The tube wave reflection from borehole fracture

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!