In the application of the parabolic projection technique to geological assessments of the world's conventional oil resources, as with other similar approaches, there is the implied assumption that sufficient oil will be discovered in time from the resource base to avoid a flat plateau peak. In the latter situation, the supply of oil from newly discovered reserves is insufficient to allow the increase in production required to form a normal peak. To test this possibility, the parabolic technique was modified to allow an approximate estimate of the oil produced by year from discoveries made after 2003. A first production parabola was calculated using the normal procedure from which a second production parabola was deducted calculated on the basis that no new discoveries were made after that year. The difference in the cumulative totals between the two parabolas was taken to represent the future production that results from discoveries occurring later than 2003. This quantity of oil must be available from new discoveries to allow the peak to form in an unconstrained way.

The cumulative quantity of oil required from new discoveries made after 2003 to avoid a plateau peak was compared with the cumulative quantity of oil resulting from two low- discovery scenarios. In the first, it was assumed that oil would be discovered at the rate of 10 gigabarrels (GB) per year in 2003 and this rate would decline at 3% thereafter; in the second, the rate was assumed to be 5 GB per year in 2003 with the same rate of decline of 3% per year. In both cases, sufficient oil was discovered to allow an unconstrained peak that was reached in 2015. The crossover point where insufficient oil would be limiting and so result in a plateau peak for these two scenarios was 2048 and 2033 respectively. Given that these discovery scenarios were at the low end of the expected range, there is little possibility that the rate of discovery itself will ever constrain the shape of the peak in world production. This calculation, however, does not deal with the related question as to whether the newly discovered oil could actually be produced in time due to other factors such as delays resulting from its location in ultra deep water or in hostile environments. This latter issue is beyond the scope of this note.