Cracking simulation models

The cracking simulation model developed by the Laboratorium voor Petrochemische Techniek contains 1680 reaction networks for some 550 hydrocarbons. The components involved in the model are normal and iso-paraffins and olefins up to C25, 5- and 6-ring naphthenes up to C20 and aromatics up to C20. The computation of the reaction networks for the heavy components requires many hours. 

In conclusion, the model performs well within the purely inductive frequency range. Both simplifications, the impedance boundary condition on the rod and the current sheet approximation with complex material properties, were successfully applied to the FEA model in 2D as well in 3D. As a result, the total element number was reduced by a factor of 3. Consequently, the simulation model allows extensive parameter studies for several types of cracks measured with different encircling coils. 

The cracked plate model is a classical example in Fracture Mechanics and its relative simplicity allows a detailed and complete study of different simulation techniques. A thorough description of this model can be found in (Ardillon Venturini 1995). 

In this paper, the Subset Simulation (SS) and Line Sampling (LS) methods have been considered for improving the efficiency of Monte Carlo Simulation (MCS) in the estimation of system failure probability. A structural reliability model of hterature, i.e. the cracked plate model, has been taken as benchmark to test the two methods. 

Both the simulation model for the detailed calculation of the flue gas pattern in the furnace and the process gas pattern in the cracking tubes are based on the Reynolds-Averaged Navier-Stokes mass, momentum, energy, and species balance equations described in Section 12.5. Turbulent momentum, species, and... 

Sundaram,K.Mo and G.F.Froment. "A Comparison of Simulation Models for Empty Tubular Reactors".Chem.Eng.Sci.v34(1979) 117-124. Sundaram,K.M. and G.F.Froment. "Two-dimensional Model for the Simulation of Tubular Reactor for Thermal Cracking", Chem. Eng, Sci, v35 (1980) 364-371,... 

In the work reported here the coil and the fire box were simulated simultaneously by means of an optimized computer package in which the design of the radiant section of the furnace is an extension and refinement of Hottel s zone method (3 ). In this paper the approach is applied to the simulation of an industrial ethane cracking furnace. The only adaptable parameter left in the simulation model is a burner design factor, namely the fraction of the heat generated in the burner that is transferred to the burner cup. The parameter is determined by matching the exit conver s ion. 

The six oil lumps each represent a reasonably narrow boiling range of compounds and thus the cracking order is assumed to be one (Jacob et al., 1976 Weekman, 1979). The equations for the Riser Simulator model can then be expressed as follows for the weight fractions of the three heavy oil lumps ... 

Liguras, D.K. and Allen, D.T., "Structural Models for Catalytic Cracking. 1. Model Compound Reactions. 2. Reactions of Simulated Oil Mixtures", Ind. Eng. Chem. Res. 28,665-683 (1989). 

Bazant, Z.P. Pang, S.D. Vofechovsky, M. and Novak. D. 2007. Energetic-statistical size effect simulated by SEEM with stratified sampling and crack band model. International Journal for Numerical Methods in Engineering (Wiley), 71(11) 1297-1320, Rep. Dept, of Civil Eng., Northwestern University, Evanston, Illinois. 

For refined finite element analysis, the fracture behavior of concrete and masonry can be simulated with continuum elements based on the nonlinear fracture mechanics concept. In these elements, cracks are modeled in a smeared fashion, i.e., with a material stress—strain law representing distributed crack development in... 

The simulation of the actual distortion of the eddy current flow caused by a crack turns out to be too time consuming with present means. We therefore have developed a simple model for calculating the optimum excitation frequencies for cracks in different depths of arbitrary test sarriples Using Equ. (2.5), we are able to calculate the decrease in eddy current density with increasing depth in the conductor for a given excitation method, taking into account the dependence of the penetration depth c on coil geometry and excitation frequency. 

For precise 3D-FEM simulations, a huge number of nodes is required (>30,000), which results in calculation times of several hours (sun spare 20) for one model. In order to decrease the number of nodes, we took advantage of the symmetry of the coils and calculated only a quarter or half of the test object. The modelled crack has a lenght of 15 mm, a height of 3 mm and is in a depth of 5 mm. The excitation frequency was 200 Hz. 

Catalytic crackings operations have been simulated by mathematical models, with the aid of computers. The computer programs are the end result of a very extensive research effort in pilot and bench scale units. Many sets of calculations are carried out to optimize design of new units, operation of existing plants, choice of feedstocks, and other variables subject to control. A background knowledge of the correlations used in the "black box" helps to make such studies more effective. 

Figure 10.15 shows the simulated temperature distribution in the electrolyte for the single-cell stack model. In this calculation, the cell operating voltage is set at 0.16 V at which the electrolyte sheet cracked in the internal heat evolution test. In Figure 10.15, it can be observed that the temperature is almost 1273 K outside the anode/electrolyte/cathode area where heat is generated. Near the fuel inlet at the channel, the temperature increases steeply and the maximum temperature spreads over a wide area to the downstream of the fuel flow the maximum temperature difference in the electrolyte is around 60 K. 

Their analysis of experimental data shows that tensile strength was the only parameter that varied as a function of particle size. Model simulation indicate that larger lumps were stronger than smaller lumps which is contradictory to Waters et al. [8], Teo and Waters [9], and Griffith [10] theory of fracture, which implies that larger particle are more likely to contain larger cracks and hence be more susceptible to breakage. 

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