The Effect of Layered Modulus on Hydraulic-Fracture Modeling and Fracture-Height Containment
- Kaimin Yue (University of Texas at Austin) | Jon E. Olson (University of Texas at Austin) | Richard A. Schultz (University of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- May 2019
- Document Type
- Journal Paper
- 2019.Society of Petroleum Engineers
- effective modulus, height containment, layered formation, modulus contrast, hydraulic fracturing
- 25 in the last 30 days
- 154 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Oil and gas production from unconventional reservoirs, which are usually stratified with layers having different mechanical properties, generally requires the aid of hydraulic-fracturing technology. Predicting hydraulic-fracture-height growth is one of the critical factors in designing successful hydraulic-fracturing treatments. It has been well-documented that the in-situ-stress contrast between adjacent layers and interface properties are the dominating factors in fracture-height containment, whereas the modulus contrast between adjacent layers is generally considered to be of secondary importance in the direct control of fracture-height containment. However, the arrest of fluid-driven fractures at soft layers is often observed in outcrops and hydraulic-fracture-diagnostic field tests. The objective of this study is to investigate fracture-height containment resulting from the modulus contrast between adjacent layers.
To illustrate the effect of modulus contrast on fracture-height containment, this study proposes a new approach that uses the effective modulus of a layered reservoir. We use 2D finite-element models to evaluate the effective modulus of a layered reservoir, considering the effects of modulus values, fracture-tip location, height percentage of each rock layer, layer location, the number of layers, and the mechanical anisotropy. Then, the effect of modulus contrast on fracture-height growth is investigated with an analysis of the stress-intensity factor, taking into account the change of the effective modulus as the fracture tip propagates from the stiff layer to the soft layer.
This study shows that the detail of layering does not affect the effective modulus and the only important parameters are fracture-tip locations, modulus values, and the height percentage of each rock layer. In addition, this study empirically derives two approximations of effective moduli depending on fracture-tip locations: the modified height-weighted mean and the modified height-weighted harmonic average. Results from combining linear-elastic fracture mechanics with the effective-modulus approximations show that height growth will be inhibited by the soft layer because of a reduced stress-intensity factor.
The effective moduli can be applied to other hydraulic-fracture models to take into account the layering effect. This study also shows that soft layers inhibit hydraulic-fracture-height growth in layered reservoirs. As a result, hydraulic-fracture-height containment within a stratified rock stack can be better evaluated by comparing the modulus contrast between adjacent layers.
|File Size||915 KB||Number of Pages||16|
Abbas, S., Gordeliy, E., Peirce, A. et al. 2014. Limited Height Growth and Reduced Opening of Hydraulic Fractures Due to Fracture Offsets: An XFEM Application. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 4–6 February. SPE-168622-MS. https://doi.org/10.2118/168622-MS.
Adachi, J. I., Detournay, E., and Peirce, A. P. 2010. An Analysis of the Classical Pseudo-3D Model for Hydraulic Fracture With Equilibrium Height Growth Across Stress Barriers. Int J Rock Mech Min Sci 47 (4): 625–639. https://doi.org/10.1016/j.ijrmms.2010.03.008.
AlTammar, M. J. and Sharma, M. M. 2017. Effect of Geological Layer Properties on Hydraulic Fracture Initiation and Propagation: An Experimental Study. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 24–28 January. SPE 184871-MS. https://doi.org/10.2118/184871-MS.
Barree, R. D. 1983. A Practical Numerical Simulator for Three-Dimensional Fracture Propagation in Heterogeneous Media. Presented at the SPE Reservoir Simulation Symposium, San Francisco, 15–18 November. SPE-12273-MS. https://doi.org/10.2118/12273-MS.
Boussinesq, M. J. 1885. Application des Potentiels à l’Étude de l’Équilibre Et du Mouvement des Solides Élastiques: Principalement au Calcul des Déformations Et des Pressions Que Produisent, dans Ces Solides, des Efforts Quelconques Exercés sur une Petite Partie de Leur Surface ou de Leur Intérieur: Memoire Suivi de Notes Etendues sur Divers Points de Physique Mathematique et d’Analyse (Application of Potentials to the Study of the Equilibrium and the Movement of Elastic Solids, Mainly to the Computation of the Deformations and the Pressures Which Produce in These Solids Any Efforts Exerted on a Small Part of Their Surface or Their Interior; Followed by Extended Notes on Various Points of Mathematical Physics and Analysis, in French). Paris: GauthierVillars.
Breyer, J. A., Denne, R. A., Kosanke, T. et al. 2013. Facies, Fractures, Pressure, and Production in the Eagle Ford Shale (Cretaceous) Between the San Marcos Arch and the Maverick Basin, Texas, USA. Presented at the Unconventional Resources Technology Conference, Denver, 12–14 August. https://doi.org/10.1190/urtec2013-159.
Chen, Z. 2012. Finite Element Modeling of Viscosity-Dominated Hydraulic Fractures. J Pet Sci Eng 88–89 (June): 136–144. https://doi.org/10.1016/j.petrol.2011.12.021.
Cleary, M. P. 1980. Analysis of Mechanisms and Procedures for Producing Favorable Shapes of Hydraulic Fractures. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 21–24 September. SPE 9260-MS. https://doi.org/10.2118/9260-MS.
Clifton, R. J. and Wang, J.-J. 1988. Multiple Fluids, Proppant Transport, and Thermal Effects in Three-Dimensional Simulation of Hydraulic Fracturing. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 2–5 October. SPE-18198-MS. https://doi.org/10.2118/18198-MS.
Comer, J. B. 1991. Stratigraphic Analysis of the Upper Devonian Woodford Formation, Permian Basin, West Texas and New Mexico. Report of Investigations No. 201, Bureau of Economic Geology, University of Texas at Austin, Austin, Texas.
Cooke, M. L. 1997. Predicting Fracture Localization in Folded Strata From Mechanical Stratigraphy and Fold Shape: Case Study of East Kaibab Monocline, Utah. Int J Rock Mech Min Sci 34 (3–4): 56.e1–56.e12. https://doi.org/10.1016/S1365-1609(97)00248-7.
Daneshy, A. A. 1978. Hydraulic Fracture Propagation in Layered Formations. SPE J. 18 (1): 33–41. SPE-6088-PA. https://doi.org/10.2118/6088-PA.
Dassault Systèmes. 2013. Abaqus Standard User’s Manual, Version 6.13. Providence, Rhode Island: Simulia.
Donovan, A. D. and Staerker, T. S. 2010. Sequence Stratigraphy of the Eagle Ford (Boquillas) Formation in the Subsurface of South Texas and Outcrops of West Texas. GCAGS Trans. 60: 861–899.
Ferrill, D. A., McGinnis, R. N., Morris, A. P. et al. 2014. Control of Mechanical Stratigraphy on Bed Restricted Jointing and Normal Faulting: Eagle Ford Formation, South Central Texas. AAPG Bull 98 (11): 2477–2506. https://doi.org/10.1306/08191414053.
Fisher, K. and Warpinski, N. 2011. Hydraulic Fracture-Height Growth: Real Data. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November. SPE-145949-MS. https://doi.org/10.2118/145949-MS.
FracProPT. 2007. FracProPT Manual. www.fracpro.com.
Gu, H. and Siebrits, E. 2008. Effect of Formation Modulus Contrast on Hydraulic Fracture Height Containment. SPE Prod & Oper 23 (2): 170–176. SPE-103822-PA. https://doi.org/10.2118/103822-PA.
Huang, J., Ma, X., Shahri, M. et al. 2016. Hydraulic Fracture Growth and Containment Design in Unconventional Reservoirs. Presented at the 50th US Rock Mechanics/Geomechanics Symposium, Houston, 26–29 June. ARMA-2016-412.
Jeffrey, R. G. and Bunger, A. 2007. A Detailed Comparison of Experimental and Numerical Data on Hydraulic Fracture-Height Growth Through Stress Contrasts. Presented at the SPE Hydraulic Fracturing Technology Conference, College Station, Texas, 29–31 January. SPE-106030-MS. https://doi.org/10.2118/106030-MS.
Jeffrey, R. G. Jr., Brynes, R. P., Lynch, P. J. et al. 1992. An Analysis of Hydraulic Fracture and Mineback Data for a Treatment in the German Creek Coal Seam. Presented at the SPE Rocky Mountain Regional Meeting, Casper, Wyoming, 18–21 May. SPE-24362-MS. https://doi.org/10.2118/24362-MS.
Jing, L. 2003. A Review of Techniques, Advances and Outstanding Issues in Numerical Modelling for Rock Mechanics and Rock Engineering. Int J Rock Mech Min Sci 40 (3): 283–353. https://doi.org/10.1016/S1365-1609(03)00013-3.
Jones, R. M. 1975. Mechanics of Composite Materials. New York City: Hemisphere Publishing.
Lawn, B. R. and Wilshaw, T. R. 1975. Fracture of Brittle Solids. Cambridge, UK: Cambridge University Press.
Lee, J. C. and Keer, L. M. 1986. Study of a Three-Dimensional Crack Terminating at an Interface. J. Appl. Mech. 53 (2): 2: 311–316. https://doi.org/10.1115/1.3171757.
Liu, S. and Valko, P. P. 2015. An Improved Equilibrium-Height Model for Predicting Hydraulic Fracture Height Migration in Multi-Layered Formations. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 3–5 February. SPE-173335-MS. https://doi.org/10.2118/173335-MS.
Marion, D. P. 1990. Acoustical, Mechanical, and Transport Properties of Sediments and Granular Materials. PhD dissertation, Stanford University, Stanford, California (February 1990).
McClure, M. W. and Horne, R. N. 2013. Discrete Fracture Network Modeling of Hydraulic Stimulation: Coupling Flow and Geomechanics. Berlin: Springer.
Mullen, J. 2010. Petrophysical Characterization of the Eagle Ford Shale in South Texas. Presented at the Canadian Unconventional Resources and International Petroleum Conference, Calgary, 19–21 October. SPE-138145-MS. https://doi.org/10.2118/138145-MS.
NSI Technologies. 2010. Manual for StimPlan. https://www.nsitech.com/stimplan-software/.
Olson, J. E. 1995. Fracturing From Highly Deviated and Horizontal Wells: Numerical Analysis of Non-Planar Fracture Propagation. Presented at the Low Permeability Reservoirs Symposium, Denver, 19–22 March. SPE-29573-MS. https://doi.org/10.2118/29573-MS.
Ortiz, A. C., Hryb, D. E., Marti´nez, J. R. et al. 2016. Hydraulic Fracture Height Estimation in an Unconventional Vertical Well in the Vaca Muerta Formation, Neuquen Basin, Argentina. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 9–11 February. SPE-179145-MS. https://doi.org/10.2118/179145-MS.
Palmer, I. D. and Craig, H. R. 1984. Modeling of Asymmetric Vertical Growth in Elongated Hydraulic Fractures and Application to First MWX Stimulation. Presented at the SPE Unconventional Gas Recovery Symposium, Pittsburgh, Pennsylvania, 13–15 May. SPE-12879-MS. https://doi.org/10.2118/12879-MS.
Perkins, T. K. and Kern, L. R. 1961. Widths of Hydraulic Fractures. J Pet Technol 13 (9): 937–949. SPE-89-PA. https://doi.org/10.2118/89-PA.
Philipp, S. L., Afs_ar, F., and Gudmundsson, A. 2013. Effects of Mechanical Layering on Hydrofracture Emplacement and Fluid Transport in Reservoirs. Front. Earth Sci. 1: 4. https://doi.org/10.3389/feart.2013.00004.
Reuss, A. 1929. Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung Für Einkristalle. Z Angew Math Mech 9 (1): 49–58. https://doi.org/10.1002/zamm.19290090104.
Rice, J. R. 1968. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. J. Appl. Mech. 35 (2): 379–86. https://doi.org/10.1115/1.3601206.
Rodrigues, N., Cobbold, P. R., Loseth, H. et al. 2009. Wide Spread Bedding-Parallel Veins of Fibrous Calcite (‘Beef’) in a Mature Source Rock (Vaca Muerta Fm, Neuquén Basin, Argentina): Evidence for Overpressure and Horizontal Compression. J Geol Soc 166 (4): 695–709. https://doi.org/10.1144/0016-76492008-111.
Settari, A. and Cleary, M. P. 1986. Development and Testing of a Pseudo-Three-Dimensional Model of Hydraulic Fracture Geometry. SPE Prod Eng 1 (6): 449-466. SPE-10505-PA. https://doi.org/10.2118/10505-PA.
Shel, E. 2017. Influence of the Elastic Moduli Contrast on the Height Growth of a Hydraulic Fracture. Presented at the SPE Russian Petroleum Technology Conference, Moscow, 16–18 October. SPE-187834-MS. https://doi.org/10.2118/187834-MS.
Shlyapobersky, J. 1989. On-Site Interactive Hydraulic Fracturing Procedures for Determining the Minimum In-Situ Stress From Fracture Closure and Reopening Pressures. Int J Rock Mech Min Sci 26 (6): 541–548. https://doi.org/10.1016/0148-9062(89)91432-0.
Siebrits, E. and Peirce, A. P. 2002. An Efficient Multi-Layer Planar 3D Fracture Growth Algorithm Using a Fixed Mesh Approach. Int J Numer Methods Eng 53 (3): 691–717. https://doi.org/10.1002/nme.308.
Simonson, E. R., Abou-Sayed, A. S., and Clifton, R. J. 1978. Containment of Massive Hydraulic Fractures. SPE J. 18 (1): 27–32. SPE-6089-PA. https://doi.org/10.2118/6089-PA.
Smith, M. B., Bale, A. B., Britt, L. K. et al. 2001. Layered Modulus Effects on Fracture Propagation, Proppant Placement, and Fracture Modeling. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. SPE-71654-MS. https://doi.org/10.2118/71654-MS.
Sneddon, I. N. 1946. The Distribution of Stress in the Neighborhood of a Crack in an Elastic Solid. Proc R Soc Lond A Math Phys Sci 187 (1009): 229–260. https://doi.org/10.1098/rspa.1946.0077.
Sone, H. and Zoback, M. D. 2013. Mechanical Properties of Shale Gas Reservoir Rocks—Part 1: Static and Dynamic Elastic Properties and Anisotropy. Geophysics 78 (5): D381–D382. https://doi.org/10.1190/geo2013- 0050.1.
Teufel, L. M. and Clark, J. A. 1984. Hydraulic Fracture Propagation in Layered Rock: Experimental Studies of Fracture Containment. SPE J. 24 (1): 19–32. SPE-9878-PA. https://doi.org/10.2118/9878-PA.
van Eekelen, H. A. M. 1982. Hydraulic Fracture Geometry: Fracture Containment in Layered Formations. SPE J. 22 (3): 341–349. SPE-9261-PA. https://doi.org/10.2118/9261-PA.
Vernik, L. and Milovac, J. 2011. Rock Physics of Organic Shales. The Leading Edge 30 (3): 318–323. https://doi.org/10.1190/1.3567263.
Voigt, W. 1910. Lehrbuch der Kristallphysik. Berlin: B. G. Teubner. https://doi.org/10.1007/978-3-663-15884-4.
Wang, W., Olson, J. E., and Prodanovic´, M. 2013. Natural and Hydraulic Fracture Interaction Study Based on Semi-Circular Bending Experiments. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Denver, 12–14 August. URTEC-1576910-MS. https://doi.org/10.15530/URTEC-1576910-MS.
Wang, W., Olson, J. E., Prodanovic´, M. et al. 2018. Interaction Between Cemented Natural Fractures and Hydraulic Fractures Assessed by Experiments and Numerical Simulations. J Pet Sci Eng 167 (August): 505–516. https://doi.org/10.1016/j.petrol.2018.03.095.
Warpinski, N. R. 2011. Measurements and Observations of Fracture-Height Growth. Oral presentation of Technical Presentation Session 6 given at the US EPA Technical Workshop for the Hydraulic Fracturing Study: Chemical & Analytical Methods, Arlington, Virginia, 24–25 February.
Warpinski, N. R., Schmidt, R. A., and Northrop, D. A. 1982. In-Situ Stresses: The Predominant Influence on Hydraulic Fracture Containment. J Pet Technol 34 (3): 653–664. SPE-8932-PA. https://doi.org/10.2118/8932-PA.
Weng, X., Chuprakov, D., Kresse, O. et al. 2018. Hydraulic Fracture-Height Containment by Permeable Weak Bedding Interfaces. Geophysics 83 (3): 137–52. https://doi.org/10.1190/geo2017-0048.1.
Wu, K. and Olson, J. E. 2015. Simultaneous Multi-Fracture Treatments: Fully Coupled Fluid Flow and Fracture Mechanics for Horizontal Wells. SPE J. 20 (2): 337–346. SPE-167626-PA. https://doi.org/10.2118/167626-PA.
Yue, K. 2015. Study of Brittle/Ductile Layering Effect on Fracture Geometry and Mechanical Behavior by Tri-Axial Testing. Master’s thesis, University of Texas at Austin, Austin, Texas (May 2015).
Yue, K., Olson, J. E., and Schultz, R. A. 2016. Calibration of Stiffness and Strength for Layered Rocks. Presented at the 50th US Rock Mechanics/Geomechanics Symposium, Houston, 26–29 June. ARMA-2016-460.
Yue, K. 2017. Height Containment of Hydraulic Fractures in Layered Reservoirs. PhD dissertation, University of Texas at Austin,Austin, Texas (August 2017).
Zhang, X. and Jeffrey, R. G. 2006. Numerical Studies on Crack Problems in Three-Layered Elastic Media Using an Image Method. Int J Fract 139 (3–4): 477–493. https://doi.org/10.1007/s10704-006-0054-y.
Zhang, X., Jeffrey, R. G., and Thiercelin, M. 2007. Deflection and Propagation of Fluid-Driven Fractures at Frictional Bedding Interfaces: A Numerical Investigation. J Struct Geol 29 (3): 396–410. https://doi.org/10.1016/j.jsg.2006.09.013.
Zhang, X., Jeffrey, R. G., Bunger, A. P. et al. 2011. Initiation and Growth of a Hydraulic Fracture From a Circular Wellbore. Int J Rock Mech Min Sci 48 (6): 984–995. https://doi.org/10.1016/j.ijrmms.2011.06.005.