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PIERS Online
Vol. 4
No. 5
2008
pp: 551-555A Parallel, Fourier Finite-Element Formulation with an Iterative Solver for the Simulation of 3D LWD Measurements Acquired in Deviated WellsDavid Pardo, M. J. Nam, Carlos Torres-Verdin, and M. Paszynski doi:10.2529/PIERS071204150229 Downloads: 793 Abstract:We describe a new method to simulate resistivity measurements acquired with induction logging instruments in deviated wells. The method combines: (1) a highly efficient iterative solver, (2) a parallel implementation, (3) a Fourier Finite-Element (FFE) formulation in a non-orthogonal system of coordinates, and (4) a 2D hp-Finite Element (FE) goal-oriented self-adaptive grid-refinement strategy.We apply the new method to simulate measurements acquired with a logging-while-drilling (LWD) instrument operating at 1.75 MHz in a 55-degree deviated well. Numerical results confirm the high-accuracy and efficiency of the method. An error level below 1% is achieved in reservoirs with high-contrast in electrical resistivity using an average CPU time of 1-3 minutes per logging position. References:1. Avdeev, D. B., A. V. Kuvshinov, O. V. Pankratov, and G. A. Newman, "Three-dimensional induction logging problems, part 1: An integral equation solution and model comparisons," Geophysics, Vol. 67, 413-426, 2002. 2. Davydycheva, S., V. Druskin, and T. Habashy, "An efficient finite-difference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media," Geophysics, Vol. 68, 1525-1536, 2003. 3. Demkowicz, L., Computing with hp-adaptive Finite Elements, Volume I: One and Two Dimensional Elliptic and Maxwell Problems, Chapman and Hall, 2006. 4. Druskin, V. L., L. A. Knizhnerman, and P. Lee, "New spectral Lanczos decomposition method for induction modeling in arbitrary 3-D geometry," Geophysics, Vol. 64, 701-706, 1999. 5. http://graal.ens lyon.fr/MUMPS/, MUMPS: A Multifrontal Massively Parallel Sparse Direct Solver, 2008. 6. Lu, X. and D. L. Alumbaugh, "One-dimensional inversion of three-component induction logging in anisotropic media," SEG Expanded Abstract, Vol. 20, 376-380, 2001. 7. Newman, G. A. and D. L. Alumbaugh, "Three-dimensional induction logging problems, part 2: A finite-difference solution," Geophysics, Vol. 67, 484-491, 2002. 8. Pardo, D., V. Calo, C. Torres-Verdin, and M. J. Nam, "Fourier series expansion in a nonorthogonal system of coordinates for the simulation of 3D DC borehole resistivity measurements," Computer Methods in Applied Mechanics and Engineering, Vol. 197, No. 1-3, 1906-1925, April, 2008. 9. Pardo, D., L. Demkowicz, C. Torres-Verdin, and M. Paszynski, "Simulation of resistivity logging-while-drilling (LWD) measurements using a self-adaptive goal-oriented hp-finite element method," SIAM Journal on Applied Mathematics, Vol. 66, No. 6, 2085-2106, 2006. 10. "A goal oriented hp-adaptive finite element strategy with electromagnetic applications, Part II: electrodynamics," Computer Methods in Applied Mechanics and Engineering, Vol. 196, 3585-3597, 2007. 11. Pardo, D., C. Torres-Verdin, and L. Demkowicz, "Feasibility study for two-dimensional frequency dependent electromagnetic sensing through casing," Geophysics, Vol. 72, No. 3, F111-F118, 2007. 12. Pardo, D., C. Torres-Verdin, M. J. Nam, M. Paszynski, and V. Calo, "Fourier series expansion in a non-orthogonal system of coordinates for the simulation of 3D AC borehole resistivity measurements," Computer Methods in Applied Mechanics and Engineering, March, 2008. in press, 10.1016/j.cma.2008.03.007 13. Wang, T. and J. Signorelli, "Finite-difference modeling of electromagnetic tool response for logging while drilling," Geophysics, Vol. 69, 152-160, 2004. |
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