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Journal of Porous Media

Impact factor: 1.035

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v14.i5.50
pages 423-435


C. P. Krishnamoorthy
Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India
Abhijit P. Deshpande
Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India
S. Pushpavanam
Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India


In this work, we investigate experimentally as well as numerically a drainage displacement system; i.e., a non-wetting fluid displacing a wetting fluid in a porous medium. Experiments were carried out in a horizontal rectangular channel packed with a monolayer of glass beads. The displacement of a higher viscosity wetting fluid (silicone oil) by a lower viscosity non-wetting fluid (air) is studied. Similarly, the displacement of a lower viscosity wetting fluid (silicone oil) by a higher viscosity non-wetting fluid (glycerol) is also studied. Flow structures, such as viscous fingering and stable displacement, were obtained. The behavior of the flow in the experiments was simulated using a pore network model. The model consists of a network of tubes of equal lengths inclined at 45±. The radius of the tubes is assumed to follow a random distribution to ensure a realistic representation of a porous medium. The pressure distribution across the network is obtained by assuming laminar flow in each tube. The Hagen-Poiseuille equation is used after including the effect of capillary pressure to determine the flow velocity in each tube. The displacement of the interface for each time step is restricted to 2.5−.0% of the tube length and the maximum velocity in the network is used to calculate this time interval. The movement of the interface inside the tube is calculated using a second-order Runge-Kutta method. Once the interface reaches a node, the volume of the fluid entering the neighboring tubes is determined by the pressure drop across them. We have varied the capillary number, Ca (μν/σA), and viscosity ratio, M, and have obtained two different flow regimes, viscous fingering and stable displacement. The residual amount of defending fluid present in the network model is calculated for the two regimes of drainage displacements. It is found that when stable displacement occurs, the system has significantly less amount of defending fluid present for the same duration of time as compared with the case when viscous fingering is exhibited. The fronts of the invading fluid during viscous fingering at different capillary numbers are self-similar with a fractal dimension of 1.3 that matches with the experimental results.