Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 14906−14917
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Multiscale Velocity Unified Theory To Characterize Microscale Structure of Electrodes and Transfer Mechanism in CO2 Capture Yunsong Yu,† Wancheng Ding,† Zaoxiao Zhang,*,†,‡ and Geoff G. X. Wang§ †
School of Chemical Engineering and Technology and ‡State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, China § School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
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S Supporting Information *
ABSTRACT: Electrodes and transfer processes are the key to thermal electrochemical CO2 capture. The lifetime of electrodes and capture performance are significantly affected by the microscale (micro- and nanocrystalline) structural change and transfer mechanism. Experimental and timeconsuming theoretical studies are expensive, and it is difficult to understand microscale structural changes and transfer mechanism due to a lack of relevant unified knowledge. Thus, a time-saving multiscale velocity unified theory was developed by synergizing the molecular motion and matter movement. The theory well predicts the microscale structural change in electrodes and quantifies the chemical reaction and heat and mass transfer under normal and superhigh/superlow operating conditions. A porous electrode and U-shaped multilayer electrode were designed, and the lifetime of electrodes increased by 30%. The U-shaped multilayer electrode self-repairs its microscale structure, and its mass transfer coefficient increased by 15%. The theory simplifies the computational fluid dynamics and molecular dynamics simulation.
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INTRODUCTION CO2 capture significantly mitigates the CO2 level on a large scale. Thermal electrochemical process, membrane separation, and absorption have been developed as efficient technologies for CO2 capture.1−3 During thermal electrochemical CO2 capture (TECC), CO2 absorption occurs in the absorber as conventional amine absorption, and CO2 desorption proceeds by integrating the electrochemical method and thermal desorption.1,4 In the electrochemical method, electrodes and transfer processes (chemical reaction, heat and mass transfer) are the keys to obtaining a high performance. The lifetimes of electrodes and capture efficiency are significantly affected by the structural change (dynamic structure) and transfer mechanism. However, the structural changes in electrodes and the transfer mechanism in TECC are not well understood. Thus, it is essential to study the structural change in electrodes and transfer mechanism in TECC, providing guidance for the self-repair design and improving the capture efficiency to achieve a long-term operation. Extensive studies have been performed to understand the detailed structural changes in materials and the transfer mechanism.1,5−7 Usually, the micro- and nanostructures and transfer mechanism are studied experimentally or theoretically. However, the experiments and theoretical analyses are expensive, and sometimes it is difficult to achieve satisfactory results due to dynamic characteristics. Simultaneously, the unified knowledge of structural changes in electrodes and the transfer mechanism is still not enough. To reduce the analysis © 2019 American Chemical Society
cost and achieve unified knowledge, it is essential to develop a unified theory. By deeply analyzing TECC from the view of multiscale, it is found that molecular motion, chemical reaction, and heat and mass transfer are the main driving forces for CO2 capture. These driving forces show the traits of multiscale velocity, i.e., very fast molecular motion and fast chemical reaction, relatively slow heat transfer and slow mass transfer. The chemical reaction and heat and mass transfer can be classified into the matter movement compared with the molecular motion. Thus, this work aims to develop a multiscale velocity unified theory based on the synergy of molecular motion and matter movements. If such a unified theory can be developed accurately, it can be used to determine the complex structural changes of electrodes only by the basic parameters (pressure, temperature, etc.). Moreover, this will solve the problem that the dynamic micro- and nanostructures are hard to be obtained at the operation conditions by the experiment. Simultaneously, the unified theory can be employed to describe the unknown structures of micromaterials and nanomaterials.8,9 More importantly, the multiscale velocity unified theory can be extended to analyze the chemical reaction and heat and mass transfer processes in CO2 capture. This possibility can be Received: Revised: Accepted: Published: 14906
March 8, 2019 July 19, 2019 July 23, 2019 July 23, 2019 DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
Article
Industrial & Engineering Chemistry Research attributed to the fact that the chemical reaction and heat and mass transfer processes show similar multiscale velocity characteristics (fast chemical reaction, relatively slow heat transfer, and slow mass transfer) in CO2 capture. This will help to improve the CO2 capture process. The energy dissipation method was used to develop the unified theory. This method can be used to describe the energy change after considering the interactive effects of the multiscale velocities. According to the method, the energy before being unified is equal to the sum of energy after being unified and the energy dissipation amount. This satisfies the energy conservation rule. The unified mechanism involves the following: the interactive effects of multiscale velocities produce energy dissipations and gradually attenuate the multiscale effects, thus finally changing the multiscale velocities into a one-scale velocity. Thus, it can be reasonably assumed that the multiscale velocities can produce the stability characteristic naturally when the energy dissipation between multiscale velocities is properly controlled; i.e., the multiscale velocities are synergized. The idea here is to achieve a synergy for multiscale velocities using a velocity triangle. The formation of a velocity triangle reduces the energy dissipation by weakening the velocity slip between multiscale velocities. This is reasonable because the velocity triangle has the stability characteristic. Moreover, by analogy, the interior angle of the velocity triangle can be considered as the synergy angle developed in the field synergy theory.10 It is possible to use the interior angle of the velocity triangle to determine energy dissipation because the synergy angle has clearly quantified the energy dissipation in the field synergy theory. Based on these considerations, the multiscale velocity unified theory can be schematically shown in Figure 1.
The various materials used in CO2 capture have their own molecular motion velocities and matter movement velocities. They are used to develop the unified theory. For typical CO2 capture involving three types of matter (electrodes, CO2, and solutions), the energy balance is developed by considering kinetic energy and energy dissipation as follows: E1 + E21 = E23 + Ek
(1)
where E1 is the kinetic energy of matter. The subscripts “2” and “3” represent the maximum and minimum kinetic energies of three types of matter, respectively. E21 and E23 represent the energy dissipation, and Ek represents the unified energy correlating to reaction and transfer process. The energy dissipation can be developed by extending the field synergy. If the velocity does not reach the synergy state (the velocities required to produce the velocity triangle), i.e., the velocity triangle is not generated, the minimum velocity should be unified according to the energy dissipation of maximum velocities and original minimum velocities. This will be described later. This is reasonable according to the velocity slip mechanism and field synergy theory by considering that the multiscale velocity becomes one-scale velocity as the synergy reaches. Moreover, the best synergy occurs as the synergy angle becomes zero, indicating that the minimum energy dissipation is produced by directly unifying the velocity through energy dissipation. This energy dissipation process makes the random molecular motion relatively ordered. When the velocity triangle structure is established, the energy dissipations E21 and E23 are deduced using the field synergy theory10,13 as follows: E21 = v2v1 cos α
(2)
E23 = v2v3 cos β
(3)
where α and β are the interior angles of the velocity triangle. The velocities v1, v2, and v3 refer to the molecular motion velocities or matter movement (such as the amine solution flow on the surface of electrodes) velocities. If the matter is static, only the molecular motion velocities are considered. These angles show the synergy effects between molecular motion and matter movements. Here, the molecular motion is considered to change from the initial state to a unified state because of matter movement and reaction. The initial state of molecular motion can be transformed into the unified state using the energy dissipation equation ÄÅ ÉÑ Å Ñ 2 ∇·ρhvv − ∇·ηhÅÅÅÅ∇v + (∇v)T − ∇·vI ÑÑÑÑ = −h∇p + f ÅÅÇ ÑÑÖ 3
Figure 1. Multiscale velocity unified theory for CO2 capture.
As shown in Figure 1, the multiscale velocity unified theory can be used to quantify the structural changes in electrodes and typical chemical reaction and heat and mass transfer in CO2 capture and other processes. This is because these processes always involve multiscale information exchange, typically represented by molecular motion and matter movement.
(4)
where ρ and h refer to the density of a solution with dissolved CO2 and molecular fraction (considering the molecular number over the molecular numbers of the system) in the CO2 capture system. I is the unit tensor. p is the pressure, and f is the integrated force between the molecular motion, matter movement, and reaction. f is the sum of forces shown in Figure 2 and the other forces present in the phases, including the body force, drag force, and gravity. The body force and drag force are cited from the literature.10,12 The initial state of v is the velocity of the molecule. Additionally, the chemical and electrochemical reaction rates are usually scalar quantities and out of order, which can be transformed into a unified state due to matter movements and
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METHOD OF MULTISCALE VELOCITY UNIFIED THEORY To develop the multiscale velocity unified theory, the key is to determine the velocity triangle of materials. The basic principle is to develop the velocity triangle by following the energy conservation rule. First, the matter movement velocity is determined using the momentum equation in CO2 capture, as reported in the literature.11,12 14907
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
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Industrial & Engineering Chemistry Research
Figure 2. Force formation by velocity triangle to influence the material structure.
molecular motions. This can be determined using the following equation: ∇·ρhvc − ∇·∇(ρhDc) = s
(5)
where ρ and h are the reactant density and fraction, respectively. D is the diffusivity. c is the concentration. s is the source term owing to the molecular motion, matter movement, and reaction. This can be described as a function of reaction rate and concentration: s=
d(ρc) − ρk dt
Figure 3. Velocity triangle impact on material structure from parallel, vertical, and inclination cuts.
by parallel cut, vertical cut, and inclination cut. Because of these cuts, the structure can be a rectangle, triangle, line, and circle. During these shapes, the triangle structure is a typical structure because the velocity triangle is produced. In the triangle structure, the microstructure diameter can be theoretically calculated from the diameter of the circumcircle shown in Figure 4. The circumcircle is the circle of length
(6)
The initial state of v can be correlated with the scalar quantity of the chemical reaction rate and electrochemical reaction rates k as follows: v = k /(ca)
(7)
where a is an active chemical or electrochemical surface area. After determining the energy dissipation, the unified velocity of the CO2 capture system can be deduced as follows: vk = Ek /v0
(8)
where v0 is the reference velocity. Here, the velocity triangle is developed by considering three types of matter. In the case of two types of matter, the velocity triangle is considered as an isosceles triangle by considering two equal velocities. For one type of matter, the velocity triangle is considered as an equilateral triangle with three equal velocities. These considerations are acceptable because the molecular motion state can be assumed as the same for one matter under the same condition. Therefore, there are two and three equal velocities for the case of two and three types of matter, respectively. When the matter number is more than three, it is possible to first consider three matters and then consider the rest of matters step by step. However, the case of over three matters is not taken as the objective of this study, and hence it is not analyzed in detail here. Based on the unified velocity of CO2 capture, the electrode structure in CO2 capture can be determined precisely. Using the unified velocity, the structural change can be determined by the velocity triangle shown in Figures 2 and 3. As shown in Figures 2 and 3, the velocity triangle produces the force effects and finally applies the overall force on the material. The force makes the structural change of the material
Figure 4. Microstructure diameter model based on the circumcircle of velocity triangle.
triangle, produced by the side length of velocity triangle multiplied with time. It is reasonable that the microstructure becomes stable as the molecular motion and matter movements are synergized. Subsequently, the microstructure diameter d can be calculated using time average as follows: t
d=
∫0 1 (v1v2v3/S) dt t1
(9)
where t1 is the time period and S is the area of the velocity triangle. According to the energy dissipation, the nanocrystalline size of material dc can be expressed as follows: v dc = b d va (10) 14908
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
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Industrial & Engineering Chemistry Research where vb and va are the velocity before and after energy dissipation, respectively. According to the structural change determined by the multiscale velocity unified theory, the self-repairing of electrodes involves the recovery of the microstructure and nanocrystalline structure after CO2 capture by controlling the molecular motion and matter movement.
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METHOD OF NUMERICAL SOLUTION The numerical solution was used to solve the multiscale velocity unified model using the finite volume method. The multiscale velocity unified method can significantly reduce the computation cost because the energy dissipation equation actually correlates with the multiscale velocity. This correlation does not require the simultaneous computation of multiscale velocities, thus significantly saving the computation cost. Thus, in the following 80 μm × 60 μm electrode surface discussed, 1 024 000 (512 × 200) grid numbers were used to simulate the nanocrystalline structure. The unified velocity helps to achieve the time parallel computation for the two-scale calculation, thus saving a significant amount of computation time. The detailed numerical solution procedure is shown in Figure S1.
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MODELING AND EXPERIMENT TO VALIDATE MULTISCALE VELOCITY UNIFIED THEORY To test the multiscale velocity unified theory, the experimental results were used. The case of a chemical reaction between CO2 and monoethanolamine (MEA) solutions in a cubic box with a length of 10 Å was used to validate the unified theory. In the molecular dynamics (MD) simulation, periodic boundary conditions (PBC) and a Nose−Hoover thermostat were used for the simulation environment. The results of MD simulation and unified theory simulation are shown in Figures 5, parts a and b, respectively. The mean squared displacement curve is consistent with the literature results,14 verifying the accuracy of MD. As shown in Figure 5a, the velocities of MEA, CO2, and H2O molecules after energy dissipation were used to construct the velocity triangle during the simulation. At the times of 450, 700, and 1000 ps, the velocity triangles are clearly shown in Figure 5a. At the balance point, the velocity triangle is the smallest triangle, thus producing less energy dissipation. These results are consistent with the calculation of multiscale velocity unified theory, thus strongly validating the simulation. The calculations shown in Figure 5b confirm that the ordered movement of CO2 molecule can be obtained using the unified theory and fits well with Hellriegel’s model developed using the statistical method.15 A typical zone of 4 μm × 3 μm on the interface is considered when adding a typical body force of 15 kg/m2/s2. As shown in Figure 5b, the body force makes the molecule move in a relative order. For validating the structural change, the structures of fibers before and after CO2 absorption were simulated as shown in Figure6. The fibers included the nontreated and treated fibers of Stipa tenacissima (S. tenacissima). The experimental condition was set at 298 K. The S. tenacissima fiber was treated with CO2 and water. The triangles, circles, and rectangles in yellow color were obtained and fitted with the scanning electron microscopy (SEM) scanning results16 shown in Figure 6b. The average deviations for the triangle, circle, and rectangle circumferences were predicted to be 17, 12, and 14% away from the reading data of SEM results, respectively. The
Figure 5. Velocity triangle in the MD (simulation box 10 Å × 10 Å × 10 Å) (a) and molecular motion in the interface of gas−liquid phases (b).
Figure 6. Structural change owing to multiscale velocity effects: (a) before CO2 absorption and (b) after CO2 absorption (SEM scanning, length of S. tenacissima fiber at 298 K 1520 μm). Adapted with permission from ref 16. Copyright 2015 Elsevier Ltd.
positions of triangles, circles, and rectangles were determined as the velocity triangle was generated in the simulation process. Moreover, from the velocity triangle, the average microstructure length of fiber was calculated as 15−20 μm before CO2 absorption. This result fits the SEM scanning result shown in Figure 6a. The average microstructure length of the fiber was simulated as 10−18 μm after CO2 absorption. This result also fits the SEM scanning result shown in Figure 6b. 14909
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
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Industrial & Engineering Chemistry Research The microstructure reduction can be attributed to the reaction between CO2 and OH groups. The orderly structure identified by the sets of triangles appears after CO2 absorption. This qualitatively validates the multiscale velocity triangle theory because it is based on the disorder transformation into the relatively ordered transformation. This is also consistent with the literature results.16
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RESULTS Results of Cu Electrode in TECC. The validated multiscale velocity unified theory was used to predict the Cu
Figure 10. Crystalline size obtained using multiscale velocity (32−89 nm obtained from SEM).
Figure 7. Structure of Cu electrode used in TECC: (a) before capture and (b) after capture (Cu−MEA−CO2 system, microstructure length 4.5−12.5 μm).
Figure 11. Porous electrode and U-shaped multilayer electrode in the improved process of TECC.
Table 1. Typical Cu Amine Crystalline Sizea nanocrystalline size/nm Cu amine
original electrode
porous electrode
U-shaped multilayer electrode
CuMEA CuTEA CuDEA
52.83 (53) 41.78 48.76 (49.51)
47.55 39.11 43.88
43.21 32.05 38.59
Figure 8. Microstructure length of Cu electrode before and after CO2 capture (T = 363 K, CO2 loading 0.37 mol/mol, and 0.5 V). a
The values in parentheses are cited from the literature.19,21
electrode structure in CO2 capture. In the advanced TECC, a Cu electrode was used as the anode and cathode, and MEA was used. This is designed to barricade Cu dissolution by maintaining a low electrode potential. By thermal heating, a low concentration of oxygen is obtained in the cathode side, and thus the cathodes for acidic CO2 capture are inhibited successfully. The electrodes are the key units that provide the CO2 desorption driving force for CO2 capture. A large thermal and electrical conductivity of the Cu electrode and the integration of thermal and electrochemical desorption intensify the CO2 desorption, reducing the energy consumption and regenerating more CO2 effectively. MEA was selected because the CO2 absorption using MEA has the advantages of a high reaction rate and relatively high stability in an electrochemical environment. Additionally, MEA is normally used for the
Figure 9. XRD patterns of Cu complex and Cu oxide in Cu−MEA system.
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DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
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Figure 14. XRD patterns of U-shaped multilayer electrode under CO2 absorption (a) and under CO2 desorption (b) (desorption at 363 K).
Figure 12. Microstructure diameter (a) and SEM results obtained after cycles (b) of U-shaped multilayer electrode self-repair by CO2 absorption and desorption (time period 30 min, microstructure diameter range 3−10 μm).
Figure 13. CO2 bubbles in the surface of conventional electrode (a) and U-shaped multilayer electrode (b) (1 min after the reaction starts).
chemical absorption of CO2. Thus, MEA was selected to compare with a similar system. The Cu electrode was installed in a reactor of 0.1 m × 0.8 m. The electrode distance was set as 4 cm.The voltage applied was 1−2 V. The current density at the anode side was 0.03−0.1 A/cm2, and the current density at the cathode side was 0.0005−0.001 A/cm2. The order of magnitude of the current density is similar to the literature range.17 The MEA concentration is at 30% weight fraction. The desorption temperature was set at 353−363 K. This provides a higher thermal diffusivity of ions, reduces the resistance for electrochemical reaction, and increases the
Figure 15. Multiscale velocity unified theory for typical cases (a) and dynamic process of the multiscale velocity change (b).
reaction rate. However, the energy consumption and copper dissolution are increased as the temperature increases further. Thus, the temperature was set at 353−363 K to balance the energy consumption and CO2 desorption. The CO2 loading ranged from 0.3 to 0.46 mol/mol. An electrode was installed at a position of 0.3 m from the top of the reactor. An IRMES infrared analyzer was used to detect the desorbed CO2 in the 14911
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
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Figure 16. Unified multiscale velocity mechanism (A) and velocity triangle structure of chemical reaction case (B), heat transfer case (C), and mass transfer case (D).
TESCAN MAIA3LMH instrument. For the SEM analysis, the electrode surface was skinned off after the CO2 absorption. The skinned-off points were set at the top, middle, and bottom. By comparing the X-ray diffraction (XRD) results of skinnedoff samples, a slight difference was observed between the curves. Thus, SEM analysis was performed only for the sample from the middle section. As shown in Figure 7, the multiscale velocity unified theory predicted the triangle, circle, and rectangle structures (in yellow), which fit the scanned SEM images obtained from the quantitative view, with circumference deviations of 10−18%. In a further comparison, the microstructure length in the area of 80 μm × 60 μm is shown in Figure 8. The predicted microstructure length is consistent with the experimental data obtained from the SEM results. To analyze the crystal size, the components of electrodes must be determined first. Thus, the XRD patterns of electrodes were obtained, as shown in Figure 9. According to the multiscale velocity triangle, the nanocrystalline size is shown in Figure 10. The simulated nanocrystalline size obtained using the multiscale velocity triangle theory varied from 32 to 89 nm, consistent with the results obtained from the XRD patterns. These results also have the same order of magnitude reported in the literature.18−21 Simultaneously, the crystal size is consistent with the deduced results by SEM as shown in
Figure 17. Mass transfer coefficient versus nanocrystalline size.
process. The Cu anode dissolved slightly due to the presence of CO2 reaction products with MEA. However, the dissolution rate is very slow because the solution was refreshed quickly owing to liquid flow. Thus, the Cu dissolution is not currently considered. The Cu electrode was scanned by SEM using a 14912
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
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Industrial & Engineering Chemistry Research Table 2. Chemical Reaction Rate Constants Predicted by Multiscale Velocity Unified Theory molecular motion velocity of H2O (m/s)
system
amine concn (kmol/m3)
molecular motion velocity of amine (m/s)
original
CO2−MEA−H2O CO2−TEA−H2O CO2−AMP−H2O CO2−DIPA−H2O CO2−DEA−H2O CO2−AEEA−H2O CO2−PZ−H2O CO2−2DMAE−H2O CO2−DEMEA−H2O CO2−MDEA−H2O
0.1−10 0.1−5 0.1−7 0.1−7 0.1−2 0.1−1.2 0.8−5 0.1−7 0.1−7 0.1−7
113.64 73.32 94.07 79.48 89.90 87.73 91.32 96.38 82.09 84.7
209.34 211.32 209.34 216.19 217.26 211.04 211.04 214.49 209.29 217.94
chem reaction rate const (m3/kmol/s)
unified
molecular velocity of CO2 (m/s)
velocity involved with chem reaction calcd using velocity triangle (m/s)
this work
lit. data
− 138 − − − − − − − −
133.89 135.01 133.89 138.28 138.96 134.98 134.98 137.19 133.86 139.39
38810.397 6127.41 34745.09 33936.71 35974.82 34014.16 34655.45 36475.61 32621.45 35242.11
4084.14−7690.94 4.69−8.82 604.41−1181.88 845.03−2336.92 2257.35−3226.21 9309.77−12161.85 20243.83−129867.16 45.10−88.18 35.40−85.76 2.52−6.05
3703−840028 4.594−6034 100−81028 258535 650−317028 3717−1210025 21311−3160125 32−9527 79.829 2.5−6.228
Table 3. Heat Transfer Coefficients Predicted by Multiscale Velocity Unified Theory heat transfer coeff (kW/m2/K)
system natural air convective heat transfer supercritical CO2 heat transfer propane heat transfer CO2 hydrate mixture Na fluid and tube
fluid flow velocity (m/s)
molecular motion velocity of fluid (m/s)
molecular motion velocity of heat transfer interface (m/s)
A unified velocity (m/s)
velocity involved with heat transfer (m/s)
2.45
3.682
2.969
2.45
10.746
0.4
2.92
2.63
0.4
1.75
4
2.92
2.97
4
0.76
2.44
2.54
0.76
2
5.07
4.06
2
15.7 0.063 13.2
this work 7.705
lit. data 7.822
8751.91
865433
5980.74
515036
315
35032
1670
178024
angle, thus controlling the synergy of molecular motion and solution movement on the Cu electrode. The U-shaped multilayer electrode was designed to achieve more synergy of molecular motion and solution movement in both sides of the electrodes rather than in one side only. Based on the multiscale velocity triangle theory, the results obtained for porous and U-shaped multilayer electrodes are shown in Table 1. As shown in Table 1, the porous electrode reduced the crystal size by 10%. The U-shaped multilayer electrode reduced the crystal size as high as 23%. This is because in the case of porous electrode and U-shaped multilayer electrode, the velocity triangle closes at a shorter period due to a small contact angle and fast electrochemical reaction, thus making the crystalline structure smaller. Moreover, the force is balanced better in the case of porous electrode and U-shaped multilayer electrode, making the crystalline structure more regular and thus producing a smaller crystal size. These results indicate that the porous electrode and U-shaped multilayer electrode have a longer lifetime than the conventional electrode. This is because a smaller crystal size provides more contact area between the molecules of solutions and electrodes. The product such as MEAcomplex can be more easily regenerated in the smaller crystal size case, making the electrode maintain a high performance. Owing to these traits, the self-repair structure is achieved by making the CO2 absorption and desorption occur inside the U-shaped multilayer electrode. The results are shown in Figure 12. According to the results shown in Figure 12a and calculation,
Figure 7 and the velocity transformation shown in eq 10. For CO2 desorption in the TECC process, the CuMEA complex intensifies the CO2 desorption. This is because CuMEA immediately coordinates with the desorbed MEA and enhances the reaction equilibrium shift of MEACOO− and MEA+ to MEA and CO2. Thus, the crystalline CuMEA complex is welcome. The crystalline CuMEA complex can be controlled by adjusting the interior angles of the multiscale velocity triangle. As shown in Figure 10, the interior angles of the multiscale velocity triangle should be controlled around 43−72°. The values of two angles can be attributed to different contact situations between CO2, amine solutions, and Cu electrodes. According to the multiscale velocity triangle simulation, these two angles can be obtained by controlling the temperature at 368 K, CO2 loading at 0.32 mol/mol, and liquid fluid flow velocity at 0.5 m/s, and by using other methods such as designing proper electrodes. Results of Designed Porous Electrode and U-Shaped Multilayer Electrode. Based on the results, the electrode was designed in a porous electrode and U-shaped multilayer electrode to synergize the molecular motion and matter movement as shown in Figure 11. The porous and U-shaped electrodes were prepared using the electropolishing method. An annealing operation at 400−600 K was used for both electrodes in the air. To obtain the porous structure, phosphoric acid of 80−90% weight fraction was used. Mechanical bending was used to prepare the U-shaped electrode. The porous electrode was to reduce the contact 14913
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
0.01125 4.81 × 10−3 4.81 × 10−3 2.48 × 10−3
CO2−AMP CO2−MEA CO2−DEAB CO2−MDEA
0.002694 1.46 × 10−3 1.46 × 10−3 1.39 × 10−3
liquid (B) 0.543 4.54 1.6 0.4
original 0.013128 5.33 × 10−3 5.96 × 10−3 1.35 × 10−3
unified (C) × × × ×
5.3 × 10−5 4.94 × 10−5 5.65 × 10−5 6.02 × 10−6 2.89 1.26 1.26 1.26
E 10−5 10−5 10−5 10−5
velocity related to diffusion (m/s)
D
calcd intermediate velocity by velocity triangle of A, B, and C (m/s)
14914
temp (K)
3209 1123 548 4.2 3 × 107
B
Ar CH4 H2O Po He
A
CO2 CO2 CO Po He
system
439.27 259.86 227.55 7.27 162 657.1
molecular motion velocity of A (m/s) 686.79 406.28 283.81 7.27 162 657.1
molecular motion velocity of B (m/s) 439.27 259.86 227.55 7.27 162 657.1
virtual velocity for triangle (m/s) 471 675.31 165 064.31 80 547.85 52.91 264 573 248 41
velocity related to chem reaction by velocity triangle (m/s)
2.8 × 10
10
4
4
2.82 × 10 −5.23 × 10 2.47 × 104−5.25 × 104
m3/kmol/s
× × × ×
10−9 10−9 10−9 10−9
kmol/m3/s
10.32 × 106
s
chem reaction rate const
7.33 4.45 7.31 7.95
lit. data
0.546 29.4 0.849 0.231
this study
0.623 26.730 0.9130 0.2731
lit. data
mass transfer coeff (kmol/m3/h)
3.579 × 10436 4.89 × 10437 4.782 × 10−7−1.12 × 10−638 11.95 × 10639 3.15 × 101040
velocity involved with mass transfer calcd by velocity triangle of D, E, and F (m/s)
4.74 × 10−7−2.73 × 10−6
7.32 × 10−5 4.66 × 10−5 6.54 × 10−5 6.7 × 10−5
F
unified liquid velocity (m/s)
Table 5. Superhigh and Superlow Temperature Systems Predicted Using Multiscale Velocity Unified Theory
gas (A)
system
fluid flow velocity (m/s)
velocity related to chem reaction (m/s)
Table 4. Mass Transfer Coefficients Predicted by Multiscale Velocity Unified Theory
Industrial & Engineering Chemistry Research Article
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
Article
Industrial & Engineering Chemistry Research
electrode system is 40% larger than that in the conventional electrode. As shown in Figure 14a, CuCOO is observed the most under CO2 absorption. This is why a larger capacity is obtained in the U-shaped multilayer electrode. Additionally, more CuMEA complex is observed in Figure 14b under CO2 desorption compared with the conventional electrode shown in Figure 9. This suggests that a U-shaped multilayer electrode significantly intensifies the CO2 capture. According to the selfrepair results mentioned above, the lifetime of U-shaped multilayer electrode is theoretically increased by 30% over the conventional electrode. Based on these results, the multiscale velocity unified theory actually represents the multiscale idea because it synergizes the molecular motion and matter movement. It can precisely characterize the micro- and nanocrystalline structural changes in electrodes and guide the self-repair design for electrodes in CO2 capture. There is a great opportunity to extend the multiscale velocity unified theory to other fields. Discussion of Extended Application To Analyze the Transfer Process. To test the extended application of the multiscale velocity unified theory, the chemical reaction case and heat and mass transfer case in CO2 capture and beyond are given as typical examples. Here, the chemical reaction case and mass transfer case were selected to demonstrate the mass change quantification using the multiscale velocity unified theory. The heat transfer case was used to present the energy conversion using the multiscale velocity unified theory. Using the multiscale velocity unified theory, the models for these three cases were developed, as shown in the Supporting Information. Based on the model described above, the multiscale velocity unified theory can be used to predict the chemical reaction rate and heat and mass transfer coefficient, as shown in Figures 15−17. As shown in Figure 15a, the integration of reaction and heat and mass transfer is quantified using the multiscale velocity unified theory. The dynamic process of multiscale velocity change is shown in Figure 15b. According to the multiscale velocity unified theory, the mass transfer coefficient was predicted using the procedure shown in Figures 15 and 16. The results are shown in Figure 17, indicating the power to correlate the mass transfer coefficient with the nanocrystalline size. The U-shaped multilayer electrode shows a 15% higher mass transfer coefficient than the porous electrode. To maintain the high performance of the U-shaped multilayer electrode, the set position of the electrode can be controlled to adjust the matter movement because the fluid flow velocity is different in the reactor. The width or diameter of the electrode can be also controlled because it affects the contact area. To control the molecular motion, it is effective to adjust the temperature, voltage, and surface structure of the electrode. For typical CO2 absorption, the operating parameters and conditions are shown in Tables S1−S3.22−36 The calculation results are shown in Tables 2−4. As shown in Tables 2−4, the prediction error is below 16%. Thus, the multiscale velocity unified theory can predict the chemical reaction at normal and superhigh and superlow temperatures, as shown in Table S4 and Table 5. The superhigh and superlow temperature systems include CO2 reaction in Ar environment at 3209 K,37 CO2 reaction with CH4 at 1128 K,38 CO and H2O reaction at 548 K and 0.1 MPa,39 Po decay at 4.2 K,40 and He and He atomic reaction at 30 000 000 K.41 As shown in Table 5, the multiscale velocity unified theory provides the precise results.
Figure 18. Application of multiscale velocity unified theory to simplify the CFD calculation.
Figure 19. Application of multiscale velocity unified theory to simplify the MD simulation for diffusivity.
the porous electrode and U-shaped multilayer electrode capture CO2 with 8 and 20% larger capacity than the conventional electrode because the microstructure and nanocrystalline structure are almost recovered in a recycle. This is proven by the almost identical microstructure and nanocrystalline structure diameter before CO2 absorption and after CO2 desorption (at the eighth cycle) as shown in Figure 12a. The open-circuit potentials obtained after the 8th cycle, 14th cycle, and 18th cycle show a slight difference (in Figure S2). This also validates the self-repair characteristic. This is further validated by the SEM results shown in Figure 12b. As shown in Figure 12b, an obvious self-repair structure is observed compared with the results shown in Figure 7b. The reason for self-repair is that the CO2 absorption and CO2 desorption inside the U-shaped multilayer electrode provide an additional force for the CO2−amine−electrode system, thus synergizing the molecular motion and matter movement from the two sides of the electrodes rather than from one side in the conventional system. This is proven by more CO2 bubbles as detected using a High Speedsense Camera shown in Figure 13 and the XRD patterns shown in Figure 14. As shown in Figure 13, the CO2 bubble diameter in the U-shaped multilayer 14915
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
Industrial & Engineering Chemistry Research The multiscale velocity unified theory also affords to simplify the computational fluid dynamics (CFD) simulation for CO2 capture. This involves the mass transfer, heat transfer, and fluid flow.2,42 In the CFD simulation, the difficulties are focused on the solution of the mass transfer equation, heat transfer equation, and momentum equation. The velocity triangle relationship based on the mass transfer coefficient, heat transfer coefficient, and fluid flow velocity provides an additional constraint condition for the mass transfer equation, heat transfer equation, and momentum equation. For example, for the CFD simulation of CO 2 absorption in the reactor,12,43,44 the CFD simulation time was reduced by 30% by applying the multiscale velocity unified theory (Figure 18). For a complex system such as astronautics and deep ocean, the multiscale velocity unified theory is expected to simplify the CFD simulation in the future. MD has the ability to predict CO2 diffusivity in solutions. However, MD normally consumes much computational cost. The multiscale velocity unified theory uses molecular velocity to directly predict the CO2 diffusivity instead of costing too much computational time (Figure 19). The prediction error is below 7% compared with the literature data.45,46 The results mentioned above suggest that the multiscale velocity unified theory is powerful enough to simplify the CFD and MD simulations. This has great value for predicting a new complex system.
ACKNOWLEDGMENTS
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REFERENCES
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CONCLUSIONS The developed multiscale velocity unified theory well predicted the micro- and nanocrystalline structural changes in electrodes in TECC. According to the multiscale velocity unified theory, a porous electrode and U-shaped multilayer electrode were designed, and the lifetime of the electrode increased by 30%. The U-shaped multilayer electrode reduced the crystal size as high as 23% and increased the capacity by 20%. More importantly, the U-shaped multilayer electrode selfrepaired its micro- and nanocrystalline structures by controlling the molecular motion and matter movements and increased the mass transfer coefficient by 15%. Additionally, the multiscale velocity unified theory well predicted the transfer properties under normal operating conditions and superhigh or superlow temperatures, thus significantly simplifying CFD and MD simulations. ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b01303.
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Financial support of the National Natural Science Foundation of China (Nos. 51506165 and 21736008) is gratefully acknowledged. This work is also supported by the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2019JM-052), “Fundamental Research Funds for the Central Universities” and Fundamental Research Funds For the Central Universities (Creative Team Plan No. cxtd2017004).
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Article
Multiscale velocity unified theory to determine the chemical reaction and heat and mass transfer, procedure to solve the multiscale velocity unified model, open circuit potentials during a few cycles, operating conditions in chemical reaction, and heat and mass transfer cases (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Zaoxiao Zhang: 0000-0002-0960-4308 Notes
The authors declare no competing financial interest. 14916
DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
Article
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DOI: 10.1021/acs.iecr.9b01303 Ind. Eng. Chem. Res. 2019, 58, 14906−14917
