Modeling and Multi-objective Optimization of a Packed Bed Reactor for Sulfur Dioxide Removal by Magnesium Oxide Using Non-dominated Sorting Genetic Algorithm II

Nowadays, protecting the environment is of utmost importance worldwide, and sulfur dioxide is one of the main pollutants in the atmosphere. This work proposes a new method for simultaneous SO2 removal by MgO, and production of magnesium sulfate in a packed bed reactor for which breakthrough curves have been obtained. Furthermore, the effect of important operating parameters, including temperature, SO2 concentration, and gaseous flow rate was investigated. Experiments showed that increasing the temperature improved the breakthrough lifetime, but the increase in concentration and flow rate reduced the lifetime. The experimental results were predicted successfully by applying the Random Pore Model (RPM). Finally, the Non-dominated Sorting Genetic Algorithm II (NSGA II) that is a technique for multi-objective optimization, was employed to determine the best operating parameters for SO2 removal by magnesium oxide in the packed bed reactor.


Introduction
Nowadays, protecting the environment, and air pollutant removal processes are of great importance all over the world. Acid rain is one of the major environmental problems, and it can destroy the forests and aquatic animals. The most important factor resulting in the formation of acid rains is the presence of SO 2 in the atmosphere. Sulfuric acid is produced as the result of SO 2 and water vapor reaction, and falling to the ground with rain 1,2 .
The main sources of SO 2 emission are metallurgical and coal-fired power plants (stationary units), and vehicles that consume high sulfur content fuel (mobile units) 3 . Many attempts have been made in order to reduce the sulfur dioxide emission to the atmosphere in the world. In many countries, the sulfur content of gasoline and gas oil should be below 10 ppm (Euro 5 standard) 4 . These low-sulfur-content fuels are produced by deep hydrotreating processes in refineries 5,6 . Furthermore, in stationary units, flue gas desulfurization (FGD) processes are applied to adsorb or absorb sulfur dioxide and control the level of SO 2 in the exhaust gases.
FGD processes are categorized into the throwaway systems for low SO 2 concentration, including coal-fired power plants, and regenerative systems for high SO 2 concentration such as metallurgical units 3 . The common adsorbents in throw-away systems are CaO, MgO, and Fe 2 O 3. The main reaction in throw-away FGD systems based on MgO is: 2 2 4 MgO+ SO +1/2O MgSO → On the other hand, magnesium sulfate is usually produced as a result of reaction between MgO and sulfuric acid. MgSO 4 is mainly used in agriculture as a fertilizer. The increasing global demand for agricultural products has resulted in the increase of MgSO 4 production. The other applications of magnesium sulfate are in medical, food preparation, and construction industries 7 .
The conventional methods of magnesium sulfate production are extraction of mineral kieserite, and MgO reaction with H 2 SO 4 . In the first method, kieserite is dissolved in water and MgSO 4 product is obtained by crystallization process. In the second method, MgO (from magnesite calcination) is reacted with H 2 SO 4 producing MgSO 4 and then crystallization is used to increase the purity of the final product 8 .
The conducted research on the ability of MgO to capture SO 2 in FGD systems are much fewer, compared to the calcium oxide. Jae et al. studied MgO-based sorbents in a fixed bed reactor to adsorb sulfur dioxide 9 . They prepared regenerable sorbents by adding cerium and iron as additives into the MgO-based sorbents. Based on their results, the efficiency of the sorbents and the rate of reaction had improved by using these additives.
Zhang et al. adsorbed SO 2 by using natural magnesite 10 . They declared that calcination temperature is a key parameter and that it affects adsorption capacity of sorbents. The adsorption capacity was reported to be 140.7 mg g -1 .
Prezepiorski et al. studied the adsorption of SO 2 from air by using MgO/carbon sorbents 11 . Furthermore, they considered the effect of operating parameters such as temperature, porosity, and humidity, and analyzed the adsorption mechanism.
Zermeno et al. used natural magnesite in packed bed reactor and obtained the experimental breakthrough profiles of the reactor 12 . They announced that natural magnesite had a good adsorption capacity. They also declared that natural magnesite could be considered as a good alternative for CaO.
Lee et al. studied the removal of sulfur dioxide by magnesium oxide 13 . They improved the adsorption capacity of sorbents by adding titanium dioxide. Their sorbents were prepared by co-precipitation method. They improved the adsorption capacity of the sorbent by adding TiO 2 from 38 g sulfur g -1 to 44 g sulfur g -1 .
Based on the analysis carried out by Magnabosco, MgO can be used as a suitable adsorbent for SO 2 removal in the regenerator of FCC unit 14 19 . They revealed that the product of MgO+SO 2 reaction was sulfite, bisulfite, and sulfate.
Zhao and Zou tested micro-sized MgO slurry and MgO nanofluids slurry in wet desulfurization process 20 . They found that the efficiency of MgO nanofluids was better than that of micro-sized MgO slurry.
Many attempts have been made to model gas-solid reactions. We were able to predict the performance of real systems by efficient application of modeling and simulation 21 . Furthermore, modeling and simulation along with the application of mathematical tools such as genetic algorithm, can lead to the discovery of optimum operating parameters of the various processes.
Dry FGD process is an important type of non-catalytic gas-solid reactions that SO 2 adsorbed by adsorbents like MgO, CaO, and CuO. Kinetic study of these reactions is an appropriate tool for improvement of FGD process through design and optimization of the related reactors. For this reason, various models including shrinking core model, volume reaction model, grain model, modified grain model, nucleation model, single pore model, and random pore model (RPM) are developed. RPM and modified grain model are able to consider incomplete conversion due to volume increase of the pellet during the reaction. Complicated RPM theory assumes that the reaction occurs on the inner surfaces of cylindrical pores of the sorbent in the series of holes that have a pore size distribution (PSD).
Bahrami et al. used RPM to simulate SO 2 removal by CuO as a regenerative process 22 . The experimental operating parameters in their work included temperature (400-600 °C) and sulfur dioxide concentration (1250-5000 ppm). They compared the experimental data with the values predicted by RPM. They declared that RPM could predict the experimental conversion-time data with a high degree of accuracy.
Moshiri et al. adsorbed SO 2 in a packed bed reactor by using CaO 23 . Their experimental breakthrough curves were modeled by RPM. They found that RPM could accurately predict the experimental data.
Betancur et al. studied gasification process by thermogravimetry and modeled the experimental data by grain model, RPM and hybrid modification RPM 24 . They concluded that RPM and hybrid modified RPM were the most precise models.
Lopez et al. considered CaO reaction with carbon dioxide, and evaluated the effect of inert support 25 . They applied RPM to calculate the kinetic parameters.
Montagnaro et al. modeled the CaO+SO 2 reaction by RPM 26 . They then compared the experimen-tal results with the RPM. They announced that the model could correlate the experimental data.
Removal of sulfur dioxide with CuO in a thermogravimeter was examined by Yu et al. 27 The experimental results were predicted by volume reaction model, grain size model, RPM and pore-blocking model.
Nouri et al. evaluated the adsorption of CO 2 by lime in a packed bed reactor and obtained the experimental breakthrough curves 28 . Furthermore, the acid washing technique was used in their study to improve the adsorption capacity of lime. Finally, they predicted the experimental breakthrough curves with RPM.
In our previous studies, the kinetic parameters of MgO+SO 2 reaction were calculated by RPM and the adsorption capacity of MgO was improved by acid washing method, and the experimental conversion-time and breakthrough curves were compared with the natural sample 29,30 . Finally, RPM was applied to model the experimental data.
Process optimization has become an interesting area of research during recent years, and as a result, attempts have been made to find the best operating conditions for different chemical processes. Optimization will maximize the process performance and minimize the operating costs. Furthermore, the optimization results can be used as the optimum conditions for large-scale industrial units operations 31,32 .
Wu et al. applied multi-objective optimization for hydrotreating process 33 . They optimized the process to minimize the operating cost and SO 2 emission to the environment. They found that the operating cost and emission of sulfur dioxide would be reduced in high temperatures and low pressures.
Zhou et al. considered multi-objective optimization of SO 2 removal by activated coke and found the best sorbent preparation parameters 34 . They found that the best operating conditions were at 924 °C, oxygen concentration 5.9 %, and vapor concentration 20 %.
Bayon et al. optimized the operation of a thermal power plant to minimize SO 2 and NO x emissions to the environment 35 .
Bakhshi Ani et al. simulated a trickle-bed hydrotreating reactor and used multi-objective optimization to find the best operating conditions of the process 5 . They also considered the effect of operating parameters such as temperature, pressure, LHSV, and H 2 /oil.
Liu et al. simulated desulfurization tower by CFD tool and optimized the related operating parameters 36 . They found that CFD could accurately predict the experimental data.
To the best of our knowledge, no previous research has been conducted on RPM for MgO+SO 2 packed bed reaction, and a few attempts have been made to investigate the behavior of packed bed reactor for adsorption of SO 2 by MgO. Furthermore, no one has reported the best operating conditions for SO 2 removal in packed bed reactor so far. Therefore, in the present study, the tests were performed to obtain the experimental breakthrough curves of natural MgO in the packed bed reactor. The effects of important operating parameters, such as SO 2 concentration, temperature, and gaseous flow rate on lifetime of the breakthrough curves were investigated experimentally. Then, RPM as a comprehensive and precise model that considers the structural changes of sorbents was applied to simulate the experimental results. The possibility of magnesium sulfate production as a useful by product in the SO 2 removal process by MgO is also considered.
Finally, NSGA II as a technique for multi-objective optimization was employed to determine the best operating parameters for SO 2 removal by magnesium oxide in the packed bed reactor.

Materials and methods
Natural magnesium carbonate/oxide was supplied from the Nehbandan mine (Iran), in the form of spherical particles of about 6 mm in diameter. The composition of the mineral sample is presented in Table 1. The data in this table was obtained from the XRF analysis results. Highly pure SO 2 (99.95 %) and zero air (mixture of pure oxygen and nitrogen) were the gases used in this research.
The experimental setup included tubular reactor (310 stainless steel, 1.5 cm inner diameter, and 6 cm height), K-type thermocouple, vertical furnace, two MFCs (mass flow controller), and online mass spectrometer (MS). The schematic diagram of the apparatus is presented in Fig. 1.
The calcination process was applied to prepare a highly porous MgO from magnesium carbonate/ oxide directly in the packed bed reactor as part of the experimental setup. In this process, the sample was heated to the operating reaction temperature (500-600 °C) for about 30 min under zero-air stream. The porosity of the sample increased due to the release of H 2 O and CO 2 molecules from mineral magnesium carbonate/oxide.
After the calcination process, SO 2 was mixed in zero-air in the predefined concentration, and it was injected to the reactor to start the adsorption/ reaction. MS continuously monitored outlet gases from the reactor. The experimental breakthrough curves were obtained from MS results. Table 2 shows the operating conditions of the experiments.
Packed bed reactor modeling RPM as a comprehensive and real model was employed in this study to simulate the packed bed reactor behavior and predict the breakthrough curves. This model was developed by Bhatia and Perlmutter and its main assumptions are [37][38][39] : -Pseudo-steady state approximation; -Negligible bulk flow effect; -Isothermal condition for system; -Irreversible and first order reaction.
The RPM governing equations with the initial and boundary conditions are 22 : In equation (1), ψ is the main RPM parameter obtained from the whole PSD of the calcined sample. The packed bed reactor differential equations were derived from the mass balance as follows 37 : For bulk gas in the reactor: For the reactant gas in the pellet: The f(x) in equation (10) is inserted from the right-hand side of equation (3).
For the solid reactant: The variables of the packed bed reactor are expressed as follows: The parameters of the system are presented as follows: The energy consumption in calcination process to reach and maintain the reactor at desired temperature can be calculated from the following equation based on the energy balance: The solution method for solving nonlinear RPM and packed bed reactor partial differential equations was developed in MATLAB ® based on the finite element method. The details about the solution method has been already described in our previous study 23 . The explanation for all of the symbols that have been used in Eq. (2) to (24) are given in the nomenclature part.

Optimization
One of the well-known optimization tools is genetic algorithm (GA) that is based on Darwinian evolution. The main operators of GAs are crossover, recombination, mutation, and selection 40 . The first step in GA is the random selection of a population from the parent chromosomes. The evolution of selected population to the better chromosomes is applied by GA main operators. The chromosomes for recombination are chosen in the selection stage. The new offspring chromosomes are generated in recombination stage from two parents after finishing the selection stage. Then, the children enter the mutation stage. In the mutation stage, new features are added to the population by creating new chromosomes from one child 41 .
Srinivas and Deb introduced the Non-dominated Sorting Genetic Algorithm (NSGA) in 1995. In 2000, Deb proposed NSGA II to solve some difficulties of NSGA 42 . NSGA II utilizes the elite strategy to sort parents' and children populations. The diversity of solutions was enhanced by using crowded comparison operator in NSGA II. In this study, the evaluation tool in NSGA II was the packed bed reactor model and the energy consumption equation. The calculation work flow chart of NSGA II is presented in Fig. 2.

Model validation
As mentioned, packed bed reactors with suitable sorbents can be used in air pollutants removal processes, such as FGD (SO 2 elimination), and CO 2 concentrating from flue gases. In these reactors, evolution of the breakthrough curve (measuring pollutant outlet concentration versus time) is essential, since breakthrough curve determines effective lifetime of a packed bed reactor in the aforementioned environmental engineering processes. Consequently, mathematical modeling for accurate prediction of breakthrough curve of a packed bed reactor is of great importance.
The experimental breakthrough curve of exit sulfur dioxide from the natural MgO reaction in the packed bed at 600 °C, 1 vol. % SO 2 concentration, and 1.67⋅10 -6 m 3 s -1 (100 cc min -1 ) zero-air flow (base case) is presented in Fig. 3. Based on the results, the breakthrough time is about 210 min.
The breakthrough curve of natural magnesium oxide in the packed bed was predicted by the RPM.
The required parameters to predict the curve by RPM are represented in Table 3 from our previous studies 29,30 . The RPM main parameter (ψ) was calculated from the whole PSD (micro, meso, and macro) of the calcined magnesium oxide pellets. The axial dispersion (D L ) is the sole fitting parameter obtained from the shape of the experimental breakthrough curve. Fig. 3 demonstrates good agreement between the model curve and experimental data. Fig. 4 illustrates the effect of SO 2 concentration on the breakthrough time. The breakthrough time was reduced from 210 min to 160 min by increasing SO 2 concentration from 1 vol.% (base case) to 2 vol.% due to the input of more sulfur dioxide reactant (versus the base case) to the packed bed reactor.
The effect of zero-air flow rate on the breakthrough time is presented in Fig. 5. The breakthrough time decreased from 210 to 120 min by increasing zero-air flow rate from 1.67⋅10 -6 m 3 s -1 (100 cc min -1 , base case) to 3.34⋅10 -6 m 3 s -1 (200 cc min -1 ). This effect was due to reduction in gaseous flow residence time versus the base case condition 43 .
The effect of temperature on the breakthrough time of packed bed reactor is shown in Fig. 6. The breakthrough time was reduced from 210 to 50 min by decreasing the temperature from 600 °C (base case operating temperature) to 500 °C. The reduction was the consequence of the decreased reaction rate. Similar behavior was also observed in the adsorption of SO 2 with CuO in the packed bed reactor 22 .
In Figs. 4 to 6, the values predicted by the model are in relatively good agreement with the experimental breakthrough curve data.

Magnesium sulfate production
During the process of SO 2 removal by MgO, magnesium sulfate is also produced. Magnesium sulfate is widely used in agriculture and various industries. Simultaneous MgSO 4 production as a valuable compound is an advantage of using MgO as adsorbent for SO 2 removal. The combination of SO 2 removal system with MgSO 4 production unit can improve the economic feasibility of FGD unit. Fig. 7 shows the XRD analysis of the sample, before and after reaction with SO 2 in the packed bed reactor. The analysis shows that MgSO 4 was produced as a result of MgO+SO 2 +1/2O 2 FGD reaction. The average overall conversion of MgSO 4 in the packed bed reactor system from RPM is presented in Fig. 8 for the base case. During the early stages of the process, the kinetics and pore diffusion controlled the reaction. Then, the product layer diffusion controlled the overall reaction, and consequently, the conversion rate decreased. In this process, the produced MgSO 4 is soluble in water and can be easily separated from the unreacted MgO.

Comparison of MgO FGD performance with other sorbents
In this section, the performance of MgO in SO 2 removal process was compared with other common sorbents, such as CuO, CaO, and Fe 2 O 3 for sulfur dioxide abatement according to the available literature data in the field. The basis of this comparison were breakthrough time and the rate constant values. It is worth mentioning that both parameters might not be reported in the literature for all of these sorbents.
A complete kinetics study of SO 2 +CuO reaction was carried out in a thermogravimeter by Bahrami et al. 22 They asserted that the rate constant for CuO at 500 °C was 4.37⋅10 -8 m s -1 , while this value for MgO was 6.01⋅10 -6 m s -1 at the same temperature. High reaction rate of MgO with SO 2 showed that it had better adsorption capacity than CuO at an equal residence time.
Bahrami et al. also conducted another research on the SO 2 removal in a packed bed reactor by CuO pellets 37 . They stated that the CuO breakthrough time at 600 °C and SO 2 concentration of 2500 ppm was about 550 min. The breakthrough time of MgO curve at 600 °C and SO 2 concentration of 10000 ppm was about 200 min. By applying curve fitting on the experimental results of Bahrami et al., at similar operating conditions, we concluded that the breakthrough times for MgO and CuO were approximately the same.
CaO is the common adsorbent in the throwaway FGD systems. The kinetics study of Moshiri et al. on CaO+SO 2 reaction demonstrated that the rate constant of CaO+SO 2 reaction at 600 °C was 3.12⋅10 -7 m s -1 44 . At the same temperature, the reaction rate constant for MgO+SO 2 was 1.11·10 -5 , which was higher than the corresponding value of CaO+SO 2 reaction.
The packed bed tests of SO 2 +CaO reaction were carried out by Dasgupta et al. 45 The results of their study indicated that the maximum breakthrough time in CaO was 60 min obtained at SO 2 concentration of 1 vol.%, temperature of 950 °C and reactor length of 15 cm. For MgO, the breakthrough time at SO 2 concentration of 1 vol.%, with reactor length of 6 cm, and temperature of 600 °C was 210 min. This implied higher adsorption capacity of MgO in comparison with CaO. The better performance of MgO reduced the number of adsorbent replacement cycles of the packed bed reactor, and as a result, the efficiency of the process would increase and operating costs decrease.
Selvakumar investigated the removal of SO 2 by ferric oxide in a packed bed reactor 46 . The results of their study indicated that the breakthrough time of vol.% with reactor length of 6 cm was about 19 min. For MgO, the breakthrough time at SO 2 concentration of 1 vol.% with reactor length of 6 cm and temperature of 500 °C was 50 min. The results of comparing breakthrough times show that MgO adsorption capacity is very much higher than that of Fe 2 O 3 . The comparison of MgO rate constant with other sorbents is summarized in Table 4.

Optimization results
In this study, the performance of packed bed reactor for SO 2 removal was optimized. The optimization was carried out by NSGA II method and the Pareto-optimal solutions figure was obtained. Pareto-optimal solutions correspond to a situation in which the solutions are not dominated with respect to each other. Moving from a Pareto solution to the next one will result in a certain amount of gain in one objective and a certain amount of sacrifice in the other.
The two target objectives of the optimization were: -to maximize the packed bed reactor breakthrough time (at C/C 0 = 0.1) -to minimize the energy consumption in calcination process Genetic algorithms are commonly used for minimizing the objective function f(x). If a function is to be minimized, -f(x) or 1/f(x) should be considered as the objective functions.
The best parameters for maximizing breakthrough lifetime and minimizing the energy consumption are shown in Table 6. It can be found that improvement in breakthrough time will result in energy consumption increase. All solutions in Pareto-optimal space can be considered as the answer, but the best one has to be selected by the user based on the operating and maintenance costs, experience, and environmental issues. According to the results presented here, the optimum SO 2 concentration, zero-air flow rate, and temperature are 1 vol.%, 1.67⋅10 -6 m 3 s -1 (100 cc min -1 ), and 500-643 °C, respectively. The SO 2 concentration and zero-air flow rate were approximately the same in all solutions, and therefore, the appropriate temperature had to be selected. The breakthrough time of chromosomes 12 and 29 were rather similar, but the energy consumption of chromosome 12 was lower than of chromosome 29. Therefore, the situation of chromosome 12 could be considered the appropriate solution. In chromosome 12, the temperature, breakthrough time, and energy consumption were 572.55 °C, 308.52 min, 82.76 kJ, respectively. This chromosome is shown by an arrow in Fig. 9.

Conclusion
In this study, SO 2 adsorption experiments were carried out in a packed bed reactor by MgO to obtain the breakthrough curves. Furthermore, the effect of important operating parameters including temperature, SO 2 concentration, and zero-air flow rate was investigated. Increasing the temperature improved the breakthrough time, but the increase in concentration and flow rate reduced the lifetime. The possibility of simultaneous production of magnesium sulfate, as a useful by product in the process of SO 2 removal by MgO, was considered. The XRD analysis verified that MgSO 4 is produced as a result of MgO+SO 2 reaction. The experimental results were correlated by applying RPM. The finite element method was used for solving RPM packed bed equations, and the results were compared with the obtained experimental data. There was a satisfactory agreement between the RPM values predicted by the model and the experimental breakthrough curve data.
The comparison of MgO performance with other sorbents for SO 2 removal was also carried out in this research. The reaction rate and the breakthrough time of MgO were mostly higher than other sorbents. As a result, the application of MgO in dry FGD systems could improve the efficiency of these units.  Finally, NSGA II was employed as a technique for multi-objective optimization to determine the best operating parameters for the removal of SO 2 by magnesium oxide in the packed bed reactor. The optimization goals were to maximize reactor breakthrough time and minimize its energy consumption. The bounds on temperature, SO 2 concentration, and zero-air flow rate were used. The Pareto-optimal solutions were obtained and the optimal operating parameters were determined. The optimum SO 2 concentration, zero-air flow rate, and temperature are 1 vol.%, 1.67⋅10 -6 m 3 s -1 (100 cc min -1 ), and 500-643 °C, respectively.