Numerical Simulation and Optimization of Microwave Heating Effect on Coal Seam Permeability Enhancement
Abstract
:1. Introduction
- The electric field profile must be homogeneous, either by using state stirrers or by rotating the reaction cavity itself.
- The geometry of the reactor must be well designed considering the depth of microwave penetration.
- The temperature and pressure inside the reaction chamber must be controlled for a continuous control of the process parameters.
- The costs of the reactor and spare parts must be considered.
- Safety and leakage of microwaves must be considered.
2. Theory
2.1. Symbols
2.2. Maxwell Equations
2.3. Heat Transfer
2.4. Mass Transfer
2.5. System Design
2.6. Initial Conditions
2.7. Boundary Conditions
2.8. Assumptions
- The microwave only heats the specimen placed inside it and has no effect on the air or the glass container on which the specimen is placed.
- The wall material is assumed to be copper.
- The specimens placed in the microwave oven are isotropic and homogeneous.
- The electrical, magnetic and thermal properties of coal are constant.
- The motion of water molecules in the magnetic and electric field is simplified as a fixed mass transfer.
- The chemical reaction of objects is ignored (the ignition temperature of coal is 360 °C [20]).
3. Methodology
4. Tests and Simulations
4.1. Coal Moisture Capacity
4.2. Effect of Microwave Operating Frequency
4.3. Effect of the Microwave Power and Heating Time
4.4. Effect of the Waveguide Port Location
4.5. Effect of the Waveguide Chamber Size
4.6. Place of Coal
5. Changing Cavity Size
5.1. Coal Moisture Capacity
5.2. Microwave Frequency
5.3. Microwave Time and Power
5.4. Waveguide Place
5.5. Waveguide Size
5.6. Place of Coal
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Name | Symbol | Name | Symbol | Name | Symbol |
---|---|---|---|---|---|
electric field intensity (V/m) | E | electric current density (A/m2) | J | relative permittivity | εr |
magnetic field intensity (A/m) | H | electric charge density (C/m3) | P | free space wave number | k0 |
electric flux density (C/m) | D | permeability (H/m) | μ | conductivity | σ |
magnetic flux density (Wb/m) | B | relative permeability | μr | angular frequency | ω |
magnetic current density (V/m2) | M | permittivity (F/m) | ε | surface normal vector | N |
density (kg/m3) | ρ | heat flux (W/m2) | q | mass averaged velocity vector (m/s) | u |
specific heat capacity at constant stress (J/(kg·K)) | Cp | material’s conductivity | k | reaction rate for the species (mol/(m3·s)) | R |
absolute temperature (K) | T | time | t | diffusive flux vector (mol/(m2·s) | Jm |
heat source (W/m3) | Q | concentration of species (mol/m3) | c | Cutoff frequency | fc |
velocity vector of translational motion (m/s) | U | diffusion coefficient (m2/s) | Dc | Speed of light | C0 |
wavelength | λ | moisture conductivity | km | dynamic viscosity (kg/m·s) | v |
Rayleigh number | RaL | specific moisture capacity | Cm | mass transfer coefficient | kc |
length | L |
Width (mm) | Depth (mm) | Height (mm) | Radius (mm) | |
---|---|---|---|---|
Microwave oven | 267 | 270 | 188 | - |
Waveguide | 50 | 78 | 18 | - |
Glass plate | - | - | 6 | 113.5 |
Sample | - | - | 60 | 25 |
Name | Units | Values | |||
---|---|---|---|---|---|
Material | - | Coal | Glass | Copper | Air |
Relative permittivity (ε′-jε″) | - | Variable | 2.55 | 1 | 1 |
Relative permeability (μ′-jμ″) | - | 1 | 1 | 1 | 1 |
Electrical conductivity | S/m | 0.02 | 0 | 5.998 × 107 | 0 |
Thermal conductivity | W/(m·k) | 0.478 | - | 400 | 0.0256 |
Density | Kg/m3 | 1300 | - | 8960 | 1.204 |
Heat capacity at constant pressure | J/(kg·K) | 4186.8 | - | 385 | 1015.1 |
Specific Moisture Capacity (Cm %) | Real Permittivity (ε′) | Imaginary Permittivity (ε″) | Diffusion Coefficient (D m2/s) |
---|---|---|---|
0.5 | 0.578 | 0.161 | 1.47 × 10−2 |
1 | 0.852 | 0.178 | 7.37 × 10−3 |
2 | 1.401 | 0.211 | 3.69 × 10−3 |
3 | 1.949 | 0.245 | 2.46 × 10−3 |
4 | 2.498 | 0.278 | 1.84 × 10−3 |
4.7 | 2.882 | 0.301 | 1.57 × 10−3 |
5 | 3.046 | 0.311 | 1.47 × 10−3 |
6 | 3.595 | 0.345 | 1.23 × 10−3 |
7 | 4.143 | 0.378 | 1.05 × 10−3 |
8 | 4.692 | 0.411 | 9.22 × 10−4 |
9 | 5.240 | 0.444 | 8.19 × 10−4 |
10 | 5.789 | 0.478 | 7.37 × 10−4 |
Parameter | Unit | Value | |||||
---|---|---|---|---|---|---|---|
Power | W | 500 | 1000 | 1500 | 2000 | 2500 | 3000 |
Time | s | 600 | 300 | 200 | 150 | 120 | 100 |
Waveguide | Width (m) | Height (m) | Depth (m) |
---|---|---|---|
1 | 0.078 | 0.018 | 0.05 |
2 | 0.078 | 0.039 | 0.05 |
3 | 0.078 | 0.018 | 0.1 |
4 | 0.064 | 0.018 | 0.05 |
5 | 0.091 | 0.018 | 0.05 |
z1 = 0.022 | z2 = 0.042 | z3 = 0.062 | z4 = 0.082 | z5 = 0.102 | z6 = 0.122 | |
---|---|---|---|---|---|---|
x1 = 0.03 m | 8871.3 | 8972.2 | 8216.8 | 5301.3 | 5633 | 10,621 |
x2 = 0.1335 m | 13,468 | 7576.1 | 7252.4 | 14,502 | 8077.2 | 7613 |
x3 = 0.237 m | 10,248 | 10,938 | 11,740 | 8768.7 | 11,305 | 17,366 |
Waveguide | Width (m) | Height (m) | Depth (m) |
---|---|---|---|
1 | 0.078 | 0.018 | 0.05 |
2 | 0.078 | 0.039 | 0.05 |
3 | 0.078 | 0.018 | 0.1 |
4 | 0.064 | 0.018 | 0.05 |
5 | 0.091 | 0.018 | 0.05 |
z1 = 0.022 | z2 = 0.042 | z3 = 0.062 | z4 = 0.082 | z5 = 0.102 | z6 = 0.122 | |
---|---|---|---|---|---|---|
x1 = 0.03 m | 48,921 | 17,035 | 12,489 | 17,755 | 18,440 | 12,992 |
x2 = 0.1485 m | 25,998 | 15,330 | 16,072 | 17,902 | 14,317 | 14,453 |
x3 = 0.267 m | 22,924 | 18,672 | 13,708 | 15,357 | 28,802 | 23,911 |
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Jebelli, A.; Mahabadi, A.; Ahmad, R. Numerical Simulation and Optimization of Microwave Heating Effect on Coal Seam Permeability Enhancement. Technologies 2022, 10, 70. https://doi.org/10.3390/technologies10030070
Jebelli A, Mahabadi A, Ahmad R. Numerical Simulation and Optimization of Microwave Heating Effect on Coal Seam Permeability Enhancement. Technologies. 2022; 10(3):70. https://doi.org/10.3390/technologies10030070
Chicago/Turabian StyleJebelli, Ali, Arezoo Mahabadi, and Rafiq Ahmad. 2022. "Numerical Simulation and Optimization of Microwave Heating Effect on Coal Seam Permeability Enhancement" Technologies 10, no. 3: 70. https://doi.org/10.3390/technologies10030070