Write a reaction used for the preparation of wrought iron from cast iron

Wrought iron is the purest form of iron. Write a reaction used for the preparation of wrought iron from cast iron. How can the impurities of sulphur, silicon and phosphorus be removed from cast iron?

(i)$Fe_{2}O_{3}$ + 3C--------> 2Fe + 3CO
This reaction takes place in reverberatory furnace lined with haematite.
(ii)The haematite oxidises S to $S{{O}_{2}}$ ,Si to SiO2 and P to P4O10). Sometimes limestone is added as flux. Impurities of S, Si and P oxidise and pass into slag. The metal is removed and freed from slag- by passing through rollers.