Crack core model

Kinetics models of gas-solid non-catalytic reaction include uniform conversion model (UCN), multiple fine particle model (GPM), crack core model (CCM), phase-change model (PCM), change void model (CVM), thermal decomposition model (TDM), shrinking core model with multi-step reactions, and multi-step reaction model of formation porous structure in reaction etc. Among these models, the shrinking core model (SCM) is the most important and most widely used. For conversion of solid it is also the most simple and practical model. Commonly it is suitable for experimental data. However, it can only be used in some reactions of many solid reactions. A more complex model must be used in other cases. 

The reduction in a wet atmosphere has been found by scanning electron microscopy to follow the cracking-core model [98, 132]. 

A classic example of the use of the unreacted core model is that of Weisz and Goodwin who studied the regeneration of fluidized-bed cracking catalyst. Although the cracking catalyst was porous, at a reaction temperature of 700° C the global rate was... 

To give a flavor of the approach, we consider a simple lumped kinetic model for resid thermal cracking. The model needs to account for an induction time for coke formation, which is due to the phase separation of a second liquid phase formed from partially converted asphaltene cores. That is, coke forms when the solubility limit is exceeded. Wiehe developed a simple frrst-order kinetic model based on solubility classes, as follows... 

The simulations in this paper give failure modes sequences very similar to the actual ones observed in the experiments. The model predicts the formation of shear-dominated inter-layer (or interfacial) cracks that initiate first and that such cracks grow very dynamically, their speeds and shear nature being enhanced by the large wave mismatch between the core and the face sheet. The triggering of the complex mechanism of the intra-layer failure of the core structure is also well reproduced. 

At this point, it is worth enquiring if these calculations have any relationship to reality. While it is very difficult to obtain information on crack extension in reactor coolant circuits for a variety of reasons, Tang etal. [63] published the data shown in Fig. 35. The data refer to the extension of a crack adjacent to the H-3 weld on the inner surface of the core shroud of a GE BWR in Taiwan. The authors had monitored the growth of the crack as a function of time after the eleventh outage for refueling. The reactor model was the same as that employed in our previous modeling and the coolant chemistry conditions could be estimated with sufficient accuracy to make a comparison between the observed and calculated crack extensions... 

Cylindrical samples of a water-swellable polymer were immersed in water for different times. The profile of the water front moving from the surface to the inner core of the sample is visualized (Ghi et al. 1997) and compared with model calculations of the water transport. The Fickian nature of the diffusion process is proved. As a result of stress formation during the diffusion processes, cracks were formed. From analysis of T2 the presence of two types of water within the polymer follows a less mobile phase of water that is interacting strongly with the polymer matrix and a more mobile phase within the cracks. 

The finite element method is already estabhshed in modelling for eddy current sensors the same as analytical methods. For example, reference [1] solves for the absolute impedance of core-less coils, and [2], [3] solve for the induced voltage in the coil. The problem with these analytical models is the dependency on the crack size, shape and location, and the equations needs to be modified all the time. Consequently, the results may not necessarily be comparable. When the FEA is used instead, the results remain comparable for changed model parameters. Hence, the aim of this study is to build a 3D model to calculate the complex coil impedance for encircling coils that measure rods with any kind of cracks. In doing so, two main simplifications are applied as follows. 

Given that the asymptotic states in response to ATWS initiators are safe, it remains to show that the dynamic transition to the asymptotic state will not engender damaging conditions on the in-core structures. A plant dynamic code, which can model the STAR-H2 balance of plant, was not available at the time when this report was prepared. Such a code is being developed first for the STAR-LM, which has a simpler (SC-C02 Bra)hon cycle) balance of plant. In the future, after further refinement of the Ca-Br water cracking cycle, that dynamics code will be modified for applicability to the STAR-H2. 

---