Calculation of Relative Permeability Curve at Different Position in
Long Core Displacement Experiment

doi:10.11885/j.issn.1674-5086.2013.03.20.01

Abstract

Abstract:

Relative permeability is an empirical parameter，which interprets the complex effects of the flow of the multi-phase
and incompressible fluid in porous media，so as to calibrate Darcy’s single phase flow equation. The relative permeability can
be influenced by many factors，such as fluid saturation，physical rock properties，wettability，saturation history，overburden
stress，clay and fines content，temperature，interfacial tension，viscosity，magnitude of initial phase saturations，and displacement
rates and capillary outlet phenomena. Based on the results of Huan Guanren and Shen Pingping’s derivation of relative
permeability curve and by considering the character in the displacement experiment whose core arrangement is heterogeneous
in one dimension and harmonious arrangement，we got the relationship between cumulative core length and harmonious average
permeability by Matlab. And then we reversely solved the relationship between absolute permeability and cumulative
core length. We also converted the discrete model into the continuous model. By substituting the above results into the single
dimension homogenous model，we obtained the relative permeability curve in different position of the displaced cores in WC
oilfield. The result is reliable except for few points that fitted poorly.

Key words: relative permeability curve, heterogeneity, long core displacement, fit

Sun Lei1, Yan Chenghai1, Pan Yi1, Chen Liang2, Li Shilun1. Calculation of Relative Permeability Curve at Different Position in
Long Core Displacement Experiment[J]. 西南石油大学学报(自然科学版), DOI: 10.11885/j.issn.1674-5086.2013.03.20.01.

0
/ / Recommend

Add to citation manager EndNote|Ris|BibTeX

URL: http://journal15.magtechjournal.com/Jwk_xnzk/EN/10.11885/j.issn.1674-5086.2013.03.20.01

http://journal15.magtechjournal.com/Jwk_xnzk/EN/Y2014/V36/I2/139

References

[1] Krause M H. Modeling and investigation of the influence

of capillary heterogeneity on relative permeability[

C]. SPE 160909，2012.

[2] Sheng Q，Thompson K E，Fredrich J T. Numerical prediction

of relative permeability from micro CT images：comparison

of steady-state versus displacement methods[C].

SPE 147431，2011.

[3] Bennion D B，Thomas F B. Recent improvements in experimental

and analytical techniques for the determination

of relative permeability data from unsteady state flow experiments[

C]//10th Techncial Conference and Exposition，

Port of Spain，Trinidad，SPE 1991.

[4] 赵春鹏，岳湘安. 特低渗透油藏超前注水长岩芯实验研

究[J]. 西南石油大学学报：自然科学版，2011，33（3）：

105–108.

Zhao Chunpeng，Yue Xiang’an. Long-core experimental

study on advance water injection of extralow permeability

reservoir[J]. Journal of Southwest Petroleum University：

Science & Technology Edition，2011，33（3）：105–108.

[5] 桓冠仁，沈平平. 一种非稳态油水相对渗透率曲线计

算方法[J]. 石油勘探与开发，1982（2）：52–58.

Huan Guanren，Shen Pingping. Calculating relative permeability[

J]. Petroleum Exploration and Development，

1982（2）：52–58.

[6] Li Heng，Chen Shengnan，Yang Daoyong，et al.

Ensemble-based relative permeability estimation using

B-spline model[J]. Transport in Porous Media，2010，

85（3）：703–721.

[7] 邓英尔，刘慈群. 两相流体非线性渗流模型及其应

用[J]. 应用数学和力学，2003，24（10）：1049–1056.

Deng Ying’er，Liu Ciqun. Mathematical model of twophase

fluid nonlinear flow in low-permeability porous media

with applications[J]. Applied Mathematics and Mechanics，

2003，24（10）：1049–1056.

[8] 王坤，张烈辉. 考虑应力敏感超低渗油藏油水相对渗透

率的计算[J]. 石油天然气学报，2011，33（11）：117–119.

Wang Kun，Zhang Liehui. Calculation of relative permeability

of extra-low permeability reservoirs considering

stress sensitivity[J]. Journal of Oil and Gas Technology，

2011，33（11）：117–119.

[9] 王金勋，刘庆杰，杨普华，等. 应用逾渗理论计算非稳

态法油水相渗曲线[J]. 石油勘探与开发，2001，28（2）：

79–82.

Wang Jinxun，Liu Qingjie，Yang Puhua，et al. Calculating

the relative permeability from displacement experiments

based on percolation theory[J]. Petorleum Exploration and

Development，2001，28（2）：79–82.

[10] 向祖平，张烈辉，陈辉，等. 相渗曲线对油水两相渗流

数值试井曲线的影响[J]. 西南石油大学学报，2007，

29（4）：74–78.

Xiang Zuping，Zhang Liehui，Chen Hui，et al. Influnce

of the relative permeability curve on numerical well test

curve of oil-water-phase flow[J]. Journal of Southwest

Petroleum Univesity，2007，29（4）：74–78.

[11] 杨小平. 精确计算相对渗透率的方法[J]. 石油勘探与开

发，1998，25（6）：63–66.

Yang Xiaoping. A method to calculate the relative permeability

accurately[J]. Petorleum Exploration and Development，

1998，25（6）：63–66.

[12] Johnson E F，Bossler D P，Bossler V O. Calculation of

relative permeability from displacement experiments[C].

SPE 1023，1959.

[13] 王学武，杨正明，时宇，等. 核磁共振研究低渗透砂岩

油水两相渗流规律[J]. 科技导报，2009，27（15）：56–58.

Wang Xuewu，Yang Zhengming，Shi Yu，et al. Experimental

study of water-oil two-phase fluid flow in low permeability

reservoir by nuclear magnetic resonance[J]. Science

& Technology Review，2009，27（15）：56–58.

[14] 李士伦，张正卿，冉新权. 注气提高石油采收率技

术[M]. 成都：四川科学技术出版社，2001.

[15] 张志涌. 精通Matlab R2011a[M]. 北京：北京航空航天

大学出版社，2011.