# Theoretical Prediction of the Efficiency of Hydrogen Production via Alkane Dehydrogenation in Catalytic Membrane Reactor

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling and Calculations

#### 2.1. Description of the Reactor and the Mathematical Model

- The steady-state conditions are considered;
- The convective radial transfer is negligible;
- The axial dispersion is negligible (D/u·L < 0.01);
- The internal mass and energy transport limitations inside the catalyst pellets, as well as external mass and heat transfer resistances at the surface of the pellets, are negligible.

#### 2.2. Parameters of the Mathematical Model

#### 2.3. Reaction Kinetics

#### 2.3.1. Ethane Dehydrogenation

_{2}H

_{6}↔ C

_{2}H

_{4}+ H

_{2}, ΔH

_{298}= 137 kJ mol

^{−1}

_{2}O

_{3}catalyst with a granule diameter of 3.35 mm and a height of 3.63 mm, are used [27]. The reaction rate of ethane dehydrogenation is described as follows:

#### 2.3.2. Propane Dehydrogenation

_{3}H

_{8}↔ C

_{3}H

_{6}+ H

_{2}, ΔH

_{298}= 124 kJ mol

^{−1}

_{3}H

_{8}↔ C

_{2}H

_{4}+ CH

_{4}, ΔH

_{298}= 81 kJ mol

^{−1}

_{2}H

_{4}+ H

_{2}↔ C

_{2}H

_{6}, ΔH

_{298}= −137 kJ mol

^{−1}

#### 2.4. Numerical Solution of the Model Equations

## 3. Results and Discussion

_{p}) values less than or equal to 0.45 nm increases as along the reactor length as with the growth of d

_{p}(Figure 2a). At d

_{p}values above 0.45 nm, the profiles exhibit a falling tendency. The outlet conversion values tend to be near 39% (Figure 3).

_{p}value here is 0.5 nm. Propane conversion at such a value of the pore diameter reaches 86%, and the corresponding outlet hydrogen concentration in the shell side is equal to 0.08 m.f.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Model Equations

## Appendix B. List of Symbols

_{i}

^{t,c,m,s}—concentrations, kmol m

^{−3}

_{p}

^{t,s}—heat capacity of gas mixture, kJ g

^{−1}K

^{−1}

_{ei}

^{t,c,m}—effective coefficient of radial diffusion of component i, m

^{2}s

^{−1}

_{ij}—molecular diffusivity for component i in a binary mixture of i and j, m

^{2}s

^{−1}

_{m}

^{t,c,m}—coefficient of molecular diffusion, m

^{2}s

^{−1}

_{kn}—Knudsen diffusion coefficient, m

^{2}s

^{−1}

_{k}—diameter of catalyst, m

_{r}—diameter of membrane reactor, m

_{p}

^{c}—pore diameter of ceramic support, m

_{p}—membrane pore diameter, nm

^{t,s}—gas flow rate, ml min

^{−1}

_{j}—heat effect of reaction j, kJ mol

^{−1}

_{i}—molecular weight of ith compound, g mol

^{−1}

_{R}—number of reactions within the tube side of reactor

_{t,s}—number of components within the tube side/shell side of reactor

_{0}—pressure at normal conditions, atm

_{i}

^{t,s,c,m}—partial pressure of components, atm

_{1,2,3}—radial coordinate into the tube side, in the ceramic support, in membrane, m

_{cap}—capillary radius, m

_{r}—reactor radius, m

^{−1}K

^{−1}

_{sp}

_{1,sp2}—specific surface area, m

^{−1}

_{0}—temperature at normal conditions, K

^{t,s,c,m,w}—temperature, K

_{av}—average temperature, K

_{i}—average thermal velocity of molecule, cm s

^{−1}

_{l}

^{t,s}—axial velocity, m s

^{−1}

_{j}—rate of reaction, kmol kg

^{−1}s

^{−1}

_{i}—mole fraction of ith component

_{1,2}—heat-transfer coefficient between the membrane and fixed bed catalyst (shell); between the exterior wall of reactor and fixed bed catalyst (shell), kJ m

^{−2}s

^{−1}K

^{−1}

^{−1}

_{c,m}—ceramic support and membrane thickness, m

^{t,c,m}—porosity of catalyst layer (tube side); ceramic support and membrane

_{ij}—stoichiometric coefficient for ith component into jth reaction

^{t}

_{ef}—effective coefficient of radial thermal conductivity, J m

^{−1}s

^{−1}K

^{−1}

^{c,m}—thermal conductivity of the ceramic support, membrane, J m

^{−1}s

^{−1}K

^{−1}

^{−1}s

^{−1}

_{G}

^{t,s}—gas density, kg m

^{−3}

_{k}

^{t}—density of catalyst, kg m

^{−3}

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**Figure 2.**Hydrogen concentration profiles vs. reactor length for various diameters of the membrane pores: (

**a**) ethane dehydrogenation; (

**b**) propane dehydrogenation.

**Figure 4.**Hydrogen concentrations along the reactor length during the dehydrogenation process in a catalytic membrane reactor (d

_{p}= 0.45 nm) and a tubular reactor: (

**a**) ethane dehydrogenation; (

**b**) propane dehydrogenation.

**Figure 8.**Critical dimensions (CD) of the main reagent and product molecules used for the modelling: (

**a**) ethane; (

**b**) ethylene; (

**c**) propane; (

**d**) propylene.

**Figure 9.**Concentration profiles along the reactor length: ethylene in the tube side (

**a**); propylene in the tube side (

**b**); sum of ethane and ethylene in the shell side (

**c**); sum of propane and propylene in the shell side (

**d**).

Parameter, Dimension | Value | Parameter, Dimension | Value |
---|---|---|---|

L, m | 0.15 | T^{w}, °C | 500 |

r_{1}, m | 0.39 × 10^{−2} | T_{in}^{t,s}, °C | 100 |

d_{r}, m | 0.2 × 10^{−1} | P^{t}, atm | 1.5 |

δ_{c}, m | 0.11 × 10^{−2} | P^{s}, atm | 1 |

δ_{m}, m | 4 × 10^{−6} | G^{t}, ml·min^{−1} | 22 |

d_{p}^{c}, m | 1 × 10^{−6} | G^{s}, ml·min^{−1} | 75 |

d_{k}, m | 0.15 × 10^{−2} | $C{}^{t}{}_{{C}_{n}{H}_{2n+2},in}$, m.f. | 0.1 |

ρ_{k}^{t}, g·m^{−3} | 0.2 × 10^{7} | ${C}^{t}{}_{{N}_{2},in}$, m.f. | 0.9 |

ε^{t} | 0.5 | μ_{g}, kg m^{−1} s^{−1} | 1.67 × 10^{−5} |

ε^{c} | 0.28 | λ^{c,m}, J m ^{−1} s^{−1} K^{−1} | 0.1 |

ε^{m} | 0.14 |

Reaction Rate and Rate Constant Equations | Reaction Rate Constant at T_{0}, mmol·g^{−1}min^{−1}bar^{−1} | Activation Energy, kJ mol^{−1} |
---|---|---|

$-{w}_{{\mathrm{C}}_{3}{\mathrm{H}}_{8}}=\frac{{k}_{1}({P}_{{\mathrm{C}}_{3}{\mathrm{H}}_{8}}-({P}_{{\mathrm{C}}_{3}{\mathrm{H}}_{6}}{P}_{{\mathrm{H}}_{2}}/{K}_{eq}))}{1+({P}_{{\mathrm{C}}_{3}{\mathrm{H}}_{6}}/{K}_{{\mathrm{C}}_{3}{\mathrm{H}}_{6}})}$ ${k}_{1}={k}_{01}{\mathrm{exp}}^{[-{E}_{a1}/R((1/T)-(1/{T}_{0}))]}$ ${K}_{{\mathrm{C}}_{3}{\mathrm{H}}_{6}}={K}_{0}{\mathrm{exp}}^{[-\Delta H/R((1/T)-(1/{T}_{0}))]}$ | k_{01} = 0.5242$\Delta H$ = −85.817 kJ mol ^{−1}K _{0} = 3.46 | E_{a1} = 34.57 |

$-{w}_{2}={k}_{2}{P}_{{\mathrm{C}}_{3}{\mathrm{H}}_{8}}$ ${k}_{2}={k}_{02}{\mathrm{exp}}^{[-{E}_{a2}/R((1/T)-(1/{T}_{0}))]}$ | k_{02} = 0.00465 | E_{a2} = 137.31 |

$-{w}_{3}={k}_{3}{P}_{{\mathrm{C}}_{2}{\mathrm{H}}_{4}}{P}_{{\mathrm{H}}_{2}}$ ${k}_{3}={k}_{03}{\mathrm{exp}}^{[-{E}_{a3}/R((1/T)-(1/{T}_{0}))]}$ | k_{03} = 0.000236 | E_{a2} = 154.54 |

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**MDPI and ACS Style**

Shelepova, E.V.; Vedyagin, A.A.
Theoretical Prediction of the Efficiency of Hydrogen Production via Alkane Dehydrogenation in Catalytic Membrane Reactor. *Hydrogen* **2021**, *2*, 362-376.
https://doi.org/10.3390/hydrogen2030019

**AMA Style**

Shelepova EV, Vedyagin AA.
Theoretical Prediction of the Efficiency of Hydrogen Production via Alkane Dehydrogenation in Catalytic Membrane Reactor. *Hydrogen*. 2021; 2(3):362-376.
https://doi.org/10.3390/hydrogen2030019

**Chicago/Turabian Style**

Shelepova, Ekaterina V., and Aleksey A. Vedyagin.
2021. "Theoretical Prediction of the Efficiency of Hydrogen Production via Alkane Dehydrogenation in Catalytic Membrane Reactor" *Hydrogen* 2, no. 3: 362-376.
https://doi.org/10.3390/hydrogen2030019