Influence of the Condensable Hydrocarbons on an Integrated Fischer

Jul 18, 2017 - Significant mass transfer limitation was observed for Fischer–Tropsch synthesis in the assumed liquid-filled spots. Hydrocracking exh...
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Influence of the Condensable Hydrocarbons on an Integrated Fischer−Tropsch Synthesis and Hydrocracking Process: Simulation and Experimental Validation Chenghao Sun,† Zhuohui Luo,† Akash Choudhary,‡ Peter Pfeifer,† and Roland Dittmeyer*,† †

Institute for Micro Process Engineering, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, D-76344, Germany Department of Chemical Engineering, Indian Institute of Technology, Madras, 600036, India

‡

ABSTRACT: Process simplification by integrating Fischer−Tropsch synthesis (FTS) with hydrocracking (HC) in a microstructured reactor was studied experimentally and by modeling and simulation. A simplified model was created to investigate the experimentally observed FTS and HC performance in the presence of larger amounts of liquid. It is assumed that part of the catalyst would be blocked if the liquid fraction exceeds a threshold. The liquid blocking would cause enlarged diffusion resistance or even inaccessible regions in the catalyst bed, particularly in microstructured reactors with broad flat channels such as the annular geometry of this study. Significant mass transfer limitation was observed for Fischer−Tropsch synthesis in the assumed liquid-filled spots. Hydrocracking exhibits limited response to internal diffusion limitation. Good agreement with experimental data was obtained here by assuming inaccessible local regions in the packed bed. Identical cross section-averaged effectiveness factors of 0.6−0.7 were obtained for the liquid-filled sections in both FTS and HC.

1. INTRODUCTION To meet the severe energy requirements caused by increasing fuel demand and air pollution, great efforts are being exerted in the utilization of renewables and the reduction of CO2 emission.1−4 The power-to-fuel process,3 which converts CO2 and electricity into fuels, exhibits promising potential. In the power-to-fuel process, surplus electricity, for example, from fluctuating renewable energy, is used to produce hydrogen via water electrolysis. The hydrogen, on one hand is applied in the reverse water gas shift reaction to convert CO2 into CO,5 and on the other hand is transferred into fuels together with the CO by Fischer−Tropsch synthesis (FTS)6 and hydrocracking (HC). Very often power from wind energy or photovoltaics is distributed and highly unsteady with limited availability. CO2 may also not be available locally in large quantities. This makes traditional large-scale plants less feasible, economically. Therefore, tailored small-scale plants with simplified and intensified process layout are of great importance for power-to-fuel applications. Process simplification by combining FTS with HC is drawing more and more attention.7−11 Different configurations to obtain bifunctional (FTS and HC) catalyst structures (particle level and bed level) have been developed. The heavy hydrocarbons could be effectively cracked. FTS is a surface catalyzed polymerization reaction to convert syngas (CO and H2) into hydrocarbons ranging from methane to heavy wax. Cobalt-based catalysts have been widely used because of the high activity and selectivity for long-chain hydrocarbons. Higher H2 partial pressure is favorable for high syngas conversion, while a more complex behavior is observed © XXXX American Chemical Society

for CO depending on the CO partial pressure. At low partial pressure the reaction rate obeys a first order dependency for CO. With increasing CO partial pressure the partial reaction order gradually decreases and finally approaches a value of −1 for very high CO partial pressure.12 The Anderson−Schulz− Flory (ASF) distribution is usually applied to describe the hydrocarbon distribution, in which the chain growth probability is affected both by the catalyst and the reaction conditions.13 With the increase of temperature and H2/CO ratio, the chain growth probability decreases.14 To predict the entire product distribution and to avoid deviations caused by the ASF distribution for low carbon number products, detailed kinetic models were recently developed which also consider the readsorption of olefins.15−18 However, in most of these studies the vapor−liquid equilibrium (VLE) in the reactor is ignored despite that a liquid phase would appear along the fixed-bed reactor with the accumulation of heavy hydrocarbons. The presence of a liquid phase could strongly affect the FTS performance for several reasons: First, diffusion in the liquid phase is much slower than in the gas phase. Hence the presence of a condensed phase both inside the catalysts pores or attached to the external surface may cause mass transport limitations. In Special Issue: Tapio Salmi Festschrift Received: Revised: Accepted: Published: A

March 31, 2017 July 3, 2017 July 18, 2017 July 18, 2017 DOI: 10.1021/acs.iecr.7b01326 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research addition, a liquid phase in contact with the active sites could lead to change of the catalytic properties, for example, due to a solvent effect. Caldwell and van Vuuren were the first to consider the importance of VLE in the FTS modeling.19 Both Raoult’s Law19−22 and more complicated equations of state23−26 were adopted to calculate the VLE. Ideal vapor and liquid phase behavior was proven to describe the FTS system with reasonable accuracy.27−29 More recently, Jess and coworkers also studied the influence of the condensed phase on the reaction performance in FTS and in particular the phenomenon of pore filling by long-chain hydrocarbons.30,31 They found that industrial-size FTS catalyst pellets operate under severe internal diffusion limitation.30 Moreover, the pores in such pellets cannot be regarded dry even for low values of the chain growth probability, that is, down to 0.75. At the same time pore filling is fast only during the initial stage, whereas the time required for complete filling may be as long as months or even years.31 The fuel selectivity of FTS is more or less tied to the ASF distribution. To improve yield and productivity of fuels, this limitation can be broken by cracking the FTS wax into middle distillates.32−37 The HC of hydrocarbons is carried out on catalysts with both acidic and hydrogenation/dehydrogenation sites.38 n-Paraffins are dehydrogenated first. Then reversible isomerization occurs followed by cracking of the i-paraffins. HC has been intensively studied from model molecules to real FTS wax. Hydrocarbons with longer chain length exhibit higher HC reaction rates. CO and water, which are typically present in the FTS reactor effluent, are unfavorable for HC.11,39,40 Because of the complexity of the reaction system, isomers with the same carbon number are generally lumped in kinetic models.41−46 Recently, the VLE was considered in the modeling of HC, too.47−49 Different from FTS, HC would lead to the opposite situation by converting liquid-phase components into gaseous components along the catalyst bed. The combination of FTS with HC was first reported in the 1970s.50 Sequential and hybrid catalyst bed concepts were developed.8,10,39,51,52 Multifunctional catalysts with both FTS and HC activity were proposed.53−57 However, there is still a lot of controversy in the literature due to the complexity of the system. Computational modeling of one-stage combined FTS and HC could help by elucidating the interactions between the different reactions in the integrated process. Till now, only limited information on this is available.7 Considering the VLE in the modeling marks a step toward the real situation. Yet this is extremely complicated as partial or complete pore filling, surface wetting, solvent effects on activity and selectivity, and even temporary local blockage of the flow in the packed-bed all may occur. In turn three-dimensional timedependent patterns may exist. In this contribution, a simplified 1D approach was developed to simulate an integrated FTS-HC process taking into account the appearance of a condensed phase and its retarding effect on the reaction in regions of high liquid phase fraction via a single factor related to the local VLE. The modified model was validated with experimental results and compared to the model ignoring liquid phase effects. The concentration profile and reaction performance along the reactor were analyzed for a sequential FTS-HC arrangement.

Figure 1. Microannular reactor and options considered for arrangement of the FTS and HC catalysts. Figure reproduced with permission from ref 58. Copyright 2017 Elsevier.

reactor in down-flow mode. A microannular reactor with 1.5 mm thick catalyst bed was applied to obtain isothermal operation (Figure 1). Axial dispersion could be neglected and plug flow behavior assumed for this reactor. Co−Re/γ-Al2O3 (20 wt % Co, 0.5 wt % Re, 3 μm γ-Al2O3) and Pt-ZSM-5 (0.5 wt % Pt, 1.5 μm H-ZSM-5 with Si/Al 40) were selected as FTS and HC catalysts, respectively. Before testing, both catalysts were pelletized, crushed, and sieved to obtain a size fraction of 50−100 μm. The catalysts were diluted with α-Al2O3 (50−100 μm) and carefully loaded into the reactor to guarantee homogeneous packing. A 1 g portion of FTS catalyst and 1 g of HC catalyst were used in the combined bed. Both combined FTS-HC and FTS reference were studied at the same conditions, that is, T = 225−255 °C, H2/CO = 1.6−2.0, WHSVsyngas = 6−12 g/(gFT‑cat·h), P = 30 bar.

3. MODELING In this work, H2, CO, N2, H2O, and hydrocarbons from C1 to C50 were considered as chemical species. For simplification, it was assumed that n- and i-paraffins with the same carbon number would have the same thermodynamic properties. 3.1. FTS and HC Kinetic Models. The FTS kinetic model reported by Kwack et al. was applied in this work.16 The model is based on a detailed kinetic mechanism in which CH2 insertion is dominant. For simplification, olefin readsorption is not considered. Only n-paraffins would be produced from FTS. The reaction rate expressions of the different species are rCH4 = k CH4A1/DEN

(1)

rC2H6 = k 2k GA CH2 /(k GA CH2 + k 2AH)A1/DEN

(2)

⎛ ⎞i − 2 k GA CH2 k GA CH2 ⎟⎟ A1/DEN ri = ki⎜⎜ ⎝ k GA CH2 + kiAH ⎠ k GA CH2 + k 2AH (i ≥ 3)

(3)

50

rCO = −∑ iri i=1

2. EXPERIMENTAL DATA The integration of FTS and HC in the same reactor was studied in sequential and hybrid configurations (Figure 1). As described elsewhere,58 the experiments were carried out in a fixed-bed

(4)

50

rH2 = rCO −

∑ (i + 1)ri i=1

B

(5) DOI: 10.1021/acs.iecr.7b01326 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research ⎛ A ⎜ DEN = ⎜1 + AH + A CH2 + 1 AH ⎝ ⎛ ⎜1 + ⎜ ⎝ ⎞⎞ ⎟⎟ ⎟⎟ ⎠⎠

50

R form, n , i = 0.097

(2R cr, j/(j − 6))

(i = 4−46)

j=i+4

(12-3)

⎛ ⎞i − 2 k GA CH2 k GA CH2 ⎜ ⎟⎟ ∑⎜ (k GA CH2 + k 2AH) i = 2 ⎝ k GA CH 2 + k iAH ⎠ 50

50

R form,3 =

∑ (R cr,j/(j − 6)) (12-4)

j=7

2

50

ADS = c H2(1 +

kINA CH2 AH2 /(k GA CH2

+ k CH4AH)

AH = (K H2c H2)0.5

(7)

(kINAH)2 + 4kINk G/kik COK COcCO )

/(2kINk G/ki)

riso, i = R iso, i + R form,iso, i − R cr, i

(9)

where k is the reaction rate constant; K is the adsorption equilibrium constant; c is the concentration; subscript i denotes the carbon number of the paraffin; subscripts IN and G denote chain initiation and chain growth, respectively. For determining parameter estimates for this kinetic model by regression, only results obtained at CO conversions below 50% were adopted. Because of the low amount of condensed phase formed under such conditions no effect on the reaction rate is expected beyond the phenomenon of pore filling. The absence of internal diffusion limitation for the particle size of 50−100 μm used in the experiments, even for the case of complete pore filling, was confirmed by calculations using a heterogeneous model solving the reaction-diffusion equations for spherical particles with 100 μm diameter and liquid diffusion coefficients for all components calculated according to established methods. For gas phase diffusion, the binary diffusivity was acquired according to Fuller’s method.59,60 Blanc’s Law was used to obtain the mixture diffusivity.61 The diffusivity in liquid hydrocarbons was calculated using Wilke’s method,62 for which C30H62 was adopted to represent the liquid. For HC the kinetic model reported by Gambaro et al. was applied.45 The hydrogenation/dehydrogenation steps were assumed to be in quasi-equilibrium, and olefins were not considered. All isomers with the same carbon number were lumped to a pseudocomponent “iso-paraffin”. The overall reaction rate expression for each component comes from three items: isomerization (eq 10), cracking (eq 11), and formation from cracking of longer-chain molecules (eq 12). R iso, i = k iso, i(cn , i − c iso, i /Keq, i)/(ADS)

(10)

R cr, i = kcr, ic iso, i /(ADS)

(11)

(14)

riso,4 = R form,iso,4

(16)

(i = 6−50)

(17)

rn,5 = −R iso,5 + R form,n,5 + 0.4R cr,6

(18)

rn, i = R form,n, i + 0.4R cr,6

(19)

(i = 3, 4)

(i = 1, 2)

(20)

50

rH2 =

∑ R cr,i 6

(21)

where subscripts n and iso of r indicate n-paraffin and isoparaffin, respectively. Parameter estimates were obtained for this kinetic model by regression as well. Again, only results obtained at CO conversions below 50% in the FTS stage were adopted. In both systems the kinetic parameters were estimated with the least-squares method using the lsqnonlin function in Matlab (release 2017a). 3.2. Vapor−Liquid Equilibrium. In line with literature, ideal behavior was assumed for both vapor and liquid phase in the FTS and HC system.27−29 Raoult’s Law (eq 22) was adopted in this study to calculate the VLE. K i = yi /xi = Pivap/P

(22)

where yi and xi are the molar fractions of species i in vapor and liquid phase, respectively; Pvap is the vapor pressure of species i i;27 P is the system pressure; Ki is the vapor−liquid equilibrium constant of species i. The local mole flow in the reactor (n, xi) is split into a vapor (nV, xV,i) and a liquid (nL, xL,i) phase fraction. The Rachford− Rice flash eq (eq 23, 24)63 is used to calculate the composition and fraction of the vapor and the liquid phase.

(2R cr, j/(j − 6)) + R cr,(i + 3)/(j − 3)

R form,iso,47 = R cr,50/(i − 3)

(i = 6−50)

(15)

ri = 0.4R cr,6

j=i+4

(i = 4−46)

(13)

riso,5 = R iso,5 + R form,iso,5

rn, i = −R iso, i + R form,n, i

50

∑

4

where k is the reaction rate constant; Keq is the equilibrium constant of isomerization; K is the Langmuir adsorption equilibrium constant; c is the concentration; subscripts i and j denote the carbon number of the paraffin; subscripts n and iso of Rform, K, and c indicate n-paraffin and iso-paraffin, respectively. The reaction rate expressions of each species are given by

(8)

A CH2 = ( −kINAH +

R form, iso , i = 0.903

50

∑ cn,iK n,i + ∑ c iso,iK iso,i) 1

(6)

A1 =

∑

(12-1)

∑ (12-2)

i

C

xi(K i − 1) =0 1 + nV /n(K i − 1)

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Industrial & Engineering Chemistry Research Table 1. Estimated FTS Kinetic Parameters parameter K H2 kCO·KCO k0INa k0Ga kCH4 k2 ki EIN EG

estimated value

95% confidence interval

1.18 × 10−4

2.18 × 10−5

5.82 × 10−2b 6.03 × 10−1 3.75 × 10−1 18.9b 1.08 3.75 7.99 × 104 9.95 × 104b

8.25 × 10−1c 2.53 × 10−2 5.32 × 10−1 3.55 × 10−1 5.6 × 103

units

definition

bar−1

adsorption constant

mol/(kg·s·bar) mol/(kg·s) mol/(kg·s) mol/(kg·s)

chain initiation constant chain growth constant termination constant of CH4

mol/(kg·s) mol/(kg·s) J/mol J/mol

termination constant of C2H6 termination constant of CiH(2i+2) activation energy of initiation activation energy of growth

Assumed to be temperature-dependent, k = k0 exp(−Ea/R·(1/T − 1/Tref)), Tref = 503.15 K. bAdopted from literature.16 cThe large confidence interval is due to correlation between the parameters. a

Figure 2. Comparison of the FTS experimental data with the simulated results: (a) CO conversion, (b) product distribution. Note that the simulation results for homogeneous and heterogeneous models basically fall on the same curves.

xi =

xi 1 + nV /n(K i − 1)

Thermochemical properties of the hydrocarbon CNLH2NL+2 were adopted for the liquid. The concentrations of H2, CO, H2O, and N2 in the liquid were calculated using Henry’s Law.27 The hydrocarbon solubility in the liquid was calculated according to van Vuuren et al.64 3.3. Reactor Model. The reactor was modeled as a 1D cascade of cells in which each of the two fluid phases is well mixed. For large number of cells the cascade approaches an ideal plug flow reactor model. For further simplification, additional assumptions were adopted: (a) steady-state; (b) isothermal; (c) isobaric. The material balance in one reactor cell is given in eq 28.

(24)

where xi is the mole fraction of species i in the entire system; nV and n represent the molar amounts of the vapor phase and of the entire system, respectively. The vapor pressure of C6+ hydrocarbons was calculated using the method reported by Marano and Holder (eq 25−27).27 Pivap = exp(2.72709 + A(i − 1.126231) − B exp( −0.619226(i − 1.126231)0.416321))

(25)

A = 15.8059 − 1496.56/T − 2.17342 log(T ) + 7.27763 × 10−7T 2 + 37876.2/T 2

u0c0, iscross = uciscross + ji scat (26)

where u0 and u denote the linear flow velocity at the inlet and outlet of the cell, respectively; c0,i and ci stand for the concentration of species i at inlet and outlet, accordingly; scross is the cross-sectional area of the reactor cell; ji is the molar flux of species i related to the external surface area of the solid catalyst present in the reactor cell; scat is the total external surface area of the catalyst in the reactor cell.

B = −5.75509 − 7.56568/T + 0.0857734 log(T ) − 1.41964 × 10−5T 2 + 267209/T 2

(28)

(27)

vap

where P is the vapor pressure in bar; T is the temperature in K; i is the carbon number of the hydrocarbon species. For a flash calculation, a hypothetical vapor pressure was formulated for the noncondensable components (H2, CO, H2O, N2, C1−C5) based on data extracted from Aspen Plus calculations of the VLE of a FTS output using the ideal model. Being mainly composed of condensed heavy hydrocarbons, the liquid was represented by a single hydrocarbon species having a carbon number equivalent to the average carbon number in the condensed phase, that is, Mw,L = ∑(Mw,i·xL,i) = 14·NL + 2, where NL is the average carbon number of the liquid.

4. RESULTS AND DISCUSSION 4.1. Estimation and Validation of FTS and HC Kinetic Parameters. Kinetic parameters for the FTS and HC kinetic models were estimated based on the experimental data using the least-squares method in Matlab (lsqnonlin). 4.1.1. Estimated FTS Kinetics. The FTS kinetic parameters are listed in Table 1. To validate the estimates, a homogeneous D

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Industrial & Engineering Chemistry Research Table 2. Estimated HC Kinetic Parametersa parameter

estimated value

Kn,i Kiso,i k0iso,i, mb k0iso,i, nb k0cr,i, mb k0cr,i, nb Keq,i Eiso,i, mb Eiso,i, nb Ecr,i, mb Ecr,i, nb

8.43·(Bn,i + 1)c 4.61·(Biso,i + 1)c 1.34 × 10−5 3.29 1.02 × 10−9 10.57 104·(i2 − 9) + 1530·(i − 3)c 2.26 × 104 4.57 × 10−3 3.50 × 104 0.621

95% confidence interval

units

definition

3.93 × 10−4d 8.99d 4.36 × 10−9d 1.22

MPa−1 MPa−1 mol/(g·h)

adsorption constant of n-paraffin adsorption constant of i-paraffin isomerization constant

mol/(g·h)

cracking constant isomerization equilibrium constant

6.99 × 105d 9.35d 2.62 × 104d 1.30 × 10−1

J/mol J/mol

activation energy of isomerization activation energy of cracking

a k = k0 exp(−Ea/R·(1/T − 1/Tref), Tref = 632.15 K; k = kiso; kcr. Bn,i = (ei·0.251−2 − e−i·0.251+2)/(ei·0.251−2 + e−i·0.251+2). Biso,i = (ei·0.11−2 − e−i·0.11+2)/ (ei·0.11−2 − e−i·0.11+2). by = m*in; y = k0iso,i, k0cr,i, Eiso,i, Ecr,i cAdopted from the literature.45 dThe large confidence intervals are due to correlation between the parameters.

Figure 3. HC product distribution at different temperatures (feed from the FTS at 30 bar, H2/CO 1.8, and WHSV 6). Note that the simulation results for the homogeneous and heterogeneous model basically fall on the same curves.

model without consideration of mass transport was adopted. The simulated results were compared with the experimental data. As shown in Figure 2a, the simulated results could reasonably fit the experimental data at CO conversion lower than 50%. At 255 °C and WHSV 6 an overestimation of CO conversion was observed in the homogeneous model (77% vs 67%). For product distribution, reasonable agreement was obtained between the experimental data and the simulated results, despite the chain growth probability (α) being a little overestimated with increasing temperature. Overall, the estimated kinetics could well predict the FTS experimental results. Possible reasons of the overestimation at high CO conversion are addressed further below. 4.1.2. Estimated HC Kinetics. The HC kinetic parameters were estimated based on the results of experiments with the

FTS effluent obtained at the same temperature as input (Table 2). The validation using the homogeneous model is shown in Figure 3. At 225 °C a slight deviation from the experimental data is observed, where the cracking is a little underestimated in the homogeneous model. At 235 and 245 °C good agreement is obtained between the experimental data and the simulated results. The regressed kinetics can reasonably well predict the experimental data from 225 to 245 °C. However, a significant deviation was observed at 255 °C. The cracking is overestimated in the simulation and more light hydrocarbons were obtained. In conclusion, an overestimation of conversion both in FTS and HC was observed at 255 °C. In addition, the experimentally obtained product distribution cannot be reproduced well by the model for these conditions. E

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Industrial & Engineering Chemistry Research 4.2. Vapor−Liquid Equilibrium and Liquid Phase Effect. A liquid phase would be formed along with the accumulation of long-chain hydrocarbons in FTS catalyst pores, as well as in the catalyst bed. The reduced diffusivity and different solubility of the syngas would influence both catalyst effectiveness and product selectivity. On the contrary, the liquid would be gradually consumed in HC. Figure 4 shows the

Figure 5. Pore filling at different temperatures at the FTS inlet.

At the FTS inlet, that is, with extremely low liquid fraction, the catalyst pores would be filled within several hours, which indicates that for a small particle size of 100 μm the pores would be completed filled with liquid hydrocarbons all over the reactor. Even though HC consumes heavy hydrocarbons, complete pore filling of the HC catalyst was assumed in analogy to the situation at the FTS inlet. 4.2.2. Influence of Reaction-Diffusion in the Catalyst Particle. Complete pore filling with liquid was obtained over the entire catalyst bed. To figure out whether the overestimation at 255 °C in both FTS and HC is caused by internal mass transport limitation in the liquid, a heterogeneous model solving the reaction-diffusion equations for spherical particles with 100 μm diameter was established (see Table 3 for additional parameters used in these simulations).

Figure 4. Hydrocarbon distribution in the vapor and the liquid phase for a typical FTS product (245 °C, 30 bar, 48% CO conversion, liquid fraction 0.5 mol %).

hydrocarbon distribution of a typical FTS output in vapor and liquid phase, respectively. Nearly all C1−C10 hydrocarbons are in the vapor phase. Similarly, the noncondensable H2, CO, N2, and H2O are also in the vapor phase. Almost all C31+ are in the liquid phase. With reaction going on, the composition of the liquid phase would change, which therefore also affects the reaction. The liquid increases or decreases gradually in the FTS or HC section, respectively. At 255 °C the high CO conversion indicates a high liquid fraction in FTS, which could cause a negative influence on the reaction and be responsible for the lower experimental conversion compared to the model. Similar reasoning is applicable to HC. At 255 °C the FTS effluent with a large fraction of liquid would be fed into the HC section, which could also be negative to the reaction and explain the overestimation in the simulation. The influence of the liquid depends on its amount (catalyst particle partially filled, completely filled, or even spilled) and composition (diffusivity, solubility). To study its effects, the local profile of the liquid should be determined first. 4.2.1. Accumulation of Liquid Hydrocarbons in FTS Catalyst Pores. The local accumulation of hydrocarbons in FTS catalyst particles was investigated using the pore filling model reported by Pöhlmann et al.31 The accumulation rate of liquid hydrocarbons in FTS is given by the interplay of formation in the pore and evaporation out of the pore. Only hydrocarbons with a carbon number larger than 10 (C11+) were assumed to be condensable. The liquid hydrocarbons in the pore were assumed to be in VLE. The evaporation was assumed to be limited only by external diffusion into the bulk gas phase. Pore filling of the 100 μm FTS catalyst particle at the bed inlet was analyzed. As shown in Figure 5, after a quick liquid filling at the beginning, the pore filling slows down. At 225 °C the catalyst pore is completely filled within 460 min. With an increase of the temperature, the time required for complete pore filling reduces to around 80 and 40 min at 245 and 255 °C, respectively.

Table 3. Properties of the Catalyst Applied in the Heterogeneous Model catalyst

apparent density [kg/m3]

particle size [μm]

porosity

tortuosity

FTS HC

1445 1500

100 100

0.5 0.5

3 3

The influence of internal diffusion on FTS is shown in Figure 6. The liquid fraction increases along with the CO conversion. The catalyst effectiveness factor for consumption of H2 and CO along the FTS section is plotted in Figure 6a. At 255 °C and syngas WHSV 6, the effectiveness factor is about 0.985 at the inlet. With increase of CO conversion, it goes down and reaches a value around 0.957 at the end of the FTS section, which indicates that pore diffusion even in a liquid-filled state would only have very limited influence on the FTS performance. Normalized concentration profiles of H2 and CO across the catalyst particle at the end of the FTS section are shown in Figure 6b. The CO concentration at the catalyst center reaches about 86% of the surface concentration. Somewhat larger concentration gradients were obtained for H2, for which the concentration in the center is about 62% of the surface concentration. According to the reaction kinetics, the reaction order decreases at higher conversion, which then explains the still high effectiveness factor despite the already marked concentration gradients. CO conversion and hydrocarbon distribution for the heterogeneous model almost fall on the same curves as for the homogeneous model (Figure 2). The interaction of reaction and diffusion was also studied for the HC catalyst particles and the conditions in which an F

DOI: 10.1021/acs.iecr.7b01326 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 6. Influence of internal diffusion on FTS assuming fully liquid-filled pores: (a) effectiveness factor and liquid fraction along the FTS section; (b) concentration profile across the catalyst particle at the FTS outlet.

Figure 7. Influence of internal diffusion on HC assuming fully liquid-filled pores: (a) effectiveness factor and liquid fraction along the HC section; (b) concentration profile across the catalyst particle at the HC outlet.

reactor was adopted. The homemade FTS and HC catalysts were pelletized and crushed to 50−100 μm, which indicates that the shape of catalyst particle is irregular. A rather wide size distribution of the void spaces between the catalyst particles in the bed would be formed in the 1.5 mm thick annular catalyst packing. With a relatively high liquid fraction, the heavy hydrocarbons would also condense in the catalyst packing where they could block smaller spaces around the catalyst particles (Figure 8). Stagnant extra-particle liquid would lead to

overestimation of conversion was obtained. Heavy hydrocarbons from FTS would be cracked into lighter ones. The effectiveness factors for consumption of the main cracking reactants (C20, C30, and C50) are plotted in Figure 7a. Identical effectiveness factors are obtained for C20, C30, and C50. The values larger than unity reflect the negative reaction order of hydrocracking. With a decrease of the liquid fraction along the HC section, the effectiveness factor decreases. Hence, the effect of internal diffusion on the rate of HC can be ignored. Normalized concentration profiles of different hydrocarbons across the catalyst particle at the HC outlet are plotted in Figure 7b. Negligible concentration gradients were obtained across the catalyst particle for all hydrocarbons. An identical product distribution was obtained in the heterogeneous and the homogeneous model (Figure 3). The analysis of the interplay of reaction and diffusion in a single catalyst particle shows that internal mass transport does not limit the performance of FTS and HC within the studied range. The filling of liquid hydrocarbons in catalyst pores is probably not the reason for the experimentally observed lower CO conversion in FTS and lower light hydrocarbon fraction in HC obtained at 255 °C. As reported elsewhere,11,58 reasonable catalyst stability was obtained for both FTS and HC catalysts, which indicates catalyst deactivation is also not the reason. Hence, there must be other factors responsible for the reduced reaction performance. 4.2.3. Blocking of the External Catalyst Surface by Liquid along the Reactor. In this study, an annular micropacked-bed

Figure 8. Scheme of the assumed catalyst particle blocking by liquid along the reactor. G

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Industrial & Engineering Chemistry Research an increased diffusion resistance, as such regions would behave like larger particles filled with stagnant liquid. Eventually, part of the catalyst particles would even be inaccessible to the flow if channeling occurs. The annular gap geometry could be particularly critical regarding channeling caused by partial blocking by liquid. The net effect is a reduction of the catalyst effectiveness over the reactor cross-section, which could explain the inferior experimental performance of both FTS and HC compared to the simulation. As depicted in Figure 8, a transitional region would exist in FTS, where small void spaces in the catalyst bed would be gradually blocked by heavy hydrocarbons with the increase of CO conversion. HC would possess the opposite situation starting from blocking to gradual unblocking due to the consumption of heavy hydrocarbons. To study the influence of local blocking by liquid, a simplified model was created. The blocked catalyst particles were treated as fictitious agglomerates with enlarged size to describe the increased diffusional distance. Instead of making a detailed description of the complicated transitional region, a simple step function was adopted in this model (Figure 8). Considering that the blocking depends on the local liquid fraction, a defined value was used to evaluate the amount of liquid along the reactor. If the local liquid fraction is above this value, blocking was assumed. For the case of mild blocking (agglomerates), the enlarged diffusional distance was applied. For the case of severe blocking (channeling), the accessible amount of catalyst was reduced. As shown in Figures 2 and 3, at 245 °C the simulated results using the heterogeneous model are in good agreement with the experimental data, which indicates that catalyst blocking is negligible. With further increase of the liquid fraction, a deviation between experimental and simulation results was obtained at 255 °C. Therefore, the liquid fraction of the FTS effluent at 245 °C was adopted as a switching value to describe the liquid-phase blocking effect. For FTS a liquid fraction of 0.31 mol % was identified as being the threshold for liquid blocking. If the liquid fraction exceeds this threshold, hypothetical agglomerates generated by liquid filling the small voids between the catalyst particles were assumed. With an agglomerate size of 500 μm (5 times of the catalyst particle), good agreement was obtained between the simulated CO conversion and the experimental data (Figure 9a). Severe internal diffusion limitation was observed in these hypothetical agglomerates. At the outlet of the FTS section, both H2 and CO exhibit large concentration gradients across the particle (Figure 9b), where the H2 concentration even drops to zero toward the center. An inner part of the agglomerate (∼300 μm diameter) is not used for the reaction at all. The conversion and the liquid phase fraction profile along the FTS section are shown in Figure 9c. At the beginning of the FTS section, the CO effectiveness factor is close to 1. With an increase of CO conversion, more and more heavy hydrocarbons would be produced. At around 53% of the length of the FTS section, the liquid fraction exceeds the threshold and the effectiveness factor drops to around 0.7. Beyond that point the increase of CO conversion and liquid fraction along the reactor is reduced due to the retarding effect of liquid blocking. Liquid blocking can explain the inferior FTS experimental performance compared to the simulation at high CO conversion. The influence of hypothetical agglomerates created by liquid-filled voids on HC was analyzed accordingly.

Figure 9. Influence of the liquid blocking on FTS performance: (a) CO conversion; (b) concentration gradient in hypothetical agglomerates; (c) development along FTS section).

The same agglomerate size of 500 μm was adopted first to investigate the effects of an enlarged diffusional distance on HC. However, similar results were still obtained as for the homogeneous model (Figure 10a), where the fraction of light hydrocarbons is much higher than detected experimentally. The effectiveness factor is even higher than for the case without liquid blocking (Figure 10b). Increasing the diffusional distance 5 times has no negative influence on the HC performance, which is apparently caused by the slow reaction rate combined with the negative reaction order under the studied conditions. The same behavior was observed with further increasing the agglomerate size to 800 μm. Consequently, an enlarged internal diffusion resistance in hypothetical catalyst particle agglomerates is not the reason for the inferior HC performance at 255 °C. However, if a liquidH

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Figure 10. HC performance at hypothetical agglomerates of different size: (a) production distribution; (b) effectiveness factor.

Figure 11. Influence of the liquid blocking on HC performance: (a) product distribution; (b) development along HC section.

filled void space would block certain regions of the crosssection of the annular packed bed completely, channeling would be the result and, as depicted in Figure 8, part of the catalyst would be bypassed and thus inaccessible to the reactants. It is assumed that such phenomenon could particularly happen in flat wide channels where the large width-to-height ratio of the cross-section makes the distribution of the flow more difficult. To analyze the influence of liquid-induced channeling in the HC catalyst packing, a factor describing the inaccessible area was introduced into the heterogeneous model. A liquid fraction threshold value of 0.50 mol % was determined together with a blocking factor of 0.6 (indicating that 40% of the catalyst are not accessible due to channeling). At the inlet of the HC section the liquid amount is above the threshold and hence it is assumed that only 60% of the catalyst is accessible to the reactants. Along with cracking of the heavy hydrocarbons, the liquid fraction is reduced and the catalyst packing would recover to blocking-free. As shown in Figure 11b, a turningpoint was obtained at around 73% of the HC section. Beyond this point the decrease of the liquid fraction would accelerate and a C5−C20 (liquid fuel) mass fraction of 72% is achieved at the end. Good agreement with the experimental product distribution was observed based on these assumptions (Figure 11a). Even though different forms of liquid blocking are assumed for FTS (liquid leads to hypothetical agglomerates) and HC (liquid leads to channeling) and it is not obvious why channeling should not occur in the FTS section as well, the

negative influence of the presence of liquid hydrocarbons on both reactions was confirmed and similar cross-section averaged effectiveness factors (0.6−0.7) were obtained for the liquid-affected regions, which indicates that the assumption of liquid blocking is reasonable.

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CONCLUSION Simplified small-scale power-to-fuel plants based on microstructured reactors hold promising potential for the targeted energy transition to a low-carbon future. Process simplification by integrating FTS with HC in a micropacked-bed reactor was studied experimentally and by modeling and simulation. In the presence of a high amount of liquid, inferior experimental performance of both FTS and HC was observed. Local blocking of void spaces in the catalyst bed is proposed as a tentative explanation. For FTS the effect on the reaction rate could be matched by assuming local liquid-filled spots of typically five times the diameter of the catalyst particles, whereas for HC this would not explain the observed experimental results. Blocked access to larger regions of the catalyst bed caused by channeling instead is assumed in this case to account for a reduction of the effective reaction rate suggested by the experimental data. A one-dimensional heterogeneous model implementing a simple step change to switch liquid blocking on (FTS) or off (HC) beyond a certain threshold value of the liquid phase fraction was created to investigate the influence of the liquid blocking. Negative effects of the liquid blocking were confirmed in FTS and in HC, and similar catalyst effectiveness factors around 0.6−0.7 were I

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obtained for the blocked sections. As the annular micropackedbed reactor has a slit height comparable to larger microstructured reactors, the study of possible liquid blocking could also be important for practical implementation of FTS and HC in microstructured reactors.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +49-721-608-23114. Fax: +49-721-608-23186. ORCID

Roland Dittmeyer: 0000-0002-3110-6989 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support of this work via provision of a Ph.D. scholarship to C. Sun by China Scholarship Council.

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NOMENCLATURE T = temperature (°C) P = pressure (bar) WHSV = weight hourly space velocity (g/(gFT‑cat.·h)) c = concentration (mol/m3) i = carbon number of species i mcat = catalyst mass w = mass fraction of hydrocarbons u = velocity s = surface area j = material flux n = molar amount x = molar fraction k = reaction rate constant K = equilibrium constant E = activation energy (J/mol) Rj,i = reaction rate of species i in reaction j (mol/(gcat·h)) ri = reaction rate of species i

Subscripts and Superscripts

i = species i V = vapor L = liquid cat = catalyst n = n-paraffin iso = isomerization reaction for Riso,i, kiso,i and Eiso,i; i-paraffin for others cr = cracking reaction form = formation reaction G = chain growth IN = chain initiation eq = equilibrium Abbreviations

FTS = Fischer−Tropsch synthesis HC = hydrocracking VLE = vapor−liquid equilibrium ASF = Anderson−Schulz−Flory

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