Crude oil and natural gas depletion may be modelled by a diffusion process based upon a constrained life-cycle. Here we consider the Generalized Bass Model. The choice is motivated by the realistic assumption that there is a self-evident link between oil and gas extraction and the spreading of the modern technologies in wide areas such as transport, heating, cooling, chemistry and hydrocarbon fuels consumption. Such a model may include deterministic or semi-deterministic regulatory interventions. Statistical analysis is based upon nonlinear methodologies and more flexible autoregressive structure of residuals. The technical aim of this paper is to outline the meaningful hierarchy existing among the components of such diffusion models. Statistical effort in residual component analysis may be read as a significant confirmation of a well-founded diffusion process under rare but strong deterministic shocks. Applications of such ideas are proposed with reference to world oil and gas production data and to particular regions such as mainland U.S.A., U.K., Norway and Alaska. The main results give new evidence in time-peaks location and in residual 90%90\% times to depletion.