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. 2023 Oct 31;8(45):42522–42539. doi: 10.1021/acsomega.3c05193

Modeling and Experimental Investigation of Sulfurous Compounds Removal from Gas Condensate through Ultrasound-Assisted Oxidative Desulfurization Method

Ameneh Taghizadeh †, Maryam Asemani †,*, Feridun Esmaeilzadeh ‡, Abolhasan Ameri †
PMCID: PMC10652721  PMID: 38024750

Abstract

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This study employed an ultrasound-assisted oxidative desulfurization process (UAOD) to investigate the degradation of three sulfurous compounds in the synthetic gas condensate. Various parameters, including oxidizers (hydrogen peroxide, sodium peroxide, potassium superoxide), promoters (formic acid, acetic acid), catalysts (phosphotungstic acid, ferrous(II) sulfate, zirconium dioxide, vanadium pentoxide, aluminum oxide γ, copper(II) oxide), and phase transfer agents (isobutanol, tetraoctylammonium bromide, and tetra-n-butylammonium fluoride), were examined to identify the optimal combination for reducing sulfurous compounds in the UAOD process. The influence of the extraction stage and reactor vessel material on the desulfurization efficiency was also investigated. Results revealed that hydrogen peroxide, formic acid, phosphotungstic acid, and isobutyl alcohol were the most effective oxidizers, promoters, catalysts, and phase transfer agents, respectively. Response surface methodology was used to determine the optimal conditions by evaluating different concentrations of these reagents within specific ranges. The study considered ranges such as 10–70 vol % of hydrogen peroxide, 5–70 vol % of formic acid, 1–30 wt % of phosphotungstic acid, 1–30 vol % of isobutanol, and 5–40 min of ultrasonic ripple time. Empirical models were developed for each sulfurous compound type, providing optimal conditions for sulfur removal with an error margin of less than 0.1%. The validity of the suggested models was confirmed through an industrial data analysis. Additionally, it was observed that increasing the number of extraction stages improved desulfurization efficiency, and using a stainless-steel reactor vessel was more suitable than using a glass vessel.

1. Introduction

Gas wells often produce natural gas and gas condensate, which commonly contain sulfurous compounds at levels that exceed acceptable thresholds for industrial use and other applications. Sulfur compounds in petroleum feedstocks contribute to environmental pollution and can harm the performance of engines and emission control systems.1 Therefore, developing effective desulfurization methods is crucial to comply with increasingly stringent environmental regulations and improve the quality of refined fuels.

Various desulfurization methods have been proposed, including hydrodesulfurization (HDS), deep hydrodesulfurization (deep HDS), biodesulfurization, oxidative desulfurization (ODS), and ultrasound-assisted ODS (UAOD). HDS, the most commonly used method, is expensive and ineffective at removing aromatic sulfurous compounds. Modifications to HDS, such as using more active catalysts, longer reaction times, and higher temperatures (>400 °C) and pressures (>1000 atm), yield only marginal improvements in aromatic sulfurous compound removal. This process requires high temperatures and pressures, metallic catalysts, and extended reaction times.2,3 Furthermore, this necessitates the establishment of a hydrogen production plant due to excessive hydrogen consumption. HDS is also associated with reduced removal efficiency, a significant increase in strongly aromatic sulfurous compounds, a shorter catalyst life span, and elevated operational costs.4 Biodesulfurization processes are conducted at low temperatures and pressures with the assistance of microorganisms to degrade sulfurous compounds in crude oil.5 However, this approach lacks mature technology, stable reactions, and reasonable reaction times.6 ODS involves a chemical reaction between an oxidant and sulfur, eliminating the need for high pressures or temperatures.7 While ODS can oxidize sulfurous compounds, it suffers from drawbacks such as the quantitative and qualitative reduction of fuel due to oxidants and the loss of valuable fuel components if an inappropriate solvent is chosen.8 To address the limitations of conventional desulfurization methods, the ultrasound-assisted oxidative desulfurization process (UAOD) has emerged as an innovative approach with several advantages. UAOD is a novel method that offers a quicker, safer, and more cost-effective oxidation process. It can efficiently remove both aliphatic and aromatic sulfurous compounds under low-pressure and low-temperature conditions, achieving a high yield of sulfur-to-sulfone conversion. It features short reaction times and is free from chemical hazards or the production of hazardous byproducts.1,9 Additionally, UAOD is characterized by the use of recyclable catalysts.1,9

The UAOD process involves adding an oxidizing agent such as hydrogen peroxide (H2O2) to a sulfur-containing petroleum fraction, followed by exposure to ultrasonic irradiation. This generates reactive species, such as hydroxyl radicals (•OH), that are capable of oxidizing sulfur compounds. The oxidized sulfur species can then be separated from the desulfurized petroleum fraction using conventional techniques, such as extraction or distillation. UAOD offers advantages such as milder operating conditions compared to those of conventional methods, shorter reaction times, enhanced selectivity for sulfur compounds, and reduced catalyst usage. Importantly, UAOD can be seamlessly integrated into existing refining processes with minimal modifications, making it an appealing choice for the petroleum industry

Several studies have explored the effectiveness of the UAOD process in desulfurizing various petroleum fractions. Pouladi et al.10 employed sulfuric acid (H2SO4), nitric acid (HNO3), and nitrogen dioxide (NO2) as oxidizing agents to optimize gas condensate desulfurization, achieving a remarkable sulfur removal efficiency of 95.61%. Alibolandi et al.11 utilized ozone gas as an oxidizer to model and optimize gas condensate desulfurization, successfully removing 95.8% of sulfurous compounds under optimal conditions. In another study, Sinhmar et al.12 achieved complete removal of sulfurous compounds from simulated diesel, including dibenzothiophene, using a combination of oxidizing agents (hydrogen peroxide, acetic acid, and potassium persulfate) in the UAOD process. Mofidi and Shahhosseini13 employed a deep eutectic solvent (DES) in the UAOD process to remove dibenzothiophene (DBT) from diesel fuel, resulting in the removal of 97.53% of sulfurous compounds under optimal conditions. Desai et al.14 applied the UAOD method to eliminate sulfurous compounds from model fuel (MF) containing DBT, achieving an impressive 99% removal rate. Fan et al.15 introduced the Mo/Ti-TUD-1 catalyst in the UAOD method, achieving a 99% efficiency on a model oil and a 55.1% sulfurous removal rate for Saudi superlight oil. Additionally, Yu et al.16 utilized a mixture of hydrogen peroxide, acetic acid, and copper(II) sulfate (CuSO4) as an oxidizing agent and achieved a 48.68 wt % reduction in sulfur content from a heavy crude oil of Iran with a sulfurous content of 38,638 ppm. These studies collectively validate the effectiveness of the UAOD process in desulfurizing gas condensates. However, it is important to note that despite ongoing research on UAOD for sulfur removal from gas condensates, there remains a need for comprehensive investigations in this area. Most existing research has primarily focused on light or heavy oil samples, with limited attention given to the simultaneous removal of all sulfur compounds in the gas condensate, including aliphatic thiol, aliphatic sulfide, and aromatic thiophene.

Shayegan et al.17 highlighted that the ultrasound-assisted oxidative desulfurization (UAOD) process inherently generates heat without the need for an external heat source. In their study investigating the temperature effect on desulfurization of sulfurous components from gas oil, the researchers explored a temperature range of 20 to 90 °C, with the upper limit set as the boiling point of the most volatile component in the mixture.18−20 However, two key limitations emerged with increasing temperature: (1) the degradation of hydrogen peroxide at high temperatures, specifically above 80 °C, and (2) the evaporation of lighter gas oil components. Additionally, as the temperature increased, the effective creation of cavitation and the intensity of the cavitation collapse decreased. Consequently, to address these constraints, the researchers maintained a constant temperature of approximately 35 ± 2 °C throughout their experiments.21,22 As a result, all experiments in this study were conducted at 35 ± 2 °C, ensuring the feasibility of the UAOD process while avoiding temperature-related issues.

In desulfurization, choosing materials, including oxidizers, promoters, catalysts, and phase transfer agents, is paramount to achieving efficient sulfur removal from hydrocarbon feedstocks. Their well-established utility and effectiveness often guide the selection of these materials in prior desulfurization studies conducted by researchers worldwide. Oxidizers such as hydrogen peroxide, sodium peroxide, and potassium superoxide have been extensively utilized due to their strong oxidizing properties, which facilitate the conversion of sulfur compounds into more readily removable forms. Promoters such as formic and acetic acids are commonly employed to enhance the desulfurization process by facilitating the action of oxidizers and catalysts. Catalysts, including phosphotungstic acid, ferrous(II) sulfate, zirconium dioxide, vanadium pentoxide, aluminum oxide γ, and copper(II) oxide, have played pivotal roles in desulfurization reactions by promoting the breakdown of complex sulfur compounds and aiding in their extraction. Phase transfer agents like isobutanol, tetraoctylammonium bromide, and tetra-n-butylammonium fluoride have been instrumental in transferring sulfur species from the hydrocarbon phase to the aqueous phase, further enhancing sulfur removal efficiency. These materials have a well-established track record in the desulfurization literature, with numerous studies showcasing their effectiveness in reducing the sulfur content in various hydrocarbon matrices. Table 1 reviews previous studies conducted on UAOD, highlighting the importance of solvent and oxidizing mixture selection. By leveraging the knowledge accumulated from prior research, this study has strategically chosen these materials as the basis for experimental investigations, aiming to contribute to ongoing efforts to develop more efficient and environmentally friendly desulfurization processes.

Table 1. Effect of the Solvent Type and Oxidant Mixture on the UAOD Efficiency.

operating condition feedstock oxidant mixture solvent type and content of sulfurous compounds removal efficiency (%) refs
75 °C, 3 rounds of extraction for different times diesel oil tetradactyl ammonium bromide + phosphotungstic acid + hydrogen peroxide acetonitrile various types and contents 98.5 Mei et al.23
70 °C with ultrasonication for 10 min diesel fuel hydrogen peroxide + acetic acid + iron sulfide acetonitrile various types and contents 98 Ibrahim et al.24
50 °C, 4 rounds of extraction for 3 h model diesel cadmium oxide catalyst + hydrogen peroxide + acetic acid acetonitrile various types and contents 99.5 Zhao et al.25
ultrasonication for 10 min kerosene formic acid + hydrogen peroxide acetonitrile various types and contents 95 Babushkina et al.26
ultrasonication for 76 min and 4 rounds of extraction kerosene phosphotungstic acid supported on active carbon + hydrogen peroxide acetonitrile various types and contents 99 Gildo et al.27
70 °C model diesel fuel hydrogen peroxide + acetic acid N, N-dimethylformamide dibenzothiophene 98 Margeta et al.28
40 °C with ultrasonication for 15 min diesel fuel hydrogen peroxide + acetic acid + iron sulfide N, N-dimethylformamide dibenzothiophene 98 Dai et al.29
62 °C with ultrasonication for 17 min and 3 rounds of extraction gasoil hydrogen peroxide + acetic acid + iron sulfide + isobutanol methanol dibenzothiophene 90 Shayegan et al.17
90 °C with ultrasonication for 9 min and 3 rounds of extraction diesel oil hydrogen peroxide + acetic acid methanol dibenzothiophene 80 Duarte et al.30
50 °C diesel oil hydrogen peroxide + acetic acid + phosphotungstic acid + tetradactyl ammonium bromide sodium hydroxide dibenzothiophene 86 Shamseddini et al.31
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The primary objective of this study was to utilize the UAOD process for the degradation of linear and cyclic sulfur compounds found in synthetic gas condensates. Three specific sulfurous compounds were chosen, namely, tert-butyl mercaptan representing aliphatic thiol, dipropyl sulfide representing aliphatic sulfide, and benzothiophene representing aromatic thiophene. These compounds were initially present in concentrations ranging from 100 to 3000 ppm in n-heptane. To enhance the performance of the UAOD process, an oxidizer mixture comprising an oxidant, promoter, catalyst, and phase transfer agent was employed. Numerous oxidizers, promoters, catalysts, and phase transfer agents were tested individually, followed by a comprehensive exploration of different combinations to determine the most effective oxidizing mixture. Subsequently, empirical models were developed for each type of sulfurous compound to predict optimal conditions for sulfur removal. Notably, this study is pioneering, as it investigates a wide range of three distinct sulfur compounds simultaneously. It also examines various values and types of oxidizers, promoters, catalysts, and phase transfer agents to optimize the UAOD process. Besides, the impact of the extraction stage and reactor vessel material was examined on the desulfurization efficiency. This article introduces three valuable mathematical models that predict sulfur removal efficiency for tert-butyl mercaptan, dipropyl sulfide, and benzothiophene. Finally, the validity of the suggested models was confirmed by using industrial data.

2. Experimental Section

2.1. Materials and Instruments

All of the chemicals used in this study were obtained from Merck and used without further purification. The chemicals include formic acid (CH2O2, 99%), acetic acid (C2H4O2, 99%), hydrogen peroxide (H2O2, 30%), sodium peroxide (Na2O2, 99%), potassium superoxide (K2O, 98%), phosphotungstic acid (H3P(W3O10)4, 97%), ferrous(II) sulfate (FeSO4, 99.5%), zirconium dioxide (ZrO2, 99.99%), vanadium pentoxide (V2O5, ≥99.6%), aluminum oxide γ (Al2O3, 99.99%), copper(II) oxide (CuO, ≥99.0%), isobutanol (C4H10O, 99%), tetraoctylammonium bromide (C32H68BrN, 98%), tetra-n-butylammonium fluoride (C16H36FN, 98%), n-heptane (C7H16, 99%), tert-butyl mercaptan (C4H10S, 98%), dipropyl sulfide (C6H14S, 98%), benzothiophene (C8H6S, 98%), and N,N-dimethylformamide (DMF) (HCON(CH3)2, 99.8%). An XOS TSA (total sulfur analyzer) manufactured in the U.S.A. was used to analyze the sulfur levels in the gas-condensate samples. The TSA used in this research adheres to the ASTMD 7039 methodology, specifically designed to analyze gas-condensate samples.

2.2. Experimental Setup

An ultrasonic bath apparatus manufactured in Iran (VCLEAN 1-L6) was employed to conduct the experiments. This apparatus boasted adjustable temperature and water circulation capabilities and operated at 150 W and 40 kHz frequency. It also had a 6 L capacity and was used to sonicate the samples in two cylindrical vessels: the first reactor was made of SS-304 with a volume of 100 mL, and the second reactor was a Pyrex beaker with the same volume. Additionally, a hot plate with a magnetic stirrer manufactured by the IKA company (Yellow Line, model MSH basic, Germany) was used at a setting of 2000 rpm. To weigh the samples and take measurements, a laboratory precision balance (Sartorius PRACTUM 224–1S, Germany) with a precision of 0.1 mg and a sampler with an accuracy of 0.01 ppm were used. The steps for conducting the experiments are illustrated in Figure 1.

Figure 1.

Figure 1

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Schematic diagram of the UAOD process of sulfurous compounds removal in samples: GC1, GC2, and GC3.

2.3. Experimental Procedure

In this study, gas-condensate systems contained two groups of sulfurous compounds: aliphatic species, such as thiols (mercaptans), and sulfides, as well as aromatic species, such as thiophene, benzothiophene, and dibenzothiophene. Generally, three representative samples were designated to examine the removal of each group of sulfurous compounds. The first group, represented by GC1, consisted of N-heptane with the addition of tert-butyl mercaptan or 2-methyl-2-propane thiol, in the range 100–3000 ppm, to represent aliphatic thiols. The second group, represented by GC2, consisted of N-heptane with the addition of dipropyl sulfide, in the range 100–3000 ppm, to represent aliphatic sulfides. Lastly, GC3 consisted of N-heptane with benzothiophene, representing aromatic thiophenes in the 100–3000 ppm range.

To achieve the most effective oxidizer mixture, a variety of compounds were utilized, including hydrogen peroxide, sodium peroxide, and potassium superoxide as the oxidizer; formic acid and acetic acid as the promoter; phosphotungstic acid, ferrous(II) sulfate, zirconium dioxide, vanadium pentoxide, aluminum oxide γ, and copper(II) oxide as the catalyst; and isobutanol, tetraoctylammonium bromide, and tetra-n-butylammonium fluoride as the phase transfer agent. These compounds were combined in various ways, as outlined in Table 2. Three separate mixtures were created to prepare the samples, each containing a consistent sulfur content of 3000 ppm of distinct sulfurous compounds. The oxidizer mixture was then added to each of the samples. After this, the samples were sonicated for 22 min in an ultrasonic bath whose temperature was kept constant at 35 ± 2 °C by a PID controller. Following the predetermined ultrasonication time, the samples were removed from the bath and allowed to rest for 10 min. The resulting mixture was then divided into an organic phase on top and an aqueous phase at the bottom. The organic phase was separated and mixed twice with 10 mL of DMF (equivalent to half the volume of the hydrocarbon sample) as the extractor and agitated for 10 min by a magnetic stirrer at 300 rpm. After each extraction, the organic phase became clearer, eventually appearing like the original n-heptane as oxidized sulfurous compounds were efficiently removed. Finally, the organic phase sample was collected for total sulfur analysis, and the sulfur removal efficiency (SRE%) was calculated using eq 1. Figure 2 shows the steps of the experiment.

2.3. 1

Table 2. Experimental Results to Obtain the Optimal Combination of the Oxidizer Mixture.

      oxidizer blend
  
run synthetic samples (100 mL) initial concentration of sulfur (ppm) oxidant (40 mol %) promoter (37.5 mol %) catalyst (15.5 wt %) SRE (%)
1 CG1 3000 hydrogen peroxide     43.42
2 CG1 3000 sodium peroxide     31.21
3 CG1 3000 potassium superoxide     43.01
4 CG2 3000 hydrogen peroxide     35.71
5 CG2 3000 sodium peroxide     27.91
6 CG2 3000 potassium superoxide     32.02
7 CG3 3000 hydrogen peroxide     36.51
8 CG3 3000 sodium peroxide     29.71
9 CG3 3000 potassium superoxide     32.01
10 CG1 3000 hydrogen peroxide formic acid   77.96
11 CG1 3000 hydrogen peroxide acetic acid   76.02
12 CG2 3000 hydrogen peroxide formic acid   68.57
13 CG2 3000 hydrogen peroxide acetic acid   66.97
14 CG3 3000 hydrogen peroxide formic acid   61.73
15 CG3 3000 hydrogen peroxide acetic acid   60.87
16 CG1 3000 hydrogen peroxide formic acid phosphotungstic acid 98.31
17 CG1 3000 hydrogen peroxide formic acid ferrous(II) sulfate 97.12
18 CG1 3000 hydrogen peroxide formic acid zirconium dioxide 80.47
19 CG1 3000 hydrogen peroxide formic acid vanadium pentoxide 87.96
20 CG1 3000 hydrogen peroxide formic acid aluminum oxide γ 93.56
21 CG1 3000 hydrogen peroxide formic acid copper(II) oxid 95.26
22 CG2 3000 hydrogen peroxide formic acid phosphotungstic acid 97.02
23 CG2 3000 hydrogen peroxide formic acid ferrous(II) sulfate 96.21
24 CG2 3000 hydrogen peroxide formic acid zirconium dioxide 68.08
25 CG2 3000 hydrogen peroxide formic acid vanadium pentoxide 83.05
26 CG2 3000 hydrogen peroxide formic acid aluminum oxide γ 91.78
27 CG2 3000 hydrogen peroxide formic acid copper(II) oxide 94.06
28 CG3 3000 hydrogen peroxide formic acid phosphotungstic acid 97.21
29 CG3 3000 hydrogen peroxide formic acid ferrous(II) sulfate 95.97
30 CG3 3000 hydrogen peroxide formic acid zirconium dioxide 72.36
31 CG3 3000 hydrogen peroxide formic acid vanadium pentoxide 83.31
32 CG3 3000 hydrogen peroxide formic acid aluminum oxide γ 91.99
33 CG3 3000 hydrogen peroxide formic acid copper(II) oxide 94.71
34 CG1 3000 hydrogen peroxide formic acid phosphotungstic acid 99.96
35 CG1 3000 hydrogen peroxide formic acid phosphotungstic acid 99.17
36 CG1 3000 hydrogen peroxide formic acid phosphotungstic acid 98.61
37 CG2 3000 hydrogen peroxide formic acid phosphotungstic acid 98.77
38 CG2 3000 hydrogen peroxide formic acid phosphotungstic acid 98.51
39 CG2 3000 hydrogen peroxide formic acid phosphotungstic acid 97.18
40 CG3 3000 hydrogen peroxide formic acid phosphotungstic acid 99.84
41 CG3 3000 hydrogen peroxide formic acid phosphotungstic acid 98.99
42 CG3 3000 hydrogen peroxide formic acid phosphotungstic acid 97.53
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Figure 2.

Figure 2

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Schematic diagram illustrating the steps of the experiment created by Ameneh Taghizadeh.

2.4. Experimental Design

To execute the Central Composite Design (CCD) with an α of 2, six variables, and five levels coded as (−2), (−1), (0), (+1), and (+2) according to eq 2, Design Expert Version 13 software was utilized.

2.4. 2

where, N is the total number of experiments, denoted by the CCD, and K considers the number of variables. Additionally, nc represents the central points. Based on eq 2, the design involved 64 factorial points, 12 axial points, and 10 central points, resulting in 86 experiments for each gas-condensate sample, namely, GC1, GC2, and GC3. Thus, the overall number of experiments required was 258.

2.5. Optimization

By employing numerical optimization, experiments can be focused on achieving a particular objective. In contrast to previous studies that solely concentrated on the sulfur content of specific wells, this study permits the estimation of the desulfurization efficiency under particular conditions. The current research offers insights into the ideal conditions for varying sulfur content levels, facilitating the anticipation of the desulfurization efficiency in optimal scenarios. To validate the optimal conditions, conducting the confirmed experiments recommended by CCD becomes essential. The confirmed experiments were executed according to the optimum conditions.

2.6. Effect of Extraction Stage and Reactor Vessel Material

This study investigated the impact of the extraction stage and reactor vessel material on the desulfurization efficiency. To achieve this, a polar solvent called DMF was utilized for extraction using a solvent-to-hydrocarbon ratio of 2:1. Subsequently, experiments were carried out at the optimal points determined for GC1, GC2, and GC3. Each sample underwent three different experiments. First, two extraction stages were conducted using a glass reactor vessel. Second, two extraction stages were performed using a stainless-steel reactor vessel. Lastly, three extraction stages were executed using the most suitable reactor vessel type, either glass or stainless steel.

2.7. Field Data

After successfully removing mercaptan from the GC1 with a desulfurization efficiency of 99.93% using UAOP under optimal conditions, a comparison was conducted between two industrial gas-condensate samples containing mercaptan compounds before and after the H2S polishing process. These samples were obtained from the Fifth Gas Refinery, Phases 10 and 11 of the South Pars Complex, Iran, and their respective characteristics are listed in Tables 2 and 3. The total sulfur contents of the industrial samples (IS1 and IS2) were measured at 1726.30 and 1521.87 ppm, respectively. The optimal operating conditions were extracted using Design Expert software, and a constant value of X1 was entered in the optimization section for the first model. This resulted in the determination of the optimal points for removing the specified amount of sulfur from both industrial samples.

Table 3. Compositions of Gas Condensates, Prepared from the Fifth Gas Refinery, Phases 10 and 11 of the South Pars Complex, Iran.

property method industrial sample 1 (ppm) industrial sample 2 (ppm)
Sp. Gr. 60/60 °F ASTM D4052 0.740 0.732
total sulfur ASTM D7039 1726.30 1521.87
mercaptans ASTM D3227 2400 2243
H2S ASTM D1159 20 5
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3. Results and Discussion

3.1. Optimizing the Type and Magnitude of the Variables

In this study, initially, 42 different experiments were accomplished to find the best types of oxidizer, promoter, catalyst, and phase transfer agent. According to the findings presented in Table 4, the optimal selections for oxidizers, promoters, catalysts, and phase transfer agents were hydrogen peroxide, formic acid, phosphotungstic acid, and isobutanol, in that order.

Table 4. Experimental Results for the Removal of Mercaptan (SRE%(CG1)), Sulfide (SRE%(CG2)), and Thiophene Compound (SRE%(CG3)) by UAOD Method from the Three-Sample Synthetic Gas Condensate with the Help of RSM Based on CCD.

  variables
  
  X1 X2 X3 X4 X5 X6 SRE (%)
run ppm code vol % code vol % code wt % code vol % code min code GC1 GC2 GC3
1 825 –1 25 –1 21.3 –1 8.3 –1 8.3 –1 13.8 –1 99.59 96.11 86.13
2 2275 1 25 –1 21.3 –1 8.3 –1 8.3 –1 13.8 –1 99.88 97.93 98.31
3 825 –1 55 1 21.3 –1 8.3 –1 8.3 –1 13.8 –1 98.58 94.45 82.41
4 2275 1 55 1 21.3 –1 8.3 –1 8.3 –1 13.8 –1 99.85 96.12 97.73
5 825 –1 25 –1 53.8 1 8.3 –1 8.3 –1 13.8 –1 99.78 96.78 87.46
6 2275 1 25 –1 53.8 1 8.3 –1 8.3 –1 13.8 –1 99.90 98.41 98.62
7 825 –1 55 1 53.8 1 8.3 –1 8.3 –1 13.8 –1 99.47 95.48 84.21
8 2275 1 55 1 53.8 1 8.3 –1 8.3 –1 13.8 –1 99.86 97.14 97.97
9 825 –1 25 –1 21.3 –1 22.8 1 8.3 –1 13.8 –1 99.68 96.42 89.23
10 2275 1 25 –1 21.3 –1 22.8 1 8.3 –1 13.8 –1 99.91 98.15 98.47
11 825 –1 55 1 21.3 –1 22.8 1 8.3 –1 13.8 –1 98.75 95.16 86.96
12 2275 1 55 1 21.3 –1 22.8 1 8.3 –1 13.8 –1 99.87 96.69 98.13
13 825 –1 25 –1 53.8 1 22.8 1 8.3 –1 13.8 –1 99.92 97.23 90.13
14 2275 1 25 –1 53.8 1 22.8 1 8.3 –1 13.8 –1 99.96 98.86 98.96
15 825 –1 55 1 53.8 1 22.8 1 8.3 –1 13.8 –1 99.49 95.97 88.63
16 2275 1 55 1 53.8 1 22.8 1 8.3 –1 13.8 –1 99.89 97.77 98.26
17 825 –1 25 –1 21.3 –1 8.3 –1 22.8 1 13.8 –1 99.73 96.83 94.12
18 2275 1 25 –1 21.3 –1 8.3 –1 22.8 1 13.8 –1 99.92 98.31 99.36
19 825 –1 55 1 21.3 –1 8.3 –1 22.8 1 13.8 –1 98.85 95.29 89.13
20 2275 1 55 1 21.3 –1 8.3 –1 22.8 1 13.8 –1 99.89 97.07 99.01
21 825 –1 25 –1 53.8 1 8.3 –1 22.8 1 13.8 –1 99.93 97.98 95.09
22 2275 1 25 –1 53.8 1 8.3 –1 22.8 1 13.8 –1 99.97 99.13 99.45
23 825 –1 55 1 53.8 1 8.3 –1 22.8 1 13.8 –1 99.51 96.73 91.98
24 2275 1 55 1 53.8 1 8.3 –1 22.8 1 13.8 –1 99.90 97.98 99.19
25 825 –1 25 –1 21.3 –1 22.8 1 22.8 1 13.8 –1 99.86 98.02 95.08
26 2275 1 25 –1 21.3 –1 22.8 1 22.8 1 13.8 –1 99.97 99.09 99.46
27 825 –1 55 1 21.3 –1 22.8 1 22.8 1 13.8 –1 99.13 96.31 92.73
28 2275 1 55 1 21.3 –1 22.8 1 22.8 1 13.8 –1 99.94 97.92 99.21
29 825 –1 25 –1 53.8 1 22.8 1 22.8 1 13.8 –1 99.95 98.83 96.56
30 2275 1 25 –1 53.8 1 22.8 1 22.8 1 13.8 –1 99.99 99.55 99.59
31 825 –1 55 1 53.8 1 22.8 1 22.8 1 13.8 –1 99.70 97.64 93.16
32 2275 1 55 1 53.8 1 22.8 1 22.8 1 13.8 –1 99.95 98.56 99.43
33 825 –1 25 –1 21.3 –1 8.3 –1 8.3 –1 31.3 1 99.65 96.87 90.72
34 2275 1 25 –1 21.3 –1 8.3 –1 8.3 –1 31.3 1 99.83 97.73 96.41
35 825 –1 55 1 21.3 –1 8.3 –1 8.3 –1 31.3 1 98.90 95.31 87.12
36 2275 1 55 1 21.3 –1 8.3 –1 8.3 –1 31.3 1 99.31 95.91 94.16
37 825 –1 25 –1 53.8 1 8.3 –1 8.3 –1 31.3 1 99.80 97.58 91.52
38 2275 1 25 –1 53.8 1 8.3 –1 8.3 –1 31.3 1 99.85 98.03 97.02
39 825 –1 55 1 53.8 1 8.3 –1 8.3 –1 31.3 1 99.58 95.91 88.96
40 2275 1 55 1 53.8 1 8.3 –1 8.3 –1 31.3 1 99.83 96.59 95.71
41 825 –1 25 –1 21.3 –1 22.8 1 8.3 –1 31.3 1 99.72 97.10 94.31
42 2275 1 25 –1 21.3 –1 22.8 1 8.3 –1 31.3 1 99.87 97.96 98.14
43 825 –1 55 1 21.3 –1 22.8 1 8.3 –1 31.3 1 99.05 95.97 89.21
44 2275 1 55 1 21.3 –1 22.8 1 8.3 –1 31.3 1 99.42 96.31 97.71
45 825 –1 25 –1 53.8 1 22.8 1 8.3 –1 31.3 1 99.93 97.73 95.89
46 2275 1 25 –1 53.8 1 22.8 1 8.3 –1 31.3 1 99.94 98.33 98.73
47 825 –1 55 1 53.8 1 22.8 1 8.3 –1 31.3 1 99.65 96.59 92.13
48 2275 1 55 1 53.8 1 22.8 1 8.3 –1 31.3 1 99.84 97.03 97.95
49 825 –1 25 –1 21.3 –1 8.3 –1 22.8 1 31.3 1 99.78 97.53 95.89
50 2275 1 25 –1 21.3 –1 8.3 –1 22.8 1 31.3 1 99.91 98.13 99.06
51 825 –1 55 1 21.3 –1 8.3 –1 22.8 1 31.3 1 99.16 96.06 92.33
52 2275 1 55 1 21.3 –1 8.3 –1 22.8 1 31.3 1 99.55 96.91 98.19
53 825 –1 25 –1 53.8 1 8.3 –1 22.8 1 31.3 1 99.94 98.17 97.66
54 2275 1 25 –1 53.8 1 8.3 –1 22.8 1 31.3 1 99.96 98.89 99.22
55 825 –1 55 1 53.8 1 8.3 –1 22.8 1 31.3 1 99.62 96.93 93.18
56 2275 1 55 1 53.8 1 8.3 –1 22.8 1 31.3 1 99.86 97.65 98.67
57 825 –1 25 –1 21.3 –1 22.8 1 22.8 1 31.3 1 99.88 98.47 97.72
58 2275 1 25 –1 21.3 –1 22.8 1 22.8 1 31.3 1 99.93 98.69 99.17
59 825 –1 55 1 21.3 –1 22.8 1 22.8 1 31.3 1 99.41 96.90 96.05
60 2275 1 55 1 21.3 –1 22.8 1 22.8 1 31.3 1 99.73 97.58 98.63
61 825 –1 25 –1 53.8 1 22.8 1 22.8 1 31.3 1 99.97 98.96 98.02
62 2275 1 25 –1 53.8 1 22.8 1 22.8 1 31.3 1 99.99 99.11 99.33
63 825 –1 55 1 53.8 1 22.8 1 22.8 1 31.3 1 99.75 97.85 96.89
64 2275 1 55 1 53.8 1 22.8 1 22.8 1 31.3 1 99.89 97.99 98.99
65 100 –2 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.19 96.32 89.31
66 3000 2 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.96 98.77 99.84
67 1550 0 10 –2 37.5 0 15.5 0 15.5 0 22.5 0 99.52 97.93 98.02
68 1550 0 70 2 37.5 0 15.5 0 15.5 0 22.5 0 99.69 96.62 94.98
69 1550 0 40 0 5.0 –2 15.5 0 15.5 0 22.5 0 99.12 96.55 92.27
70 1550 0 40 0 70.0 2 15.5 0 15.5 0 22.5 0 99.83 98.89 96.09
71 1550 0 40 0 37.5 0 1.0 –2 15.5 0 22.5 0 99.35 96.83 96.33
72 1550 0 40 0 37.5 0 30.0 2 15.5 0 22.5 0 99.75 98.06 99.22
73 1550 0 40 0 37.5 0 15.5 0 1.0 –2 22.5 0 99.27 96.38 93.07
74 1550 0 40 0 37.5 0 15.5 0 30.0 2 22.5 0 99.52 98.11 99.42
75 1550 0 40 0 37.5 0 15.5 0 15.5 0 5.0 –2 99.45 97.18 95.71
76 1550 0 40 0 37.5 0 15.5 0 15.5 0 40.0 2 99.95 98.66 98.21
77 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.12 97.7 97.38
78 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.14 97.72 97.38
79 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.12 97.69 97.39
80 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.12 97.69 97.39
81 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.13 97.69 97.41
82 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.1 97.67 97.39
83 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.12 97.68 97.39
84 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.11 97.69 97.39
85 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.12 97.68 97.39
86 1550 0 40 0 37.5 0 15.5 0 15.5 0 22.5 0 99.12 97.69 97.39
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After determining the best type of oxidizer, promoter, catalyst, and phase transfer agent, optimizing these parameters based on the CCD method was tried. Table 5 displays the experiments suggested by the experimental design and the obtained results, outlining the independent variables under consideration in this study. These variables comprise the sulfur content for each of GC1, GC2, and GC3 (X1), the oxidant (10–70 vol % of hydrogen peroxide) (X2), the enhancer (5–70 vol % of formic acid) (X3), the catalyst (1–30 wt % of phosphotungstic acid) (X4), the phase transfer agent dosage (1–30 vol % of isobutanol) (X5), and the ultrasonic time (5–40 min) (X6). In addition, certain factors remained constant throughout the research, such as the sonication power of 150 W, the sonication frequency of 40 kHz, and the stirring of a magnetic stirrer at 300 rpm. The ultrasonic bath temperature was maintained at 35 ± 2 °C under atmospheric pressure for 10 min in each extraction round.

Table 5. Analysis of Variance (ANOVA) for the RSM for Three Synthetic Gas Condensate Samples.

  ANOVA
 coefficient of quadratic equation in terms of coded factors
source model type sum of squares Df mean square F-value P-value CG1 GC2 GC3
  GC1 9.69 27 0.3591 21.48 <0.0001 significant +99.13    
  GC2 90.51 27 3.35 66.48 <0.0001 significant   +97.71  
  GC3 1382.21 27 51.19 108.29 <0.0001 significant     +97.44
X1 GC1 1.74 1 1.74 104.02 <0.0001 +0.1554    
GC2 19.28 1 19.28 382.39 <0.0001   +0.5175  
GC3 726.38 1 726.38 1536.58 <0.0001     +3.18
X2 GC1 1.49 1 1.49 89.33 <0.0001 –0.1440    
GC2 29.08 1 29.08 576.75 <0.0001   –0.6356  
GC3 62.14 1 62.14 131.46 <0.0001     –0.9290
X3 GC1 1.25 1 1.25 74.81 <0.0001 +0.1318    
GC2 11.49 1 11.49 227.82 <0.0001   +0.3994  
GC3 17.91 1 17.91 37.89 <0.0001     +0.4988
X4 GC1 0.1790 1 0.1790 10.70 0.0018 +0.0499    
GC2 6.28 1 6.28 124.49 <0.0001   +0.2953  
GC3 54.51 1 54.51 115.32 <0.0001     +0.8701
X5 GC1 0.2775 1 0.2775 16.58 0.0001 +0.0621    
GC2 16.92 1 16.92 335.48 <0.0001   +0.4847  
GC3 223.84 1 223.84 473.51 <0.0001     +1.76
X6 GC1 0.0120 1 0.0120 0.7177 0.4004 +0.0129    
GC2 0.4705 1 0.4705 9.33 0.0034   +0.0808  
GC3 28.79 1 28.79 60.91 <0.0001     +0.6324
X1X2 GC1 0.6221 1 0.6221 37.17 <0.0001 +0.0986    
GC2 0.0150 1 0.0150 0.2976 0.5875   +0.0153  
GC3 25.11 1 25.11 53.12 <0.0001     +0.6264
X1X3 GC1 0.3122 1 0.3122 18.65 <0.0001 –0.0698    
GC2 0.1444 1 0.1444 2.86 0.0960   –0.0475  
GC3 4.20 1 4.20 8.88 0.0042     –0.2561
X1X4 GC1 0.0207 1 0.0207 1.23 0.2711 –0.0180    
GC2 0.1892 1 0.1892 3.75 0.0576   –0.0544  
GC3 16.72 1 16.72 35.37 <0.0001     –0.5111
X1X5 GC1 0.0260 1 0.0260 1.55 0.2176 –0.0202    
GC2 0.2809 1 0.2809 5.57 0.0216   –0.0663  
GC3 69.91 1 69.91 147.89 <0.0001     –1.05
X1X6 GC1 0.2268 1 0.2268 13.55 0.0005 –0.0595    
GC2 3.30 1 3.30 65.51 <0.0001   –0.2272  
GC3 73.64 1 73.64 155.77 <0.0001     –1.07
X2X3 GC1 0.3496 1 0.3496 20.89 <0.0001 +0.0739    
GC2 0.2048 1 0.2048 4.06 0.0485   +0.0566  
GC3 0.3798 1 0.3798 0.8034 0.3738     +0.0770
X2X4 GC1 0.0074 1 0.0074 0.4445 0.5076 +0.0108    
GC2 0.1073 1 0.1073 2.13 0.1501   +0.0409  
GC3 2.02 1 2.02 4.27 0.0432     +0.1777
X2X5 GC1 0.0166 1 0.0166 0.9904 0.3238 +0.0161    
GC2 0.0977 1 0.0977 1.94 0.1693   +0.0391  
GC3 0.3585 1 0.3585 0.7584 0.3874     +0.0748
X2X6 GC1 0.0001 1 0.0001 0.0076 0.9310 –0.0014    
GC2 0.0030 1 0.0030 0.0600 0.8074   –0.0069  
GC3 0.3985 1 0.3985 0.8429 0.3624     –0.0789
X3X4 GC1 0.0074 1 0.0074 0.4445 0.5076 –0.0108    
GC2 0.0380 1 0.0380 0.7541 0.3888   –0.0244  
GC3 0.1796 1 0.1796 0.3799 0.5401     –0.0530
X3X5 GC1 0.0395 1 0.0395 2.36 0.1299 –0.0248    
GC2 0.0400 1 0.0400 0.7932 0.3768   +0.0250  
GC3 0.5130 1 0.5130 1.09 0.3019     –0.0895
X3X6 GC1 0.0044 1 0.0044 0.2622 0.6105 +0.0083    
GC2 0.2836 1 0.2836 5.62 0.0211   –0.0666  
GC3 0.0523 1 0.0523 0.1107 0.7406     +0.0286
X4X5 GC1 0.0017 1 0.0017 0.1017 0.7510 +0.0052    
GC2 0.3844 1 0.3844 7.62 0.0077   +0.0775  
GC3 6.18 1 6.18 13.08 0.0006     –0.3108
X4X6 GC1 0.0001 1 0.0001 0.0076 0.9310 +0.0014    
GC2 0.0663 1 0.0663 1.31 0.2562   –0.0322  
GC3 1.33 1 1.33 2.82 0.0987     +0.1442
X5X6 GC1 0.0019 1 0.0019 0.1144 0.7364 +0.0055    
GC2 0.0452 1 0.0452 0.8955 0.3479   –0.0266  
GC3 0.9096 1 0.9096 1.92 0.1707     –0.1192
X12 GC1 0.3581 1 0.3581 21.39 <0.0001 +0.1021    
GC2 0.0970 1 0.0970 1.92 0.1707   –0.0530  
GC3 19.17 1 19.17 40.55 <0.0001     –0.7470
X22 GC1 0.4126 1 0.4126 24.65 <0.0001 +0.1096    
GC2 0.5001 1 0.5001 9.92 0.0026   –0.1205  
GC3 2.43 1 2.43 5.13 0.0272     –0.2657
X32 GC1 0.2042 1 0.2042 12.20 0.0009 +0.0771    
GC2 0.0030 1 0.0030 0.0602 0.8070   –0.0092  
GC3 24.57 1 24.57 51.98 <0.0001     –0.8457
X42 GC1 0.3156 1 0.3156 18.85 <0.0001 +0.0958    
GC2 0.2098 1 0.2098 4.16 0.0459   –0.0780  
GC3 0.0965 1 0.0965 0.2042 0.6530     +0.0530
X52 GC1 0.1120 1 0.1120 6.69 0.0122 +0.0571    
GC2 0.5642 1 0.5642 11.19 0.0014   –0.1280  
GC3 3.73 1 3.73 7.89 0.0068     –0.3295
X62 GC1 0.6108 1 0.6108 36.50 <0.0001 +0.1333    
GC2 0.0566 1 0.0566 1.12 0.2937   +0.0408  
GC3 0.7806 1 0.7806 1.65 0.2039     –0.1507
residual GC1 0.9707 58 0.0167          
GC2 2.92 58 0.0504          
GC3 27.42 58 0.4727          
lack of fit GC1 0.9697 49 0.0198 178.11 <0.0001      
GC2 2.92 49 0.0597 335.56 <0.0001      
GC3 27.42 49 0.5595 8393.06 <0.0001      
pure error GC1 0.0010 9 0.0001          
GC2 0.0016 9 0.0002          
GC3 0.0006 9 0.0001          
cor total GC1 10.67 85            
GC2 93.43 85            
GC3 1409.63 85            
fit statistics GC1 R2 = 0.9090, adj-R2= 0.8666, pred-R2= 0.7319, model precision = 18.0658
GC2 R2 = 0.9687, adj-R2= 0.9541, pred-R2= 0.8994, model precision = 41.8028
GC3 R2 = 0.9805, adj-R2= 0.9715, pred-R2= 0.9510, model precision = 45.0703
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Table 6 displays the results of the analysis of variances (ANOVA), where the combination of high F-statistics and small p-values indicates both the validity of the models and the significance of the coefficients in the built models. For the three gas-condensate samples, variables with p-values less than 0.05 substantially impact the response and, therefore, cannot be disregarded. Additionally, the table reveals exceptional correlation coefficients (R2) for all three models, which measure the relationship between the response and independent variables and their interactions. In essence, R2 serves as an indicator of how closely the model predictions resemble the experimental data. The minor differences between the adjusted correlation coefficient (RAdj2) and the predicted correlation coefficient (RPred2) for all three samples demonstrate the reliability of the mathematical model presented.

Table 6. Compassion of the Predicted and Experimental Results of the Three-Sample Synthetic Gas Condensate Containing Mercaptan, Sulfide, and Thiophene Compounds.

sample   X1 (ppm) X2 (vol %) X3 (vol %) X4 (wt %) X5 (vol %) X6 (min) predicted R2 experimental R2
GC1 actual 1357.60 48.05 69.72 8.96 5.60 11.33 100.0 99.93
coded –0.26 0.53 1.98 –0.90 –1.36 –1.27
GC2 actual 1618.14 12.54 67.66 27.95 18.93 5.83 99.71 99.63
coded 0.09 –1.83 1.85 1.71 0.47 –1.90
GC3 actual 2972.64 30.08 27.83 5.04 22.91 20.22 100.0 99.81
coded 1.96 –0.66 –0.59 –1.44 1.02 –0.26
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3.2. Introducing the Mathematical Models

Drawing from the CCD, eq 3 can be utilized to articulate the quadratic association linking the response and variables

3.2. 3

The equation comprises various components, including the response variable for sulfur removal efficiency denoted as YSER%. The parameters X1,..., and Xi are coded parameters, while α0 is the interception term, and α1,..., αi represent the regression coefficients for linear effects. Furthermore, αii corresponds to the regression coefficients for squared effects, αij is the regression coefficient for interaction effects, and ε denotes the error component.

Using the encoded values of various variables presented in Table 6, a quadratic form for each of the three samples was expressed in eqs 45–6.

3.2. 4
3.2. 5
3.2. 6

3.3. Statistical Graphs

Figure 3(a1,a2,a3) demonstrates the comparison between the model and empirical data, exhibiting a favorable level of agreement. On the other hand, Figure 3(b1,b2,b3), which showcases the deviation model, allows for the comparison of the impacts of individual parameters on the model. In this regard, the variables’ center points in Table 4 are designated as code 0. A pronounced incline implies a heightened level of sensitivity, whereas a comparatively gentle incline signifies a lack of sensitivity. Notably, the response was observed to be sensitive to all inputs.

Figure 3.

Figure 3

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Comparison of quadratic model results and corresponding experimental data: (a) model-predicted vs actual efficiency and (b) diversion plot of the model.

3.4. UAOD Mechanism

UAOD is a process that utilizes both the aqueous and organic phases. In this particular study, the oxidants and enhancers used were hydrogen peroxide and formic acid, respectively. The catalyst used was phosphotungstic acid, also known as polyoxometalate acid, while isobutyl alcohol acted as a phase transfer agent. A competitive reaction takes place during catalytic oxidation in the aqueous phase involving two mechanisms. The first mechanism involves the reaction of formic acid with hydrogen peroxide, resulting in the formation of performic acid and subsequent decomposition to produce free radicals of *OOH. The second mechanism involves the reaction of hydrogen peroxide with phosphotungstic acid to produce proxy-poly(tungstate) anions. Depending on the components present in the aqueous phase, both mechanisms may occur simultaneously, as in this study, where both catalyst and promoter were used. Both mechanisms may occur simultaneously, and the relative dominance of each depends on the quantities of hydrogen peroxide, formic acid, and phosphotungstic acid used. Therefore, in this study, these parameters were optimized to harness the combined potential of both mechanisms, ultimately maximizing the sulfur removal efficiency. Mechanism (1) comprises eqs 7–10, in which the oxidant attacks the enhancer to oxidize and produce free radicals. As a result of the presence of these free radicals, sulfurous compounds are subsequently oxidized.

3.4. 7
3.4. 8
3.4. 9
3.4. 10

According to Wan et al.,32 the second mechanism involves the oxidation of sulfurous compounds upon attacking the catalyst with an oxidant. When there is an excess of hydrogen peroxide, phosphotungstic acid, acting as the catalyst, undergoes oxidation and becomes polyoxometalate acid. The polyoxometalate acid then forms a proxy-metal complex with active oxygen, which binds with isobutyl alcohol, a phase transfer agent, and is transferred to the organic phase. The sulfurous compounds are then oxidized by the proxy metals, resulting in the production of sulfones in the aqueous phase. The reduced proxy-metal compound in the ionic phase undergoes ion exchange with the phase transfer agent and is then returned to the aqueous phase where it is reoxidized by hydrogen peroxide. This cycle continues until all sulfur or oxidizer is consumed. Emulsion induction by UAOD facilitates the phase transfer of the metal-proxy complex and isobutanol.

3.5. Analysis of the Contours

3.5.1. Effect of Initial Mercaptan Content

In Figure 4, the desulfurization efficiency of mercaptan (GC1) is displayed as a function of the ratio of X1 to X6. As depicted in all of the figures, desulfurization efficiency improves with increasing mercaptan content. This is due to the fact that higher mercaptan content allows for greater selectivity of aqueous phase components to react with mercaptans, while also preventing side reactions of free radicals. At low sulfur content, free radicals are produced during the reaction of hydrogen peroxide and acid, which then react with each other to produce oxygen and water, thereby diluting the acid in the aqueous phase. In Figure 4(a), there are two distinguishable regions for the effect of hydrogen peroxide on desulfurization. Low sulfur content requires a low amount of hydrogen peroxide, while for high sulfur content, even low or high hydrogen peroxide levels have the same results, but the middle amounts decrease efficiency. Therefore, low dosages of hydrogen peroxide should be used in any case.

Figure 4.

Figure 4

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Mutual effects of sulfur (mercaptan) content of n-heptane (i.e., gas condensate) against hydrogen peroxide (a), formic acid (b), phosphotungstic acid (c), isobutyl alcohol (d), and ultrasonication time (e) in terms of desulfurization efficiency.

Hydrogen peroxide imposes dual negative and positive effects on desulfurization efficiency as it contributes in two mechanisms at the same time to form free radicals: (1) reaction with formic acid to produce performic acid and (2) reaction with phosphotungstic acid to form epoxy metals. Thus, the hydrogen peroxide content must be adjusted based on the formic acid and phosphotungstic acid contents. If the dosage of hydrogen peroxide exceeds the consumption rates of acids, the high reactivity of hydrogen peroxide leads to the release of oxygen and extra water, diluting the aqueous phase and suppressing the desulfurization efficiency.

In Figure 4(b), for low mercaptan levels, a higher promoter content leads to a higher desulfurization efficiency, while, at high sulfur levels, there is little effect. Similarly, in Figure 4(c), the catalyst (phosphotungstic acid) has a direct effect on desulfurization but with a much weaker intensity than in Figure 4(b). Phosphotungstic and formic acids compete with each other and follow two different mechanisms of desulfurization when reacting with hydrogen peroxide. The effect of the catalyst is smaller than that of formic acid, but this does not rule out the advantage of using the catalyst since it forms poly(polyoxometalate) to become a proxy-metal complex with active oxygen that can be transferred between the aqueous and organic phases. This indicates that the amount of phosphotungstic acid as a catalyst is directly and positively linked to the mercaptan content. It can be observed from Figure 4(c) that the catalyst has the greatest impact on the desulfurization efficiency only at low doses, and additional doses of the catalyst do not have a significant effect on the desulfurization efficiency. Therefore, it is recommended to use lower doses of the catalyst for mercaptan removal. Figure 4(d) indicates that a higher dosage of the phase transfer agent improves desulfurization. The phase transfer agent has one aqueous end and one organic end, which helps to connect the aqueous and organic phases, maintaining their continuous attachment. Ultrasonic waves play a significant role in connecting the two phases when ultrasonication is employed. The low slope of changes in the response with changing the phase transfer agent implies that the ultrasonic waves have a more significant impact on the response, which justifies the lower use of the phase transfer agent. Based on Figure 4(e), the best response is expected with the shortest ultrasonication time, with the desulfurization efficiency only slightly improving as the ultrasonication time increases. This demonstrates the advantage of ultrasonication, as it yields positive effects in a short amount of time.

3.5.2. Effect of Initial Sulfide Content

Figure 5(a) shows that increasing the sulfide content in n-heptane (GC2) improves the efficiency of desulfurization. When there is an excess of sulfide in the hydrocarbon phase, the selectivity of the aqueous phase and the reactivity of sulfides increase, promoting the conversion of sulfidic compounds into sulfones and enhancing the desulfurization efficiency. However, when the sulfide content is low, the chances of secondary reactions increase, reducing the desulfurization efficiency. Figure 5(a) also demonstrates that as the sulfur content increases, the amount of hydrogen peroxide needed decreases, depending on the dosages of the enhancer and the catalyst. The highest desulfurization efficiency occurs when there are high levels of sulfur (sulfide) and formic acid, as shown in Figure 5(b). Figure 5(c) indicates that the dosage of phosphotungstic acid, as the catalyst, is directly related to the sulfide content of the sample, following a trend similar to that for formic acid but at a slower rate. Furthermore, Figure 5(d) demonstrates that using a higher dosage of the phase transfer agent can enhance the desulfurization efficiency. Ultrasonication time is also a factor, as a long time allows for the accumulation of microemulsions in the oxidation reaction medium, increasing the contact surface between the aqueous and organic phases and thus promoting the conversion of sulfide compounds into sulfones. However, according to Figure 5(e), the optimal response is obtained with a minimal ultrasonication time.

Figure 5.

Figure 5

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Mutual effects of sulfur (sulfide) content of n-heptane (i.e., gas condensate) against hydrogen peroxide (a), formic acid (b), phosphotungstic acid (c), isobutanol (d), and ultrasonication time (e) in terms of desulfurization efficiency.

3.5.3. Effect of Initial Thiophene Content

As the benzothiophene content in (GC3) increased, Figure 6 demonstrated an improvement in the desulfurization efficiency. The experimental results indicated that higher sulfur contents in the gas-condensate sample resulted in a greater desulfurization efficiency, which may be due to the influence of ultrasonic waves. The removal efficiency of sulfur increased with the oxidant up to a certain level, regardless of the sulfur content of the sample, indicating a direct correlation between sulfur content and desulfurization efficiency. In Figure 6(a), it was observed that the desulfurization efficiency decreased as the hydrogen peroxide dosage increased for a given sulfur (thiophene compound) content, with the best results obtained at higher sulfur contents and lower hydrogen peroxide dosages. This could be attributed to an increase in the aqueous phase and the dependency of hydrogen peroxide dosage on enhancer and catalyst dosages. Therefore, optimal adjustment of hydrogen peroxide dosage was necessary. Figure 6(b) shows that at a given sulfur (thiophene) content, the desulfurization efficiency increased with formic acid dosage up to a certain level, beyond which it decreased due to the undesired effect of the aqueous phase and dependence of formic acid dosage on hydrogen peroxide dosage. This implied that the dosage of the two substances needed to be optimized to maintain the alkalinity of the sample within a certain range, with the best results obtained at higher sulfur contents and moderate formic acid dosages. Figure 6(c) demonstrates that desulfurization efficiency increased with increasing catalyst dosage (phosphotungstic acid), and a direct correlation was observed between the sulfur content and catalyst dosage. This was because a higher amount of polyoxometalate (a product of the reaction between hydrogen peroxide and phosphotungstic acid) provided for improved conversion of thiophene compounds to sulfones, thereby enhancing removal efficiency. In Figure 6(d), the most favorable results were obtained at higher concentrations of sulfur and the phase transfer agent. To enhance sulfur removal, isobutanol was utilized as a phase transfer agent to aid in the transfer of oxidized sulfur contents from the organic phase to the aqueous phase. Hence, the desulfurization efficiency rose with an increase in the isobutanol dosage. Figure 6(e) shows the impact of reaction time on the sulfur content. At lower sulfur contents, the desulfurization efficiency improved with an increase in ultrasonication time. However, at higher sulfur contents, the desulfurization efficiency increased only marginally with an extension in sonication time, indicating the need to optimize the sonication time. A lower demand for ultrasonication is implied as the higher the sulfur content of the sample, the faster the oxidation reaction occurs. These results indicate that all variables, such as the dosages of oxidant, enhancer, catalyst, and phase transfer agent, as well as the ultrasonication time, significantly depend on the content of thiophene compounds in the sample.

Figure 6.

Figure 6

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Mutual effects of sulfur (thiophene) content of n-heptane (i.e., gas condensate) against hydrogen peroxide (a), formic acid (b), phosphotungstic acid (c), isobutanol (d), and ultrasonication time (e) in terms of desulfurization efficiency.

3.6. Optimization

The objective of the current research is to identify the most effective parameters for various sulfur contents. Optimization of the ultrasound-assisted oxidation technique involves reducing the oxidant consumption and oxidation time while maintaining an efficiency level exceeding 99.99%. This necessitates optimization of the mathematical model with the aid of software. Design Expert software has the advantage of enabling users to determine optimal conditions for desulfurizing gas-condensate samples with sulfur content ranging from 100 to 3000 ppm. This allows for the estimation of desulfurization efficiency under specific conditions, unlike previous studies that only focused on the sulfur content of particular wells. The present research provides optimal conditions for different levels of sulfur content, enabling estimation of the anticipated desulfurization efficiency under optimal conditions. Through mathematical modeling, the software determined 100 optimal points that had the same level of desirability, with example optimal points shown in Table 7. By conducting experiments under the optimal conditions of Table 7, the maximum efficiency of sulfur removal for mercaptan, sulfide, and thiophene compounds was 99.93, 99.63, and 99.81%, respectively.

Table 7. Characteristics of the Industrial Gas Condensate.

property method unit IS1 IS2
Sp. Gr. 60/60 °F ASTM D4052   0.740 0.732
total sulfur ASTM D7039 ppm (wt %) 1726.30 1521.87
mercaptans ASTM D3227 ppm (wt %) 2400 2243
H2S ASTM D1159 ppm (wt %) 20 5
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3.7. Effect of the Extraction Stage and Reactor Vessel Material

Figure 7 shows that the maximum efficiency was achieved when the reactor vessel material was changed from glass to stainless steel. Therefore, the findings revealed the significance of the ultrasonic container material, with metal containers exhibiting greater wave transmission to the sample, resulting in an increase in removal efficiency (red color curve). Additionally, it was observed that as the number of extraction steps increased, the removal efficiency also increased (green color curve than the blue color one). However, the increase in yield during the third stage was not significantly notable compared to the second stage. Thus, it is advisable to augment the number of extraction steps only in situations where the complete elimination of sulfur is necessary.

Figure 7.

Figure 7

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Effects of the number of extraction stages and vessel material on the desulfurization efficiency for synthetic gas-condensate samples containing mercaptans (GC1), sulfides (GC2), and thiophenes (GC3).

3.8. Field Data

Using Design Expert software, the optimal operating conditions were extracted for desulfurization of both industrial samples, as demonstrated in Table 8. Based on the results (Figure 8), it was found that using two-stage extraction with DMF (with a solvent-to-hydrocarbon ratio of 2:1) on IS1 and IS2 resulted in desulfurization efficiencies of 97.96 and 99.13%, respectively. To enhance the mercaptan removal efficiency under optimal conditions, the number of extraction stages was increased from two to three and also the reactor vessel material was switched from glass to stainless steel. These modifications led to desulfurization efficiencies of 99.61 and 99.98% for IS1 and IS2, respectively, as depicted in Figure 8. These outcomes underscored the effectiveness of UAOD for mercaptan removal. The results verified that the model accurately identified the optimal conditions for desulfurization and accurately predicted its efficiency. The negligible disparity in mercaptan removal efficiency between the synthetic gas condensate (GC1, 100%) and industrial sample was due to the presence of hydrogen sulfide in the industrial gas-condensate sample.

Table 8. Experimental Results of the Synthetic and Industrial Samples Using the Optimal Conditions Obtained from the Proposed Model.

  actual of variable
  
system X1 (ppm) X2 (mol %) X3 (mol %) X4 (wt %) X5 (mol %) X6 (min) results of experimental (2-stage, NNDMF solvent, glass vessel) (%)
GC1 1357.6 48.0 69.7 8.9 5.6 11.3 99.93
IS1 1726.3 23.9 38.2 21.2 4.4 36.3 97.96
IS2 1521.8 10.0 40.5 9.0 4.3 31.5 99.13
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Figure 8.

Figure 8

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Comparison of the results of desulfurization between GC1, IS1, and IS2 under optimal conditions for different numbers of extraction stages and reactor vessel materials.

4. Conclusions

In this research, UAOD was utilized for removing sulfurous compounds from gas condensates. Results show that the best combination of the mixture in removing different sulfurous compounds is hydrogen peroxide as the optimal oxidant, formic acid as the optimal promoter, phosphorus tungstic acid as the optimal catalyst, and isobutanol as the optimal phase transfer agent. Experimental results showed that most of the sulfur content was removed upon the first extraction stage, with the two-stage and three-stage extraction procedures returning more or less the same results (at each stage, the solvent-to-gas-condensate ratio was set to 1:2). At optimal points, the GC1, GC2, and GC3 models (under two-stage extraction in a glass-made sonoreactor vessel) ended up removing the sulfurous compounds at 99.93, 99.63, and 99.86%, respectively. To enhance the removal efficiency, three extraction stages were practiced in a stainless-steel reactor vessel, which led to 100% removal of mercaptans, 99.81% removal of sulfides, and 99.94% removal of benzothiophene. The desulfurization efficiency of 99.98% on industrial gas-condensate sample 2 confirmed the validity of the mathematical modeling. The results provide for determining optimal conditions for different levels of sulfur content in the gas condensate and conversely predict the achievable desulfurization efficiency under a given set of conditions.

Acknowledgments

The authors are grateful to Shiraz Branch, Islamic Azad University, and Shiraz University for supporting this research.

The authors declare no competing financial interest.

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