The microscopic analysis of high forchheimer number flow in porous media

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

“…A wide range of critical particle Reynolds numbers is given in the literature for the onset of nonlinear laminar flow. For example, Bear (1972), Hassanizadeh and Gray (1987), Ma and Ruth (1993) and Comiti et al (2000) suggested critical particle Reynolds numbers ranging between 1 and 15. Other studies, such as Scheidegger (1974), obtained higher maximal critical particle Reynolds numbers up to a value of 75.…”

“…Other studies, such as Scheidegger (1974), obtained higher maximal critical particle Reynolds numbers up to a value of 75. Ma and Ruth (1993) and Lage (1998) introduced new criteria to evaluate the onset of nonlinear flow by means of a "Forchheimer number," based on the intrinsic permeability and the non-Darcy coefficient b in the Forchheimer equation. However, such criteria require experimentally or empirically determined values for the Forchheimer coefficients a and b, while criteria such as the particle Reynolds number require only the average grain size in order to estimate the onset of nonlinear flow in a given porous media.…”

“…A smooth transition was observed from nonlinear laminar flow, to the onset of small vortices and eddies in some pore spaces, to eventually, development of fully turbulent flow in the porous medium (e.g., Dybbs and Edwards 1984;Seguin et al 1998). In the literature, this nonlinearity in the laminar flow regime is ascribed to different microscale processes (e.g., Hassanizadeh and Gray 1987;Ma and Ruth 1993;Skjetne and Auriault 1999;Hill and Koch 2002;Nield 2002). In general, it is assumed that the deviation from the linear Darcy's law at increased Reynolds numbers is due to the occurrence of microscopic inertial forces (e.g., Bear 1972;Macdonald et al 1979;Venkataraman and Rao 1998).…”

“…Other studies, such as Panfilov et al (2003) and Panfilov and Fourar (2006), showed that the main mechanisms of energy dissipation that contribute to the nonlinear flow term are due to both recirculation of eddies in closed streamline regions, as well as streamline deformation in the main area of flow. Ma and Ruth (1993) showed that the onset of nonlinearity cannot be fully described by microscopic inertial terms using a simple tube model. Hassanizadeh and Gray (1987) stated that the onset of nonlinear flow behavior is due to the occurrence of interfacial drag forces at increased flow velocities and inertial forces become significantly important at particle Reynold numbers of about 100.…”

“…These studies showed that microscopic analysis should be used to fully understand macroscopic nonlinear laminar flow behavior in a given complex pore structure for a given Reynolds number. Overall, the geometry of the pore structure (such as tube-like or blob-like pore surfaces), as well as the total fluid-solid interface and its interface roughness, largely determine the flow resistance due to drag force terms in the Forchheimer coefficient b (e.g., Ma and Ruth 1993;Liu et al 1995;Thauvin and Mohanty 1998;Panfilov and Fourar 2006;Chaudhary et al 2013). …”