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

The mechanism behind the NMR surface-relaxation times (T_1S,2S) and the large T_1S/T_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 n-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 n-heptane shows a power-law dependence on the concentration of n-heptane (φ_C7) in the polymer matrix, consistent with Archie's model of tortuosity. We calculate the autocorrelation function G(t) for ¹H-¹H dipole-dipole interactions of n-heptane in the polymer matrix and use this to generate the NMR frequency (f₀) dependence of T_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 n-heptane in the polymer matrix. For weak confinement (φ_C7 > 50 vol %), we find that T_1S/T_2S ≃ 1. Under strong confinement (φ_C7 ψ 50 vol %), we find that T_1S/T_2S ψ 4 increases with decreasing φ_C7 and that the dispersion relation T_1S ∝ f₀ 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.