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Tube Wave Reflection from Borehole Fractures: An Analytical and Finite-Difference Study

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15 diapositives · 293 Views · Jul 14, 2014

This paper by Andrey Ponomarenko explores the importance of estimating the effective width of fractures within boreholes and how this can be achieved through the reflection coefficient of tube waves. Utilizing both analytical models and finite-difference (FD) simulations, the study examines the interaction of tube waves with an infinite horizontal fracture. Results show excellent agreement between analytical and FD methods, demonstrating the potential for analytical formulas to estimate fracture system parameters efficiently and enhance well productivity.

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Tube Wave Reflection from Borehole Fractures: An Analytical and Finite-Difference Study
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  1. The tube wave reflection from borehole fracture Author: Andrey Ponomarenko, laboratory for elastic media dynamics Faculty of Physics Saint-Petersburg State University JASS 2008

  2. The effective width of the fracture is important to be estimated. Why? • How can we obtain knowledge about it??? • from the reflection coefficient of the tube wave!

  3. the analytical model considering calculation of the coefficients comparing results with FD modeling

  4. 1)The model of the tube and fracture • Fracture is infinite in the horizontal plane and perpendicular to the borehole • Fracture z- coordinate is z=0

  5. 2) Symmetrical guided wave in the fracture can be obtained from the dispersion equation for the slab of fluid bounded on each side by a semi-infinite elastic media

  6. Fracture is infinite in the horizontal plane and perpendicular to the borehole • Fracture z- coordinate is z=0

  7. 3) equations: • Continuity of pressure in the “cylinder”: • Continuity of liquid flow through the “cylinder”: • Euler equation for non-viscous liquid:

  8. 4)Equations for calculations and obtained results

  9. Finite-difference model • The model have cylindrical symmetry • The value of the grid steps is less than the smallest ratio

  10. Finite-difference seismogram

  11. Comparison of the finite-difference modeling results and analytic approach (task I) Excellent agreement between analytic approach and finite-difference modeling black – FD, red - analytic

  12. Comparison of the finite-difference modeling results and analytical approach (task II) • Another tube radius (0.031 m), other media parameters, different fractures • The discrepancy is increasing but not too much!

  13. Conclusions • The analytical formula of the wave coefficients werederived • We can obtain better physical insight into the interaction of the tube wave with the fracture • The analytic approach were made which showed excellent agreement with finite-difference modeling both for the absolute values of reflection coefficient and for the seismogram • It is clear that we can use analytical formula for the cases with wide range of models • It is possible to use obtained formula for the estimating of the well-fracture's system parameters and, consequently, the well productivity. And it requests too less time than the time of finite-difference code's similar calculations.

  14. References • S.Kostek, D.Johnson, K.Winkler, B.Hornby. “The interaction of tube wave with borehole fracture”. Geophys.vol.63,#3, 809-815 • B.Plyushchnkov, V. Turchaninov. “Finite-difference code for acoustic logging modeling. Operation instructions”. KIAM RAS. Moscow, 2003 • S.Ziatdinov, A.Bakulin, B.Kashtan. “Tube waves from a horizontal fluid-filled fracture of a finite radius”. SEG New Orleans 2006 Annual Meeting abstracts.

  15. Thank you for attention!