Ind. Eng. Chem. Res. 2006, 45, 1047-1057
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Modeling and Product Grade Optimization of Fischer-Tropsch Synthesis in a Slurry Reactor Fabiano A. N. Fernandes Departamento de Engenharia Quimica, UniVersidade Federal do Ceara, Campus UniVersitario do Pici, Bloco 709, 60455-760 Fortaleza, CE, Brazil
Fischer-Tropsch synthesis is an important chemical process for the production of liquid fuels and olefins. In recent years, the abundant availability of natural gas and the increasing demand for olefins, diesel, and waxes have led to a high level of interest to further develop this process. A mathematical model of a slurry reactor used for syngas polymerization was developed, and carbon monoxide polymerization was studied from a modeling point of view. Simulation results show that different parameters affect syngas conversion and carbon product distribution, such as temperature, operating pressure, catalyst holdup, and syngas composition. Optimization of several hydrocarbon products were done in order to search for the best operating conditions for their production. Introduction Fischer-Tropsch synthesis (FTS) was discovered nearly 80 years ago, but until now its application in producing liquid fuels and other chemicals has not been fully explored, due especially to economic reasons. In recent years, FTS has become a subject of renewed interest particularly in the context of the conversion of remote natural gas into liquid transportation fuels and due to an escalation in the price of oil. Natural gas, biomass, and coal can be converted to carbon monoxide and hydrogen (synthesis gas) via existing processes, such as steam reforming, carbon dioxide reforming, partial oxidation, and catalytic partial oxidation, followed by the FT synthesis reaction:
CO + (1 + m/2n)H2 f (1/n)CnHm + H2O
(1)
FT synthesis can be carried out in iron-, cobalt-, and ruthenium-based catalysts. Fe-based catalysts are much less expensive than Co-based catalysts, which can be an important economic factor for the process, especially because the catalyst has to be replaced due to deactivation. Fe-based catalysts also present higher productivities than Co-based catalysts at higher pressures and space velocities;1 thus this evidence must be further studied. When iron catalysts are used, carbon monoxide polymerization occurs in combination with the water gas shift reaction (WGS):
CO + H2O T CO2 + H2
(2)
Many researchers have been working on catalyst development,2,3 on reactor design,4-7 and on the commercial applications of the Fischer-Tropsch synthesis,8,9 but few investigations have been done to optimize production of specific products. In part, this lack of information and research is due to a poor comprehension of the FTS mechanism and CO polymerization kinetics.10,11 At the present time, the mechanism of the Fischer-Tropsch reaction is still not fully understood. The Fischer-Tropsch reaction yields predominantly straight-chain hydrocarbons (Rolefins and alkanes), and there is general agreement that the reaction may be viewed as a methylene polymerization reaction where the monomer unit (dCH2) is not initially present. The products are formed by hydrogenation of CO to generate the methylene monomer, in situ. Polymerization occurs through initiation of chains, competing chain propagation, and chain
termination steps. The product distributions tend to obey Anderson-Schulz-Flory (ASF) chain-length statistics, but this is not always true, and many researchers have reported deviations from ASF theory.12-14 Theories for ASF deviations are based on the superposition of two ASF distributions and rely on the dual site theory,14 secondary chain growth of readsorbed alkenes theory,10,13 and the dual mechanism of chain growth theory.15,16 Iron catalysts are more likely to obey a dual mechanism of chain growth theory. In this work a mathematical model of a slurry reactor used for syngas polymerization was developed and carbon monoxide polymerization was studied from a modeling point of view based on the kinetics of an iron catalyst obeying a dual mechanism theory. Optimization of several hydrocarbon products was done in order to search for the best operating conditions for their production. Slurry Reactor The bubble column slurry reactor consists of a tower where the synthesis gas and liquid phase (liquid + catalyst) are fed through the bottom of the column. The liquid phase is fed at very low velocities so that the liquid products can be continuously withdrawn. The synthesis gas goes through the reactor as bubbles and exchanges mass with the liquid phase. In a commercial process the velocity of the gas is high enough to produce large and small bubbles and the reactor operates at a heterogeneous regime or churn-turbulent flow regime. The slurry reactor is also provided with thousands of cooling tubes or cooling coils, with a heat exchange surface that can be as high as 20 m2 per m3 of reactor.17 The cooling tubes are used to remove the heat released by the FTS reaction and to control the reactor temperature, ensuring the isothermal conditions inside the reactor, despite the high heat of reaction (∆H ) -170 kJ/ mol of CO).17-21 Mathematical Model Slurry Reactor Model. The mathematical model of the bubble column slurry reactor is based on the model presented by Maretto and Krishna,4 Krishna and Sie,5 and van der Laan and Beenackers.11 The basic assumptions made for the reactor were the following: steady-state operation; isothermal conditions; large-bubble flow in plug-flow regime due to its velocity; constant slurry velocity; assumption of hydrocarbon products in the gas and liquid phases to be in equilibrium at the reactor
10.1021/ie0507732 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/06/2006
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Table 1. Kinetic Parameters for Fischer-Tropsch Synthesis in Iron Catalyst and for Water Gas Shift2 a kFTS a kWGS K1 K2
0.1106 [mol/kg‚s‚MPa] 3.016 0.0292 [mol/kg‚s] 85.81 3.07
a Obtained experimentally2 at T ) 270 °C, P ) 0.5-3.0 MPa, and H : 2 CO ) 0.67-1.7.
outlet; negligible mass and heat transfer resistances between the catalyst and the liquid; location of the gas-liquid mass transfer limitation in the liquid phase; intrinsic kinetics for Fischer-Tropsch synthesis and water gas shift reactions. The kinetic model for the FTS reaction on an iron catalyst and that for the WGS reaction are given by
RFTS )
RWGS )
kFTSPCOPH2
(3)
PCO + aPH2O
(
kWGS PCOPH2O -
)
(4)
(PCO + K2PH2O)
2
The gas-phase mass balance for component i in the large bubbles and the gas-phase balance for component i in the small bubbles are
[
]
l l Ci,G d(UG - UDF)Ci,G + (kLa)li GL - Ci,L ) 0 dh mi
(5)
s Ci,G UDF in s ) ) +(kLa)si GL - Ci,L (Ci,G - Ci,G H mi
(6)
[
]
The mass balance for component i in the completely mixed liquid phase is
1
∫
H
H
l (kLa)i,G 0
(
l Ci,G
miGL
)
- Ci,L dh +
s (kLa)i,G n
(
s Ci,G
mGL i
)
- Ci,L + US
νijRj - Ci,L ) 0 ∑ H j)1
LPFP
(7)
where j are the reactions: 1, FTS; 2, WGS. The boundary conditions at the reactor entrance are h ) 0 f l s in Ci,G ) Ci,G ) Ci,G . The mass transfer coefficients of component i for large and small bubbles are given by the correlations
( ) ( )
(kLa)si ) (kLa)sref
Di Dref
0.5
(kLa)li ) (kLa)lref
Di Dref
0.5
(8)
(9)
where Dref ) 2.0 × 109 m2/s, (kLa) lref ) 0.5B, and (kLa) sref ) DF. The molar flow rate of the gas phase will change due to reaction. The superficial velocity was assumed to be a linear function of the overall carbon monoxide conversion (XCO).
UG ) [1 + RCXCO]Uin G where RC ) -0.67.
temperature [°C] total pressure [MPa] hydrogen to carbon monoxide ratio gas superficial velocity [m/s] liquid velocity [m/s] solids holdup catalyst apparent density [kg/m3] reactor bed height [m] reactor diameter [m]
270 1.0-3.0 0.5-2.0 0.25-0.45 0.01 0.10-0.25 647 30.0 7.0
Table 3. Gas Properties (T ) 270 °C; P ) 1.3 MPa)a CO H2 CO2 H2O
diffusivity [m2/s]
Henry constant
17.2 × 10-9 45.5 × 10-9 24.9 × 10-9 31.7 × 10-9
2.48 2.96 2.05 1.06
a Diffusivity and Henry constants for other pressures used in the simulations were obtained according to the procedures and equations described in refs 22 and 23.
Liquid, total gas, and small-bubble holdup, as well as smallbubble velocity, are calculated as
PCO2PH2 K1
Table 2. Operating Conditions and Reactor Parameters
(10)
(
)
0.8P VS,ref
(11)
)
(12)
G ) B + DF(1 - B)
(13)
L ) 1 - G - P
(14)
UDF ) DFVS,ref 1 +
(
DF ) DF,ref 1 +
0.7P DF,ref
where VS,ref ) 0.095 m/s and DF,ref ) 0.27. Due to the assumption of isothermal conditions in the reactor, which can be considered based on academic and patent reports,17-21 only the mass balances and population balances for the hydrocarbon species were considered in this work. As such, all heat produced by the reaction is considered to be removed by the cooling tubes of the reactor. To solve the mathematical model, first, initial estimates were provided for the gas concentration in the liquid phase and in the small bubbles (step 1). These values were used to numerically integrate eq 5 (step 2), and after that to solve the algebraic equations 6 and 7 (step 3), obtaining new values for gas concentration in the liquid and the small bubble phases. An iterative procedure was created to run steps 2 and 3 until the concentrations in all phases converged. The numerical integration was carried out using a fifth-order Runge-Kutta method. The kinetic parameters for the reaction are presented in Table 1, the operating conditions used in the simulations are presented in Table 2, and the gas properties are presented in Table 3. The overall kinetic rates for the Fischer-Tropsch reaction and the WGS reaction were taken from Raje and Davis.2 Calculation and values for the mass transfer coefficients, diffusivities, solubility coefficients, solids holdup, and bubble holdup were based on the works of Krishna’s group.4,5,21 Kinetic Model. The kinetic model used to simulate the CO polymerization and product distribution assumes that the alkyl and alkenyl mechanisms act together in the FT synthesis. The alkyl mechanism can be represented by the following reactions: ki1
•CH2 + •H 98 R(1)
initiation
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1049 kp1
R(n) + •CH2 98 R(n+1)
Table 4. Kinetic Parameters for CO Polymerization in Iron Catalyst (at 270 °C)
propagation
kpar
R(n) + •H 98 P(n) reduction by surface hydride giving an alkane kolef
R(n) 98 P)(n) β-hydride elimination giving an olefin (termination) The alkenyl mechanism can be represented by the following reactions: ki2
•CH2 + •CH 98 R(2)
initiation
kp2
R′′(n) + •CH2 98 R′′(n+1)
propagation
kolef2
R′′(n) 98 P)(n) reduction giving an olefin (termination) Methane and ethane are formed by the following reactions: kmet
R(1) + •H 98 P(1) reduction by surface hydride giving methane kO
•CH2 + •CH2 98 P)(2) 2
methylene termination
The mass balance for the FTS is given by the following set of equations:
[R(1)] )
kp
(15)
ki2RFTS kp2
(16)
kpRFTS [R(n-1)] kpRFTS + kparPH2 + kolef
(17)
kp2RFTS [R′′(n-1)] kp2RFTS + kolef2
(18)
[R′′(2)] ) [R(n)] )
kiPH2
[R′′(n)] )
d[P(1)] ) kmetPH2[R(1)] dt
(19)
d[P(2)] ) ketPH2[R(2)] dt
(20)
d[P)(2)] ) kO2RFTS2 dt
(21)
d[P(n)] ) kparPH2[R(n)] dt
(22)
d[P)(n)] ) kolef[R(n)] + kolef2[R′′(n)] dt
(23)
The development of the mass balances assumes that the quasisteady state is applied to the concentration of the propagating species (as assumed for the zero-order moment of live polymers), the consumption of methylene units is proportional to the global reaction rate, and the concentration of hydrogen in the polymerization site is proportional to the partial pressure of hydrogen in the reaction media. The kinetic parameters for the CO polymerization are presented in Table 4.
ki [MPa-1] ki2 [mol/h] kp [h/mol] kp2 [h/mol] kpar [MPa-1‚h-1] kolef [h-1] kolef2 [h-1] kmet [MPa-1‚h-1] ket [MPa-1‚h-1] kO2 [h/mol]
0.4963 8.054 0.3530 0.4206 0.02314 0.003487 0.04792 0.06386 0.02421 0.09994
The model has been validated using the data reported by Raje and Davis2 and Donnelly and Satterfield24 and has provided a satisfactory fitting (samples are shown in Figure 1). Variance analysis was done using the software Statistica 6.0, which showed that the model is significant within 99% confidence. For the sample shown in Figure 1a, the regression coefficient R2 for paraffin and olefin was respectively 0.999 and 0.955. The F-test presented the values of 6596 for paraffin and 148 for olefin, which are more than 3 times the listed F values (11.26 and 12.25 for 99% confidence respectively for paraffin and olefin), guaranteeing that the model is very significant. For the sample shown in Figure 1b the regression coefficient R2 for paraffin and olefin was respectively 0.996 and 0.975. The F-test presented the values of 2067 for paraffin and 271 for olefin, which are more than 3 times the listed F values (11.26 and 12.25 for 99% confidence respectively for paraffin and olefin). The total hydrocarbon number of moles was also tested and returned a regression coefficient R2 of 0.994 and an F value of 1278, also more than 3 times the listed F value (8.53 for 99% confidence level). Hydrocracking and Hydroisomerization. Production of paraffins of a specified carbon number range in high yields is not possible by direct FTS, but may be achieved by directing the synthesis toward heavy paraffins, which are subsequently cracked selectively in a second reactor. This cracking process has to break the heavy paraffins into fragments that should be predominantly in the diesel range (if diesel is the desired product), and it should not break the paraffins already in the diesel range. This hydrocracking (HC) and hydroisomerization (HI) can be done over a bifunctional (acid/metal) catalyst capable of having its reactivity increased with increasing carbon number of the paraffin. Hydrocracking catalysts are bifunctional catalysts characterized by the presence of acidic sites, which provide the cracking function, and of metal sites with hydrogenation-dehydrogenation function. Typical acidic supports are amorphous oxides or mixtures of oxides, zeolites, and silicoaluminaphosphates. Pt, Pd, and bimetallic systems (i.e., Ni/Mo, Ni/W, Co/Mo, in the sulfided form) are the most commonly used metals. Conditions favorable for this reaction are 3.0-5.0 MPa total pressure and at temperatures between 300 and 350 °C.25,26 Figure 2a shows the relative reactivity (RR) of hydrocarbons over a dual-functional catalyst,25 which presents an exponential behavior as a function of the number of carbons in the hydrocarbon chain, which can be fit by the equation
RR ) 0.00182 exp(0.626n)
(24)
The kinetic rate constant for the hydrocracking and hydroisomerization for a hydrocarbon with 10 carbons is given by eq25, and the reaction rates for higher hydrocarbons are obtained by multiplying eqs 24 and 25.
kHC ) 1.336 × 1017 exp
(-25173 T )
(25)
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Figure 1. Carbon number distributions of paraffin and olefin products for (a) H2:CO ) 0.67, PT ) 1.3 MPa, and T ) 270 °C and (b) H2:CO ) 1.70, PT ) 1.3 MPa, and T ) 270 °C. Symbols refer to experimental data2 and lines to model simulation results.
Figure 2. Relative reactivity for hydrocracking (a) and cracking probability (b) as a function of hydrocarbon carbon number. Symbols refer to experimental data.25
On the basis of the kinetic rate constants and relative reactivity of each hydrocarbon chain, a cracking probability was calculated (Figure 2b). All hydrocarbons (paraffins and olefins) with 10 carbons or more were multiplied by the cracking probability for the specific carbon number, resulting in a new carbon number distribution for the synthesis after HC and HI. The procedure was not applied to hydrocarbons with less than 10 carbons because the cracking probability for them is insignificant at the conditions applied. Results and Discussion Fischer-Tropsch synthesis in slurry reactors is a very complex system with many process variables that should be accounted for: gas superficial velocity, suspension velocity, catalyst holdup, total pressure, and H2:CO ratio. Studies on how gas velocity and catalyst holdup affect conversion and total production of hydrocarbons have been extensively made by several authors,4-7,21 but few studies have been made on how these parameters affect the product distribution.11,21,27 In this work, several simulations were made to understand the effect of several operating conditions on the product distribution, especially in the range of transportation fuels. The simulation study assumes that the rate laws for the FTS and WGS kinetics are valid for the entire range of the varied process
parameters. Some extrapolations were done but kept near the experimental regime of Raje and Davis2 and Donnelly and Satterfield.24 The extrapolation on pressure was more significant, but was kept within the limits defined in a related work by Davis28 which stated that for this catalyst the effect of pressure (from 0.5 to 3 MPa) over the overall kinetic rate is not significant. This information is also supported by Dry29 and Iglesia et al.30 On the other hand, temperature has an enormous effect on the kinetic rate laws and therefore was unchanged. Influence of H2:CO Ratio. In general, conversion of syngas increases with H2:CO ratio. As the H2:CO ratio approaches 2.0, the amount of syngas converted to hydrocarbons (FTS) and water (WGS) increases. As conversion increases, the WGS reaction increases its rate due to the production of more water by the FTS reaction, and although CO conversion may be at 66% (30 atm, UG ) 0.25 m/s, H2:CO ) 1.0), the hydrocarbon yield is at 58% (Figure 3). The case presented herein is based on an iron-based catalyst, which presents high hydrocarbon production. Some iron catalysts in the literature present a higher spread between the production of hydrocarbons and CO2 (due to the WGS reaction), and thus the hydrocarbon yield for these catalysts can be as low as 50% of the CO conversion. Hydrogen is responsible for the termination of hydrocarbon chains into paraffins. As such, an increase in the H2:CO feed ratio will increase the partial pressure of H2 in the reaction media
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1051
Figure 3. CO conversion as function of H2:CO ratio for two different gas superficial velocities (conditions: 30 atm, 270 °C, P ) 0.1). Solid lines represent total syngas conversion. Dashed lines represent hydrocarbon yield.
and thus increase the termination rate into paraffins (Figure 4a). At low H2:CO ratios, the fraction of olefin production is at its maximum since the amount of hydrogen is small enough to not produce great quantities of paraffins. As the H2:CO ratio increases, the termination into paraffin increases and the ratio of olefin to paraffin tends to zero.
Figure 4b shows the weight fraction of higher olefins (C5+) that are produced by the reaction. As the H2:CO ratio increases, the production of higher olefins decreases steeply, since chain termination occurs preferably toward paraffins. Production of paraffins is higher toward light gases and diminishes toward waxes (Figure 4b,c). Higher production of gasoline is around 0.6 H2:CO ratio, while higher production of diesel and waxes is approximately at 0.5 H2:CO ratio. Above these ratios the production of liquefied petroleum gas (LPG) and light gases are favored. An increase in the velocity enhances the production of transportation fuels since the higher gas superficial velocity adds more gas into the reactor, increasing the concentration of the reagents in both the liquid phase and gas phase as an effect of the residence time in the reactor (Figure 5). The increase in the carbon monoxide partial pressure is higher than the increase in the hydrogen partial pressure, so the propagation rate increases more than the termination rate (influenced by the hydrogen partial pressure), leading to an increase in the average hydrocarbon chain length. Influence of Total Pressure. Figure 6 shows that an increase in the total pressure in the system reduces CO conversion and hydrocarbon yield. The rate of the FTS reaction is directly proportional to the total pressure; the rate of the WGS is not directly affected by the total pressure, but is coupled to the H2O partial
Figure 4. Weight fractions of (a) paraffins and olefins, (b) higher olefins and gasoline, (c) diesel and waxes, and (d) diesel after hydroisomerization and hydrocracking (conditions: 30 atm, 270 °C, P ) 0.1).
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Figure 5. Partial pressure of carbon monoxide and hydrogen in the slurry reactor for two different gas superficial velocities: (a) in the liquid phase (calculated by the liquid-phase concentrations and Henry coefficients); (b) in the gas phase (conditions: 30 atm, 270 °C, P ) 0.1).
Figure 6. CO conversion as a function of total pressure for two different gas superficial velocities (conditions: 270 °C, H2:CO ) 0.6, P ) 0.1). Solid lines represent CO conversion. Dashed lines represent hydrocarbon yield.
pressure, which depends on the conversion level. The H2O partial pressure also inhibits the FTS reaction, and its increase causes the conversion to decrease. On the other hand, the productivity (tons per hour) is favored by the increase in total pressure since the reaction rate is proportional to the total pressure. Lower pressures favor the WGS reaction, and the FTS reaction can be responsible only for 51% of the CO consumption (at PT ) 5 atm, UG ) 0.25 m/s, H2:CO ) 0.6), while higher pressures favor the FTS reaction and CO consumption by this reaction is as high as 91% (at PT ) 30 atm, UG ) 0.45 m/s, H2:CO ) 0.6). At higher superficial velocities (UG ) 0.45 m/s), the FTS reaction presents a maximum CO conversion at 30 atm, lowering very rapidly the CO conversion before this pressure level. Production of paraffins is increased as total pressure rises, reaching a maximum at 20 atm where, after this point, the paraffin fraction changes only slightly. Production of paraffins is higher at higher superficial velocities (for pressures above 12 atm) (Figure 7a). The amount of higher olefins (C4+) is maximum at 23 atm for a superficial velocity of 0.25 m/s syngas (Figure 7b). Gasoline production is favored above 30 atm and high superficial velocities, after which the amount of gasoline produced decreases. Lower superficial velocities change the gasoline maximum production to higher pressures but at lower rates (Figure 7b). Diesel and wax production increases as pressure
rises. After isomerization and hydrocracking the amount of diesel that can be produced is as high as 9.2% (Figure 7c,d). These results show that the total pressure of the system is a major factor to be defined depending on the most desired product to be produced. As a rule of thumb, the higher the pressure, the higher the chain length of the hydrocarbon that is produced by the reaction. Influence of Catalyst Holdup. As a general rule, the increase in the amount of catalyst loaded to the reactor will increase the CO conversion. The hydrocarbon yield increases as more catalyst is used, but the rate of the WGS reaction also increases by the same factor and, as catalyst holdup increases, the conversion and the H2O partial pressure increase. The higher H2O partial pressure enhances the CO shift to CO2 (Figure 8). On the other hand, the increase in the amount of catalyst in the reactor will diminish the average chain length due to the competitive chain propagation. As the amount of catalyst in the reactor increases, the amount of active sites for chain propagation also increases and will compete for the available carbon monoxide and hydrogen available in the reaction media, leading to shorter hydrocarbon chains. As a result, an increase in the catalyst holdup will decrease the weight fractions of gasoline, diesel, and waxes produced during the reaction (Figure 9). Product Optimization Optimization of the FTS was conducted searching for the operating conditions (pressure, H2 and CO concentrations, gas superficial velocity, and catalyst holdup) that result in the highest production of gasoline, diesel, and higher olefins. Although it is known that the temperature is an important parameter in the FTS process, we currently do not have enough information on how the temperature affects the product distribution, so all optimizations performed in this work are at constant temperature (270 °C). A program in Fortran was developed in order to maximize the production of these products, using the quasi-Newton method and a finite-difference gradient. For diesel production, the maximum production is at the point where the amount produced of diesel plus waxes (that can go through hydrocracking and hydroisomerization) is at a maximum. The search for the optimum operating conditions is time-consuming and the system presents some local maxima that need to be avoided, so several initial values for the maximization procedure were used and the best values shown in Tables 5-8. Hydrocarbon yield, production, and mass fractions of each product have different maximum points, so the optimization
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Figure 7. Weight fractions of (a) paraffins and olefins, (b) higher olefins and gasoline, (c) diesel and waxes, and (d) diesel after hydroisomerization and hydrocracking (conditions: 270 °C, H2:CO ) 0.6, P ) 0.1).
target products in offshore platforms. Table 5 presents a summary of the optimal operating conditions for maximum yields of gasoline, diesel, waxes, and olefins. Table 6 presents the production distribution for the optimum conditions for the following optimization problem:
Find: PT, H2:CO ratio, UG, and P Maximize: product yield (g of product/g of total hydrocarbon) max{Φ )
∑wi}
where the product is gasoline, diesel, diesel after HC and HI, waxes, or higher olefins within the ranges of the following operating conditions (constraints): Figure 8. CO conversion as a function of catalyst holdup for two different gas superficial velocities (conditions: 30 atm, 270 °C, H2:CO ) 0.6). Solid lines represent CO conversion. Dashed lines represent hydrocarbon yield.
function can focus on one of these factors. Figure 10 shows the behavior of the system for the profiles of mass fractions of gasoline and diesel in the product distribution and of the production of these products in tons per hour for the conditions presented in Table 2. The focus presented herein is on the maximum production and on the maximum yield (maximum mass fraction) of gasoline, diesel, waxes, and higher olefins, which are the main
1.0 e PT e 3.0 MPa 0.5 e H2:CO e 2.0 0.25 e UG e 0.45 0.1 e P e 0.4 The higher concentration of reacting gases in the reaction media (high pressure and gas superficial velocity) associated with low catalyst holdup are the best operating conditions to maximize the yield of the FTS reaction into transportation fuels.
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Figure 9. Weight fractions of (a) paraffins and olefins, (b) higher olefins and gasoline, (c) diesel and waxes, and (d) diesel after hydroisomerization and hydrocracking (conditions: 30 atm, 270 °C, H2:CO ) 0.6).
Figure 10. (a) Weight fractions of gasoline and diesel in product distribution; (b) production of gasoline and diesel [tons/h] (conditions: 30 atm, 270 °C, UG ) 0.45 m/s, P ) 0.1).
The H2:CO ratio for all liquid fuels was at 0.6, showing that low H2:CO ratios are more indicated to maximize product seletivity, since they generate longer hydrocarbon chains. On the other hand, olefins (C4+) are favored by moderate pressures and high H2:CO ratio. Table 7 presents a summary of the optimal operating conditions for maximum production (tons per hour) of gasoline, diesel, waxes, and higher olefins. Table 8 presents the production
Table 5. Optimal Operating Conditions for Maximum Yields of Gasoline, Diesel, Waxes, and Higher Olefins optimal yield of
H2:CO ratio
press. [MPa]
catal holdup
UG [m/s]
gasoline, diesel, and waxes diesel after HC + HI olefins (C4+) higher olefins (C15+)
0.60 0.60 2.00 0.60
3.0 3.0 2.1 3.0
0.1 0.1 0.1 0.1
0.45 0.45 0.45 0.45
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1055 Table 6. Product Distribution (Weight Fraction) of Reactor Operating at Optimum Conditions for Maximum Yields of Gasoline, Diesel, Waxes, and Higher Olefins total paraffin 0.57
paraffins olefin 0.43
0.57
0.43
light gases
LPG
gasoline
diesel
olefins diesel HC + HI
waxes
Maximum Gasoline, Diesel, and Wax Yield 0.13 0.10 0.04 0.19
ethene
propene
C4+
C15+
0.21
0.08
0.02
0.09
0.26
0.06
0.21
Maximum Diesel Yield After Hydrocracking and Hydroisomerization 0.08 0.13 0.10 0.04 0.19 0.02
0.09
0.26
0.06
Maximum Olefin Yield (C4+) 0.02 0.00
0.45
0.55
0.29
0.07
0.07
0.04
0.03
0.14
0.36
0.02
0.57
0.43
0.21
0.08
Maximum Higher Olefin Yield (C15+) 0.13 0.10 0.04 0.19
0.02
0.09
0.26
0.06
Table 7. Optimal Operating Conditions for Maximum Production of Gasoline, Diesel, Waxes, and Higher Olefins optimal production of
H2:CO ratio
press. [MPa]
catal holdup
UG [m/s]
gasoline diesel waxes diesel after HC + HI olefins (C4+) higher olefins (C15+)
1.36 1.11 0.90 1.10 1.75 1.33
3.0 3.0 3.0 3.0 3.0 3.0
0.1 0.1 0.1 0.1 0.1 0.1
0.45 0.45 0.45 0.45 0.45 0.45
distribution for the optimum conditions for the following optimization problem:
Find: PT, H2:CO ratio, UG, and P Maximize: product production (tons of product/h)
∑wi}
max{Φ ) RFTSFppVR
where the product is gasoline, diesel, diesel after HC and HI, waxes, or higher olefins within the ranges of the following operating conditions (constraints):
1.0 e PT e 3.0 MPa 0.5 e H2:CO e 2.0 0.25 e UG e 0.45 0.1 e P e 0.4 When the maximization focuses on the mass production of the desired product, the operating conditions are different from the conditions for maximum yields. Pressure, catalyst holdup, and gas superficial velocity are the same for all products since maximum production is associated with high gas concentration and few active sites leading to longer hydrocarbon chains. The
H2:CO ratios for maximum production are higher than for maximum yield, for a tradeoff from reducing the average chain length toward a higher mass production associated with higher propagation rates. As shown in Table 8, when diesel is the desired product the production of gasoline is at 5.51 tons/h, but when the H2:CO ratio increases, the average chain length diminishes, producing more gasoline, and its production rises, yielding 5.70 tons/h of gasoline. Hydrocracking (HC) and hydroisomerization (HI) of waxes and higher olefins can boost diesel production, enhancing the maximum production from 3.81 to 7.78 tons/h after HC and HI, a 104% increase. The same analogy can be drawn to olefin production, where the decrease in the H2:CO ratio favors the production of higher olefins (C15+). The evaluation of the reactor volume specific productivity is important to measure the reactor performance. According to Krishna’s group and van der Laan research,4-6,11,21,31 the total hydrocarbon production for an economical FTS process should range between 50 and 80 kg‚h-1‚m-3. Van der Laan31 has provided valuable information on the FTS process, correlating the process conditions with product distribution. Analyzing van der Laan’s31 results, one can observe that the optimal H2:CO ratio for diesel production is between 0.67 and 1.0, which is in accordance with the results obtained herein. Van der Laan’s31 data also show that the production of liquid fuels is optimized when the reactor volume specific productivity is between 50 and 60 kg‚h-1‚m-3. Herein, a reactor volume specific productivity between 40 and 50 kg‚h-1‚m-3 was obtained, which is 1720% lower than the results obtained by van der Laan’s catalyst. Regarding the product distribution, the catalyst studied by Raje and Davis2 and optimized herein presents better performance in the production of gasoline and kerosene, yielding up to 19.6 kg‚h-1‚m-3, while van der Laan’s catalyst yielded 14.8 kg‚h-1‚m-3. The production of diesel and waxes is lower than that from the van der Laan catalyst, but the amount of higher olefins (C15+) is at the same level (32-37% depending on the
Table 8. Product Distribution (Weight Basis) of Reactor Operating at Optimum Conditions for Maximum Production of Gasoline, Diesel, Waxes, and Higher Olefins (tons/h) total
paraffins diesel
olefins waxes
diesel HC + HI
paraffin
olefin
light gases
LPG
gasoline
ethene
propene
C4+
C15+
24.12
19.74
9.65
3.68
5.70
Maximum Gasoline Production 3.73 1.49
7.63
1.10
3.99
12.28
2.41
7.71
1.06
3.81
11.44
2.37
7.65
1.00
3.57
10.82
2.28
Maximum Diesel Production After Hydrocracking and Hydroisomerization 3.56 5.50 3.81 1.60 7.78 1.06
3.81
11.43
2.37
23.73
18.65
9.32
3.56
5.51
Maximum Diesel Production 3.81 1.53
22.44
17.63
8.82
3.37
5.20
Maximum Wax Production 3.73 1.64
23.72
18.63
9.32
23.98
20.42
10.21
24.09
19.71
9.64
3.77
5.33
Maximum Olefin Production (C4+) 3.41 1.24 7.00
1.15
4.17
12.43
2.35
3.50
Maximum Higher Olefin Production (C15+) 5.69 3.94 1.31 7.88
1.31
3.94
11.83
2.63
1056
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
operating conditions). When operating at conditions that favor the production of olefins, the catalyst studied herein presents a higher olefin-to-paraffin ratio (57%) than that obtained by van der Laan (37%). A decision on which optimum point to choosesmaximum production or maximum yieldsmay depend on economic reasons. Running the system with the operating conditions that favor maximum yield will lead to lower costs on recycling and burning of unwanted products (light gases and LPG), but production will be lower for the same reactor size. However, running the system with the operating conditions that favor maximum production will lead to higher recycling costs, which may be compensated by the enhanced production rate. Conclusions Fischer-Tropsch synthesis can be used to produce transportation fuels from natural gas, and the polymerization conditions can be set to maximize the production of a certain product generated by the FTS reaction, such as gasoline, diesel, waxes, and others. According to the simulations, the optimum operating condition to maximize diesel production and yield needs a low catalyst holdup and high pressures and gas superficial velocity leading to improvements in the propagation rate and decreasing the termination rate. Higher H2:CO ratios favor production of low molecular weight products such as gasoline, while lower H2: CO ratios direct the production toward heavy hydrocarbons. The catalyst developed by Raje and Davis2 and optimized herein has shown good performance for the production of gasoline and kerosene with high reactor volume specific productivity of hydrocarbons in the range of these products, as well as high olefin-to-paraffin ratio, which can be interesting for the production of co-monomers for the polymer industry and lubricant additives.
kL‚) volumetric mass transfer coefficient [s-1] miGL ) solubility coefficient (Henry constant) Pi ) partial pressure [MPa] PT ) total pressure in the reaction zone [MPa] P(n) ) paraffin containing n carbons [mol] P)(n) ) olefin containing n carbons [mol] Ri ) rate of reaction i [mol/s‚kgcat] R(n) ) alkyl propagating species containing n carbons [mol] R′′(n) ) alkenyl propagating species containing n carbons [mol] RFTS ) overall Fischer-Tropsch reaction rate T ) temperature [K] UDF ) small bubbles rising velocity [m/s] UG ) gas superficial velocity [m/s] US ) suspension velocity [m/s] VR ) reactor bed volume [m3] wi ) weight fraction of hydrocarbon with i carbons in the product distribution XCO ) carbon monoxide conversion ) holdup ν ) stoichiometric coefficient F ) density [kg/m3] Φ ) objective function Superscripts l ) large bubble s ) small bubble Subscripts DF ) small bubbles G ) gas phase L ) liquid phase P ) solid phase (catalyst) S ) suspension Literature Cited
Acknowledgment The author gratefully acknowledges the financial support of the Brazilian research funding institution CNPq/CTPetros Conselho Nacional de Desenvolvimento Cientı´fico. Nomenclature A ) area [m2] Ci,j ) concentration of component i in phase j [mol/m3] D ) diffusivity [m2/s] H ) reactor height [m] ket ) ethane formation rate constant [MPa-1‚h-1] kHC ) hydrocracking rate constant [h-1] ki ) initiation rate constant for the alkyl mechanism [MPa-1] ki2 ) initiation rate constant for the alkenyl mechanism [mol/ h] kmet ) methane formation rate constant [MPa-1‚h-1] kO2 ) ethylene formation rate constant [h/mol] kolef ) termination by b-elimination rate constant for the alkyl mechanism [h-1] kolef2 ) termination rate constant for the alkenyl mechanism [h-1] kp ) propagation rate constant for the alkyl mechanism [h/mol] kp2 ) propagation rate constant for the alkenyl mechanism [h/mol] kpar ) termination rate constant for the alkyl mechanism yielding paraffin [MPa-1‚h-1] Ki ) equilibrium constant of reaction i or adsorption coefficient of component i
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ReceiVed for reView June 30, 2005 ReVised manuscript receiVed November 7, 2005 Accepted December 2, 2005 IE0507732
