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Secondary Current Distribution in a Zinc Electrowinning Cell
Introduction
In a zinc electrowinning cell, zinc deposition is the desired main reaction at the cathode, whereas oxygen is evolved at the anode. A good alignment of the electrodes is required to achieve a uniform current distribution. Even small spatial deviations of the electrode placement in the cell may increase the tendency for short circuits and loss of current efficiency.
This model, which reproduces the results of Bouzek and others (Ref. 1), investigates the effect of the cathode alignment in a zinc electrowinning cell.
Model Definition
The model geometry is shown in Figure 1.
Figure 1: Modeled geometry.
The geometry is a unit cell containing a single electrolyte domain where the anodes and cathodes are modeled as electrode surfaces on the boundaries. The end of the electrodes are isolated using edge strips of isolating material. The stationary problem is solved using a parametric study, investigating the impact of displacing the cathode in the horizontal direction for a range of different values between −60 mm to +40 mm.
Concentration gradients in the electrolyte are neglected. This implies that a secondary current distribution is assumed. The model is set up using the Secondary Current Distribution interface using a constant conductivity of 36.2 S/m in the electrolyte.
At the cathode, zinc ions are reduced according to
Hydrogen evolution may also occur at the cathode according to
On the anode, oxygen is evolved:
Butler-Volmer expressions are used to describe the electrode reaction kinetics for all electrode reactions:
where the overpotentials for the electrode reactions, η, are defined by:
Using the Nernst equation, the equilibrium potentials, Eeq,are calculated according to:
where E0 is the standard electrode potential for the respective reactions, and ai denotes the species activity.
The anode and cathode surfaces are modeled using two Electrode Surface nodes, where the electrode reactions above are defined. The electric potential is set to 0 V at the anode and to 3.597 V at the cathode. The voltage of the cathode is thus the cell voltage. All other boundaries are isolated.
Results and Discussion
Figure 2 and Figure 3 show the electrolyte potential distribution for a cathode dislocation of -60 mm and +40 mm, respectively. The difference in electrolyte potential between the two plots is due to the change of available electrode surface areas, which causes a difference in the average overpotentials at the electrodes.
Figure 2: Electrolyte potential distribution for a cathode displacement of -60 mm.
Figure 3: Electrolyte potential distribution for a cathode displacement of +40 mm.
Figure 4 and Figure 5 show the electrolyte current density and streamlines of the electrolyte current for the same cathodes as in Figure 2 and Figure 3. The location of the maximum in electrolyte current is located toward the end of the shorter electrode.
Figure 4: Electrolyte current density distribution for a cathode displacement of -60 mm.
Figure 5: Electrolyte current density distribution for a cathode displacement of +40 mm.
Figure 6 shows a line graph of the total current density at the cathode for different cathode displacements. The most uniform current density is found for a cathode displacement of −20 mm.
Figure 6: Electrode density at the cathode for different cathode displacements normalized to the electrode density at x = 0.
Reference
1. K. Bouzek, K. Korve, O.A. Lorentsen, K. Osmundsen, I. Rousar, and J. Thonstad, “Current Distribution at the Electrodes in Zinc Electrowinning Cells,” J. Electrochemical Society, vol. 142, no. 1, 1995.
Application Library path: Electrodeposition_Module/Verification_Examples/zn_electrowinning
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D.
2
In the Select Physics tree, select Electrochemistry>Primary and Secondary Current Distribution>Secondary Current Distribution (cd).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Stationary.
6
Click  Done.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file zn_electrowinning_parameters.txt.
Geometry 1
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type l6+l2+l3.
4
In the Height text field, type 2*d4+d1+d5+d2.
5
Click  Build Selected.
Rectangle 2 (r2)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type l6+disp.
4
In the Height text field, type d4.
5
Click  Build Selected.
Rectangle 3 (r3)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type l5.
4
In the Height text field, type d5.
5
Locate the Position section. In the y text field, type d2+d4.
6
Click  Build Selected.
Rectangle 4 (r4)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type l6+disp.
4
In the Height text field, type d4.
5
Locate the Position section. In the y text field, type d4+d1+d5+d2.
6
Click  Build Selected.
Rectangle 5 (r5)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type l2.
4
In the Height text field, type d3+d4.
5
Locate the Position section. In the x text field, type l6+disp.
6
Click  Build Selected.
Rectangle 6 (r6)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type l4.
4
In the Height text field, type d5+2*d6.
5
Locate the Position section. In the x text field, type l5.
6
In the y text field, type d2+d4-d6.
7
Click  Build Selected.
Rectangle 7 (r7)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type l2.
4
In the Height text field, type d3+d4.
5
Locate the Position section. In the x text field, type l6+disp.
6
In the y text field, type d4+d1+d5+d2-d3.
7
Click  Build Selected.
Difference 1 (dif1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object r1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Find the Objects to subtract subsection. Select the  Activate Selection toggle button.
5
Select the objects r2, r3, r4, r5, r6, and r7 only (I.e. the other six rectangles).
6
In the Geometry toolbar, click  Build All.
The geometry is now complete.
Definitions
Anode
1
In the Definitions toolbar, click  Explicit.
2
Right-click Explicit 1 and choose Rename.
3
In the Rename Explicit dialog box, type Anode in the New label text field.
4
Click OK.
5
In the Settings window for Explicit, locate the Input Entities section.
6
From the Geometric entity level list, choose Boundary.
7
Select Boundaries 3 and 5 only.
Cathode
1
In the Definitions toolbar, click  Explicit.
2
In the Model Builder window, right-click Explicit 2 and choose Rename.
3
In the Rename Explicit dialog box, type Cathode in the New label text field.
4
Click OK.
5
In the Settings window for Explicit, locate the Input Entities section.
6
From the Geometric entity level list, choose Boundary.
7
Select Boundaries 2 and 6 only.
Integration 1 (intop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, locate the Source Selection section.
3
From the Geometric entity level list, choose Point.
4
Select Point 4 only.
Secondary Current Distribution (cd)
Electrolyte 1
1
In the Model Builder window, under Component 1 (comp1)>Secondary Current Distribution (cd) click Electrolyte 1.
2
In the Settings window for Electrolyte, locate the Electrolyte section.
3
From the σl list, choose User defined. In the associated text field, type sigma_l.
Electrode Surface 1
1
In the Physics toolbar, click  Boundaries and choose Electrode Surface.
2
In the Settings window for Electrode Surface, locate the Boundary Selection section.
3
From the Selection list, choose Anode.
4
Locate the Electrode Phase Potential Condition section. In the φs,ext text field, type phisext.
Oxygen evolution
1
In the Model Builder window, expand the Electrode Surface 1 node.
2
Right-click Electrode Reaction 1 and choose Rename.
3
In the Rename Electrode Reaction dialog box, type Oxygen evolution in the New label text field.
4
Click OK.
5
In the Settings window for Electrode Reaction, locate the Equilibrium Potential section.
6
In the Eeq text field, type E_O2.
7
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Butler-Volmer.
8
In the i0 text field, type i0_O2.
9
In the αa text field, type alphaa_O2.
10
In the αc text field, type alphac_O2.
Electrode Surface 2
1
In the Physics toolbar, click  Boundaries and choose Electrode Surface.
2
In the Settings window for Electrode Surface, locate the Boundary Selection section.
3
From the Selection list, choose Cathode.
Zinc reaction
1
In the Model Builder window, expand the Electrode Surface 2 node.
2
Right-click Electrode Reaction 1 and choose Rename.
3
In the Rename Electrode Reaction dialog box, type Zinc reaction in the New label text field.
4
Click OK.
5
In the Settings window for Electrode Reaction, locate the Equilibrium Potential section.
6
In the Eeq text field, type E_Zn.
7
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Butler-Volmer.
8
In the i0 text field, type i0_Zn.
9
In the αa text field, type alphaa_Zn.
10
In the αc text field, type alphac_Zn.
Electrode Surface 2
In the Model Builder window, click Electrode Surface 2.
Hydrogen evolution
1
In the Physics toolbar, click  Attributes and choose Electrode Reaction.
2
Right-click Electrode Reaction 2 and choose Rename.
3
In the Rename Electrode Reaction dialog box, type Hydrogen evolution in the New label text field.
4
Click OK.
5
In the Settings window for Electrode Reaction, locate the Equilibrium Potential section.
6
In the Eeq text field, type E_H.
7
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Butler-Volmer.
8
In the i0 text field, type i0_H.
Initial Values 1
1
In the Settings window for Initial Values, locate the Initial Values section.
2
In the phil text field, type 1.
Global Definitions
Default Model Inputs
Set up the temperature value used in the entire model.
1
In the Model Builder window, under Global Definitions click Default Model Inputs.
2
In the Settings window for Default Model Inputs, locate the Browse Model Inputs section.
3
In the tree, select General>Temperature (K) - minput.T.
4
Find the Expression for remaining selection subsection. In the Temperature text field, type T.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
From the Element size list, choose Extremely fine.
4
Click  Build All.
Study 1
Parametric Sweep
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
disp (Cathode displacement in parametric sweep)
0.04 0.02 0 -0.01 -0.02 -0.04 -0.06
m
5
In the Study toolbar, click  Compute.
Results
Electrolyte Potential (cd)
The default plot shows the electrolyte potential for the last displacement value in the sweep, that is -60 mm. Compare the plot in the Graphics window with that in Figure 2. Visualize the potential for the displacement +40 mm as follows:
1
Click the  Zoom Extents button in the Graphics toolbar.
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Parameter value (disp (m)) list, choose 0.04.
4
In the Electrolyte Potential (cd) toolbar, click  Plot.
Compare the result with that in Figure 3.
2D Plot Group 5
Next, visualize the electrolyte current density field for the same two displacement values in a combined surface and streamline plot.
1
In the Home toolbar, click  Add Plot Group and choose 2D Plot Group.
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Dataset list, choose Study 1/Parametric Solutions 1 (sol2).
Surface 1
1
Right-click 2D Plot Group 5 and choose Surface.
2
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Secondary Current Distribution>cd.IlMag - Electrolyte current density magnitude - A/m².
Streamline 1
1
In the Model Builder window, right-click 2D Plot Group 5 and choose Streamline.
2
In the Settings window for Streamline, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Secondary Current Distribution>cd.Ilx,cd.Ily - Electrolyte current density vector.
3
Select Boundaries 3 and 5 only.
Electrolyte current density
1
In the Model Builder window, click 2D Plot Group 5.
2
In the 2D Plot Group 5 toolbar, click  Plot.
Compare the resulting plot with that in Figure 4.
3
In the Settings window for 2D Plot Group, locate the Data section.
4
From the Parameter value (disp (m)) list, choose 0.04.
5
In the 2D Plot Group 5 toolbar, click  Plot.
Compare the result with the plot in Figure 5.
6
Right-click 2D Plot Group 5 and choose Rename.
7
In the Rename 2D Plot Group dialog box, type Electrolyte current density in the New label text field.
8
Click OK.
1D Plot Group 6
Finally, reproduce the plot of the current density distribution at the anode shown in Figure 6.
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, locate the Data section.
3
From the Dataset list, choose Study 1/Parametric Solutions 1 (sol2).
4
Click to expand the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Anode current density distribution for different cathode displacements.
6
Locate the Plot Settings section. Select the y-axis label check box.
7
In the associated text field, type Electrode current density (Normalized at x=0).
Cathode current distribution
1
Right-click 1D Plot Group 6 and choose Line Graph.
2
Select Boundary 6 only.
3
In the Settings window for Line Graph, locate the y-Axis Data section.
4
In the Expression text field, type cd.itot/comp1.intop1(cd.itot).
5
Locate the x-Axis Data section. From the Parameter list, choose Expression.
6
In the Expression text field, type x.
7
Click to expand the Legends section. Select the Show legends check box.
8
In the 1D Plot Group 6 toolbar, click  Plot.
9
Right-click Line Graph 1 and choose Rename.
10
In the Rename Line Graph dialog box, type Cathode current distribution in the New label text field.
11
Click OK.