Transport mechanism with porous catalysts

Heat and mass transfer processes always proceed with finite rates. Thus, even when operating under steady state conditions, more or less pronounced concentration and temperature profiles may exist across the phase boundary and within the porous catalyst pellet as well (Fig. 2). As a consequence, the observable reaction rate may differ substantially from the intrinsic rate of the chemical transformation under bulk fluid phase conditions. Moreover, the transport of heat or mass inside the porous catalyst pellet and across the external boundary layer is governed by mechanisms other than the chemical reaction, a fact that suggests a change in the dependence of the effective rate on the operating conditions (i.e concentration and temperature). 

Whereas the pore-flow mechanism describes transport through porous UF, NF and RO membranes show a transient structure between porous and non-porous, with probably also sorption-diffusion as part of the transport mechanism. Nanofiltration is a relatively new membrane process with a nominal MWCO in the range of 200-1000 Da. Its application in water treatment has been growing rapidly, but the nonaqu-eous application is still an emerging field. All efforts to enlarge catalysts become superfluous when the membranes are capable of retaining off-the-shelf TMCs. 

Chemical reaction and mass transfer are two unique phenomena that help define chemical engineering. Chapter 8 described problems involving chemical reaction and mass transfer in a porous catalyst, and how to model chemical reactors when the flow was well defined, as in a plug-flow reactor. Those models, however, did not account for the complicated flow situations sometimes seen in practice, where flow equations must be solved along with the transport equation. Microfluidics is the chemical analog to microelectro-mechanical systems (MEMS), which are small devices with tiny gears, valves, and pumps. The generally accepted definition of microfluidics is flow in channels of size 1 mm or less, and it is essential to include both distributed flow and mass transfer in such devices. 

The overall rate of reaction is equal to the rate of the slowest step in the mechanism. When the diffusion steps (1.2. 6. and 7 in Table 10-2) are very fast compared with the reaction steps (14. and 5), the concentrations in the immediate vicinity of the active sites are indistinguishable from those in the bulk Ouid. In this situation, the transport or diffusion steps do not affect the overall rate of the reaction. In other situations, if the reaction. steps are very fast compared with the diffusion steps, mass transport does affect the reaction rate. In systems where diffusion from the bulk gas or liquid to the catalyst surface or to the mouths of catalyst pores affects the rate, changing the flow conditions past the catalyst should change the overall reaction rate. In porous catalysts, on the other hand, diffusion within the catalyst pores may limit the rate of reaction. Under these circumstances, the overall rate will be unaffected by external flow conditions even though diffusion affects the overall reaction rate. 

Surface diffusion is yet another mechanism that is invoked to explain mass transport in porous catalysts. An adsorbed species may be transported either by desorption into the gas phase or by migration to an adjacent site on the surface. It is this latter phenomenon that is referred to as surface diffusion. This phenomenon is poorly understood and the rate of mass transfer by this process cannot be predicted with a reasonable degree of accuracy. Classic discussions of this subject are presented by Satterfield (14) and Barrer (15), while modem animations are contained in Wikipedia (16). 

The dimensionless substrate concentration profile in a porous membrane, where the biocatalyst is entrapped, depends on the Thiele modulus heterogeneous catalyst, since it allows for the estimation of the penetration depth within the support and can also be used to identify the mechanism that controls the process rate. The Thiele modulus can be interpreted as a ratio between a diffusion time (SVD if.s) and a kinetic time (A a/ max) or, equivalently, as a ratio between a characteristic kinetic rate Vmax/ m AS = AS and a merely diffusive transport mechanism, characterized by (D s s/S) x (A5/5). When (/) 1 kinetics is the limiting step, the process rate coincides with the reaction rate and the concentration profile is uniform, completely penetrating the support. 

Pores, and especially mesopores (with sizes between 2 and 50 nm) and micropores (with sizes less than 2 nm), play an essential role in physical and chemical properties of industrially important materials like adsorbents, membranes, catalysts etc. In addition to pore structural characterization described above, the description of transport phenomena in porous materials has received attention due to its importance in many applications such as drying, moisture transport in building materials, filtration etc. Although widely different, these applications present many similarities since they all depend on the same type of transport phenomena occurring in a porous media environment. In particular, transport in mesoporous media and the associated phenomena of multilayer adsorption and capillary condensation have been investigated as a separation mechanism for gas mixtures [29]. 

One PEFC developer (10) devised an alternative plate structure that provides passive water control. Product water is removed by two mechanisms (1) transport of liquid water through the porous bipolar plate into the coolant, and (2) evaporation into the reactant gas streams. The cell is similar in basic design to other PEFCs with membrane, catalysts, substrates, and bipolar plate components. However, there is a difference in construction and composition of the bipolar plate ... 

Oxygen transport in the catalyst layer may differ from transport in the GDL due to the nonnegligible impact of its small pores with radii of 0.01 am. In these pores, oxygen transport is controlled by the Knudsen diffusion mechanism (see below). For a detailed discussion of transport mechanisms in the porous CL and GDL, see Hinebaugh et al. (2012), Wang (2004), and Weber and Newman (2004a). 

Apecetche et al. [1] studied viscous and diffusive transport with simultaneous reaction in non-isobaric porous catalyst particles by use of the dusty gas model. A binary gaseous mixture under isothermal conditions was studied taking into account mass transfer due to the following mechanisms viscous flow, non-equimolar... 

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... 

The species diffusivity, varies in different subregions of a PEFC depending on the specific physical phase of component k. In flow channels and porous electrodes, species k exists in the gaseous phase and thus the diffusion coefficient corresponds with that in gas, whereas species k is dissolved in the membrane phase within the catalyst layers and the membrane and thus assumes the value corresponding to dissolved species, usually a few orders of magnitude lower than that in gas. The diffusive transport in gas can be described by molecular diffusion and Knudsen diffusion. The latter mechanism occurs when the pore size becomes comparable to the mean free path of gas, so that molecule-to-wall collision takes place instead of molecule-to-molecule collision in ordinary diffusion. The Knudsen diffusion coefficient can be computed according to the kinetic theory of gases as follows... 

Purwanto and Delmas [10] proposed the addition of co-solvent (ethanol) to enhance the solubility of 1-octene in the aqueous phase so that the overall reaction rate was increased, and their kinetic study led to a rate model similar to that in homogeneous liquid systems consistently from the point of view of bulk reaction mechanism. Chaudhari et al. [11] reported the improvement of the hydroformylation rate by addition of a small amount of PPhj to the biphasic system to enrich the effective catalyst species at the liquid-liquid interface. Kalck et al. [12] tested two more approaches to improve the mass transfer rate of biphasic hydroformylation of 1-octene and 1-decene with catalyst precursor [Rh2(/i-S Bu)2(CO)2(TPPTS)3j use the phase-transfer agent /i-cyclodextrin to transport the substrate into the aqueous phase to react there (see Section 2.2.3.2.2), and the supported aqueous-phase (SAP) catalyst to increase the reaction area due to the high specific surface area of porous silica (see Section 2.6). The improved conversion and TOF gave informative suggestions for the reaction mechanisms. 

As mentioned previously, the catalyst layer is applied to either a GDM or to a decal (applying to the PEM directly is also explored). The GDM allows the reactant to transport from the flow-field channels on the plates to the catalyst layer, and allows the product to transport from the catalyst layer to the flow-field channels on the plates so it must be porous, typically with porosity as high up to 80% and with pore size in lO s pm. The GDM also provides mechanical support for the catalyst layer or the catalyst-coated membrane (CCM). The GDM transports heat and electrons between the plates and the catalyst layers as well, so it must conduct electrons and heat. 

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