Uncertainty Quantification in Rate Transient Analysis of Multi-Fractured Tight Gas Wells Exhibiting Gas–Water Two-Phase Flow

The production performances of fractured tight gas wells are closely related to several complex and unknown factors, including the formation properties, fracture parameters, gas–water two-phase flow, and other nonlinear flow mechanisms. The rate transient analysis (RTA) results have significant uncertainties, which should be quantified to evaluate the formation and fracturing treatment better. This paper provides an efficient method for uncertainty quantification in the RTA of fractured tight gas wells with multiple unknown factors incorporated. The theoretical model for making forward predictions is based on a trilinear flow model, which incorporates the effects of two-phase flow and other nonlinear flow mechanisms. The normalized rates and material balance times of both water and gas phases are regarded as observations and matched with the theoretical model. The unknowns in the model are calibrated using the ensemble Kalman filter (EnKF), which applies an ensemble of multiple realizations to match the observations and updates the unknown parameters step by step. Finally, a comprehensive field case from Northwestern China is implemented to benchmark the proposed method. The results show that the parameters and rate transient responses have wide ranges and significant uncertainties before history matching, while all the realizations in the ensemble can have good matches to the field data after calibration. The posterior distribution of each unknown parameter in the model can be obtained after history matching, which can be used to quantify the uncertainties in the RTA of the fractured tight gas wells. The ranges and uncertainties of the parameters are significantly narrowed down, but the parameters are still with significant uncertainties. The main contribution of the paper is the provision of an efficient integrated workflow to quantify the uncertainties in RTA. It can be readily used in field applications of multi-fractured horizontal wells from tight gas reservoirs.