According to Needham's Science and Civilization of China volume 5-13, it talks about mining petroleum and natural gas. Natural gas was mined in China around 300CE.

He cited Way(1916) saying petroleum was seen more as a necessary evil as it produce the black smoke and smell when burnt. They also made lubricant, carbon for inksticks, medical remedy paste from petroleum. There was never a large demand for petroleum so not much technology advancement was made for it. However, by Song there was oil drilling, possibly due to refined petroleum was used for flamethrower which increase the demand for oil.

In that volume, he only briefly mention natural gas and said more would be talk about in salt production section, which I am trying to find it. I may not have that volume of Science and Civilization of China laying around.