Integral methods to assess ventilation rates in operational spaces, with a framework that provides assessment via uncertainty quantification
File(s)
Published version
Author(s)
Finneran, Joshua
Burridge, Henry C
Type
Journal Article
Abstract
We present a novel formulation of the integral method for quantifying effective ventilation rates from metabolic carbon dioxide (CO2) measurements, applicable to general operational indoor environments (transient and spatially heterogeneous), and 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 vari able ventilation rates, and uncertain CO2 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 CO2 variability both between different classrooms and within specific classrooms. A key finding is that CO2 measurements in operational classrooms taken over periods as short as 30 minutes 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 CO2 generation rates, which remain significant even when averaged over approximately 30 occupants.
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 CO2 variability both between different classrooms and within specific classrooms. A key finding is that CO2 measurements in operational classrooms taken over periods as short as 30 minutes 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 CO2 generation rates, which remain significant even when averaged over approximately 30 occupants.
Date Issued
2026-01-15
Date Acceptance
2025-10-26
Citation
Building and Environment, 2026, 288
ISSN
0360-1323
Publisher
Elsevier BV
Journal / Book Title
Building and Environment
Volume
288
Copyright Statement
© 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Publication Status
Published
Article Number
113910
Date Publish Online
2025-10-29