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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 $ϕ_{C7}$. 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 ($ϕ_{C7} > 50$ vol%), we find that $T_{1S}/T_{2S} \simeq 1$. Under strong confinement ($ϕ_{C7} \lesssim $ 50 vol%), we find that the ratio $T_{1S}/T_{2S} \gtrsim 4$ increases with decreasing $ϕ_{C7}$, 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.