Novel Method Based on Electric Field Simulation and Optimization for

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Novel Method Based on Electric Field Simulation and Optimization for Designing an Energy-Saving Magnesium Electrolysis Cell Ze Sun,† Yun Zhao,† Guimin Lu,*,‡ Ping Li,† Jin Wang,† and Jianguo Yu*,†,‡ †

State Key Laboratory of Chemical Engineering and ‡National Engineering Research Center for Integrated Utilization of Salt Lake Resources, East China University of Science and Technology, Shanghai 200237, China ABSTRACT: In this study, on the basis of simulation of the electric field, the design optimization methods for 120 and 250 kA magnesium electrolysis cells were developed. A 3D numerical model was built to simulate the electric field at the steady state to obtain the minimum resistance voltage which has a significant effect on the energy consumption in the magnesium electrolysis process. The major optimization was focused on adjustment of structural parameters, such as the relative positions of the anode and cathode, electrolyte height in the cell, and so on. An orthogonal design approach was used to optimize the structural parameters in a 120 kA cell, and the optimization criterion was applied to magnify the design of a 250 kA cell. The resistance voltage in the optimized 250 kA cell was computed, and the minimum resistance voltage was 1631.3 mV among the provided solutions. Hence, the developed model and simulation results would be useful for the design optimization of a magnesium electrolysis cell.

1. INTRODUCTION Magnesium, the eighth most abundant element in the earth’s crust, is widely used, especially in the energy-saving and environmental protection industries, because of its contribution to reduction of energy consumption and greenhouse gas emissions. With more attention to energy and the environment, magnesium will hold greater promise as a new weight-saving replacement for denser steel and aluminum alloys, and demands for magnesium will increase sharply in the future. It is known that there are two main magnesium production technologies: the electrolytic process and thermal reduction process. According to a report by James,1 the electrolytic process is a promising way to produce magnesium. However, there are over 10 kinds of different structure electrolysis cells used for magnesium production. Among them, the best one in commercial application is the diaphragmless electrolysis (DLE) cell2 designed by Norsk Hydro. The main characteristics of the DLE cell are both a high amperage load and a high current efficiency. Now main relevant scholars from Russia35 still keep active on the progress of the diaphragmless electrolysis cell. Like aluminum production, the process to produce primary magnesium is one of the most energy intensive industrial processes. The main factors for the loss of energy include current efficiency and voltage of the electrolysis cell. Factors which have significant effects on the current efficiency and voltage of the electrolysis cell include the shapes of the electrodes, anode cathode distance, current density, and so on. To design a new energy-saving electrolysis cell, a lot of work to improve the current efficiency and reduce the voltage of the electrolysis cell needs to be done. In early cell designs,6 a higher current efficiency was usually obtained by increasing the anodecathode distance, but that would result in a higher cell voltage. The current efficiency is typically in the range from 80% to 90%. Dow Chemical Co.7 reported that around 94% current efficiency could be reached when the current density is in the range of 0.71.2 A 3 cm2. Over the past decade, U.S. Magnesium Corp.8 r 2011 American Chemical Society

has successfully developed a new high-efficiency M-cell. The cell was optimized in many aspects, such as the current density, electrode geometry, electrode distance, magnesium separating compartment, cell thermal balance, and current efficiency. Some scholars in India and Turkey also did a lot of work to obtain a type of economical cell. Rajagopalan9 developed a low-energy intensive cell by utilizing the positive aspects of modular and multipolar cells. G€uden10 designed a cell like the HallHerault cell used for aluminum electrolysis. Following G€uden’s work, in recent years, a lot of work on the current density11 and hydrodynamics12 has been done to improve this kind of cell. The above-mentioned research work was done by experimental methods, which takes up a lot of money, time, and labor sources. In recent decades, mathematical modeling and computer simulation have become effective tools for solution of problems.1315 The simulation approach makes it possible to study the effect of each factor in many numerical experiments without more money and to evaluate the cell responses to variation of design parameters on a computer. However, reports about the simulation for the magnesium electrolytic process are few. Shcherbinin16,17 investigated the effects of the anode cathode distance, amperage, and air temperature on the heat balance in a magnesium electrolysis cell by the mathematical simulation of the three-dimensional temperature and electric field. Sun18,19 studied the flow field in a magnesium electrolysis cell by simulation, where the effect of an electromagnetic field was considered. Usually, there are three classical choices for the numerical solution of partial differential equations (PDEs), such as the finite difference method (FDM), the finite element method (FEM), and the finite volume method (FVM). These three methods are Received: May 13, 2010 Accepted: April 1, 2011 Revised: March 16, 2011 Published: April 01, 2011 6161

dx.doi.org/10.1021/ie101091p | Ind. Eng. Chem. Res. 2011, 50, 6161–6173

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Figure 1. Schematic drawing of the magnesium electrolysis cell: L = 2.91 m; W = 1.87 m; H = 1.40 m; h1 = 2.20 m; h2 = 0.95 m; D1 = 0.14 m; D2 = 0.26 m; D3 = 0.19 m; D4 = 0.07 m; ACD = 0.07 m; I, electrolysis compartment; II, metal separating compartment.

Table 1. Geometric Parameters Used for the Simulations value for the param (m)

120 kA symbol cell

distance between the cathode and the back wall

D1

distance between the cathode end and the cell bottom

D2

0.26

distance between the cathode top and the electrolyte surface D3

0.19

distance between the cathode and the partition

0.07

D4

0.14

widely used in electrochemical systems, especially in fuel cell research. Sukkee20 developed a multidimensional model to simulate proton exchange membrane fuel cells by the FVM, and Jain21 studied the optimization of polymer electrolyte fuel cell cathodes using the FDM. In this study, the FEM was utilized to design an advanced magnesium electrolysis cell. Numerical simulation studies on aluminum reduction cells were successfully applied with the help of the software ANSYS. Most of them were aimed at optimizing the thermoelectric field,22 electromagnetic field,23 thermo-electromechanical field,24 and magnetohydrodynamic (MHD) models.2527 As known to us, there are six important physical fields in the molten salt electrolysis cell,28,29 which include the electric field, magnetic field, temperature field, flow field, concentration field, and stress field. Among the six fields, the electric field involving the current and potential distribution is the energy foundation of operation and source of the other physical fields in reduction cells. Therefore, this study was aimed at optimizing the electric field distribution to develop a more economical cell, mainly focused on investigating how to reduce the resistance voltage by the adjusting cell structure parameters, such as the anode cathode distance, thickness of the anodes, thickness of the cathodes, and so on.

2. DESCRIPTION OF THE NUMERICAL SIMULATION 2.1. Configuration of the Electrolysis Cell. A 120 kA magnesium electrolysis cell is chosen as an example for design optimization. The geometric configuration of the cell is complicated,

Figure 2. Mesh for the magnesium electrolysis cell.

but it can be simplified to a half-model due to its symmetry. Figure 1 shows the schematic configuration of a 120 kA cell. The half-cell has the general shape of a cube with dimensions of 2.91 1.87 1.40 m, eight installed anodes with dimensions of 0.95 1.14 0.15 m, nine cathodes with dimensions of 0.95 1.14 0.05 m, and an anodecathode distance of 0.07 m. Other important parameters used for optimization are detailed in Table 1. 2.2. Mathematical Model. In the electrolysis process, direct current is inducted into the anodes, uniformly passing through the fused salt and then flowing out of the cathodes. Unlike previously proposed models 28,29 of thermoelectric transport in a magnesium electrolysis cell, the model described and solved in this study focuses on the voltage drop in the electric field. The basic assumptions made in the model are as follows: (1) The electrolysis process is at a steady state. (2) Current transport occurs the same way in the whole electrolysis cell. 6162

dx.doi.org/10.1021/ie101091p |Ind. Eng. Chem. Res. 2011, 50, 6161–6173


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(3) The resistances of the electrolyte, anodes, and cathodes are constant. (4) The influences between the two half parts of the cell are ignored. According to the assumption that the current is independent of time and there are no extra charges, the control equations of the conduction can be simplified to the Laplace equation as follows: ! ! ! D 1 DV D 1 DV D 1 DV þ þ ¼0 ð1Þ Dx Fx Dx Dy Fy Dy Dz Fz Dz n

n

∑ V ¼ i∑¼ 1 IR i¼1

ð2Þ

where V is the potential, I is the current, R is the resistance, and Table 2. Physical Parameters of the Electric Field30 average resistivity of resistivity of the

resistivity of the

the fused salt and liquid

anode (Ω 3 m)

cathode (Ω 3 m)

magnesium (Ω 3 m)

5.50 10

6

3.15 10

7

4.50 103

Fx, Fy, and Fz are the material resistivities in the x, y, and z axial directions, respectively. In eq 2, the summation symbol means to sum the voltages of all elements in the computational domain, such as the anode, the cathode, the electrolyte, and half of the cell. For the anode, n = 100 612, for the cathode, n = 34 892, for the electrolyte, n = 236 548, and for the half electrolysis cell, n = 372 052. In this study, the materials are isotropic, so the equation can be simplified as D DV D DV D DV þ þ ¼0 ð3Þ Dx Dx Dy Dy Dz Dz To solve the finite element equation, the method of separation of the variables is adopted. The numerical values of the current I, scalar potential V, and current density are obtained after calculation. 2.3. Finite Element Analysis. With the rapid increase of computer power in the past decade, the FEM has become an essential step in the design or modeling of a physical phenomenon in various engineering disciplines. In this work, the commercial software ANSYS was used to calculate the electric field in the magnesium electrolysis cell. To investigate the factors which have effects on the cell voltage and bypass current, a finite element (FE) model was built, which

Figure 3. Voltage variations with the cathode extension distance (where (a) = (b) þ (c) þ (d)). 6163



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Figure 4. Voltage variations with alteration of D4 (where (a) = (b) þ (c) þ (d)).

is shown in Figure 2. Three kinds of materials were used, the properties of which are presented in Table 2. To control errors to less than 5% for the mesh independence tests in industrial applications, the convergence of the FE models is checked by modifying the number and size of the meshing. In addition, the main challenges for studying the electric field of fused salt electrolysis are the boundary conditions and the complexity of the electrolytic process. Hence, a large number of elements for each model are needed to ensure the accuracy of the simulation results, while too many elements would take up a lot of time to compute. Thus, the numerical model with more than 300 000 elements is chosen as a compromise between accuracy and computation time. Each part of the model is meshed into hexahedral grids. From Figure 2, it can be found that the numerical model used in the present study can reasonably predict the electric field inside the magnesium electrolytic cell. Two types of boundary conditions, current and voltage potential, are loaded, which are shown as follows and in Figure 2: (1) At each top of the anodes, a current of 7.5 kA is applied, for a total current of 60 kA. (2) At each end of the cathodes, a voltage potential of zero is applied. (3) The symmetric boundary is applied on the x = 0 plane.

3. RESULTS AND DISCUSSION 3.1. Effect of the Relative Position of the Cathode and Anode in the Electric Field. Cell voltage is one of the most

important operational parameters. During the past 50 years, cell voltage has been reduced steadily, and its now seems to have reached a constant level at 4.85.3 V.8 Cell voltage is mainly composed of the decomposition voltage, overvoltage, anode voltage, cathode voltage, and electrolyte voltage. In this work, the resistance voltage, including the anode voltage, cathode voltage, and electrolyte voltage, is studied. There are many impact factors for the resistance voltage, such as the components of the electrolyte and the anode and cathode materials. To investigate the effects of the cell structure on the resistance voltage, the electric field obtained by FEM simulation is first analyzed, and the effects of positional parameters D1, D2, D3, and D4 in the cell on the resistance voltage are evaluated. 3.1.1. Effects of Extension of the Cathode Downward on the Resistance Voltage. To study the influence of the cathode width on the resistance voltage, all variables in the cell are kept constant, except the parameter D2 shown in Figure 1. The values of D2 are changed from 0.01 to 0.15 m, and the results are shown in Figure 3. From Figure 3, the voltages of the electrolyte, cathodes, 6164



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and resistance decrease as the offset distance D2 increases from 0.01 to 0.12 m and change slightly from 0.12 to 0.15 m. In the electrolysis process, the partial current at the end of the anodes usually goes through the electrolyte between the ends of the cathodes and the cell bottom and then back to the cathodes, but here most of it directly flows to the cathodes. That is the main reason why the electrolyte voltage goes downward. However, when the downward extended distance reaches 0.12 m, little bypass current continues going downward toward the electrolyte bottom, so the resistance voltage differences and electrolyte voltage differences change just a little. The simulation results of the cathode voltage present a descending trend from 109 to 108 mV. However, the anode voltage increases from 484 to 488 mV due to the higher current density at the anodes’ ends, and finally the maximum voltage drop is about 27.7 mV. 3.1.2. Effect of Cathode Extension toward the Partition Wall on the Resistance Voltage. To attempt to prevent current from going through the metal separating compartment and save energy, the cathode was extended toward the partition wall. Extending the cathode toward the partition wall means to shorten D4, as shown in Figure 1. This can prevent part of the bypass current from going into the metal separating

compartment. Parts a and b of Figure 4 show that there was a nearly linear decrease between the voltage and offset distance, and these two curves were very similar to each other. The reason is that the cathode changes cut down the distance of the bypass current, so the potential was reduced a lot. Meanwhile, the anode voltage and cathode voltage also changed a little with an increase of the offset distance. Figure 4c shows that the cathode voltage rose while the offset distance increased from 0.01 to 0.07 m, but the anode voltage almost stayed steady in Figure 4d. Consequently, the total reduced value of the anode and cathode was 25.2 mV, which shows that it is beneficial to lengthen the cathode toward the partition wall. 3.1.3. Effect of Cathode Extension toward the Back Wall on the Resistance Voltage. There is 0.14 m distance between the cathode and the back wall in the primary 120 kA cell. The current density is large in this region, and the voltage produced by this partial electrolyte should not be ignored. Therefore, it is necessary to investigate the voltage change by extending the cathode toward the back wall. Parts a and b of Figure 5 show the resistance voltage decreased as the offset distance was increased from 0.01 to 0.12 m and then 6165



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increased sharply. This obviously shows that 0.12 m is the critical point for the resistance voltage reaching the lowest value. This is because the ratio of the working areas of the anode and cathode is the best value when D1 = 0.12 m. Under this condition, the current flows the shortest distance in the electrolyte. Thus, the electrolyte voltage also reached the lowest value. Figure 5c shows that the anode voltage stayed steady, and in the Figure 5d, the cathode voltage linearly decreased due to the larger working area relative to constant current. 3.2. Effect of the Electrolyte Height on the Resistance Voltage. Usually there is a conventional operation liquid level for the electrolyte. For the cell studied, there is a 0.19 m distance from the surface of the electrolyte to the cathode top and a 0.26 m distance from the bottom of the electrolyte to the cathode end. These parts contain a lot of electrolyte; thus, the voltage drop produced by this partial electrolyte cannot be ignored. To obtain the lowest voltage, simulation of the electric field in these parts of the electrolyte was conducted to investigate the influence of the electrolyte height on the resistance voltage. 3.2.1. Effect of the Distance between the Electrolyte Surface and the Cathode Top on the Resistance Voltage. The current density of the electrolyte surface is very high, so this partial electrolyte voltage should be investigated by changing the height of the electrolyte. Parts a and b of Figure 6 show the resistance

and electrolyte voltages decreased with increasing distance from 0.01 to 0.10 m and then increased after 0.11 m. This indicates that the electrolyte current is sensitive to the distance between the electrolyte surface and the top of the cathode. As known to us, the voltage of the partial electrolyte above the top of the cathode drops definitely as the height of this partial electrolyte is cut down, since less bypass current goes to the electrolyte above the top of the cathode. Because the value of the current remains the same, the bypass current density of the other regions except the electrolyte above the cathode in the whole cell increases. Therefore, when the reduced voltage from the electrolyte above the top is less than the increased voltage produced by increasing the bypass current of the other regions, the total voltage increases conversely. That is the main reason for what happens in Figure 6a,b. In Figure 6c,d, the anode voltage and the cathode voltage basically stay steady. They have little impact on the voltage differences. The maximum voltage drop reached 18.3 mV, which demonstrates that the level of electrolyte needs to be taken into account in designing a new cell. 3.2.2. Effects of the Distance between the Cathode End and the Cell Bottom on the Resistance Voltage. In fact, it is necessary to leave room for sludge, but partial current from the anode end goes through this part. From the point of saving energy, the 6166



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Figure 7. Voltage variations with alteration of the distance from the cathode end to the cell bottom (where (a) = (b) þ (c) þ (d)).

Table 4. Orthogonal Design (L9(3)4) and Simulation Results

Table 3. Factors and Levels (A)

(B)

(C)

(D)

level

downward/m

forward/m

backward/m

shorten D3/m

1

0.11

0.12

0.05

0.09

2

0.13

0.11

0.06

3

0.15

0.10

0.07

test number

A

B

C

D

result/mV

1

1

1

1

1

1722.517

2

1

2

2

2

1718.736

0.10

3

1

3

3

3

1715.488

0.11

4

2

1

2

3

1715.779

5

2

2

3

1

1717.144

6

2

3

1

2

1718.726

7

3

1

3

2

1713.693

8 9

3 3

2 3

1 2

3 1

1719.167 1716.772

relationship between distance and voltage needs to be studied. Figure 7a shows that the resistance voltage almost remained steady when the offset distance was increased from 0.01 to 0.16 m and sharply increased as the offset was increased from 0.17 to 0.20 m. This means that the distance between the cathode end and the cell bottom should stay under 0.17 m. If the distance exceeds 0.17 m, the energy consumption will increase sharply in real industrial design. Parts c and d of Figure 7 show that the electrode voltage basically was not affected during this process. 3.3. Optimization and Comparison of Magnesium Electrolysis Cells. As in the above discussion, five factors have been observed to have effects on the resistance voltages, and these parameters’ interactions are not observed. To find the optimal design conditions in the magnesium electrolysis cell, here the

orthogonal design approach is used to find the optimum point among the five factors. The orthogonal design approach is constructed on the basis of combinatorial theory and is widely used in experimental designs. The orthogonal experiment is that in which the experiment strategies are arranged and the experiment results are analyzed according to the orthogonal array. It is applied to multifactor and multi-index experiments. According to the results presented in sections 3.1 and 3.2, four of the five factors have a significant effect on the resistance 6167



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Figure 8. Potential distribution contours in 120 kA cells.

Table 5. Parameters of the Orthogonal Design of a 250 kA Cell test number

number of anodes

cell length, L/m

cell width, W/m

cell height, H/m

height of the cathode, h/m

width of the cathode, b/m

1 2

12 12

1.73 1.73

2.41 2.32

1.29 1.34

0.9 0.95

1.66 1.57

3

12

1.73

2.50

1.24

0.85

1.75

4

12

1.73

2.61

1.19

0.80

1.86

5

14

1.99

2.17

1.29

0.9

1.42

6

14

1.99

2.10

1.34

0.95

1.35

7

14

1.99

2.25

1.24

0.85

1.5

8

14

1.99

2.35

1.19

0.80

1.60

9 10

16 16

2.25 2.25

1.99 1.93

1.29 1.34

0.9 0.95

1.24 1.18

11

16

2.25

2.07

1.24

0.85

1.32

12

16

2.25

2.15

1.19

0.80

1.40

13

18

2.51

1.85

1.29

0.9

1.1

14

18

2.51

1.80

1.34

0.95

1.05

15

18

2.51

1.92

1.24

0.85

1.17

16

18

2.51

1.99

1.19

0.80

1.24

voltage. The fifth factor, the distance between the electrolyte bottom and the end of the cathode, was eliminated due to little effect on optimization. Without considering interactions, the scheme is obtained by using the orthogonal array L9(34). The pairs for any two columns contain all possible combinations under three levels: (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3). We can use a few of the simulation results to represent the full consideration of the variables. Using the orthogonal design approach, a lot of time and energy can be saved. The research factors and levels are detailed in Table 3, where nine orthogonal design tests are needed to accomplish the goal. The detailed design approach and the relative simulation results are presented in Tables 3 and 4. Among the orthogonal design tests in Table 4, test 7 obtained the lowest voltage, 1713.7 mV. The optimum formula was formed for the 120 kA magnesium electrolysis cell. Compared with the original cell, the reduced voltage value reached 77.6 mV, which will save 81 572 kW 3 h for a single cell every year. From the contours of these two cells in Figure 8, compared with the potential distributions in regions I and II, the structure of the

optimized cell was obviously effective in reducing the voltage. Regions III and IV represent the potential produced by bypass current from the anode. It is clear that less bypass current went through region IV, and the optimum 120 kA cell can obviously save energy. 3.4. Design of a New Energy-Saving Electrolysis Cell. There are a lot of parameters that should be considered to design a new electrolysis cell, which include the amperage, cell voltage, current density, current efficiency, feeding, cell temperature, and anode and cathode shapes. On the basis of the previous design for a 120kA cell, a new cell with 250 kA is designed by the optimal strategy, where the cell voltage and cathode and anode sizes are the main variables; the others are set to be constant. The final design target for the new cell is the lowest Ohmic voltage, including the anode voltage, cathode voltage, and electrolyte voltage. Our goal is to design an energy-saving magnesium electrolysis cell. 3.4.1. Comparison among Different Cells with Different Numbers of Anodes. The first step is to verify the construction of the cell, which contains anodes, cathodes, and electrolyte. 6168



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Figure 9. Voltage distribution of different cathode heights (where (a) = (b) þ (c) þ (d)).

Figure 10. Voltage variations with alteration of the cathode thickness.

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Figure 11. Voltage variations with alteration of the anode thickness.

Table 6. Orthogonal Design and Simulation Results for Simple Verification of the Optimized 250 kA A/m

D3/m

C/m

result/mV

test 17 test 18

0.15 0.14

0.1 0.09

0.07 0.06

1631.312 1634.760

test 19

0.15

0.09

0.06

1634.965

test 20

0.15

0.1

0.06

1632.870

test 21

0.15

0.09

0.07

1634.583

Relevant publications, such as papers written by Gopalakrishna,7 Thayer,8 and Rajagopalan,9 indicate that a narrow anodecathode distance and a high current density are beneficial for design. Therefore, in the present study, the anodecathode distance was set to 0.03 m, the current density of the anode was 0.7 A 3 cm2, and the thicknesses of the anode and cathode were 0.15 and 0.05 m, respectively. Equations 4, 5, 6, and 7 were used to calculate the profile of the anodes, cathodes, and cell. F ¼

I ¼ 2nhb i

ð4Þ

L ¼ 0:3n þ 0:12 þ 0:15n þ 0:05ðn þ 1Þ

ð5Þ

W ¼ b þ 0:02 þ 0:07 þ 0:16 þ 0:50

ð6Þ

H ¼ 0:20 þ h þ 0:19

ð7Þ

where the variables F, I, i, n, h, b, L, W, and H represent the total working area of the anodes, amperage, current density of the anode, number of anodes, working height of the cathode, cathode width, cell length, cell width, and cell height, respectively. According to experience in industrial practice, four types of electrolysis cells with 12, 14, 16, and 18 anodes were used to investigate voltage drops. There are 16 solutions due to 4 working heights of the cathode. Detailed parameters are given in Table 5. The data in Table 5 are based on the half model of the magnesium electrolysis cell. All the solid models were meshed into over 1 million hexahedrons. The mesh independence tests

were carried out to establish the effect of the mesh size on the calculated results. Computations of 16 tests were carried out, and the level of results residuals was less than 105. Figure 9a shows that the resistance voltage decreased as the number of anodes increased from 12 to 18. The total voltage of the cell with 18 anodes was the lowest. The resistance voltage achieved the lowest value when the working height of the anode was 0.80 m. There is an approximately linear relationship between the height of the cathode and the Ohmic voltage drop for every type of cell. The voltage differences at different heights of the cathode were almost equal to each other, as shown in Figure 9a,c,d. Figure 9c shows that the cathode voltage decreased with increasing working height of the cathode. However, there were few changes in the anode voltage drop from 12 anodes to 18 anodes, which is shown in Figure 9d. 3.4.2. Comparison among Different Cells with Different Thicknesses of the Anode and Cathode. Test 16, the most outstanding cell above, can obtain the lowest voltage, 2119.2 mV. However, the anode and cathode voltages take about 0.47 fraction, but only 0.35 fraction in the optimized 120 kA cell. Hence, the next step was planning to reduce the ratio, and major work was done on the influence of the anode and cathode thicknesses on the voltage. The simulation model was based on test 16, and the anode was reduced from 2.2 to 2.0 m. Figure 10a presents a decreased voltage of the cathode, which dropped from 221.7 to 139.5 mV as the thickness increased from 0.05 to 0.08 m. The same phenomenon happened in Figure 10b, and the final result was reduced by 137.7 mV. In Figure 10b, the cell with a 0.08 m thickness of the cathode behaved the best and was used for investigating the effect of the anode thickness on the voltage. Figure 11a shows that there was a linear decrease with an increase of the anode thickness from 0.15 to 0.20 m, the same as in Figure 11b, and the maximum resistance voltage difference reached 207.7 mV. The value of the voltage reduced on the anode was 162.1 mV, which takes 0.78 fraction. This suggests that the thickness of the anode has a significant effect on the resistance voltage. 3.4.3. Developing a New Cell with 18 Anodes on the Basis of the Optimum 120 kA Cell. To obtain the optimum cell with 18 6170



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Figure 12. Potential distribution of contours in 250 kA cells.

Figure 13. Vectors of current density in the metal separating compartment.

anodes, according to the successful design of the 120 kA cell, the downward extended distance of the cathode relative to the anode, the reduced distance between the electrolyte surface and the cathode top, and the extended distance of the cathode relative to the anode in the direction toward the partition wall were considered in this part and orderly substituted by factors A, D3, and C. On the basis of the results in section 3.4.2, 0.08 m was selected for the cathode thickness and 0.20 m for the anode thickness. Table 6 presents the variables and corresponding simulated results. Test 17 was based on the optimum condition of the 120 kA cell, and it was verified that test 17 obtained the lowest resistance voltage by comparison with the other four tests. Compared with the simulation result (1689.2 mV) of the original cell with 18 anodes, the resistance voltage of the optimum 250kA cell was 58.0 mV lower. Parts a and b of Figure 12 show that the electric potential distributions are different, mainly focusing on the metal separating compartment and regions A and B. In theory, the current should not go through this part. However, if using the electrolysis magnesium cell without optimization, a large fraction of current will pass this region due to the large current. In Figure 12b, the metal separating compartment behaved perfectly, with only little resistance voltage. Region D in Figure 13a represents the surface of the electrolyte in the metal separating compartment, and the

details are shown in Figure 13b. From the viewpoint of current density, region C shows that most of the bypass current from the anode went back to the cathode surface after a short path in the vertical plane of region C. Hence, the current density of the metal separating compartment was very low. The maximum was 125.62 A 3 m2, which is shown in Figure13b. Region F in Figure 13b represents the bypass current from the anode. Region G refers to partial backflow of the bypass current. The current density value in this region is very small relative to the anode current density. This phenomenon means that the optimized cell was beneficial in reducing the electrolyte voltage in the metal separating compartment. In short, from the above simulated results, the design of the optimum 250 kA cell was in agreement with the guidelines obtained from optimization of the 120 kA cell, which are beneficial in gaining a better potential distribution and a lower cell voltage. If the decomposition and over voltages are 2.735 V, the external voltage is assumed to be 0.25 V, and then the theoretical cell voltage could attain a values of 4.616 V. Compared with the electrolyzers8 in commercial use, this cell is more competitive in cell voltage.

4. CONCLUSIONS 3D electric field simulation was first conducted to design and optimize the magnesium electrolysis cell. The effects of the 6171


Industrial & Engineering Chemistry Research anodecathode distance and cell configuration on the resistance voltage were investigated by 3D simulation. The simulation results indicate that the cathode size and cell configuration have significant effects on the resistance voltage distribution, and good design results can be obtained by the reasonable modification of the cell structural parameters. Five cell relevant structural factors are studied, and their effects on the resistance voltage are analyzed for further design optimization of a 120 kA cell. The simulation results show that the cathodes need to be longer and wider than the anodes. By comparison of cells with different working heights and thicknesses of the cathode and anode, it was confirmed that the 250 kA simulation model based on 120 kA optimization criteria was able to achieve a lower voltage than cells in commercial use. In conclusion, the design optimization approach, FE models, and simulation results presented in this work will be useful to understand the effect of the electric field on the cell voltage and will play an important role in the design and operation of advanced magnesium electrolysis cells.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (J.Y.); [email protected] (G.L.). Fax: 86-21-64252826. Tel.: 86-21-64252826.

’ ACKNOWLEDGMENT We acknowledge the financial support provided by National Natural Science Foundation of China (Grant 50874048), National High-tech R&D Program (Grant 2009AA06Z102), and the Fundamental Research Funds for the Central Universities. ’ NOMENCLATURE A = downward extended distance of the cathode relative to the anode (m) b = width of the cathode (m) C = extended distance of the cathode relative to the anode in the direction toward the partition wall (m) D1 = distance between the cathode and the back wall (m) D2 = distance between the cathode and the cell bottom (m) D3 = distance between the cathode top and the electrolyte surface (m) D4 = distance between the cathode and the partition (m) F = total working area of the anodes (m2) H = cell height (m) ACD = anodecathode distance (m) h1 = height of the anode (m) h2 = height of the cathode (m) I = mean current (A) i = current density of the anode (A 3 m2) L = cell length (m) n = number of anodes R = mean resistance (Ω) V = mean voltage potential (V) W = cell width (m) Greek Letters

F = material resistivity (Ω 3 m)

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