There is paper "Development of oil formation theories and their importance for peak oil" (2010) - http://uu.diva-portal.org/smash/get/diva2:338107/FULLTEXT01.pdf about oil origins and their relations for finite oil supply.
Abiotic petroleum formation theories are largely irrelevant to the debate about peak oil,
unless it is assumed that the most extreme version of the abiotic oil theory, namely the "strong one" is a reality. However, such spectacular claims necessitate comprehensive and convincing evidence. In what might be a reasonably realistic version of the abiotic theory, massive abiotic oil discoveries and their rapid development would be able, at most, to postpone the date of the peak by some years or decades in the weak case, but it would not be able to remove the notion of an ultimate production peak at some time. Peak oil is a matter of extraction rates and flows, not oil formation theories.
With biogenic formation there are algae and bit of plants (no animals) were buried and converted into oil in some specific conditions (no oxygen, depth no more than 5 km, specific temperature) in several hundreds millions of years.
Usual oil production can lift only up to 20-40 % of oil in the underground (with massive water flooding of reservoir), this is called oil recovery factor. Only very expensive and rare process, Enhanced oil recovery will change this percentage to 30-60.
Human extracted around 15-20% of this in 1 hundred years; the rate of extraction is millions time faster than rate of formation. In next 50-100 years it may be possible to extract 15-20% more of oil; more then half can't be extracted.
For abiotic oil genesis the paper gives two variants, weak and strong. Weak have no difference for finite oil from biogenic; and strong have no evidence to be true. Also, human will increase production rate while he can, and sometimes out extraction rate will be greater than any replacing rate (same peak of oil, just bit later):
The "weak" abiotic oil theory: oil is abiotically formed at rates not higher than those that petroleum geologists assume for oil formation according to the conventional biogenic
The "strong" abiotic theory: oil is formed at a speed sufficient to replace the oil
reservoirs as we deplete them, that is, at a rate something like 10 000 times faster than
known in conventional petroleum geology. In some cases, this version of theory claims
that there exist true "oceans of oil" deep within the earth.
Author's description of both theories:
The weak abiotic theory does not change the fact that we are extracting oil much faster
than it is being generated. For this reason, it does not change the fundamentals of peak oil theory. Nor does it remove the concept of a production peak at some point. In fact, one can easily swap biogenic petroleum formation theory for weak abiotic oil genesis and still derive the same type of arguments for a coming peak since it is production flows that matter. Mankind is still using oil much faster than it is regenerated by nature and sooner or later the oil reserves will be depleted and force the onset of decline and peak production, regardless of biogenic or weak abiotic oil formation theory.
Strong abiotic oil genesis is a completely different topic, as it would imply that oil is created naturally at least as fast as we are currently extracting it or even faster. In the most convenient (from a human viewpoint) version of the theory, the wells being exploited today are connected to ultra-deep reservoirs that slowly (or rapidly) refill them. In this version, the theory allows for a virtually endless plateau production at some level of oil consumption. However, at some point production will eventually match the creation rate and, consequently, limit oil utilization. Therefore, the arrival of a maximum sustainable production level is still valid but it would be a plateau rather than a peak. This occurrence would likely postpone the "end of oil" far into the future and cause it to occur only when futuristic energy sources ought to have been invented.
It goes without saying, however, that even the most enthusiastic supporter of the abiotic
oil theory cannot show any evidence for the "strong" version of the theory, at least in the papers published in scientific journals. It is another matter in the popular press, where wild claims have often been made. Such claims are more the result of wishful thinking than any quantitative evaluation based on scientific methodology.
So, there will be peak, when humankind will produce some amount of oil per day (around 95-100 millions of barrels), and after this event oil production will decline. There will be a lot of oil underground, but with time it is harder and harder to get it out. Under "harder" I mean several things: high price of oil (100 $ / barrel or 200$ / barrel) is not enough to keep 95 mbbl/day level of production; we need to invest some energy into EOR processes and oil lifting. There is last point - when you need to invest same amount of energy to get the barrel which is equal to the energy of this oil barrel (EROEI = 1) - https://en.wikipedia.org/wiki/Energy_returned_on_energy_invested (PS: biodiesel and Ethanol corn have 1.3 EROEI which is very low; shale oil was estimated at EROEI=3, and Canadian bitumen tar sands was estimated as EROEI=3).
PS: Fortune article you linked was about White Tiger Field. Online copy of article http://archive.fortune.com/magazines/fortune/fortune_archive/2003/02/17/337289/index.htm and oil is in basement rock (it is true):
"With the White Tiger Field in Vietnam, 90% of the production is coming from basement rock, where there were never any fossils,"
but the next phrase is false:
"What they've been teaching us in school about oil coming from fossils is wrong."
Wikipedia says that Tiger has its oil in granite, but the original source of this oil is fossil https://en.wikipedia.org/wiki/B%E1%BA%A1ch_H%E1%BB%95_oil_field
Bạch Hổ is not the only oil field convincingly shown to be hosted in granite; however, inspection of the seismic profile of the area shows faulted basement passive margin which is sealed by an onlapping sedimentary sequence.
It is plausible that the oil has migrated laterally from the lowermost, mature sediments into the fault systems within the granite. The seismic profile shows a definite basement horst with onlapping sedimentary source rocks, draped by a reservoir seal. This trap view would see the oil migrate up the horst bounding faults from the lower source units, into the trap unit draped over the top.
Upon examination of the source rock and oil content, petrogeologists have emphasized that the oil's components indicate a lacustrine organic facies with lipid-rich, land-plant debris and fresh-water algal material, refuting theories of abiogenic origin in this area.
Wikipedia has wrong link for , the correct one is http://archives.aapg.org/explorer/2005/02feb/vietnam.cfm (can somebody fix it?) - DAVID BROWN, Offshore Plays Boosting Production. Vietnam Finds Oil in the Basement, AAPG EXPLORER, February 2005
Wallace G. Dow, an AAPG member and consultant in The Woodlands, Texas, calls the Cuu Long oil "paraffinic, classic lacustrine crude" expelled into fractured basement from lower source rock.
"The oils in the basement are virtually identical to the oils in the sandstone sitting around the basement," Dow said.
"This is the key -- they migrate updip through faults into the basement, in horst blocks," he said.
Dow emphasized that the oil's components indicate a lacustrine organic facies with lipid-rich, land-plant debris and fresh-water algal material, refuting theories of abiogenic origin in this area.