#### Abstract

The existence of H_{2}S has limited the biogas energy promotion. The traditional photodegradation of H_{2}S is usually conducted in the presence of O_{2}, yet this is unsuitable for biogas desulfurization which should be avoided. Therefore, the ultraviolet degradation of H_{2}S in the absence of O_{2} was investigated for the first time in the present study from a mathematical point of view. Light wavelength and intensity applied were 185 nm and 2.16 × 10^{−12} Einstein/cm^{2}·s, respectively. Firstly, the mathematical model of H_{2}S photodegradation was established with MATLAB software, including the gas flow distribution model and radiation model of photoreactor, kinetics model, mass balance model, and calculation model of the degradation rate. Then, the influence of the initial H_{2}S concentration and gas retention time on the photodegradation rate were studied, for verification of the mathematical model. Results indicated that the photodegradation rate decreased with the increase in initial H_{2}S concentration, and the maximum photodegradation rate reached 62.8% under initial concentration of 3 mg/m^{3}. In addition, the photodegradation rate of H_{2}S increased with the increase in retention time. The experimental results were in good accordance with the modeling results, indicating the feasibility of the mathematical model to simulate the photodegradation of H_{2}S. Finally, the intermediate products were simulated and results showed that the main photodegradation products were found to be H_{2} and elemental S, and concentrations of the two main products were close and agreed well with the reaction stoichiometric coefficients. Moreover, the concentration of free radicals of H• and SH• was rather low.

#### 1. Introduction

During anaerobic digestion which is considered as one of the most important biomass-based renewable energy techniques to reclaim clean fuel of biogas [1], hydrogen sulfide (H_{2}S) is also produced in addition to CH_{4} and CO_{2}, with content of 0.3%–0.4% [2]. H_{2}S is a foul acid gas, and it can result in the serious corrosion of pipeline, instruments, and equipment. In addition, H_{2}S endangers human health and causes environmental pollution. When the biogas containing H_{2}S is utilized as energy (such as burning, power generation, etc.), H_{2}S will be converted into SO_{2} and cause serious air pollution [3]. Therefore, the existence of H_{2}S has limited the biogas energy promotion, and effective approaches are required for H_{2}S removal from biogas.

treatment methods include physical, chemical, biological, and combinatorial technologies. The direct degradation of H_{2}S for production of hydrogen and sulfur has been the research focus of domestic and foreign researchers, since it can effectively control the H_{2}S pollution produced during oil, gas, coal, and mineral processing and also achieve the recycling of hydrogen energy. The main methods of H_{2}S degradation for hydrogen and sulfur production include thermal degradation [4, 5], electrochemical degradation [6], photocatalytic degradation [7–9], and plasma degradation [10, 11]. Herein, photocatalytic degradation of H_{2}S is the most promising technology due to the high treatment efficiency and reaction rate.

Currently, researches on photocatalytic degradation of H_{2}S are mostly conducted under the condition of O_{2} [12–14]. Nevertheless, there is potential of explosion with O_{2} presented during photocatalytic degradation of H_{2}S from biogas. Moreover, a by-product of ozone (O_{3}) is produced and further treatment was required. Photocatalytic degradation of H_{2}S with the absence of O_{2} can avoid the abovementioned problems, which is quite suitable for H_{2}S removal from biogas and other gas treatments requiring anaerobic conditions. In addition, conventional UV light sources for degradation, such as mercury vapor lamps and high-pressure xenon lamps, are incapable of producing intense light near UV or deep UV lights. The self-made high-frequency discharge vacuum ultraviolet (VUV) lamp has lots of advantages compared with the conventional UV lamps and microwave discharge electrodeless lamps, such as high efficiency, high radiation intensity, high ratio of 185 nm light, and long service life [12, 15].

Therefore, in the present study, the photodegradation of H_{2}S with VUV lamp in the absence of O_{2} was studied. Firstly, the photodegradation model was built using the MATLAB software, and then the effect of initial H_{2}S concentration and retention time on H_{2}S degradation performance was investigated and compared with the modeling result. Moreover, the reaction kinetics and mechanism of H_{2}S degradation in the absence of O_{2} were discussed. We hope the research result can help the effective H_{2}S removal under anaerobic conditions.

#### 2. Materials and Methods

##### 2.1. Reactor and Experiments

Figure 1 schematically depicts the H_{2}S photodegradation reactor used in this study. The reactor was designed as cylindrical in shape to avoid the dead space for photodegradation and the potential uneven gas distribution within the reactor. A cylindrical VUV lamp was placed on top of the reactor, and its connection with the reactor was sealed with corrosion-resistant and high temperature-resistant silica gel. A high-frequency generator was connected with the VUV lamp via an external circuit. A porous plate-like gas distribution device was installed at the gas inlet, and thus, the incoming gas can evenly flow upwards. The gas outlet was installed at the top of the reactor. To avoid short flow, the gas inlet and outlet were placed on different sides of the reactor. For the sake of shielding the high-frequency electromagnetic radiation and preventing the corrosion of the reactor caused by H_{2}S, the body of the reactor was made of SUS304 stainless steel.

The diameter and height of the reactor were 15 and 14 cm, respectively. The total volume of the reactor was 2.5 L, with the effective volume of 2.0 L when the cylindrical UV lamp with a height of 5.8 cm and diameter of 4 cm was placed.

Figure 2 is diagrammatic sketch of the cylindrical photoreactor with a cylindrical light source for radiation field modeling, where is the light intensity at point within the reactor, is the UV intensity at wavelength , and and are the horizontal distance and vertical distance of a random particle from the center of the UV lamp, respectively. is the length of the UV lamp. is the absorption coefficient of the medium in the reactor at the wavelength of . and are the radii of the cylindrical UV lamp and the cylindrical reactor, respectively.

##### 2.2. Experimental Methods

In order to investigate the degradation efficiency of H_{2}S with only the high-frequency electrodeless VUV lamp without addition of O_{3}, OH, and photocatalyst, the reactor was firstly dried, and Ar was flushed into the reactor with a 10 L/min flow rate for an hour to expel the residual O_{2} and H_{2}O in the pipeline. During the whole experiment, Ar gas was continuously flushed to exclude the effects of O_{3} and OH on H_{2}S degradation.

##### 2.3. Analytical Methods

H_{2}S concentration was determined with methylene blue spectrophotometry under a wavelength of 660 nm [16].

#### 3. Results and Discussion

##### 3.1. Mathematical Modeling of H_{2}S Photodegradation

###### 3.1.1. Gas Flow Distribution Model

The rate of gas flow was determined by both the annular space of the reactor and the retention time. As the diameter of the reactor and the UV lamp were 15 cm and 4 cm, respectively, the rate of the gas flow was calculated as 20–40 L/min when the retention time was set as 3–6 s. Considering that the concentration of H_{2}S in the gas influent was low, the constant could be calculated based on the physical properties of the incoming gas. The calculated at room temperature with Ar as carrier gas was 203–406.

The velocity () of a particle at the radius of away from the center axis of the annular reactor can be determined according to the following equation [13]: where is the known average velocity and , , and are the radius of the UV lamp, the radius of the reactor, and the horizontal distance between the particle and the center axis of the annular reactor, respectively.

Based on (1), the simulated maximum velocity was no more than 5.8 m/s (as shown in Figure S1), and then the calculated was also no more than 609. The above values were all far below the critical value of laminar flow (2300) and indicated a typical laminar flow pattern in the reactor (the calculation was provided in the Supplementary Materials).

###### 3.1.2. Radiation Field Model

The light intensity () at point within the reactor can be expressed with (2) [17].

The simulated three-dimensional model of the light intensity by the cylindrical VUV lamp at the center of the photoreactor with diameter and height of 15 cm and 14 cm, respectively, is shown in Figure 3. The white area was occupied by the VUV lamp with diameter and height of 4 cm and 5.8 cm, respectively, as scaled in the figure coordinate axis. According to Figure 3, light intensity decreased rapidly with the increase in the distance from the center of the light source.

In order to verify the result of the light intensity distribution model in the reactor, a UV radiation meter was applied to measure the UV_{254} intensity at 5–35 cm away from the lamp wick of the cylindrical lamp. In the meantime, the light intensity at the same position was calculated based on the UV light radiation field model and then was compared with the measured value to verify the results of the model. As shown in Figure 4, the results indicated that the calculated value and the measured values were close, indicating that (2) was feasible to predict the radiation intensity distribution.

###### 3.1.3. Photochemical Reaction Kinetics Model

The photochemical reaction kinetics equation involving component can generally be presented as the following equation.
where is the molar concentration of component (mol/L), is the quantum efficiency, is the molar absorption coefficient (L/mol·cm), is the optical length (cm), and is the light radiation intensity (Einstein/cm^{2}·s). It should be noted that the VUV light absorption by other components of the initial biogas, including the typical CH_{4} and CO_{2}, could be neglected [18].

Equation (3) has an exponential term, making the calculation complicated. When , (3) can be reasonably approximated to the following expression:

Asili and De Visscher [13] proposed another equation for calculating the photochemical reaction rate (molecule/cm^{3}·s):
where is the molar concentration of component (molecule/cm^{3}), is the quantum efficiency, is the absorption cross section of component , and is the photon flux (photon/cm^{2}·s).

The comparison of (4) and (5) revealed that both equations reflect the same reaction behavior, though (4) describes the concentration change macroscopically while (5) describes it microscopically. Both equations describe the chemical changes that occur when the reacting components absorb a certain amount of energy.

###### 3.1.4. Mass Balance Model

Firstly, the Peclet number in the photoreactor was calculated, revealing the numerical zone of 132–263. represented the relative proportion of convection to diffusion. When is larger than 40, the dominant mass transfer type was convection at the airflow direction. As the main gas flow pattern was a laminar flow, the main mass transfer pattern at the vertical direction was diffusion. According to the empirical equation, for H_{2}S-air mixed gas, the diffusion coefficient at the vertical direction can be expressed as [19]
where is the diffusion coefficient (cm^{2}/s), is the gas temperature (K), and is the gas pressure.

For a random component of the photochemical reaction system in the annular photoreactor, its partial differential equation of mass conservation can be represented as
where is the velocity of the gas molecule at current position (cm/s), is the molar concentration of the component (mole/cm^{3}), is the vertical distance between a random position and the gas inlet (cm), is the horizontal distance between a random position and the linear light source, is the diffusion coefficient of the component at the radical direction (cm^{2}/s), and is the photochemical reaction rate (mole/cm^{3}·s).

The boundary condition of the partial differential equation (7) was assumed as the no-flow boundary, and the inlet gas concentration was considered as constant.

###### 3.1.5. Calculation Model of Degradation Rate

For a random component in the photochemical reaction system, the degradation degree can be expressed as where is the random component in the photochemical reaction system at the gas outlet and is the initial concentration of at the inlet. For a tubular reactor, the average concentration of the random component at the gas outlet can be expressed as where is the velocity of the gas molecule at the present position (cm/s), and are the radius of the VUV lamp and the reactor (cm), and is the horizontal distance between a random position and the linear light source.

The velocity of the component in the reactor can be calculated using (1) and (2) and can be used to acquire the light intensity of a random position in the reactor. Then, the acquired data can be used in (4) and (7).

Equation (4) is an ordinary differential equation (ODE). Although (7) is a partial differential equation (PDE), it can be converted into a series of ODEs using MATLAB ODE15s for equation solution. Then, (8) and (9) are used for solving the degradation rate of the target component and correlate with experimental data.

##### 3.2. Major Influence Factors on H_{2}S Photodegradation

###### 3.2.1. Initial H_{2}S Concentration

The influence of the initial H_{2}S concentration on the degradation rate under retention time of 6 s is profiled in Figure 5. Results showed that the degradation rate continuously decreased with the increase in the initial H_{2}S concentration, which was similar to the situation with O_{2} present [12]. As shown, when the initial H_{2}S concentration was 3 mg/m^{3}, the maximum degradation rate was about 62.8%. When the initial H_{2}S concentration reached 25 mg/m^{3}, the degradation rate decreased to 36.2%. UV light can only pass a relatively short distance in vacuum, and also there were no oxidative free radicals to assist degradation [20]; therefore, the degradation rate was comparatively lower than that with the presence of O_{2} [12, 21]. Moreover, no SO_{4}^{2−} in the photodegradation products of H_{2}S was detected although it was confirmed as the main product in a previous study [22], and H_{2} and elemental sulfur were the possible products. Yet, solid S was also not observable throughout the whole experiment. The first reason was the rather low particle settling velocity calculated by Stokes formula, and another reason was the very low H_{2}S concentration and high airflow velocity. Therefore, it was difficult for the sulfur particle to settle on the internal reactor walls and no deposition of elemental sulfur was observed.

###### 3.2.2. Gas Retention Time

Under the initial H_{2}S concentration of 12 mg/m^{3}, the simulation of the H_{2}S degradation profile based on modeling and the experimental data are compared in Figure 6. The experimental results indicated that the degradation rate was significantly affected when gas retention time in the reactor was less than 12 s. Specifically, when gas retention time was 3 s and 6 s, the degradation rate was 22.0% and 48.1%, respectively, indicating that the degradation efficiency proportionally increased with gas retention time. With higher gas retention time, the increasing rate of the degradation efficiency became slower. For instance, when gas retention time was 24 s, the degradation efficiency was 74% and only increased by 30% compared with that at gas retention time of 6 s. However, it still could not reach 100% degradation with the further increase in gas retention time.

The dead zone was placed in a position far away from the lamp, and so H_{2}S was hard to be degraded thoroughly. Longer retention time was beneficial for increasing the degradation rate; however, the energy consumption was also increased. Therefore, the appropriate retention time should be selected considering the initial H_{2}S concentration, equipment cost, and operating cost.

The root-mean-square error (RMSE) for this model simulation was as small as 0.0622. A -test was conducted for comparing the simulation data and experimental data, and the test result accepted the null hypothesis with a possibility of 96.72%, indicating that the simulation data and the experimental data were consistent. This proves that the model to simulate the degradation efficiency in the photodegradation reactor was feasible.

##### 3.3. Mechanism of H_{2}S Photodegradation Using Only VUV Light

Wilson et al. [23] studied the direct degradation of H_{2}S by photon of a near ultraviolet band. Results showed that a photon with a wavelength less than 270 nm could directly photodegrade H_{2}S into H· and SH·, and SH· could be degraded into H· and S· with a photon wavelength less than 230 nm, as shown in (10) and (11). The possible reactions during the direct photodegradation of H_{2}S are listed as follows:

By referring to the chemical dynamics database of the National Institute of Standards and Technology (NIST) and the related literatures, the rate constants can be acquired for the above reactions and are summarized in Table 1. A photon participates in reactions (10) and (11), and the molar absorption coefficients for wavelengths of 185 nm and 254 nm can be obtained by converting the absorptivity data summarized in Table 1.

Based on (10), (11), (12), (13), (14), and (15), the degradation rate equation of the various intermediates during hydrogen sulfide photodegradation in the absence of O_{2} could be established. As photon is presented in (10) and (11), let ((4)), denoting , , , , , and as the rate constants for (10), (11), (12), (13), (14), and (15). The reaction rate equations for each component can be expressed as follows:

Then, the reaction rate equations for , , , , and (from (16), (17), (18), (19), and (20)) were integrated into the UV-photodegrading reactor model, and the photodegradation effect without O_{2} was simulated under the following conditions: the initial concentration was set as 12 mg/m^{3} with Ar as the carrier gas. The concentration evolution of , , , , and were calculated 2 cm away from the UV light with MATLAB software and demonstrated by the logarithmic scale in Figure 7.

It was revealed that the final products of photodegradation were mainly and , and their concentrations were close to each other, which was in accordance with the stoichiometric coefficients of the photodegradation reaction. Moreover, the simulated concentrations of and radicals were rather low, which were about two orders of magnitude lower than and .

Finally, we tried to build the analytical equation connecting the rate of consumption and its concentration and light intensity using steady-state approximation for radicals. Firstly, let (16) be equal to zero, as shown in (21).

Then, (21) and (22) could be obtained combining (16) and (21), as follows.

Then, was substituted with (4), and the analytical equation connecting the rate of consumption and its concentration and light intensity using steady-state approximation for the radical could be obtained as (24).

#### 4. Conclusions

In the present study, the mathematical model of ultraviolet degradation of with the absence of O_{2} was established, and the influence of the initial concentration and gas retention time on the photodegradation rate were studied and for verification of the model. The main findings were as follows.
(1)The photodegradation rate decreased with the increase in initial concentration, and the maximum photodegradation rate was about 62.8% under initial concentration of 3 mg/m^{3}.(2)The photodegradation rate increased with the increase in retention time.(3)Experimental results were in good accordance with the modeling results.(4)The main photodegradation products were and elemental S based on mathematical modeling. Concentrations of both products were close and agreed well with the reaction stoichiometric coefficients.

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Authors’ Contributions

Jian-hui Xu and Bin-bin Ding contributed equally to this work and should be considered co-first authors.

#### Acknowledgments

The authors gratefully acknowledge the financial support of the Development of Social Science and Technology in Dongguan (Key) (2017507101426).

#### Supplementary Materials

Calculation of Reynolds number (Re): the calculation formula for Re was , where *ρ*, *v*, and *μ* were the gas density (1.169 g/cm^{3}), velocity, and viscosity coefficient (18.448 *μ*Pa·s) of Ar gas, respectively, and d was the equivalent diameter of the photoreactor. The diameter (*d*) was 0.15 cm. The velocity (*v*) was 0.019–0.038 m/s based on the gas flow rate (, where *Q* was 20–40 L/min and *S* was obtained based on the diameter of 15 cm). Then the calculated Re was about 203–406. In addition, the velocity based on the simulation of (1) was no more than 0.058 m/s (as shown in Figure S1), and Re was about 609. Both the above values indicated a typical laminar flow pattern in the reactor. Figure S1: the simulated gas flow velocity by (1).* (Supplementary Materials)*