Multiscale and Multiphase Model of Fixed-Bed Reactors for Fischer

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Multiscale and Multiphase Model of Fixed Bed Reactors for Fischer-Tropsch Synthesis: Optimization Study Marko Stameni#, Vladimir Diki#, Milos Mandic, Branislav Todic, Dragomir B. Bukur, and Nikola Nikacevic Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04914 • Publication Date (Web): 07 Feb 2018 Downloaded from http://pubs.acs.org on February 12, 2018

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Multiscale and Multiphase Model of Fixed Bed Reactors for Fischer−Tropsch Synthesis: Optimization Study Marko Stamenića, Vladimir Dikića, Miloš Mandića, Branislav Todićb, Dragomir B. Bukurb,c, Nikola M. Nikačevića,* a

Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade 11000,

Serbia b c

Chemical Engineering Program, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Artie McFerrin Department of Chemical Engineering, Texas A&M University, MS 3122,

College Station, Texas 77843-3122, United States *

phone: +381113303652; e-mail: [email protected]

Abstract Our previously developed mathematical model is used for parametric sensitivity and optimization study of conventional and milli-scale fixed-bed reactors (FBR) for Fischer-Tropsch Synthesis (FTS). Five indicators are chosen to analyze the influence of eight parameters on the FBRs performance. Results show the scale of the effects caused by changing single parameter values, and highlight the most important ones. Subsequently, the model is used to perform a rigorous multivariable optimization of FBRs performance in steady-state. Three optimization functions are used, depicting different reactor costs. Four design parameters (tube length and diameter, particle diameter and catalyst layer thickness) and five operating parameters (inlet and wall temperature, inlet pressure, H2/CO ratio, velocity) are optimized simultaneously. Results indicate that optimal results, in terms of reactor design and operating parameters, and FBR performance, highly depend on the selected objective function and values of constrained parameters (especially methane selectivity and partial pressure of water). Keywords: Fischer-Tropsch Synthesis; Fixed-Bed Reactor; Parametric sensitivity; Optimization Highlights: •

The performance of FBRs for FTS is analyzed using multiscale and multiphase model

•

Comprehensive sensitivity analysis highlights the key design and operating parameters

•

Multivariable and constrained NLP optimization is performed 1 ACS Paragon Plus Environment

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•

Different designs obtained when different optimization functions are used

1. Introduction Fischer-Tropsch synthesis (FTS) is the key element of the gas to liquid (GTL) process, in which synthesis gas, a mixture of carbon monoxide (CO) and hydrogen (H2), is converted into a range of hydrocarbons (HCs), mainly paraffins and olefins, with water as by-product1,2. Multitubular fixed bed reactors (MTFBR) with catalysts based on cobalt (Co) or iron (Fe) are the most often used type of commercial reactors for FTS, including large scale facilities in South Africa, Qatar and Malaysia3-7. In comparison with other types of reactors, FBRs offer advantages such as easy separation of the products from the catalyst and relatively easy scale-up, while the challenges in the design of the reactor and catalyst are related to preventing high pressure drop, enabling good heat removal and avoiding the negative influence of diffusion limitations8. Cobased catalysts are preferable for working at lower temperatures (190 to 230 °C) and in the absence of the water-gas-shift reaction9. The choice of operating and design parameters is essential for obtaining high productivity of the desired products. The influence of operating parameters, such as conversion level, inlet pressure, temperature and hydrogen to carbon monoxide (H2/CO) molar ratio, on the product slate of the FTS has been extensively studied10-21. Although the exact reaction mechanism of the FTS is still a subject of the scientific debate, it is generally accepted that operating parameters influence the intrinsic kinetics of the three key steps of this polymerization-type reaction; namely, the chain initiation, propagation and termination9. In this way, the operating parameters influence the rate of FTS and selectivity towards HCs of different length. Experimental studies reveal that although increasing temperature has a positive effect on the rate of FTS, the overall influence on the product slate is negative, as the selectivity to methane, a major undesired product, is higher at higher temperatures10,12-16. Consequently, selectivity to C5+ HCs is lower. It is generally considered that increase of temperature leads to faster increase in rates of chain termination compared to rates of chain propagation, thus leading to higher selectivities toward lower molecular weight HCs21. Increase of pressure generally has a positive effect on FTS reaction rate and selectivity towardsC5+HCs17-20. Lowering of the H2/CO ratio has been reported to positively influence the selectivity towards higher HCs10,12,14.

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Design parameters, such as the reactors tube diameter and length, and catalyst particle diameter, influence hydrodynamics inside the reactor, and consequently the rate of heat transfer through the reactor wall. Additionally, catalyst particle diameter is the essential parameter for occurrence of negative effects of diffusion limitations. In most industrial FBRs for FTS, due to pressure drop requirements, Co-based catalyst pellets have diameter between 1-3 mm2. Under the conditions of pronounced diffusion limitations, the concentration of the reactant species inside the catalyst pores could become extremely low, leading to low reaction rates and lower catalyst effectiveness factor22. Moreover, the local H2/CO ratio could become very high, due to higher diffusivity of hydrogen through the liquid wax-filled pores of the catalyst23. This has a negative effect on the selectivity toward HCs with 5 or more carbon atoms (C5+ HCs), which are considered the desired products of FTS23-25. In order to avoid the negative influence of strong pore diffusional limitations and satisfy low pressure drop requirements, the use of egg-shell distribution of catalyst has been proposed in several studies 24, 26-28. Another option to accomplish this is to reduce the scale of the reactor by exploiting micro- or milli- reactors in which catalyst is deposited in a way to ensure short diffusion lengths29-31. Apart from alleviating the influence of diffusion limitations, micro- and milli- reactor configurations significantly facilitate heat removal, another important feature of FTS related to energy consumption. In an actual GTL facility, syngas preparation is considered to be the largest contributor, with more than 50 %, to overall capital costs6, 32,33. The contribution of a FTS section to overall costs depends on the type of reactor and operating conditions. However, for energy loses, FTS section is reportedly the largest contributor, with about 50 %, to overall losses of a GTL facility33. Obviously, an economic analysis of a GTL process requires accounting for the techno-economic aspects of natural gas processing, production of synthesis gas, FTS process, products postprocessing, as well as current and predicted market conditions, which is beyond the scope of this study. Here, we focus on the FTS section of a GTL process and investigate the influence of design and operating parameters on the performance and economics of a MTFBR for FTS. In the first part of the present study we use a new comprehensive multiscale and multiphase model, developed by us previously34, to perform a parametric sensitivity analysis on the influence of design and operating parameters on the performance of a FBR for FTS. The analysis is performed on two


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types of FBRs: a conventional and milli-scale reactor, in order to compare the magnitude of the effects caused by changing a single design and/or operating parameter. In the second part of this study we use the aforementioned comprehensive model to perform a multivariable deterministic optimization of the performance of FBR. Literature data on optimization of the design and/or operating parameters for a FTS FBR are scarce, with only a few utilizing Co-based catalysts35-38. In these studies, a relatively low level of details in the description of the phenomena occurring in a FTS FBR is employed, especially at the particle scale level, which may limit the validity of optimization results. Therefore, in this study, we used a detailed model for optimization. Three different objective functions (OF) are used to optimize the performance of FBRs. All three OFs maximize the productivity of the C5+ products for minimal fixed costs of a FBR. Three OFs differ in formulation, reflecting the three possible dominant contributions to the overall fixed costs. A total of 9 design and operating parameters were used as optimization parameters (control variables), simultaneously. The ranges of optimization variables are set widely, in order to cover possible optimal solution from conventional scale to milli-scale FBR, including wide operation windows. However, realistic process constraints have been imposed. Further, for each OF two different values of key constraints have been set (tight and relaxed cases), giving a total of 6 optimization solutions. 2. Methods 2.1. Mathematical model Mathematical model used in this study for parametric sensitivity and optimization analysis has been previously described in details34. It is a comprehensive, multiscale and multiphase (heterogeneous) model for FBRs which includes a high level of details in description of the phenomena occurring in the FBR for FTS. Its most important features are: •

Use of detailed kinetics for product formation (116 components in reaction rates, and 28 components in material balances);

•

Accounting for external and internal (intra-particle) mass and heat transfer resistances;

•

Accounting for non-ideal phase equilibrium between the gas and the liquid;

•

Describing the formation and flow of liquid inside the reactor;

•

Using full momentum balance (1D) for description of fluid dynamics inside the reactor;



•

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Describing radial heat transfer through modified overall heat transfer coefficient for each phase.

Reaction kinetics was modeled using data obtained in experiments with Re-promoted Co catalyst supported on alumina (25%Co/0.48%Re/Al2O3)39. The model was compared against several sets of experimental data from the literature, and it has been found that it predicts well trends of changes of selectivity and conversion with a change of different process variables34. 2.2 Parametric sensitivity analysis In our previous publication34, the model was used to make a comparison between the performances of two FBRs: a centi-scale FBR with egg-shell distribution of catalyst, and a milliscale FBR with uniform distribution of catalyst, for one set of values of design and operation parameters (base cases). Results from this investigation showed that milli scaled FBR provides qualitatively similar results (CO conversion, product selectivity and productivity) as the conventional FBR, for a similar catalyst mass, while having a much lower reactor volume, considerably higher reactor wall surface area and a vast number of reactor tubes. In order to compare the effects of operating and design parameters of a centi-scale (conventional) and milli-scale FBR for FTS in more depth, a parametric sensitivity analysis was performed with ranges of several operating and design parameters shown in Table 1. Table 1.Ranges of operating and design parameters for parametric sensitivity analysis Range: min - max Parameter

Base case

Centi-scale Milli-scale Centi-scale Milli-scale

Design Catalyst layer thickness, µm 50-200 -* 100 -* Particle diameter, mm 1–3 0.2 – 0.7 1.5 0.4 Tube diameter, mm 15 – 35 5 – 11 25 7 Reactor length, m 8 – 16 0.5 – 3 12 2 Operating H2/CO feed ratio, 1.2 – 2.4 2.0 **** Inlet temperature , K 468 – 493 473 Inlet pressure, bar 15 – 45 25 ** Inlet superficial. gas velocity , m/s 0.15 – 0.50 0.07 – 0.20 0.30 0.13 *** Space velocity , nL/grcat/h 3.06 - 9.19 2.78 - 8.33 5.10 4.63 * catalyst is assumed to be uniformly distributed throughout the whole particle volume 5 ACS Paragon Plus Environment

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**

reactor length was simultaneously adjusted in order to keep the similar mean residence

time for all values of velocity ***

calculated based on inlet velocity and other process conditions

****

in all simulations, the temperature of the reactor wall (coolant) was assumed to be

constant and equal to the inlet temperature Operating parameters are the same for both cases, with the exception of the inlet gas velocity, which is assumed to be lower in the case of milli-FBR. In order to clearly depict trends in changes of performance indicators, ranges of parameters values were set widely for both conventional and milli-scale FBR. Table 1 also shows base-case conditions for both types of FBRs. Despite the difference in inlet velocity, the calculated space velocity at normal conditions is fairly similar for both base-cases. In our study the total inlet molar flow rate in MTFBR (Ftot,in) was fixed at 1800 mol/s, for all variations of parameters. When the influence of one parameter on the reactor performance was analyzed, the other parameters were kept constant at the corresponding base-case conditions, with the exception of changing inlet velocity. When the inlet velocity is changed, the reactor length was varied simultaneously in order to keep the mean gas phase residence time nearly constant. In this way, the influence of the inlet velocity is decoupled from the influence of the residence time (i.e. conversion). It is important to notice that when the pressure is changed, the inlet superficial velocity is kept constant, again to decouple the effects. The number of tubes (N) in a MTFBR was calculated by dividing the total molar flow rate by molar flow rate per tube Ft,in : N=

Ftot ,in Ft ,in

(1)

Molar flow rate per tube is calculated by multiplying the inlet concentration (Cin), inlet superficial velocity (uin) and the tube cross-section area (As): (2)

Ft ,in = Cinuin As

Finally, the inlet concentration is obtained from inlet pressure (Pin) and temperature (Tin), according to the ideal gas law:



Cin =

Pin RTin

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(3)

Therefore, when the inlet pressure was changed, the inlet molar flow rate per tube also changed, and consequently the calculated number of tubes in a MTFBR changed as well (since total molar flow is fixed). It should be noted that we have considered a feed consisting of reactants only, without inert (decoupling the influence of pressure and composition). Furthermore, in the case of milli-scale system catalyst is assumed to be uniformly distributed throughout the whole particle, therefore the catalyst layer thickness corresponds directly to the particle radius. Model equations were solved in gPROMS. Detailed description of the numerical methods used for solving equations of the comprehensive mathematical model is given in the previous article34. To facilitate solving the model equations in parametric sensitivity analysis, results from a simulation with the previous value of the varying parameter were used as initial guesses for the subsequent simulation. In some cases, usually at parameter values close or equal to the range limit, initialization procedure had to be applied, which is explained in detail in our previous study34. Nevertheless, with this analysis the robustness of the comprehensive model for FTS in a FBR was confirmed, as it was successfully applied over wide ranges of operating and design parameters. 2.3 Optimization Three objective functions, defined in equations 4-6, were chosen for optimization of the performance of a MTFBR for FTS. Objective functions (OFs) comprise the productivity of C5+ fraction of HCs, which commonly represents the main products of the FTS, with respect to the reactor volume (VR [m3rea]) or mass of catalyst (mcat [tcat]) or the reactor wall specific area (aR [m2/m3rea]): OF1 =

OF 2 =

PC5+

(4)

VR PC5+

(5)

mcat


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OF 3 =

PC5+

(6)

aR

where is the daily production of C5+ [t/day]. Accordingly, the goal of the optimizations is to maximize values of the three OFs. The above defined OFs have been selected to be simple, while reflecting the dominant economic costs of a FBR for FTS. Fixed costs of a FBR, in general contain many aspects: costs for reactor construction material, costs of catalyst particles, the cost of their manufacturing, installation, maintenance, depreciation, costs for auxiliary equipment etc. Since it is difficult to obtain realistic prices for all these aspects, we decided to select three design parameters that are most suitable for representing the fixed costs, separately. Namely, OF1 depicts reactor volume as the most important parameter. The reactor volume is dominant only in cases where available space for the reactor is limited, for example at off-shore installations. OF2 assumes that the cost of catalyst and its preparation (egg-shell distribution with a support) is dominant. Finally, OF3 assumes that the main costs are related to the reactor construction material, reactor manufacturing and installation. Consequently, depending on the selected OF different optimal results, i.e. designs and conditions may be expected. In this optimization study, we used a fixed inlet molar flow rate of syngas (1800 mol/s), i.e. the capacity demand was assumed to be fixed. Thus, the cost of syngas production is equal for all optimization cases and has no effect on results. Moreover, it is assumed that the variations of process conditions (inlet pressure, temperatures and feed H2/CO ratio), which are related to operating costs, would not significantly affect the total cost, i.e. that these expenses, coming from variation of conditions, would be relatively small compared to fixed reactor costs. It is therefore assumed that the fixed costs are dominant, and optimization searches for maximum of productivity of higher HCs for minimal reactor fixed costs. In order for optimizations results to be within physically and technically feasible region, additional constraints have been implemented, apart from those defined by the mathematical model. These constraints, presented in Table 2, include methane selectivity, CO conversion, H2O partial pressure, total pressure drop, reactor temperature, difference between inlet and reactor wall temperature, and tube to particle diameter ratio.



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Methane is the main undesired product in FTS, partial pressure of water has been shown to strongly influence catalyst deactivation17, 21, while pressure drop is related to energy consumption. Since there are no reliable data revealing the values of these key parameters in commercial facilities, we have chosen two sets of values as constraints for these parameters. In cases 1.1, 2.1 and 3.1 lower values (further on referred as tight) for these parameters were used as constraints, while in cases 1.2, 2.2 and 3.3 higher values (relaxed) were used (see Table 2). Consequently, a total of six optimizations (two sets of constraints for each of the three OFs) were performed. Table 2. Values and ranges for optimization parameters and constraints used in optimization study Objective function OF1 OF2 OF3 Unit ∙ ∙ ∙ Case

1.1

1.2

2.1

2.2

3.1

3.2

6.0 6.0 6.0

8.0 8.0 8.0

Optimization constraints: maximum(if not indicated otherwise) CH4 selectivity, % H2O pressure, bar Pressure drop, bar CO conversion, % Temperature, K Tin-Twall, K Tube to particle dia. ratio, -

6.0 6.0 6.0

8.0 8.0 8.0

6.0 8.0 6.0 8.0 6.0 8.0 Min 20.0 513.0 10.0 Min 10.0

Optimization parameters: min - max Catalyst layer thickness, µm Particle diameter, mm Tube diameter, mm Reactor length, m H2/CO feed ratio, Inlet temperature, K Inlet pressure, bar Inlet superficial gas velocity, m/s Wall temperature, K

50 - 500 0.1 - 5.0 2 - 50 0.5 - 30 1.1 - 3.0 463 - 503 15 - 50 0.05 - 1.0 453 - 493


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A total of 9 design and operating parameters were chosen as optimization (control) variables, as shown in Table 2. The ranges of operating parameters values, in which the optimal solution is to be found, were set widely enough to allow for innovative solutions and to cover both the conventional and milli-scale reactor design in a single optimization run. On the other hand, the limits on optimization parameters are set to represent possible and technically realizable conditions for low temperature FTS. Optimization of design and process parameters was conducted using one of the intrinsic gPROMS optimization algorithms: NLPSQP (non-linear programming, sequential quadratic programming). Program receives user defined initial guesses for all parameters and iteratively changes parameter values in order to improve the objective function and its derivatives while satisfying imposed constraints. Obtained solution (objective function, its derivative and constraints) are returned back iteratively to have another step in optimization until the optimized solution is obtained based on optimization criteria. Since NLP methods do not ensure finding global minima/maxima, in order to avoid local solutions, multiple optimization runs, with different starting points, i.e. initial values of optimization parameters, have been performed. For each of the six optimization cases (Table 2) at least 8 optimization runs have been conducted, starting from both centi- and milli-scale FBR designs and with different initial values of optimization parameters. Final solution is chosen once several (at least 3) runs obtain equal or very similar set of results, primarily in terms of the objective function and optimization parameters. 3. Results and discussion 3.1 Parametric sensitivity 3.1.1 Influence of design parameters The influence of design parameters on the selected performance indicators, namely: C5+ productivity (P [ (S+, [

!"-,

./)%

!"#$%%&

]), CO conversion (XCO [

!"#$%%& !"#'()%

]), pressure drop per reactor length (∆P/L[

]), CH4 selectivity

01

]) and the difference between

maximum temperature obtained inside the reactor and the inlet temperature (∆Tmax [K]) is presented in Figures 1 and 2 for the centi- and milli-scale FBR, respectively. Comparing the 10 ACS Paragon Plus Environment


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results depicted in Figures 1 and 2, it can be deduced that changing the design parameters, within ranges shown in Table 1, produces mostly similar results on both FBR scales.

Figure 1. Influence of design parameters (catalyst layer thickness – a) and e), particle diameter – b) and f), tube diameter – c) and g), reactor length – d) and h)) on performance indicators (C5+ productivity – •, CH4 selectivity – ▲, CO conversion – ■, pressure drop – ♦, maximum temperature difference – ◄) for centi-scale FBR. Changing the catalyst layer thickness has the strongest influence on CH4 selectivity (Figure 1a), indicating the negative influence of diffusion limitations on selectivity. Increase in δ from 0.1 to 0.2 mm leads to increase in CH4 selectivity from below 6 to almost 16 %. This is in agreement with our recent study23, in which it was found that, for the same catalyst, diffusion limitations exist for δ larger than 0.13 mm. The plateau of CO conversion for δ larger than 0.15 mm (Figure 1a) is also due to diffusion limitations, as the concentration of CO significantly drops along the


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catalyst layer, making FTS reaction rate very low (low effectiveness factor). For δ smaller than 0.15 mm, in the absence of considerable diffusion limitations, there is a significant increase in CO conversion with increase in δ, a consequence of larger amount of deposited catalyst in the reactor. The combined effect of increase of δ on XCO and CH4 selectivity leads to increase in C5+ productivity at lower δ values (Figure 1a), due to prevailing higher conversions, and subsequent slight decrease at higher δ due to prevailing higher methane selectivity (lower C5+ selectivity). Increase in δ also results in higher ∆Tmax (Figure 1e) due to higher conversion, i.e. larger amount of heat is being generated. Analysis of the influence of changing particle diameter (dp) on the CH4 selectivity, CO conversion and ∆Tmax reveal significant differences in the effects caused on different reactor scales. In the centi-FBR CH4 selectivity is practically insensitive to changes in dp (Figure 1b), due to the same catalyst layer thickness, while CO conversion (Figure 1b) and ∆Tmax (Figure 1f) significantly decrease. The latter is the consequence of the fact that the amount of catalyst in the reactor is smaller for larger particles (at constant catalyst layer thickness) and less heat is generated. On the other hand, in milli-FBR CH4 selectivity sharply increases if dp is larger than 0.4 mm (Figure 2a), while the change in CO conversion (Figure 2a) and ∆Tmax (Figure 2d) is almost negligible. Since particles in milli-FBR are completely filled with the catalyst (uniform catalyst distribution), these observations are the result of diffusion limitations which become significant for particles with diameter larger than 0.4mm (which is in agreement with 23). Thus, CH4 selectivity increases and reaction rates become very small, which is analogous to the case of changing δ in the centi-scale FBR (Figures 1a and 1e). Changes in productivity of C5+ per catalyst mass with dp (Figures 1b and 2a) are minor on both scales, whereas pressure drop per reactor length expectedly rises with decrease in dp (Figures 1f and 2d). Pressure drop per length is very high in the milli-FBR (Figure 2d), which is consistent with experimental measurements performed by Knobloch et al40. However, since a much lower reactor length is used for milli-FBR (2m), the total pressure drop is acceptable. Changing the tube diameter (dt) and the reactor length (L) induces similar effects on both scales and on all performance indicators. Increase in dt, with other parameters at base case values, directly causes less effective cooling and, thus, higher temperatures are obtained inside the reactor (Figures 1g and 2e). This is consistent with the literature on conventional FTS FBRs, which shows tube diameters bellow 5 cm are preferred for cobalt-based catalysts2. Even though milli-FBRs provide significant improvement in terms of heat removal41, somewhat larger 12 ACS Paragon Plus Environment


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increase in ∆Tmax is obtained for milli-FBR (see Fig. 2), as a consequence of higher heat generation in a more compact reactor (higher catalyst loading per reactor volume). Consequently, higher reaction rates (FTS is an exothermic reaction) result in higher CO conversions (Figures 1c and 2b). The C5+ productivity also increases with dt (Figures 1c and 2b), indicating that the increase in CO conversion (higher productivity) prevails over the increase in C1-C4 selectivity due to higher reaction temperature. The influence of dt on pressure drop per length is practically insignificant (Figures 1g and 2e), because for different tube diameters inlet velocity is maintained constant.

Figure 2. Influence of design parameters (particle diameter – a) and d), tube diameter – b) and e), reactor length – c) and f)) on performance indicators (C5+ productivity – •, CH4 selectivity – ▲, CO conversion – ■, pressure drop – ♦, maximum temperature difference – ◄) for milli-FBR.


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The effect of increase in reactor length on selectivities and CO conversion (Figures 1d and 2c) is directly related to higher residence times and larger mass of catalyst. The latter is the reason for decrease in C5+ productivity per catalyst mass in spite of having a higher CO conversion (Figures 1g and 2e). Pressure drop per length and ∆Tmax are generally not affected much by changing L (Figures 1h and 2f), given that all important parameters, such as velocity and particle size are kept constant. Methane selectivity is decreasing with increase of the tube length (Figures 1d and 2c), due to increase of water content with conversion, and water is known to inhibit CH4 production17,21. The influence of the formed liquid phase on the performance of a FBR can be considerable, as it affects the two important features of this type of reactor, namely the pressure drop and heat removal. Our analysis showed that, on the conventional scale, the particle diameter is the most influential parameter regarding liquid holdup. By decreasing the particle diameter from 3 to 1 mm, the liquid holdup increases from 2.79 to 6.23 %. This is the consequence of significantly higher CO conversion for smaller particles (Figure 1b), as explained above. Higher CO conversion is also the reason for increase in liquid holdup with increase in the reactor length and the catalyst layer thickness, although the effect is not as pronounced as in the case of particle diameter (the increase is from 4.03 to 5.27 % and from 3.64 to 4.74 % for the reactor length and the catalyst layer thickness, respectively). In the case of milli-FBR the highest influence on the liquid holdup comes from the reactor length, i.e. higher conversion due to a longer residence time (Figure 2e). The increase from 0.5 to 3 m causes the increase in liquid holdup from 4.23 to 7.96 (88 % increase). The influence of particle diameter is somewhat smaller (increase from5.39 to7.13 % with decreasing diameter from 0.7 to 0.2 mm). 3.1.2 Influence of operating parameters Figures 3 and 4 show the influence of selected operating parameters on the performance of centiand milli-scale FBR for FTS, respectively. As can be seen, the influence of operating parameters on performance indicators has very similar trends for both reactor scales. An increase in inlet H2/CO molar ratio (FR) (Figures 3a and 4a) and inlet temperature (T) (Figures 3b and 4b) leads to increase in CO conversion, productivity and CH4 selectivity, which is consistent with literature reports10,12,14. CO conversion, and thus C5+ productivity, generally 14 ACS Paragon Plus Environment


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increases with increase in FR (Figure 3a) due to higher rates of hydrogenation; on the other hand, chain termination is also favored at higher FRs, which influences higher CH4 selectivity11, 21, 34. The combined effect of these two opposite trends is crucial for obtaining the desired product slate and productivity. High conversions lead to having more liquid in the reactor which should increase pressure drop. However, the pressure drop decreases with increase in FR (Figures 3a and 4a) and T (Figures 3f and 4f), as a consequence of the effect of lower gas densities of the reaction mixture prevailing over the opposite effect of the formed liquid. Compared to FR, increase in T has a more pronounced effect on increase of C5+ productivity per catalyst mass and CO conversion, due to considerable increase of temperatures in the reactor (see ΔTmax increase, Figures 3e, 3f, 4e and 4f) and thus higher reaction rates. However, CH4 selectivity increases faster with an increase of inlet temperature, and thus C5+ productivity per catalyst mass for a centi-scale FBR (Figure 3b) reaches a plateau after inlet T of 483, in spite of increase of CO conversion. This effect justifies the need to introduce the constraint on CH4 selectivity in the optimization, although the objective functions comprises C5+ productivity and thus (somewhat) includes selectivity.


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Figure 3. Influence of operating parameters (H2/CO molar ratio – a) and e), temperature – b) and f), pressure – c) and g), reactor length, superficial velocity – d) and h)) on performance indicators (C5+ productivity – •, CH4 selectivity – ▲, CO conversion – ■, pressure drop – ♦, maximum temperature difference – ◄) for centi-FBR. The influence of pressure, for a fixed value of the inlet velocity, on performance indicators might seem ambiguous because an increase in pressure leads to significant decrease in CO conversion (Figure 3c), but also to slight increase, up to 25 bar, and then relatively constant valueof C5+ productivity (Figure 3c). At higher pressures, gas density increases, leading to decrease of gas velocity gradients (continuity equation). Thus, higher pressure results in increase of average velocity, and consequently shorter residence times, despite the fact that the inlet velocity is kept constant. Moreover, higher density and velocity increase Reynolds number, and thus the heat transfer coefficient. Therefore, increase in pressure leads to efficient cooling and lower temperatures (see ΔTmax decrease, Figure 3g). Higher Reynolds number is also causing higher pressure drop when the inlet pressure is increased (see ΔP/L increase, Figure 3g). Both shorter residence time and lower temperature are responsible for a sharp drop in CO conversion, with an increase of pressure. On the other hand, for higher pressures and fixed inlet superficial velocity, the inlet molar flow rate per tube is higher (as explained in Methods section). Since the total inlet molar flow in the reactor is fixed, higher pressure corresponds to smaller number of tubes, i.e. less total catalyst mass in the MTFBR (with equal catalyst mass per tube). Therefore, despite the considerable decrease in CO conversion, C5+ productivity per catalyst mass is not decreasing



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(Figures 3c). Similar qualitative trends with respect to the effect of inlet pressure have been observed for the milli-FBR (see Figures 4c and 4g). Increasing inlet velocity together with extending reactor length, results in slight decrease in CO conversion and productivity per catalyst mass, regardless of the similar residence times(Figures 3d and 4d). This is mainly due to lower reaction rates, as a consequence of decrease in temperature (see ΔTmax, Figures 3h and 4h) due to better heat removal at higher velocities. As expected pressure drop per meter increases significantly with increase of velocity (Figures 3h and 4h).

Figure 4. Influence of operating parameters (H2/CO molar ratio – a) and e), temperature – b) and f), pressure – c) and g), reactor length, superficial velocity – d) and h)) on performance indicators (C5+ productivity – •, CH4 selectivity – ▲, CO conversion – ■, pressure drop – ♦, maximum temperature difference – ◄) for milli-FBR. 17 ACS Paragon Plus Environment

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The influence of operating parameters on the liquid holdup is similar for the centi- and the milliscale FBRs. Increase in pressure, in the defined range, leads to decrease in liquid holdup from 4.99 to 3.49 % and from 7.02 to 5.34 % for the centi- and the milli-FBR, respectively. On the other hand, an increase in temperature or the inlet H2/CO ratio increases the liquid holdup. The increase is, in the case of temperature change, from 4.33 to 5.45 % and from 6.28 to 8.44 for the centi- and the milli-FBR, respectively. With increase in inlet H2/CO ratio, the liquid holdup increases from 3.82 to 4.86 % for the centi-FBR and from 5.69 to 7.06 % for the milli-FBR. In summary, the change of liquid holdup is mainly related to changes in conversion and C5+ total productivity (amount of liquid formed), and it is less dependent on multiphase fluid dynamics. Sensitivity analysis revealed that the inlet FR and temperature have the highest influence on C5+ productivity per catalyst mass and CO conversion, whereas CH4 selectivity is most sensitive to changes in the inlet temperature and the catalyst layer thickness. For pressure drop per unit length, the most significant parameters are, expectedly, particle diameter and inlet velocity, whereas for heat management (ΔTmax) it is the inlet temperature and then the inlet velocity. Similar trends are observed for the milli- and the centi scale reactors, but there are some obvious differences regarding the scale of the change. The influence of catalyst layer thickness and particle diameter on C5+ productivity and CH4 selectivity is more pronounced in the centi-FBR, whereas the influence of tube diameter on the maximum temperature difference in the reactor is larger in the milli-FBR. Changes in C5+ productivity, CO conversion and CH4 selectivity, induced by changing operating parameters, are very similar for FBRs at both scales. The influence of all parameters, design and operating, on pressure drop per meter is significantly more pronounced in the milli-FBR. Obviously, the interplay of the effects of operating and design parameters on the performance of FBR for FTS is complex, and frequently the trends are opposite. Thus, selecting the optimal values based on single parameter sensitivity analysis is not rigorous enough and probably not possible. In the next section we present the results of a comprehensive mathematical optimization in which a number of operating and design parameters are varied and optimized simultaneously. 3.2 Optimization study



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Results of optimization study, for 6 cases defined in subsection 2.3, are presented in Table 3. Values of optimized (control) parameters are presented in Figure 5, along with values for basecases (Centi- and Milli-FBR, Table 1). Table 3. Results of the optimization study Objective function OF1 Unit Case

∙ 1.1 1.2

OF2

OF3

∙

∙

2.1

3.1

2.2

OF 1, t/(m3 day) 8.08 13.64 1.68** 6.63** OF2, t/(t day) 10.45** 17.58** 11.01 18.80 -1 OF3, t/(m day) 0.35** 0.42** 1.22** 0.68** Productivity C5+, 1000 t/year 59.4 71.7 58.3 72.9 CH4 selectivity, % 6.0 8.0 6.0 8.0 C2 - C4 selectivity, % 4.95 4.94 5.39 5.98 C5+ selectivity, % 89.05 87.06 88.61 86.02 CO conversion, % 36.90 45.50 35.99 45.83 H2O outlet pressure, bar 6.0 7.9 6.0 8.0 Pressure drop, bar 1.0 1.0 0.7 0.5 Pressure drop per length, bar/m 0.495 1.111 0.046 0.141 Outlet temperature, K 470.6 487.6 469.1 482.7 Max temperature, K 476.4 487.6 476.4 486.6 Tin-Twall, K 10.0 10.0 10.0 10.0 Number of tubes, in 000 174.30 274.20 8.66 60.72 Total reactor volume, m3 20.14 14.40 94.83 30.13 Total catalyst mass, t 15.59 11.18 14.51 10.62 Reactor specific area, m2/m3 468.9 464.0 131.1 293.7 Tube to particle dia. ratio, 21.59 47.36 10.00 15.13 Outlet superficial gas velocity, m/s 0.12 0.07 0.18 0.12 Gas phase mean residence time, s 4.74 3.46 25.45 7.69 Space velocity*, nL/grcat/h 10.03 13.91 10.48 14.26 Outlet liquid holdup, % 5.26 5.75 2.65 4.30 Outlet real liquid velocity, mm/s 3.92 2.75 11.70 6.37 * calculated based on inlet velocity and other conditions ** calculated after the results are obtained (not used in the optimization)

3.2

2.59** 3.65** 9.03** 14.75** 2.58 3.94 75.3 115.1 6.0 8.0 6.37 7.81 87.63 84.19 36.79 54.64 6.0 8.0 6.0 8.0 0.300 0.400 472.4 488.2 472.4 488.9 2.6 0.0 2.03 2.20 79.59 86.34 22.85 21.41 80.0 80.0 24.04 28.40 0.38 0.40 16.20 14.43 6.85 7.31 3.50 4.30 17.40 19.10

3.2.1 Productivity per reactor volume Results related to OF1 reveal that, regardless of the values of the constrained parameters, the optimal design is a milli-scale FBR containing catalyst particles with practically uniform catalyst distribution (see Figure 5c and d, cases 1.1 and 1.2).This result is not unexpected, since milli19 ACS Paragon Plus Environment

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reactors in general have smaller volumes, and this design may be valuable for small capacity facilities (capacity lower than the one used in this study). Comparing the results (Table 3 and Figure 5) obtained with tight and relaxed values of constrained parameters, it can be seen that CH4 selectivity and H2O partial pressure at outlet are both at the defined maximum, as well as the difference between the inlet and reactor wall (coolant) temperature. Although in both cases (1.1 and 1.2) the proposed design is a milli-FBR, there are differences in the values of several optimized parameters (Figure 5e-i), as well as in OF1 (Table 3), depending on the values of constrained parameters. Allowing higher values of CH4 selectivity (case 1.2) resulted in higher inlet temperature, while the values for pressure and H2/CO ratio are close to, or at, the defined maximum, for both cases. Increasing temperature induces higher reaction rates for case 1.2, and thus smaller particles (less catalyst mass, see Table 3) and shorter residence times (less volume, see reactor lengths) are employed. On the other hand, due to lower inlet velocity, the obtained optimal number of tubes in the MTFBR is significantly higher for case 1.2 (274.2 compared to 174.3 thousands). Comparing the two cases in terms of pressure drop, it can be concluded that in case 1.2 the effect of smaller particles is somewhat compensated by the lower inlet velocity. Nevertheless, the resulting pressure drop per length is higher in case 1.2 (1.111 compared to 0.495 bar/m) while the total pressure drop is similar for both cases, due to smaller reactor length in case 1.2. Results obtained with OF1 show that relaxing values of selected constrained parameters (case 1.2) reduces the reactor volume by 28.5 % (14.40 compared to 20.14 m3) and increases C5+ productivity per reactor volume (OF1) by 68.8 % (13.64 compared to 8.08 t/m3/day). 3.2.2 Productivity per catalyst mass To reiterate, using OF2 should result in less catalyst, which may important in the case when costs of catalyst material and its preparation are dominant. This is especially important for novel Co based catalyst promoted by Re, and also for demanding catalyst particle designs (specific shapes and/or catalyst distribution, such as egg-shell or similar). It should be noted that this study utilizes kinetic parameters obtained with alumina supported catalyst having 25% Co and 0.48%Re by weight, so for calculating costs related to catalyst, the percentages, i.e. precise composition, have to be taken into account. Moreover, the OF2, as productivity of C5+ per catalyst mass is commonly used as a performance indicator for FTS reactors42. 20 ACS Paragon Plus Environment


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Figure 5. Optimized parameters (reactor length – a) , tube diameter – b), particle diameter – c), catalyst layer thickness – d), inlet temperature – e), reactor wall temperature – f), inlet pressure – g), H2/CO feed ratio – h), inlet gas velocity – i) for 6 optimization cases (1.1,1.2,2.1,2.2,3.1,3.2). Results from optimization study with OF2 reveal that the optimal design for case 2.1 is a conventional scale FBR (Figure 5a-d). The result for case 2.2 are not so straightforward, since the values of reactor length (3.41 m), tube diameter (13.62 mm) and particle diameter (0.90 mm) fall between those for conventional and milli-scale design. As in the case of OF1, optimization results are strongly influenced by the choice of constrained values of CH4 selectivity and H2O partial pressure (Figure 5). Relaxing the values of constrained parameters had a considerable influence on the optimal design of the FBR, as considerably smaller particle, catalyst layer thickness, tube diameter and length are obtained for case 2.2 (Figure 5a-d). On the other hand, the number of tubes is significantly increased for the smaller 21 ACS Paragon Plus Environment

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reactor (8.66 thousands for 2.1 and 60.72 for 2.2, Table 3), because total inlet flow is fixed, and thus more tubes of smaller diameter are needed. The similar trend is observed for OF1 when constraints on CH4 selectivity and H2O partial pressure are relaxed. Again the most probable reason for down-scaling the reactor is that increased CH4 selectivity (for case 2.2), allows the use of higher inlet temperature which increases reaction rates. Generally, the optimized values of operating parameters are for both cases (2.1 and 2.2, Figure 5e-i) similar to the respective ones obtained with maximizing productivity per reactor volume (OF1), indicating that both optimizations follow a similar path, in which temperature is used as a governing operating parameter, with inlet pressure and H2/CO ratio having maximum values. Relaxing constraint on the magnitude of partial pressure of water results in higher conversions (cases 2.2 and 1.2) and this contributes significantly to increase in productivity. The overall results show that relaxation of constraints leads to 26.8 % lower catalyst mass (10.62 compared to 14.51 t) and 70.7 % higher C5+ productivity per catalyst mass (18.80 vs 11.01 t/t day). 3.2.3 Productivity per reactor specific area For the third objective function (OF3), which requires the minimal reactor construction material and related costs, the obtained optimal design is a large scale conventional FBR with egg-shell distribution of the catalyst (Figure 5a-d). Optimal solution was found, for both cases, at the highest allowable value of tube diameter (50 mm), a parameter which has the highest influence on the reactor specific area. This is directly related to the minimum number of tubes used (around 2000). As in the case of OF1 and OF2, the constraints on values of CH4 selectivity and H2O partial pressure are crucial for optimal solution, but for OF3 the total pressure drop also has an important role, as the optimum is at the maximum allowable value in both cases (6.0 and 8.0 bar for 3.1 and 3.2, respectively). However, the pressure drop per unit length is relatively low for both cases because of the use of large particles, although gas velocities are now higher. Optimized values of operating parameters for OF3 differ considerably from the ones obtained using OF1 and/or OF2, and this will be discussed in the following subsection. The differences in results between cases 3.1 and 3.2, are now less pronounced, i.e. values of reactor design parameters are similar (Figure 5a-d), as well the values of OF3 (Table 3). Higher inlet temperature and conversion are obtained for case 3.2 and these results in higher C5+ productivity 22 ACS Paragon Plus Environment


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(115.1 Mt/y for 3.2 vs. 75.3 Mt/y for 3.1). Since the reactor tubes have the same dimensions (i.e. specific surface areas, see Table 3), the increased productivity is the reason for increasing OF3 by 52.7 %, when the constraints are relaxed (3.94 t/m-1/day for case 3.2 compared to 2.58 t/m1

/day for case 3.1).

3.2.4 Comparison of results for different OFs and base cases From the above analysis it is obvious that applying different optimization functions resulted in three quite different designs of the FBR (Figure 5a-d). For obtaining maximum C5+ productivity per reactor volume, FTS should be performed in a milli-scale FBR. On the other hand, if priority is maximizing C5+ productivity per reactor tube specific area, the proposed design is a FBR of a large-scale, so-called conventional reactor. For maximizing C5+ productivity per catalyst mass (OF2), large-scale and mid-scale FBR are possible solutions, depending on the applied constraints. Since the inlet molar flow is fixed for all cases (same capacity demand), the resulting number of tubes varies significantly, from around 274 thousand for the milli-FBR (case 1.2) to approximately 2 thousand for the conventional scale (case 3.1). Values of reactor volumes and specific areas differ strongly and are directly related to the OF applied, whereas the catalyst mass and total C5+ productivity do not change as much (see Table 3). It can be noticed that total C5+ productivity has the highest value in case 3.2. This is a consequence of the combined effect of large reactor volume/catalyst mass and high CO conversion. Such high absolute value of C5+ productivity has not been reached in other cases, because the objective functions take also into account the capital costs (catalyst mass, reactor volume), and the optimal ratio is obtained at lower values of total productivity (catalyst mass and volume increase faster than productivity for 1.1-2 and 2.1-2). The resulting optimal values of operating parameters are not significantly different for the three OFs (Figure 5e-i). In fact, for OF1 and OF2, although completely different designs are obtained, the proposed values of inlet and wall temperature, pressure and molar H2/CO ratio are almost the same for the cases 1.1 and 2.1, as well as for the cases 1.2 and 2.2. It is important to notice that optimal solutions, for both OF1 and OF2, imply the use of high pressure (50 bar) and high feed molar ratio (3). Having high pressures is beneficial, as for the same residence time, i.e. conversion level, higher productivity per volume / catalyst mass and efficient cooling can be achieved, as shown and elaborated in Section 3.2.1.


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High H2/CO molar ratio might seem unexpected as an optimal solution, mainly due to its negative influence on CH4 selectivity, which has been shown in our parametric sensitivity analysis. However, it is obvious that this negative influence is, in cases 1.1, 1.2, 2.1 and 2.2, minimized by very low optimal values of the catalyst layer thickness, i.e. diffusion lengths, as well as by use of mild temperatures. On the other hand, higher H2/CO molar ratio significantly increases the productivity of C5+ fraction of HCs, through increase in CO conversion, which is also shown and elaborated in Section 3.2.1. Higher than usual reactants molar feed ratios are comparable to those obtained by Moazami et al.44, who in their study obtained value of 2.6 as optimal for maximizing C5+ and minimizing CH4 selectivity, which in their optimal case was 6.57 %. Also, Lillebøet al.43, in experiments with rhenium-promoted cobalt/alumina catalyst (with very similar composition to the catalyst used in our current study), showed that it is possible to obtain high CO conversion at high H2/CO ratio (2.55 was maximum in their experiments), while maintaining high C5+ selectivity. At H2/CO ratio 2.55, pressure of 20 bar and temperature 483 K, CH4 selectivity was 9.5 %, and C5+ selectivity was 81.5 %, which is comparable to the results in our sensitivity and optimization study (Figure 4 and Table 3). On the other hand, Kaskeset al.36 in their optimization analysis of a FBR performance found that the optimal H2/CO molar ratio for maximizing C5+ productivity per reactor volume is 1. However, they did not include a wide range of values for catalyst particle diameter or the possibility of egg-shell catalyst distribution, and their optimal particle diameters are higher than 1 mm. With larger particles diffusional limitations are strongly pronounced, and therefore the optimal solution requires low H2/CO molar ratios. Results are somewhat different in the case of OF3 where the resulting inlet temperature, pressure and molar H2/CO ratio are lower than for the other two OFs. In this case a lower inlet temperature and molar H2/CO ratio are obtained, to keep CH4 selectivity at the desired level, since the ratio of catalyst layer to particle diameter is higher and thus diffusion limitations start to be important. Somewhat lower optimal inlet pressure is most probably related to maximum allowable total pressure drop, which is reached in the case of OF3 (see Table 3). As discussed in Section 3.2.1 the use of higher pressure increases the pressure drop. In all cases the critical constrained parameters were CH4 selectivity and H2O partial pressure. The obtained values of these parameters were at their upper limits in all cases. Additional crucial parameter for OF1 and OF2 was the difference between the inlet and the wall temperature, 24 ACS Paragon Plus Environment


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whereas for OF3 it was the total pressure drop, both of which were at their defined respective maximums. The optimal difference between Tin and Tw (cooling medium) at maximal value for OF1 and OF2 indicates that ‘aggressive’ cooling is needed, probably due to high reaction rates per reactor volume (high heat generation). In the case of OF3 the difference Tin and Tw is much lower, despite larger tube diameters, because the catalyst is distributed over a long reactor length, and higher gas velocities are used. The obtained values of all OFs for all cases are compared in Figure 6. The horizontal axis is divided in 8 parts, each part representing the values of three OFs for each case (1.1-3.2) with addition of two parts for the base case conditions (Centi- and Milli-FBR, Table 1). The values of OFs at the ordinate are relative, i.e. normalized with regard to the highest obtained value of certain OF. Therefore, for OF1 the relative value 1 is obtained for the case 1.2, for OF2 it is the case 2.2, and for OF3 it is the case 3.2 (see Table 3). It should be noted that for cases 1.1 and 1.2 values of bars OF1 are obtained within the optimization, while the bars OF2 and OF3 (dimmed color bars) are calculated subsequently in simulation using obtained optimal values of parameters. The same applies to cases 2.1, 2.2 and 3.1, 3.2 and related OFs. For milli- and centiFBR values of all three OFs are calculated using the base case conditions, presented in Table 1.

Figure 6.Comparison of objective functions (OF) for all optimization cases and base-cases 25 ACS Paragon Plus Environment

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Figure 6 clearly indicates that the values of OFs depend crucially on the values of constrained parameters. The differences in the values of OFs for cases with tight (1.1, 2.1 and 3.1) and relaxed (1.2, 2.2, and 3.2) constraints, are significant. The comparison of OF bars for base-cases clearly shows that for the milli-scale the highest value has OF1, while for the centi-FBR OF3 and OF2 are similar. Furthermore, the gain from optimization is clearly observable by making comparison to the base-cases. For OF1, the optimized solution with very similar CH4 selectivity (case 1.1) is around 44 % higher than for the milli-base case. For OF3 (case 3.1), the increase is 80 % from the centi-base case. For OF2, the optimized solution with similar methane selectivity (2.1) is around 47 % higher than centi-base case, and around 51 % higher than milli-base case. It is interesting to notice that the values of OF2 (C5+ productivity per catalyst mass) are relatively high for cases 1.1, and 1.2, in which OF1 was used in optimization (see Figure 6). Similar trend can be observed for 3.2 and 3.1, though OF2 is now slightly lower (when OF3 is used in optimization). Therefore, it may be concluded that, in the given ranges of optimization and constrained parameters, when OFs productivity of C5+ per volume / specific area are used, the result would also give a fairly good value for productivity of C5+ per catalyst mass. 4. Conclusions A rigorous multiscale mathematical model34 was used to perform a comprehensive parametric sensitivity analysis of the performance of two types of FBRs for FTS: a conventional (centiscale) FBR and a milli-scale FBR. The influences of the design (catalyst layer thickness, particle and tube diameter, and reactor length) and operating (inlet H2/CO molar ratio, temperature, pressure and velocity) parameters on the selected performance indicators such as: C5+ productivity per catalyst mass, CH4 and C5+ selectivity, pressure drop and maximum temperature difference inside the reactor, are analyzed. Parameters with highest positive influence on C5+ productivity per catalyst mass and CO conversion are inlet temperature and molar H2/CO ratio. On the other hand, catalyst layer thickness and particle diameter for particles with egg-shell and uniform catalyst distribution, respectively, have the highest negative influence on CH4 selectivity. Pressure drop is, expectedly, highly influenced by changing particle diameter and inlet velocity. Similar trends in changes of performance indicators with changing a single parameter are observed for milli- and centi- scale, with some obvious differences regarding the magnitude of 26 ACS Paragon Plus Environment


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the induced change. The influence of catalyst layer thickness and particle diameter on C5+ productivity and CH4 selectivity is more pronounced in FBR on the centi-scale, while the influence of tube diameter on maximal temperature difference is larger in milli-FBR. Furthermore, the influences of all parameters (design and operating) on pressure drop per meter are more significant in milli-FBR. Further, the same mathematical model was used to perform a rigorous multivariable optimization of a FBR performance, with three optimization functions used to depict different reactor costs. The results show that the choice of objective function and the values of constrained parameters, strongly influence the obtained optimal design of the FBR. Maximal C5+ productivity per reactor volume, is obtained in milli-FBRs with narrow and short reactor tubes (dt < 8 mm, L < 2 m), and small catalyst particles with uniform distribution of catalyst (dp < 0.4 mm). On the other hand , maximal C5+ productivity per reactor specific area is obtained in large scale conventional FBRs with wide and long reactor tubes (dt = 50 mm, L = 20 m) and large particles with egg-shell distribution of catalyst (dp > 1.8 mm, δ < 0.15 mm). Results for maximizing C5+ productivity per catalyst mass strongly depend on selected constraints. Namely, with relaxing the values of constrained performance parameters the optimal design shifts from conventional to mid-scale FBR. In all cases, relaxing the constraints significantly increases the C5+ productivity per reactor volume / catalyst mass / reactor specific area. The crucial constraints are CH4 selectivity and partial pressure of H2O. The former allows higher temperatures, whereas the latter allows higher conversions, which both directly increase productivity per volume / catalyst mass / specific area. On the other hand, the gain in C5+ productivity per reactor volume / catalyst mass / reactor specific area is achieved with a penalty of having higher CH4 selectivity (undesired product), higher H2O partial pressure (potential catalyst deactivation) and in one case high pressure drop (high operating costs). In all optimization cases, diffusion lengths are short, which is crucial for satisfying conservative demand on CH4 selectivity. The main operating parameter is proved to be inlet temperature. Although mild inlet temperature is used, it rises considerably when constraints are relaxed (related to CH4 selectivity and increased productivity). Moreover, higher pressures (50 bar) and H2/CO ratios (3.0) are preferred for maximizing C5+ productivity per reactor volume and catalyst 27 ACS Paragon Plus Environment

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mass, while mild values of these parameters (34-41 bar and 2.0 for pressure and H2/CO ratio, respectively) were optimal for maximizing C5+ productivity per reactor specific area. Optimized solutions considerably outperform base-cases – C5+ productivity per reactor volume is 44 % higher for the optimized solution (case 1.1) in comparison to milli-FBR base case with the same CH4 selectivity, while C5+ productivity per specific area (case 3.1) is 80 % higher for the optimized case compared to centi-FBR base-case. Finally, when optimization per reactor volume or specific area is performed, the obtained (calculated) productivity per catalyst mass has similar value as in the case itself is used in optimization. Acknowledgments This research was made possible by a grant (NPRP Grant No. 7- 559-2- 211) from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. References (1)

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Figure 1. Influence of design parameters on performance indicators for centi-scale FBR 57x45mm (300 x 300 DPI)



Figure 2. Influence of design parameters on performance indicators for milli-FBR 59x47mm (300 x 300 DPI)


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Figure 3. Influence of operating parameters on performance indicators for centi-FBR 58x45mm (300 x 300 DPI)



Figure 4. Influence of operating parameters on performance indicators for milli-FBR 58x45mm (300 x 300 DPI)


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Figure 5. Optimized parameters for 6 optimization cases 203x144mm (300 x 300 DPI)



Figure 6. Comparison of objective functions (OF) for all optimization cases and base-cases 144x97mm (150 x 150 DPI)


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Multiscale and Multiphase Model of Fixed-Bed Reactors for Fischer

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