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.
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.
The solution methodology of a three-dimensional hydraulic fracturing simulator (MFRAC-II) for use on personal computers is described. The Simulator is design oriented and user-friendly with menu- driven pre- and post-processors. It has been formulated and structured to be used as an everyday design tool. The coupled rock and fluid mechanics equations governing fracture propagation are presented. These non-linear partial differential equations are then transformed and solved using integral methods. The criteria for fracture propagation and the effect fracture toughness and confining stress contrast has on fracture propagation are also discussed. Comparative studies with full 3-D hydraulic fracturing simulators are included to illustrate the diversity of MFRAC-II. These comparison studies range from fractures dominated by pure rock mechanics (fracture toughness) to fractures dominated by viscous driven fluids. The fractures range from highly uncontained to very well contained fractures (1/3 ⩽ L/H ➝ ∞).
A new solution methodology for pseudosteady-state behaviorof a well with a finite-conductivity vertical fracture isformulated using a reservoir/fracture domain resistivityconcept. The formulation encompasses a transformed resistivitydomain based on an equivalent or effective wellbore radius. Theresulting pseudosteady solution is presented in the form of thedimensionless productivity index (JD). Some of the major advantages of this pseudosteady solutionfor finite-conductivity vertical fractures are 1) the methodologyis based on fundamental principles, 2) the solution is analyticaland easily implemented, 3) the equations are formulated forrectangular reservoirs, 4) the model includes wellbore flow(i.e., wellbore radius effect) which is important for low-conductivity fractures, and 5) the formulation accounts for apiece-wise continuous linearly varying fracture conductivityincluding: proppant tail-ins, over-flushing, pinch zones, chokedflow (internal), and external skin mechanisms. The stimulation ratios for finite-conductivity fractures withan undamaged well are compared with those of McGuire and Sikora[1] (1960), and Holditch[2] (1974). The accuracy andvalidity of the pseudosteady model is also illustrated bycomparison with the works of Prats[3,4] (1961,1962), Gringartenet al.[5,6] (1974), Cinco-Ley et al.[7–10] (1978,1981), Barker and Ramey[11] (1978), and Valko and Economides[12] (1998). A summary of the fundamental building blocks, effectivewellbore radius concept, pseudo-skin functions and fractureskin are discussed. An improvement to Gringarten'sdimensionless productivity solution for infinite-conductivityvertical fractures in rectangular closed reservoirs is alsopresented. Introduction Since hydraulic fracturing is one of the most widely used andaccepted methods for enhancing well performance, pressuretransient analysis of fractured reservoirs has become aninvaluable tool in determining the productivity increase andbenefits of fracturing. McGuire and Sikora[1] (1960) published a classic paper on"The Effect of Vertical Fractures on Well Productivity"whereby they used an electric analogue computer to study theeffect of finite-conductivity vertical fractures on theproductivity of wells in expanding fluid-drive reservoirs (i.e., pseudosteady-state behavior). These curves are still one of themost widely referenced and used diagnostic plots forproductivity forecasting. The McGuire and Sikora curvesdemonstrate the productivity increase benefits from hydraulicfracturing as a function of fracture length (penetration) andrelative fracture conductivity.
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