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.

In this paper, we use a commercial reservoir simulator to solve the transient response in a segment of a hydraulically fractured horizontal well. This is a triple porosity medium in which matrix blocks deplete into the two fracture networks simultaneously. The proposed model is used to analyze the actual rate data from a tight oil well. It is assumed that the obtained results would characterize the mean estimate of the corresponding fracture parameters. Additional heterogeneous models of fracture properties including its total number and intensity (spacing) are assigned stochastically and subjected to flow simulations to demonstrate their impact on production performance. The resulting production profiles converge to those of dual and triple porosity models at the limiting cases. Uncertainties due to pressure interference between natural fractures and inter-well fracture communication are also investigated. The variability (spread) of the simulation results would capture the sensitivity due to uncertainty in fracture distributions. Our results also show that history-matched fracture half-length strongly depends on the number of micro-fractures implemented in the static simulation model. The estimated value of fracture half-length significantly decreases by increasing the number of micro-fractures from zero, representing the dual porosity system.

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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