High-Resolution X-Ray Computed Tomography of Macroporous Karst for Permeability Measurement and Non-Darcian Flow Via Lattice Boltzmann Models

The permeability of macroporous karstic rocks is extremely difficult to measure in a laboratory setting due to flow-rate limitations of the measuring apparatus, and issues related to the maintaining and measuring the extremely small gradients needed to sustain Darcian flow regimes. High-resolution X-ray computed tomography (HRXCT) can provide digital reconstructions of porous media that are essential for detailed pore-scale flow modeling. The HRXCT provides rendering data for lattice Boltzmann calculation of permeability in samples with well-connected macropores.

Samples representative of biomoldic and trace-fossil related macroporosity were collected from the Fort Thompson Formation and Miami Limestone of the Biscayne aquifer in southeastern Florida and scanned using HRXCT methods that provided resolutions on the order of 0.3 mm per pixel. Permeability measurements were conducted using lattice Boltzmann techniques applied to seven renderings of samples created from the HRXCT scans. Non-Darcian inertial flows were avoided by applying extremely small gradients while making the permeability measurements. The lattice Boltzmann method was verified against analytical solutions for pipe and conduit flow. Measured permeabilities derived from lattice Boltzmann methods correspond to hydraulic conductivity values ranging from 0 m/s (for a sample lacking well-connected macroporosity) to 167 m/s (vertical), and are as much as five orders of magnitude greater than the largest values typically reported by testing laboratories.

Non-Darcian effects are of considerable interest if they occur under field-scale conditions and lattice Boltzmann models permit investigation of the potential significance of non-Darcian effects. For one limestone sample from the Biscayne aquifer with extremely high, well-connected macroporosity, it is concluded that non-Darcian behavior due to inertial flow under field-scale gradients could effectively reduce the apparent hydraulic conductivity by nearly 50 percent.