An intercomparison of the pore network to the Navier\u2013Stokes modeling approach applied for saturated conductivity estimation from X-ray CT images

Abstract

Different modeling techniques can be used to estimate the saturated conductivity of a porous medium based on computed tomography (CT) images. In this research, two methods are intercompared: direct modeling using the Navier–Stokes (NS) approach and simplified geometry pore network (PN) modeling. Both modeling approaches rely on pore media geometry which was determined using an X-ray CT scans with voxel size 2 μm. An estimate of the saturated conductivity using both methods was calculated for 20 samples prepared from sand with diverse particle size distributions. PN-estimated saturated conductivity was found to be statistically equivalent to the NS-determined saturated conductivity values. The average value of the ratio of the PN-determined conductivity to the NS-determined conductivity (KsatPN/NS) was equal to 0.927. In addition to the NS and PN modeling approaches, a simple Kozeny-Carman (KC) equation-based estimate was made. The comparison showed that the KC estimate overestimated saturated conductivity by more than double (2.624) the NS estimate. A relationship was observed between the porous media specific surface and the KsatPN/NS ratio. The tortuosity of analyzed samples was estimated, the correlation between the porous media tortuosity and the specific surface of the samples was observed. In case of NS modelling approach the difference between pore media total porosity and total porosity of meshes, which were lower, generated for simulations were observed. The average value of the differences between them was 0.01. The method of NS saturated conductivity error estimation related to pore media porosity underestimation by numerical meshes was proposed. The error was on the average 10% for analyzed samples. The minimum value of the error was 4.6% and maximum 19%.