Arabian Journal for Science and Engineering

, Volume 44, Issue 12, pp 10513–10523 | Cite as

Relative Permeability Model Taking the Roughness and Actual Fluid Distributions into Consideration for Water Flooding Reservoirs

  • Zhongwei Wu
  • Chuanzhi CuiEmail author
  • Yongmao Hao
  • Yeheng Sun
  • Guangzhong Lv
  • Du Sun
  • Zifan Zhang
Research Article - Petroleum Engineering


Reservoir relative permeability is greatly important to the development of water flooding reservoirs. Currently, most researches on relative permeability have not taken the roughness of pore surface and actual fluid distributions into consideration. In this paper, a novel relative permeability model for water flooding reservoirs taking the roughness and actual fluid distributions into consideration has been proposed by using the fractal theory. The novel model contains some key parameters, all of which have clear physical meanings, such as the immobile liquid film thickness, relative roughness, tortuosity fractal dimension \( D_{\text{T}} \) and pore fractal dimension \( D_{\text{f}} \). The predicted results of the novel fractal relative permeability model are consistent with published experimental data. That verifies the correctness of the novel fractal relative permeability model. Finally, sensitive factor analysis of novel relative permeability model is conducted. We can find that the wetting fluid relative permeability decreases as the immobile wetting fluid film thickness or relative roughness increases. When the tortuosity fractal dimension or pore fractal dimension increases, the wetting relative permeability and non-wetting relative permeability will both decrease. An increase in maximum pore diameter or the decreasing of minimum pore diameter results in the reduction in fractal dimension of flow channel and discontinuous saturation. The increasing of maximum pore diameter results in an increase in the relative permeability of wetting fluid. The minimum pore diameter has tiny effect on the relative permeability.


Water flooding reservoir Relative permeability Fractal Relative roughness Immobile wetting fluid film 



This work was supported by the Fundamental Research Funds for the Central Universities through Grant Number 18CX06011A, China University of Petroleum Graduate Innovation Engineering Project through Grant Number (Grant No: YCX2018013), National Massive Oil & Gas Field and Coal-bed Methane Development Program through Grant Number 2016ZX05010-002-007, National Science and Technology Major Demonstration Project ‘Tight Oil Development Demonstration Project of Bohai Bay Basin Jiyang Depression’ through Grant Number 2016ZX05072006-004 and Natural Science Foundation of Shandong Province, China through Grant Number ZR2017MEE054.


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Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  • Zhongwei Wu
    • 1
    • 3
  • Chuanzhi Cui
    • 1
    Email author
  • Yongmao Hao
    • 1
  • Yeheng Sun
    • 2
  • Guangzhong Lv
    • 2
  • Du Sun
    • 2
  • Zifan Zhang
    • 3
  1. 1.College of Petroleum EngineeringChina University of Petroleum (East China)QingdaoPeople’s Republic of China
  2. 2.Research Institute of Exploration and DevelopmentShengli Oilfield Company SINOPECDongyingPeople’s Republic of China
  3. 3.School of Mining and Petroleum, Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada

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