26 Aug 2021

Fugacity and Multi-Media Models: A Personal Odyssey

Don Mackay, Trent University and University of Toronto

Back in the 1970s, I had the privilege of working with George Baughman of the U.S. Environmental Protection Agency lab at Athens, Georgia, on his Exposure Analysis Modeling System (EXAMS). Baughman had a vision that multi-box evaluative models of chemical in fate in aquatic systems could identify and quantify relative rates of processes of fate and exposure of chemicals and ultimate exposures. I heartily agreed, and this conviction propelled me on a trajectory to develop and apply multi-media models to the fate of chemicals in the environment. I saw two opportunities to innovate. First was to include all media into which the chemical could partition, including the atmosphere and biota. Second, was the controversial suggestion to use fugacity instead of concentration to describe the multi-media partitioning of organic chemicals between all relevant environmental media.

I wrote an article, “Finding Fugacity Feasible,” for Environmental Science and Technology in 1979 outlining these ideas. It suggested that for teaching purposes, it was useful to proceed in four levels of increasing complexity and fidelity to real systems. Level I simply described equilibrium partitioning between media boxes. Level II introduced reaction and advection. Level III introduced intermedia box-to-box transport under steady-state conditions in which chemical concentrations do not change with time. Level IV was similar to Level III but treated more complex unsteady-state or dynamic conditions in which concentrations can change with time, as occurs in reality. Levels I to III used simple algebraic equations, whereas Level IV involved differential equations. Students responded positively to these models.

I was very fortunate to be encouraged at SETAC by individuals from the chemical industry, especially Brock Neely of Dow Chemical. We conceived of a model 1 m2 “unit world” consisting of a column of air, water, soil, sediment and biota. Neely was understandably interested in bioconcentration of hydrophobic chemicals such as DDT between water and fish, a process that Jerry Hamelink showed is essentially equi-fugacity of the substance between water and fish. We also had invaluable support from Christina Cowen (Ellsberry) of Procter and Gamble, who saw the merits of applying models to the fate of domestic and personal care products. With Cowen, Antonio di Guardo and Sally Patterson, we later devised the EQuilibrium Criterion (EQC) model, which treats a more realistic area of 100,000 km²–about the area of Ohio. Calculations can be done at the same four levels of complexity. I was sold on the SETAC “3 pillar principle” of collaboration between academia, government and business. The underlying math in fugacity modeling is simple and was conveniently done using “fugacity forms,” similar to income tax forms but much more pleasant. Accordingly, in 1992, I wrote the first edition of “Multimedia Environmental Partitioning: The Fugacity Approach,” which contained fugacity forms that were particularly useful for assigning large numbers of individual problems to students of chemical fate assessment in the environment. Copying assignments was very difficult!

These calculations were particularly valuable and attractive for educating students about the wide variability of chemical fates in the environment, as well as the causes. All they needed was blank fugacity forms to fill in the quantities, a slide rule or a hand calculator, and physical chemical property data. Accordingly, my colleagues Wan Ying Shiu and Kuo Ching Ma compiled chemical property data and specimen evaluations in a series of four “Illustrated Handbooks of Physical Chemical Property Data and Environmental Fate for Organic Chemicals.” The handbooks contain only real experimental data since we were skeptical about the use of available quantitative structure activity relationships.

Then disaster struck!

Desktop computers became available and spreadsheets such as Excel replaced my beloved fugacity forms. There was increased reliance on more accurate QSARS. Disaster struck again with the invention of the Internet, email and spreadsheets, and huge almost unbelievable property databases became widely available. Given encouragement, our group (too numerous to mention individually) applied fugacity models to diverse evaluative and real systems. A particular focus was the Great Lakes Areas of Concern, models of urban and rural regions, and the indoor environment. Much progress was made in fugacity modeling of bioconcentration, bioaccumulation and biomagnification (a simple fugacity increase in animals driven by lipid solvent depletion). We also tackled the global distribution of chemicals by long-range atmospheric transport and fractionation, and we applied fugacity to toxicokinetic models exploiting the pioneering work of Mel Andersen. Passive sampling devices (simply fugacity meters) became popular. They were and continue to be successfully applied in water and air and can be used to measure fugacities directly in the environment.

In 1995, I moved from the bustling University of Toronto to the quieter Trent University and with industry and government support set up, with Eva Webster, the Canadian Environmental Modelling Centre to promote environmental modeling in general and fugacity models in particular, again on the SETAC principle of three pillars. A second edition of the fugacity book was needed and was published in 2001.

Progress continued with advances in chemical property estimation, and cheeky chemists were now claiming that they can calculate certain properties such as Kow from first principles better than they can be measured! My colleague at Trent, Mark Parnis, understands better these “first principles” computations and how we could better present examples of modeling techniques using spreadsheets. In 2020, we compiled the third edition of “Multimedia Environmental Models: The Fugacity Approach“ (CRC Press) with an emphasis on teaching the fundamentals of environmental model-building, making models available over the internet and encouraging readers to build their own models. A doctoral student who includes a fugacity model in their dissertation is guaranteed to pass because the examiners likely do not understand the subtleties of fugacity models.

A glimpse into a murky future.

It has been a joy to watch others exploit the concept of fugacity when seeking to understand and quantify organic chemical fate in the environment. Fugacity has contributed to explaining the toxicokinetics of baseline narcosis. Can it contribute to toxicodynamics?

A 2018 ES&T paper by Li Li, Jon Arnot and Frank Wania has demonstrated the power of comprehensive multi-media models by describing the fate of polycholorianted biphenyls (PCBs) in the Baltic region, including changing emissions, steady state and dynamic multimedia near-field and far-field partitioning, bioaccumulation, human uptake and intergenerational transport, all transparently expressed using fugacity. Model “blocks” are used to facilitate application to other chemicals. We need more examples of this type to convince reluctant regulators of the potential of models to “manage” chemicals.

The example in Li, Arnot and Wania’s paper suggests that fugacity can play a key role in chemical management, not only by describing the distribution of chemicals in the environment but by showing that chemicals can coexist with humans in an ecosystem in situations where multi-media fugacities are maintained below a certain “no-effect” level. It is clearly impossible to monitor and evaluate the hundreds of thousands of chemicals of commerce that contaminate our ecosystems and us as individuals. But what we can (and should) do is model chemical use and discharges, fate in the environment and exposures, exploiting emerging predictive property estimation methods and the power of modern information technology. Skeptics will raise issues of model validation, but even achievable order of magnitude estimations of fugacities and concentrations from multi-media models may be adequate to identify most “bad actors.” At least it would be a start towards addressing the issue of environmental contamination by chemicals. It raises the possibility of using fugacity as a global synoptic indicator of contamination. It could be a tangible step towards a “greener” and more sustainable environment by assisting efforts to define an “operating space” within which humanity can enjoy the benefits of a diversity of chemicals, while avoiding adverse effects.

Now age 85, I can happily sit back and watch others apply and promote fugacity. To assist progress, I have requested all my royalties from the fugacity books and handbooks be paid to SETAC to support young enthusiastic environmental students who are the scientists of tomorrow. I hope they too can exploit the three pillars of SETAC and continue the fugacity odyssey.

Author’s contact information: [email protected]