Suppose people in China start using the same amount per person as we do in the United States. How many barrels per year will they use then?

I assume you are referring only to crude oil consumption. The United States in 2015 consumed 6.97 billion barrels of petroleum products. The population of the United States in 2015 was approximately 321 million and the population of China was approximately 1.4 billion.

If the per capita crude oil consumption in China were to equal that in the US, the total crude oil consumed in China would be approximately 6.97*10^9/321*10^6*1.4*10^9. This is approximately equal to 3.03*10^10 or 30.3 billion barrels of crude oil.

If people in China start to consume crude oil at the same rate as those in the United States they would consume approximately 30.3 billion barrels of crude oil in a year.

The global production of crude oil in 2015 was approximately 35.5 billion barrels. If the Chinese consume as much crude oil as Americans, they would use up almost all the crude oil produced on Earth.