(560jb) Two-Dimensional Heterogeneous Reactor Model for an Exothermic Reaction Exhibiting Deactivation By Fouling: Modeling and Computational Strategy

inter-ideograph;line-height:115%"> 115%">Two-dimensional heterogeneous reactor model for an exothermic reaction
exhibiting deactivation by fouling: modeling and computational strategy

inter-ideograph;line-height:115%">Javier
Ibáñez,^a Jeroen Poissonnier,^a and Joris Thybaut^a

6.0pt;margin-left:0cm;text-align:justify;text-justify:inter-ideograph;
line-height:115%">Abstract:

line-height:115%">This
contribution reports on a two-dimensional heterogeneous reactor model for a
fixed bed catalytic reactor. The model considers temperature and concentration
gradients in both phases. The gas-phase chemical reaction, is highly exothermic
and presents particularities that cannot be tackled with the effectiveness
factor approach. Notably, deactivation by fouling is considered, simultaneously
addressing active site disappearance and pore blockage. The computational
effort is alleviated employing efficient numerical integration algorithms and
applying a quasi-steady state approach.

inter-ideograph;line-height:115%"> 115%;color:black">1. Introduction

inter-ideograph;text-indent:21.25pt;line-height:115%"> 11.0pt;line-height:115%;color:black">The generally considered idealization of a
packed bed reactor consists of a homogeneous model in which temperature and
concentration gradients within all phases are considered negligible. For reactions
presenting rapid kinetics and pronounced exothermicity, the gradients between
phases become non-negligible. Under these circumstances, a two-dimensional
heterogeneous reactor model becomes the appropriate choice. This more
fundamental approach becomes especially relevant when catalyst deactivation
takes place, since well-described local conditions are key to accurately
simulate the evolution of catalytic activity. 

inter-ideograph;text-indent:21.25pt;line-height:115%"> 11.0pt;line-height:115%;color:black">In this work we aim to model the
performance evolution for a packed bed reactor in which an exothermic reaction,
represented as A + B ↔ C, with ∆Hº ≈ 110.0 kJ·mol^-1
is carried out. A deactivation of the pellet shell has been experimentally
observed, in which the porosity of the catalyst is lost in the outer layers,
whereas the core maintains its original state. Nonetheless, the plugged pores
hinder the diffusion of the reactants and render the pellet inactive. In the
following we describe a two-dimensional heterogeneous model, as described by de
Wasch et al. ¹, accounting for catalyst
deactivation by fouling and pore blockage.

inter-ideograph;line-height:115%"> 115%;color:black">2. The modeling approach

inter-ideograph;text-indent:21.25pt;line-height:115%"> 11.0pt;line-height:115%;color:black">The set of main features and assumptions
considered in the heterogeneous packed bed reactor model are as follows:

margin-bottom:0cm;margin-left:39.25pt;margin-bottom:.0001pt;text-align:justify;
text-justify:inter-ideograph;text-indent:-18.0pt;line-height:115%">1.     
Concentration
and temperature gradients exist in the axial and radial directions on the fluid
phase.

margin-bottom:0cm;margin-left:39.25pt;margin-bottom:.0001pt;text-align:justify;
text-justify:inter-ideograph;text-indent:-18.0pt;line-height:115%">2.     
The
chemical reaction occurs exclusively in the solid phase.

margin-bottom:0cm;margin-left:39.25pt;margin-bottom:.0001pt;text-align:justify;
text-justify:inter-ideograph;text-indent:-18.0pt;line-height:115%">3.     
The
solid phase consists of finite cylindrical pellets, presenting concentration
and temperature gradients in the axial and radial directions.

margin-bottom:0cm;margin-left:39.25pt;margin-bottom:.0001pt;text-align:justify;
text-justify:inter-ideograph;text-indent:-18.0pt;line-height:115%">4.     
The
catalyst pellets are considered of negligible size with respect to the tubular
reactor and are exposed to homogeneous boundary conditions.

margin-bottom:6.0pt;margin-left:39.1pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-17.85pt;line-height:115%"> line-height:115%;color:black">5.     
The
mass and heat transfer resistance at the fluid-solid interphase are considered.

margin-bottom:6.0pt;margin-left:39.1pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-17.85pt;line-height:115%"> line-height:115%;color:black">6.     
The
deactivation mechanism proceeds via coke deposition and is modeled by means of
a decrease of the effective molecular diffusivity.

6.0pt;margin-left:21.25pt;text-align:justify;text-justify:inter-ideograph;
line-height:115%">In
order to derive the balances over the reactor and pellets, their spatial
coordinates are discretized in concentric hollow cylinders, as depicted in
Figure 1(a).

6.0pt;margin-left:21.25pt;text-align:justify;text-justify:inter-ideograph;
line-height:115%">Particularly,
the fluid phase continuity equations are as follows:

6.0pt;margin-left:21.25pt;text-align:justify;text-justify:inter-ideograph;
line-height:115%">

6.0pt;margin-left:21.25pt;text-align:justify;text-justify:inter-ideograph;
line-height:115%">The
boundary conditions applied correspond to those of the inlet at z=0, while the
symmetry condition applies at r=0 and wall conditions at r=R_t:

6.0pt;margin-left:21.25pt;text-align:justify;text-justify:inter-ideograph;
line-height:115%">

6.0pt;margin-left:21.25pt;text-align:justify;text-justify:inter-ideograph;
line-height:115%">The
solid phase mass and heat transfer occur solely by means of diffusion and are
respectively described by the following expressions:

6.0pt;margin-left:21.25pt;text-align:justify;text-justify:inter-ideograph;
line-height:115%">

6.0pt;margin-left:0cm;text-align:justify;text-justify:inter-ideograph;
text-indent:21.25pt;line-height:115%"> 115%;color:black">Neumann boundary conditions apply at the outer surface of the
pellet, whereas symmetry conditions apply at r and z = 0.

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text-indent:21.25pt;line-height:115%"> 115%;color:black">

6.0pt;margin-left:0cm;text-align:justify;text-justify:inter-ideograph;
text-indent:21.25pt;line-height:115%"> 115%;color:black">The deactivation is considered to proceed by fouling and pore
clogging, since a decrease of the net porosity is observed in the pellet shell.
Such mechanism occurs in a set of consecutive steps: first, the coke precursor
adsorbs on the active sites; second, the precursor is transformed into actual
coke which further grows in the catalyst pores, hindering the diffusion of
reactants and finally blocking their access. Theoretical approaches based on
percolation theory have been proposed to model the evolution of the
accessibility of the active sites as a function of coke content ². The success of these
models is based upon a good description of the pore structure, which might only
be known for purely crystalline catalysts. A more practical approach was
proposed by Nevicato et al. ³. A semi-empirical
expression was developed based on a mechanistic description of the sequence of
steps involved in the deactivation process. For the case of diffusion-limited
reactions, the following expression could be derived:

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text-indent:21.25pt;line-height:115%"> 115%;color:black">

6.0pt;margin-left:0cm;line-height:115%"> line-height:115%;color:black">Finally, the following expressions are used to
describe the main reaction and coke deposition rates:

6.0pt;margin-left:0cm;line-height:115%"> line-height:115%;color:black">

6.0pt;margin-left:0cm;text-align:justify;text-justify:inter-ideograph;
text-indent:21.25pt;line-height:115%"> 115%;color:black">By combining the above set of PDEs, the reactor model can be solved
accounting for the effect of coke deposition in the catalyst deactivation.
Depictions of the model outputs can be visualized in Figure 1(b-c), which
illustrates a mapping of the concentration of A within a catalyst pellet and
the evolution of the center-line axial temperature profiles with time on
stream. The computational effort is effectively alleviated by automatically
switching between the steady state solution and the deactivation function. In
this approach, the reactor equations are solved at steady state and assumed to
remain invariant for a finite amount of time. The deactivation functions are
then computed at these invariant conditions, allowing to update the map of
catalytic activity in the reactor. The automatic switching is based on the
evolution of this activity map, which assures an accurate solution and saves
computational effort. 

6.0pt;margin-left:0cm;text-align:justify;text-justify:inter-ideograph;
line-height:115%">3.
Conclusions

6.0pt;margin-left:0cm;text-align:justify;text-justify:inter-ideograph;
text-indent:21.25pt;line-height:115%"> 115%;color:black">A two-dimensional heterogeneous reactor model is here
proposed. This model describes the time evolution of a packed bed reactor,
considering interphase and intraparticle concentration and temperature
gradients. The experimentally observed catalyst shell deactivation is described
by means of a semi-empirical expression. This approach parts from a mechanistic
basis, lumping the consecutive processes of active site coverage, growth of
coke chains and pore blockage into a single expression. For the case of mass
transfer limited reactions, the coke concentration can be linked with the
effective diffusivity. This relation is here used to describe the evolution of
the catalytic activity. Finally, the computational effort required for the
complex transient modeling is minimized by automatically switching between the
steady state solution and the deactivation function.

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inter-ideograph;line-height:115%;page-break-after:avoid">Glossary

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line-height:115%">4.
References

none">1.        de Wasch, A. P. & Froment, G. F. A two
dimensional heterogeneous model for fixed bed catalytic reactors. Chem. Eng.
Sci. 26, 629–634 (1971).

none">2.        Froment, G. . Modeling of
catalyst deactivation. Appl. Catal. A Gen. 212, 117–128 (2001).

none">3.        Nevicato, D., Pitault, I.,
Forissier, M. & Bernard, J. R. The activity decay of cracking catalysts:
chemical and structural deactivation by coke. Stud. Surf. Sci. Catal. 88,
249–256 (1994).