### abstract

- © Copyright 2015, Society of Petroleum Engineers. This study introduces a novel approach to model the hydraulic fractures in a shale reservoir using a common stochastic method called "random-walk." The goal of this work is to capture part of the "complexity" of a fracture/fracture network that has been generated by a hydraulic fracturing treatment and to attempt to characterize this fracture network using reservoir performance signatures. The steps involved in this work are: • Stochastic generation of a "random-walk" fracture pattern constructed as a scaled numerical model. • Assessment of the "random-walk" fracture using sensitivity analyses which consider the following elements: - The tortuosity (i.e., the actual length to ideal length ratio) - The tendency to branch (or split). - The number of branching stages - the number of branches was held constant for a given set of cases. • Comparison of the mass rate and beta mass rate-derivative performance of the various "randomwalk" fracture cases compared to the "standard" model of a planar fracture. The primary results of this work are: • Generation of pressure distributions (maps) at given times (i.e., "time slices") to qualitatively assess each complex-pattern during transient production. The pressure distribution figures (i.e., maps) are used to qualitatively determine the presence of fracture interference(s) and to identify a time interval where those interferences occur. • Creation of a graphical correlation of reservoir performance in terms of cumulative recovery as a function of the fracture volume and "fracture complexity" (i.e., the number of branches). • Creation of an empirical correlation between the number of branches in a given fracture pattern and the value of the mass rate beta-derivative during transient flow (we observed that the mass rate beta-derivative is essentially constant during transient flow regardless of the fracture network configuration, as such this constant value of the mass rate beta-derivative was selected for correlation). This work provides an alternative description of hydraulic fractures in unconventional shale-gas reservoirs which, in concept, captures the complexity of the hydraulic fracture as a stochastic fracture network. Early-time rate performance is believed to be an indicator of the geometry of the hydraulic fracture pattern. A fracture with a higher level of "complexity" yields higher values of mass rate beta-derivative when the fractures components are interfering with each other. Therefore, mass rate curves could be used as a diagnostic tool that helps the identification of the fracture geometric features.