Experimental Optimization and Modeling of Sodium Sulfide Production from H2S-Rich Off-Gas via Response Surface Methodology and Artificial Neural Network

The existence of hydrogen sulfide (H2 S) in the gas effluents of oil, gas and petrochemical industries causes environmental pollution and equipment corrosion. These gas streams, called off-gas, have high H2 S concentration, which can be used to produce sodium sulfide (Na2 S) by H2 S reactive absorption. Na2 S has a wide variety of applications in chemical industries. In this study, the reactive absorption process was performed using a spray column. Response Surface Methodology (RSM) was applied to design and optimize experiments based on Central Composite Design (CCD). The individual and interactive effects of three independent operating conditions on the weight percent of the produced Na2 S (Y ) were investigated by RSM: initial NaOH concentration (10-20% w/w), scrubbing solution temperature (40-60 °C) and liquid-to-gas volumetric ratio (15 × 10−3 to 25 × 10−3 ). Furthermore, an Artificial Neural Network (ANN) model was used to predict Y . The results from RSM and ANN models were compared with experimental data by the regression analysis method. The optimum operating conditions specified by RSM resulted in Y of 15.5% at initial NaOH concentration of 19.3% w/w, scrubbing solution temperature of 40 °C and liquid-to-gas volumetric ratio of 24.6 × 10−3 v/v.


INTRODUCTION
Many effluent gas streams in oil, gas and petrochemical industries, called off-gas, are similar to gases resulting from thermal cracking and hydrotreating plants, which contain hydrogen sulfide (H 2 S).The existence of H 2 S in the offgas can cause environmental pollution and equipment corrosion.H 2 S is a highly toxic gas which has a narcotic effect on the nervous system including paralysis of the olfactory nerves.The sense of smell can no longer be relied upon after a short exposure [1].Depending on H 2 S concentration, composition and flow rate of the off-gas, and the desired specifications of the refined off-gas, there are many commercial processes for H 2 S removal from the off-gas streams.The most common and widely used methods of removing H 2 S are absorption into alkaline solution, physical absorption, oxidation, dry sorption, membrane permeation and adsorption [2,3].H 2 S absorption into NaOH solution is one of the main methods to produce sodium sulfide (Na 2 S) and H 2 S removal.Other methods to produce Na 2 S are reduction of sodium sulfate (Na 2 SO 4 ) by solid carbonaceous materials, reduction of Na 2 SO 4 by gaseous reducing agents, exchange decomposition of barium sulfide (BaS) with sodium sulfate, carbonate, and hydroxide as well as an electrolytic method [4].When off-gas contains high concentrations of H 2 S, producing Na 2 S becomes feasible alongside H 2 S removal from off-gas using absorption into NaOH solution.In other words, Na 2 S production and H 2 S removal from off-gas can occur simultaneously in one process.However, when the main objective of the process is H 2 S removal from off-gas and considering the fact that NaOH solution cannot be easily regenerated, NaOH scrubbers are most often applied for removing small quantities of acid gases containing H 2 S [5,6].
The absorption of H 2 S from off-gas into NaOH solution results in production of Na 2 S through two reversible reactions: Na 2 S is highly hygroscopic, and its solubility in water increases with increasing temperature.This valuable product has a wide variety of applications in chemical industries: It is widely used in pulp and paper industries in the Kraft process, in leather and tanning industries as the depilation agent for raw hides, in textile industries as a bleach and mordant in dyeing cotton fabric, in the photography industry to protect developer solutions from oxidation, and in dyestuff and dye printing industries as a dye agent in solving thion dye and production of sulfur dyes.Na 2 S is also used in pharmaceutical-grade chemicals production and in water treatment as an oxygen scavenger agent.It is also used as a metals precipitant in desulfurizing rayon and cellophane, elastomers, lubricants, and organic compounds, as well as in man-made fibers.Other applications include recovery of metals as the insoluble sulfides and ore flotation as a reducing agent, production of a sulfonation and sulfomethylation agent and sodium thiosulfate (Na 2 S 2 O 3 ) as well as sodium hydrosulfide (NaHS) in the medical and chemical industries [7][8][9][10][11].
The reactive absorption of H 2 S from off-gas into NaOH solution to produce Na 2 S can be performed in gas-liquid contactor devices such as spray, packed and tray columns.A spray column is an appropriate gas-liquid contactor device, because precipitation of Na 2 S at normal temperatures may ordinarily clog the internal apparatus in a continuous process.In practice, a fine spray of NaOH solution is brought into contact with off-gas inside a spray column in order to remove H 2 S by chemical absorption and produce Na 2 S solution.High-efficiency, low-pressure drops, operability in a wide range of liquid-to-gas flow rate ratios and low investment costs are other advantages of using spray columns [12].The high solubility of H 2 S in NaOH solution and prevention of foaming are other reasons to use spray columns [12,13].
There have been several studies on Na 2 S and NaHS production by H 2 S absorption into NaOH solution.Maschwitz studied a continuous process to produce a high-concentration NaHS solution in the range of 25-30% w/w by H 2 S absorption from gas mixtures containing H 2 S (0.25-20% w/w) and hydrocarbons into NaOH solution in packed columns [14].Other works on production of NaHS solution utilized waste gas and waste soda liquid in oil refineries [15], and by reaction of Na 2 S with pure H 2 S in a closed-reaction system including a reaction chamber [16].Akiba presented a production method of an anhydrous alkali metal sulfide such as anhydrous sodium sulfide by bubbling an alkali metal hydroxide solution in an aprotic organic solvent, with the hydrogen sulfide temperature between 50 and 250 °C [17].
Brons and Myers [18] studied a continuous process of putting heavy oils containing sulfuric compounds into contact with NaOH solution at a temperature of 380-450 °C for a sufficient time to form sodium sulfide (10% w/w) and removal of organically bound sulfur in the form of mercaptans, sulfides and thiophenes.Then, the produced Na 2 S was used to form metal sulfides [18].The results of our literature review indicate that there is no comprehensive information on production of Na 2 S solution using high H 2 S content (%25% v/v) off-gas stream through reactive absorption process of H 2 S into NaOH solution in a spray column.
In this study, Response Surface Methodology (RSM) was employed as a statistical method for design of experiments of reactive absorption of off-gas including H 2 S into NaOH solution to produce Na 2 S in a spray column.The experiments were performed at the Iran Chemical Industrial Investment Company (Isfahan, Iran) to use H 2 S-rich offgas from the effluent gas of the hydrotreating unit.RSM was applied to investigate the individual and interactive effects of initial NaOH concentration (C 0 ), scrubbing solution temperature (T) and liquid-to-gas volumetric ratio (L/G) on the weight percent of produced Na 2 S (Y).The ranges of the above-mentioned parameters are 10-20% w/w, 40-60 °C, and 15 9 10 À3 to 25 9 10 À3 v/v, respectively.The range for C 0 was selected to maintain the scrubbing solution pH higher than 13.5, hence producing Na 2 S to subsequently produce NaHS with higher selectivity, and to minimize sulfide precipitation problems [5,19].The range of 40-60 °C is suitable for T, because of the decrease in the rate of reactions (1) and (2) at lower temperatures and the decrease of the solubility of H 2 S into NaOH solution at higher temperatures, thus decreasing Na 2 S production [19].For L/G, the satisfactory operation conditions were obtained in the range of 15 9 10 À3 to 25 9 10 À3 v/v.By applying L/G values outside of this range, operating problems such as coning and flooding phenomena take place.Within the mentioned ranges, RSM was used to optimize the operating conditions and determine the maximum value of Y.
In addition to applying the RSM model, the Artificial Neural Network (ANN) model was implemented to predict Y using MATLAB (Version 8.1.0.604).Furthermore, the model results were compared with experimental data by the coefficient of determination (R 2 ), Mean Square Error (MSE) and Absolute Average Deviation (AAD).

Materials
H 2 S-rich off-gas in the experiments was supplied from the effluent gas of the hydrotreating unit at the Iran Chemical Industrial Investment Company (Isfahan, Iran).The molar composition of the off-gas is 25.0% hydrogen sulfide, 33.1% hydrogen, 5.5% methane, 5.0% butane, 16.4% ethane, 11.7% propane, 0.6% iso-butane, 1.8% N-pentane, 0.4% iso-pentane and 0.5% C 6+ .The NaOH solution of 10-20% w/w was prepared from the industrial grade of NaOH solution (47% w/w, Bandar Imam petrochemical Co.).All of the chemicals used for titration analyses of NaHS and Na 2 S were obtained from Merck Company (95-99%).

Experimental Apparatus and Procedure
The experiments were carried out in a lab-scale spray column.Figure 1 shows the schematic diagram of the labscale plant for Na 2 S production.The spray column was a stainless steel cylinder (5 cm ID 9 103 cm) (5) including a shower head with several holes (2.3 mm ID).The flow rates of inlet and outlet gas streams to and from the spray column were measured by glass tube gas flow meters (AMC-RGD, Azmoon motamam Co.) (1,9).Before offgas loading the spray column, it was heated to the desired operating temperature of 40-60 °C by electric heaters (4).The H 2 S content of off-gas in the inlet and outlet of the spray column were measured by Dräger-tubes (Dräger Safety AG & Co. KGaA) (2) which were suitable for H 2 S detection in the range of 0.2-7% v/v and 2-40% v/v, respectively.In all experiments, inlet gas pressure and flow rate were set at 1 bar g and 100 L/min, respectively.The outlet gas stream from the spray column and H 2 S analyzer section entered high-concentration NaOH solution tank (3).Subsequently, the outlet gas stream from the NaOH solution tank (3) was transferred to the furnace.Before releasing off-gas stream, the prepared NaOH solution in the range of 10-20% w/w were kept in the fresh NaOH solution tank (30 cm ID 9 69 cm) (12).About 10 L of the solution were transferred to the collecting tank (46 cm ID 9 37 cm) (6) for startup of experiments.The collecting tank was equipped with a mixer (7) and steam coils (8) to obtain a welldispersed solution with the desired temperature.
The H 2 S in the off-gas was absorbed into scrubbing NaOH solution in a counter-current pattern to produce Na 2 S solution.Initially, before reaching steady state conditions for the scrubbing system, the NaOH solution in the collecting tank was recycled by the pump (10), and the valve belonging to the fresh NaOH solution tank (12) was kept closed.Samples were collected from the collection tank and their pH values were measured with a pH meter (Metrohm Co.) (18).When the sample pH was below 13.5, a fresh NaOH solution stream was added to the recycle stream by the pump (15) to keep pH !13.5 during absorption in order to produce Na 2 S instead of NaHS.The fresh NaOH solution was heated to the desired operating temperature by electric heaters ( 14) before being fed into the spray column.In steady state operation of the continuous process, the flow rate of fresh NaOH solution was equivalent to the liquid outlet stream from the spray column.The flow rates of liquid phases were controlled by the rotameters (11,16,17).The output solution stream was collected in the solution tank (19).When steady state was reached, the sampling was performed and kept for further titration analysis.The produced Na 2 S solutions can reach commercial-grade quality by evaporating water from the solution.The water evaporation stage was not performed in this study.

Titration Analysis
All collected samples were analyzed by standard titration technique with aqueous hydrochloric acid (HCl) to determine concentration of sulfides [20].The weight percent of each component of Na 2 S, NaHS and NaOH in the collected samples can be determined by this titration analysis.
Thymolphthalein and bromophenol were used as indicators to determine the content of Na 2 S and NaHS in solution, respectively.

RSM Model and Experimental Design
RSM is a mathematical and statistical technique that is based on fitting a full quadratic model to the experimental data [21,22].There are three stages in RSM: (1) design of experiments specified by response variables, independent variables and their levels and statistical procedure such as Central Composite Design (CCD); (2) carrying out the designed experiments and applying regression analysis using RSM to obtained results; (3) optimization of response surface model.Additionally, RSM allows evaluating the statistical significance of individual process variables, as well as the interaction between variables [23][24][25].RSM was employed to investigate the effect of the variables of initial NaOH concentration (X 1 ), scrubbing solution temperature (X 2 ) and liquid-to-gas volumetric ratio (X 3 ) and their interactions on the weight percent of the produced Na 2 S (Y).CCD with three variables (C 0 , T and L/G) and three levels was used to obtain the optimum conditions for Na 2 S production.RSM fitted a full-quadratic equation with the experimental data to provide a reasonable response surface modeling through regression analysis in MINITAB software (version 16).In order to investigate the effects of variables with different magnitude of value, coded variables (Z i ) were applied instead of uncoded variables (X i , i = 1-3).These variables were coded by the following equation: where X i , X i.c and DX i are the real value, real value at center point and step change in the variable i (i = 1-3), respectively.Table 1 shows the coded and uncoded levels of independent variables employed in RSM design.The experiments randomly designed by RSM involved six axial points and eight cube points which repeated twice, and six center points.As mentioned earlier, RSM provides a second-orderpolynomial equation including linear and quadratic variables with interaction terms [26] as in Equation ( 4): where Y represents the response variable (weight percent of produced Na 2 S), Z i is a coded variable, b 0 , b i , b ii , b ij are regression coefficients for the constant term, the square term and the interaction term, respectively, and e is residual factor associated with the experiments.The statistical analysis of the RSM was carried out in the form of analysis of variance (ANOVA) which presents the sources of variation, the degrees of freedom, sum of squares and the mean square for the model.ANOVA also includes F-value and probability (p-values) employed to determine whether the predictors or factors are significantly related to the response.In addition to ANOVA, R 2 and the adjusted coefficient of determination (Adj.R 2 ) were applied to verify the model validity.

ANN Model Description
ANN is an alternative modeling tool to the polynomial regression model, which can describe the complex nonlinear relationships between experimental data.A common ANN architecture is a Multi-Layer Feed Forward (MLFF) network.It consists of an input layer, one or more hidden layers and an output layer.Each layer involves processing units called neurons which operate independently of others [27,28].In the current study, a MLFF network was applied with the architecture as shown in Figure 2: an input layer included three operating conditions as input neurons, an output layer with one neuron, and one hidden layer which its neurons can change to gain the best ANN performance.The selection of one hidden layer was sufficient for accurate statistical prediction.
An ANN model inherently needs more experimental data than RSM to have an efficient and accurate prediction.But, ANN can also build a satisfactory model even with relatively less data, if the data were collected from experiments that matching the experimental design [29].The relationship between the components of a MLFF network can be represented by the following equation: where y jk is the neuron j's output from k's layer, b jk is the bias weight for neuron j in layer k, and w ijk are the weights representing the strength of the connection between the ith neuron and jth neuron.F k is the activation transfer functions.Three types of activation transfer functions were used: sigmoidal function, hyperbolic tangent and linear function.
Sigmoidal function is the most common activation transfer function [30,31].
The MLFF optimization was carried out in four stages: (1) determining the Back-Propagation Learning Algorithm (BPLA); (2) specifying the optimum number of neurons in the hidden layer; (3) estimating the initial values of weights and biases for Equation ( 5); (4) updating the weights and biases to obtain optimum ANN performance up to the minimum network error like MSE.Since the experimental data used in ANN had different ranges, all input and output experimental data were normalized to the range of 0-1.This data normalization was performed to prevent disorder in the learning process and gain homogenous results and higher ANN performance [32,33].

Analysis of RSM
In this study, a set of 20 experiments was employed to obtain the full quadratic model using CCD with three independent variables and three levels for each variable.This design of experiments was used to evaluate both the individual and the interactive effects of the operating conditions, and to determine the optimal operating conditions.Table 2 shows the set of 20 runs for experimental and predicted Y as the results of the experiments.Table 3 shows the calculated coefficients of the regression model (Eq.4).Statistical tests of t-value and p-value from Table 3 were employed to clarify the significance of each term in Equation ( 4).In this study, highly significant, significant and insignificant coefficients have p-value < 0.001, 0.001 p-value < 0.05 and p-value !0.05, respectively.Therefore, the quadratic polynomial model without insignificant coefficients for Y was obtained as the following equation: The results presented in Table 3 indicate that linear and square C 0 were highly significant (p-value < 0.001).On the other hand, due to the effectiveness of C 0 on the prime cost and the possibility of creating the operating problems, its importance will be doubled.The linear terms of T and L/G, and all the interaction terms except C 0 -L/G were significant (0.001 p-value < 0.05).The other terms containing the square terms of T and L/G and the interaction term C 0 -L/G were insignificant.
Analysis of variance for Y as a response surface quadratic model is presented in Table 4 and includes the statistic tests of F-value and p-values.In Table 4, p-value !0.05 for the lack-of-fit and p-value 0.001 for the regression model of Y obtained via analysis of variance (ANOVA) confirmed the fitted model.R 2 and Adj.R 2 employed to validate the RSM model were calculated to be 0.9824 and 0.9666, respectively.These values indicated that the model developed by RSM precisely agrees with the experimental results.

ANN Model
The weight percent of the produced Na 2 S was modeled by MLFF network on the basis of operating conditions as input data.In this work, a three-layered network as shown in Figure 2 was used applying the log-sigmoid transfer function called "logsig" at the hidden layer and a linear transfer function called "purelin" at the output layer.Logsig and purelin transfer functions are defined by the following equations: The optimum BPLA and number of neurons in the hidden layer were identified by trial-and-error.The best ANN performance was determined based on the minimum MSE of the training and prediction set.Seventy five percent of the CCD experimental data with two replications was randomly applied in the training process and the remaining 25% was used in test and validation processes.Table 5 shows the calculated MSE for different sets of ANN parameters.The results represented in Table 5 indicate that applying the logsig activation transfer function, Levenberg-Marquardt (L-M) learning algorithm, and five neurons in one hidden layer for the MLFF results in the minimum MSE.As shown in Figure 3, this optimized MLFF network represents the best validation performance of MSE 2.4115 9 10 À6 .Figure 4 shows the satisfactory agreement between the data predicted by ANN and experimental data.

Individual and Interactive Effects of Operating
Conditions on Y The operating conditions of C 0 , T and L/G are three variables that affect spray column performance.Their individual and interactive effects on Y were investigated to find out the best experimental and efficient operating conditions.Three-dimensional response surfaces plots and twodimensional contour plots can indicate the interactive effects of the independent variables on the response variable.These plots were visualized by the weight percent of the produced Na 2 S versus initial NaOH concentration, scrubbing solution temperature and liquid-to-gas volumetric ratio in Figures 5 and 6.The third independent variable was kept at central point (Z i = 0) in Figures 5  and 6.
Figure 5 shows the response surface and contour plots for the effect of initial NaOH concentration and liquid-to-gas volumetric ratio on Y at scrubbing solution temperature of 50 °C.Because of the direct effect of initial NaOH concentration on the production of Na 2 S as described in Equations ( 1) and ( 2), C 0 is an important and efficient independent variable to increase Y.The main reason for the positive effects on Y of increasing C 0 is the enhancement of active and available moles of the absorbent solution which penetrates into gas-liquid interface and reacts with H 2 S, thereby increasing the absorption rate and enhancement factor.Figure 5 confirms this activity within the range of the scrubbing solution temperatures.Moreover, Table 3 displays a positive linear effect of C 0 (p-value < 0.001) on the response variable.The increase in C 0 also had a negative effect on Y by increasing the density and viscosity of scrubbing solution.Therefore, H 2 S molecular diffusion coefficients and H 2 S solubility decrease due to acid-base equilibrium (Eq. 1 and 2), which reduces Y. Additionally, at constant pressure of the spray nozzle, the increase in density and viscosity of scrubbing solution led to production of drops with larger diameters, thus providing smaller liquid-gas interfaces.The positive and negative effects of initial NaOH concentration cancel each other and thus Y is almost independent of C 0 at C 0 > 17.5% w/w, especially at L/G higher than 20 9 10 À3 , as shown in Figure 5.This effect is due to reciprocal positive linear (p-value < 0.001) and negative quadratic effects (p-value < 0.001) of Z 1 and negative Z 1 -Z 2 interaction effect (p-value < 0.05) on Álvarez-Cruz et al. obtained similar results regarding the effect of C 0 on H 2 S absorption [5].They concluded at higher concentration of NaOH solution (1 and 2 M), H 2 S dissolution was less.In addition, Yincheng et al. studied the effect of initial NaOH and NH 3 concentration on CO 2 removal efficiency and acquired similar results with this study [34].
Increase in scrubbing solution temperature had two effects on Y. Increasing the scrubbing solution temperature provided positive effects on Y by increasing the rate of reactions ( 1) and ( 2) to produce more Na 2 S, reducing the solution viscosity and, therefore, producing drops with smaller diameter and more liquid-gas interfacial area.
In addition, increasing the scrubbing solution temperature leads to negative effects on Y due to: 1. decrease in H 2 S solubility in scrubbing solution; 2. release of H 2 S from solution to gas phases due to exothermic reactions of ( 1) and (2); 3. increase in water evaporation rate from solution, and therefore, increase in resistance against H 2 S transition to liquid phase.As summarized in Table 3, the scrubbing solution temperature had a negative linear (p-value < 0.05) effect and the negative interaction of Z 1 -Z 2 (p-value < 0.05) and Z 2 -Z 3 (p-value < 0.05) effects on Y.The effect on Y scrubbing solution temperature varied depending on which effect was dominant.The reciprocal effects of L/G and T at C 0 15% w/w in the surface and contour plots of Figure 6 show that the negative effects of T on Y were generally dominant in the considered range for T.
The prediction of spray column performance is difficult due to the complexity of its hydrodynamics.The spray column performance is influenced by several droplet specifications: size, distribution, velocity, collision, distortion, internal recirculation, and oscillation and coalescence between droplets [35].Additionally, L/G is an effective and important design parameter for absorption columns from a process economics perspective.Increasing L/G can occur by increase in liquid flow rate or decrease in gas flow rate.Increasing liquid flow rate at constant gas flow rate resulted in L/G enhancement, the diameter of droplets increased at constant spraying pressure and therefore, the total liquid-gas interfacial area and hence Y were increased.This enhancement of Y occurs due to some reasons: (1) the reactive absorption of H 2 S at the liquid film of NaOH solution (Hatta number > 2) [36]; (2) increasing collision of droplet and gas; (3) increase in mass transfer coefficient of gas because of increased velocity of droplets.Increasing L/G could cause a negative effect on Y by increasing both the rate of droplet coalescence and the thickness of liquid film on the wall of the spray column, thereby reducing liquid-gas interfacial area.On the other hand, the droplet coalescence raises the weight of droplets and the droplet falling rate which in turn reduces the contact time of two phases and therefore a decrease in Y. Figure 5 shows that Y increased approximately 11% by enhancement of L/G from 15 9 10 À3 to 21.5 9 10 À3 (v/v) and then remained constant, because the positive and negative effects of L/G enhancement cancel each other.Bandyopadhyay and Biswas obtained similar results in spray columns for the effect of L/G on SO 2 scrubbing using water and dilute NaOH [37] and for CO 2 capture into NaOH solution [38].Their experimental results of reference [37] in a range of L similar to this study support the claim that increasing L/G from 15 9 10 À3 to 18.6 9 10 À3 at constant G of 6 Nm 3 /h, increases the sauter mean diameter (d 32 ) of drops 17.6% and 5.6% of the total droplet surface area, although it decreases the number of droplets 23.6%.Zhang et al. acquired the same trend for the effect of L/G on the removal efficiency of SO 2 using seawater as an absorbent [39].Both Figure 5 and the interaction coefficient of Z 1 -Z 3 with p-value !0.05 in Table 3 show that the interaction effect of Z 1 -Z 3 on Y was negligible.
As mentioned earlier, T and L/G had two effects on Y. Figure 6 indicates that the interaction of T and L/G with the coefficient of À0.4787 and p-value < 0.05 presented in Table 3 had a significant effect on Y.

Comparison Between Results of RSM and ANN Models
The precision and accuracy of RSM and ANN models were compared using R 2 , MSE and AAD values.Table 6 shows that the ANN model with larger R 2 and smaller MSE and AAD values is superior to the RSM model in predicting Y.
Additionally, the ANN model is not limited to number of experiments and it is applicable to complicated non-linear processes [21,28].

Optimization of Operating Conditions
The optimum Y is predicted by analytical optimization of RSM.RSM estimated the sets of operating conditions that resulted in maximum Y (15.7 ± 0.1% w/w).These sets of operating condition were employed to determine the

CONCLUSION
The H 2 S reactive absorption in the spray column into NaOH solution was employed to define the weight percent of the produced Na 2 S insight from experimental, RSM and ANN models.The results show that Na 2 S production from H 2 S-rich off-gas is a suitable and reasonable way to achieve Na 2 S besides removing the principal portion of H 2 S from off-gas.Therefore, it can be applied as a pretreatment process.The effects of initial NaOH concentration, scrubbing solution temperature and liquid-to-gas volumetric ratio on Y were investigated.The experimental results showed that the linear and quadratic terms of initial NaOH concentration play a significant role on Y. Additionally, the linearity of scrubbing solution temperature and liquid-togas volumetric ratio and the interactions between initial NaOH concentration and scrubbing solution temperature, scrubbing solution temperature and liquid-to-gas volumetric had significant effects on the produced Na 2 S.An ANN model was developed, for which the results agreed well with experimental data when the MLFF network with the logsig activation transfer function, L-M training algorithm and 5 neurons in the single hidden layer was utilized.The comparison between the results of RSM and ANN models indicates that ANN model has higher precision than RSM model, based on comparison with the experimental data.However, both models could accurately describe Y based on regression analyses of R 2 , MSE and AAD.
The maximum weight percent of the produced Na 2 S of 15.5% was achieved at optimum operational conditions by a numerical and graphical analysis at an initial NaOH concentration of 19.3% w/w, scrubbing solution temperature of 40 °C and liquid-to-gas volumetric ratio of 24.6 9 10 À3 v/v.The achieved Na 2 S solution will be able to convert to the commercial-grade quality of Na 2 S solution by evaporating excess water from the solution.

Figure 2 Architecture
Figure 2 Architecture of the three-layered MLFF network.

Figure 3
Figure 3 Plot of MSE of predicted data by ANN model and experimental results versus epochs.

Figure 4 ScattergramFigure 5 Figure 6
Figure 4 Scattergram of modeled normalized Y by ANN versus exprimental normalized Y for training and all data.

TABLE 1
Coded and uncoded levels of independent variables employed in RSM design.

TABLE 2
Experimental and predicted data by RSM and ANN models for Y from the set of experiments performed based on CCD.

TABLE 3
Calculated regression coefficients for quadratic polynomial model of Y.

TABLE 4
Analysis of variance (ANOVA) of the fitted quadratic polynomial model for Y.
a Degree of freedom; b Sequential sums of squares; c Adjusted sum of squares; d Adjusted mean squares; e p-value < 0.001 highly significant; 0.001 p-value < 0.05 significant; p-value !0.05 not significant.

TABLE 5
Performance comparison of 15 ANN with different BLPA and number of neurons in the hidden layer.

TABLE 6
Comparison of precision and accuracy of RSM and ANN models.Y i , Ŷ i , and " Y i are the experimental data, modeling data and average of experimental data, respectively.n for RSM model is the number of experimental data and for ANN model is n op 9 n dp which n op is the number of output parameters, and n dp is the number of data patterns. *