Correction to : Mining, Metallurgy & Exploration (2022) 39:1679–1686

https://doi.org/10.1007/s42461-022-00628-7

Several corrections are needed in the article. They are as follows:

  • In the “Abbreviations” section, it is τ instead of T. It is, then, “τ: time required for complete sulfation”.

  • The font size of reaction (2) in part 2 Physico-chemistry of sulfation should be smaller to be coherent with the other reactions in the list.

  • In the expression of equation (8), delete Âă. Therefore, it is \(\text{z=(}\overline{\mathrm{u}}\text{t+x)/L}\) 

  • In expression (9), delete Âă. So, it is \(\displaystyle\mathrm{C}_{\mathrm{T}}(\uptheta)=\frac{\mathrm{C}_{\mathrm{T}}}{\mathrm{C}_{\mathrm{T}}^{0}}=\frac{1}{2[\pi\theta(\mathrm{D}_{\mathrm{a}}/\mathrm{\overline{u}}\mathrm{L})]}\exp-\left[\frac{(1-\theta)^{2}}{4\theta(\mathrm{D}_{\mathrm{a}}/\mathrm{\overline{u}}\mathrm{L})}\right]\) 

  • In expression (10), it is τ instead of T. It is then \(\overline{{t}}/\tau=1-(1-\mathrm{X}_{\text{Cu}})^{1/3}\) 

  • τ = …

  • In expression (11), equals symbol is missing and the upper limit of the integral is τ(di) and not T(di). Thus, it is

    $$\displaystyle\mathrm{\overline{X}}_{\mathrm{A}}(\mathrm{n})=\sum\Delta \psi(\mathrm{d}_{\mathrm{i}})\left[{\int\limits_{0}^{\tau(\mathrm{d}_{\mathrm{i}})}}\mathrm{X}_{\mathrm{A}}(\mathrm{d}_{\mathrm{i}}) \mathrm{E}(\mathrm{t})_{\mathrm{n}}\text{dt}\right]$$

  • In expression (12), delete Âă. Therefore, it is

    $$\displaystyle\mathrm{E}(\mathrm{t})_{\mathrm{n}}=\frac{\mathrm{n}^{\mathrm{n}}}{\mathrm{\overline{t}}_{\mathrm{i}}(\mathrm{n}-1)!}\left(\frac{\mathrm{t}}{\mathrm{\overline{t}}_{\mathrm{i}}}\right)^{\mathrm{n}-1}\exp - \left(\frac{\mathrm{t}}{\mathrm{\overline{t}}_{\mathrm{i}}}\right)$$

  • In the sentence “In Fig. 8, the calculated fraction of copper extracted as a function of the number of backmixed reactors in series and the dimensionless average reaction time \(\theta=\mathrm{t}/\theta=\mathrm{t}/\mathrm{\overline{t}}.\), with t being the reaction time required to obtain 0.1 wt% Cu (10 h), is shown.”, the correct formula for dimensionless average reaction time is \(\theta=\mathrm{t}/\mathrm{\overline{t}}\).