Integral methods to assess ventilation rates in operational spaces, with a framework that provides assessment via uncertainty quantification

We present a novel formulation of the integral method for quantifying effective ventilation rates from metabolic carbon dioxide ( CO 2 ) measurements, applicable to general operational indoor environments (transient and spatially heterogeneous), and to other tracer gases. This formulation provides new insights into the contributing factors to uncertainty, determining that in classrooms spatial heterogeneity is the dominant source of uncertainty relative to those from variable ventilation rates, and uncertain CO 2 generation rates from occupants. The integral method is assessed against common alternatives (decay, equilibrium, and build-up methods) using a new framework that solves the general scalar conservation equation following dynamically selected inputs from prescribed probability distributions using Monte Carlo methods. Compared to alternatives, integral methods provide similar or superior accuracy but are shown to be more widely applicable to any time period, while equilibrium methods are the most restrictive in their application. A simulated dataset, representative of UK secondary school classrooms, is generated and validated against measured CO 2 variability both between different classrooms and within specific classrooms. A key finding is that CO 2 measurements in operational classrooms taken over periods as short as 30 min can yield meaningful estimates of the effective ventilation rate, with 95% confidence intervals typically within ± 30 % . Deploying multiple sensors can mitigate this uncertainty, e.g. to around ± 14 % using four sensors. Further uncertainty reductions are challenging, not least, due to the uncertainties in CO 2 generation rates, which remain significant even when averaged over approximately 30 occupants. • Integral formulation applies to transient, heterogeneous operational indoor spaces. • Statistical parametrisation of classrooms enables quantifying uncertainty. • CO 2 -based ventilation rate estimates have ＋/- 30% uncertainty (95% conf.). • Using 4 sensors reduces uncertainty to ±14% in typical classroom settings.