Species sensitivity, coefficient

Formulas for safety factors are calculated according to cumulative properties, species sensitivity coefficient, and occurrence of delayed adverse effects (Sidorov 1980). It should be noted that the safety factor is designed mainly to allow for the potentially higher sensitivity of humans to specific pesticides than laboratory animals. This factor should also ensure the safety of a selected dose or concentration if new, unexpected adverse properties are identified for the substance in question. The final adjustment of health standards is based on clinical and epidemiological examinations of people exposed to that substance. 

The sensitivity analysis is an important tool that evaluates the response of a model due to changes of one or more parameters. Among the sensitivity analysis methods are the Direct Sensitivity Analysis (DSA), Principal Component Analysis (PCA), Normalized Rate Sensitivity Coefficients (NRSC), and Overall Normalized Species Sensitivity Coefficients (ONSS) [7]. 

Calculate and plot the time-dependent species profiles for an initial mixture of 50% H2 and 50% Cl2 reacting at a constant temperature and pressure of 800K and 1 atm, respectively. Consider a reaction time of 200ms. Perform a sensitivity analysis and plot the sensitivity coefficients of the HC1 concentration with respect to each of the rate constants. Rank-order the importance of each reaction on the HC1 concentration. Is the H atom concentration in steady-state ... 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

The sensitivity coefficient can be either positive or negative an increase in parameter A, can lead to increases or decreases in c,. In fact, for some times r, X, could be positive, and for other times, negative. Different species c, also respond to changes in a parameter differently, in both magnitude and sign. 

The ratio of the LD50 for less sensitive animals to that of more sensitive ones is defined as a coefficient of species sensitivity (CSS). If this coefficient is less than three, the differences are considered nonessential. A CSS of three to nine characterizes a moderate degree of species difference a CSS over nine indicates a great degree of species sensitivity to the chemical and necessitates very careful extrapolation of experimental results to humans (Sanotsky and Ivanova 1975, Krasovsky et al. 1986). 

The above analyses of species concentrations and net reaction rates clearly indicate which reactions and which chemical species are most important in this reaction mechanism, under the particular conditions considered. However, for purposes of refining a reaction mechanism by eliminating unimportant reactions and species and by improving rate parameter estimates and thermochemical property estimates for the most important reactions and species, it would be helpful to have a quantitative measure of how important each reaction is in determining the concentration of each species. This measure is obtained by sensitivity analysis. In this approach, we define sensitivity coefficients as the partial derivative of each of the concentrations with respect to each of the rate parameters. We can write an initial value problem like that given by equation (35) in the general form... 

Because the initial species concentrations are independent of the rate constants, the initial conditions for these sensitivity coefficient equations are that all Ski — 0 at t — 0. Integrating these equations, along with the equations for the species concentrations, provides all the sensitivity coefficients as a function of time. For the case of the rate equations given by equation (35), letting the hrst I parameters be the forward rate constants and the second I parameters be the reverse rate constants, the function fk can be written (using new summation subscripts / and m) as... 

Note that if the concentrations and reaction rates have already been computed and stored, then this is a set of linear differential equations (with non-constant coefficients) for the sensitivity coefficients. Note also that each sensitivity coefficient depends only on the sensitivity coefficients of the other species to the same parameter, but not on sensitivity coefficients with respect to other parameters. Thus, the sensitivity coefficients with respect to a given parameter (K of them) are coupled and must be computed simultaneously, but it is not necessary to solve for all the sensitivity coefficients (2 x / x of them) simultaneously. 

Continuing with the example based on the reaction mechanism of Table 10, the equations for the sensitivity coefficients (equation (50)) were integrated numerically using Matlab. For a mechanism of this size, it was feasible to solve for the species concentrations (15 of them) and all the sensitivity coefficients (39 x 15x2 = 1170 of them) simultaneously. Rather than examining the sensitivity coefficients themselves, it is often more informative to examine scaled or normalized sensitivity coefficients. These are usually defined as... 

The sensitivity coefficients defined by equation (43) relate the absolute change in a solution variable (species concentration) to an absolute change in a parameter (rate constant), and thus have units that depend on the units of the rate constant, which in turn depend on the overall reaction order. The scaled sensitivity coefficients defined by equation (51) relate fractional changes in a solution variable to fractional changes in a parameter. Thus, for example, if <7, = 1, then a 10% increase in parameter dj will lead to a 10% increase in solution variable Likewise, if [Pg.236]

Taken together, the analyses of species concentrations, reaction rates, and scaled sensitivity coefficients for this particular example and conditions provide a clear and consistent picture of which species and reactions are most important in the overall process of AICI3 decomposition and reaction with H2 to produce AlCl and HCl. From the 39 reactions included in Table 10, just 5 seem to be essential. These... 

Another tool available to the modeler is sensitivity analysis of the results. The normalized sensitivity coefficient s for some property P (such as bum rate, species concentration, or temperature) due to variation in some parameter a (such as a rate constant) is given by... 

An obvious next stage is to treat each species separately and quantify differences in species sensitivities in terms of specific target/water or target/octanol partition coefficients. But it would be useful if the correlation techniques were identical such that inter-species comparisons can be made more easily. 

Fig. 8. Sensitivity coefficients of speed of Hz/O2/N2 flames (( ) = 1.6, D = 0.077, 0.09, and 0.209) doped with 0.04% TMP to rate constants of reactions (l)-(3) involving P-containing species modeling is based on mechanism (Jayaweera et al., 2005)...

In the general case, we have to investigate how a small change of rate coefficient kj changes the production rate dyjdt of product T,. This effect appears in the local rate sensitivity coefficient d(AcJAt)ldkj (see Sect. 5.2). If this coefficient is much higher for reaction j than for the other reaction steps, then reaction j is the ratedetermining step of the production of species i (Turanyi 1990). 

The Green function has a very clear physical meaning it shows the effect of changing the initial concentrations on the model solution therefore, its elements were also called initial concentration sensitivity coefficients. Using the notation of Eq. (5.11), gij(t,s) shows the effect of changing the concentration of species j at time s on the calculated concentration of species i at time t. This effect can be very small (this is typical when at time t the system is close to the equilibrium or the stationary point) or can be very large, such as when species j is an autocatalyst. Therefore, the Green function is not only an auxiliary variable for the calculation of the sensitivity matrix, but it can be used directly for the analysis of reaction mechanisms (Nikolaev et al. 2007). 

The summation refers to all the Nr reaction steps. For the calculation of lifetime not only the chemical lifetime t,- is taken into account but also the residence time in a reactor and the species rate of diffusion. The half-normalised local sensitivity coefficient 3T,/3 In A shows the effect of perturbing the A-factor of reaction step I on concentration T and Vy is the corresponding stoichiometric coefficient. The index (LOI)jy estimates the error of the calculadcHi of the concentration of species j due to the application of the QSSA on species i. 

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