Tortuosity estimate through paramagnetic gas diffusion in rock saturated with two fluids using T2 (z, t) low-field NMR

Abstract

Petrophysical interpretation of 1H NMR relaxation responses from saturated rocks is complicated by paramagnetic species present in fluids. Oxygen dissolved in liquids is one common example. Dipolar interactions of oxygen’s unpaired electron spins with the magnetic moment of fluid nuclei provide a strong relaxation mechanism known as paramagnetic relaxation enhancement (PRE). As a result even low concentrations of dioxygen in its common triplet ground state significantly shorten longitudinal and transverse relaxation times of host fluids. This effect may be employed similarly to any standard tracer technique to study pore connectivity in porous media by detecting a change of oxygen concentration due to diffusion resolved in time and space. Since relaxation enhancement effect is likely stronger in non-wetting phase than in wetting one (where surface relaxation process dominates) this difference can be utilized to study wettability in immiscible multiphase systems. We use a relaxation time contrast between air-saturated and oxygen-free fluids to evaluate oxygen concentration change within two fluid phases saturating rock, to estimate time required to establish equilibrium concentration and to calculate a mutual diffusion coefficient of oxygen. A spatially- and time-resolved T2(z,t) experiment provides the time-dependent oxygen concentration change along the fully- and partially-saturated carbonate core plug exposed to air saturated oil at its inlet. We derive an effective mutual diffusion coefficient of oxygen and accordingly a tortuosity estimate as a function of position along the core and rock saturation. The spatially resolved oxygen diffusion-based tortuosity is compared to simulated conductivitybased tortuosity. The latter is calculated on a high-resolution micro-tomographic image of Mount Gambier limestone by solving the Laplace equation for conductivity.