The effect of viscosity ratio on the dispersal of fracturing fluids into groundwater system

  • Qian Sang
  • Ping Chen
  • Mingzhe DongEmail author
  • Guo Tao
Original Article


In the development of oil and gas reservoirs, the transport of miscible fluids in porous rocks is a key issue for oil and gas recovery. The simplified unidirectional flow model is employed to investigate the effects of the viscosity ratio on dispersion in semi-infinite homogenous media. The viscosity is supposed to be unsteady due to changing component concentration over time. In cases of both a viscosity ratio larger and less than 1, the pollutant concentration and flow velocity are computed at different initial conditions and viscosity ratios. The analytical solutions are then developed by introducing new variables and transforming the equation governing advection–diffusion equation in semi-infinite homogeneous media with a continuous source. A comparison of the numerical solution with the analytical solution revealed a similarity over 98%, highlighting the usability of the analytical solution. If the viscosity ratio is larger than 1, flow velocity declines exponentially and concentration attenuates with transporting time. In addition, the timescale plays a significant role and the effects become more prominent in long-term transport. In the case of a viscosity ratio less than 1, both the timescale and viscosity ratio variables have little influence on the changing speed of the concentration profile. This work helps to predict the position and the time required to reach the harmless pollutant concentration when monitoring fracturing fluids transportation into groundwater system and would be especially useful in designing and interpreting laboratory experiments studying the miscible flow.


Unsteady flow Viscosity ratio Advection–diffusion equation Temporary velocity Numerical solution Analytical solution 



This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and China Scholarship Council for sponsoring as a visiting student (No. 2009644010) in University of Calgary.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chemical and Petroleum Engineering DepartmentUniversity of CalgaryCalgaryCanada
  2. 2.State Key Laboratory of Petroleum Resource and ProspectingChina University of PetroleumBeijingChina

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