Hubbert passed out a pre-print, marked "Subject to Correction," at the regional American Petroleum Institute conference in San Antonio in 1956. His presentation was on March 8, 1956. Hubbert and his wife had been in Europe much of 1955, and he only got the formal invitation to present in December 1955, after bumping into someone at another conference in Denver. So, even with help from other Shell staff, he had to put together a paper hurriedly, addressing not just oil but natural gas, coal, and nuclear.
What Hubbert had to work with, for U.S. oil (meaning, in 1956, the Lower 48 states as Alaska and Hawaii had not yet joined the union), is shown at the top of pdf page 5 of a recent paper by Stanford physicist Amos Nur. It shows a shaded area with extraction data through 1954.
Hubbert also had an estimate of the expected Lower 48 ultimate, which he tweaked to get 150 billion barrels (150 Gb). There was not a lot of analysis that went into it. But going back to the Nur graph, we see that Nur, just like Hubbert in 1956, has it marked off in rectangular grids. The Y axis is in Gb/year, and the X axis is in years. Multiplying them cancels out the year unit, producing Gb. So any particular area of the graph (e.g., one rectangle, or the area underneath the upslope of the extraction-rate line) is a quantity of oil in Gb. One rectangle is 25 Gb, and if the supposition was that there 150 Gb was the ultimate total extraction quantity, then only 150 Gb could fit underneath the line as it proceeded into the future. That is, only the equivalent of six rectangles could fit underneath it.
U.S. and Texas oil in 1956 were in their heyday. The Railroad Commission of Texas was the OPEC of its era. Pretty much everybody else seemed to think U.S. Lower 48 oil was still plentiful. For instance, from Nur we can see that only about two rectangles of the estimated six had been consumed, over 95 years of oil industry history. There were still four rectangles to go, and a lot of history. Not that much more thought, apparently, was given to the topic.
Hubbert's analysis was that to fit the equivalent of six rectangles under the line, the line had to take a downturn in the near future. Consequently he drew a bell curve, albeit I think without ever calling it that, saying simply that however the line progressed, it couldn't resemble anything too different from his drawing, if only 150 Gb were to snuggle under it.
From the 150 Gb, he got a peak year of (i.e., bell curve maxing out and topping out in) 1965.
But the San Antonio paper was a preprint, and in the next six weeks Hubbert was apprised of a January 1956 federal-government publication containing a paper by Wallace Pratt, then of Carlsbad, New Mexico. Pratt for his paper had surveyed 25 industry experts, and among other questions sought estimates of the Lower 48 ultimate. From 22 replies, the highest figure he got was 200 Gb, from the prestigious Dallas firm of DeGolyer and McNaughton. (Everette DeGolyer is mentioned early on in Simmons' book. FDR sent DeGolyer to Saudi Arabia during WWII to assess that country's oil potential. DeGolyer was a big donor to Southern Methodist University, and the main library there is named after him. The company he and Lewis McNaughton founded is still in business and still prestigious.) A like number of 200 Gb came from a 1952 book by another author who Pratt mentioned but had not included in the survey. The upshot was that Hubbert and Pratt traded correspondence, more about Pratt advising Hubbert not to go out on such a prognosticatopm limb (where other pessimists had gone before, very wrongly) than about the 200 Gb. However, by mid-April Hubbert had revised his graph and sent it to Pratt. The revision drew two bell curves, one for 150 Gb and the other for 200 Gb. That was what Shell published, with some editorial changes, in June 1956. The 200 Gb estimate produced a peak year of 1970. The publshed version, in turn, was duplicated (I think) in an American Petroleum Institute annual publication, called Drilling and Production Practice, which came out at or slightly after the end of 1956. So it likewise had two graphs rather than one, and that and/or the June 1956 publication were what most people had access to, as opposed to the preprint before its correction.
The June 1956 Shell version is online. See Figure 21 on pdf page 32.
Thus Hubbert predicted that, at the outside, the rate of Lower 48 oil extraction would hit a maximum (i.e., a peak, or "Hubbert Peak") in 1970. That was precisely on the money, with the caveat that it was the outside chronological end of a range that had a 1965 peak year on the other end. Even so, with the two graphs, the 1970 was prescient enough to make Hubbert eventually famous.
Partly the prognostication fame came from Hubbert sticking to his guns. After 1956, the main way of challenging his analysis was to conclude that the 200 Gb was just wrong. Other estimates came out, progressively going higher and higher, fracturing a relative industry consensus that had been reflected in the Pratt survey results.
A separate analysis, friendly to Hubbert's, came out in February between Pratt's January paper and Hubbert's March presentation in San Antonio. It was by Joseph E. Pogue and Kenneth E. Hill of Chase Manhattan. Hubbert later in 1956 exchanged correspondence with both of them, as well, and it may (emphasis, may) have been Hill who gave Hubbert the idea for more complicated mathematical tinkering looking at data for cumulative extraction, proven reserves, and discovery. Discovery, with barrels per year as the Y axis unit, was not a smooth line, so Hubbert converted the Y axis to cumulative barrels of discovery. This produced an S curve, and one looked for a flattening as it proceeded, suggesting approximately where the upper cumulative limit, or ultimate, would be. Extraction graphed the same way would be a similar S curve with a time lag. As Campbell or Laherrere would say today, you can't extract what hasn't been discovered. The one follows the other.
The more complicated math led to a series of papers, apparently begun with one Hubbert presented at a conference in Midland, Texas, in 1958 (which I have not yet located), and followed by another he presented in Dallas in 1959 (which had an error Hubbert had to advise people of and correct). Eventually he got a chance to write the energy portion of a natural resources study by the National Academy of Sciences for President Kennedy. His analysis, while more mathematical than that of 1956, suggested a Lower 48 ultimate comfortably in the 150 Gb to 200 Gb range, validating 1956.
It got published in 1962, but not before an estimate of 590 Gb emanated from the U.S. Geological Survey, influenced heavily by Vincent McKelvey who some years later became USGS director. There was scientific politicking, maybe even backstabbing, and given the discrepancy between Hubbert's number and the much larger USGS number, Hubbert's paper didn't get a chance to make a public splash all on its own. For President Kennedy purposes, it got downplayed, and thus a second Hubbert message, attempting to tell the country that we needed to get busy contemplating an energy transition to something else, ended up again diluted. McKelvey and Hubbert exchanged correspondence on the discrepancy in 1962, McKelvey eventually deciding they needed to agree to disagree. Over the years he grew more adversarial, essentially a Hubbert nemesis on the topic. Hubbert retired from Shell in Houston in 1964, and went to work for the USGS, where he was given other assignments besides estimating oil quantities.
He continued publishing outside the USGS, in journals, and already by the end of 1962, in National Academy of Sciences circles, was challenging the methodology that produced the adversarial 590 Gb, which was based on barrels of discoveries per feet of well drilling. This led to a 1967 Hubbert paper showing that discoveries per foot were declining. By even more complicated mathematics than 1962, he arrived back within the original 150 Gb to 200 Gb range.
The U.S. peaked in 1970. The USGS only minimally backed down from its estimated ultimate, and even then not until 1974. It backed down more in 1975, after coming under fire from a new National Academy of Sciences referee attempt. Eventually, with the advent of the Carter Administration, McKelvey was forced to resign.
Stewart Udall, Secretary of the Interior under President Kennedy, began figuring out in 1971 that he had been misled by his subordinates, including the USGS, while secretary in the 1960s. He consequently befriended Hubbert, who previously as secretary he hadn't even known was his employee. Udall published a book, The Energy Balloon, in 1974 contemporaneous with the first energy crisis. He did some public blistering of the "boomer geologists" and the "paper discoveries" of oil that had led the country astray and allowed it to get blindsided from an energy policy standpoint.
Hubbert brought much of his math and analytical evolution all together in a lengthy Congressional publication, prepared for Senator Henry "Scoop" Jackson, in 1974. That in turn got expanded in a 1980 paper, published in 1982, that was the full culmination of Hubbert's evolving prognostication methodology. (We are talking lots of equations.) It takes some effort to get hold of, usually requiring an interlibrary loan and a microfilm viewer/printer.
Prudhoe Bay was discovered in 1968, and resultant oil began to flow through the Alaskan pipeline in 1977. The Alaskan oil extraction rate peaked in 1988, I think. The U.S. all-time maximum, even with Alaska and Hawaii added as the 49th and 50th states, remained at 1970, although 1985 got reasonably close to 1970. But Alaska helped, as did Mexican oil, as did North Sea oil, etc., such that the OPEC nations had to impose quotas to avoid gluts. That situation, and Hubbert's death in 1989, created a bit of a peak-oil lull before various successors (Buzz Ivanhoe, Joseph Riva, Colin Campbell, Jean Laherrere, Brian Fleay, Walter Youngquist, Richard Duncan, Kenneth Deffeyes, Matthew Simmons) created analytical momentum looking beyond a U.S. peak toward a world peak. The Internet, beginning with Jay Hanson's dieoff website and energyresources list, as well as the hubbertpeak.com website of Ron Swenson and Francis de Winter, began to popularize the topic, as did Richard Heinberg's publication of The Party's Over.