A decoupling method to compute near field and far field exposure concentrations

In the near field/far field (NF/FF) dispersion construct, the analytical solutions for the NF and FF concentration equations, respectively denoted CNF(t) and CFF(t) in mg/m3, are coupled in their mathematical derivation. Depending on the form of the contaminant emission rate function G(t) (mg/min), deriving CNF(t) and CFF(t) can range from being relatively easy to impossible. A method is presented to more easily approximate these concentration functions. The method decouples the NF and FF equations by treating the NF as an isolated well-mixed space with volume VNF (m3) and supply/exhaust airflow rate β(m3) and treating the FF as an isolated well mixed-space with volume V (m3) and supply/exhaust airflow rate Q (m3). Assuming that each space contains a source with the same contaminant emission rate function G(t), a contaminant concentration function is derived for the FF zone, denoted CWMR1(t), and an independent contaminant concentration function is derived for the NF zone, denoted CWMR2(t). Deriving a concentration function for a single zone is far easier than deriving coupled concentration functions. It is shown that the sum CWMR1(t) + CWMR2(t) provides an excellent approximation of CNF(t) and that CWMR1(t) provides an excellent approximation of CFF(t). A discrete-time numerical solution for the CNF(t) and CFF(t) system based on a Markov matrix is also presented.