Browsing Petroleum Engineering by Subject "Bayesian field theory"
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Using rate transient analysis and bayesian algorithms for reservoir characterization in hydraulically fractured horizontal gas wells during linear flowMulti-stage hydraulically fractured horizontal wells (MFHWs) are currently a popular method of developing shale gas and oil reservoirs. The performance of MFHWs can be analyzed by an approach called Rate transient analysis (RTA). However, the predicted outcomes are often inaccurate and provide non-unique results. Therefore, the main objective of this thesis is to couple Bayesian Algorithms with a current production analysis method, that is, rate transient analysis, to generate probabilistic credible interval ranges for key reservoir and completion variables. To show the legitimacy of the RTA-Bayesian method, synthetic production data from a multistage hydraulically fractured horizontal completion in a reservoir modeled after Marcellus shale reservoir was generated using a reservoir (CMG) model. The synthetic production data was analyzed using a combination of rate transient analysis with Bayesian techniques. Firstly, the traditional log-log plot was produced to identify the linear flow production regime, which is usually the dominant regime in shale reservoirs. Using the linear flow production data and traditional rate transient analysis equations, Bayesian inversion was carried out using likelihood-based and likelihood-free Bayesian methods. The rjags and EasyABC packages in statistical software R were used for the likelihood-based and likelihood-free inversion respectively. Model priors were based (1) on information available about the Marcellus shale from technical literature and (2) hydraulic fracture design parameters. Posterior distributions and prediction intervals were developed for the fracture length, matrix permeability, and skin factor. These predicted credible intervals were then compared with actual synthetic reservoir and hydraulic fracture data. The methodology was also repeated for an actual case in the Barnett shale for a validation. The most substantial finding was that for all the investigated cases, including complicated scenarios (such as finite fracture conductivity, fracturing fluid flowback, heterogeneity of fracture length, and pressure-dependent reservoir), the combined RTA-Bayesian model provided a reasonable prediction interval that encompassed the actual/observed values of the reservoir/hydraulic fracture variables. The R-squared value of predicted values over true values was more than 0.5 in all cases. For the base case in this study, the choice of the prior distribution did not affect the posterior distribution/prediction interval in a significant manner in as much as the prior distribution was partially informative. However, the use of noninformative priors resulted in a loss of precision. Also, a comparison of the Approximate Bayesian Computation (ABC) and the traditional Bayesian algorithms showed that the ABC algorithm reduced computational time with minimal loss of accuracy by at least an order of magnitude by bypassing the complicated step of having to compute the likelihood function. In addition, the production time, number of iterations and tolerance of fitting had a minimal impact on the posterior distribution after an optimum point--which was at least one-year production, 10,000 iterations and 0.001 respectively. In summary, the RTA-Bayesian production analysis method implemented in relatively easy computational platforms, like R and Excel, provided good 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, improved identification of optimization opportunities and ultimately improved ultimate recovery from shale gas resources.