Diffusion effects through catalyst particles

The effective diffusivity is obtained from D, but must also take into account the two features that (1) only a portion of the catalyst particle is permeable, and (2) the diffusion path through the particle is random and tortuous. These are allowed for by the particle voidage or porosity, p, and the tortuosity, rp, respectively. The former must also be measured, and is usually provided by the manufacturer for a commercial catalyst. For a straight cylinder, rp = 1, but for most catalysts, the value lies between 3 and 7 typical values are given by Satterfield. 

The characteristic times on which catalytic events occur vary more or less in parallel with the different length scales discussed above. The activation and breaking of a chemical bond inside a molecule occurs in the picosecond regime, completion of an entire reaction cycle from complexation between catalyst and reactants through separation from the product may take anywhere between microseconds for the fastest enzymatic reactions to minutes for complicated reactions on surfaces. On the mesoscopic level, diffusion in and outside pores, and through shaped catalyst particles may take between seconds and minutes, and the residence times of molecules inside entire reactors may be from seconds to, effectively, infinity if the reactants end up in unwanted byproducts such as coke, which stay on the catalyst. 

The GDE for hydrochloric acid electrolysis is characterised by micro-scale hydraulic problems connected with the competition between the gas phase (oxygen), which has to diffuse towards the catalyst, and the liquid phase (water), which must be released. This competition is managed basically by a flow-through structure provided with hydrophobic channels of relatively large diameter. These are formed from PTFE (the binder of the structure) and catalyst particles and account for regulating the gas phase. Hydrophilic channels with smaller diameters (one order of magnitude smaller), which are located in the micro-porous carbon particles of the catalyst support (e.g. Vulcan XC-72), act as water absorbers. A consequence of the electrolysis process is that the catalyst itself is partially covered by liquid. This reduces its effectiveness and accounts for extra voltage. 

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... 

No experiments with variation in particle size of the silica gel have been done to study intraparticle diffusion effects. In silica gel such diffusion would be only through the pores (analogous to the macropores of a polystyrene) since the active sites lie on the internal surface. The silica gel used by Tundo had a surface area of 500 m2/g and average pore diameter of 60 A.116). Phosphonium ion catalyst 28 gave rates of iodide displacements that decreased as the 1-bromoalkane chain length increased from C4 to Cg to C16, The selectivity of 28 was slightly less than that observed with soluble catalyst hexadecyltri-n-butylphosphonium bromide U8). Consequently the selectivity cannot be attributed to intraparticle diffusional limitations. 

For liquid-phase catalytic or enzymatic reactions, catalysts or enzymes are used as homogeneous solutes in the hquid, or as sohd particles suspended in the hquid phase. In the latter case, (i) the particles per se may be catalysts (ii) the catalysts or enzymes are uniformly distributed within inert particles or (hi) the catalysts or enzymes exist at the surface of pores, inside the particles. In such heterogeneous catalytic or enzymatic systems, a variety of factors that include the mass transfer of reactants and products, heat effects accompanying the reactions, and/or some surface phenomena, may affect the apparent reaction rates. For example, in situation (iii) above, the reactants must move to the catalytic reaction sites within catalyst particles by various mechanisms of diffusion through the pores. In general, the apparent rates of reactions with catalyst or enzymatic particles are lower than the intrinsic reaction rates this is due to the various mass transfer resistances, as is discussed below. 

Another important catalyst characteristic is porosity. Particularly when heavy feeds are processed, high pore volumes and pore diameters are required to reduce pore diffusion limitations. These limitations occur when the intrinsic rate of reaction is high compared with the rate of diffusion of the reactants through the catalyst particle to the active surface. The catalyst is then not used effectively, and reaction rates and selectivity become functions of particle size. If the kinetics of the reaction are known, it is possible to estimate from theory the reaction rate or threshold above which a catalyst of known size will begin to exhibit diffusion limitations. 

Another type of stability problem arises in reactors containing reactive solid or catalyst particles. During chemical reaction the particles themselves pass through various states of thermal equilibrium, and regions of instability will exist along the reactor bed. Consider, for example, a first-order catalytic reaction in an adiabatic tubular reactor and further suppose that the reactor operates in a region where there is no diffusion limitation within the particles. The steady state condition for reaction in the particle may then be expressed by equating the rate of chemical reaction to the rate of mass transfer. The rate of chemical reaction per unit reactor volume will be (1 - e)kCAi since the effectiveness factor rj is considered to be unity. From equation 3.66 the rate of mass transfer per unit volume is (1 - e) (Sx/Vp)hD(CAG CAl) so the steady state condition is ... 

The effective diffusivity Dn decreases rapidly as carbon number increases. The readsorption rate constant kr n depends on the intrinsic chemistry of the catalytic site and on experimental conditions but not on chain size. The rest of the equation contains only structural catalyst properties pellet size (L), porosity (e), active site density (0), and pore radius (Rp). High values of the Damkohler number lead to transport-enhanced a-olefin readsorption and chain initiation. The structural parameters in the Damkohler number account for two phenomena that control the extent of an intrapellet secondary reaction the intrapellet residence time of a-olefins and the number of readsorption sites (0) that they encounter as they diffuse through a catalyst particle. For example, high site densities can compensate for low catalyst surface areas, small pellets, and large pores by increasing the probability of readsorption even at short residence times. This is the case, for example, for unsupported Ru, Co, and Fe powders. 

One of the popular methods for evaluating effective diffusivities in heterogeneous catalysts is based on gas chromatography. A carrier gas, usually helium, which is not adsorbed, is passed continuously through a column packed with catalyst. A pulse of a diffusing component is injected into the inlet stream and the effluent pulse recorded. The main advantages of this transient method are its applicability to particles of arbitrary shapes, and that experiments can be carried out at elevated temperatures and pressures. Haynes [1] has given a comprehensive review of this method. 

An interesting technique for the measurement of intraparticle diffusivity as well as longitudinal diffusion in the particle bed has been described by Deisler and Wilhelm (21). It deviates from all other techniques mentioned in that it is based on a dynamic flow study, analyzing the effect of the particles on the propagation of a sinusoidal variation of composition of a binary gas mixture passed through the catalyst bed. The authors have demonstrated the versatility of their general technique for determination of diffusion properties, as well as adsorption equilibria between the solids and the gas composition employed. If this general technique were modified to measure specifically the particle diffusivity, a very convenient and accurate method may result. 

One aspect of mass transport that is not easily measured is the effect on the reaction rate caused by the diffusion of the reactants through the pores of the catalyst particle to reach an active site and the migration of product molecules back through the pores to the liquid/solid interface and into the solution.24 As discussed in Chapter 13 most metal catalysts are prepared by impregnating a... 

The ways in which reaction parameters affect a two phase batch reaction are similar to those considered above for the three phase systems. Since there is no gas phase, agitation only serves to keep the catalyst suspended making it more accessible to the dissolved reactants so it only has a secondary effect on mass transfer processes. Substrate concentration and catalyst quantity are the two most important reaction variables in such reactions since both have an influence on the rate of migration of the reactants through the liquid/solid interface. Also of significant importance are the factors involved in minimizing pore diffusion factors the size of the catalyst particles and their pore structure. 

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