“…Over time, this method of combining asymptotic solutions proved quite to be successful in developing models in many applications. Recently, it has been applied to two-phase flow in circular pipes (Awad, 2007;Muzychka and Awad, 2010), minichannels (Awad, 2007;Muzychka and Awad, 2010;Awad and Muzychka, 2010), and microchannels (Awad, 2007;Muzychka and Awad;2010). Moreover, Awad and Butt (2009a,b,c) have shown that the asymptotic method works well in petroleum industry applications for flows through porous media, liquid-liquid flows, and flows through fractured media.…”