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On the Use of Steady-State Optimal Initial Operating Conditions for Control Scheme Implementation of a Fixed-Bed Fischer–Tropsch Reactor

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Abstract

A control scheme implementation for a fixed-bed Fischer–Tropsch synthesis (FTS) reactor using the optimal initial operating conditions at steady-state is developed. The proposed approach consists of solving a nonlinear constrained optimization problem for a fixed-bed FTS reactor with incorporation of a control scheme in the cooling jacket in order to find the optimal values of the initial operating conditions of temperature, gas-hourly space velocity (GHSV), pressure and coolant flow velocity under a steady-state regime that maximizes CO conversion and \({\mathrm{C}}_{5+}\) product selectivities. Such optimal operating conditions at steady-state are used to evaluate the dynamic behavior of the reactor under the proportional-integral control (PIC) scheme action that is implemented in the cooling jacket. An extended dynamic one-dimensional pseudohomogeneous model of a fixed-bed FTS reactor recently reported in the literature is used. The obtained results show the importance of the implementation of dynamic control strategies for the FTS carried out in a fixed-bed reactor, since they allow for ensuring the thermal control of such highly exothermic reactions and assure better reactor performance in terms of high CO conversion and liquid products selectivity (C5+).

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Abbreviations

A j :

j-th pre-exponential factor of FTS reaction, (J/mol)

C i :

Molar concentration of component i, (mol/m3)

C i ,0 :

Initial molar concentration of component i, (moli/m3)

\(C_{{{\text{P}}_{{{\text{mix,G}}}}}}\) :

Specific heat capacity of the gaseous mixture, (J/(Kg K))

\(C_{{{\text{P}}_{i}}}\) C Pi :

Specific heat capacity of component i, (J/(Kg K))

d p :

Average particle diameter, (m)

d t :

Diameter of the reactor tube, (m)

E a, j :

j-th Activation energy according to the Arrhenius equation, (J/mol)

f p :

Friction factor, (dimensionless)

h int :

Convective heat transfer coefficient on the side wall, (W/m2 K)

h ext :

Convective heat transfer coefficient on the side FTS reaction, (W/m2 K)

L B :

Catalytic bed length, (m)

m j :

j-th Reaction order for partial pressure of CO, (dimensionless)

Mmix,G :

Molecular weight of the gas mixture, (Kgmix/molmix)

n j :

j-th Reaction order for partial pressure of H2, (dimensionless)

p i :

Partial pressure of component i, (Pa)

P T :

Total system pressure, (Pa)

R j :

j-th reaction rate of Fischer–Tropsch synthesis, (mol/(Kgcat·s))

R :

Ideal gas constant, (8.314471 J/(mol K))

T :

Absolute temperature, (K)

T 0 :

Initial system temperature, (K)

u s :

Superficial gas velocity, (m3/(m2·s))

U r :

Overall heat transfer coefficient, (W/(m2·K))

y i :

Molar fraction of component i, (dimensionless)

z :

Axial coordinate, (m)

β :

Volume fraction of active site of the solid particles, (dimensionless)

δ W :

Tube wall thickness, (m)

ΔH FTS ,j :

j-th reaction heat (reaction enthalpy) of the Fischer–Tropsch synthesis, (J/Kg)

ε B :

Porosity of the catalytic bed, (m3(G+L)/m3)

λ w :

Thermal conductivity of the reactor wall, (J/(m·s·K))

μ i :

Dynamic viscosity of component i, (Kg/(m·s))

μ mix ,G :

Dynamic viscosity of the gaseous mixture, (Kg/(m·s))

ρ B :

Catalytic bed density, (Kg/(m3cat))

ρ mix ,G :

Density of gas mixture, (Kg/m3)

υ j :

Stoichiometric coefficient for the hydrogen consumption kinetic rate

B:

Referred to the catalytic bed reactor

calc:

Calculate value

CO:

Molecular carbon monoxide

exp:

Experimental value

FTS:

Fischer–Tropsch synthesis

G:

Gas

H2 :

Molecular hydrogen

i :

Component

mix:

Mixture

p:

Particle

r:

Referred to the reactor

s:

Referred to superficial velocity

t:

Reactor tube

W:

Water

0:

Initial condition

f :

Phase

m :

Reaction order for carbon monoxide

n :

Reaction order for hydrogen

Re:

Reynolds number

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Acknowledgements

The authors thank to the Instituto Mexicano del Petróleo for the financial support. C.I.M. thanks to the Consejo Nacional de Ciencia y Tecnología (CONACyT) for the PhD scholarship.

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Authors and Affiliations

  1. Instituto Politécnico Nacional, CICATA-Legaria. Legaria 694, Col. Irrigación, 11500, Mexico City, Mexico

    César I. Méndez & Fernando Trejo

  2. Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte 152, Col. San Juan Bartolo Atepehuacan, 07730, Mexico City, Mexico

    Jorge Ancheyta

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  1. César I. Méndez
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Méndez, C.I., Trejo, F. & Ancheyta, J. On the Use of Steady-State Optimal Initial Operating Conditions for Control Scheme Implementation of a Fixed-Bed Fischer–Tropsch Reactor. Arab J Sci Eng 47, 6099–6113 (2022). https://doi.org/10.1007/s13369-021-05897-w

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