Method and system for synthesizing alpha-olefin and POE (polyolefin elastomer) from coal base

The invention belongs to the technical field of synthesis of a polyolefin elastomer POE and a raw material alpha-olefin thereof, and particularly relates to a method and a system for synthesizing alpha-olefin and a POE polyolefin elastomer from a coal base. A coal base is used as a raw material; a mixed oil product generated by Fischer-Tropsch synthesis in the Fischer-Tropsch synthesis unit is primarily separated by a Fischer-Tropsch stripping tower to obtain light naphtha rich in alpha-olefin; enriching the content gt of C5-C7 components in the light naphtha through a low-temperature oil washing, absorption and elution process; the alpha-pentene/hexene/heptene product is respectively obtained through separation and purification of a light component removal tower and a heavy component removal tower of an alpha-olefin separation device, and the alpha-hexene product can be directly used as a synthesis raw material such as POE (polyolefin elastomer) and does not need to be subjected to separation treatment for s