The Mathematical Model of Non-Equilibrium Effects in Water-Oil Displacement

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Fractal Prediction Model of Spontaneous Imbibition Rate (2011, methodology): “These include the Washburn equation (Washburn 1921), the Handy model (Handy 1960), the Li-Horne model (2001, 2004, 2006a) and the models proposed by Barenblatt et al. (2002) as well as by Zimmerman and Bodvarsson (1991). The value of m in the model derived by Cai et al. (2010) could be equal to 0.”
On Barenblatt's Model of Spontaneous Countercurrent Imbibition (2004, background): “A survey of major contributions in this area has been presented elsewhere (Barenblatt et al., 2003).”
Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media (2008, methodology): “Another recently proposed class of model modifications has been the use of dynamic capillary pressure [42, 68, 67, 66, 12, 11] which accounts for the dynamic flow rates via S 7→ Pc(x, S, dS dt ).”