Deterministic and stochastic analyses to quantify the reliability of uncertainty estimates in production decline modeling of shale gas reservoirs

Abstract

Decline curve analysis seeks to predict the future performance of oil and gas wells by fitting a mathematical function to historical production data and extrapolating its trend into the future. A recurring issue associated with decline curve analysis centers on the reliability of these predictions. To evaluate the reliability of decline curve predictions, stochastic analyses, such as the bootstrap method, can be used to generate a range of cumulative production or estimated ultimate recovery outcomes. By comparing whether the actual cumulative production of a series of wells falls between certain probabilistic estimates generated by the bootstrap method, the reliability of the bootstrap method and the mathematical models used to fit a curve to the historical production data can be evaluated. In addition, the reliability of predications based on certain numbers of months of production data can be examined. Although prior research implemented the bootstrap method with the Arps model to predict future production or evaluate and improve the reliability of stochastic estimates in conventional wells, this research is the first to also use the Duong model as well, use various ranges of months of production data to determine decline model parameter values, and use shale gas production data to evaluate the reliability of both deterministic and stochastic estimates based on decline curve analyses. Based on an examination of historical production data from horizontal and vertical gas wells in the Barnett Shale, this research finds that when 12 or more months of production data are available, the bootstrap method can be used to reasonably predict the next five years of production for both vertical and horizontal wells. Increasing the number of months of available generally improves both the reliability and precision of predictions. The range of values by which deterministic and stochastic predictions vary from the actual cumulative production of groups of wells deceases by about 5% to 10%, and the median values of such distributions of predictions become about 10% to 15% closer to the actual production values, as an additional 6 to 12 months of data become available for modeling decline curve parameter values. The research methodology undertaken in this research can be easily applied to production data from other formations to assist engineers in making predictions about the future performance of wells in other geologic and geographic contexts.