component was allowed to join the liquid component iii to obtain a liquid component iv present in a line 20 the compositions of the liquid component iii the off gas and the liquid component iv are set forth in table 1 then the liquid component iv was heated to 380 u00b0 c to be evaporated and then introduced into an expander 6 at a pressure of 109 kg cm 2 g then the pressure of the liquid component iv was released to 6 kg cm 2 g and the pressure energy generated by the pressure release was recovered the energy recovered in the pressure release was 32 000 kw the component iv the pressure of which had been released to 6 kg cm 2 g was introduced into an olefin production means 7 and converted into a lower olefin fraction v the energy recovered in the pressure release was used as a power of a compressor for recovering the later described lower olefins obtained by the olefin production means 7 the resulting lower olefin fraction v was introduced into a fractional distillation means 8 to obtain fractions of ethylene propylene and butene a mixed liquid of methanol dme and water in a weight ratio of 10 20 8 methanol dme water was used as a starting material the mixed liquid was introduced into a tubular reactor inner diameter 10 mm length 600.