Heat transfer effects internal transport

The mass transfer effects cause, in general, a decrease of the measured reaction rate. The heat transfer effects may lead in the case of endothermic reactions also to a decrease of the equilibrium value and the resulting negative effect may be more pronounced. With exothermic reactions, an insufficient heat removal causes an increase of the reaction rate. In such a case, if both the heat and mass transfer effects are operating, they can either compensate each other or one of them prevails. In the case of internal transfer, mass transport effects are usually more important than heat transport, but in the case of external transfer the opposite prevails. Heat transport effects frequently play a more important role, especially in catalytic reactions of gases. The influence of heat and mass transfer effects should be evaluated before the determination of kinetics. These effects should preferably be completely eliminated. 

Antonini, T Gallucci, K., Foscolo, P.U. (2014) Oxygen transport by ionic membrane conductors to a biomass steam gasifier mass and heat transfer effects in the char burning process, iconBM International conference on BioMass, 4-7 May 2014, Florence, Italy. 

The general problem of diffusion-reaction for the overall effectiveness factor D is rather complicated. However, the physical and chemical rate processes prevailing under practical conditions promote isothermal particles and negligible external mass transfer limitations. In other words, the key transport limitations are external heat transfer and internal mass transfer. External temperature gradients can be significant even when external mass transfer resistances are negligibly small. 

Essentially all of the surface, of porous catalyst pellets is internal (see page 295). Reaction and mass and heat transfer occur simultaneously at any position within the pellet. The resulting intrapellet concentration and temperature gradients cause the rate to vary with position. At steady state the average rate for a whole pellet will be equal to the global rate at the location of the pellet in the reactor. The concentration and temperature of the bulk fluid at this location rhay not be equal to those properties at the outer surface of the pellet. The effect of such external resistances can be accounted for by the procedures outlined in Chap. 10. The objective in the present chapter is to account for internal resistances, that is, to evaluate average rates in terms of the temperature and concentration at the outer surface. Because reaction and transport occur simultaneously, differential... 

To conclude, an overall summary of calculations based on the above results indicates that the usual order of events as transport limitations occur is to begin with no limitations—chemical reaction controls throughout the pellet. Next, internal pore diffusion begins to have an effect, followed by external heat transfer... 

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. 

The rates at which chemical transformations take place are in some circumstances strongly influenced by mass and heat transfer processes (see Sections 12.3 to 12.5). In the design of heterogeneous catalytic reactors, it is essential to utilize a rate expression that takes into account the influence of physical transport processes on the rate at which reactants are converted to products. Smith (94) has popularized the use of the term global reaction rate to characterize the overall rate of transformation of reactants to products in the presence of heat and mass transfer limitations. We shall find this term convenient for use throughout the remainder of the chapter. Global rate expressions then include both external heat and mass transfer effects on the reaction rate and the efficiency with which the internal... 

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. 

Though the term "slurry refers to a suspension of fine solid particles in a liquid, the term slurry reactor is often used for a three-phase system, where both gas bubbles and solid particles are suspended in a liquid phase. For a solid/liquid/gas process, slurry reactors have two obvious advantages the possibilities for very large solid/liquid surface areas and for good heat transfer to the reactor wall. Therefore the volumetric capacity of slurry reactors can be relatively large. However, effective separation of the fine catalyst from the liquid phase may offer considerable technical problems. One possibility is an external separation, e.g. with centrifuges or hydrocyclones, and a transport of a concentrated catalyst slurry back into the reactor. More often internal filters are used, usually consisting of porous tubes (sintered stainless steel, or ceramics), that are cleaned every few minutes by a periodic reversal of the flow. 

In addition to these kinetic steps, there are also physical processes of heat and mass transfer to be considered. The external transport problem is one of heat and species exchange through the boundary layer between the surrounding bulk fluid and the catalyst surface (Figure 5). Concentration and temperature gradients are necessarily present in this case and would have to be accounted for in the modeling equations. Also, there is often an internal transport problem of heat conduction through the catalytic material -- and in the case of porous catalyst particles, an internal diffusion problem as well. Internal transport problems are beyond the scope of this paper. It must be noted, however, that any model intended to describe real-life systems will have to account for these effects. 

As pointed out earlier, the major external resistance is that of mass transfer, and therefore, the effect of external heat transfer can be neglected. Furthermore, internal (intraparticle) transport effects can be neglected in slurry reactors except under some unusual reaction conditions since the size of the catalyst particles is of the order of 100 microns. In trickle-beds, however, both the internal heat and mass transport effects can be important. 

The coupled heat and liquid moisture transport of nano-porous material has wide industrial applications in textile engineering and functional design of apparel products. Heat transfer mechanisms in nano-porous textiles include conduction by the solid material of fibers, conduction by intervening air, radiation, and convection. Meanwhile, liquid and moisture transfer mechanisms include vapor diffusion in the void space and moisture sorption by the fiber, evaporation, and capillary effects. Water vapor moves through textiles as a result of water vapor concentration differences. Fibers absorb water vapor due to their internal chemical compositions and structures. The flow of liquid moisture through the textiles is caused by flber-liquid molecular attraction at the surface of fiber materials, which is determined mainly by surface tension and effective capillary pore distribution and pathways. Evaporation and/or condensation take place, depending on the temperature and moisture distributions. The heat transfer process is coupled with the moisture transfer processes with phase changes such as moisture sorption and evaporation. 

This equation is valid for the general case, where the effective rate is influenced by external as well as internal heat and mass transfer. In real situations, however, one or more of the transport steps involved frequently proceed at a rate substantially above that of the chemical reaction. If this happens, these steps may be neglected without significantly affecting the observable reaction rate. Hence, the system may be simplified. The extent of simplification depends on which of the transport steps can be neglected. In the following, the different cases, which occur in practical situations, are discussed separately. 

For interphase limitations (boundary layer effects) the situation seems, at first glance, as simple as that for internal gradients, since most correlations for heat-and mass-transfer eoeffieients show a proportionality to the flow velocity of the surrounding fluid, u", where normally 0.6 < n < 1. At the lower velocities associated in particular with laboratory reactor operation, however, n tends to be closer to 0.6 than to 1, and the transport coefficients become insensitive to flow velocity and changing flow velocity is not an effective diagnostic. 

---