In this paper, we compare the Gaussian plume and puff atmospheric dispersion models with a focus on characterizing methane emissions on oil and gas production sites. We find that the Gaussian puff model outperforms the Gaussian plume model in terms of correlation coefficient and RMSE between CMS observations and model predictions. We provide open-source implementations of the Gaussian puff model for a general 3D grid and a specialized version for point-in-space sensor networks, which can be easily implemented in a parallel architecture and scaled up for use on distributed computing systems. These implementations were motivated by the need for a dispersion model fast enough to be used for near real-time methane leak detection and largescale applications to help quantify emissions at hundreds of oil and gas sites across an oil basin. While our algorithms are tailored to rapid emission mitigation on oil and gas sites, the proposed implementations can be easily adapted for use in numerous applications involving the modeling of near-field dispersion. Finally, we provide physically-motivated guidelines for setting simulation parameters for the Gaussian puff model in Section 4.2 since they affect both simulation accuracy and computational cost.