A play-by-play geological assessment of the remaining petroleum resources and historical records for past drilling and discoveries of a basin provide the basic information for assessing the future supply potential of a basin. Estimates are made of the number of wells required for the development of each prospect identified by the geological assessment and the associated supply costs. A discovery process model can be used to project future discovery rates and associated costs of the basin development. Alternatively, these projections can be derived by extrapolation of trends in the historical discovery rates and supply costs with the constraint of the geologically estimated ultimate recoverable potential. Various mathematical formulae have been used to make these extrapolations. This paper proposes a discovery process model that provides approximate consistency with the projections of discovery rates and supply costs derived from the extrapolations of trends in the historical data. The model is estimated using the results of a detailed assessment of the wells required to develop the individual prospects given by a play-by-play geological assessment and the associated supply costs. The Canadian Energy Research Institute recently used the proposed discovery model in a study of the Canadian natural gas supply potential.