Computers have been used in the industry since at least the 1970s. These days, every major oil company has $XXX million in supercomputers cranking through seismic data in a number of extremely computationally intensive ways. Reservoir simulation is also computationally intensive, but can be done at the individual workstation level.

Here's a paper from May 1985 titled "Applications of supercomputers in the petroleum industry" - https://journals.sagepub.com/doi/abs/10.1177/003754978504400.... Found that without even looking for oldest example.