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.