Model of stationary gas network

Modern problems of quantitative risk assessment require a development of more sophisticated types of so-called formation models. The formation models give all the information about an accidental leakage due the depressurization needed for quantitative estimation of the dangerous substances accumulating in the environment and further calculation of impact factors on humans, buildings etc. Common type of depressurization is a release of gaseous substances throughout the accidental hole on the surface of apparatus or pipeline. The pipeline connecting two vessels and a hole occurred on the pipeline as well as streams of vapour phase moving inside the pipelines and throughout the hole is a classical example of graph theory transport network problem. Thereby the model of stationary gas network based on equations of subsonic and choked adiabatic flow (for ideal gas) with accounting of mixing processes has been proposed. The solution with applying of graph theory, linear algebra and numerical analysis has been found.The gas net is represented as an oriented graph with nodes as a pressure-points and lines as pipelines. Case of incorrect estimation of flows directions has been studied and the problem of solving algorithm’s self-correction has been arisen. The method of incidence matrix correction during solving process has been developed and applied. The Newton’s method of non-linear equations system solving has been applied and specific method of Jacoby matrix correction has been developed.The behaviour of gas network model has been studied on example of a hydrocarbons’ mixture leakage from an accidental hole on the pipeline connecting two vessels. Results of numerical simulation experiments showed good agreement of model with basic laws of ideal gas adiabatic flow movement and gas network system in general. The directions of flows were in agreement with pressures’ differences on the lines as well as material and energy conservation laws have been observed. Model can be applied in numerical risks analysis for modelling of accidental processes of gaseous substances leaks as well as for the transport problems of chemical technology or educational purposes.

Embracing Uncertainty: Modeling Uncertainty in EPMA—Part II

This, the second in a series of articles present a new framework for considering the computation of uncertainty in electron excited X-ray microanalysis measurements, will discuss matrix correction. The framework presented in the first article will be applied to the matrix correction model called “Pouchou and Pichoir's Simplified Model” or simply “XPP.” This uncertainty calculation will consider the influence of beam energy, take-off angle, mass absorption coefficient, surface roughness, and other parameters. Since uncertainty calculations and measurement optimization are so intimately related, it also provides a starting point for optimizing accuracy through choice of measurement design.