Characterizing Hydraulic Fracturing With a Tendency-for-Shear-Stimulation Test
- Mark McClure (University of Texas at Austin) | Roland Horne (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- May 2014
- Document Type
- Journal Paper
- 233 - 243
- 2014.Society of Petroleum Engineers
- 5.9.2 Geothermal Resources, 5.6.4 Drillstem/Well Testing, 1.10 Drilling Equipment, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation
- gas shale, geothermal, well testing, shear stimulation, hydraulic fracturing
- 8 in the last 30 days
- 830 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
The classical concept of hydraulic fracturing is that a single, planar, opening mode fracture propagates through the formation. In recent years, there has been a growing consensus that natural fractures play an important role during stimulation in many settings.There is not universal agreement on the mechanisms by which natural fractures affect stimulation, and these mechanisms may vary depending on formation properties. One potentially important mechanism is shear stimulation, in which increased fluid pressure induces slip and permeability enhancement on pre-existing fractures. We propose a tendency-for-shear-stimulation (TSS) test as a direct, relatively unambiguous method for determining the degree to which shear stimulation contributes to stimulation in a formation. In a TSS test, fluid injection is performed while maintaining the bottomhole fluid pressure slightly less than the minimum principal stress. Under these conditions, shear stimulation is the only possible mechanism for permeability enhancement (except, perhaps, thermally induced tensile fracturing). A TSS test is different from a conventional procedure because injection is performed at a specified pressure (rather than a specified rate).With injection at a specified rate, fluid pressure may exceed the minimum principal stress, and it may cause tensile fractures to propagate through the formation. If this occurs, it will be ambiguouswhether stimulation was because of shear stimulation or tensile fracturing. Maintaining pressure less than the minimum principal stress ensures that the effect of shear stimulation can be isolated. Low-rate injectivity tests could be performed before and after the TSS test to estimate formation permeability. An increase in formation permeability would indicate that shear stimulation has occurred. The flow-rate transient during injection may also be interpreted to identify shear stimulation. Numerical simulations of shear stimulation were performed with a discrete-fracture-network (DFN) simulator that couples fluid flow with the stresses induced by fracture deformation. These simulations were used to qualitatively investigate how shear stimulation and fracture connectivity affect the results of a TSS test. Two specific field projects are discussed as examples of a TSS test, the Enhanced Geothermal Systems (EGS) projects at Desert Peak, Nevada, and Soultz-sous-Forêts, France.
|File Size||1000 KB||Number of Pages||11|
Baisch, Stefan, Weidler, Ralph, Vörös, Robert et al. 2006. Induced Seismicity During the Stimulation of a Geothermal HFR Reservoir in the Cooper Basin, Australia. Bull. Seismological Soc. Am. 96 (6): 2242–2256. http://dx.doi.org/10.1785/0120050255-PA.
Barton, N., Bandis, S., and Bakhtar, K. 1985. Strength, Deformation, and Conductivity Coupling of Rock Joints. International J. Rock Mechanics and Mining Sci. & Geomechanics Abstracts 22 (3): 121–140. http://dx.doi.org/10.1016/0148-9062(85)93227-9-PA.
Benato, S., Reeves, D.M., Parashar, R. et al. 2013. Computational Investigation of Hydro-Mechanical Effects on Transmissivity Enhancement During the Initial Injection Phases at the Desert Peak EGS Project, NV. Paper presented at the Thirty-Eighth Workshop on Geothermal Reservoir Engineering, Stanford, California.
Bird, R. Byron, Stewart, Warren E., and Lightfoot, Edwin N. 2006. Transport Phenomena, second edition, New York: John Wiley & Sons, Inc.
Blanton, Thomas. 1982. An Experimental Study of Interaction Between Hydraulically Induced and Pre-Existing Fractures. Paper SPE 10847 presented at the SPE Unconventional Gas Recovery Symposium, Pittsburgh, Pennsylvania, 16–18 May. http://dx.doi.org/10.2118/10847-MS.
Bowker, Kent A. 2007. Barnett Shale Gas Production, Fort Worth Basin: Issues and Discussion. AAPG Bull. 91 (4): 523–533. http://dx.doi.org/10.1306/06190606018-PA.
Bradley, Andrew M. 2012. H-Matrix and Block Error Tolerances. arXiv:1110.2807, source code available at https://pangea.stanford.edu/research/CDFM/software/index.html, paper available at http://arvix.org/abs/1110.2807.
Brown, D.W. 1989. The Potential for Large Errors in the Inferred Minimum Earth Stress When Using Incomplete Hydraulic Fracturing Results. International J. Rock Mechanics and Mining Sci. & Geomechanics Abstracts 26 (6): 573–577. http://dx.doi.org/10.1016/0148-9062(89)91437-X.
Bruel, D. 1995. Heat Extraction Modelling From Forced Fluid Flow Through Stimulated Fractured Rock Masses: Application to the Rosemanowes Hot Dry Rock Reservoir. Geothermics 24 (3): 361–374. http://dx.doi.org/10.1016/0375-6505(95)00014-H.
Bruel, Dominique. 2007. Using the Migration of the Induced Seismicity as a Constraint for Fractured Hot Dry Rock Reservoir Modelling. International J. Rock Mechanics and Mining Sci. 44 (8): 1106–1117. http://dx.doi.org/10.1016/j.ijrmms.2007.07.001.
Chabora, Ethan, Zemach, Ezra, Spielman, Paul et al. 2012. Hydraulic Stimulation of Well 27-15, Desert Peak Geothermal Field, Nevada, USA. Paper presented at the Thirty-Seventh Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California.
Chipperfield, S.T., Wong, J.R., Warner, D.S. et al. 2007. Shear Dilation Diagnostics: A New Approach for Evaluating Tight Gas Stimulation Treatments. Paper SPE 106289 presented at the SPE Hydraulic Fracturing Technology Conference, College Station, Texas, 29–31 January. http://dx.doi.org/10.2118/106289-MS.
Cipolla, Craig, Warpinski, Norman, Mayerhofer, Michael et al. 2008. The Relationship Between Fracture Complexity, Reservoir Properties, and Fracture Treatment Design. Paper SPE 115769 presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 21–24 September. http://dx.doi.org/10.2118/115769-MS.
Cipolla, C.L., Lolon, E.P., Erdle, J.C. et al. 2010. Reservoir Modeling in Shale-Gas Reservoirs. SPE Res Eval & Eng 13 (4): 638–653. http://dx.doi.org/10.2118/125530-PA.
Cladouhos, Trenton, Petty, Susan, Larson, Ben et al. 2009. Towards More Efficient Heat Mining: A Planned Enhanced Geothermal System Demonstration Project. GRC Trans. 33: 165–170.
Cladouhos, Trenton T., Clyne, Matthew, and Nichols, Maisie et al. 2011. Newberry Volcano EGS Demonstration Stimulation Modeling. Geothermal Resources Council Trans. 35: 317–322.
Dahi-Taleghani, Arash and Olson, Jon. 2009. Modeling Simultaneous Growth of Multiple Hydraulic Fractures and Their Interaction With Natural Fractures. Paper SPE 119739 presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 19–21 January. http://dx.doi.org/10.2118/119739-MS.
Damjanac, Branko, Gil, Ivan, Pierce, Matt et al. 2010. A New Approach to Hydraulic Fracturing Modeling in Naturally Fractured Reservoirs. Paper presented at the 44th US Rock Mechanics Symposium and 5th US-Canada Rock Mechanics Symposium, Salt Lake City, Utah.
Dempsey, D., Kelkar, S., Lewis, K. et al. 2013. Modeling Shear Stimulation of the Desert Peak EGS Well 27-15 Using a Coupled Thermal-Hydrological-Mechanical Simulator. Paper presented at the 47th United States Rock Mechanics/Geomechanics Association Symposium, San Francisco, California.
Ehlig-Economides, Christine. 1979. Well Test Analysis for Wells Produced at a Constant Pressure. PhD Thesis, Stanford University.
Esaki, T., Du, S., Mitani, Y. et al. 1999. Development of a Shear-Flow Test Apparatus and Determination of Coupled Properties for a Single Rock Joint. International J. Rock Mechanics and Mining Sci. 36 (5): 641–650. http://dx.doi.org/10.1016/S0148-9062(99)00044-3.
Evans, Keith F. 2005. Permeability Creation and Damage Due To Massive Fluid Injections Into Granite At 3.5 Km At Soultz: 2. Critical Stress and Fracture Strength. J. Geophysical Research 110 (B4). http://dx.doi.org/10.1029/2004JB003169.
Evans, Keith F., Genter, Albert and Sausse, Judith. 2005. Permeability Creation and Damage Due To Massive Fluid Injections Into Granite at 3.5 Km at Soultz: 1. Borehole Observations. J. Geophysical Research 110 (B4). http://dx.doi.org/10.1029/2004JB003168.
Fan, Li, Thompson, John, and Robinson, John. 2010. Understanding Gas Production Mechanism and Effectiveness of Well Stimulation in the Haynesville Shale Through Reservoir Simulation. Paper SPE 136696 presented at the Canadian Unconventional Resources and International Petroleum Conference, Calgary, Alberta, Canada, 19–21 October. http://dx.doi.org/10.2118/136696-MS.
Fisher, M.K., Heinze, J.R., Harris, C.D. et al. 2004. Optimizing Horizontal Completion Techniques in the Barnett Shale Using Microseismic Fracture Mapping. Paper SPE 90051 presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 26–29 September. http://dx.doi.org/10.2118/90051-MS.
Fu, Pengcheng, Johnson, Scott M., and Carrigan, Charles R. 2012. An Explicitly Coupled Hydro-Geomechanical Model for Simulating Hydraulic Fracturing in Arbitrary Discrete Fracture Networks. International J. Numerical and Analytical Methods in Geomechanics. http://dx.doi.org/10.1002/nag.2135.
Gale, Julia F.W., Reed, Robert M. and Holder, Jon. 2007. Natural Fractures in the Barnett Shale and Their Importance for Hydraulic Fracture Treatments. AAPG Bull. 91 (4): 603–622. http://dx.doi.org/10.1306/11010606061.
Gu, H. and Weng, X. 2010. Criterion for Fractures Crossing Frictional Interfaces at Non-Orthogonal Angles. Paper presented at the 44th US Rock Mechanics Symposium and 5th US-Canada Rock Mechanics Symposium, Salt Lake City, Utah.
Gu, Hongren, Weng, Xiaowei, Lund, Jeffrey et al. 2011. Hydraulic Fracture Crossing Natural Fracture at Non-Orthogonal Angles, a Criterion, Its Validation and Applications. Paper SPE 139984 presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 24–26 January. http://dx.doi.org/10.2118/139984-MS.
Hettkamp, T., Baumgärtner, J. Baria, R. et al. 2004. Electricity Production From Hot Rocks. Paper presented at the Twenty-Ninth Workshop on Geothermal Reservoir Engineering, Stanford University.
Horne, Roland N. 1995. Modern Well Test Analysis: A Computer-Aided Approach, second edition. Palo Alto, California: Petroway, Inc.
Ito, Hisatoshi. 2003. Inferred Role of Natural Fractures, Veins, and Breccias in Development of the Artificial Geothermal Reservoir at the Ogachi Hot Dry Rock Site, Japan. J. Geophysical Research 108 (B9). http://dx.doi.org/10.1029/2001JB001671.
Ito, T. and Hayashi, K. 2003. Role of Stress-Controlled Flow Pathways in HDR Geothermal Reservoirs. Pure and Applied Geophysics 160 (5): 1103–1124. http://dx.doi.org/10.1007/PL00012563.
Jeffrey, Robert, Zhang, Xi, and Thiercelin, Marc. 2009. Hydraulic Fracture Offsetting in Naturally Fractured Reservoirs: Quantifying a Long-Recognized Process. Paper SPE 119351 presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 19–21 January. http://dx.doi.org/10.2118/119351-MS.
Jing, Z., Willis-Richards, J. Watanabe, K. et al. 2000. A Three-Dimensional Stochastic Rock Mechanics Model of Engineered Geothermal Systems in Fractured Crystalline Rock. J. Geophysical Research 105 (B10): 23663–23679. http://dx.doi.org/10.1029/2000JB900202.
Jupe, A.J., Green, A.S.P., and Wallroth, T. 1992. Induced Microseismicity and Reservoir Growth at the Fjällbacka Hot Dry Rocks Project, Sweden. International J. Rock Mechanics and Mining Sciences & Geomechanics Abstracts 29 (4): 343–354. http://dx.doi.org/10.1016/0148-9062(92)90511-W.
Kaieda, H., Sasaki, S., and Wyborn, D. 2010. Comparison of Characteristics of Micro-Earthquakes Observed During Hydraulic Stimulation Operations in Ogachi, Hijiori, and Cooper Basin HDR Projects. Paper presented at the World Geothermal Congress, Bali, Indonesia.
Kamal, Medhat M. ed. 2009. Transient Well Testing, Vol. Monograph Series Vol. 23, Society of Petroleum Engineers.
King, G.C.P. 2007. 4.08—Fault Interaction, Earthquake Stress Changes, and the Evolution of Seismicity. In Treatise on Geophysics, ed. G. Schubert 225–255. Amsterdam: Elsevier.
King, George. 2010. Thirty Years of Gas Shale Fracturing: What Have We Learned? Paper SPE 133456 presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September. http://dx.doi.org/10.2118/133456-MS.
Kohl, T. and Hopkirk, R.J. 1995. “FRACTURE”—A Simulation Code for Forced Fluid Flow and Transport in Fractured, Porous Rock. Geothermics 24 (3): 333–343. http://dx.doi.org/10.1016/0375-6505(95)00012-F.
Kohl, T. and Mégel, T. 2007. Predictive Modeling of Reservoir Response to Hydraulic Stimulations at the European EGS Site Soultz-Sous-Forêts. International J. Rock Mechanics and Mining Sci. 44 (8): 1118–1131. http://dx.doi.org/10.1016/j.ijrmms.2007.07.022.
Lanyon, G.W., Batchelor, A.S., and Ledingham, P. 1993. Results From a Discrete Fracture Network Model of a Hot Dry Rock System. Paper presented at the Eighteenth Workshop on Geothermal Reservoir Engineering, Stanford University.
Laubach, Stephen E., Olson, Jon E., and Gale, Julia F.W. 2004. Are Open Fracture Necessary Aligned With Maximum Horizontal Stress? Earth and Planetary Science Lett. 222: 191–195. http://dx.doi.org/10.1016/j.epsl.2004.02.019.
Ledésert, Béatrice, Hebert, Ronan, Genter, Albert et al. 2010. Fractures, Hydrothermal Alterations and Permeability in the Soultz Enhanced Geothermal System. Comptes Rendus Geosci. 342 (7–8): 607–615. http://dx.doi.org/10.1016/j.crte.2009.09.011.
Liu, Enru. 2005. Effects of Fracture Aperture and Roughness on Hydraulic and Mechanical Properties of Rocks: Implication of Seismic Characterization of Fractured Reservoirs. J. Geophysics and Eng. 2 (1): 38–47. http://dx.doi.org/10.1088/1742-2132/2/1/006.
Lutz, S.J., Hickman, S. Davatzes, N. et al. 2010. Rock Mechanical Testing and Petrological Analysis in Support of Well Stimulation Activities at the Desert Peak Geothermal Field, Nevada. Paper presented at the Thirty-Fifth Workshop on Geothermal Reservoir Engineering, Stanford University.
Mahrer, Kenneth D. 1999. A review and perspective on far-field hydraulic fracture geometry studies. J. Petrol. Sci. and Eng. 24 (1): 13–28. http://dx.doi.org/10.1016/S0920-4105(99)00020-0.
Mayerhofer, Michael, Lolon, Elyezer, and Warpinski, Norman et al. 2010. What Is Stimulated Reservoir Volume? SPE Prod & Oper 25 (1): 89–98. http://dx.doi.org/10.2118/119890-PA.
McClure, M.W. 2012. Modeling and Characterization of Hydraulic Stimulation and Induced Seismicity in Geothermal and Shale Gas Reservoirs. PhD Thesis, Stanford University, Stanford, California.
McClure, M.W. and Horne, R.N. 2010a. Discrete Fracture Modeling of Hydraulic Stimulation in Enhanced Geothermal Systems. Paper presented at the Thirty-Fifth Workshop on Geothermal Reservoir Engineering, Stanford University.
McClure, Mark W. and Horne, Roland N. 2010b. Numerical and Analytical Modeling of the Mechanisms of Induced Seismicity During Fluid Injection. Geothermal Resources Council Trans. 34: 381–396.
McClure, M.W. and Horne, Roland N. 2011. Investigation of Injection-Induced Seismicity Using a Coupled Fluid Flow and Rate/State Friction Model. Geophysics 76 (6): WC181–WC198. http://dx.doi.org/10.1190/geo2011-0064.1.
McClure, M.W. and Horne, R.N. 2012. The Effect of Fault Zone Development on Induced Seismicity. Paper presented at the Thirty-Seventh Workshop on Geothermal Reservoir Engineering, Stanford, California.
McClure, Mark W. and Horne, Roland N. 2013a. Discrete Fracture Network Modeling of Hydraulic Stimulation: Coupling Flow and Geomechanics: Springer Briefs in Earth Sciences, Springer.
McClure, M.W. and Horne, R.N. 2013b. Is Pure Shear Stimulation Always the Mechanism of Stimulation in EGS? Paper presented at the Thirty-Eighth Workshop on Geothermal Reservoir Engineering, Stanford, California.
Murphy, H.D. and Fehler, M.C. 1986. Hydraulic Fracturing of Jointed Formations. Paper SPE 14088 presented at the International Meeting on Petroleum Engineering, Beijing, China, 17–20 March. http://dx.doi.org/10.2118/14088-MS.
Mutlu, O. and Pollard, D.D. 2008. On the Patterns of Wing Cracks Along in Outcrop Scale Flaw: A Numerical Modeling Approach Using Complementarity. J. Geophysical Research 113 (B6). http://dx.doi.org/10.1029/2007JB005284.
Nagel, Neal, Gil, Ivan, Sanchez-Nagel, Marisela et al. 2011. Simulating Hydraulic Fracturing in Real Fractured Rocks—Overcoming the Limits of Pseudo3D Models. Paper SPE 140480 presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 24–26 January. http://dx.doi.org/10.2118/140480-MS.
Olson, Jon E. 2004. Predicting Fracture Swarms—The Influence of Subcritical Crack Growth and the Crack-Tip Process Zone on Joint Spacing in Rock. In The Initiation, Propagation, and Arrest of Joints and Other Fractures, ed. J.W. Cosgrove and T. Engelder, 73–88. London: Geological Society, Special Publications, Geological Society of London.
Olson, Jon E., Laubach, Stephen E., and Lander, Robert H. 2009. Natural Fracture Characterization in Tight Gas Sandstones: Integrating Mechanics and Diagenesis. Bull. Am. Assoc. Petrol. Geolog. 93 (11): 1535–1549. http://dx.doi.org/10.1306/08110909100.
Palmer, Ian, Moschovidis, Zissis, and Cameron, John. 2007. Modeling Shear Failure and Stimulation on the Barnett Shale After Hydraulic Fracturing. Paper SPE 106113 presented at the SPE Hydraulic Fracturing Technology Conference, College Station, Texas, 29–31 January. http://dx.doi.org/10.2118/106113-MS.
Pine, R.J. and Batchelor, A.S. 1984. Downward Migration of Shearing in Jointed Rock During Hydraulic Injections. International J. Rock Mechanics and Mining Sci. & Geomechanics Abstracts 21 (5): 249–263. http://dx.doi.org/10.1016/0148-9062(84)92681-0.
Rachez, X. and Gentier, S. 2010. 3D-Hydromechanical Behavior of a Stimulated Fractured Rock Mass. Paper presented at the World Geothermal Congress, Bali, Indonesia.
Rahman, M.K., Hossain, M.M., and Rahman, S.S. 2002. A Shear-Dilation-Based Model for Evaluation of Hydraulically Stimulated Naturally Fractured Reservoirs. International J. for Numerical and Analytical Methods in Geomechanics 26 (5): 469–497. http://dx.doi.org/10.2118/10.1002/nag.208.
Renshaw, C.E. and Pollard, D.D. 1995. An Experimentally Verified Criterion for Propagation Across Unbounded Frictional Interfaces in Brittle, Linear Elastic Materials. International J. Rock Mechanics and Mining Sci. & Geomechanics Abstracts 32 (3): 237–249. http://dx.doi.org/10.1016/0148-9062(94)00037-4.
Riahi, Azadeh and Damjanac, Branko. 2013. Numerical Study of Hydro-Shearing in Geothermal Reservoirs With a Pre-Existing Discrete Fracture Network. Paper presented at the Thirty-Eighth Workshop on Geothermal Reservoir Engineering, Stanford, California.
Rice, James R. 1993. Spatio-Temporal Complexity of Slip on a Fault. J. Geophysical Research 98 (B6): 9885–9907. http://dx.doi.org/10.1029/93JB00191.
Rogers, Stephen, Elmo, Davide, Dunphy, Rory et al. 2010. Understanding Hydraulic Fracture Geometry and Interactions in the Horn River Basin Through DFN and Numerical Modeling. Paper SPE 137488 presented at the Canadian Unconventional Resources and International Petroleum Conference, Calgary, Alberta, Canada, 19–21 October. http://dx.doi.org/10.2118/137488-MS.
Roussel, Nicolas and Sharma, Mukul. 2011. Strategies To Minimize Frac Spacing and Stimulate Natural Fractures in Horizontal Completions. Paper SPE 146104 presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 30 October–2 November. http://dx.doi.org/10.2118/146104-MS.
Segall, Paul. 2010. Earthquake and Volcano Deformation. Princeton, New Jersey: Princeton University Press.
Segall, Paul and Pollard, David D. 1983. Nucleation and Growth of Strike Slip Faults in Granite. J. Geophysical Research 88 (B1): 555–568. http://dx.doi.org/10.1029/JB088iB01p00555.
Shou, K.J. and Crouch, S.L. 1995. A Higher Order Displacement Discontinuity Method for Analysis of Crack Problems. International J. Rock Mechanics and Mining Sci. & Geomechanics Abstracts 32 (1): 49–55. http://dx.doi.org/10.1016/0148-9062(94)00016-V.
Tester, J. ed. 2006. The Future of Geothermal Energy: Impact of Enhanced Geothermal Systems (EGS) on the United States in the 21st Century, Massachusetts Institute of Technology.
Valley, B. and Evans, K. 2007. Stress State at Soultz-Sous-Forêts to 5 Km Depth From Wellbore Failure and Hydraulic Observations. Paper presented at the Thirty-Second Workshop on Geothermal Reservoir Engineering, Stanford University.
Warpinski, N.R., Lorenz, J.C., Branagan, P.T. et al. 1993. Examination of a Cored Hydraulic Fracture in a Deep Gas Well. SPE Prod & Fac 8 (3): 150–158. http://dx.doi.org/10.2118/22876-PA.
Warpinski, N.R. and Teufel, L.W.. 1987. Influence of Geologic Discontinuities on Hydraulic Fracture Propagation. J. Pet Tech 39 (2): 209–220. http://dx.doi.org/10.2118/13224-PA.
Warpinski, N.R., Wolhart, S.L., and Wright, C.A. 2001. Analysis and Prediction of Microseismicity Induced by Hydraulic Fracturing. Paper SPE 71649 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September–3 October. http://dx.doi.org/10.2118/71649-MS.
Weidler, R. 2000. Hydraulic Stimulation of the 5 km Deep Well GPK-2, Bureau de Recherches Géologiques et Minières (BRGM).
Weidler, R., Gerard, A.,Baria, A. et al. 2002. Hydraulic and Micro-Seismic Results of a Massive Stimulation Test at the 5 Km Depth at the European Hot-Dry Rock Test Site Soultz, France. Paper presented at the Twenty-Seventh Workshop on Geothermal Reservoir Engineering, Stanford University.
Weng, Xiaowei, Kresse, O., Cohen, C.-E. et al. 2011. Modeling of Hydraulic-Fracture-Network Propagation in a Naturally Fractured Formation. SPE Prod & Oper 26 (4). http://dx.doi.org/10.2118/140253-PA.
Willis-Richards, J., Green, A.S.P., and Jupe, A.J. 1995. A Comparison of HDR Geothermal Sites. Paper presented at the World Geothermal Congress, Florence, Italy.
Willis-Richards, J., Watanabe, K., and Takahashi, H. 1996. Progress Toward a Stochastic Rock Mechanics Model of Engineered Geothermal Systems. J. Geophysical Research 101 (B8): 17481–17496. http://dx.doi.org/10.1029/96JB00882.
Witherspoon, P.A., Wang, J.S.Y., Iwai, K. et al. 1980. Validity of Cubic Law for Fluid Flow in a Deformable Rock Fracture. Water Resources Research 16 (6): 1016–1024. http://dx.doi.org/10.1029/WR016i006p01016.
Wu, R., Kresse, O., Weng, X. et al. 2012. Modeling of Interaction of Hydraulic Fractures in Complex Fracture Networks. Paper SPE 152052 presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 6–8 February. http://dx.doi.org/10.2118/152052MS.
Zhou, Jian, Chen, Mian, Jin, Yan et al. 2008. Analysis of Fracture Propagation Behavior and Fracture Geometry Using a Tri-Axial Fracturing System in Naturally Fractured Reservoirs. International J. Rock Mechanics and Mining Sci. 45 (7): 1143–1152. http://dx.doi.org/10.1016/j.ijrmms.2008.01.001.
Zhou, Xiaoxian and Ghassemi, Ahmad. 2011. Three-Dimensional Poroelastic Analysis of a Pressurized Natural Fracture. International J. Rock Mechanics and Mining Sci. 48 (4): 527–534. http://dx.doi.org/10.1016/j.ijrmms.2011.02.002.
Zimmermann, G., Reinicke, A., Brandt, W. et al. 2008. Results of Stimulation Treatments at the Geothermal Research Wells in Grob Schönebeck/Germany. Paper presented at the Thirty-Third Workshop on Geothermal Reservoir Engineering, Stanford University.