simulation of trickle bed electrochemical reactor …
TRANSCRIPT
SIMULATION OF TRICKLE BED ELECTROCHEMICAL REACTOR FOR
HYDROGEN PEROXIDE SYNTHESIS
_______________________________________
A Thesis
presented to
the Faculty of the Graduate School
at the University of Missouri-Columbia
_______________________________________________________
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
_____________________________________________________
by
ZHOUZHOU LU
Dr. Yangchuan Xing, Thesis Supervisor
JULY 2019
The undersigned, appointed by the dean of the Graduate School, have examined the
thesis entitled
SIMULATION OF TRICKLE BED ELECTROCHEMICAL REACTOR FOR
HYDROGEN PEROXIDE SYNTHESIS
presented by Zhouzhou Lu,
a candidate for the degree of master of science,
and hereby certify that, in their opinion, it is worthy of acceptance.
_______________________________________
Professor Yangchuan Xing
_______________________________________
Professor David Retzloff
_______________________________________
Professor Qingsong Yu
iii
TABLE OF CONTENTS
LIST OF TABLES ......................................................................................................... v
LIST OF FIGURES ...................................................................................................... vi
ABSTRACT ................................................................................................................ viii
Chapter
1. SYMBOLS .......................................................................................................... 1
2. TABLES .............................................................................................................. 3
3. INTRODUCTION .............................................................................................. 9
4. EXPERIMENTAL SECTION .......................................................................... 12
4.1 Materials. ..................................................................................................... 12
4.2 C-PTFE Cathode. ........................................................................................ 12
4.3 H2O2 Generation Procedures. .................................................................... 13
5. PARAMETERS ESTIMATION ....................................................................... 15
5.1 Effective diffusion coefficient..................................................................... 15
5.2 Liquid holdup. ............................................................................................. 16
5.3 Wetting efficiency. ...................................................................................... 17
5.4 Oxygen evolution kinetics........................................................................... 18
6. MODEL DESCRIPTION.................................................................................. 19
6.1 Mass transport model. ................................................................................. 21
6.2 Electrochemical model. ............................................................................... 22
6.3 Fluid dynamics model. ................................................................................ 23
7. RESULTS AND DISCUSSION ....................................................................... 24
7.1 H2O2 concentration distribution. ............................................................... 24
7.2 Effect of the KOH concentration. ............................................................... 26
7.3 Effect of the KOH flow rate. ....................................................................... 30
iv
7.4 Effect of the O2 flow rate. .......................................................................... 33
7.5 Effect of the applied voltage. ...................................................................... 36
8. CONCLUSIONS ............................................................................................... 39
REFERENCES ............................................................................................................ 40
v
LIST OF TABLES
Table Page
Table 1. Equations implemented into the model ........................................................... 3
Table 2. Boundary conditions implemented into the model .......................................... 4
Table 3. Properties equations ......................................................................................... 5
Table 4. Parameters used in the model .......................................................................... 6
Table 5. Reactions in electro-synthesis of alkaline peroxide ......................................... 8
Table 6. Tafel slope value for different applied voltage ................................................ 8
vi
LIST OF FIGURES
Figure Page
Figure 1. Flow diagram of electrolysis in continuous mode for the production of
hydrogen peroxide ...................................................................................................... 14
Figure 2. Construction of the divided-cell TBER ...................................................... 15
Figure 3. 2D geometry of the divided-cell TBER used in simulation ......................... 19
Figure 4. (a) H2O2 concentration distribution at 6 mol/L KOH, 2.0 V, 1.5 L/min O2
flow rate and 15 mL/min electrolyte flow rate at 20 ℃ from the divided-cell reactor
simulation ..................................................................................................................... 25
Figure 4. (b) H2O2 concentration distribution at 6 mol/L KOH, 2.0 V, 1.5 L/min O2
flow rate and 15 mL/min electrolyte flow rate at 20 ℃ from the undivided reactor
simulation ..................................................................................................................... 25
Figure 5. (a) H2O2 generation as a function of KOH concentration at 2.0 V, 1.5
L/min O2 flow rate and 15 mL/min electrolyte flow rate at 20 ℃ for modeled and
experimental runs. ........................................................................................................ 28
Figure 5. (b) H2O2 current efficiency as a function of KOH concentration at 2.0 V,
1.5 L/min O2 flow rate and 15 mL/min electrolyte flow rate at 20 ℃ for modeled
runs ............................................................................................................................... 28
Figure 6. (a) Current density of reaction (1) vs. Cell Depth with change of KOH
concentration. ............................................................................................................... 29
Figure 6. (b) Current density of reaction (2) vs. Cell Depth with change of KOH
concentration. ............................................................................................................... 29
Figure 7. (a) H2O2 concentration as a function of electrolyte flow rate at constant O2
flow rate of 1.5L/min in 6.0 M KOH, 2.0 V and 20 ℃ for modeled and experimental
runs. .............................................................................................................................. 31
Figure 7. (b) H2O2 current efficiency as a function of electrolyte flow rate at constant
O2 flow rate of 1.5L/min in 6.0 M KOH, 2.0 V and 20 ℃ for modeled runs. ............ 31
Figure 8. (a) Current density of reaction (1) vs. Cell Depth with change of KOH flow
rate................................................................................................................................ 32
Figure 8. (b) Current density of reaction (2) vs. Cell Depth with change of KOH flow
rate................................................................................................................................ 32
vii
Figure 9. (a) H2O2 concentration as a function of O2 flow rate at constant electrolyte
flow rate of 15 mL/min in 6.0 M KOH at applied potential of 2.0 V at 20 ℃ for
modeled and experimental runs. .................................................................................. 34
Figure 9. (b) H2O2 current efficiency as a function of O2 flow rate at constant
electrolyte flow rate of 15 mL/min in 6.0 M KOH at applied potential of 2.0 V at
20 ℃ for modeled runs. ............................................................................................... 34
Figure 10. (a) Current density of reaction (1) vs. Cell Depth with change of O2 flow
rate................................................................................................................................ 35
Figure 10. (b) Current density of reaction (2) vs. Cell Depth with change of O2 flow
rate................................................................................................................................ 35
Figure 11. (a) H2O2 generation as a function of applied potential in 2.0 M KOH, 15
mL/min electrolyte flow rate, 1.5 L/min O2 flow rate and 20 ℃ for modeled and
experimental runs. ........................................................................................................ 37
Figure 11. (b) H2O2 current efficiency as a function of applied potential in 2.0 M
KOH, 15 mL/min electrolyte flow rate, 1.5 L/min O2 flow rate and 20 ℃ for
modeled runs. ............................................................................................................... 37
Figure 12. (a) Current density of reaction (1) vs. Cell Depth with change of applied
voltage .......................................................................................................................... 38
Figure 12. (b) Current density of reaction (2) vs. Cell Depth with change of applied
voltage .......................................................................................................................... 38
Figure 13. Concentration of OH− at the anode surface vs. Cell Height with change of
applied voltage in 2.0 M KOH，15 mL/min electrolyte flow rate, 1.5 L/min O2 flow
rate and 20 ℃ for modeled runs. ................................................................................. 39
viii
ABSTRACT
A 2D multi-physics, multi-component model was developed to analyze the effects of
electrolyte concentration, flow rates and applied voltage on the performance of a trickle
bed electrochemical reactor for hydrogen peroxide synthesis. The trickle bed reactor
with a porous cathode composed of carbon black and polytetrafluoroethylene was
designed in our previous work. An important feature of the reactor was a divided-cell
structure of the cathode, which resulted in a much-improved performance. In order to
describe various phenomena that affect the behavior of the system, it is desirable to
model the divided cell TBER for H2O2 generation. The simulation used three main
models including the electrochemical model, the mass transfer model, and the fluid
dynamics model to solve the coupled voltage (charge), mass and momentum balance.
The simulation results were compared with the experimental data, showing reasonably
good agreements for different variables. Also, the distribution results of the divided cell
model were compared with the undivided ones and did show a better improvement on
the distribution of the H2O2 concentration. The model can be used as an optimization
tool for further improvement of the trickle bed electrochemical reactor.
1
1. Symbols
𝑎𝑉 Electrochemically active area per unit catalyst volume, 𝑚2/𝑚3
𝑎𝑒𝑓𝑓 Effective active area per unit catalyst volume, 𝑚2/𝑚3
𝐶𝑜2 Concentration of 𝑂2 in electrolyte, mol/𝑚3
𝐶𝑜20 Solubility of oxygen in pure water at 298K and 0.1 MPa, mol/𝑚3
𝐶𝐻𝑂2 Concentration of HO2− in electrolyte, mol/𝑚3
𝐶𝑂𝐻 Concentration of OH− in electrolyte, mol/𝑚3
𝑑𝑝 Particle diameter, m
𝐷𝑂2 Diffusivity of oxygen, 𝑚2𝑠−1
𝐷𝐻𝑂2 Diffusivity of per hydroxyl ion, 𝑚2𝑠−1
𝐷𝑂𝐻 Diffusivity of hydroxyl ion, 𝑚2𝑠−1
𝐷𝑂20 Diffusivity of oxygen at infinite dilution, 𝑚2𝑠−1
𝐷𝐻𝑂20 Diffusivity of perhydroxyl ion at infinite dilution, 𝑚2𝑠−1
𝐷𝑂𝐻0 Diffusivity of hydroxyl ion at infinite dilution, 𝑚2𝑠−1
𝐷𝑂2𝑒𝑓𝑓
Effective diffusivity of oxygen, 𝑚2𝑠−1
𝐷𝐻𝑂2𝑒𝑓𝑓
Effective diffusivity of per hydroxyl ion, 𝑚2𝑠−1
𝐷𝑂𝐻𝑒𝑓𝑓
Effective diffusivity of hydroxyl ion, 𝑚2𝑠−1
𝐸𝑒𝑞1 Equilibrium potential for reaction (1) (V)
𝐸𝑒𝑞2 Equilibrium potential for reaction (2) (V)
𝐸𝑒𝑞3 Equilibrium potential for reaction (3) (V)
𝐸0,𝑒𝑞1 Standard equilibrium potential for reaction (1) (V)
𝐸0,𝑒𝑞2 Standard equilibrium potential for reaction (2) (V)
𝐸0,𝑒𝑞3 Standard equilibrium potential for reaction (3) (V)
𝐹 Faraday’s constant (96486), 𝑐 𝑚𝑜𝑙−1
𝐹𝑡 Force term, 𝑘𝑔 𝑚−2 𝑠−2
𝑔 Gravity acceleration, 𝑚 𝑠−2
𝐺𝑀 Inlet mass flow rate of O2, 𝑘𝑔 𝑚−2 𝑠−1
𝐺𝑉 Inlet volume flow rate of O2, L/min
H Henry’s constant for oxygen in KOH, 𝑀𝑃𝑎 𝐿 𝑚𝑜𝑙−1
𝐻0 Henry’s constant of oxygen in pure water at 298K and 0.1 MPa,
𝑀𝑃𝑎 𝐿 𝑚𝑜𝑙−1
𝑖𝑙 Electrolyte current density, 𝐴 𝑚−2
𝑖𝑠 Electrode current density, 𝐴 𝑚−2
𝑖𝑣 Volumetric current density, 𝐴 𝑚−3
𝑖𝑙𝑜𝑐 Local current density, 𝐴 𝑚−2
2
𝑖0 Exchange current density, 𝐴 𝑚−2
I unit vector
𝐾𝑠 Setschenow constant
𝑘10 Electrochemical rate constant for reaction (1)
𝑘20 Electrochemical rate constant for reaction (2)
L𝑀 Inlet mass flow rate of electrolyte, 𝑘𝑔 𝑚−2 𝑠−1
𝐿𝑉 Inlet volume flow rate of electrolyte, 𝑚L/min
n number of participating electrons
𝑛′ unit vector
N Concentration flux, 𝑚𝑜𝑙 𝑚−2 𝑠−1
𝑃 Pressure, Pa
𝑄 Volumetric current density source term, 𝐴 𝑚−3
𝑟𝑤 Reactor width, m
𝑟ℎ Reactor height, m
𝑟𝑑 Reactor depth, m
𝑟𝑚 Thickness of diaphragm, m
S Concentration source term, mol 𝑚−3 𝑠−1
T Temperature, K
𝑢𝑙 Liquid flow rate, m/s
𝑢𝑔 Gas flow rate, m/s
𝑈𝐿 Inlet liquid flow rate, m/s
𝑈𝐺 Inlet gas flow rate, m/s
𝑊𝑒𝑓𝑓 Wetting efficiency
𝛼1 Charge transfer coefficient for single step of reaction (1)
𝛼2 Charge transfer coefficient for single step of reaction (2)
𝜀𝑝 Porosity of reactor
𝜀𝑙 Liquid hold-up
𝜌𝑙 Density of electrolyte, kg/𝑚3
𝜌𝑔 Density of oxygen, kg/𝑚3
𝜇𝑙 Viscosity of electrolyte, Pa∙s
𝜇𝑔 Viscosity of oxygen, Pa∙s
𝜎𝑠 Conductivity of electrode, S/m
𝜎𝑙 Conductivity of electrolyte, S/m
𝜎𝐿 surface tension of KOH, N/m
κ permeability, 𝑚2
3
2. Tables
Table 1 Equations implemented into the model
Equation Eq.
number
Domain
Mass transport ∇ ∙ 𝜏𝑖 + 𝑢 ∙ ∇𝐶𝑖 = 𝑅𝑖 + 𝑆𝑖 1 1-5
𝜏𝑖 = −𝐷𝑖𝑒𝑓𝑓
∇𝐶𝑖 2 1-5
𝑁𝑖 = −𝐷𝑖𝑒𝑓𝑓
∇𝐶𝑖 + 𝑢 ∙ 𝐶𝑖 3 1-5
Cathode 𝑅𝑖 =
𝜈𝑖𝑖𝑉
𝑛𝐹
4 2-5
Anode −𝑛′ ∙ 𝑁𝑖 = ∑ 𝑅𝑖,𝑚
𝑚
5 B1
𝑅𝑖 =
𝜈𝑖𝑖𝑙𝑜𝑐
𝑛𝐹
6 B1
Electrochemical ∅𝑙 = 𝑝ℎ𝑖𝑙 7 1-5
∅𝑠 = 𝑝ℎ𝑖𝑠 8 1-5
Electrolyte ∇ ∙ 𝑖𝑙 = 𝑄𝑙 9 1-5
𝑖𝑙 = −𝜎𝑙∇∅𝑙 10 1-5
Cathode ∇ ∙ 𝑖𝑙 = 𝑄𝑙 + 𝑖𝑉,𝑡𝑜𝑡𝑎𝑙 11 2-5
𝑖𝑙 = −𝜎𝑙,𝑒𝑓𝑓∇∅𝑙 12 2-5
−𝜎𝑙,𝑒𝑓𝑓 = 𝑓𝑙𝜎𝑙 13 2-5
∇ ∙ 𝑖𝑠 = 𝑄𝑠 − 𝑖𝑉,𝑡𝑜𝑡𝑎𝑙 14 2-5
𝑖𝑠 = −𝜎𝑠,𝑒𝑓𝑓∇∅𝑠 15 2-5
−𝜎𝑠,𝑒𝑓𝑓 = 𝑓𝑠𝜎𝑠 16 2-5
𝑖𝑉,𝑡𝑜𝑡𝑎𝑙 = ∑ 𝑖𝑉,𝑚
𝑚
+ 𝑖𝑉,𝑑𝑙 17 2-5
Reaction.1 𝜂 = ∅𝑠 − ∅𝑙 − 𝐸𝑒𝑞1 18 2-5
𝐸𝑒𝑞1 = 𝐸0,𝑒𝑞1 − (
𝑅𝑇
2𝐹) ln (
𝐶𝐻𝑂2𝐶𝑂𝐻
𝑃𝑜2)
19 2-5
𝑖0,1 = 2𝐹𝑘1
0𝐶𝑂2 exp [(−𝐸1
𝑅) (
1
𝑇
−1
288)] exp (
−𝛼1𝐹𝐸𝑒𝑞1
𝑅𝑇)
20 2-5
𝑖𝑙𝑜𝑐,1 = −𝑖0,1 × 10𝜂/𝐴𝑐,1, 21 2-5
𝑖𝑉,1 = 𝑎𝑒𝑓𝑓 ∙ 𝑖𝑙𝑜𝑐,1 22 2-5
Reaction.2 𝜂 = ∅𝑠 − ∅𝑙 − 𝐸𝑒𝑞2 23 2-5
𝐸𝑒𝑞2 = 𝐸0,𝑒𝑞2 − (
𝑅𝑇
2𝐹) ln (
𝐶𝑂𝐻3
𝐶𝐻𝑂2)
24 2-5
𝑖0,2 = 2𝐹𝑘2
0𝐶𝐻𝑂2 exp [(−𝐸2
𝑅) (
1
𝑇
−1
288)] exp (
−𝛼2𝐹𝐸𝑒𝑞2
𝑅𝑇)
25 2-5
4
𝑖𝑙𝑜𝑐,2 = −𝑖0,2 × 10𝜂/𝐴𝑐,2 26 2-5
𝑖𝑉,2 = 𝑎𝑒𝑓𝑓 ∙ 𝑖𝑙𝑜𝑐,2 27 2-5
Anode 𝑛′ ∙ 𝑖𝑙 = 𝑖𝑡𝑜𝑡𝑎𝑙 28 B1
𝑖𝑡𝑜𝑡𝑎𝑙 = ∑ 𝑖𝑙𝑜𝑐,𝑚
𝑚
+ 𝑖𝑑𝑙 29 B1
Reaction.3 𝜂 = ∅𝑠,𝑒𝑥𝑡 − ∅𝑙 − 𝐸𝑒𝑞3 30 B1
𝐸𝑒𝑞3 = 𝐸0,𝑒𝑞3 − (
𝑅𝑇
4𝐹) ln (
𝐶𝑂𝐻4
𝑃𝑜2)
31 B1
𝑖𝑙𝑜𝑐,3 = 𝑖0,3 ×
𝐶𝑂𝐻
𝐶𝑟𝑒𝑓× 10𝜂/𝐴𝑎
32 B1
Fluid dynamic-
Liquid 0 = ∇ ∙ [−𝑝𝑙𝐼 +
𝜇𝑙
𝜀𝑝(∇𝑢𝑙 + (∇𝑢𝑙)𝑇)
−2
3
𝜇𝑙
𝜀𝑝
(∇ ∙ 𝑢𝑙)𝐼]
− (𝜇𝑙𝜅−1 + 𝛽𝐹|𝑢𝑙| +𝑄𝑚
𝜀𝑝2
) 𝑢𝑙
+ 𝐹𝑡)
33 1-5
𝜌𝑙 ∙ ∇ ∙ 𝑢𝑙 = 𝑄𝑚 34 1-5
Fluid dynamic-
Gas 0 = ∇ ∙ [−𝑝𝑔𝐼 +
𝜇𝑔
𝜀𝑝(∇𝑢𝑔 + (∇𝑢𝑔)
𝑇)
−2
3
𝜇𝑔
𝜀𝑝(∇ ∙ 𝑢𝑔)𝐼]
− (𝜇𝑔𝜅−1 + 𝛽𝐹|𝑢𝑔|
+𝑄𝑚
𝜀𝑝2
) 𝑢𝑔 + 𝐹𝑡)
35 1-5
𝜌𝑔 ∙ ∇ ∙ 𝑢𝑔 = 𝑄𝑚 36 1-5
Table 2 Boundary conditions implemented into the model
Equation Eq. number Boundary
Mass transport
No Flux −𝑛′ ∙ 𝑁𝑖 = 0 37 2,3,13-16
Inflow 𝐶𝑖 = 𝐶0,𝑗 38 12
Outflow −𝑛′ ∙ 𝐷𝑖∇𝐶𝑖 = 0 39 5
Impermeable −𝑛′ ∙ 𝑁𝑖 = 0 40 4,6,8,10
re-distribution 𝑐𝑖 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑖 41 5,7,9,11
Electrochemical
Insulation −𝑛′ ∙ 𝑖𝑙 = 0 42 2,3,5,12
−𝑛′ ∙ 𝑖𝑠 = 0 43 2,3,5,12
Fluid dynamic-
Liquid
Wall-no slip 𝑢𝑙 = 0 44 1-3,13-16
Inlet 𝑢𝑙 = −𝑈𝐿𝑛′ 45 12
5
Outlet 𝑛′𝑇
[−𝑝𝑙𝐼 +𝜇𝑙
𝜀𝑝
(∇𝑢𝑙 + (∇𝑢𝑙)𝑇)
−2
3
𝜇𝑙
𝜀𝑝
(∇ ∙ 𝑢𝑙)𝐼] 𝑛′
= −𝑝0
46 5
Fluid dynamic-
Gas
Wall-no slip 𝑢𝑔 = 0 47 1-3,13-16
Inlet 𝑢𝑔 = −𝑈𝐺𝑛′ 48 12
Outlet 𝑛′𝑇
[−𝑝𝑔𝐼 +𝜇𝑔
𝜀𝑝(∇𝑢𝑔 + (∇𝑢𝑔)
𝑇)
−2
3
𝜇𝑔
𝜀𝑝(∇ ∙ 𝑢𝑔)𝐼] 𝑛′
= −𝑝0
49 5
Table 3 Properties equations
Quantity Relation Source
Inlet mass flow rate 𝐿𝑀 =
𝐿𝑉𝜌𝑙
𝑟𝑤𝑟𝑑
Measured
𝐺𝑀 =
𝐺𝑉𝜌𝑔
𝑟𝑤𝑟𝑑
Measured
Inlet flow rate 𝑈𝐿 =
𝐿𝑉
𝑟𝑤𝑟𝑑
Measured
𝑈𝐺 =
𝐺𝑉
𝑟𝑤𝑟𝑑
Measured
Oxygen Solubility 𝐶𝑜2 =
𝑃𝑂2
𝐻
[1, 2]
log (
𝐶𝑜2
𝐶𝑜20) = 𝐾𝑠𝐶
[1, 2]
H =
𝐻0
𝐶𝑂2/𝐶𝑂2
0 [1, 2]
Species diffusivity 𝐷𝐻𝑂2 =
0.001𝐷𝐻𝑂20 𝑇
298𝜇𝑙
[3]
𝐷𝑂𝐻 =
0.001𝐷𝑂𝐻0 𝑇
298𝜇𝑙
[3]
𝐷𝑂2 =
0.001𝐷𝑂20 𝑇
298𝜇𝑙
[3]
Effective diffusivity 𝐷𝐻𝑂2
𝑒𝑓𝑓=
𝜀𝑝
𝜀𝑝−1/2
∙ 𝐷𝐻𝑂2 [4]
𝐷𝑂𝐻𝑒𝑓𝑓
=𝜀𝑝
𝜀𝑝−1/2
∙ 𝐷𝑂𝐻 [4]
𝐷𝑂2
𝑒𝑓𝑓=
𝜀𝑝
𝜀𝑝−1/2
∙ 𝐷𝑂2 [4]
6
Specific surface 𝑎𝑉 =
6(1 − 𝜀𝑃)
𝑑𝑝
Measured
Wetting efficiency 𝑛𝐶𝐸
= 1
− exp [−1.35𝑅𝑒𝐿0.333𝐹𝑟𝐿
0.235𝑊𝑒𝐿−0.170 (
𝑎𝑉𝑑𝑝
𝜀𝑝2
)
−0.0425
]
[5]
𝐹𝑟𝐿 =
𝑎𝑉𝐿𝑀2
𝜌𝑙2𝑔
[5]
𝑊𝑒𝐿 =
𝐿𝑀2
𝜎𝐿𝜌𝑙𝑎𝑉
[5]
𝑅𝑒𝐿 =
𝜌𝑙𝑈𝐿𝑑𝑝
𝜇𝑙
[5]
Effective surface 𝑎𝑒𝑓𝑓 = 𝑎𝑉 ∙ 𝑛𝐶𝐸 Measured
Liquid hold-up 𝜀𝑙 = 10^(−0.42𝑋𝐺
0.24𝑅𝑒𝐿0.14 (
𝑎𝑉𝑑𝑘
1 − 𝜀𝑝)
−0.14
） + 0.05 [6]
𝑋𝐺 =𝑈𝐺√𝜌𝑔
𝑈𝐿√𝜌𝑙
[6]
𝑑𝑘 = 𝑑𝑝 √16𝜀𝑝
3
9𝜋(1 − 𝜀𝑝)2
3
[6]
Conductivity 𝜎𝑙 = −2.041𝐶𝑂𝐻 − 0.0028𝐶𝑂𝐻2 + 0.005332(𝐶𝑂𝐻 ∙ 𝑇)
+ 207.2 (𝐶𝑂𝐻
𝑇) + 0.001043𝐶𝑂𝐻
3
− 0.0000003(𝐶𝑂𝐻2 ∙ 𝑇2)
[7]
Correction factor 𝑓𝑙 =
2𝜀𝑝
3 − 𝜀𝑝
[3]
Table 4 Parameters used in the model
Parameter Meaning Value Source
𝒓𝒘 Reactor width 0.06m Measured
𝒓𝒉 Reactor height 0.05m Measured
𝒓𝒅 Reactor depth 0.014m Measured
𝒓𝒎 Thickness of diaphragm 0.001m Measured
T Temperature 293K Measured
𝜺𝒑 Porosity of reactor 0.55 Measured
𝒅𝒑 Particle diameter 20 𝜇𝑚 Measured
𝝆𝒍 Density of electrolyte 1087.3 kg/𝑚3 [8]
𝝆𝒈 Density of oxygen 2.237 kg/𝑚3 [9]
𝝁𝒍 Viscosity of electrolyte 0.00123 Pa*s [8]
𝝁𝒈 Viscosity of oxygen 2.04E-5 Pa*s [9]
𝑫𝑯𝑶𝟐𝟎 Diffusivity of perhydroxyl ion
at infinite dilution
1.5 × 10−9 𝑚2𝑠−1 [3]
7
𝑫𝑶𝑯𝟎 Diffusivity of hydroxyl ion
at infinite dilution
5.3 × 10−9 𝑚2𝑠−1 [3]
𝑫𝑶𝟐𝟎 Diffusivity of oxygen
at infinite dilution
2.4 × 10−9 𝑚2𝑠−1 [3]
𝑪𝒐𝟐𝟎 Solubility of oxygen in pure water
at 298K and 0.1 MPa
1.3 × 10−3 𝑚𝑜𝑙 𝐿−1 [1, 2]
𝑯𝟎 Henry’s constant of oxygen in
pure water at 298K and 0.1 MPa
76.9 𝑀𝑃𝑎 𝐿 𝑚𝑜𝑙−1 [1, 2]
𝑲𝒔 Setschenow constant -0.175 [1, 2]
𝑬𝟎,𝒆𝒒𝟏 Standard equilibrium potential
for reaction (1)
-0.076 V [3]
𝑬𝟎,𝒆𝒒𝟐 Standard equilibrium potential
for reaction (2)
0.878 V [3]
𝑬𝟎,𝒆𝒒𝟑 Standard equilibrium potential
for reaction (3)
0.401 V [3]
𝒌𝟏𝟎 Electrochemical rate
constant for reaction (1)
4.92E-7 m/s [10]
𝒌𝟐𝟎 Electrochemical rate
constant for reaction (2)
1.6E-9 m/s [10]
𝜶𝟏 Charge transfer coefficient
for single step of reaction (1)
0.543 [10]
𝜶𝟐 Charge transfer coefficient
for single step of reaction (2)
0.268 [10]
𝒊𝟎,𝟑 Exchange current density
for reaction (3)
1.1e-7 𝐴/𝑚2 [11]
𝝈𝒔 Conductivity of carbon 450 S/m [12]
g Gravity 9.8 m/s Measured
𝝈𝑳 surface tension of KOH 7.85× 10−2 N/m [13]
𝑳𝑽 Inlet volume flow rate of KOH 15 mL/min Measured
𝑮𝑽 Inlet volume flow rate of 𝑂2 1.5 L/min Measured
𝑷𝒊𝒏 Inlet pressure of 𝑂2 1.7× 105 Pa Measured
𝑪𝒊𝒏,𝑶𝟐 Inflow concentration of
dissolved 𝑂2
1.1874 𝑚𝑜𝑙/𝑚3 Measured
𝑪𝒊𝒏,𝑶𝑯 Inflow concentration of OH 2000 𝑚𝑜𝑙/𝑚3 Measured
𝑪𝒊𝒏,𝑯𝑶𝟐 Inflow concentration of 𝐻𝑂2 0.001 𝑚𝑜𝑙/𝑚3 Measured
𝑪𝟎,𝑶𝟐 Initial concentration of
dissolved 𝑂2
0.7076 𝑚𝑜𝑙/𝑚3 Measured
𝑪𝟎,𝑶𝑯 Initial concentration of OH 2000 𝑚𝑜𝑙/𝑚3 Measured
𝑪𝟎,𝑯𝑶𝟐 Initial concentration of 𝐻𝑂2 0.1 𝑚𝑜𝑙/𝑚3 Measured
𝑪𝒓𝒆𝒇 Reference concentration 1000 𝑚𝑜𝑙/𝑚3 Measured
8
Table 5 Reactions in electro-synthesis of alkaline peroxide
Reaction 𝐄𝟎 𝐕 𝐯𝐬. 𝐍𝐇𝐄 𝐚𝐭 𝟐𝟗𝟖𝐤(𝐏𝐇 = 𝟏𝟒)
Cathode
𝑂2 + 𝐻2𝑂 + 2𝑒− → 𝑂𝐻− + 𝐻𝑂2− -0.076 reaction (1)
𝐻𝑂2− + 𝐻2𝑂 + 2𝑒− → 3𝑂𝐻− +0.878 reaction (2)
Anode
4𝑂𝐻− → 𝑂2 + 2𝐻2𝑂 + 4𝑒− +0.401 reaction (3)
𝑂𝐻− + 𝐻𝑂2− → 𝑂2 + 𝐻2𝑂 + 2𝑒− -0.076 reaction (4)
Table 6 Tafel slope value for different applied voltage
Applied Voltage (V) 1 1.5 2 2.5 3
Tafel slope (mV/decade) 43 93 140 160 180
9
3. Introduction
Hydrogen peroxide is one of the most powerful and environmentally friendly
oxidants, which is widely used in pulp bleaching [14], wastewater treatment[15],
detoxifying cyanide wastes [16]，synthesis of chemicals [17], and degradation of
organic contaminants [18]. Commercially available H2O2 is produced primarily by
the anthraquinone autoxidation process [19], but electrochemical methods have now
received more attention [20-22]. Electrochemical technology for hydrogen peroxide
generation and application have advantages in producing chemicals in small quantities
at sites and also avoiding the cost of transportation. The main problem for applying
electrolytic routes is that the low solubility of oxygen in aqueous electrolyte solution
often limits the production rate and efficiency [11]. This problem can be resolved by
using a three-dimensional high surface area such as a porous electrode. A trickle bed
electrochemical reactor composed of Vulcan-XC72 carbon black and PTFE(or C-PTFE)
has been developed in our previous work [23]. More importantly, a divided cathode was
designed and used in the TBER, which demonstrated a much higher production rate of
hydrogen peroxide [23]. To interpret the effect of different parameters on the
performance of the trickle bed reactor, it is desirable to model the divided cell TBER
for H2O2 generation.
Trickle bed reactors (TBRs) are fixed bed reactors in which a gas phase and a liquid
phase flow concurrently downward through catalyst particles while reactions take place.
The word “TRICKLE” itself describes its operational characteristics in which liquid
intermittently flows over the solid catalyst in the form of films or rivulets or droplets
10
[24]. TBRs are widely used in chemical processing, such as hydrogenation of citral [25],
wastewater treatment [26], removal of volatile organic compounds [27], and production
of H2O2 [28].
The first step in simulating the TBERs is to assess the flow pattern. Four distinct flow
regimes were identified by Chaudhari and Ramachandran (1983) [29]: (1). Trickle flow
regime; (2). Pulse flow regime; (3). Spray flow regime; (4). Bubbly flow regime. These
flow patterns mainly depend on the packing density, gas and liquid velocities, particle
size, and physical properties of the aqueous phases [30]. At low gas and liquid flow
rates like our experimental conditions, gas-liquid interaction is small, and liquid flows
in the form of films or rivulets over the packed particles. This flow regime is known as
the trickle flow regime or low interaction regime. All subsequent calculations such as
estimating hydrodynamic parameters are based on the characteristics of the flow pattern
[24].
After estimating the main design parameters, the reaction kinetics need to be
simulated. The reaction process of oxygen on the electrode is a complex multi-electron,
multi-step continuous reaction. The reduction reaction of 𝑂2 basically has two
reaction processes, one is a four-electron reduction reaction in which no hydrogen
peroxide is formed, and the other is a reduction in 𝐻𝑂2−, and 𝐻𝑂2
− may be further
reduced to 𝑂𝐻− [31]. The oxygen reduction process is largely determined by the
cathode material used. Carbon is an effective electrocatalyst for the cathodic reduction
of 𝑂2 to 𝐻2𝑂2 in the alkaline electrolyte and is also a relatively poor 𝐻2𝑂2
decomposition catalyst [11]. Electrochemical kinetics are related to electrode potential,
11
conduction resistance, gas-liquid mass transfer, which increases the coupling difficulty
of the simulation [32].
The interaction between different phases and the complexity of the bed structure
cause several difficulties in simulating the hydrodynamics in a trickle bed reactor.
Usually, multilayer or multiscale models are used to simulate processes occurring at
different scales with different research purposes [24]. The macroscale process models
treat the entire packed bed as the porous media and use averaged transport equations to
simulate the fluid flow [33, 34]. It can provide the macroscopic information but does
not give information on the local flow and transport occurring within the bed. The
macroscale method is widely used to simulate fluid flow in the packed bed [35, 36].
Microscopic process models are useful for developing better closure terms for
macroscale flow models. Volume of the fluid (VOF) method developed by Hirt and
Nichols (1981) [37] is one of the most widely used methods in studying the detailed
gas-liquid interaction. The flow field predicted by the VOF models can be used to
examine various intricate details of the interaction of a liquid drop and flat surface [30,
38]. Taking both the macroscale and microscale processes into consideration, the
Eulerian-Eulerian approach of the two-dimensional multifluid models with spatial
variation of the porosity appears to be more suitable for reactor engineering applications
[24].
Earlier works on modeling a conventional single-cell trickle bed reactor for hydrogen
peroxide generation has been done by Oloman [39] and Sudoh [40]. These models
assume that the entire system is under isothermal operations and the reactions are
12
controlled by electrochemical kinetics, so the accuracy of the mass transfer equations
and hydrodynamic equations involved in the model is relatively insufficient. Also, these
models ignore the electrode potential gradient and do not take into account the effect of
effective resistance. A perforated bipole electrochemical reactor for hydrogen peroxide
generation was modeled by N. Gupta [3]. This model is a more comprehensive one
since it involved the electrode potential gradient, mass transport effect, pressure and
temperature gradients. However, this model is used for the particular case of a
perforated bipole reactor with superficial current densities up to 5 kA m2 , which is
super larger than the current density of conventional TBRs. This thesis intends to
describe a model for the divided-cell trickle bed electrochemical reactor and compare
the modeling results with experimental data.
4. Experimental section
4.1 Materials.
Carbon black (Vulcan-XC72) was obtained from Cabot Corporation. PTFE aqueous
suspension (60 wt % dispersion in water), KOH (85%), and molybdic acid
(NH4)6Mo7O24 ∙ 4H2O were purchased from Sigma-Aldrich. H2SO4 (98%) was
purchased from Alfa Aesar, and HNO3 aqueous solution was purchased from Fisher
Scientific. Carbon cloth was obtained from the Fuel Cell store. High purity deionized
water (Millipore, ＞18.2 MΩ ∙ cm) was used to prepare the electrolyte solution in all
experiment.
4.2 C-PTFE Cathode
13
The composite of the C-PTFE cathode was prepared by mixing carbon black with an
appropriate amount of PTFE (60 wt % in solution) at a mass ratio of 2:1 of C/PTFE.
The mixture was placed and pressed in a divided frame to make porous C-PTFE blocks.
These blocks were taken out and dried overnight under vacuum at 80 ℃ and then
sintered at 360 ℃ for 2h. A second bed with undivided cathode following the work of
Lei et al. [41] was also fabricated by coating C-PTFE on a carbon cloth until the
appropriate thickness was obtained. Before use, the carbon black was treated
ultrasonically in a mixture of H2SO4 and HNO3 acids for 2h at 60 ℃ to increase its
hydrophilicity and create more surface oxygen functional groups, considered to be
beneficial for H2O2 production.
4.3 𝐇𝟐𝐎𝟐 Generation Procedures
H2O2 generation in concentrated KOH solution was carried out in a continuous flow
mode using the trickle bed electrochemical reactor with C-PTFE composite cathode as
illustrated in Figure 1 [23]. Oxygen and electrolyte are combined in a tee and delivered
together in a two-phase flow to the TBER. The gas-liquid flow enters the trickle bed
reactor from the top of the cathode frame and then goes down through the C-PTFE
cathode where 𝐻2𝑂2 generation occurs. The cathode frame with dimensions of 60mm
X 50mm X14mm (width, height, depth) is divided by three stainless steel mesh as
shown in Figure 2. This division into a sectional cathode improves the performance of
the TBER by the even distribution of electrolyte and oxygen in the cathode bed. The
electrolyte that comes from the bottom of the reactor was circulated back in a
continuous mode, and unreacted oxygen was flowing out with the electrolyte from the
14
outlet. All electrolysis experiments are conducted in a potentiostatic model with a
constant voltage at room temperature. The concentration of the produced H2O2 was
evaluated using a peroxymolybdate method. In this method, a sample of 0.5 mL of the
solution was added to 5 mL of (2.4 mM) (NH4)6Mo7O24 in（0.5M）H2SO4 solution,
and a Genesys 20 Spectrophotometer was used to quantify H2O2 concentration at
wavelength of 350 nm.
The detail experimental set-up of the divided-cell trickle bed electrochemical reactor
and corresponding experimental results are as previously published [23]. The content
described below was carried out to provide further information on reactor parameters,
mass transfer and reaction kinetics necessary for the TBER simulation.
Figure 1. Flow diagram of electrolysis in continuous mode for the production of hydrogen
Peroxide [23].
15
Figure 2. Construction of the divided-cell TBER [23].
5. Parameter Estimation
5.1 Effective diffusion coefficient.
In porous media, the effective diffusion coefficient is different from the real diffusion
coefficient. This is because the effective diffusion cross section is smaller than the cross
section of the free fluid. Another reason is that the actual distance the molecule must
move from one point to another in the porous material is longer than the linear distance
between these points. As a result, the real concentration gradient is less than the
apparent concentration gradient. In Fick's first law, the ratio of the actual distance to the
straight-line distance is introduced by multiplying the diffusion coefficient by a
tortuosity (𝜏 > 1):
𝑁𝑖 = −𝐷𝑖𝑒𝑓𝑓
∇𝑐𝑖 = −𝜀
𝜏𝐷𝑖∇𝑐𝑖
There are standard correlations relating the tortuosity to the porosity:
Millington-Quirk [42]:
16
𝜏 = 𝜀−13
Bruggeman [4]:
𝜏 = 𝜀−12
Bruggeman correlation is used in our model since it is more commonly used in the
simulation of electrochemical systems [43].
5.2 Liquid holdup
In the trickle bed electrochemical reactor, the liquid holdup is an important parameter
which has a further impact on other parameters such as wetting efficiency, effective
conductivity of the electrolyte, mass transfer coefficient and so on. According to some
work done by previous researchers [6, 30, 44-46], the factors that affect the change of
the liquid holdup mainly include particle size, gas-liquid flow rate and the properties of
the fluid.
For smaller particles, the specific surface area of the particles is larger, resulting in a
higher liquid holdup. In the low interaction area, the liquid holdup is not sensitive to
the gas flow rate. The liquid holdup decreases with the gas flow rate increases only at
moderate or high gas-liquid flow rates. In contrast, the liquid holdup increases as the
liquid flow rate increases. Most liquid holdup correlations contain Reynolds numbers
that represent changes in gas and liquid viscosity. For high viscous liquids, the liquid
holdup is higher because the solid-liquid shearing force at this time is greater than the
gas-liquid interaction. The effect of surface tension is significant for small particles
(less than 1~2mm) with a strong capillary effect. The liquid holdup indicates the
influence of the liquid surface tension by introducing the Weber number.
17
After considering the factors mentioned above, we chose Ellman’s equation (shown
in Table 3) [6] to predict the liquid holdup, since most of the influencing factors are
covered in this formula
5.3 Wetting efficiency
For trickle bed electrochemical reactors, partial wetting harms reactor performance
since the electrochemical reaction must be performed on the wetted catalyst surface.
The difference in the degree of wetting of the particles is caused by the non-uniform
flow of liquid on the surface of the catalyst particles.
The liquid distributor directly affects the wetting efficiency. Poorly designed
spreaders can result in non-uniform distribution and poor distribution of liquids. To
improve the uniform distribution of liquid and gas, we used a divided-cell trickle bed
electrochemical reactor and did get better results than an undivided one [23].
Particle diameter also affects the wetting efficiency of the porous bed. The larger the
particle diameter, the lower the wetting efficiency due to less capillary effect and liquid
holdup [5, 47-49]. For small particles, strong liquid-solid interaction is beneficial to
liquid spreading and increasing wetting efficiency.
In addition to the particle diameter, the wetting efficiency is strongly dependent on
the liquid flow rate [5, 47-49]. The liquid flow rate of most trickle bed reactors is very
low. At this time, the liquid is insufficient to cover the surface of the catalyst, and partial
wetting is inevitably caused. Increasing the liquid flow rate increases the wetting
efficiency [50].
Considering the favorable effect of the divided-cell reactor on the liquid distribution,
18
we chose the equation referred in Mills & Dudukovic’s researches [5] (which has a
higher predict results compared to other correlations [24]) to estimate the wetting
efficiency.
5.4 Oxygen evolution kinetics
Oxygen evolution reaction (reaction (3) in Table 5) occurs at the anode surface,
corresponding to the reduction of oxygen in the porous cathode. In many of the
studies[51-53], varying Tafel slope was reported for the oxygen evolution reaction
when changing the current densities, with the higher values obtained at higher current
densities. According to the researches from Damjanovic et al. [54], there are four
possibilities can cause the change in the anodic Tafel slope: (1) different reaction
pathways, (2) change in the electrode substrate, (3) change in the rate-controlling step,
(4) influence of potential controlled conditions (i.e., high coverage by intermediates).
It is proposed by Damjanovic et al. that the most likely explanation for the change in
the anodic Tafel slopes is the increase in the concentration of intermediates at high
potentials [11]. For nickel oxide, the transformation of nickel from a low state (Ni2+)
to a higher state (Ni3+) will lead to the change in Tafel slopes for oxygen evolution
[55].
After considering the complexity of the oxygen evolution reaction kinetics, we chose
the data from P.W.T. Lu and S. Srinivasan’s researches in which the current exchange
density equals 1.1 × 10−7 𝐴/𝑚2 and Tafel slope equals 43 mV (By using Ni
electrode, 25℃) [56] as the initial kinetics value for the oxygen evolution reaction at
low current densities. Then we keep the exchange current density constant and increase
19
the Tafel slope as the voltage increases. The Tafel slope value with different applied
voltage is shown in Table 6.
Figure 3. 2D geometry of the divided-cell TBER used in simulation.
6. Model description
A 2D multi-physics, multi-component model was developed to analyze the effects of
electrolyte concentration, flow rates and applied voltage on the performance of a trickle
20
bed electrochemical reactor. The 2D geometry of the entire model mainly consists of
four divided cathode domain, one diaphragm domain, one anode surface boundary, one
inlet, one outlet boundary and three re-distribution boundaries as illustrated in Figure
3. In order to describe various phenomena that affect the behavior of the system, we
made the multi-physics into three main models including the electrochemical model,
the mass transfer model and the fluid dynamics model.
Equations and boundary conditions implemented into the model are illustrated in
Table 1 and Table 2. For computing the simulations, the model requires some
correlation equations to calculate useful property parameters, for example, diffusion
coefficients, wetting efficiency, liquid hold-up, as reported in Table 3. Meanwhile, the
initial values that are used in both equations and boundary conditions, for example,
reactor size, material properties, inlet flow rates, are listed in Table 4. And the correlated
reactions involved in the TBER are shown in Table 5.
The basic model assumptions, applied to the various domains and boundaries, are:
1. An isothermal system.
2. Gas phases follow ideal gas law.
3. Only considering reaction (1) and reaction (2) take place in the cathode and
reaction (3) at the anode surface, no other chemical reactions are considered.
4. The model is operated under steady-state condition.
5. Slip wall conditions are applied to all walls.
6. Neglect the effect of electric field migration
The following sections describe each model in detail.
21
6.1 Mass transport model
Mass transport is accounted for by the general transport of diluted species in porous
media equation, Eq (1) and convection-diffusion equation, Eq (3), coupled with Stokes-
Brinkman equations and electrochemical model. One of the important parameters in Eq
(2) and Eq (3) is the effective diffusion coefficient 𝐷𝑖𝑒𝑓𝑓
, described in Table 3. The
subscript index “i” means the respective species and the superscript index “eff” means
that the effective diffusion coefficient which takes the porosity into consideration. The
model calculates the species fluxes at the catalyst surface by the general
electrochemical reaction equation, Eqs (4) and (6), with ∑ 𝜈𝑜𝑥𝑂𝑥 + 𝑛𝑒 ↔𝑜𝑥
∑ 𝜈𝑟𝑒𝑑𝑅𝑒𝑑𝑟𝑒𝑑 . For reaction (1), the number of participating electrons for n and
stoichiometric coefficient for 𝜈𝑖 are: 𝑛1 = 2 , 𝜈1,𝑂2= −1 , 𝜈1,𝑂𝐻 = 1 , 𝜈1,𝐻𝑂2
= 1 .
For reaction (2), the numerical values for 𝑛2 and 𝜈𝑖 are: 𝑛2 = 2 , 𝜈2,𝑂𝐻 = 3 ,
𝜈2,𝐻𝑂2= −1 . For reaction (3), the numerical values for 𝑛3 and 𝜈𝑖 are: 𝑛3 = 4 ,
𝜈3,𝑂2= −1, 𝜈1,𝑂𝐻 = 4.
The model performs calculations according to these assumptions and boundary
conditions:
1. Abundant water.
2. Liquid film thickness is thin enough. So, no concentration difference needs to be
added when using the Tafel equation for reaction (1) and reaction (2).
3. A thin impermeable barrier boundary condition is used to prevent hydrogen
peroxide from diffusing to the anode for side reactions, as shown in Eq. (40).
4. Three re-distribution boundary conditions are used to make sure the inputs
22
(chemical species) for the second cell are those outputs (and concentration
averaged) from the first cell, and so on.
5. The inlet/outlet flow and initial values used for the simulation are listed in Table
4.
6.2 Electrochemical model
Considering the effect of overpotential and the resistance of electrolyte solution, the
Secondary Current Distribution (SCD) model is used to simulate the electrochemical
behaviors. Eqs (7)-(17) show the Ohm’s Law that used to calculate the current density
at the electrode and the electrolyte. For the porous cathode, the effective conductivity,
described in Eqs (13) and (16) is an essential parameter that will affect the behavior of
the system. The kinetics of all three reactions can be explained by the Tafel equation
which is the simple model of the Butler-Volmer equation when the reaction moves in a
preferential direction, as Eqs (21), (26), (32). The overpotential is calculated by Eqs
(18), (23), (30), and the corresponding equilibrium potential is defined by Nernst
equations, Eqs (19), (24), (31). Exchange current density of reaction (1) and reaction
(2) is correlated with the concentration of the species by using Eqs (20) and (25).
Assuming constant exchange current density for reaction (3). No concentration
difference is included in the Tafel equation for reaction (1) and reaction (2). However,
for reaction (3), the concentration difference of 𝑂𝐻− at the anode surface is considered
by using Eq (32). Finally, 𝑎𝑒𝑓𝑓 is the effective active area per unit catalyst volume and
is used to calculate 𝑖𝑉, Eqs (22), (27).
In conclusion, the model performs calculations according to these assumptions and
23
boundary conditions:
1. No migration effect of HO2−.
2. The kinetics of three reactions can be explained by the Tafel equation.
3. No initial electrolyte potential and electrode potential.
4. Assuming constant exchange current density for reaction (3) but different Tafel
slopes when changing the applied voltage.
5. Considering the concentration difference of OH− at the anode surface for
reaction (3).
6.3 Fluid dynamics model
In order to analyze the effect of porous structure, Stokes-Brinkman equations are
used, as shown in Eqs (33)-(36). The model performs separate calculations for the fluid
flow in the liquid and gas phases, so the effects of the interaction between each phase
are not taken into consideration. From the perspective of fluid dynamics mechanics,
this part should not be ignored. But since our operating conditions are in the low
interaction zone, and the purpose of this research is to simulate the macroscopic reactor
performance, we decided to simplify the fluid dynamics by neglecting the gas-liquid
interaction.
The model performs calculations according to these assumptions and boundary
conditions:
1. Neglecting interaction between each phase.
2. The inlet/outlet flow and initial values used for the simulation are listed in Table 4.
24
7. Results and Discussion
7.1 𝐇𝟐𝐎𝟐 concentration distribution
Figure 4a and Figure 4b show the H2O2 concentration distribution at 6 mol/L KOH,
2.0 V, 1.5 L/min O2 flow rate and 15 mL/min electrolyte flow rate at 20 ℃ from the
divided-cell reactor simulation and the undivided reactor simulation, respectively. The
divided cell structure does have a good improvement on the H2O2 concentration
distribution. From both two Figures, we can see that the active volume of the porous
cathode is basically confined to a narrow region closest to the diaphragm. This is
attributed to the fact that the conductivity of the electrode is much higher than the
electrolyte conductivity. On the other hand, although the maximum H2O2
concentration value in the divided cell model is far less than that in the undivided one,
the average H2O2 concentration value at the bottom of the reactor is almost the same
in both models. According to these, we can conclude that the divided cell TBER is a
better choice than the undivided one.
25
Figure 4. (a) H2O2 concentration distribution at 6 mol/L KOH, 2.0 V, 1.5 L/min O2
flow rate and 15 mL/min electrolyte flow rate at 20 ℃ from the divided-cell reactor
simulation. (b) H2O2 concentration distribution at 6 mol/L KOH, 2.0 V, 1.5 L/min O2
flow rate and 15 mL/min electrolyte flow rate at 20 ℃ from the undivided reactor
simulation.
26
7.2 Effect of the KOH concentration
The modeling results and the experimental results of H2O2 generation as a function
of KOH concentration at 2.0 V, 1.5 L/min 𝑂2 flow rate and 15 mL/min electrolyte flow
rate at 20 ℃ are shown in Figure 5a. The H2O2 concentration increases with
increasing the KOH concentration, reaching the maximum value and then decreases.
This kind of change is mainly due to two reasons. One reason is the solubility of oxygen
in KOH solution; the other is the conductivity of KOH electrolyte. With KOH
concentration increasing, the amount of O2 dissolved in the electrolyte decreases,
which limits the amount of the reactant in the O2 reduction reaction. Meanwhile, when
KOH concentration is increased, the conductivity of the electrolyte rises first but then
decreases after the KOH concentration larger than 6 mol/l, which can be calculated by
the equation mentioned in Table 3. From Figure 6a, we can see that the current density
of reaction (1) increases with the concentration of KOH rising from 2 mol/l to 6mol/l
and then decreases, which is corresponding to the change of the electrolyte conductivity.
However, the simulated results obtained the maximum H2O2 concentration at a KOH
concentration of 4 mol/L instead of 6 mol/L that got from the experiment. According to
this difference, we can conclude that in the model, during the KOH concentration
increases from 4 mol/L to 6 mol/L, the negative effect of low oxygen solubility is
greater than the positive effect of increasing conductivity.
From Figure 5b, we can see the current efficiency of reaction (1) decreases with
increasing KOH concentration. These changes are attributed to the rise in the current
density of reaction (2) as shown in Figure 6b. From the view of general chemical
27
reactions, an increase in the OH− concentration will inhibit the occurrence of reaction
(2). However, the results obtained by the simulation are reversed to that. This is because
electrochemical reactions differ from ordinary chemical reactions. In addition to the
concentration of reactants and products, electrochemical reactions are also affected by
other factors including the exchange current density, electrical resistance, overpotential
and so on. As the OH− concentration increases, the overpotential of reaction (2)
increases, which is the main reason for an increase in the current density of reaction (2).
Moreover, since from 2 mol/L KOH solution to 6 mol/L KOH solution, the current
efficiency has always been decreasing, we can conclude that at least when both current
density of reaction (1) and reaction (2) increasing, the ratio of the increase in current
density of reaction (2) is higher than that in current density of reaction (1).
28
Figure 5. (a) H2O2 generation as a function of KOH concentration at 2.0 V, 1.5 L/min
O_2 flow rate and 15 mL/min electrolyte flow rate at 20 ℃ for modeled and
experimental runs. (b) H2O2 current efficiency as a function of KOH concentration at
2.0 V, 1.5 L/min O2 flow rate and 15 mL/min electrolyte flow rate at 20 ℃ for
modeled runs.
29
Figure 6. (a) Current density of reaction (1) vs. Cell Depth with change of KOH
concentration. (b) Current density of reaction (2) vs. Cell Depth with change of KOH
concentration.
30
7.3 Effect of the KOH flow rate
When considering the impact of the electrolyte flow rate, the model results in Figure
7a indicate that when the electrolyte flow rate increases, the average concentration of
H2O2 decreases. The advantages of increasing electrolyte flow rate are that it increases
liquid holdup, which further increases the active reaction area. However, it also
increases the thickness of the liquid film, which delays the species transfer inside the
liquid. Meanwhile, the accumulation of H2O2 inside the reactor is an important aspect
that affects the H2O2 concentration. Rising the electrolyte flow rate makes the H2O2
much more difficult to accumulate in the reactor, which further decreases the H2O2
concentration.
From Figure 8a and Figure 8b we can see that with an increase in the KOH flow rate,
the current density of reaction (1) almost keeps the same and the current density of
reaction (2) decreases. The reason why the current density of the reaction (1) can be
kept stable is that we assume no influence of the liquid film thickness. Therefore,
changing the liquid flow rate does not affect the concentration of oxygen on the catalyst
surface, and thus does not affect the electrochemical kinetics of reaction (1). Based on
this, we can infer that as the liquid flow rate increases, the decrease in H2O2
concentration is mainly due to the fact that the liquid flows faster in the reactor and the
H2O2 cannot accumulate well. Also, the reduction of H2O2 concentration affects the
equilibrium potential, overpotential and current density of reaction (2). From Figure 8b
we can see that the current density of reaction (2) decreases when we increase the KOH
flow rate, which further increases the current efficiency of reaction (1) as shown in
31
Figure 7b.
Figure 7. (a) H2O2 concentration as a function of electrolyte flow rate at constant O_2
flow rate of 1.5L/min in 6.0 M KOH, 2.0 V and 20 ℃ for modeled and experimental
runs. (b) H2O2 current efficiency as a function of electrolyte flow rate at constant O2
flow rate of 1.5L/min in 6.0 M KOH, 2.0 V and 20 ℃ for modeled runs.
32
Figure 8. (a) Current density of reaction (1) vs. Cell Depth with change of KOH flow
rate. (b) Current density of reaction (2) vs. Cell Depth with change of KOH flow rate.
33
7.4 Effect of the 𝐎𝟐 flow rate
When considering the change of O2 flow rate, the experimental data of the H2O2
concentration increased first and then decreased, while the simulation results remained
almost unchanged as shown in Figure 9a. Theoretically, increasing the O2 flow rate
can increase the interaction between gas and electrolyte, which leads to a decrease in
liquid film thickness and liquid holdup. These effects lead to an advantage in improving
the mass transfer of O2 from gas to the liquid-solid interface and a disadvantage in
decreasing the active reaction area. However, since both the gas flow rate and the liquid
flow rate in our experiments are low, the liquid holdup is not sensitive to the change of
the O2 flow rate. Meanwhile, we assumed O2 fully dissolved in the electrolyte, and
the liquid film thickness is thin enough to neglect the effect of concentration
polarization, which eliminates the impact of liquid film thickness. Also, under the low
gas-liquid interaction area, the liquid flow rate is not sensitive to the change of the gas
flow rate. In summary, when increasing the O2 flow rate, the dissolved O2
concentration on the reaction surface is still stable, and no effect works on the H2O2
generation and accumulation in the liquid. These factors lead to steady kinetics for both
reaction (1) and reaction (2) like shown in Figure 10a and Figure 10b.
From Figure 9b, we can see that although the current density of reaction (1) and
reaction (2) almost the same when increasing the O2 flow rate, the current efficiency
of reaction (1) still have a trend in decreasing.
34
Figure 9. (a) H2O2 concentration as a function of O2 flow rate at constant electrolyte
flow rate of 15 mL/min in 6.0 M KOH, 2.0 V and 20 ℃ for modeled and experimental
runs. (b) H2O2 current efficiency as a function of O2 flow rate at constant electrolyte
flow rate of 15 mL/min in 6.0 M KOH, 2.0 V and 20 ℃ for modeled runs.
35
Figure 10. (a) Current density of reaction (1) vs. Cell Depth with change of O2 flow
rate. (b) Current density of reaction (2) vs. Cell Depth with change of O2 flow rate.
36
7.5 Effect of the applied voltage
Figure 11a shows the simulation results and experimental results of H2O2
generation as a function of applied potential in 2.0 M KOH, 15 mL/min electrolyte flow
rate, 1.5 L/min O2 flow rate and 20 ℃. The model results show the concentration of
H2O2 increases with increasing the applied voltage until it reaches the maximum value.
These results are attributed to the rise in the overpotential of all reactions, which further
affect their current density respectively. From Fig 12a and Fig 12b, we can find that
although the current densities of reaction (1) and reaction (2) increase with the increase
of voltage, the magnitude of the change is not significant. Therefore, we can conclude
that as the applied voltage increases, most of the voltage is supplied to the anode as the
overpotential for the O2 evolution reaction. As the applied voltage further increases,
electrochemical reactions continue to accelerate, which results in the fact that the
concentration of OH− at the anode surface finally decreases to zero as shown in Figure
13. At this time, the system is controlled by the mass transfer step of OH− from liquid
to the anode surface. Increasing the applied voltage will not increase the H2O2
concentration anymore when the OH− concentration limits the anode reaction.
With increasing in the applied voltage, the current efficiency of H2O2 generation
decreases as shown in Figure 11b.
37
Figure 11. (a) H2O2 generation as a function of applied potential in 2.0 M KOH, 15
mL/min electrolyte flow rate, 1.5 L/min O2 flow rate and 20 ℃ for modeled and
experimental runs. (b) H2O2 current efficiency as a function of applied potential in
2.0 M KOH, 15 mL/min electrolyte flow rate, 1.5 L/min O2 flow rate and 20 ℃ for
modeled runs.
38
Figure 12. (a) Current density of reaction (1) vs. Cell Depth with change of applied
voltage. (b) Current density of reaction (2) vs. Cell Depth with change of applied
voltage.
39
Figure 13. Concentration of OH at the anode surface vs. Cell Height with change of
applied voltage in 2.0 M KOH, 15 mL/min electrolyte flow rate, 1.5 L/min O2 flow
rate and 20 ℃ for modeled runs.
8. Conclusions
A model has been developed to simulate the divided cell trickle bed electrochemical
reactor for hydrogen peroxide. The simulation results show good agreement with the
experimental ones, which can further guide the design and improvement of the trickle
bed electrochemical reactor. The divided-cell trickle bed reactor does have a better
improvement on the distribution of the H2O2 concentration, which can further
increase the effective reaction area for the in situ application. With increasing the KOH
concentration, the decrease in oxygen solubility has a significant influence on the
reduction of hydrogen peroxide concentration. 4 mol/L or 6 mol/L KOH solution seems
to be the better choices. Reaction (2) is not inhibited as the concentration of inlet KOH
40
increases. Conversely, the current density of reaction (2) increases, resulting in a
decrease in current efficiency of H2O2 generation. The simulation results for the
change of the KOH flow rate and the change of the O2 flow rate are a little different
from the experimental ones. These differences are due to the simplification of the model
and the errors in some correlation equations. But at least we can conclude that
increasing the electrolyte flow rate and the gas flow rate does not have much impact on
improving our TBER performance. When the applied voltage increases, most voltage
is supplied to the anode surface as the overpotential for the O2 evolution reaction,
which greatly reduces the energy efficiency. Meanwhile, with 2 mol/L KOH, the mass
transfer of OH− from liquid to the anode surface will finally become the control step
for the whole system. An attempt can be made to replace the anode plate with a porous
anode while introducing KOH solution into the porous anode. This improvement can
eliminate mass transfer limitations of OH− at the anode at lower KOH concentrations
while eliminating fluid flow dead zones. In order to get better modeling results on the
effect of the KOH and O2 flow rate, a more comprehensive hydrodynamic model with
Interphase coupling terms and spatial variation of the porosity is under consideration.
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