Mathematical model estimating releases

Mathematical models are also used for estimating releases, but these are usually relatively simple. For example, if it is known that X kg of a chlorofluorocarbon is manufactured annually, and Y percent enters spray cans, and Z percent of a spray can is usually left unexhausted, then XY(100-Z)/10 kg of that CFC are released to the atmosphere per year. The average discharge rate (kg/sec) nationwide then can be computed easily. (For simplicity in this example, we ignore the contributions from leaking discarded cans and changes in production and use levels.)... 

When chemicals are released in the environment, their hazard potential to human or ecological receptors depends upon the extent of contact between the receptors and the chemical. This exposure level is not only influenced by where, when and how much of the chemical is released, but also on its movement and changes in air, water, soil or biota relative to the locations of the receptors. Risk is defined as the probability of some adverse consequence in the health context, or as the probability times the extent of the consequence in the technology context. In this paper we shall examine and discuss how mathematical models are used to generate estimates of risk when more than one of the environmental media must be considered in tracing pathways connecting sources with receptors. The principal objective here is to place in perspective the... 

Leak Estimation - A mathematical model of the probability and amount of potential hydrocarbon releases that may occur from selected processes or locations. 

Intracellular fluxes can be estimated more precisely through 13C tracer experiments. Following 13C feeding to a cell it is possible to analyze metabolic products, such as amino acids, and measure 13C enriched patterns, so to be able to reconstruct the flux distribution from the measured data [91]. To obtain flux data from the labeling patterns, two techniques can be applied NMR [92, 93] and MS [94, 95]. Due to the low intracellular concentration of metabolites, these are often difficult to measure therefore the analysis of the labeling pattern of amino acids in proteins is used as input for flux quantification. Here proteins are hydrolyzed to release labeled amino acids and further analyzed by NMR of GC-MS. Once NMR or MS spectra are recorded, the next step is the quantitative interpretation of the isotopomer data by using mathematical models that describe the relationship between fluxes and the observed isotopomer abundance [96, 97], Some of the mathematical approaches used include cumulative isotopomer (cumomers) [98], bondomers [99], and fractional labeling [100], For a more comprehensive review on the methods we refer to Sauer [91]. 

Biomarkers of Exposure and Effect. Currently, the only biomarker of exposure that has been identified is the presence of radioactivity, released by plutonium, in the urine. The presence of this activity in the urine is specific to plutonium exposure and can be used to monitor short- term, intermediate, or long-term exposure. Although the detection of plutonium radioactivity in the urine is not a direct measurement of exposure, estimates may be derived using mathematical models. 

Fire and Smoke Models - A mathematical estimation model depicting the duration and extent of heat, flame and smoke that may be generated from the ignition of a hydrocarbon release. The results of these estimates are compared against protection mechanisms (e.g., firewater, fireproofing, etc.) afforded to the subject area to determine adequacy. 

Concern about fission-product release from coated reactor fuel particles and fission-product sorption by fallout particles has provided stimulus to understand diffusion. In a fallout program mathematics of diffusion with simple boundary conditions have been used as a basis for (1) an experimental method of determining diffusion coefficients of volatile solutes and (2) a calculational method for estimating diffusion profiles with time dependent sources and. time dependent diffusion coefficients. The latter method has been used to estimate the distribution of fission products in fallout. In a fission-product release program, a numerical model which calculates diffusion profiles in multi-coated spherical particles has been programmed, and a parametric study based on coating and kernel properties has provided an understanding of fission product release. 

The UFP emission rate of a laser printer cannot be determined using the same techniques as for the (S)VOC case. Here, the superposition of particle release and deposition has to be solved mathematically. Using this method, different types of emitting behavior ( constant emitter or initial-burst emitter ) can be identified for the printer under observation (Schripp et al, 2008). It was mentioned above that the determination of the emission rate of a VOC allows the calculation of the air concentration in a model room. For particulate emissions this is not the case. If the deposition in the room is unknown an estimation of the particle concentration development is not possible even though the emission rate of the printer is known (Wensing et al, 2008). 

The use of computer modeling for rapidly and easily estimating the effects from explosions, fires, and gas releases is almost commonplace in risk evaluations for the hydrocarbon industry. Specialized risk consultants and even insurance risk offices can now offer a variety of software products or services to conduct mathematical consequence modehng of most hydrocarbon adverse events. Even major petroleum companies have bought... 

Combustible Vapor Dispersion (CVD)— A mathematical estimation of the probability, location, and distance of a release of combustible vapors that will exist until dilution naturally reduces the concentration to below the lower explosive limit (LEL), or will no longer be considered ignitable (typically defined as 50% of the LEL). For basic studies, the normal expected wind direction is utilized (based on historical wind rose data). Real-time modeling is sometimes used during incident occurrence to depict area of vapor coverage on plant maps for visual understanding of the affected areas based on wind speeds and direction. 

---