In the transitory contact mode, the desulphurization can be determined by performing sulphur balance:

(1)

 is rate of injection of slag powder,  is sulphur in steel at time t. integration of equation 1 and putting the limit

and we get,

(2)

Similarly in the permanent contact zone sulphur balance

(3)

Where W is amount of top slag, and  is initial S in slag and  is final sulphur in slag. Re- arrangement of equation 3 gives

(4)