A couple of minor points: Here is a slightly revised graph. The data above represents the mideast "internal consumption" divided by the total production. Per the BP review, the middle east only exports about 20% of its refinery production outside the region. For this graph I have added to this figure the natural gas usage, converted to BOE. The mideast actually consumes 90% of the natural gas it is currently producing.
Since about 1985 the ratio of production to consumption has gone up by only about 5%. At this rate of increase, they will still be able to pump oil for a long time. However, this rate of increase will almost certainly not be linear. As they approach the maximum production rate, there will be a discontinuity, no doubt.
The growth rate of natural gas consumption in the middle east is about 7.5%. This is a doubling every 10 years. 90% of the natural gas produced in the middle east is used internally in the middle east. At this rate of increase, the currently stated reserves of natural gas in the middle east will run out in about 2048. I suppose they will hit "peak gas" and go into decline before then. So, presumably, if they are indeed using most of their natural gas to generate power to provide the energy for oil production, this will at some point be a big problem This will probably be the source of the discontinuity.
Thirdly, I am not ready to say that this consumption of energy is necessarily directly related to the pumping of that oil, but I don't think it is necessarily important for this to be the case. The amount of energy those guys are consuming is the amount it is taking to run their society in some orderly way, and take care of the population to a sufficient extent so they can produce oil. Think of it as the "overhead" involved in oil production. You can make the argument that it is going to take an increasing amount of energy to keep the people happy enough to keep the stuff running, and that is equally important if not more so than whatever amount they use to run the actual pumps and drilling rigs. This is especially true in light of the population increase in some of these areas.
Fourthly, I agree with whoever said that these guys will run their equipment even though EROEI is negative, as long as they pump oil, for critical petrochemicals and non-energy usage. At that point, you will have to compute it based on "money returned on money invested".
But. to return to the original point: It is clear that at some point, the internal usage in these places will be sufficiently large so as to not allow them to continue to export. This will be especially true if they start to go into decline. The data at hand at the moment do not allow us to figure out exactly what that point will be. Seahorse is probably right, though, we will be able to tell by reading the numbers on the gas pump.