Characterization of the Relative Permeability Relationship Based on a Weibull Model

doi:10.11885/j.issn.1674-5086.2015.10.29.01

Abstract

Abstract: This study aims to solve the large inaccuracy in characterizing the relative permeability relationship at ultra low and ultra high water saturations in gas reservoirs. We conducted a thorough analysis of measured experimental data for relative permeabilities of rock core samples. We found a good linear relationship between the natural log of water and oil relative permeability ratio, ln(K_rw/K_ro), and double natural log of normalized water saturation, ln(ln 1/SS_wn). These two parameters fit a Weibull function. On this basis, a new equation for the relationship between relative permeability is proposed based on a Weibull model; this improves the fitting calculation for the relative permeability fractional flow equation. Compared to traditional methods used in reservoir physics, this method and the relative permeability fractional flow equation derived from it, can significantly improve the fitting accuracy for water production rate in the ultra low to medium water cutting period.

Key words: Weibull function, phase permeability characteristics, fractional flow equation, water content

CLC Number:

TE33

LIU Xilei. Characterization of the Relative Permeability Relationship Based on a Weibull Model[J]. 西南石油大学学报(自然科学版), 2017, 39(3): 141-146.

0
/ / Recommend

Add to citation manager EndNote|Ris|BibTeX

URL: http://journal15.magtechjournal.com/Jwk_xnzk/EN/10.11885/j.issn.1674-5086.2015.10.29.01

http://journal15.magtechjournal.com/Jwk_xnzk/EN/Y2017/V39/I3/141

References

[1] 秦积舜,李爱芬. 油层物理学[M]. 东营:石油大学出版社,2001.
[2] 李传亮. 油藏工程原理[M]. 北京:石油工业出版社, 2005.
[3] 邴绍献. 特高含水期相渗关系表征研究[J]. 石油天然气学报,2012,34(10):118-120. doi:10.3969/j.issn.1000-9752.2012.10.028 BING Shaoxian. Study on relative permeability equation adapted at ultra-high water-cut stage[J]. Journal of Oil and Gas Technology, 2012, 34(10): 118-120. doi: 10.3969/j.-issn.1000-9752.2012.10.028
[4] 张金庆,孙福街. 相渗曲线和水驱曲线与水驱储量的关系[J]. 新疆石油地质,2010,31(6):629-631. ZHANG Jinqing, SUN Fujie. Quantitative relationship between relative permeability curve, water drive curveand waterflood reserve[J]. Xinjiang Petroleum Geology, 2010, 31(6): 629-631.
[5] 薛颖,石立华,席天德. 童氏水驱曲线的改进及应用[J]. 西南石油大学学报(自然科学版),2015,37(1): 141-145. doi:10.11885/j.issn.1674-5086.2012.12.20.02 XUE Ying, SHI Lihua, XI Tiande. Tong's water drive curve improvement and its application[J]. Journal of Southwest Petroleum University (Science & Technology Edition), 2015, 37(1): 141-145. doi: 10.11885/j.issn.1674-5086.2012.12.20.02
[6] 蒋炳金,唐海,吕栋梁,等. 用相对渗透率曲线研究薄层底水油藏产水规律[J]. 新疆石油地质,2006,27(5): 588-590. doi:10.3969/j.issn.1001-3873.2006.05.022 JIANG Bingjin, TANG Hai, LÜ Dongliang, et al. Research on water production law of reservoir with thin thickness and bottom water using relative permeability curve[J]. Xinjiang Petroleum Geology, 2006, 27(5): 588-590. doi: 10.3969/j.issn.1001-3873.2006.05.022
[7] 耿站立,孙福街,田冀. 多层砂岩油藏层内纵向非均质性表征方法探索[J]. 西南石油大学学报(自然科学版),2011,33(4):96-100. doi:10.3863/j.issn.1674-5086.2011.04.017 GENG Zhanli, SUN Fujie, TIAN Ji. Exploration on reservoir heterogeneity characterization in reservoir numerical modeling of multi-substratum sandstone reservoir[J]. Journal of Southwest Petroleum University (Science & Technology Edition), 2011, 33(4): 96-100. doi: 10.3863/j.-issn.1674-5086.2011.04.017
[8] 吕成远. 油藏条件下油水相对渗透率实验研究[J]. 石油勘探与开发,2003,30(4):102-104. doi:10.3321/j.-issn:1000-0747.2003.04.033 LÜ Chengyuan. Experimenal study on oil-water relative permeability under natural reservoir conditions[J]. Petroleum Exploration and Development, 2003, 30(4): 102-104. doi: 10.3321/j.issn:1000-0747.2003.04.033
[9] 董大鹏. 非稳态相渗实验数据的处理方法[J]. 西南石油大学学报(自然科学版),2014,36(6):110-116. doi: 10.11885/j.issn.1674-5086.2012.08.30.07 DONG Dapeng. Processing method to the data of relative permeability in unsteady state displacement[J]. Journal of Southwest Petroleum University(Science & Technology Edition), 2014, 36(6): 110-116. doi: 10.11885/j.issn.1674-5086.2012.08.30.07
[10] 戴胜群,付波,洪秀娥,等. 油藏综合相渗曲线拟合方法[J]. 油气藏评价与开发,2011,1(3):1-4. doi:10.-3969/j.issn.2095-1426.2011.03.001 DAI Shengqun, FU Bo, HONG Xiu'e, et al. The methods to fit the curve of integrated relative permeability in reservoir[J]. Reservoir Evaluation and Development, 2011, 1(3): 1-4. doi: 10.3969/j.issn.2095-1426.2011.03.-001
[11] 孙雷,闫成海,潘毅,等. 长岩芯驱替中不同位置的相渗曲线计算[J]. 西南石油大学学报(自然科学版), 2014,36(2):139-144. doi:10.11885/j.issn.1674-5086.-2013.03.20.01 SUN Lei, YAN Chenghai, PAN Yi, et al. Calculation of relative permeability curve at different position in long core displacement experiment[J]. Journal of Southwest Petroleum University (Science & Technology Edition), 2014, 36(2): 139-144. doi: 10.11885/j.issn.1674-5086.2013.03.-20.01
[12] 刘西雷. 基于分形理论计算相渗分流量曲线[J]. 大庆石油地质与开发,2015,34(1):59-62. doi:10.3969/J.-ISSN.1000-3754.2015.01.012 LIU Xilei. Relative permeability fractional flow curve calculation based on fractal theory[J]. Petroleum Geology and Oilfield Development in Daqing, 2015, 34(1): 59-62. doi: 10.3969/J.ISSN.1000-3754.2015.01.012
[13] 陈田勇,毛鑫,刘仕银,等. 利用分形理论计算相对渗透率曲线以南襄盆地双河油田核桃园组六油组为例[J]. 石油与天然气地质,2012,33(4):578-581, 590. doi:10.11743/ogg20120412 CHEN Tianyong, MAO Xin, LIU Shiyin, et al. Fractal theory-based calculation method of relative permeability curves: A case study from the Hetaoyuan Formation in Shuanghe Oilfield, Nanxiang Basin[J]. Oil & Gas Geology, 2012, 33(4): 578-581, 590. doi: 10.11743/-ogg20120412
[14] 黄祥峰,张光明,郭俊磊,等. 计算油藏相渗曲线的新方法及应用[J]. 石油地质与工程,2013,27(1):53-55. doi:10.3969/j.issn.1673-8217.2013.01.014 HUANG Xiangfeng, ZHANG Guangming, GUO Junlei, et al. New measurement methods for relative permeability curve and its application[J].Petroleum Geology and Engineering, 2013, 27(1): 53-55. doi: 10.3969/j.issn.1673-8217.2013.01.014
[15] 凡哲元,袁向春,廖荣凤,等. 制作含水率与采出程度关系理论曲线常犯错误及解决办法[J]. 石油与天然气地质,2005,26(3):384-387. doi:10.3321/j.issn:0253-9985.2005.03.021 FAN Zheyuan, YUAN Xiangchun, LIAO Rongfeng, et al. Conunon problerns and solutions in plotting thcoretical curves of water-cut vs. recovery percent of reserves[J]. Oil and Gas Geology, 2005, 26(3): 384-387. doi: 10.3321/j.-issn:0253-9985.2005.03.021
[16] 王华,邴绍献,张海燕,等. 特高含水期水驱油效率计算新方法[J]. 断块油气田,2013,20(2):201-203. doi: 10.6056/dkyqt201302016 WANG Hua, BING Shaoxian, ZHANG Haiyan, et al. A new method suitable for water-oil displacement efficiency calculation in extra-high water cut period[J]. Fault-block Oil & Gas Field, 2013, 20(2): 201-203. doi: 10.6056/-dkyqt201302016
[17] 丁剑霆,程凯,杨晓丰. Weibull分布及其在混凝土断裂能试验数据分析中的应用[J]. 黑龙江工程学院学报(自然科学版),2009,23(1):14-16. doi:10.3969/j.-issn.1671-4679.2009.01.005 DING Jianting, CHENG Kai, YANG Xiaofeng. Weibull distribution and its application in trial data analysis of fracture energy[J]. Journal of Heilongjiang Institute of Technology, 2009, 23(1): 14-16. doi: 10.3969/j.issn.1671-4679.2009.01.005
[18] 王亮,谭洪卫,季亮. 基于Weibull统计特性的风速条件下的自然通风[J]. 太阳能学报,2014,35(2):345-350. doi:10.3969/j.issn.0254-0096.2014.02.026 WANG Liang, TAN Hongwei, JI Liang. Natural ventilation under wind speed condition based on Weibull statistic characteristics[J]. Acta Energiae Solaris Sinica, 2014, 35(2): 345-350. doi: 10.3969/j.issn.0254-0096.2014.02.-026
[19] 宫平志,刘斌,郑彬,等. 相渗曲线处理新方法-半归一化法[J]. 石油化工应用,2015,34(9):32-35. doi: 10.3969/j.issn.1673-5285.2015.09.007 GONG Pingzhi, LIU Bin, ZHENG Bin, et al. A new method for processing relative permeability curves-Seminormalization method[J]. Petrochemical Industry Application, 2015, 34(9): 32-35. doi: 10.3969/j.issn.1673-5285.-2015.09.007
[20] 李宁,孙雷,潘毅,等. 油水相渗曲线归一化新方法研究[J]. 复杂油气藏,2015,8(1):38-40,51. doi:10.-16181/j.cnki.fzyqc.2015.01.009 LI Ning, SUN Lei, PAN Yi, et al. A new method for normalizing oil-water relative permeability curves[J]. Complex Hydrocarbon Reservoirs, 2015, 8(1): 38-40, 51. doi: 10.16181/j.cnki.fzyqc.2015.01.009