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Water resources research v.52 no.9, 2016년, pp.7284 - 7310   SCI SCIE
본 등재정보는 저널의 등재정보를 참고하여 보여주는 베타서비스로 정확한 논문의 등재여부는 등재기관에 확인하시기 바랍니다.

Analytical and numerical investigations of spontaneous imbibition in porous media

Nooruddin, Hasan A. (Department of Earth Science and Engineering, Imperial College London, UK ); Blunt, Martin J. ( );
  • 초록  

    Abstract We present semianalytical solutions for cocurrent displacements with some degree of countercurrent flow. The solution assumes a one‐dimensional horizontal displacement of two immiscible incompressible fluids with arbitrary viscosities and saturation‐dependent relative permeability and capillary pressures. We address the impact of the system length on the degree of countercurrent flow when there is no pressure drop in the nonwetting phase across the system, assuming negligible capillary back pressure at the inlet boundary of the system. It is shown that in such displacements, the fractional flow can be used to determine a critical water saturation, from which regions of both cocurrent and countercurrent flow are identified. This critical saturation changes with time as the saturation front moves into the porous medium. Furthermore, the saturation profile in the approach presented here is not necessarily a function of distance divided by the square root of time. We also present approximate solutions using a perturbative approach, which is valid for a wide range of flow conditions. This approach requires less computational power and is much easier to implement than the implicit integral solutions used in previous work. Finally, a comprehensive comparison between analytical and numerical solutions is presented. Numerical computations are performed using traditional finite‐difference formulations and convergence analysis shows a generally slow convergence rate for water imbibition rates and saturation profiles. This suggests that most coarsely gridded simulations give a poor estimate of imbibition rates, while demonstrating the value of these analytical solutions as benchmarks for numerical studies, complementing Buckley‐Leverett analysis.


    Key Points Semianalytical solutions for co‐current displacements with some degree of counter‐current flow Saturation profiles are not necessarily a function of distance divided by the square‐root of time Most coarsely gridded simulations give a poor estimate of imbibition rates


  • 주제어

    spontaneous imbibition .   immiscible displacements .   analytical solutions .   counter‐current flow .   cocurrernt flow .   fractional flow.  

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