Because of the direct correlation with # of rigs, the job loss will be linear with the loss of # rigs. However, the current situation is that each rig that is still working is getting more efficient and productive on a daily basis. So much so now, that there are fewer rigs coming online to produce the same amount of oil that we had before the drop in oil prices. This is where the job loss will be. Some of it is due to automation, but most of it is due to the efficiency gains in the drilling and completion process itself.
http://www.otterwoodcapital.com/static/media/uploads/2016/03...
There's no real demand for new rigs right now. In the downturn, though, the rig and rig equipment companies are making more labor-efficient rigs and equipment. So when new rigs come online, they won't raise labor demand the way new rigs used to.
I am sure robots will replace a lot of these jobs, but I don't see this article providing much evidence that it is happening substantially.