Recent interest in the development of Marcellus and Utica plays has renewed attention on the problem of reliable estimation of recoverable reserves from low-permeability shale gas formations. Over-optimistic results obtained from the commonly used Arps hyperbolic model has led to the development of alternative decline curve analysis models based on empirical considerations (e.g., Duong's power law model) or mechanistic considerations (e.g., Valko's SEDM). This work addresses the practical difficulty of discriminating between such models (including a new mechanistic model proposed for decline curve analysis based on the Weibull growth curve) from limited production data. The paper also presents a new approach to aggregating estimated ultimate recovery (EUR) forecasts from multiple plausible models using the Generalized Likelihood Uncertainty Estimation (GLUE) methodology.
Two field examples are presented to demonstrate the performance of Hyperbolic, SEDM, Duong and Weibull models. Model parameters are estimated via nonlinear regression using Excel-SOLVER, from which 30-year EUR estimates are generated. The GLUE procedure is then used for determining the likelihood of each model by weighting the results with [1/RMSE^2], and computing the weighted mean and standard deviation for the 30-year EUR. For the first example (with 15 years of data), excellent visual fits are obtained for both rate and cumulative production with all four models. However, 30-year EUR estimates from the Arps and Duong models are on the high side and the SEDM and Weibull models are on the low side. The uncertainty in the mean amounts to only ~2%. For the second example (with 52 months of data), the trends are very similar, albeit with greater separation in the 30-year EUR forecasts and a higher uncertainty in the mean EUR (~7%).
These results reinforce earlier findings that multiple alternative models can provide equally good fits to limited-duration production data, but yield very different 30-year EUR forecasts. The GLUE approach provides a robust methodology for aggregating such analyses and quantifying the uncertainty of the EUR forecast.