# How to (thermodynamically) model the aluminum electrolysis using FactSage

As a member of the Centre for Research in Computational Thermochemistry (CRCT, Polytechnique Montreal) that develops the FactSage software, it is always a pleasure to share my knowledge on thermochemistry. This post will show you how to simply model the conventional aluminum electrolysis process (i.e. the Hall-Héroult process) using FactSage.

Let’s start by reviewing the fundamental aspects of the extractive metallurgy of aluminum. Aluminum is an abundant element in the earth’s crust. Unfortunately, it’s high affinity for oxygen and the conditions that prevail during the genesis of the bauxite mineral (i.e. the most common mineral that contains aluminum that is industrially processed) give us some engineering challenges in order to obtain metallic aluminum as it is naturally available mostly in its 3+ oxidation state.

Alumina is first extracted from bauxite using the Bayer’s process which leads to smelter’s grade alumina (about 99.5% of purity, Na2O being the most abundant impurity). This alumina is then dissolved in a cryolite bath (stoichiometric composition Na3AlF6). This molten salt appears to be the most efficient way of liberating Al3+ cations that are subsequently reduced in the electrolysis cell.

The cryolite bath also acts as the electrolyte for the Hall-Heroult smelting process which involves the following overall oxydo-reduction reactions:

$2\underline{Al_{2}O_{3}}+3C(graphite) \longleftrightarrow 4Al(liq.)+3CO_{2}(gas); K_{eq.1}$                                               eq.1

$2\underline{Al_{2}O_{3}}+6C(graphite) \longleftrightarrow 4Al(liq.)+6CO(gas); K_{eq.2}$                                                 eq.2

with

$\Delta G_{eq.1}(T)=\Delta G^{0}_{eq.1}(T)+R\cdot T\cdot ln{ \frac{a_{Al}^4 \cdot P_{CO_2}^3}{a_{Al_2O_3}^2 \cdot a_C^3}}$                                                                                eq.3a

$\Delta G^{0}_{eq.1}(1010^oC)=+1346 kJ$                                                                                                                  eq.3b

$\Delta G_{eq.2}(T)=\Delta G^{0}_{eq.2}(T)+R\cdot T\cdot ln{ \frac{a_{Al}^4 \cdot P_{CO}^6}{a_{Al_2O_3}^2 \cdot a_C^6}}$                                                                                eq.4

$\Delta G^{0}_{eq.2}(1010^oC)=+1185 kJ$                                                                                                                  eq.4b

In eqs. 3 and 4, the activity of Al2O3 is referred to the corundum allotrope. We explained in a previous post that eq.1 is kinetically favored under industrial electrolysis conditions.

The following oxidation reactions therefore take place at the anode:

$C(graphite) +2O^{-2}\rightarrow CO_2(gas) + 4e^-$                                                                                        eq.5a

$C(graphite) +O^{-2}\rightarrow CO(gas) + 2e^-$                                                                                             eq.5b

while the following reduction reaction takes place at the cathode:

$Al^{3+} +3e^-\rightarrow Al(liq.)$                                                                                                                            eq.6a

Also sometime written as:

$\underline{AlF_3} +3Na^+ +3e^-\rightarrow Al(liq.)+\underline{3NaF}$                                                                                        eq.6b

Assuming i) no dusting of the anode as well as ii) no solubility of carbon in cryolite, the mass balance of reacted carbon in the cell, nCreac., can be defined as follows:

$n_{C}^{reac.}=n_{CO_{2}}+n_{CO}$                                                                                                                                     eq.7

The charge balance based on eqs. 5a and 5b, assuming that Na+ is the only ionic species that carries the electrical current in the electrolyte, is written as:

$4n_{CO_{2}}+2n_{CO}=-n_{Na}$                                                                                                                              eq.8

Finally, the CO2/CO molar ratio is introduced:

$R_{\frac{CO_2}{CO}}=\frac{n_{CO_2}}{n_{CO}}$                                                                                                                                                   eq.9

By combining eqs. 7 to 9, we obtain the following mass balance:

$-(4R_{\frac{CO_2}{CO}}+2)\cdot(\frac{1}{1+R\frac{CO_2}{CO}})\cdot n_C^{reac.}=n_{Na}$                                                                                        eq.10

We can therefore modulate the amount of Na+ cations that migrate from the anode to the cathode knowing the specific CO2/CO molar ratio of the gas exhausting the cell.

The example below shows how to set the conditions in the Equilib module in order to mimic the oxydation reactions at the anode when <B> mole of C is consumed for some imposed  CO2/CO ratio in a normal operation mode (no anode effect).

In this example, the <A> parameter is calculated as follows:

$=(4R_{\frac{CO_2}{CO}}+2)\cdot(\frac{1}{1+R\frac{CO_2}{CO}})$                                                                                             eq.12

A special component selection for the cryolite solution (called B-Bath in the FTHall database) is made so that carbon cannot dissolve in the cryolite in this simplified example:

The following equilibrium state at the anode is calculated by FactSage:

The next example shows how to set the conditions in the Equilib module in order to mimic the associated reduction reaction at the cathode when <B> mole of C is consumed at the anode for some imposed  CO2/CO ratio in a normal operation mode (no anode effect):

FactSage calculates the following equilibrium state at the cathode:

It is to be noted that an important reduction of the activity of Al2O3 (i.e. a low wt.% in cryolite) will significantly increase the energy requirement for the reactions 5a and 5b to occur. Because of that, non desirable reactions may take place at the anode (phenomenon called the anode effect) :

$C(graphite) +4F^{-}\rightarrow CF_4(gas) + 4e^-$                                                                                             eq.13

Here is another example that leads to an anode effect:

With the following equilibrium state at the anode:

Finally, the thermodynamic simulation of the electrolysis process can be improved by:

1. Considering the real transport number of mobile ions in the cryolite (ex.: F-, Na+, Ca+, etc.) when defining the charge balance equation.
2. Considering the presence of carbon in the cryolite (ex.: carbonate and carbides species)
3. Considering the dusting effect.