Abstract
A numerical modeling framework is described that is able to calculate the coupled processes of fluid flow, geomechanics, and rock failure for application to general engineering problems related to reservoir stimulation, including hydraulic fracturing and shear stimulation. The numerical formulation employs the use of an embedded fracture modeling approach, which provides several advantages over more traditional methods in terms of computational complexity and efficiency. Specifically, the embedded fracture modeling strategy avoids the usual requirement that the discretization of the fracture domain conforms to the discretization of the rock volume surrounding the fractures. As fluid is exchanged between the two domains, conservation of mass is guaranteed through a coupling term that appears as a simple source term in the governing mass balance equations. In this manner, as new tensile fractures nucleate and propagate subject to mechanical effects, numerical complexities associated with the introduction of new fracture control volumes are largely negated. In addition, the ability to discretize the fractures and surrounding rock volume independently provides the freedom to choose an acceptable level of discretization for each domain separately. Three numerical examples were performed to demonstrate the utility of the embedded fracture model for application to problems involving fluid flow, mechanical deformation, and rock failure. The results of the numerical examples confirm that the embedded fracture model was able to capture accurately the complex and nonlinear evolution of reservoir permeability as new fractures propagate through the reservoir and as fractures fail in shear.
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References
Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Khalid Aziz and Anonin Settari (1979)
Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. 2nd edn. Wiley (2006)
Crouch, S.L., Starfield, A.M.: Boundary Element Methods in Solid Mechanics. Allen and Unwin, London (1983)
Ding, D.Y., Wu, Y.S., Jeannin, L.: Efficient simulation of hydraulic fractured wells in unconventional reservoirs. J. Pet. Sci. Eng. 122, 631–642 (2014)
Economides, M.J., Nolte, K.G.: Reservoir Stimulation. 3rd edn. Wiley (2000)
Geertsma, J., de Klerk, F.: A rapid method of predicting width and extent of hydraulically induced fractures. SPE J. 21(12), 1571–1581 (1969)
Gidley, J.L., Holditch, S.A., Nierode, D.E., Veatch, Jr. R.W.: Recent advances in hydraulic fracturing. SPE Monogr. Ser. 12 (1990)
Gringarten, A.C., Ramey Jr. H.J., Raghavan, R.: Unsteady-state pressure distributions created by a well with a single infinite-conductivity vertical fracture. SPE J. 14(4), 347–360 (1974)
Hajibeygi, H., Karvounis, D., Jenny, P.: A hierarchical fracture model for the iterative multiscale finite volume method. J. Comp. Phys. 230(24), 8729–8743 (2011)
Horne, R.N.: Modern Well Test Analysis: A Computer-Aided Approach, 2nd edn. Petroway Inc., Palo Alto (1995)
Howard, G., Fast, C.R.: Optimum fluid characteristics for fracture extension. Drill. Prod. Pract. 24, 261–270 (1957)
Hunsweck, M.J., Shen, Y., Lew, A.J.: A finite element approach to the simulation of hydraulic fractures with lag. Int. J. Numer. Anal. Meth. Geomech. 37, 993–1015 (2013)
Jaeger, J.C., Cook, N.G.W., Zimmerman, R.: Fundamentals of Rock Mechanics, 4th edn. Blackwell Publishing Ltd., Oxford (2007)
Karimi-Fard, M., Durlofsky, L., Aziz, K.: An efficient discrete-fracture model applicable for general purpose reservoir simulators. SPE J. 9(2), 249–262 (2004)
Karvounis, D.: Simulations of Enhanced Geothermal Systems with an Adaptive Hierarchical Fracture Representation. PhD dissertation, ETH Zurich, Zurich (2013)
Karvounis, D., Gischig, V., Wiemer, S.: EGS probabalistic seismic hazard assessment with 3-D discrete fracture modeling. In: Proceedings of the Thirty-Ninth Workshop on Geothermal Reservoir Engineering, Stanford (2014)
Kazemi, H.: Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. SPE J. 9(4), 451–462 (1969)
Kim, J., Tchelepi, H., Juanes, R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. SPE J. 16(2), 249–262 (2011)
Lee, S.H., Jensen, C.L., Lough, M.F.: Efficient finite-difference model for flow in a reservoir with multiple length-scale variations. SPE J. 5(3), 268–275 (2000)
Lee, H.S., Cho, T.F.: Hydraulic characteristics of rough fractures in linear flow under normal and shear load. Rock Mech. Rock Eng. 35(4), 299–318 (2002)
Li, L., Lee, S.H.: Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media. SPE Reserv. Eval. Eng. 11(4), 750–758 (2008)
McClure, M.W., Horne, R.N.: Investigation of injection-induced seismicity using a coupled fluid flow and rate/state friction model. Geophysics 76(6), 181–198 (2011)
McClure, M.W.: Modeling and characterization of hydraulic stimulation and induced seismicity in geothermal and shale gas reservoirs. PhD dissertation, Stanford University, Stanford (2012)
McClure, M.W., Horne, R.N.: Discrete Fracture Network Modeling of Hydraulic Stimulation: Coupling Flow and Geomechanics. SpringerBriefs in Earth Sciences, Springer (2013)
Moinfar, A., Varavei, A., Sepehrnoori, K., Johns, R.T.: Development of a novel and computationally efficient discrete-fracture model to study IOR processes in naturally fractured reservoirs. Paper SPE 154246 presented at the Eighteenth SPE Improved Oil Recovery Symposium, Tulsa (2012)
Moinfar, A., Varavei, A., Sepehrnoori, K., Johns, R.T.: Development of a coupled dual continuum and discrete fracture model for the simulation of unconventional reservoirs. Paper SPE 163647 presented at the SPE Reservoir Simulation Symposium, The Woodlands (2013)
Norbeck, J., Huang, H., Podgorney, R., Horne, R.: An integrated discrete fracture model for description of dynamic behavior in fractured reservoirs. In: Proceedings of the 39th Workshop on Geothermal Reservoir Engineering, Stanford (2014)
Norbeck, J.H., Horne, R.N.: An embedded fracture modeling framework for fluid flow, geomechanics, and fracture propagation. In: Proceedings of the International Conference on Discrete Fracture Network Engineering, Vancouver, British Columbia, Canada (2014)
Norbeck, J., Horne, R.: Injection-triggered seismicity: An investigation of porothermoelastic effects using a rate-and-state earthquake model. In: Proceedings of the 40th Workshop on Geothermal Reservoir Engineering, Stanford (2015)
Olson, J.E.: Fracture aperture, length and pattern geometry development under biaxial loading: a numerical study with applications to natural, cross-jointed systems. In: Lewis, H., Couples, G.D (eds.) The Relationship between Damage and Localization, pp 123–142. Geological Society, London, Special Publications, The Geological Society of London (2007)
Peaceman, D.W.: Interpretation of well-block pressures in numerical reservoir simulation. SPE J. 23(3), 531–543 (1978)
Pluimers, S.: Hierarchical Fracture Modeling Approach. MSc thesis, Delft University of Technology, Delft (2015)
Rangarajan, R., Chiaramonte, M.M., Hunsweck, M.J., Shen, Y., Lew, A.J.: Simulating curvilinear crack propagation in two dimensions with universal meshes. Int. J. Numer. Meth. Eng. (2014)
Segall, P.: Earthquake and Volcano Deformation. Princeton University Press, Princeton (2010)
Shewchuk, J.R.: Triangle: Engineering a 2D quality mesh and delaunay triangulator. Lect. Notes Comput. Sci. 1148, 203–222 (1996)
Shiozawa, S., McClure, M.W.: EGS designs with horizontal wells, multiple stages, and proppant. In: Proceedings of the 39th Workshop on Geothermal Reservoir Engineering, Stanford (2014)
Shou, K.J., Crouch, S.L.: A higher order displacement discontinuity method for analysis of crack problems. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 32(1), 49–55 (1995)
Snow, D.T.: A parallel plate model of fractured permeable media. PhD dissertation, University of California, Berkeley (1965)
Valko, P., Economides, M.J.: Hydraulic Fracture Mechanics. Wiley, Chichester (1995)
Vermylen, J.P., Zoback, M.D.: Hydraulic fracturing, microseismic magnitudes, and stress evolution in the Barnett shale, Texas, USA. Paper SPE 140507 presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands (2011)
Vinsome, P.K., Westerveld, J.: A simple method for predicting cap and base rock heat losses in thermal reservoir simulators. J. Can. Pet. Tech. 19(3), 87–90 (1980)
Warren, J.E., Root, P.J.: The behavior of naturally fractured reservoirs. SPE J. 3(3), 245–255 (1963)
Willis-Richards, J., Watanbe, K., Takahashi, H.: Progress towards a stochastic rock mechanics model of engineered geothermal systems. J. Geophys. Res. 101(B8), 17481–17496 (1996)
Zoback, M.D.: Reservoir Geomechanics. Cambridge University Press, Cambridge (2007)
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Norbeck, J.H., McClure, M.W., Lo, J.W. et al. An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation. Comput Geosci 20, 1–18 (2016). https://doi.org/10.1007/s10596-015-9543-2
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DOI: https://doi.org/10.1007/s10596-015-9543-2
Keywords
- Embedded fracture modeling
- Reservoir geomechanics
- Hydraulic fracture
- Shear stimulation
- Fractured reservoir simulation