Reversible Molten Catalytic Methane Cracking Applied to Commercial Solar-Thermal Receivers
Abstract
:1. Introduction
2. Materials and Methods
2.1. Reversible Catalytic Molten Methane Cracking Kinetics
2.2. Thermal Reactor Model
3. Results
3.1. Validation of Reversible Catalytic Molten Methane Cracking Kinetics
3.2. Solar Reactor Screening and Evaluation
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Appendix A.1. Greek Variable Definitions
α | fractional | effective absorptivity of a receiver surface from ray tracing |
ε | fractional | effective emissivity of a receiver surface from ray tracing |
η | % | energy efficiency of a solar receiver in hydrogen production |
ø | meters | diameter of a vessel. |
ρ | kg/m3 | density of molten 27% nickel, 73% bismuth [33,34] |
ρgas | kg/m4 | gas density |
ρinlet | kg/m5 | gas density at a reactor tube inlet temperature and pressure |
σ | W/(m2K4) | Stefan–Boltzmann constant [5.67…×10–8 W/(m2K4)] |
σYS(T) | Pa | Inconel temperature-dependent yield strength [46] |
Appendix A.2. English Variable Definitions
Abubble | m2 | area of bubble |
Abubblers | m2 | area of gas emanation on a gas distributor |
Atube | m2 | cross-sectional area of a bubbler (reactor) tube |
b | bubbles | number of bubbles initiated by a gas distributor |
ḃ | bubbles/sec | rate of bubble emanation from a gas distributor |
Cp,i | J/(mol·Kelvin) | heat capacity of chemical species i |
Ef | J/mol | forward reaction activation energy (Table 1) |
Er | J/mol | reverse reaction activation energy (Table 1) |
F | fractional | view factor [16] |
g | m/s2 | acceleration of gravity (9.81 m/s2) |
Gr | unitless | Grashoff number |
h | W/(m2Kelvin) | convective heat transfer coefficient to air [43] |
hwall | W/(m2Kelvin) | convective heat transfer coefficient to molten metal [44] |
H | meters | reactor tube manifold height |
ΔHrxn | J/mol | enthalpy of reaction |
kf | m/sec | forward Arrhenius preexponential (Table 1) |
kr | m4/sec | reverse Arrhenius preexponential (Table 1) |
k(T) | W/(m·Kelvin) | Inconel thermal conductivity at temperature T [46] |
Kc | mol/m3 | concentration equilibrium constant |
n | integer | number of tubes in a receiver manifold |
ṅinlet | mol/sec | mole flow of reactor tube gaseous feed |
nC | moles | moles of solid carbon |
nCH4 | moles | moles of gaseous methane |
nH2 | moles | moles of gaseous hydrogen |
ṅC | mol/sec | mole flow of solid carbon |
ṅCH4 | mol/sec | mole flow of gaseous methane |
ṅH2 | mol/sed | mole flow of gaseous hydrogen |
Nu | unitless | Nusselt number |
N(r) | W/m2 | flux at radial coordinate r in an Inconel tube wall |
Pe | unitless | Peclet number |
Pinlet | Pascals | reactor tube feed pressure |
P(z) | Pascals | axial pressure in a reactor tube at elevation z |
Qconvection | Watts | receiver losses to ambient air by natural convection |
Qfield | Watts | solar energy incident on a heliostat field reflective area |
Qradiative | Watts | receiver emissive losses by radiation |
Qwall | Watts | energy that trespasses a reactor tube interior wall |
Q(z) | m3/sec | volumetric flow at elevation z in a reactor tube |
r | meters | radial coordinate |
rbubble | meters | radius of a bubble |
rbubble,inlet | meters | initial radius of a bubble entering a reactor tube |
R | J/(mol·Kelvin) | gas constant |
ℜ | meters | inner radius of a reactor tube |
S | m2 | surface area of a solar receiver |
t | seconds | time coordinate |
T | Kelvin | isothermal reaction temperature |
Ts | Kelvin | outer Inconel solar receiver surface temperature |
Tw | Kelvin | inner Inconel reactor tube wall temperature |
vbubbler | m/sec | initial velocity of a bubble entering a reactor tube |
V | m3/sec | feed volumetric flow into a reactor tube |
Vbubble | m3 | volume of a bubble |
Vbubble,inlet | m3 | initial volume of a bubble entering a reactor tube |
w | meters | reactor tube Inconel wall thickness |
X | % | methane conversion to hydrogen gas |
yCH4 | fractional | mole fraction of gaseous methane |
yH2 | fractional | mole fraction of gaseous hydrogen |
z | meters | axial coordinate (elevation in a reactor tube) |
Z | unitless | compressibility factor from the SRK equation of state [35] |
Appendix B
Physical Property Correlations
Species | a1 | a2 | a3 | a4 |
---|---|---|---|---|
CH4 | 18.386286 | 5.470402(10−2) | 1.034479(10−5) | −9.833387(10−9) |
C | −5.394667 | 5.812952(10−2) | −4.177213(10−5) | −1.071678(10−8) |
H2 | 28.653517 | 7.762754(10−4) | 1.324842(10−7) | 6.664873(10−10) |
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Power Tower | Beam-Down | ||||
---|---|---|---|---|---|
Best Objective | Best Efficiency | Best Objective | Best Efficiency | ||
objective, ηX | %2 | 33 | 22 | 152 | 102 |
efficiency, η | % | 1.4 | 1.7 | 7.22 | 9 |
conversion X | % | 23.6 | 12.9 | 21.1 | 11.3 |
isothermal reaction, T | Kelvin | 1325 | 1265 | 1315 | 1255 |
inlet pressure, Pinlet | atm | 21.71 | 65.13 | 24.67 | 69.10 |
facility power, Qfield | MW | 144.3 | 190.0 | 24.7 | 34.1 |
convective losses, Qconvective | MW | 39.6 | 72.5 | 10.5 | 15.22 |
radiative losses, Qradiative | MW | 38.1 | 42.4 | 1.4 | 1.00 |
H2 produced | mol/sec | 44.88 | 73.73 | 39.23 | 64.31 |
reactor height, H | meters | 8.5 | 10.4 | 8.5 | 10.4 |
tube radius, ℜ | meters | 0.48 | 0.48 | 0.41 | 0.45 |
surface temperature, Ts | Kelvin | 1365 | 1330 | 1348 | 1318 |
wall temperature, Tw | Kelvin | 1350 | 1300 | 1337 | 1289 |
wall thickness, w | cm | 6.10 | 8.40 | 3.85 | 7.47 |
heliostat area, Amirrors | km2 | 0.18 | 0.24 | 0.03 | 0.04 |
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Rowe, S.C.; Ariko, T.A.; Weiler, K.M.; Spana, J.T.E.; Weimer, A.W. Reversible Molten Catalytic Methane Cracking Applied to Commercial Solar-Thermal Receivers. Energies 2020, 13, 6229. https://doi.org/10.3390/en13236229
Rowe SC, Ariko TA, Weiler KM, Spana JTE, Weimer AW. Reversible Molten Catalytic Methane Cracking Applied to Commercial Solar-Thermal Receivers. Energies. 2020; 13(23):6229. https://doi.org/10.3390/en13236229
Chicago/Turabian StyleRowe, Scott C., Taylor A. Ariko, Kaylin M. Weiler, Jacob T. E. Spana, and Alan W. Weimer. 2020. "Reversible Molten Catalytic Methane Cracking Applied to Commercial Solar-Thermal Receivers" Energies 13, no. 23: 6229. https://doi.org/10.3390/en13236229