Mathematical Modeling of Fischer-Tropsch Synthesis ...

I NTERNATIONAL J OURNAL OF C HEMICAL R EACTOR E NGINEERING Volume 7

2009

Article A23

Mathematical Modeling of Fischer-Tropsch Synthesis in an Industrial Slurry Bubble Column Nasim Hooshyar∗

Shohreh Fatemi†

Mohammad Rahmani‡

∗

University of Tehran, [email protected] University of Tehran, [email protected] ‡ Amirkabir University of Technology, Tehran, [email protected] ISSN 1542-6580 c Copyright 2009 The Berkeley Electronic Press. All rights reserved. †

Mathematical Modeling of Fischer-Tropsch Synthesis in an Industrial Slurry Bubble Column∗ Nasim Hooshyar, Shohreh Fatemi, and Mohammad Rahmani

Abstract The increase in society’s need for fuels and decrease in crude oil resources are important reasons to make more interest for both academic and industry in converting gas to liquids. Fischer-Tropsch synthesis is one of the most attractive methods of Gas-to-Liquids (GTL) processes and the reactor in which, this reaction occurs, is the heart of this process. This work deals with modeling of a commercial size slurry bubble column reactor by two different models, i.e. single bubble class model (SBCM) and double bubble class model (DBCM). The reactor is assumed to work in a churn-turbulent flow regime and the reaction kinetic is a Langmuir-Hinshelwood type. Cobalt-based catalyst is used for this study as it plays an important role in preparing heavy cuts and the higher yield of the liquid products. Parameter sensitivity analysis was carried out for different conditions such as catalyst concentration, superficial gas velocity, H2 over CO ratio, and column diameter. The results of the SBCM and DBCM revealed that there is no significant difference between single and double bubble class models in terms of temperature, concentration and conversion profiles in the reactor, so the simpler SBCM with less number of model parameters can be a good and reliable model of choice for analyzing the slurry bubble column reactors. KEYWORDS: Fischer-Tropsch, slurry bubble column reactors, hydrodynamic, flow regime

∗

Shohreh Fatemi, corresponding author whom to be addressed, Tel./Fax: +98(21)61112229, Email: [email protected].

Hooshyar et al.: Modeling of Fischer-Tropsch Synthesis in a Slurry Bubble Column

1

1

Introduction

Rapid development of the world economy and dramatic increase in the international oil price has made the global energy and environmental problems increasingly serious. The demand for middle distillate that can be distillated directly from crude oil and also can be produced by converting coal and natural gas using Fischer- Tropsch reaction, is growing in recent years( Wang et al., 2007). Most of the natural gas resources around the world are not reachable and there is a need to convert them to some other products such as gasoline and kerosene (middle distillate) to easy to transfer. Since Fisher-Tropsch Synthesis (FTS) was invented eighty years ago, it has become one of the most concerned methods in converting gas to liquid. The users of this method for producing distillates in industrial scales are limit; Shell and Sasol oil companies are the main users. After invention of this method, many researchers are trying to design and make reactors to produce heavy paraffin. Good reactor sizing and operational conditions will gain desired products. FTS is a highly exothermic reaction and the slurry bubble column reactor (SBCR) is the ideal reactor of choice for this purpose. This is, due to the possibility of achieving near isothermal conditions because of relatively high heat transfer coefficients to cooling agent. The slurry reactor also possesses the advantage of lower operating and reactor construction costs. In these reactors, gas is usually the discontinuous phase rising in the form of bubble through a continuous liquid or slurry phase. In this method catalyst recovery is possible, depreciation rate is low, mass transfer is done at a high rate and reaction can be done in a high temperature. Pressure drop in SBCRs is less than one bar and fabrication is more economic than the other kinds of three-phase reactors. The main issue of these reactors is scale up because of the problem in gathering and recovery of the fine catalyst particles. The mathematical modeling of the SBCs is influenced by the hydrodynamics in three- phase flow systems and depends on many parameters such as gas velocity, pressure, column diameter, inlet gas temperature, slurry properties and solid concentration. Heretofore, two different flow regimes are introduced for analyzing of the SBCs; “Single bubble” and “Double bubble” class flow. Dynamic models can be used for the simulation of the start-up, shut-down or transition operation (change in process set points), however, because of the computational complexity until newly SBCRs have been exclusively modeled in the steady state operation, De Swart and Krishna (2002) just newly proposed the first dynamic model of the FT in slurry bubble column reactors. Deckwer et al.(1982) and Mills et al.(1996) have developed their model on single bubble flow regime concept and, oppositely Krishna et al.(Maretto and Krishna, 1999; Van der Laan et al., 1999; Krishna and Sie, 2000; Krishna et al., 2001; De Swart and Krishna, 2002) and Fernandes (Fernandes, 2007; Fernandes

Published by The Berkeley Electronic Press, 2009

International Journal of Chemical Reactor Engineering

2

Vol. 7 [2009], Article A23

and Teles, 2007) employed the double-bubble flow regime. The double-bubble class regime is a more complex and time-consumed model; also more model parameters are needed for the computation. These two different models which have been developed on the base of Axial Dispersion (AD) are introduced in this article. The main purpose of our work is to figure out the difference between the single bubble and double bubble class model at transitional conditions for FTS in SBC reactors. 2

Fischer-Tropsch synthesis

Fischer-Tropsch Synthesis is combination of two reactions: Fischer-Tropsch (FT) and Water-Gas-Shift (WGS) reactions: CO + 2H2 → -(CH2)- + H2O

(1)

CO + H2O ↔ CO2 + H2

(2)

Mainly cobalt and iron are used as the reaction catalyst. Supports used for these catalysts are Titania, Silica and Alumina. In presence of cobalt catalyst, WGS reaction rate is very slow and inappreciable. In contrary, in presence of iron, WGS is noticeable. Iron catalyst deactivates rapidly in comparison to cobalt catalyst because of deposition of coke on the catalyst surface(Maretto and Krishna, 1999). These evidences would leads to more concerns to cobalt catalyst although the high accessibility and the low price of iron. In present work the kinetic equation used for FT synthesis is based on the rate of synthesis gas consumption suggested by Yates and Satterfield (1991) in which CO adsorption on the active sites and hindering the reaction rate is considered as following: − RCO + H 2 =

aPH 2 PCO

(1 + bPCO )

(3)

2

In equation (3), a and b are assumed to be temperature dependent constants, a representing kinetic parameter and b an adsorption coefficient and were determined by means of curve fitting over experimental data:

⎛ 4494 ⎞ 2 a = 8.1113 ×10−9 exp ⎜ − ⎟ ⎡⎣ mol/(s.kg cat .Pa ) ⎤⎦ T ⎝ ⎠

http://www.bepress.com/ijcre/vol7/A23

(4)


⎛ 8236 ⎞ b = 1.2473 ×10−12 exp ⎜ ⎟ ⎝ T ⎠

[1/Pa ]

3

(5)

The cobalt catalyst used was Co/MgO on SiO2 support. Ranges of operating condition were: 220-240 °C, 5-15 bar, inlet feed H2/CO 1.5-3.5(Yates and Satterfield, 1991). As the reaction is taking place in liquid phase in contact to the solid; therefore the partial pressures of equation 3 were converted to the gas concentration using the assumption of ideal gas law by the equation of Pi = Ci RT . Then Ci was converted to the liquid concentration using Henry's law for hydrogen and carbon monoxide. 3

Mathematical modeling

3.1

Hydrodynamic

A slurry bubble column reactor is a complicated reaction system because it consists of different gaseous compounds, liquids and solid particles. The hydrodynamics in a gas-liquid or gas-liquid-solid reactor are characterized by different flow regimes(Behkish, 2004; Hooshyar and Fatemi, 2008). In these columns, two flow patterns have been observed: the homogeneous and the heterogeneous, mainly depending on the superficial gas velocity. The homogeneous regime exists at low superficial gas velocities and changes to heterogeneous regimes with an increase in the gas velocity. In homogeneous regime the gas velocity is usually less than 0.05 m/s. Under this condition, the gas bubble, do not affect the liquid motion and almost no liquid mixing is observed. As the gas velocity and the gas fraction are increased, the uniform flow losses its stability and the flow regime transients from the homogeneous to heterogeneous. Then the instability quickly develops and there is strong interaction among gas bubbles and both coalescence and break up of bubbles are observed. This is the “churn-turbulent” as a part of heterogeneous flow(Mudde et al., 2009), where the larger gas bubbles move in a plug flow manner, creating liquid recirculation as well as back mixing. The smaller gas bubbles, on the other hand are entrained within the liquid re-circulation. The hydrodynamic behavior, heat and mass transfer and mixing behavior are quiet different in homogeneous and heterogeneous regimes. The transition from bubbly to heterogeneous regime is delayed with increasing pressure and is advanced with increasing solid concentration. Therefore the gas holdup and volumetric mass transfer coefficient are increased with increasing pressure and decreasing solid concentration(Behkish, 2004).



4


In modeling of FTS in a slurry bubble column two different theories can be distinguished; one is on the base of Deckwer (Deckwer et al., 1980; and 1982) and the other one on Krishna theory(Krishna et al., 1999; Maretto and Krishna, 1999; Krishna and Sie, 2000; De Swart and Krishna, 2002). Deckwer used a single bubble class flow regime and assumed that gas bubbles exist in a single size and their diameter distribution is narrow. Krishna explained that in the churnturbulent flow regime the gas phase can be split up in a ‘large’ bubble population and a ‘small’ bubble population. The superficial gas velocity, Usg is split in two parts: a part of gas rises through the column in the form of ‘small’ bubbles at a superficial gas velocity Udf; the remainder rises through the column in the form of ‘large’ bubbles at a superficial gas velocity (Usg - Udf ). The large bubbles travel up through the column at high velocities (in the range of 1-2 m/s) and have the effect of churning up the slurry phase(De Swart and Krishna, 2002). Figure (1) shows a schematic representation of these two models. Usg,H U

sg,H

Usg,H

Uss

Uss

Z=H

Z=H

Z=0

Z=0

Us Ud

(a)

Usg0-Udf

Usg0

Usg0

Uss (b)

Figure 1. Schematic representation of Slurry Bubble Column Reactor for: (a) Double Bubble Class Model (DBCM), (b) Single Bubble Class Model (SBCM) 3.2

Fischer-Tropsch slurry reactor models

In this work the axial dispersion (AD) is adopted to describe the characteristics of the flow in slurry bubble columns for FTS which provides a convenient method for describing flow patterns of the gas, liquid and solid catalyst that exist between the limits of plug-flow and complete back mixing. The AD has the ability to be accounted for different classes of bubbles that may exist. The mathematical model



5

proposed by Mills et al.(1996) is used as a basis but extended for both SBCM and DBCM and summarized in table1 by using down coming assumptions: • Transport of the solid catalyst is described by a sedimentation-dispersion type model. • Intraparticle temperature gradients are absent, so that the catalyst is in thermal equilibrium with liquid phase. • The gas phase is in thermal equilibrium with liquid phase. • The slurry phase is non volatile. • Heat is removed by internal tubes. • The volume of the heat transfer tubes is small compared to the empty reactor volume. • The gas velocity is changed along the bed because of chemical reaction and defined by the contraction factor as following(Levenspiel, 1999):

α=

(

)

(

Vg X CO + H 2 = 1 − Vg X CO + H 2 = 0

(

Vg X CO + H 2 = 0

)

)

(6)

Using this approach, the superficial gas velocity is given by:

(

U sg = U sg 0 1 + α X CO + H 2

)

(7)

where:

X CO + H 2 =

1+U X H2 1+ I

(8)

I = CG ,CO / CG , H 2 at the reactor inlet and U = υCO / υ H 2 denotes the molar usage factor for carbon monoxide to hydrogen(Deckwer et al., 1982). • The superficial gas velocity of small bubbles is constant. • The resistance of mass transfer between the gas and liquid phase is located in the liquid phase. • The reaction performs on the surface of fine catalyst particles with non significant diffusion resistance. The mean diameter of catalyst particle is 50µm and the effectiveness factor is taken unity because of very small particle diameters. • Movement of catalyst particles is a random diffusive process and can be described by ascribing a dispersion coefficient for the solid. Their movement is under gravity and their velocity is equal to the terminal settling velocity of



6


the solid particles(Ramachandran and Chaudhari, 1983). As there is a uniform solid concentration in slurry phase a steady condition can be assumed for mass balance of catalyst: d 2 Cs dCs Dc + U ct =0 2 dz dz

(9)

Boc exp ( − Bocζ ) 1 − exp ( − Boc )

Then Cs (ζ ) = Cs

(10)

(

)⎦

and Boc = Pec ⎡U ct / U g 0 − U ss / U sg 0 (1 − ε g ) ⎤

⎣

(11)

While Peclet number for particle is defined as follow(Ramachandran and Chaudhari, 1983): ⎛ U Pec = 13 ⎜ sg ⎜ gD T ⎝

(

⎡ ⎞ ⎢1 + 0.009 Rec U sg / gDT ⎟⎢ 0.85 ⎟ 1 + 8 U sg / gDT ⎠⎢ ⎣

(

)

)

−0.8

⎤ ⎥ ⎥ ⎥⎦

(12)

Here Rec is the Reynolds number of solids. Table 1. Mathematical models for single bubble class and double bubble class model Single class model Double class model Mass balance for ith component in Mass balance for ith component in large bubbles is: gas phase is1: εg

∂Ci , g ∂t

=

∂ ∂z

(ε g E g

∂Ci , g ∂z

)−

∂ ∂z

− k L ,i a (Ci* − Ci , L )

Ci* = Ci , g / mi

(U sg Ci , g )

εb

∂Ci , g ,l arg e ∂t

=

∂ ∂z

−

(ε b Eg ,l arg e

∂Ci , g ,l arg e ∂z

)

∂

[(U sg − U df )Ci , g ,l arg e ] ∂z − k L ,i ,l arg e al arg e (Ci*,l arg e − Ci , L ) Ci*,l arg e = Ci , g ,l arg e / mi

1 . In calculation i=1,2,…,ns and ‘ns’ is the total number of species and ‘nr’ is number of independent reactions.



7

Table 1. (Continued) Mass balance for ith component in Mass balance for ith component in small liquid phase: bubbles is: εL

∂Ci , L ∂t

=

∂ ∂z

(ε L EL

∂Ci , L ∂z

)−

∂ ∂z

(U ss Ci , L )

ε small

∂Ci , g , small ∂t

+ k L ,i a (C − Ci , L ) * i

=

∂

(ε small Eg , small

∂z

−

∂Ci , g , small ∂z

)

∂

(U df Ci , g , small ) ∂z − k L ,i , small asmall (Ci*, small − Ci , L )

nr

−Csε L ρ P ∑ υij R j j =1

Ci*, small = Ci , g , small / mi

Mass balance for ith component in liquid phase is: εL

∂Ci , L ∂t

=

∂

(ε L EL

∂Ci , L

)−

∂

(U ss Ci , L ) ∂z ∂z ∂z + k L ,i ,l arg e al arg e (Ci*,l arg e − Ci , L ) + k L ,i , small asmall (Ci*, small − Ci , L ) nr

−Cs ε L ρ p ∑ υij R j j =1

Heat balance is derived as: ρ s C psε L

∂T ∂t

=

∂ ∂z

(ε L λax

∂T ∂z

) − U ss ρ s C ps

∂T ∂z

nr

−α eff aw (T − Tc ) +Cs ε L ∑ ( −ΔH Ri ) R j j =1

To solve these equations boundary and initial conditions are needed for unsteady state mode. These B.Cs and I.Cs are represented in table 2.



8


Table 2. Boundary conditions and Initial conditions for single bubble class and double bubble class model Single Bubble Class Model

Double Bubble Class Model

For initial conditions (at t=0):

For initial conditions (at t=0):

Ci , g = Ci , L = 0

Ci , g ,l arg e = Ci , g , small = Ci , L = 0

T = Tc

T = Tc

For boundary conditions:

For boundary conditions:

At z=0

At z=0

Ci , g = Ci , g 0

Ci , g ,l arg e = Ci , g 0

∂ ∂z

(ε L EL

ε L λax

∂T ∂z

∂Ci , L ∂z

)=

∂ ∂z

(U ss Ci , L )

= U ss ρ s C ps (T − Tc )

ε df Eg , small ∂ ∂z

(ε L EL ∂T

ε L λax

At z=H ∂Ci , g ∂z

=

∂z ∂Ci , L ∂z

)=

= U sg 0 (Ci , g , small _ Ci , g 0 ) ∂ ∂z

(U ss Ci , L )

= U ss ρ s C ps (T − Tc )

At z=H ∂Ci , L ∂z

=

∂T ∂z

∂Ci , g , small

=0

∂z

=

∂Ci , g ,l arg e ∂z

=

∂Ci , L ∂z

=

∂T ∂z

=0

And

And Ci , g 0 = Py0 / ZRTi

3.3

∂z

∂Ci , g , small

(Z=1.01)

Ci , g 0 = Py0 / ZRTi

(Z=1.01)

Model parameters

The operating conditions and physical properties of system are summarized in table 3 and 4. Table 5 shows the hydrodynamic and mass transfer correlations of both models. Table 3. Operational conditions (De Swart and Krishna, 2002) Operating conditions

Value

Dimension

Reactor Pressure (P)

3.0

MPa



9

Table 3. (Continued) Reactor diameter (DT)

7.5

m

Reactor height (H)

30.0

m

Inlet temperature of syngas (Ti)

501

K

Temperature of coolant (Tc)

501

K

Area for heat transfer (aw)

10

m2(m3 reactor)-1

Superficial inlet gas velocity (Usg0)

0.1

m/s

Slurry velocity (Uss)

0.01

m/s

Table 4. Physical properties Properties

Value or Definition

Dimension

Liquid phase properties (C16H34)(Maretto and Krishna, 1999) 2.9×10-4

Pa

Surface tension of liquid phase(σ)

0.01 Pa. m

Pa. m

Liquid density (ρL)

640

kg m-3

Heat conductivity of liquid (λL)

0.113

W m-1 K-1

Liquid viscosity(ηL)


10



Table 4. (Continued) Heat capacity of the liquid (CPL) Diffusion coefficient of CO at 240°C (DL,CO) (Erkey et al., 1990) Diffusion coefficient of H2 at 240°C (DL,H2)(Erkey et al., 1990)

1500

J kg-1K-1

45.5×10-9

m2.s

17.2×10-9

m2.s

Catalyst properties (silica support)(Maretto and Krishna, 1999) Particle diameter (dp)

50×10-6

m

Particle density (ρP)

647

kg m-3

Heat capacity of the catalyst particle (CPC)

992

J kg-1K-1

Heat conductivity of particle (λP )

1.7

W m-1 K-1

Slurry properties(De Swart and Krishna, 2002) Cs ρ P

Catalyst weight fraction in suspension

wc =

Suspension density

ρ s = Cs ρ P + (1 − Cs ) ρ L

Suspension specific heat

C ps = wc C pc + (1 − wc )C pL

Suspension viscosity

η s = η L (1 + 4.5Cs )

Suspension heat conductivity

λs = λL

Suspension effective axial heat conductivity

λax = EL C ps ρ s

Cs ( ρ P − ρ L ) + ρ L

2λL + λ p − 2Cs (λL − λ p ) 2λ L + λ p + C s ( λ L − λ p )


Kg m-3 J kg-1K-1 Pa. s W. m-1. K-1 W. m-1. K-1


11

Table 5. Hydrodynamic, mass and heat transfer parameters Single Bubble Class Model εb = 0.3

1 D (U −Udf )0.22 0.18 T

(U −Udf )4/ 5 (ρg / ρgref )0.5

(Maretto and Krishna, 1999) and ρ gref = 1.3kg .m −3 (( k L a )i , g / ε b ) = 0.5 Di , L / DL , ref

(Maretto and Krishna, 1999), DL,ref =2×10-9 m2/s PeL = U sg 0 H / EL

Double Bubble Class Model εdf = εtrans = 2.16exp(−13.1ρg−0.1ηL0.16σ0.11)exp(−5.86Cs )

(De Swart and Krishna, 2002)

Udf=Utrans=Vsmallεtrans (Maretto and Krishna, 1999) Vsmall = 2.25

σ σ 3 ρ L −0.273 ρ L 0.03 ( ) ( ) η L gη L4 ρg

(De Swart and Krishna, 2002) EL = 0.768U sg0.320 DT1.34

(Deckwer et al., 1982)

εb = 0.3

1 D (U −Udf )0.22 0.18 T

(U −Udf )4/ 5 (ρg / ρgref )0.5

(Maretto and Krishna, 1999)

αeff = 0.1(ρsCpsUsg )(Usg3 ρs / gηs )−1/4 (ρsCps / λs )−1/2

(( k L a )i ,l arg e / ε b ) = 0.5 Di , L / DL , ref

(Deckwer, et al., 1982)

(Maretto and Krishna, 1999)

Peg=UsgH/Eg

Eg = 5 × 10−5 (U sg / ε g )3 DT1.5

(Mills et al, 1996)

(( k L a )i , small / ε b ) = 0.5 Di , L / DL , ref

(Maretto and Krishna, 1999) Peg,large=100.0 (De Swart and Krishna, 2002) Peg,small=PeL=Usg0H/EL EL = 0.768U sg0.320 DT1.34

(Deckwer, et al., 1982) 4

Computer implementation

The reactor model is consisted of 3ns+1 partial differential equations for double bubble class model and 2ns+1 PDE for single bubble class model which have to be solved together. This set of equations is solved using Matlab pdepe solver. In our calculations two species of CO and H2 were considered therefore ns=2. Here it is clear that the DBCM has more equations to be solved than SBCM.



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5

Results and discussion

5.1

Simulation results


By solving the coupled set of partial differential equations, gas velocity, reactant concentrations in both gas and liquid phases, conversion and temperature profiles are determined at transitional state and steady state either. The simulation results are presented in this section. For better discussion on simulation results the temperature, concentration, time and distance variables were made dimensionless. The ith concentration in gas and liquid phase and all other relevant parameters have been normalized and summarized in table 6. The transitional behaviors of the FTS are simulated in a slurry bubble column with diameter of 7.5 m and height of 30 m. the assumption is that, at τ=0, the hydrogen and carbon monoxide concentration in gas and in liquid phases are zero. Figure (2) shows the hydrogen dimensionless profile in gas phase through the reactor dimensionless length which reaches the steady state mode during 7 minutes (420 second) in two different flow regimes (SBCM and DBCM). As this figure illustrates, the hydrogen concentration decreases through the reactor length and in almost 7 minutes after the start-up the profile reaches a steady mode.

Variable

Table 6. Dimensionless parameters Definition

θ

T/Tc

ζ

z/H

τ

tUsg0/H

In Double bubble class model: yi,large

Ci , g ,l arg e / Ci , g 0

yi,small

Ci , g , small / Ci , g 0

xi

mi Ci , L / Ci , g 0

In Single bubble class model: yi

Ci , g / Ci , g 0

xi

mi Ci , L / Ci , g 0



13

(a)

Figure 2. Dimensionless Hydrogen concentration in:(a) DBCM and (b) SBCM, DT=7.5 m, H=30.0 m, H2/CO=2.0, Usg0=0.1 m/s. Simulation results revealed that it takes more time for the reaction to heat up the reactor and to reach the steady conditions. As the Figure (3) shows, it takes 3 hours to the reactor to heat up 13 K and achieve a constant temperature of 513 K. 514

Temperature, K

512 510 508

SBCM

506

DBCM

504 502 500 0

1

2

Time, hr

3

4

5

Figure 3. Temperature in a slurry bubble column reactor vs. time for DBCM and SBCM: DT=7.5 m, H=30.0 m, H2/CO=2.0, Usg0=0.1 m/s.



14


Figure (4) shows the hydrogen concentration profiles in gas and liquid phases. Also conversion profiles over dimensionless length of reactor are depicted for both DBCM and SBCM. It can be seen that the concentration in gas and liquid phases decrease from their maximum. Figure (4) illustrates that the concentration in small bubbles in double bubble class model shows the same behavior as it shows in liquid phase. This phenomenon is due to the back mixed characteristic of small bubbles which are always in equilibrium with liquid phase.

ylargeH2 ,ysmallH2, xH2 and H2 conversion

1 0.9

(a)

0.8 0.7

ylargeH2

0.6

ysmallH2

0.5

xH2 H2 conversion

0.4 0.3 0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

reactor length, ξ (z/H) 1

(b)

0.9

yH2,xH2 and H2 conversion

0.8 0.7

yH2

0.6

xH2

0.5

H2 conversion

0.4 0.3 0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

reactor length, ξ (z/H)

Figure 4. Hydrogen concentration and conversion profile in a slurry bubble column reactor in: (a) DBCM, (b) SBCM. DT=7.5 m, H=30.0 m, H2/CO=2.0, Usg0=0.1 m/s.



15

Double bubble class model (DBCM) and single bubble class model (SBCM), are compared in Figure (5) and (6). Figure (5) shows the comparison between superficial gas velocity vs. dimensionless reactor length in TBCN and SBCM. There is a decrease in superficial gas velocity through the reactor and this is due to the dependency of gas velocity with conversion. An increase in conversion leads to decrease in superficial gas velocity.

Figure 5. Superficial gas velocity profiles for DBCM and SBCM, DT=7.5 m, H=30.0 m, H2/CO=2.0, Usg0=0.1 m/s. In Figure (6-a) and (6-b), syngas conversion and dimensionless H2 concentration in SBCM and DBCM are compared. These figures indicate that there is no significant difference among the results of double bubble class model and single bubble class model, so SBCM as a simpler model is favored to predict the slurry bubble column performance.



16


Figure 6. Comparison of simulation resulted curves from DBCM and SBCM, DT=7.5 m, H=30.0 m, H2/CO=2.0, Usg0=0.1 m/s. 5.2

Sensitivity analysis

All wanted in a slurry bubble column reactor is approaching to an optimal conversion and it is affected by inlet superficial gas velocity, catalyst loading syngas inlet ratio and reactor diameter. The purpose of this part is to evaluate the effect of these important parameters on syngas conversion as well as to compare the two different models against each other in their ability to predict the reactor behaviors. From Figure (7) one can see that the effect of increase in inlet syngas ratio is to increase the amount of syngas conversion for both SBCM and DBCM. Regarding to the stoichimetry of the FT kinetic, the usage ratio of the hydrogen to carbon monoxide is two. Using the inlet ratio less than this amount causes in lack of hydrogen and decrease in syngas conversion.



17

(a)

Figure 7. Influence of increased inlet syngas ratio on conversion in: (a) DBCM and (b) SBCM, DT=7.5m, H=30.0m, Usg0=0.1 m/s. Another effective parameter on syngas conversion is catalyst loading in the reactor. Increasing catalyst concentration which is defined here as volume fraction, Cs, increases conversion for both the SBCM as well as for the DBCM and is shown in Figure (8).

Figure 8. Influence of increased slurry concentration, Cs, on syngas conversion in: (a) DBCM and (b) SBCM vs, Usg0=0.1 m/s, DT=7.5 m, H=30 m, H2/CO=2.0. The effect of superficial gas velocity studied on the syngas conversion is shown in Figure (9) for both of the SBCM and DBCM. Increasing the inlet



18


syngas conversion, [-]

superficial gas velocity will result in decreasing conversion due to the decrease in residence time.

Figure 9. Influence of increased inlet superficial gas velocity on syngas conversion in: (a) DBCM and (b) SBCM, DT=7.5 m, H=30.0m, H2/CO=2.0. The last effect evaluated in this study is the influence of column diameter on syngas conversion. Figure (10) presents the result of such evaluation for both two models. It can be seen nearly in most parts of the reactor from the entrance, increasing column diameter, for the same volumetric gas flow rate, would results higher syngas conversion for both models. However there are two opposite effects; the first one is increasing the space time and the second one is decreasing the catalyst volume fraction, therefore we observe decreasing conversion at higher length of the reactor. However the results show more sensitivity against the inlet gas velocity rather than column diameter.



19

Figure 10. Influence of increased reactor diameter on syngas conversion in: (a) DBCM and (b) SBCM, Usg0=0.1 m/s, H=30.0 m, H2/CO=2.0. 6

Conclusions

The dynamic behavior of FTS is simulated in this work at churn turbulent flow regime for both single and double bubble class flow regimes, considering axial dispersion term in both liquid and gas phases. The modelling results represent that there is no need really to make the assumption of dividing gas phase into two bubble size distribution while the small bubble shows the behaviour as well as liquid phase. Therefore single bubble class model can predict the behaviour of the slurry bubble reactor with less computational complexity while using less parameter. The sensitivity analysis showed that system is sensible to inlet gas ratio, column diameter, and inlet gas velocity and also catalyst loading but, it is more sensitive to the inlet gas velocity and less to the reactor diameter. The sensitivity analysis also represent that DBCM does not present additional benefits over SBCM. Notations a alarge

Mol/(s.kgcatPa2) m2/m3

asmall

m2/m3

aw

m2/m3

Kinetic parameter Gas-liquid specific area for large bubbles Gas-liquid specific area for small bubbles Cooling tube specific external surface area referred to the total reactor volume



20

b Cg Ci,g0

1/Pa mol/m3 mol/m3

Ci,g,small

mol/m3

Ci,g,large

mol/m3

Ci,L CP,L CP,s CP,C Cs

mol/m3 J/kg K J/kg K J/kg K -

Cs

-

Dc dP DL DT Ea Eg,large

m2/s M m2/s m J/mol m2/s

Eg,small

m2/s

Eg

m2/s

EL

m2/s

g H -∆HR I

m2/s m J/mol -

kL,i,small

1/s

kL,i,large

1/s

mi

-


Adsorption coefficient Gas phase concentration Concentration of i in the gas phase at reactor inlet Concentration of i in small bubbles Concentration of i in large bubbles Concentration of i in liquid Heat capacity of the liquid Heat capacity of the slurry Heat capacity of the catalyst Solid volume fraction in gas free slurry Mean Solid volume fraction in gas free slurry Solid phase diffusivity Particle diameter Liquid phase diffusivity Column diameter Activation energy Axial dispersion coefficient of the large bubbles Axial dispersion coefficient of the small bubbles Axial dispersion coefficient of gas phase Axial dispersion coefficient of the liquid phase Accelerating due to gravity Reactor height Heat of reaction Molar ratio of H2/CO at the reactor inlet Volume mass transfer coefficient of I with small bubbles Volume mass transfer coefficient of I with large bubbles Henry’s coefficient



nr

-

ns P Pe RFTS t T Tc U

Pa mol/s s K K -

Uct

m/s

Udf

m/s

Usg (Usg-Udf)

m/s m/s

Uss Utrans

m/s m/s

Vsmall Wc

m/s -

xi

-

Xi yi,large

-

yi,small

-

z

m

Greek letters αeff

W/m2 K

α εg εb εL

-

21

Number of independent reaction Number of species Total pressure Peclet number FTS kinetic reaction Time Temperature Cooling temperature Usage ratio of H2/CO at the reactor inlet Settling velocity of the catalyst particle in a swarm Superficial velocity of gas through the dense phase Superficial gas velocity Superficial gas velocity through the dilute phase Superficial slurry velocity Superficial gas velocity at regime transition Rising velocity of small bubble Weight fraction catalyst in gas free slurry Dimensionless i concentration in liquid phase Conversion of i Dimensionless i concentration in large bubbles Dimensionless i concentration in small bubbles Height above the gas distributor Slurry to internal coil wall conversion heat transfer coefficient Modified contraction factor Gas holdup Holdup in large bubbles Liquid hold up



22

εsmall εtrans ηL ηs θ λax

Pa s Pa s W/ m K

λc

W/ m K

λL λs ξ ρg ρL ρP ρs τ

W/ m K W/ m K Kg/m3 Kg/m3 Kg/m3 Kg/m3 -


Holdup in small bubbles Holdup in transition point Liquid viscosity slurry viscosity Dimensionless temperature Effective axial heat conductivity of the liquid-solid suspension Heat conductivity of the catalyst particle Heat conductivity of the liquid Heat conductivity of the slurry Axial coordinate, z/H Gas density Liquid density Particle density Slurry density Dimensionless time

References

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23

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