Estimation of the flammability zone boundaries with thermodynamic and empirical equations

The flammability zone boundaries are very important properties to prevent explosions in the process industries. Within the boundaries, a flame or explosion can occur so it is important to understand these boundaries to prevent fires and explosions. Very little work has been reported in the literature to model the flammability zone boundaries. Two boundaries are defined and studied: the upper flammability zone boundary and the lower flammability zone boundary. Three methods are presented to predict the upper and lower flammability zone boundaries: The linear model The extended linear model, and An empirical model The linear model is a thermodynamic model that uses the upper flammability limit (UFL) and lower flammability limit (LFL) to calculate two adiabatic flame temperatures. When the proper assumptions are applied, the linear model can be reduced to the well-known equation yLOC = zyLFL for estimation of the limiting oxygen concentration. The extended linear model attempts to account for the changes in the reactions along the UFL boundary. Finally, the empirical method fits the boundaries with linear equations between the UFL or LFL and the intercept with the oxygen axis. xx Comparison of the models to experimental data of the flammability zone shows that the best model for estimating the flammability zone boundaries is the empirical method. It is shown that is fits the limiting oxygen concentration (LOC), upper oxygen limit (UOL), and the lower oxygen limit (LOL) quite well. The regression coefficient values for the fits to the LOC, UOL, and LOL are 0.672, 0.968, and 0.959, respectively. This is better than the fit of the "zyLFL" method for the LOC in which the regression coefficient’s value is 0.416.

Loss on ignition as a method for estimating organic and carbonate content in sediments: reproducibility and comparability of results

Five test runs were performed to assess possible bias when performing the loss on ignition (LOI) method to estimate organic matter and carbonate content of lake sediments. An accurate and stable weight loss was achieved after 2 h of burning pure CaCO3 at 950 °C, whereas LOI of pure graphite at 530 °C showed a direct relation to sample size and exposure time, with only 40-70% of the possible weight loss reached after 2 h of exposure and smaller samples losing weight faster than larger ones. Experiments with a standardised lake sediment revealed a strong initial weight loss at 550 °C, but samples continued to lose weight at a slow rate at exposure of up to 64 h, which was likely the effect of loss of volatile salts, structural water of clay minerals or metal oxides, or of inorganic carbon after the initial burning of organic matter. A further test-run revealed that at 550 °C samples in the centre of the furnace lost more weight than marginal samples. At 950 °C this pattern was still apparent but the differences became negligible. Again, LOI was dependent on sample size. An analytical LOI quality control experiment including ten different laboratories was carried out using each laboratory's own LOI procedure as well as a standardised LOI procedure to analyse three different sediments. The range of LOI values between laboratories measured at 550 °C was generally larger when each laboratory used its own method than when using the standard method. This was similar for 950 °C, although the range of values tended to be smaller. The within-laboratory range of LOI measurements for a given sediment was generally small. Comparisons of the results of the individual and the standardised method suggest that there is a laboratory-specific pattern in the results, probably due to differences in laboratory equipment and/or handling that could not be eliminated by standardising the LOI procedure. Factors such as sample size, exposure time, position of samples in the furnace and the laboratory measuring affected LOI results, with LOI at 550 °C being more susceptible to these factors than LOI at 950 °C. We, therefore, recommend analysts to be consistent in the LOI method used in relation to the ignition temperatures, exposure times, and the sample size and to include information on these three parameters when referring to the method.

A second order in time modified Lagrange-Galerkin finite element method for the incompressible Navier-Stokes equations

We introduce a second order in time modified Lagrange--Galerkin (MLG) method for the time dependent incompressible Navier--Stokes equations. The main ingredient of the new method is the scheme proposed to calculate in a more efficient manner the Galerkin projection of the functions transported along the characteristic curves of the transport operator. We present error estimates for velocity and pressure in the framework of mixed finite elements when either the mini-element or the $P2/P1$ Taylor--Hood element are used.

A method for estimating posterior BAC distributions for persons involved in fatal traffic accidents.

National Highway Traffic Safety Administration, Washington, D.C.

An efficient numerical method for highly oscillatory ordinary differential equations /

"Supported in part by the Department of Energy under contract ENERGY/EY-76-S-02-2383, and submitted in partial fulfillment of the requirements of the Graduate College for the degree of doctor of philosophy."

An implicit method for the solution of elliptic partial differential equations.

Supported in part by National Science Foundation under Grant No. U.S. NSF-GJ-328.

A method for solving polynomial equations by continued fractions.

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