An apparatus comprising a rotary kiln and intended for improved combustion of a secondary fuel supplied in a first stream to the rotary kiln, whereby the rotary kiln has burner assembly with a main burner for supplying primary fuel and a plurality of feed channels for various media extending parallel to a main axis of the burner assembly, one of said feed channels being a secondary fuel channel for supplying the first stream of secondary fuel, characterised in that a tubular oxygen lance for supplying an oxygen-rich gas, or an oxygen-rich liquid, is positioned in or on another one of said feed channels, called oxygen channel, said lance having an angled nozzle at its feed end such that when, in operation, oxygen-rich gas or oxygen-rich liquid emerges from the angled nozzle and a second stream is formed of oxygen-rich gas or oxygen-rich liquid which impacts the first stream of secondary fuel at an angle thereto.