Dynamic Modeling and Control of an Integrated Reformer-Membrane-Fuel Cell System
Abstract
:1. Introduction
2. System Description
2.1. Fuel Processing Subsystem: Auto Thermal Reformer
Mathematical Model of Auto Thermal Reformer
2.2. Fuel Purification Subsystem: Palladium Based Membrane Separation
Mathematical Model of Palladium Membrane Separation
2.3. Power Generation Subsystem: PEMFC
Mathematical Model of PEMFC
2.4. Integrated Reformer Membrane Fuel Cell System
2.5. Numerical Solution of the Integrated System
2.6. Controllability Analysis and Choice of Pairing
3. Case Studies: Dynamic Analysis and Control of the Integrated System
3.1. Case Study 1: Open Loop Simulation for Start-up of Integrated Reformer-Membrane-Fuel Cell System
Relative Gain Array (RGA) Analysis
3.2. Case Study 2: Integrated System Delivering Target Power Demand
3.3. Case Study 3: Disturbance in both the Reformer Inlet Feed Concentration and Coolant Temperature
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
ratio of water molecules per proton (molecules proton) | |
heat of reaction (kJ mol) | |
packing bed porosity | |
effectiveness factor of reaction j | |
over potential (V) | |
effective thermal conductivity (W(mK)) | |
water viscosity (g cms) | |
density of the catalyst bed (kg m) | |
density of the catalyst pellet (kg m) | |
density of the fluid (kg m) | |
density of the solid (kg m) | |
density of dry membrane of fuel cell (g cm) | |
ionic conductivity of the fuel cell membrane (Ohm cm) | |
Pd membrane poisoning caused by the adsorption of | |
A | heat exchange area per unit length (cm) |
area of the fuel flow pipe to the reformer inlet (m) | |
activity of water in stream k | |
external catalyst surface area per unit volume of catalyst bed (mm) | |
Pd membrane surface area (m) | |
molar concentration of species i in the gas phase (mol m) | |
molar heat capacity (J(g mol K)) | |
concentration of water in the membrane of fuel cell (mol cm) | |
molar concentration of in the line pack (mol m) | |
molar concentration of species i in the solid phase (mol m) | |
specific heat of the catalyst bed (J (kg K)) | |
specific heat of the fluid (J (kg K)) | |
control valve 1 flow coefficient | |
control valve 2 flow coefficient | |
concentration of water at k interface of the membrane of fuel cell (mol cm) | |
D | diffusion coefficient of water in membrane of fuel cell (cm s ) |
d | fuel cell channel height (cm) |
axial dispersion coefficient (m s ) | |
e | membrane area per unit length (cm) |
activation energy for permeability (J mol) | |
F | Faraday’s constant (C mol) |
f | cross-section of solid in fuel cell (cm) |
opening of control valve 1 (%) | |
opening of control valve 2 (%) | |
piping geometry factor | |
h | fuel cell channel width (cm) |
gas to solid heat transfer coefficient (W ms) | |
I | current density (A cm) |
exchange current density (A cm) | |
k | heat conduction coefficient (W (cmK)) |
condensation rate constant (s) | |
parameter corresponding to the viscous loss term (Pa s m) | |
parameter corresponding to the kinetic loss term (Pa s m) | |
gas to solid mass transfer coefficient of component i (m s) | |
Pd membrane thickness (m) | |
M | molar flow rate (mol s) |
equivalent weight of dry membrane of fuel cell (g mol) | |
n | pressure exponent |
number of electrons taking part in charge reactions | |
molar flux of species i (mol s cm) | |
P | pressure (atm) |
vapor pressure of water in channel | |
permeability of Pd membrane (mol (msPa) | |
permeability pre-exponential factor (mol (msPa) | |
methane fuel storage pressure (atm) | |
R | gas constant (J (mol K)) |
rate of consumption or formation of species i (mol (kgs)) | |
rate of reaction j (mol (kgs)) | |
t | time (s) |
reformer gas temperature (K) | |
fuel cell membrane thickness (cm) | |
fuel cell solid temperature (K) | |
gas temperature at the exit of heat exchanger 1 (K) | |
ambient temperature (K) | |
methane fuel storage temperature (K) | |
U | convective heat transfer coefficient (W cm K) |
u | superficial gas flow velocity (m s) |
V | volume of the line pack (m) |
cell voltage (V) | |
open circuit voltage (V) | |
W | molecular weight (kg mol) |
X | ratio of pressure drop to the absolute inlet pressure |
x | direction along the fuel cell channel length (cm) |
Y | expansion factor |
Z | compressibility factor |
z | axial dimension (m) |
Suffixes
a | anode |
c | cathode |
g | gas |
m | line pack |
s | solid |
sat | saturation |
w | water |
Appendix A. Data for the Base Case
Parameter | Values |
(mol m) | 9.1705 |
(mol m) | 4.1273 |
(mol m) | 0.0001 |
(mol m) | 9.1705 |
(mol m) | 0.0001 |
(mol m) | 0.0001 |
(mol m) | 15.5287 |
(K) | 815 |
(K) | 815 |
(mol m) | 0.001 |
(mol s) | |
(mol s) | |
(mol s) | 0 |
(mol s) | 0 |
(mol s) | |
(mol s) | |
(K) | 353 |
(K) | 353 |
(K) | 340 |
(K) | 342 |
Appendix B. Parameter Values Used for Simulation
Parameter | Values |
0.4 | |
z (m) | 0.2 |
(m s) | |
(m) | 1200 |
(kg m) | 1870 |
(kg m) | 1122 |
(J kg K) | 850 |
(kJ mol) | 206.2 |
(kJ mol) | 164.9 |
(kJ mol) | −41.1 |
(kJ mol) | −802.7 |
(K) | 0.07 |
(K) | 0.06 |
(K) | 0.7 |
(K) | 0.05 |
(K) | |
0.2 | |
(m) | 0.0064 |
(m) | 0.0001 |
R (J mol K) | 8.314 |
n | 0.67 |
(mol m s Pa) | 0.4 |
(J mol) | 8000 |
x (cm) | 10 |
h (cm) | 0.1 |
d (cm) | 0.1 |
F (C mol) | 96484.69 |
(s) | 100 |
(atm) | 1 |
(atm) | 1 |
(W cm K) | 0.025 |
(cm) | 0.4 |
(W cm K) | 0.025 |
(cm) | 0.4 |
(J g mol K) | 75.38 |
(mol s) | |
(g cm) | 2 |
(J g mol K) | 1 |
(W cm K) | 0.005 |
e (cm) | 0.1 |
(W cm K) | 0.025 |
(K) | 350 |
(V) | 1.1 |
(cm) | 0.01275 |
2 | |
(A cm) | 0.01 |
0.667 | |
0.67 | |
Y | 1 |
(kg mol) | 0.016 |
Z | 1 |
(atm) | 2 |
V (m) | 0.00025 |
0.002 | |
(kg mol) | 0.002 |
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Electrode | Reactions |
---|---|
Anode | |
Cathode | |
Overall |
Loop | Controller | Ratio | |||
---|---|---|---|---|---|
Pressure controller | PID | 0.3 | 0.0001 | 0.4 | - |
Power controller | P | 0.1 | - | - | - |
Temperature controller | PID | −0.1 | −0.0001 | −0.05 | |
Air to ratio controller | Ratio | - | - | - | 5 |
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P. S., P.; Gudi, R.D.; Bhartiya, S. Dynamic Modeling and Control of an Integrated Reformer-Membrane-Fuel Cell System. Processes 2018, 6, 169. https://doi.org/10.3390/pr6090169
P. S. P, Gudi RD, Bhartiya S. Dynamic Modeling and Control of an Integrated Reformer-Membrane-Fuel Cell System. Processes. 2018; 6(9):169. https://doi.org/10.3390/pr6090169
Chicago/Turabian StyleP. S., Pravin, Ravindra D. Gudi, and Sharad Bhartiya. 2018. "Dynamic Modeling and Control of an Integrated Reformer-Membrane-Fuel Cell System" Processes 6, no. 9: 169. https://doi.org/10.3390/pr6090169