Mathematical model assessment

Malanchuk, J.L. and H.P. Kollig. 1985. Effects of atrazine on aquatic ecosystems a physical and mathematical modeling assessment. Pages 212-224 in T.P. Boyle (ed.). Validation and Predictability of Laboratory Methods for Assessing the Fate and Effects of Contaminants in Aquatic Ecosystems. ASTM Spec. Tech. Publ. 865. American Society for Testing and Materials, 1916 Race Street, Philadelphia, PA 19103. 

Uses mathematical models to assess gas cloud movements. Uses gas detectors and weather sensors to alert user of release, and provides plume dispersion, effects, and response information. 

The development of mathematical modelling techniques is proving to be a significant advance in the assessment of the bimetallic corrosion hazard in real systems. 

The capability to constmct mathematical models that more fully incorporate the basic chemistiy and physics of a system provides a mechanism for assessing understanding of fundamental phenomena in a system by comparing predictions made by the model with experimental data. 

FIGURE 20.8 Relative tradeoffs between physical (microcosm) and mathematical models as affected by effluent complexity. (From U.S. EPA, Assessing the Geochemical Fate of Deep-Well-Injected Hazardous Waste A Reference Guide, EPA/625/6-89/025a, U.S. EPA, Cincinnati, OH, June 1990.)... 

Mathematical Modeling Application to Environmental Risk Assessments... 

This gives an example of fate modeling in which the risks of an insect growth inhibitor, CGA-72662, in aquatic environments were assessed using a combination of the SWRRB and EXAMS mathematical models.. Runoff of CGA-72662 from agricultural watersheds was estimated using the SWRRB model. The runoff data were then used to estimate the loading of CGA-72662 into the EXAMS model for aquatic environments. EXAMS was used to estimate the maximum concentrations of CGA-72662 that would occur in various compartments of the defined ponds and lakes. The maximum expected environmental concentrations of CGA-72662 in water were then compared with acute and chronic toxicity data for CGA-72662 in fish and aquatic invertebrates in order to establish a safety factor for CGA-72662 in aquatic environments. 

The major objective of this presentation is to illustrate how an environmental risk assessment of a chemical can be made using mathematical models which are available at the present time. CGA-72662, a CIBA-GEIGY insect growth inhibitor, is used as an example to show how a risk assessment can be carried out using the SWRRB runoff model coupled to the EXAMS fate model. 

Zhou et al. [55], The most effective method to assess the capacity is the flow simulation which includes volumetric formulas and more reservoir parameters rather than other methods [56], Mass balance and constitutive relations are accounted in mathematical models to capacity assessment and dimensional analysis consists of fractional flow formulation with dimensionless assessment and analytical approaches [33], From the formulations demonstrated by Okwen and Stewart for analytical investigation, it can be deduced that the C02 buoyancy and injection rate have affected the storage capacity [57], Zheng et al. have indicated the equations employed in Japanese and Chinese methodology and have noted that some parameters in Japanese relation can be compared to the CSLF and DOE techniques [58]. 

The quantitative water air sediment interaction (Qwasi) model was developed in 1983 in order to perform a mathematical model which describes the behavior of the contaminants in the water. Since there are many situations in which chemical substances (such as PCBs, pesticides, mercury, etc.) are discharged into a river or a lake resulting in contamination of water, sediment and biota, it is interesting to implement a model to assess the fate of these substances in the aquatic compartment [34]. 

ECETOC (1994) HAZCHEM. A mathematical model for use in risk assessment of substances. Special report n. 8. European Centre for Ecotoxicology and Toxicology of Chemicals, Brussels... 

Fuzzy logic is often referred to as a way of "reasoning with uncertainty." It provides a well-defined mechanism to deal with uncertain and incompletely defined data, so that one can make precise deductions from imprecise data. The incorporation of fuzzy ideas into expert systems allows the development of software that can reason in roughly the same way that people think when confronted with information that is ragged around the edges. Fuzzy logic is also convenient in that it can operate on not just imprecise data, but inaccurate data, or data about which we have doubts. It does not require that some underlying mathematical model be constructed before we start to assess the data. 

Other major early contributions of biochemical engineering have been in the development of the artificial kidney and physiologically based pharmacokinetic models. The artificial kidney has been literally a lifesaver. Pharmacokinetic models divide the body of an animal or human into various compartments that act as bioreactors. These mathematical models have been used very successfully in developing therapeutic strategies for the optimal delivery of chemotherapeutic drugs and in assessing risk from exposure to toxins. 

A mathematical model for nonideal flow in a vessel provides a characterization of the mixing and flow behavior. Although it may appear to be an independent alternative to the experimental measurement of RTD, the latter may be required to determine the parameters) of the model. The ultimate importance of such a model for our purpose is that it may be used to assess the performance of the vessel as a reactor (Chapter 20). 

When evaluating the safety of chemicals in humans, it is very important to know the fate of chemicals in the human body and the amounts of exposure in daily activity. This section reviews the metabolic reactions of pyrethroids in humans, and the biomonitoring of pyrethroid metabolites in human urine for the exposure assessment. Mathematical modeling is a useful tool to predict the fate of chemicals in humans. This section also deals with the recent advance of mathematical modeling of pyrethroids to predict the pharmacokinetics of pyrethroids. 

The fundamental basis for virtually all a prion mathematical models of air pollution is the statement of conservation of mass for each pollutant species. The formulation of a mathematical model of air poUution involves a number of basic steps, the first of which is a detaUed examination of the basis of the description of the diffusion of material released into the atmosphere. The second step requires that the form of interaction among the various physical and chemical processes be specified and tested against independent experiments. Once the appropriate mathematical descriptions have been formulated, it is necessary to implement suitable solution procedures. The final step is to assess the ability of the model to predict actual ambient concentration distributions. 

---