Diffusion effects within catalyst

For a completely realistic interpretation of diffusion effects within catalyst particles, a heterogeneous reactor model is required. In a heterogeneous model, separate balance... 

The steam reformer model can handle feeds from methane to naphtha, with all the t5q)ical components that are present in natural gas, as well as recycled S5mthesis purge gas, or hydrogen recovery unit tail gases. Naphtha feed is characterized as about 30 chemical species, some of which are pure components, and some are hydrocarbon fractions (pseudo components). Each hydrocarbon species participates in a reaction that includes adsorption onto the catalyst, reforming, and desorption. The model includes diffusion effects within the catalyst, as well as heat transfer resistance from the bulk gas to the catalyst surface. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Recall than both A and B must diffuse into the catalyst for a bimolecular reaction to occur. This can create fairly complex concentration profiles of the two reactants within the catalyst, and the overall effectiveness factor is more complex than with the assumptions above. 

In the laboratory experiments, DOC monolith samples (length 7.5 cm, diameter 1.4 cm) with rather thin catalyst layer coating ( 25 pm) were employed to minimize the internal diffusion effects. The samples were placed into a thermostat to suppress the formation of temperature-gradients along the channels. In the course of each experiment, the temperature of the inlet gas and the monolith sample was increased at a constant rate of /min within the range of 300-800 K. The exhaust gases at the inlet of the converter were simulated by synthetic gas mixtures with defined compositions and flow rates (cf. individual figure captions all gas mixtures contained 6% C02 and 6% H20). 

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 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 ... 

Based on the studies on the KD306-type sulfur-resisting methanation catalyst, the non-isothermal one-dimensional and two-dimensional reaction-diffusion models for the key-components have been established, which were solved using an orthogonal collocation method. The simulation values of the effectiveness factors for the methanation reaction ch4 and the shift reaction fco2are in fair agreement with the experimental values, which indicates that both models are able to predict intraparticle transport and reaction processes within catalyst pellets. 

The modeling equations contain two key dimensionless parameters a Thiele modulus ( o) and a Peclet number (Peo) they characterize reaction/diffusion processes within the catalyst pellets and convection effects within the interpellet voids, respectively (81). Accordingly, both quantities depend on catalyst properties and reactor conditions. 

The probability of readsorption increases as the intrinsic readsorption reactivity of a-olefins (k,) increases and as their effective residence time within catalyst pores and bed interstices increases. The Thiele modulus [Eq. (15)] contains a parameter that contains only structural properties of the support material ( <>, pellet radius Fp, pore radius 4>, porosity) and the density of Ru or Co sites (0m) on the support surface. A similar dimensional analysis of Eqs. (l9)-(24), which describe reactant transport during FT synthesis, shows that a similar structural parameter governs intrapellet concentration gradients of CO and H2 [Eq. (25)]. In this case, the first term in the Thiele modulus (i/>co) reflects the reactive and diffusive properties of CO and H2 and the second term ( ) accounts for the effect of catalyst structure on reactant transport limitations. Not surprisingly, this second term is... 

Many models use an apparent reaction rate [59], with an Arrhenius-type temperature dependence and, as a result, consider the diffusion and reaction on the interior surface of the catalyst only under certain restrictive assumptions. It is important to incorporate mass transfer effects within the washcoat in the model to give a realistic description of the processes in the monolith [54,60]. 

For the reaction under consideration, values of the reaction rate as a function of concentration and catalyst decay time may be obtained by numerical differentiation of the experimental data obtained by Prasad and Doraiswamy (1974) at various space velocities and catalyst decay times in a fixed-bed reactor. The bed length was maintained small enough to give isothermal conditions to within 2°C. It was also ensured that the feed velocity was high enough, and the particle size small enough, to eliminate external and internal diffusion effects, respectively. The kinetic parameters, including decay time, will vary with the type of silica gel used. The data obtained for the silica gel used are summarized in Table CS3.1. 

Catalyst supports such as silica and alumina have low thermal conductivities so that temperature gradients within catalyst particles are likely in all but the finely ground powders used for infrinsic kinetic studies. There may also be a film resisfance fo heaf fransfer af fhe exfemal surface of the catalyst. Thus the internal temperatures in a catalyst pellet may be substantially different than the bulk gas temperature. The definition of the effectiveness factor, Equation 10.23, is unchanged, but an exothermic reaction can have reaction rates inside the pellet that are higher than would be predicted using the bulk gas temperature. In the absence of a diffusion limitation, rj > 1 would be expected for an exothermic reaction. (The case > 1 is also possible for some isothermal reactions with weird kinetics.) Mass transfer limitations may have a larger... 

CBb molar concentration of liquid phase component B, mol m-3 Deff effective diffusivity within catalyst particle, m2 s l Dj liquid-phase diffusivity, m2 s 1 E enhancement factor for gas-liquid reaction... 

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