A robust predictive tool for estimating CO2 solubility in potassium based amino acid salt solutions

Ebrahim Soroush ,Shohreh Shahsavari,Mohammad Mesbah *,Mashallah Rezakazemi,Zhi'en Zhang

1 Young Researchers and Elites Club,Ahvaz Branch,Islamic Azad University,Ahvaz,Iran

2 Department of Chemical Engineering,Sahand University of Technology,Tabriz,Iran

3 Young Researchers and Elites Club,Science and Research Branch,Islamic Azad University,Tehran,Iran

4 Department of Chemical Engineering,Shahrood University of Technology,Shahrood,Iran

5 School of Chemistry and Chemical Engineering,Chongqing University of Technology,Chongqing 400054,China

6 Key Laboratory of Low-grade Energy Utilization Technologies and Systems,Ministry of Education of China,Chongqing University,Chongqing 400044,China

1.Introduction

Annual emission of a large quantity of Greenhouse Gases(GHG)endangers the environment and is the main reason ofglobal warming and climate change.It is estimated that a considerable amount of global warming,approximately more than 55%,is related to the CO2,which is present in the atmosphere.Consequently,decreasing CO2emissions is a harsh necessity and requires immediate attention[1–4].

Absorption by aqueous alkanol-amine solutions is the mostcommon method for processes dealing with CO2elimination from flue gas streams[5–7].The most preferred chemical solvents for absorption of CO2are the aqueous solution of amines(primary,secondary,tertiary,and sterically hindered)due to their amazing thermal degradation resistance,low hydrocarbons loading capacity,high rate of absorption,and reasonable cost[8].Nevertheless,high consumption of energy,equipment corrosion,fouling,and foaming are inevitable drawbacks of utilizing amine solutions[8].

In recent decades,Ionic Liquids(ILs)have been suggested as new CO2absorbers.Due to their low vapor pressures,they have low vaporization rate.However,ILs face some problems as CO2solvent including high viscosity,high cost,and low CO2loading[9].In the past decade,as a potential substitute for alkanol-amines,amino acid salt solutions have been welcomed[10].Despite that,alkanolamines are cheaper;the amino acid salt solutions are superior in many ways.Due to their ionic essence,they have high chemical reactivity,low vapor pressures,and low viscosities,are stable to oxidative degradation,and capable of establishing proper binding energy with CO2[11].CO2absorption by amino acid salt solutions may produce some precipitation in the liquid phase,which shifts the reactions in the direction of forming more products and consequently an increase of CO2absorption[12,13].

Some investigators have studied the absorption of CO2via amino acid salt solutions.Sodium glycinate solutions were investigated by Song et al.[14]for CO2absorption.They used solutions of 10 wt%,20 wt%,and 30 wt%for CO2absorption with the range ofpartialpressure from 0.1 to 200 kPa at the temperatures 303,313,and 323 K.The outcomes stated that the loading capacity reduces by increasing concentration ofthe amino acid salt.Mu?oz etal.[15]studied CO2absorption with 1-molar solution of the potassium salts of threonine,proline,serine,arginine,ornithine,histidine,glycine,and taurine at 293 K and 100 kPa.They concluded that these amino acid salt solutions have a CO2loading like monoethylamine(MEA).

Portugal et al.[15]used potassium threonate and potassium glycinate for CO2absorption.They stated that despite no precipitation was observed during the experiments,the order of magnitude for CO2absorption using the amino acid is equal to the MEA.In addition,they found out that an increase in the potassium glycinate concentration decreases the CO2loading.Majchrowicz and Brilman[16]studied the potassium L-prolinate solution in absorbing CO2.They concluded the CO2loading decreases with increasing molar concentration of potassium L-prolinate.In addition,they observed some precipitation in the absorption process using 3-molar L-prolinate solution at 285 K.

Wei et al.[17]examined the CO2loading capacity of potassium taurate aqueous solution along with density and viscosity.They indicated that the CO2loading increases when the concentration of potassium taurate increases.Mazinani etal.[32]investigated the CO2absorption at low partial pressures using potassium lysinate.Their results indicated that the CO2solubility decreases by increase in the concentration of potassium lysinate and operating temperature.

Literature experimental data for equilibrium solubility of CO2into some amino acid salt solutions are collected and they are limited in the range of operating conditions and accuracy.Basically,the CO2loading for amino acid salt solutions depends on the solvent type,temperature,pressure,and concentration of solvent.There are several experimental data on CO2absorption with amino acid salt solutions in the literature[10,11,14,18,19].Nevertheless,they cover only a narrow range of temperature and concentration,which does not satisfy the requirements for applications.In addition,equilibrium data points are needed to assess the system reliability.However,the experimental measurements in all ranges for all types of solutions are impractical and rather expensive.Though developing methods for estimating CO2loading of amino acid salt solutions is of vital importance.

Several thermodynamic models could be found in the literature that can predict the CO2loading.In some empirical base models such as Kent–Eisenberg[20]which is applicable to some CO2absorption systems[21],non-idealities are assumed lumped in equilibrium constants.Some models which are developed using the excess Gibbs free energy,such as the models introduced by Austgen et al.[22],Clegg and Pitzer[23],the electrolyte-NRTL modelofChen and Evans[24],and Deshmukh and Mather[25].There are some equations of state(EoS)which try to designate non-idealities of the amino acid absorption systems.Thermodynamic models such as SAFT and CPA could be applicable for predicting CO2absorption using amino acid salts,albeit the lack of data on critical and some physical properties of amino acid solutions is a major problem.

In this study,we are trying to develop a rebuts predictive mathematical model for estimating CO2solubility in potassium based amino acid salt solutions by using neural networks and assess the in fluential parameters of the absorption process with resultant model.

2.Methodology

An important step in designing a network is the determination of number of hidden layers.It is believed that all kinds of nonlinear mapping could be performed by using a network which has just one hidden layer[26–28].MLP is broadly used for prediction,approximation,pattern classi fication,and recognition.MLP can predictissues stochastically which are not linearly separable.Hence,in this study,single-hiddenlayer MLP was selected to predict acid gas absorption in the different amino acid salt solutions.

2.1.Multilayer perceptron(MLP)

An MLP is a feed-forward artificialneuralnetwork ofsimple neurons called perceptrons with single or multiple layers between input and output layer with the back-propagation learning algorithm.Fig.1 displays the graphical of the MLP with one hidden layer in the prediction of CO2solubility in different amino acid solutions.Each MLP layer contains one or more neurons directionally connected with the neurons from the nextand the previous layer.Allthe neurons in MLP are similar.The values regained from the former layerare summed up with weights and bias which are individual for each neuron.The summation is transformed using the activation function which can be also changed foreach neuron.In this study,tangent sigmoid activation function was used for hidden layer while a linear function was used for the output layer[28–31].

However,MLP using a back-propagation algorithm is the standard algorithm for any chemical engineering problems and the subjectof ongoing research in the prediction of acid gas absorption in different amino acid salt solutions.

Fig.1.The structure of MLP with one hidden layer containing 12 neurons.

Table 1 Range of Data for each amino acid salt solution system

2.2.Data

For training,the network,255 data points of CO2absorption at various operating conditions in different amino acid salt solutions were gathered from numerous literature review and were reported in Table A1.The range of data for each amino acid salt solution system was reported in Table 1.These data are divided into three classes named training(70%,179 data points),validation(15%,38 data points),and testing(15%,38 data points)datasets.The data selection was carried out randomly.

For creating an ANN,the independent inputs must be de fined.It is essentialto determine criteria to discriminate the types ofamine saltsolutions.Moreover,operating conditions are imperative asthey in fluence the solubility of acid gases.Based on empirical experience,acid gas absorption into amino salt solutions depends on amine salt solution's type,temperature,equilibrium partial pressure of CO2,and the molar concentration ofthe solution.Some other parameters such as molecular weight and the boiling point of amino acid salts may be taken into account as a characteristic of amino salt solutions.With varying the amino salt solutions type and concentration,the apparent boiling pointand molecular weightalso varies.The boiling pointand molecular weight were chosen because of its availability.

2.3.Optimum ANN architecture

2.3.1.ANN training

The optimum ANN architecture must be designed after de fining the number of input variables.For this purpose,trial and error was used to reach the best layer,the optimum number of neurons in each layer and the finest transfer function.MATLAB neural network toolbox was used to implementthe model.Levenberg–Marquardt(LM)back-propagation method was selected for the training network.

2.3.2.Selecting the optimal ANN structure

To examine the ANNability forprediction ofacid gassolubility in different amino acid salt solutions,conventional regression analysis including mean square error(MSE),average absolute relative deviation(AARD)percent,and the coefficientofdetermination(R2)were utilized.The R2indicates how the ANN estimation is associated with the data sets.In this study,the number of optimum neurons in the hidden layerwasfound iteratively to reach the minimum value ofMSE.However,the developed ANN with the least MSE and AARD was selected during the training procedure.

3.Result and Discussion

3.1.MLP accuracy

In order to select,the optimal number of the neurons in the hidden layer,a trial and error technique,by increasing the number of neurons and monitoring the statistical parameters for the resultant networks was used.As shown in Table 2,the MLP with the 12 neurons in the hidden layer shows the finest results.For a better visual examination,the AARD and R2for the different number of neurons in the hidden layer are plotted in Fig.2(a)and(b),respectively.As it could be seen increasing the number of neurons in the hidden layer results in better performance of the network until it reaches 12 neurons,where a further increase in the number of neurons will increase the error and decrease the accuracy.The suggested network has the minimum MSE of 0.0011,which is an acceptable error trend,minimum AARD of 5.54%that indicates proper error distribution,and maximum R2of 0.9828 as a demonstration of excellent agreement between predicted and experimental data.

It is worth mentioning that in addition to the remarkable results of training and validation data,the suggested network has a satisfactory error trend and accuracy for testing subset.The MSE of 0.0015,AARD of6.56%,and R2of0.9742 oftesting data show an acceptable generalization for the proposed MLP.

In an attempt to provide a more sensible visual understanding for the performance of the proposed model a graphical analysis was conducted.The reliability of the suggested network is examined by a cross plotin Fig.3.The training,validation and testing data are specifiedwith differentcolorsforachieving a more discreetoutlook.The accumulation of data points around the 45 degree line indicates the robustness of the network and reasonable agreement between experimental and prognosticated values.The figure shows that there is no considerable over or underestimation of the individual data.

Table 2 Tested networks and their statistical parameters

Fig.2.(a)AARD for different number of neurons in the hidden layer(b)R2 for different number of neurons in the hidden layer.

In Fig.4,all experimental data were plotted against their corresponding predicted values.As itis obvious fromthe figure,the proposed MLP can prognosticate CO2in an appropriate mannerforthe whole data range.Additionally,to ensure thatthe modelperforms well in modeling each individual system of the amino acid salt solution,a through statistical analysis was performed on each of the systems,which could be found in Table 3.The order of MSE for all four systems is an indication of outstanding error trend and network capability in distinguishing each individual amino acid salt system.

3.2.Outlier diagnostics

Individualorcollections ofdata thatdeviate from the behaviorofthe majority of data population are known as outliers.All mathematical models that require data collection face a high chance of probable outliers that threaten the reliability of the model.These doubtful values may harm the model or decline the preciseness of its predictions.The errors,which occur in experimental measurements,are known as the main source of outliers[34–38].An essential stage in developing a model is identification and elimination of the outliers.One of the common statistical methods used for outlier recognition is known as the Leverage approach.The details ofthis method and its formulation could be found elsewhere[34–38].

In an attempt to investigate the data quality and applicability domain of the proposed MLP,an outlier diagnostic was conducted via Leverage approach.Fig.5 shows the William plot for the predictions of the model.As it can be seen the accumulation of the data in the 0≤H≤0.071 and-3≤R≤3 area indicates the statistical validity of the MLP and that the all of the data points are in the applicability domain of the network.

3.3.Sensitivity analysis

Fig.3.Cross plot assessment of training,validation and testing subsets for predicting CO2 loading(Selected network 5-12-1).

Fig.4.Comparing the experimental data and results of MLP model.

Table 3 The statistical analysis of each amino acid salt solution system

In an attempt to examine the effect of each input parameter on CO2loading,extend our understanding of absorption process,and uncertainties of the variables a sensitivity analysis was conducted.The overall effect of each independent parameter on CO2was examined via relevancy factor(r)with directionality.The Pearson correlation[39,40]:

Fig.5.Outlier diagnostics of the data set.

Here LiandL designate the i th and the average value of CO2loading,respectively.The symbols Vi,jandVjshow the i th and average value of the j th input variable,respectively.The value of relevancy factor may vary between+1 to-1.A positive value of relevancy factor designates an increasing relation among the parameters while a negative value of r specifies a decreasing relation.When the relevancy factor has a value of 0,itcould be concluded thatthe parameters have no relations.Fig.6 illustratesthe relevancy factorofeach variable.In the firstglance one may notice that the most in fluential parameter on CO2loading is the partial pressure ofCO2and by increasing its value the CO2loading increase significantly.The figure clearly shows that second important parameter affecting the CO2loading is the concentration ofamino acid saltin the solution;nevertheless,the negative value ofits relevancy factor indicates thatithas an adverse effect.The system temperature and boiling point of the amino acid salts also have the adverse effect on the CO2loading,but due to the magnitude of their relevancy factor,it can be understood that they have just a slight effect on the CO2loading.It is interesting to note that the zero value of relevancy factor for the molecular weight of amino acid salts indicates that this parameter has no effect on the CO2loading.

Fig.6.The relevancy factor for each of the input parameters.

4.Conclusions

In this study,a multilayer perceptron neural network algorithm as a supervised learning method has been suggested to prognosticate the CO2loading of amino acid salt solutions as a function of CO2partial pressure,molecular weight of amino acid salts,boiling point of amino acid salts,molar concentration of the solution,and temperature.In this manner,the data points of CO2absorption by different amino acid salt solutions for training,validation,and testing the model were gathered from dependable literature sources.Through a trial and error procedure,the best three layers network was selected to model the CO2loading.One of the most significant features of using MLP is that high theoretical knowledge or human experience throughout the training procedure is not required.Therefore,theoretical knowledge has not been used and the MLP training process is solely founded on the experimental data.Graphical and statistical measures designate that the suggested MLP can predict CO2loading with acceptable accuracy.Furthermore,it was confirmed that the suggested network is capable of predicting the actual physical behavior of absorption process.The relevancy factor indicated that CO2partial pressure is the most crucial variable in the model and has a positive effect on the CO2loading while the concentrations of the amino acid salts as the second important variables have a negative effect.Furthermore,it was found that the molecular weight of amino acid salts has no role on the CO2loading;but system temperature and boiling point of amino acid salts have a weak negative effect.In addition,the Leverage statistical algorithm was used to guarantee the data quality.

Nomenclature

AARD average absolute relative deviations,%

ANN artificial neural network

BP boiling point of amino acid salt,°C

C molar concentration of the solution,mol·L-1

GHG greenhouse gases

H hat matrix

Lii th value of the predicted CO2loading

L average value of the predicted CO2loading

LM Levenberg–Marquardt

MEA monoethylamine

MLP multilayer perceptron

MSE mean square error

MWmolecular weight of amino acid salt

PCO2equilibrium partial pressure of CO2,kPa

R2correlation coefficient

T temperature,K

Vi,j i th value of the j th input variable

Vjaverage value of the j th input variable

α CO2loading,mol CO2·(mol amino acid salt)-1

Supplementary Material

Supplementary data to this article can be found online athttps://doi.org/10.1016/j.cjche.2017.10.002.

References

[1]S.Shirazian,A.Marjani,M.Rezakazemi,Separation of CO2by single and mixed aqueous amine solvents in membrane contactors: fluid flow and mass transfer modeling,Eng.Comput.28(2)(2012)189–198.

[2]M.Rezakazemi,A.E.Amooghin,M.M.Montazer-Rahmati,et al.,State-of-the-art membrane based CO2separation using mixed matrix membranes(MMMs):an overview on current status and future directions,Prog.Polym.Sci.39(5)(2014)817–861.

[3]S.M.R.Razavi,et al.,Simulation of CO2absorption by solution of ammonium ionic liquid in hollow- fiber contactors,Chem.Eng.Process.Process Intensif.108(2016)27–34.

[4]M.Rezakazemi,I.Heydari,Z.Zhang,Hybrid systems:combining membrane and absorption technologies leads to more efficient acid gases(CO2and H2S)removal from natural gas,J.CO2Util.18(2017)362–369.

[5]M.Fasihi,S.Shirazian,A.Marjani,et al.,Computational fluid dynamics simulation of transport phenomena in ceramic membranes for SO2separation,Math.Comput.Model.56(11–12)(2012)278–286.

[6]A.Mansourizadeh,A.F.Ismail,CO2stripping from water through porous PVDF hollow fiber membrane contactor,Desalination 273(2)(2011)386–390.

[7]M.Mesbah,et al.,Mathematical modeling and numerical simulation of CO2removal by using hollow fiber membrane contactors,Iran.J.Oil Gas Sci.Technol.(2017)https://doi.org/10.22050/IJOGST.2017.48143(in press).

[8]S.Ma'mun,R.Nilsen,H.F.Svendsen,et al.,Solubility of carbon dioxide in 30 mass%monoethanolamine and 50 mass%methyldiethanolamine solutions,J.Chem.Eng.Data 50(2)(2005)630–634.

[9]S.D.Kenarsari,D.Yang,G.Jiang,et al.,Review of recent advances in carbon dioxide separation and capture,RSC Adv.3(45)(2013)22739–22773.

[10]T.Payagala,D.W.Armstrong,Chiral ionic liquids:a compendium of syntheses and applications(2005–2012),Chirality 24(1)(2012)17.

[11]P.S.Kumar,et al.,Density,viscosity,solubility,and diffusivity of N2O in aqueous amino acid salt solutions,J.Chem.Eng.Data 46(6)(2001)1357–1361.

[12]P.S.Kumar,J.A.Hogendoorn,S.J.Timmer,et al.,Equilibrium solubility of CO2 in aqueous potassium taurate solutions:part 2.Experimental VLE data and model,Ind.Eng.Chem.Res.42(12)(2003)2841–2852.

[13]M.Rezakazemi,Z.Niazi,M.Mirfendereski,et al.,CFD simulation of natural gas sweetening in a gas-liquid hollow- fiber membrane contactor,Chem.Eng.J.168(3)(2011)1217–1226.

[14]H.-J.Song,S.Lee,S.Maken,et al.,Solubilities of carbon dioxide in aqueous solutions of sodium glycinate,Fluid Phase Equilib.246(1)(2006)1–5.

[15]D.M.Mu?oz,A.F.Portugal,A.E.Lozano,et al.,New liquid absorbents for the removal of CO2from gas mixtures,Energy Environ.Sci.2(8)(2009)883–891.

[16]M.Majchrowicz,D.Brilman,Solubility of CO2in aqueous potassium L-prolinate solutions—absorber conditions,Chem.Eng.Sci.72(2012)35–44.

[17]S.C.-C.Wei,G.Puxty,P.Feron,Amino acid salts for CO2capture at flue gas temperatures,Energy Procedia 37(2013)485–493.

[18]H.-J.Song,M.-G.Lee,H.Kim,et al.,Density,viscosity,heat capacity,surface tension,and solubility of CO2in aqueous solutions of potassium serinate,J.Chem.Eng.Data 56(4)(2011)1371–1377.

[19]U.E.Aronu,E.T.Hessen,T.Huang-Warberg,et al.,Vapor–liquid equilibrium in amino acid salt system:experiments and modeling,Chem.Eng.Sci.66(10)(2011)2191–2198.

[20]R.L.Kent,B.Eisenberg,Better data for amine treating,Hydrocarb.Process.55(2)(1976)87–90.

[21]P.S.Kumar,J.A.Hogendoorn,P.H.M.Feron,et al.,Equilibrium solubility of CO2 in aqueous potassium taurate solutions:part 1.Crystallization in carbon dioxide loaded aqueous salt solutions of amino acids,Ind.Eng.Chem.Res.42(12)(2003)2832–2840.

[22]D.M.Austgen,et al.,Model of vapor-liquid equilibria for aqueous acid gasalkanolamine systems using the electrolyte-NRTL equation,Ind.Eng.Chem.Res.28(7)(1989)1060–1073.

[23]S.L.Clegg,K.S.Pitzer,Thermodynamics of multicomponent,miscible,ionic solutions:generalized equations for symmetrical electrolytes,J.Phys.Chem.96(8)(1992)3513–3520.

[24]C.C.Chen,L.B.Evans,A local composition modelfor the excess Gibbs energy of aqueous electrolyte systems,AIChE J.32(3)(1986)444–454.

[25]R.Deshmukh,A.Mather,A mathematical model for equilibrium solubility of hydrogen sul fide and carbon dioxide in aqueous alkanolamine solutions,Chem.Eng.Sci.36(2)(1981)355–362.

[26]G.Cybenko,Approximation by superpositions of a sigmoidal function,Math.Control Signals Syst.2(4)(1989)303–314.

[27]M.Rezakazemi,S.Razavi,T.Mohammadi,et al.,Simulation and determination of optimum conditions of pervaporative dehydration of isopropanol process using synthesized PVA–APTEOS/TEOS nanocomposite membranes by means of expert systems,J.Membr.Sci.379(1–2)(2011)224–232.

[28]M.Rostamizadeh,M.Rezakazemi,K.Shahidi,et al.,Gas permeation through H2-selective mixed matrix membranes:experimental and neural network modeling,Int.J.Hydrog.Energy 38(2)(2013)1128–1135.

[29]M.Rezakazemi,T.Mohammadi,Gas sorption in H2-selective mixed matrix membranes:experimental and neural network modeling,Int.J.Hydrog.Energy 38(32)(2013)14035–14041.

[30]M.Rezakazemi,A.Dashti,M.Asghari,et al.,H2-selective mixed matrix membranes modeling using ANFIS,PSO-ANFIS,GA-ANFIS,Int.J.Hydrog.Energy 42(22)(2017)15211–15225.

[31]N.Azizi,M.Rezakazemi,M.M.Zarei,An intelligent approach to predict gas compressibility factor using neural network model,Neural Comput.&Applic.(2017)1–10.

[32]S.Mazinani,R.Ramazani,A.Samsami,et al.,Equilibrium solubility,density,viscosity and corrosion rate of carbon dioxide in potassium lysinate solution,Fluid Phase Equilib.396(2015)28–34.

[33]S.Shen,Y.Yang,Y.Wang,et al.,CO2absorption into aqueous potassium salts of lysine and proline:density,viscosity and solubility of CO2,Fluid Phase Equilib.399(2015)40–49.

[34]P.J.Rousseeuw,A.M.Leroy,Robust Regression and Outlier Detection,Vol.589,John Wiley&Sons Inc.,Hoboken,New Jersey,2005.

[35]M.Mesbah,E.Soroush,V.Azari,et al.,Vapor liquid equilibrium prediction of carbon dioxide and hydrocarbon systems using LSSVM algorithm,J.Supercrit.Fluids 97(2015)256–267.

[36]M.Mesbah,E.Soroush,A.Shokrollahi,et al.,Prediction of phase equilibrium of CO2/cyclic compound binary mixtures using a rigorous modeling approach,J.Supercrit.Fluids 90(2014)110–125.

[37]E.Soroush,M.Mesbah,A.Shokrollahi,et al.,Prediction of methane uptake on different adsorbents in adsorbed natural gas technology using a rigorous model,Energy Fuel 28(k)(2014)6299–6314.

[38]E.Soroush,M.Mesbah,A.Shokrollahi,et al.,Evolving a robust modeling tool for prediction of natural gas hydrate formation conditions,J.Unconv.Oil Gas Res.12(2015)45–55.

[39]M.Mesbah,E.Soroush,M.Rostampour Kakroudi,Predicting physical properties(viscosity,density,and refractive index)of ternary systems containing 1-octyl-3-methyl-imidazolium bis(tri fluoromethylsulfonyl)imide,esters and alcohols at 298.15 K and atmospheric pressure,using rigorous classi fication techniques,J.Mol.Liq.225(2017)778–787.

[40]M.Mesbah,E.Soroush,M.Rezakazemi,Development of a least squares support vector machine model for prediction of natural gas hydrate formation temperature,Chin.J.Chem.Eng.25(9)(2017)1238–1248.