title: On the formulation of environmental fugacity models and their numerical solutions.
abstract: Multimedia models based on chemical fugacity, solved numerically, play an important role in investigating and quantifying the environmental fate of chemicals such as persistent organic pollutants. These models have been used extensively in studying the local and global distribution of chemicals in the environment. The present study describes potential sources of error that may arise from the formulation and numerical solution of environmental fugacity models. The authors derive a general fugacity equation for the rate of change of mass in an arbitrary volume (e.g., an environmental phase). Deriving this general equation makes clear several assumptions that are often not articulated but can be important for successfully applying multimedia fugacity models. It shows that the homogeneity of fugacity and fugacity capacity in a volume (the homogeneity assumption) is fundamental to formulating discretized fugacity models. It also shows that when using the fugacity rather than mass as the state-variable, correction terms may be necessary to accommodate environmental factors such as varying phase temperatures and volume. Neglecting these can lead to conservation errors. The authors illustrate the manifestation of these errors using heuristic multimedia fugacity models. The authors also show that there are easily avoided errors that can arise in mass state-variable models if variables are not updated appropriately in the numerical integration scheme. Environ Toxicol Chem 2016;35:2182-2191. © 2016 SETAC.
authors.affiliation: Griffith School of Environment, Griffith University, Brisbane, Queensland, Australia.
authors.forename: Michael L
authors.initials: ML
authors.lastname: Bates
authors.affiliation: Environmental Futures Research Institute, Griffith University, Brisbane, Queensland, Australia.
authors.forename: Marie
authors.initials: M
authors.lastname: Bigot
authors.affiliation: Griffith School of Environment, Griffith University, Brisbane, Queensland, Australia.
authors.forename: Roger A
authors.initials: RA
authors.lastname: Cropp
authors.affiliation: Department of Earth, Atmospheric and Planetary Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
authors.forename: Darren
authors.initials: D
authors.lastname: Engwirda
authors.affiliation: Center for Global Change Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
authors.forename: Carey L
authors.initials: CL
authors.lastname: Friedman
authors.affiliation: Griffith School of Environment, Griffith University, Brisbane, Queensland, Australia.
authors.forename: Darryl W
authors.initials: DW
authors.lastname: Hawker
mesh_terms: D003198:Computer Simulation; D004784:Environmental Monitoring / Q000379:methods*; D004785:Environmental Pollutants / Q000032:analysis* / Q000737:chemistry; D005544:Forecasting; D008956:Models, Chemical; D008962:Models, Theoretical; D014835:Volatilization
chemical_list: D004785:Environmental Pollutants
keywords: Environmental modeling; Environmental partitioning; Fate modeling; Fugacity modeling; Persistent organic pollutants (POPs); State-variable