The complex fracture network created by multistage hydraulic fracturing has been recently described by a triple porosity model. Existing triple porosity models typically assume sequential flow from matrix to micro fractures and from micro fractures to hydraulic fracture. Modeling simultaneous depletion of a matrix block into both micro and hydraulic fractures entails solution of a two dimensional continuity equation that is challenging by analytical or even semi-analytical methods. In addition, analysis with analytical models and type-curves provides deterministic and homogeneous estimates, rendering uncertainty analysis of fracture properties difficult. This paper systematically investigates applying stochastic models of fracture heterogeneity for production data analysis. It illustrates efficient integration of numerical simulations with analytical solutions to quantify the uncertainty in production performance predictions. Information derived from this sensitivity or uncertainty analysis can be used to evaluate existing fracturing operation and to optimize future multi-stage hydraulic fracturing operations.
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