CFD Modeling of Reactor Concepts to Avoid Carbon Deposition in Pyrolysis Reactions

2.1 Falling Film Reactor

In methane pyrolysis, the liquid film serves only as a protective barrier and heat carrier. The concept is shown in Fig. 1. Methane enters the reactor at the bottom, while liquid metal is introduced at the top of the reactor. The countercurrent flow allows using the film to preheat the incoming gas and to cool the reaction product. Another advantageous effect is the separation of the products. Hydrogen escapes at the top of the reactor, while solid carbon is transported via the falling film to the bottom.

For the model of the falling film reactor rotational symmetry is assumed and the inlet and outlet pipes are neglected. The reactor consists of the falling film region with outer radius r_a of 0.0125 m and a length L_F of 1 m. Above the film region, a box with radius r_B of 0.0225 m and a length L_B of 0.1 m is located.

A mixture of methane and hydrogen with T_G0 = 600 K and a molar ratio of 9:1 is fed to the reactor with a volume flow of 1 L min⁻¹. Due to low gas volume flow and ambient pressure, the gas flow is simulated laminar and incompressible.

Molten liquid tin is used as film medium with a volume flow of 1 L min⁻¹ at a reference temperature of 600 K. This leads to a mass flow of 0.12 kg s⁻¹ and a minimum volume flow per wetted unit of perimeter of 0.76 m³m⁻¹h⁻¹, which is between 0.5–1.5 m³m⁻¹h⁻¹ where complete wetting of the wall is achieved ¹⁹. The film Reynolds number for the given conditions is Re > 400 so that a turbulent film regime can be expected ²⁰. The Reynolds number is given by

()

using liquid mass flow rate , outer radius r_a and dynamic viscosity η_L. The thermophysical properties of liquid tin could be calculated by Eqs. 5–8 ^21-23.

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The inlet temperature of the molten tin varies between T_L0 = 600 K for furnace operation with a furnace temperature T_fur = 1300 K as shown in Fig. 1 and T_L0 = 1300 K for heating with the hot film.

To avoid a computationally expensive two-phase (gas-liquid) simulation, the flow of the falling film is reduced to a moving wall boundary condition as shown in Fig. 3. Film thickness for turbulent films could be calculated by a correlation of Brauer ²⁴

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where ν_L represents the kinematic viscosity. The superficial velocity in turbulent film is equal to the mean wave velocity which could be calculated by a correlation of Helbig ²⁵

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with maximum laminar film velocity w_max,lam in cylindrical coordinates given by Eq. 19.

Besides the surface velocity, the film temperature serves as a boundary condition. To calculate the film temperature T_L, a differential equation is set up according to Fig. 4b.

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The specific heat flow describes the specific heat loss due to the heating of the cold gas where characterizes the specific heat flow through the wall. The equation for can be set up according to Fig. 4a and is given by

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Here λ_L represents the thermal conductivity, d_W the wall thickness and α_WL the heat transfer coefficient between wall and liquid.

Methane pyrolysis is simulated as a simple global reaction as used by Catalan et al. for the optimization of a bubble column reactor ²⁶. The equations for calculating the reaction rate are given below.

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The heat sink that occurs in the endothermic pyrolysis reaction is

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The carbon is modeled as inert, spherical particles with a fixed diameter. For this purpose, particle injection points as shown in Fig. 5 are inserted at a total number of 153 locations in the reactor. By means of the reaction rate (Eq. 12), the mass flow of carbon can be calculated for the volume element ΔV in which the injection point lies.

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During the pyrolysis process, particles of different sizes are formed. These range from primary particles (d = 5 · 10⁻⁸ m) to carbon agglomerates (d = 1.28 · 10⁻⁶ m) ²⁷. Depending on the residence time in the reactor and the temperature, the primary particles grow and carbon agglomerates will form. The growth process is not represented by the model at first. Initially, the model is only intended to check how efficiently particles of different sizes can be separated by the reactor concepts. Therefore, six different particle sizes are injected from each given particle size range.

2.2 Rotating Film Reactor

The basic concept of the rotating reactor does not differ much from the falling film reactor. The gas and liquid flow are fed into the reactor at different ends as shown in Fig. 2. The film is formed by rotating the tube that connects two static vessels on the left and right ends.

Similar to the falling film reactor, rotational symmetry is assumed. Volume flows of gas and liquid as well as inlet temperatures and composition of the operating media are identical to the falling film reactor model. Since the rotation of the gas flow creates turbulence, the k-ω-SST model is used to describe the gas flow.

The complete wetting of the wall in a rotating film reactor depends on the rotational frequency. The most uniform form of wetting is achieved within annular flow regime. Using a correlation of Chatterjee et al. ²⁸ a rotational frequency rpm of 2000 min⁻¹ has been calculated to guarantee annular flow for the given conditions.

The film flow is assumed to be a rotating hollow cylinder with film surface velocity w_max. The surface velocity w_max could be calculated from laminar velocity profile of the film by

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The constant C₁ can be calculated by integrating the velocity profile:

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The film thickness is calculated by forming a mean value over the reactor length from the correlation of Suppiah ²⁹

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Heat transfer, pyrolysis reaction and particle model are identical to the falling film reactor.

2.3 Porous Wall Reactor

The reactor concept shown in Fig. 6 is based on a patent to produce carbon black and chlorinated hydrocarbons ¹⁸. The exothermic energy from the chlorination reaction is used for the pyrolysis reactions of the chlorinated hydrocarbons to generate the solid carbon, thus requiring no heat introduction via the walls. A protective layer is built up near the reactor walls by using the product gas hydrogen chloride. After the area of radial inflow, there is an additional pipe section in which no radial inflow is introduced.

For the concept of this porous wall reactor, the length and width ratios were adjusted to those of the patent and scaled up. The zone where the reaction takes place has a diameter of 100 mm and a length of 500 mm, of which 300 mm correspond to the porous wall.

As gas phase components methane, chlorine, chloromethane, hydrogen chloride and gaseous carbon are considered. The reaction is divided into two reaction steps: the chlorination of methane to methyl chloride and hydrogen chloride as well as the reaction of methyl chloride with chlorine to carbon and hydrogen chloride. The complex mechanism of the chlorination, pyrolysis and carbon generation kinetics were simplified to the two-step reaction, as the generation of carbon out of the gas phase is not part of the simulation. The patent states for inlet volume flow rate ratio of CH₄:Cl₂:HCl ≈ 0.9:2:6, while 90 % of the HCl gas enters the reactor via the sidewalls, there is no carbon accumulation on the reactor walls ¹⁸. This ratio was adjusted to a total volume flow rate of 534 L min⁻¹, with all gases having an inlet temperature of 773 K and atmospheric pressure.

The solid carbon is implemented by injection of particles. To estimate the mass of the carbon, a complete conversion of the methane is assumed, with the mass distributed into different particle sizes ranging from 0.001 to 0.201 mm. The particles are mainly injected into the mixing zone of the reactor in a shape of a hollow cone.

3.1 Falling Film and Rotating Film Reactor

In order to be able to compare the results of falling film and rotating film reactor, the operating parameters and the geometries have to be chosen similarly as described in Sect. 2. Tab. 1 compares the characteristic film parameters of the film flow for the falling film and the rotating film reactor.

The comparison of film thickness δ and maximum velocities w reveals the biggest difference between the two reactors. Since the film thickness is an order of magnitude greater, the maximum film speed in the rotating film reactor is only a quarter of the speed in the falling film. This leads to less backmixing in the gas phase due to countercurrent flow. Due to the thin film and the high film velocity in the falling film reactor a possible detachment of the film might create non-wetted zones. This might result in carbon deposition, which needs to be avoided. Higher mass flows could solve this problem leading to even higher film speeds.

3.1.1 Heat Input by Furnace

For a maximum furnace temperature of 1300 K, the heat input into the reactor is investigated. For this purpose, the dimensionless axial temperature profiles of the furnace, the wall film and the reactor center and the reaction rates in the film region and the reactor center are shown in Fig. 7.

Regarding the temperature profiles for both reactors, furnace and film temperature are equal. The advantage of the rotating film reactor becomes apparent when looking at the temperature in the center of the reactor. Due to the high velocities in the falling film, the gas velocity in the center of the reactor increases. Therefore, the maximum temperature is located at x* = 0.65 whereas the maximum film temperature can be found at x* = 0.25. In comparison, the slower film and gas velocity in the rotating film reactor are advantageous for the heat input. The maximum temperature in the center of the rotating film reactor is higher than in the falling film reactor. This could also be seen by the higher reaction rate in the reactor center although the difference seems to be very small for this temperature level. Furthermore, the reaction gas cools down much faster in the rotating film reactor. This prevents methane from reacting in the outlet area where no protective film is present.

3.1.2 Heat Input by the Hot Film

Alternatively, the heat can also be carried into the reactor by a previously heated film flow at 1300 K. For this purpose, 80 % of the reactor is insulated starting from the film inlet. The other 20 % are used for film cooling with a wall temperature of 600 K. The dimensionless temperatures and reaction rates for falling and rotating film reactor are shown in Fig. 8.

The center of the falling film reactor is heated more slowly than that of the rotating film reactor. This is again due to the slower gas velocities. Furthermore, in the insulated area (x* > 0.2) almost a constant temperature level is reached. Within the rotating film reactor, the heat can be quickly removed at the end of the film zone, which allows a clear reaction zone to be defined. With regard to the reaction rate, it is noticeable that it is higher at x* = 0.2 in the rotating film reactor than in the falling film reactor. Due to the lower film speed, less product is mixed back, which increases the reactant concentration locally ensuring a higher reaction rate. The demonstrated reaction rates lead to the following conversions: 17 % for the falling film reactor and 19 % for the rotating film reactor. The difference does not seem very large, but it should be noted that in the falling film reactor the gas flow could not be cooled down so that a part of the reaction takes place in the volume above the film zone. With the rotating film reactor, no reaction takes place in this zone.

3.1.3 Particle Separation

As shown in Fig. 5, particles are injected at 153 locations. Each particle is tracked to find the location where it escapes. The mass flow of the particle injection is coupled via Eq. 14 to the reaction rate. Thus, more particles are produced in the zones of high temperatures than in cold zones. The growth of particles from primary particles to carbon agglomerates is not considered. Therefore, six different particle sizes are injected. Based on the different particle sizes, a final assessment can be made as to whether all types of particles can be separated. Fig. 9 shows which particles have left the reactor via each boundary. For the falling film reactor at least a third of the particles leave the reactor via the outlet. These are the particles injected near the reactor center (Fig. 9a).

In the rotating film reactor (Fig. 9b), more than 90 % of the particles of each size leave the reactor via the wall film. Due to the rotation, even the smallest particles with a diameter of 50 nm are pushed out of the reactor center towards the wall film.

3.2 Porous Wall Reactor

This concept includes the addition of multiple gas inlets in a tubular reactor. On the one hand, the addition of inert gas in the inlet area of the reactants methane and chlorine prevents them from directly contacting on another, avoiding the carbon deposition at the inlet mixing zone. On the other hand, the introduction of the inert gas through porous walls along the reactor ensures that the chlorination reaction mainly takes place at the center of the tube.

The reaction takes place immediately behind the inlet of the axial HCl inlet. Only small amounts of methane and methane chloride are found at the outlet (Tab. 2).

Since no heat loss via the walls is assumed in the reactor, the average temperature at the outlet is 1735 K. The maximum temperature of around 2000 K is reached locally at the outlet near the center. The HCl coats the complete wall until the outlet, even in the region with no radial inlet, resulting in an outlet temperature at the walls of around 800 K.

Fig. 10 shows the trajectory of the particles in the reactor. For this purpose, 2000 particles were injected into the mixing area. Particles touching the sidewalls are marked as trapped. Particles flowing through the axial exit surface are marked as escaped. The trajectory of the particles shows that the particles are pushed into the center of the reactor and thus remain away from the wall. In the simulation, less than 1 % of the particles remained trapped in the reactor. Heat generation accelerates the flow in the center of the reactor, resulting in a flow channel. The simulation confirms the results of the claims in the patent that the particles are carried out of the reactor.