“…Two-phase flow of immiscible fluids in porous media has attracted the attention of many research groups during the last 30 years (Payatakes, 1982;Lenormand et al, 1983;Dias and Payatakes, 1986a,b;Lenormand et al, 1988;Blunt and King, 1991;Vizika et al, 1994;Avraam and Payatakes, 1995a,b;Aker et al, 1998;Xu et al, 1998;Knudsen and Hansen, 2002;Tsakiroglou et al, 2003;Valvatne and Blunt, 2004;Li et al, 2005;Theodoropoulou et al, 2005;Joekar-Niasar et al, 2008;Aggelopoulos and Tsakiroglou, 2008;Tallakstad et al, 2009a;Raoof and Hassanizadeh, 2012). There is a broad variety of relevant application areas such as the enhanced oil recovery (Lackner and Torsaeter, 2006), the CO 2 storage in deep saline aquifers and depleted oil reservoirs (Berg and Ott, 2012), the soil contamination and reconstitution (Gao et al, 2013), the performance of proton exchange membranes in fuel cells (Wang et al, 2010).…”