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Linear hydraulic fracture with tortuosity: Conservation laws and fluid extraction

Introduction Modelling process Conservation laws Fluid extraction Conclusion. Linear hydraulic fracture with tortuosity: Conservation laws and fluid extraction. M. R. R. Kgatle and D. P. Mason School of computational and applied mathematics University of the Witwatersrand.

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Linear hydraulic fracture with tortuosity: Conservation laws and fluid extraction

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  1. Introduction Modelling process Conservation laws Fluid extraction Conclusion Linear hydraulic fracture with tortuosity: Conservation laws and fluid extraction M. R. R. Kgatle and D. P. Mason School of computational and applied mathematics University of the Witwatersrand Energy Postgraduate Conference 2013

  2. Introduction Modelling process Conservation laws Fluid extraction Conclusion Introduction • Hydraulic fracturing Natural fractures and man-made fractures

  3. Introduction Modelling process Conservation laws Fluid extraction Conclusion ooo Modeling process • Problem description Propagation of a pre-existing hydraulic fracture with length x=L(t) and width z=H at the fracture entry

  4. Modelling formulation Introduction Modelling process Conservation laws Fluid extraction Conclusion ooo

  5. Introduction Modelling process Conservation laws Fluid extraction Conclusion ooo

  6. Introduction Modelling process Conservation laws Fluid extraction Conclusion ooo Conservation laws

  7. Introduction Modelling process Conservation laws Fluid extraction Conclusion ooo

  8. Introduction Modelling process Conservation laws Fluid extraction Conclusion ooo • Interpretation of working conditions obtained from conservation laws Obtained from conservation laws Working conditions curves

  9. Introduction Modelling process Conservation lawsFluid extraction Conclusion ooo Fluid extraction

  10. Introduction Modelling process Conservation lawsFluid extraction Conclusion ooo Fluid extraction

  11. Introduction Modelling process Conservation lawsFluid extraction Conclusion ooo

  12. Introduction Modelling process Conservation lawsFluid extraction Conclusion ooo

  13. Introduction Modelling process Conservation lawsFluid extraction Conclusion ooo

  14. Introduction Modelling process Conservation lawsFluid extractionConclusion Conclusion • Conservation laws suggest parameters that lead to analytical solutions. • A new solution is obtained. • Fluid always flows out of the closed fracture at the fracture entry. • No pockets of fluid left in the fracture. • Analysis of flux shows that there’s fluid flow in the forward and backward directions during fluid extraction. • Maximum rate for fluid extraction is the limiting working condition.

  15. Acknowledgements Gratitude to NRF, SANHARP, for funding and to the School of Computational and Applied Mathematics, Wits University, for academic support. References • A. D. Fitt, A. D. Kelly and C. P. Please. Crack propagation models for rock fracture in a geothermal energy reservoir. SIAM J Appl Math, 55: 1592-1608, 1995. 2. A. P. Oron and B. Berkowitz. Flow in rock fractures: The local cubic law assumption re-examined. Water Resources Research, 34: 2811-2825, 1998. 3. A. G. Fareo and D. P. Mason. Group invariant solutions for a pre-existing fluid-driven fracture in permeable rock. Nonlinear Analysis: Real World Applications, 12: 767-779, 2011.

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