The Mathematical Model of Nonequilibrium Effects in Water-Oil Displacement

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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).”
Real-time 3D imaging of Haines jumps in porous media flow (2013, methodology): “These rapid pore-scale events are essential to the upscaling of multiphase flow because they make up a significant fraction of the energy dissipation within the system (15, 16) and contribute to relative permeability (14) and to macroscopic nonequilibrium effects (12).”
Universal scaling of spontaneous imbibition for water‐wet systems (2012, background): “Some authors ([Barenblatt et al., 2003; Le Guen and Kovscek, 2006]; for a recent overview see Hall [2007]) argue that nonequlibrium effects are especially important for the case of countercurrent SI due to the filling process of the pores by the wetting fluid.”
Pore‐scale displacement mechanisms as a source of hysteresis for two‐phase flow in porous media (2016, background): “…hysteresis is usually accounted for by empirical extensions to the constitutive Pc(Sw)relationship that either address the difference between drainage and imbibition [Mualem, 1974; Kool and Parker, 1987] or dynamic effects [Barenblatt et al., 2003; Hassanizadeh et al., 2002; Mitkov et al., 1998].”