The Kinetics of Reactions in the Mechanism of Ultraviolet Degradation of H₂S Combined with the Non-Appearance of O₂ Using the Homotopy Perturbation Method

Anaerobic digestion, which is regarded as the most important strategy for producing renewable energy from biomass to recover clean biogas fuel, see [1], produces hydrogen sulphide [H₂S], which contains 0.3%–0.4% of the material CH₄ and CO₂, see [2]. H₂S is a foul acid gas with the potential to cause significant corrosion in equipment, instruments, and pipelines. Furthermore, H₂S has a negative impact on people’s health and the environment. When the biogas is used for energy (burning, generating power, etc.), the H₂S in it is converted to SO₂, which may significantly worsen air pollution (see [3]). Thus, the presence of H₂S impedes the promotion of biogas energy, and H₂S must be extracted from biogas using effi cient methods. H₂S techniques include biological, chemical, physical, and combinatorial technologies. The direct decomposition of H₂S to produce sulphur and hydrogen is a research topic for both domestic and international researchers because it allows for the recycling of hydrogen energy while also efficiently managing the H₂S pollution generated during the processing of coal, oil, gas, and minerals. Thermal [4,5], electrochemical [6], photocatalytic [7-9], and plasma degradation [10,11] are the primary H₂S degradation processes that produce hydrogen and sulphur. Photocatalytic H₂S degradation is the most promising technique available today due to its high treatment efficacy and reaction movement [12] (Figure 1-3).

Wilson et al. [13] investigated the direct photodegradation of hydrogen sulphide (H₂S) in the approaching Ultraviolet (UV) band. Photons with wavelengths below 270 nm can initiate degradation of H₂S, resulting in the formation of hydroxyl radicals (H·) and sulfhydryl radicals (SH·). Moreover, further photon exposure, particularly with wavelengths less than 230 nm, facilitated the transformation of SH· into H· and sulphur radicals (S·), as confirmed by experimental evidence (1), and (2). These reactions demonstrate the complex interplay between H₂S and UV radiation, focusing on the formation of reactive intermediates such as radicals and their subsequent reactions with oxygen and other environmental species. Further research into these reaction pathways is critical for understanding the fate and impact of H₂S photodegradation in various environmental settings.

The degradation rate equation for each intermediate during the photodegradation of hydrogen sulphide in the absence of oxygen can be determined using the relevant literature, the Technology’s chemical dynamics database, and the National Institute of Standards based on (1), (2), (3), (4), (5), and (6), respectively. As a photon is presented in (1) and (2), the rate constants are denoted by kobs₁, kobs₂, k₃, k₄, k₅, and k₆. The reaction rates of each component can be expressed using the equations below:

The initial conditions are given below:

and the boundary conditions are

Many researchers in engineering and physics have recently used the Homotopy perturbation method to solve a wide range of nonlinear problems [14-19]. This method combines a conventional perturbation scheme with topology. J. H. He, used the Homotopy perturbation method to solve the light hill equations [20], Duffing equations [21], and Blasius equations [22]. This method is notable for its efficiency, precision, and applicability. The Homotopy perturbation method uses the surrounding parameter p as a small parameter, and (Appendix A) it only takes a few duplications to find an asymptotic result. Using HPM (Appendix B), analytical expressions for the concentrations of H₂S, H., SH., H₂, and S are obtained using the homotopy perturbation method from these equations, giving the following results:

(Calculation was provided in the Supplementary Materials)

Proposed Model of H₂S Photodegradation

The cylindrical VUV lamp is placed in the centre of the photoreactor’s virtualized three-dimensional representation of light intensity, with a diameter of 15 cm and a height of 14 cm, as shown in (Figure 3). The VUV lamp in the white region measures 4 cm in diameter and 5.8 cm in height, as depicted in the illustration. Figure 3 shows how the intensity of light rapidly decreases as one moves away from the light source’s centre, see [12].

Major Influence Factors on H₂S Photodegradation

Equations (14)-(18) represent the approximate analytical expressions for the concentrations of H₂S, H., SH., H₂, and S. Figure 3 depicts the concentration evolution of H₂S, H., SH., H₂, and S calculated 2cm away from ultraviolet light and displayed by the analytical solution (14)-(18). Figure 4 depicts influence concentration for various values (analytical) as compared to experimental results [12]. Figure 5 depicts the impact of initial gas retention and H₂S concentration duration on photodegradation rate. Constant k₃ and k₆ increased, as did the concentration of H₂S and kobs1 has decreased. Figure 6 shows that the simulated concentration of H. radicals increased, whereas kobs₁, k₁, and k₅ decreased. kobs₂ and k₄ have increased and H. concentration decreased. Figure 7 also shows that the concentration SH. increased, kobs₁, k₅ increased, and kobs₂ and k₆ decreased. Figure 8 depicts the accelerating rate of degradation. Figure 9 indicates that the simulated concentration S increased, decreased, and increased. Mathematical analysis of the simulated concentrations for the elements of H₂S photodegradation by Ultra Violet in the absence of oxygen. The concentration changes of H₂S, H., SH., H₂, and S. The model incorporates a set of steady-state nonlinear reaction-diffusion equations. Applying the homotopy perturbation scheme to these equations yields analytical expressions for concentrations.

In the article’s overall conclusion and future development, the proposed model of UV degradation of H₂S was determined without the presence of oxygen, and the impact of the initial H₂S concentration and gas preservation duration on the photodegradation experiment was associated with the analytical results. In this work, the nonlinear differential equations in the VUV degradation are solved analytically using HPM, and an approximate and closed analytical representation form of the concentration of H₂S, H., SH., H₂, and S is provided. These novel analytical findings provide an intuitive understanding of the system and allow parameter optimization for VUV photodegradation of H₂S in the absence of oxygen.

The authors declare no competing financial interest.

Table 1:

The data sets used and/or analysed during the current study are available from the corresponding author upon reasonable request.

Methodology, Validation and Investigation: K. Saranya; Resource, Visualization and Writing-Original draft: M. Suguna; Visualization, Formal Analysis and Writing-review and editing: Salahuddin. All authors have read and agreed to the published version of the manuscript.

No potential conflict of interest was reported by the authors.

This research is supported by the Deanship of Graduate Studies and Scientific Research at Jazan University in Saudi Arabia, under Project number GSSRD-24..

The authors gratefully acknowledge the funding of the Deanship of Graduate Studies and Scientific Research, Jazan University, Saudi Arabia, through Project Number: GSSRD-24.

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