A new decline curve is presented, reproducing the succession of various flow regimes such as the classical linear flow and pseudo steady state. The formulation also enables the decline curve to reproduce a succession of periods with power-law behavior, as predicted by recent work on anomalous diffusion. By construction, this decline curve is fully consistent with RTA concepts and the predictions of physical models. The decline curve is obtained by numerically integrating, in the material balance time domain, a “base function” defined as a succession of straight lines reproducing the successive flow regimes, linked with continuous transition periods. By construction, the base function follows the characteristic evolution of the rate-normalized pressure derivative on a loglog plot, which ensures the physical consistency of the obtained decline curve. Once the curve is matched, its parameters can then be used to infer combinations of physical parameters. Two approaches are possible:
(1) In the absence of bottomhole pressures, a classical match and forecast of the instantaneous rate or of the cumulative can be performed in the real time domain directly, with only 3 parameters.
(2) If a bottomhole pressure history is available, the evolution of the rate-normalized pressure and its derivative can first be displayed on a loglog plot, where the different regimes emerging can be rigorously identified, and the corresponding lines traced.Once the different straight lines have been positioned, they are automatically linked with continuous transition periods, and seamlessly integrated into the final decline curve. The forecast can be made either by extending the last observed flow regime, or by using a more conservative regime.
The proposed decline curve reproduces the successive emergence of expected flow regimes and is fully consistent with the predictions of currently available physical models – including recent anomalous diffusion models. The parameters of the curve can be used to estimate combinations of the corresponding physical model parameters. As consequence, the proposed approach bridges the gap between empirical decline curve techniques and the physical concepts used for rate transient analysis.