Empirical decline curve analysis remains the primary tool for the estimation of ultimate recovery of unconventional shale wells, and correspondingly, the associated economic value. Yet, certain DCA parameters are difficult to determine directly from production data, especially early in a well's life. This is particularly true of the hyperbolic exponent, or b-parameter, in the Arps equation. We present a novel workflow for mathematically rigorous inference of the b-parameter by use of an automatic regression engine.
Forecasting production works well when there is considerable history (multiple years) of data. While it is possible to estimate the initial decline from short production histories (two to three months), this is not true of the b-parameter. We adopt a Bayesian framework using maximum likelihood estimation to determine the value of the b-parameter as an inference between a prior distribution and the data likelihood. We implement this framework in an automatic regression engine and provide a workflow to forecast hundreds of wells. We provide heuristics for estimating the prior distribution of the b-parameter. We compare how alternatives of the prior for the b-parameter influence the EUR and use hindcasting to compare the quality of the fit using our new method versus a weak prior.
We find that traditional automatic regression fails to accurately determine the value of the b-parameter from short periods of production data. This can lead to unstable estimations of ultimate recovery. By use of a prior distribution, an analyst has a simple workflow for creating automatic forecasts that more closely reflect a b-parameter determined by empirical analysis, such as from a data set of analog wells. This in turn gives the analyst a greater degree of control over the model fit generated by the automatic regression engine. Moreover, we provide evidence that using a well-chosen prior for the b-parameter provides superior fit to future (unobserved) production time-rate data than a traditional automatic regression.
One of the principal challenges of creating an automatic regression engine is providing accurate fits to low quality or short periods of production data. Nonetheless, an accurate automatic regression engine is invaluable to analysts and/or engineers who must make forecasts for tens of thousands of unconventional shale wells across one or more basins. We provide a new input for an automatic regression engine—the prior distribution for the b-parameter—that enables a workflow to improve forecast accuracy for tens of thousands of wells in only minutes of compute time.
