Pore geometry effects on intrapore viscous to inertial flows and on effective hydraulic parameters

In this article, the effects of different diverging-converging pore geometries were investigated, and the microscale fluid flow and effective hydraulic properties from these pores were compared with that of a pipe from viscous to inertial laminar flow regimes. The flow fields are obtained using computational fluid dynamics, and the comparative analysis is based on a new dimensionless hydraulic shape factor beta, which is the specific surface scaled by the length of pores. Results from all diverging-converging pores show an inverse pattern in velocity and vorticity distributions relative to the pipe flow. The hydraulic conductivity K of all pores is dependent on and can be predicted from beta with a power function with an exponent of 3/2. The differences in K are due to the differences in distribution of local friction drag on the pore walls. At Reynolds number (Re) similar to 0 flows, viscous eddies are found to exist almost in all pores in different sizes, but not in the pipe. Eddies grow when Re -> 1 and leads to the failure of Darcy's law. During non-Darcy or Forchheimer flows, the apparent hydraulic conductivity K-a decreases due to the growth of eddies, which constricts the bulk flow region. At Re > 1, the rate of decrease in K-a increases, and at Re >> 1, it decreases to where the change in K-a approximate to 0, and flows once again exhibits a Darcy-type relationship. The degree of nonlinearity during non-Darcy flow decreases for pores with increasing beta. The nonlinear flow behavior becomes weaker as beta increases to its maximum value in the pipe, which shows no nonlinearity in the flow; in essence, Darcy's law stays valid in the pipe at all laminar flow conditions. The diverging-converging geometry in pores plays a critical role in modifying the intrapore fluid flow, implying that this property should be incorporated in effective larger-scale models, e.g., pore-network models.