Inferring ventilation rates with quantified uncertainty in operational rooms using point measurements of carbon dioxide: Classrooms as a case study

We present a robust integral method to estimate the daily mean per-person ventilation rate Q¯pp based on carbon dioxide (CO2) concentration measurements in operational spaces, and limited other data. The method makes no assumptions regarding the ventilation provision throughout the day, nor requires the room to be in a steady state, nor the air within to be well-mixed. We demonstrate that several integral parameters remain reliably close to a value of unity, despite large variations in room conditions. Evaluating the likely distributions of integral parameters provides a method to quantify the uncertainty bounds and therefore assess the reliability of these ventilation estimates. Taking school classrooms as a case study, estimates of Q¯pp based on measured CO2 are shown to exhibit uncertainty bounds (of 95% confidence intervals) of approximately ±24% if no other data than the classroom timetable is available. Deploying four CO2 sensors within a classroom is expected to halve the uncertainty bounds to around ±12%. Moreover, the framework presented herein evidences that when the same classroom experiences similar usage on two different days, the relative per-person ventilation rate achieved during these two days can be simply determined by the ratio of their integral excess CO2 concentrations. These significant findings offer great scope to facilitate more reliable ventilation estimates, particularly from large-scale data sets of CO2 measured in operational spaces, to better inform assessments of indoor air quality.