Net Carbon Consumption in Aluminum Electrolysis: Impact of Anode Properties and Reduction Cell-Operation Variables

Abstract

In the Hall–Héroult aluminum production process, the amount of carbon consumed per ton of aluminum produced is an important metric. Deviations from ideal conditions in the reduction cells contribute to the discrepancy between the theoretical carbon consumption and the actual Net Carbon Consumption (NCC). Previous work from the authors, focused on predicting the net carbon consumption for individual anodes using partial least squares, was based on data collected by an anode-tracking system. In this paper, the importance of each aluminum production step to the NCC is identified and a link to the green anode properties is established. The data collected were analyzed using the sequential multi-block partial least-squares algorithm. The data were split in different blocks, determined by the manufacturing process sequence. The modeling showed that the top three most important blocks were alumina feeding metrics, baked anode properties, and green anode properties. Local green anode homogeneity was defined as resistivity variability metrics, calculated from the green anode resistance measurements. This local green anode homogeneity was found to be greater for anodes with low NCC.

Graphical Abstract

Appendices

Appendices

Appendix 1: SMB-PLS Pseudo-code

See Table 3

Table 3 Pseudo-code for the SMB-PLS algorithm [17]

Appendix 2: PLS Metrics

Within the PLS and SMB-PLS algorithms, two metrics can be calculated. One is the Hotelling’s $\text {T}^\text {2}$ and it represents the distance from the origin to the projection of the point onto the latent variable space, shown in Eq. 6 [19]. That is to say, it is a measure of the variables’ magnitude. It is the sum of the squared ratio of the score value $t_{i,a}$ to the standard deviation $s_a$ of the score vector, where i is the observation number, and a the component number of the model using A components.

$$\begin{aligned} T_i^2 = \sum ^{A}_{a=1} \left( \frac{t_{i,a}}{s_a} \right) ^2 \end{aligned}$$

(6)

The second metric is the Squared Predicted Error (SPE) and it represents the distance from the model plane to the observation in high-dimensional space, calculated by Eq. 7 [19]. In other words, it is related with the correlation structure of the variables for each observation, as compared to the model. To calculate it the residual vector ${\textbf {e}}$ between the actual and predicted observation is used, where i is the observation number and a is the component number out of the A components of the model.

$$\begin{aligned} {\text {SPE}}_i = \sqrt{\mathbf{e}^T_{i,A}{} \mathbf{e}_{i,A}} \end{aligned}$$

(7)

Appendix 3: List of Abbreviations for Figs. 7 and 8

See Tables 4 and 5

Table 4 Variable abbreviations for Fig. 7

Table 5 Variable abbreviations for Fig. 8