Mass transfer internal concentration profiles

The influence of the mass transfer resistance on the purity and on the steady state internal concentration profiles are shown in Figs. 9-11 and 9-12. A higher value for the mass transfer coefficient corresponds to a situation where mass transfer resistance is less important, and a better performance of the SMB will be obtained with sharper internal concentration profiles. 

Fig. 9-12. Effect of the mass transfer resistance on the internal concentration profiles ...

There is no influence of the concentration profile on selectivity in the case of equal order kinetics for the two reaction paths. If 2> the effective selectivity will be influenced by internal diffusion. As the influence of the internal concentration profile becomes more pronounced with increasing reaction order, the product selectivity will diminish, if the desired reaction has a higher order than the undesired. Otherwise, if the desired reaction has a lower kinetic order, the selectivity will be improved with increasing internal mass transfer resistance. 

Figure 8.8 Internal mass transfer resistance and catalyst deactivation concentration profiles inside a catalyst particle-lactose hydrogenation to lactitol and by-products (sponge Ni).

In the general case where the active material is dispersed through the pellet and the catalyst is porous, internal diffusion of the species within the pores of the pellet must be included. In fact, for many cases diffusion through catalyst pores represents the main resistance to mass transfer. Therefore, the concentration and temperature profiles inside the catalyst particles are usually not flat and the reaction rates in the solid phase are not constant. As there is a continuous variation in concentration and temperature inside the pellet, differential conservation equations are required to describe the concentration and temperature profiles. These profiles are used with intrinsic rate equations to integrate through the pellet and to obtain the overall rate of reaction for the pellet. The differential equations for the catalyst pellet are two point boundary value differential equations and besides the intrinsic kinetics they require the effective diffusivity and thermal conductivity of the porous pellet. 

Diffusion of reactants to the external surface is the first step in a solid-catalyzed reaction, and this is followed by simultaneous diffusion and reaction in the pores, as discussed in Chapter 4. In developing the solutions for pore diffusion plus reaction, the surface concentrations of reactants and products are assumed to be known, and in many cases these concentrations are essentially the same as in the bulk fluid. However, for fast reactions, the concentration driving force for external mass transfer may become an appreciable fraction of the bulk concentration, and both external and internal diffusion must be allowed for. There may also be temperature differences to consider these will be discussed later. Typical concentration profiles near and in a catalyst particle are depicted in Figure 5.6. As a simplification, a linear concentration gradient is shown in the boundary layer, though the actual concentration profile is generally curved. 

Fig. 2.1-11 Concentration profile ofthe educt A during mass transfer through a laminar bounda layer of thickness (5 (external mass-transfer resistance) and a cylindrical catalyst pore of length L (internal mass-transfer resistance).

A large number of catalytic reactions are exothermic and are accompanied by thermal effects. For relatively fast intrinsic kinetics as compared to the mass and heat transfer phenomena, the development of internal temperature gradients can be expected. Heat and mass transfer balances have to be solved simultaneously to estimate concentration and temperature profiles under steady-state conditions. 

Figure 4.41. Possible cases of concentration profiles s versus z in L S bioprocessing with partially aerobic biofilms (1) fully penetrated biofilm, (2) shallow biofilm, (3) deep biofilm with incomplete penetration. Profiles A-C represent the situations of combined external and internal mass transport limitations. The thickness of individual films of mass transfer resistance (<5l2 < s) ire indicated (5s, represents the active layer of biomass (aerobic biofilm). Increasing turbulence at the L S interface increases the concentration profile, as shown in l2-...

It is assumed that the mass tiansfer occurs in the layers on both sides of the phase boundary. According to the model, the mass transfer is caused by molecular diffusion. Therefore, a linear concentration profile is built up in the boundary layers. At the phase boundary itself, thermodynamic equilibrium is reached. More or less empirical correlations for the mass transfer coefficients /I and for the effective phase interface area are usually provided by the simulation program for different column internals (random packings, structured packings, and trays). The necessary diffusion coefficients can again be calculated according to Section 3.3.6. 

Figure 2.3 Reactant concentration profiles in different global rate regimes I, external mass transfer limitation II, pore diffusion limitation III, both external and internal mass transfer limitations IV, no mass transfer limitations on the intrinsic rate.

Since the reactant concentrations along the pores and within the particles are lower than the external surface concentrations, the overall effect of internal mass transfer resistances is to reduce the actually observed global rate below that measured at exterior surface conditions. It can be stated for isothermal effectiveness factors that r]concentration profile showing the pore diffusion-affected surface reaction is labeled as II in Figure 2.3. 

For endothermic reactions, fi<0, and the p curves at each value clearly indicate that the internal effectiveness factor ri will always be less than unity, since both the temperature and the reactant concentration decline toward the center of the particle. In this case, the impact of heat transfer decreases, but the effect of mass transfer becomes almost negligible. An approximate solution can be obtained by ignoring the concentration profile and solving the differential energy balance (Eq. 2.69) by assuming that the reactant concentration is equal to Cas within the particle ... 

Consider a catalyst particle located in a fluid medium where both external and internal mass transfer limitations affect the global rate. The reactant concentration profile for this situation is represented by curve III in Figure 2.3. The isothermal overall effectiveness factor, Q, expressed in terms of bulk fluid conditions, is derived primarily for first-order reactions using... 

A pillar structure of small rectangular posts was incorporated near the outlet of the reaction channel to retain the catalyst. The reaction was studied in the temperature range of 80-120 °C and at inlet pressures up to 5 bar. Benzyl alcohol conversion and benzaldehyde selectivity at 80 and 120 °C were very close to those from conventional glass stirred reactors. The best conversion of benzyl alcohol of 95.5% with selectivity to benzaldehyde of 78% was obtained for a micropacked bed reactors with catalyst sizes of 53-63 pm and a catalyst bed length of 48 mm at 120 °C and 5 bar. The effect of catalyst particle size on the reaction was examined with two ranges of particle size 53-63 pm and 90-125 pm. Lower conversion was obtained with particle sizes of 90-125 pm, indicating the presence of internal mass transfer resistances. In situ Raman measurements were performed and could be used to obtain the benzaldehyde concentration profile along the catalyst bed. 

Internal mass transfer is usually considered to be diffusional and, consequently, frequently described using a single effective diffusion coefficient (Deff). The flux of a compound, therefore, depends both on its diffusion coefficient and the slope of the concentration profile... 

For (Bi) j > 10, the preponderant part of the resistance, over 90%, resides in the internal phase. Mass transfer to and from that phase is described by Pick s equation (a PDF), and the uptake or release of solute can be read from Figure 4.6, Chapter 4, or calculated from the "long-time" solution (an ordinary differential equation [ODE]) listed in Table 4.4. Internally, the concentration profile varies with time externally it is flat and constant, with interface concentration Cg equal to the bulk fluid concentration Cp (see Figure 5.1a). 

Consider the case of a nonisothermal reaction A B occurring in the interior of a spherical catalyst pellet of radius R (Figure 6.4). We wish to compute the effect of internal heat and mass transfer resistance upon the reaction rate and the concentration and temperature profiles within the pellet. If Z)a is the effective binary diffusivity of A within the pellet, and we have first-order kinetics, the concentration profile CA(f) is governed by the mole balance... 

In the previous chapters tve discussed the influence of internal mass and heat transfer by neglecting external transport phenomena. Hence, we assumed that concentrations and temperature at the outer surface of the catalyst particle and the bulk of the fluid are the same. But this assumption is not justified under certain conditions and concentration and temperature profiles inside and outside the porous catalyst must be considered. 

Mass and heat transport may influence the effective rate of heterogeneously catalyzed and gas-solid reactions. External profiles of concentration and temperature may be established in the boundary layer between the surface of the particles and the fluid, and internal gradients may develop in the particles (although for industrial practice the influence of internal heat transfer can be usually neglected). Deviations from the ideal zero-gradient situation are usually considered by effectiveness factors. 

---