An equation-of-state for methane for modeling hydrogen attack in ferritic steels
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INTRODUCTION
STEELS exposed to high pressure and high temperature hydrogen undergo permanent damage resulting in marked reduction of strength and ductility. This problem, known as hydrogen attack (HA), is due to nucleation, growth, and coalescence of methane bubbles along the grain boundaries.l-H The phenomenon has been observed in both petroleum and synthetic ammonia industries for many years.~2 Engineering practice for the selection of "safe" operating regimes of hydrogen partial pressure, PH2, and temperature, T, has been based on the empirical Nelson Curves. ~2These curves for various broad alloy classes and qualitative failure criteria were derived largely from historical operating experience. The more rigorous operating regimes of proposed coal conversion plants, and the potential consequences of failure of large pressure vessels in these systems suggests that a better method of predicting HA failures based on some understanding of the underlying physical mechanisms is desirable.' The driving force for the growth of the bubbles is the pressure of methane gas in the bubbles which is formed by reaction between carbon present in the steel and the absorbed hydrogen. Hence, accurate knowledge of methane pressure is necessary to model hydrogen attack kinetics. One of the major deficiencies in previous attempts 6'1~ to model HA has been improper treatment of methane pressure. In particular, models had used approximate equationsof-state for methane and, generally, assumed an equality between the methane fugacity,fca,, and pressure Pcs4- It will be shown in the present paper that this assumption breaks down at high fugacities ffca4>80 MPa) and leads to serious errors in estimation of rates of bubble growth during HA. In order to calculate methane pressures accurately it is necessary to identify an appropriate equation-of-state which is valid at high temperatures and pressures. Such information was not available in the literature in an acceptably accurate and convenient form. Therefore, an equation-of-state for methane has been developed. Further, this equation-of-state was used to relate methane fugacity, which is governed by the reaction thermodynamics, to mechanical pressures. G. R. ODETTE,Professorand Vice-Chairman,and S. S. VAGARALI, Assistant Research Engineer, are both with the Departmentof Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106. Manuscript submittedFebruary23, 1981. METALLURGICALTRANSACTIONSA
II.
EQUILIBRIUM METHANE FUGACITY
In general, for equilibrium conditions the overall methane reaction involves dissolution of carbides I• + XM [1] Y Y with a forward reaction free energy of AGo ealculated from thermodynamic data for methane, hydrogen, the carbide, and the solid solution alloy. The equilibrium fugacity is given by [~ f~n 4 =
"~l/y
K 0~(aM)X/y t r v n 2 ,~2 ,
[2]
where K0 is the equilibrium reaction constant
a%
K 0 = exp
[3]
--~l,
and aMxcy, aM are "standard-state" carbide and metal activities, respectively. 1 In alloy steels there may be several metal
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