Fugacity models

Application of Fugacity Models to the Estimation of Chemical Distribution and Persistence in the Environment... 

An attractive feature of the fugacity models is that they can be applied at various levels of complexity, depending on the perceived modelling need and the availability of data. The determinants of complexity are believed to be as follows. 

Equilibrium. Equilibrium between compartments can be expressed either as partition coefficients K.. (i.e. concentration ratio at equilibrium) or in the fugacity models as fugacity capacities and Z. such that K.. is Z./Z., the relationships being depicted in Figur 1. Z is dellned as tfte ratio of concentration C (mol/m3) to fugacity f (Pa), definitions being given in Table I. 

We illustrate these concepts by applying various fugacity models to PCB behavior in evaluative and real lake environments. The evaluative models are similar to those presented earlier (3, 4). The real model has been developed recently to provide a relatively simple fugacity model for real situations such as an already contaminated lake or river, or in assessing the likely impact of new or changed industrial emissions into aquatic environments. This model is called the Quantitative Water Air Sediment Interactive (or QWASI) fugacity model. Mathematical details are given elsewhere (15). 

The evaluative fugacity model equations and levels have been presented earlier (1, 2, 3). The level I model gives distribution at equilibrium of a fixed amount of chemical. Level II gives the equilibrium distribution of a steady emission balanced by an equal reaction (and/or advection) rate and the average residence time or persistence. Level III gives the non-equilibrium steady state distribution in which emissions are into specified compartments and transfer rates between compartments may be restricted. Level IV is essentially the same as level III except that emissions vary with time and a set of simultaneous differential equations must be solved numerically (instead of algebraically). 

The QWASI fugacity model contains expressions for the 15 processes detailed in Figure 2. For each process, a D term is calculated as the rate divided by the prevailing fugacity such that the rate becomes Df as described earlier. The D terms are then grouped and mass balance equations derived. 

Figure 2A. Diagram of processes included in the QWASI fugacity model showing D values for a trichlorobiphenyl in a lake similar to Lake Michigan.

The QUASI fugacity model was then run for a trichlorobiphenyl in a lake the size of Lake Michigan, being approximately 60,000 times the size of the evaluative environment. A detailed justification for the selection of D values is beyond our scope here but in selecting values, we have relied on recent reports by Neely (11), Rogers (15), Armstrong and Swackhamer (16), Thomann (17), and Andren (18). 

Progress can best be made by applying these models to new and existing chemicals at all scales, i.e. to real environments such as Lake Michigan, to rivers, or small ponds, to microcosms and ultimately to laboratory flasks in which one process is isolated for study. The fugacity models described here will, it is hoped, contribute to the integration of such disparate data into more accurate profiles of chemical behavior in the environment. 

Mackay, D. Paterson, S. "Fugacity Models for Predicting the Environmental Behavior of Chemicals", report prepared for Environment Canada 1982. 

Mackay, D. Joy, M. Paterson, S. "AQuantitative Water Air Sediment Interaction (QWASI) Fugacity Model for Describing Chemical Fate in Lakes and Rivers" submitted to Chemosphere, 1983. 

The earliest or Level I fugacity models simulate the simple situation in which a chemical achieves equilibrium between a number of phases of different composition and volume. The prevailing fugacity is simply/ = M/Y.V, x Z where M is the total quantity of chemical (mol), V, is volume (m3), and Z, is the corresponding phase Z value (mol Pa-1 m-3). Although very elementary and naive, this simulation is useful as a first indication of where a chemical is likely to partition. It is widely used as a first step in chemical fate assessments. 

Besides the fugacity models, the environmental science literature reports the use of models based on Markov chain principle to evaluate the environmental fate of chemicals in multimedia environment. Markov chain is a random process, and its theory lies in using transition matrix to describe the transition of a substance among different states [39,40]. If the substance has all together n different kinds of states,... 

The current version of CalTOX (CalTOX4) is an eight-compartment regional and dynamic multimedia fugacity model. CalTOX comprises a multimedia transport and transformation model, multi-pathway exposure scenario models, and add-ins to quantify and evaluate variability and uncertainty. To conduct the sensitivity and uncertainty analyses, all input parameter values are given as distributions, described in terms of mean values and a coefficient of variation, instead of point estimates or plausible upper values. 

Mackay D, Diamond M (1989) Application of the QWASI (quantitative water air sediment interaction) fugacity model to the dynamics of organic and inorganic chemicals in lakes. Chemosphere 18 1343-1365... 

Mackay D, Paterson S (1991) Evaluating the multimedia fate of organic chemicals a level III fugacity model. Environ Sci Technol 25 427-436... 

Devillers J, Bintein S (1995) CHEMFRANCE a regional level III fugacity model applied to France. Chemosphere 30(3) 457 176... 

Mackay D, Joy M, Paterson S (1983) A quantitative water, air, sediment interaction (Qwasi) fugacity model for describing the fate of chemicals in lakes. Chemosphere 12(7/8) 981-997... 

While QWASI is an easy to use multimedia fate modeling tool, it has been originally designed as a fugacity model. Even though an adaptation to ionic substances exists and it has been applied to lead before, it needs to be recognized that it does not take speciation of metals into account. This adds to the overall uncertainty of results. 

Mackay D, Paterson S, Joy M (1983) Application of fugacity models to the estimation of chemical distribution and persistence in the environment. In Swann Eschenroeder (eds) Fate of chemicals in the environment. American Chemical Society Symposium Series 225 175-196... 

---