Diffusion catalyst boundary layer

Step 8. Product species diffuse across the fluid boundary layer at the external surface of the catalyst ... 

Regime of transport limitation, here

diffusion through the hydrodynamic boundary layer. The apparent activation energy under these conditions gets close to zero. Every educt molecule reacts instantaneously on the outer catalyst surface, no educt diffusion inside the catalyst particle takes place. 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

The resulting values are shown in Table 4. As expected, the diffusion coefficients of prenal and citral are smaller in water than in n-hexane. Since the mass transport coefficients in each boundary layer directly correlate with the diffusion coefficient (Eq. 3), this result confirms the assumption that the overall mass transport resistance can be predominantly referred to the aqueous catalyst phase ... 

In Section 17.8.3 we discussed the catalytic combustion of methane within a single one of the tubes in a honeycomb catalyst, illustrated in Fig. 17.18. The high velocity, and thus the dominance of convective over diffusive transport, makes the boundary layer approximations valid for this system. We will model the catalytic combustion performance in one of the honeycomb channels in this problem. 

In this equation, if the rate of diffusion is faster than that of the catalytic reaction at the surface (ko kc), the Arrhenius plot of rr gives the apparent activation energy Ec of kc. This is the reaction-controlled condition. On the other hand, if the rate of the catalytic reaction is faster than that of diffusion (kc 2> kid, the Arrhenius plot of rr gives the characteristics of temperature dependence of ko. This is the diffusion-controlled condition. Under diffusion-controlled conditions, the transferred reactant decreases at once at the surface (Cs = 0) because of the fast catalytic reaction rate. The gas flow along the catalyst surface forms a boundary layer above the surface, and gas molecules diffuse due to the concentration gradient inside the layer in the thickness direction. As the total reaction... 

The rate o oxidation o ammonia at atmospheric pressure on single wires and ribbons has been determined as a function of a gas flow rate and catalyst size. In agreement with boundary layer diffusion theory the function rx, where r is the average rate of reaction/unit area, and x is the length of the surface measured in the direction of gas flow, is directly proportional to gas velocity. 

The rate of reaction at atmospheric pressure can be estimated by equating the rate of the surface reaction given by 2 to the rate of diffusion through the mass transfer boundary layer at the catalyst surface. 

Surface reaction with diffusion and heat transfer resistance In fast exothermic reactions, in addition to grad c, also grad T (TG Ts) is present in the boundary layer between the gas bulk phase and the catalyst surface. For the outer effectiveness factor qext this means that... 

The heterogeneous catalyst particles in the reactor are surrounded by a boundary layer of gas or liquid, which can be considered as a static him around the particle. A reactant molecule has to diffuse through this boundary layer via film diffusion (1). As most catalysts have pores, the reactant molecule also has to diffuse through the pores in order to approach the active site, the pore diffusion process (2). Inside the pores, the reactant molecules adsorb at or near the active center and react (3, 4). The resulting product molecules desorb (5) and return back into the fluid phase via pore diffusion (6) and film diffusion (7). Further details on this can be found in general textbooks [1-3]. 

As described in Section 4.1.1.2, in most catalytic reactions, the reactant molecules diffuse through a boundary layer and through the pores to the active center, react, and diffuse back. If the velocity of any of these two diffusion processes is smaller than the conversion of the reactants at the active center, the overall reaction rate for the whole process is limited by the mass transport and not by the chemical reaction. If the reaction is influenced by mass transport effects, a comparison of the catalytic activity of different catalysts is impossible ... 

In such a three-phase system, a different spatial concentration profile occurs, as shown in Figure 4.1.11, as compared to a two-phase system, cf. Figure 4.1.2. The gaseous reactant molecules first have to cross the boundary layer between the gas and liquid phase. In the liquid phase, they have to diffuse through the boundary layer between the liquid and the solid particle. The remaining way is the same as for a heterogeneous catalyst in the gas phase, as described in a previous Section 4.1.1.2. 

Transport of the reactants by diffusion and convection out of the bulk gas stream, through a laminar boundary layer, to the outer surface of the catalyst particles, and further through the pore system to the inner surface (pore walls)... 

Figure 6.1.1 depicts the concentration profile of a reactant in the vicinity of a catalyst particle. In region 1, the reactant diffuses through the stagnant boundary layer surrounding the particle. Since the transport phenomena in this region occur outside the catalyst particle, they are commonly referred to as external, or... 

For a solid-catalyzed reaction to take place, a reactant in the fluid phase must first diffuse through the stagnant boundary layer surrounding the catalyst particle. This mode of transport is described (in one spatial dimension) by the Stefan-Max well equations (see Appendix C for details) ... 

Reactants and products must diffuse through high-molecular-weight liquid hydrocarbons during FT synthesis. The liquid phase may be confined to the mesoporous structure within catalyst pellets or extend to the outer surface and the interstitial spaces between pellets, depending on the reactor design and hydrodynamic properties. In packed-bed reactors, the characteristic diffusion distance equals the radius of the pellets plus the thickness of any liquid boundary layer surrounding them. Intrapellet diffusion usually becomes... 

To begin our discussion on the diffusion of reactants from the bulk fluid to the external smface of a catalyst, we shall focus attention on the flow past a single catalyst pellet. Reaction takes place only on the catalyst and not in the fluid surroimding it. The fluid velocity in the vicinity of the spherical pellet will vaiy with position aroimd the sphere. The hydrodynamic boundary layer is usually defined as the distance from a solid object to where the fluid velocity is 99% of the bulk velocity U. Similarly, the mass transfer boundary layer thickness, 8, is defined as the distance from a solid object to where the concentration of the diffusing species reaches 99% of the bulk concentration. 

Diffusion to and from the bulk gas to the external catalyst surface, represented as an external mass-transfer process across a film or boundary layer concentration gradient. For nonporous catalyst this is the only mass-transfer step. 

Above the catalyst surface, substance A will be transported by diffusion, mainly in the x-direction. In a thin layer close to the wall, the diffusion boundary layer, mass transport by convection is negligible, and from (2.338) we obtain the diffusion equation valid for steady one-dimensional diffusion without chemical reaction... 

They conclude that surface diffusion and/or gaseous PtOa transport in a boundary layer can best explain their observations. Thus loss of metal in the oxygen-rich regime is consistent with Pt02(g) formation. It also provides an explanation of catalyst activation by facetting since the oxygen pressure adjacent to active zones will be low relative to that adjacent to inactive zones Pt will then preferentially evaporate from the inactive zones. 

In industrial practice, the most convenient way of accounting for mass-transfer effects is to view the penetrable catalyst particle as a pseudo-homogeneous phase. Obstruction of mass transfer by the solid material in the particle then is reflected by an "effective" intraparticle mass-transfer or diffusion coefficient that is appropriately lower than in the contacting fluid. If this approach is taken, two fundamentally different mass-transfer situations appear Mass transfer to and from the particle across an adherent boundary layer is affected by the reaction only in that the latter sets the boundary condition at the particle. Here, mass transfer and reaction are sequential and occur in different parts of the system, and the slower of the two is the bottleneck and dictates the overall rate and its temperature dependence. Within the particle, however, mass transfer and reaction occur simultaneously and in the same volume element. Here, the reaction introduces a source-or-sink term into the basic differential material balance. If the reaction is slow, it alone controls the overall rate and its temperature dependence. If mass transfer is slow, both reaction and mass transfer affect the rate, and the apparent reaction order and activation energy are the arithmetic means of those of reaction and mass transfer. 

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