Probing the water distribution in porous model sands with two immiscible fluids: A nuclear magnetic resonance micro-imaging study

Abstract

The effect of the structural heterogeneity of porous networks on the water distribution in porous media, initially saturated with immiscible fluid followed by increasing durations of water injection, remains one of the important problems in hydrology. The relationship among convergence rates (i.e., the rate of fluid saturation with varying injection time) and the macroscopic properties and structural parameters of porous media have been anticipated. Here, we used nuclear magnetic resonance (NMR) micro-imaging to obtain images (down to ∼50μm resolution) of the distribution of water injected for varying durations into porous networks that were initially saturated with silicone oil. We then established the relationships among the convergence rates, structural parameters, and transport properties of porous networks. The volume fraction of the water phase increases as the water injection duration increases. The 3D images of the water distributions for silica gel samples are similar to those of the glass bead samples. The changes in water saturation (and the accompanying removal of silicone oil) and the variations in the volume fraction, specific surface area, and cube-counting fractal dimension of the water phase fit well with the single-exponential recovery function {f(t)=a[1-exp(-λt)]}. The asymptotic values (a, i.e., saturated value) of the properties of the volume fraction, specific surface area, and cube-counting fractal dimension of the glass bead samples were greater than those for the silica gel samples primarily because of the intrinsic differences in the porous networks and local distribution of the pore size and connectivity. The convergence rates of all of the properties are inversely proportional to the entropy length and permeability. Despite limitations of the current study, such as insufficient resolution and uncertainty for the estimated parameters due to sparsely selected short injection times, the observed trends highlight the first analyses of the cube-counting fractal dimension (and other structural properties) and convergence rates in porous networks consisting of two fluid components. These results indicate that the convergence rates correlate with the geometric factor that characterizes the porous networks and transport property of the porous networks.