Can we delay peak by upping extraction rate?

Yes.

But at a price.

I first created a simplified oil shock model¹ with a constant extraction rate (relative to reservoir size) and a clear primary peak. As an experiment I added a progression of linear increases in the extraction rate timed to start at the original peak position. I intended the increases to offset the decline in production and thus move the peak to the future.

As the following curves show, this linear shock does shift the peak, but not as much as one might intuitively predict. The amount of shift seems to fairly quickly reach an asymptotic value of perhaps 8 years total "delayed gratification", independent of rate increase. And then we get punished on the backside.

Why does this delay reach an asymptote? I suppose one could prove this but my gut tells me that it most likely occurs because the real decline exhibits an exponential decrease which swamps any linear increase in extraction rate. The increases simply cannot keep up with this relentless decline in reserves. In the worst case, even adding a 40% extraction rate per year at 2040 won't cut it.

The Cliff Notes summary

Try sucking the juice out of a Sno-Cone until you start seeing white ice. At that point, it doesn't matter how hard you suck. If you try real hard you might get one last slurp of flavor. But you might as well let it melt and get some Kool-Aid out of the rest.

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¹ Single discovery spike in 1960, with rates of fallow=build=maturation=0.1/year.