Theoretically, Primary Recovery comes to an end, when a pressure equilibrium is established between the oil field and the atmosphere. Will it ever happen in REALITY?
I think that the posed problem is more complex.
Below an answer attempt.
The primary oil recovery is depending from the pressure difference between the natural reservoir and the extraction wellbore, strongly depending from the pressure conditions in the natural drive system (e.g. water drive, gas cap drive or combination drive system).
The oil production come to end theoretically when the pressure in the natural system decreases to thus of wellbore pressure value, but practically earlier.
When the Oil field is in direct contact with the atmosphere (i.e. free oil surface) the recovery can occur when in the wellbore through extraction a lower oil level that the free oil level is created and so, an oil conning around the wellbore occurs. The oil production come to end theoretically when both levels become equal, but practically earlier.
Maybe a paper published by me years ago can be interesting for you, which you can find on the following web site:
https://www.researchgate.net/publication/265880656_Analytical_solution_for_design_of_large_free-LNAPL_pancake-like_lens_recovery_using_a_well_network
Best regards
Dear all, regarding the productivity of the well, it is not beneficial to wait for the equilibrium pressure to set, rather it is anticipated by starting the secondary oil recovery by injection of water, CO2,.... For the same reason tertiary oil recovery starts when water amount production becomes important, most presumably an indication of fingering occurrence. My Regards
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