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## Combining ozone and UV-light for energy efficient removal of SO_x in low-
temperature flue gas

Reference number: 19-422

Marc Rovira, Klas Engvall, and Christophe Duwig
Department of Chemical Engineering, KTH Royal Institute of Technology,
SE-10044 Stockholm, Sweden

ABSTRACT

The potential of a combined ozone O3 ultraviolet (UV) light reactor for gas-
phase oxidation of flue gas pollutants has been evaluated in this work. For
this, numerical simulations of a continuously stirred tank reactor (CSTR) have
been performed for the analysis of sulfur dioxide SO2 removal. Chemical
kinetics have been coupled with modeling of the radiation intensity
distribution produced by a UV lamp with five different radiation models. A
grid convergence study and an optimization of the number of discrete point
light sources employed for some of the radiation models was carried out. The
effect of residence time and reactor size on the removal of SO2 have also been
analyzed. Overall, results for the abatement of SO2 in an O3-UV reactor under
optimized conditions suggest that this approach is suitable for sustainable
air cleaning applications.

### 1\. Introduction

There is currently a wide consensus that poor air quality leads to adverse
heals effects in humans. The World Health Organization estimates that 90% of
the world population lives in areas that do not meet their air quality
guidelines and attributes more than 3 million premature deaths each year to
outdoor airborne emissions [1]. One of the six priority pollutants considered
by international air standards is the family of gaseous sulfur oxides (SO_x)
of which sulfur dioxide (SO2) can be found in much greater concentration [2].
Health effects of SO2 exposure are more pronounced in susceptible populations
such as children and the elderly. For children, increased asthma [3, 4],
rhinitis [4], pneumonia and acute bronchitis [5] hospitalizations are linked
to higher SO2 levels. The environment is also affected by high SO2 emissions
mainly through acid rain.

Since the USA announced the first version of the Clean Air Act in 1963, there
has been a global effort to reduce SO2 pollution from human sources as
anthropogenic emissions account for close to 99% of total emissions [6]. The
main industrial sources include vehicle and refinery emissions as well as
emissions from the burning of coal [7]. Furthermore, the presence of SO2 in
exhaust gasses is proportional to the concentration of sulfur in the fuel
employed. Although some industries such as the automotive have been quick to
tackle SO2 emissions, others like the shipping industry are still large
pollutant sources. In 2014, the marine industry was found to be responsible
13% of global SO2 emissions [8]. Although many vessels have embraced low
sulfur emissions, upcoming legislation is bound to be even more strict. The
regulations in the MARPOL Annex VI have been adopted by the International
Maritime Organisation (IMO) and define the extent of admissible air pollution
impact of ships [9]. Taking effect in 2020, the revised MARPOL Annex VI
reduces the “Global Sulfur Cap” from 3.5% to 0.50% and 0.1% in sulfur Emission
Control Areas [10]. Hence, the shipping industry will require drastic measures
to meet these targets. A similar trend is seen in industrial flue gas
emissions [11, 12].

Apart from employing low-sulfur fuels when possible, most industries remove
SO2 by employing gas cleaning systems. In these solutions SO2 is treated along
with NO_x. However, most implementations do so individually. For flue gas,
independent denitration (i.e. selective catalytic reduction (SCR) with
ammonia) and desulfurization (i.e. wet flue gas desulfurization WFGD) systems
result in costly technologies that are expensive to operate and install [13,
14]. Hence, multi-pollutant removal solutions are quickly becoming a prominent
research topic. One such technology, which uses oxidation by ozone (O3) to
treat exhaust gases, was recently review by Lin et al. [15]. Although this
method achieves high denitrification efficiency, its main limitation of is
that O3 selectively oxidises NO [16]. Hence, the direct oxidation of SO2 by
ozone is not significant. Current solutions employ pre-ozonation to increase
the oxidation state of NO and thus its solubility to improve removal before a
wet scrubber [15]. Although this process can achieve high removal
efficiencies, the treatment of the residual liquid employed in the scrubbing
process increases operational costs and limits its applicability. Hence,
although oxidative removal of NO by O3 is feasible, other alternatives for the
simultaneous oxidation of SO2 are required.

Advanced oxidation processes (AOPs) that use hydroxyl radicals (^.OH) for
water purification and disinfection have been employed for wastewater
treatment for over three decades [17, 18]. Recently, this knowledge has been
applied to the gas-phase removal of exhaust gas pollutants with notable
success [19, 20, 21]. Here, direct exposure of the primary oxidant, usually
hydrogen peroxide (H2O2), to ultraviolet (UV) light at a particular wavelength
creates ^.OH. This radical is then able to effectively simultaneously oxidize
and remove multiple pollutants. Benefits of gas-phase AOPs include low
operational costs, little sensitivity to temperature and relative humidity
conditions, high oxidizing power, and the lack of formation of secondary
undesired products [22, 14].

An alternative to H2O2 as the primary oxidant for gas-phase AOPs is O3. This
has the advantage of directly oxidizing NO while indirectly oxidizing SO2 when
exposed to UV light. Some studies that dealt with industrial pollution removal
in gas-phase AOPs with O3 include the work of Montecchio et al. [23, 23] for
volatile organic compounds (VOCs) and the work of the research group of M.
Johnson [24, 22, 25] for reduced sulfur compounds. However, to the best of the
authors’ knowledge, there are no studies that investigate the potential for
radical oxidation of SO2 with O3 via UV light in the context of multi-
pollutant removal solutions for cooperative denitration and desulfurization.
Hence, in the present work numerical simulations of SO2 abatement by O3 and UV
light in an idealized chemical reactor will be performed. In the following
sections, details of the modeling approach will be provided along with the
results obtained and a discussion of the conclusions that can be drawn from
them.

### 2\. Methods for simulation and analysis

As described by Ducoste and Alpert [26], simulating a UV-driven AOP system
requires modeling of three different physical aspects that are interconnected.
These are the modeling of fluid dynamics, chemical kinetics, and UV light
distribution. In the following, the implementation of the modeling of each
element will be described individually after presenting the reactor
configuration that will be modeled.

#### 2.1. Reactor configuration and conditions

The geometry of the modeled reactor is an annular cylinder where the reactor
and the lamp have the same length. Dimensions for it have been taken from
Montecchio et al. [23]. Fig 1 shows an illustration of the cross-section of
the reactor. In the present study, the effect of reactor geometry has been
studied. To do so, as in the work by Montecchio et al. [23] three different
reactors have been analyzed. All three reactors have the same conditions
except their outer radius varies. The relevant conditions for the three
reactors studied, including the geometry and thermodynamic parameters, are
presented in Table I.

Figure 1: Sketch of the two-dimensional cross-section of the annular UV reactor employed. Not to scale. Table I: Parameters and conditions for the simulated CSTR reactor. All conditions are adapted from Montecchio et al. [23].  Parameter | Symbol | Value | Units
---|---|---|---
Lamp and reactor length | $L$ | 0.28 | m
Lamp sleeve (inner radius) | $r_{in}$ | 0.0115 | m
Small reactor radius | $r_{A,out}$ | 0.0425 | m
Medium reactor radius | $r_{B,out}$ | 0.0675 | m
Big reactor radius | $r_{C,out}$ | 0.0820 | m
Low-pressure UV lamp power | $P$ | 17 | W
UV lamp efficiency at $\lambda=254$ nm | $\eta_{\lambda=254}$ | 0.33 | -
Operating temperature | $T$ | 298 | K
Operating pressure | $p$ | 1 | atm

#### 2.2. Reactor modeling

In the present modeling approach, the fluid dynamics of the reactor were
simplified to consider ideal mixing. By doing so, the concentrations of all
species are assumed to be homogeneous throughout the reactor, often referred
to as a continuously stirred tank reactor (CSTR). This is done to reduce the
overall complexity of the implementation, which in turn reduces both the
number of unknown variables in the model and the time required to produce
results. This is advantageous in order to evaluate the sensitivity of the
model to different initial conditions, geometries, chemical kinetics, and UV
models. Furthermore, although the mixing is modeled as perfect, this approach
provides an upper bound to what can be expected in more complex simulations
and experimental studies.

In this work, the CSTR model as implemented in Cantera was employed [27].
Cantera is an open-source package that aids in solving numerical chemistry
problems and can be executed in Python 3 [28]. This software was used to solve
the time-dependent equations that govern the evolution of the chemical species
and the thermodynamic state of the reactor.

Figure 2: Illustration of the arrangement simulated for the CSTR reactor in
Cantera [27].

A sketch of the reactor network simulated can be seen in Fig. 2. Firstly, an
infinite reservoir of the gas mixture is defined. The composition of the
mixture tank is defined by the user by setting the initial conditions of the
molar fraction of each of the species that are desired to react together. This
mixture is considered perfectly mixed and is simulated overall as a perfect
gas. In the present case, the simplest simulation included only air (as N2 and
O2), SO2, O3 and water vapour (H2O). Initial temperature and pressure
conditions also have to be defined at this stage and were set to 295 K and 1
atm. Upstream of the tank a mass flow controller object is defined, which is
fully described by the user-defined residence time once the volume of the
reactor tank is fixed. It is then in the reactor object where the time loop is
simulated until the user-defined maximum simulation time. Only here are
reactions allowed to be carried out and hence composition changes with time.
Downstream of the reactor, a pressure valve is simulated by setting a pressure
valve coefficient which defines the efficiency to maintain the defined reactor
pressure. Finally, a capture tank object is defined at the end of the network
to store the resulting species from the reactions occurring in the stirred
reactor.

#### 2.3. Chemical kinetic modeling

The information regarding the reactions that occur in the gas mixture in
Cantera is stored in a kinetic mechanism. These files are the main chemical
input to the model and have to be in the pre-defined Cantera format (CTI). The
mechanism file stores elements and species of the gas as well as the
thermodynamic properties of each specie. Following this, the chemical
equations for the reactions between all defined species are provided. Each
reaction is then modeled with a modified Arrhenius equation and thus the
values for the pre-exponential factor $A$, the exponential factor $n$, and
activation energy for the reaction $E_{a}$ must be provided. This allows the
Cantera to numerically solve the system of ordinary differential equations
(ODEs) describing the reaction mechanism in order to determine reaction rate
coefficients.

Table II: Reduced kinetic mechanism based on the mechanism proposed by Meusinger et al. [25]. Here the units of the pre-exponential factor $A$ depend on the order the reaction. It is [$\mathrm{s}^{-1}$] for first order reactions, [$\mathrm{cm}^{3}\;\mathrm{molecule}^{-1}\;\mathrm{s}^{-1}$] for second order reactions and [$\mathrm{cm}^{6}\;\mathrm{molecule}^{-2}\;\mathrm{s}^{-1}$] for third order reaction. R13 represents the photolysis of ozone by UV light.  ID |  Reaction | $A$ | $n$ |  $E_{a}/\mathrm{R}$ [K]
---|---|---|---|---
R1 |  O + O3 -> 2 O2 | 8.00E-12 | 0 | 2060
R2 |  O(^1D) + H2O -> 2 ^.OH | 1.63E-10 | 0 | -65
R3 |  O(^1D) + N2 -> O + N2 | 1.79E-11 | 0 | -110
R4 |  O + ^.OH -> O2 + H | 2.40E-11 | 0 | -110
R5 |  O + HO2 -> ^.OH + O2 | 2.70E-11 | 0 | -224
R6 |  H + O2 + M -> HO2 + M | 2.17E-29 | -1.1 | 0
R7 |  ^.OH + O3 -> HO2 + O2 | 1.70E-12 | 0 | 940
R8 |  ^.OH + HO2 -> H2O + O2 | 4.80E-11 | 0 | -250
R9 |  ^.OH + SO2 -> HSO3 | 7.07E-11 | -0.7 | 0
R10 |  O + SO2 + M -> SO3 + M | 4.00E-32 | 0 | 1000
R11 |  SO3 + H2O -> H2SO4 | 1.20E-15 | 0 | 0
R12 |  HSO3 + O2 -> HO2 + SO3 | 1.30E-12 | 0 | 330
R13 |  O3 ->[h$\nu$] O(^1D) + O2 | $k_{\mathrm{UV}}$ | 0 | 0

The kinetic mechanisms employed in the present work was originally developed
by Meusinger et al. [25]. This mechanism employs only the most relevant
reactions among the 150 reactions provided, as predicted by their model. This
reduced mechanism has a total of 13 reactions. The reactions and Arrhenius
constants for the reduced mechanism are presented in Table II.

Reactions R1-R12 presented in Table II are thermal reactions while R13 is a
photolytic reaction. Although the reaction rate of thermal reactions can be
modeled by a modified Arrhenius equation, photolysis reactions cannot be
generally modeled in the same way. If we consider a general photochemical
reaction (A ->[h$\nu$] B), this can decomposed into three steps [29]. Here,
$h$ is the Planck constant ($6.626\times
10^{-34}\;\mathrm{J\>s\>photon^{-1}}$) and $\nu$ is the frequency of the
radiated UV light. Hence, $Q_{\lambda}=h\nu$ is the energy of one photon at a
given wavelength. Firstly an activation step (A ->[h$\nu$] A^*) occurs when
the initial ground state species absorbs a photon and produces an
electronically excited version of the original specie. Once this activate
species is created it can take two different paths. A deactivation step (A^*
-> A) occurs when the additional energy from the photon absorption is lost (by
either a radiative mechanism such as fluorescence or by a non-radiative
mechanism such as heat loss) and the activate specie returns to its original
ground state. In the context of photo-activated reactions, this is often a
negative outcome as it reduces the efficiency of the overall photochemical
reaction. Finally, a reaction step (A^* -> B) takes place when the excited
species is converted to the desired photochemical product.

The reaction rate for the photochemical activation step
$r^{\lambda}_{(\ch{A->A^{*}})}$ is directly proportional to the photon energy
absorbed by the specie [29]. Here the subscript described which reaction the
reaction rate is referring to and the superscript $\lambda$ indicates the
wavelength for which the photochemical reaction takes place (usually given in
$\mathrm{nm}$). The expression for the reaction rate of the photochemical
activation step for species A is at a certain wavelength $\lambda$ is:

$r^{\lambda}_{(\ch{A->A^{*}})}=e_{\lambda,A}^{\prime}=\frac{\lambda}{N_{A}hc}e_{\lambda,A}$
(1)

where $c$ is the speed of light ($2.998\times 10^{8}\;\mathrm{m\>s^{-1}}$),
$N_{A}$ is the Avogadro number ($6.023\times 10^{23}\;\mathrm{mol^{-1}}$). The
photon-based effective energy absorbed by A is $e_{\lambda,A}^{\prime}$ and is
often referred to as the local volumetric rate of photon absorption or LVRPA
in $\mathrm{{einstein}\>s^{-1}\>m^{-3}}$ which is equivalent to
$\mathrm{mol}$-$\mathrm{photon}\mathrm{\>s^{-1}\>m^{-3}}$ [30]. This can be
converted to the energy-based effective energy absorbed by A, $e_{\lambda,A}$,
also known as the local volumetric rate of energy absorption or LVREA (in
$\mathrm{{W}\>m^{-3}}$) by multiplying $e_{\lambda,A}^{\prime}$ by the energy
contained in one mole of photons at a given wavelength (i.e.
$Q_{\lambda,\mathrm{mol}}=N_{A}h\frac{c}{\lambda}$).

For the deactivation and reaction steps, their respective reaction rates can
be formulated by considering both as first order thermal reactions:

$r_{(\ch{A^{*}->A})}=k_{(\ch{A^{*}->A})}[\ch{A^{*}}]$ (2)

$r_{(\ch{A^{*}->B})}=k_{(\ch{A^{*}->B})}[\ch{A^{*}}]$ (3)

where $k_{(\ch{A^{*}->A})}$ and $k_{(\ch{A^{*}->B})}$ are the reaction rate
constants for the deactivation and reaction step, respectively and
$[\ch{A^{*}}]$ is the concentration of species A^* in
$\mathrm{{mol}\>m^{-3}}$. Putting Eqs 1 \- 3 together the time evolution of
the concentration of species A^* can be written as:

$\dfrac{d[\ch{A^{*}}]}{dt}=r^{\lambda}_{(\ch{A->A^{*}})}-r_{(\ch{A^{*}->A})}-r_{(\ch{A^{*}->B})}$
(4)

It can be assumed that the concentration of the photo-activated intermediate
species A^* reaches a quasi-steady state and so
$\dfrac{d[\ch{A^{*}}]}{dt}\approx 0$ [29]. Therefore, the quasi-steady state
concentration of species A^* can be expressed as:

$[\ch{A^{*}}]=\dfrac{e_{\lambda,A}^{\prime}}{k_{(\ch{A^{*}->A})}+k_{(\ch{A^{*}->B})}}$
(5)

Therefore, the rate of consumption of A, $r_{A}$, which equals the rate of
formation of B, $r_{B}$, can be written for the overall photochemical reaction
as:

$-r_{A}=r_{B}=k_{(\ch{A^{*}->B})}[\ch{A^{*}}]=\dfrac{k_{(\ch{A^{*}->B})}}{k_{(\ch{A^{*}->A})}+k_{(\ch{A^{*}->B})}}e_{\lambda,A}^{\prime}=\phi_{\lambda}e_{\lambda,A}^{\prime}$
(6)

where $\phi_{\lambda}$ is the quantum yield for the overall reaction at a
given wavelength.

Another description for the quantum yield can be obtained by defining the
overall photochemical reaction rate in such a way that it satisfies the first
and second laws of photochemistry [31]. The first law states that it is only
the light absorbed by a species which can effectively produce a photochemical
change. This law is also known as the Grotthus-Draper law. The second law,
known as the Stark-Einstein law, says that each photon can at most cause
photochemical change of one single molecule which has absorbed it. Therefore,
it defines that the primary quantum yields of a molecule must sum one. Hence,
the quantum yield itself is defined as the number of molecules of the reactant
species A consumed per unit time, $n(A)$, over the total number of photons
absorbed $\Phi_{p}^{abs}$ [32]:

$\phi_{\lambda}=\dfrac{dn(\ch{A})/dt}{\Phi_{p}^{abs}}$ (7)

Converting the number of molecules of A, $n(\ch{A})$, to the concentration [A]
by [32]:

$dn(\ch{A})=[\ch{A}]N_{A}dV$ (8)

where $dV$ is an infinitesimally small volume element that contain $dn$
molecules of A. Rearranging, one can write an expression for the consumption
of A [32]:

$-r_{A}=-\dfrac{d[\ch{A}]}{dt}=\phi_{\lambda}\dfrac{\Phi_{p}^{abs}}{N_{A}V}=\phi_{\lambda}e_{\lambda,A}^{\prime}=\phi_{\lambda}\frac{\lambda}{N_{A}hc}e_{\lambda,A}$
(9)

for which we obtain the same expression as Eq. 6. This is the equation that
will allow expressing the photochemical reaction kinetics. However, first, the
local volumetric rate of energy absorption $e_{\lambda,A}$ must be obtained.
This will be discussed in Section 2.3. Note that as the reactor is assumed to
be perfectly mixed, the reaction rate will only depend on time assuming fixed
geometry and constant lamp power output. Hence, despite Eq. 9 being also
applicable to any individual point in the reactor, for the present work the
reaction rates will be defined for the whole volume. For this to be achieved,
the LVRPA or LVREA will be required to be volume-averaged quantities as the
remainder will no have a spatial dependency. Defining this explicitly, the
rate of consumption of A for the present CSTR reactor is defined as:

$-\dfrac{d[\ch{A}]}{dt}=\phi_{\lambda}\langle
e_{\lambda,A}^{\prime}\rangle_{V}=\phi_{\lambda}\frac{\lambda}{N_{A}hc}\langle
e_{\lambda,A}\rangle_{V}$ (10)

#### 2.4. UV distribution modeling

In a general annular photoreactor where we can assume that the characteristic
length is much larger than the UV radiation wavelength, the general transport
equation for single-wavelength radiations, also known as the radiation
transport equation (RTE) reads as follows [33, 34]:

$\underbrace{\dfrac{1}{c}\dfrac{\partial I_{\lambda}}{\partial
t}\vphantom{\int_{4\pi}}}_{\text{Transient}}+\underbrace{\dfrac{\partial
I_{\lambda}}{\partial s}\vphantom{\int_{4\pi}}}_{\text{Along
$s$}}=\underbrace{j_{\lambda}\vphantom{\int_{4\pi}}}_{\text{Emission}}-\underbrace{\alpha_{\lambda}I_{\lambda}\vphantom{\int_{4\pi}}}_{\text{Absorption}}-\underbrace{\sigma_{\lambda,s}I_{\lambda}\vphantom{\int_{4\pi}}}_{\text{Out-
scattering}}+\underbrace{\dfrac{\sigma_{\lambda,s}}{4\pi}\int_{4\pi}I_{\lambda}(\textbf{{\^{s}}}_{i})\varphi_{\lambda}(\textbf{{\^{s}}}_{i},\textbf{{\^{s}}})d\Omega_{i}}_{\text{In-
scattering}}$ (11)

where $I_{\lambda}$ is the radiation intensity in
$\mathrm{{einstein}\>m^{-2}\>s^{-1}}$ at a given radiation wavelength
$\lambda$, $s$ is the radiation ray path and $\alpha_{\lambda}$ is the
(Naperian) absorption coefficient of the medium in $\mathrm{m^{-1}}$. A
thorough description of the remainder terms can be found in Modest et al.
[33]. Given that the boundary conditions are steady, the ration field will
instantaneously reach a steady-state and the transient term can be neglected
[34]. This is valid only when the speed of light is much larger than the ratio
between the characteristic length and the characteristic time. Nevertheless,
this is the case in most engineering applications [33]. In UV reactors,
temperatures are generally sufficiently low to assume that the emission from
black-body radiation is negligible [35]. Hence, the emission term can be
neglected. Finally, as the considered medium (i.e. air or water) does not have
a large concentration of solid particles or scattering can be generally
assumed to be non-elastic, the in- and out-scattering terms can be neglected
[36]. This simplification is also known as the purely absorbing medium [34].
Therefore, the final expression for the RTE when all relevant assumptions are
made reads:

$\dfrac{\partial I_{\lambda}}{\partial s}+\alpha_{\lambda}I_{\lambda}=0$ (12)

which, when integrated is:

$I_{\lambda}=I_{\lambda,0}\>\exp\left({-\int_{0}^{l}\alpha_{\lambda}ds}\right)$
(13)

where $I_{\lambda,0}$ is the radiation intensity without absorption and $l$ is
the distance from the light radiation source to the point at which the
radiation intensity $I_{\lambda}$ is going to be computed. Applying the
definition of the absorption coefficient for the medium (i.e. the mixture of
species) and the additive property Eq. 13 can be expressed as [32]:

$I_{\lambda}=I_{\lambda,0}\>\exp\left({-\int_{0}^{l}\sum_{i=1}^{N}\varepsilon_{\lambda,i}[\>i\>]\ln
10\>ds}\right)$ (14)

where $i$ is each individual species in the medium, $N$ is the total number of
species contained in the medium, $[\>i\>]$ is the concentration of the i-th
specie and $\varepsilon_{\lambda,i}$ is the wavelength dependent molar decadic
absorption coefficient in $\mathrm{m^{2}\>{mol}^{-1}}$ of the i-th specie. The
$\ln 10$ term is required to convert from the Naperian absorption coefficient
$\alpha_{\lambda}$ to the molar decadic absorption coefficient
$\varepsilon_{\lambda,i}$ [32]. Assuming that the the molar absorption
coefficient is path-independent and the concentration of each species is
homogeneous because the medium perfectly mixed:

$I_{\lambda}=I_{\lambda,0}\>\exp\left(\ln
10\>l\sum_{i=1}^{N}\varepsilon_{i,\lambda}[\>i\>]\right)$ (15)

In this form the simplified RTE in Eq. 15 is often referred to as the Beer-
Lambert Law. This simple equation describes how the different species present
in the medium through which a radiation ray is traveling partially absorb its
energy to reduce the incoming intensity. Eq. 14 is suited for the description
of the radiation intensity at a single point in the annular reactor domain.

The LVRPA for species A which undergoes photochemical change can be expressed
as [37, 38, 30]:

$e_{\lambda,A}^{\prime}=\alpha_{\lambda,A}I_{\lambda}$ (16)

substituting in Eq. 15 and expressing the Naperian absorption coefficient of
species A in terms of the molar decadic absorption coefficient and the
concentration of species A the LVRPA equation reads:

$e_{\lambda,A}^{\prime}(\mathbf{x},t)=\ln
10\>\varepsilon_{A,\lambda}[\ch{A}(t)]I_{\lambda,0}(\mathbf{x})\>\exp\left(\ln
10\>l(\mathbf{x})\sum_{i=1}^{N}\varepsilon_{i,\lambda}[i(t)]\right)$ (17)

where the dependencies of each term with respect to space (described as a
spatial vector $\mathbf{x}$) and time $t$) have been made explicit. As was the
case for Eq. 15, Eq. 17 describes the LVRPA for a single point in the reactor.
To calculate the LVRPA for the whole reactor, the hollow cylinder volume was
discretized. This will be discussed in detail in Section 3. For each mesh
element, the radiation intensity $I_{\lambda}$ was computed taking the value
calculated at the cell center. Then the volume-averaged radiation intensity is
computed as:

$\langle
I_{\lambda}\rangle_{V}=\dfrac{\sum\limits_{j=1}^{M}V_{j}I_{j,\lambda}}{\sum\limits_{j=1}^{M}V_{j}}$
(18)

where $M$ is the total number of cell elements, $V_{j}$ is the volume of the
$j$-th element and $I_{j,\lambda}$ is the radiation intensity of the $j$-th
element. Therefore, the equation that described the volume-averaged LVRPA
reads:

$\langle e_{\lambda,A}^{\prime}\rangle_{V}=\ln
10\>\varepsilon_{A,\lambda}[\ch{A}]\langle I_{\lambda}\rangle_{V}$ (19)

If Eq. 19 is substituted into Eq. 10 we obtain a pseudo-first order reaction
rate equation for the photochemical reaction A ->[h$\nu$] B:

$-\dfrac{d[\ch{A}]}{dt}=\phi_{\lambda}\ln
10\>\varepsilon_{A,\lambda}[\ch{A}]\langle
I_{\lambda}\rangle_{V}=k_{\mathrm{UV}}[\ch{A}]$ (20)

where $k_{\mathrm{UV}}$ is a function of the geometry of the reactor and the
discretization of it, the UV lamp characteristics and the radiation model
employed and the concentrations of the different radiation-absorbing species
(including $\ch{A}$) which are themselves a function of time.

The only remaining unknown is $I_{\lambda,0}$. This will be calculated using
several possible radiation models. Generally, these models can be divided into
incidence and emission models. The former assumes a radiation distribution
inside the reactor while the latter models the type of radiation emitted by
the source. Usually emission models are preferred as incidence models require
experimental parameters [35]. Comprehensive reviews of these models can be
found elsewhere in the literature [35, 39, 40] so only the models employed in
the present work will be described briefly. All models presented in the
following are known as line source models. Here, the UV lamp emission is
modeled as coming from a one-dimensional line. Other models that simulate the
UV lamp as a two-dimensional surface or a three-dimensional volume also exist
but the line source models are simpler and offer reasonable accuracy [35]. The
nomenclature for these models is not consistent throughout the literature,
however, in the present work the terminology employed by Liu et al. [39] will
be used as their application (i.e. AOPs for water treatment) is closer to the
intended application of this study. Note that the following models are usually
presented in the literature including absorption (i.e. $I_{\lambda}$ instead
of $I_{\lambda,0}$) but will be described in their simpler form as absorption
will be treated separately. For all cases, the origin of the coordinate system
will be placed at the center of the UV lamp. These models and their equations
are:

  * •

Radial model (RAD): the radial model is the most simple radiation model and
was first introduced by Harris and Dranoff [41]. This model assumes that the
light source is only emitting UV radiation in the radial direction and hence
can be considered a one-dimensional model. Mathematically, for any point in
the domain, this reads:

$I_{\lambda,0}(r)=\frac{P_{\lambda}^{\prime}}{2\pi rL}$ (21)

where $r$ is the radial coordinate (i.e. the radial distance from the lamp
center to a specific point inside the reactor) $L$ is the length of the lamp
and $P_{\lambda}^{\prime}$ is the useful UV lamp power emitted a specific
wavelength $\lambda$ in $\mathrm{einstein\>s^{-1}}$. Note that
$P_{\lambda}^{\prime}$ can be obtained from $P_{\lambda}$, the useful UV lamp
power emitted a specific wavelength $\lambda$ in $\mathrm{W}$, as:

$P_{\lambda}^{\prime}=Q_{\lambda,\mathrm{mol}}P_{\lambda}=Q_{\lambda,\mathrm{mol}}P\eta_{\lambda}$
(22)

where $P$ is the UV lamp power in $\mathrm{W}$ and $\eta_{\lambda}$ is the UV
lamp efficiency at a specific wavelength $\lambda$.

  * •

Multiple points source summation (MPSS): originally introduced by Jacob and
Dranoff [42], the MPSS model divides the lamp into several equispaced point
light sources along the lamp centerline. These light sources, unlike in the
RAD model, are not limited to emitting light in a single direction, but do so
in all available directions. This is often referred to as spherical emission.
As in an annular photoreactor, there is azimuthal symmetry, this model is two-
dimensional. The radiation intensity without absorption from one single point
light source $k$ to a single point in the domain is:

$l_{k,\lambda,0}(r,z)=\frac{P_{\lambda}^{\prime}/N_{ls}}{4\pi\rho^{2}}$ (23)

where $z$ is the axial coordinate (i.e. the axial distance from the lamp
center to a specific point inside the reactor), $N_{ls}$ is the total number
of light sources and $\rho$ can be described as:

$\rho=\sqrt{r^{2}+(z-h)^{2}}$ (24)

where $h$ is the axial distance from the lamp center to the point light
source. Then the total radiation intensity (without considering absorption)
for any point in the domain is:

$I_{\lambda,0}(r,z)=\sum\limits_{k=1}^{N_{ls}}l_{k,0,\lambda}(r,z)$ (25)

The MPSS model introduces the unknown parameter of the total number of light
sources with which to discretize the UV lamp. This parameter will be addressed
in Section 3.

  * •

Multiple segment source summation (MSSS): the MSSS model was an extension of
the MPSS model introduced by Bolton (as cited by Liu et al. [39]). Here, the
apparent overprediction of the MPSS model was tackled by assuming that the
light emission from the point light sources was diffuse rather than spherical.
This amounts to considering the point light sources as finite cylindrical
segments. This reads:

$l_{k,\lambda,0}(r,z)=\frac{P_{\lambda}^{\prime}/N_{ls}}{4\pi\rho^{2}}\cos\left(\theta\right)$
(26)

where $\theta$ is defined as the angle formed between the radial direction and
the direction that connects the point in the domain at which the radiation
intensity is being calculated with the $k$-th point light source:

$\theta=\arctan{\dfrac{|z-h|}{r}}$ (27)

Then, the total radiation intensity is computed following Eq. 25.

  * •

Line source integration (LSI): the LSI model was first introduced by Jacob and
Dranoff [42] and later assessed by Blatchley [43] for collimated-beam AOP
reactors. Formally, this method is equivalent to the MPSS with an infinite
number of discrete point light sources. Therefore, it is the integral version
of the MPSS. Without considering the absorption of the medium, the LSI model
has an analytical solution:

$I_{\lambda,0}(r,z)=\frac{P_{\lambda}^{\prime}}{4\pi
rL}\left(\arctan{\frac{L/2+z}{r}}+\arctan{\frac{L/2-z}{r}}\right)$ (28)

It should be noted that when this model is employed all absorption is
neglected. This includes the absorption of the photo-activated species which
is therefore not physical. Although some efforts have been made to include
absorption terms a posteriori (i.e. after integration) [23] experimental
fitting is required. This defeats the purpose of a priori modeling and hence
the LSI model will only be employed for evaluating the value of the MPSS model
with an infinite number of point light sources.

  * •

Modified LSI (RAD-LSI): the RAD-LSI model was proposed by Liu et al. and
incorporates both the RAD and LSI models together. This is done because the
LSI model is able to correctly predict far-field radiation intensities but not
the near-field distribution. This happens because, when approaching the UV
lamp, most radiation incident on a point will come from the light source
immediately close to it. Hence, close to the lamp the radiation can be through
as being is mostly radial and so the RAD model will better predict the near
field. Formally this is described as:

$I_{\lambda,0}(r,z)=\mathrm{min}\left[\mathrm{RAD},\;\mathrm{LSI}\right]=\mathrm{min}\left[\frac{P_{\lambda}^{\prime}}{2\pi
rL},\;\frac{P_{\lambda}^{\prime}}{4\pi
rL}\left(\arctan{\frac{L/2+z}{r}}+\arctan{\frac{L/2-z}{r}}\right)\right]$ (29)

where $\mathrm{min}\left[\mathrm{RAD},\;\mathrm{LSI}\right]$ is minimum
function between the RAD and LSI models.

Often when discussing the models presented above in the context of water
treatment AOPs, great importance is given to evaluate the effect of additional
terms that change the radiation intensity distribution [44, 39]. These terms
are mainly absorption, reflection, and refraction. For air, Liu et al. argue
that the latter two terms can be omitted [39]. Nevertheless, for cases with
low absorption neglecting reflection could yield lower performance. The effect
of the absorption of the medium should be evaluated separately because it will
depend on the species present and the wavelength at which the reactor will be
operating. As presented in Eq. 15, the Beer-Lambert law describes the
reduction in radiation intensity by an exponential term with accounts for the
distance traveled by a UV light ray $l$, the concentration of the $i$-th
species and how much that species absorbs light. The latter parameter
$\varepsilon_{\lambda,i}$ is often reported in the literature indirectly as
the (Naperian) absorption cross-section coefficient $\sigma_{\lambda,i}$ in
$\mathrm{cm^{2}}$. To obtain the former from the latter Eq. 30 can be used:

$\varepsilon_{\lambda,i}=\frac{\sigma_{\lambda,i}N_{A}}{10^{4}\ln{10}}$ (30)

Note that Eq. 30 yields $\varepsilon_{\lambda,i}$ in S.I. units (i.e.
$\mathrm{m^{2}\>{mol}^{-1}}$) but is only valid for $\sigma_{\lambda,i}$ in
$\mathrm{cm^{2}}$ as it is in these units how this value is given in the
literature.

A valuable resource for obtaining accurate and updated values for the
absorption cross-section coefficient of different species is the MPI-Mainz
UV/VIS Spectral Atlas [45]. Table III presents the values for the absorption
cross-section coefficients for the species in the kinetic mechanism as
presented in Table III. Specific references are mentioned when more than one
option was available. The references employed were selected based on recency
and/or if the publication was a review paper. The temperature and wavelength
at which these values are evaluated are as close as possible to the operating
conditions of the reactor modeled (i.e. 300 K and 254 nm).

Table III: Absorption cross-section coefficients for different species present in the present reactor simulations. All values were obtained from the MPI-Mainz UV/VIS Spectral Atlas [45] for the species in gas phase at $\sim 300$ K and for UV radiation at a radiation wavelength of 254 nm, except otherwise stated.  Species | Absorbtion cross section, $\mathrm{cm^{2}}$ | Reference
---|---|---
O3 | 1.132935E-17 | Hodges et al. [46]
O2 | 1.477865E-24 | Bogumil et al. [47]
N2 | Not reported above 150 nm | Spectral Atlas [45]
SO2 | 1.551258E-19 | Bogumil et al. [47]
H2O | Approaches 0 | Ranjan et al. [48]
HO2 | 2.63E-19 | Tyndall et al. [49]
SO3 | 1.34E-20 | Burkholder et al. [50]
H2SO4 | 7.19E-22 (at 248 nm) | Farahani et al. [51]

To simplify the computations, the contribution of some species to medium
absorption was neglected. Species with very low or negligible absorption
cross-section coefficients like N2, H2O, O2 or H2SO4 were not considered.
Furthermore, the concentration of others such as HO2 and SO3 will be too low
to have a meaningful impact. Hence only O3 and SO2 are considered as UV
radiation-absorbing species for a wavelength of 254 nm.

### 3\. Results and discussion

#### 3.1. Grid convergence

One of the earliest decisions that must be taken to simulate the UV CSTR is
how the discretization of the control volume will be performed. As has been
presented in Section 2.4, all the radiation models employed are either one-
dimensional or two-dimensional. This defines, at most, only two unknowns which
are the number of cell elements along the radial coordinate, $n_{r}$, and
along the axial coordinate, $n_{z}$.

To evaluate which value for the total number of cells is high enough to ensure
good accuracy for a simple simulation was performed using the LSI model. The
small reactor radius is employed and both coordinates are discretized with the
same number of points. Fig. 4 shows the convergence of the value for the
volume-averaged radiation intensity (VARI) with increasing number of cells.
Both the absolute value of the VARI as well as the relative rate of change
(i.e. the absolute value of the change between one simulation and the next) is
presented. As can be seen, above 100 cells there is little change in the VARI.
This corresponds to 10 cells in each direction. Nevertheless, to ensure a
value below 0.1% for the relative rate of change of the VARI a the number of
cells chosen for the subsequent studies is 225, which corresponds to 15 cells
in each direction. When a larger reactor (i.e. larger outer radius) is
employed the number of cells will be increased to maintain the ratio between
the hollow cylinder radius and the number of cells in the radial direction
constant.

Figure 3: Evolution of the the volume averaged radiation intensity (VARI) for
different total number of cells using the LSI method. Left: total value of the
VARI. Right: relative rate of change of the VARI between successive
simulations in %.

#### 3.2. Optimization of the number of point light sources

Although in the original work by Jacob and Dranoff [42] less than $0.1\%$
error was achieved with only 10 light sources, a more recent work by Bolton
[44] suggests that less than $1\%$ is usually achieved with close to 1000
discretization points. Current implementations of the MPSS model tend to use
the recommendation of Bolton despite the large discrepancy between both
values. Unfortunately, a large number of discrete point light sources leads to
a considerable increase in the computation cost. Furthermore, if the radiation
field is evaluated in each iteration of a time loop inside a reactor
discretized with many cell elements even simple CSTR simulations can be
costly.

To tackle this the defining property of the LSI model was employed. As the LSI
model is the MPSS model without absorption in the limit when the number of
discrete point light sources ($N_{ls}$) tends to infinity, a simple error
equation can be written as:

$\epsilon=\frac{|I_{\lambda,0}^{\mathrm{MPSS}}-I_{\lambda,0}^{\mathrm{LSI}}|}{I_{\lambda,0}^{\mathrm{LSI}}}$
(31)

where $\epsilon$ is the error incurred. Hence, for fixed conditions several
values for $I_{\lambda,0}^{\mathrm{MPSS}}$ can be computed until the error is
as small as a user-defined tolerance. Such computation has been implemented in
the present work. The evolution of the error with the number of light sources
can be seen in Fig. 4. Here all the error incurred in for all integer values
of $N_{ls}$ from 1 to 1000 is plotted. As can be observed, although a clear
trendline is visible, there is considerable variability that appears
unpredictable. Hence, although using a very large value for $N_{ls}\sim 1000$
can yield low error for this specific configuration $\sim 0.1\%$, the same or
even lower errors can be achieved by using much lower values. It can be seen
that close to $N_{ls}=400$ two distinct values produce sharp valleys which
yield substantially low errors. Therefore, finding the lowest possible value
of $N_{ls}$ that produces the desired error is a worth-while time investment.

Figure 4: Evolution of the error for the MPSS model without considering the
absorption of the medium (as compared to its integrated form, the LSI model)
with the discrete number of light sources employed to model the UV lamp.

Considering the large errors that are incurred in by some of the main
assumptions in the current work (e.g. ideal mixing causing perfectly
homogeneous concentrations) the target error for present computations was
fixed to $1\%$. As a rule of thumb less than 50 points were required for all
studied conditions in order to produce this error. In particular, for the 225
cell mesh, only 24 points were enough to obtain a 0.95% error with respect to
the same LSI simulation. The speedup achieved by this optimization was also
tested. For all mesh sizes studied, the case with the computed optimum value
of $N_{ls}$ was around 7 times faster than the case using 1000 points. This
optimum value of $N_{ls}$ is also employed when using the MSSS method,
however, the value is not computed using the MSSS method but rather by using
the MPSS method and comparing it with the results from the LSI prediction.

#### 3.3. Parametric study

In the following subsection, the different parameters that make up the CSTR UV
simulation as explained above will be evaluated. This will be done by
selectively varying some of the different values and aiming to establish an
optimum or ideal range within possible trade-offs. Some parameters that were
found to not significantly affect the removal rate of SO2 were not shown here.
These include the initial concentration of SO2, the relative humidity (i.e.
concentration of water vapor), and the gas temperature. All of these were
tested within a reasonable rage starting from the baseline conditions of the
simulation. The data shown for each simulation are obtained for the final
simulation time when results are considered converged in time.

##### Radiation model.

The five different radiation models presented in Section 2.4 have been
compared under equal conditions. The reactor employed was the smallest of the
three (see Table I) and was discretized with 225 mesh elements. For the MPSS
and MSSS models, the previously obtained optimum value of $N_{ls}=24$ was
employed. A total of 300 parts per million (ppm) of SO2 and 10,000 ppm of H2O
were employed. The concentration of O3 was varied to account for a range of
molarity ratios (i.e. O3/SO2). A deliberately short residence time of 10 s was
defined to better assess the differences between models.

Figure 5: Evolution of the percentage removal of SO2 for different molarity
ratios and different radiation models. Left: Molarity ratio from 0 to 1.
Right: Zoomed view, molarity ratio from 0.5 to 0.7.

Fig. 5 shows the removal of SO2 by UV-O3 at different molarity ratios for the
five models described. As expected the LSI model produces the highest SO2
removal as it is an idealized model without absorption. However, this
absorption is low for the present case as only 300 ppm of SO2 and at most 300
ppm of O3 are actively absorbing UV radiation at $\lambda=254$ nm. Hence, the
MPSS can be observed to perform similarly to the LSI under these conditions.
This low light absorption for gas-phase UV-O3 systems was already reported by
Montecchio et al. [23]. The RAD and RAD-LSI models also yield very similar
results owing to the nature of the RAD-LSI formulation. However, the MSSS
model provides a considerably lower prediction for SO2 removal efficiency. As
noted by Bolton (as cited by Liu et al. [39]), the MSSS was developed to
tackle the overprediction of the MPSS model. The present results are in line
with those obtained by Liu et al. [39] when using the MSSS in air. Namely, the
MSSS model produces the lowest volume-average radiation intensity. In their
work, the MSSS model was capable of reproducing experimental actinometric data
better than the other models. Therefore, this model was chosen for the
remainder parametric studies.

Overall, all simulations irrespective of the radiation model employed follow a
similar trend. Initially, from molarity ratio 0 to 0.7, a linear response is
observed. Increasing the molarity ratio leads to an increase in SO2 removal.
For the models which predict a higher fluence rate the proportionality
constant between molarity ratio and SO2 removal is higher and so the gradient
of their trendline is steeper. From molarity ratio 0.7 to 1 the linearity
decays progressively into a plateau reaching a maximum removal of 96-98%
depending on the model.

##### Residence time.

The efficiency of a UV reactor will be directly related to the ability of the
photochemically active species to absorb UV radiation. Hence, increasing the
exposure time of a particular species to UV light will improve photochemical
conversion. This exposure can be evaluated by varying the residence time
$\tau$ in seconds of the present simulations. Following the previous study of
the different reactor models, the MSSS model was employed for this analysis.
Other parameters and conditions remained the same.

Figure 6: Evolution of the percentage removal of SO2 for different molarity
ratios and different residence times $\tau$ in s. Note that the line
corresponding to $\tau=1000$ s is barely visible as it lies just beneath the
line corresponding to $\tau=10000$ s.

Fig. 6 shows the effect of the residence time on the overall removal
efficiency of SO2. As can be observed the residence time has a major impact on
the resulting abatement of SO2. For $\tau=1$ s just about 20% removal is
achieved with equal initial SO2 and O3 concentrations. Here, the slope is less
than one. Statistically, this implies that for every 1 ppm of input O3, less
than one 1 ppm of SO2 is removed. Therefore, fast flow through the reactor is
discouraged. Nevertheless, it should be noted that these idealized CSTR
simulations assume ideal mixing. In reality, getting as close as possible to
ideal mixing conditions will have to be done by turbulent mixing. At lower
speeds, fluid flows tend to be laminar which do not promote mixing and so
should be avoided. Hence, although higher residence times are ideal, these
should not be achieved by lowering flow speeds. Therefore, a geometry-specific
reactor has to be set up so that both relatively high residence times and
turbulent mixing occur simultaneously. Increasing the residence time to
$\tau=10$ s a notable increase in SO2 removal is achieved. At this time-scale,
the slope of the graph approaches unity. Hence, the input concentration of O3
manages to remove close to that same concentration of SO2. Therefore, close to
100% removal is achieved at a molarity ratio equal to 1. Further increasing
the residence time to $\tau=100$ s the value of the slope approaches a value
of 2. This implies that any initial concentration of O3 manages to remove
twice that concentration of SO2 from the gas phase. The peak close to 100%
removal is achieved in the vicinity of molarity ratio 0.5. This is the natural
limit for this reaction, which can be seen by inspecting the original kinetic
mechanism for the CSTR UV reactor in Table II. As observed, under ideal
conditions one mole of O3 produces one mole of oxygen singlets O(^1D). These
singlets then react with water vapor to produce two moles of hydroxyl radicals
^*OH which finally react one-to-one with one mole of SO2. This will happen if
no other scavenging reaction occurs and the hydroxyl radicals only selectively
oxidize SO2. Under these conditions, one mole of O3 can oxidize two moles of
SO2. As seen in Fig. 6, this ideal limit can be approached with long residence
times. However, increasing the residence time above $\tau=100$ s to
$\tau=1000$ s or even $\tau=10000$ s produces diminishing returns. Therefore,
the residence time for this reactor should be in the order of magnitude of
$\tau=100$ s to achieve a good trade-off between high removal efficiency and
reasonable residence times.

##### Reactor size.

Finally, following Montecchio et al. [23], the size of the reactor was
studied. This was done for three different outer radius sizes as shown in
Table. I. Fig. 7 shows the results of this parameter study. As can be
observed, the impact of the reactor size for the selected dimension is not
very large for molarity ratios below 0.2 or above 0.8. Around molarity ratio
equals 0.5 the effect of the reactor size is more visible. Here, the smaller
reactor is able to perform better and remove a higher percentage of initial
SO2. Increasing the reactor outer radius will in turn increase the reactor
volume and decrease the abatement efficiency. Therefore, to improve the
removal of SO2, the aspect ratio of the reactor must be large, with the axial
length being much larger than the radial length.

Figure 7: Evolution of the percentage removal of SO2 for different molarity
ratios and different reactor sizes. Left: Molarity ratio from 0 to 1. Right:
Zoomed view.

#### 3.4. Time-dependent results

To conclude the results section, some detailed results with temporal
resolution will be shown. Unlike previous sections, results shown here are one
for a single simulation with the optimum or desired conditions obtained from
the parametric studies. This includes the MSSS model, the smallest reactor
size, and a residence time of $\tau=100$ s. Here, a molarity ratio of 0.5 was
chosen. Results with temporal resolution enable an understanding of the time
scales of different reactions.

Fig. 8 shows the time dependant concentration of six relevant species in the
UV reactor. First, SO2 and O3 can be seen to follow a similar trend as one is
being converted to oxygen singlets O(^1D) by the UV light while the other is
being oxidized by the hydroxyl radicals ^.OH. The time-scale at which both
take place appears to be almost identical, which implies that the intermediate
steps that are between O3 depletion and SO2 removal happen fast. This
hypothesis is further substantiated by observing the evolution of O(^1D) and
^.OH. As can be seen, both remain at negligible concentration values which
implies that all molecules being generated are instantaneously being consumed.
Something similar happens to SO3 which is an intermediate species. After SO2
reacts with ^.OH it produces HSO3 which reacts with the abundant O2 to produce
SO3. However, again this species is being consumed at least as fast as it is
being produced due to its constant low concentration. When SO3 reacts with the
water vapor present in the gas mixture it is converted into H2SO4 which can be
also seen in Fig. 8 in much higher concentrations.

Figure 8: Temporal evolution of the concentration of different important
species for the CSTR UV simulation.

### 4\. Conclusions and future outlook

In the current study, simulations of a CSTR reactor were performed to analyze
the abatement of SO2 by O3 via UV light. To do so, an annular reactor was
discretized and several radiation models were employed to simulate the volume-
average radiation intensity. The theory employed has been described in detail
and equations have been derived. The information regarding radiation
distribution was employed to numerically evaluate the reaction rate of a
photochemically active step. This step converted O3 to oxygen singlets which
gave rise to hydroxyl radicals which end up oxidizing the main pollutant SO2.
The fundamental concepts of photochemical modeling were presented. The
chemical process was simulated using the Cantera [27] software in python [28].
For this, a chemical kinetic mechanism was required, which was adapted from
Meusinger et al. [25].

To understand and minimize the error committed in the simulations, a grid
convergence study was undertaken. A low number of mesh elements ($\sim 200$)
were found to be enough for obtaining low errors. Some radiation models
require the discretization of the UV lamp into point light sources or
segments. To obtain acceptable errors and minimize the computational cost, a
method to obtain the optimum value of the discrete light sources to be used
was developed. It was shown that for the present configuration, a low number
of light sources ($<50$) was enough to obtain errors smaller than 1%.

The results presented here include a parametric study on several simulation
variables. When the different models were assessed the LSI and MPSS models
were observed to predict similarly high overall SO2 removal. Following, the
RAD and RAD-LSI models presented lower removal due to their mainly radial
conceptualization of the direction of the emitted UV light. Finally, the MSSS
method produced the lowest removal rate of SO2 as was expected from the
literature. The residence time was also studied. In this parametric analysis,
it was observed to be the most impact variable. Low residence times
($1<\tau<10$ s) yielded poor pollutant removal rates. Very high residence
times ($1000<\tau<10000$ s) produced much higher SO2 removal but results were
almost identical, showing diminishing returns for such large values. Hence a
moderate residence time of $\tau=100$ s was observed to be a reasonable
compromise. The reactor size was also studied. This variable was seen to have
a moderate effect on removal rates for the range studied. Nevertheless, it was
concluding that reactors that have a low radial length compared to their axial
lengths will perform better. Hence, large aspect ratios are desirable.
Finally, time-dependent results were presented. Here, the evolution of some of
the key species in the present chemical process was studied. It was shown that
some intermediate species such as O^1D, ^.OH and SO3 are consumed at an equal
or faster rate than they are produced. All in all, results show that the
application of the present methods constitutes a viable strategy for gas-phase
pollutant removal systems.

Further developments to the present work include several aspects not directly
evaluated here. For instance, a validation case could be set up. Chemical UV
reactors are dependant on many aspects such as geometry, chemical species, UV
lamp characteristics, and placement. Hence, either another detailed
experimental results should be replicated or a new experimental work should be
undertaken. A more complex version of the chemistry employed here could be
studied. Hence, more complex mechanisms should be studied to assess how
performance varies with an increasing number of intermediate species and/or
scavenging molecules. Similarly, this reactor could be configured in series
with a NO_x-O3 system. This will both simulate a more realistic scenario - as
NO_x and SO_x tend to coexist in exhaust gases - and evaluate the selectivity
of hydroxyl radical oxidation. Here, the reflection of UV light from the
reactor walls has not been addressed. This process would require experimental
measurements of the material, roughness, and fouling over time of the wall.
Furthermore, the effect of several UV lamps and their placing could be
evaluated. Finally, scrapping the idealization of chemical homogeneity from
perfect mixing could lead to more realistic simulations. This would entail
more complex and time-consuming computational fluid dynamics simulations (CFD)
coupled with both the local radiation model and the local chemistry kinetic
rates. Under this framework, more detailed radiation models could be studied
(i.e. the discrete ordinate method [39]) and more complex turbulent modeling
such as large-eddy simulations (LES) could be employed.

### Acknowledgements

This work has been funded by ÅForsk (grant 19-422) with complementary
financing from Formas (Swedish Research Council for Sustainable Development).

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