Analytical single-well models have been particularly useful in forecasting production rates and estimated ultimate recovery (EUR) for the massive number of wells in unconventional reservoirs. In this work, a physics-based decline-curve model accounting for linear flow and material balance in horizontal multistage-hydraulically-fractured wells is introduced. The main characteristics of pressure diffusion in the porous media and the fact that the reservoir is a limited resource are embedded in the functional form, such that there is a transition from transient to boundary-dominated flow and the EUR is always finite. Analogously to the frequently used Arps (1945) hyperbolic model, the new model has only three parameters, where two of them define the decline profile and the third one is a multiplier.
This model is applied to a large data set in a work flow that incorporates heuristic knowledge into the history matching and uncertainty quantification by assigning weights to rate measurements. The heuristic rules aim to lessen the effects of nonreservoir-related variations in the production data (e.g., temporary shut-in caused by fracturing in a neighboring well) and emphasize the reservoir dynamics to perform reliable predictions. However, there are additional degrees of freedom in the way these rules define the values of the weights; therefore, a criterion is established that “calibrates” the uncertainty in the probabilistic models by adjusting the parameters in the heuristic rules. Uncertainty quantification and calibration are performed using a Bayesian approach with hindcasts. This methodology is implemented in an automated framework and applied to 992 gas wells from the Barnett Shale. A comparison with the Arps (1945) hyperbolic model, the Duong (2011) model, and stretched exponential model for this data set shows that the new model is the most conservative in terms of estimated reserves.