Joint numerical microscale simulations of multiphase flow and NMR relaxation behavior in porous media using Lattice Boltzmann methods

Abstract

Nuclear magnetic resonance (NMR) relaxometry is a useful tool to estimate transport and storage properties of rocks and soils. However, as there is no unique relation between the NMR signal and these properties in rocks, a variety of empirical models on deriving hydraulic properties from NMR relaxometry data have been published. Complementary to laboratory measurements, this paper introduces a numerical framework to jointly simulate NMR relaxometry experiments and two-phase flow on the micrometer scale. Herein, the NMR diffusion equations were tied to an established Lattice Boltzmann algorithm used in computational fluid dynamics. The numerically simulated NMR data were validated for both surface-limited and diffusion-limited relaxation regimes using analytical solutions available for fully and partially watersaturated simple pore geometries. Subsequently, simulations were compiled using a complex pore space derived from three-dimensional computer tomography (CT) data of an unconsolidated sand and the results were compared to respective NMR T 1 relaxometry data. The NMR transients simulated for different water saturations matched the measured data regarding initial amplitudes (i.e., porosity and saturation) and relaxation behavior (i.e., distribution of water-saturated pores). Thus, we provide a simulation tool that enables study of the influences of structural and physicochemical properties, such as pore connectivity and pore coupling, surface relaxivity, or diffusivity, on partially saturated porous media, e.g, rocks or soils, with NMR T 1 relaxometry data.

A critical mini-review on the low-field nuclear magnetic resonance investigation of pore coupling effects in near-surface environments

“…Two main simulation methods are predominant in literature: Random Walk (e.g., Talabi, 2008) and Finite Elements (e.g., Mohnke and Klitzsch, 2010;Mitchell et al, 2019). Furthermore, Mohnke et al (2014) developed a Boltzmann Lattice framework, allowing for the joint simulation of NMR relaxation and transport properties in unsaturated environments. Several versions of the Random Walk method have been developed deviating from the traditional fix-step-size technique: in the First Arrival or First Passage approach (e.g., Toumelin et al, 2003;Mitchell et al, 2019) the step-size of the walkers depends on its proximity to the pore wall, while, in the Variable-Step-Size approach (e.g., Zhang et al, 2011;Carneiro et al, 2013), each walker moves at changing step-sizes with its own internal clock.…”

“…The study of pore coupling effects has so far been limited to fully-saturated conditions. The NMR method, nevertheless, has great potential for studying unsaturated conditions and fluid-flow processes in the vadose zone (Costabel and Yaramanci, 2011;Walsh et al, 2014;Flinchum et al, 2019;Tian, 2021); it can provide information regarding water availability, distribution and movement, and has already been used to study infiltration mechanisms (e.g., Walsh et al, 2014), draining processes (e.g., Mohnke et al, 2014), water availability for plants in form of rock moisture (e.g., Rempe and Dietrich, 2018;Schmidt and Rempe, 2020;Zhang and Zhang, 2021), among others.…”