3D PRINTED KARST LIMESTONE CORE FOR APPARENT HYDRAULIC CONDUCTIVITY MEASUREMENT UNDER NON-DARCIAN FLOW

The Biscayne Aquifer is an epigenetic karst aquifer that is the water supply for most of Southeast Florida. Many aquifer strata contain highly interconnected 2-cm diameter touching-vug pores. The size and abundance of these pores leads to very high hydraulic conductivity (K) that cannot be quantified using standard methods for many reasons including non-Darcian flow and difficulty obtaining representative samples and shaping them to fit permeameters.

To circumvent this last challenge, we created a 3-D printed 25-cm long x 10-cm diameter core based on computed tomography of a rock sample and made K measurements on it. We previously reported on using high viscosity glycerol to measure true hydraulic conductivity at low Reynolds numbers and found K = 13.1 +/- 3.9 m s^-1 (Garcia, 2013). In addition, we made Lattice Boltzmann simulations of flow in the core and computed a nearly identical K (14.8 m s^-1).

The high viscosity fluid K measurements did not extend into the non-Darcian flow regime, but Lattice Boltzmann calculations were able to predict the effects of non-Darcian flow up to hydraulic gradients of approximately 10^-3; this allowed fitting a Forchheimer model to the simulation results that can estimate apparent K at any gradient.

The current work uses water to measure apparent K at higher gradients (approximately 10^-3 to 10^-1) and Reynolds numbers. Results are consistent with the Forchheimer model based on Lattice Boltzmann simulations and show about an order-of-magnitude reduction in apparent K as gradients exceed 6 x 10^-3 and Reynolds numbers exceed 40,000. Another factor of 2 reduction occurred at gradients approaching 10^-1 and Reynolds numbers of 220,000.

These results experimentally confirm a dramatic 20-fold reduction of apparent hydraulic conductivity due to non-Darcian flow, which was previously only predicted on the basis of Lattice Boltzmann simulations. Ks at extreme low and high gradients and Reynolds number regimes expected in these rocks have now been measured. Intermediate gradients from about 10^-5 to 10^-3, which are most relevant to regional aquifer behavior, have not yet been accessible to laboratory quantification and will likely require intermediate viscosity fluid substitution, or measurement of head differences using very high resolution transducers or laser interferometry.