So in the North Sea, where flaring gas at high volumes (as another poster mentioned) is banned, this is actually done a lot. Typically you have a field producing lots of oil and some gas ("associated gas"). Building infrastructure and pipelines to process and ship out the gas is too expensive given the small volumes, so the natural gas is reinjected into the reservoir, only the oil is produced and exported. Then after the oil production becomes depleted after many years, one can switch to producing the (now more concentrated) natural gas.
Apart from reducing CO2 emissions and giving potential for future profits from gas production, the reinjection strategy also maintains higher reservoir pressure thus boosting oil production. The fact that gas is flared at some fields speaks volumes of how crazy the oil industry is.
The Statfjord field is a prime example of a field with reinjection and subsequent gas production.
