Approximate bayesian computation for probabilistic decline curve analysis in unconventional reservoirs

Abstract

Predicting the production rate and ultimate production of shale resource plays is critical in order to determine if development is economical. In the absence of production from the Shublik Shale, Alaska, Arps' decline model and other newly proposed decline models were used to analyze production data from oil producing wells in the Eagle Ford Shale, Texas. It was found that shales violated assumptions used in Arps' model for conventional hydrocarbon accumulations. Newly proposed models fit the past production data to varying degrees, with the Logistic Growth Analysis (LGA) and Power Law Exponential (PLE) models making the most conservative predictions and those of Duong's model falling in between LGA and PLE. Using a regression coefficient cutoff of 95%, we see that the LGA model fits the production data (both rate and cumulative) from 81 of the 100 wells analyzed. Arps' hyperbolic and the LGA equation provided the most optimistic and pessimistic reserve estimates, respectively. The second part of this study investigates how the choice of residual function affects the estimation of model parameters and consequent remaining well life and reserves. Results suggest that using logarithmic rate residuals maximized the likelihood of Arps' equation having bounded estimates of reserves. We saw that approximately 75% of the well histories that were fitted using the logarithmic rate residual had hyperbolic b-values < 1, as opposed to 40% using the least squares error function--an 87.5% increase. This is because they allow the most recent production data to be weighted more heavily, thereby ensuring that the fitted parameters reflect the current flow regime in the drainage area of the wells. In the third part of this work, in order to quantify the uncertainty associated with Decline Curve Analysis (DCA) models, a methodology was developed that integrated DCA models with an approximate Bayesian probabilistic method based on rejection sampling. The proposed Bayesian model was tested by history matching the simulation results with the observed production data of 100 gas wells from the Barnett Shale and 21 oil wells from the Eagle Ford Shale. For example, in Karnes County, the ABC P90-P50-P10 average interval per well was 170-184-204 MSTB, while the true average cumulative production per well was 183 MSTB. The ABC methodology coupled with any deterministic DCA model will help in long-term planning of operations necessary for optimal/effective field development.