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.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractTo hydraulically fracture a well requires large investments in equipment, horsepower, materials and manpower.An engineer can be overwhelmed with the selection of completion fluids, perforation strategy and treatment size, as well as coordination of frac crews. In the end, however, the primary characteristic of the treatment that provides any economic benefit is a conductive fracture that economically increases well production.Although the primary goal of a hydraulic fracture is to create a highly conductive flowpath, it is often the most poorly understood parameter in the treatment, with pressure transient and rate transient testing frequently indicating disappointingly short fractures of limited conductivity. In order to design an optimized fracture treatment, it is imperative that numerous factors be understood, including proppant embedment, formation spalling, temperature degradation, conductivity loss over time, non-Darcy flow, multiphase flow, non-uniform proppant distribution, cyclic stress, gel damage, fines migration, and other effects. This paper introduces many of these factors and describes their individual impacts on fluid flow within propped hydraulic fractures. It will also demonstrate the cumulative effect of many of these factors upon fracture conductivity and calculate the corresponding impact on well performance. A fracture treatment optimized to accommodate these damage factors will be shown to differ dramatically from treatments in which these phenomena were ignored.The authors present field data demonstrating that these effects are not only real, but can substantially impact well productivity. A field study in which the operator intentionally designed fractures to better accommodate these effects will be shown to significantly improve conductivity and fracture half length, as well as production and profitability. Readers of this paper will be armed with a more realistic view of fracture conductivity and fluid flow within propped fractures which, when incorporated into fracture designs, will yield more optimal fracture stimulations, improved production rates, and superior economic returns.

Hydraulic fracturing and horizontal drilling are the two key technologies that have made the development of unconventional shale formations 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 multicluster per stage fracture treatments in horizontal wellbores create a large stimulated reservoir volume (SRV) that increases both production and estimated ultimate recovery (EUR). This paper presents a new analytical solution methodology for predicting the behavior of multiple patterned transverse vertical hydraulic fractures intercepting horizontal wellbores. The numerical solution is applicable for finite-conductivity vertical fractures in rectangular shaped reservoirs. The mathematical formulation is based on the method of images with no flow boundaries for symmetrical patterns. An economics procedure is also presented for optimizing transverse fracture spacing and number of fracture stages/clusters to maximize the Net Present Value (NPV) and Discounted Return on Investment (DROI). The advantages of this approximate analytical production solution for multiple finite-conductivity vertical transverse fractures in horizontal wells and corresponding optimization procedure include: 1) the solution is based on fundamental engineering principles, 2) the production and interference of multiple transverse fractures are predicted to a first-order, and 3) it provides the basis for optimizing fracture and cluster spacing based on NPV and DROI, not just initial production rate. The methodology provides a simple way to predict the production behavior (including interaction) and associated economics of multi-stage/multi-cluster transverse fracture spacing scenarios in horizontal wellbores. The high initial production (IP) rates from multiple transverse fractures and the late time production decline as a result of fracture interference is discussed. Numerous examples are presented illustrating the method for optimizing (maximizing NPV and DROI) multiple transverse vertical hydraulic fractures in horizontal wellbores. Application of this technique will help provide the design engineer with a better tool for designing and optimizing multi-stage/multi-cluster transverse hydraulic fractures in horizontal wellbores. The governing production equations and fundamental procedure for NPV and DROI optimization of transverse fractures in a horizontal wellbore are discussed.

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