Uncertainty quantification in unconventional reservoirs using conventional bootstrap and modified bootstrap methodology

Abstract

Various uncertainty quantication methodologies are presented using a combination of several deterministic decline curve analysis models and two bootstrapping algorithms. The bootstrapping algorithms are the conventional bootstrapping method (CBM) and the modied bootstrapping method (MBM). The combined deterministic-stochastic combination models are applied to 126 sample wells from the Permian basin. Results are presented for 12 to 72 months of production hindcast given an average well production history of 120 months. Previous researchers used the Arps model and both conventional and modied bootstrapping with block re-sampling techniques to reliably quantify uncertainty in production forecasts. In this work, we applied both stochastic techniques to other decline curve analysis models∎namely, the Duong and the Stretched Exponential Production Decline (SEPD) models. The algorithms were applied to sample wells spread across the three main sub-basins of the Permian. A description of how both the deterministic and stochastic methods can be combined is provided. Also, pseudo-codes that describes the methodologies applied in this work is provided to permit readers to replicate results if necessary. Based on the average forecast error plot in the Permian Basin for 126 active wells, we can also conclude that the MBM-Arps, CBM-Arps, and MBM-SEPD combinations produce P50 forecasts that match cumulative production best regardless of the sub-basin and amount of production hindcast used. Regardless of concerns about the coverage rate, the CBM-Arps, MBM-Arps, CBM-SEPD, and MBMSEPD algorithm combinations produce cumulative P50 predictions within 20% of the true cumulative production value using only a 24-month hindcast. With a 12 month-hindcast, the MBM-Arps combined model produced cumulative P50 predictions with a forecast error of approximately 20%. Also, the CBM-SEPD and MBM-SEPD models were within 30% of the true cumulative production using a 12- month hindcast. Another important result is that all the deterministic-stochastic method combinations studied under-predicted the true cumulative production to varying degrees. However, the CBM-Duong combination was found to severely under-predict cumulative production, especially for the 12-month hindcast. It is not a suitable model combination based on forecast error, especially when hindcast fractions on the low end of the spectrum are used. Accordingly, the CBM- Duong combination is not recommended, especially if production history of no more than 24 months is available for hindcasting. As expected, the coverage rate increased, and the forecast error decreased for all the algorithm combinations with increasing hindcast duration. The novelty of this work lies in its extension of the bootstrapping technique to other decline curve analysis models. The software developed can also be used to analyze many wells quickly on a standard engineering computer. This research is also important because realistic estimates of reserves can be estimated in plays like the Permian basin when uncertainty is correctly quantied.