Pseudo-homogeneous approximation

Therefore, once again invokingthe pseudo-homogeneous approximation, the equations we mustsolveare ... 

A highly concentrated suspension of flocculated kaolin in water behaves as a pseudo-homogeneous fluid with shear-thinning characteristics which can be represented approximately by the Ostwald-de Waele power law, with an index of 0.15. It is found that, if air is injected into the suspension when in laminar flow, the pressure gradient may be reduced even though the flowrate of suspension is kept constant, Explain how this is possible in slug flow and estimate the possible reduction in pressure gradient for equal volumetric flowrates of suspension and air. 

The pseudo-homogeneous assumption means that both the solid and fluid phases are are considered a single phase. Therefore, we avoid considering mass and heat transfer from and to the catalytic pellets. This model assumes that the conqionent concentrations and the temperature in the pellets are the same as those in the fluid phase. This assumption is approximated when the catalyst pellet is small and mass and heat transfer between the pellets and the fluid phase are rapid. The reaction rate for this model, called the global reaction rate, includes heat and mass transfer. If heat and mass transfer are made insignificant, then the reaction rate is called the intrinsic reaction rate. 

Figure 6.41 shows that the o-Xylene conversion predicted by the pseudo-homogeneous model is lower than all the three steady states of the heterogeneous model until a length of approximately 0.32 m when the conversion predicted by the pseudo-homogeneous model exceeds that of the heterogeneous model and reaches a value of 1.0. 

The design of such gas-solid catalytic reactors can be approximated by a pseudo-homogeneous model with gas phase in plug flow. In the case of very exothermic reactions accounting for radial dispersion of heat and mass might be useful to prevent excessive particle overheating. The reaction time must find a compromise with the hydrodynamic design, namely the maximum gas velocity and pressure drop. 

Finally, we recall that the relative extent of each reaction phase and the relative magnitudes of the rate constants determine the extent to which a pseudo-homogeneous model approximation may be applied to a three-phase process. If there are no transport limitations in or between phases (cf. Fig. 4.28) (if, for example, ol), one may ignore the differential equations pertaining to mass transport, and the system of equations is reduced to that appropriate for a pseudohomogeneous model. 

The heterogeneous catalytic reforming reactions are supposed to take place on the gas-solid interface. In heterogeneous catalysis no species enter into the solid phase, hence for this process the species mass balance are solved only in the gas phase. For the adsorption process the reaction actually takes place within the solid adsorbent material. However, in the modeling approach employed by Wang et al. [161] a pseudo-homogeneous reaction model was adopted so that the CO2 capture reaction was approximated by a particle surface reaction thus the overall diffusion... 

The simplest model is pseudo-homogeneous, one-dimensional and ideal, where solid and gas phases are analysed as a one single phase and no axial and radial mixing is taken into account. Obviously, this type of model is very easily implemented but, on the other hand, it can only give a first approximation assessment. 

In a series of papers by Leung and coworkers (AlChE J., 32, 1743-1746 [1986] 33, 524-527 [1987] 34, 688-691 [1988] J. Loss Prevention Proc. Ind., 2[2], 78-86 [April 1989] 3(1), 27-32 [Januaiy 1990] Trans. ASME J. Heat Transfer, 112, 524-528, 528-530 [1990] 113, 269-272 [1991]) approximate techni ques have been developed for homogeneous equilibrium calculations based on pseudo-equation of state methods for flashing mixtures. 

In this section the classical continuum theory of mixtures is reviewed [15]. In this concept the multiphase mixture is treated as a single homogeneous continuum. Thereby the balance principle can be applied to derive conservation laws for the macroscopic pseudo-fluid in analogy to the single phase formulation examined in chap 1. Approximate constitutive equations are postulated for the expected macroscopic behavior of the phases. 

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