Uncertainty quantification of gas production in the Barnett shale using time series analysis

Abstract

Deterministic methods for evaluating uncertainty in production forecasts for unconventional shale plays are either unreliable or time intensive. This thesis presents an improved methodology for quantifying uncertainty in production forecasts using Logistic Growth Analysis (LGA) and time series modeling. The applicability of the proposed method is tested by history matching production data and providing uncertainty bounds for forecasts from eight Barnett Shale counties. The 80% confidence interval (CI) generated by this method successfully bracketed true production values for all the counties, even when approximately one-third of the data was used for history matching. In the methodology presented, the trend in the production data was determined using two different non-linear regression schemes. The predicted trends were subtracted from the actual production data to generate two sets of stationary residual time series. Time series analysis techniques (Auto Regressive Moving Average models) were thereafter used to model and forecast residuals. These residual forecasts were incorporated with trend forecasts to generate our final 80% CI. To check the reliability of the proposed method, I tested it on 100 gas wells with at least 100 months of available production data. The CIs generated covered true production 84% and 92% of the time when 40 and 60 months of production data were used for history matching, respectively. An auto-regressive model of lag 1 best fit the residual time series in each case. The proposed methodology is an efficient way to generate production forecasts and to reliably estimate uncertainty for short to medium time periods. It includes uncertainty due to parameter estimation using two different regression schemes. It also incorporates the uncertainty due to the variance of the residuals. The method is computationally inexpensive and easy to implement. The utility of the procedure presented is not limited to gas wells; it can be applied to any type of well or group of related wells.