Plugging pore models

Newson (1975) was among the first to develop a pore plugging model of demetallation to predict catalyst life. By using the pore structure model of Wheeler (1951), the pellet was assumed to have N pores of identical length but with a specified distribution of pore radii. Metal deposition was assumed to be a first-order reaction over an outer fraction of the pore length and to have a uniform thickness. This model showed that the broadness of the size distribution had little effect on the catalyst life for the same average radii, but that increasing the radii from 45 to 65 A more than doubled the catalyst life. The restricted form of the diffusivity (see Section IV,B,5) was not employed in this model. 

The maximum sulfation observed is considerably smaller than the theoretical limit of 59 percent. This observation, together with the decrease in rate constant Kg with extent of sulfation, can be explained by models which assume that the reaction is retarded by a product layer of CaSO of low porosity through which the SO2 must diffuse in order to reach the unreacted CaO. Such a hypothesis has formed the basis for the development of several models to quantitatively fit sulfation data, of which the grain model (11, 12) and the pore-plugging model (13, 14) are the most notable. 

In the present communication, a brief description of the pore plugging model is presented and its differences with that of Ramachandran and Smith (7 ) are examined. An analytical calculation of the time required to plug the pore is presented. In addition, a perturbation solution for small times is used to motivate the formulation of a semianalytical version of the collocation method for two point boundary value problems with steep concentration profiles. 

Assuming isothermal conditions and neglecting bulk flow, radial concentration gradients in the pore and external mass transfer resistance, the following dimensionless form of the pore plugging model is derived ( ). 

The pore plugging model for gas-solid reactions given by eqs. (9) and (10) is integrated numerically by the use of orthogonal collocations ( ). The values of c, g, g2 are evaluated at the collocation points as functions of time, in order to evaluate conversion as a function of time, an outer radius, r, is defined so that for each pore the volume of the available solid reactant is given by, 2 2. The value... 

The pore plugging model predictions are now compared with experimental data obtained by Hartman and Coughlin (6,10) on the sulfation of calcined limestone. 

Figure 3. Pore plugging model prediction of the % total conversion change with time for different values of k. Same constants as in Figure 2...

This review will only focus on the modeling efforts in pore diffusion and reaction in single-catalyst pellets which have incorporated pore plugging as a deactivation mechanism. A broad literature exists on the deactivation of catalysts by active site poisoning, and it has been reviewed by Froment and Bischoff (1979). The behavior of catalytic beds undergoing deactivation is... 

Dautzenberg et al. (1978) considered a pore mouth plugging model in which the local pore radius (initially uniform) changes with time according to... 

Haynes apd Leung (1983) formulated a similar configurational diffusion model combining the effects of active site poisoning as well as pore plugging on the HDM reaction. In this case the reaction form in the conservation equation is multiplied by a deactivation function which accounts for the loss of intrinsic activity, (1 - ) is frequently chosen, where x is the fractional coverage of the sites. Other forms of the site deactivation function have been discussed by Froment and Bischoff (1979). The deactivation was found to depend on a dimensionless parameter given by... 

The effects of metal deposition on catalyst pore plugging were not included in this computation of Wei and Wei (1982). Rather, this model... 

A refined model can be written to describe deactivation by diffusion and fouling within a catalyst pellet or crystal. Nevertheless, it cannot be used for modelling a whole reactor which demands in itself, a complex model to be solved. We propose a simple decay function which can be easily introduced in the kinetic equations of a reactor model. This function is experimentally determined. It has a physical meaning and it allows to describe different behaviours of feedstocks between pure site fouling and strong diffusional limitation by pore plugging. 

Figure 5 shows the simulation of the reaction kinetic model for VO-TPP hydro-demetallisation at the reference temperature using a Be the network with coordination 6. The metal deposition profiles are shown as a function of pellet radius and time in case of zero concentration of the intermediates at the edge of the pellet. Computer simulations were ended when pore plugging occurred. It is observed that for the bulk diffusion coefficient of this reacting system the metal deposition maximum occurs at the centre of the catalyst pellet, indicating that the deposition process is reaction rate-determined. The reactants and intermediates can reach the centre of the pellet easily due to the absence of diffusion limitations. 

The points on figure 3 are built using this calculation method. The shape of the obtained deactivation function is different from the common exponential decrease, but it has been experimentally obtained with cracking reactbns on pure zeolites 119], Mann 110] found the same characteristic shape when modelling a catalyst deactivation by pore plugging under diffusion limitation, which is the case of cracking catalysis [8]. 

Alternately, models have been analyzed that view deactivation as involving pore plugging. In this case the connectivity of the void network would be reduced as the interconnections between neighboring pores are filled. The inherent problem in the testing of this model is that connectivity is not measured directly. Our ability to quantify void connectivity still requires advances in... 

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