Calculation method of equilibrium composition in the carbon-hydrogen-oxygen system and its application to environments o
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INTRODUCTION
A T high temperatures, equilibrium considerations help explain effects of gas environments on materials. Most of the environmental effects of the C-H-O system are controlled by oxygen potential and carbon activity, which play major roles on oxidation (reduction) and carburization (decarburization) of the materials in industrial applications. ~-5 On the basis of the equilibrium theory, graphical representations of chemical potentials succeeded in our systematic understandings of gas environments for chemical plants, such as high-temperature gas-cooled reactors, coal gasification systems, and combustion systems. 2-5 Since the isopotential phase diagrams were expressed by a function of mutual ratios of gram atoms of C, H, and O, thermodynamic characterization was obtained from the diagrams without calculating equilibria of individual environments. However, experimenters of the materials were often driven by necessity to turn back to calculation of the equilibria, since experimental conditions of environments tended to vary over a wide range of temperature, pressure, and composition. The calculation of the equilibria would be sometimes more informative and beneficial than the isopotential diagrams if the calculation method were simple and accurate. For calculation of the equilibrium composition, the method was basically established by Brinkley et al. 6'7'~ The procedure is to select equilibria of concerned chemical reactions and next to solve them as multi-variable equations together with mass-balance equations of atoms. Calculations have been made by using a digital computerY -~~ because the actual calculation processes were fairly complicated. Here, we present a simpler method for the equilibrium calculation of the C-H-O system. This method is applicable for cases of carbon activity ac = 1 (soot precipitation) and ac < 1 (no sooting) using the identical set of the equilibria, while, in most of the calculation methods to date, the cases of ac = 1 and < 1 were classified and two sets of N. K1SHIMOTO is with Nuclear Materials Division, National Research Institute for Metals, Tsukuba Laboratories, Sakura-Mura, Ibaraki 305, Japan. H. YOSHIDA, formerly with Nuclear Materials Division, is now with Energy Materials Research Group, National Research Institute for Metals, Nakameguro, Tokyo 153, Japan. Manuscript submitted December 31, 1982. METALLURGICALTRANSACTIONS B
equilibria were employed corresponding to the two cases. The classification e__nabled o__ne to avoid discontinuity of derivatives (e.g., 80/apo2, OC/Oac) at ac = 1, which sometimes made the Newton-Raphson method invalid in the vicinity of ac = 1. Contrarily, we focus on carbon precipitation, AC, as a calculation technique and form an idea of imaginary carbon-precipitation (AC < 0) and imaginary change in total molar number on the way to the final equilibrium, as will be discussed later. The presented method is suitable for programmable calculators instead of access to larger computers and basically accurate as well as existing programs. 4"1~To
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