Electronic Supplementary Information: Gliding arc plasma for CO2 conversion: better insights by a combined experimental and modelling approach Weizong Wang*,1, Danhua Mei2, Xin Tu2 and Annemie Bogaerts1 1. Research group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, B-2610 Wilrijk-Antwerp, Belgium 2. Department of Electrical Engineering and Electronics, University of Liverpool, Brownlow Hill, Liverpool L69 3GJ, United Kingdom E-mail:
[email protected],
[email protected]
1. Model description: governing equations and boundary conditions The species density continuity equations read as follows:
ns t
Gs (ug
)ns Sc,s
(S1)
where ns is the species density, Gs is the species flux in a reference frame moving with the gas velocity ug, and Sc,s is the collision term representing the net number of particles produced (when a positive value) or lost (when negative) in the volume reactions. The index ‘s’ represents all the species considered in the model, except for , and the ground state of CO2. Indeed, the number density of is simply determined by electrical neutrality in the plasma, i.e., from the calculated densities of the electrons and of the negative and other positive ions. The number density of ground state CO2 is obtained by subtracting the sum of the number densities of all other species from the total species number density. The latter is determined from the following gas state equation:
P
ne kTe
N
ne
(S2)
ns kTg
(S3)
ns
where ne, ns, k, Te, Tg and N are the electron number density, the number density of the various other species s, the Boltzmann constant, the electron temperature, the gas temperature and the total species number density, respectively. We assume that the local pressure inside the plasma is constant (i.e., equal to atmospheric pressure), while the electron and gas temperature are calculated with eq. S6 and S12 below) The drift-diffusion approximation is used to calculate the species fluxes Gs in eq. (S1) as follows:
Gs
qs qs
s ns Eamb
(S4)
Ds ns
Here qs is the charge of the given species type, Ds is the diffusion coefficient and μs is the mobility of the corresponding species. Their values can be found in our previous work [1]. The ambipolar electric field Eamb is derived from the densities, diffusion coefficients and mobilities of the various charged species: 1
Eamb =
DCO
2
nCO
DO
2
nO
2
nCO
nCO
3
nO
CO2
2
DCO
2
nCO
O2
2
DO
3
nO
CO3
3
nO
DO
2
nO
O
2
O2
nO
De ne
2
ne
The electron energy equation is solved for the average electron energy density ne
ne t where
e
e
G ,e (ug
)ne
Ed2 ne
e
(S5)
e
e:
Pbb
e
(S6)
is the average electron energy, from which the average electron temperature is evaluated
as Te = (2/3)
e in eV. Pbb is the power used to initiate the back-breakdown events (see below).
The plasma electric conductivity is defined as:
=e(nCO
CO2
2
nO
O2
2
nCO
nO
CO3
3
O
nO
2
O2
ne e )
(S7)
where e is the elementary charge. The first term in the right hand side of equation (S6) represents the Joule heating term and the second term is the total electron elastic and inelastic collision energy loss term with e being negative values. The electron energy density flux
qs qs
Gs
s ns Eamb
G ,e
is expressed as follows (S8)
Ds ns
where D ,e is the electron energy diffusion coefficient and , e is the electron energy mobility. The electron energy mobility is written as: ,e =
5 3
(S9)
e
The electron energy diffusion coefficient is:
D ,e =
2 3
e
(S10)
,e
The applied electric field Ed is calculated by the following derivation, which is obtained by summing equation S1 for the charged species.
(
)
qe ( DCO
2
nCO
2
DO
2
nO
2
DCO
3
nCO
3
DO
nO
De ne )
(S11)
where is the electric potential. The gas heat transfer equation is solved for the gas translational temperature Tg:
Cp
Tg t
C pug
Tg
(k g Tg ) Pe,el
Rj H j
(S12)
j
∑ where is the total mass density of the ionized gas (i.e., the sum of the mass densities of all heavy species). The first and second term in the right hand side of equation (S12) represent the 2
power transferred from the electrons to the heavy particles by elastic collisions and the power consumed by the heavy particle reactions (with H j being positive or negative in case of heat consumed or released in the reaction j). Rj is the reaction rate of reaction j, defined as:
Rj
kj
l
(S13)
nl
where kj is the rate coefficient of reaction j, and nl stands for the number density of the various reactants l in this reaction. The thermal conductivity of a gaseous mixture k g is evaluated by the Chapman-Enskog method *2+-*3+. The specific heat at constant pressure C p is determined by
k 1M
Cp =
(S14)
where k and M are the Boltzmann constant and the molar weight of the gaseous mixture, respectively. The specific heat ratio of the gaseous mixture,
N
-1
s
= ns s
, is determined as
s
(S15)
1
where γs is the specific heat ratio of species s. The specific heat ratio is taken as 1.67 for the atomic species and 1.40 for the diatomic molecules (CO and O2). For CO2, we only have to take into account the heat capacity due to translational and rotational degrees of freedom, as well as the vibrational symmetric mode levels that are not described by an individual species. The neutral gas flow, which is responsible for the arc displacement, is described by a simplified version of the Navier-Stokes equations, which provide a solution for the mass density and the massaveraged velocity.
( ug ) 0
t ug t
(S16)
( ug ug )
where p is the gas pressure,
( pI
( u g ( u g )T ))
(S17)
is the gas viscosity, I is the unit matrix and the superscript ‘T’ stands
for the tensor transpose operation. In our case, the inertial term at the left hand side in equation (S17) is not included in the 2D model, i.e. in the regime of Stokes flow. The Navier-Stokes equations are first solved separately, and subsequently, the obtained velocity distribution is used as input data in the other equations, describing the plasma behavior and the gas heating. The above partial differential equations are subjected to appropriate boundary conditions. We set zero species fluxes and zero electron energy flux at all boundaries. A thermal insulation condition is used for the gas heat balance equation. For the electric potential equation, the cathode potential Vc is derived from Ohm’s law based on the value of the total arc current at the cathode, the external resistor value and the total applied voltage (i.e., potential difference over the resistor and the arc). The anode is connected to the ground. For the gas flow, a laminar inflow boundary condition for the 3
flow is used at the inlet of the reactor. This assumption of a laminar flow is reasonable because of the low gas flow rate adopted here. At the gas outlet, the gas pressure is set to atmospheric pressure. On the cathode and anode walls, the velocity follows a so-called “no slip” boundary condition, i.e. zero tangential velocity.
2. Experimental validation of the model Figure S1 presents the applied voltage and corresponding discharge current as a function of time, for one cycle of the applied voltage (or two gliding arc cycles), at a gas flow rate of 2.5 L/min and a discharge power of 40 W. From these data, we can obtain the average voltage drop and average current, which yield an average arc impedance. In combination with the radius and average length of the arc, which are obtained from the high speed camera recordings, illustrated in Figure S2, we can obtain the average arc electrical conductivity, from which the electron density can be calculated, as explained in the main paper.
Figure S1 Discharge voltage and corresponding discharge current as a function of time for one cycle of the applied voltage, at a gas flow rate of 2.5 L/min and a discharge power of 40 W. The dashed line (t = 0 ms) corresponds to the starting time of our simulation.
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Figure S2 Time evolution of the CO2 gliding arc discharge, during one half cycle of the applied voltage, corresponding to one gliding cycle (gas flow rate 2.5 L/min, plasma power 40 W, 5000 frames/s, exposure time of 50 μs). The number corresponds to the frame number in the sequence of the high speed camera recordings. From these images, we could deduce that the arc radius and average arc length are ca. 1 mm and 15 mm, respectively.
3. Thermal CO2 conversion and corresponding energy efficiency In order to evaluate the performance of the GA plasma for CO2 conversion and to illustrate the non-equilibrium character, we compare the results with the pure thermal conversion, calculated as a function of gas temperature. The thermal conversion of CO2 is calculated as ( )( )
[
( (
) ( ) ) ( )
]
[
( (
)
( )
) (
)
]
(S18)
where nCO2 is the total CO2 number density and v is the gas velocity. During the derivation of equation (S18), a constant mass flow rate Qm= ρ(t)v(t) is assumed. It is assumed that the initial temperature of the gas is 300 K and the gas temperature reaches Tg at a time t. is the mass density, which is evaluated as: 𝑤
𝑚𝑎𝑥 ∑𝑖=1
(S19)
𝑖 𝑖
where mi is the mass of species i , and the summation is taken over all species, including CO2 molecules, but also CO, O, O2, and corresponding ions, where 𝑤𝑚𝑎𝑥 denotes the total number of species in the mixture. The energy efficiency of thermal CO2 conversion is calculated as: 5
𝜂
( )
(
𝐻
𝑚𝑜𝑙,
𝐻𝑚𝑖𝑥 (
)
)
(S20)
where nmol,CO (kg-1) is the number of CO molecules per kilogram, HCO is the CO formation enthalpy per molecule (2.93 eV, or4.69 × 10-19 J) and Hmix(Tg) (J/kg) can be written as: 𝐻𝑚𝑖𝑥 ( )
𝐻( )
𝐻(3
𝐾)
(S21)
The specific energy input (SEI; expressed here in J) is evaluated in this case as the specific enthalpy change of the mixture Hmix (J/kg) divided by the total number of species per kilogram at the initial state nt(kg-1) when the dissociation has not yet taken place. 𝑆𝐸𝐼( )
𝐻𝑚𝑖𝑥 (
)
(S22)
𝑡
The specific enthalpy 𝐻( ) is determined from the calculated chemical equilibrium composition using the standard well known thermodynamic formula *5+. Figure S3 illustrates the CO2 conversion and corresponding energy efficiency, calculated with the above formulas, as a function of the gas temperature. From these data, we can plot the energy efficiency vs conversion, i.e., the so-called thermal conversion limit, as shown in figure 3 of the main paper.
Figure S3 Calculated theoretical thermal conversion and energy efficiency as a function of temperature in pure CO2 at a pressure of 1 atm.
4. Time evolution of the rates of the different CO2 loss and formation processes
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Figure S4 Time evolution of the rates of the different CO2 loss (a) and formation (b) processes, spatially-integrated over the reactor, at a gas flow rate of 2.5 L/min and a discharge power of 40 W. The numbers of the curves correspond to the reactions listed in table 3 of the main paper. In figure S4, we plot the time evolution of the most important loss and formation rates of CO2, spatially integrated over the entire reactor, at a gas flow rate of 2.5 L/min and a discharge power of 40 W. Initially, at around 0.01 ms, electron impact dissociation from the CO2 ground state (process L1g in figure S4) is the most important loss process for CO2, which is attributed to the relatively large potential difference across the electrodes and hence the large electric field, yielding electrons with high enough energy for dissociation from the ground state. However, due to the low electron density at this time, the absolute rate of this process is limited. After ignition of the arc, i.e. at 0.1 ms, the electric field drops dramatically (as can be observed from the significant drop in the applied voltage; see figure S1), and thus, the rate of this process drops, while electron impact dissociation from the CO2 vibrational levels (L1v) becomes more important. Indeed, vibrational excitation becomes more important at lower electric field, and thus lower electron energy, and the subsequent dissociation from the vibrational levels also requires less energy for the electrons than dissociation from the ground state. When time evolves, dissociation upon collision of the CO2 vibrational levels with O atoms (L2v) becomes the dominant loss mechanism, starting from t = 1 ms, as is clear from figure S4. This is partly due to the higher gas temperature obtained in the arc, which increases the reaction rate of this process. This explains why the rate of the same process, but with ground state CO2 molecules, also rises with time. However, by comparing the reaction rates of the dissociation upon collision of O atoms with ground and vibrational levels, it is clear that dissociation from the vibrational levels is far more important, due to the increasing concentration of the vibrational levels in the arc, which can 7
help to overcome the high reaction energy barrier of CO2 splitting upon collision with O atoms. After t = 7 ms, when the discharge current drops, the reactions rates of L2g and L2v go down, because of the drop in plasma temperature. Similarly, the rates of the dissociation of CO2 (in both ground state and vibrational levels) upon collision with other heavy particles (i.e., L3g and L3v) show the same trends, following the evolution of discharge current and hence the plasma temperature. However, their rates are lower than the dissociation upon collision with O atoms. The reactions with 𝑂 − ions forming 𝑂− ions (i.e., L4g and L4v) are almost negligible compared to the other processes, and their rates also show the same drop after t = 7 ms, because of the drop in electron number density. Finally, when the GA enters into the relaxation stage, after t = 8.5 ms, the rates of the CO2 splitting reactions involving electrons (i.e., L1g and L1v, as well as L4g and L4v) show a (slight) increase again, because a higher reverse polarity voltage is imposed across the electrodes, and the electron temperature and electron number density will again gradually increase. It is obvious from this figure that, integrated over time of one entire GA cycle, dissociation of the vibrationally excited levels upon collision with O atoms (L2v) is by far the most important loss process for CO2, with an overall contribution of 80 % (see figure 6 of the main paper). As far as the CO2 formation is concerned, the recombination of CO with O2 (F1) is clearly the most important, but the recombination of CO with O atoms (F2) dominates the CO2 formation till 0.1 ms. This is logical, because at this short time, CO2 dissociates into CO and O atoms, and the O atoms did not yet have the time to recombine into O2. The recombination of CO with 𝑂− ions (F3) is negligible in the whole GA cycle. Finally, it is clear that the rates of the CO2 formation reactions (F1, F2 and F3) first increases and then decrease, following the temporal evolution of the CO concentration within the arc channel, as well as of the gas temperature (see figure S5). As the CO2 formation reactions are the limiting factors for energy-efficient CO2 conversion by the GA plasma, we need to look for solutions on how to overcome these limitations, in order to further improve the GA based CO2 conversion.
Figure S5 Time evolution of the maximum CO molar fraction and gas temperature along the symmetry plane, for the same conditions as in figure S4.
5. Occurrence of the back-breakdown events in a CO2 GA We employ the following algorithm for a distance controlled back-breakdown *6+. 8
1. We first define the period between consecutive back-breakdown events and a time dependent function tbb which represents the different time instants when the back-breakdown takes place. This function is the sum of several Gaussian functions, each one being displaced in time and centered at the time of the back-breakdown events. 2. We find the positions of maximum electron density at the electrodes ((x1, y1) and (-x1, y1)) and at the symmetry axis (x = 0, y2). These numbers approximately determine the current position of the arc. 3. We use these numbers (x1, y1, y2) to define the position of the back-breakdown event, i.e. to define the spatial function of the back breakdown addition to the heating term. More specifically, the y position of the back-breakdown event is defined as ybb=y1+(y2-y1)*ry, assuming ry = 0.5. The x position of the back-breakdown event is xbb=rx*(ybb-y2)*x1/(y1-y2), assuming rx = 0.5. The formulas are deduced from the shape of the region surrounded by the arc. 4. A heating term used to initiate the back-breakdown is added to the electron energy equation (Eq. S6). The minimum heat source used for producing the back-breakdown is 1010 W/m3, and thus the expression with only one time function term is as follows: 1
W
[m3 ]
exp(
(
(𝑦−𝑦 1
) [𝑚])
)
exp(
(𝑥) (𝑥 )
)
exp(
(
( − 1
) [ ])
)
(S6)
Figure S6 presents the time evolution of the electron number density, the gas temperature and the CO molar fraction, illustrating a single back-breakdown event for the same conditions as in figure S1. By adding the heating term Pbb between the arc tails, the average electron energy rapidly increases there and leads to a fast CO2 ionization. With the accumulation of the produced electrons, the back-breakdown channel becomes conductive and a new arc is established, because this new channel provides a shorter electric current path and a lower resistance. As a result, the potential difference across the old channel drops and cannot further sustain the discharge there. The plasma density gradually decays and the old discharge channel disappears. Together with the occurrence of the back-breakdown channel, the current flowing into the old channel decreases and the power used to heat the residual plasma channel reduces to zero. As a result, the plasma temperature there decreases and the gas temperature in the newly established channel starts to increase due to the VT relaxation, which converts the vibrational energy, stored in the vibrational levels by electron impact vibrational excitation and VV relaxation, into translational energy. As we can see in figure S7, when the back-breakdown events would occur too often, they will continuously cool the GA. Thus, too many back-breakdown events will lower the overall gas temperature, because the heat is now spread over a larger domain and not only within the initial arc channel. This lower gas temperature can have either beneficial effects (because of (i) reduced VT relaxation, thus promoting the vibrational kinetics, and (ii) reduced recombination between CO and O2)or detrimental effects (because of reduced dissociation of CO2 upon collision with neutral species) on the overall CO2 conversion. It is clear that for the conditions under study, the lower temperature, in combination with the larger fraction of the CO2 gas treated by the arc, have a positive effect on the CO2 conversion, as is clear from figure 11 of the main paper.
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Figure S6 Time evolution of the electron number density (a, in m-3), the gas temperature (b) and the CO molar fraction (c), during a back-breakdown event at a flow rate of 5 L/min.
Figure S7 Time evolution of the maximum gas temperature along the symmetry plane at a gas flow rate of 5.0 L/min, for different cases, i.e., without back-breakdown (1); one back-breakdown at 5 ms 10
(2); two back-breakdowns, at 5 ms and 6 ms (3); three back-breakdowns, at 5 ms, 6 ms and 7 ms (4); and five back-breakdowns, at 5 ms, 5.5 ms, 6 ms, 6.5 ms and 7 ms (5). Furthermore, as indicated in figure S6 (c), the CO molar fraction in the new discharge channel after the back-breakdown event gradually increases because CO2 is being continuously processed by the new arc. In contrast, the local CO molar fraction in the old channel gradually decreases due to the recombination reaction of CO into CO2, as well as the diffusion and gas convection process, which gradually transport CO out of the old discharge channel. We can also find that the occurrence of back-breakdown establishes a new conducting channel in the upstream of the old arc, causing a delay of the arc velocity with respect to the gas flow velocity. Reference [1] W. Z. Wang, A. Berthelot, St. Kolev, X. Tu, A. Bogaerts, CO2 conversion in a gliding arc plasma: 1D cylindrical discharge model, Plasma Sources Sci. Technol. 25 (2015) 065012. [2] W. Z. Wang, J. D. Yan, M. Z. Rong, A. B. Murphy, J. W. Spencer, Thermophysical properties of high temperature reacting mixtures of carbon and water in the range 400–30,000 k and 0.1–10 atm. part 2: transport coefficients, Plasma Chem Plasma Process 32 (2012) 495-518. [3] W. Z. Wang, M. Z. Rong, Y. Wu, J. D. Yan, Fundamental properties of high-temperature SF6 mixed with CO2 as a replacement for SF6 in high-voltage circuit breakers, J. Phys. D: Appl. Phys. 47 (2014) 255201. [4] W. Z. Wang, A. Bogaerts, Effective ionisation coefficients and critical breakdown electric field of CO2 at elevated temperature: effect of excited states and ion kinetics, Plasma Sources Sci. Technol. 25 (2015) 055025. [5] W. Z. Wang, A. B. Murphy, J. D. Yan, M. Z. Rong, J. W. Spencer and M. T. C. Fang, Thermophysical properties of high-temperature reacting mixtures of carbon and water in the range 400–30,000 K and 0.1–10 atm. part 1: equilibrium composition and thermodynamic properties, Plasma Chem. Plasma Process 32 (2012) 75-96. [6] S. R. Sun, St. Kolev, H. X. Wang, A. Bogaerts, Coupled gas flow-plasma model for a gliding arc: investigations of the back-breakdown phenomenon and its effect on the gliding arc characteristics, Plasma Sources Sci. Technol. 26 (2016) 015003.
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