A transfer function technique to describe odor causing VOCs transport in a ventilated airspace with mixing/adsorption heterogeneity

A model describing odor causing volatile organic compounds (VOC-odor) transport in a ventilated airspace influenced by heterogeneity of adsorption surface of ambient aerosol and air mixing pattern is proposed and analyzed based on a transfer function modeling technique. In this study an advection–reaction impulse/step response function for VOC-odor is assumed. The system process presented by an ensemble transfer function is solved analytically in the Laplace domain. The analytical results are then numerically inverted using a modified fast Fourier transform algorithm. The model requires the specification of probability density function for residence time of airflow and for both equilibrium linear partitioning and first-order mass transfer rate parameters to quantify the specific air mixing pattern and transport processes. The model predicts the ensemble mean VOC-odor concentrations for a variety of adsorption kinetics and mixing pattern combinations as a function of the boundary impulse/step response inputs as well as residence time and adsorption rate statistics. The general behavior of output VOC-odor profiles is analyzed through the effects of mean adsorption rate coefficient, mean linear partitioning constant, mixing efficiency, mean residence time and coefficient of variations of both linear partitioning and rate coefficients. It * Corresponding author. E-mail address: [email protected] (C.-M. Liao). 0096-3003/02/$ see front matter 2002 Elsevier Science Inc. All rights reserved. PII: S0096 -3003 (02 )00224-2 Applied Mathematics and Computation 140 (2003) 255–277 www.elsevier.com/locate/amc indicates that when mixing/adsorption heterogeneity exists, simple complete mixing assumption and simple distribution of rate constant is inherently not sufficient to represent a more generally distributed mixing/adsorption process of VOC-odor transport in a ventilated airspace. 2002 Elsevier Science Inc. All rights reserved.