You are here
Home > BLOG > An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation

An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation

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.

7 Discussion and concluding remarks

In this work, we developed a novel numerical modeling framework based on the embedded fracture modeling (EFM) approach as an effective technique to model reservoir stimulation processes such as hydraulic fracturing and shear stimulation. The EFM approach was implemented in a reservoir model that couples fluid flow, mechanical deformation, and rock failure processes. In order to verify the accuracy of the embedded fracture model, the present model was compared to a more traditional discrete fracture model (DFM) in three separate numerical examples. In each example, the EFM performed rermarkably well and yielded results that matched the DFM to within an acceptable margin of error.

In this paper, we demonstrated that the EFM is extremely well-suited for fracture propagation problems. In the EFM framework, newly formed fracture control volumes can be integrated into the numerical model with relative ease. The ability to discretize the fracture and matrix rock domains separately ensures that fractures are able to propagate without the numerical constraints associated with traditional approaches that employ conforming meshes. We showed that it is possible to coarsen the matrix discretization and still obtain a reasonable degree of accuracy using the EFM approach. Once a fracture discretization has been defined for a DFM, however, it is very difficult to arbitrarily coarsen the matrix discretization in the same fashion that is possible with EFM. This has important implications when moving towards increased problem complexity, for instance, when considering interaction between propagating fractures and natural fractures, branching and curving fractures, or three dimensions. Issues associated with numerical discretization in these complex scenarios can set practical limitations on the utility of reservoir modeling, and are largely overcome in the EFM framework.

Two approximate models were also developed and compared to both EFM and DFM. These models are referred to as the one-dimensional leakoff and zero leakoff approximation models, and were observed to provide useful constraints on reservoir stimulation behavior at significantly reduced computational effort. For very low matrix permeabilities, all models were observed to provide similar results. As matrix permeability increased, the two approximate models diverged from the EFM and DFM models. Further investigation must be performed in order to better classify the range of geologic and operational parameters over which each of the models retain a high level of accuracy.

It has become clear that geomechanics can play an important role in many different facets of reservoir engineering practice. For example, mechanisms that enable permeability creation during hydraulic fracturing are controlled largely by mechanical effects. Shear slip events commonly observed during microseismic monitoring operations of fluid injection treatments help reservoir engineers define the stimulated region. The reservoir model described in this paper can be applied in practical settings to help design and optimize reservoir management strategies or in research settings to better understand fundamental reservoir processes.

Acknowledgments We thank the industrial affiliates of the Stan- ford Center for Induced and Triggered Seismicity for partial financial support of this work. The financial support of the Cockrell School of Engineering at The University of Texas at Austin is also gratefully acknowledged. The numerical simulations were performed at the Stanford Center for Computational Earth and Environmental Science (CEES) using their high performance computing (HPC) resources.

References

  • 1. Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Khalid Aziz and Anonin Settari (1979)
  • 2. Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. 2nd edn. Wiley (2006)
  • 3. Crouch, S.L., Starfield, A.M.: Boundary Element Methods in Solid Mechanics. Allen and Unwin, London (1983)
  • 4. 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)
  • 5. Economides, M.J., Nolte, K.G.: Reservoir Stimulation. 3rd edn. Wiley (2000)
  • 6. Geertsma, J., de Klerk, F.: A rapid method of predicting width and extent of hydraulically induced fractures. SPE J. 21(12), 1571–1581 (1969)
  • 7. Gidley, J.L., Holditch, S.A., Nierode, D.E., Veatch Jr. R.W.: Recent advances in hydraulic fracturing. SPE Monogr. Ser. 12 (1990)
  • 8. 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)
  • 9. 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)
  • 10. Horne, R.N. Modern Well Test Analysis: A Computer-Aided Approach, 2nd edn. Petroway Inc., Palo Alto (1995)
  • 11. Howard, G., Fast, C.R.: Optimum fluid characteristics for fracture extension. Drill. Prod. Pract. 24, 261–270 (1957)
  • 12. 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)
  • 13. Jaeger, J.C., Cook, N.G.W., Zimmerman, R. Fundamentals of Rock Mechanics, 4th edn. Blackwell Publishing Ltd., Oxford (2007)
  • 14. 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)
  • 15. Karvounis, D.: Simulations of Enhanced Geothermal Systems with an Adaptive Hierarchical Fracture Representation. PhD dissertation, ETH Zurich, Zurich (2013)
  • 16. Karvounis, D., Gischig, V., Wiemer, S.: EGS probabalistic seismic hazard assessment with 3-D discrete fracture modeling. In: Pro- ceedings of the Thirty-Ninth Workshop on Geothermal Reservoir Engineering, Stanford (2014)
  • 17. Kazemi, H.: Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. SPE J. 9(4), 451–462 (1969)
  • 18. 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)
  • 19. 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)
  • 20. 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)
  • 21. 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)
  • 22. 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)
  • 23. McClure, M.W.: Modeling and characterization of hydraulic stimulation and induced seismicity in geothermal and shale gas reservoirs. PhD dissertation, Stanford University, Stanford (2012)
  • 24. McClure, M.W., Horne, R.N.: Discrete Fracture Network Modeling of Hydraulic Stimulation: Coupling Flow and Geomechanics. SpringerBriefs in Earth Sciences, Springer (2013)
  • 25. 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)
  • 26. 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)
  • 27. 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)
  • 28. 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)
  • 29. 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)
  • 30. 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)
  • 31. Peaceman, D.W.: Interpretation of well-block pressures in numerical reservoir simulation. SPE J. 23(3), 531–543 (1978)
  • 32. Pluimers, S.: Hierarchical Fracture Modeling Approach. MSc thesis, Delft University of Technology, Delft (2015)
  • 33. 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)
  • 34. Segall, P.: Earthquake and Volcano Deformation. Princeton University Press, Princeton (2010)
  • 35. Shewchuk, J.R.: Triangle: Engineering a 2D quality mesh and delaunay triangulator. Lect. Notes Comput. Sci. 1148, 203–222 (1996)
  • 36. Shiozawa, S., McClure, M.W.: EGS designs with horizontal wells, multiple stages, and proppant. In: Proceedings of the 39th Work- shop on Geothermal Reservoir Engineering, Stanford (2014)
  • 37. 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)
  • 38. Snow, D.T.: A parallel plate model of fractured permeable media. PhD dissertation, University of California, Berkeley (1965)
  • 39. Valko, P., Economides, M.J.: Hydraulic Fracture Mechanics. Wiley, Chichester (1995)
  • 40. Vermylen, J.P., Zoback, M.D.: Hydraulic fracturing, microseis- mic 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)
  • 41. 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)
  • 42. Warren, J.E., Root, P.J.: The behavior of naturally fractured reservoirs. SPE J. 3(3), 245–255 (1963)
  • 43. 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)
  • 44. Zoback, M.D.: Reservoir Geomechanics. Cambridge University Press, Cambridge (2007)

Jack H. Norbeck
[email protected]

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http:// creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Emanuel Martin
Emanuel Martin is a Petroleum Engineer graduate from the Faculty of Engineering and a musician educate in the Arts Faculty at National University of Cuyo. In an independent way he’s researching about shale gas & tight oil and building this website to spread the scientist knowledge of the shale industry.
http://www.allaboutshale.com

Leave a Reply

4 + twenty =

Top