A method of upgrading a hydrocarbon feedstock, the method characterized by the steps of: supplying the hydrocarbon feedstock to an oxidation reactor, the hydrocarbon feedstock comprising sulfur-containing compounds; contacting the hydrocarbon feedstock with an oxidant in the presence of a catalyst in the oxidation reactor under conditions sufficient to selectively oxidize sulfur compounds present in the hydrocarbon feedstock to produce a hydrocarbon stream that comprises hydrocarbons and oxidized sulfur-containing compounds; supplying the hydrocarbon stream to an extraction vessel and separating the hydrocarbon stream into an extracted hydrocarbon stream and a mixed stream by extracting the hydrocarbon stream with a polar solvent, the mixed stream comprising the polar solvent and the oxidized sulfur-containing compounds and wherein the extracted hydrocarbon stream has a lower concentration of the sulfur containing-compounds than the hydrocarbon feedstock; separating the mixed stream using a distillation column into a first recovered polar solvent stream and a first residue stream; supplying the first residue stream to a coker to produce a coker vapors stream; supplying the extracted hydrocarbon stream to an adsorption column, the adsorption column being charged with an adsorbent suitable for the removal of oxidized compounds present in the extracted hydrocarbon stream, the adsorption column producing a high purity hydrocarbon product stream and a second residue stream, the second residue stream containing a portion of the oxidized compounds; and supplying spent adsorbent comprising residual oils from the adsorption column to the coker for disposing the spent adsorbent after completion of an adsorption cycle, wherein the adsorbent comprises a non-carbon based adsorbent, and the spent adsorbent acts as a slag material to cool reactor walls of the coker and the coker produces the coker vapors stream with ash. supplying the hydrocarbon feedstock to an oxidation reactor, the hydrocarbon feedstock comprising sulfur-containing compounds; contacting the hydrocarbon feedstock with an oxidant in the presence of a catalyst in the oxidation reactor under conditions sufficient to selectively oxidize sulfur compounds present in the hydrocarbon feedstock to produce a hydrocarbon stream that comprises hydrocarbons and oxidized sulfur-containing compounds; supplying the hydrocarbon stream to an extraction vessel and separating the hydrocarbon stream into an extracted hydrocarbon stream and a mixed stream by extracting the hydrocarbon stream with a polar solvent, the mixed stream comprising the polar solvent and the oxidized sulfur-containing compounds and wherein the extracted hydrocarbon stream has a lower concentration of the sulfur containing-compounds than the hydrocarbon feedstock; separating the mixed stream using a distillation column into a first recovered polar solvent stream and a first residue stream; supplying the first residue stream to a coker to produce a coker vapors stream; supplying the extracted hydrocarbon stream to an adsorption column, the adsorption column being charged with an adsorbent suitable for the removal of oxidized compounds present in the extracted hydrocarbon stream, the adsorption column producing a high purity hydrocarbon product stream and a second residue stream, the second residue stream containing a portion of the oxidized compounds; and supplying spent adsorbent comprising residual oils from the adsorption column to the coker for disposing the spent adsorbent after completion of an adsorption cycle, wherein the adsorbent comprises a non-carbon based adsorbent, and the spent adsorbent acts as a slag material to cool reactor walls of the coker and the coker produces the coker vapors stream with ash.