A post combustion apparatus comprising: a) a furnace flue inlet that is configured to connect to a furnace and to permit ingress of furnace exhaust gas into the post combustion apparatus, thereby defining an extreme upstream location of furnace exhaust gas entering the apparatus; b) a post combustion exhaust chamber comprising an inlet and an outlet, the outlet defining the extreme downstream location of processed furnace exhaust gas exiting the apparatus, such that gas flows between said extreme upstream location and said extreme downstream location; c) a cooler comprising an inlet, connected to the furnace flue inlet, an outlet and a cooling element; d) a mixing chamber comprising an inlet, connected to the outlet of the cooler, an outlet, and a post-combustion gas fuel injection port located downstream of the mixing chamber inlet that is configured to introduce and mix post-combustion gas fuel with furnace exhaust gas; e) a non-return valve interposed between the cooler outlet and the mixing chamber inlet, which non-return valve is configured to permit the flow of gas substantially in one direction only from the cooler to the mixing chamber; f) a combustion expansion chamber comprising an inlet, connected to the mixing chamber outlet, and an outlet connected to the post combustion exhaust chamber inlet; g) an igniter located downstream of the fuel injection port within the mixing chamber or the combustion expansion chamber; h) a gas power system connected to the cooler downstream the cooler and connected to the non-return valve upstream the non-return valve and configured to drive furnace exhaust gas and particulates from the furnace flue inlet downstream through the post combustion apparatus and to the post combustion exhaust chamber outlet; i) wherein a cross-sectional combustion expansion chamber area, bounded by internal walls of the combustion expansion chamber and perpendicular to the gas flow, is larger than a cross-sectional mixing chamber area, defined by internal walls of the mixing chamber and perpendicular to the gas flow; and j) wherein a cross-sectional post combustion exhaust chamber area, bounded by internal walls of the post combustion exhaust chamber and perpendicular to the gas flow, is larger than the cross-sectional mixing chamber area. a) a furnace flue inlet that is configured to connect to a furnace and to permit ingress of furnace exhaust gas into the post combustion apparatus, thereby defining an extreme upstream location of furnace exhaust gas entering the apparatus; b) a post combustion exhaust chamber comprising an inlet and an outlet, the outlet defining the extreme downstream location of processed furnace exhaust gas exiting the apparatus, such that gas flows between said extreme upstream location and said extreme downstream location; c) a cooler comprising an inlet, connected to the furnace flue inlet, an outlet and a cooling element; d) a mixing chamber comprising an inlet, connected to the outlet of the cooler, an outlet, and a post-combustion gas fuel injection port located downstream of the mixing chamber inlet that is configured to introduce and mix post-combustion gas fuel with furnace exhaust gas; e) a non-return valve interposed between the cooler outlet and the mixing chamber inlet, which non-return valve is configured to permit the flow of gas substantially in one direction only from the cooler to the mixing chamber; f) a combustion expansion chamber comprising an inlet, connected to the mixing chamber outlet, and an outlet connected to the post combustion exhaust chamber inlet; g) an igniter located downstream of the fuel injection port within the mixing chamber or the combustion expansion chamber; h) a gas power system connected to the cooler downstream the cooler and connected to the non-return valve upstream the non-return valve and configured to drive furnace exhaust gas and particulates from the furnace flue inlet downstream through the post combustion apparatus and to the post combustion exhaust chamber outlet; i) wherein a cross-sectional combustion expansion chamber area, bounded by internal walls of the combustion expansion chamber and perpendicular to the gas flow, is larger than a cross-sectional mixing chamber area, defined by internal walls of the mixing chamber and perpendicular to the gas flow; and j) wherein a cross-sectional post combustion exhaust chamber area, bounded by internal walls of the post combustion exhaust chamber and perpendicular to the gas flow, is larger than the cross-sectional mixing chamber area.