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  SPE-170965-MSOptimal Hydraulic Fracture Angle in Productivity Maximized Shale WellDesign Nadav Sorek, Jose A Moreno, Ryan Rice, Guofan Luo, and Christine Ehlig-Economides, Texas AM University Copyright 2014, Society of Petroleum EngineersThis paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Amsterdam, The Netherlands, 27–29 October 2014This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s) Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s) The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied The abstract must contain conspicuous acknowledgment of SPE copyright Abstract In general, hydraulic fractures propagate perpendicular to the horizontal well axis whenever the drillingdirection is parallel to the principal minimum stress plane However, operators frequently drill horizontalwells parallel to lease boundaries resulting in slanted hydraulic fracture planes at angles less than 90degrees from the well axisThis study provides a model for the inclined fracture case It applies and further extends the unified fracture design approach for rectangular drainage areas, relating the dimensionless proppant number to themaximum productivity index in pseudo-steady state conditions When simulating flow in shale reservoirs,the stimulated shale volume was represented as a rectangular drainage area that varies with changingangle, but preserves total area Similarly, fracture length and width varies with changing angle, but total propped fracture volume stays constantResults show that for any given set of reservoir and proppant properties along with a given proppantmass, as long as the created fractures drain the same stimulated rock volume, there exists a well directionresulting in maximized well productivity that is not necessarily parallel to the minimum stress directionIn addition, results yield two main correlations The first one relates the optimal fracture angle to proppant number, for a given ratio of well spacing to primary-fracture spacing In this way, operators canchoose the drilling azimuth that would maximize production The second correlation determines theoptimal ratio of well spacing to primary-fracture spacing as a function of proppant number for a givenfracture angle This can be applied when selecting the optimum number of fracture stages given a wellspacing plan and fracture angle Two case studies show the application of these findings In the end, thiswork provides a simple framework for well design incorporating slanted hydraulic fractures Introduction Industry experience suggests that horizontal shale gas development is enhanced by drilling in the direction parallel to the local minimum principal horizontal stress (   H,min ) (Zinn et al, 2011) Because US mineral leases frequently are rectangular areas with NS and EW boundaries, operators often drill parallel to thelease boundaries, prioritizing well saturation over optimum fracture length propagation (Zinn et al, 2011)This practice leads to creation of hydraulic fracture planes that are slanted at an angle less than 90 degreeswith the well axis  Extensive research has investigated the effects of angled fractures on well productivity Zinn et al(2011) utilized theoretical and empirical data to address the impact of wellbore azimuth on well performance in the Marcellus Shale Zinn’s results showed that for each degree a well was suboptimal tominimum horizontal stress, EUR decreased by 725 Mscf per foot of effective lateral length Next,Olorode and Freeman (2013) supported Zinn’s findings by demonstrating superior well performance for wells with orthogonal hydraulic fractures, 90 degrees from the wellbore axis (Olorode et al, 2013)Unified Fracture Design (UFD) methodology (Economides et al, 2002), indicates the hydraulicfracturing treatment design that maximizes well productivity for any set of reservoir and proppant properties and a given injected proppant mass This methodology introduces the concept of proppantnumber (  N   p ), which describes the weighted ratio of propped fracture volume to a square reservoir volumeLater on, Daal and Economides (2006) and  Sabaev et al (2006) extended the definition of   N   p  to elongated rectangular reservoir drainage volumesThis study applies and further extends the UFD approach to show that for any given set of reservoir and proppant properties along with a given proppant mass, as long as the created fractures define the samestimulated rock volume, there exists a well direction resulting in maximized well productivity that is not parallel to the minimum stress direction First, we establish a correlation between the proppant number and the optimum drainage area aspect ratio Then, this correlation is used to express what the optimumfracture angle is for a specific proppant number Because we are considering ultra-low reservoir  permeabilities, we demonstrate the motivation for modeling proppant numbers larger than the maximumvalue of 100 found in previous applications Methodology In the following section, we establish a correlation between proppant number (  N   P  ) and optimaldrainage area aspect ratio (  A r    X  e / Y  e ) This correlation eventually translates into an expression relating proppant number (N P ) and optimal fracture angle In this way, the determination of one of two design parameters, optimal horizontal drilling direction or fracture spacing is achieved It continues withdemonstrating the need for expanding previous UFD publications and describing the implemented method Motivation The base case describes a horizontal well drilled in a direction parallel to the minimum horizontal stresswith hydraulic fractures propagating perpendicular to the well axis (    90°) As the trajectory azimuthdeviates from this base case scenario, fracture angles decrease (    90°) Following the methodology presented by Song and Ehlig-Economides (2011), this work models the multiple transverse fracture horizontal well as one fracture fully penetrating a rectangular drainage area; the well model multiplies thesingle fracture result by the number of fractures in the well No-flow boundaries are set at the fracture tipsand at the locations interference occurs between two adjacent fractures Fig 1 shows a schematic for the base case, as well as the streamlines for the pseudo-steady state flow regime modelAs the well path deviates from the minimum horizontal stress, the angle at which the hydraulic fractureextends will begin to decrease, thereby altering the fracture geometry Rather than modeling the changein geometry with a parallelepiped shaped Stimulated Shale Volume (SSV), an equivalent rectangular SSVis defined using a different aspect ratio established by    ° and   X  e  /Y  e By adjusting fracture width, fracturespacing, and half-length accordingly, the stimulated shale area remains constant, and thus total SSV isconserved Fig 2 illustrates this concept Note from Fig 2 the new drainage area parameters ( and ), which are a function of the angle atwhich the fracture deviates (for the purpose of this work, the superscript tag denotes deviated fractureangle parameters) In addition, the well and fracture spacing ( Y e  and   X  e ,  respectively) remain constant,irrespective of the fracture angle Next, assuming no additional capital is invested in the fracture treatment, 2 SPE-170965-MS  we set proppant mass constant and thus maintain the same proppant number As a result, fracturehalf-length ( x f  ) and width ( w ) become a function of the fracture angleThe geometric relations between parameters are as follow:(1) Note that fracture area and SSV are conserved:(2) Next, two aspect ratios are defined:(3)(4)Where,  A r  and are the aspect ratio of the base  (    90°)  and modified case  (   < 90°) , respectivelyReorganizing Eq 1 yields,(5) Figure 1—Reservoir and fracture geometry schematic Pseudo-steady state flow regime model (Song and Ehlig-Economides, 2011) Figure 2—Fracture drainage area arrangement after fracture angle deviation SPE-170965-MS 3







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