COMSOL 6.3 - Carbon Deposition in Heterogeneous Catalysis

Carbon Deposition in Heterogeneous Catalysis

Carbon deposition onto the surface of solid catalysts is commonly observed in hydrocarbon processing. Carbon deposits can affect both the activity of catalysts as well as the flow of gas through a catalyst bed.

This example investigates the thermal decomposition of methane into hydrogen and solid carbon with two models. In the first model, the isothermal process occurring in an ideal reactor is simulated with the Reaction Engineering interface. The influence of carbon deposition on catalyst activity is also considered. In the second model, the effect that the carbon deposits have on the porosity and the fluid flow is studied. The second simulation takes both time and space dependencies into account.

Model Definition

CHEMISTRY

Methane decomposes over a Ni/Al2O3 catalyst according to the overall chemical reaction

(1)

Under atmospheric pressure, the temperate ranging from 490°C to 590°C and a volume fraction of hydrogen between 0 and 40%, the following reaction rate expression has been reported in the literature (Ref. 1):

(2)

where

(3)

and

The constant k0 in Equation 3 is 2.31·10−5 mol/(m3·s), supposing the amount of catalyst being 1 g/m3. The unit for pressure in Equation 2 is bar.

IDEAL REACTOR MODEL

This model treats the isothermal decomposition of methane (Figure 2) in a perfectly mixed batch reactor with constant volume. The species mass balances are summarized by

The rate term, Ri (SI unit: mol/(m3·s)) for each species, takes into account the reaction stoichiometry coefficients, νi, the reaction rate reported in Equation 2, r mol/(m3·s), and the catalyst activity, a:

The mass balances of the reacting species are then

The time dependence of the catalytic activity is expressed by

where

where ka0 is 8.324·106 (m3/mol)3·s. Solving the mass balances provides the evolution of the species concentrations over time. The fact that carbon is in the solid phase is taken into account by removing its effect on gas phase physical properties. The pressure in the reactor is a function of only the methane and hydrogen concentrations:

SPACE- AND TIME-DEPENDENT MODEL

The second model takes fluid flow, mass transport, heat transfer, and the chemical reaction into account. It is created by the Generate Space-Dependent Model feature available in the Reaction Engineering interface.

Figure 1: Methane enters from the left and reacts in the porous catalytic bed. The wall of the bed is heated.

Equations

The space-dependent model solves coupled momentum, mass, and energy balances together with a void fraction balance. The fluid flow is laminar, the concentrations high (no solvent is present), and porous media with variable porosity exist within the reactor. Additionally, the impact of heating is studied. The following physics interfaces are used in this example:

•

Chemistry

•

Transport of Concentrated Species

•

Heat Transfer in Porous Media

•

Laminar flow

•

Domain ODEs and PDEs

The Domain ODEs and PDEs interface solves a balance for the void fraction, or porosity, of the bed given by

where MC (kg/mol) is the carbon molar weight, and ρsoot (kg/m3) is the deposited carbon density. The equation states that the porosity decreases with the formation rate r of carbon in the pores. The porosity ε on the right hand side is needed to correct the reaction rate to pore volume base, and MC/ρsoot gives the unit 1/s. This equation can be implemented in the Domain ODEs and DAEs interface, resulting in a porosity distribution across the catalytic bed as a function of time. The initial porosity of the bed is assumed to be ε = 0.4.

The porosity is related to the permeability of the porous domain by (Ref. 2)

The reactor geometry (see Figure 1) is set up in 2D axisymmetry in the model as the angular gradients are negligible.

Results and Discussion

IDEAL REACTOR MODEL

Figure 2 shows the concentration transients of methane, hydrogen, and deposited carbon as methane decomposes over a Ni/Al2O3 catalyst. The compositions are displayed both with and without catalyst deactivation. From the change in concentrations with time, the reaction rate with constant catalyst activity is higher than when catalyst deactivation is accounted for.

Figure 2: Concentration transients of methane decomposition over a Ni/Al2O3 catalyst for two catalyst conditions: 1) deactivation; 2) constant activity.

Figure 3 shows the deactivation of the catalyst activity during methane decomposition. The activity decreases rapidly at the early stage of reaction, then decreases slowly.

Figure 3: Change of catalyst activity with reacting time.

SPACE- AND TIME-DEPENDENT MODEL

Figure 4 shows the velocity profile (surface) and pressure difference (contour) in the reactor at the end of the simulation. The flow velocity of gas is lower within the porous catalytic bed. The figure also displays the pressure drop across the bed.

Figure 4: Velocity flow field and pressure drop within the porous catalyst bed after 20,000 s. Surface plot displays the velocity (SI unit: m/s) and contour plot the pressure (SI unit: Pa).

Figure 5 shows the temperature distribution after 50 s and 500 s. It takes approximately 300 s for the bed to heat up to the same temperature as the walls (850 K).

Figure 5: Temperature distribution within the reactor after 50 s and 500 s.

Figure 6 shows a comparison of the concentration distributions for methane and hydrogen at 50 s and 500 s. The concentration of methane decreases fast as soon as the bed is sufficiently heated (Figure 5).

Figure 6: Concentration distribution of methane within the reactor at 50 s and 500 s.

The concentration distribution of methane and hydrogen is displayed along the centerline of the porous catalyst bed in Figure 7. The figure shows in detail that the production of hydrogen varies with time and temperature.

Figure 7: Concentration distribution of CH4 and H2 along the center of the porous catalyst bed at 50 s and 500 s.

Figure 8 illustrates that the porosity varies within the bed at 20,000 s and that the pores may become completely clogged near the bed inlet with time.

Figure 8: Porosity distribution within the porous catalyst bed at 20,000 s.

References

1. S.G. Zavarukhin and G.G. Kuvshinov, “The kinetic model of formation of nanofibrous carbon from CH4–H2 mixture over a high-loaded nickel catalyst with consideration for the catalyst deactivation”, J. Appl. Catal. A, vol. 272, pp. 219–227, 2004.

2. E.A. Borisova and P.M. Adler, “Deposition in porous media and clogging on the field scale”, Phys. Rev. E, vol. 71, p. 016311-1, 2005.

Chemical_Reaction_Engineering_Module/Reactors_with_Porous_Catalysts/carbon_deposition

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