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 from a point source, using a case study in west Texas. The case study examines a 10 kg/hr source at a height of 5.5m, representative of the emission pattern from a liquid storage tank. Using site specific meteorological data and dispersion modeling, emission detection performance was characterized. For this case study, infinite duration emission events were detected within 1 hour to multiple days, depending on the numbers of sensors deployed. The percentage of fixed duration emission events that were detected ranged from less than 30% to more than 90%, depending on the emission event duration and the number of sensors deployed. Because the dispersion modeling for the case study region predicted relatively narrow plumes, with steep concentration gradients, the benefit of using sensors with low detection thresholds was less important to system performance than the number of sensors deployed and the positioning of the sensors. While these results are specific to this case study, the analysis framework described in this work can be broadly applied in the evaluation of continuous emission monitoring network designs. Overall, while there can be time delays in continuous monitoring systems detecting continuous infinite duration emission events, and while some fixed duration emission events may not be detected, the detection efficiencies for continuous monitoring networks are greater than efficiencies for periodic short duration measurements, such as monthly or quarterly inspections.