Particle maximum temperature difference between

Baddour [26] retained the above model equations after checking for the influence of heat and mass transfer effects. The maximum temperature difference between gas and catalyst was computed to be 2.3°C at the top of the reactor, where the rate is a maximum. The difference at the outlet is 0.4°C. This confirms previous calculations by Kjaer [120]. The inclusion of axial dispersion, which will be discussed in a later section, altered the steady-state temperature profile by less than O.S°C. Internal transport effects would only have to be accounted for with particles having a diameter larger than 6 mm, which are used in some high-capacity modern converters to keep the pressure drop low. Dyson and Simon [121] have published expressions for the effectiveness factor as a function of the pressure, temperature and conversion, using Nielsen s experimental data for the true rate of reaction [119]. At 300 atm and 480°C the effectiveness factor would be 0.44 at a conversion of 10 percent and 0.80 at a conversion of 50 percent. 

When Thiele modulus is high. Cm is effectively zero and the maximum temperature difference between particle center and its external surface is equal to ... 

Here, T and Ca are the temperature and concentration at any point within the particle, while Tg and Cas are the boundary values at the outer surface, respectively. As evident in Equation 2.68, the heat of reaction AH, and the transport properties D, and k, are the essential parameters. This relationship, which was originally derived by Damkohler in 1943 [9], is valid for all kinetics and applies to all particle geometries. The only implicit assumption made is that of symmetry, that is, the assumption that Tj and C s are uniform over the entire boundary surface. Using this expression, it is possible to find the maximum temperature difference between the surface and the center of particle, which occurs when the reactant is used up before it reaches the center AT x is influenced by C s in addition to AH D and... 

Example 4.5.4 Maximum temperature difference between particle and fluid... 

If we assume that external mass transport has no influence (thus the concentration of oxygen at the external surface equals the gas-phase concentration), we can use Eq. (4.5.99) to estimate the maximum temperature difference between the external surface and the center of the spherical coke particle ... 

When the Thiele modulus is large Cam is effectively zero and the maximum difference in temperature between the centre and exterior of the particle is (- AH)DeCAJke. Relative to the temperature outside the particle this maximum temperature difference is therefore 0. For exothermic reactions 0 is positive while for endothermic reactions it is negative. The curve in Fig. 3.6 for 0 = 0 represents isothermal conditions within the pellet. It is interesting to note that for a reaction in which -AH- 10 kJ/kmol, ke= lW/mK, De = 10 5m2/s and CAa> = 10 1 kmol/m3, the value of Tu - Tx is 100°C. In practice much lower values than this are observed but it does serve to show that serious errors may be introduced into calculations if conditions within the pellet are arbitrarily assumed to be isothermal. 

Estimate the maximum possible difference between the tenqieratuie at the center of the catalyst particle and the temperature at its ext nal surface. 

This technique measures the temperature difference between a sample and a reference, as temperature is increased. A plot of the temperature difference (thermogram) reveals exothermic and endothermic reactions that may occur in the sample. Temperature for thermal events, such as phase transitions, melting points, crystallization temperatures, and others, can he determined by this method. Maximum temperature capability of DTA is in excess of 1000 °C under air or other gas atmospheres. A typical heat-up rate for DTA is in the range of 10—20 °C/min, although slower rates are possible by using a typical optimum sample weight of 50—100 mg. The sample should be ground to particles finer than 100 mesh. 

To achieve the maximum coating opacity the opacifter particle size should be between 0.2 and 0.3 ]lni. A good opacifter should not be soluble in the vitreous system, should have a refractive index substantially different from the refractive index of the system, should be inexpensive, easily milled to a submicrometer particle size, and thermally stable at the film s firing temperature. 

The accuracy of SDV was assessed by Morikita et. al. [184] who showed that the maximum difference between the arithmetic means of irregular particles by SDV and microscopic measurements was about 10%. Hishida et al. [185] recorded a maximum difference of 4% owing to beam wandering due to temperature gradients and concluded that the maximum error with increasing flame size cannot exceed 15%. 

Slurry bubble column reactor for methanol and other hydrocarbons productions from synthesis gas is an issue of interest to the energy industries throughout the world. Computational fluid dynamics (CFD) is a recently developed tool which can help in the scale up. We have developed an algorithm for computing the optimum process of fluidized bed reactors. The mathematical technique can be applied to gas solid, liquid-solid, and gas-liquid-solid fluidized bed reactors, as well as the LaPorte slurry bubble column reactor. Our computations for the optimum particle size show that there is a factor of about two differences between 20 and 60 pm size with maximum granular-like temperature (turbulent kinetic energy) near the 60 pm size particles. 

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