1. Introduction
The petrochemical industry is an important industry that meets the needs of the whole world. It is inevitable that various waste gases will be released from this industry, as it uses crude oil and natural gas as resources. One of these gases is hydrogen sulfide, which is a poisonous gas and is found in high concentrations in refinery acid waste gases. Due to its high abundance, H2S removal takes place in the Claus sulfur recovery unit in refineries. The Claus unit is a part of the refinery that does not attract attention and is not studied much as long as it operates properly. However, since this unit is controlled by strict environmental regulations, its failure to operate efficiently could lead to the closing down of the refinery. For this reason, every improvement that can be made to this unit will contribute to the efficiency of refineries, increase financial gains, reduce losses, and limit the negative impact on the environment by providing the conditions determined by the regulations.
The Claus is a recovery process in which some of the hydrogen sulfide oxidizes and turns into sulfur dioxide, and then the remaining H
2S reacts with the SO
2 to form hydrogen gas and elemental sulfur. Depending on the process conditions and feed gas composition, sulfur recovery efficiency will be 94–98%; if the residual gas is sent to the incineration unit, sulfur recovery efficiency may rise up to 99.99% [
1,
2]. Approximately 60–70% of the hydrogen sulfide conversion in the process occurs in the thermal step [
3]. In order to increase the sulfur recovery efficiency, many researchers have studied thermal furnace modeling, and in the first of these modeling studies, constrained equilibrium models were used to predict product distribution from the Claus reaction furnace. Bennett and Meisen evaluated 36 chemical species, including nitrogen compounds and radicals, and reported equilibrium calculations in the H
2S–air system at temperatures up to 2000 K [
4]. Khudenko et al. performed a Claus reaction furnace equilibrium calculation under oxygen-rich conditions using the Gibbs energy minimization method [
5]. As a result, they found that the oxygen-based Claus process could reduce equipment dimensions. Monnery et al. [
6] applied various methods such as Gibbs energy minimization, Fisher monograph and Western Research correlations to determine the reaction furnace’s output, and they determined that the results of these methods were not compatible with the results obtained before and after the waste heat boiler was applied. Selim et al. investigated the critical roles of other gases besides H
2S in determining the optimum operating temperature required for maximum sulfur recovery [
7]. ZareNezhad and Hosseinpour presented a general formulation for determining the Claus reaction furnace temperature, equilibrium compositions and optimum air ratio using the Gibbs free energy minimization method [
8].
Up to today, the research has evolved to focus on kinetic model-based studies. Since 1999, both simplified and detailed kinetic models have begun to be developed for the reaction furnace. Dowling and Clark aimed to apply a more stringent reversible kinetic model and use a more robust data regression technique [
9]. Monnery et al. carried out laboratory and modeling studies together; they compared the separation of HS and sulfur conversion as a result of the second Claus reaction with that occurring under furnace conditions by combining their results with the results of previous studies [
6]. Pierucci et al. modeled a thermal reactor with a detailed kinetic design based on an approach that included 130 species and more than 1500 elementary reactions. They aimed to present a meaningful phenomenological furnace model based on the non-equilibrium approach in order to achieve a detailed kinetic design [
10]. Jones et al. defined a reaction set including independent reactions and used a four-step method to determine the product distribution of the measured waste heat boiler output. Their study was limited to the waste heat boiler output [
11]. Manenti et al. modeled the thermal step of a sulfur recovery unit including the reaction furnace and waste heat boiler using a kinetic model containing 146 species and 2412 reactions [
12]. In another study in the same year, they aimed to develop their own kinetic models by considering the Claus process’ conditions. Unlike in the literature, their kinetic parameters explain the presence of light hydrocarbons, ammonia and other species. The work provides a review of the major phenomena involved in reacting systems containing sulfur compounds [
13]. In another study, Manenti et al. used a kinetic model with 140 species and 2400 reactions to optimize elemental sulfur recovery and steam production [
14].
In another study, an industrial sulfur recovery unit reaction furnace was modeled using equilibrium and combined modeling [
15]. Nabikandi and Fatemi modeled and simulated an industrial Claus sulfur recovery process. Furnace and Claus reactors were comparatively modeled with two different approaches: the equilibrium and the kinetic method [
16]. Zarei et al. modeled reaction furnace and waste heat boiler methods separately and together, using two different reaction schemes containing the same reaction rate expressions [
17]. A dynamic model was introduced for the reaction furnace simulation, and all the existing kinetic information was used in this model, but complex reactions with free radicals were neglected Pahlavan and Fanaei [
18] in order to prevent complexity. Adewale et al. examined the hydrogen and sulfur degradation of H
2S using the process simulator [
19]. Andoglu et al. developed a reduced kinetic model for a reaction furnace and compared the results with detailed kinetic mechanism [
20]. In the study of Fazlollahi et al., using both numerical modeling and simulation, the effects of oxygen and acid gas enrichment on the reaction furnace temperature and sulfur recovery were studied [
21]. Mahmoodi et al. developed a CFD model for a thermal furnace using the reduced kinetic model [
22]. Dell’Angelo et al. proposed a machine learning method to determine the mechanisms of their reduced kinetic model for the reaction furnace [
23].
Recently, optimization studies on Claus process units have been encountered. Researchers used different algorithms and methods for optimization. Kazempour et al. detailed the multi-objective optimization of modeling and the thermal part of the Claus process with a kinetic model utilizing a response surface method (Central Composite Design). Sensitivity analysis was performed with a simulator software to investigate the effects of fuel and air inlet flow rates, steam inlet temperature, oven pressure and waste heat boiler (WHB) output temperature on sulfur recovery efficiency, steam production and H
2S/SO
2 ratio [
3]. Ghahraloud et al. aimed to model and optimize an industrial modified Claus process in order to achieve maximum sulfur recovery using a genetic algorithm. The decision variables here were the inlet temperatures of the oven and fixed bed reactors, the distribution of feeding throughout the oven and the air flow rate in the furnace [
24]. Zarei performed optimization work with the fmincon function in Matlab for maximizing the sulfur conversion and reducing total emissions from the thermal furnace, with the temperature, pressure, and oxygen amount in the feed as control variables [
25]. Rahman et al. simulated the thermal part in Chemkin Pro and the catalytic part in Aspen Hysys using a detailed kinetic model; they performed optimization studies using a genetic algorithm and artificial neural networks in Matlab [
26]. Zahid et al. modeled the Claus process, validated it with industrial data and performed an optimization study using pinch analysis [
27]. Johni and OmidbakhshAmiri simulated SRU using the Aspen HYSYS, and environmental, energy, and economic features of the process based on special criteria (profit, weighted global warming potentials, and energy consumption) were analyzed. After the sensitivity analysis of the process, single- and multi-objective optimizations were carried out using genetic algorithm [
28].
In the optimization studies, the reaction furnace was considered alone as the only reactor in the thermal step; the waste heat boiler was not taken into account, or it was considered as a simple heat exchanger. This assumption ignores the reformation of hydrogen sulfide with a sudden temperature drop in the waste heat boiler, where the gas mixture leaving the furnace at high temperatures is cooled before entering the catalytic reactors, thus introducing an error into the calculation of amounts of components at the end of the thermal step. This study aims to optimize the thermal section of the Claus process by considering the waste heat boiler as a reactor with heat exchange instead of a basic heat exchanger. As the first step, the reaction furnace and the waste heat boiler will be modeled as reactors on a kinetic basis using reduced kinetic models with 11 and 2 global reactions, respectively. As the second step, both units will be optimized together in the thermal section of the Claus process to maximize the sulfur and steam production using a genetic algorithm and statistical analysis.
4. Conclusions
This study aimed to model and optimize the thermal section of the Claus process. At first, reduced kinetic models were proposed for the reaction furnace and waste heat boiler, and these models were validated with the detailed kinetic scheme shown in the literature. Thus, it has been demonstrated that instead of a detailed kinetic model including more than 2000 elemental reactions, which is cumbersome when applied to the ensuing calculations and is difficult to modify, a reduced kinetic model with 11 global reactions can be used.
A waste heat boiler is generally considered as a simple heat exchanger in the literature; instead, it is here modeled as a plug flow reactor with heat transfer. The simulation results show that recombination reactions cannot neglect the hydrogen sulfide ratio and temperature. Modeling the boiler as a reactor instead of a heat exchanger was a more realistic and revelatory approach.
After the modeling and simulation studies, single-objective and multi-objective optimizations were carried out on the Claus thermal step in the MATLAB environment. The aim was to maximize the sulfur production at the exit of the thermal section, which is the main goal of using sulfur recovery units. First, the simulation of the thermal step was considered as the experimental setup; simulations were carried out according to Taguchi’s suggestions and the results were analyzed, and a 24% increase in sulfur production was achieved. In the second step, a single-objective optimization problem was studied, wherein the objective was to maximize the sulfur production and the constraint was to keep the ratio of hydrogen sulfide to sulfur dioxide at around 2. The genetic algorithm (ga) solver was used, and the improvement in the objective function was 14.1%. In the third step, maximizing the steam produced in the waste heat boiler was included as a secondary objective, and the constraint was considered as the third objective, using the gamultiobj solver to solve it. The results of the multi-objective optimization problem show increases of up to 30% and 41% in sulfur production and steam production, respectively, as the conditions changed.
As a result of the improvements in the operating parameters of the Claus process revealed by the model employed in this study, the process can be rendered more cost-effective and environmentally friendly.