Quantifying mechanical ventilation performance: The connection between transport equations and Markov matrices

Most people spend approximately 90% of their lives indoors. Thus, designing effective ventilation systems is essential to mitigating problems with indoor air quality. The measures of mechanical ventilation design performance considered in this study are age of air, air residual life time, air residence time, and ventilation effectiveness. This paper presents two different methods to help quantify these measures. The first method is based on transport equations, where a continuous representation of these quantities are calculated. The second method is based on Markov matrices, where a discrete representation of these quantities are calculated. We show 1) how both the continuous and discrete methods are related and 2) that the age of air and residual life time are adjoints. A new transport equation for residual life time along with methods for these quantities using Markov matrices are established. The two approaches are validated and compared using previously established experimental data. The results show that both approaches provide similar results. Using these techniques allows for the quantities of residual life time and residence time to be integrated into the design processes. This paper provides a simple framework that enables designers to get a comprehensive picture of the ventilation systems they design.