Multimedia mass balance

Mackay D (1998) Multimedia mass balance models of chemical distribution and fate. In Schuurmann G, Markert B (eds) Ecotoxicology. Wiley, New York, pp 237-257... 

To understand the impact of individual processes on the compartmental distribution of DDT, model runs with a non-steady-state, zero-dimensional, multimedia mass balance box model (MPI-MBM) [Lammel (2004)] were conducted in addition to MPI-MCTM experiments. Parameterisations of intra- and intercompartmental mass exchange and conversion process in MPI-MBM are similar to those in MPI-MCTM. A detailed description of differences and a comparison of both models can be found in Lammel et al (2007). The DDT emissions were the global mean temporally varying DDT applications for the years 1950 to 1990. A repeating annual cycle around constant mean temperatures was simulated. Surface and air temperatures differ by 14 K constantly. 

SimpleBox is a multimedia mass balance model of the so-called Mackay type. It represents the environment as a series of well-mixed boxes of air, water, sediment, soil, and vegetation (compartments). Calculations start with user-specified emission fluxes into the compartments. Intermedia mass transfer fluxes and degradation fluxes are calculated by the model on the basis of user-specified mass transfer coefficients and degradation rate constants. The model performs a simultaneous mass balance calculation for all the compartments, and produces steady-state concentrations in... 

Of particular importance is the contamination of soil, because it receives pollutants from the atmosphere (e.g., sulfates and nitrates resulting from oxidation of nitrogen and sulfur oxides, and metals from smelters) and from the hydrosphere (e.g., sediments that concentrate heavy metals from aqueous bodies and mining operations). In multimedia mass-balance models, soil is an important sink as well as a conduit for mass transfer to vegetation and shallow groundwater. 

The calculation of characteristic times aids in the interpretation of multimedia mass balance for environmental compartments by conveying how long it will take for the compartment or phase to adjust as a result of each rate process. Obviously, the shorter characteristic time processes are the most important with respect to chemical fate. The following simple example demonstrates the use of fugacity, Z values, D values, and characteristic times when interpreting the results of mass balances. 

The multimedia urban model (MUM) is a fugacity-based mass balance model that treats the movement of POPs in an urban environment and links emissions to ambient chemical concentrations, and thus outdoor exposure (Diamond et al., 2001). MUM considers longterm, average conditions of chemical transport and transformation among six environmental compartments in urban areas (air, soil, surface water, sediment, vegetation and surface film see Figure 6.1) shows a concepmal version of the model). The model does not estimate event-specihc processes as do meteorological-based air or stormwater models. 

In multimedia box models, the environmental fate of a chemical is described by a set of coupled mass-balance equations for all boxes of the model. These equations include terms for degradation, inter-media exchange such as settling and resuspension of particles, and transport with air and water flows [19,20]. Equations for different boxes are coupled by inter-media exchange terms (linking different environmental media) and terms for trans-... 

Even if the data input requirements for kinetics/rates models are met, difficult problems remain regarding the sensitivity and overall reliability of the predictions made. One approach to validating and refining these models is to gather mass balance information on the environmental distributions of well-known chemicals. This involves multimedia sampling under well-defined environmental conditions and known chemical input rates. The chemical mass balance between the environmental media is then compared to model predictions. These mass-... 

Multimedia environmental models often incorporate the concept of fugac-ity into mass balance calculations. As pioneered by Dr. Donald Mackay and described in Table 2.3, fugacity models can reflect four levels of sophistication [64]. Level III fugacity models are commonly used to describe the fate and transport of a chemical released to the environment that undergoes degradation and advective transport between compartments. One such model is described below. 

Multimedia environmental models perform mass balances on chemicals in the environment and can predict the resulting concentrations in various environmental compartments. Many models incorporate the concept of fugacity to allow for the deviations of the natural world from ideal behavior. 

Although LCA contains elements of the tools discussed earlier in this chapter—mass balance, multimedia modeling of environmental fate and transport, and risk characterization— it is a distinct discipline with its own jargon, precepts, and limitations. 

To illustrate the use of Z andD values in a simple multimedia model, we present below a steady-state mass balance for an air-water-sediment system representing a small lake with inflow and outflow. It is an application of the quantitative water air sediment interaction (QWASI) model that is available from the Web site www.trentu.ca/cemc. The chemical is similar in properties to a volatile hydrocarbon such as benzene. Table 3.3 lists the lake properties, the chemical input rates in the inflowing water, its properties as partition coefficients, Z values and D values for all the transport and reaction rates. 

A final note. The interface compartment concept has application for the next generation of multimedia compartment box models and other models as well. Presently several of these models use versions of Ohm s law as noted above as well as other procedures. The numerical results produced appear to be reasonable and provide good approximations apparently. However, without the additional mass balance provided by applying the interface compartment concept, the advective transport processes fail to impact the magnitude of the interface concentfation. This influences the flux and finally the media mass concentrations. Comparative model studies using the present-day approaches of combining interface fluxes and the IC model approach need to be performed and the results evaluated. Such studies may aid the development of a more realistic and appropriate approaches for connecting chemical flux between multimedia environmental compartments. 

Our approach here is essentially that of McKone and Benett (2003), which is based on the Jury et al. (1983) model. It is incorporated within the latest version of the CalTOX model (McKone, 1993) and the original version of the TRIM (USEPA, 2003) model, but also used in other models such as BETR (MacLeod et al., 2001). This approach uses one or more soil compartment layers while maintaining a structure that links easily to other compartments such as air and vegetation in multimedia models. This approach begins by setting up the differential equations describing the mass balance in soil and accounting for diffusion in air and water phases, advection via water, bioturbation, and chemical transformation. Erom the steady-state analytical solution to these equations, which can be applied stepwise to different layers, one develops an equivalent compartment model that uses compartment-based inventories and transfer factors. 

As noted above, there are cases where we need more accurate representations of how chemical concentration varies with depth. For example, we may be interested in transfers of chemicals from air to shallow ground water or want to consider how long-term applications of pesticides to the soil surface can impact terrestrial ecosystems—including burrowing creatures. However, we also wish to maintain a simple mathematical mass-balance structure of the multimedia model. To illustrate how we can set up a multilayer model that accurately captures soil mass transport processes, we next derive a vertical compartment structure with an air and three soil compartments, but any number of environmental compartments and soil layers can be employed in this scheme. Figure 8.6 provides a schematic of three soil layers linked to an air compartment and carrying pollutants downward to a saturated zone. We represent the inventory in each vertical compartment i, as M, (mol), transformation rate constants as kt, and transfer factors as ky (d ). The latter account for the rate of transfer between each i and j compartment pair. 

---