“…In this type of drilling operation, fluid pressure must be maintained at a higher level than the formation pressure, but the pressure difference must not be so high to avoid fluid invasion into the formation rock (Belkin et al, 2005). Although more experimental investigation is carried out on Aphron fluid filtration and its related parameters (Sebba, 1987) (Brookey, 1998) (Ivan et al, 2001) (Ramirez et al, 2002) (Bjorndalen and Kuru, 2008), a few modeling works were carried out in the literature (Belkin et al, 2005), recently Alizadeh and Khamehch have published some works on the Aphron modeling and flow through porous medium (Alizadeh and Khamehchi, 2015a) (Alizadeh and Khamehchi, 2015b) (Alizadeh and Khamehchi, 2016a) (Alizadeh and Khamehchi, 2016b) (Alizadeh and Khamehchi, 2016c) When a solid free fluid is created due to environmental issues, the use of Aphron drilling fluids is considered. Bridging in the front of the porous media in near wellbore zone, in fractured or depleted reservoirs, reduces the formation damage and fluid depth of invasion into the formation.…”