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. 2021 May 5;6(19):12459–12469. doi: 10.1021/acsomega.0c06158

Evaluation of CO2 Absorption by Amino Acid Salt Aqueous Solution Using Hybrid Soft Computing Methods

Amir Dashti †,*, Farid Amirkhani †, Amir-Sina Hamedi ‡, Amir H Mohammadi §,*
PMCID: PMC8154155  PMID: 34056396

Abstract

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Amino acid salt (AAs) aqueous solutions have recently exhibited a great potential in CO2 absorption from various gas mixtures. In this work, four hybrid machine learning methods were developed to evaluate 626 CO2 and AAs equilibrium data for different aqueous solutions of AAs (potassium sarcosinate, potassium l-asparaginate, potassium l-glutaminate, sodium l-phenylalanine, sodium glycinate, and potassium lysinate) gathered from reliable references. The models are the hybrids of the least squares support vector machine and coupled simulated annealing optimization algorithm, radial basis function neural network (RBF-NN), particle swarm optimization–adaptive neuro-fuzzy inference system, and hybrid adaptive neuro-fuzzy inference system. The inputs of the models are the CO2 partial pressure, temperature, mass concentration in the aqueous solution, molecular weight of AAs, hydrogen bond donor count, hydrogen bond acceptor count, rotatable bond count, heavy atom count, and complexity, and the CO2 loading capacity of AAs aqueous solution is considered as the output of the models. The accuracies of the models’ results were verified through graphical and statistical analyses. RBF-NN performance is promising and surpassed that of other models in estimating the CO2 loading capacities of AAs aqueous solutions.

1. Introduction

Carbon dioxide (CO2) footprint is one of the most impactful environmental issues contributing to global warming. Various human activities such as deforestation, fossil fuel combustion for transportation, industries, and so on are the main sources of CO2 emission.1,2 Climate change due to greenhouse gases is now threatening our habitation on earth more than ever; therefore, scientists are actively upgrading CO2 capture technologies to mitigate CO2 pollution. These technologies can be generally categorized into pre-combustion, oxy-combustion, and post-combustion levels.3,4 Adsorption, cryogenic separation, membrane separation, absorption, and so on are examples for the abovementioned classification.5−9 The most prevalent technique among them is chemical absorption due to its high absorption rate and capacity.10 However, a suitable solvent selection comprises multiple facets such as CO2 loading capacity, absorption/desorption rate, regeneration rate, toxicity, corrosion, volatility, and so on.11

Alkanolamine aqueous solutions and other types of amine aqueous solutions of primary, secondary, tertiary, and sterically hindered amine solutions have been used and proposed for CO2 capturing from flue and industrial gas streams. One of the most widely used chemical absorbents among them is the aqueous monoethanolamine (MEA) solution featuring a fast absorption rate, acceptable thermal stability, low hydrocarbon loading capacity, and cost effectiveness. Despite these, the disadvantages are high energy consumption and high vaporization rate, solvent degradation causing corrosion, foaming, and fouling in vessels and pipelines.10−12 Ionic liquids are other types of CO2 absorbents with a low vaporization rate. However, they suffer from a low CO2 absorption rate, high cost, and high viscosity.13

In the past decade, amino acid salt (AAs) aqueous solutions, which are the products of amino acids and alkaline compounds, have shown a superior potential for replacing alkanolamines in CO2 capture and separation. AAs aqueous solutions have high chemical reactivity due to a higher value of pKa than that of amine aqueous solutions. Accordingly, the high surface tension of AAs enables them to properly bind to CO2.14 They are also more stable against oxidative degradation, with low viscosity and low volatility due to the ionic structure.11,15 Nonetheless, AAs are more costly and heavier than MEA, which may result in higher absorber size in some high-fraction CO2 gas streams such as biogas.16

Few researchers have tried to experimentally measure the equilibrium solubility of CO2 in AAs aqueous solutions under different operating conditions, CO2 partial pressures, and absorbent concentrations. In a study, Kang et al.(17) reported the solubility of CO2 in different amino acid-based aqueous solutions. Those compounds were 4 M potassium sarcosinate (K-SAR), a mixture of 1.5 M potassium alaninate and piperazine (K-ALA–PZ), and a mixture of 1.5 M potassium serinate and piperazine (K-SER–PZ) in a temperature range of 313.15–353.15 K. In another study,18 a solution of potassium prolinate (KPr) mixed with piperazine (PZ) in 1, 4, and 10 wt % concentrations was used to measure the solubility of CO2, which shows a very high loading capacity. The experimental conditions were ranging at 4.8–2383.2 kPa CO2 partial pressure and a temperature of 293.15–323.15 K. Both studies concluded that the absorbate solubility decays with an increase in temperature. In some cases, precipitation of AA may occur, which results in shifting the reaction toward products and further CO2 absorption.19,20 Kumar et al.(19) measured the solubility of CO2 in potassium taurate aqueous solution in a temperature range of 298–313 K and concentration range of 0.5–4 M. They developed a simple model to interpret the observed crystallization of one of the products during the equilibrium.

Another category of studies focused on measuring the thermophysical properties of AAs to estimate CO2 absorption. In a study,21 the thermophysical properties of various AAs aqueous solutions were measured in temperature and concentration ranges of 298–333 K and 0.25–3.5 M, respectively. Using the analogy of N2O and CO2 and employing Schumpe’s method, CO2 solubility was estimated based on N2O solubility measurements. In a similar study, Garcia et al.(22) measured viscosity, electrolytic conductivity, density, and the refractive index of potassium for sodium salt aqueous solutions of a-aminobutyric acid at 303.15–343.15 K to correlate these properties under different operating conditions.

As mentioned earlier, limited information is available on the solubility of CO2 in AAs aqueous solutions under different operating conditions because performing experimental studies is normally time-consuming, expensive, and dangerous in some cases. Moreover, experimental results are normally reported in limited ranges of operating conditions.23−25 Although models require experimental data for verification and validation, an in-depth understanding and sensitivity analysis of CO2 and AAs aqueous solution vapor–liquid equilibrium (VLE) require advanced models.

Thermodynamic models utilize different principles to predict/estimate CO2 solubility in AAs aqueous solutions. For instance, the Kent and Eisenberg26 model, which is empirical-based, considers non-idealities lumped in equilibrium constants. Another category of models such as Austgen et al.,27 Clegg and Pitzer,28 the electrolyte–NRTL model of Chen and Evans,29 and Deshmukh and Mather30 uses excess Gibbs free energy. Also, there are some equations of state (EoS) that characterize the non-idealities of CO2 and AAs aqueous solutions VLE. Although these EoS such as SAFT and CPA can reasonably predict/estimate CO2 solubility in AAs aqueous solutions, they suffer from lack of information available regarding some thermophysical properties of AAs.

Machine learning as a powerful tool can predict/estimate equilibrium properties for CO2 absorption using measured data.31−34 To predict/estimate outputs of a regeneration system in a gas sweetening plant, Salooki et al.(35) used an artificial neural network (ANN) method. They used some input variables including the inlet temperature of reflux, the difference between inlet and outlet condenser temperatures, and so on to build the ANN. In a similar study,36 support vector machine (SVM) and ANN methods were compared to estimate the process output variables of the same plant; consequently, the SVM showed a better agreement with experimental data. Accordingly, Ghiasi and Mohammadi37 used the same tools to predict/estimate the circulation rate of MEA aqueous solution. In another study,38 an adaptive neuro-fuzzy inference system (ANFIS) was employed to model the CO2 loading capacity of MEA, DEA, and TEA aqueous solutions used in the CO2 removal from natural gas streams. The results were significantly improved compared to their previous LSSVM model. As mentioned earlier, the most commonly used machine learning techniques in the literature are the ANN, LSSVM, and ANFIS. A comprehensive review of these methods for modeling of CO2 equilibrium absorption is given elsewhere.39

This study aimed to develop hybrids of machine learning methods (soft computing methods) to model the CO2 loading capacities of AAs aqueous solutions. For this purpose, we employed least squares support vector machine and coupled simulated annealing optimization algorithm (CSA-LSSVM), radial basis function neural network (RBF-NN), particle swarm optimization–ANFIS (PSO-ANFIS), and hybrid ANFIS models as the machine learning methods.

2. Model Development

2.1. Least Squares Support Vector Machine

One of the most powerful strategies that is frequently used in data mining to process data and recognize patterns is the SVM.40−42 The SVM builds a function as follows43

2.1. 1

in which φ(x) is the kernel function, wT represents the transpose of the weight vector of the output layer, and b denotes the bias term. x in this equation stands for the matrix vector with the N × n dimension, in which N is the number of data points and n represents the number of input parameters to the model. Later on, wT and b need to be optimized via the following objective function in eq 2, which should be minimized and is exposed to the subsequent constraints in eq 3(44−46)

2.1. 2
2.1. 3

where x, y, and ε are the input vector, output vector, and fixed precision term of the interpolating function, respectively. ξk and ξk* are positive slack terms. The Lagrangian form of this equation can be applied to solve the minimization problem in the previous equation as follows47

2.1. 4
2.1. 5
2.1. 6

ak and ak* denote Lagrangian multipliers in the preceding equations. After applying the Lagrangian multipliers and related constraints, the SVM function of the minimization problem can be expressed as given below47

2.1. 7

in which K represents the Kernel function.

Pelckmans et al.(40) introduced a modified version of the SVM, which mathematically solves several linear equations to obtain the best solution. The LSSVM model presents the optimization function and the constraint in eqs 8 and 9 instead of the traditional way of optimizing the error in the SVM47

2.1. 8
2.1. 9

where ek and μ indicate the error and an tunable variable corresponding to the LSSVM architecture model, respectively. Likewise, the Lagrangian form of the objective function as given below helps us to solve the optimization problem47

2.1. 10

By solving the system of equations presented in eq 10, one can obtain the 2N + 2 equation with 2N + 2 unknown parameters (αk, ek, w, and b). Therefore, the LSSVM variables will be set by solving the abovementioned equations. In this work, we choose the RBF out of existing kernel functions, which is defined as follows47

2.1. 11

in which σ2 suggests the tunable variable of the LSSVM model. These two variables σ2 and μ can be tuned/adjusted by minimizing the cost function, which is the mean squared error (MSE) of the LSSVM model and actual values as follows48

2.1. 12

where ypred denotes the values provided by the LSSVM and yexp represents the experimental data values. In the current study, we used the CSA method introduced by Xavier-de-Souza et al.(49) to adjust the value of these parameters. The LSSVM and CSA are normally coupled to reach the best performance in terms of accuracy and reliability.

2.2. Radial Basis Function Neural Network

The RBF neural network is one of the subcategories of the ANN, which can classify the complex systems and specify the type of associated non-linearity with them. The RBF-NN is a three-layer feed-forward network composed of an input, hidden, and output layer.50 The input layer is responsible for transmitting the input vector to the hidden layer by a transfer function. The number of input nodes in the input layer is equal to the number of input parameters to the model. In the next step, the hidden layer transmits the input data to a higher dimensioned space in the hidden space.51 All nodes in the hidden layer, unlike other neural networks, are located at a specific point with a particular radius. The amount of space involving the input vector and the center is computed in each neuron.52 A RBF transfers this calculated space from the hidden layer to the output layer. In the present work, we used the Gaussian transfer function as shown in eq 13 as the basis function of RBF because of a smoother response53

2.2. 13

in which r denotes the Euclidean distance between the input vector and RBF and σ is the spread coefficient that represents the smoothness of the interpolation, which is adjusted by users. Ultimately, the output layer linearly sums up all the outputs of the hidden layer as expressed below53

2.2. 14

where ∥x – c∥ is the Euclidean distance involving the input vector and RBF center, c denotes the RBF center, x represents the input vector, and ω is the weight that connects the nodes. Also, j = 1, ... , N where N represents the number of neurons in the hidden layer and k = 1, ... , M where M indicates the input vector size.

Two important parameters that determine the performance of the RBF-NN are the spread coefficient and the maximum number of neurons (MNN). Thus, it is critical to assign an optimal value for these parameters to obtain a precise and reliable result from this method.

2.3. Adaptive Neuro-Fuzzy Inference System

The ANFIS combines the principles of the ANN and fuzzy logic to overcome the shortcomings of each model individually.54 The ANFIS consists of anodes in a five-layer network to build an inference system for predicting/estimating parameters in non-linear systems.55,56 The fuzzy logic helps us to construct this inference through the training step.57 The ANFIS utilizes membership functions (MFs) to define each node output Oij, in which i is the number of nodes in layer j. The MF for a node is as follows58

2.3. 15
2.3. 16

where x or y represents the input vector of the node, Oi1 represents the MF of a fuzzy set (A1, A2, B1, or B2) and it sets the amount that the input vector correlates to the quantifier A, Ai or Bi-2 denotes linguistic label of the adaptive node, and μAior μBi-2 is the MF of set A or B. The MF, which is normally generalized bell functions, is as follows58

2.3. 17

The MF takes a different shape by changing the parameter set pi, qi, and ri. In the second layer, the node function is multiplied by the input signals to produce the output as follows58

2.3. 18

wi represents the firing strength. In the next layer, firing strength is normalized by the sum of all firing strengths as follows58

2.3. 19

In the fourth layer, each node, using the normalized firing strength w̅i and parameter set ai, bi, and ci referred to as consequence parameters, computes the output as expressed below58

2.3. 20

In the last layer, the summation of all input signals evaluates the final output as follows58

2.3. 21

It is worth noting that in the current study, we used a genetic algorithm (PSO) to find the optimum value for MFs.

3. Development of Models

In this study, we developed hybrid models to estimate the CO2 loading capacities of AAs aqueous solutions. The CO2 loading capacity function is as follows

3. 22

in which PCO2 (kPa) is the CO2 partial pressure in equilibrium, T (K) represents the temperature, wt % is the mass concentration of the solution, MwAAs (g/mol) denotes the molecular weight of AAs, HBD, HBA, RB, and HA are the hydrogen bond donor count, hydrogen bond acceptor count, rotatable bond count, and heavy atom count, respectively. “Training” and “testing” of the experimental data were randomly chosen with 80–20% ratio with a range presented in Table 1. In order to build up the models, PCO2 (kPa), T (K), wt %, MwAAs (g/mol), HBD, HBA, RB, HA, and complexity are regarded as the input parameters and CO2 loading capacity (α, mole of CO2 per mole of AAs) is considered as the output parameter. The input and output data are introduced to MATLAB software. The training data set is utilized to train the models, and the test data set is used to evaluate the accuracy of the models. In order to obtain the best LSSVM model, μ and σ2 should be obtained using the CSA algorithm. In order to find the optimum structure of the ANFIS model, hybrid and PSO algorithms were used. The spread coefficient and the MNN are the key parameters among the other adjusting parameters in the RBF-NN model, which directly affect the model performance. In this work, we employed a trial and error approach to pick optimum values for these parameters. In other words, we defined various RBF-NN structures by adjusting the values for these two variables. These functions then assigned the optimum values to these parameters by minimizing the MSE between the output of the model and the target.

Table 1. Detail of the Data Used in This Study.

AAs temperature (K) weight % CO2 partial pressure (kPa) CO2 loading ref.
potassium sarcosinate 353.2 50.9 4.6–950.6 0.41–0.83 (59)
potassium l-asparaginate 313.2–353.2 8.5–34 7.2–951.2 0.17–1.22 (59)
potassium l-glutaminate 313.2–353.2 9.2–36.8 5.1–871.4 0.28–1.44 (59)
sodium l-phenylalanine 303.15–333.15 0.1–0.25 1.5–23.11 0.164–1.75 (60)
sodium glycinate 313.15–333.15 5–25 0.06–773.5 0.0023–1.749 (61)
potassium lysinate 298.2–353.2 9–41.2 0.47–115.26 0.641–1.781 (62)
total 298.2–353.2 0.1–50.9 0.06–951.2 0.0023–1.781  
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4. Results and Discussion

As mentioned earlier, the LSSVM model requires the CSA algorithm to calculate the optimum values for μ and σ2 parameters. These values were calculated as 526.74 and 5.29, respectively.

Because no explicit model was found in the literature to determine the minimum number of MFs,63,64 we used a trial and error method to estimate it, and Gaussian-type MFs achieved the best result. The ANFIS based on FCM included 14 rules, and the model properties are reported in Table 2. We set the model training as 1500 epochs. The model with the minimum test error was selected as the main one. A hybrid learning method was used for parameter estimation. In addition, we employed PSO65−67 to evaluate the optimal values and train the ANFIS model.

Table 2. Developed ANFIS Properties Employed for the Estimation of CO2 Absorption by AAs Aqueous Solutions.

variable value
fuzzy type Sugeno-type
initial FIS Genfis3
MF Gaussian
output MF linear
optimization technique hybrid
no. of fuzzy rules 14
epoch no. 1500
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The literature suggests a generalized Gaussian function for the MFs in the fuzzy subdomain.68−73Table 3 reports PSO-ANFIS model properties used to estimate CO2 absorption by the AAs aqueous solutions. The optimum values for the spread coefficient and MNN were obtained as 65 and 195, respectively. Changes in the MSE, which is necessary to track in each step, are shown in Figure 1.

Table 3. Variables in the PSO-ANFIS Model Used for the Estimation of CO2 Absorption by AAs Aqueous Solutions.

parameter description/value
Iterations 100 200 500 100 200 500 100 200 500 100
amount of particles 10 10 10 20 20 20 30 30 30 50
initial inertia weight (Wmin) 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
inertia weight damping ratio (Wdamp) 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
cognitive acceleration (C1) 1 1 1 1 1 1 1 1 1 1
social acceleration (C2) 2 2 2 2 2 2 2 2 2 2
no. of fuzzy rules 10 10 10 10 10 10 10 10 10 10
R2 (test data) 0.7318 0.7749 0.7459 0.7430 0.7563 0.7706 0.7748 0.7936 0.7886 0.7880
% AARD (test data) 21.54 18.21 20.93 20.05 19.92 17.92 17.50 16.68 18.17 17.20
parameter description/value
iterations 200 500 100 200 500 100 200 500 200 500
amount of particles 50 50 75 75 75 100 100 100 200 200
initial inertia weight (Wmin) 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
inertia weight damping ratio (Wdamp) 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
cognitive acceleration (C1) 1 1 1 1 1 1 1 1 1 1
social acceleration (C2) 2 2 2 2 2 2 2 2 2 2
no. of fuzzy rules 10 10 10 10 10 10 10 10 10 10
R2 (test data) 0.8332 0.8157 0.7522 0.7858 0.8152 0.7903 0.8133 0.8291 0.8877 0.8177
% AARD (test data) 14.40 16.57 17.29 14.49 14.36 16.67 16.41 15.27 11.07 13.22
parameter description/value
iterations 1000 500 1000 500 800 1000 1200 2000 2000 500
amount of particles 200 150 150 250 250 250 250 250 300 400
initial inertia weight (Wmin) 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
inertia Weight Damping Ratio (Wdamp) 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
cognitive acceleration (C1) 1 1 1 1 1 1 1 1 1 1
social acceleration (C2) 2 2 2 2 2 2 2 2 2 2
no. of fuzzy rules 10 10 10 10 10 10 10 10 10 10
R2 (test data) 0.8340 0.7826 0.8432 0.8171 0.8301 0.8769 0.9221 0.8625 0.8697 0.8316
% AARD (test data) 11.81 14.82 12.87 13.82 12.95 10.61 10.00 11.77 11.37 14.02
parameter description/value
iterations 1000 1200 1200 1200 1200 1200 1200 1200    
amount of particles 400 250 250 250 250 250 250 250    
initial inertia weight (Wmin) 0.5 0.5 0.1 0.7 0.9 0.5 0.5 0.5    
inertia Weight Damping Ratio (Wdamp) 0.99 0.99 0.99 0.99 0.99 0.1 0.5 0.75    
cognitive acceleration (C1) 1 2 1 1 1 1 1 1    
social acceleration (C2) 2 1 2 2 2 2 2 2    
no. of fuzzy rules 10 10 10 10 10 10 10 10    
R2 (test data) 0.8231 0.7978 0.9160 0.8137 0.9103 0.9182 0.9293 0.8395    
% AARD (test data) 10.56 17.54 11.79 13.45 9.446 9.750 7.661 13.75    
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Figure 1.

Figure 1

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Convergence of the RBF-NN to the best structure.

4.1. Model Accuracy and Validation

The models’ performance is validated through graphical and statistical methods. Figure 2 compares the values estimated by the model against the experimental data used in this work. The correlation coefficients of the regression line for the RBF-NN are higher than those of the other models, and the best fit line significantly lies over the 45° line, indicating a good agreement between model results and real measurements. Considering the correlation coefficient of 0.9752 for the RBF-NN, the model output displays a superior fit with actual data. Figure 3 illustrates the consistency of models’ output versus the experimental data in terms of relative deviation for absorption of CO2 by the solutions. According to Figure 3, the maximum relative deviations for the CSA-LSSVM, RBF-NN, PSO-ANFIS, and hybrid ANFIS are 1.54, 6.66, 21.21, and 21.62, respectively.

Figure 2.

Figure 2

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Regression plot for the absorption of CO2 prognostication by (a) LSSVM, (b) RBF-NN, (c) PSO-ANFIS, and (d) ANFIS.

Figure 3.

Figure 3

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Relative deviation of the estimated CO2 absorption values for both test and train data points by (a) LSSVM, (b) RBF-NN, (c) PSO-ANFIS, and (d) ANFIS.

Obviously, the lowest relative deviation belongs to the PSO-ANFIS because the relative error of this model lies in the range of 0–0.3. Figure 4 depicts the model estimations versus the actual data point index to gain a realistic sense of model precision; the result indicates a good fit between model results and real measurements.

Figure 4.

Figure 4

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Actual CO2 absorption versus estimated data at testing and training stages for (a) LSSVM, (b) RBF-NN, (c) PSO-ANFIS, and (d) ANFIS.

Four additional data analysis parameters including the correlation factor (R2), average absolute relative deviation (AARD), standard deviation (STD), and root mean squared error (RMSE) are shown in Table 4 to demonstrate the models’ performances. In the following equations, x stands for the CO2 absorption56

4.1. 23
4.1. 24
4.1. 25
4.1. 26

Table 4. Accuracies of Different Models.

  parameter
model train test total
LSSVM
R2 0.9326 0.9036 0.9262
MSE 0.0078 0.0111 0.0085
STD 0.3263 0.3170 0.3244
% AARD 59.40 13.45 50.23
RBF-NN
R2 0.9913 0.9155 0.9753
MSE 0.0010 0.0103 0.0028
STD 0.3390 0.3450 0.3402
% AARD 6.86 9.33 7.350
PSO-ANFIS
R2 0.9519 0.9293 0.9464
MSE 0.0056 0.0084 0.0061
STD 0.3285 0.3354 0.3298
% AARD 19.07 7.66 16.79
ANFIS
R2 0.9451 0.9157 0.9390
MSE 0.0064 0.0095 0.0070
STD 0.3310 0.3176 0.3283
% AARD 15.76 10.09 14.63
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The RBF-NN model results in a higher correlation coefficient and lower MSE, AARD %, and STD, which conveys a more promising performance for this model against other models. Table 5 demonstrates the % AARD, which is estimated by the developed models. As can be seen, except in the case of potassium l-asparaginate that the ANFIS AARD is lower than other models’ AARDs, the RBF-NN AARD is lower than other models’ AARD in other cases.

Table 5. % AARD for Each AAs Aqueous Solution Estimated by the Developed Model.

  % AARD
  
AAs LSSVM RBF-NN PSO-ANFIS ANFIS no. data
potassium sarcosinate 4.20 0.427 7.95 3.64 12
potassium l-asparaginate 5.59 4.23 6.48 3.88 91
potassium l-glutaminate 6.11 2.87 5.17 3.90 100
sodium l-phenylalanine 16.90 6.43 10.56 15.89 63
sodium glycinate 226.1 24.44 17.50 47.71 123
potassium lysinate 5.88 1.88 5.17 6.25 237
total 50.23 7.35 16.79 14.63 626
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Accordingly, Figure 5 provides a more clear picture to evaluate the aforementioned parameters and endorses the excellence of the RBF-NN in estimating the CO2 absorption compared to other models.

Figure 5.

Figure 5

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Absorption of CO2 by an aqueous solution of 0.25 wt % sodium l-phenylalanine at 313.15 K. Experimental data.60

Figures 6 and 7 demonstrate the impact of pressure at various temperatures and concentrations of aqueous sodium l-phenylalanine (Na-Phe) solution. According to these figures at a given temperature and concentration, CO2 absorption increases as the CO2 pressure rises, which directly affects the CO2 loading. The reason is that an increase in pressure reproduces the collision of gas molecules on the solution surface, which subsequently helps CO2 molecules diffuse into the solution to a greater extent.74Figure 6 shows the effect of temperature on the loading. Since the absorption is an exothermic process, as per Le Chaterlier’s principle, an increase in temperature results in a decrease in CO2 absorption.75 Therefore, temperature impacts CO2 solubility conversely. Accordingly, as Figure 7 depicts, CO2 loading decreases as Na-Phe concentration increases in the solution. CO2 loading is defined as the absorbed moles of CO2 per mole of AAs in the solution. Consequently, because Na-Phe moles increase more rapidly compared with absorbed CO2 moles, the CO2 loading declines as Na-Phe concentration increases.60

Figure 6.

Figure 6

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Absorption of CO2 by an aqueous solution of 0.2 wt % sodium l-phenylalanine at different temperatures. Experimental data.60

Figure 7.

Figure 7

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Absorption of CO2 by different aqueous solutions of sodium l-phenylalanine solution at 313.15 K. Experimental data.60

4.2. Sensitivity Analysis

To investigate the effects of input parameters on the CO2 and AAs aqueous solution equilibrium, a sensitivity analysis was performed. The relevancy factor (r) with directionality in Pearson correlation helps us to gain a clearer understanding of the input parameter influences on the system as follows76,77

4.2. 27

in which Li and L̅ denote the ith and the average values of CO2 loading, respectively, and Vj,i and V̅j represent the ith and average values of the jth input variable, respectively. The relevancy factor ranges from −1 to 1, where a negative value indicates a decreasing correlation between the input variables and the loading, a positive value indicates the opposite, and zero means no correlation. Figure 8 clearly illustrates that the RB value impacts the loading the most with an increasing correlation. The molecular weight (Mw) of the AAs is the second noticeable factor that raises the loading as it increases. Moreover, there are two other parameters that slightly influence CO2 loading. Temperature and amine concentration have a negative effect on the loading.

Figure 8.

Figure 8

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Sensitivity analysis of the RBF-NN model.

5. Conclusions

Four hybrid machine learning models were developed to estimate CO2 loading capacities of AAs aqueous solutions, namely, potassium sarcosinate, potassium l-asparaginate, potassium l-glutaminate, sodium l-phenylalanine, sodium glycinate, and potassium lysinate as a function of temperature, mass concentration of AAs in the aqueous solution, molecular weight of AAs, HBD, HBA, RB, HA, and complexity. The four methods are the CSA-LSSVM, RBF-NN, PSO-ANFIS, and hybrid ANFIS, among which the RBF-NN outperformed other methods in estimating the CO2 loading capacities of AAs aqueous solutions. The AARD %s of the model results and actual data are 13.4, 9.3, 7.6, and 10 for CSA-LSSVM, RBF-NN, PSO-ANFIS, and hybrid ANFIS models, respectively. For training and testing, experimental data points covering different AAs aqueous solutions and gathered from reliable references were utilized. The RBF-NN could estimate the CO2 loading capacities of AAs aqueous solutions with acceptable accuracy.

The authors declare no competing financial interest.

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