SPE-170965-MS

Optimal Hydraulic Fracture Angle in Productivity Maximized Shale WellDesign

Nadav Sorek, Jose A. Moreno, Ryan Rice, Guofan Luo, and Christine Ehlig-Economides, Texas A&M University

Copyright 2014, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Amsterdam, The Netherlands, 2729 October 2014.

This 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 axis.

This study provides a model for the inclined fracture case. It applies and further extends the unifiedfracture 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 totalpropped fracture volume stays constant.

Results 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 direction.

In addition, results yield two main correlations. The first one relates the optimal fracture angle toproppant 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.

IntroductionIndustry experience suggests that horizontal shale gas development is enhanced by drilling in the directionparallel to the local minimum principal horizontal stress (H,min) (Zinn et al, 2011). Because US mineralleases 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 wellperformance in the Marcellus Shale. Zinns results showed that for each degree a well was suboptimal tominimum horizontal stress, EUR decreased by 7.25 Mscf per foot of effective lateral length. Next,Olorode and Freeman (2013) supported Zinns findings by demonstrating superior well performance forwells 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 proppantproperties and a given injected proppant mass. This methodology introduces the concept of proppantnumber (Np), which describes the weighted ratio of propped fracture volume to a square reservoir volume.Later on, Daal and Economides (2006) and Sabaev et al. (2006) extended the definition of Np to elongatedrectangular reservoir drainage volumes.

This study applies and further extends the UFD approach to show that for any given set of reservoirand 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 notparallel to the minimum stress direction. First, we establish a correlation between the proppant numberand 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 reservoirpermeabilities, 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 (NP) and optimaldrainage area aspect ratio (ArXe/Ye). This correlation eventually translates into an expression relatingproppant number (NP) and optimal fracture angle. In this way, the determination of one of two designparameters, optimal horizontal drilling direction or fracture spacing is achieved. It continues withdemonstrating the need for expanding previous UFD publications and describing the implementedmethod.

MotivationThe base case describes a horizontal well drilled in a direction parallel to the minimum horizontal stress

with hydraulic fractures propagating perpendicular to the well axis (90). As the trajectory azimuthdeviates from this base case scenario, fracture angles decrease (90). Following the methodologypresented by Song and Ehlig-Economides (2011), this work models the multiple transverse fracturehorizontal 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 thebase case, as well as the streamlines for the pseudo-steady state flow regime model.

As 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 Xe/Ye. 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 (Ye and Xe, respectively) remain constant,irrespective of the fracture angle. Next, assuming no additional capital is invested in the fracture treatment,

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we set proppant mass constant and thus maintain the same proppant number. As a result, fracturehalf-length (xf) and width (w) become a function of the fracture angle.

The 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, Ar and are the aspect ratio of the base (90) and modified case (

From Eq. 5 the fracture angle is defined as,

(6)

Obtaining the optimal fracture angleThe UFD approach strives for conditions that maximize the pseudo-steady state productivity index

(JDPSS). Though in many shale reservoir cases transient flow regime persists for a long period until a PSSflow is present, the authors belief is that a good design should minimize the transient period. Because ofthis, (JDPSS) is still considered a valid key performance index, even for shale reservoirs.

Productivity index is defined as,

(7)

While dimensionless productivity index in oil field units is:

(8)

Eq. 8 holds valid for both transient flow and pseudo-steady state (PSS) flow. In pseudo-steady stateflow, JD becomes approximately constant (JDPSS).

Next, Daal and Economides (2006) adjusted the proppant numbers definition for irregular shapeddrainage areas as:

(9)

Where kf and k are the proppant and reservoir permeabilities, respectively. Vfrac and Vres are the fractureand reservoir volumes, while w and Ye are the fracture and stimulated reservoir width, respectively. Xf andXe represent fracture half-length and stimulated reservoir area length, respectively. Reservoir thicknessand fracture height are represented as h and assumed equal. The penetration ratio ((2xf)/Xe) is representedas Ix. Lastly, the fracture dimensionless conductivity is represented as CfD).

Economides et al. (2002) showed that proppant number correlates to a maximum and uniqueproductivity index (in PSS flow), which corresponds to an ideal fracture conductivity. Daal and Econo-mides (2006) and Sabaev et al. (2006) developed this concept further to account for rectangular drainageareas. Fig. 3 illustrates three different aspect ratios from Daal and Economides work, as well as therelation between CfD, Np and JDPSS.

The dashed lines in Fig. 3 represent fully penetrating fractures (Ix(2xf)/Xe). For our purposes, weconsider high proppant numbers in order to model low permeability reservoirs. Fig.3 shows that for highproppant numbers, the maximum productivity coincides with full penetration of the reservoir by thefractures. Therefore, for a specific drainage area and high proppant numbers, the maximum (JDPSS) isassociated with full reservoir penetration.

Figure 3UFD Type Curves for aspect ratios equal to one, two, and four (Daal and Economides, 2006)

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Consequently, Fig. 3 also reveals that for a given proppant number, different JD values are obtaineddepending on the drainage area aspect ratio. Because of this, each proppant number is associated with anoptimum aspect ratio that maximizes well productivity. This concept is illustrated in Fig. 4

The green line on the right plot of Fig. 4 implies that one can derive a unique relation between proppantnumber and optimal aspect ratio. Thus, expressing Eq. 4 and 5 in terms of these parameters results in,

(10)

(11)

Eq. 11 is an important result of this work. If a unique relation between proppant number and optimalaspect ratio is found, then Eq. 11 could be expressed as a function of Np. As a result, opt can calculatedin advance since Np is a function of initial model parameters (e.g. Xe,Ye). For practical purposes, previousknowledge of the optimal fracture angle (and direction of H,min) allows the operator to choose the correctoptimum drilling azimuth. By doing so, field development and economics can be optimized. In thefollowing section, a relation between opt and Np is developed for high proppant numbers (Np100) inorder to simulate flow in shale reservoirs.

Modeling MethodsFor modeling purposes, GASSIM simulator was used to simulate flow in hydraulically fractured

reservoirs (Lee and Wattenbarger, 1996). GASSIM is a single-phase numerical simulator for simulatingliquid and real gas flow. To reduce computation time, we used symmetry and simulated only one fourthof the drainage area by considering only one half the fracture length and width. The simulation was rununder constant-pressure production and stopped only when the productivity index reached a constantvalue at pseudo-steady state. We applied logarithmic gridding to simulate flow from the matrix to thefracture and from the fracture to the well. In addition, hydraulic fractures fully penetrated the drainagearea. Simulations considered different aspect ratios ranging from one to 2,000, as well as differentproppant numbers ranging from 100 to 1,000,000.

ResultsFig. 5 and Fig. 6 summarize the simulation results. Fig. 5 shows the relation between productivity indexat pseudo-steady state conditions and aspect ratio for different proppant numbers. For each proppant

Figure 4JDmax for different proppant number values ranging from 0.1 to 100. On the left, the horizontal axis is 1/AR (Daal and Economides, 2006).On the right, the horizontal axis is AR (Sabaev et al, 2006).

SPE-170965-MS 5

number there is a distinctive concave-like function, which exhibits an absolute maximum JDPSS value. Theblack line intercepts the corresponding maximum JDPSS value for each proppant number. For Np100, theAr value corresponding to the maximum JDPSS is 7. This value matches the Sabaevs results shown in Fig.4. Dall and Economides work did not predict a maximum value for Np100 because none of theirsimulations considered aspect ratios between 5 and 10, thereby missing the maximum point.

One should recognize that these productivity indices values decrease for horizontal wells due to chokeskin effect (Wei and Economides, 2005). However, the overall total trend remains the same.

By using the results shown in Fig. 5 and applying a logarithmic regression, we correlate the proppantnumber to the optimal aspect ratio. A plot of this correlation is shown in Fig. 6.

Figure 5Relation between productivity index and aspect ratio for varying proppant number values

Figure 6Correlation between optimal aspect ratio and proppant number

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A practical approximation for the equation shown on Fig. 6 would be

(12)

Now, by substituting Eq. 12 into Eq. 10 and Eq. 11 we get

(13)

(14)

Eq. 13 and 14 are the main resulting correlations of this work. Eq. 13 can be applied in thedetermination of the optimal fracture stage spacing (Ye) given a predefined well spacing plan (Xe). Note,that we consider a stage as a single primary hydraulic fracture. Fig. 7 shows a relationship of fracture stagespacing with respect to proppant number for different fracture angles.

Finally, Eq. 14 describes the valuable relationship between opt and Np. Eq. 14 suggests that byknowing the aspect ratio (Xe/Ye) and proppant number, one can determine what the optimal fracture anglewould be. With this information, the drilling azimuth that maximizes production can be easily determined.Fig. 7 shows a relationship of fracture angle with respect to proppant number for different drainage areaaspect ratio values.

Fig. 7 shows a relationship of fracture stage spacing with respect to proppant number for differentfracture angles (assuming well spacing of 1,000 feet). This is a different case, where the fracture anglesare predetermined. We can see that for all proppant numbers, as angles decrease the optimal fracturestage-spacing increases. In other words, lower fracture angle can lead to a fewer primary hydraulicfractures.

Fig. 8 shows a type curve plot of optimal fracture angles as a function of proppant number for differentaspect ratios. As the proppant number increases, the optimal angle decreases. Similarly, the decrease inproppant number is associated with an increase in fracture angle up to 90. This behavior is explained bythe fact that as fracture angle decreases, the fracture length extension increases and fracture widthdecreases as to conserve propped fracture volume. Thus, as the fracture becomes longer and the contact

Figure 7Relation between proppant number and fracture spacing for varying fracture angles.

SPE-170965-MS 7

with the reservoir increases, the fracture width decreases and so does the fracture conductivity. However,at high proppant numbers, the benefit of having an elongated fracture overcomes the drawbacks fromfracture conductivity reduction associated with the decrease of fracture width.

Example ApplicationLet us assume a rectangular lease with a length (a), equal to 5,000 feet and width (b), equal to 2,000 feet.We also assume a homogenous stress regime with a principle minimum horizontal stress, which lie in theazimuth of 30 to 210 (See Fig. 9 below).

The operator intends to drill two multi-fractured horizontal wells (nw2) and to pump 1,000,000 lb.of proppant. Reservoir and proppant properties are shown in Table 1.

The propped volume (Vp) and reservoir volume (Vr) are

Figure 8Relation between proppant number and fracture angle for varying drainage area aspect ratio values

Figure 9Lease dimension, top view. The red lines represent the principle minimum horizontal stress (sHmin).

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The proppant number can be calculated from Eq. 8,

Then, Eq. 11 can obtain an optimal aspect ratio,

Next, we consider two cases. In Case 1, the operator wants to determine the optimal drilling azimuththat will create an optimal fracture angle and to align the lease boundaries parallel and perpendicular tothe well axis. In Case 2, the direction of drilling is predetermined, by state regulation for example, andthe operator wants to know the optimal fracture spacing that will optimize production.

Case 1 The well design calls for hydraulic fracture spacing of 100 ft (equal to fracture spacing, Ye).Thus, the number of fractures per well is

The well spacing is

Now, we can obtain the optimal fracture angle by using Eq. 11

Consequently, we can obtain optimal drilling direction. Since the fracture is expected to propagateperpendicular to Hmin plane, the fracture azimuth is expected to be

The drilling azimuth then would be

The results are illustrated also in Fig. 10 below. Note that the stimulated area remains constant.

Case 2 Let us assume the state regulation mandates drilling parallel to the lease boundary, from east towest. In that case, the fracture angle from the well axis would be 30, as shown in Fig. 11. Note that if

Table 1Reservoir and fracture properties for case studies.

Property Description Value [units]

k Reservoir permeability 5.10-4 [md]

kf Proppant permeability 10,000[md]

SG Proppant specific gravity 2.65

p Proppant porosity 0.38

h Reservoir height 100[ft]

Mp Proppant mass 1,000,00[lb]

SPE-170965-MS 9

regulations allow drilling from north to south, that would results in a 60 fracture angle, which is nearlythe optimal angle from case 1, and thus it would be a better option in that sense.

First, we calculate the ratio of well spacing to fracture spacing using Eq. 10

The resulting fracture spacing is

As a result, the number fractures per well will be

With each fracture containing 29411.8 lb.The results are illustrated also in Fig. 10 below. Note that the stimulated area remains constant.

ConclusionsThis study applies unified fracture design principles to determine the angle between a horizontal well andcreated hydraulic fractures that will maximize the well productivity. We found that, as long as themulti-fractured well drains the same stimulated shale volume, the angle between the horizontal well andthe created hydraulic fractures that maximizes the well productivity for a given total proppant mass is not

Figure 10Optimal drilling azimuth (green), fracture azimuth (yellow) and minimum horizontal stress azimuth (red).

Figure 11Case 2- Drilling azimuth (green), fracture azimuth (yellow) and minimum horizontal stress azimuth (red).

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necessarily 90. Instead, we show that the optimum angle depends on the proppant number determinedbased on the total proppant mass, the well drainage volume, and fracture and shale permeability values.We also showed that smaller fracture angle might lead to less required primary fractures. Or, alternatively,when the well must be drilled parallel to EW and NS lease boundaries even if this direction is not parallelthe minimum stress direction, we show how to find the fracture spacing that maximizes the wellproductivity, again for a given total proppant volume.

Nomenclature

nf number of fractures, fracturesB formation volume factor, res bbl/STBCfD dimensionless fracture conductivity, dimensionlessh reservoir/fracture thicknes, ftIx penetration ratio, fractionJ productivity index, STB/D/psiJD dimensionless productivity index, dimensionlesskf fracture permeability, mdk formation permeability, md

average pressure in the reservoir, psiapwf well flowing pressure, psiaq flow rate, STB/DVf fracture volume, ft3Vres reservoir volume, ft3w fracture width, ftw= inclined fracture width, ft

Inclined fracture length, ftXe well spacing, ftxf 90 fracture half length, ft

Inclined fracture half length, ft optimal drainage ratio, fraction

(Ye/Xe)opt optimal perforation spacing to well acing ratio, fractionYe perforation spacing, ft

distance between two adjusted inclined fractures, ft

Greek variables

p proppant porosity, fraction viscosity, cp angle, degree

ReferencesDaal, J. A., and Economides, M. J. 2006. Optimization of Hydraulically Fractured Wells in Irregularly

Shaped Drainage Areas. Paper SPE 98047 presented at the SPE International Symposium and Exhibitionon Formation Damage Control, Lafayette, Louisianna, 15-17 February. http://dx.doi.org/10.2118/98047-MS

Economides, M. J., Oligney, R. E., and Valko, P. 2002. Unified Fracture Design: Bridging the Gapbetween Theory and Practice. Vol.1, Alvin, TX:

Lee, J., and Wattenbarger, R. A. 1996. Gas Reservoir Engineering. Vol. 5, 349. Richardson, TX:Textbook Series, Spe.

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Olorode, O., Freeman, C. M., Moridis, G. et alet al. 2013. High-Resolution Numerical Modeling ofComplex and Irregular Fracture Patterns in Shale-Gas Reservoirs and Tight Gas Reservoirs. SPEReservoir Evaluation & Engineering 16(04): 44355 http://dx.doi.org/10.2118/152482-PA

Sabaev, V. V., Mach, J. M., Wolcott, D. S. et alet al. 2006. Vertically Fractured Well Performance inRectangular Drainage Area. Paper SPE 101048 presented at the SPE Russian Oil and Gas TechnicalConference and Exhibitio, Moscow, Russia, 3-6 October. http://dx.doi.org/10.2118/101048-MS

Song, B., and Ehlig-Economides, C. A. 2011. Rate-Normalized Pressure Analysis for Determinationof Shale Gas Well Performance. Paper SPE 144031 presented at the North American Unconventional GasConference and Exhibition, The Woodlands, Texas, 14-16 June. http://dx.doi.org/10.2118/144031-MS

Wei, Y., and Economides, M. J. 2005. Transverse Hydraulic Fractures from a Horizontal Well. PaperSPE 94671 presented at the SPE Annual Technical Conference and Exhibition, Dallas, 9-12 October.http://dx.doi.org/10.2118/94671-MS

Zinn, C. J., Blood, D., and Morath, P. 2011. Evaluating the Impact of Wellbore Azimuth in theMarcellus Shale. Paper SPE149468 presented at the SPE Eastern Regional Meeting, Colombus, OH, 1January. http://dx.doi.org/149468-MS

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Optimal Hydraulic Fracture Angle in Productivity Maximized Shale Well DesignIntroductionMethodologyMotivationObtaining the optimal fracture angleModeling Methods

ResultsExample ApplicationCase 1

Case 2

ConclusionsReferences