Modelling of Microchannel Reactors for Fischer-Tropsch Synthesis

Cao Huili; Tang Xiaojin

(SINOPEC Research Institute of Petroleum Processing, Beijing 100083)

Abstract: The Fischer-Tropsch synthesis is an important step in coal liquefaction, natural gas liquefaction, and biomass liquefaction. In recent years, the use of microchannel reactors for Fischer-Tropsch synthesis has received widespread attention. Since thermocouples and other sensors cannot be placed easily in a microchannel reactor, it is very vital to establish a model to provide calculated results highly compatible with the experimental data. This paper mainly introduces the establishment and solution of microchannel reactor models for Fischer-Tropsch synthesis. General mass transfer differential equations, heat transfer differential equations and related parameters (such as reaction rates, dispersion coefficient, and convective heat transfer coefficient) are listed. To solve the models, numerical solutions, such as the CFD simulation methods and the programming methods, are reviewed. It is recommended that a more accurate solution strategy is the combination of CFD simulation and programming methods.

Key words: Fischer-Tropsch synthesis; microchannel reactor; modelling

1 Introduction

The Fischer-Tropsch synthesis has a history of more than 90 years[1]. It is an important step in coal liquefaction,natural gas liquefaction, and biomass liquefaction.Specifically, the Fischer-Tropsch synthesis reaction is a process for preparing hydrocarbon compounds from syngas[2]. The basic reactions of Fischer-Tropsch synthesis are shown in Equation (1) — Equation (3)[3]. At present,the research on Fischer-Tropsch synthesis mainly focuses on two aspects: new catalysts and reactor optimization[4].

Commercial reactors for Fischer-Tropsch synthesis include the fixed bed reactors, the slurry bed reactors,and the fluidized bed reactors[5]. The advantages of fixed bed reactors are: (i) Fluid flow is close to plug flow; (ii)Catalyst loading is high; (iii) Subsequent separation and catalyst recovery steps are not required, which can reduce time and operating costs; (iv) There are different catalysts for high temperature and low temperature conditions,and many types of hydrocarbons could be produced; (v)This process can be readily commercialized. However,in addition to the major drawback of insufficient heat transfer, the fixed bed reactors have problems associated with high pressure drop and diffusion limitations[6-8].The advantages of the slurry bed reactors are: (i) The structure of a slurry reactor is simple; (ii) The heat transfer performance is excellent; (iii) Catalysts could be easily replaced; (iv) The pressure drop is small.However, separation of liquid products from catalysts is very difficult for slurry reactors[9-11]. The advantages of the fluidized bed reactors are: (i) It is easy to achieve continuous process and automation control; (ii) Fluidized bed reactors have good heat transfer characteristics;(iii) It is easy to facilitate continuous regeneration and circulation of catalyst particles. The disadvantages of fluidized bed reactors mainly involve the strong impact and friction effects for solid catalysts during the flow process, which can cause the attrition of catalyst particles and leakage of reactor. Also, the residence time of the reactants is widely distributed in fluidized bed reactors,which could reduce the yields of target products[12-14].

The reactors mentioned above are suitable for large scale industrial production, while the microchannel reactors were developed in the 1990s[15]for small syngas production due to small size and flexible operation[16](as shown in Figure 1[17]). More importantly, the mass transfer and heat transfer performance of microchannel reactors are much better than the conventional reactors with smaller reaction space, shorter molecular diffusion distance, and larger specific surface area[18-19]. Ying, et al.[20]performed a Fischer-Tropsch synthesis experiment in a microchannel reactor using the cobalt-based catalyst. They found that the CO conversion rate in the microchannel reactor was 84% (493 K, 20 bar, 13 900 h-1),while the CO conversion in the fixed bed reactor was 69% (498 K, 20 bar, 14400 h-1). The CO conversion rate in the microchannel reactor is higher even at lower temperatures and smaller GHSV (gas hourly space velocity). Rai, et al.[21]also found that the conversion of CO in a microchannel reactor (over 92%) was higher than that in a fixed bed reactor (70%) using the same Cobased catalysts. They also studied effects of temperature,pressure, GHSV, and H2/CO ratio on CO conversion and CH4selectivity. Sun, et al.[22]carried out the Fe-based Fischer-Tropsch synthesis in a microchannel reactor,while they studied the effects of temperature, pressure,GHSV, and H2/CO ratio on CO conversion, and proposed the reaction rate correlation and reaction mechanisms. The current research on microchannel reactors for the Fischer-Tropsch synthesis remains in the laboratory scale. The industrialization proposal needs to consider issues such as the hot spots, the reactor materials, and the catalysts.However, thermocouples and other sensors cannot be placed easily in a microchannel reactor so temperature detection in a microchannel reactor is difficult. Therefore,it is very essential to establish a microchannel reactor model for the Fischer-Tropsch synthesis to obtain the temperature distribution of a reactor and determine the hot spots positions for the purpose of safe and efficient industrial applications.

In this study, the mass transfer and heat transfer models of microchannel reactors for the Fischer-Tropsch synthesis are reviewed including the model establishment and the model solution methods.

2 Model Equations

2.1 Mass transfer

The mass transfer differential equation is shown in Equation (4)[23]. The two items on the left side of the equation are unsteady term and convection item, and the two items on the right side are dispersion term and source term.

whereR=,ris the reaction rate of each component,iiMiis the molar mass of each component, andDis the dispersion coefficient.

The mass transfer models can be divided into the pseudohomogeneous models and the heterogeneous models.The difference between pseudo-homogeneous models and heterogeneous models is that the heterogeneous models should consider the internal diffusion effect. In other words, the mass transfer and the heat transfer within catalyst particles need to be considered for heterogeneous models[24]. Na, et al.[19]established a two-dimensional pseudo-homogeneous model of a microchannel reactor for the Fischer-Tropsch synthesis. The mass transfer differential equation consists of the unsteady term, the convection term, the dispersion term, and the source term, as shown in Equation (5). Hosukoglu, et al.[25]established a two-dimensional heterogeneous model of a microchannel reactor. In the model, the mass transfer differential equation for fluid phase consists of the convection term and the dispersion term, and the mass transfer differential equation for catalyst pellets consists of the convection term, the dispersion term, and the source term, as shown in Equation (6) and Equation (7).

Figure 1 Schematic of a microchannel reactor assembly[17]

2.2 Heat transfer

The heat transfer differential equation is expressed as Equation (8)[23]. Similar to mass transfer, the two terms on the left side of the equation are the unsteady term and the convection item, and the first term on the right side is the dispersion term, while the other three terms on the right side are the source items. For a fluid which is incompressible and has a small viscosity, the heat transfer differential equation is shown in Equation (9).

The heat transfer models can be divided into the pseudohomogeneous heat transfer models and the heterogeneous heat transfer models. Shin, et al.[26]established a one-dimensional pseudo-homogeneous model of a microchannel reactor for the Fischer-Tropsch synthesis,and the heat transfer differential equation consists of the convection term, the heat conduction term, and the source term, as shown in Equation (10). Hosukogluet, et al.[25]established a two-dimensional heterogeneous model of a microchannel reactor. In the model, the heat transfer differential equation for fluid phase consists of convection term and dispersion term, and the heat transfer differential equation for catalyst pellets consists of convection term,dispersion term and source term, as shown in Equation(11) and Equation (12).

2.3 Model parameter

2.3.1 Kinetics of Fischer-Tropsch synthesis

There are three basic reactions of Fischer-Tropsch synthesis as shown in Equation (1) — Equation (3).Kinetic equations for these reactions in microchannel reactors are shown in Table 1.

2.3.2 Dispersion coefficient

The values of the axial dispersion coefficient and the radial diffusion coefficient are important parameters for Equation (4). The axial dispersion coefficient can be described by molecular diffusion and fluid mechanics, as shown in Equation (13)[31]. Similarly, the radial dispersion coefficient can be described by molecular diffusion and turbulent dispersion, as shown in Equation(14)[31].

2.3.3 Convective heat transfer coefficient

The computational correlations of convective heat transfer coefficient could generally be divided into a pure empirical type and a semi-empirical type. The pure empirical correlations are usually directly related to experimental parameters by dimensionless processing[26,32-33].The semi-empirical correlations are usually based on the theory of heat transfer, and could be used more widely.The convective heat transfer coefficient correlations are shown in Table 2. Moreover, the convective heat transfer coefficient can be easily calculated from the Nusselt number, as shown in Equation (15). Therefore, the correlation of Nusselt number is also listed in Table 2.

Where,kis the thermal conductivity of fluid.

Table 1 Kinetic equations for Fischer-Tropsch synthesis in microchannel reactors

Table 2 Correlations of convective heat-transfer coefficient

3 Model Solution

At present, the above models can only be solved by numerical methods because the above differential equations are extremely complicated and impossible to be solved by analytical methods. Numerical computation methods were developed in the early 1960s. With the development of computers, numerical methods have become an important research method in the study of transfer processes.

3.1 CFD simulation

CFD simulation is often used to numerically solve differential equations by commercial software, and a discrete distribution of the flow or temperature field over a continuous region could be obtained. Common commercial CFD softwares include ANSYS CFX,ANSYS FLUENT, and COMSOL Multiphysics (formerly FEMLAB). The fluid-solid coupling function of COMSOL Multiphysics is more powerful than ANSYS.Cao, et al.[36]established a three-dimensional pseudohomogeneous model of a microchannel reactor for the cobalt-based Fischer-Tropsch synthesis and solved the model using Femlab. The results of simulation are shown in Figure 2. The temperature difference within the microchannel reactor is less than 1 K.

Figure 2 Temperature pro file in a microchannel reactor(P = 2.0 MPa, H2/CO = 2, GHSV=17 894 h-1)[36]

Arzamendi, et al.[37]proposed a CFD model of a microchannel reactor for the cobalt-based Fischer-Tropsch synthesis by ANSYS CFX. Figure 3 (a) is the temperature distribution of the solid state module. The temperature difference within the block is less than 3 K,and the average temperature of the solid is about 490.2 K,which is close to the average temperature of the coolant.Figure 3 (b) is a temperature pro file of the syngas fluid,the temperature of which drops from 523.15 K at the inlet to 491.4 K at the outlet. However, the temperature of the fluid in the reaction channel is almost constant at 498 K.

Figure 3 Temperature distribution of solid modules and the fluid(GHSV=30 000 h-1, H2/CO = 2)[37]

Kshetrimayum, et al.[38]used ANSYS FLUENT 14.5 for CFD simulation of a microchannel reactor for the cobalt-based Fischer-Tropsch synthesis. Figure 4 shows the temperature distribution of the reaction channel and the cooling channel. It can be seen that the hot spot is in the upper left corner, and the temperature difference in the reaction channel reaches 12 K. Thus, they proposed to add a cooling channel above the reaction channel, as shown in Figure 5. In this way, the temperature difference in the reaction channel drops to 8 K.

Figure 4 Temperature distributions of the reaction channel and the cooling channel (GHSV = 5 000 h-1)[38]

Park, et al.[39]used COMSOL Multiphysics 5.2 for CFD modeling of a microchannel reactor with the cobalt-based catalysts. Figure 6 (a) shows the CO conversion profile,where the CO conversion can reach 35%. The temperature pro file of the catalytic bed is shown in Figure 6 (b), and the temperature difference in the catalyst bed is no more than 5 K.The CFD simulation is theoretically strong but its fluidsolid coupling function is weak. In a simulation process,the fluid-solid coupling models with high matching degree must be selected by simplifying conditions to obtain better results. In addition, the CFD simulation methods cannot solve the problem of fluid volume change, and the internal diffusion of catalysts is difficult to describe.

Figure 5 Temperature distribution of the reaction channel with additional coolant layer (GHSV=5 000 h-1)[38]

Figure 6 CO conversion pro file and temperature pro file of the catalytic bed (SV=15 762 mL/(gcat·h))[39]

3.2 Programming method

Programming method is used to solve the mass transfer differential equation and the heat transfer differential equation by writing an algorithm, which can be executed in MATLAB, FORTRAN, and C/C++. FORTRAN and C/C++ have fast operation speed and high computational efficiency for large data. MATLAB’s algorithm is more flexible and its data processing is simple[40]. Currently, the programming methods for solving microchannel reactor models have rarely been studied due to the complex boundary conditions so that the programming methods are illustrated by the fixed bed reactor models. Programming methods use fitting regression in the process of modeling,which can get more accurate results and solve the fluidsolid coupling problem.

Moazamiand, et al.[41]used MATLAB to calculate the mass transfer differential equation of a fixed bed reactor for the Fischer-Tropsch synthesis, and obtained the concentration distribution of each component along the reactor under different experimental conditions, as shown in Figure 7.

Figure 7 Concentration pro file under different experimental conditions[41]

Ghouri, et al.[42]used MATLAB combined with the experimental data to fit the kinetic parameters of Fischer-Tropsch synthesis in a fixed-bed reactor,and solved the mass transfer differential and the heat transfer differential equations. The CO conversion rate and methane selectivity data under different syngas flow rates were simulated and compared with the experimental results as shown in Figure 8. The simulated values of CO conversion rate are slightly different from the experiments, and the difference between the simulated and the experimental values of methane selectivity is negligible. The temperature distribution in the fixed-bed reactor under different syngas flow rates was also obtained as shown in Figure 9. It can be seen from the Figure 9 that the larger the flow rate of the syngas is, the smaller the temperature difference in the reactor would be.

Figure 8 Comparison of simulated (triangle) and experimental values (square) of CO conversion (a)and CH4 selectivity (b)(T = 513 K, P = 20 bar)[42]

Although the CFD simulation methods are convenient and the functions of commercial software are powerful, their basic theories lack necessary mathematical foundation,such as convergence and error estimation[43]. In addition,the fluid-solid coupling problem, the fluid volume change problem and the internal diffusion problem in catalyst cannot be solved well. The programming methods can make up for these deficiencies, so their development is absolutely necessary. However, for reactor structures with complex boundary conditions, the programming methods need to rely on high computer performance. Moreover,flow fields are usually simpli fied when the programming methods are applied.

4 Conclusions

Modelling of microchannel reactors for the Fischer-Tropsch synthesis is reviewed in two aspects: model establishment and model solution. The general forms of mass transfer differential equations and heat transfer differential equations are respectively provided. In addition, the pseudo-homogeneous models and the heterogeneous models established in literature are summarized, and the correlations of related parameters such as reaction rates, dispersion coefficient, and convective heat transfer coefficient are listed. At this stage, the calculations of these parameters still require an in-depth research to obtain more accurate values.

Nowadays, the model solution mainly depends on numerical solution methods. The numerical solution methods include CFD methods and programming methods.CFD simulation is theoretically strong but its fluidsolid coupling function is weak. Programming methods can get very useful results if using high-performance computers. Thus, the combination of programming methods and CFD methods can not only solve problems of fluid-solid coupling, fluid volume change and internal diffusion in catalyst, but also make calculations more efficient with enough information of flow fields.

Figure 9 Temperature distribution in the reactor(T = 513 K, P = 20 bar)[42]

Acknowledgement:We gratefully acknowledge the financial support from the SINOPEC (No.119001).

Nomenclature

C—Concentration, mol/m3

d—Diameter of inert particles, m

D—Dispersion coefficient

Dax—Axial dispersion coefficient, m2/s

Dra—Radial dispersion coefficient, m2/s

Dm—Molecular diffusion coefficient, m2/s

D'm—Effective molecular diffusion coefficient, m2/s

h—Convective heat transfer coefficient, W/(m2·K)

k—Thermal conductivity, W/(m·K)

L—Reactor length, m

M—molar mass, g/mol

P—Pressure, Pa

Pem'—Effective Peclet number of inert particle

r—Reaction rate, mol/(m3·s)

t—Time, s

T—Temperature, K

us—Super ficial gas velocity, m/s

Δz—Space step, m

εB—Catalyst porosity

ρ—Density, kg/m3

τ—Tortuosity factor