Critical Role of Confinement in the NMR Surface Relaxation and Diffusion of <i>n</i>-Heptane in a Polymer Matrix Revealed by MD Simulations

Abstract

The mechanism behind the NMR surface-relaxation times (<i>T</i>_1S,2S) and the large <i>T</i>_1S/<i>T</i>_2S ratio of light hydrocarbons confined in the nanopores of kerogen remains poorly understood and consequently has engendered much debate. Toward bringing a molecular-scale resolution to this problem, we present molecular dynamics (MD) simulations of ¹H NMR relaxation and diffusion of <i>n</i>-heptane in a polymer matrix. The high-viscosity polymer is a model for kerogen and bitumen that provides an organic "surface" for heptane. Diffusion of <i>n</i>-heptane shows a power-law dependence on the concentration of <i>n</i>-heptane (ϕ_C7) in the polymer matrix, consistent with Archie's model of tortuosity. We calculate the autocorrelation function <i>G</i>(<i>t</i>) for ¹H-¹H dipole-dipole interactions of <i>n</i>-heptane in the polymer matrix and use this to generate the NMR frequency (<i>f</i>₀) dependence of <i>T</i>_1S,2S as a function of ϕ_C7. We find that increasing molecular confinement increases the correlation time, which decreases the surface-relaxation times for <i>n</i>-heptane in the polymer matrix. For weak confinement (ϕ_C7 > 50 vol %), we find that <i>T</i>_1S/<i>T</i>_2S ≃ 1. Under strong confinement (ϕ_C7 ≲ 50 vol %), we find that <i>T</i>_1S/<i>T</i>_2S ≳ 4 increases with decreasing ϕ_C7 and that the dispersion relation <i>T</i>_1S ∝ <i>f</i>₀ is consistent with previously reported measurements of polydisperse polymers and bitumen. Such frequency dependence in bitumen has been previously attributed to paramagnetism; instead, our studies suggests that ¹H-¹H dipole-dipole interactions enhanced by organic nanopore confinement dominate the NMR response in saturated organic-rich shales.