Abstract A solution methodology and mathematical formulation for an induced hydraulic Discrete Fracture Network (DFN) numerical simulator is presented. Although most conventional fracture treatments result in bi-wing fractures, there are naturally fractured formations that provide geomechanical conditions that enable hydraulically induced discrete fractures to initiate and propagate both vertical and horizontal fractures in the three principal planes. The fundamental first-order DFN continuity, mass, momentum, and constitutive equations are developed and formulated for a pseudo-three-dimensional (P3D) hydraulically induced fracture system. The theoretical foundation and concepts for multiple, cluster, complex, and discrete fracture network growth are presented. Discrete fracture interactions as a result of fluid loss and mechanical interference are discussed and included in the modeling. A new extended wellbore pressure loss and storage concept in the fracture mid-field is introduced. The Extended Wellbore Storage (EWS) region in the fracture mid-field accounts for the high fracture pressures observed when fracturing in horizontal or highly deviated wellbores and the associated steep pressure decline during closure. Numerous proppant transport scenarios are formulated and presented for the transport of proppant in the dominant and secondary fracture network system. Application of this technology will provide the operator with a systematic approach for designing, analyzing, and optimizing multi-stage/multi-cluster transverse DFN induced hydraulic fractures in horizontal wellbores. This paper provides the foundation for predicting the propagation and behavior of discrete fracture networks in shales and unconventional formations along with the associated generated Stimulated Reservoir Volume (SRV). Numerous parametric and case studies are provided illustrating the technology and engineering application of the DFN modeling. Introduction Hydraulic fracturing and horizontal drilling are the two key technologies that have made the development of shale formations commercially economical. Hydraulic fracturing has been the major and relatively inexpensive stimulation method used for enhanced oil and gas recovery in the petroleum industry since 1949. The multi-stage and multi-cluster per stage fracture treatments in horizontal wellbores create a large stimulated reservoir volume (SRV) (see Mayerhofer et al. (2008)) that increases both production and estimated ultimate recovery (EUR). As stated above, most conventional fracture treatments result in bi-wing fractures. However, some naturally fractured coal and shale formations have geomechanical properties that allow hydraulically induced discrete fractures to initiate, propagate and create complex fracture networks. The microseismic data collected during a fracture treatment can be a very useful diagnostic tool to calibrate the fracture model by inferring DFN areal extent, fracture height and half-length. Pressure history matching of the fracture treatment and production analyses are additional diagnostic procedures the engineer can use as assurance of the created DFN and SRV. Davidson et al. (1993) presented detailed minifrac evaluation results for the Gas Research Institute?s (GRI) fourth Staged Field Experiment (SFE 4) conducted in the Frontier formation of southwest Wyoming. This paper presented a discussion on the possibility of multiple hydraulic fractures being created in formations that contain natural fractures, including numerous references cited in the literature identifying the existence of multiple fractures created during the hydraulic fracturing process. The authors presented scenarios whereby multiple fractures could be initiated from a vertical wellbore, including: 1) each fracture could be propagating from the wellbore originating from a different set of perforations or 2) one main fracture may be extended from the wellbore and a secondary fracture may split off, forming a fracture spray. Their paper also presented an analysis of abnormally high fracture treating pressures caused by complex fracture growth.

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