Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
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Simulation of eccentricity effects on short- and long-normal logging measurements using a Fourier-hp-finite-element method

Self-adaptive hp 유한요소법을 이용한 단.장노말 전기검층에서 손데의 편향 효과 수치모델링

  • 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))
  • 남명진 (한국지질자원연구원 지구환경연구본부) ;
  • ;
  • ;
  • 황세호 (한국지질자원연구원 지구환경연구본부) ;
  • 박권규 (한국지질자원연구원 지구환경연구본부) ;
  • 이창현 (한국지질자원연구원 지구환경연구본부)
  • Received : 2009.11.10
  • Accepted : 2009.12.09
  • Published : 2010.02.18
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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.

전기검층은 지층의 전기비저항을 측정하는 물리검층법으로 전극배열에 따른 전기비저항 변화에서 지층내의 수포화도를 평가하는데 이용된다. 전기검층은 시추공 효과 및 인접한 지층의 두께와 전기비저항 들에 의해 많은 영향을 받는다. 이러한 시추공 효과 및 인접 지층의 영향은 시추공 내에서 전기검층 손데가 중심으로부터 편향되었을 때 더 커진다. 노말검층 손데가 시추공 내에서 편향되었을 때, 단노말과 장노말 검층자료의 정확한 해석의 기초를 마련하기 위해 검층손데의 편향에 의한 전기검층 자료의 왜곡을 수치모델링을 이용하여 분석하였다. 이를 위해 노말검층 손데의 편향으로 인한 3차원적 기하학적 구조를 단순화 시킬 수 있는 새로운 좌표 체계를 제안하고, 이 좌표계에서 Fourier 급수 전개(Fourier series expansion)를 수행하였다. 여러 개의 서로 연동된 이차원 문제들을 풀기 위하여 이차원 hp goal-oriented high-order self-adaptive hp (h는 셀의 크기, p는 근사 차수를 의미) 유한요소법에 기초한 알고리즘을 적용하였다. 이 알고리즘은 모델링 영역 내에서 자동적으로 각 격자 셀에서의 h와 p를 바꿔가면서 최적의 격자를 생생하여 원하는 정밀도의 해를 도출할 수 있다. 수치모델링 결과, 이 연구에서 제안한 알고리즘으로 정확하고 신뢰성 있는 해를 얻을 수 있었다. 검층손데의 편향 영향은 시추공경이나 시추공 이수의 전기비저항이 큰 경우, 그리고 지층의 전기비저항이 낮은 경우에 큰 것을 알 수 있었다.

Keywords

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