To address these issues, we present a modern computationally-efficient algorithm to simulate the Gaussian puff model. This new implementation, distinct from both naive and regulatory-grade models , employs dynamic spatiotemporal thresholds to reduce unnecessary computations and achieves a speedup of two orders of magnitude over a naive implementation. This feature renders the algorithm suitable for application at different scales, from sparse sensor networks to dense grid-level simulations. Additionally, the lightweight implementation allows for higher spatial and temporal resolution than regulatory-grade implementations and only requires practically available meteorological information. Another important contribution of this work is to provide the first (to our knowledge) direct comparison of the Gaussian plume and puff models in the context of modeling methane emissions on oil and gas sites, finding that the Gaussian puff outperforms the Gaussian plume across multiple measure-of-fit metrics. Note that while we focus on applications related to oil and gas sites in this work, the proposed implementations can be easily adapted to different near-field atmospheric transport modeling applications.