TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Unit: The waste gas cooler is cylindrical first cylinder member, second cylinder member coaxially positioned at the inner peripheral side of the first cylinder member in the cylinder shape whose outer diameter is more small diameter than the internal diameter of this first cylinder member, it has the third cylinder member coaxially positioned at the inner peripheral side of the second cylinder member in the cylinder shape whose outer diameter is more small diameter than the internal diameter of this second cylinder member; the water-flow path is formed between the internal peripheral surface of the first cylinder member, and the outer peripheral surface of the second cylinder member, and the waste gas flow path is formed between the internal peripheral surface of the second cylinder member, and the outer peripheral surface of the third cylinder member, and in between, the CO selective-oxidation device or the methanation device has been positioned at the outer peripheral side of the first cylinder member. The combustion gas which circulated the combustion gas flow path is exhausted as waste gas from an exhaust gas pipe. The first cylinder member or the third cylinder member is formed in substantially cup shape opened to the down side, respectively. Cross section of the combustion gas flow path is formed larger than the cross section of the water-flow path. The flow-path cross section is large formed in the end vicinity of the axial direction of the water-flow path, and the storage part which can store the water is provided in it. When the water circulates between the internal peripheral surface of the first cylinder member, and the outer peripheral surface of the second cylinder member, the first cylinder member is an upper end of this first cylinder member. Having an opening part which can pass the water, the second cylinder member has the bulging part bulged in the position corresponding to the opening part at the first cylinder member side, when the water circulates between the internal peripheral surface of the second cylinder member, and the outer peripheral surface of the third cylinder member, the second cylinder member is an upper end of this second cylinder member. Having an opening part which can pass the water, the third cylinder member had the bulging part bulged in the position corresponding to the opening part at the second cylinder member side. The water circulates between the internal peripheral surface of the first cylinder member, and the outer peripheral surface of the second cylinder member, and the combustion gas circulates between the internal peripheral surface of the second cylinder member, and the outer peripheral surface of the third cylinder member; the CO selective-oxidation device or the methanation device is positioned at the outer peripheral side of the first cylinder member; and the CO-modifying device has been positioned at the outer peripheral side of the CO selective oxidation device or the methanation device.