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Optimization of operating conditions of the Fischer–Tropsch synthesis based on multi-objective differential evolution algorithm

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Abstract

A study on the Fischer–Tropsch synthesis was investigated employing a one-dimensional non-isothermal model in a fixed-bed reactor over a Co/Al2O3 catalyst. The reaction kinetic follows a semi-empirical approach. Under multiple operating conditions and compared to experimental results, the presented model appropriately describes the product distribution. Afterward, optimizations using single- and multi-objective differential evolution (DE) algorithms were conducted. The minimum CH4 selectivity and maximum CO conversion were obtained, through the single-objective DE optimization. The results indicate that the improvement of one objective is only reached by making reductions to the other objective, i.e., a trade-off between objectives. The optimal operating conditions employing the multi-objective algorithm found GHSV = 4002.17 \({\text{Nml}}\;{\text{g}}_{{{\text{cat}}}}^{ - 1} {\text{h}}^{ - 1}\), H2/CO = 2.7, T = 501.63 K, P = 22.7 bar, and no inert content (%N2 = 0). Conditions that yielded optimized CO conversion and CH4 selectivity, respectively, of 60.21 and 6.65%.

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Abbreviations

C j :

Molar concentration of species j [mol m−3]

C p :

Mixture heat capacity [J Kg−1 K−1]

d p :

Catalyst particle diameter [m]

d i :

Reactor inner diameter [m]

L :

Reactor length [m]

M m :

Average molar mass [g mol−1]

P :

Total pressure [bar]

R :

Universal gas constant [J mol−1 K−1]

r :

H2/CO molar ratio

r FT :

Global Fischer–Tropsch reaction rate [\({\text{mol g}}_{{{\text{cat}}}}^{ - 1} {\text{ s}}^{ - 1}\)]

r j :

Rate of consumption/production of species j [\({\text{mol g}}_{{{\text{cat}}}}^{ - 1} {\text{ s}}^{ - 1}\)]

r WGS :

Water–gas shift reaction rate [\({\text{mol g}}_{{{\text{cat}}}}^{ - 1} {\text{ s}}^{ - 1}\)]

S Cn :

Hydrocarbon selectivity n [%]

T :

Temperature [°C] or [K]

T w :

Reactor inner wall temperature [°C] or [K]

U :

Overall heat transfer coefficient [W m−2 K−1]

u s :

Superficial velocity [m s−1]

x CO :

Carbon monoxide conversion [%

ASF:

Anderson–Shultz–Flory

BDF:

Backward differentiation formula

CSTR:

Continuous stirred tank reactor

DE:

Differential evolution

FBR:

Fluidized bed reactor

FTS or FT:

Fischer–Tropsch synthesis

GHSV:

Gas hourly space velocity [\({\text{Nml g}}_{{{\text{cat}}}}^{ - 1} {\text{ h}}^{ - 1}\)]

HTFT:

High-temperature Fischer–Tropsch

LTFT:

Low-temperature Fischer–Tropsch

MODE:

Multi-objective differential evolution

PBR:

Packed or fixed-bed reactor

RMSE:

Root-mean-square error

SBR:

Slurry bed reactor

STTR:

Straight through transport reactor

TOPSIS:

Technique for order of preference by similarity to ideal solution

WGS:

Water–gas shift

0 :

Initial condition

i :

Reaction "i"

j :

Chemical species "j"

n :

Carbon number

α n :

Chain growth probability

ΔH i :

Enthalpy of reaction i [KJ mol−1]

ε :

Reactor bed porosity

θ :

Catalysis active sites

μ m :

Mixture viscosity [Pa s]

ρ b :

Catalytic bed density or bulk density [Kg m−3]

ρ f :

Fluid density [Kg m−3

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Acknowledgements

The authors would like to thank the National Council of Scientific and Technological Development of Brazil—CNPq (Grants Number: 307966/2019-4-PQ, 405101/2016-3-Univ), PRONEX ‘Fundação Araucária’ 042/2018 for financial support of this work.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Pontifical Catholic University of Paraná, Curitiba, Brazil

    Vinícius Reisdorfer Leite & Viviana Cocco Mariani

  2. Department of Chemical Engineering, Federal University of Paraná, Curitiba, Brazil

    Éliton Fontana

  3. Department of Electrical Engineering, Federal University of Parana, Curitiba, Parana, Brazil

    Viviana Cocco Mariani

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Leite, V.R., Fontana, É. & Mariani, V.C. Optimization of operating conditions of the Fischer–Tropsch synthesis based on multi-objective differential evolution algorithm. J Braz. Soc. Mech. Sci. Eng. 44, 490 (2022). https://doi.org/10.1007/s40430-022-03785-4

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