Simultaneous Optimization of Sulfur Recovery Efficiency and Thermal Energy Generation in the Catalytic Section of the Sulfur Recovery Unit Simulated Based on Reaction Kinetics

Abstract

The Claus process is widely used in refineries for sulfur recovery, significantly reducing sulfur dioxide emissions. In line with this, the current study presents the simulation and multiobjective optimization of the Claus sulfur recovery process catalytic section. The catalytic reactors were modeled by using Aspen HYSYS software and then validated with industrial data from the South Pars refinery in Iran. The work was based on critical parameters that influence the efficiency of sulfur recovery and energy generation with added value to the balance between environmental and operational outcomes. Sensitivity analysis of the catalytic bed depth and cross-sectional area in combination with the inlet temperature on the performance of the reactors was performed by evaluating H₂S conversion, COS, and CS₂ hydrolysis as well as sulfur yield. The optimization was carried out using the response surface methodology to achieve maximum sulfur recovery, efficient energy utilization, and optimal H₂S/SO₂ ratios. From the obtained results, it is evident that the enhancements of recovery effectiveness were very pronounced; hence, the potential of the kinetic modeling and optimization strategies had been proven true. Most essentially, this overall approach lays the foundation for insights into improving the operational efficiency of sulfur recovery units with a minimum environmental impact.

1. Introduction

In the past, sulfur present in fossil fuels would usually end up in products from refineries, thereby causing significant sulfur dioxide pollution in the atmosphere. Many countries in the world have strict regulations regarding the concentration of sulfur trapped inside fossil fuels and the amount of sulfur dioxide that should be emitted into the atmosphere. Consequently, fossil fuels must undergo desulfurization. ,

For economic reasons, refining coal to produce cleaner fuel is less common. Large amounts of coal are used in major plants such as power stations. In some facilities, coal is converted to gas through partial oxidation to produce gaseous fuel or syngas for chemical processes. Additionally, significant amounts of coal are still used to produce coke for steelmaking and other industries. In all these cases, sulfur appears as hydrogen sulfide in the gaseous fuel and as ammonium sulfides in sour water. Various methods have been developed to separate sulfur from acidic gas streams. Among these, the Claus process, despite being the oldest, is the most widely used. , This is due to several factors, including the higher quality of sulfur produced by the Claus process.

Simulation plays a crucial role in understanding and improving the sulfur recovery unit (SRU) by allowing detailed analysis and optimization of various process parameters. Ibrahim simulated an SRU using SULSIM, validating the results and conducting case studies to analyze the impact of parameters such as combustion air inlet temperature and reactor feed rates on plant performance. Nabgan aimed to characterize SRUs through simulation using Aspen HYSYS, focusing on the complete conversion of sour gas to product and environmental protection by minimizing SO₂ emissions. The study emphasized the importance of feed composition and flow rates for hydrogen sulfide conversion efficiency.

Hashemi et al. , also employed Aspen HYSYS to simulate an SRU based on the modified Claus process with a split flow configuration. The results, validated against data from the South Pars gas refinery, confirmed the accuracy and reliability of the simulation in representing real-world operations.

The optimization of operating conditions is essential in industrial processes, and over the past two decades, this has driven a notable increase in simulation-based industrial process optimization. Optimization studies are thus of central importance for increasing the efficiency and effectiveness of SRUs. Several studies have contributed to this area by developing models and applying advanced optimization techniques. , Over the past two decades, several optimization methodologies have been applied to improve process performance, including genetic algorithms (GA), artificial neural networks (ANN), and the response surface methodology. Each of these methodologies has its unique advantages, and the choice depends on the requirements of the optimization task. , Rahman et al. developed a multiobjective optimization model for SRUs, validated with plant data. Their approach utilized Chemkin Pro and Aspen HYSYS for simulating the thermal and catalytic sections, respectively, and integrated these simulations with MATLAB for optimization using GA and ANN. Similarly, Zarei et al. focused on controlling operating variables to achieve optimal conditions, such as maintaining the H₂S to SO₂ ratio at 2 and reducing carbonyl sulfide (COS) emissions from the waste heat boiler.

Manenti et al. combined a kinetic model, which includes 2400 reactions and 140 species, implemented in a reactor network to describe the thermal furnace and waste heat boiler. Such a detailed kinetic network provided the base for a detailed Claus process simulation that allowed integrated plant-scale process energy optimization. The integration with GA optimization was further researched by Ghahraloud et al. This study modeled and optimized the Claus process for maximum recovery of sulfur, for which it showed an improvement in recovery efficiency by 4.63%. The process also considered autothermal reactors to improve sulfur recovery and reduce emissions. Johni and OmidbakhshAmiri went a step further in carrying out single and multiobjective optimizations using Aspen HYSYS and MATLAB. Their work focused on the influence of feed temperature, molar flow rate, and combustion air temperature on energy consumption and emissions.

Kazempour et al. have done multiobjective optimization of the thermal section of the Claus process using RSM. Based on industrial data from the South Pars refinery, the process performance achieved high sulfur recovery efficiency, including the generation of steam and the H₂S/SO₂ ratio, with significant process performance improvement and fuel consumption reduction. Performance assessment of the SRUs has to be undertaken through effective appraisal of different configurations of the process for any improvement possibilities. The studies conducted by Rahman et al. and Ghahraloud et al. provided insights into optimizing process parameters to enhance sulfur recovery and reduce emissions. It can be seen from their studies that the results of such complex schemes can be advanced strongly using a combination of simulation and optimization techniques. A comprehensive kinetic model by Manenti et al. gives an integrated approach to process simulation for the accurate prediction of conversion of acid gas, recovery of sulfur, and generation of steam. Other investigations by Ibrahim and Nabgan highlighted the critical role of simulation in performance assessment. A study of the effects of different operational parameters offered salient information for the optimization of SRU operations in order to reduce the environmental impact.

The reviewed literature indicates that optimization and simulation are needed to make sulfur recovery units highly efficient and effective. In addition, techniques including genetic algorithms and response surface methods, with an integrated approach with simulation tools, can be used to optimize such chemical processes in a completely accurate and comprehensive manner. , Simulation tools based on an integrated approach, such as Aspen HYSYS and SULSIM, have been seen to provide detailed insights into process dynamics that meet major requirements relating to the effectiveness of performance assessment while also ensuring the feasibility of optimal operating conditions. , Together, these studies contribute to a deeper understanding of SRUs and pave the way for further innovations in sulfur recovery technologies.

In most previous works, simulation and kinetic studies of the sulfur recovery process were worked out. Some studies have been performed with respect to the optimization of this process. However, none involves maximizing the sulfur production efficiency and thermal energy generation simultaneously. The catalytic section of the sulfur recovery process was modeled by using Aspen HYSYS software. After simulation and validation by the industrial data of the sulfur recovery unit of the South Pars Field in Iran, a comprehensive sensitivity analysis was done to find effective parameters for the performance of the catalytic section of the sulfur recovery process. The multiobjective optimization of the parameters was then carried out in the second step using RSM.

This work exploits the potential of RSM in order to perform the multiobjective optimization of the catalytic section of the Claus process. This has the major advantage of the capability to pinpoint optimum conditions within relatively minimal computing efforts, although this is to be done by considering all interaction effects of multiple variables simultaneously. In contrast to one-variable-at-a-time-based methods, which simply run in a linear, sequential process by changing only one variable at a time and holding others fixed, RSM encompasses a larger design space within a single comprehensive model to discover optimum trade-off interactions between various objectives.

It thus becomes even more appropriate for industrial use cases that incorporate operational constraints and more than one objective that can be combined, such as maximum sulfur recovery efficiency and minimum undesirable byproducts. Compared with other earlier research works that were largely focused on single-objective optimization and constant parameters, this brings an application of RSM to a new multiobjective optimization that has both sulfur recovery efficiency and thermal energy generation maximized simultaneously. This study makes RSM in Aspen HYSYS simulations give a result that is even more accurate as well as having a practical aspect in the sense of its possible industrial implementation. The approach is validated on the data taken from the South Pars refinery in Iran, thereby giving it real relevance and applicability to real operation.

This research outcome is to be used to fill the gap that exists between theory and practice for the actual realization of sulfur recovery unit efficiency and sustainability. The remaining sections are based on the methodology, results, and implications from this work and focus particularly on the novel approach of the RSM used for optimizing the catalytic section of the Claus process.

2. Methodologies

2.1. Modeling

The Claus process consists of two main parts. The first part is thermal, while the other part is called the catalytic part and mainly concerns the creation of reaction conditions for the H₂S present in the feed and the SO₂ produced in the furnace to finally produce elemental sulfur. This operation is generally conducted in two or three catalytic reactors. Preheaters that increase the temperature at the reactor inlet and condensers to liquefy the sulfur are two indispensable needs of this part.

Due to the effect of the catalyst on the progress of reaction of sulfur recovery from the acid gas, the catalytic stage has a lower heat load and a lower temperature than the thermal stage. The ability to convert acid gas to sulfur in direct flow mode is low; therefore, the need for a catalytic step to achieve a higher percentage of sulfur recovery becomes completely clear. In the temperature range of 153–300 °C in catalytic reactors, suitable conditions are provided to achieve high sulfur recovery because both the temperature is low enough to cause the thermodynamic progress of the Claus reaction and the necessary speed is provided for the reaction from a kinetic point of view.

The presence of consecutive catalytic reactors after the furnace ultimately provides the possibility of achieving a high recovery percentage of sulfur. Catalytic reactors are insulated, and due to the adiabatic nature of the reactors, the temperature changes will be observed throughout the reactor. However, the decrease in the intensity of the reactions from the first to the third reactor is also reduced by the amount of temperature changes. The division of sulfur recovery into several stages is due to the fact that the amount of sulfur recovered from the input flow is the basis, not the amount of liquefied sulfur, so reaching the lowest volume and cost with a higher percentage of recovery is the goal of designing these units, and finally, it leads to the division of recovery and liquefaction in several stages. The design of catalytic beds is generally standard for operational conditions with an inlet volumetric flow rate of 20–40 m³, and the height of the bed is also in the range of 0.9–1.6 m due to the prevention of a severe pressure drop.

The catalyst used in the Claus reaction typically consists of activated alumina (γ-Al₂O₃), which is a crystalline phase of aluminum oxide. This material serves as a support for active components, such as metal oxides or sulfides, which enhance catalytic activity for hydrolysis and sulfur recovery reactions. A protective layer with a high density of about 1360–1600 kg/m³ and a height of 75–150 cm is placed on top of the catalytic bed whose density is also about 650–700 kg/m³. For units with low capacity (less than 100 tons per day), the reactors coupled to each other can be used in such a way that three catalytic beds are placed in one shell, and separating plates separate them from each other.

In modeling the Claus process, the catalytic section may be subjected to both equilibrium and kinetic models; in the present work, a kinetic model was applied.

2.1.1. Kinetic Modeling of the Catalytic Part

Kinetic modeling is a method that can be used to model catalytic reactors. This method, which is the chosen method of this investigation, has more complex conditions and assumptions than the furnace, and this is due to the presence of catalyst grains that overshadow the fluid passage. The kinetic modeling of the reactions that take place in the catalytic reactors is as follows.

Table presents all reactions that take place in catalytic reactors. The hydrolysis reactions of carbonyl sulfide (COS) and carbon disulfide (CS₂) (nos. 2 and 3) occur in only the first catalytic reactor, and the rest occur in all three catalytic reactors.

1. Reactions that Take Place in Catalytic Reactors.

no.	reaction
1	${\mathrm{H}}_2\mathrm{S}+\frac{1}{2}{\mathrm{SO}}_2\rightleftarrows {\mathrm{H}}_2\mathrm{O}+\frac{3}{16}{\mathrm{S}}_8$
2	${\mathrm{CS}}_2+2{\mathrm{H}}_2\mathrm{O}\rightleftarrows {\mathrm{CO}}_2+2{\mathrm{H}}_2\mathrm{S}$
3	${\mathrm{CS}}_2+2{\mathrm{H}}_2\mathrm{O}\rightleftarrows {\mathrm{CO}}_2+2{\mathrm{H}}_2\mathrm{S}$
4	${\mathrm{S}}_8\rightleftarrows {\mathrm{S}}_6$
5	${\mathrm{S}}_8\rightleftarrows {\mathrm{S}}_2$
6	${\mathrm{S}}_6\rightleftarrows {\mathrm{S}}_2$

The gas exiting the furnace enters the condenser after its temperature drops in the waste heat boiler (WHB), and the temperature drops to the sulfur dew point and the liquefied sulfur is separated from the gas stream. Then, before entering the catalytic reactor, it passes through a heater to increase its temperature to about 300 °C. In addition to preventing the formation of liquid sulfur and the poisoning of catalysts, this action provides the activation energy required for the Claus reaction and also accelerates the reaction with an increasing temperature.

The main reaction in catalytic reactors is the Claus reaction, which can be seen below.

$${\mathrm{H}}_2\mathrm{S}+\frac{1}{2}{\mathrm{SO}}_2\rightleftarrows {\mathrm{H}}_2\mathrm{O}+\frac{3}{16}{\mathrm{S}}_8$$ 1

In 1997, Tong et al. at the University of Canada presented the complete kinetics. The presented mechanism was the result of his and his colleagues’ work in 1992 and 1995 on bauxite, aluminum oxide, and titanium oxide catalysts and their comparison with industrial data, which led to the kinetics presented in 1997.

$$R_{{\mathrm{H}}_2\mathrm{S}}=\frac{k_{\mathrm{S}}\left[P_{{\mathrm{H}}_2\mathrm{S}}{P}_{{\mathrm{SO}}_2}^{0.5}-\left(\frac{1}{K}\right)P_{{\mathrm{H}}_2\mathrm{O}}{P}_{{\mathrm{S}}_6}^{0.25}\right]}{[1+K_{{\mathrm{H}}_2\mathrm{O}}(P_{{\mathrm{H}}_2\mathrm{O}}){]}^2}$$ 2

where $K=\sqrt{K_{\mathrm{E}}}$ and K _E is the thermodynamic equilibrium constant. The parameters mentioned in eqs – are calculated as follows:

$$K_{{\mathrm{H}}_2\mathrm{O}}=K_0\exp (-\frac{\mathrm{\Delta }{H}_{{\mathrm{H}}_2\mathrm{O}}}{RT})$$

$$k_{\mathrm{S}}=k_0\exp (-\frac{E_{\mathrm{S}}}{RT})$$

$$K_{\mathrm{E}}=9.502\times {10}^{-7}\exp \left(\frac{1.11\times {10}^4}{T}\right)1/{\mathrm{kPa}}^{0.5}$$

$$k_0=6.91\mathrm{kgmol}/\mathrm{kg}\mathrm{h}{\mathrm{kPa}}^{1.5}$$

$$E_{\mathrm{S}}=30.77\mathrm{kJ}/\mathrm{gmol}$$

$$K_{0,{\mathrm{H}}_2\mathrm{O}}=0.3381/\mathrm{kPa}$$

$$\mathrm{\Delta }{H}_{{\mathrm{H}}_2\mathrm{O}}=0\mathrm{kJ}/\mathrm{gmol}$$

In 1998, Shangguan et al. investigated the kinetics of hydrolysis reactions for an alumina base catalyst with three active substances γ (gamma), K₂O (potassium oxide), and K₂O-Pt (potassium oxide-platinum). The space velocity of the gases was 5000–1000 1/h, and the temperature range was 30–140 °C. From their series of experiments, the results with the K₂O-Pt active substance catalyst were better than others, and the following results were obtained as hydrolysis kinetics. The constants of eq for the COS hydrolysis reaction are shown in Table , and the constants of eq for the CS₂ hydrolysis reaction are shown in Table .

$$K=A\exp (-\frac{E}{RT})$$ 3

2. Constants of Equation for the COS Hydrolysis Reaction.

	γ-alumina	Al-K2O	Al-K2O-Pt
Ea [kJ/gmol]	57.8	52.5	44.71
A [1/s]	7.66 × 108	2.72 × 108	2.18 × 107

3. Constants of Equation for the CS₂ Hydrolysis Reaction.

	γ-alumina	Al-K2O	Al-K2O-Pt
Ea [kJ/gmol]	55.53	38.70	35.37
A [1/s]	1.25 × 108	1.01 × 108	4.43 × 107

In 1997, Tong et al. conducted research to provide kinetics for COS and CS₂ hydrolysis reactions. In this research, they investigated the effect of sulfation of the catalyst surface on the hydrolysis of COS and CS₂, as well as the effect of changing the shape of the catalyst grain and the height of the catalyst bed on the hydrolysis reactions. The strength of their work is to present the kinetics for two hydrolysis reactions and one main Claus reaction in the conditions where these three are investigated simultaneously. The kinetics provided by them is as follows.

$$-R_i=\frac{k_i{P}_i{P}_{{\mathrm{H}}_2\mathrm{O}}}{1+K_{{\mathrm{H}}_2\mathrm{O}}(P_{{\mathrm{H}}_2\mathrm{O}})}$$ 4

The subscript i indicates the type of compound, COS or CS₂. The parameters mentioned in eq are calculated using the constants in Table and as follows:

$$K_i=K_0\exp (-\frac{\mathrm{\Delta }{H}_i}{RT})$$

$$k_{\mathrm{s}}=k_0\exp (-\frac{E_i}{RT})$$

4. Constants Related to Equation .

	COS	CS2
k0 [kgmol/kg h (kPa)1.5]	2.30	19.75
E i [kJ/gmol]	25.27	40.41
K0,H2O [1/kPa]	1.25	3.43
ΔH H2O [kJ/gmol]	83.22	98.10

The spherical catalyst, which is the most available catalyst, has the lowest progress rate for the hydrolysis of COS and CS₂.

2.1.2. Reactions between Sulfur Allotropes

The conversion of allotropes of sulfur into each other is one of the reactions that take place. So far, many allotropes for sulfur have been discovered. However, because this element is generally seen in nature in three forms S₂, S₆, and S₈, we considered these three as the main types of sulfur element in the process. According to the research of Gamson and Elkins in 1953, the rate of conversion of these three allotropes to each other is dependent only on temperature, which is presented in Figure .

1.

Molar ratio of different allotropes of sulfur at different temperatures. Redrawn from ref .

As it is clear from the figure, S₂ is the only dominant species at high temperatures and in places such as the furnace, while at temperatures related to the catalytic stages, S₆ and S₈ species are competing with each other, and of course, the relative superiority of S₈ is evident. Using the MATLAB program Curve Fitting Toolbox Plots module, we calculate the isometric diagram of sulfur allotropes in the form of a second degree equation that can be used in Aspen HYSYS:

$$\mathrm{mole}\mathrm{percent}\mathrm{of}{\mathrm{S}}_2=4.666\times {10}^{-4}{T}^2-4.979\times {10}^{-1}T+126.4$$ 5

$$\mathrm{mole}\mathrm{percent}\mathrm{of}{\mathrm{S}}_6=4.862\times {10}^{-4}{T}^2-6.854\times {10}^{-1}T-192$$ 6

$$\mathrm{mole}\mathrm{percent}\mathrm{of}{\mathrm{S}}_8=3.431\times {10}^{-5}{T}^2-2.086\times {10}^{-1}T+172.1$$ 7

In the mentioned equations, T is in Kelvin.

In order to define the mentioned allotropes in the simulator program due to the lack of this information in the database of the software, a function was written in MATLAB software by using the method of numerical derivation using the finite difference method with a fourth-degree error. , Also, by numerical integration of enthalpy, we find the C_p coefficient. ,

In the environment of ASPEN, in the hypothetical species section, it is possible to simulate allotropes of sulfur by defining the relations of heat capacity and standard enthalpy of formation and their other physical and chemical properties with the help of the entered relations and molecular weight estimated. ,

2.2. Description of the Process

The Claus process furnace consisting of seven irreversible reactions and five equilibrium reactions was simulated by Aspen HYSYS software. Catalytic reactors were modeled according to the conditions mentioned in the previous sections with simulation software, and this modeling was validated using refinery data of the South Pars region.

Figure illustrates the block flow diagram (BFD) of the entire process, covering both the thermal and catalytic sections.

2.

Block flow diagram (BFD) of the entire Claus process. Redrawn from ref .

In the condenser, water is used as a coolant to reduce the temperature and condense sulfur elements into a liquid at this stage, resulting in low-pressure steam as the output.

2.3. Operating Conditions

The operating conditions in the simulation are obtained from the industrial data provided by the South Pars refinery. These parameters include the temperature, pressure, and feed composition for each reactor. Inlet temperatures for catalytic reactors were set in the range of 200–240 °C, while pressures were within the range of 139–177 kPa.

Acid gas and air feed molar flow rates were kept constant, 728.1 and 730.0 kgmol/h, respectively. This ensures an almost constant value of the ratio H₂S/SO₂ close to the theoretical. During the experiment run, the three reactors were identically charged with the same type of catalyst and the same specific surface area and porosity characteristics.

This detailed elaboration of the actual operating conditions provides a strong basis for understanding the input parameters and their sensitivities to the simulated results, besides allowing for comparability and reproducibility by other studies.

The catalytic reactors were modeled as plug flow reactors (PFR) in Aspen HYSYS. This selection was made because the PFR model closely mimics the behavior of catalytic reactors, where reactions occur progressively along the reactor length with continuous changes in composition and temperature. The plug flow assumption is particularly suitable for the Claus process as the high gas velocity minimizes backmixing, ensuring efficient conversion.

2.4. Equation of State

Thermodynamic relations are used to determine the thermodynamic characteristics of mixtures and flows. The basis of this application is the selection of the appropriate equation of state for the mixtures and operating conditions.

Due to the presence of a gas phase, the use of the equation of state has priority over activity models. The majority of the process takes place at low pressure and high temperature, which provides the basis for using the ideal gas equation of state, but to ensure the performance of the equation of state at all points in the process, the PR equation of state can be used.

Our chosen equation in this model is the SRK equation of state:

$$P=\frac{RT}{V-b}-\frac{a}{V(V+b)}$$

in which

$$a={\mathrm{\Omega }}_a\frac{R^2{T}_{\mathrm{c}}^2}{P_{\mathrm{c}}}\alpha T_{\mathrm{r}}$$

$$b={\mathrm{\Omega }}_b\frac{R{T}_{\mathrm{c}}}{P_{\mathrm{c}}}$$

This equation gives results that are very close to those obtained using the PR equation of state, but by definition, it has greater accuracy in smaller operating ranges (T > −143 and P < 5000 psia) and is close to the ideal state. The SRK equation is one of the most widely used equations of state and is used as one of the equations of state in calculations due to its widespread use in determining the phase behavior of mixtures. Constants related to the SRK equation of state are shown in Table .

5. Constants Related to the SRK Equation of State.

U	b
W	0
αT r	[1 + C 1(1 – (T/T c)0.5)]2
C 1	0.480 + 1.574ω + 0.176ω2
Ω a	0.42748
Ω b	0.08664

2.5. Optimization Methods

The optimization process utilized the response surface methodology (RSM) to perform multiobjective optimization, with the primary goals of maximizing sulfur recovery and thermal energy generation while maintaining the H₂S/SO₂ ratio close to the desired value of 2. This method is based on central composite design with the weight fraction for each variable and object and exhibits a collection of responses with desirability. Key input variables, such as the inlet temperature, catalytic bed depth, and cross-sectional area, were systematically varied within defined ranges to explore their effects on process performance. A desirability function was employed to simultaneously balance these objectives, ensuring that the optimized conditions achieved practical relevance for industrial applications.

3. Results and Discussion

The simulation results point out some trends in sulfur recovery efficiency, energy use, and minimization of byproducts that are strongly related to the Claus process reaction kinetics and thermodynamic principles. As an example, hydrolysis reactions of COS and CS₂ in the first catalytic reactor will be strongly influenced by the inlet temperature and residence time, which determine the availability of activation energy and the direction of equilibrium shifts. Similarly, in the second and third reactors, it can be observed that the conversion efficiency of H₂S decreases successively, which is due to a decrease in the concentration of reactants and saturation of catalyst activity.

The changes that take place along the catalytic bed height for all the reactors are elaborated in Figures S1–S4. More precisely, Figure S1 details how enthalpy and temperature change across the catalytic bed and underlines the fact that the Claus reaction is exothermic while hydrolysis reactions show endothermic behavior. This underlines again the importance of an optimal temperature gradient to balance reaction progress with equilibrium.

Figure S2 highlights variation in the molar flow rates of the main components and reaction rates in the first reactor with dominance of COS and CS₂ hydrolysis: the steep gradient at the bed inlet from the reaction rate indicates that the inlet conditions are very critical for ensuring the effective startup of these reactions.

Figures S3 and S4 extend this further to the second and third reactors, respectively, showing that reaction velocities and changes in molar flow further taper as reactant concentrations are reduced. These trends further validate the observed drop in efficiencies through the reactors and provide a quantitative basis for optimization of bed depth and gas flow distribution.

The deviations in the H₂S/SO₂ ratios included in Table are indicative of the sensitivity of the process to operating conditions; ratios near the desired value of 2 were achieved under optimum conditions. The analysis hence underlines the importance of tight control of parameters such as the inlet temperature and bed geometry to achieve high recovery efficiencies.

9. Comparison of the Molar Flow of Components in the Output of Reactors for Industrial Data and Modeling.

	data			kinetic model			rel. deviation			deviation %
composition (kgmol/h)	R1	R2	R3	R1	R2	R3	R1	R2	R3	R1	R2	R3
H2S	23.99	8.16	4.98	24.58	8.18	4.97	–0.59	–0.02	0.01	–2.46	–0.30	0.21
SO2	10.77	2.86	1.27	11.08	2.86	1.28	–0.31	0.00	–0.01	–2.88	–0.16	–0.86
N2	552.37	552.37	552.37	552.37	552.37	552.39	0.00	0.00	–0.02	0.00	0.00	0.00
CO	27.51	27.51	27.51	27.51	27.51	27.51	0.00	0.00	0.00	0.00	0.00	0.00
CO2	337.18	337.18	337.18	337.16	337.18	337.18	0.02	0.00	0.00	0.01	0.00	0.00
COS	0.50	0.50	0.50	0.51	0.50	0.50	–0.01	0.00	0.00	–2.80	0.00	0.00
S2	0.15	0.01	0.00	0.12	0.01	0.00	0.03	0.00	0.00	20.00	0.00	0.00
S6	3.00	0.53	0.17	3.15	0.54	0.16	–0.15	–0.01	0.01	–5.00	–1.32	4.00
S8	9.63	3.47	1.27	9.45	3.46	1.28	0.18	0.01	–0.01	1.87	0.29	–0.86
H2O	355.68	371.50	337.18	355.08	371.49	337.18	0.60	0.01	0.00	0.17	0.00	0.00
H2	14.63	14.63	14.63	14.63	14.63	14.63	0.00	0.00	0.00	0.00	0.00	0.00
CS2	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

3.1. Validation of the Model (Comparison of Modeling and Validation Results)

To model this process, the input data of one of the South Pars refineries were used. The intended evaluation for the catalytic section was examined in the form of output flow from each catalytic reactor with the mentioned data. The comparison of flows was done in the form of a comparison between the concentration of different compounds and the general characteristics of the flows. Considering the operational conditions of the mentioned refinery and including them in the simulation, we achieved an acceptable accuracy for the next steps. The amount of error and deviation from the actual conditions are given in the graphs and tables. The reasons for the small differences will also be explained below.

The desired feed in this modeling was the feed of one of the South Pars refinery units, which is actually the outflow from the top of the desorption tower of the gas treating unit. The feed gas entering the desulfurization unit has the following specifications (Table ).

6. Specification of Input Feed to the Sulfur Recovery Unit.

specification	acid gas	air
molar flow (kgmol/h)	728.1	730.0
temperature (°C)	240	240
pressure (kPa)	177	1.82
Composition of input feed (gmol %)
H2S	0.4616	0.0000
CH4	0.0018	0.0000
SO2	0.0000	0.0000
N2	0.0001	0.7586
O2	0.0000	0.2011
CO	0.0000	0.0000
CO2	0.4989	0.0003
COS	0.0000	0.0000
CS2	0.0000	0.0000
S2	0.0000	0.0000
S8	0.0000	0.0000
H2O	0.0375	0.0400
H2	0.0000	0.0000

3.1.1. Comparison of the Catalytic Section

In the catalytic section of the unit, there are three reactors with alumina-type catalytic beds, along with preheaters before each reactor and condensers after each reactor, all three reactors having the same dimensions reported in Table .

7. Characteristics of Catalytic Reactors.

2/7 m	reactor diameter
6 m	reactor length
34/35 m3	reactor volume
1/4 m	catalytic bed height
36,000 kg	weight of the catalyst in the reactor
30 m3	volume of the catalyst in the reactor

After passing through the WHB and cooling, the output stream from the furnace enters a condenser to lower the temperature of the stream below the dew point of sulfur and liquefy it so that it can be separated. This flow is ready to enter the furnace after passing through the preheater.

One of the reasons for preheating the stream is to prevent sulfur from liquefying inside the reactor and to avoid sulfation of the catalyst. Another reason is to raise the temperature to accelerate the reactions, provided that thermodynamically, it does not interfere with the progress of the exothermic Claus reaction. For the first catalytic reactor, this preheating has another reason, and it is to ensure the progress of COS and CS₂ hydrolysis reactions in the catalytic bed, so that the catalyst poisoning for these two compounds is not provided. The input streams to the catalytic reactors have the characteristics mentioned in Table . The presence of a small amount of sulfur in the inlet flow to the reactors is not a problem because the efficiency of separation of elemental sulfur in the condenser is not 100%. Of course, with the increase in temperature, this amount of sulfur enters the reactor in a gaseous form, and the probability of the catalyst being sulfated is greatly reduced.

8. Characteristics of Input Flow to Catalytic Reactors in Industrial Data.

stream property	first reactor	second reactor	third reactor
molar flow (kgmol/h)	1352.85	1323.59	1352.85
temperature (°C)	240	210	200
pressure (kPa)	162	150	139
Composition of input flow (kgmol/h)
H2S	79.47	23.99	8.16
SO2	39.99	10.77	2.86
N2	552.37	552.37	552.37
CO	27.51	27.51	27.51
CO2	334.23	334.23	337.18
COS	3.45	0.50	0.50
S2	0.00	0.01	0.00
S6	0.16	0.20	0.09
S8	0.85	0.75	0.73
H2O	300.20	371.50	374.69
H2	14.63	14.63	14.63

In the kinetic model, the high speed of the gas entering the reactor indicates the turbulent state of the fluid in the plug-type reactor. This high speed makes it possible to ignore the concentration gradient between the mass of the gas phase and the surface of the catalyst. Tables and present a comparison of the output data from the catalytic reactors for the refinery data and the model output.

10. Comparison of Output Flow Characteristics of Reactors for Industrial Data and Modeling.

	data			kinetic model			rel. deviation			deviation %
total stream properties	R1	R2	R3	R1	R2	R3	R1	R2	R3	R1	R2	R3
temperature (°C)	299.23	226.86	203.45	308.20	226.60	204.50	–8.97	0.26	–1.05	–3.00	0.11	–0.52
molar flow rate (kgmol/h)	1335.42	1318.72	1277.06	1335.64	1318.73	1277.08	–0.22	–0.01	–0.02	–0.02	0.00	0.00
molecular weight (kg/kgmol)	31.54	29.79	29.29	31.72	31.72	31.72	–0.18	–1.93	–2.43	–0.57	–6.48	–8.30
actual density (kg/m3)	1.05	1.05	1.00	0.93	0.93	0.93	0.12	0.12	0.07	11.43	11.43	7.00
viscosity (cP)	0.02	0.02	0.02	0.02	0.02	0.02	0.00	0.00	0.00	0.00	0.00	0.00
heat flow (MW)	–58.65	–60.31	–60.77	–57.92	–57.92	–57.92	–0.73	–2.39	–2.85	1.24	3.96	4.69
molar enthalpy (kJ/kgmol)	–158,107.93	–164,652.05	–166,432.50	–156,500.00	–156,500.00	–156,500.00	–1607.93	–8152.05	–9932.50	1.02	4.95	5.97
mass heat capacity (kJ/kg K)	1.16	1.20	1.16	1.19	1.19	1.19	–0.03	0.01	–0.03	–2.59	0.83	–2.59
thermal conductivity (W/m K)	0.04	0.04	0.03	0.04	0.04	0.04	0.00	0.00	–0.01	2.50	2.50	–30.00

Available error values are shown for the various components participating in the reaction. All errors are within the reliable range, except for S₂. For the S₂ species, it is because the balance of different allotropes of sulfur is not only dependent on temperature, but other factors are also effective; so far, no general report has been presented regarding the balance of allotropes of sulfur. However, finally, due to the importance of mass flow rate of sulfur in the SRU unit and the existence of a difference, which is 0.63% less than the refinery data, it shows the acceptability of the model. The differences for the second and third reactors are 0.06 and 0.17%, respectively.

The sources of these deviations between the model predictions and real data, especially for the catalytic reactors, were analyzed. It can be seen from Table that the relative deviations of H₂S and SO₂ conversion rates increase gradually from reactor 1 to reactor 3. This is because of accumulating errors from a number of factors:

• Catalyst activity and deactivation: This model assumes the uniform activity of the catalyst that may not realistically account for any deactivation as time progresses; in particular, reactor 3 has a lower temperature and may enhance such deactivation.

• Equilibrium assumption: Equilibrium constants of transformation between sulfur allotropes do not fully model the dynamic equilibrium of temperature and pressure and, further, of the distribution of sulfur species, which justifies the given difference in concentration of S₂.

• Measurement uncertainties: There are deviations because of the variability in industrial data; this view is more applicable to minor components such as COS and CS₂.

In this regard, a sensitivity analysis is provided in the Supporting Information to show the variation in model predictions accounting for catalyst deactivation, among other equilibrium parameters.

According to the presented results, the model has a high capability in simulating the SRU unit with the Claus process. The reason for some differences in other characteristics of the flows is the use of thermodynamic equations by the simulator software to obtain the properties of the flows, and these relationships are sometimes slightly different from the experimental relationships.

Figures S1–S4 show the enthalpy changes, temperature changes, changes in the molar flow rate of the components, and reaction speeds for different components through the height of the catalytic bed of catalytic reactors.

3.2. Sensitivity Analysis

Among the parameters examined for selection in the sensitivity analysis, only three parameters were found to have a significant impact: the inlet temperature, reactor bed height, and reactor cross-sectional area. Key parameters were subjected to a wide range for sensitivity analysis. The inlet stream temperature ranged from 200 to 400 °C, encompassing a wide operational range that affects both the reaction kinetics and overall catalytic process performance. A catalytic bed depth between 1 and 2 m was defined, which will greatly affect the residence time in the system and the final catalytic interaction. Moreover, the range of the cross-sectional area of the catalytic bed was taken into account from about 5 to 38 m², influencing the flow pattern and the associated pressure drop. Those ranges were chosen to ensure that their impact on the performance of the system could be investigated under a range of operating conditions.

3.2.1. The Effect of the Temperature of the Inlet Flow to the Reactors

Temperature is a fundamental parameter in reactors, as it governs both the reaction kinetics and thermodynamic equilibrium. Higher temperatures enhance the reaction rates, particularly in the first catalytic reactor, by providing the activation energy required for faster kinetics. However, due to the exothermic nature of the Claus reaction, lower temperatures shift the equilibrium favorably toward the production of elemental sulfur. Achieving optimal reaction conditions requires balancing these kinetic and thermodynamic effects to maximize the efficiency. The effect of temperatures of the inlet streams to all reactors on the performances of the catalytic reactors can be seen in Figures –. Figure shows the effect of the temperature of the inlet stream to the first reactor, and Figure shows how changes in the temperature of the inlet stream to the first reactor affect sulfur production and sulfur recovery efficiency.

3.

Effect of temperature of the inlet stream to the first reactor on (a) H₂S/SO₂ ratio, (b) conversion percentage of COS and CS₂, (c) temperature of the output stream from the first reactor, and (d) percentage conversion of H₂S.

6.

Effect of temperature of the inlet flow to the third reactor on (a) percentage conversion of H₂S, (b) H₂S/SO₂ ratio at the outlet of the third reactor, (c) temperature of the outlet stream from the third reactor, and (d) changes in the amount of sulfur recovery.

4.

Changes in the amount of sulfur recovery versus the inlet temperature to the first catalytic reactor.

The increase in sulfur production efficiency is due to the presence of preheaters before catalytic reactors, which do not have much of an effect on initial costs. Decreasing the temperature to less than 200 °C increases the possibility of sulfur condensation in the inlet flow to the catalytic reactors, which leads to a sulfated catalyst. Although the melting point of sulfur is about 162 °C, the minimum temperature limit has been started from 200 °C to ensure the absence of sulfur fog and increase the reaction speed in the sensitivity analysis. The increase in the efficiency of sulfur recovery and the consequent increase in the mass flow rate of sulfur produced with a constant and close to linear trend are evident for all three catalytic reactors. The increase in temperature in the first reactor is very important due to the importance of hydrolysis of COS and CS₂ compounds compared to the next two reactors. Also, due to the higher activation energy of hydrolysis reactions compared to the Claus reaction, the temperature increase becomes more important.

Increasing the temperature, although it reduces the H₂S conversion rate and lowers the conversion percentage to below 53% at temperatures above 263 °C, due to the H₂S/SO₂ ratio approaching 2, results in an increased H₂S conversion rate in the subsequent reactor. The increase in the percentage of conversion is dominant in the next two reactors and increases the overall efficiency of sulfur recovery.

The sensitivity analysis in the catalytic section has no effect on medium pressure steam production and has a negligible effect on the medium pressure steam production parameter. So, presenting their diagrams, it has been omitted.

In the sensitivity analysis, the outlet temperature of each reactor is examined, and the reactor outlet is the inlet flow to the condenser and affects the steam production rate in the condenser. So, this parameter is related to the steam production rate and thermal energy generation. The mentioned process for increasing the temperature of the inlet flow to the first catalytic reactor can be seen in the same way for the second and third catalytic reactors.

The effect of temperature of the inlet flow to the second reactor can be seen in Figure . Increasing the temperature of the second reactor decreases the percentage of H₂S conversion, and this is associated with the approach of the H₂S/SO₂ ratio. So, the conversion percentage in the third reactor increases. However, the effect of the second reactor on the efficiency of sulfur production is much higher than the third reactor, so the percentage of total H₂S conversion decreases. With the hydrolysis of the COS and CS₂ compounds in the first reactor to H₂S, the ratio of H₂S/SO₂ after the first reactor is higher than 2.

5.

Effect of temperature of the inlet flow to second reactor on (a) temperature of the output stream from the second reactor, (b) percentage conversion of H₂S, (c) H₂S/SO₂ ratio, and (d) changes in the amount of sulfur recovery.

As shown in Figure , in the third reactor, increasing the temperature over 350 °C causes the Claus reaction to progress in the opposite direction.

3.2.2. The Effect of the Height of the Catalytic Bed

Due to the vertical movement of acid gases in the catalytic bed from top to bottom, increasing the height of the catalytic bed increases the length of the gas passage and, as a result, increases the residence time inside the reactor. Although this causes an increase in the efficiency of sulfur recovery, the excessive increase in the depth of the bed leads to adverse consequences such as more pressure drop and an increase in initial costs for designing and building a larger reactor and the need for more catalyst. By increasing every 10 cm to the depth of the bed, about 5% is added to the H₂S conversion, the higher conversion rate causes the H₂S/SO₂ ratio to increase, and the progress rate of the conversion percentage decreases. Figures – present the effect of the catalytic bed depth of the reactors on the performance of the catalytic reactors.

7.

Effect of catalytic bed depth of the first reactor on (a) conversion percentage of COS and CS₂, (b) percentage conversion of H₂S, (c) temperature of the outlet flow from the first reactor, and (d) ratio of H₂S/SO₂ in the outlet of the first reactor.

10.

Effect of catalytic bed depth of the third reactor on (a) percentage conversion of H₂S, (b) ratio of H₂S/SO₂ in the outlet of the reactor, (c) temperature of the outlet flow from the reactor, and (d) amount of sulfur recovery.

8.

Amount of sulfur recovery vs the depth of the catalytic bed of the first reactor.

9.

Effect of catalytic bed depth of the second reactor on (a) temperature of the outlet flow from the second reactor, (b) ratio of H₂S/SO₂ in the outlet of the second reactor, (c) percentage conversion of H₂S, and (d) amount of sulfur recovery.

Increasing the depth of the catalytic bed, although it increases the initial costs, with a linear process, increases the efficiency of sulfur recovery in the whole process. A similar trend can be seen in relation to the increase in the depth of the catalytic bed for the second and third catalytic reactors.

Figures – illustrate that with longer residence times, which is increased by increasing the catalytic bed depth, sulfur recovery efficiencies are increased. This is associated, however, with increased pressure drops and higher initial cost. An increase in bed depth is linearly related to the conversion of H₂S but does not extend beyond a critical value, after which further additions in bed height would show decreasing returns because of excessive bed height.

3.2.3. The Effect of the Cross-Sectional Area of the Catalytic Bed

The area of the catalytic bed in catalytic reactors has a direct effect on the progress of the Claus reaction in the first to third reactors and on the hydrolysis reactions in the first reactor. Despite the fact that this issue is effective in the dimensions of the reactor, it increases the initial costs. However, it is effective in sulfur recovery efficiency and increases this parameter. Also, the presence of more and bigger support plates and the heavy weight of the catalysts will make it more difficult to replace the catalysts. Increasing the catalyst area causes a decrease in the speed of the gas passing through the bed and leads to an increase in the residence time of the compounds inside the reactor. It is evident in all the graphs that the percentage of H₂S conversion increases in all three catalytic reactors and the hydrolysis of COS and CS₂ compounds in the first reactor progresses with a lower slope in the bigger areas. The effect of the cross-sectional area of the catalytic bed on the performances of the catalytic reactors can be seen in Figures –.

11.

Effect of the cross-sectional area of the catalytic bed in the first reactor on (a) temperature of the outlet flow from the reactor, (b) ratio of H₂S/SO₂ in the outlet of the reactor, (c) conversion percentage of COS and CS₂, and (d) conversion percentage of H₂S.

14.

Effect of the cross-sectional area of the catalytic bed in the third reactor on (a) temperature of the outlet flow from the reactor, (b) ratio of H₂S/SO₂ at the outlet of the reactor, (c) conversion percentage of H₂S, and (lower right) changes in the amount of sulfur recovery.

12.

Changes in the amount of sulfur recovery vs the cross-sectional area of the catalytic bed in the first catalytic reactor.

13.

Effect of the cross-sectional area of the catalytic bed in the second reactor on (a) ratio of H₂S/SO₂ in the outlet of the reactor, (b) temperature of the outlet flow from the reactor, (c) conversion percentage of H₂S, and (lower right) changes in the amount of sulfur recovery.

The mentioned process for the first catalytic reactor can be seen in the second and third catalytic reactors in the same way.

Larger cross-sectional areas decrease gas velocities, increasing residence time and giving better conversion rates for both the H₂S and hydrolysis reactions, as can be realized from Figures –. This is, however, at the expense of larger reactor dimensions and, consequently, larger costs; thus, a trade-off between efficiency and economic feasibility must be made.

3.3. Optimization

In the “Sensitivity Analysis” section, we found that the performance of each reactor depends on three parameters: the inlet temperature, cross-sectional area of the catalytic bed, and bed depth. Therefore, in order to optimize the catalytic part of the process, we optimize each reactor separately and consider the ratio of H₂S/SO₂, which is an effective factor on the performance of subsequent reactors. For all reactors, the parameters mentioned in the ranges are shown in Table . Tables S1, S2, and S3 exhibit the results obtained from simulation in 20 different conditions to be used to calculate the optimal values of the H₂S conversion, the H₂S/SO₂ ratio, the low-pressure (LP) steam, the consumed energy of the preheater in each reactor, and the amount of hydrolysis of COS and CS₂ in the first reactor.

11. Range of Independent Variables for the Optimization.

	inlet T (°C)	bed depth (m)	cross-sectional area of the bed (m2)
for all reactors	200–300	1.2–1.6	10–30

For catalytic reactors, the direct effect of energy on the production of low-pressure (LP) steam was considered. The amount of hydrolysis of COS and CS₂ compounds in the first reactor has been considered with the condition that it is greater than the base amount and without a coefficient. So, the optimization was done by focusing on the maximum amount of H₂S conversion and the H₂S/SO₂ ratio being closer to two, both with a coefficient of one and considering low-pressure steam production as the second priority. Among the set of numerical optimization answers by the software, the answers presented in Table have been selected with a degree of desirability for the optimization of the first reactor, 0.88 for the second reactor, and 0.9 for the third reactor 0.95.

12. Optimum Values for Purposes of Catalytic Reactors.

reactor	H2S conv. (%)	H2S/SO2	COS conv. (%)	CS2 conv. (%)	LP steam (kgmol/h)	consumed energy (kW)
1	71.56	1.83	91.72	100	274.3	2552
2	63.95	2.64			163.1	1038
3	42.02	3.99			163.1	1469

Due to the multiobjective optimization of catalytic reactors, it is not possible to present a diagram in three-dimensional space. For this reason, it was presented at a specific temperature and only as a sample, as can be seen in Figure .

15.

Example of the response surface provided for the rate of H₂S conversion in the first catalytic reactor for changes in the depth and cross-sectional area of the catalytic bed at a temperature of 260 °C.

Again, to present the diagram in three-dimensional space, it was necessary to keep one of the parameters constant. The degree of desirability of the responses for the third reactor is shown in Figure as an example. It is known that at a temperature of 300 °C due to the reduction of H₂S conversion, the desired responses occur in the high depth and cross-sectional area of the catalytic bed.

16.

Diagram of the degree of desirability of the responses for changes in the cross-sectional area and depth of the catalytic bed of the third reactor at a constant temperature of 300 °C.

The optimization results characterized significant performance enhancements across all reactors. In the case of the first reactor, the optimal conditions improved the H₂S conversion compared to baseline values while maintaining a H₂S/SO₂ ratio close to the desired value of 2. COS and CS₂ conversion efficiencies were also characterized with the presented optimization strategy.

The optimization of configurations for the second and third reactors resulted in further gains in H₂S conversion and increased low-pressure steam generation. Energy consumption analysis showed that higher conversion rates are usually associated with higher energy consumption for scenarios with increased temperature or reactor size. However, the gains in terms of overall sulfur recovery and efficiency of the process outweigh these costs, making the optimization strategy practically useful for industrial applications.

4. Conclusions

In an industrial unit like the Claus process, where the primary focus is on improving environmental conditions and economic factors are secondary, enhancing efficiency is of particular importance. This study applied various assumptions to develop and simulate a model aimed at optimizing the sulfur recovery. We investigated the effects of multiple parameters on the sulfur recovery efficiency, reduction of undesirable compounds, energy efficiency, and production of medium- and low-pressure steam.

The analysis considered the kinetics of three equilibrium reactions and the transformations among sulfur allotropes (S₆, S₂, and S₈) for the first catalytic reactor. For the second and third catalytic reactors, the focus shifted to the absence of two equilibrium hydrolysis reactions. Sensitivity analysis explored the impact of the inlet temperature, catalytic bed depth, and cross-sectional area on optimizing H₂S conversion, the H₂S/SO₂ ratio, low-pressure steam production, and energy consumption. Additionally, for the first reactor, the COS and CS₂ conversion rates were also optimized.

The tailored, multicriteria-based adjustments led to significant enhancements in reactor efficiency and output. The results, as indicated by the degree of desirability, demonstrate the effectiveness of the optimization strategy in achieving the desired operational parameters and overall reactor performance.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.4c10709.

• (Figures S1–S4) Enthalpy changes in the height of the catalytic bed of the catalytic reactors; temperature changes in the height of the catalytic bed of catalytic reactors; changes in the molar flow rate of the components in the height of the catalytic bed of the first reactor; changes in the molar flow rate of components at the height of the catalytic bed of the first, second, and third reactors; reaction speed for different components in the first, second, and third reactors according to the height of the catalytic bed; (Tables S1–S3) calculation scenarios and their results for the optimization of the first, second, and third catalytic reactors (PDF)

The authors declare no competing financial interest.