Transport in Porous Media

, Volume 130, Issue 3, pp 947–968 | Cite as

Modeling of Co-current Spontaneous Imbibition Oil Recovery from Partially Covered Homogeneous Hydrocarbon Reservoir

  • Tufan Ghosh
  • G. P. Raja SekharEmail author
  • Debasis Deb


In this paper, an approximate integral equation solution for a horizontal, unsteady flow of two viscous incompressible fluids is derived. Wettability variation of the porous medium is also considered in the present study. The non-wetting phase recovery fraction is obtained in terms of dimensionless time for 1D model from the derived solution. The derived approximate recovery fraction has been compared with the existing experimental data and empirical correlations for spontaneous imbibition from water-wet medium. It is observed that the normalized water saturation profiles show sharp gradients indicating some instability of the water front. Hence, a linear stability analysis is developed to study viscous instability of the co-current spontaneous imbibition. Viscous instability phenomenon for a two-phase oil–water system is also discussed. The corresponding instability number related to co-current imbibition recovery is estimated. The present study clearly spells out the effect of the instability number on the recovery process and estimates a critical instability number for co-current spontaneous imbibition.


Two-phase flow Co-current imbibition Wettability Linear stability analysis Instability number 



We thank the anonymous referee for useful suggestions which improved the quality of the manuscript. One of the authors (TG) acknowledges the support from the institute in the form of institute research fellowship (Grant No. IIT/Acad/PGS&R/F. II/2/15/MA/90J09) of Indian Institute of Technology Kharagpur. TG is also thankful to Mr. Timir Karmakar for his useful suggestions and discussions on this manuscript.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia
  2. 2.Department of Mining EngineeringIndian Institute of Technology KharagpurKharagpurIndia

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