Characterization of Hydraulically-Induced Shale Fracture Network Using An Analytical/Semi-Analytical Model

A model describing hydraulic fracture network growth is presented in this paper. The model is fully constrained by accounting for mechanical interactions between injected fluid and fracture walls and among nearby fractures and by satisfying observation data including wellbore pressure and microseismic event distribution. It may be solved analytically or semi-analytically, depending on whether a quasi-steady approximation is made. The mathematical framework of the model is first discussed to certain detail. The model is then applied to a Barnett Shale case to illustrate the procedures of characterizing a hydraulically induced fracture network via inverse modeling and predicting the growth of the fracture network using forward modeling. Detailed information including fluid pressure, fracture width, fracture permeability, fracture volume and the surface area of fracture walls are also obtained during the course of modeling. It is further applied to carry out parameter sensitivity analysis. Its potential in realtime applications is also discussed. Introduction Due to its extremely low permeability, gas shale needs to be hydraulically stimulated for economical production. Compared to the traditional bi-wing hydraulic fractures which are seen in many conventional reservoirs, fracture networks created in gas shale are often complex. The actual cause of this complexity is not yet fully established, but some mine-back experiments (Van As and Jeffrey 2000) and field observations of natural hydraulic fractures (see for examples Pollard and Avdin 1988; Cook and Underwood 2000) suggest that natural fractures prevent the creation of a single tensile fracture and promote the creation of fracture offsets and multi-branched fractures. This is especially true in some shales where tensile natural fractures are not aligned with the current principal stress direction because they were created in a era where the stress directions were different. It is still assumed that the majority of the hydraulically induced fractures propagate normal to the far-field least compressive stress, creating the so-called fracture “fairway”. Shear displacement along pre-existing, often sealed (see for example Gale et al. 2007), natural fractures or discontinuities or even induced shear fractures might also occur and contribute to the complexity (Warpinski 1988; Rahman et al. 2002; Warpinski et al. 2004; Palmer et al. 2005; Palmer 2007). However there are indications of induced microseismic activity being related not just to stress effects but also to actual fluid movement (Fisher et al. 2004; Warpinski et al. 2008), suggesting a volumetric hydraulic fracturing process (Shapiro and Dinske 2007). Complex fracture patterns have significant consequences for the design of the fracturing treatment (Jeffrey et al. 1992; Midlin and Fitch 1988; Daneshy 2003; Zhang and Jeffrey 2006). The fracture width of each branch of this complex fracture network is obviously smaller than that of a single fracture, and the conventionally used proppant might not be able to be transported to the tip of the fracture network. Finally, the pressure response during the treatment might be very different from that of a conventional treatment. Understanding the hydraulic fracturing process and the resultant fracture network are of essential importance for better design, planning and sometimes real-time execution of a hydraulic fracturing job and for production optimization. However, the very complexity poses a great challenge to the modeling effort. Recent work has investigated in detail the propagation of a single hydraulic fracture with (Zhang et al. 2007) or without (Hossain and Rahman 2008) its interaction with preexisting natural fractures. Other models have been developed to quantify the growth of complex hydraulic fracture networks. Most of them (Sahimi 1995; Fomin and Hasida 2005; Napier and Bakers 2006; Tezuka et al. 2008; Olson and Dahi-Taleghani 2009) examine the behavior of hydraulic fractures in a formation embedded with predefined, deterministic or stochastic, natural fractures or flaws. Mechanical interactions between fluid and fracture walls and among nearby fractures