3.1 Numerical simulation of CO2 mineralization using calcium carbide slag and optimum process parameters
The mass transfer and heat pipe outlet water temperature for CO2 mineralization with calcium carbide slag were studied by controlling the length-to-diameter ratio (A), blade inclination angle (B), blade spacing (C), and blade diameter (D) in the device. The numerical simulation was carried out by designing orthogonal experiments, and the gradient was divided, as shown in Table 3. The 3D physical model of the mixing device centered on (0,0,0) was established using Solidworks software (Fig. 3). The model includes a slurry inlet and outlet, a CO2 source phase, and a heat pipe (screw thread spacing of 10 cm), The data from domestic and foreign studies on the degree of mineralization promoted by different factors were summarized, from which the rotational speed, pressure, solid–liquid ratio, and slurry entry speed were set to 2000 rpm, 5 Mpa, 0.25, and 0.8 m/s, respectively.
The length–diameter ratio, blade angle, spacing, and diameter of the mixing device are 1.5-3, 15–45°, 3–6 cm and 11–14 cm, respectively, and were equally divided into four gradients for orthogonal numerical simulation. The gradient was divided as shown in Table 3.
Table 3
Gradients in the orthogonal simulation.
Group
|
Factor
|
A
|
B
|
C
|
D
|
1
|
1.5
|
15°
|
3 cm
|
11 cm
|
2
|
2
|
25°
|
4 cm
|
12 cm
|
3
|
2.5
|
35°
|
5 cm
|
13 cm
|
4
|
3
|
45°
|
6 cm
|
14 cm
|
Note: The inlet speed of the heat pipe (water temperature 300 K) was 2 m/s |
The degree of mineralization and the heat pipe outlet water temperature were calculated when the mass of the CaCO3 outlet was stable. Sixteen groups of mineralization degree data and heat pipe outlet water temperature were obtained by orthogonal simulation, as shown in Table 4.
Table 4
Mineralization degree and water temperature after orthogonal simulation.
Group
|
Factor
|
Result
|
A
|
B
|
C
|
D
|
A (%)
|
T (K)
|
1
|
1,600
|
4.5
|
0.1
|
0.2
|
82.74
|
303.82
|
2
|
1,800
|
5
|
0.15
|
0.2
|
67.48
|
305.47
|
3
|
2,000
|
5.5
|
0.2
|
0.2
|
79.02
|
306.34
|
4
|
2,200
|
6
|
0.25
|
0.2
|
45.59
|
308.21
|
5
|
1,600
|
5
|
0.2
|
0.4
|
84.59
|
315.24
|
6
|
1,800
|
4.5
|
0.25
|
0.4
|
82.94
|
316.20
|
7
|
2,000
|
6
|
0.1
|
0.4
|
81.19
|
306.21
|
8
|
2,200
|
5.5
|
0.15
|
0.4
|
80.12
|
308.50
|
9
|
1,600
|
5.5
|
0.25
|
0.6
|
80.90
|
322.21
|
10
|
1,800
|
6
|
0.2
|
0.6
|
78.13
|
317.52
|
11
|
1,200
|
4.5
|
0.15
|
0.6
|
76.97
|
311.54
|
12
|
2,200
|
5
|
0.1
|
0.6
|
80.29
|
307.23
|
13
|
1,600
|
6
|
0.15
|
0.8
|
78.58
|
315.50
|
14
|
1,800
|
5.5
|
0.1
|
0.8
|
80.56
|
309.64
|
15
|
2,000
|
5
|
0.25
|
0.8
|
80.62
|
322.90
|
16
|
2,200
|
4.5
|
0.2
|
0.8
|
81.79
|
317.51
|
K11
|
81.70
|
81.11
|
81.20
|
68.71
|
|
|
K12
|
77.28
|
78.25
|
75.79
|
82.21
|
|
|
K13
|
79.45
|
80.15
|
80.88
|
79.07
|
|
|
K14
|
71.95
|
70.87
|
72.51
|
80.39
|
|
|
R1
|
9.75
|
10.24
|
8.69
|
13.50
|
|
|
K21
|
314.19
|
312.27
|
306.73
|
305.96
|
|
|
K22
|
312.21
|
312.71
|
310.25
|
311.54
|
|
|
K23
|
311.75
|
311.67
|
314.15
|
314.63
|
|
|
K24
|
310.36
|
311.86
|
317.38
|
316.39
|
|
|
R2
|
3.83
|
1.04
|
10.65
|
10.43
|
|
|
Note: A is the mineralization degree, and T is the water temperature. Kij represents the average mineralization degree and outlet temperature rise corresponding to level I in column j. Rj stands for kmax −Kmin in column j. |
The range of Rj reflects the influence of this factor on the degree of mineralization or temperature rise. The greater the Rj value, the greater the influence of this factor on the results. As can be seen from Table 4, for the degree of mineralization, R1 follows the order: A > D > B > C. For the heat pipe outlet water temperature, R2follows the order: A > D > C > B. Therefore, factor A has the greatest influence on both the degree of mineralization and the heat pipe outlet water temperature.
Table 5
Numerical simulation—Analysis of variance for mineralization degree.
|
A
|
B
|
C
|
D
|
Error
|
Sum of squared deviation
|
1831.33
|
40.31
|
9.41
|
190.16
|
2071.21
|
Degree of freedom
|
3.00
|
3.00
|
3.00
|
3.00
|
12.00
|
Fratio
|
3.54
|
0.08
|
0.02
|
0.37
|
|
Fcritical (0.05)
|
3.49
|
3.49
|
3.49
|
3.49
|
|
Significant
|
Significant
|
|
|
|
|
Note: Fratio represents F value, Fcritical value (0.05) represents significance level 0.05 |
Table 6
Numerical simulation—Analysis of variance for heat pipe outlet water temperature.
|
A
|
B
|
C
|
D
|
Error
|
Sum of squared deviation
|
245.51
|
3.93
|
12.48
|
18.72
|
280.63
|
Degree of freedom
|
3
|
3
|
3
|
3
|
12.00
|
Fratio
|
3.50
|
0.06
|
0.18
|
0.27
|
|
Fcritical (0.05)
|
3.49
|
3.49
|
3.49
|
3.49
|
|
Significant
|
Significant
|
|
|
|
|
Combined with the data in Tables 5 and 6, the analysis of variance shows that when the mineralization degree is an objective function (Wu et al. 2020), the Fratio for factors A, B, and D (3.54, 0.08, and 0.37, respectively) is greater than that when the heat pipe outlet water temperature is the objective function (3.50, 0.06, and 0.27, respectively). Thus A4B1D4 was selected under the objective function of the mineralization degree. When the heat pipe outlet water temperature is the objective function, the Fratio (0.18) of factors A, B, and D is greater than that when the mineralization degree is the objective function (0.02). Therefore, C4 was selected as the objective function for the heat pipe outlet water temperature. The optimal combination is A4B1C4D4, that is, the length-to-diameter ratio of the mixing device is 3, and the angle, spacing, and diameter of the blade are 15°, 6 cm, and 14 cm, respectively, which is the fourth group of sixteen orthogonal simulations.
3.2 Analysis of CO2 mineralization and quantification of heat extraction for mixing device
The length-to-diameter ratio of the mixing device has the greatest influence on the mineralization capacity and the heat pipe outlet water temperature. To a certain extent, increasing the length of the mixing device can increase the contact time between the calcium carbide slag and CO2, leading to greater reaction, a longer heat exchange time between the heat pipe and the high-temperature slurry in the mixing device, and improved heat exchange efficiency. Group 4 of the numerical simulation data was imported into TECPLOT post-processing software, and the nephograms of the CaCO3 concentration and temperature distribution (after the mass of CaCO3 at the outlet stabilized) were obtained (Fig. 4).
The nephograms of the CaCO3 concentration and temperature distribution show that the CaCO3 concentration and temperature were high near the entrance and low near the exit. This is because a large amount of heat is released after the reaction of Ca(OH)2 and CO2 to form CaCO3, which increases the temperature of the slurry containing CaCO3, resulting in a similar CaCO3 concentration distribution and temperature distribution. Table 4 shows that after the mass of CaCO3 at the outlet stabilized, the degree of mineralization and the temperature of the outlet reached 78% and 319.21 K, respectively. The calculation indicates that the mixing device with the A4B1C4D4 structure parameters can mineralize about 2.14 t of CO2 and consume 4.53 t carbide slag within one hour, which is equivalent to the CO2 released by complete combustion of 0.957 t coal. In addition, 2.35 m3 of water can be heated from 300 K to 319.21 K for the mineralization of 1 t CO2, where the amount of heat extracted reached 189.60 MJ.