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4.5 Ohmic Bath Voltage

The Ohmic Bath Voltage (U_Ω) is the sum of voltage drop in the electrolyte (U_ACD) due to the electrical resistance of the bath and the bubble voltage drop (U_bub). The horizontal orientation of the anodes in the Hall-Héroult-cell causes gas accumulation beneath the surface, reducing the electrically conducting volume. This increases of the effective resistivity of the electrolyte with the resulting increase of the bath voltage is called bubble voltage drop.

(4.5.1)

4.5.1. Electrolyte Voltage Drop

Ohm's Law combines the electric current (I) and the electrical resistance (R) to determine the electrical voltage or tension (U).

(4.5.2)

The electrical resistance of the electrolyte (R_ACD) is written as:

(4.5.3)

where the anodic fanning factor (f_A) takes care that the surface of the anode table (A_A) changes during electrolysis. A_A is calculated using the dimensions of new anodes.
Introducing R_ACD into Ohm's Law (Equ. 4.5.2) and using the electrical anodic current density (j_A) one finds the expression to calculate the voltage drop in the electrolyte (U_ACD) from the anode cathode distance (ACD), the anodic current density (j_A) and the electrical conductivity of the electrolyte (κ):

(4.5.4)

4.5.2. Fanning Factors

The Hall-Héroult electrolysis process consumes the newly set prebaked carbon anodes e.g. the sharp corners are gradually rounded off. The anode attains a steady state shape after six to nine days.

Fanning of the Electrolysis Current.

The electrolysis reactions consume the sharp corners of the carbon anodes. The ideal current distribution is changed (ACD: anode to cathode distance, A_A: surface of the anode table of new anodes). The anodic (f_A) and the cathodic (f_C) fanning factors take care of this surface change.

In order to calculate the electrical resistance e.g. the ohmic voltage drop across the bath, the calculation account for these variations in current density and cross sectional areas by using the so called Anodic (f_A) and Cathodic Fanning Factor (f_C). The Anodic (j_A) and the Cathodic Current Density (j_C) is then written:

(4.5.5)

The Geometric Anode Table Surface (A_A) is calculated by assuming that all prebaked anodes of a cell are new:

(4.5.6)

AlWeb and AlPrg estimate the value of the anodic fanning factor with relations that were taken from the literature [Lit. Equ. 33-35]. The anodic fanning factor (F_A) is the ratio of the electrolytic effective anode table surface (A_eff) over the geometric anode table surface (A_A, Equ. 4.5.6).

(4.5.7)

AlWeb and AlPrg calculate (A_eff) using Equ. 4.5.8:

(4.5.8)

Depending on the orientation of th eanode surface in the electrolyte AlWeb and AlPrg apply in Equ. 4.5.8 an individual correction of the anode dimensions F_i. There are two equations available: Equ. 4.5.9A is taken form [Lit.] and Equ. 4.5.9B comes from an spreadsheet that Warren Haupin distributed at the 1998 TMS-Meeting. AlWeb and AlPrg use Equ. 4.5.9B.

(4.5.9A)

(4.5.9B)

AlWeb and AlPrg calculate the average distances d_i of the Equs. 4.5.8. in the following way:

(4.5.10)

The correction of the anode length (Δl) and anode width (Δl) and of the average anode length (L_A) and average anode width (W_A) is given by:

(4.5.11)

4.6 Bubble Voltage Drop

The horizontal orientation of the anode in the Hall-Héroult-cell causes gas accumulation beneath the surface, reducing the electrically conducting area. This increases the effective resistivity of the electrolyte with the resulting increase of the bath voltage referred to as bubble voltage drop.
[Lit.] reviews the different bubble resistance models and introduces the following equation:

(4.6.1)

The relations for the bubble layer thickness (d_bub):

(4.6.2)

and the surface coverage (φ) were again taken from Haupins paper [Lit. Equ.30 and 31, p. 534]:

(4.6.3)