NOVELTY - A gaseous coolant is heat-exchanged in LNG heat exchanger (1). LNG is gasified into natural gas and changed to temperature lower than gaseous coolant temperature. The gaseous coolant is condensed into liquid to be filled in storage tank (3). The liquid coolant is filled in a flash evaporation tank (A) and partial liquid coolant is filled in a flash evaporation tank (B). The partial liquid coolant is vaporized. The catalyst solution and mixed source material are respectively cooled to the temperature required for butyl rubber synthesis.    USE - Production of LNG cold energy for butyl rubber synthesis.    ADVANTAGE - The method eliminates heat of polymerization through corresponding heat exchanger to meet the needs of temperature and cold degree of butyl rubber synthesis.    DETAILED DESCRIPTION - A gaseous coolant from a liquefied natural gas (LNG) and gaseous coolant buffer tank (2) is heat-exchanged at an LNG heat exchanger. LNG is gasified into natural gas and changed to a temperature slightly lower than the gaseous coolant temperature. The gaseous coolant is condensed into liquid to be filled in a liquid coolant storage tank. The liquid coolant in liquid coolant storage tank is filled in a flash evaporation tank (A), the pressure is controlled, and the temperature of liquid coolant in the flash evaporation tank is maintained at -100 degrees C or less. A partial liquid coolant is filled in a flash evaporation tank (B), pressure is controlled, and temperature of the liquid coolant in tank (B) is maintained at -110 degrees C or less. The partial liquid coolant in tank (A) is filled into a catalyst heat exchanger (6) and a source material heat exchanger (7) at controlled flow rate, and is vaporized to tank (A) after cooling the catalyst solution and mixed source material. The catalyst solution and mixed source material are respectively cooled to the temperature required for butyl rubber synthesis. The liquid coolant in tank (B) is filled into a polymerization kettle heat exchanger (8) and vaporized to tank (B) after heat-exchange and vaporization. The gaseous coolants from tanks (A,B) are combined and filled into a compressor (10) through a temperature controller (9). The gaseous coolant is filled into the gaseous coolant buffer tank after compression. The compressor provides power for coolant circulation. Also claimed is, the LNG cold energy production system equipped with LNG heat exchanger, gaseous coolant buffer tank, liquid coolant storage tank, flash evaporation tanks, catalyst heat exchanger, source material heat exchanger, polymerization kettle heat exchanger, temperature controller, and compressor. The coolant is ethane or ethylene.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of the production of LNG cold energy.    LNG heat exchanger (1)    Gaseous coolant buffer tank (2)    Liquid coolant storage tank (3)    Catalyst heat exchanger (6)    Source material heat exchanger (7)    Polymerization kettle heat exchanger (8)    Temperature controller (9)    Compressor (10)