After the publication of the Darcy's law in 1856 (Darcy, 1856), Hiegen in Germany attempted to repeat Darcy's experiments. However, he did not find a stable relationship between pressure gradients and flow rate. In 1885, Newell conducted the first test on a consolidated rock sample. He reported the relationship between velocity and gradient is more than Darcy's proportion and found that there was a Pre-Darcy effect. Subsequently, a number of researchers expressed deviation from Darcy law. In 1999, Prada and Civan observed the threshold gradient for the onset of Pre-Darcy flow during flow of water through consolidated rock samples at velocity of about 4 ft/day [1]. In 2004, Longmuir reviewed all available investigations in Pre-Darcy flow. He concluded that this effect is significant where predictions involve processes that change fluid gradients established in the field and it can affect improved oil recovery [2]. In 2008, Cheng et al. used quadratic and power law formulations in terms of Reynolds numbers for correlating the experimental results covering Darcy to non-Darcy flows through porous media [3]. In 2014, Bagci et al. characterized Flow Regimes in Packed Beds of Spheres from Pre-Darcy to Turbulent. They used two particle size of 1mm and 3mm in their experiments. Results of their experiments added to the divergence of available data on pressure drop in packed beds of spheres [4]. In 2016, Siddiqui et al. experimentally investigated the departure from Darcy's law and compared experimental data of low permeability rocks with high permeable rocks from published data sets. They used an organic fluid (soltrol-130) as a working fluid, and observed that Pre-Darcy effect exists due to fluid/rock interaction [5]. The next work in the field of Pre-Darcy effect was performed by Kundu et al. They characterized Darcy and Non-Darcy flow regimes both experimentally and numerically. They used water as a working fluid with different types of porous medium. The functional relat