ARTICLE pubs.acs.org/EF
FischerTropsch Synthesis in a Fixed Bed Reactor Alex Moutsoglou* and Posi Praveen Sunkara Mechanical Engineering Department, South Dakota State University, Brookings, South Dakota 57007, United States ABSTRACT: A numerical simulation that models the FischerTropsch (FT) synthesis in a tubular multitube reactor packed with an iron-based catalyst is conducted to assess the effects of process parameters on product distribution. The study adopts the alkyl and alkenyl mechanisms in predicting the formation of paraffins and olefins. The effects of the desorbed hydrocarbons on the gaseous flow and reaction kinetics are accounted for in the computational algorithm. The extent of the variation of the syngas molar feed ratio, reactor inlet pressure, and reactor length on paraffin and olefin selectivities and mass flow rates is documented. Three distinct regions of the FT synthesis in the packed tube are documented. In the first region, the polymerization reactions are characterized with the absence of termination reactions that result in chain propagation reactions reaching higher carbon atom numbers with increasing axial length. The beginning of the second region is marked with the initial formation of desorbed species. The second region is characterized initially with chain termination reactions reaching higher carbon atom numbers with increasing axial length. This results in the decrease of the extent of the chain propagation reactions to lower carbon atom numbers, which itself limits the termination reactions to lower carbon atom numbers. This is the only region where liquid olefin and paraffins are formed, as the end of the second region is marked with the propagation reactions not reaching carbon number atoms beyond n = 19. In the third region, with the chain propagation reactions keep diminishing to lower carbon atom numbers, the termination reactions themselves decrease to lower carbon atom numbers. This region is characterized with constant gas flow rates, as in the absence of desorbed liquids any decrease in syngas results in the formation of low carbon number gaseous olefins and paraffins.
’ INTRODUCTION Conversion of lignocellulosic feedstock into transportation fuels is a topic that is currently being studied quite extensively. The main conversion processes in achieving this are fast pyrolysis and FischerTropsch (FT) synthesis. Both processes have been shown to be viable procedures in converting biomass to liquid fuels. The three major processes in the FT technology are synthesis gas preparation, FT synthesis, and product upgrading. Current interest is in producing syngas from gasification of lignocellulosic feedstock. FT synthesis can proceed at either low temperatures (200240 °C, LTFT) using an iron or cobalt catalyst or high temperatures (300350 °C, HTFT) using an iron catalyst. Slurry and fixed bed reactors are typically used in LTFT, while fluidized bed reactors are common in HTFT. The thermochemistry taking place in an FT reactor is complex but can be generalized as follows:1
ð3Þ
As the desired products are the heavier hydrocarbons, the FT reaction is predominant. It is noted that the FT reaction models only the formation of olefins but not paraffins. The extent of the WGS reaction depends on the bed catalyst. Generally, for cobalt catalysts the extent of the WGS reaction is negligible, and this reaction may be treated as a one way reaction producing a small amount of carbon dioxide. On the other hand, for iron catalysts at high temperatures, the WGS reaction approaches equilibrium. In this case, the direction of the WGS reaction depends on the gas composition. In the FT synthesis, the H2 to CO ratio (consumption or usage ratio) for cobalt catalysts is determined primarily by the FT reaction, with a significant influence from the methanation reaction. In these instances, the usage ratio typically ranges from 2.06 to 2.16. For iron catalysts, when the WGS reaction is in equilibrium, the combined usage ratio for the FT and WGS reactions is difficult to pin down and depends on the feed gas composition and can dip below 2. For the forward shift reaction the combined usage ratio is 0.5. Conversion can be expressed as the rate of consumption of CO þ H2. As the CO and H2 are in opposite sides of the WGS reaction, the rate of consumption of CO þ H2 is independent of the extent of the WGS reaction. A more useful concept in expressing conversion is in terms of the rate of consumption of CO þ CO2. This approach is valid even if CO2 is produced rather than consumed. It is also independent of the extent of the WGS reaction as CO and CO2 are in opposite sides of the equation. With this approach, the amount of carbon in the products can be
ð4Þ
Received: January 29, 2011 Revised: March 21, 2011 Published: March 22, 2011
Methanation Reaction CO þ 3H2 f CH4 þ H2 O
ð1Þ
FischerTropsch (FT) Reaction nCO þ 2nH2 f ðCH2 Þn þ nH2 O
ð2Þ
Alcohol Formation nCO þ 2nH2 f Cn H2n þ 2 O þ ðn 1ÞH2 O WaterGas Shift (WGS) Reaction CO þ H2 O T CO2 þ H2 r 2011 American Chemical Society
2242
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directly equated to the amount of carbon consumed. This is not the case for the CO þ H2 conversion, where in addition one needs to know the ratio of carbon to hydrogen and oxygen in the products. In order to describe the distribution of the products produced by the FT process, the product selectivity is utilized. The product selectivities are best expressed on a carbon atom basis. Thus, for a hydrocarbon CnHm, the carbon atom selectivity Sn is defined from Sn ¼
moles of Cn Hm producedn total moles of C converted
’ FT REACTION MECHANISMS The FT synthesis is a polymerization reaction where the monomers CH2 are formed on the catalyst surface from the gaseous reactants hydrogen and carbon monoxide. All proposed reaction pathways in the FT synthesis include (i) chain initiation, (ii) chain propagation, and (iii) chain termination. A model that combines the alkyl and alkenyl mechanisms in simulating the FT reaction pathways is adopted in this study.1 According to the alkyl mechanism, chain initiation takes place via dissociative CO chemisorption that generates surface carbon and surface oxygen. Subsequently, surface oxygen is removed from the surface by reaction with adsorbed hydrogen yielding H2 O or with adsorbed carbon monoxide yielding CO2, while surface carbon is hydrogenated to form successively “CH” (methylidyne), the monomer “CH2” (methylene), and the chain initiator “CH3” (methyl) on the catalyst surface CH2 þ • H f Rð1Þ
chain initiation
ð6Þ
where the alkyl group R(n) = CnH2nþ1 and R(1) = CH3. Chain propagation takes place by successive incorporation of methylene to alkyl groups. •
RðnÞ þ CH2 f Rðn þ 1Þ
n ¼ 1, 2, 3, :::
RðnÞ þ • H f PðnÞ
n ¼ 2, 3, 4, :::
chain termination to n-paraffins
ð8Þ or via β-hydride abstraction to form R-olefins, E(n) = CnH2n. RðnÞ f EðnÞ þ • H
n ¼ 3, 4, 5, :::
chain termination to R-olefins
ð9Þ
ð5Þ
Product selectivities can also be expressed on a mass basis of the total carbon products. As most hydrocarbon products are made up of methylene “CH2” building blocks, the carbon atom selectivities and mass selectivities result in similar numbers except for low molecular alkanes and oxygenated compounds. It is more convenient to express the product selectivities on a carbon atom basis, and that is the approach taken in this study. An important design factor in the overall FT process is the matching of the H2/CO ratio in the syngas composition to the usage ratio of the FT synthesis process. The usage ratio itself depends on the overall product selectivity, which in turn depends on several factors in the reactor. The FT reaction produces a wide range of hydrocarbon and oxygenated hydrocarbon atoms. In one extreme, the selectivity of methane can vary from 1 to 100%, while on the other end, the selectivity of long chain linear waxes can vary from 0 to 70%. The intermediate carbon number products between these extremes are only produced in limited amounts.
•
Thus, the methyl group changes to ethyl, the ethyl to n-propyl, the npropyl to n-butyl, and so on. Chain termination occurs by either reduction to form n-paraffins (alkanes), P(n) = CnH2nþ2
In the alkenyl mechanism, the chain initiator is taken to be a vinyl surface group CHdCH2 which forms through the coupling of methylidyne CH and methylene CH2 •
CH þ • CH2 f Q ð2Þ
chain initiation
where the alkenyl group Q(n) = CnH2n1 and Q(2) = C2H3. Chain propagation takes place by successive incorporation of methylene to alkenyl groups. Q ðnÞ þ • CH2 f Q ðn þ 1Þ
n ¼ 2, 3, 4, :::
ð7Þ
chain propagation
ð11Þ Thus, the vinyl group C2H3 changes to allyl C3H5, the allyl to butenyl C4H7, and so on. Chain termination occurs by surface reduction of an alkenyl species to yield R-olefins. Q ðnÞ þ • H f EðnÞ
n ¼ 3, 4, 5, :::
chain termination to R-olefins
ð12Þ The alkenyl mechanism fails to explain the primary formation of n-paraffins. Methane and ethylene are formed by reactions that do not involve propagating species and therefore are governed by different reactions. Methane is formed by termination of methyl • CH3 which reacts with surface hydrogen at a higher rate than termination of R(n) species when n > 2. Rð1Þ þ • H f Pð1Þ
ð13Þ
Ethylene is formed by the reaction of two methylene species rather than termination of an R(2) or Q(2) species. •
CH2 þ • CH2 f Eð2Þ
ð14Þ
The alkyl mechanism does not form ethylene as there is a stable methylCH3 at the end of the propagating species. Neither the alkyl nor the alkenyl mechanisms are able to explain the formation of oxygenates in the FT synthesis. The carbon number product distribution depends on several operating factors including reactor temperature and pressure, the kind of catalyst used, the amount and type of promoter present, and the reactor type. The main products of the FT synthesis are R-olefins and n-paraffins, along with some oxygenate and branched compounds. Several mathematical models have been developed in predicting the FT product distribution. The simplest basic model depicting the stepwise chain growth concept is that of AndersonSchulzFlory distribution given as wi ¼ Ri 1 ð1 RÞ2 i
chain propagation
ð10Þ
ð15Þ
where, wi is the mass fraction of the ith carbon number and R is the chain growth probability. 2243
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’ COMPUTATIONAL ALGORITHM In the present study, a fixed bed vertical multitube reactor filled with iron catalyst is considered for the FT synthesis. Synthesis gas with a known H2/CO molar ratio and inlet pressure pi is forced through the tubes of length L, which are maintained at a temperature T. The pressure at the exit of the reactor is kept at a constant value of pe. A kinetic model developed by Fernandes2 that is based on the alkyl and alkenyl mechanisms described earlier is adopted. For the alkyl mechanism, mass balances for eqs 69 result in dRð1Þ ¼ ki ½• CH2 ½• H kp ½• CH2 Rð1Þ dt
With the above simplifications, the system of eqs 1624 can be rewritten as
RðnÞ ¼
dEðnÞ ¼ kolef RðnÞ dt
n ¼ 2, 3, 4, :::
n ¼ 3, 4, 5, :::
ð16Þ
ð18Þ
Similarly for the alkenyl mechanism, mass balances for eqs 1012 result in dQ ð2Þ ¼ ki ½• CH2 ½• CH2 kp2 ½• CH2 Q ð2Þ dt dQ ðnÞ ¼ kp2 ½• CH2 Q ðn 1Þ kp2 ½• CH2 Q ðnÞ dt n ¼ 3, 4, 5, ::: dEðnÞ ¼ kolef 2 Q ðnÞ dt
n ¼ 3, 4, 5, :::
ð29Þ
n ¼ 3, 4, 5, :::
ki2 RFTS kp2
kp2 RFTS Q ðn 1Þ kp2 RFTS þ kolef 2
dEðnÞ kolef RðnÞ þ kolef 2 Q ðnÞ ¼ dz u ð21Þ ð22Þ
dPð1Þ ¼ kmet ½• HRð1Þ dt
ð23Þ
dEð2Þ ¼ kO2 ½• CH2 ½• CH2 dt
ð24Þ
In the above equations R, P, Q, and E are all in moles per kilogram catalyst. In the FischerTropsch synthesis, the propagating alkyl and alkenyl species R(n) and Q(n) are being formed and consumed constantly at very fast rates, that leads to the quasi-steady-state assumption that the concentrations of R(n) and Q(n) can be taken to be constant. This allows the elimination of the time derivatives in eqs 16, 17, 20, and 21, reducing these equations to algebraic form. In the above set of equations the concentrations [•CH2] and [•H] are not directly known. The concentration of methylene is taken to be proportional to the well documented overall FischerTropsch reaction rate RFTS of eq 2 given in moles per hour gram catalyst from kFTS pCO pH2 pCO þ apH2 O
dPð2Þ ket pH2 ¼ Rð2Þ dz u
ð25Þ
where pCO, pH2, and pH2O are the partial pressures of the reactants and products of eq 2. The surface hydrogen concentration [•H] is taken to be proportional to its adsorption rate, which can be written in terms of its partial pressure pH2.
ð30Þ ð31Þ
n ¼ 3, 4, 5, :::
dEð2Þ kO RFTS 2 ¼ 2 u dz
ð20Þ
Finally, mass balances for methane and ethylene formation can be written from eqs 13 and 14 to give
RFTS ¼
ð28Þ
Q ð2Þ ¼
Q ðnÞ ¼
n ¼ 2, 3, 4, ::: ð27Þ
dPð1Þ kmet pH2 ¼ Rð1Þ dz u
kpar pH2 dPðnÞ ¼ RðnÞ dz u
ð19Þ
ð26Þ
kp RFTS Rðn 1Þ kp RFTS þ kpar pH2 þ kolef
dRðnÞ ¼ kp ½• CH2 Rðn 1Þ kp ½• CH2 RðnÞ dt n ¼ 2, 3, 4, ::: ð17Þ kolef RðnÞ kpar ½• HRðnÞ dPðnÞ ¼ kpar ½• HRðnÞ dt
ki pH2 kp
Rð1Þ ¼
ð32Þ
ð33Þ n ¼ 3, 4, 5, :::
ð34Þ
where the olefin productions from the alkyl and alkenyl mechanisms have been combined in eq 34. In eqs 2830, 33, and 34, the time derivatives were converted to axial derivatives using d/dt = (d/dz)(dz/ dt), where dz/dt = u is the local gas superficial velocity at any axial location in the bed. To close the system of eqs 2634 along with eq 25, the partial pressures appearing in these equations need to be established as a function of position in the reactor. This is achieved by considering overall mass balances for the constituents of the synthesis gas flowing in the reactor. From the FischerTropsch reaction, eq 2, and the watergas reaction, eq 4, the mass conservation of species equations can be written as3 dN_ CO ¼ Fcat Að RFTS RWGS Þ dz
ð35Þ
dN_ H2 ¼ Fcat Að 2RFTS þ RWGS Þ dz
ð36Þ
dN_ H2 O ¼ Fcat AðRFTS RWGS Þ dz
ð37Þ
dN_ CO2 ¼ Fcat ARWGS dz
ð38Þ
· where N are the species mole flow rates, Fcat is the density of the catalyst, A is the cross-sectional area of the tube in which the gas is flowing, and RFTS given from eq 25 is the overall reaction rate of the FT reaction 2. RWGS is the watergas reaction rate in moles per hour gram catalyst. pCO2 pH2 pCO pH2 O K1 RWGS ¼ kWGS ð39Þ ðpCO þ K2 pH2 O Þ2 2244
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found following Ergun’s equation5
Table 1. Kinetic Constants for the FischerTropsch and WaterGas Reactions in Iron Catalysts4 kFTS
0.39816 mol/h 3 gcat 3 MPa
a
3.016
kWGS
0.10512 mol/h 3 gcat
K1
85.81
K2
3.07
dp u 1 φ 150ð1 φÞμ ¼ þ 1:75Fu 3 dz dcat φ dcat F is the gas mixture density estimated from the ideal gas law
ki ki2
0.4963 1/MPa 8.054 h 3 gcat/mol
kp
0.3530 gcat/mol
kp2
0.4206 gcat/mol
kpar
0.02314 1/h 3 MPa 0.003487 1/h 3 gcat
kolef2
0.04792 1/h 3 gcat
kmet
0.06386 1/h 3 MPa
ket kO2
0.02421 1/h 3 MPa 0.09994 h 3 gcat2/mol
N_ H2 O pH2 O ¼ p N_ CO þ N_ H2 þ N_ H2 O þ N_ CO2 þ
yiolef ¼
nG
∑ yk k¼1
olef
N_ ipar N_ CO þ N_ H2 þ N_ H2 O þ N_ CO2 nG
∑ N_ k k¼1
par
nG
∑ N_ k k¼1
par
þ
∑ N_ k
k¼1
par
þ
nG
∑ N_ k
k¼1
par
þ
nG
∑ N_ k k¼1
par
þ
∑ N_ k
k¼1
par
þ
olef
for i e nG ð47Þ
nG
olef
for i e nG
ð48Þ
and the molecular weights of paraffins and olefins are given as Mkolef ¼ kMC þ 2kMH
ð49Þ
nG
∑ N_ k
olef
k¼1
The viscosity of any gaseous component (except H2O) in the mixture is estimated using Sutherland’s formula6 μi ¼ μ0i
nG
∑ N_ k
k¼1
nG
∑ N_ k k¼1
ð50Þ
where T0 is the reference temperature in Rankine, μ0 is the gas viscosity at the reference temperature T0, T is the actual temperature in Rankine, and c is Sutherland’s constant.7 The viscosity of water vapor is estimated from ref 8. The viscosity of the gas mixture appearing in eq 44 is then calculated using the semiempirical formula of Wilke9
olef
μ¼
nG
∑ N_ k
k¼1
0:555T0 þ ci T 3=2 0:555T þ ci T0
olef
yi μi
m
∑ i¼1
m
∑ yi Φij
j¼1 nG
nG
∑ N_ k k¼1
þ
∑ N_ k k¼1
Mkpar ¼ kMC þ ð2k þ 2ÞMH nG
ð46Þ
Mkolef
N_ iolef N_ CO þ N_ H2 þ N_ H2 O þ N_ CO2 þ
N_ CO2
pCO2 ¼ p N_ CO þ N_ H2 þ N_ H2 O þ N_ CO2 þ
Mkpar þ
þ
ð42Þ yCO2 ¼
par
yipar ¼
ð41Þ yH2 O ¼
nG
∑ yk k¼1
The mole fractions of the gaseous paraffins and olefins in the gas mixture flowing in the packed tube are found from
ð40Þ
N_ H2 pH ¼ 2 ¼ p N_ CO þ N_ H2 þ N_ H2 O þ N_ CO2 þ
where the molecular weight of the gas mixture is calculated from
þ
kolef
pCO N_ CO ¼ p N_ CO þ N_ H2 þ N_ H2 O þ N_ CO2 þ
ð45Þ
MG ¼ yCO MCO þ yH2 MH2 þ yH2 O MH2 O þ yCO2 MCO2
The kinetic constants appearing in the FT and WGS reactions are given in Table 1 for iron catalysts from the experiments of Raje and Davis4 for a reactor temperature of 270 °C, reactor pressure of 1.3 MPa, and molar syngas feed ratios of H2/CO = 0.67 and 1.7. The remaining kinetic parameters appearing in eqs 2634 were established by Fernandes2 using the empirical data of Raje and Davis4 for iron catalysts at 270 °C, and are given in Table 2. At any axial location z of the reactor tube, the partial pressures can be calculated from the definition of mole fractions:
yH2
pMG RT
F¼
Table 2. Kinetic Parameters for CO Polymerization in Iron Catalyst2
yCO ¼
ð44Þ
1 Mi Φij ¼ 1þ Mj 8
olef
ð43Þ The summation terms above represent the total mole flow rates of the gaseous paraffins and olefins desorbed at any axial location z and mixed with the syngas flowing down the tube, while p represents the total pressure at that axial location. In the analysis, paraffins and olefins with carbon number of 19 or less are assumed to be gaseous, thus nG = 19. The variation of the total pressure with axial location in the reactor tube packed with catalyst of diameter dcat and having a porosity φ, is
!1=2 2 !1=2 32 Mj 1=4 5 μ i 41 þ μj Mi
ð51Þ
In estimating the viscosity of the gas mixture from eq 51 only the viscosities of the CO, H2, CO2, and H2O are accounted for in the summations (m = 4). The superficial velocity of the gas that appears in eqs 2830, 33, 34, and 44 is defined from u 2245
m_ G FA
ð52Þ
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· where mG is the total mass flow rate of the gaseous products at any axial position, calculated from m_ G ¼ ½N_ CO þ N_ H2 þ N_ H2 O þ N_ CO2 þ
nG
∑ N_ k k¼1
par
þ
nG
∑ N_ k k¼1
olef
MG
· and N_ H2/NCO2 = 1, 1.5, and 2. To start solving the system of equations, a guess for the superficial velocity is made at the top of the reactor. The mole flow rates for CO, H2, CO2, and H2O are then calculated from FuA N_ i ¼ yi MG
ð53Þ It is noted that the mass flow rate of the gas flowing down the packed tube changes as CO and H2 adsorb to catalyst surface while desorbed paraffins and olefins are reintroduced back to the stream, some in gaseous (n < 20) and some in liquid form (n g 20). In eqs 4043, 47, 48, and 53, the mole flow rates of the gaseous paraffins and olefins appear and need to be determined. The system of kinetic reaction eqs 2634 provides estimates for the desorbed paraffins and olefins, as well as for the alkyls R(n) and alkenyls Q(n) on the catalyst, in moles per kilogram of catalyst. The mole flow rate of the carbon adsorbed on the catalyst is the rate of carbon conversion at any axial location calculated from N_ Cdesorbed ¼ ðN_ CO þ N_ CO2 Þz ¼ 0 ðN_ CO þ N_ CO2 Þz
ð54Þ
where the mole flow rates of CO and CO2 can be found from solving eqs 3538. Next, from the solution of the system of kinetic eqs 2634, the carbon number selectivity, i.e., fraction of carbon atoms present in each paraffin or olefin (both gaseous and liquids) divided by the total number of carbon atoms in all paraffins, olefins, and propagating alkyl and alkenyl species at each axial location can be written as Snpar ¼
nPðnÞ nF
∑
i¼1
paraffins
Snolef ¼
iPðiÞ þ
nF
∑
i¼2
ð55Þ
iEðiÞ þ nF RðnF Þ þ nF Q ðnF Þ
ð59Þ
with F and MG estimated from eqs 45 and 46, respectively. The partial pressures of the gaseous mixture are then determined from eqs 4043. With RFTS and RWGS calculated from eqs 25 and 39, equations 2634 along with eqs 3538 and 44 are solved simultaneously to obtain the mole per kilogram catalyst of R(n), Q(n), P(n), and E(n), as well as, the · · mole flow rates N_ CO, NH2, N_ H2O, NCO2, and total pressure p, at the new axial location. Then using eqs 5458, the mole flow rates of the desorbed paraffins and olefins are calculated. Treating all paraffins and olefins with a carbon number less than 20 as gaseous, a new gas mixture molecular weight, gas density, mass flow rate, and superficial velocity is estimated from eqs 4553 for the new axial location. This procedure is then repeated until the bottom of the reactor is reached, where the calculated pressure at the exit of the reactor is checked against its known assigned value of 0.1 MPa. A NewtonRaphson scheme with underrelaxation is then used to correct the initial guess of the inlet superficial velocity, and the iterations are continued until the deviation between the calculated and assigned pressure values at the exit is less than 104 MPa. Numerical results are obtained with up to a carbon number of n = 30. Numerical tests on the effects of the axial step size employed in the RungeKutta integration are conducted. Axial step sizes of 2 mm (when L = 2 m) to 3.5 mm (when L = 3.5 m) are determined to be sufficiently small for grid independence, where deviations are found to be less than 0.1%.
olefins
nEðnÞ nF
nF
paraffins
olefins
∑ iPðiÞ þ i∑¼ 2 iEðiÞ þ nF RðnF Þ þ nF Q ðnF Þ i¼1
ð56Þ
where nF represents the highest carbon atom accounted for in the computational simulation. Results presented in this study are for nF = 30. The mole flow rates of the desorbed paraffins and olefins at each axial location z can then be construed from Snpar N_ Cdesorbed n
ð57Þ
Sn N_ C N_ nolef ¼ olef desorbed n
ð58Þ
N_ npar ¼
The fixed bed reactor for the FT synthesis consists of a multitube reactor, each tube of diameter dtube and length L, packed with an ironbased catalyst. Synthesis gas with a known composition is fed at the top of the reactor and passes through the packed tubes. Water passes outside of the tubes to cool the gases and maintain the reactor temperature at a constant value. The reactor pressure at the inlet and exit of the bed are assumed known. For the numerical calculations presented in the Results section, the following values are assigned: tube diameter dtube = 2.5 cm, tube length L = 2, 2.5, 3, and 3.5 m, apparent catalyst density Fcat = 647 kg/m3, catalyst diameter dcat = 70 μm, fixed bed porosity φ = 0.6, reactor temperature T = 270 °C, reactor inlet pressure pi = 3, 3.5, and 4 MPa, reactor exit pressure pe = 0.1 MPa. Holding the exit pressure constant at the atmospheric value provides a common basis for independently assessing the effects of process parameters on product selectivities. The initial mole fractions of all hydrocarbons in the entering synthesis gas are taken as zero at the top of the reactor. At the inlet, the mole fractions of the synthesis gas are assigned the values yH2O = 0, yCO2 = 0,
’ RESULTS To validate the computational algorithm, a mass balance is performed in the reactor. Results for an inlet pressure of 4 MPa, a reactor length of 3 m, and two H2/CO molar feed ratios of 1.5 and 2 are presented in Table 3. As shown, a mass balance of C where carbon is counted entering as CO and CO2 and leaving as CO, CO2, paraffins, and olefins (both as gases and liquids), along with any carbon propagating as alkyl and alkenyl in the catalyst results in an exact match within a hundredth accuracy. Paraffins and olefins up to carbon number 30 are computed in the algorithm. A corresponding mass balance of monatomic H, entering as H2 and H2O while leaving as H2, H2O, paraffins, and olefins (both as gases and liquids), along with any H propagating as alkyl and alkenyl results in a slight mismatch, as shown for both cases in the table. This is because of the limitation of the FT reaction to model the formation of olefins but not paraffins, resulting in C and H adsorbing to the catalyst always on a 1 to 2 ratio as predicted by the FT and WGS reactions, eqs 2 and 4. Although this ratio is maintained in the olefin formation CnH2n, this is not the case when paraffins CnH2nþ2 are formed. When the extra hydrogen in paraffins CnH2nþ2 is accounted for, the differences between entering and exiting masses in the last column of Table 3 are recovered. A mass balance of O entering and leaving as CO, CO2, and H2O resulted in a zero error within two decimal places accuracy. Finally, an overall mass balance for all species entering and leaving produced exactly the same balance error as that generated for the balance of H due to the omission of any CnH2nþ2 in the FT reaction eq 2. In Table 4, the mole ratio (H/C)utilized calculated by two different methods, is depicted for the same two cases as those for Table 3. The (H/C)converted is calculated by taking the ratio of the H consumed (difference of H entering and leaving as H2 and 2246
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Table 3. Elemental and Total Mass Balances as Calculated from the Numerical Simulations entering mass in exiting mass in converted mass in
mass in paraffins
mass in olefins
mass in propagating alkyl
produced [g/h]
produced [g/h]
and alkenyl [g/h]
syngas [g/h]
syngas [g/h]
syngas [g/h]
C
5853.10
2850.41
3002.69
H
1964.72
1460.76
503.96
105.61 586.54
O
pi = 4 MPa, L = 3 m, H2/CO = 2, pe = 0.1 MPa 480.93 2521.76
total mass
mass balance
synthesized [g/h] inout [g/h]
9.58 1012
3002.69
0
423.24
1.64 1012
528.86
24.90
2945.00
1.12 1011
3531.54
24.90
pi = 4 MPa, L = 3 m, H2/CO = 1.5, pe = 0.1 MPa 450.18 2442.29 1.72 1011
7796.69
7796.69
15614.52
12107.87
3506.65
C
6639.54
3747.06
2892.48
2892.48
0
H O
1671.53 8844.28
1186.07 8844.28
485.46
97.25
409.91
2.94 1012
507.15
21.69 0
17155.34
13777.41
3377.94
547.43
2852.20
2.02 1011
3399.63
21.68
total
Total
0
H2O) to the C consumed (difference of C entering and leaving as CO and CO2) is found to equal to 2 mol of H per mole of C, regardless of the feed ratio, reactor length, or inlet pressure. This is the case, because the C and H on the catalyst first react to form the monomer CH2, as illustrated by the FT reaction (eq 2), for both the alkyl and alkenyl mechanisms while not accounting for the extra two hydrogen atoms formed per mole of paraffin in CnH2nþ2. The same mole ratio (H/C)synthesized is more accurately calculated from the H and C found in the paraffins, olefins, alkyls, and alkenyls and is shown to deviate from the ratio of 2 found above, as it truly accounts for all hydrocarbons formed. The variation of the pressure, gas density, mass flow rate, and superficial velocity in the packed tube as a function of axial position in the reactor are shown in Figures 15, for a reactor length of L = 3 m, inlet pressure pi = 4 MPa, and three inlet H2/ CO molar feed ratios of 1, 1.5, and 2. In Figure 1, the pressure is shown to decrease almost linearly until near the end of the reactor, where it is seen to drop very quickly to match the exit pressure. Ergun’s eq 44 dictates that the pressure gradient is a function of the superficial velocity and the density. As seen from Figures 2 and 5, both density and superficial velocity vary only slightly in the first part of the reactor, while both vary drastically near the latter part of the tube. As the density decreases with decreasing pressure (eq 45), the superficial gas velocity increases to conserve mass. With the mass flow rate of the gas remaining constant over the latter part of the reactor (see Figures 3 and 4), the increase in the superficial gas velocity causes the sharp decrease of the pressure seen in Figure 1. The variation of the feed ratio does not have any effect on the pressure distribution, as indicated in Figure 1, although it does seem to have a pronounced effect on the gas density and mass flow rates. It is also noted that Ergun’s equation does not account for the desorbed hydrocarbons that are in the liquid phase (paraffins and olefins with carbon atom numbers of equal or greater than 20). One would predict that in the presence of liquid trickling down the packed tube, the slope of the pressure would be a greater negative number. The variation of the gas density with axial location is plotted in Figure 2. As can be seen from eq 45, for an isothermal reactor, the density is affected by the pressure and the molecular weight of the gas. At a constant feed ratio H2/CO, the primary factor is the pressure, and thus, the density generally follows the trend of the pressure shown in Figure 1: a slow decrease for about half the reactor length, followed by a sharp decrease, especially near the
Table 4. Molar (H/C)utilized Calculated from the Numerical Simulations (H/C)converted
(H/C)synthesized
pi = 4 MPa, L = 3 m, H2/CO = 2, pe = 0.1 MPa 2
2.1 pi = 4 MPa, L = 3 m, H2/CO = 1.5, pe = 0.1 MPa
2
2.09
latter part of the tube. The density decrease with the H2/CO feed ratio is directly attributable to the decrease of the gas molecular weight, with increasing H2/CO ratios. Mass flow rates flowing down the packed tube are plotted in Figure 3 for an inlet molar feed ratio of H2/CO = 2, inlet pressure pi = 4 MPA, and reactor length L = 3 m. At the inlet of the packed reactor tube the total mass flow rate entering consists of syngas made up of H2 and CO alone. The fluid flowing downstream consists of syngas (H2, CO, CO2, and H2O) along with paraffins, CnH2nþ2, and olefins, CnH2n. There are also alkyl, CnFH2nFþ1, and alkenyl, CnFH2nF1, that propagate on the iron based catalyst. In the study, paraffins and olefins with carbon atom numbers n < 20 are treated as gaseous, while those with n g 20 are considered liquid. As the polymerization reactions are extended up to n = 30, the alkyl and alkenyl propagating on the catalyst surface correspond to C30H61 and C30H59, respectively. In Figure 3, at any axial location, the difference between the syngas and total gas represents the desorbed gaseous paraffins and olefins (n < 20), while that between the total gas and total gas and liquid is an account of the desorbed liquid paraffins and olefins (n g 20). Finally, the difference between the total gas and liquid and the total mass flowing in tube and propagating in catalyst represents the amount of alkyl and alkenyl that propagate on the catalyst surface. As shown in the figure, the total mass flow rate in the packed tube consisting of the flowing mass (syngas, paraffins, and olefins) and propagating mass (alkyl and alkenyl) remains constant at the initial value verifying the overall conservation of mass of species. As hydrogen and carbon monoxide adsorb to the catalyst throughout the reactor length, the syngas is shown to decrease continuously along the length of the tube. The adsorption of hydrogen and carbon monoxide is proportional to their corresponding partial pressures, which in turn are directly related to the total gas pressure and mole fractions. Thus, the highest 2247
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Figure 1. Axial variation of gas pressure.
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Figure 4. Axial variation of mass flow rate.
Figure 5. Axial variation of superficial gas velocity. Figure 2. Axial variation of gas density.
Figure 3. Axial variation of mass flow rate.
adsorption rates occur at the inlet of the tube, which coincide with the largest decreases in the syngas flow rate. As can be seen from the figure, for the first 0.5 m of the tube there is no desorption of paraffins or olefins, and as such, the adsorbed mass of H2 and CO on the catalyst is converted to the propagating
alkyl and alkenyl species. This suggests that the polymerization reactions are characterized solely by chain propagation reactions reaching higher carbon atom numbers with increasing axial length. From this point on, paraffins and olefins start desorbing from the catalyst and are added to the flow stream in the tube. Around x = 0.8 m, the propagating alkyl and alkenyl rates reach a maximum that corresponds to a minimum of the flowing stream of mass (syngas, paraffins, and olefins). Beyond this point, the sharp decrease of the propagating alkyl and alkenyl contributes to the corresponding fast rate of increase in the desorbed paraffins and olefins, causing the flowing mass stream in the tube to increase, as shown in the figure. Thus, the second region starts with chain termination reactions reaching higher carbon atom numbers with increasing axial length (and thus desorption of liquid species), resulting in limiting the extent of the chain propagation reactions to lower carbon atom numbers. This in turn starts limiting the termination reactions themselves to lower carbon atom numbers. Around x = 1.9 m, the propagating alkyl and alkenyl at n = 30 are depleted resulting in the flowing mass of gas and liquid making up the total mass flow entering the reactor tube. Beyond x = 1.9 m, desorption of liquid paraffin and olefins ceases. This indicates that the end of the second region is marked with the propagation reactions not reaching carbon number atoms beyond n = 19. The constant liquid flow rate guarantees a constant gas flow rate. This assures that the continuing 2248
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Figure 6. Variation of inlet superficial velocity with inlet pressure and inlet feed ratio.
adsorption of H2 and CO, that occurs at decreasing rates, is balanced out by desorption of low carbon number gaseous paraffins and olefins. Thus, in the third region, where the chain propagation reactions keep diminishing to lower carbon atom numbers with increasing axial distance, the termination reactions themselves decrease to lower carbon atom numbers. Corresponding mass flow rates for inlet feed ratios of H2/CO = 1.5 and 1 are plotted in Figure 4. As can be seen from Figures 3 and 4, lower feed ratios result in higher mass flow rates, as lower H2/ CO mole fractions result in higher gas molecular weights, larger densities, and thus larger mass flow rates. For the same inlet pressure and packed tube length, the axial location where the propagating alkyl and alkenyl species is a maximum (and the flowing gas and liquid flow rate is a minimum) occurs around x = 0.8 m for all three inlet feed ratios. The axial location, where the propagating species are depleted and the desorption of liquid paraffins and olefins ceases, decreases as the H2/CO feed ratio increases, since the FT reaction rate increases with increasing H2/CO feed ratio resulting in higher adsorption rates of H2 and CO as attested from the decrease of syngas . It is for the same reason that the amounts of gaseous and liquid paraffins and olefins produced in the tube, as noted from Figures 3 and 4, decrease as the feed ratio decreases. The axial variation of the superficial gas velocity in the packed tube is shown in Figure 5. The superficial gas velocity, as defined from eq 52, is inversely proportional with pressure and gas molecular weight and proportional to the total gas mass flow rate. Initially, for a given feed ratio, the superficial gas velocity despite the decrease in pressure goes through a slight minimum that coincides with the minimum of the total gas mass flow rate shown in Figures 3 and 4. Beyond that point, as the total gas mass flow rate increases and then levels off while the pressure continues to decrease, the superficial gas velocity is found to increase. Near the latter part of the tube, the superficial gas velocity exhibits a sharp increase that follows the sharp decrease of the pressure. The increase of the superficial gas velocity with increasing initial H2/ CO feed ratio is due to the corresponding decrease in the gas molecular weight. It is noted that the superficial gas velocity for a fixed length reactor reflects the residence time of the gas, with larger velocities corresponding to lower residence times, and thus reaction times. As explained earlier, the inlet superficial velocity is determined in the computational model through a NewtonRaphson
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Figure 7. Variation of inlet superficial velocity with reactor length and inlet feed ratio.
iterative scheme that employs under-relaxation. Converged values for the inlet superficial velocities as a function of inlet pressure are plotted in Figure 6 for a tube length of 3 m and exit pressure of 0.1 MPa. As expected from basic momentum concepts, greater inlet pressures will result in greater superficial velocities. The increase of the inlet superficial velocity with increasing H2/CO feed ratio is again due to the decrease in density with increasing H2/CO ratios. Inlet superficial velocities as a function of the reactor length are plotted in Figure 7 for an inlet pressure of 4 MPa. With the inlet and exit pressures fixed, the momentum eq 44 dictates that higher velocities are required in shorter reactors, verifying the decreasing values of the inlet velocities with reactor length. Again, the increase of the inlet superficial velocities with increasing H2/CO feed ratios is due to the decrease in density with increasing feed ratios. Conversion performance relates to the overall consumption of reactants rather than the formation of products. For reasons discussed earlier, the rate of conversion is best expressed in terms of the rate of carbon conversion, which is equal to the overall rate of consumption of CO and CO2. rate of carbon conversion ¼ ðN_ CO þ N_ CO2 Þinlet ðN_ CO þ N_ CO2 Þexit
ð60Þ
Conversion expressed in this way is not affected by CO2 being produced or consumed. The calculated amount of carbon consumed is directly equal to the amount of carbon in the FT products. As discussed earlier with the FT reaction producing the (CH2) monomer, the ratio of H/C is 2 regardless of the reactor parameters. As a result, the rate of carbon conversion is exactly the same as that for the total H2 conversion, defined as rate of H2 conversion ¼ ðN_ H2 þ N_ H2 O Þinlet ðN_ H2 þ N_ H2 O Þexit
ð61Þ
The rate of total carbon conversion (or the rate of total H2 conversion) as a function of the syngas feed ratio is plotted for the three inlet pressures in Figure 8 and for the four reactor lengths in Figure 9. As illustrated in Figure 8, for a fixed reactor length, the carbon conversion rate increases with both inlet pressure and with H2/CO feed ratio. An increase in pressure, and hence partial pressures, increases the adsorption and reaction rates, promoting 2249
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Figure 8. Variation of total carbon conversion rate with inlet feed ratio and inlet pressure.
Figure 10. Variation of fraction of total carbon conversion with inlet feed ratio and inlet pressure.
Figure 9. Variation of total carbon conversion rate with inlet feed ratio and reactor length.
Figure 11. Variation of fraction of total carbon conversion with inlet feed ratio and reactor length.
the rate of carbon consumption. An increase in the molar feed ratio H2/CO results in an increase in the mole fraction of hydrogen and a decrease in the mole fraction of carbon monoxide. As can be seen from eq 25, an increase in the partial pressure of H2 increases the FT reaction rate RFTS, while a decrease in the partial pressure of CO tends to decrease it. With the effect of the increase of pH2 dominating over the retarding effect of the decrease of pCO, an increase in H2/CO results in an increase of the carbon conversion rate. It is noted that total carbon conversion rate is independent of the extent of the WGS reaction, eq 4, since CO and CO2 are on opposite sides of the equation. The rate of total carbon conversion versus feed ratio for four reactor lengths is plotted in Figure 9 for an inlet pressure of 4 MPa. The conversion rate is shown to increase with both reactor length and feed ratio for a fixed inlet and outlet pressure. The longer reactor lengths provide longer residence times (smaller superficial velocities) for the carbon monoxide and hydrogen to adsorb and react with the catalyst, thus increasing the carbon conversion rate (see eqs 2834). For a fixed reactor length, an increase in the feed ratio again, as discussed in the above paragraph, enhances the FT reaction rate resulting in an increase in the carbon conversion rate.
The fraction of total carbon conversion defined as fraction of carbon conversion ¼
ðN_ CO þ N_ CO2 Þinlet ðN_ CO þ N_ CO2 Þexit ðN_ CO þ N_ CO2 Þinlet
ð62Þ is plotted versus the H2/CO feed ratio for the three pressures with a reactor length of 3 m in Figure 10. The fraction of carbon conversion increases with increasing feed ratio, but decreases with increasing inlet pressure. The decrease of the fraction of carbon conversion with inlet pressure is due to the increasing carbon molar rates at the inlet of the reactor (denominator of eq 62) that result from the corresponding increase of the superficial inlet velocity with pressure, plotted in Figure 6, despite the increase in the conversion rate (numerator of eq 62) with the inlet pressure. The fraction of carbon conversion versus the H2/CO feed ratio for the four reactor lengths is plotted in Figure 11 for an inlet pressure of 4 MPa. The fraction of carbon conversion is shown to increase with feed ratio, as well as with increasing reactor length. The increase of the fraction of carbon conversion with increasing reactor length is due to both the increase in the conversion rate illustrated in Figure 9 (numerator of eq 62), and 2250
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Figure 12. Variation of usage ratio with inlet feed ratio and inlet pressure.
the decrease of the carbon flow rate at the inlet illustrated in Figure 7 (denominator of eq 62) with decreasing inlet superficial velocity. Despite the increase of the inlet superficial velocity (see Figure 7) and thus the denominator of eq 62, the increase in the FT reaction rate with the feed ratio results in the increase of the fraction of carbon conversion with increasing H2/CO feed ratio, as shown in Figure 11. The usage ratio H2/CO is defined from ðH2 =COÞusage ¼
N_ H2in N_ H2out N_ COin N_ COout
ð63Þ
and is a measure of the ratio of the decrease of H2 to that of CO. The production of synthesis gas is a major cost factor in the FT process. Thus, as mentioned earlier, it is essential that as much of the synthesis products (CO, H2, and CO2) are consumed to provide useful products. One way to assess this is to compare the usage ratio (eq 63) to the supplied inlet feed ratio. In Figure 12, at a given supplied feed ratio, the usage ratio is shown to increase with an increase in inlet pressure. An increase in total pressure increases the partial pressures of H2 and CO, promoting the adsorption of both and consequently their consumption. The usage ratio thus increases since more H2 is consumed than CO as dictated by eqs 14. As the supplied H2/CO feed ratio increases, the mole fraction of H2 increases while that of CO decreases, resulting in the increase of the usage ratio. For feed ratios H2/CO of both 1 and 1.5, the usage ratio for all three pressures always exceeds the feed ratio, indicating that (H2/CO)out < (H2/CO)in and that there would be extra H2 entering the reactor. For these two feed ratios, this mismatch is amplified with an increase in pressure. Conversely, for the feed ratio of 2, the usage ratio is found to be less than the feed ratio for all three pressures. This would indicate that (H2/CO)out > (H2/CO)in and that there would be extra CO entering the reactor. As can be seen, for each inlet pressure, the usage ratio increases with the feed ratio. This is because the carbon conversion rate increases with increasing feed ratio, as illustrated in Figure 8, resulting in greater consumption of hydrogen than carbon monoxide, and hence a greater usage ratio. One can also see in Figure 12, that for an inlet pressure of 4, a feed ratio of around 1.92 approximately matches the usage ratio. Plots of H2/CO usage ratio versus H2/CO feed ratio for four different reactor lengths at an inlet pressure of 4 MPa are shown in Figure 13. As seen from the figure, for a given feed ratio and inlet and exit pressures, a decrease in the reactor length increases
Figure 13. Variation of usage ratio with inlet feed ratio and reactor length.
the usage ratio. This is due to the decrease in the carbon conversion rate with decreasing reactor length, illustrated in Figure 9. At a given reactor length and a fixed inlet pressure, an increase in the feed ratio results in higher usage ratios. Again for feed ratios of 1 and 1.5, the usage ratio exceeds the feed ratio, resulting in (H2/CO)out < (H2/CO)in. The mismatch between the two ratios decreases with an increase in reactor length, resulting in higher carbon conversion rates and lower usage ratios. Conversely, for the feed ratio of 2, the usage ratio is found to be less than the feed ratio, indicating that (H2/CO)out > (H2/ CO)in. It can be seen that for a reactor length of 2 m, a feed ratio around 1.936 approximately matches the usage ratio. With the watergas shift reaction of eq 4 being close to equilibrium for iron catalysts considered in this study, the usage ratio depends on the feed gas composition as the direction of the WGS reaction depends on the feed ratio. By examining the FT and WGS reactions, eqs 2 and 4, the usage ratio may vary from 2, with no CO2 in the feed, to infinity, with no CO in the feed. However, the case with no CO2 in the feed is likely to cause CO2 to be a product, as is the case in this study with the usage ratio dropping below 2. The product distribution of a FischerTropsch process depends on many reaction variables, the type of reactor, and the catalyst used. The main products of the FT synthesis are Rolefins and n-paraffins with some side oxygenate and branched compounds. Mazzone and Fernandes3 varied the inlet superficial gas velocity, inlet pressure, and H2/CO ratio independently, while presenting their results. With the dependence of the density and thus mass flow rate on inlet pressure, their choice of independent variables is at best ambiguous. Also, for a given inlet pressure and reactor length, a change in the entering H2/ CO ratio changes the inlet velocity and mass flow rate. In addition, the exit pressure is a variable that was not reported. In their model, the effects of the desorbed gaseous paraffins and olefins mixing with the flowing synthesis gas, accounted for in eqs 4048, 52, and 53, were left out of the analysis. Also, no information on the handling of the axial variation of the density, superficial velocity, and gas molecular weight was reported. The most direct way to assess the effects of the process parameters on the FT product is to plot the carbon atom selectivities as defined from eq 5. The change of the flow rate entering the reactor with pressure, reactor length, and H2/CO 2251
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Figure 14. Variation of total selectivity of paraffins with inlet feed ratio and inlet pressure.
Figure 16. Variation of total selectivity of olefins with inlet feed ratio and inlet pressure.
Figure 15. Variation of total selectivity of paraffins with inlet feed ratio and reactor length.
Figure 17. Variation of total selectivity of olefins with inlet feed ratio and reactor length.
ratio is thus accounted for in the definition of the selectivities. The total selectivities for all paraffins and olefins leaving the reactor
hydrogen on catalyst surface promotes the rate of termination of paraffins. In the alkyl mechanism, olefin formation occurs by hydrogen abstraction (see eq 9); therefore an increase in the adsorbed hydrogen on the catalyst would tend to decrease the termination of the alkyls as olefins. In contrast, in the alkenyl mechanism which predicts only the formation of olefins, olefin termination occurs via hydrogen reduction, as seen from eq 12. Thus, an increase in the hydrogen on the catalyst would tend to increase olefin formation. With the alkyl mechanism dominating, at a constant syngas feed ratio, the total olefin selectivity is found to decrease with either decreasing inlet pressure (Figure 16) or with increasing reactor length (Figure 17). These trends are exactly reverse of those for paraffins depicted in Figures 14 and 15. This is because with negligible alkyl and alkenyl rates at the exit of the reactor (see Table 3), at a given inlet pressure, reactor length, and syngas feed ratio, the total selectivities of paraffins and olefins add up to unity, as attested from eqs 55, 56, and 64. An increase in the syngas feed ratio is shown to promote the total selectivity of paraffins while stifling the total selectivity of olefins. An increase in the H2/CO feed ratio results in the increase of the H2 mole fraction (partial pressure) and decrease in the CO mole fraction (partial pressure). As discussed earlier, the increase in the H2/CO feed ratio augments the FT reaction
Stotpar ¼
30
∑ Sn n¼1
par
Stotolef ¼
30
∑ Sn n¼2
olef
ð64Þ
are plotted in Figures 1417, where the carbon atom selectivities are estimated at z = L from eqs 55 and 56, respectively, for paraffins and olefins. As the reaction rates of olefin desorption are much greater than those for paraffins, the total olefin selectivities are of the order of 0.820.86, whereas the corresponding paraffin selectivities are in the range of 0.180.14. At a constant syngas feed ratio, the total selectivity of paraffins is shown to increase with either a decrease in inlet pressure (Figure 14) or an increase with reactor length (Figure 15). This can be attributed to the fact that either a decrease in the inlet pressure or an increase in the reactor length reduces the gas velocities in the reactor, as depicted by Figures 6 and 7, respectively. Reduced reactor velocities increase gas residence times resulting in enhanced fraction of total carbon (or hydrogen) conversion, as illustrated in Figures 10 and 11. As paraffins are formed by the addition of H to alkyls (see eq 8), an increase in adsorbed
2252
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Figure 18. Variation of selectivity of paraffins with carbon number and inlet feed ratio.
Figure 19. Variation of selectivity of olefins with carbon number and inlet feed ratio.
rate (see eq 25) contributing to enhanced formation of the monomer CH2 and, thus, an increase in total fraction of carbon (and hydrogen) conversion as shown in Figures 10 and 11. Again, the increase of hydrogen on catalyst, as discussed above, promotes paraffin termination (see Figures 14 and 15), while reducing olefin formation as illustrated in Figures 16 and 17. The carbon atom selectivities of paraffins CnH2nþ2 and olefins CnH2n, as given from eqs 55 and 56, respectively, are plotted in Figures 1823 as a function of carbon atom number for n = 130. It is noted again that desorbed hydrocarbons with a carbon atom number of n = 20 or greater are considered to be in the liquid state. As the rate of desorption of olefins is greater than paraffins, the selectivity of olefins by far exceeds those of paraffins with the exception of methyl (n = 1) and ethyl (n = 2) group. The paraffin methane (CH4) is the only FT product formed with n = 1 since methylene (CH2) acts as the monomer in the synthesis reaction. With no olefin desorbed at n = 1, methane has the highest rate of desorption than any other paraffin. For n = 2, the low formation of the olefin ethylene (C2H4) is due to the fact that ethylene is formed by the reaction of two methylene species, rather than the termination of C2H5 or C2H3. As shown in the figures, the selectivity of the paraffins beyond methane initially dips at n = 2, then increases slightly, quickly going through a peak at n = 3 or 4, and subsequently drops steadily with
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increasing carbon atom number. For the olefins, after the low selectivity of ethylene (n = 2), the selectivity of olefins increases sharply, going through a maximum and then decreases steadily with increasing atom numbers. These trends are consistent with polymerization reactions, as noted in eq 15, where the probability of formation of hydrocarbons decreases with increasing carbon number. Carbon atom selectivities for paraffins and olefins are plotted in Figures 18 and 19, respectively, for an inlet pressure pi = 4 MPa, reactor length of L = 3 m, and three molar syngas feed ratios. Paraffins are formed by the addition of H to alkyls (see eq 8). As discussed earlier, an increase in the syngas feed ratio, H2/CO, will naturally increase the mole fraction of H2, thus increasing the rate of termination of paraffins. The significantly larger paraffin termination rates at small carbon atom numbers (n = 1, 2) that result with increasing feed ratio, diminish the propagation of the alkyls resulting in the decrease of the carbon selectivity for paraffins for n = 8 and beyond with increasing H2/CO feed ratio, causing the crossover of the lines plotted in Figure 18. As documented earlier, an increase in the H2/CO ratio diminishes the olefin formation via the alkyl mechanism, while enhancing it via the alkenyl mechanism due to the increase of the H2 mole fraction. Consequently, an increase in the syngas feed ratio results in the decrease of olefin selectivities up to n = 11 due to the steep increases in the low carbon number paraffins coupled with the low selectivity of ethylene, and in the increase of olefin selectivities beyond n = 11, demonstrated in Figure 19, complimenting the decreasing selectivity of paraffins at large carbon atoms with H2/CO shown in Figure 18. The carbon number selectivities of paraffins and olefins at three different inlet pressures and for an inlet syngas feed ratio of H2/CO = 2 and reactor length of L = 3 m, are plotted in Figures 20 and 21, respectively. A decrease in the inlet pressure while maintaining a constant H2/CO feed ratio, results in a decrease in gas velocities, thus increasing the fraction of carbon (hydrogen) conversion rates which favors the formation of paraffins at the expense of olefin formation according to the alkyl mechanism, while at the same time enhancing the olefin formation as predicted by the alkenyl mechanism. As shown in Figure 20, a decrease in the inlet pressure results in enhanced paraffins selectivities at lower carbon number, followed by crossover due to the diminishing propagation of alkyl species
Figure 20. Variation of selectivity of paraffins with carbon number and inlet pressure. 2253
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Figure 21. Variation of selectivity of olefins with carbon number and inlet pressure.
Figure 23. Variation of selectivity of olefins with carbon number and reactor length.
with increasing carbon atom numbers. The crossover occurs at a much higher carbon atom number and is hardly noticeable in the figure due to the low selectivities of paraffins. The effect of the inlet pressure is much more pronounced for the olefin selectivities depicted in Figure 21, where a decrease in the inlet pressure increases the olefin selectivities for up to carbon atom number n = 9. This is due to the increase of olefin formation via the alkenyl mechanism that results from higher carbon and hydrogen conversion rates with decreasing pressure (decreasing gas velocities) that favor termination of growing chains and thus promote the formation of light paraffin and olefin products. Consequently, the propagating alkyl and alkenyl species increase with increasing inlet pressure, promoting the formation of large chain olefins and paraffins. Thus, as seen in Figure 21, for a carbon number of n > 9 an increase in the inlet pressure is shown to increase the olefin selectivities. The effects of the reactor length on paraffin and olefin selectivities are depicted in Figures 22 and 23, respectively. The results are for an inlet pressure of 4 MPa, outlet pressure of 0.1 MPa, and a syngas molar feed ratio of H2/CO = 2. As discussed earlier, at a constant inlet pressure, an increase in the reactor length increases residence time favoring the fraction of carbon (hydrogen) conversion rate. This again favors the termination rates of light paraffins and olefins as discussed above,
resulting in the increase of the selectivity of paraffins (for n e 9) and olefins (for n e 7), as shown in Figures 22 and 23, respectively. Higher termination rates at low carbon numbers with increasing reactor lengths cause the propagating alkyl and alkenyl species to decrease. This decrease results in the crossover of the paraffin selectivities for n > 9 (Figure 22) and olefin selectivities for n > 7 (Figure 23), where an increase in the reactor length is found to diminish the paraffin and olefin selectivities. The carbon atom selectivities for several carbon atom range fuel products are summarized in Table 5 as a function of inlet syngas feed ratios, reactor inlet pressures, and lengths. The mass flow rates for paraffins CnHnþ2, and olefins CnH2n, leaving the reactor, as a function of the carbon number n, are plotted in Figures 2429. The mass flow rates are calculated by multiplying the mole flow rates of paraffins and olefins, given from eqs 57 and 58, respectively, with their corresponding molecular weights given from eq 49. 2 ð65Þ m_ kpar ¼ Skpar N_ Cdesorbed MC þ 2 þ MH k
Figure 22. Variation of selectivity of paraffins with carbon number and reactor length.
m_ kolef ¼ Skolef N_ Cdesorbed ½MC þ 2MH
ð66Þ
As seen from the equations above, the variation of the mass flow rates of paraffins and olefins with syngas molar feed ratio, inlet reactor pressure, and reactor length directly follows the trends of the carbon number selectivities discussed in Figures 1823 and that of the total carbon conversion rate discussed in Figures 8 and 9. As shown in Figures 24, 25, and 26, the mass flow rate of methane is by far the largest among paraffins. There is a sharp decrease in the production of ethane (n = 2) that goes through a quick peak, then decreases gradually with increasing carbon atom numbers. These trends are consistent with those for paraffin selectivities discussed earlier. As seen from the three figures, at low to moderate carbon atom numbers, the mass flow rate of paraffins increase with increasing molar syngas feed ratio (Figure 24), decreasing inlet pressure (Figure 25), and increasing reactor length (Figure 26). These effects decrease with increasing carbon atom number and completely diminish beyond n = 13 in Figure 24, n = 24 in Figure 25, and n = 13 in Figure 26. 2254
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Table 5. Calculated Selectivities of Conventional Fuels (TR = 270 °C, pe = 0.1 MPa, O = 0.6) H2/CO total paraffins total olefins SNG LPG light petroleum heavy petroleum petroleum kerosene diesel middle distillates softwax carbon number
130
130
12
34
57
810
510
1112
1320
1120
2130
1
0.251
0.749
0.147 0.319
0.253
0.127
0.380
0.050
0.083
0.132
0.021
1.5
0.287
0.713
0.176 0.288
0.238
0.126
0.364
0.051
0.092
0.143
0.028
2
0.318
0.682
0.203 0.272
0.227
0.122
0.348
0.051
0.095
0.145
0.032
1
0.250
0.750
0.148 0.344
0.257
0.121
0.378
0.045
0.070
0.114
0.016
1.5 2
0.288 0.319
0.712 0.681
0.179 0.311 0.206 0.292
0.243 0.231
0.121 0.118
0.363 0.348
0.047 0.047
0.079 0.082
0.126 0.129
0.021 0.024
1
0.250
0.750
0.150 0.375
0.258
0.112
0.370
0.039
0.056
0.095
0.010
1.5
0.289
0.711
0.182 0.338
0.245
0.114
0.359
0.042
0.065
0.107
0.015
2
0.322
0.678
0.211 0.316
0.234
0.111
0.345
0.042
0.068
0.111
0.017
1
0.228
0.772
0.127 0.304
0.259
0.137
0.395
0.055
0.093
0.148
0.025
1.5
0.252
0.748
0.145 0.276
0.245
0.137
0.382
0.057
0.106
0.163
0.034
2
0.272
0.728
0.161 0.262
0.236
0.134
0.371
0.058
0.111
0.168
0.038
1 1.5
0.240 0.271
0.760 0.729
0.138 0.313 0.161 0.283
0.256 0.242
0.131 0.131
0.388 0.373
0.052 0.054
0.087 0.098
0.139 0.152
0.023 0.031
2
0.296
0.704
0.183 0.268
0.232
0.128
0.360
0.054
0.102
0.155
0.035
1
0.251
0.749
0.147 0.319
0.253
0.127
0.380
0.050
0.083
0.132
0.021
1.5
0.287
0.713
0.176 0.288
0.238
0.126
0.364
0.051
0.092
0.143
0.028
2
0.318
0.682
0.203 0.272
0.227
0.122
0.348
0.051
0.095
0.145
0.032
pi = 4 MPa
1
0.259
0.741
0.155 0.324
0.250
0.124
0.374
0.048
0.079
0.127
0.020
L = 3.5 m
1.5
0.302
0.698
0.190 0.292
0.234
0.121
0.355
0.049
0.087
0.136
0.027
2
0.338
0.662
0.222 0.273
0.221
0.116
0.337
0.048
0.089
0.137
0.030
pi = 4 MPa L=3m pi = 3.5 MPa L=3m pi = 3 MPa L=3m pi = 4 MPa L=2m pi = 4 MPa L = 2.5 m pi = 4 MPa L=3m
Figure 24. Variation of mass flow rate of paraffins with carbon number and inlet feed ratio.
Figure 25. Variation of mass flow rate of paraffins with carbon number and inlet pressure.
The absence of any crossover in these graphs, in contrast with those that were encountered in the selectivity plots, is due to the increase in the carbon conversion rate with increasing syngas feed ratio, increasing inlet pressure, and increasing reactor length, as depicted in Figures 8 and 9. Corresponding mass flow rates of olefins are plotted in Figures 2729. As can be seen, ethylene has the lowest mass flow rates of olefins, and it is not affected by the variation of syngas feed ratio, inlet pressure, or reactor length. Beyond ethylene, the olefin mass flow rates are shown to go through a quick maximum around n = 4 (butanele) and, then, gradually decrease with increasing carbon atom number. In Figure 27, the
mass flow rate of olefins decreases with increasing molar syngas feed ratio for n e 5, while it is shown to increase for n g 6 with increasing H2/CO. This is again due to the increase of the H2 mole fraction with increasing H2/CO that retards the olefin termination by the alkyl mechanism at low carbon atoms, while enhancing olefin formation via the alkenyl mechanism. In Figure 28, the olefin mass flow rates are shown to increase with increasing inlet pressure. As can be seen from Figure 27 and 28, the inlet syngas feed ratio and inlet pressure, respectively, are found to significantly affect the olefin mass flow rates at large carbon atom numbers. In Figure 29, the mass flow rate of olefins is shown to increase with increasing reactor length. These effects are the largest at n = 3 (propylene), and decrease with 2255
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Figure 26. Variation of mass flow rate of paraffins with carbon number and reactor length.
Figure 27. Variation of mass flow rate of olefins with carbon number and inlet feed ratio.
Figure 28. Variation of mass flow rate of olefins with carbon number and inlet pressure.
increasing carbon atom number until they completely diminish beyond n = 16.
ARTICLE
Figure 29. Variation of mass flow rate of olefins with carbon number and reactor length.
’ CONCLUSIONS The effects of reactor length, inlet pressure, and syngas feed ratio on paraffin and olefin selectivities and mass flow rates in a FischerTropsch synthesis have been documented. The carbon conversion rate is found to increase with inlet pressure, reactor length, and syngas molar feed ratio, while the usage ratio is shown to increase with inlet pressure and molar feed ratio and to decrease with increasing reactor length. The total selectivity of paraffins is shown to increase with increasing syngas feed ratio and reactor length and to decrease with increasing inlet pressure. On the other hand, the total selectivity of olefins is found to decrease with increasing syngas feed ratio and reactor length, while increasing with increasing inlet pressure. At low to moderate carbon atom numbers, the mass flow rate of paraffins increase with increasing syngas feed ratio, decreasing inlet pressure, and increasing reactor length. These effects subside with increasing carbon number. The mass flow rate of methane is by far the greatest among paraffins. Mass flow rates of olefins exceed corresponding paraffin rates except for n = 2, where the mass flow rate of ethylene is the lowest of olefins. The mass flow rates of olefins decrease with increasing syngas feed ratio at low carbon atom numbers, but increase with the feed ratio at large carbon atom numbers. Olefin mass flow rates are shown to increase with increasing inlet pressure and reactor length. Finally, three distinct stages of the polymerization reactions are identified. At the initial stage, all of the adsorbed syngas is converted to propagating alkyl and alkenyl species with increasing carbon atom numbers, as chain termination reactions do not occur at this stage. The second stage is characterized with desorption of olefins and paraffins, as chain termination reactions become significant, decreasing the propagation reaction rates to lower carbon numbers. Eventually, the decreasing propagation reactions at lower carbon numbers in turn limit the termination reactions to lower carbon numbers themselves. The second stage ends with the ceasing of desorption of liquid olefin and paraffins. At the last stage, the absence of desorbed liquids results in constant gas flow rates, as any decrease in syngas results in the formation of low carbon number gaseous olefins and paraffins. 2256
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ARTICLE
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work has been supported through funds provided by the Department of Transportation under grant DTOS59-07-G00054 and Department of Defense under grant W911NF-092-0024. ’ REFERENCES (1) Steynberg, A. P., Dry, M. E., Ed. Studies in Surface Science and Catalysis FischerTropsch Technology; Elsevier: New York, 2004; Vol. 152. (2) Fernandes, F. A. N. Polymerization kinetics of FischerTropsch reaction on iron based catalysts and product grade optimization. Chem. Eng. Technol. 2005, 28, 930–938. (3) Mazzone, L. C. A.; Fernandes, F. A. N. Modeling of FischerTropsch synthesis in a tubular reactor. Latin Am. Appl. Res. 2006, 36, 141–148. (4) Raje, A. P.; Davis, B. H. FischerTropsch synthesis over ironbased catalysts in a slurry reactor. Reactor rates, selectivities and implications for improving hydrocarbon productivity. Catal. Today 1997, 36, 335–345. (5) Ergun, S. Fluid flow through packed columns. Chem. Eng. Prog. 1952, 48, 89–94. (6) Sutherland, W. The viscosity of gases and molecular force. Philos. Mag. 1893, 36, 507–531. (7) Flow of Fluids Trough Valves, Fittings, and Pipe; Crane, 1988. (8) Kim, W. Viscosity of liquid water and water vapor. Bull. Korean Chem. Soc. 1990, 11, 180–181. (9) Wilke, C. R. A viscosity equation for gas mixtures. J. Chem. Phys. 1950, 18, 517–519.
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