1 Introduction

Aluminum production is growing steadily since the invention of the Hall–Héroult process in 1886. The basic design of the cell has not changed much since its invention. As shown in Fig. 1, top down, a Hall–Héroult cell is made of a carbon anode followed by cryolite-based electrolyte (a liquid at the operating temperature of the cell of ~ 960 °C), molten aluminum, carbon cathode, collector bar and various insulation layers. A solidified electrolyte layer on the side walls in contact with the liquid bilayers called the ledge protects the side insulation layers. A solid crust layer above the molten electrolyte and the anode protects the electrolyte bath from the ambience humidity and oxygen, in addition to minimizing the top heat losses. An outer steel case houses all these components for structural integrity. Current enters the cell through the carbon anode hung from a steel yoke and comes out from the cathode via a collector bar. It follows vertically in the high resistive electrolyte bath and horizontally in the collector bar. Multiple cells are arranged side by side in a potline, as depicted in Fig. 2, and several potlines are present in a typical aluminum smelter. A number of successful attempts have been made to improve the basic Hall–Héroult cell in terms of alumina feeding, anode and cathode materials, effective process control, low energy consumption, high productivity and better stability [1,2,3,4]. Generally, the energy consumption in the electrolysis process for production of 1 kg of aluminum falls in the range of 12–15 kWh [5,6,7]. The energy efficiency of this process is about 45–50%, i.e., more than half of the electrical energy input to a modern Hall–Héroult cell for the aluminum production is lost as heat. So, finding opportunities to minimize the specific energy consumption is a high priority for primary aluminum producers. Some of the big opportunities lie in the: (a) development of inert anode [8], (b) designing of stable, drained cathode lining [2, 8, 9] and (c) effective control of metal pad turbulence [10,11,12].

Fig. 1
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Schematic diagram of a Hall–Héroult cell

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Fig. 2
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Arrangement of cells in a pot line

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Mainly, the specific energy consumption in a cell depends on cell voltage and current efficiency. A 100% current efficiency is not possible because of ineluctable back reactions of aluminum with dissolved carbon dioxide present in electrolyte [13, 14]. In general, the voltage drop in a modern, high-capacity Hall–Héroult cell has come down to as low as 3.7 V [5]. A typical Ohmic voltage drop in some of the important cell components is shown in Table 1 [15].

Table 1 Cell voltage distribution
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Voltage drop in the electrolyte is directly proportional to anode cathode distance (ACD). However, decreasing ACD is constrained by instability [16], whose sources are:

  1. (i)

    The Kelvin–Helmholtz instability of the mean flow

  2. (ii)

    Magneto-hydro-dynamics (MHD)

The disturbing phenomenon at interface between two parallel and horizontal streams of different velocities and densities is called the Kelvin–Helmholtz instability [17], whereas the destabilizing mechanism of electromagnetic (Lorentz) force which creates interface deflection is the result of MHD flow. The collective voltage drops in carbon anode and stub–anode interface is known as anodic voltage drop. Richard et al. [18] mentioned that 25% of anodic voltage drop occurs at stub–anode interface. The rest is contributed by resistivity of anode material. Since it is nearly impractical to reduce the resistivity of anode significantly [4], attention is given to a cathode voltage drop (CVD) defined as the difference of electric potential between metal pad surface and the outside end of the collector bar. Nearly, half the magnitude of the CVD is incurred in the metal collector bar [19]. The only viable way to minimize the CVD is to increase the conductivity of the carbon block–collector bar assembly. Significant efforts are currently directed toward increasing the thermal efficiency of the cell by using a Cu insert in the conventional carbon steel collector bar [20,21,22,23,24,25,26,27].

Kaenel and Antille [20] have reported an energy saving of 0.5–1.0 kWh/kgAl and a productivity increase of 10–20% in a 170 kA concept cell as a result of a decrease in ACD and the cell voltage and an increase in cell amperage which was possible by a change in the metal pool height achieved by a change in carbon block design and the use of a copper insert. A study by Gagnon et al. [21] found that the use of a copper insert is economically beneficial; however, a detailed energy balance was not performed. In another of a simulation study, a decrease in Lorentz force of 50% with a concomitant decrease in the CVD was predicted due to the improvement in current distribution in the molten metal as result of using a copper collector bar in place of steel. However, the energy balance of the pot was not performed [22]. A design optimization study by Blais et al. [23] found that the optimum design of the cathode should give uniform current distribution at the surface of the cathode block. Such a design had a wedge shaped Cu insert at the bottom of the steel bar. The wedge shape spanned in horizontal as well as in vertical directions. The enhancement of cathode life was projected to be 20% with a CVD of 93 mV. However, like majority of simulation studies, the issue pertaining to the ledge profile and the energy imbalance as a result of a use of insert was not addressed.

In this paper, a thermoelectric balance, including ledge profile evolution and the stability, under steady-state operation of an aluminum reduction cell with an insert-free base and a set of Cu insert models is studied computationally. With the introduction of a Cu insert, a reduction in heat generation occurs due to a reduction in the CVD results. The heat imbalance in a cell employing a Cu insert with respect to the insert-free smelting pot is quantified. Noninvasive strategies to counter the heat imbalance resulting from the introduction of a Cu insert are further investigated. It is demonstrated that an increase in the cell current with the introduction of a Cu insert not only increases the productivity but it also decreases the specific energy consumption, without adversely affecting the stability.

2 Model Description

In this section, various elements of the model such as the geometry, governing equations, boundary conditions and assumptions are explained. The section ends with the description of a very critical model element: the numerical procedure to extract the steady-state ledge profile. A ledge is a solidified electrolyte region at the side of the cell in contact with the molten electrolyte and liquid aluminum. Due to extreme corrosiveness of the molten fluorides to virtually all known materials including the ceramics and refractories, the formation of this layer in between the liquid phases and the refractory lining material (e.g., SiC) enhances the cell life. However, a certain minimum heat flux is to be allowed for the formation of a steady-state ledge profile.

2.1 Model Geometry

It is an enormous challenge to simulate a complete Hall–Héroult cell. The inherent symmetry (Fig. 3) of the cell, however, allows us to study only the half of the portion undeneath an anode by making assumptions of a long, high-capacity cell with no corner effect. A slice model of a Hall–Héroult cell was built in ANSYS Mechanical Enterprise 17.0 (ANSYS, Inc., Canonsburg, USA), as shown in Fig. 4. The ledge domain is split into two parts by the interface plane separating the electrolyte and the metal bath for extraction of ledge profile as explained in Sect. 2.4. The cathode carbon block and collector bar assembly are modeled with and without a cylindrical copper bar insert. The insert-free model is named the base case and the rest are insert case/s.

Fig. 3
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Schematic of the top view of a pot/cell

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Fig. 4
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Front view of the Cu insert slice model showing all participating domains studied in this work

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The copper insert inside a collector bar is shown in Fig. 5a, and the complete model geometry with a sample nonconformal mesh is shown in Fig. 5b. The model cases, I-VI, are defined based on length (L1 = 1625 mm and L2 = 1910 mm) and diameter of the insert (Table 2).

Fig. 5
figure 5

a Collector bar-copper insert assembly. b Nonconformal meshed slice model with a refined mesh in the ledge region. The Cu insert resides inside of the collector bar and is not seen in b

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Table 2 Length (L) and diameter (D) of the copper insert studied under insert models
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2.2 Governing Equations

The steady-state thermo-electrical energy balance (Joule Heating) was studied. The governing equations for the electric potential, V, are:

$$\nabla \cdot J = 0$$
(1)
$$J = \sigma E$$
(2)
$$E = - \nabla V$$
(3)

where J is current density, E is electric field strength, and σ is electrical conductivity.

The governing equations for the thermal energy balance are:

$$Q = J \cdot E$$
(4)
$$\rho C_{p} \frac{\partial T}{{\partial t}} - \nabla \cdot \left( {k\nabla T} \right) = Q$$
(5)

where \(\rho\) is density, \(C_{p}\) is heat capacity, k is thermal conductivity of the material and Q is Ohmic heat source. The volumetric Ohmic heat generation (Q: internal heat source) is coupled with the steady-state heat balance equation.

The radiation heat transfer is taken care by increasing the convective heat transfer coefficient value by a suitable factor [28]. Nonlinear variations in material properties such as the electrical and thermal conductivities, σ and k, with temperature are taken from the previous study [26]. All parameters used in this model are given in Table 3.

Table 3 Electrical and thermal conductivities in the material domains
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A pure conduction heat transfer model is solved in the fluid media wherein the heat transfer by convection in the liquid phases is accounted by defining an effective conductivity [35] as below:

$$K_{{{\text{eff}}}} = LU\rho C_{p}$$
(6)

where L is characteristic length equals to 4A*/P [36], A* is cross-section area of electrolyte under anode, P is wetted perimeter and U is characteristic velocity taken as the mean velocity of 0.1(m/s) in the liquid phases [37]. The calculated Peclet number is of the order of 105 for electrolyte and of 106 for liquid aluminum. It is clear that the heat transfer by convection dominates. Therefore, the use of an effective thermal conductivity defined by Eq. (6) for the liquid layers has been used which minimizes the complexity of the problem with little compromise on the accuracy.

Finally, this thermo-electrical coupled model is based on the following main assumptions under the steady state:

  1. (i)

    Mass transfer in the cell is intricately linked to heat balance in the cell. However, no material balance is performed in this model. Under steady-state operation of the cell, it is assumed that there is no net mass imbalance with regard to the input and output streams of the cell and, there is a net fixed amount of heat (~ 7 kWh/kgAl) that leaves the cell with the output material streams (liquid Al, exhaust gases, anode removal and muck layer removal etc.) whose effects are time-averaged to model the steady-state operation of the cell.

  2. (ii)

    Heat transfer by the convection in fluid layers is not modelled explicitly. Instead, its’ effect is indirectly modelled by the use of enhanced conductivity, Keff.

  3. (iii)

    Heat loss due to radiation is not modelled explicitly. Instead, an enhanced heat transfer coefficient at the surfaces is used to account for the radiative heat loss.

  4. (iv)

    There is no fluctuation in voltage drop due to instabilities in molten aluminum and electrolyte layer.

  5. (v)

    Bath composition of electrolyte is fixed and uniform.

  6. (vi)

    The thickness of crust above anode is uniform.

  7. (vii)

    Ambient temperature is 22 °C, and it is not affected by a change in pot heat loss.

2.3 Boundary Conditions and Computational Methods

The galvanostatic electrical boundary condition was applied at the end of the collector bar wherein an outward pointing cell current was drawn (Fig. 6a). A constant voltage of 0 V was imposed at the top surface of the anode yoke. As solid surfaces are not perfectly smooth, atomic level contact takes place at some discrete points only. These gaps in contact surfaces create obstacle to electricity, giving rise to contact resistance. These resistances exist at:

  • Stub–anode and

  • Ramming paste–collector bar interfaces.

    In addition, interfacial electrode reactions happen at anode (solid–liquid) and cathode (liquid–liquid interface) with a large activation potential drop. Thus, extra contact resistances, basically fitting parameters in the model, are added at these interfaces to account for the effects such as:

  • the CO2 bubble effect at the anode–electrolyte interface

  • Cathodic polarization at the electrolyte–metal bath interface

  • Resistance due to sludge at the metal–carbon block interface

Fig. 6
figure 6

a Galvanostatic electrical boundary conditions. b Convective heat transfer boundary conditions at external surfaces (symmetry surfaces do not allow any normal heat flux)

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In the electrolysis process, some undissolved alumina combined with the electrolyte freeze on the surface of cathode carbon block called the sludge. The deposited sludge layer is thin and is not modelled geometrically. However, its high resistive effect is taken into account by defining a suitable contact impedance of 7 × 10−6 (Ω.m2) [26] at metal bath–carbon block interface. It is important to note that the nature of contact in Cu/steel interface may add extra resistance to the cell structure. However, low valued contact impedance of the order of 10−9 (resistance × area, even in dynamic electrical contact [38]) is negligible compared to other impedances as Cu–steel contact is static metallurgical joint in this model. Also, the cylindrical Cu insert provides minimum contact surface without affecting the cell symmetry. The surface contact impedances are given in Table 4. All outer surfaces except the surfaces representing the top of the stem and the collector bar have been electrically insulated because of either a symmetry plane or an electrical insulation.

Table 4 Electrical contact resistances at various interfaces
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As regards the thermal boundary conditions, these are shown in Fig. 6b. Unlike the electrical contact resistance, there is no need of any thermal contact resistance as radiation takes place even if surfaces are not in contact. The radiative heat transfer assumes more importance at higher temperature and the thermal equilibrium is reached fast at the internal boundaries. The heat from the outer surface of the model (surface that are exposed to atmosphere) is lost to the surroundings via convection and radiation, modeled as below:

$$Q_{{\text{L}}} = hA\left( {T_{{\text{s}}} - T_{{\text{a}}} } \right)$$
(7)

where QL is heat loss, h is convective heat transfer coefficient that also account for the heat transfer by radiation [28], A is exposed surface area, Ts and Ta are the temperature of the outer surface and surrounding atmosphere, respectively.

Finally, FEM (finite element method) simulation for the slice model is performed by using the built-in physics-controlled mesh (shown in Fig. 5b) in coupled Thermal-Electric Analysis System ANSYS Mechanical Enterprise 17.0® (ANSYS® Academic Research, Release 17.0, Help System, ANSYS, Inc.) for all the domains except ledge. A fine mesh is desired in the ledge for the purpose of extracting the steady-state ledge profile, and it was performed by employing “body sizing” operation over the ledge region available under mesh branch of the model tree. It was made sure that the element size/quality was good enough to render all the simulation results virtually grid independent.

2.4 Extraction of Ledge Profile

The steady-state ledge profile in all cases is obtained by an iterative procedure, wherein we first find the steady-state solution for a given approximate ledge geometry. The solution will have higher than a liquidus temperature of 940 °C in part of the ledge in the vicinity of the electrolyte and the metal bath. This solution becomes un-physical due to the fact that part of the ledge is at higher than liquidus temperature. Such ledge portions should be molten. To obtain a solution with a more realistic ledge profile, the model is rerun by treating the ledge cells having a temperature greater than 940 °C as molten electrolyte or liquid Al. Again, in the resulting solution, we may expect some ledge elements, less in number than in the very first case, having a temperature in excess of 940 °C which need to be assigned to liquid phases. Thus, the model is rerun, again, after assigning electrolyte/liquid Al material properties to these high temperature ledge cells. This procedure is repeated until the number of elements undergoing the changes contribute to less than 0.1% of the total ledge volume between successive iterations.

3 Results and Discussion

Over 50% of the electrical energy input to a pot degenerates into heat. A portion of the input energy is used in heating the reactants and pot-room gases entrained into the exhaust to the electrolysis temperature. The consumption of this heat and the reaction enthalpy is explicit in the process and, is assumed constant. The components of the inevitable voltage drop [39] for decomposition, external (from collector bar to the anode stub) and overvoltages (assumed constant) are:

  1. (a)

    Reaction enthalpy at bath temperature (5.655 kWh/kgAl)

  2. (b)

    Al2O3, carbon and entrained gas heat up to the reaction temperature (0.577 kWh/kgAl)

  3. (c)

    Other reactions and heat up (0.341 kWh/kgAl).

The above inevitable energy losses demand/consume energy corresponding to 1.986 V of the total voltage drop [39]. The remaining heat input is lost to the pot-room ambience by the conduction, convection and radiation. This is the heat loss related to the irreversibilities in the process which cannot be avoided completely although it can potentially be minimized further. In this work, a thermoelectric simulation of the evitable heat losses is performed in order to explore the avenues for further energy savings. The total cell voltage is the sum of voltage drops corresponding to the evitable and inevitable terms (e.g., for the base case the total voltage drop is 4.156 V of which 1.986 V times the current make up for the inevitable energy loss and the rest is the losses related to irreversibilities).

3.1 Cell Voltage Drop

The voltage drop corresponding to the evitable heat loss in the base model (2.17 V) is shown in Fig. 7, which includes a voltage drop of 0.230 V (in anode), 1.6 V (electrolyte) and 0.34 V (cathode). These voltage drops in the respective domains compare well with the corresponding experimental values reported in the literature in Table 1. For the insert I case, the evitable voltage drop is found to be 2.074 V (Fig. 7), dropping by 96 mV as compared with the base case. This voltage drop corresponds to a reduction in the CVD due to a gain in conductivity of the cathode assembly with the use of a copper insert. Although the cell energy consumption, all things being equal, drops in commensurate with a drop in the cell voltage with the use of an insert. This could lead to an undesirable heat imbalance in the cell. Under steady-state operation of the cell, the heat input should equal to the heat output at the temperature of the cell operation. A drop in the CVD will reduce the total heat input to the cell running at a fixed cell current. Heat losses at the operating temperature will be higher than the heat input leading to cell cooling. This condition is highly undesirable and should be avoided, say by increasing the cell current if possible (Sect. 3.5). Alternatively, the cell lining/insulation can be improved to reduce the heat losses, keeping the ledge profile and cell stability undisturbed [27].

Fig. 7
figure 7

Cell potential (V) distribution: a base case, b Cu insert I

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3.2 Cell Energy Consumption

The cell voltage drop is directly related to the energy consumption in a Hall–Héroult cell. The energy consumption [15] in the cell per kg of aluminum, called the specific energy consumption (SEC), is calculated as:

$${\text{SEC}} = 3 \times 96485({\text{Coulomb}}/{\text{mol}}) \times U(V) \times 1000g/27({\text{g}}\,{\text{mol}}^{ - 1} )/{\text{CE}}( - )({\text{J}}/{\text{kgAl}}) = 2.978U/{\text{CE}}({\text{kWh}}/{\text{kgAl}})$$

where U is total cell voltage drop and CE is current efficiency. The factor 3 arises from the fact that the reduction of Al3+ requires three Faraday electricity for the production of one mole (27 g) of Al. The SEC has been found to be 13.759 kWh for the base case at 90% CE.

3.3 Cell Temperature Distribution

The temperature profile of the insert-free base case is shown in Fig. 8a. In an insert case I, as the thermal conductivity of cathode block assembly increases, the heat leakage out of the cell at a given temperature will also increases as compared with the base case as found in Fig. 8b. Moreover, there is less heat generation in the cathode due to a drop in the CVD by 96 mV from the CVD value in the base case of 0.340 V. As a result, the average electrolyte temperature drops down to 1207 K in the insert I case (Fig. 8b), with the cell current, the cell insulation and the cell operation/reactions the same as in the base case. The aluminum reduction pot with insert cannot operate at a bath temperature as low as 1207 K. Thus, a proportionate ramp up in the cell current or insulation fortification or a combination thereof will be needed to rebalance the cell thermally without compromising the cell stability. In the subsequent section, the cell current is increased to offset the thermal effect of the insert and its’ influence on cell stability is also studied.

Fig. 8
figure 8

Cell temperature distribution, a base case, b copper insert I case with the same current as the base case of 3100A

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The isotherm lines in the base model are shown in Fig. 9, which are in excellent qualitative agreement with an isotherm reported by Taylor et al. [14]. The isotherms are important characteristics of the model, which demonstrate the accuracy of the model, where improper heat balance will result a freezing point isotherm inside carbon block only to reduce the cell life by frost heave damage or swelling of carbon block due to solidification of penetrating salt [40]. Freezing isotherm well below the carbon block, on the other hand, is undesirable as a salt penetration to this level will damage the insulation.

Fig. 9
figure 9

Temperature isotherms (°C) of insert-free case showing freezing isotherms (940 °C) running just under the carbon block

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The evolution of the ledge profile at each pass/iteration is shown in Fig. 10 for the base model. No appreciable change in the ledge profile is noticed after fourth iteration which has been taken as the steady-state ledge profile. As shown in Fig. 11, nearly the same temperature and ledge profile as the base case are obtained in the insert cases when the simulation is run with an increased cell current. The cell voltage drop is 47 mV less (Fig. 11a) as compared with the base case (Fig. 7a) even though the cell current is raised by 70 A.

Fig. 10
figure 10

Evolution of the profile at various stages of the base case model runs: Left to right run# 0 to run#4. The red region shows the initial portion of the ledge that needed to be converted to electrolyte domain because of its’ higher temperature

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Fig. 11
figure 11

Insert model I run at an increased cell current of 3170 A: a cell potential, b calculated temperature and c the ledge profile. In c, the red region is liquid electrolyte and the rest is solidified ledge

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3.4 Cell Stability

Instability in the metal pad region caused principally by the MHD flows is the most undesirable effect in a Hall–Héroult cell. An interaction of horizontal current density with the vertical magnetic field leads to a high Lorentz force acting on the liquid metal [41, 42]. As the cell current increases in the insert model to maintain the heat balance, it also increases the magnetic field around the cell. An increase in the magnetic field strength will lead to an undesirable increase in the Lorentz forces in the liquid metal only to enhance the magnitude of MHD wave perturbation [43, 44]. Thus, unless the magnitude of the horizontal component of the current density in the metal decreases proportional to the increase in the magnetic field, the cell operation may become unstable with the use of a Cu insert. Current density (J) has three components Jx (along short side of the cell), Jz (along long side of the cell) and Jy (along height). Due to inherent symmetry of the 3D slice model, the z-component is very small and the x-component dominates the total horizontal current density. Thus, the magnitude of the x-component of current density is mainly responsible for the MHD instability. The variation of Jx, in the molten aluminum bath, with and without copper insert is shown in Fig. 12.

Fig. 12
figure 12

Horizontal component of current density: a base model, b Cu insert model

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It is seen that the range of –ve current densities (x-component) has gone down significantly, by a factor of 10 with respect to the values in the base model. Although a localized increase of the + ve current density is observed near to the ledge profile, its volumetric effect is negligible. Therefore, the use of an insert has also been found to be good from the point of view of cell stability. It is furthermore observed that the cell stability improvement with the use of a Cu insert is not always guaranteed. Bojarevics [25] have demonstrated computationally that the use of a Cu insert improves the cell stability to a point where a reduction in anode to cathode distance (ACD) of 2 mm was possible in the case of 180 kA TRIMET pot. However, a use of Cu insert destabilizes a 500 kA concept cell to a point where an increase in ACD of 3 mm would be required for stable cell operation.

3.5 Parametric Studies

The following parameters are varied to study their effect:

  1. (i).

    Length of copper insert (L mm)

  2. (ii).

    Diameter of copper insert (D mm)

The L and D parameters in the insert models (Table 2) influence the CVD as shown in Fig. 13. An increase in diameter by 4 mm decreases the CVD by 8 mV. However, the CVD drops by 0.175 mV with per mm increase in the length. The drop in the CVD is further dependent on positioning of the insert of a fixed length inside the collector bar [26]. Positioning of the insert further away from the center of the cell gives the maximum drop in the CVD. However, it also leads to a higher heat loss due to an increase in the thermal conductivity in the side region [26]. Since the thermal balance of the reduction cell is disrupted when copper insert is used, the cell current needs to be further increased, gradually, until the operating temperature of the electrolyte bath is restored. At this juncture, the cell current and the cathode voltage drop (CVD) of the stable and thermally balanced Cu insert cells are recorded for energy calculations. Interestingly, the additional energy consumed owing to incremental current is lower for insert cases I–V (Fig. 14). It indicates that with the use of a copper insert in the collector bar, the SEC goes down with a concomitant increase in productivity, which is proportional to the cell current. The SEC decreases by 0.2 kWh/kg and productivity increases by 2.5% for the insert III case. However, for insert V case, production rate will increase by 5.4% for the same SEC as in the base model. Two new operating regions, marked as A and B (Fig. 14), could be proposed for a better operational and economic efficiency than the base case operation. The choice for the Region A is obviously the low SEC values and, for the region B is the increased productivity at a fixed SEC. Beyond the region B, it may not be economical to use the Cu insert model as the increase in current will simply consume more energy compared to base case. However, the increase in the SEC above region B is accompanied by an increase in the productivity. On a flip side, an increase in current directly increases the erosion of the cathode block [23]. Thus, a trade-off between the productivity increase, SEC and the cell life dictates the economics of the process over lifetime of a cell and, this is a complex optimization challenge which is outside the scope of this work.

Fig. 13
figure 13

Effect of diameter and length of copper insert on CVD

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Fig. 14
figure 14

Variation of energy and productivity for all models

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Finally, the model has a major limitation of assuming the inevitable losses to be a fixed parameter, closely related to the material balance in the cell. In addition, the locality of these heat sources are not accounted either. Although the results obtained in the present paper are expected to change a little if we couple an electrochemistry-based mass transfer model accounting for the inevitable heat losses, the conclusions about the effect of an insert on the energy balance and the cell stability will hold in all probability. A more rigorous thermoelectric model, coupled to pot-level MHD flows and the electrochemical reactions, is a desirable goal.

4 Concluding Remarks

A slice, thermoelectric model of a Hall–Héroult cell was developed for a conventional cell employing an insert-free collector bar, termed the base model as well as for a cell with a copper insert in the collector bar, termed the insert model. Finite element method (FEM)-based simulations were carried out to determine the components of voltage drops, steady-state ledge profile, cell stability and the overall heat balance. It was demonstrated that a reduction in the cathode voltage drop of 96 mV resulted by the use of a copper insert (Fig. 7) over the base case. However, the cell heat balance was adversely affected in the insert case due to: (i) the increase in the thermal conductivity leading to an increase in the heat flux at a given temperature and (ii) the decrease in the Ohmic heat generation at the same electrical current as in the insert-free base case, and (iii) due to a decrease in the CVD, potentially leading to an electrolyte freeze.

One scheme to counter the heat imbalance in the insert case/s, without touching the cell insulation in the parent, base case, was by increasing the cell current by an amount required to maintain the electrolyte superheat. It at first appeared that the cell stability worsened with an increase in the cell current. On the contrary, a significant reduction in the range of the horizontal current density—the component responsible for the instability—in liquid metal pool compared to base case resulted. Thus, the cell operation with increased current density in the insert case was deemed to be as stable as the base case.

Parametric studies demonstrated that the CVD dropped linearly with the length of copper insert of fixed diameter. A linear trend in the CVD drop was also found with increment in diameter of copper insert of fixed length (Fig. 13). The variation of the SEC and the cell current in all cases highlighted the advantages of copper insert collector bar assembly over the insert-free, base case—i.e., the use of a Cu insert could increase the plant productivity by over 5% (Fig. 14) at the same SEC as in the base case. Moreover, with a change in insert design, an increase in productivity with a concomitant decrease in the SEC (see the region in Fig. 14 marked A) could be achieved. Lastly, it could also be possible to decrease the ACD with an increase in cell insulation, if the cell stability stayed intact with the use of an insert, broadening further the possible gain in energy efficiency and productivity. The economic advantage of using a Cu insert in the cathode assembly potentially outweighed the cost incurred in implementing this design.