Improving the measurement of air change rates using the decay method: Quantifying the uncertainty of the well-mixed assumption and identifying the required sampling locations

¹ Department of Civil and Building Engineering, Université de Sherbrooke, 2500 boul. de l’Université, J1K 2R1, Sherbrooke, Québec, Canada
² Centre for Zero Energy Building Studies, Concordia University, 1515 St. Catherine W., H3G 2W1, Montreal, Québec, Canada

^* Corresponding author: dahai.qi@usherbrooke.ca

Abstract

Improving building ventilation has emerged as a vital imperative in today’s post-Covid-19 era, while accurately estimating air change rates continues to present a considerable challenge. For more than fifty years, the decay method has been employed for this purpose, assuming the well-mixed condition that rarely occurs. However, existing mixing models (e.g., K or E_z) are limited in addressing this gap since their reported data are subjective and inconsistent across different standards (ASHRAE and AIHA). Therefore, we developed a novel modified decay method that includes two proposed factors: the uniformity index (U_i) and the sampling factor (S_f). These two factors help to quantify the well-mixed assumption’s uncertainty and identify the minimum required sampling locations for tracer measurements. The modified decay method is tested in a classroom, measuring the spatial variations of CO₂ using automated data acquisition. The proposed method significantly reduced the error caused by the well-mixing assumption of estimated air change rates from 26% to 3%. The sampling locations are identified as a function of the zone’s geometry. The findings of this study can be used to improve the ventilation performance of buildings.