Synthesis and Mathematical Modelling of the Preparation Process of Nickel-Alumina Catalysts with Egg-Shell Structures for Syngas Production via Reforming of Clean Model Biogas
Abstract
:1. Introduction
2. Theory/Calculation
- i.
- The catalyst support consists of distinct, dry, homogenous, and isotropic catalytic particles of cylindrical geometry, non-deformable and not interacting.
- ii.
- The total amount of the impregnating solution is sufficient to fill the water pore volume of the support.
- iii.
- The impregnating solution is a Newtonian and incompressible liquid.
- iv.
- The support pore surface is water wet. The capillary force can be characterized by a single average pore size.
- v.
- The size of the pores of the support is in the order of several nanometers so that gravity force is negligibly small compared with viscous and capillary forces, but the pores are large enough so that exclusion of the solutes is avoided.
- vi.
- Inertial forces are negligible and quasi steady-state approximation is justified.
- vii.
- Air initially filling the pore space is either totally entrapped and compressed in the center of the pellet or totally escaped from it.
- viii.
- Imbibition can be thought as one-phase radial plug flow through the porous support material with the sharp liquid front separating the advancing liquid and the receding air. The cylindrical pellets are long enough so that edge effects can be ignored. Darcy’s law is applicable, and the absolute permeability of the porous support is the pertinent parameter.
- ix.
- Hydrodynamic dispersion of the active species is taken into account through a dispersion coefficient that combines effective diffusivity and mechanical dispersion.
- x.
- Non-equilibrium processes such as dynamic contact angle, surface viscosity, and dynamic surface tension are not important. Dynamics of thin liquid films do not influence imbibition flow.
- xi.
- Surface diffusion of the active species does not take place.
- xii.
- Deposition of the active species on the supporting material pore surface takes place through isothermal adsorption (sorption and desorption), the overall rate of which is described by a consistent physicochemical deposition model.
3. Results and Discussion
3.1. Catalysts Characterization
3.1.1. Physicochemical Properties
3.1.2. Crystal Structure
3.1.3. Electron Microscopy
3.2. Model Implementation
3.3. Biogas Reforming over Ni/Al2O3 Catalysts
3.3.1. Catalytic Activity
3.3.2. Catalysts Stability
4. Materials and Methods
4.1. Catalysts Preparation
4.2. Catalysts Characterization and Testing
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
inverse measure of the capillary force, dim/less | |
concentration of aqueous solution of ammonium hydroxide, NH4OH, M | |
average pore diameter, m | |
initial concentration of the impregnating liquids, M | |
dispersion coefficient of the k-th active species, m2/s | |
Nickel dispersion coefficient, m2/s | |
rate of adsorption of the k-th active species, dim/less | |
absolute permeability, m2 | |
Langmuir isotherm adsorption constant of the k-th active species, | |
Nickel Langmuir isotherm adsorption constant, | |
modified Langmuir adsorption constant of the k-th active species, dim/less | |
Nickel modified Langmuir adsorption constant, dim/less | |
generalized mass transfer coefficient based on Langmuir isotherm of the k-th active species, dim/less | |
adsorption kinetic constant of the k-th active species, m3·pore volume | |
Nickel adsorption kinetic constant, m3·pore volume m solid volume/kg·s | |
desorption kinetic constant of the k-th active species, m solid/s | |
Nickel desorption kinetic constant, m solid/s | |
Nickel Langmuir isotherm adsorption constant, | |
pellet average length, m | |
relative adsorption capacity of the k-th active species, dim/less | |
Nickel relative adsorption capacity, dim/less | |
saturation surface concentration of the k-th active species, kg/m3 solid volume | |
Nickel saturation surface concentration, kg/m3 solid volume | |
dimensionless pressure | |
atmospheric pressure, N/m2 | |
capillary pressure, N/m2 | |
local (time dependent) Péclet number of the k-th active species, dim/less | |
characteristic (time independent) Péclet number of the k-th active species, dim/less | |
Nickel characteristic (time independent) Péclet number, dim/less | |
radial coordinate, m | |
liquid front position, m | |
pellet radius, m | |
pellet surface area, m2/kKg | |
local (time dependent) Stanton number of the k-th component, dim/less | |
characteristic (time independent) Stanton number of the k-th component, dim/less | |
Nickel characteristic (time independent) Stanton number, dim/less | |
time, s | |
characteristic imbibition time, s | |
imbibition termination time, s | |
impregnating solution concentration of the k-th component, dim/less | |
local (time dependent) interstitial liquid pore velocity, m/s | |
local (time dependent) interstitial liquid pore velocity, dim/less | |
characteristic (time independent) interstitial liquid pore velocity, dim/less | |
pellet pore volume, m3 pore volume/kg | |
mean pore radius, m | |
specific catalytic surface, m2 solid surface/m3 total volume | |
surface tension, Ν/m | |
ε | porosity, m3 pore volume/m3 total volume |
equilibrium contact angle, radian | |
dimensionless surface concentration of the k-th component | |
dimensionless Nickel surface concentration | |
viscosity of the impregnating solution, Pa s | |
ratio of solid to pore pellet volume, m3 solid volume/m3 pore volume | |
dimensionless radial space coordinate | |
dimensionless liquid front position | |
termination liquid front position, dim/less | |
pellet bed density, kKg/m3 | |
mass concentration of the k-th active species in the liquid (fluid) phase, kg/m3 pore volume | |
equilibrium mass concentration of the k-th active species in the liquid (fluid) phase, kg/m3 pore volume | |
Nickel mass concentration in the liquid (fluid) phase, kKg/m3 pore volume | |
initial mass concentration of the k-th active species in the impregnating liquid, kKg/m3 liquid volume | |
Nickel initial mass concentration in the impregnating liquid, kKg/m3 liquid volume | |
mass concentration of the k-th active species in the solid phase, kKg/m3 solid volume | |
Nickel mass concentration in the solid phase, kg/m3 solid volume | |
dimensionless capillary pressure | |
dimensionless time variable | |
imbibition termination time, dim/less | |
dimensionless radial space coordinate with respect to liquid front position |
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Catalyst | SBET (m2 g−1) | ICP (Ni, wt%) | Crystalline Phase (XRD) | Ni Species Particle Size (nm) |
---|---|---|---|---|
6Ni/Al-edf | 173 | 5.90 ± 0.9 | γ-Al2O3, NiAl2O4 + | 12.1 ± 1.2 |
16Ni/Al-edf | 137 | 16.80 ± 0.8 | γ-Al2O3, NiAl2O4 +++ | 17.2 ± 1.9 |
6Ni/Al-wet | 163 | 5.91 ± 0.3 | γ-Al2O3, NiAl2O4 ++ | 14.1 ± 1.7 |
16Ni/Al-wet | 141 | 15.87 ± 0.7 | γ-Al2O3, NiAl2O4 ++++ | 25.1 ± 2.1 |
Element | Atomic (%) Periphery, 6Ni/Al-wet | Atomic (%) Center, 6Ni/Al-wet | Atomic (%) Periphery, 6Ni/Al-edf | Atomic (%) Center, 6Ni/Al-edf | Atomic (%) Periphery, 16Ni/Al-wet | Atomic (%) Center, 16Ni/Al-wet | Atomic (%) Periphery, 16Ni/Al-edf | Atomic (%) Center, 16Ni/Al-edf |
---|---|---|---|---|---|---|---|---|
Al K | 91.68 | 92.38 | 92.18 | 95.47 | 80.65 | 86.11 | 80.05 | 95.20 |
Ni K | 8.32 | 7.62 | 7.82 | 4.53 | 19.35 | 13.89 | 19.95 | 4.80 |
Total | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
Study | Ref. [54] | Ref. [46] | Ref. [89] | This Study (6Ni/Al-edf) | This Study (16Ni/Al-edf) | |
---|---|---|---|---|---|---|
Solution Properties | C° = n/a | C° = 0.0012–0.003 M | C° = 0.002 M | C° = 0.17 M | C° = 0.34 M | |
Estimated Parameters | pH = 5.2 | pH = 6.2 | pH = 10.6 | pH = 7.0 | pH = 7.0 | |
Kp (l mol−1) | 326 | 408 | 1422 | 715 ± 842 | 781 ± 226 | |
ns (μmol m−2) | 0.50 | 0.60 | 1.82 | 46.45 ± 19.16 | 133.71 ± 8.51 | |
DL (m2 s−1) | - | - | - | 2.93 10−8 ± 1.66 10−8 | 2.50 10−8 ± 8.28 10−1 |
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Latsiou, A.I.; Bereketidou, O.A.; Charisiou, N.D.; Georgiadis, A.G.; Avraam, D.G.; Goula, M.A. Synthesis and Mathematical Modelling of the Preparation Process of Nickel-Alumina Catalysts with Egg-Shell Structures for Syngas Production via Reforming of Clean Model Biogas. Catalysts 2022, 12, 274. https://doi.org/10.3390/catal12030274
Latsiou AI, Bereketidou OA, Charisiou ND, Georgiadis AG, Avraam DG, Goula MA. Synthesis and Mathematical Modelling of the Preparation Process of Nickel-Alumina Catalysts with Egg-Shell Structures for Syngas Production via Reforming of Clean Model Biogas. Catalysts. 2022; 12(3):274. https://doi.org/10.3390/catal12030274
Chicago/Turabian StyleLatsiou, Angeliki I., Olga A. Bereketidou, Nikolaos D. Charisiou, Amvrosios G. Georgiadis, Dimitrios G. Avraam, and Maria A. Goula. 2022. "Synthesis and Mathematical Modelling of the Preparation Process of Nickel-Alumina Catalysts with Egg-Shell Structures for Syngas Production via Reforming of Clean Model Biogas" Catalysts 12, no. 3: 274. https://doi.org/10.3390/catal12030274