Summary
The main objective of this work is to improve robust, repeatable interpretation of reservoir characteristics using rate transient analysis (RTA). This is to generate probabilistic credible intervals for key reservoir and completion variables. This resulting data-driven algorithm was applied to production data from both synthetic and actual case histories. Synthetic production data from a multistage, hydraulically fractured horizontal completion in a reservoir modeled after the Marcellus Shale reservoir were generated using a reservoir model. The synthetic production data were analyzed using a combination of RTA and Bayesian techniques. First, the traditional log-log plot was produced to identify the linear flow production regime. Using the linear flow production data and traditional RTA equations, Bayesian inversion was carried out using two distinct Bayesian methods. The “rjags” and “EasyABC” packages in the open-source statistical software R were used for the traditional and approximate inversion, respectively. Model priors were based on (1) information available about the Marcellus Shale from technical literature and (2) results from a hydraulic fracturing forward model. Posterior distributions and credible intervals were produced for the fracture length, matrix permeability, and skin factor. These credible intervals were then compared with true reservoir and hydraulic fracturing data. The methodology was also repeated for an actual case in the Barnett shale. The most substantial finding was that for nearly all the investigated cases—including complicated scenarios (such as including finite fracture conductivity, fracturing fluid flowback, and heterogeneity in fracture length in the reservoir/hydraulic fracturing forward model)—the combined RTA-Bayesian model provided a 95% credible interval that encompassed the true values of the reservoir/hydraulic fracture parameters. We also found that the choice of the prior distribution did not affect the posterior distribution/credible interval in a significant manner as long as it was moderately concentrated and consistent with engineering science. Also, a comparison of the approximate Bayesian computation (ABC) and the traditional Bayesian algorithms showed that the ABC algorithm reduced computational time by at least an order of magnitude with minimal loss in accuracy. In addition, the production history used, the number of iterations, and the tolerance of fitting in the ABC analysis had a minimal impact on the posterior distribution after an optimal point, which were determined to be at least 1-year production history, 10,000 iterations, and 0.001, respectively. In summary, the RTA-Bayesian production analysis method was implemented using relatively user-friendly computational platforms [R and Excel® (Microsoft Corporation, Redmond, Washington, USA)]. This methodology provided reasonable characterization of all key variables such as matrix permeability, fracture length, and skin when compared to results obtained from analytical methods. This probabilistic characterization has the potential to enable better understanding of well performance ranges expected from shale gas wells. The methodology described here can also be generalized to shale oil systems during linear flow.
The use of well-production data in quantifying gas-reservoir heterogeneity
