This dissertation presents methodologies to forecast the recoverable oil volume in sedimenary basins and to explain the evolution of the discovery process. The evolution of the discovery process is modeled as the product of two mathematical functions of opposing trends, namely, the control function, increasing, which represents the degree of knowledge and information acquired in the exploration region, and the condition function, decreasing, indicating that the exploration condition worsens with time as a consequence of the area depletion. Three new methodologies are proposed using nonlinear control functions to explain the influence of technological progress in the reserves accrual. Acting as a proxy for exploratory effort, the drilling footage is used as an explanatory variable for both the control and the condition functions. The aforementioned methodologies were tested using a dataset of five petroliferous basins. After evaluating the explicative capacity by fitting the models to the historical data, out of sample forecast were made for a horizon of 3 and 10 years. The results using a dataset of four different basins indicate that the drilling footage can improve the long-term forecast. The analysis in the residues of the proposed models indicates that the models captured the information contained in the data and satisfactorily describes the process of evolution of discoveries in the observed series.