Artificial neural network models for the prediction of CO2 solubility in aqueous amine solutions

International Journal of Greenhouse Gas Control 39 (2015) 174–184

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International Journal of Greenhouse Gas Control journal homepage: www.elsevier.com/locate/ijggc

Artificial neural network models for the prediction of CO2 solubility in aqueous amine solutions Guangying Chen a , Xiao Luo a,∗ ∗ ∗ , Haiyan Zhang b,∗∗ , Kaiyun Fu a , Zhiwu Liang a,∗ , Wichitpan Rongwong a , Paitoon Tontiwachwuthikul a , Raphael Idem a a Joint International Center for CO2 Capture and Storage (iCCS), Provincial Hunan Key Laboratory for Cost-effective Utilization of Fossil Fuel Aimed at Reducing Carbon-dioxide Emissions, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, PR China b Department of Petroleum and Chemical Engineering, Qinzhou University, Qinzhou, Guangxi 535000, PR China

a r t i c l e

i n f o

Article history: Received 5 December 2014 Received in revised form 24 April 2015 Accepted 5 May 2015 Keywords: CO2 solubility Amine solutions Back-propagation neural network Radial basis function neural network

a b s t r a c t CO2 equilibrium solubility is an important parameter used to evaluate the performance of absorption solvents in CO2 capture processes. Back-propagation neural networks (BPNN) and radial basis function neural networks (RBFNN) were proposed to predict the CO2 solubility in 12 known amine solutions. Both of the models were firstly conducted in monoethanolamine, diethanolmine and methyldiethanolamine solutions to evaluate their effectiveness, and were then applied in nine other amine solutions to further verify their adaptability. The results showed that both BPNN and RBFNN models provided excellent agreements with the experimental values for all the amine solutions with average absolute relative errors and root mean square errors less than 10%. A comparison between the predicted results and those of the eight published models showed that the proposed ANN models performed better than the literature models. Furthermore, scalability analysis was carried out to evaluate the adaptability of BPNN and RBFNN models in terms of the wide input parameter ranges. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction The post-combustion capture process that uses an amine solvent is one of the most widely employed CO2 capture technologies because of its high absorption performance and suitability for industrial applications (Rao and Rubin, 2002; Amann and Bouallou, 2009; Tontiwachwuthikul et al., 2011). As one of the most important parameters for the absorption of CO2 in reactive chemical solvents, solubility of CO2 in solution (i.e., equilibrium CO2 loading) has received much attention in the process of CO2 capture due to its crucial role in the evaluation of the absorption effectiveness of the absorbent (Liang et al., 2011; Porcheron et al., 2011). Up to now, a variety of amine solvents have been screened and studied for the CO2 capture process, and measurements of CO2 solubility in these amine solutions have been performed by various researchers so far. Monoethanolamine (MEA), diethanolmine (DEA) and methyldiethanolamine (MDEA) are the mostly studied amines

∗ Corresponding author. Tel.: +86 13618481627; fax: +86 73188573033. ∗∗ Corresponding author. Tel.: +86 15807770798. ∗ ∗ ∗Corresponding author. Tel.: +86 18627329998. E-mail addresses: x [email protected] (X. Luo), [email protected] (H. Zhang), [email protected] (Z. Liang). http://dx.doi.org/10.1016/j.ijggc.2015.05.005 1750-5836/© 2015 Elsevier Ltd. All rights reserved.

and have been researched for decades (Jones et al., 1959; Lawson and Garst, 1976; Jou et al., 1982; Kennard and Meisen, 1984; Shen and Li, 1992; Ermatchkov et al., 2006a; Aronu et al., 2011). Recently, some novel amine solvents (such as 2-amino-2-methyl1-propanol (AMP), piperazine (PZ), 4-(diethylamino)-2-butanol (DEAB), and 2-(Diethylamino) ethanol (DEEA)) have been experimentally investigated (Tontiwachwuthikul et al., 1991; Kamps et al., 2003; Daneshvar et al., 2004b; Dong et al., 2010; Bougie and Iliuta, 2011; Rebolledo-Morales et al., 2011; Sema et al., 2011; Dash et al., 2012; Kumar and Kundu, 2012; Arshad et al., 2014). All of those studies determined the CO2 solubility at various conditions such as amine concentrations (C), operation temperatures (T) and CO2 partial pressures (PCO2 ), and have achieved high measurement accuracies with good repeatability. In addition to traditional experimental measurements, a number of thermodynamic models have been established to analyze and correlate the equilibrium solubility of CO2 within different operating conditions, such as Kent-Eisenberg model (Kent and Eisenberg, 1976; Fouad and Berrouk, 2012), electrolyte-NRTL model (Chen and Evans, 1986), Deshmukh-Mather model (Deshmukh and Mather, 1981) and extended UNIQUAC model (Haghtalab and Dehghani Tafti, 2007; Aronu et al., 2011). These well-established models were developed based on the vapor–liquid equilibrium (VLE) the-

G. Chen et al. / International Journal of Greenhouse Gas Control 39 (2015) 174–184

Nomenclature a Output value of the neuron ai The prediction value of the ith input data Aj The matrix of output values of the jth layer (j = 1–3) AARE Average absolute relative error Absolute relative error ARE AMP 2-Amino-2-methyl-1-propanol ANN Artificial neural network Bias b Bj Bias matrix of the jth layer (j = 1–3) BPNN Back-propagation neural network C Amine concentration C1 , C2 , C3 , C4 Regression coefficient Diethanolmine DEA DEAB 4-(Diethylamino)-2-butanol DEEA 2-(Diethylamino)-ethanol Transfer function of the jth layer (j = 1–3) fi g The momentum factor Henry’s constant for CO2 HCO2 k Current training iteration ki Equilibrium constants MAE Methyl amino ethanol 3-(Methylamino)-propylamine MAPA MDEA Methyldiethanolamine MEA Monoethanolamine MIPA 1-Amino-2-propanol Monoproanolamine MPA n The number of inputs pmin The minimum value among all the pi variable pmax The maximum value among all the pi variables The normalized value of input variable pi pn,i PCO2 CO2 partial pressure Input vector P PZ Piperazine Correlation coefficient R RBFNN Radial basis function neural network Root mean square error RMSE [RR’NH]0 The initial amine concentration ti The target value of the ith input data T Operation temperature Triisopropanolamine TIPA wi The weight of the ith input parameter pi W The weight vector related to P Wj Weights matrix of the jth layer (j = 1–3) Greek symbols ˛ Equilibrium CO2 loading Learning rate  ıi Radius or width of the ith hidden neuron pi − i  Euclidean distance between pi and i i The center vector of the i hidden neuron

ory, and reflected the thermodynamic properties of the CO2 -amine systems. However, there are still some limitations on the accuracy and range on those prediction models, which sometimes are only suitable for the specific amine solutions. For example, Benamor and Aroua (Benamor and Aroua, 2005) applied the DeshmukhMather model to determine the CO2 solubility in DEA and MDEA solutions as well as their mixtures at various conditions of amine concentrations (2–4 M), temperatures (30–50 ◦ C) and CO2 partial pressures (0.09–100 kPa). Although the average absolute relative errors (AAREs) for DEA and MDEA were barely acceptable (4.84% and 10.72%, respectively), the lack of studied amines (only two) and

175

the narrow ranges of concentration and temperature still hindered its subsequent applicability. Artificial neural network (ANN) is an artificial intelligence method that mimics human brain’s operation and computation performance, and processes information using certain mathematical principles. ANNs have powerful and effective nonlinear regression ability, and can reflect the system’s complexity and the input-output data groups’ inherent relationship with high confidence and precision (Hagan et al., 1996). These special capabilities have made them applicable in many areas such as machine automation, environmental science and engineering, petroleum engineering, and chemical engineering (Ozcan et al., 2006; Benardos and Vosniakos, 2007; Feng et al., 2011; Chen et al., 2014; Fu et al., 2014). In this study, two types of ANN models (i.e., back-propagation neural network (BPNN) and radial basic function neural network (RBFNN)) are proposed to predict CO2 solubility in 12 amine solutions for wide ranges of amine concentrations, temperatures and CO2 partial pressures. The amines used in this work mainly include: (i) three typical amines, i.e., MEA, DEA, and MDEA, and (ii) nine other novel amines, i.e., 2-amino-2-methyl-1-propanol (AMP), piperazine (PZ), triisopropanolamine (TIPA), monoproanolamine (MPA), 1-amino-2-propanol (MIPA), 4-(diethylamino)-2-butanol (DEAB), methyl amino ethanol (MAE), 2-(Diethylamino)- ethanol (DEEA) and 3-(Methylamino)-propylamine (MAPA). As these 12 amines covered all the three amine categories (i.e., primary, secondary and tertiary), accurate predictions of the CO2 solubility by using ANN models can be considered to overcome the limitations of theoretical models that may only be applicable to specific amines. Therefore, this study will show the applicability of ANN models for the prediction of CO2 solubility in all amine types. The study involved initially setting and training the adjustable configuration parameters of the BPNN and RBFNN models during the training processes to obtain optimized network models. The performances of these well-established models were then evaluated by comparing their prediction results with experimental data as well as the predicted results of eight numerical models proposed in the literature. In addition, scalability analysis was performed to evaluate the adaptability of BPNN and RBFNN models for predicting the CO2 solubility in various amine solutions in terms of the wide input parameter ranges. 2. Theory 2.1. Reaction mechanisms of CO2 solubility in aqueous amine solutions As is well known, CO2 absorption into an amine solution combines both physical and chemical absorptions. In order to obtain the CO2 equilibrium solubility, the concentration of CO2 in the aqueous solution needs to be calculated. The reaction of CO2 with primary and secondary amines can be explained by the zwitterion mechanism (Caplow, 1968) as expressed in the following equilibrium equations: Amine deprotonation reaction: + K1

RR NH2 ↔RR NH + H

+

(1)

Carbamate hydrolysis reaction: K2

−

RR NCOO + H2 O↔RR NH + HCO3 −

(2)

Bicarbonate formation reaction: K3

CO2 + H2 O↔HCO3 − + H+

(3)

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G. Chen et al. / International Journal of Greenhouse Gas Control 39 (2015) 174–184

Carbonate formation reaction: K4

HCO3 − + H2 O↔CO3 2− + H+

(4)

B = K2 [RR’NH2 ] + K1 K2

K5

H2 O↔H+ + OH−

(5)

Water is regarded as the reference solvent for all the chemical equilibrium equations mentioned above. The equilibrium constants of each reaction (Ki , i = 1, 2, . . ., 5) can be described by using KentEisenberg model, as expressed in terms of concentration in Eqs. (6)–(10):

K2 =

[RR’NH][H+ ] [RR’NH2 ] [RR’NH][HCO3 − ]

(7)

[RR’ NCOO− ]

(8)

[HCO3 ]

(10)

It is well known that the equilibrium constants K1 –K5 are in terms of temperature and can be expressed as: ln K = C1 + C2 /T + C3 ln T + C4 T

(11)

where C1 –C4 are the regression coefficients related to each amine solution. In addition, the physical solubility of CO2 absorption in amine solutions can be expressed by Henry’s law: PCO2 = HCO2 [CO2 ]

(12)

where PCO2 is the partial pressure of CO2 and measured during the experiment; HCO2 is the Henry’s law constant for CO2 , which is also a function of temperature and share the same expression form with K (shown in Eq. (11)). Regression coefficients (i.e., C1 –C4 ) for K and HCO2 can be obtained from the literature. There are some balance equations in the system of amine-H2 OCO2 as follows: Amine mass balance: [RR’NH]0 = [RR’NH] + [RR’NH2 + ] + [RR’NCOO− ]

(13)

[RR’NH]0 ␣ = [RR’NCOO− ] + [CO2 ] + [HCO3 − ] + [CO3 2− ]

(14)

where ␣ is the equilibrium CO2 loading, mol CO2 /mol amine. Charge balance: [H+ ] + [RR’NH2 + ] = [HCO3 − ] + [RR’NCOO− ] + 2[CO3 2− ] +[OH− ]

(15)

Besides, Eqs. (6)–(10), (13) and (15) can be reduced to a single polynomial equation (Eq. (16)) according to the concentration of hydrogen ion ([H+ ]), and [H+ ] can be obtained through the solution of this equation. The polynomial equation and its coefficients are expressed below (Aroua and Mohd Salleh, 2004).







+ B H+

−K1 K2 K3 [CO2 ] − K1 K2 K5 − 2K2 K3 K4 [CO2 ]

(16d)

E = −K1 K3 [CO2 ](K3 [CO2 ] + K5 ) − 2K1 K2 K3 K4 [CO2 ]

(16e)

5

+F H+ + G = 0



+ C H+

4



+ D H+

3



+ E H+

−2K1 K32 K4 [CO2 ]2

(16f)

Moreover, Eq. (14) can be modified using Eqs. (6)–(13) to obtain the final calculation formula of equilibrium CO2 loading (␣).



PCO2 HCO2 [RR’NH]0



1+



K3 [RR’NH]0 +

K2 [H ] +

2 (16)

2

K2 [H+ ] K1

+



+

K3 PCO

2

HCO

K3 K4 + 2

[H ]

+

K3 +

[H ]

(17)

2

From Eqs. (1)–(17), it can be concluded that CO2 solubility (i.e., equilibrium CO2 loading) is influenced by the amine concentration [RR’NH]0 (also written as C), temperature (T) and CO2 partial pressure (PCO2 ).The reactions of CO2 with tertiary amines are similar to those of CO2 with primary and secondary amines except that the tertiary amine cannot directly react with CO2 to form carbamate, but act as a base to catalyze the hydration of CO2 . The chemical equilibrium reaction of CO2 with aqueous tertiary amines can be approximated as: RR’R”NH+ + HCO3 − ↔ RR’R”N + CO2 + H2 O

(18)

Also, the calculation of CO2 solubility in tertiary amine could be expressed as a function of C, T and PCO2 . 2.2. Basic description of artificial neural networks (ANN) The basic structure units of an ANN are neurons, which are completely interconnected with neurons in adjacent layers by means of direct communication linked with associated weights (w), bias (b) and transfer functions, as shown in Eq. (19): a = f (WP + b) = f (˙wi pi + b)

where [RR’NH]0 is the initial amine concentration, mol/L. Carbon mass balance:

6

(16c)

D = K1 K3 [RR’NH2 + ][CO2 ] − 2K1 K3 [RR’NH]0 [CO2 ]

␣=

−

K5 = [H ][OH ]



−K2 (K1 [RR’NH]0 + K5 )

(9)

−

A H+

C = K1 K2 [RR’NH2 + ] + [CO2 ](K1 K3 − K2 K3 )

F=

+ [CO23 ][H ]

+

(16b)

(6)

−

[HCO3 − ][H+ ] K3 = [CO2 ] K4 =

(16a) +

Water ionization reaction:

K2 =

A = K2

(19)

where a is the output value of this neuron, P is the input vector, W is the weight vector related to P, and wi is the weight of the ith input parameter pi . An intact ANN is usually multiple-layered, which consists of one input layer, one output layer, and at least one hidden layer. Once the variables are imported from an external source to the network, they are received firstly by the input layer and orderly passed to the hidden layer(s) and then to the output layer. In an ANN model, the outputs of the former layer are the inputs of next adjacent layer, and the outputs of the last layer are the target values. Through linear or nonlinear combination of P, W, b and transfer functions, information stores into the network and then the prediction results are obtained. If the results are satisfactory, the network is ready to be used for forecasting. This type of procedure is highly amendable to predict the CO2 solubility in amine solutions, and two ANN approaches (i.e., back-propagation neural network (BPNN) and radial basis function neural network (RBFNN)) are considered for this purpose in this study.

G. Chen et al. / International Journal of Greenhouse Gas Control 39 (2015) 174–184

Predicted CO2 loading (mol/mol)

1.2

177

BPNN(AARE=4.31%) RBFNN(AARE=4.93%)

1.0

0.8

0.6

0.4

(a) for MEA 0.2 0.2 1.0

0.4

0.6

0.8

1.0

1.2

Experimental CO2 loading (mol/mol)

Predicted CO2 loading (mol/mol)

BPNN(AARE=4.89%) RBFNN(AARE=5.17%) 0.8

0.6

0.4

0.2

(b) for DEA 0.0 0.0 1.5

0.2

0.4

0.6

0.8

1.0

Experimental CO2 loading (mol/mol)

Fig. 1. The typical architectures of BPNN and RBFNN: (a) the general topology of a three-layer back-propagation neural network; (b) the schematic architecture of a radial basis function neural network.

2.2.1. Back-propagation neural network (BPNN) BPNN refers to a multilayer feed-forward network with backpropagated learning process, which is based on the steepest gradient method and is considered to be one of the most widely used network architectures (Rummelhart, 1986). The architecture of a typical three-layer BPNN is displayed in Fig. 1(a). The BPNN models used in this work are established through the following steps according to the basic principles and working mechanisms: (1) Data collection: collect the required data, and divide all input/output data pairs into two parts, i.e., training dataset and testing dataset. (2) Data normalization: all data are normalized (between −1 and 1) initially in order to decrease the sample distribution range, accelerate the calculation and training speed, and then acquire good prediction results. It is well known in the literature that this data preprocessing procedure is indispensable, especially when the values of these input/output variables differ by more than one order of magnitude. Data normalization is performed according to the formula given in Eq. (20): pn,i = 2

pi − pmin −1 pmax − pmin

(20)

Predicted CO2 loading (mol/mol)

BPNN(AARE=3.96%) RBFNN(AARE=5.49%)

1.0

0.5

(c) for MDEA 0.0 0.0

0.5

1.0

1.5

Experimental CO2 loading (mol/mol) Fig. 2. Comparison between the predicted CO2 solubility values and the experimental ones in MEA, DEA and MDEA solutions.

where pn,i is the normalized value of input variable pi (i = C, T and PCO2 ), pmin and pmax are the minimum and maximum value among all the pi variables, respectively. (3) Network configuration confirmation: all network configuration parameters (i.e., hidden layers, number of neurons in each hidden-layer, training algorithm, transfer functions, and so on) are modified by a trial and error method to obtain the optimized network structure. (4) Information transfer: information flows towards a feedforward propagation process, as the input layer receives the input data and passes them to hidden-layer(s) and then to the output layer, which is also demonstrated in Eq. (21) (for a three-layer

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G. Chen et al. / International Journal of Greenhouse Gas Control 39 (2015) 174–184

Table 1 Literature experimental data that used for the solubility prediction in CO2 -amine systems. Amine

CMEA (mol/L)

T (◦ C)

PCO2 (kPa)

␣

Number of data points

References

MEA

1–9.8

25–170

0.1–10000

0.211–2.152

577

DEA

1–4

30–205

0.492–4373

0.081–1.167

226

MDEA

0.42–8

25–200

1.7–7565

0.016–1.833

485

AMP

1–11.2

20–120

1.077–6987

0.103–2.49

507

PZ

0.1–12

15–120

0.065–9560

0.073–2.77

301

TIPA MPA MIPA DEAB MAE DEEA MAPA

2 2–5 3.33–13.32 1–5 1–4 5 1–2

30–70 40–130 40–120 25–60 30–50 40–120 40–120

10.73–78.42 2.5–704.9 0.2–2436.4 9–100 1–355.9 0.6–577.1 0.3–534.5

0.06–0.501 0.19–1.024 0.213–1.114 0.52–1.03 0.366–1.162 0.015–1.038 0.345–1.875

25 101 60 60 72 91 94

(Jones et al., 1959; Lee et al., 1976; Austgen et al., 1991; Shen and Li, 1992; Jou et al., 1995; Park et al., 2002; Daneshvar et al., 2004a; Ma’mun et al., 2005 Aronu et al., 2011; Xu and Rochelle, 2011) (Lawson and Garst, 1976; Kennard and Meisen, 1984; Haji-Sulaiman et al., 1998) (Jou et al., 1982; Chakma and Meisen, 1987; Shen and Li, 1992; Kuranov et al., 1996; Rho et al., 1997; Kamps et al., 2001; Park and Sandall, 2001; Ma’mun et al., 2005 Ermatchkov et al., 2006a) (Tontiwachwuthikul et al., 1991; Seo and Hong, 1996; Silkenbäumer et al., 1998; Kundu et al., 2003; Dash et al., 2011; Pahlavanzadeh et al., 2011; Shariff et al., 2011; Dash et al., 2012; Tong et al., 2012) (Kamps et al., 2003; Derks et al., 2005; Ermatchkov et al., 2006b; Dugas and Rochelle, 2009; Kadiwala et al., 2010; Bougie and Iliuta, 2011) (Daneshvar et al., 2004b) (Dong et al., 2010) (Rebolledo-Morales et al., 2011) (Sema et al., 2011) (Kumar and Kundu, 2012) (Arshad et al., 2014) (Arshad et al., 2014)

CO2

(mol/mol)

BPNN): A3 = f3 (W3 A2 + B3 ) = f3 (W3 (f2 (W2 A1 + B1 )) + B3 = f3 (W3 (f2 (W2 (f1 (W1 P + B1 )) + B3 )

(21)

where Aj, Wj and Bj are the matrix of output values, weights and biases of the jth layer respectively, and fj is the transfer function (j = 1–3). (5) Error calculation: calculate the errors between the network outputs and the desired ones. If the errors are acceptable, training is stopped and the optimized network architecture is obtained. (6) Weights and biases adjustment: If the calculated errors are unacceptable, they are back propagated and the connection weights and biases are adjusted along with the reverse path of the information transfer. Weights and biases are adjusted according to Eqs. (22) and (23), respectively. wk+1 = wk + k gk

(22)

bk+1 = bk + k gk

(23)

where  is the learning rate, g is the momentum factor and k is current training iteration. (7) Steps 4–6 are repeated until the network is able to predict the given output within the desired tolerance.

It should be noted that although the performance of BPNN has been successfully validated by some researchers, it has the drawbacks of slow learning convergence rate and can easily be trapped in a local minimum or over-fitting. Therefore, more and deeper investigation should be done to quicken the learning rate as well as to avoid local minimum or over-fitting problems. 2.2.2. Radial basis function neural network (RBFNN) RBFNN is a feed-forward network with only one hidden layer. According to the literature, the most notable characteristic of RBFNN lies in its hidden layer structure, which uses distance function (e.g., Euclidean distance) as the “base” and the radial basis function (e.g., Gaussian function) as the transfer function (Park and Sandberg, 1991; Beatson and Newsam, 1992). The radial basis function is presented as a nonnegative nonlinear function with a radial symmetry center in n-dimensional space. Every hidden neuron of RBFNN has a data center, the farther the neuron from the center, the lesser its activation. This is its main difference from BPNN and other multilayer perceptrons. The architecture of RBFNN is shown in Fig. 1(b). There are several radial basis functions, the one used in this study is the Gaussian function, which is also the most widely used one and can be represented in Eq. (24):

Table 2 The best BPNN structures for CO2 solubility prediction in 12 amine solutions. Amine

Parameters N

MEA DEA MDEA AMP PZ TIPA MPA MIPA DEAB MAE DEEA MAPA

1 1 2 2 2 1 1 1 1 1 1 1

N1 5 10 12 11 10 4 3 4 3 3 4 3

N2

f1

f2

f3

Tr



g

Mi

G

/ / 7 13 6 / / / / / / /

Tansig Tansig Logsig Tansig Tansig Tansig Tansig Tansig Tansig Tansig Tansig Tansig

/ / Logsig Tansig Tansig / / / / / / /

Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin

Trainlm Trainlm Trainlm Trainlm Trainlm Trainlm Trainlm Trainlm Trainlm Trainlm Trainlm Trainlm

0.02 0.002 0.002 0.003 0.0015 0.0008 0.003 0.003 0.003 0.003 0.003 0.003

0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85

10000 10000 10000 10000 10000 10000 10000 10000 10000 10000 10000 10000

0.0012 0.001 0.00015 0.0001 0.0003 0.0003 0.0007 0.0005 0.0007 0.0007 0.0001 0.0007

Note: N is the number of hidden layer, N1–2 are the number of neurons in hidden layer 1 and 2, respectively, f1–3 are the transfer functions of each layer respectively, Tr is the training algorithm, Mi is the maximum iterations, and G is the goal error.

G. Chen et al. / International Journal of Greenhouse Gas Control 39 (2015) 174–184

often refers to the input data themselves, which (i) makes it difficult to reflect the real relationship between input and output, and (ii) increases the training time because of the large number of initial center points. This matter can be solved through the selection of proper data samples.

Predicted CO2 loading (mol/mol)

2.4

AMP PZ TIPA MPA MIPA DEAB MAE DEEA MAPA

1.8

1.2

-10%

3. Data collection

(a) for BPNN 0.6

1.2

1.8

2.4

Experimental CO2 loading (mol/mol)

2.4

Predicted CO2 loading (mol/mol)

+10%

0.6

0.0 0.0

AMP PZ TIPA MPA MIPA DEAB MAE DEEA MAPA

1.8

1.2

+20%

-20%

0.6

(b) for RBFNN 0.0 0.0

0.6

179

1.2

1.8

2.4

As is well known, data acquisition is of great importance for obtaining a good dataset that can effectively reflect the underlying nonlinearities, complexities and intricacies of the targeted system behavior. For an ANN model, the more datasets as the inputs and the more equality of the data distribution, the better prediction accuracy as a consequence. In an ANN model, all the input datasets were divided into two parts: training datasets and testing datasets. The former is used to train the ANN model to get the optimal network structure and ensure a good prediction performance, while the latter is used to evaluate the accuracy and stability of the well-trained network. About 75% of the total datasets were used for training the network while the other 25% were used for testing the already well-trained model (Tahmasebi and Hezarkhani, 2010). The reason is that if a small proportion of training datasets was used, the network cannot be well trained, and the prediction results (output data) will not be very satisfactory. On the contrary, if a small proportion of testing datasets was used, the reliability of the network cannot be well validated. That is why a reasonable ratio of training and testing datasets of 3:1 was selected and applied in the present work. The data used in this study were collected from available literature, and all the data units were modified to maintain consistency. Many datasets were gathered to make up the whole database, which corresponded to each CO2 -amine systems. All the amine types, the three parameters that have impacts on the CO2 solubility (i.e., C, T and PCO2 ), the input/target parameters ranges, the number of data points and the data sources are given in Table 1.

Experimental CO2 loading (mol/mol) Fig. 3. The comparison between the predicted CO2 solubility values and the corresponding experimental values in 9 novel amine solutions.

4. Results and discussion 4.1. The optimized BPNN and RBFNN network configurations

˚i (p) = e

−

pi −i 2 ı2 i

(24)

where i denotes the center vector of the ith hidden neuron, pi − i  is the Euclidean distance between pi and i , and ıi is the radius or width of the ith hidden neuron. It can be seen clearly that the smaller ıi is, the narrower is the width of the radial basis function, and the higher is the selectivity of the resulting radial basis function. Similar with BPNN, the design of a RBFNN mainly includes data collection, network structure modification and parameter optimization three main aspects; the complete procedure can be summarized as follows: (1) Selecting proper input-output patterns and normalizing them into [−1, 1] to obtain good datasets. (2) Determining the data center and width of the radial basis function and the weights information between hidden layer and output layer. (3) Building the main body of the RBFNN and modifying its structure using the trial and error method. This step is critical as it creates and trains the RBFNN simultaneously, consequently, the final network configuration can be obtained at the end of this step. Through the above-mentioned steps, the RBFNN can be established and well-trained up to the desired error. However, it may need more hidden neurons than BPNN because the input space of neurons is small. Furthermore, the data center of each neuron

CO2 equilibrium solubilities in 12 amine solutions were predicted by means of BPNN and RBFNN models. The predicted results were compared with their correlated experimental data respectively so as to verify the effectiveness and accuracy of the BPNN and RBFNN models. The BPNN and RBFNN models were developed and optimized by using the neural network toolbox in Matlab. During the training process, the network configuration parameters (such as (i) hidden-layer number, neurons in each hidden-layer, transfer functions, training algorithm, learning rate and iterations of BPNN; and (ii) neurons in hidden-layer, radial basis function, number of data center, width of data center, maximum number of hidden neurons and goal error of RBFNN) were determined. And the final optimized network structures were listed in Tables 2 and 3 respectively. 4.2. Performance evaluation of BPNN and RBFNN models for predicting the CO2 solubility in 12 amine solutions The prediction performances of BPNN and RBFNN models were evaluated using three statistical parameters that can reflect the relationship between the predicted and the target values, i.e. the correlation coefficient (R), the average absolute relative error (AARE), and the root mean square error (RMSE). These evaluation indexes can display how well the model’s prediction results

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Table 3 The best RBFNN structures for CO2 solubility prediction in 12 amine solutions. Amine

Parameters Nr

MEA DEA MDEA AMP PZ TIPA MPA MIPA DEAB MAE DEEA MAPA

Table 4 The comparison of BPNN and RBFNN results for CO2 solubility prediction in 12 amine solutions.

R

210 71 315 216 221 14 17 26 14 29 39 26

f

Gaussian function Gaussian function Gaussian function Gaussian function Gaussian function Gaussian function Gaussian function Gaussian function Gaussian function Gaussian function Gaussian function Gaussian function

Nc

Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin Purelin

432 161 369 356 221 17 65 45 41 53 65 62

Wc 0.45 0.85 0.58 0.25 0.8 0.5 1.5 3.5 1.5 1.5 0.3 1.5

Amine

G 0.0006 0.002 0.0003 0.0009 0.001 0.0003 0.003 0.001 0.003 0.003 0.0002 0.003

MEA DEA MDEA AMP PZ TIPA MPA MIPA DEAB MAE DEEA MAPA

Note: Nr is the number of neurons in radial basis layer, R is the radial basis function, f is the transfer function of hidden-output layer, Nc is the number of data center, and Wc is the width of data center.

matched the experimental values, and their expressions are listed in Eqs. (25)-(27), respectively:

 ⎡ ⎤  n  2  ⎢ (ai − ti ) ⎥  ⎢ ⎥  ⎢ i=1 ⎥ R = 1 − ⎢ n ⎥  ⎣ ⎦  2

(25)

ti

i=1

1 ai − ti | | × 100 n ti n

AARE =

(26)

i=1

  n   1 ai − ti 2 RMSE =  × 100 n

i=1

(27)

ti

In these three formulas, n is the number of inputs; ai and ti are the predicted and target values of the ith input data, respectively. Firstly, BPNN and RBFNN models were employed to predict the CO2 solubility in MEA, DEA and MDEA amine solutions. Fig. 2(a)–(c) present the predicted CO2 solubility for the testing datasets of MEA, DEA and MDEA solutions, respectively. From the figures, it can be concluded that: (i) all the predicted CO2 solubility values match well with the experimental values with ARE (absolute relative error) under 20%; (ii) for MEA, DEA and MDEA solutions, the percentages of predicted datasets with ARE under 10% are 91.7%, 86.2%, 94.8% for BPNN and 87.6%, 86.2% and 85.3% for RBFNN, respectively. It can be inferred from these results that the newly developed ANN models provide good performances for the prediction of CO2 solubility in these three typical amine solutions.

BPNN

RBFNN

R

AARE (%)

RMSE (%)

R

AARE (%)

RMSE (%)

0.9983 0.9982 0.9988 0.9992 0.9982 0.9994 0.9996 0.9997 0.9999 0.9997 0.9997 0.9993

4.31 4.89 3.96 3.27 4.78 3.07 2.64 2.16 1.32 2.22 1.92 3.51

5.6 6.49 6.06 4.49 6.58 4.07 3.36 2.65 1.68 3.4 2.6 4.72

0.9983 0.9973 0.9971 0.9974 0.9968 0.9986 0.9993 0.9994 0.9999 0.9995 0.9992 0.9986

4.93 5.17 6.0 6.08 7.39 4.65 3.25 2.83 1.39 2.56 3.22 4.71

6.36 6.84 8.05 8.63 9.11 6.58 4.46 3.35 1.82 3.81 3.8 6.05

Secondly, other nine amine solutions were chosen to check the applicability of BPNN and RBFNN models in the prediction of CO2 solubility. The predicted CO2 solubility values of each amine solvent using BPNN and RBFNN models are listed in Fig. 3. For the CO2 solubility prediction using the BPNN models, the percentage of predicted datasets with ARE under 10% are larger than 90% for almost all of the amines except for PZ (which is 86.25%) and equal to 100% for TIPA, MPA, MIPA, DEAB and DEEA. While for the CO2 solubility prediction using RBFNN models, the percentages of predicted datasets with ARE under 10% are 100% for MIPA, DEAB and DEEA, 94.7% and 94.4% for MAE and MPA respectively, and less than 90% for AMP, PZ, TIPA and MAPA. All these prediction results show the effectiveness of the newly developed ANN models, implying their wide adaptability in different amine solutions. Table 4 lists the R, AARE and RMSE values of BPNN and RBFNN models for all the 12 amine solutions. As can be seen from the table, all the prediction results fit favorably well with their corresponding experimental values, since the R values of all models are larger than 0.99, and all the AARE and RMSE values are less than 10%. Furthermore, the ANN models show excellent performances for the prediction of CO2 solubility in several novel amine solutions (i.e., DETA, MPA, MIPA, DEAB, MAE and DEEA), as all their R values are greater than 0.999, and the AARE and RMSE values are less than 5% for both BPNN and RBFNN models. It also should be noted that the prediction result of DEAB is the best one, for the R, AARE and RMSE values for BPNN and RBFNN are found to be 0.9999, 1.32%, 1.68% and 0.9999, 1.39%, 1.82%, respectively. Furthermore, the AARE values of the BPNN and RBFNN models were also compared with eight numerical models from literature that were used for CO2 solubility prediction in different amine solutions, as shown in Table 5. It can be seen obviously that the new developed BPNN and RBFNN models show good prediction

Table 5 The comparison of BPNN and RBFNN models with eight published correlations for CO2 solubility prediction in 12 amine solutions. Prediction method

BPNN RBFNN (Dash et al., 2011) (Sema et al., 2011) (Pahlavanzadeh et al., 2011) (Dong et al., 2010) (Hussain et al., 2010) (Benamor and Aroua, 2005) (Derks et al., 2005) (Haji-Sulaiman et al., 1998) a

AARE (%) MEA

DEA

MDEA

AMP

PZ

TIPA

MPA

MIPA

DEAB

MAE

DEEA

MAPA

4.31 4.93 / / / / 4.1 / / /

4.89 5.17 / / / / 16.77 4.84 / 6.27

3.96 5.49 / / / / / 10.72 / 12.59

3.27 6.08 10.5 / 12.29 / / / / /

4.78 7.39 / / / / / / 15.7 /

3.07 4.65 / / / / / / / /

2.64 3.25 / / / 17.5 / / / /

2.16 2.83 / / / / / / / /

1.32 1.39 / 7.1a / / / / / /

2.22 2.56 / / / / / / / /

1.92 3.22 / / / / / / / /

3.51 4.71 / / / / / / / /

refers to the AARE value of the Li-Shen model (the best one) used in Sema et al., 2011.

G. Chen et al. / International Journal of Greenhouse Gas Control 39 (2015) 174–184

12

181

10

BPNN RBFNN

BPNN RBFNN 8

AARE%

AARE%

9

6

6

4

3 2

0

0

0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0

1.0-

20

40

60

100

120

140

160

180

o

Experimental CO2 loading (mol/mol)

Temperature( C) 15

15

BPNN RBFNN

BPNN RBFNN

12

12

9

9

AARE%

AARE%

80

6

6

3

3

0

0 1M

1.64M

2M

2.5M 3.75M

5M

5.9M 6.9M 7.4M 9.8M

MEA Concentration (mol/L)

1

10

100

1000

10000

PCO2 (kPa)

Fig. 4. The predicted AARE values of MEA solution in terms of different CO2 loadings, T, C, and PCO2 .

performances in all 12 amine solutions, while those published models provide acceptable results in only one or two amine solutions within their predicting capacity. These results demonstrate the high prediction capacities of the ANN models compared to those numerical models. Besides, according to the parameter values listed in Table 4 and the scatter plots presented in Figs. 2–3, it can be found that the BPNN and RBFNN have great capacities to predict the CO2 solubility with high accuracy and stability. The values of performance evaluation parameters (i.e., R, AARE and RMSE) show a further proof about the capability and adaptability of the ANN models for the CO2 solubility prediction in various amine solutions, and indicate the benefits of the application of ANN models for the CO2 solubility prediction. However, it can also be seen that the BPNN performs slightly better than the RBFNN for the CO2 solubility prediction. This phenomenon is probably due to the characteristics of the error back propagation of BPNN models, which lead to a more accurate result through the adjustment of initially generated weights and biases and the re-training of the network to the desired error. In addition, the neurons in hidden layer(s) of the BPNN models are much less than that of the RBFNN models, which can reduce the training time and decrease the complexities of the network configurations.

4.3. Scalability evaluation of BPNN and RBFNN models for predicting the CO2 solubility in various amine solutions As was shown above, the ANN models have been well validated with excellent prediction performances through the comparisons with the corresponding experimental values as well as several literature numerical models. However, there can not clearly show the scalability of the BPNN and RBFNN models for CO2 solubility prediction in wide range of experimental conditions (various T, C, and PCO2 ) and in various amine solutions. In order to get better understanding of that, an in-depth investigation was carried out to obtain the prediction accuracy of BPNN and RBFNN models in terms of the subdivided input parameter ranges, which were displayed as the AARE values of each parameter range. Taking the prediction results of MEA and PZ (which represent the most widely used amine solvent and the amine with the largest prediction AARE value in this study) for example. Figs. 4 and 5 present the predicted AARE values of MEA and PZ solutions in terms of different parameter ranges, including the CO2 loadings, T, C, and PCO2 . It can be seen from these two figures that both BPNN and RBFNN models perform well at the wide input parameter ranges and CO2 loading ranges (almost all of the AARE values are under 10%). Since the two amines (MEA and PZ) were chosen as examples due to their particularity, the results

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15

10

BPNN RBFNN

12

8

9

6

AARE%

AARE%

BPNN RBFNN

6

3

4

2

0

0 0-0.2 0.2-0.40.4-0.60.6-0.80.8-1.01.0-1.21.2-1.41.4-1.61.6-1.81.8-2.0 2.0-

20

40

60

100

120

o

Temperature( C)

Experimental CO2 loading (mol/mol) 15

15

BPNN RBFNN

BPNN RBFNN

12

12

9

9

AARE%

AARE%

80

6

6

3

3

0

0 0-1.0

1.0-2.0

2.0-4.0

5

8

12

1

10

100

1000

10000

PCO2 (kPa)

PZ Concentration (mol/L)

Fig. 5. The predicted AARE values of PZ solution in terms of different CO2 loadings, T, C, and PCO2 .

showed in Figs. 4–5 can be extrapolated to other amine solutions. It also should be declared that the datasets for CO2 solubility in TIPA and DEEA solutions are deficient, since they have only one amine concentration and relative narrow T and PCO2 ranges (which can be seen in Table 1), so the prediction accuracies are uncertain when extrapolating our prediction results to other parameter ranges. However, as mentioned in Section 3, ANN model has better prediction accuracy with more input datasets. Since our ANN models have very excellent prediction accuracies for TIPA and DEEA solutions with only 25 and 91 datasets (all the AARE values are under 5%), which can be an indication about the performances of ANN models from the reverse perspective. From the analysis above, it was known that ANN models perform well in predicting the CO2 solubility in single amine solutions. However, it is uncertain about the prediction performances of them for hybrid amine solutions. More investigations need to be done to have better study about it. 5. Conclusion Two kinds of ANN models, BPNN and RBFNN, were successfully developed in this paper to predict the CO2 equilibrium solubilities in 12 amine solutions. The predicted results of BPNN and RBFNN models were in good agreements with the experimental data over

a wide range of amine concentrations, temperatures, and equilibrium CO2 partial pressures. The results also showed that the newly developed ANN models in this work have good performance compared with other eight literature models. Besides, it was found that the BPNN models perform slightly better than the RBFNN models in all the amine types. Moreover, scalability analysis was carried out to evaluate the adaptability of BPNN and RBFNN models in terms of the wide input parameter ranges. It was found that all the AARE values were acceptable (almost all of them were under 10%). Acknowledgements The financial supports from the National Natural Science Foundation of China (NSFC-Nos. U1362112, 21406057 and 21446012), Innovative Research Team Development Plan-Ministry of Education of China (MOE-No.IRT1238), National Key Technology R&D Program (MOST-Nos. 2012BAC26B01 and 2014BAC18B04), Specialized Research Fund for the Doctoral Program of Higher Education(MOE-No.20130161110025), Key project of international & regional scientific and technological cooperation of Hunan provincial science and technology plan (2014WK2037), China’s State “Project 985” in Hunan University–Novel Technology Research & Development for CO2 Capture, and China Outstanding Engineer Training Plan for Students of Chemical Engineering

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