Superficial velocity surface diffusion

Here, ae is the effective thermal diffusivity of the bed and Th the bulk fluid temperature. We assume that the plug flow conditions (v = vav) and essentially radially flat superficial velocity profiles prevail through the cross-section of the packed flow passage, and the axial thermal conduction is negligible. The uniform heat fluxes at each of the two surfaces provide the necessary boundary conditions with positive heat fluxes when the heat flows into the fluid... 

In many problems of mass transfer in a solid porous medium with a large specific surface area (as with catalysts), with or without a chemical reaction, the solutes are considered to be carried only by diffusion (molecular, superficial or Knudsen diffusion), the molecular barycentric velocity being... 

Film diffusion is usually the controlling step in dilute solutions which are moving at a low superficial velocity through the fixed bed whereas internal diffusion is limiting in high concentration solutions. Dealing with macroreticular resins with a permanent pore volume, BET surface and a defined pore size distribution, pore diffusion can be described by an approach which is based on the conservation of ions in a spherical shell and diffusion steps. 

E21.1 Hydrogenation of particular oil is performed in a liquid phase catalytic reactor (plug flow reactor (PFR)) containing catalytic particles (pellets—spherical diameters) of 1 cm. The external concentration is 1 kmol/L and on the particle surface is 0.1 kmol/L at a superficial velocity of 0.1 m/s. Verify if there are mass effects. There will be a change if the particle diameter is equal to 0.5 cm Neglect the effects in diffusive pores (Fogler, 2000). Additional data ... 

The void fraction should be the total void fraction including the pore volume. We now distinguish Stotai from the superficial void fraction used in the Ergun equation and in the packed-bed correlations of Chapter 9. The pore volume is accessible to gas molecules and can constitute a substantial fraction of the gas-phase volume. It is included in reaction rate calculations through the use of the total void fraction. The superficial void fraction ignores the pore volume. It is the appropriate parameter for the hydrodynamic calculations because fluid velocities go to zero at the external surface of the catalyst particles. The pore volume is accessible by diffusion, not bulk flow. 

Here, the parameter F = Uo]dJ2De( — t) considers the effect of intraparticle diffusion, Pe = V dJlEzi. takes into account the effect of axial dispersion, S = 3(1 — e)Kt/U0L considers the effect of total external mass-transfer resistance, and A0 = /j (l — )k dp/2UoL considers the effect of surface reaction on the conversion. In these reactions L/0l, s the superficial liquid velocity, dp is the particle... 

Example 10-1 Experimental, global rates are given in Table 10-2 for two levels of conversion of SOj to SO3. Evaluate the concentration difference for SO2 between bulk gas and pellet surface and comment on the significance of external diffusion. Neglect possible temperature differences. The reactor consists of a fixed bed of x -in. cylindrical pellets through which the gases passed at a superficial mass velocity of 147 lb/(hr)(ft ) and at a pressure of 790 mm Hg. The temperature of the catalyst pellets was 480°C, and the bulk mixture contained 6.42 mole % SOj and 93.58 mole % air. To simplify the calculations compute physical properties on the basis of the reaction mixture being air. The external area of the catalyst pellets is 5.12 ft /lb material. The platinum covers only the external surface and a very small section of the pores of the alumina carrier, so that internal diffusion need not be considered. 

In these fluidized bed fermenters, the reaction rate is controlled by the superficial flow velocity and its effects on the diffusion of substrate from the bulk of the medium to the enzymatically active surface, by the enzymatic reaction at the surface, or by diffusion of the reactant products back into the bulk of the medium being fermented. 

Reynolds number (ND Vm) diffusion time =Dal/kt (s) reaction time , see equation (15.25) (s) vessel diameter (m) superficial gas velocity (m/s) dispersion volume (m ) liquid volume without gassing (m ) number of mixed zones in loop CfA-CLA (moles/m ) gas hold-up per unit dispersion volume liquid hold-up per unit dispersion volume gas volumetric recirculation rate per unit gas feed rate mean liquid circulation time (s) mean liquid residence time (s) liquid viscosity (Pa s) gas viscosity (Pa s) liquid density (kg/m ) gas density (kg/m ) surface tension (N/m) yield stress (Pa)... 

Surface reaction (pore diffusion negligible) dp, [ ], [fiJb temperature, replacement of active by inactive catalyst particles Superficial liquid velocity (above certain minimum) Superficial gas velocity ... 

Superficial gas velocity Uj (empty reactor) Partial pressure of oxygen (assumed to be constant) poi Diameter of catalyst particle dp Density of catalyst particle Pp External surface area of catalyst particle Am Kinematic viscosity of gas mixture v Molecular diffusion coefficient of o-xylene in air D .x Effective diffusion coefficient of o-xylene in the catalyst Deff.o-x Pseudo-first-order rate constant k = (fem.i + m,i)PT P02 Reynolds number Rcp — 2.46ms 0.21 bar 3mm 1800 kgm l.lm kg 5.5 X 10 m s" 2.5 X 10 m s" 2.5 X 10 m s- 2.5 X 10 m kg s 134... 

Water evaporates from a strangely shaped surface into a flowing stream of hydrogen (15 m/sec, 38 C, 1 atm). Heat transfer studies for air flowing past a similarly shaped object at a superficial mass velocity of 21.3 kg/m sec show that h = 2.3G , where h is the heat transfer coefficient and G is the mass velocity. Find the water evaporation rate into the hydrogen if hydrogen-water vapor diffusivity is 0.775 cm /sec. 

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