Browse > Article

Simulation of eccentricity effects on short- and long-normal logging measurements using a Fourier-hp-finite-element method  

Nam, Myung-Jin (Korea Institute of Geoscience and Mineral Resources (KIGAM))
Pardo, David (IKERBASQUE, Basque Foundation for Science and BCAM - Basque Centre for Applied Mathematics)
Torres-Verdin, Carlos (Department of Petroleum and Geosystems Engineering, The University of Texas)
Hwang, Se-Ho (Korea Institute of Geoscience and Mineral Resources (KIGAM))
Park, Kwon-Gyu (Korea Institute of Geoscience and Mineral Resources (KIGAM))
Lee, Chang-Hyun (Korea Institute of Geoscience and Mineral Resources (KIGAM))
Publication Information
Geophysics and Geophysical Exploration / v.13, no.1, 2010 , pp. 118-127 More about this Journal
Abstract
Resistivity logging instruments are designed to measure the electrical resistivity of a formation, and this can be directly interpreted to provide a water-saturation profile. However, resistivity logs are sensitive to borehole and shoulder-bed effects, which often result in misinterpretation of the results. These effects are emphasised more in the presence of tool eccentricity. For precise interpretation of short- and long-normal logging measurements in the presence of tool eccentricity, we simulate and analyse eccentricity effects by combining the use of a Fourier series expansion in a new system of coordinates with a 2D goal-oriented high-order self-adaptive hp finite-element refinement strategy, where h denotes the element size and p the polynomial order of approximation within each element. The algorithm automatically performs local mesh refinement to construct an optimal grid for the problem under consideration. In addition, the proper combination of h and p refinements produces highly accurate simulations even in the presence of high electrical resistivity contrasts. Numerical results demonstrate that our algorithm provides highly accurate and reliable simulation results. Eccentricity effects are more noticeable when the borehole is large or resistive, or when the formation is highly conductive.
Keywords
eccentricity; finite-element method; hp; normal logging; self-adaptivity;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Demkowicz, L., 2006, Computing with hp-adaptive finite elements. Volume I: One and two dimensional elliptic and Maxwell problems: Chapman and Hall.
2 Doll, H. G., 1951, The laterolog: A new resistivity logging method with electrodes using an automatic focusing system: Petroleum Transactions of the AIME, 192, 305–316.
3 Heuveline, V., and Rannacher, R., 2003, Duality-based adaptivity in the hp-finite element method: Journal of Numerical Mathematics, 11, 95–113. doi:10.1515/156939503766614126
4 Oden, J. T., and Prudhomme, S., 2001, Goal-oriented error estimation and adaptivity for the finite element method: Computers & Mathematics with Applications, 41, 735–756. doi:10.1016/S0898-1221(00)00317-5
5 Pardo, D., Demkowicz, L., Torres-Verdín, C., and Paszynski, D., 2006a, Simulation of resistivity logging-while-drilling (LWD) measurements using a self-adaptive goal-oriented hp-finite element method: SIAM Journal on Applied Mathematics, 66, 2085–2106. doi:10.1137/050631732
6 Pardo, D., Torres-Verdín, C., and Demkowicz, L., 2007, Feasibility study for two dimensional frequency dependent electromagnetic sensing through casing: Geophysics, 72, F111–F118. doi:10.1190/1.2712058
7 Pardo, D., Torres-Verdín, C., Nam, M. J., Paszynski, M., and Calo, V. M., 2008, Fourier series expansion in a non-orthogonal system of coordinates for the simulation of 3D alternating current borehole resistivity measurements: Computer Methods in Applied Mechanics and Engineering, 197, 3836–3849. doi:10.1016/j.cma.2008.03.007
8 Tsang, L., Chan, A., and Gianzero, S., 1984, Solution of the fundamental problem of resistivity logging with a hybrid method: Geophysics, 40, 1596–1604.
9 Howard, A. Q., and Chew, W. C., 1992, Electromagnetic borehole fields in a layered, dipping-bed environment with invasion: Geophysics, 57, 451–465. doi:10.1190/1.1443259
10 Pirson, S. J., 1963, Handbook of well log analysis for oil and gas formation evaluation: Prentice Hall Inc.
11 Paraschivoiu, M., and Patera, A. T., 1998,Ahierarchical duality approach to bounds for the outputs of partial differential equations: Computer Methods in Applied Mechanics and Engineering, 158, 389–407. doi:10.1016/S0045-7825(99)00270-4
12 Zhang, L., Poulton, M. M., and Wang, T., 2002, Borehole electrical resistivity modeling using neural networks: Geophysics, 67, 1790–1797. doi:10.1190/1.1527079
13 Pardo, D., Demkowicz, L., Torres-Verdín, C., and Tabarovsky, L., 2006b, A goal-oriented hp-adaptive finite element method with electromagnetic applications. Part I: electrostatics: International Journal for Numerical Methods in Engineering, 65, 1269–1309. doi:10.1002/nme.1488
14 Anon., 1969, Resistivity departure curves, Schlumberger Document No. 3: Schlumberger Well Surveying Corporation.
15 Doll, H. G., 1953, The microlaterolog: Petroleum Transactions of the AIME, 198, 17–31.
16 Hakvoort, R. G., Fabris, A., Frenkel, M. A., Koelman, J. M. V. A., and Loermans, A. M., 1998, Field measurements and inversion results of the high-definition lateral log: 39th Ann. Log. Symp., Soc. Prof. Log Analysts, paper C.
17 Tabarovsky, L. A., Goldman, M. M., Rabinovich, M. B., and Strack, K.-M., 1996, 2.5-D modeling in electromagnetic methods of geophysics: Journal of Applied Geophysics, 35, 261–284. doi:10.1016/0926-9851(96)00025-0
18 Tamarchenko, T., and Druskin, V., 1993, Fast modeling of induction and resistivity logging in the model with mixed boundaries: 34th Ann. Log. Symp., Soc. Prof. Well Log Analysts, paper GG.
19 Anon., 1949, Resistivity departure curves, Schlumberger Document No. 3: Schlumberger Well Surveying Corporation.
20 Prudhomme, S., and Oden, J. T., 1999, On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors: Computer Methods in Applied Mechanics and Engineering, 176, 313–331. doi:10.1016/S0045-7825(98)00343-0
21 Nam, M. J., Pardo, D., and Torres-Verdín, C., 2009, Simulation of DC dual-laterolog measurements in complex formations: A Fourier-series approach with nonorthogonal coordinates and self-adapting finite elements: Geophysics, 74, E31–E43. doi:10.1190/1.3000681
22 Tamarchenko, T., Frenkel, M., and Mezzatesta, A., 1999, Three-dimensional modeling of resistivity devices. In M. Oristaglio, and B. Spies, (Eds), Three-dimensional electromagnetic, Soc. Expl. Geophys., 600–610.