Computer simulation of flow through a lattice flow-cell model

For single-phase flow through a network model of a porous medium, we report (1) solutions of the Navier-Stokes equation for the flow, (2) micro-particle imaging velocimetry (PIV) measurements of local flow velocity vectors in the “pores throats” and “pore bodies,” and (3) comparisons of the computed and measured velocity vectors. A “two-dimensional” network of cylindrical pores and parallelepiped connecting throats was constructed and used for the measurements. All pore bodies had the same dimensions, but three-different (square cross-section) pore-throat sizes were randomly distributed throughout the network. An unstructured computational grid for flow through an identical network was developed and used to compute the local pressure gradients and flow vectors for several different (macroscopic) flow rates. Numerical solution results were compared with the experimental data, and good agreement was found. Cross-over from Darcy flow to inertial flow was observed in the computational results, and the permeability and inertia coefficients of the network were estimated. The development of inertial flow was seen as a “two-step” process: (1) recirculation zones appeared in more and more pore bodies as the flow rate was increased, and (2) the strengths of individual recirculation zones increased with flow rate. Because each pore-throat and pore-body dimension is known, in this approach an experimental (and/or computed) local Reynolds number is known for every location in the porous medium at which the velocity has been measured (and/or computed).