Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
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Suggestion of the Modified Archie's Formula for Calculating Water Saturation of Clean Sandstone and Carbonate Rocks

청결 사암 및 탄산염암의 물 포화도 산출을 위한 수정 Archie 경험식의 제안

  • Lee, Sang-Hee (Energy and Mineral Resources Dept., Dong-A University) ;
  • Ko, Eun-Ji (Dongnam Regional Infrastructure Tech. Management Center) ;
  • Kim, Jin-Hoo (Energy and Mineral Resources Dept., Dong-A University)
  • 이상희 (동아대학교 에너지.자원공학과) ;
  • 고은지 (동남권 건설교통기술 지역거점센터) ;
  • 김진후 (동아대학교 에너지.자원공학과)
  • Received : 2015.07.23
  • Accepted : 2015.08.24
  • Published : 2015.08.31
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Abstract

The water saturation ($S_w$), which is very important to estimate hydrocarbon reserves in the reservoir, has been determined from resistivity index (RI) by using the Archie's formula. However, in many cases, it has been reported that n is not constant for a given formation and it could be varied with water saturation. In addition, it frequently happens that the line obtained by linear regression analysis on log-log scale does not pass through the origin. In order to overcome these drawbacks, we suggested a modified Archie's formula, which can handle almost all the RI vs. $S_w$ cross-plots whether the trend is straight or curved and whether it passes through the origin or not. We also demonstrated that how to determine conductivity exponent ${\mu}$, critical water saturation $S_c$, and saturation distribution factor b in the laboratory to use the modified Archie's formula. Since the modified Archie's formula takes into account pore structure, pore water distribution, and wettability of reservoir such as clean sandstone and carbonate rocks, it might improve field applicability.

저류층의 탄화수소 매장량 평가에 있어서 매우 중요한 물 포화도($S_w$)는 Archie의 경험식을 이용하여 전기비저항지수(RI )로부터 구할 수 있다. 그러나 많은 경우, Archie 경험식에 사용되는 포화도 지수 n은 상수가 아니며, 물 포화도에 따라 변하는 것으로 알려져 있다. 또한 RI vs. $S_w$ 자료를 log-log 축에서 회귀분석하면 원점을 지나지 않는 경우도 흔히 발생한다. 본 연구에서는 이러한 단점을 극복하고자 수정 Archie 경험식을 제안하였는데, 이 식은 RI vs. $S_w$ 대비도표의 추세가 직선이든 곡선이든, 원점을 지나든 아니든 모두 표현할 수 있는 장점을 갖는다. 수정 Archie 경험식을 사용하기 위해서는 전도성 지수 ${\mu}$, 임계 물 포화도 $S_c$, 포화 분포 계수 b 등의 계수를 결정해야 하는데, 이들 계수를 실내실험을 통하여 결정하는 방법을 제시하였다. 수정 Archie 경험식은 청결 사암 및 탄산염암 등 저류암의 공극 구조, 공극수 분포, 습윤성 등을 반영할 수 있어 현장 적용성을 높일 수 있을 것으로 생각된다.

Keywords

References

  1. Anderson, W. G., 1986, Wettability literature survey-Part 3: The effects of wettability on the electrical properties of porous media, Journal of Petroleum Technology, 1371-1377.
  2. Ara, T. S., Talabani, S., Vaziri, H. H., and Islam, M. R., 2001, In-depth investigation of the validity of the Archie equation in carbonate rocks, SPE 67204.
  3. Archie, G. E., 1942, The electrical resistivity log as an aid in determining some reservoir characteristics, Trans. AIME, 146, 54-62. https://doi.org/10.2118/942054-G
  4. Galiuk, H. S., Saadat, K., and Kazemzadeh, E., 2011, A case study of saturation exponent measurement on some carbonate cores at full reservoir conditions, International Symposium of the Society of Core Analysts held in Austin, Texas, U.S.A., 18-21 September, 2011, SCA2011-42
  5. Givens, W. W., 1986, Formation factor, resistivity index, and related equations based upon a Conductive Rock Matrix Model (CRMM), Trans. SPWLA 27th Annual Logging Symposium, Paper P.
  6. Grattoni, C. A., and Dawe, R. A., 1995, Influence of fluid distribution upon electrical resistivity of partially saturated media, SPWLA 36th Annual Logging Symposium, Paris, France, June 26-29, 1995.
  7. Grattoni, C. A., and Dawe, R. A., 1996, Electrical resistivity and fluid distribution of coexisting immiscible phases, SCA Conference, Paper No. 9625.
  8. Jing, X. D., and Archer, J. S., 1991, Special core analysis considerations in the determination of electrical properties of shaly rocks at reservoir conditions, in Worthington, P. F., and Longeron, D., eds., Advances in core evaluation II reservoir appraisal, Gordon and Breach Science Publishers, Philadelphia, pp. 309-330.
  9. Keller, G. V., 1953, Effect of wettability on the electrical resistivity of sand, Oil and Gas Journal, 51, 62-65.
  10. Koerperic, E. A., 1975, Utilization of Waxman-Smits equations for determining oil saturation in a low-salinity, shaly sand reservoir, Journal Petroleum Technology, 27, 1204-1208. https://doi.org/10.2118/5038-PA
  11. Kumar, M., Senden, T. J., Sheppard, A. P., Arns, C. H., and Knackstedt, M. A., 2011, Probing the Archie's exponent under variable saturation conditions, Petrophysics, 52, pp. 124-134.
  12. Lee, S. K., and Lee, T. J., 2008, Electrical resistivity versus water contents of core samples from a geothermal borehole in Pohang, Korea, Journal of the Korean Society for Geosystem Engineering, 45, 526-535.
  13. Lee, S. K., and Lee, T. J., 2009a, Characteristics of electrical resistivity of cylindrical cement core with respect to the conductivity and contents of pore water, Journal of the Korean Society for Geosystem Engineering, 46, 553-562.
  14. Lee, S. K., and Lee, T. J., 2009b, Electrical resistivity of cylindrical cement core with successive substitution by electrolyte of different conductivity, Jigu-Mulli-wa-Mulli-Tamsa, 12, 328-337.
  15. Lewis, M. G., Sharma, M. M., Dunlap, H. F., and Dorfman, M. H., 1988, Techniques for measuring the electrical properties of sandstone cores, The 63rd Annual Technical Conference and Exhibition, SPE No. 18178,
  16. Longeron, D. G., Argaud, M. J., and Feraud, J. P., 1989, Effect of overburden pressure and the nature and microscopic distribution of fluids on electrical properties of rock samples, SPE Formation Evaluation, 4, 194-202. https://doi.org/10.2118/15383-PA
  17. Longeron, D. G., 1990, Laboratory measurements of capillary and electrical properties of rock samples at reservoir conditions: Effect of some parameters, CSA Conference, Paper Number 9023.
  18. Montaron, B., 2007, A quantitative model for the effect of wettability on the conductivity of porous rocks, The 15th SPE Middle East Oil and Gas Show and Conference, Bahrain, SPE No. 105041.
  19. Park, S. G., 2004, Physical property factors controlling the electrical resistivity of subsurface, Mulli-Tamsa, 7, 130-135.
  20. Rasmus, J. C., 1986, A summary of the effects of various pore geometries and their wettabilities on measured and in-situ values of cementation and saturation exponents, Trans. SPWLA 27th Annual Logging Symposium, Paper PP.
  21. Sai, F. L., 2014, A study on the influence of water saturation on the resistivity index of water-wet porous sandstone, MSc. Thesis, Dong-A University.
  22. Schlumberger, 1991, Log Interpretation Chart, Schlumberger Educational Services, U.S.A., p. 5.
  23. Swanson, B. F., 1985, Microporosity in reservoir rocks-Its measurement and influence on electrical-resistivity, The Log Analyst, 26, 42-52.
  24. Worthington, P. F., and Pallatt, N., 1992, Effect of variable saturation exponent upon the evaluation of hydrocarbon saturation, SPE Formation Evaluation, SPE No. 20538. 331-336.