On Process Intensification through Membrane Storage Reactors
Abstract
1. Introduction
2. Mathematical Formulation
2.1. Limiting Reactant Conversion
2.2. Desired Product Ratio
2.3. Desired Product Recovery Fraction
3. Steam Methane Reforming (SMR) Case Study
3.1. OM 1: MSR Loading-Reaction/Storage Phase
3.2. OM 2: MSR Decarbonization/Maintenance Phase
3.3. Phase 3: MSR Unloading-Production/Emptying Phase
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
Nomenclature
English Symbols | |
Verhulst function parameter. | |
Reactor cross section area | |
Verhulst function parameter. | |
species concentration in gas phase of void and storage domains | |
effective diffusivity | |
binary diffusion coefficient | |
Reference Damköhler number | |
Pellet diameter | |
species | |
Reference axial molar flowrate | |
species | |
operating mode (OM) specific Heaviside function. | |
Rate coefficients for SMR reactions | |
Equilibrium constants for SMR reactions | |
Species adsorption constants for SMR reactions | |
Reactor Length | |
Characteristic length | |
Number of species | |
Number of reactor operating modes | |
Operating mode | |
species partial pressure in gas phase of void and storage domains | |
species dimensionless partial pressure in gas phase of void and storage domains | |
Ratio of inlet partial pressure for species i for operating mode k-1, based on operating mode k = 1 | |
Ratio of inlet partial pressure for species i for operating mode k, based on operating mode k = 1 | |
Reference pressure | |
Peclet number for convective to diffusive mass transport | |
Peclet number for membrane to convective transport | |
species reaction-based generation rate | |
species dimensionless reaction-based generation rate | |
Reference reaction generation rate | |
species produced during all OM’s | |
SMR reaction | |
SMR reaction | |
Universal Gas Constant | |
Limiting reactant used in performance metric calculations | |
species into the gas phase of the voids domain due to transport from the gas phase in the storage domain | |
species into the gas phase of the storage domain due to transport from the gas phase in the voids domain | |
Time | |
Dimensionless time | |
Reference time, chosen as the residence time | |
Temperature in all reactor domains | |
Total reactor volume | |
effective velocity | |
gas velocity in reactor void domain | |
Reference velocity, chosen as gas inlet velocity during OM 1 | |
Dimensionless gas velocity in reactor void domain | |
over all OM’s | |
Verhulst function for switching between inlet boundary conditions during OM change. | |
Reactor axial coordinate | |
Reactor dimensionless axial coordinate | |
Geek Symbols | |
Storage-void domain interfacial area per unit volume of reactor system | |
species permeance through storage medium permselective layer | |
Volume fractions of voids, catalyst, storage, gas phase in storage domain, and solid phase in storage domain | |
Catalyst effectiveness factor | |
Dimensionless number quantifying membrane permeation to convection (inverse Peclet) | |
Catalyst pellet density | |
over limiting reactant fed throughout all OM’s | |
species produced during all OMs over limiting reactant fed throughout all OM’s | |
operating mode | |
operating mode |
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Rate Coefficient or Adsorption Constant | Pre-Exponential Factor | Unit Pre-Exponential Factor | Activation Energy or Adsorption Enthalpy |
---|---|---|---|
Equilibrium Constant | Units |
---|---|
Trial | Da | Θ | |||
---|---|---|---|---|---|
1 | 1 | 1 | 0.717543 | 1.00 | 0.674081 |
2 | 1 | 10 | 0.755321 | 1.00 | 2.261037 |
3 | 1 | 30 | 0.752953 | 1.00 | 2.049624 |
4 | 1 | 40 | 0.762492 | 1.00 | 1.941365 |
5 | 1 | 50 | 0.742631 | 1.00 | 1.814203 |
6 | 2 | 1 | 0.545116 | 1.00 | 0.367633 |
7 | 2 | 10 | 0.565994 | 1.00 | 2.509012 |
8 | 2 | 30 | 0.587789 | 1.00 | 1.998005 |
9 | 2 | 40 | 0.588387 | 1.00 | 1.8797 |
10 | 2 | 50 | 0.597422 | 1.00 | 1.754175 |
11 | 4 | 1 | 0.405848 | 1.00 | 0.24924 |
12 | 4 | 10 | 0.428648 | 1.00 | 2.455872 |
13 | 4 | 50 | 0.466553 | 1.00 | 1.713176 |
14 | 6 | 1 | 0.363228 | 1.00 | 0.222919 |
15 | 6 | 10 | 0.389041 | 1.00 | 2.457342 |
16 | 6 | 50 | 0.388379 | 1.00 | 1.76623 |
Trial | Da | Θ | |||||
---|---|---|---|---|---|---|---|
1 | 1 | 1 | 0.268297 | 0.2205 | 0.925244 | 0.8505 | 0.133693 |
2 | 1 | 10 | 0.486804 | 0.2205 | 2.06218 | 0.8505 | 0.851397 |
3 | 1 | 30 | 0.51877 | 0.2205 | 2.172158 | 0.8505 | 0.874449 |
4 | 1 | 40 | 0.527766 | 0.2205 | 2.211969 | 0.8505 | 0.883636 |
5 | 1 | 50 | 0.557738 | 0.2205 | 2.317619 | 0.8505 | 0.895902 |
6 | 2 | 1 | 0.332334 | 0.2564 | 1.027561 | 0.9858 | 0.114506 |
7 | 2 | 10 | 0.555291 | 0.2564 | 2.311048 | 0.9858 | 0.828753 |
8 | 2 | 30 | 0.657883 | 0.2564 | 2.710915 | 0.9858 | 0.90206 |
9 | 2 | 40 | 0.683793 | 0.2564 | 2.797332 | 0.9858 | 0.917312 |
10 | 2 | 50 | 0.696967 | 0.2564 | 2.856135 | 0.9858 | 0.923089 |
11 | 4 | 1 | 0.406878 | 0. 2866 | 1.140335 | 1.102 | 0.122357 |
12 | 4 | 10 | 0.719437 | 0. 2866 | 2.918608 | 1.102 | 0.868964 |
13 | 4 | 50 | 0.900393 | 0. 2866 | 3.638564 | 1.102 | 0.958944 |
14 | 6 | 1 | 0.430822 | 0.2913 | 1.165753 | 1.131 | 0.122353 |
15 | 6 | 10 | 0.795136 | 0.2913 | 3.205293 | 1.131 | 0.884476 |
16 | 6 | 50 | 0.974497 | 0.2913 | 3.931581 | 1.131 | 0.972301 |
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Lowd, J., III; Tsotsis, T.; Manousiouthakis, V.I. On Process Intensification through Membrane Storage Reactors. Separations 2021, 8, 195. https://doi.org/10.3390/separations8110195
Lowd J III, Tsotsis T, Manousiouthakis VI. On Process Intensification through Membrane Storage Reactors. Separations. 2021; 8(11):195. https://doi.org/10.3390/separations8110195
Chicago/Turabian StyleLowd, John, III, Theodore Tsotsis, and Vasilios I. Manousiouthakis. 2021. "On Process Intensification through Membrane Storage Reactors" Separations 8, no. 11: 195. https://doi.org/10.3390/separations8110195
APA StyleLowd, J., III, Tsotsis, T., & Manousiouthakis, V. I. (2021). On Process Intensification through Membrane Storage Reactors. Separations, 8(11), 195. https://doi.org/10.3390/separations8110195