  The mechanism behind the NMR surface relaxation and the large $T_1$/$T_2$
ratio of light hydrocarbons confined in the nano-pores of kerogen remains
poorly understood, and consequently has engendered much debate. Towards
bringing a molecular-scale resolution to this problem, we present molecular
dynamics (MD) simulations of $^1$H NMR relaxation and diffusion of heptane in a
polymer matrix, where the high-viscosity polymer is a model for kerogen and
bitumen that provides an organic "surface" for heptane. We calculate the
autocorrelation function $G(t)$ for $^1$H-$^1$H dipole-dipole interactions of
heptane in the polymer matrix and use this to generate the NMR frequency
($f_0$) dependence of $T_1$ and $T_2$ relaxation times as a function of
$\phi_{C7}$. We find that increasing molecular confinement increases the
correlation time of the heptane molecule, which decreases the surface
relaxation times for heptane in the polymer matrix. For weak confinement
($\phi_{C7} > 50$ vol%), we find that $T_{1S}/T_{2S} \simeq 1$. Under strong
confinement ($\phi_{C7} \lesssim $ 50 vol%), we find that the ratio
$T_{1S}/T_{2S} \gtrsim 4$ increases with decreasing $\phi_{C7}$, and that the
dispersion relation $T_{1S} \propto f_0$ is consistent with previously reported
measurements of polymers and bitumen. Such frequency dependence in bitumen has
been previously attributed to paramagnetism, but our studies suggests that
$^1$H-$^1$H dipole-dipole interactions enhanced by organic nano-pore
confinement dominates the NMR response in saturated organic-rich shales,
without the need to invoke paramagnetism.
