
Fan
,
Y.
,
Pan
,
X.
, and
Wang
,
Q. Y.
, 2017
, “
Investigation on the Correlation of Mode II Fracture Toughness of Sandstone With Tensile Strength
,” Eng. Fract. Mech.
,
184
, pp. 249
–258
.10.1016/j.engfracmech.2017.09.00928.
Lu
,
C.
,
Sun
,
Q.
,
Zhang
,
W. Q.
,
Geng
,
J. S.
,
Qi
,
Y. M.
, and
Lu
,
L. L.
, 2017
, “
The Effect of High Temperature on Tensile Strength of Sandstone
,” Appl. Therm. Eng.
,
111
, pp. 573
–579
.10.1016/j.applthermaleng.2016.09.15129.
Yaseen
,
M.
,
Zemmouri
,
J.
, and
Shahrour
,
I.
, “
The Geomaterials Fracture by Thermal Process
,” Proceedings of the 39th Workshop on Geothermal Reservoir Engineering
, Stanford University, Stanford, CA, Feb. 24–29, p. 6
.https://pangea.stanford.edu/ERE/pdf/IGAstandard/SGW/2014/Yaseen.pdf30.
Shen
,
B.
,
Ko
,
T. Y.
,
Lee
,
S.
,
Kim
,
J.
,
Kim
,
T. K.
,
Lee
,
J.
,
Kim
,
H. M.
,
Park
,
E. S.
,
Wuttke
,
M. W.
, and
Backers
,
T.
, “
Rock Fracture Propagation Due to Thermal and Hydraulic Loadings
,” Proceedings of 13th IACMAG Conference
, Melbourne, Australia, Sept. 9–13, p. 7.https://publications.csiro.au/rpr/download?pid=csiro:EP105229&dsid=DS131.
Griffiths
,
L.
,
Lengline
,
O.
,
Heap
,
M. J.
,
Baud
,
P.
, and
Schmittbuhl
,
J.
, 2018
, “
Thermal Cracking in Westerly Granite Monitored Using Direct Wave Velocity, Coda Wave Interferometry, and Acoustic Emissions
,” J. Geophys. Res.: Solid Earth
,
123
, pp. 2246
–2261
.10.1002/2017JB01519132.
Glover
,
P. W. J.
,
Baud
,
P.
,
Darot
,
M.
,
Meredith
,
P. G.
,
Boon
,
S. A.
,
LeRavalec
,
M.
,
Zoussi
,
S.
, and
Reuschle
,
T.
, 1995
, “
Alpha/Beta Phase Transition in Quartz Monitored Using Acoustic Emissions
,” Geophys. J. Int.
,
120
(3
), pp. 775
–782
.10.1111/j.1365-246X.1995.tb01852.x33.
Meredith
,
P. G.
,
Knight
,
K. S.
,
Boon
,
S. A.
, and
Wood
,
I. G.
, 2001
, “
The Microscopic Origin of Thermal Cracking in Rocks: An Investigation by Simultaneous Time-of-Flight Neutron Diffraction and Acoustic Emission Monitoring
,” Geophys. Res. Lett.
,
28
(10
), pp. 2105
–2108
.10.1029/2000GL012470Copyright © 2020 by ASME
You do not currently have access to this content.
