A case history of a Catalytic Reformer fired heater assessment is used to illustrate an alternative approach to quantify some of the uncertainties associated with fired heater tube remaining life estimates. Such uncertainties include temperature and pressure history, tube wall thickness, and existing creep damage. While it is well understood that fired heater tubes are susceptible to creep and corrosion damage, it can be challenging to quantify the margin of error associated with typical analyses. For example, in order to determine estimates of remaining life, it is not unusual for analysts to use overly conservative input parameters (e.g., minimum measured thicknesses, maximum temperatures and pressures). This often results in a “worst case scenario” or “pass/fail” answer, but it does not necessarily provide insight into the effect of uncertainty. In this paper, an alternative method is utilized to predict heater tube lifetimes. The uncertainty associated with the primary input parameters for the API-579 Part 10 Omega creep procedure is characterized statistically by treating them as random variables and random processes. The probability of tubes failing by a specified time is estimated by performing Monte Carlo simulations. This study is of a practical nature, illustrating how the methodology can be used to aid in decision making.
a b s t r a c tIn this paper we study a variation on the classical problem of a ring subject to a uniform radial load. An initially circular elastic ring, modeled as an elastica, is concentric with a second circular ring, which is rigid and is either outside or inside the elastic ring. On each point of the elastic ring, the rigid ring exerts a nonuniform radial load that depends on the distance between the point and the rigid ring. The two rings can be viewed as a continuum description of the cross-section of a double-walled carbon nanotube. The force between the elastic ring and the rigid ring is a continuum approximation to the van der Waals interaction between atoms on the two walls of the double-walled tube. We use this model to study the buckling of the elastic ring as the radius of the rigid ring is varied. Our model predicts radial corrugations, a type of deformation studied recently in Sato, 2008, 2009;Shima et al., 2010).
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