Derivation of an indoor air averaging time model from the mass balance equation for the case of independent source inputs and fixed air exchange rates

Previous human activity pattern-exposure models have required improved ways for handling the serial autocorrelation of pollutant concentrations in indoor and in-transit microenvironments. Because existing models often sample concentrations from microenvironmental distributions for different averaging times, one approach for handling this autocorrelation is to develop an averaging time model for each microenvironment of importance. The paper explores a new approach for developing averaging time models: deriving the model theoretically from the mass balance equation, which describes the relationship between the time series of the input and output concentrations of any pollutant introduced into a well-mixed chamber. Beginning with the mass balance equation, the paper derives an averaging time model that predicts the mean, variance, and autocorrelation of the time series of pollutant concentrations in a well-mixed chamber for any averaging time. The paper considers the case of a discrete model in which the input source concentration is a time series of independent, piecewise-constant concentrations of equal duration while the air exchange rate remains fixed. Because the model is derived theoretically, the model is exact for the conditions specified. The goal of the research is to provide human exposure researchers with basic concepts for designing and developing useful, practical algorithms for futuremore » exposure and indoor air quality models.« less