Continuous monitoring systems, consisting of multiple fixed sensors, are increasingly being deployed at oil and gas production sites to detect methane emissions. While these monitoring systems operate continuously, their efficiency in detecting emissions will depend on meteorological conditions, sensor detection limits, the number of sensors deployed, and sensor placement strategies. This work demonstrates an approach to assess the effectiveness of continuous sensor networks in detecting infinite-duration and fixed-duration emission events. The case studies examine a single idealized source and a group of nine different sources at varying heights and locations on a single pad. Using site-specific meteorological data and dispersion modeling, the emission detection performance is characterized. For these case studies, infinite-duration emission events are detected within 1 h to multiple days, depending on the number of sensors deployed. The percentage of fixed-duration emission events that are detected ranged from less than 10% to more than 90%, depending on the number of sources, emission release height, emission event duration, and the number of sensors deployed. While these results are specific to these case studies, the analysis framework described in this work can be broadly applied in the evaluation of continuous emission monitoring network designs.