(450g) Heat Generation and Removal in Fixed-Bed Reactors for Fischer-Tropsch Synthesis

1.    
Introduction

Fischer-Tropsch synthesis (FTS) is
one of the main ways utilized commercially to convert natural gas, coal and
biomass into liquid hydrocarbon fuels and other value-added products. The most frequently
used type of reactor for FTS is a multi-tubular fixed bed reactor (FBR). Due to
the high exothermicity of FTS reaction, special care has to be taken of removal
of generated heat during the design of such reactors. Understanding the
influence of process parameters on heat generation and removal is very
important in predicting hot spots and avoiding potential temperature runaways.

Majority of previously published studies
on this topic used one-dimensional pseudo-homogeneous models of FBR reactor for
FTS [1]. Relatively little attention has been given
to the topic of heat management, despite its practical significance. Also a
common assumption was that gas-phase correlations for heat transport parameters
are applicable, even though a certain amount of liquid is present both
accumulated in the FTS catalyst pellets and trickling down the reactor bed.

We will present analysis of heat
management characteristics in FTS fixed bed reactor using a cobalt-based
catalyst. Results of a two-dimensional model simulations which incorporates the
effect of both gas and liquid phase will be presented. Based on these the
influence of various relevant process parameters on FTS FBR heat generation and
removal will be examined.

2.    
Fixed-bed reactor model

The reactor model is developed as
a two-dimensional pseudo-homogeneous model without axial mixing, where
intra-particle transport is taken into account via the component effectiveness
factor . Components
considered in the system are CO, H₂, H₂O and hydrocarbons
products CH₄, C₂, C₃, C₄ … C₂₄
and lumped C₂₅₊. The main model equations are shown below.

Two-dimensional
mass balance is given by:

                                                                 (1)

where  is the molar
concentration of component i (i = CO, H₂, H₂O
and hydrocarbons CH₄, C₂, … C₂₄ and lumped C₂₅₊),
 is superficial
velocity, z and r are axial and radial dimension,  is cross-section
area of a tube with diameter  (), is effective radial
diffusivity of species i, η_i is catalyst
effectiveness for species i,  is reactor bed
density and  is rate of
species i disappearance or formation. Rates of reactants (CO and H₂)
disappearance and products (H₂O, n-paraffin and 1-olefin) formation
are calculated at each point along the reactor bed using a hybrid kinetic
approach [2-4].

Heat
balance equation is defined as:

                                                          (2)

where T is
temperature,  is
reaction enthalpy per mole of CO consumed, , ρ is fluid phase
density, λ_er is effective radial thermal conductivity, η_co
is effectiveness factor for CO and C_p is fluid heat
capacity.  Pressure drop is calculated using Ergun’s correlation [5]. Literature
correlations considering both gas and liquid phase influence on heat transport parameters
were incorporated in the model [6, 7]. The split between the gas and the liquid phase was
estimated using Raoult’s law. Effectiveness factor values were estimated based
on recent work on the single particle modeling done in our group [8].

            The
boundary conditions needed to solve Eqs. (1) and (2) were defined as:

                                                                             (3)

                                                                     (4)

                                                                                              (5)

                                                                                              (6)

                                                                 (7)

where L is
reactor tube length, R_t is reactor tube radius, ,  and  are inlet flowrate of
species i, inlet temperature and inlet pressure, respectively,  is radial heat transfer
coefficient at the wall and  is
wall temperature.

Model equations were
discretized and solved using gPROMS software for a number of process conditions
and geometric parameters.

3.    
Results and discussion

The influence of several process
parameters (inlet flowrates and temperature, wall temperature, tube and
particle diameter) on temperature distribution in radial and axial direction
was investigated. At base case conditions used in our study (T_in =
473 K, P_in = 25 bar, H₂/CO feed ratio = 2, F_in
= 0.15 mol/s, T_wall = T_in, d_t = 2.6 cm, d_p
= 2.5 mm, L = 10 m) temperature increases in axial direction and reaches a
maximum core temperature of 479 K close to the reactor inlet (z ~ 1 m), after
which it decreases gradually along the reactor. The radial gradient inside the
tube is about 3 K at the maximum temperature position, which highlights the
importance of using two-dimensional models to represent this process.

Simulations with varying one
process parameter and keeping others constant show temperature runaway
occurring for F_in < 0.03 mol/s, T_in > 497 K and d_t
> 5.9 cm.  Thermal behavior has a very complex dependency of process
conditions and often variation of one parameter can have conflicting influences
(both positive and negative effects) on heat management. For example,
increasing inlet temperature increases the reaction rate and thus amount of
generated heat. However, it also decreases the catalyst effectiveness which
results in a lower amount of heat generation.

Varying inlet flowrate shows that
the gas phase velocity increase has a very positive effect on the heat transfer coefficient at the wall, however the
impact of gas phase composition is noticeable as well. The highest h_wall
values are achieved with pure syngas (i.e. inlet conditions), while generation
of hydrocarbons along the reactor (X_CO > 0%) changes the physical
properties of the gas phase and results in h_wall decrease.
Increasing gas phase velocity also has a positive effect on the effective
radial thermal conductivity. However, we also see a positive influence of a liquid
phase velocity. The liquid phase is generated along the reactor and thus
Reynolds number of liquid increases from 0 to 0.57 for the base case inlet and
outlet conditions, respectively, resulting in about 18% increase of λ_er.
 

Increase of particle diameter is
beneficial from standpoint of heat management, both from the perspective of
decreased heat generation due to lower effectiveness factor and higher heat
transport coefficients due to increased Reynolds numbers. However, this leads
to low productivity and poor FTS product selectivity. Increase of tube diameter
results in much higher hotspots and more likely runaways, due to higher radial
thermal resistance and lower transport coefficients related to lower gas and
liquid velocities. These effects can be somewhat alleviated by increasing the
inlet flowrate, but not completely avoided.

4.    
Conclusions

Simulation results with variation
of process parameters show that FTS fixed bed reactors are very sensitive in
terms of heat management and any large disturbance can lead to potential
temperature runaway. Reasons for this behavior of FTS fixed bed reactors are
analyzed in detail. Especially interesting and previously unknown in open
literature is the contribution which liquid phase has on heat transport in FTS
fixed bed reactors.

References

[1]        A.P. Steynberg, M.E. Dry, B.H. Davis and
B.B. Breman, in S. André and D. Mark (Editors), Studies in Surface Science and
Catalysis, Volume 152, Elsevier, 2004, p. 64.

[2]        I.C. Yates and C.N. Satterfield, Energy
& Fuels, 5 (1991) 168.

[3]        W. Ma, G. Jacobs, T.K. Das, C.M. Masuku, J.
Kang, V.R.R. Pendyala, B.H. Davis, J.L.S. Klettlinger and C.H. Yen, Industrial
& Engineering Chemistry Research, 53 (2014) 2157.

[4]        B. Todic, W. Ma, G. Jacobs, B.H. Davis and
D.B. Bukur, Catalysis Today, 228 (2014) 32.

[5]        S. Ergun, Chemical Engineering Progress, 48
(1952) 89.

[6]        A. Matsuura, Y. Hitaka, T. Akehata and T.
Shirai, Heat Transfer - Japanse Research, 8 (1979) 44.

[7]        V. Specchia, G. Baldi and S. Sicardi, Chemical
Engineering Communications, 4 (1980) 361.

[8]        M.
Mandić, B. Todić, L. Živanić, N. Nikačević and D.B.
Bukur, Industrial & Engineering Chemistry Research, 56 (2017) 2733.