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

Area of Science:

• Environmental Engineering
• Chemical Engineering
• Atmospheric Science

Background:

• Calculating contaminant dispersion in near field/far field (NF/FF) zones involves complex coupled equations.
• The difficulty of deriving analytical solutions for contaminant concentration functions CNF(t) and CFF(t) depends heavily on the emission rate function G(t).

Purpose of the Study:

• To present a novel method for approximating NF/FF contaminant concentration functions.
• To decouple the coupled NF/FF dispersion equations for easier mathematical derivation.
• To validate the accuracy of the proposed approximation method.

Main Methods:

• Decoupling NF and FF equations by treating each as an isolated well-mixed space with distinct volumes and airflow rates.
• Deriving independent contaminant concentration functions for the FF zone (CWMR1(t)) and NF zone (CWMR2(t)) assuming identical emission rates.
• Validating the approximation by comparing the sum CWMR1(t) + CWMR2(t) to CNF(t) and CWMR1(t) to CFF(t).
• Presenting a discrete-time numerical solution using a Markov matrix.

Main Results:

• The sum of independently derived FF and NF concentration functions (CWMR1(t) + CWMR2(t)) provides an excellent approximation for the coupled NF/FF concentration (CNF(t)).
• The independently derived FF concentration function (CWMR1(t)) serves as an excellent approximation for the coupled FF concentration (CFF(t)).
• The proposed decoupling method significantly simplifies the approximation of contaminant concentration functions.

Conclusions:

• The decoupling method offers a more accessible approach to approximating NF/FF contaminant concentrations compared to solving coupled equations.
• The validated approximations improve the feasibility of dispersion modeling, especially when analytical solutions are intractable.
• A numerical Markov matrix-based solution is also presented for discrete-time analysis of the NF/FF dispersion system.