- Email: [email protected]
Machine learning predictive framework for CO2 thermodynamic properties in solution
Journal of CO₂ Utilization 26 (2018) 152–159
Contents lists available at ScienceDirect
Journal of CO2 Utilization journal homepage: www.elsevier.com/locate/jcou
Machine learning predictive framework for CO2 thermodynamic properties in solution Zhien Zhanga,b,e,1, Hao Lic,
T
⁎,1
, Haixing Changb, Zhen Pand, Xubiao Luoa
a
Key Laboratory of Jiangxi Province for Persistant Pollutants Control and Resources Recycle, Nanchang Hangkong University, Nanchang 330063, China School of Chemistry and Chemical Engineering, Chongqing University of Technology, Chongqing 400054, China c Department of Chemistry and Institute for Computational and Engineering Sciences, The University of Texas at Austin, 105 E. 24th Street, Stop A5300, Austin, TX 78712, USA d College of Petroleum Engineering, Liaoning Shihua University, Fushun 113001, China e Fujian Provincial Key Laboratory of Featured Materials in Biochemical Industry, Ningde Normal University, Ningde 352100, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: CO2 absorption Solubility Amino acid salt Machine learning Artificial neural network
CO2 is the major greenhouse gas (GHG) emission throughout the world. For scientific and industrial purposes, chemical absorption is regarded as an efficient method to capture CO2. However, the observation of thermodynamic properties of CO2 in solution environment requires too much time and resources. To address this issue and provide an ultra-fast solution, here, we use machine learning as a powerful data-mining strategy to predict the CO2 solubility, density and viscosity of potassium lysinate (PL) and its blended solutions with monoethanolamine (MEA), with totally 433 data groups extracted from previous experimental literatures. Specifically, we compared the predictive performances of back-propagation neural network (BPNN) and general regression neural network (GRNN). Results show that for BPNN with only one hidden layer and a small number of hidden neurons could provide good predictive performance for CO2 solubility and aqueous solution viscosity, while a GRNN could perform better for the prediction of aqueous solution density. Finally, it is concluded that such a machine learning based predictive framework could help to provide an ultra-fast prediction for CO2-related thermodynamic properties in solution environment.
1. Introduction CO2 is one of the major greenhouse gas (GHG) emissions in the world which could deteriorate the atmospheric environment. How to capture CO2 from the polluted gas mixture has become a hot topic in the past decades [1]. Chemical absorption is regarded as a mature and efficient method for capturing CO2, which is widely used in comparison with other capture techniques (e.g., adsorption, [2] cryogenic distillation [3], and oxygen-enriched combustion [4]) due to the high absorption efficiency and absorption rate [5–7]. The selection of an excellent CO2 absorbent is a main factor determining the efficiency of CO2 absorption. At first, a physical absorbent of water and chemical absorbents of alkali (e.g., NaOH and KOH) have been widely applied to the area of CO2 absorption. However, these absorbents have their respective disadvantages. The former absorbent of water exhibits a very low CO2 absorption efficiency, and the latter one may cause the corrosion problems to the equipment [8]. Since then,
⁎
the alkanolamine solutions, including primary, secondary, tertiary, and sterically hindered amines, have been commonly used for absorbing CO2 from the gas mixture in industry. This is because they have high absorption rate, low hydrocarbon loading capacity, and excellent thermal degradation resistance, etc. But they also have drawbacks in high energy consumption, and foaming and fouling issues [9–13]. Furthermore, ionic liquids (ILs) are also attracted much attention by many scholars, however they indicate deficiencies in low CO2 loading capacity, high cost, and high viscosity which hamper their applications in CO2 capture [14,15]. In addition, amino acid salts (AASs) solutions are advantageous in low volatility owing to the ionic structure, good stability and high oxidative degradation resistance compared with common alkanolamine solutions [16,17]. Some amino acid salts show a higher CO2 absorption capacity and a faster reactivity than alkanolamines [18–20]. Kang et al. [21] studied CO2 equilibrium solubility into 4 M potassium alaninate (PA), blend of 1.5 M potassium sarcosinate (PSar) and 1 M piperazine
Corresponding author. E-mail addresses: [email protected], [email protected] (Z. Zhang), [email protected] (H. Li), [email protected] (H. Chang), [email protected] (Z. Pan), [email protected] (X. Luo). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.jcou.2018.04.025 Received 11 March 2018; Received in revised form 10 April 2018; Accepted 26 April 2018 2212-9820/ © 2018 Elsevier Ltd. All rights reserved.
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Nomenclature
GHG GRNN IL MEA PA PPr PSar PSer PT PZ RMSE
Greek letters α ρ η
solubility (mol CO2/mol solution) density (g/cm3) viscosity (mPa∙s)
Abbreviations AAS ANN BPNN
amino acid salt artificial neural network back-propagation neural network
greenhouse gas general regression neural network ionic liquid monoethanolamine potassium alaninate potassium prolinate potassium sarcosinate potassium serinate potassium taurate piperazine root mean square error
temperature, and the absorbent concentration. Experimental results reported in literature for CO2 solubility into potassium lysinate and its blended solutions are limited in operating condition range and accuracy, which are unable to assess the system reliability [26–28]. Experimental studies on CO2 solubility tests are long period and high cost in some cases. On the other hand, experimental research is more dangerous than modeling work particularly under the conditions of very high pressure and temperature. To address this issue, machine learning could be a powerful technique that directly predicts the CO2 properties in the solution environment, with the simple inputs of some easilymeasured data [29–31]. With the existing experimental data, a welltrained machine learning model could become an ultra-fast alternative for practical evaluations. Nowadays, both physical modeling and machine learning have strong potential applications for many areas, such as mechanical engineering, biomedical, energy and materials science [32–38]. In this study, we aim to use artificial neural networks (ANN) as the machine learning algorithms for the predictions of CO2 solubility in the solutions of potassium lysinate and its blends with varying
(PZ), and blend of 1.5 M potassium serinate (PSer) and 1 M PZ at 313.15–353.15 K. Hamzehie and Najibi [22] investigated the CO2 loading capacity into the mixed solutions of potassium prolinate (PPr) and PZ with total concentrations of 1, 4, and 10 wt.%. The experimental data were measured at the conditions of 4.8–2383.2 kPa CO2 partial pressure and 293.15–323.15 K operating temperature. Kumar et al. [23] measured CO2 equilibrium solubility in potassium taurate (PT) solutions in the concentration range of 0.5 and 4.0 M. The experiments were carried out at the temperatures of 298 and 313 K, and the CO2 partial pressures from 0.107 to 7.396 kPa. van Holst et al.[24] obtained the density and viscosity of various amino acid salts solutions in the concentration range of 0.25–3.5 M and the temperature range of 298333 K. They also measured N2O solubility to estimate the CO2 solubility in these solutions. Garcia et al. [25] studied the thermophysical parameters of potassium and sodium salt solutions of a-aminobutyric acid at 303.15–343.15 K. Fundamentally, the solubility of CO2 in the solutions of potassium lysinate and its blends is a function of operating pressure and
Fig. 1. (a–c) The feed forward neural network structure for the predictions of (a) CO2 solubility, (b) aqueous solution density and (c) aqueous solution viscosity. (d–f) The general regression neural network for the predictions of (d) CO2 solubility, (e) aqueous solution density and (f) aqueous solution viscosity. 153
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
the training and testing errors [46]. More comparative studies between the performances and optimizations of GRNN and BPNN (with both relatively small- and large-scale datasets) are shown in our previous reports [44]. The schematic structures of BPNN and GRNN for the predictions of solubility, aqueous solution density and viscosity are shown in Fig. 1. The loss function for all the ANNs in this study is root mean square error (RMSE). Details about the principles of BPNN and GRNN can be found in Refs.[40,41]. For the prediction of CO2 solubility, the independent variables are PL concentration, MEA concentration, total concentration, temperature and CO2 partial pressure (Fig. 1a and d). For the predictions of aqueous solution density and viscosity, the independent variables are PL concentration, MEA concentration, total concentration and temperature (Fig. 1b, c, e and f). All these independent variables can be easily measured and are potentially correlated with the dependent variables. To train an ANN model, the data were separated into two different sets: training and testing sets. The data in the training set were used for the model training, while the testing set was used to validate the predictive capacity of the model after each training. A well-trained model should have the average minimized RMSE in the testing sets. To ensure the robustness of the trained model with multiple trainings, our previous studies have shown that a sensitivity test with shuffled training and testing data are able to help to evaluate the model [44]. Compared to a conventional cross-validation method, this method could ensure an effective and much faster model validation process under different data compositions and components [30,47]. More training principles of ANNs can be found in Ref. [48]. In this study, the BPNNs with different numbers of hidden layers and neurons are represented as X-N-Y and XN-N-Y, where X is the number of input neurons, N represents the number of hidden neurons, and Y represents the number of output neurons.
concentrations, with the simple inputs of solution information and physical solution parameters. To generalize the developed methodology, we further discuss the predictive framework for the CO2 thermodynamic properties in solution environment by expanding the similar processes for the modeling and prediction of the aqueous solution density and viscosity. 2. Reaction mechanism The structure of potassium lysnate has a primary amine group (like monoethanolamine (MEA) solution) due to a carbon-nitrogen bond [39]. The equilibrium reactions between CO2 and potassium lysinate solutions are shown as follows [20,26]: k1
RNH+3 ↔ RNH2 + H+
(1)
k2
RNHCOO− + H2 O ↔ RNH2 + HCO−3
(2)
k3
CO2 + H2 O ↔ H+ + HCO−3
(3)
k4
HCO−3 ↔ H+ + CO32 −
(4)
k5
H2 O ↔ H+ + OH−
(5)
where R is lysine amino acid, and k represents the equilibrium constant for each reaction. The above chemical reaction is dominated kinetically by the direct reaction between CO2 and amino acid salt to produce a carbamate and a protonated amino acid:
CO2 + 2RNH2 ↔ RNH+3 + RNHCOO−
(6)
3. Methodology and modeling
3.2. Date collection
3.1. Modeling
Table 1 shows the range of data for CO2-PL and CO2-PL/MEA systems reported in previous literature. The input and output variables in the model and the number of datasets are given in this table. The target variables here are the values of CO2 solubility, density, and viscosity of the solution. It can be seen that a higher liquid concentration could improve the CO2 solubility results since the increase of the liquid concentration could enhance the chemical reaction between them. In addition, higher CO2 partial pressure and lower temperature result in a higher CO2 loading.
In this study, general regression neural network (GRNN) and feed forward neural network with a back-propagation (BPNN) algorithm were used for the non-linear fitting of the data [40,41]. A completed ANN model should consist of three different types of layer: input, hidden and output layers (Fig. 1) [42,43]. Each neuron in the input layer represents an independent variable. Each neuron in the output layer represents a dependent variable. Each neuron connects with all the other neurons in the other layer(s) nearby and each connection represents a numerical weight [30]. Using the weights, an activation function is used for acquiring the output values with the inputs of independent variables [44]. For BPNN, the training of a network is essentially the optimization of weights using a BP iteration method [45]. For each prediction target, an optimized BPNN should include an appropriate number of hidden layers and hidden neurons, in order to avoid under- or over-fitting. For GRNN, the hidden layer consists of two different types of layers: the pattern and summation layers (Fig. 1d–f). Unlike a conventional feed forward neural network, GRNN uses a regression method with a Gaussian function for data training. Compared with BPNN, GRNN has a fixed algorithmic network structure. Thus, it is not necessary to tune the GRNN structural information for minimizing
4. Results and discussion 4.1. Data analysis Taking the CO2 solubility as an example, the data analysis of “independent variable vs dependent variable” are plotted in Fig. 2. It can be clearly seen that for each value of the independent variable in this study, it has multiple values of CO2 solubility. None of the independent variable could have clear linear relationship with the CO2 solubility. This means that though physically there should be potential relationships between the independent variables and the CO2 solubility, linear regression or simple empirical equation of states might not be effective
Table 1 Data range of CO2 solubility, density and viscosity in PL and PL/MEA solutions. PL concentration range/M
MEA concentration range/M
No. of data
Operating pressure/kPa
CO2 partial pressure range/kPa
Temperature range/K
Solubility α/(mol CO2/mol solution)
Density ρ/(g/cm3)
Viscosity η/mPa s
Ref.
0.5–2.5 0.2001–3 0.5–2 0.26–1.98
0 0 0.5–2 0
63 220 78 72
101 101 101 101
5.4–41.47 0.069–17.444 2.64–47.52 –
298–313 313–333 303–323 298–333
0.17–1.063 – 0.511–1.05 –
1.0307–1.1738 0.9877–1.151 1.0232–1.1003 1.0008–1.1168
0.894–3.1652 0.4358–8.4071 1.005–1.514 0.5507–3.557
[26] [27] [28] [49]
154
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Fig. 2. Relationships between independent and dependent variables: (a) PL concentration vs CO2 solubility; (b) MEA concentration vs CO2 solubility; (c) total concentration vs CO2 solubility; (d) temperature vs CO2 solubility and (e) CO2 partial pressure vs CO2 solubility.
dramatically increase. Therefore, in this case, a BPNN with one hidden layer and four hidden neurons (5-4-1) could guarantee a good training result and meanwhile, have less time-consumption. To compare the performance of BPNN with GRNN, we further conducted repeated training and testing with shuffled data on BPNN 54-1 and GRNN, respectively. Three different sizes of training set were selected, including 70%, 80% and 90%. The average RMSEs were then acquired from the testing sets for model evaluation (Fig. 4). It can be clearly seen that for the prediction of CO2 solubility, BPNN with a 5-4-1 network structure significantly outperforms the GRNN, having the average RMSEs in the testing sets lower than 0.03 mol CO2/mol solution. To further evaluate the training and testing results on BPNN 5-4-1, we respectively picked a typical training and testing result for comparison (Fig. 5). It can be seen that in both the training and testing sets, the predicted values are highly close to their corresponding actual values, which indicates a good non-linear fitting performance.
for direct prediction. Therefore, to precisely predict the CO2 solubility, more complicated model is required. Since similar statistical results were found in the predictions of density and viscosity data, these additional results are not included in the paper. 4.2. CO2 solubility To search an optimal BPNN network configuration, different numbers of hidden layer and hidden neuron were selected for data training and testing. Fig. 3 shows the average testing RMSEs for the prediction of CO2 solubility, with varying hidden layer information. It can be clearly seen that with two hidden layers in a BPNN, the average RMSEs in the testing sets are generally high (Fig. 3, blue points), indicating an overfitting phenomenon. If there is only one hidden layer, the BPNN with 4–16 hidden neurons tend to show minimized average RMSEs in the testing sets. If the number of hidden neuron is lower than 4 or higher than 16, their RMSEs are relatively higher, which respectively indicates an under- and over-fitting. It should be noted that with more hidden neurons in the hidden layer, the required training time would 155
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Fig. 3. The average RMSEs of the testing sets in different BPNN hidden structures. Red points represent the BPNN with single hidden layer, with the network structure of 5-N-1 (where N represents the number of hidden neurons). Blue points represent the BPNN with two hidden layers, with the network structure of 5-N-N-1. Each point is the average testing RMSE after 20 training and testing processes with shuffled data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 6. Average RMSEs of GRNN and a BPNN 4-2-1 for the prediction of density with different training data sizes. Each point represents the average testing RMSE of 200 repeated training and testing processes with shuffled data.
Fig. 7. Average RMSEs of GRNN and a BPNN 4-2-1 for the prediction of viscosity with different training data sizes. Each point represents the average testing RMSE of 200 repeated training and testing processes with shuffled data.
4.3. Extension: Prediction of solution density and viscosity Fig. 4. Average RMSEs of GRNN and a BPNN 5-4-1 for the prediction of CO2 solubility with different training data sizes. Each point represents the average testing RMSE of 200 repeated training and testing processes with shuffled data.
With a similar method, we found that BPNN 4-2-1 could perform good model training for the prediction of both the aqueous solution density and viscosity, with minimized testing RMSEs and short timeconsumptions. Therefore, we compare the BPNN 4-2-1 with the GRNN for the prediction of the solution density (Fig. 6) and viscosity (Fig. 7),
Fig. 5. Predicted solubility values vs actual solubility values in a typical (a) training and (b) testing set using a BPNN 5-4-1. 156
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Fig. 8. Predicted solution density values vs actual density values in a typical (a) training and (b) testing set using a GRNN.
Fig. 9. Predicted solution viscosity values vs actual viscosity values in a typical (a) training and (b) testing set using a BPNN 4-2-1.
Fig. 10. The predictive framework for CO2 thermodynamic properties.
data summarized in Table 1, a GRNN is suitable for density prediction while a BPNN 4-2-1 is more suitable for viscosity prediction. To show the training and testing processes, Figs. 8 and 9 show the representative predicted-vs-actual values for the predictions of density and viscosity, respectively. It can be seen that in the training processes (Figs. 8a and 9a), though there exist several data points that deviate
respectively. Results show that for the prediction of density, GRNN has lower average testing RMSEs when the size of training set is relatively high (90%). This means that a higher proportion of training data could guarantee better training results of GRNN, compared to the BPNN. In terms of the viscosity, BPNN 4-2-1 outperforms the GRNN in all the three training sizes. Therefore, it is concluded that training with the 157
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
from the diagonal, most of them fit with the y = x line. In terms of the testing processes, all the predicted values are close to their corresponding actual values. These results indicate that our models have good precisions for interpolation analysis.
[4] G. Cau, V. Tola, F. Ferrara, A. Porcu, A. Pettinau, CO2-free coal-fired power generation by partial oxy-fuel and post-combustion CO2 capture: techno-economic analysis, Fuel 214 (2018) 423–435. [5] M. Rezakazemi, I. Heydari, Z. Zhang, Hybrid systems: combining membrane and absorption technologies leads to more efficient acid gases (CO2 and H2S) removal from natural gas, J. CO2 Util. 18 (2017) 362–369. [6] A. Baghban, A. Bahadori, A.H. Mohammadi, A. Behbahaninia, Prediction of CO2 loading capacities of aqueous solutions of absorbents using different computational schemes, Int. J. Greenh. Gas Control 57 (2017) 143–161. [7] E.F. da Silva, H.F. Svendsen, Computational chemistry study of reactions, equilibrium and kinetics of chemical CO2 absorption, Int. J. Greenh. Gas Control 1 (2) (2007) 151–157. [8] M. Wang, A. Lawal, P. Stephenson, J. Sidders, C. Ramshaw, Post-combustion CO2 capture with chemical absorption: a state-of-the-art review, Chem. Eng. Res. Des. 89 (9) (2011) 1609–1624. [9] Z. Zhang, F. Chen, M. Rezakazemi, W. Zhang, C. Lu, H. Chang, X. Quan, Modeling of a CO2-piperazine-membrane absorption system, Chem. Eng. Res. Des. 131 (2018) 375–384. [10] Z. Zhang, Comparisons of various absorbent effects on carbon dioxide capture in membrane gas absorption (MGA) process, J. Nat. Gas Sci. Eng. 39 (2016) 589–595. [11] X. Zhang, R. Zhang, H. Liu, H. Gao, Z. Liang, Evaluating CO2 desorption performance in CO2-loaded aqueous tri-solvent blend amines with and without solid acid catalysts, Appl. Energy 218 (2018) 417–429. [12] H. Liu, H. Gao, R. Idem, P. Tontiwachwuthikul, Z. Liang, Analysis of CO2 solubility and absorption heat into 1-dimethylamino-2-propanol solution, Chem. Eng. Sci. 170 (2017) 3–15. [13] H. Liu, M. Xiao, Z. Liang, P. Tontiwachwuthikul, The analysis of solubility, absorption kinetics of CO2 absorption into aqueous 1‐diethylamino‐2‐propanol solution, AlChE J. 63 (7) (2017) 2694–2704. [14] I. Iliuta, M. Hasib-ur-Rahman, F. Larachi, CO2 absorption in diethanolamine/ionic liquid emulsions – chemical kinetics and mass transfer study, Chem. Eng. J. 240 (2014) 16–23. [15] S. Rostami, P. Keshavarz, S. Raeissi, Experimental study on the effects of an ionic liquid for CO2 capture using hollow fiber membrane contactors, Int. J. Greenh. Gas Control 69 (2018) 1–7. [16] Q. Huang, S. Bhatnagar, J.E. Remias, J.P. Selegue, K. Liu, Thermal degradation of amino acid salts in CO2 capture, Int. J. Greenh. Gas Control 19 (2013) 243–250. [17] U.E. Aronu, H.F. Svendsen, K.A. Hoff, Investigation of amine amino acid salts for carbon dioxide absorption, Int. J. Greenh. Gas Control 4 (5) (2010) 771–775. [18] J. van Holst, G.F. Versteeg, D.W.F. Brilman, J.A. Hogendoorn, Kinetic study of CO2 with various amino acid salts in aqueous solution, Chem. Eng. Sci. 64 (1) (2009) 59–68. [19] Y. Yan, Z. Zhang, L. Zhang, Y. Chen, Q. Tang, Dynamic modeling of biogas upgrading in hollow fiber membrane contactors, Energy Fuel 28 (9) (2014) 5745–5755. [20] Z. Zhang, Y. Yan, L. Zhang, Y. Chen, J. Ran, G. Pu, C. Qin, Theoretical study on CO2 absorption from biogas by membrane contactors: effect of operating parameters, Ind Eng. Chem. Res. 53 (36) (2014) 14075–14083. [21] D. Kang, S. Park, H. Jo, J. Min, J. Park, Solubility of CO2 in amino-acid-based solutions of (potassium sarcosinate), (potassium alaninate + piperazine), and (potassium serinate + piperazine), J. Chem. Eng. Data 58 (6) (2013) 1787–1791. [22] M.E. Hamzehie, H. Najibi, Carbon dioxide loading capacity in aqueous solution of potassium salt of proline blended with piperazine as new absorbents, Thermochim. Acta 639 (2016) 66–75. [23] P.S. Kumar, J.A. Hogendoorn, S.J. Timmer, P.H.M. Feron, G.F. Versteeg, 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. [24] J. van Holst, S.R.A. Kersten, K.J.A. Hogendoorn, Physiochemical properties of several aqueous potassium amino acid salts, J. Chem. Eng. Data 53 (2008) 1286–1291. [25] A.A.R. Garcia, R.B. Leron, A.N. Soriano, M.-H. Li, Thermophysical property characterization of aqueous amino acid salt solutions containing α -aminobutyric acid, J. Chem. Thermodyn. 81 (2015) 136–142. [26] S. Mazinani, R. Ramazani, A. Samsami, A. Jahanmiri, B. Van der Bruggen, S. Darvishmanesh, Equilibrium solubility, density, viscosity and corrosion rate of carbon dioxide in potassium lysinate solution, Fluid Phase Equilib. 396 (2015) 28–34. [27] S. Shen, Y. Yang, Y. Wang, S. Ren, J. Han, A. Chen, CO2 absorption into aqueous potassium salts of lysine and proline: density, viscosity and solubility of CO2, Fluid Phase Equilib. 399 (2015) 40–49. [28] R. Ramazani, A. Samsami, A. Jahanmiri, B.Vd. Bruggen, S. Mazinani, Characterization of monoethanolamine + potassium lysinate blend solution as a new chemical absorbent for CO2 capture, Int. J. Greenh. Gas Control 51 (2016) 29–35. [29] Z. Liu, H. Li, K. Liu, H. Yu, K. Cheng, Design of high-performance water-in-glass evacuated tube solar water heaters by a high-throughput screening based on machine learning: a combined modeling and experimental study, Sol. Energy 142 (2017) 61–67. [30] H. Li, Z. Liu, K. Liu, Z. Zhang, Predictive power of machine learning for optimizing solar water heater performance: the potential application of high-throughput screening, Int. J. Photoenergy 2017 (2017) 1–10. [31] H. Li, X. Tang, R. Wang, F. Lin, Z. Liu, K. Cheng, Comparative study on theoretical and machine learning methods for acquiring compressed liquid densities of 1,1,1,2,3,3,3-Heptafluoropropane (R227ea) via song and Mason equation, support vector machine, and artificial neural networks, Appl. Sci. 6 (1) (2016) 25. [32] J.H. Park, Lumped Parameter Model for a Self Powered Fontan Palliation of the
4.4. Generalized predictive framework These case studies for CO2 thermodynamic properties prediction could potentially be a good way for ultra-fast analysis. A general flow chart of such a predictive framework is shown in Fig. 10. It can be seen that once a suitable predictive machine learning model is developed based on the previous experimental knowledge, a well-developed model could rapidly predict the target CO2 thermodynamic properties with an acceptable accuracy. With some widely used platforms (e.g., personal computer and Android [50]) or packages (e.g., Keras machine learning python library [51]), users can directly use a well-developed ANN model for direct prediction with simple data collection experiments of the solution properties (e.g., concentrations) and operating conditions (e.g., partial pressure and temperature) of the system. Additionally, it is worthy to mention that other state-of-the-art machine learning techniques, like support vector machine (SVM) [52], are also expected to have good predictive performances. In our case, since ANNs usually have better local-fitting capacity due to the higher degree of non-linear components, ANNs were selected as a case studies for the systems. We also expect that these approaches can also be extended to other fields such as mechanical and information systems [53,54]. 5. Conclusions Fundamentals of gas thermodynamic properties into solutions are industrially important in the gas removal field. In this paper, a welltrained machine learning model was used to predict CO2 solubility, solution density, and viscosity with various operating conditions and liquid concentrations. In total, 105, 164, and 164 data groups were employed in the predictive modeling for CO2 solubility, solution density and viscosity, respectively. The modeling results indicate that BPNN 54-1 was more suitable for predicting CO2 solubility compared with GRNN. On the other hand, a GRNN was suitable for density prediction while a BPNN 4-2-1 was more suitable for predicting viscosity. As a consequence, the proposed predictive framework has been proven useful for the rapid and accurate predictions of CO2 thermodynamic properties in the solutions. We expect that such a machine learning based predictive framework could be further applied to more thermodynamic properties of CO2-related aqueous systems. Acknowledgements We would like to acknowledge the financial support from the National Natural Science Foundation of China (No. 41572116), Open Funds of Key Laboratory of Jiangxi Province for Persistant Pollutants Control and Resources Recycle (No. ES201880049) and Fujian Provincial Key Laboratory of Featured Materials in Biochemical Industry (No. FJKL_FMBI201704), and Scientific and Technological Research Program of Chongqing Municipal Education Commission (No. KJ1709193). References [1] Z. Zhang, J. Cai, F. Chen, H. Li, W. Zhang, W. Qi, Progress in enhancement of CO2 absorption by nanofluids: a mini review of mechanisms and current status, Renew. Energy 118 (2018) 527–535. [2] S. Chaemchuen, N.A. Kabir, K. Zhou, F. Verpoort, Metal-organic frameworks for upgrading biogas via CO2 adsorption to biogas green energy, Chem. Soc. Rev. 42 (24) (2013) 9304–9332. [3] K. Maqsood, J. Pal, D. Turunawarasu, A.J. Pal, S. Ganguly, Performance enhancement and energy reduction using hybrid cryogenic distillation networks for purification of natural gas with high CO2 content, Korean J. Chem. Eng. 31 (7) (2014) 1120–1135.
158
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Hypoplastic Left Heart Syndrome, (2015). [33] T. Liu, A. Jagota, C.Y. Hui, Effect of surface tension on the adhesion between a rigid flat punch and a semi-infinite neo-Hookean half-space, Extreme Mech. Lett. 9 (2016) 310–316. [34] S. Dreiseitl, L. Ohnomachado, H. Kittler, S. Vinterbo, H. Billhardt, M. Binder, A comparison of machine learning methods for the diagnosis of pigmented skin lesions, J. Biomed. Inform. 34 (1) (2001) 28–36. [35] T. Liu, N. Nadermann, Z. He, S.H. Strogatz, C.Y. Hui, A. Jagota, Spontaneous droplet motion on a periodically compliant substrate, Langmuir 33 (20) (2017). [36] A. Widodo, B.S. Yang, Support vector machine in machine condition monitoring and fault diagnosis, Mech. Syst. Signal. Process. 21 (6) (2007) 2560–2574. [37] B. Meredig, A. Agrawal, S. Kirklin, J.E. Saal, J.W. Doak, A. Thompson, K. Zhang, A. Choudhary, C. Wolverton, Combinatorial screening for new materials in unconstrained composition space with machine learning, Phys. Rev. B 89 (9) (2014) 82–84. [38] T. Liu, A. Jagota, C.Y. Hui, A closed form large deformation solution of plate bending with surface effects, Soft Matter 13 (2) (2016) 386–393. [39] P.S. Kumar, J.A. Hogendoorn, P.H.M. Feron, G.F. Versteeg, 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. [40] D.F. Specht, A general regression neural network, IEEE Trans. Neural Netw. 2 (6) (1991) 568–576. [41] K. Hornik, M. Stinchcombe, H. White, Multilayer feedforward networks are universal approximators, Neural Netw. 2 (5) (1989) 359–366. [42] H. Li, F. Chen, K. Cheng, Z. Zhao, D. Yang, Prediction of zeta potential of decomposed Peat via machine learning: comparative study of support vector machine and artificial neural networks, Int. J. Electrochem. Sci. 10 (8) (2015) 6044–6056. [43] Z. Liu, K. Cheng, H. Li, G. Cao, D. Wu, Y. Shi, Exploring the potential relationship
[44] [45]
[46]
[47]
[48] [49]
[50] [51] [52] [53] [54]
159
between indoor air quality and the concentration of airborne culturable fungi: a combined experimental and neural network modeling study, Environ. Sci. Pollut. Res. 6 (2017) 1–8. H. Li, Z. Liu, Performance Prediction and Optimization of Solar Water Heater via a Knowledge-Based Machine Learning Method, arXiv preprint, 2017. Z. Liu, K. Liu, L. Hao, X. Zhang, G. Jin, K. Cheng, Artificial neural networks-based software for measuring heat collection rate and heat loss coefficient of water-inglass evacuated tube solar Water heaters, Plos One 10 (12) (2015) e0143624. Z. Liu, L. Hao, G. Cao, Quick estimation model for the concentration of indoor airborne culturable bacteria: an application of machine learning, Int. J. Environ. Res. Public Health 14 (8) (2017) 857. Z. Liu, H. Li, X. Zhang, G. Jin, K. Cheng, Novel method for measuring the heat collection rate and heat loss coefficient of water-in-glass evacuated tube solar water heaters based on artificial neural networks and support vector machine, Energies 8 (8) (2015) 8814–8834. H. Li, Z. Zhang, Z. Liu, Application of artificial neural networks for catalysis: a review, Catalysts 7 (10) (2017) 306. S. Shen, Y.N. Yang, Y. Bian, Y. Zhao, Kinetics of CO2 absorption into aqueous basic amino acid Salt: potassium salt of lysine solution, Environ. Sci. Technol. 50 (4) (2016) 2054–2063. Y. Chen, Adaptive android kernel live patching, Usenix Security, (2017). F. Chollet, Keras, (2015). J.A.K. Suykens, J. Vandewalle, Least squares support vector machine classifiers, Neural Process. Lett. 9 (3) (1999) 293–300. Y. Chen, Z. Wang, D. Whalley, L. Lu, Remix: on-demand live randomization, ACM Conference on Data and Application Security and Privacy, (2016), pp. 50–61. X. Wang, Y. Chen, Z. Wang, Y. Zhou, Y. Zhou, SecPod: a framework for virtualization-based security systems, Usenix Conference on Usenix Technical Conference, (2015), pp. 347–360.
Contents lists available at ScienceDirect
Journal of CO2 Utilization journal homepage: www.elsevier.com/locate/jcou
Machine learning predictive framework for CO2 thermodynamic properties in solution Zhien Zhanga,b,e,1, Hao Lic,
T
⁎,1
, Haixing Changb, Zhen Pand, Xubiao Luoa
a
Key Laboratory of Jiangxi Province for Persistant Pollutants Control and Resources Recycle, Nanchang Hangkong University, Nanchang 330063, China School of Chemistry and Chemical Engineering, Chongqing University of Technology, Chongqing 400054, China c Department of Chemistry and Institute for Computational and Engineering Sciences, The University of Texas at Austin, 105 E. 24th Street, Stop A5300, Austin, TX 78712, USA d College of Petroleum Engineering, Liaoning Shihua University, Fushun 113001, China e Fujian Provincial Key Laboratory of Featured Materials in Biochemical Industry, Ningde Normal University, Ningde 352100, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: CO2 absorption Solubility Amino acid salt Machine learning Artificial neural network
CO2 is the major greenhouse gas (GHG) emission throughout the world. For scientific and industrial purposes, chemical absorption is regarded as an efficient method to capture CO2. However, the observation of thermodynamic properties of CO2 in solution environment requires too much time and resources. To address this issue and provide an ultra-fast solution, here, we use machine learning as a powerful data-mining strategy to predict the CO2 solubility, density and viscosity of potassium lysinate (PL) and its blended solutions with monoethanolamine (MEA), with totally 433 data groups extracted from previous experimental literatures. Specifically, we compared the predictive performances of back-propagation neural network (BPNN) and general regression neural network (GRNN). Results show that for BPNN with only one hidden layer and a small number of hidden neurons could provide good predictive performance for CO2 solubility and aqueous solution viscosity, while a GRNN could perform better for the prediction of aqueous solution density. Finally, it is concluded that such a machine learning based predictive framework could help to provide an ultra-fast prediction for CO2-related thermodynamic properties in solution environment.
1. Introduction CO2 is one of the major greenhouse gas (GHG) emissions in the world which could deteriorate the atmospheric environment. How to capture CO2 from the polluted gas mixture has become a hot topic in the past decades [1]. Chemical absorption is regarded as a mature and efficient method for capturing CO2, which is widely used in comparison with other capture techniques (e.g., adsorption, [2] cryogenic distillation [3], and oxygen-enriched combustion [4]) due to the high absorption efficiency and absorption rate [5–7]. The selection of an excellent CO2 absorbent is a main factor determining the efficiency of CO2 absorption. At first, a physical absorbent of water and chemical absorbents of alkali (e.g., NaOH and KOH) have been widely applied to the area of CO2 absorption. However, these absorbents have their respective disadvantages. The former absorbent of water exhibits a very low CO2 absorption efficiency, and the latter one may cause the corrosion problems to the equipment [8]. Since then,
⁎
the alkanolamine solutions, including primary, secondary, tertiary, and sterically hindered amines, have been commonly used for absorbing CO2 from the gas mixture in industry. This is because they have high absorption rate, low hydrocarbon loading capacity, and excellent thermal degradation resistance, etc. But they also have drawbacks in high energy consumption, and foaming and fouling issues [9–13]. Furthermore, ionic liquids (ILs) are also attracted much attention by many scholars, however they indicate deficiencies in low CO2 loading capacity, high cost, and high viscosity which hamper their applications in CO2 capture [14,15]. In addition, amino acid salts (AASs) solutions are advantageous in low volatility owing to the ionic structure, good stability and high oxidative degradation resistance compared with common alkanolamine solutions [16,17]. Some amino acid salts show a higher CO2 absorption capacity and a faster reactivity than alkanolamines [18–20]. Kang et al. [21] studied CO2 equilibrium solubility into 4 M potassium alaninate (PA), blend of 1.5 M potassium sarcosinate (PSar) and 1 M piperazine
Corresponding author. E-mail addresses: [email protected], [email protected] (Z. Zhang), [email protected] (H. Li), [email protected] (H. Chang), [email protected] (Z. Pan), [email protected] (X. Luo). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.jcou.2018.04.025 Received 11 March 2018; Received in revised form 10 April 2018; Accepted 26 April 2018 2212-9820/ © 2018 Elsevier Ltd. All rights reserved.
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Nomenclature
GHG GRNN IL MEA PA PPr PSar PSer PT PZ RMSE
Greek letters α ρ η
solubility (mol CO2/mol solution) density (g/cm3) viscosity (mPa∙s)
Abbreviations AAS ANN BPNN
amino acid salt artificial neural network back-propagation neural network
greenhouse gas general regression neural network ionic liquid monoethanolamine potassium alaninate potassium prolinate potassium sarcosinate potassium serinate potassium taurate piperazine root mean square error
temperature, and the absorbent concentration. Experimental results reported in literature for CO2 solubility into potassium lysinate and its blended solutions are limited in operating condition range and accuracy, which are unable to assess the system reliability [26–28]. Experimental studies on CO2 solubility tests are long period and high cost in some cases. On the other hand, experimental research is more dangerous than modeling work particularly under the conditions of very high pressure and temperature. To address this issue, machine learning could be a powerful technique that directly predicts the CO2 properties in the solution environment, with the simple inputs of some easilymeasured data [29–31]. With the existing experimental data, a welltrained machine learning model could become an ultra-fast alternative for practical evaluations. Nowadays, both physical modeling and machine learning have strong potential applications for many areas, such as mechanical engineering, biomedical, energy and materials science [32–38]. In this study, we aim to use artificial neural networks (ANN) as the machine learning algorithms for the predictions of CO2 solubility in the solutions of potassium lysinate and its blends with varying
(PZ), and blend of 1.5 M potassium serinate (PSer) and 1 M PZ at 313.15–353.15 K. Hamzehie and Najibi [22] investigated the CO2 loading capacity into the mixed solutions of potassium prolinate (PPr) and PZ with total concentrations of 1, 4, and 10 wt.%. The experimental data were measured at the conditions of 4.8–2383.2 kPa CO2 partial pressure and 293.15–323.15 K operating temperature. Kumar et al. [23] measured CO2 equilibrium solubility in potassium taurate (PT) solutions in the concentration range of 0.5 and 4.0 M. The experiments were carried out at the temperatures of 298 and 313 K, and the CO2 partial pressures from 0.107 to 7.396 kPa. van Holst et al.[24] obtained the density and viscosity of various amino acid salts solutions in the concentration range of 0.25–3.5 M and the temperature range of 298333 K. They also measured N2O solubility to estimate the CO2 solubility in these solutions. Garcia et al. [25] studied the thermophysical parameters of potassium and sodium salt solutions of a-aminobutyric acid at 303.15–343.15 K. Fundamentally, the solubility of CO2 in the solutions of potassium lysinate and its blends is a function of operating pressure and
Fig. 1. (a–c) The feed forward neural network structure for the predictions of (a) CO2 solubility, (b) aqueous solution density and (c) aqueous solution viscosity. (d–f) The general regression neural network for the predictions of (d) CO2 solubility, (e) aqueous solution density and (f) aqueous solution viscosity. 153
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
the training and testing errors [46]. More comparative studies between the performances and optimizations of GRNN and BPNN (with both relatively small- and large-scale datasets) are shown in our previous reports [44]. The schematic structures of BPNN and GRNN for the predictions of solubility, aqueous solution density and viscosity are shown in Fig. 1. The loss function for all the ANNs in this study is root mean square error (RMSE). Details about the principles of BPNN and GRNN can be found in Refs.[40,41]. For the prediction of CO2 solubility, the independent variables are PL concentration, MEA concentration, total concentration, temperature and CO2 partial pressure (Fig. 1a and d). For the predictions of aqueous solution density and viscosity, the independent variables are PL concentration, MEA concentration, total concentration and temperature (Fig. 1b, c, e and f). All these independent variables can be easily measured and are potentially correlated with the dependent variables. To train an ANN model, the data were separated into two different sets: training and testing sets. The data in the training set were used for the model training, while the testing set was used to validate the predictive capacity of the model after each training. A well-trained model should have the average minimized RMSE in the testing sets. To ensure the robustness of the trained model with multiple trainings, our previous studies have shown that a sensitivity test with shuffled training and testing data are able to help to evaluate the model [44]. Compared to a conventional cross-validation method, this method could ensure an effective and much faster model validation process under different data compositions and components [30,47]. More training principles of ANNs can be found in Ref. [48]. In this study, the BPNNs with different numbers of hidden layers and neurons are represented as X-N-Y and XN-N-Y, where X is the number of input neurons, N represents the number of hidden neurons, and Y represents the number of output neurons.
concentrations, with the simple inputs of solution information and physical solution parameters. To generalize the developed methodology, we further discuss the predictive framework for the CO2 thermodynamic properties in solution environment by expanding the similar processes for the modeling and prediction of the aqueous solution density and viscosity. 2. Reaction mechanism The structure of potassium lysnate has a primary amine group (like monoethanolamine (MEA) solution) due to a carbon-nitrogen bond [39]. The equilibrium reactions between CO2 and potassium lysinate solutions are shown as follows [20,26]: k1
RNH+3 ↔ RNH2 + H+
(1)
k2
RNHCOO− + H2 O ↔ RNH2 + HCO−3
(2)
k3
CO2 + H2 O ↔ H+ + HCO−3
(3)
k4
HCO−3 ↔ H+ + CO32 −
(4)
k5
H2 O ↔ H+ + OH−
(5)
where R is lysine amino acid, and k represents the equilibrium constant for each reaction. The above chemical reaction is dominated kinetically by the direct reaction between CO2 and amino acid salt to produce a carbamate and a protonated amino acid:
CO2 + 2RNH2 ↔ RNH+3 + RNHCOO−
(6)
3. Methodology and modeling
3.2. Date collection
3.1. Modeling
Table 1 shows the range of data for CO2-PL and CO2-PL/MEA systems reported in previous literature. The input and output variables in the model and the number of datasets are given in this table. The target variables here are the values of CO2 solubility, density, and viscosity of the solution. It can be seen that a higher liquid concentration could improve the CO2 solubility results since the increase of the liquid concentration could enhance the chemical reaction between them. In addition, higher CO2 partial pressure and lower temperature result in a higher CO2 loading.
In this study, general regression neural network (GRNN) and feed forward neural network with a back-propagation (BPNN) algorithm were used for the non-linear fitting of the data [40,41]. A completed ANN model should consist of three different types of layer: input, hidden and output layers (Fig. 1) [42,43]. Each neuron in the input layer represents an independent variable. Each neuron in the output layer represents a dependent variable. Each neuron connects with all the other neurons in the other layer(s) nearby and each connection represents a numerical weight [30]. Using the weights, an activation function is used for acquiring the output values with the inputs of independent variables [44]. For BPNN, the training of a network is essentially the optimization of weights using a BP iteration method [45]. For each prediction target, an optimized BPNN should include an appropriate number of hidden layers and hidden neurons, in order to avoid under- or over-fitting. For GRNN, the hidden layer consists of two different types of layers: the pattern and summation layers (Fig. 1d–f). Unlike a conventional feed forward neural network, GRNN uses a regression method with a Gaussian function for data training. Compared with BPNN, GRNN has a fixed algorithmic network structure. Thus, it is not necessary to tune the GRNN structural information for minimizing
4. Results and discussion 4.1. Data analysis Taking the CO2 solubility as an example, the data analysis of “independent variable vs dependent variable” are plotted in Fig. 2. It can be clearly seen that for each value of the independent variable in this study, it has multiple values of CO2 solubility. None of the independent variable could have clear linear relationship with the CO2 solubility. This means that though physically there should be potential relationships between the independent variables and the CO2 solubility, linear regression or simple empirical equation of states might not be effective
Table 1 Data range of CO2 solubility, density and viscosity in PL and PL/MEA solutions. PL concentration range/M
MEA concentration range/M
No. of data
Operating pressure/kPa
CO2 partial pressure range/kPa
Temperature range/K
Solubility α/(mol CO2/mol solution)
Density ρ/(g/cm3)
Viscosity η/mPa s
Ref.
0.5–2.5 0.2001–3 0.5–2 0.26–1.98
0 0 0.5–2 0
63 220 78 72
101 101 101 101
5.4–41.47 0.069–17.444 2.64–47.52 –
298–313 313–333 303–323 298–333
0.17–1.063 – 0.511–1.05 –
1.0307–1.1738 0.9877–1.151 1.0232–1.1003 1.0008–1.1168
0.894–3.1652 0.4358–8.4071 1.005–1.514 0.5507–3.557
[26] [27] [28] [49]
154
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Fig. 2. Relationships between independent and dependent variables: (a) PL concentration vs CO2 solubility; (b) MEA concentration vs CO2 solubility; (c) total concentration vs CO2 solubility; (d) temperature vs CO2 solubility and (e) CO2 partial pressure vs CO2 solubility.
dramatically increase. Therefore, in this case, a BPNN with one hidden layer and four hidden neurons (5-4-1) could guarantee a good training result and meanwhile, have less time-consumption. To compare the performance of BPNN with GRNN, we further conducted repeated training and testing with shuffled data on BPNN 54-1 and GRNN, respectively. Three different sizes of training set were selected, including 70%, 80% and 90%. The average RMSEs were then acquired from the testing sets for model evaluation (Fig. 4). It can be clearly seen that for the prediction of CO2 solubility, BPNN with a 5-4-1 network structure significantly outperforms the GRNN, having the average RMSEs in the testing sets lower than 0.03 mol CO2/mol solution. To further evaluate the training and testing results on BPNN 5-4-1, we respectively picked a typical training and testing result for comparison (Fig. 5). It can be seen that in both the training and testing sets, the predicted values are highly close to their corresponding actual values, which indicates a good non-linear fitting performance.
for direct prediction. Therefore, to precisely predict the CO2 solubility, more complicated model is required. Since similar statistical results were found in the predictions of density and viscosity data, these additional results are not included in the paper. 4.2. CO2 solubility To search an optimal BPNN network configuration, different numbers of hidden layer and hidden neuron were selected for data training and testing. Fig. 3 shows the average testing RMSEs for the prediction of CO2 solubility, with varying hidden layer information. It can be clearly seen that with two hidden layers in a BPNN, the average RMSEs in the testing sets are generally high (Fig. 3, blue points), indicating an overfitting phenomenon. If there is only one hidden layer, the BPNN with 4–16 hidden neurons tend to show minimized average RMSEs in the testing sets. If the number of hidden neuron is lower than 4 or higher than 16, their RMSEs are relatively higher, which respectively indicates an under- and over-fitting. It should be noted that with more hidden neurons in the hidden layer, the required training time would 155
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Fig. 3. The average RMSEs of the testing sets in different BPNN hidden structures. Red points represent the BPNN with single hidden layer, with the network structure of 5-N-1 (where N represents the number of hidden neurons). Blue points represent the BPNN with two hidden layers, with the network structure of 5-N-N-1. Each point is the average testing RMSE after 20 training and testing processes with shuffled data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 6. Average RMSEs of GRNN and a BPNN 4-2-1 for the prediction of density with different training data sizes. Each point represents the average testing RMSE of 200 repeated training and testing processes with shuffled data.
Fig. 7. Average RMSEs of GRNN and a BPNN 4-2-1 for the prediction of viscosity with different training data sizes. Each point represents the average testing RMSE of 200 repeated training and testing processes with shuffled data.
4.3. Extension: Prediction of solution density and viscosity Fig. 4. Average RMSEs of GRNN and a BPNN 5-4-1 for the prediction of CO2 solubility with different training data sizes. Each point represents the average testing RMSE of 200 repeated training and testing processes with shuffled data.
With a similar method, we found that BPNN 4-2-1 could perform good model training for the prediction of both the aqueous solution density and viscosity, with minimized testing RMSEs and short timeconsumptions. Therefore, we compare the BPNN 4-2-1 with the GRNN for the prediction of the solution density (Fig. 6) and viscosity (Fig. 7),
Fig. 5. Predicted solubility values vs actual solubility values in a typical (a) training and (b) testing set using a BPNN 5-4-1. 156
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Fig. 8. Predicted solution density values vs actual density values in a typical (a) training and (b) testing set using a GRNN.
Fig. 9. Predicted solution viscosity values vs actual viscosity values in a typical (a) training and (b) testing set using a BPNN 4-2-1.
Fig. 10. The predictive framework for CO2 thermodynamic properties.
data summarized in Table 1, a GRNN is suitable for density prediction while a BPNN 4-2-1 is more suitable for viscosity prediction. To show the training and testing processes, Figs. 8 and 9 show the representative predicted-vs-actual values for the predictions of density and viscosity, respectively. It can be seen that in the training processes (Figs. 8a and 9a), though there exist several data points that deviate
respectively. Results show that for the prediction of density, GRNN has lower average testing RMSEs when the size of training set is relatively high (90%). This means that a higher proportion of training data could guarantee better training results of GRNN, compared to the BPNN. In terms of the viscosity, BPNN 4-2-1 outperforms the GRNN in all the three training sizes. Therefore, it is concluded that training with the 157
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
from the diagonal, most of them fit with the y = x line. In terms of the testing processes, all the predicted values are close to their corresponding actual values. These results indicate that our models have good precisions for interpolation analysis.
[4] G. Cau, V. Tola, F. Ferrara, A. Porcu, A. Pettinau, CO2-free coal-fired power generation by partial oxy-fuel and post-combustion CO2 capture: techno-economic analysis, Fuel 214 (2018) 423–435. [5] M. Rezakazemi, I. Heydari, Z. Zhang, Hybrid systems: combining membrane and absorption technologies leads to more efficient acid gases (CO2 and H2S) removal from natural gas, J. CO2 Util. 18 (2017) 362–369. [6] A. Baghban, A. Bahadori, A.H. Mohammadi, A. Behbahaninia, Prediction of CO2 loading capacities of aqueous solutions of absorbents using different computational schemes, Int. J. Greenh. Gas Control 57 (2017) 143–161. [7] E.F. da Silva, H.F. Svendsen, Computational chemistry study of reactions, equilibrium and kinetics of chemical CO2 absorption, Int. J. Greenh. Gas Control 1 (2) (2007) 151–157. [8] M. Wang, A. Lawal, P. Stephenson, J. Sidders, C. Ramshaw, Post-combustion CO2 capture with chemical absorption: a state-of-the-art review, Chem. Eng. Res. Des. 89 (9) (2011) 1609–1624. [9] Z. Zhang, F. Chen, M. Rezakazemi, W. Zhang, C. Lu, H. Chang, X. Quan, Modeling of a CO2-piperazine-membrane absorption system, Chem. Eng. Res. Des. 131 (2018) 375–384. [10] Z. Zhang, Comparisons of various absorbent effects on carbon dioxide capture in membrane gas absorption (MGA) process, J. Nat. Gas Sci. Eng. 39 (2016) 589–595. [11] X. Zhang, R. Zhang, H. Liu, H. Gao, Z. Liang, Evaluating CO2 desorption performance in CO2-loaded aqueous tri-solvent blend amines with and without solid acid catalysts, Appl. Energy 218 (2018) 417–429. [12] H. Liu, H. Gao, R. Idem, P. Tontiwachwuthikul, Z. Liang, Analysis of CO2 solubility and absorption heat into 1-dimethylamino-2-propanol solution, Chem. Eng. Sci. 170 (2017) 3–15. [13] H. Liu, M. Xiao, Z. Liang, P. Tontiwachwuthikul, The analysis of solubility, absorption kinetics of CO2 absorption into aqueous 1‐diethylamino‐2‐propanol solution, AlChE J. 63 (7) (2017) 2694–2704. [14] I. Iliuta, M. Hasib-ur-Rahman, F. Larachi, CO2 absorption in diethanolamine/ionic liquid emulsions – chemical kinetics and mass transfer study, Chem. Eng. J. 240 (2014) 16–23. [15] S. Rostami, P. Keshavarz, S. Raeissi, Experimental study on the effects of an ionic liquid for CO2 capture using hollow fiber membrane contactors, Int. J. Greenh. Gas Control 69 (2018) 1–7. [16] Q. Huang, S. Bhatnagar, J.E. Remias, J.P. Selegue, K. Liu, Thermal degradation of amino acid salts in CO2 capture, Int. J. Greenh. Gas Control 19 (2013) 243–250. [17] U.E. Aronu, H.F. Svendsen, K.A. Hoff, Investigation of amine amino acid salts for carbon dioxide absorption, Int. J. Greenh. Gas Control 4 (5) (2010) 771–775. [18] J. van Holst, G.F. Versteeg, D.W.F. Brilman, J.A. Hogendoorn, Kinetic study of CO2 with various amino acid salts in aqueous solution, Chem. Eng. Sci. 64 (1) (2009) 59–68. [19] Y. Yan, Z. Zhang, L. Zhang, Y. Chen, Q. Tang, Dynamic modeling of biogas upgrading in hollow fiber membrane contactors, Energy Fuel 28 (9) (2014) 5745–5755. [20] Z. Zhang, Y. Yan, L. Zhang, Y. Chen, J. Ran, G. Pu, C. Qin, Theoretical study on CO2 absorption from biogas by membrane contactors: effect of operating parameters, Ind Eng. Chem. Res. 53 (36) (2014) 14075–14083. [21] D. Kang, S. Park, H. Jo, J. Min, J. Park, Solubility of CO2 in amino-acid-based solutions of (potassium sarcosinate), (potassium alaninate + piperazine), and (potassium serinate + piperazine), J. Chem. Eng. Data 58 (6) (2013) 1787–1791. [22] M.E. Hamzehie, H. Najibi, Carbon dioxide loading capacity in aqueous solution of potassium salt of proline blended with piperazine as new absorbents, Thermochim. Acta 639 (2016) 66–75. [23] P.S. Kumar, J.A. Hogendoorn, S.J. Timmer, P.H.M. Feron, G.F. Versteeg, 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. [24] J. van Holst, S.R.A. Kersten, K.J.A. Hogendoorn, Physiochemical properties of several aqueous potassium amino acid salts, J. Chem. Eng. Data 53 (2008) 1286–1291. [25] A.A.R. Garcia, R.B. Leron, A.N. Soriano, M.-H. Li, Thermophysical property characterization of aqueous amino acid salt solutions containing α -aminobutyric acid, J. Chem. Thermodyn. 81 (2015) 136–142. [26] S. Mazinani, R. Ramazani, A. Samsami, A. Jahanmiri, B. Van der Bruggen, S. Darvishmanesh, Equilibrium solubility, density, viscosity and corrosion rate of carbon dioxide in potassium lysinate solution, Fluid Phase Equilib. 396 (2015) 28–34. [27] S. Shen, Y. Yang, Y. Wang, S. Ren, J. Han, A. Chen, CO2 absorption into aqueous potassium salts of lysine and proline: density, viscosity and solubility of CO2, Fluid Phase Equilib. 399 (2015) 40–49. [28] R. Ramazani, A. Samsami, A. Jahanmiri, B.Vd. Bruggen, S. Mazinani, Characterization of monoethanolamine + potassium lysinate blend solution as a new chemical absorbent for CO2 capture, Int. J. Greenh. Gas Control 51 (2016) 29–35. [29] Z. Liu, H. Li, K. Liu, H. Yu, K. Cheng, Design of high-performance water-in-glass evacuated tube solar water heaters by a high-throughput screening based on machine learning: a combined modeling and experimental study, Sol. Energy 142 (2017) 61–67. [30] H. Li, Z. Liu, K. Liu, Z. Zhang, Predictive power of machine learning for optimizing solar water heater performance: the potential application of high-throughput screening, Int. J. Photoenergy 2017 (2017) 1–10. [31] H. Li, X. Tang, R. Wang, F. Lin, Z. Liu, K. Cheng, Comparative study on theoretical and machine learning methods for acquiring compressed liquid densities of 1,1,1,2,3,3,3-Heptafluoropropane (R227ea) via song and Mason equation, support vector machine, and artificial neural networks, Appl. Sci. 6 (1) (2016) 25. [32] J.H. Park, Lumped Parameter Model for a Self Powered Fontan Palliation of the
4.4. Generalized predictive framework These case studies for CO2 thermodynamic properties prediction could potentially be a good way for ultra-fast analysis. A general flow chart of such a predictive framework is shown in Fig. 10. It can be seen that once a suitable predictive machine learning model is developed based on the previous experimental knowledge, a well-developed model could rapidly predict the target CO2 thermodynamic properties with an acceptable accuracy. With some widely used platforms (e.g., personal computer and Android [50]) or packages (e.g., Keras machine learning python library [51]), users can directly use a well-developed ANN model for direct prediction with simple data collection experiments of the solution properties (e.g., concentrations) and operating conditions (e.g., partial pressure and temperature) of the system. Additionally, it is worthy to mention that other state-of-the-art machine learning techniques, like support vector machine (SVM) [52], are also expected to have good predictive performances. In our case, since ANNs usually have better local-fitting capacity due to the higher degree of non-linear components, ANNs were selected as a case studies for the systems. We also expect that these approaches can also be extended to other fields such as mechanical and information systems [53,54]. 5. Conclusions Fundamentals of gas thermodynamic properties into solutions are industrially important in the gas removal field. In this paper, a welltrained machine learning model was used to predict CO2 solubility, solution density, and viscosity with various operating conditions and liquid concentrations. In total, 105, 164, and 164 data groups were employed in the predictive modeling for CO2 solubility, solution density and viscosity, respectively. The modeling results indicate that BPNN 54-1 was more suitable for predicting CO2 solubility compared with GRNN. On the other hand, a GRNN was suitable for density prediction while a BPNN 4-2-1 was more suitable for predicting viscosity. As a consequence, the proposed predictive framework has been proven useful for the rapid and accurate predictions of CO2 thermodynamic properties in the solutions. We expect that such a machine learning based predictive framework could be further applied to more thermodynamic properties of CO2-related aqueous systems. Acknowledgements We would like to acknowledge the financial support from the National Natural Science Foundation of China (No. 41572116), Open Funds of Key Laboratory of Jiangxi Province for Persistant Pollutants Control and Resources Recycle (No. ES201880049) and Fujian Provincial Key Laboratory of Featured Materials in Biochemical Industry (No. FJKL_FMBI201704), and Scientific and Technological Research Program of Chongqing Municipal Education Commission (No. KJ1709193). References [1] Z. Zhang, J. Cai, F. Chen, H. Li, W. Zhang, W. Qi, Progress in enhancement of CO2 absorption by nanofluids: a mini review of mechanisms and current status, Renew. Energy 118 (2018) 527–535. [2] S. Chaemchuen, N.A. Kabir, K. Zhou, F. Verpoort, Metal-organic frameworks for upgrading biogas via CO2 adsorption to biogas green energy, Chem. Soc. Rev. 42 (24) (2013) 9304–9332. [3] K. Maqsood, J. Pal, D. Turunawarasu, A.J. Pal, S. Ganguly, Performance enhancement and energy reduction using hybrid cryogenic distillation networks for purification of natural gas with high CO2 content, Korean J. Chem. Eng. 31 (7) (2014) 1120–1135.
158
Journal of CO₂ Utilization 26 (2018) 152–159
Z. Zhang et al.
Hypoplastic Left Heart Syndrome, (2015). [33] T. Liu, A. Jagota, C.Y. Hui, Effect of surface tension on the adhesion between a rigid flat punch and a semi-infinite neo-Hookean half-space, Extreme Mech. Lett. 9 (2016) 310–316. [34] S. Dreiseitl, L. Ohnomachado, H. Kittler, S. Vinterbo, H. Billhardt, M. Binder, A comparison of machine learning methods for the diagnosis of pigmented skin lesions, J. Biomed. Inform. 34 (1) (2001) 28–36. [35] T. Liu, N. Nadermann, Z. He, S.H. Strogatz, C.Y. Hui, A. Jagota, Spontaneous droplet motion on a periodically compliant substrate, Langmuir 33 (20) (2017). [36] A. Widodo, B.S. Yang, Support vector machine in machine condition monitoring and fault diagnosis, Mech. Syst. Signal. Process. 21 (6) (2007) 2560–2574. [37] B. Meredig, A. Agrawal, S. Kirklin, J.E. Saal, J.W. Doak, A. Thompson, K. Zhang, A. Choudhary, C. Wolverton, Combinatorial screening for new materials in unconstrained composition space with machine learning, Phys. Rev. B 89 (9) (2014) 82–84. [38] T. Liu, A. Jagota, C.Y. Hui, A closed form large deformation solution of plate bending with surface effects, Soft Matter 13 (2) (2016) 386–393. [39] P.S. Kumar, J.A. Hogendoorn, P.H.M. Feron, G.F. Versteeg, 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. [40] D.F. Specht, A general regression neural network, IEEE Trans. Neural Netw. 2 (6) (1991) 568–576. [41] K. Hornik, M. Stinchcombe, H. White, Multilayer feedforward networks are universal approximators, Neural Netw. 2 (5) (1989) 359–366. [42] H. Li, F. Chen, K. Cheng, Z. Zhao, D. Yang, Prediction of zeta potential of decomposed Peat via machine learning: comparative study of support vector machine and artificial neural networks, Int. J. Electrochem. Sci. 10 (8) (2015) 6044–6056. [43] Z. Liu, K. Cheng, H. Li, G. Cao, D. Wu, Y. Shi, Exploring the potential relationship
[44] [45]
[46]
[47]
[48] [49]
[50] [51] [52] [53] [54]
159
between indoor air quality and the concentration of airborne culturable fungi: a combined experimental and neural network modeling study, Environ. Sci. Pollut. Res. 6 (2017) 1–8. H. Li, Z. Liu, Performance Prediction and Optimization of Solar Water Heater via a Knowledge-Based Machine Learning Method, arXiv preprint, 2017. Z. Liu, K. Liu, L. Hao, X. Zhang, G. Jin, K. Cheng, Artificial neural networks-based software for measuring heat collection rate and heat loss coefficient of water-inglass evacuated tube solar Water heaters, Plos One 10 (12) (2015) e0143624. Z. Liu, L. Hao, G. Cao, Quick estimation model for the concentration of indoor airborne culturable bacteria: an application of machine learning, Int. J. Environ. Res. Public Health 14 (8) (2017) 857. Z. Liu, H. Li, X. Zhang, G. Jin, K. Cheng, Novel method for measuring the heat collection rate and heat loss coefficient of water-in-glass evacuated tube solar water heaters based on artificial neural networks and support vector machine, Energies 8 (8) (2015) 8814–8834. H. Li, Z. Zhang, Z. Liu, Application of artificial neural networks for catalysis: a review, Catalysts 7 (10) (2017) 306. S. Shen, Y.N. Yang, Y. Bian, Y. Zhao, Kinetics of CO2 absorption into aqueous basic amino acid Salt: potassium salt of lysine solution, Environ. Sci. Technol. 50 (4) (2016) 2054–2063. Y. Chen, Adaptive android kernel live patching, Usenix Security, (2017). F. Chollet, Keras, (2015). J.A.K. Suykens, J. Vandewalle, Least squares support vector machine classifiers, Neural Process. Lett. 9 (3) (1999) 293–300. Y. Chen, Z. Wang, D. Whalley, L. Lu, Remix: on-demand live randomization, ACM Conference on Data and Application Security and Privacy, (2016), pp. 50–61. X. Wang, Y. Chen, Z. Wang, Y. Zhou, Y. Zhou, SecPod: a framework for virtualization-based security systems, Usenix Conference on Usenix Technical Conference, (2015), pp. 347–360.