Pore-Scale Reconstruction and Simulation of Non-Darcy Flow in Synthetic Porous Rocks

We image synthetic porous rocks of varied porosity and pore size by micro–computed tomography with pore-scale finite element modeling representing the pore space for single-phase fluid flow. The simulations quantify the key features of microscale flow behavior in the synthetic cores. The smaller the permeability, the greater the critical pressure gradient required for the onset of non-Darcy fluid flows, and the easier the emergence of nonlinear seepage within the tested cores. The relationship between permeability and porosity from different methods shows a power law correlation with pressure. Structural heterogeneity and anisotropy of the pore systems are shown to have a significant impact on transport through the three-dimensional pore model—exhibiting irregular flow fields. The simulated permeabilities of the tested cores vary by a factor of 2–5 depending on the fluid flow directions. With the increase of flow seepage velocity, the flow regime deviates from Darcy linear relationship and non-Darcy behavior (inertia) leads to a reduction in the effective permeability of the core. Both experiments and modeling demonstrate that the larger the porosity and permeability, the stronger the non-linear phenomenon of the seepage within the pore space. A method is proposed to estimate the non-Darcy coefficient β based on simulation results, which provides a good prediction for all the tested cores. A new equation is established to predict the transition of flow patterns as a function of the apparent permeability K^* and Reynolds number Re. The K^*-Re model provides a theoretical approach to dynamically describe the transition from Darcy to Forchheimer flow.