SPE 115769

The Relationship Between Fracture Complexity, Reservoir Properties, and Fracture Treatment Design C.L. Cipolla, N.R. Warpinski, M.J. Mayerhofer, and E.P. Lolon, Pinnacle Technologies, and M.C. Vincent, Carbo Ceramics

Copyright 2008, Society of Petroleum Engineers This paper was prepared for presentation at the 2008 SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 21–24 September 2008. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of 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 reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent 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 may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract In many reservoirs fracture growth may be complex due to the interaction of the hydraulic fracture with natural fractures, fissures, and other geologic heterogeneities. The decision whether to control or exploit fracture complexity has significant impact on fracture design and well performance. This paper investigates fracture treatment design issues as they relate to various degrees and types of fracture complexity (i.e., simple planar fractures, complex planar fractures, and network fracture behavior), including the effect of fracture fluid viscosity on fracture complexity, proppant distribution in complex fractures, and fracture conductivity requirements for complex fractures. The impact of reservoir properties (including permeability, stress and modulus) on treatment design is also evaluated. The paper includes general guidelines for treatment design when fracture growth is complex. This includes criteria for the application of water-fracs, hybrid fracs, and crosslinked fluids.

The paper begins with an evaluation of microseismic fracture mapping data that illustrates how fracture complexity can be maximized using low viscosity fluids, which includes an example of how microseismic data can be used to estimate the permeability and spacing of secondary or network fractures. The effect of proppant distribution on gas well performance is also examined for cases when fracture growth is complex, assuming that proppant was either concentrated in a primary planar fracture or evenly distributed in a fracture network. Examples are presented that show when fracture growth is complex the average proppant concentration will likely be too low to materially impact well performance if proppant is evenly distributed in the fracture network and un-propped fracture conductivity will control gas production. This paper also extends published conductivity data for un-propped fractures and embedment predictions for partially propped fractures to lower modulus rock to provide insights into fracture design decisions. Exploiting fracture complexity may not possible when Young’s modulus is 2 x 106 psi or lower due to insufficient network conductivity resulting from asperity deformation and proppant embedment.

Fracture conductivity requirements are examined for a wide range of reservoir permeability and fracture complexity. Reservoir simulations illustrate that the network fracture conductivity required to maximize production is proportional to the square-root of fracture spacing, indicating that increasing fracture complexity will reduce conductivity requirements. The reservoir simulations show that fracture conductivity requirements are proportional k1/2 for small networks and k1/4 for large networks, indicating much higher conductivity requirements for low permeability reservoirs than would be predicted using classical dimensionless conductivity calculations (Fcd) where conductivity requirements are proportionate to reservoir permeability (k). The results show that when fracture growth is complex, proppant distribution will have a significant impact on network conductivity requirement and well performance. If an infinite conductivity primary fracture can be created, network fracture conductivity requirements are reduced by a factor of 10 to 100 depending on the size of the network. The decision to exploit or control fracture complexity depends on reservoir permeability, the degree of fracture complexity, and un-propped fracture conductivity.

The paper also examines the effect of fluid leakoff on maximum fracture area, illustrating potential limits for fracture complexity as reservoir permeability increases. Although the expected range of un-propped fracture conductivity is controlled by Young’s modulus and closure stress, in many reservoirs it can be beneficial to exploit fracture complexity when the permeability is on order 0.0001 mD by generating large fracture networks using low viscosity fluids (water-fracs). As reservoir permeability approaches 0.01 mD, fluid efficiency decreases and fracture conductivity requirements increase, fracture designs can be tailored to generate small networks with improved conductivity using medium viscosity or multiple fluids (hybrid fracs). Fracture complexity should be controlled using high viscosity fluids and fracture conductivity optimized for moderate permeability reservoirs, on order 1 mD.

2 SPE 115769

Introduction Complex growth of hydraulic fractures has been documented in mine-back experiments, providing direct observations of hydraulic fracture complexity in a variety of environments including tight sandstones and coalbed methane reservoirs.1-6 Complexity is frequently associated with the interaction of the hydraulic fracture with a pre-existing rock fabric such as natural fractures, fissures, or cleats. Unfortunately data from mine-back experiments are very limited, requiring other methods to diagnose hydraulic fracture complexity. Until recently, fracture pressure analysis was the only diagnostic available to estimate complexity.7-21 Fracture pressure analysis has been used to estimate both near-wellbore7,22 and far-field fracture complexity; the focus of this paper is far-field fracture complexity. In most cases far-field fracture complexity is deemed detrimental due to excessive fluid leakoff and/or reduced fracture width that can result in early screenouts.23,24 In many cases, fracture complexity is reduced by adding particulates that likely plug secondary fractures and/or fissures.20,25,26 In some reservoirs, however, maximizing fracture complexity is the goal of the treatment design. During the past ten years, thousands of hydraulic fracture treatments have been characterized using microseismic and tiltmeter fracture mapping technologies. These measurements have shown a surprising diversity in hydraulic fracture growth, ranging from simple planar fractures to very complex fracture systems to extreme fracture height confinement (that are not explained by variations in rock properties and stress).27-44 The occurrence of complex fracture growth is much more common than initially anticipated and is becoming more prevalent with the increased development of unconventional reservoirs. The nature and degree of the fracture complexity must be clearly understood to select the best stimulation strategy. This paper focuses on the relationship between fracture complexity, reservoir properties, and stimulation design.

Hydraulic fracture growth can be divided into four categories:

- Planar-coupled growth - Planar-decoupled growth or

fissure opening - Complex growth • Non-communicating • Communicating

- Network growth Figure 1 illustrates the various types

of fracture growth. The depictions are simplistic, but will serve as a reference for calculations and modeling presented in subsequent sections. Examples of each fracture growth category have been documented with direct fracture geometry measurements using tiltmeter and/or microseismic frac mapping or inferred from fracture pressure analyses. Large-scale fracture complexity can be measured using microseismic and/or tiltmeter fracture mapping, allowing direct detection of network fracture growth and large-scale decoupling

(fissure opening); however, it is difficult to identify small-scale fracture complexity such as complex-planar growth or limited planar-decoupled growth using hydraulic fracture mapping technologies as the resolution is typically not sufficient to distinguish these features. Therefore, fracture pressure analysis is used to determine small-scale complexity. Effect of Viscosity on Fracture Complexity

Fracture complexity is typically reduced when fluid viscosity is increased. Laboratory tests have shown that both near-wellbore and far-field fracture complexity may be reduced using high viscosity fluids.22,45 Field data have also indicated that high viscosity fluids can reduce fracture complexity.8,18-20 It is more difficult for high viscosity fluids to penetrate intersected natural fractures or fissures.45 In addition, the penetration distance into these intersected natural fractures or fissures may be significantly reduced as viscosity increases. For gas reservoirs, the penetration distance can be approximated using a limiting estimate discussed by Warpinski, et al.46 Given the expected behavior for fluid flow into essentially evacuated fractures, fluid movement is expected to obey a law similar to that for viscosity-dominated leakoff and the distance y that fluid will penetrate is estimated by Equation 1.

tgtPky =Δ

=μϕ

2 ………………….. (1)

Figure 1 - Fracture growth and complexity scenarios

Xf

Xn

ΔXs

Xf

Xn

Xf

Xn

ΔXs

Planar

Planar-decoupled

Complex Planar

Network

No communication

communication

2

SPE 115769 3

Where k is the fracture permeability, ΔP is the pressure drop inside the fracture, t is time, φ is fracture porosity, μ is fluid viscosity, and g is a constant. Additional details are provided in Appendix 1. Evaluation of Microseismic Data to Estimate Fluid Diffusion

A proper application of the relative penetration distance (Equation 1) requires some assumptions or inferences regarding the pressure drop and permeability for the fractures created with low and high viscosity fluids. These inferences will be evaluated in more detail by comparing the behavior of low and high viscosity fracture treatments. In relatively simple environments, the development of micro-seismicity may provide important information about the reservoir. Shapiro has shown that the induced seismicity can be used to extract information regarding the diffusion of fluid in a geothermal reservoir and in some cases for fracturing applications, such as a network fracture.48 This approach is applied here to network fractures to explore viscosity relationships, but particularly for cases with a well-defined geometry where the configuration is amenable for evaluation of diffusion effects. An example of an appropriate case would be a fracture in a vertical well in a reservoir like the Barnett Shale, where the primary fracture azimuth is known and the diffusion orthogonal to the fracture can be evaluated from the extending micro-seismicity. In the Barnett Shale, the composite permeability normal to the principal fracture at fracturing conditions will be a function of the opening of pre-existing healed natural fractures. In general, diffusion effects from horizontal wells in the Barnett would not be appropriate, since multiple origination points are possible (several perforation clusters per stage) and the diffusion behavior would be difficult to sort through; however, several horizontal Barnett Shale wells have been oriented so that the primary created fractures are longitudinal. In such cases, the diffusion approach is warranted since flow orthogonal to the wellbore/fracture would be indicative of the behavior of interest. Consider the fractures mapped in Warpinski, et al. (2005), with dual monitoring arrays to determine microseismicity.35 Fracture treatments were performed with a cross-linked gel treatment and, because of poor performance, re-stimulated several months later with a water-frac. The locations of the micro-seismicity orthogonal to the wellbore/fracture system can be displayed as a function of elapsed treatment time (Figure 2). The microseismic clouds clearly expand in lateral extent with time and the two treatments (gel and water) do so at a different rate. It should also be noted that the very early time data is probably not useful since the general width of a microseismic cloud around the hydraulic fracture itself may not be indicative of diffusion if the mechanism is not associated with fluid flow (e.g., stress effects around the fracture tip and location errors).

A square-root-of-time function can be fit to the microseismic envelope to estimate the diffusion according to Equation 1. For the two cases shown in Figure 2, the values of g given by the dashed lines are 50 ft/√min for the water-frac and 24 ft/√min for the gel frac. Converting to units where k is in Darcies, ΔP is in psi, t is in minutes, and μ is in cp, the behavior

can be used to solve Equation 1 for the average orthogonal system permeability, if the other parameters are known. Table 1 shows best-chosen values; note that ΔP generally denotes the difference between the fracturing pressure and the reservoir pressure, but since the fractures will not open unless the pressure exceeds the in situ stress, it is probably more appropriate to use the fracturing pressure minus the maximum horizontal stress. If the net pressure in a water-frac treatment is 500 psi, then the effective ΔP for flow through the cross fractures is more likely going to be ~300 psi (since it is acting against the maximum horizontal stress and assuming a differential of 200 psi between minimum and maximum horizontal stress). Solving Equation 1 yields:

PgkΔ

=μ2

114 ……………………. (2)

Before computing results, it is also likely that the fluid flow orthogonal to the hydraulic fracture is not going to be a

direct path. Based upon the complex microseismic development observed in water-fracs, the process could be approximated with a random walk pattern. In a random walk, it is equally likely that the extension of natural fractures could be orthogonal, sub parallel left, or sub parallel right, then the total distance traveled could be as much as three times the orthogonal distance. This is likely a maximum value, but a reasonable range appears to be 1 to 3. It is expected that gel fractures would be closer to unity (based on microseismic data) and water-fracs would be closer to the upper range of 3.

Figure 2 – Micro-seismicity orthogonal to wellbore and fracture azimuth

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4 SPE 115769

Using the “direct path” orthogonal distance, the average system orthogonal permeability for the water-frac is 950 Darcies while pumping. This is about what one would expect to get fluid movement 1,000 ft from the fracture. For the gel fracture, the value is 25,000 Darcies while pumping. This value also makes sense as higher pressures and wider fractures are required to move the much higher viscosity gel any significant distance. Although it might appear advantageous to pump gel and induce wider fractures, the orthogonal network will be much more limited in size and following fracture closure, residual gel damage must be considered. If we now add the “random” path to the water-frac calculations (using a maximum value of 3), g becomes 150 and the permeability becomes 8,550 Darcies. Table 1 summarizes the permeability estimates and assumptions used in the calculation.

Table 1 - Input Data and Estimated Permeability of Dilated Fracture (While Pumping)

Note that this calculation is independent of the volume pumped, as long as it is sufficient for the treatment to actually start developing diffusional characteristics. For the water-fracs, the diffusion is probably considerably underestimated because the

fluid from the orthogonal fractures must fill the sub parallel fractures as well. This is not likely to be the case for the gel treatments, where it is not clear if any real network develops. Taken one step farther, this analysis can be used to estimate the fracture widths from the parallel plate analogy using Equation 3:

kw 12= , in units of feet and Darcies, kxw 5101.1 −= ……………………………… (3)

The water-frac orthogonal widths during the treatment would then be 0.00035 ft (direct path) and 0.001 ft (random path), while the gel widths could range from 0.001 ft (100 cp) to 0.0017 ft (300 cp). It is tempting to now calculate volumetrics, but the large leakoff area (particularly for the water-frac) suggests that there could be a very significant percentage of leakoff. Ignoring leakoff, the volume of any one orthogonal fracture would be 105 ft3 (water-frac, direct), 300 ft3 (water-frac, random), 90 ft3 (gel frac-100 cp) and 153 ft3 (gel frac-300 cp) for the two cases, assuming the orthogonal fractures are 300 ft high and 1,000 ft long in the water-frac and 300 ft long in the gel frac (microseismic width). With no leakoff, two (bi-wing) fractures, and tiltmeter information suggesting that 40% of the fluid goes into the orthogonal fractures28, it would require 650 (direct), 226 (random), 145 (gel-100cp) and 85 (gel-300 cp) fractures to account for a treatment volume of 60,000 bbl. This fracture density equates to a spacing of 4 to 12 ft for the water-frac and 19 to 32 ft for the gel frac. The fracture spacing would be proportional to the fluid efficiency and would increase by a factor of two if fluid efficiency were 50%.

Implications of Barnett Shale Fluid Diffusion Evaluation

The fluid diffusion evaluation indicates that high viscosity fluids reduce fracture complexity, as evidenced by the much less complex microseismic pattern that is developed, smaller penetration distance, and likelihood that high viscosity fluids create fewer secondary fractures. In the example presented, the cross-linked gel frac resulted in a penetration distance of about 300 ft, while the water-frac resulted in a penetration distance of 1,000 ft (as interpreted from the microseismic event development, Figure 2). The relative penetration distance for the cross-linked gel is much greater than predicted from Equation 1, which would indicate that the penetration for a 100 to 300 cp fluid would be 7 to 11% of the penetration distance of water (includes a correction for injection time and pressure drop) – or about 70 to 110 ft. The actual penetration distance of 300 ft for the high viscosity fluid seems to indicate higher permeability (i.e., wider) secondary fractures were created with the cross-linked gel, as calculated from the diffusion behavior. The overall implications from the diffusion evaluation are that high viscosity fluid reduces fracture complexity and penetration distance (in the Barnett Shale). In addition, the application of microseismic data to estimate permeability and width of secondary (orthogonal) fractures combined with tilt mapping measurements of directional fluid movement may provide important information to estimate fracture spacing. Proppant Distribution in Complex Fractures Proppant transport in simple, planar, perfectly vertical fractures with smooth faces has been well studied and appears to be reasonably well understood; however, proppant transport when fracture growth is complex, particularly in cases where a fracture network is developed, is not as clear. This paper will evaluate several potential arrangements of proppant within fracture networks. As previously shown, network fractures are more commonly created with low viscosity fracturing fluids; unfortunately, these low viscosity fluids provide correspondingly poor proppant transport properties. For these low viscosity fluids the settling rate46 for most proppant types used in the industry exceeds five feet per minute and it is expected that most proppant particles will settle into a proppant bank at the bottom of the fracture or in notches or offsets at bed boundaries even with simple planar fracture growth. In cases of extreme fracture complexity with induced fractures only slightly wider than the proppant grains that may capture grains prior to settling or with neutrally buoyant materials78, proppant particles may arguably be sparsely distributed through the fracture network. It is also possible that large portions of the fractures will only have the residual conductivity of the closed un-propped fracture.

ΔP (psi)

μ (centipoise)

Permeability (Darcies)

Water-frac 300 1 950-8550 Cross-linked Gel Frac 800 100-300 8300-25,000

SPE 115769 5

Due to the inability to accurately model proppant transport when fracture growth is complex, proppant placement will be estimated using three limiting scenarios: (Case 1) the proppant is evenly distributed throughout the complex fracture system, (Case 2) the proppant is concentrated in a dominant planar fracture with an un-propped complex fracture system accepting fluid only and (Case 3) the proppant settles and forms “pillars” that are evenly distributed within the complex fracture system. Figure 3 and Figure 4 illustrate the three proppant distribution scenarios. In some cases, moderately complex fracture growth is approximated using multiple parallel (planar) fractures in fracture models. In these cases proppant will be distributed evenly between each planar fracture. The additional concerns of proppant settling and failing to effectively

prop the entire pay interval (Figure 4) in complex fracture systems are not addressed in this work and proppant is assumed to be evenly distributed over the fracture height. The effects of un-propped fracture height for simple planar fracture growth have been addressed by Britt, et al.69 This work indicated that in reservoirs in which kv/kh > 0.1, well productivity may not be negatively affected if 50% or more of the pay zone is propped or if un-propped fracture conductivity provides sufficient fracture flow capacity. The general conclusions of Britt likely apply to cases were fracture growth is complex, and may bode

well for naturally fissured reservoirs with enhanced vertical flow. Appendix 2 provides additional details on proppant transport and equations for estimating average proppant concentration.

Example Calculations of Proppant Concentration in Complex Fractures

Two examples are presented to illustrate the effect of fracture complexity on proppant distribution and the range of proppant concentrations that may result when complexity is high. The effect of fracture conductivity on well productivity and the relationship between fracture complexity, fracture conductivity, and well productivity will be examined later in the paper.

Barnett Shale. The Barnett Shale stimulation treatment discussed previously, a water-frac or slick-water treatment, provided microseismic measurements of fracture length, height, and network width.35 The diffusion analysis for this horizontal well stimulation

indicated a fracture spacing of ~10 ft for the water-frac, while previous reservoir simulation studies have indicated effective fracture spacing of 100 to 300 ft for vertical well stimulations using a matrix permeability of 0.0001 mD.47 The difference between the diffusion analysis and reservoir modeling could be due to limitations in the diffusion theory to accurately describe fluid flow in these complex fracture systems, differences between “effective” fracture area from production modeling and “created” area, and/or over-estimation of matrix permeability which would result in over-predicting fracture spacing from production history matching. However, the two approaches provide a reasonable bound for fracture spacing that can be used to estimate fracture area and proppant concentration. It may be possible to estimate the relative fracture spacing or density using advanced microseismic analyses, which indicates that the microseismic moment density could be a crude measure of fracture density.79 This treatment consisted of 60,000 bbl of water and 385,000 lbm of proppant and resulted in a complex fracture with a half-length of 1,500 ft, height of 300 ft, and network width of 2,000 ft. Assuming a fluid efficiency of 75% (required only for Case 3-pillar distribution), the average proppant concentrations for fracture spacing of

Figure 3 - Proppant transport scenarios (plan view)

Figure 4 - Proppant transport scenarios (side view)

Proppant in Dominant Planar Fracture

Proppant in Complex Fracture System

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high viscosity Fluid low viscosity Fluid

Pumping

Closed Fracture

Pillar Distribution Evenly Distributed

ΔXs

ΔXs

Xn

Xf

Evenly Distributed

Concentrated in a dominant fracture

Pillar Distribution

2

(Case 1)

(Case 2)

(Case 3)

6 SPE 115769

10, 50, and 150 ft are provided in Table 2. The average proppant concentration for Case 1 (evenly distributed) is very low, ranging from 0.001 to 0.015 lbm/ft2. This seems to indicate that an even distribution of proppant throughout this very complex network would result in concentrations that are probably too low to be effective and un-propped fracture conductivity would likely dominate well productivity. It should be noted that the width at end of pumping for 10-ft fracture spacing is too small to accept 40/70-mesh proppant. If the proppant is concentrated in a primary planar fracture (Case 2), the average proppant concentration would be 0.43 lbm/ft2 (independent of network fracture spacing). In Case 3, where the proppant is assumed to be evenly distributed in pillars, the average proppant concentration of the pillars would range from 0.07 to 1.0 lbm/ft2 depending on fracture spacing; however, only 1.5% of the fracture area would be propped. The very small percentage of the total fracture area that is propped in Case 3 would likely be insufficient to support the closure stress and resist fracture closure. Cases 1 and 3 do not appear to provide effective propped fractures. Therefore, in this example well productivity may be dominated by the un-propped fracture conductivity. If proppant transport is best described by Case 2, then a much higher conductivity connection to the wellbore will result compared to Cases 1 and 3 which could significantly impact productivity.

Cotton Valley Sand. Mayerhofer, et al.37, presented fracture mapping results from a Cotton Valley hybrid stimulation consisting of 10,000 bbl of slick-water and 20 lbm/1000 gal linear gel containing 300,000 lbm of proppant (equal amounts of 40/70-mesh sand and 20/40-mesh resin-coated sand). The microseismic fracture mapping indicated a fracture half-length of 1,550 ft and a height of 250 ft. The width of the microseismic event

cloud was ~200 ft, indicating relatively planar fracture growth, with no evidence of network fracture growth. Although there may be small-scale fracture complexity, the microseismic data cannot provide sufficient detail to distinguish between simple planar growth and complex planar growth. Therefore, proppant concentrations will be estimated for planar growth and complex planar growth (low degree of complexity). Fracture modeling indicated a fluid efficiency of ~70%. Table 3 shows the proppant concentrations for a simple planar fracture, three parallel fractures (Figure 1, complex planar – no communication), and a narrow 200-ft wide network with 100-ft fracture spacing (Figure 1, complex planar – communication). The results indicate that a planar fracture would have an average proppant concentration of 0.39 lbm/ft2 if proppant is evenly distributed over the fracture area. However, average proppant concentration is reduced by a factor of three (0.13 lbm/ft2) if three parallel fractures are used to approximate moderate complexity and to 0.076 lbm/ft2 if a small network was created with 100-ft fracture spacing. For all cases, only 7.6% of the fracture area is propped if the proppant settles into pillars (or to the bottom of the fracture system). In the Cotton Valley, an even distribution of proppant may result in sufficient proppant concentration if fracture complexity is low (simple planar fracture). However, a modest degree of fracture complexity could result in a partial monolayer distribution.

The Barnett Shale and Cotton Valley examples illustrate how the degree of fracture complexity can impact proppant concentration. In many cases, fracture complexity can result in sparsely distributed partial monolayer concentrations (Case 1) or insufficient propping of the fracture area (Case 3), and the subsequent well productivity my be dominated by the un-propped fracture conductivity. Even if proppant is concentrated in a single planar fracture, the un-propped fracture conductivity may be an important consideration when selecting stimulation fluids and optimizing design. Therefore, estimating the conductivity of un-propped and partially propped fractures will be an important component of stimulation design in complex environments. Conductivity of Partially Propped and Un-Propped Fractures The surface area of the fracture increases as fracture complexity increases, which can result in the distribution of proppant over a much larger area compared to a simple, single planar fracture (Figure 1). The conductivity of propped fractures has been extensively studied; especially for higher concentrations of proppant in the fracture.58-65 However, there is less understanding of the actual particle arrangement and the corresponding conductivity of a partial monolayer. The conductivity of partially propped and un-propped fractures is much more difficult to determine without accurate descriptions of the

Table 2 - Proppant Concentration, Typical Barnett Shale Treatment

Table 3 - Proppant Concentration, Typical Cotton Valley Hybrid Treatment

10 ft 50 ft 150 ftAfc(ft

2) 361,500,000 73,500,000 25,500,000Wfc(inches) - at end of pumping 0.008 0.041 0.120Cp1(lbm/ft2) 0.001 0.005 0.015Cp2(lbm/ft2) 0.43 0.43 0.43Cp3(lbm/ft2) 0.07 0.34 0.99% Propped (case 3) 1.5% 1.5% 1.5%

Fracture Spacing

Planar 3-parallel 100 ft networkAfc(ft2) 775,000 2,325,000 3,925,000Wfc(inches) - at end of pumping 0.609 0.203 0.120Cp1(lbm/ft2) 0.39 0.13 0.076Cp2(lbm/ft2) 0.39 0.13 0.39Cp3(lbm/ft2) 5.1 1.69 1.00% Propped (case 3) 7.6% 7.6% 7.6%

Fracture Spacing

SPE 115769 7

fracture face and any asperities. The importance of fracture conductivity for a partial monolayer and un-propped fracture has been emphasized with the re-introduction of water-fracs, where very low proppant concentrations are pumped.66-69 The conductivity of partially propped and un-propped fractures has been studied in the laboratory by Fredd, et al., providing important information for fracture design.70 There are very few direct field measurements of un-propped fracture conductivity to confirm the lab results presented by Fredd, but pre- and post-fracture pressure buildup results from a pure CO2 stimulation in the Ozona field71,72 indicated an un-propped fracture conductivity of 0.6 mD-ft (5,500 psi closure stress and E=5x106 psi), which is consistent with the laboratory results of Fredd. Reservoir modeling47 in the Barnett Shale has indicated the conductivity for partially propped and/or un-propped fractures could be 1 to 5 mD-ft (4,500 psi closure stress and E=6x106 psi), also within the range predicted using the Fredd data.

The Fredd data from Cotton Valley cores and the field examples noted above focus on relatively high modulus rock and moderate closure stresses. However, a relationship between closure stress and modulus is needed to extend Fredd’s work and develop guidelines for fracture design. Although attempting to extrapolate such limited data that exhibits a wide range of uncertainty is problematic, the intent is to provide general relationships to approximate fracture conductivity for un-propped fractures. The case of residual conductivity in a fracture that has been opened and then closed is one of asperity contact that has been studied extensively in the literature. Fredd provided experimental results, but earlier work by Walsh and others laid the theoretical groundwork for the expected behavior of the fracture, particularly with regard to stress.73,74 Gall, et al., studied damage to such fractures caused by leakoff fluids.75 Using a Walsh type model, the general form of the permeability is given by:

3

2 )1(ln

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡

−=

σνDECk , which is equivalent to the familiar ( )σln3

1BAk −= , ……………………………(4)

Where A, B, C and D are material/crack parameters, E is Young’s modulus, σ is the net normal stress on the fracture, and

ν is Poisson’s ratio. This type of relationship has been found to match several types of experimental data (e.g., Jones, Kranz, et al., Gall, et al., and Warpinski).2,75-77 From the form of Equation 4 on the left side, it is clear that high modulus formations and low effective stresses are more amenable to retaining conductivity. However, because of the log function, this equation does not lend itself to generalized conclusions about relative behavior without knowing the material parameters.

Nevertheless, it is possible to fit data and then use that information to make an assessment of other parameters. An example of the fit to Fredd’s data for an un-propped displaced fracture is shown in Figure 5.

Assuming the Walsh model is representative of the behavior of un-propped fractures, it can now be used to assess the effect of the modulus of the formation on the conductivity of the fractures as a function of stress level. Figure 6 shows the same data (E=6x106 psi) and extrapolations of those data for lower modulus. The conductivity drop off is dramatic with lower modulus materials. The extrapolation indicates that un-propped fractures, even when displaced and supported by asperities, will essentially close when modulus is 2 x106 psi or lower and stress exceeds 4,000 psi.

Partially Propped Fractures

Predicting the conductivity of partially propped fractures may be necessary when fracture complexity is high and fracture area is large. Fredd presented data for partially propped fractures with a proppant concentration of 0.1 lbm/ft2 (Figure 5). It would be beneficial to extrapolate these results to lower modulus rock and lower proppant concentrations to aid in fracture design when lab data are not available. Although extrapolations of such data are difficult and clearly not rigorous, the following discussion and estimations provide general relationships that should be useful when evaluating fracture treatments in complex environments.

Fredd’s work illustrated the effect of particle strength on fracture conductivity. Figure 5 shows a significant difference between the conductivity of fractures that are partially propped with sand and bauxite. When proppants are sparsely arranged

Figure 5 – Fracture conductivity for un-propped and partially propped fractures (reproduced from Fredd, et al., SPE Journal Sept. 2001)

8 SPE 115769

within a fracture, closure stresses are concentrated on fewer particles, and bauxite was measured to provide 100 times the flow capacity of white sand, even at a modest stress of 4,000 psi. Due to the higher modulus Cotton Valley core used for the tests, it is likely that the conductivity profile is dominated by particle crushing, not embedment. However, as modulus decreases, embedment effects will increase, reducing the conductivity of the partially propped fracture.

It may be possible to extend Fredd’s data by evaluating the two extreme cases: (1) conductivity is dominated by embedment and (2) conductivity is dominated by proppant crushing. When conductivity is dominated by crushing and the fracture is partially propped, higher strength particles will improve fracture conductivity. This improvement can be seen in Figure 5 (Fredd data) by comparing the bauxite conductivity to the sand conductivity. The effect of changing the size of the particles is more complicated. Based on work by Huitt and others using a Hertz cap model, it can be observed that for the same proppant concentration in the fracture, smaller particles will be more resistant to crushing.88-90 Even though small particles are not as strong as larger grains, a specified mass concentration (e.g., 0.1 lb/sq ft) composed of small particles will provide more individual grains per surface area and

more contact points to distribute the applied load. This is the reason that the reported crush diminishes with small diameter proppants. However, because of the reduced permeability provided by smaller particles, it is not certain whether the overall fracture conductivity is improved or decreased by changing particle size. Smaller proppant diameters have a distinct advantage in proppant transport characteristics along the primary fracture and potentially into the network fractures. Leonard, et al.,56 and other anecdotal sources demonstrate that 40/70 and 100-mesh proppant can be carried distances on the order of 1,000 ft in a slickwater fracture. The small diameter of these proppants also enhances their ability to penetrate into network fractures that may be significantly narrower than the primary hydraulic fracture.

In the case where embedment dominates fracture conductivity behavior for sparsely distributed proppant, it may be possible to utilize proppant embedment calculations to estimate the effects of decreasing modulus. The predicted embedment for moderate to hard rock is shown in Figure 7.61 The embedment estimates shown in Figure 7 were developed for multi-layers of proppant and are not valid for partially propped fractures where the stress on each particle will be significantly higher. Therefore, using these embedment estimates for partially propped fractures is clearly a very optimistic assumption, as proppant crushing is ignored and particle stress could be many times higher. Figure 7 provides an upper bound of stress and modulus for the application of low proppant concentrations. In the absence of crushing, it would be expected that partially propped fractures would close when embedment exceeds 0.5 grain diameters into each face of the fracture.

It may also be possible to extrapolate Fredd’s data to proppant concentrations other than 0.1 lbm/ft2 by using an effective stress that is calculated as 0.1/Cp. This approach may be a reasonable approximation for a limited range of proppant concentrations. For example, assuming that the percentage of the total load carried by the rock is constant, the effective stress for a proppant concentration of 0.05 lbm/ft2 would be twice that of 0.1 lbm/ft2. The conductivity for a partially propped fracture could then be estimated using the concentration corrected stress. This approach would indicate that ultra low proppant concentrations would likely behave similar to un-propped fractures, especially at higher stresses.

0.01

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duct

ivity

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-ft)

E=6E+6 psiE=4E+6 psiE=2E+6 psiE=1E+6 psi

Figure 6 - Effect of modulus on conductivity of un-propped fractures with shear offset, extrapolation of Fredd data using Walsh model

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ain

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s) 1E+6 psi2E+6 psi4E+6 psi6E+6 psi

Figure 7 - Proppant embedment for moderate to hard rock

SPE 115769 9

Application of Conductivity Estimates Although quantifying actual fracture conductivity for un-propped and partially propped fractures is not possible with such

a limited amount of data, it may be possible to use the available data and subsequent extrapolations to provide guidelines for fracture design when fracture complexity exists. It may be possible to approximate reasonable bounds for fracture conductivity given estimates of fracture complexity, closure stress, Young’s modulus, location and concentration of the proppant. While the effect of non-Darcy, multiphase flow, and other damage factors have been described63,64 in fully packed fractures containing multiple layers of proppant, additional guidance is needed to apply these reductions to partially or irregularly propped fractures. The fracture conductivity extrapolations for un-propped fractures shown in Figure 6 and the embedment calculations shown in Figure 7 indicate that fracture conductivity decreases rapidly for lower modulus rock, especially at higher closure stress. For example, un-propped fracture conductivity for a 2x106 psi modulus rock at 6,000 psi stress is estimated to be less than 0.01 mD-ft and embedment would be 0.5 grain diameters into each face of the fracture for a partially propped fracture (indicating a closed fracture).

Relationship Between Fracture Conductivity and Well Productivity for Complex Fractures

A series of reservoir simulations was performed to evaluate the relationship between fracture conductivity and well productivity when fracture growth is complex (vertical well). The simulations focused on low permeability gas reservoirs where water-fracs and hybrid fracs are commonly applied. A low-range permeability of 0.0001 mD was selected to represent many shale reservoirs and mid-range permeability of 0.01 mD to represent tight gas sands. Simulations were also performed using a permeability of 1 mD to represent moderate permeability reservoirs. The basic input parameters for the reservoir modeling are shown in Table 4. A fracture or network length of 1,000 ft was used for all the simulations. The reservoir modeling covered a wide range of fracture complexity, from simple planar fractures to large networks. In each case, a wide range of fracture conductivity was evaluated. When simulating medium to large

fracture networks, two scenarios were used to evaluate the effect of network conductivity on well productivity: (1) uniform fracture conductivity throughout the network and (2) an infinite conductivity primary fracture that is connected to a fracture network. In all cases the one-year cumulative production was normalized by dividing the gas production (Gp) by the infinite conductivity gas production or maximum theoretical gas production (Gpmax). For reference, the maximum achievable first-year production for each case is summarized in Table 5. The normalized production allows cases with widely varying productivity to be easily compared. First-year production values were selected to minimize the influence of boundary affects while still providing a time frame of economic relevance. Correlating parameters were identified to “collapse” the normalized production curves for each set of simulations into a single curve to emphasize the relationship between reservoir permeability, fracture complexity, fracture conductivity and well productivity. The reservoir simulations are presented in order of complexity, from simple planar fractures to large networks.

Simple Planar Fracture

As a base line, the production from a simple planar fracture for various fracture conductivities was evaluated. Figure 8 compares the normalized production for permeability of 0.0001, 0.01, and 1.0 mD. The reservoir geometry is 10,000 ft x 10,000 ft with a 1,000-ft fracture half-length. Fracture conductivity divided by the square-root of reservoir permeability (denoted FcDc) was plotted on the x-axis and appears to collapse the various permeability ranges fairly well. The simulations indicate that to achieve near maximum (+98%) one-year production requires 30,000 mD-ft, 3,000 mD-ft, and 300 mD-ft for permeability of 1 mD, 0.01 mD, and 0.0001 mD, respectively (FcDc of about 30,000 in Figure 8). A dimensionless fracture conductivity (Fcd = kfwf/kxf) of 10 to 30 is normally considered optimum; however, the optimum Fcd depends on the time selected for comparison and the reservoir permeability.83 In very tight reservoirs, conventional Fcd applications may not be

Table 4 - Reservoir Simulation Inputs

Table 5 – Summary of Reservoir Modeling: Maximum Achievable 1st Year Production (MMCF)

Case k = 0.0001 mD k = 0.01 mD k = 1 mD

Dx (Frac Spacing) = 100 ft 1867 9520 43710Dx (Frac Spacing) = 50 ft 2113 9525 43718Dx (Frac Spacing) = 25 ft 2152 9542 43777

Dx (Frac Spacing) = 100 ft 1867 9522 43731Dx (Frac Spacing) = 50 ft 2113 9529 43744Dx (Frac Spacing) = 25 ft 2152 9543 43777

Dx (Frac Spacing) = 50 ft 736 4674 39803Dx (Frac Spacing) = 25 ft 742 4683 39867

Dx (Frac Spacing) = 50 ft 736 4676 39845Dx (Frac Spacing) = 25 ft 742 4685 39885

Dx (Frac Spacing) = 5 ft 180 2682 35948

Three-Parallel Fracs 179 2669 35832

Single Frac (Xf = 1,000 ft) 139 2581 53391

Small Network 1000 x 150 ft Infinite Conductivity

Small Network 1000 x 10 ft Communicating Fractures

Small Network 1000 x 10 ft Non-Communicating Fractures

No Fracture Network

Large Network 1000 x 500 ft Uniform Conductivity

Large Network 1000 x 500 ft Infinite Conductivity

Small Network 1000 x 150 ft Uniform Conductivity

Formation depth, D 7000 ftReservoir permeability, k 0.0001, 0.01, 1 mDNet pay thickness, h 300 ftPorosity, φ 0.03 (k = 1.e-4 mD) –

0.09 (k = 1.e-2 mD) –0.18 (k = 1 mD) –

Initial pore pressure, pi 3000 psiWater saturation, Sw 0.3 –Reservoir temperature, T 180 ºFRock compressibility, cf 3.00E-06 1/psiGas viscosity, μg 0.019 cpGas gravity, γg 0.6 –

10 SPE 115769

appropriate. In this case, an Fcd of 30 would indicate fracture conductivity requirements of 30,000 mD (k=1.0 mD), 300 mD-ft (k=0.01 mD), and 3 mD-ft (k=0.0001 mD). For the 1 mD case, the fracture conductivity estimated using an Fcd of 30 is consistent with the near maximum one-year production. However, the Fcd based value of 300 mD-ft for the 0.01 mD case would generate an FcDc of 3,000 and result in about 15% less production in the first year (Figure 8). The difference becomes even greater for the very low permeability case (k=0.0001 mD), where designing a fracture to achieve an Fcd of 30 would result in about 40% less production in the first year compared to what could be achieved with a fracture conductivity 100 times higher (300 mD-ft or Fcd=3000). These results illustrate the limitations of conventional Fcd based estimates of optimum fracture conductivity and the benefits of reservoir simulation when evaluating fracture conductivity requirements.

Complex Planar Fractures

The effect of small-scale fracture complexity was evaluated for the case of five parallel fractures. Two scenarios were modeled – one with no communication between the fractures and one with an orthogonal set of fractures. Figure 9 illustrates the reservoir model used to simulate complex planar fractures (quarter symmetry).

Figure 10 summarizes the results for the simulations, illustrating the effect of fracture conductivity on first-year production. To collapse the curves, the normalized gas production is graphed as a function of fracture conductivity divided by the square-root of reservoir permeability, consistent with the single planar fracture case above.

The simulations indicate that near maximum one-year production is achieved with an FcDc of about 15,000, half that of the single planar case above. The results for the “communication” and “no communication” cases are the same. This appears to indicate that only the outside fractures are contributing to production, even when the fractures are communicating. Therefore, in the presence of small-scale fracture complexity, fracture conductivity requirements may be higher than that for a single planar fracture. For example, if typical FCD estimates of required fracture conductivity are used and single planar growth is assumed, then the design fracture conductivity would be 300 mD-ft to achieve an Fcd of 30 for k=0.01 mD and xf=1000 ft. For the fracture complexity used in this case (Figure 9), fracture conductivity may be reduced by a factor of 5 to 9 compared to a single planar fracture because the proppant would be spread over a much larger area. The corresponding FcDc values in Figure 9 for k=0.01 mD would range from 333 (33.3 mD-ft) to 600 (60 mD-ft) and result in 15 to 20% lower gas production if fracture complexity were present – but not anticipated in the design.

Network Fracture Productivity

Network fracture productivity was evaluated for small and large fracture networks. In the case of small and large fracture networks, two scenarios were evaluated: (1) uniform fracture conductivity throughout the network and (2) an infinite conductivity primary fracture that is connected to a finite conductivity network. The two cases are meant to describe the two extremes for proppant transport in complex fractures, where proppant is evenly distributed throughout the fracture network or concentrated in a primary planar fracture. Partially propped and un-propped fractures may be important when evaluating the effects of fracture conductivity on well productivity for network fracture growth.

Figure 8 - Normalized Gp for the single fracture case (one year)

Figure 9 - Reservoir Model for Complex Planar Fractures

3 Parallel Fractures

2000 ft

1000 ft

1000 ft

10 ft

3 Parallel Fractures

2000 ft

1000 ft

1000 ft

10 ft

Fracture Network

2000 ft

1000 ft

1000 ft

10 ft

Fracture Network

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1000 ft

1000 ft

10 ft

(a) No Communication (b) Communication

3 Parallel Fractures

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1000 ft

10 ft

Fracture Network

2000 ft

1000 ft

1000 ft

10 ft

Fracture Network

2000 ft

1000 ft

1000 ft

10 ft

(a) No Communication (b) Communication

SPE 115769 11

Small Network Fracture Productivity Productivity for a small fracture network was

studied using a 300-ft network width (xn) and fracture spacing (Δxs or Dx) of 25 and 50 ft. For reference, the total fracture area for the 25-ft and 50-ft spacing is 13 to 25 times larger than the single planar fracture (xf = 1000 ft for all cases). The quarter symmetry reservoir simulation model is shown in Figure 11. The reservoir simulation results for a small network are summarized in Figure 12. “Infinite FC” denotes the results for an

infinite conductivity primary fracture, while “Uniform FC” denotes the results when conductivity is uniform throughout the fracture network. For the uniform conductivity case, the normalized production will have a minimum that will equate to the one-year cumulative production for the un-stimulated reservoir. If an infinite conductivity primary fracture is created, the normalized production will have a minimum that will equate to the one-year cumulative production for an infinite conductivity single planar fracture. The benefits of exploiting fracture complexity in low permeability reservoirs is illustrated in Figure 12 by comparing the Normalized Gp for an infinite conductivity single fracture to the Normalized Gp for an infinite conductivity small network (discussed in more detail later).

In this case the normalized production results are graphed as a function of kfwf/Δxs0.5k0.5, which reasonably collapses the

results for permeability that ranges from 0.0001 to 1.0 mD. The FcDc in this case indicates that the required network fracture conductivity is proportional to the square-root of fracture spacing and permeability. The fracture conductivity required to achieve near maximum production is summarized in Table 6.

If an infinite conductivity primary fracture is created, near maximum one-year cumulative production is achieved when fracture conductivity reaches 150 to 212 mD-ft (k=1.0 mD), 15 to 21 mD-ft (k=0.01 mD) and 1.5 to 2.0 mD-ft (k=0.0001 mD) (Table 6). Compared to a small network with uniform fracture conductivity, the network fracture conductivity required to maximize first year production is 100 times lower when an infinite conductivity primary fracture is present (Table 6). This indicates that production could be significantly impacted by proppant transport behavior when fracture growth is complex.

The presence of an infinite conductivity primary fracture dominates well performance as permeability approaches 1 mD. For example, when reservoir permeability is 1 mD, production for an infinite conductivity network and a very low conductivity network differ by only 10% (Figure 12, Infinite FC, 1 mD) when an infinite conductivity primary fracture is present. This would suggest that controlling fracture complexity should be the design goal when permeability is on order 1.0 mD. However, for low permeability reservoirs, significant production enhancement above that of a single infinite conductivity fracture can be realized if sufficient network conductivity can be achieved. For example, an infinite conductivity single planar fracture in a 0.01 mD reservoir will result in a normalized Gp of about 0.55 or 55% of the maximum that could theoretically be realized from a small fracture network with 25 to 50 ft fracture spacing. Referring to

Figure 10 - Normalized Gp for complex planar fracture growth

Network is ON

2000 ft

1000 ft

1000 ft

150 ft

Network is ON

2000 ft

1000 ft

1000 ft

150 ft

Figure 11 - Small fracture network model

Figure 12 - Normalized Gp, small fracture network

Gp: Un-stimulated Reservoir

Gp: Infinite Conductivity Single Planar Fracture

Gp: Un-stimulated Reservoir

Gp: Infinite Conductivity Single Planar Fracture

12 SPE 115769

Table 6, if a network fracture conductivity of 15 to 21 mD-ft could be achieved in addition to an infinite conductivity primary fracture or a uniform fracture network with a conductivity of 1,500 to 2,121 mD-ft was created, production could almost be doubled. Tight Gas Applications. The Barnett Shale47 and Cotton Valley37 treatment sizes are representative of many tight gas stimulation treatments, with about 1,250 lbm of proppant pumped per foot of fracture height. For a hypothetical tight gas stimulation where 1,250 lbm/ft of proppant is pumped per foot of fracture height and a small fracture network is created with a fracture spacing of 50 ft and a 1,000-ft half-length (as described above), there would be 26,300 ft2 of fracture area per foot of fracture height. The average proppant concentration would be ~0.05 lbm/ft2 if the proppant were evenly distributed in the fracture network. If the proppant were distributed in pillars throughout the network, the proppant concentration at each pillar would be much higher, but only a small percentage of the total fracture area would be propped by the pillars – as was illustrated previously in the Barnett Shale and Cotton Valley examples.

Assuming a closure stress of 4,000 psi, sand proppant, and a Young’s modulus of 5x106 psi, a range of possible fracture conductivity can be estimated by extrapolating the laboratory results of Fredd, as previously discussed. The stress for a proppant concentration of 0.05 lbm/ft2 would be twice that of the 0.10 lbm/ft2 concentration used in Fredd’s tests, resulting in an effective stress of 8,000 psi on the proppant. Although the maximum stress in Fredd’s laboratory work is 7,000 psi, it is clear from Figure 5 that the conductivity for a partially propped fracture at 8,000 psi stress is less than 10 mD-ft and could be as low as 1 mD-ft if the fracture network behaves as an un-propped displaced fracture – which is possible for such low proppant concentrations.

A permeability range that covers many tight gas reservoirs is 0.0001 to 0.01 mD; 71,84 the corresponding FcDc in Figure 12 for this permeability range and a fracture conductivity of 10 mD-ft is 14 (k=0.01 mD) and 140 (k=0.0001 mD). This would indicate that when sand is distributed throughout the network (Case 1), the fracture conductivity is insufficient to maximize first year gas production, resulting in normalized one-year gas production of about 40% (k=0.01 mD) to 80% (k=0.0001 mD) of the maximum. If the fracture network behaves as a displaced un-propped fracture (kfwf=1 mD-ft), then the corresponding FcDc in Figure 12 would be ten times lower and the resulting production would be 10% (k=0.01 mD) to 40% (k=0.0001 mD) of the maximum attainable. If a stronger proppant (bauxite) provides 10 to 100 times the conductivity of sand as suggested by Figure 5, significant production gains would be achieved. It is important to note that the normalized gas production for an infinite conductivity single planar fracture is 55% (k=0.01 mD) and 18% (k=0.0001 mD) of the maximum (Figure 12) and should be used as a baseline for design decisions. Given estimates of the achievable network fracture conductivity and proppant distribution, if the network production does not exceed that of an infinite conductivity single planar fracture, then the design should be tailored to minimize fracture complexity. Therefore, network fracture growth could be detrimental to production when reservoir permeability is 0.01 mD if the proppant is evenly distributed throughout the fracture network, as sufficient network conductivity may not be achieved with partially sand-propped fractures or displaced un-propped fractures to surpass the production from an infinite conductivity single planar fracture. However, when permeability is 0.0001 mD, un-propped fracture conductivity may be sufficient to provide significant production enhancement above that of an infinite conductivity single planar fracture if some degree of shear-offset can be obtained in the fracture network. If proppant is selected to accommodate the higher effective stresses with irregularly propped fractures, it may be possible to exploit small-scale fracture complexity when permeability is 0.01 mD, even if the proppant is distributed evenly throughout the fracture network.

If all of the proppant were concentrated in a primary fracture (Case 2), the average proppant concentration would be 0.625 lbm/ft2. The resulting reference63 fracture conductivity for 40/70-mesh proppant in this primary fracture would be about 75 to 500 mD-ft for a closure stress range of 4,000 to 6,000 psi, depending on the type of proppant pumped (sand or ceramic). The realistic retained conductivity (after damage) would be significantly lower.63,64 The reference conductivity for 20/40-mesh sand would be about 250 to 750 mD-ft, while a 20/40-mesh lightweight ceramic would provide 500 to 1,500 mD-ft. Typical reductions63,64 for gel damage, cyclic stress, non-Darcy and multiphase flow generally reduce these values by over 90%. Using the results above for a single fracture (Figure 8), it would require 300 to 3,000 mD-ft to achieve near maximum first year production for a permeability of 0.0001 to 0.01 mD, respectively. Therefore, it may be possible that a near infinite conductivity primary fracture could be achieved in many tight gas reservoirs with complex fracture growth if the proppant were concentrated in the primary fracture (i.e., cannot enter into secondary fractures), proppant concentration or quality were maximized, and if damage factors were minimized by use of slick-water to reduce gel damage, etc.

Significant production enhancement could be achieved from small fracture networks with effective conductivities of 2 to 20 mD-ft for reservoir permeabilities of 0.0001 to 0.01 mD, respectively, if an infinite conductivity primary fracture were created (Figure 12). However, the network fractures would be un-propped. Referring to Figure 5 and Figure 6, the expected

Table 6 – Small Network Conductivity Requirements

Uniform Fracture Conductivity

k (mD) 50 ft 25 ft1 21213 15000

0.01 2121 15000.0001 212 150

Infinite Conductivity Primary Fracture

k (mD) 50 ft 25 ft1 212 150

0.01 21 150.0001 2 1.5

Conductivity (mD-ft) to Achieve Near-Max GpFracture Spacing

Conductivity (mD-ft) to Achieve Near-Max GpFracture Spacing

SPE 115769 13

conductivity for a displaced un-propped fracture at 4,000 to 6,000 psi closure stress would be 1 to 10 mD-ft for E=6x106 psi. Therefore, for very low permeability reservoirs like the Barnett Shale, it may be possible to maximize production without transporting proppant into the fracture network if the network fractures have shear offsets (displaced fracture case). If the network fractures do not have shear offsets (Figure 5, aligned fracture case) then sufficient conductivity cannot be obtained with un-propped fractures. For lower modulus rock, it is unlikely sufficient network conductivity can be obtained with un-propped fractures (Figure 6), even when permeability is 0.0001 mD, as fracture conductivity would likely be less than 0.1 mD-ft at stresses of 4,000 to 6,000 psi.

Moderate Permeability Applications. In the case of a uniform conductivity fracture network in higher permeability

reservoirs, achieving maximum production may not be possible due to limitations in network fracture conductivity. For example, the network fracture conductivity required to maximize first year production for a 1 mD reservoir is in excess of 15,000 mD-ft (Table 6). For reference, it would require about 2 to 10 lbm/ft2 of 12/18-mesh ceramic proppant to achieve a conductivity of 15,000 mD-ft at modest closure (4,000 to 6,000 psi) and typical retained conductivity values.61 In many cases, moderate permeability reservoirs exhibit lower Young’s modulus than their low permeability counterparts, often ranging from 1 to 3x106 psi. 19,86,87 In this modulus range it is unlikely that sufficient un-propped fracture conductivity could be retained to exploit fracture complexity (Figure 6). Embedment effects would likely render a partially propped fracture completely ineffective (Figure 7). Therefore, the only possible way to capitalize on fracture complexity would be a fully propped fracture, which is very difficult to achieve when complexity is severe.10,11,18,20,21 In this example, a 50-ft network fracture spacing would result in a fracture area of 26,300 ft2 per foot of fracture height. Given the calculation above for 12/18-mesh ceramic proppant (2 to 10 lbm/ft2), it would require 48,000 to 240,000 lb of proppant per foot of fracture height to maximize one-year production if fracture complexity were present. Even for modest fracture heights, this is an excessive amount of proppant and it is probably impossible to place such large quantities at concentrations sufficient to achieve 2 to 10 lbm/ft2 when moderate to high fracture complexity exists.

If an infinite conductivity single planar fracture is created, network fracture conductivity requirements decrease by a factor of 100 to 150-212 mD-ft (Table 6). However, in a 1 mD reservoir, achieving significant production improvements by exploiting fracture complexity is not likely. Given the conditions of the simulations, an infinite conductivity planar fracture in a 1 mD reservoir will result in a normalized first year production of 90%. Therefore, even if sufficient network conductivity could be achieved, first year gas production would only increase by about 10%; controlling fracture complexity is the key in moderate permeability reservoirs. Although it is unlikely that a treatment would be designed to create a 1,000-ft fracture half-length in most 1 mD reservoirs, fracture half-lengths of 200 to 300 ft have been reported for this permeability range in chalks and sandstone reservoirs and the same general conclusions probably apply.19,86,87

Large Network Fracture Productivity

The reservoir model used to evaluate conductivity requirements for large network fracture productivity is shown in Figure 13 (¼ reservoir symmetry), consisting of a 1,000-ft network width and a fracture half-length of 1,000 ft. Fracture spacings of 25, 50, and 100 ft were modeled. The results of the simulations are summarized in Figure 14. With the large fracture network, the correlating parameter (FcDc) that provides the best collapse of the results is fracture conductivity divided by the square-root of the fracture spacing and the fourth-root of the reservoir permeability (kfwf/Δxs

0.5k0.25). The fourth-root of permeability may reflect the bilinear nature of flow in the large fracture network, compared to more linear flow that was represented by the square-root of permeability in the correlating parameter for the small fracture network. The network conductivity required to achieve near maximum one-year production is summarized in Table 7, indicating very high conductivity requirements for the lower permeability reservoirs relative to the 1 mD case. For example, the conductivity requirements for the 0.0001 mD case are only ten times lower than the 1 mD cases, while permeability differs by a factor of 10,000 (Table 7). This is contrary to classical fracture design theory based on dimensionless fracture conductivity (FCD), where conductivity requirements are directly proportional to reservoir permeability (given the same fracture length).

Near maximum first year production is obtained when FcDc reaches about 1,000 for the large fracture network with uniform fracture conductivity. If an infinite conductivity primary fracture is created (Case 2), near maximum production is obtained when FcDc reaches about 100, indicating that ten times less conductivity is required in the network. As with the small network case, as fracture network conductivity becomes very low and fracture network permeability approaches reservoir permeability, the normalized production will reach a minimum that is equal to that of an infinite conductivity single planar fracture (or an un-stimulated reservoir for the uniform conductivity case). The resulting network conductivity requirements are shown in Table 7, indicating fracture conductivity of 500 to 1,000 mD-ft is required to achieve near maximum production when reservoir permeability is 0.0001 mD and proppant is uniformly distributed. The conductivity

Figure 13 – Reservoir model for large network

Fracture Network

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Fracture Network

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14 SPE 115769

requirements for a large network are ten times lower when an infinite conductivity primary fracture is created as compared to a uniform conductivity network (Table 7); however, the production benefits of optimizing fracture network conductivity are dependent on reservoir permeability. Figure 14 shows that an infinite conductivity single planar fracture (no network) will result in a normalized one-year gas production of less than 10% of the maximum when permeability is 0.0001 mD, about 26% of the maximum for 0.01 mD, and 83% of the maximum for 1 mD. As with the small network case, the benefits of exploiting fracture complexity are mostly limited to low permeability reservoirs (0.01 to 0.0001 mD).

Comparing the conductivity requirements for large (Table 7) and small (Table 6) networks shows that much higher network fracture conductivity is required when reservoir permeability is lower for the large network to maximize first year production. For example, a large network with 50 ft spacing in a 0.0001 mD reservoir would require 707 mD-ft to achieve near maximum first year production, while only 212 mD-ft are required when the network is small. The near maximum one-year production for the large network will be much higher than the small network, emphasizing the importance of achieving large fracture networks with adequate conductivity (if possible) in very low permeability reservoirs.

Tight Gas Applications. Suppose the same

treatment that was pumped in the small network evaluation actually develops a large network. Assuming a fracture spacing of 50 ft and 1,250 lbm of proppant pumped per foot of fracture height, the area of the large network would be 83,000 ft2 per foot of fracture height, resulting in an average proppant concentration of 0.015 lbm/ft2 (Case 1) if the proppant were evenly distributed in the fracture network. Assuming a closure stress range of 4,000 to 6,000 psi and hard rock (E=5x106 psi), fracture conductivity can be estimated from Figure 5 using an effective stress on the proppant grains that is 6.6 times (0.1 lbm/ft2 /0.015 lbm/ft2 ) larger than was represented in Fredd’s lab tests. Using this approximation of effective stress, the stress on 0.015 lbm/ft2 appears to be excessive and it is unlikely that the proppant would contribute materially to overall fracture conductivity. Therefore, the best estimate of the network conductivity would be the un-propped conductivity at 4,000 to 6,000 psi in Figure 5, which is about 1 to 10 mD-ft for an un-propped displaced fracture. As discussed previously, the distribution of the proppant in pillars (Case 3) would result in a very small percentage of the overall fracture area propped (less than 2% for most large networks) and may also behave as an un-propped fracture. Using a typical permeability range in tight and unconventional gas reservoirs, from Table 7 the required fracture conductivity to achieve near maximum first-year production is about 700 mD-ft (k=0.0001 mD) to 2,250 mD-ft (k=0.01 mD). Therefore, near maximum first-year production cannot be achieved with a uniform distribution of proppant (Case 1) or pillar distribution (Case 3).

Assuming a network fracture conductivity of 1 to 10 mD-ft, the corresponding “large network” FcDc values would be 0.44 to 4.4 (k=0.01 mD) and 1.4 to 14 (k=0.0001 mD). Using Figure 14, the resulting normalized first-year production would be about 5 to 25% of the maximum if reservoir permeability is 0.01 mD and 10 to 50% of the maximum for a reservoir permeability of 0.0001 mD. In the case of a large network with evenly distributed proppant that behaves like displaced un-propped fractures, stimulation effectiveness would likely be moderate to good for very low permeability reservoirs (i.e., shale) compared to an infinite conductivity simple planar fracture, which would result in a normalized first year gas production of about 0.10 or 10% (Figure 14). However, for tight gas reservoirs with a permeability of 0.01 mD, stimulation effectiveness would be poor, as the expected normalized first-year gas production for an infinite conductivity planar fracture would be 0.26 or 26% (Figure 14) - the same production as a large network with a uniform fracture conductivity of 10 mD-ft. Therefore, when reservoir permeability is around 0.01 mD, large fracture networks with uniform conductivity are likely

Figure 14 - Normalized Gp, large network

Table 7 – Large Network Conductivity Requirements

Uniform Fracture Conductivity

k (mD) 100 ft 50 ft 25 ft1 10000 7071 5000

0.01 3162 2236 15810.0001 1000 707 500

Infinite Conductivity Primary Fracture

k (mD) 100 ft 50 ft 25 ft1 1000 707 500

0.01 316 224 1580.0001 100 71 50

Fracture SpacingConductivity (mD-ft) to Achieve Near-Max Gp

Conductivity (mD-ft) to Achieve Near-Max GpFracture Spacing

Gp: Un-stimulated Reservoir

Gp: Infinite Conductivity Single Planar Fracture

Gp: Un-stimulated Reservoir

Gp: Infinite Conductivity Single Planar Fracture

SPE 115769 15

detrimental to production, while for much lower permeability reservoirs they are probably beneficial to production, based on the expected conductivity of 1 to 10 mD-ft.

If shear offset is not achieved and the conductivity is not represented by Fredd’s displaced un-propped fracture data, the network fracture conductivity would be much less than 0.1 mD-ft (aligned fracture, Figure 5), resulting in normalized first year gas production of 2% or lower (Figure 14). In the case of evenly distributed proppant that behaves like aligned un-propped fractures, stimulation effectiveness would be very low and fracture complexity would be detrimental – suggesting that controlling fracture complexity and creating a more planar hydraulic fracture would be desirable. In addition, for lower modulus rock, even displaced fractures will likely provide insufficient network fracture conductivity (Figure 6) and fracture complexity should be minimized in these cases.

Now let’s consider the case where an infinite conductivity primary fracture is created and proppant presumably is prohibited entry into the distant network. In this case, network conductivity will be dominated by un-propped fractures, either displaced or aligned. Un-propped displaced fractures could exhibit conductivities of 1 to 10 mD-ft. For very low permeability reservoirs like the Barnett Shale, the FcDc values would range from 1.4 to 14 (k=0.0001 mD, 50 ft fracture spacing, 1 to 10 mD-ft un-propped network conductivity) and result in first year production that is 75 to 95% of the maximum (Figure 14). When reservoir permeability is 0.01 mD, the corresponding FcDc values for 50 ft spacing and 1 to 10 mD-ft un-propped network conductivity are 0.45 to 4.5 and result in production that is 50 to 80% of the first year maximum. Therefore, if shear offsets are present, providing un-propped fracture conductivity of 1 to 10 mD-ft, it may be possible to significantly improve production if large un-propped fracture networks can be created in addition to an infinite conductivity primary fracture. As discussed previously, in the absence of shear offsets (displaced fractures), aligned un-propped fracture conductivity would be less than 0.1 mD-ft and result in insufficient conductivity to achieve even modest production benefits from network fracture growth.

Moderate Permeability Applications. As discussed for small networks, with reservoir permeability of 1 mD or higher, achieving significant production improvements above the infinite conductivity single planar fracture is not likely. Given the conditions of the simulations, an infinite conductivity planar fracture in a 1 mD reservoir will result in a normalized first year production of 83% of what could be achieved with a large fracture network (Figure 14). Even if an infinite conductivity primary fracture and a large network with sufficient network conductivity could be achieved (500 to 1,000 mD-ft), first year gas production would only increase by about 17%. Although this may equate to a large amount of gas, it is probably not possible to achieve both the desired primary fracture and network conductivity. Fluid loss will likely limit the ability to create large networks in moderate permeability reservoirs, as will the high viscosity fluids needed to place the proppant concentrations required to achieve the desired conductivity. Therefore, controlling fracture complexity is again the key in moderate permeability reservoirs.

Fluid Leakoff and Fracture Area As fracture area and reservoir permeability increase, fluid loss rates will increase dramatically. The low viscosity fluids specified to create large fracture networks generally omit gelling and wall-building components, thus fluid loss is dominated by reservoir properties and fracturing conditions. The ability to achieve large fracture networks will be limited by fluid loss behavior and there will be practical limits to the maximum fracture area that can be created. Figure 15 illustrates the effect

of fluid loss on approximate maximum fracture area for a wide range of fluid loss coefficients, assuming an injection rate of 100 BPM. The maximum fracture area was estimated by calculating the area that resulted in a leakoff rate equal to the injection rate of 100 BPM. The likely range of fluid loss coefficients that would be expected for a reservoir permeability of 0.0001 mD and 0.01 mD are shown in the figure69, allowing an approximation of the maximum area that could be achieved for injection volumes of 12,000, 24,000, and 48,000 bbl.

When permeability is very low, fracture networks in excess of 100 million square feet might be possible with large injection volumes. Referring to the Barnett Shale example that was previously presented, network fracture areas of 24 to 360 million square feet were estimated depending on fracture spacing for a typical Barnett Shale

Figure 15 - Maximum fracture area as a function leakoff coefficient

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09

0.00001 0.00010 0.00100 0.01000

Ct (ft/min1/2)

Max

imum

Fra

ctur

e A

rea

(ft2 )

48,000 bbl24,000 bbl12,000 bbl

Q=100 BPM

k ~0.01 mD

k ~0.0001 mD

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09

0.00001 0.00010 0.00100 0.01000

Ct (ft/min1/2)

Max

imum

Fra

ctur

e A

rea

(ft2 )

48,000 bbl24,000 bbl12,000 bbl

Q=100 BPM

k ~0.01 mD

k ~0.0001 mD

16 SPE 115769

fracture treatment (Table 2). This is consistent with the approximate range of fracture area from Figure 15 and the expected permeability (k ~ 0.0001 mD) and injected volume (60,000 bbl).

As permeability increases to 0.01 mD, the expected maximum fracture area for a slick-water treatment decreases to about 2 to 20 million square feet. Fracture area ranged from 0.775 to 3.1 million square feet, depending fracture complexity, in the Cotton Valley example discussed previously (Table 3) for a 10,000-bbl hybrid treatment. As permeability approaches 1 mD, fluid loss control and increased viscosity are required to reduce leakoff and improve proppant transport to allow successful placement of sufficient proppant concentrations to achieve adequate fracture conductivity. In moderate permeability reservoirs (~1 mD), generating even modest network fracture growth is unlikely with low viscosity fluids due to excessive fluid leakoff.

For reference, the fracture area for the small network example with a 300-ft fracture height would be 8 to 15 million square feet (25 and 50 ft fracture spacing). For the same fracture height and fracture spacing, the fracture area would be 25 to 49 million square feet for the large network example. Figure 15 illustrates that generating large fracture networks with slick-water may be possible only when reservoir permeability is less than 0.001 mD. As permeability approaches 0.01 mD, fluid loss will control maximum fracture area and limit treatments designs to small network growth.

Diagnosing Fracture Complexity Although it is difficult to uniquely characterize fracture complexity, it may be helpful to evaluate the degree of fracture complexity for various geologic environments. A simple approximation of fracture complexity is given by Equation 5.

f

n

xxFCI

2= ...................(5)

Figure 16 is a graph of published microseismic fracture mapping data showing the total width of the microseismic cloud versus the total length of the cloud. Several slopes are shown for reference. Network complexity appears to occur in the 0.25 to 0.5 range, but it is not very clear when the fracture is small because of normal microseismic activity that occurs away from

the fracture, as well as uncertainty in event location. Some of the network width in the smaller fractures is due to interaction with faults. Note that there is some interpretation required, as some cases do not image the entire fracture length, in which case the total fracture length was assumed to be twice the length of the observed wing. Figure 16 illustrates that many geologic environments may exhibit some degree of fracture complexity, with the shale plays generally exhibiting the highest degree of complexity and the tight gas sands low to moderate complexity. Unfortunately, a microseismic event “cloud” will typically have a minimum width of 100 to 200 ft. Therefore, for short hydraulic fractures (i.e., less than 1,000 ft) FCI may over-predict the degree of fracture complexity. An alternate approach may be to simply evaluate the width of the microseismic event pattern; when the width of the event pattern exceeds 200 ft, fracture complexity and/or network growth may be present.

Net Pressure & Fracture Complexity

Net pressure data may provide qualitative insights into fracture complexity when microseismic data are not available or the microseismic event pattern cannot distinguish between simple planar and complex planar fracture growth. Nolte and Smith80 provided a simple estimate of fissure opening pressure based on the net pressure in the fracture and the difference between the minimum and maximum horizontal stress and Poisson’s ratio (Equation 6).

)21( v

P ho −

Δ=

σ...................(6)

Warpinski2 showed fissure opening at net pressures of 850 to 1,050 psi in tight gas sands in the Piceance Basin. The actual fissure opening pressures were somewhat lower that predicted by Equation 6, but still in reasonable agreement. Therefore, in cases where a pre-existing rock fabric is present, the potential for fracture complexity may be estimated from net pressure data if the maximum horizontal stress has been determined. The analysis of minifrac pressure decline data can also provide estimates of fissure opening pressures and insights into fracture complexity.81,82

Figure 16 - Fracture Complexity Index (FCI) for various geologic environments

0

200

400

600

800

1000

1200

1400

1600

0 1000 2000 3000 4000 5000

Total Length (ft)

Tota

l Wid

th (f

t)

BossierGrand ValleyRulisonWest TavaputsBarnettDevonian SandsCanyon SandsCotton ValleyLance/Mesaverde

0.5

0.25

FCI = 1

FCI = 0.1

0

200

400

600

800

1000

1200

1400

1600

0 1000 2000 3000 4000 5000

Total Length (ft)

Tota

l Wid

th (f

t)

BossierGrand ValleyRulisonWest TavaputsBarnettDevonian SandsCanyon SandsCotton ValleyLance/Mesaverde

0.5

0.25

FCI = 1

FCI = 0.1

SPE 115769 17

Fracture complexity can also be estimated by evaluating the level of net pressure using fracture modeling techniques. Although current fracture models cannot rigorously model fracture complexity, it may be possible to approximate fracture complexity by modeling a system of interacting parallel fractures.9,19 This approach provides estimates of proppant distribution that can be used to evaluate fracture conductivity requirements and the impact of fracture complexity on well productivity. In the event fracture complexity cannot be determined from fracture mapping measurements, the application of fracture modeling and net pressure analyses may provide insights into fracture growth that are critical when selecting the appropriate treatment design.

Summary The tendency for complex fracture growth is most likely a function of the pre-existing rock fabric and the stress regime. Reservoirs with a high concentration of natural fractures or fissures are more prone to complex fracture growth. Complexity may be encouraged by dilation or shear failure depending on the interaction between the stress regime, natural fractures, and hydraulic fracture. Fracture complexity can be reduced by pumping high viscosity fluids and maximized by pumping low viscosity fluids. The decision whether to control or enhance fracture complexity will depend on reservoir permeability,

proppant distribution, and desired fracture conductivity. The fracture conductivity required to achieve near

maximum first year gas production varies considerably depending on reservoir permeability, the degree of fracture complexity, fracture spacing, and network width. Table 8 shows the fracture conductivity required to achieve near maximum first year gas production for the cases evaluated, assuming 50-ft fracture spacing for network growth. The table shows that conductivity requirements do not follow simple dimensionless conductivity design guidelines83 where conductivity requirements are directly proportional to reservoir permeability (for a given fracture length). When fracture complexity is modest, conductivity requirements are proportional to k1/2. For large fracture networks, conductivity requirements are proportional to k1/4. In the case of network fracture growth, conductivity requirements are also proportional to xs

1/2, indicating that less conductivity is required as fracture spacing decreases.

When fracture growth is complex but still planar in nature (complex planar), fracture conductivity requirements are half that of a single planar fracture; however, if the proppant is distributed evenly within fractures, the average proppant concentration and fracture conductivity would decrease as complexity increases. Therefore, to compensate for the lower average proppant concentration, the treatment design will require more focus on delivering fracture conductivity. For network fracture growth, if the proppant is concentrated in a single planar fracture with infinite conductivity, then the network conductivity requirements decrease by a factor of 100 for small networks (300 ft wide) and by a factor of 10 for large networks (1,000 ft wide). Arguably, this may be a plausible scenario for proppant transport (Case 2) in water-fracs and low-viscosity hybrid fracture treatments, which implies that un-propped fracture conductivity may play a critical role in well productivity.

To achieve 90% of the maximum first year production, fracture conductivity requirements are significantly less than that required to achieve near maximum first-year production (Table 9) and may provide additional insights for fracture design. For a large fracture network with an infinite conductivity primary fracture, 90% of the maximum first-year gas production can be achieved with a network conductivity 2.83 to 22.4 mD for low permeability reservoirs (0.0001 to 0.01 mD). When fracture growth is less complex (small network), the required network conductivity to achieve 90% of the maximum first year production is only 0.35 to 3.5 mD-ft for the same permeability range (Table 9). Therefore, it may be possible to exploit fracture complexity in low permeability reservoirs with an infinite conductivity primary fracture if un-propped fracture conductivity is 1 to 20 mD-ft. Un-propped fracture conductivity of 1 to 10 mD-ft may be possible in many tight gas environments if shear offsets result in displaced fractures (Figure 5). However, if an infinite conductivity

Table 8 - Conductivity Requirements to Achieve Near Maximum First Year Gas Production

0.0001 mD 0.01 mD 1 mDPlanar 300 3000 30000Complex Planar 150 1500 15000Small Network (U) 1 212 2100 21200Small Network (I) 1 2 21 212Large Network (U) 1 707 2240 7070Large Network (I) 1 71 224 707U = uniform conductivityI = infinire conductivity primary fractureNote 1 - 50-ft fracture spacing cases

Reservoir PermeabilityCase

Table 9 - Conductivity Requirements to Achieve 90% of Maximum First Year Gas Production

0.0001 mD 0.01 mD 1 mDPlanar 20 500 10000Complex Planar 10 100 1000Small Network (U) 1 25 212 1768Small Network (I) 1 0.35 3.5 NALarge Network (U) 1 71 224 1414Large Network (I) 1 2.83 22.4 50U = uniform conductivityI = infinire conductivity primary fractureNote 1 - 50-ft fracture spacing cases

Reservoir Permeability

Network Conductivity Requirments to Obtain 90% of Maximum 1st-year production

Case

18 SPE 115769

primary fracture is not present and the fracture conductivity is uniform throughout the network, the fracture conductivity required to achieve 90% of the maximum first-year production is increased by a factor of 10 to 100 depending on network size. In the case of uniform network conductivity, it is unlikely that fracture conductivity will be sufficient to fully exploit fracture complexity – with the exception of small networks in very low permeability reservoirs. However, even when network conductivity is significantly lower than the values shown in Table 9, significant production enhancement may still be possible by exploiting fracture complexity in many low permeability reservoirs.

Fracture Design Guidelines When Fracture Growth Is Complex The primary decision when designing fracture treatments in reservoirs that exhibit complex fracture growth is whether to control or exploit the complexity. This decision is primarily a function of reservoir permeability and achievable fracture conductivity, but also depends on Young’s modulus, the degree of complexity, and the likely proppant transport scenario. In general, fracture complexity should be minimized in moderate permeability reservoirs (k > 1 mD), as there is very little potential benefit from exploiting complexity and the fracture conductivity requirements are high. However, for low permeability reservoirs (k < 0.01 mD), exploiting fracture complexity may result in significant production enhancements. Fracture network size may be limited by excessive fluid loss, even when permeability is low (k~0.01 mD). The effects of fluid loss and network conductivity requirements will probably dictate that small networks are optimal when permeability is on order 0.01 mD and large networks are optimal when permeability is on order 0.0001 mD.

The following very general guidelines are provided for treatment design in reservoirs that exhibit complex fracture growth. However, it should be emphasized that designing treatments when fracture growth is complex is a difficult process and not easily defined using simple guidelines.

• Determine the reservoir permeability, Young’s modulus, and tendency for complex fracture growth. Fracture mapping can distinguish between network and planar fracture growth and also provide direct measurements of fracture length and height; however, fracture pressure analysis will likely be the primary method to distinguish between simple planar and complex planar growth. Fracture spacing can be estimated using reservoir modeling given the Stimulated Reservoir Volume (SRV) from fracture mapping and estimates of matrix permeability.29,30,47 The degree of complex planar fracture growth can be estimated using net pressure history matching, given fracture length and height from fracture mapping44 or less reliably using net pressure matching alone.9,18-21 It may be necessary to evaluate the effect of fluid viscosity on fracture complexity.

• If permeability is 1 mD or greater, minimize fracture complexity by pumping viscous fluids and particulate slugs. Optimize fracture conductivity based on reservoir permeability and fracture complexity. When pumping viscous fluids and particulate slugs it is unlikely that network fracture growth will be achieved and fracture conductivity requirements can be estimated based on fracture modeling estimates of proppant concentration assuming complex planar growth (i.e., number of equivalent multiple fractures).

• If permeability is 0.01 mD or less and shear offsets are possible, estimate un-propped fracture conductivity based on closure stress and Young’s modulus (Figure 6 or lab measurements on actual core). Using the un-propped conductivity, determine whether the design should target small or large network growth based on the expected production. Evaluate the production for a uniform conductivity network and a network with an infinite conductivity primary fracture to determine the appropriate proppant transport goal (although this may be very difficult to control). If un-propped fracture conductivity is insufficient to effectively exploit network fracture growth OR shear offset is unlikely, determine if sufficient propped or partially propped fracture conductivity can be achieved to exploit small network growth based on closure stress and embedment (Figure 5, Figure 7). It is assumed that sufficient proppant cannot be placed to effectively prop a large network. If sufficient propped or partially propped conductivity cannot be achieved for small network growth, then attempt to restrict fracture complexity and target the design for complex planar growth.

• Generating large fracture networks (water-fracs). Pump very large volumes of low viscosity fluid (slickwater) to maximize fracture complexity and generate large networks. In addition, low viscosity fluid will provide the best cleanup behavior. In most cases it is desirable to target an infinite conductivity primary fracture to reduce network conductivity requirements. Achieving an infinite conductivity primary fracture may require pumping relatively large amounts of proppant. Proppant type, concentration, and size will be dictated by closure stress, conductivity requirements, and proppant placement efficiency. Smaller proppants will likely be transported further in the primary fracture and possibly modest distances into the fracture network, but higher permeability proppants may be required to achieve an effectively infinite conductivity primary fracture.

• Generating small fracture networks (hybrid fracs). Pump large volumes of moderate viscosity fluid (linear gel, lower viscosity cross-linked fluid, or both) to moderate fracture complexity and improve proppant transport characteristics. Linear gel may provide adequate cleanup behavior in small networks. Ensure that an infinite conductivity primary fracture is obtained by pumping larger or higher quality proppants at greater concentrations compared to water-frac designs. In cases where obtaining an infinite conductivity in the primary fracture is difficult,

SPE 115769 19

consider using cross-linked gel in the later proppant stages, which should allow higher proppant concentrations and improve proppant transport – while also promoting primary fracture propagation.

• Completion schemes to increase complexity & fracture intensity. In many cases complexity can be enhanced by stimulating multiple perforation clusters in a horizontal well. Microseismic mapping data often shows a much wider zone of activity in such cases, although whether it is due to multiple parallel fractures or some network development is often difficult to discern. Similarly, simultaneous fracturing, sequential fracturing, fracturing of closely spaced stages, and other strategies to cause interaction between different fracture treatments is another method used to intensify the degree of fracturing. These procedures may help to divert fluid into new fractures that they might not otherwise have opened or penetrated, and mapping does appear to support that premise. The application of small diameter proppant particles, such as 40/70 or 100-mesh, may also help intensify fracturing by bridging existing fractures and forcing new ones to open.

• Obtaining sufficient network fracture conductivity. In cases where sufficient fracture conductivity cannot be obtained from un-propped fractures, consider pumping small diameter, higher strength proppants such as 70/140-mesh ceramic proppant. The higher strength proppant, combined with the much smaller diameter (compare to 40/70-mesh), may allow partial propping of network fractures further away from the wellbore.

Conclusions The following conclusions are based on a set of reservoir simulations that cover a wide range of reservoir permeability and fracture conductivity, but only a limited range of fracture growth and reservoir geometry (i.e., fixed fracture half-length and reservoir size). In addition, the evaluations focused on comparisons of first year cumulative production. However, the trends identified in this work should be applicable to a wide range of situations, although the quantitative results will vary depending of the specifics of each case.

1. Fracture complexity may be affected by fluid viscosity. In reservoirs prone to complex fracture growth, complexity can be reduced by pumping high viscosity fluid or maximized by pumping low viscosity fluid.

2. For any given treatment, as fracture complexity increases, average proppant concentration will decrease resulting in lower fracture conductivity, increased embedment effects, and less efficient cleanup.

3. With modest stresses and relatively hard formations, proppant characteristics (strength, size, resistance to embedment) have been shown to be key to retaining flow capacity with low proppant concentrations.

4. When low proppant concentrations are placed in high stress or relatively soft formations, stress concentration, particle crushing, and embedment may render such fractures only marginally more effective than un-propped fractures.

5. If proppant is evenly distributed throughout fracture networks, the resulting proppant concentrations are probably inadequate to materially contribute to network fracture conductivity. The amount of proppant pumped in typical slick-water and hybrid fracture treatments will result in average proppant concentrations << 0.1 lbm/ft2 or a propped area << 10%. In this scenario, it is probable that the majority of the created fracture area has residual conductivity similar to an un-propped fracture.

6. Although un-propped fracturing treatments are successful in some reservoirs, the production results from a wide variety of formations69,85,91-100 indicate that stimulation treatments containing proppant generally outperform treatments with no proppant. This could be evidence that, if fracture growth is complex, the proppant is concentrated in a primary fracture or is restricted to limited penetration distances into the fracture network. However, proppant could be providing other benefits (erosion, diversion, etc.) not addressed herein.

7. Un-propped fracture conductivity will likely be insufficient to exploit fracture complexity in the absence of shear offsets (displaced fractures). In addition, even with shear offsets, un-propped fracture conductivity will likely be insufficient for Young’s modulus of 2 x 106 psi or lower, as deformation of asperities will be excessive and likely result in closure of un-propped fractures.

8. Fracture complexity should normally be controlled when Young’s modulus is less than 2 x 106 psi. As Young’s modulus decreases, the ability to exploit fracture complexity becomes more challenging due to the inability to generate sufficient un-propped or partially propped fracture conductivity due to proppant embedment effects and asperity deformation. It is likely that complex fracture growth cannot be exploited when Young’s modulus is less than 2 x 106 psi and may be detrimental to stimulation effectiveness due to excessive leakoff and proppant placement problems.

9. Partially propped fracture conductivity may play an important role in production enhancement when fracture complexity is moderate if proppant can be transported into secondary fractures. The application of smaller, higher strength proppants may be the key to exploiting moderately complex fracture growth in low permeability reservoirs. However, proppant embedment will likely be excessive (i.e., greater than one particle diameter) when Young’s modulus is ≤ 2 x 106 psi for partial monolayer proppant distributions, resulting essentially in un-propped fractures.

20 SPE 115769

10. When fracture complexity is moderate to high (network growth) and proppant is not or cannot be transported into the network, creating a high conductivity primary fracture will significantly reduce network conductivity requirements. If the primary fracture exhibits infinite conductivity behavior, network conductivity requirements decrease by a factor of 10 (large networks) to 100 (small networks).

11. In moderate permeability reservoirs (~ 1 mD), fracture complexity should typically be minimized. 12. In tight reservoirs (~0.01 mD) with relatively hard rock (E=4-6 x 106 psi), significant production enhancements may

be possible by exploiting moderately complex fracture growth (small networks). In addition, when permeability is ~0.01 mD, excessive fluid loss will likely limit fracture area and make it impractical or impossible to create very large networks.

13. In very tight reservoirs (~0.0001 mD) with relatively hard rock (E=4-6 x 106 psi), significant production enhancements may be possible by exploiting very complex fracture growth (large networks).

14. Increasing fracture complexity by generating a more dense fracture network (smaller fracture spacing) reduces fracture conductivity requirements, but challenges our capability to effectively place proppant throughout the fracture.

Acknowledgments The authors would like to thank Pinnacle Technologies and Carbo Ceramics for supporting the publication of this work. Nomenclature Af = fracture area, one face (subscripts denote: c=complex, p=planar, propped=fraction of fracture area propped), L2 Cp = Proppant concentration (Case denoted by subscript 1, 2, or 3) M/L2 d = particle diameter, L E = Young’s modulus FCD = dimensionless conductivity FcDc = complex fracture conductivity correlating function FCI = fracture complexity index g = gravity, L/T2 hf = fracture height, L k = permeability, L2

khf = hydraulic fracture permeability, L2

Mp = Proppant pumped, M Po = Fissure opening pressure, M/LT2 t = time, T Vfl = Volume of fluid pumped, L3 VS = settling velocity, L/T wf = fracture width (subscripts denote: p=planar, c=complex), L xf = hydraulic fracture wing or half-length, L xn = hydraulic fracture network width (from microseismic event pattern), L Δxs,Dx = orthogonal fracture spacing, L y = distance fluid penetrates into a natural fracture or fissure, L ε = fluid efficiency ΔP = pressure drop, specifically treating pressure minus reservoir pressure, M/LT2 Δσh = Difference between minimum and maximum horizontal stress, M/LT2 v = Poisons’ ratio μ = fluid viscosity, M/LT ρf = fluid density, M/L3 ρp = particle density, M/L3 ϕ = porosity σ = stress, M/LT2

SI Metric Conversion Factors

acre x 4.046 873 e+03 = m2 bbl x 1.589 874 e-01 = m3 cp x 1.0 e-03 = Pa.s ft x 3.048 e-01 = m oF (oF – 32)/1.8 = oC lbm/gal x 1.198 264 e+02 = kg/cm2 psi x 6.894 757 e+00 = kPa

SPE 115769 21

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22 SPE 115769

30. Fisher, M.K., Heinze, J.R., Harris, C.D., Davidson, B.M, Wright, C.A., and Dunn, K.P.: “Optimizing Horizontal Completion Techniques in the Barnett Shale Using Microseismic Fracture Mapping,” paper SPE 90051 presented at the 2004 SPE Annual Technical Conference and Exhibition, Houston, Texas, September 26-29.

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38. Wolhart, S.L., Harting, T.A., Dahlem, J.E., Young, T.J., Mayerhofer, M.J., and Lolon, E.P.: “Hydraulic Fracture Diagnostics Used to Optimize Development in the Jonah Field,” paper SPE 102528 presented at the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, September 24-27.

39. Griffin, L.G., Sullivan, R.B., Wolhart, S.L., Waltman, C.K., Wright, C.A., Weijers, L., and Warpinski, N.R.: “Hydraulic Fracture Mapping of the High-Temperature, High-Pressure Bossier Sands in East Texas,” paper SPE 84489 presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 5 – 8.

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46. Warpinski, N.R., Mayerhofer, M.J., Vincent, M.C., Cipolla, C.L., and Lolon, E.P.: “Stimulating Unconventional Reservoirs: Maximizing Network Growth while Optimizing Fracture Conductivity,” paper SPE 114173 presented at the 2008 SPE Unconventional Reservoirs Conference, Keystone, Colorado, February 10-12.

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SPE 115769 23

56. Leonard, R., Woodroof, R., Bullard, K., Middlebrook, M. and Wilson, R.: “Barnett Shale Completions: A Method for Assessing New Completion Strategies,” paper SPE 110809 presented at the 2007 SPE Annual Technical Conference and Exhibition, Anaheim, California, November 11-14.

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59. Vincent, M.C.: “Proving It – A Review of 80 Published Field Studies Demonstrating the Importance of Increased Fracture Conductivity,” paper SPE 77675 presented at the 2002 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, September 29-October 2.

60. Vincent, M.C.: “Field Trial Design and Analyses of Production Data from a Tight Gas Reservoir: Detailed Production Comparisons from the Pinedale Anticline,” paper SPE 106151 presented at the 2007 Hydraulic Fracturing Technology Conference, College Station, Texas, January 29-31.

61. Stim-Lab Proppant and Fluids Consortia (1986-2007). 62. American Petroleum Institute: “Recommended Practices for Testing Sand Used in Hydraulic Fracturing Operations,” API RP 56,

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its Impact on Well Performance – Theory and Field Examples,” SPE 106301 presented at the 2007 Hydraulic Fracturing Technology Conference, College Station, Texas, January 29-31.

64. Barree, R.D., et al.: “Realistic Assessment of Fracture Conductivity for Material Selection,” paper SPE 84306 presented at the 2003 SPE Annual Technical Conference & Exhibition, Denver, Colorado, October 5-8.

65. Barree, R.D., et al.: “Closing the Gap: Fracture Half-length from Design, Buildup, and Production Analysis,” paper SPE 84491 presented at 2003 SPE Annual Technical Conference & Exhibition, Denver, Colorado, October 5-8.

66. Mayerhofer, M.J., Richardson, M.F., Walker R.N. Jr., Meehan D.N., Oehler M.W., and Browning R.R., Jr.: “Are Proppants Really Necessary?” Journal of Petroleum Technology (March 1998).

67. Mayerhofer, M.J., Richardson, M.F., Walker, R.N. Jr., Meehan, D.N., Oehler, M.W., and Browning, R.R. Jr.: “Proppants? We Don’t Need No Proppants,” SPE 38611 presented at the 1997 ATC 97 in San Antonio, Texas, October.

68. Mayerhofer, M.: “Water-fracs – Results from 50 Cotton Valley Wells,” SPE 49104 presented at the 1998 SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 27-30 September.

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Appendix 1 – Fluid Viscosity Supplement

Figure 17 shows the relative penetration distance compared to water (1 cp) as function of viscosity. The comparison assumes that all other factors are equal; however, the pressure drop and fracture permeability may differ for high viscosity fluids. The figure illustrates that even moderate viscosity fluids such a linear gels (10 to 50 cp) could reduce penetration distance by a factor of 3 to 7. High viscosity cross-linked fluids (100 to 1000 cp) would reduce penetration distance by a factor of 10 to 30 compared to water. Therefore, high viscosity fluids should reduce the degree of fracture complexity, while pumping low viscosity fluids should maximize fracture complexity. The Barnett Shale is an example of a reservoir where maximizing fracture complexity using low viscosity fluid (water) is the key to increasing well productivity47, while many North Sea Chalk reservoirs are examples where high viscosity fluids (cross-linked gels) which minimize fracture complexity are key to success.20 Appendix 2 – Proppant Transport & Distribution Supplement

The settling of proppant particles is often predicted using the relatively simple relationship shown in Equation A1 (Stokes’ Law).

( )μ

ρρ18

2pfp

s

gdV

−= ………………….(A1)

Where Vs is the particle settling velocity, ρp is the density of the particle, ρf is the density of the fluid, g is the acceleration of gravity, μ is the fluid viscosity, and dp is the diameter of the particle.

0.001

0.01

0.1

11 10 100 1000 10000 100000

Viscosity (cp)

Rel

ativ

e D

ista

nce

Figure 17 - Effect of fluid viscosity on penetration

SPE 115769 25

This form of the equation has many simplifying assumptions which are violated in actual slickwater treatments. Stokes’ Law in this form predicts the terminal settling velocity of spherical particles in stagnant Newtonian liquid without wall effects and without particle interaction. In actual treatments, realistic power-law fluids are highly turbulent near-wellbore, irregularly shaped particles settle at a velocity adequate to generate wakes requiring corrections for inertia, particles agglomerate (draft) and interact (hinder), while rough and/or inclined fracture faces complicate settling. Although Stokes’ Law has been deemed to be “grossly inadequate”49 for describing proppant placement, the general relationships are valid:

• with low viscosity (μ) fluids – proppant settling will be rapid, • settling can be slowed with reduced particle density (ρp), and most poorly recognized, • when particle diameter is reduced, settling velocity reduces exponentially.

Although more sophisticated mathematical treatments have been proposed to describe proppant settling,49,50 a predictive tool is not available to provide a precise description of the created fracture geometry, and the hindrance of particle movement by rough, inclined, stair-stepping fractures. However, the maximum distance that particles will be transported with slick-water is not exclusively a function of suspension time. Instead, in slick-water fractures, the main mode of lateral transport is actually saltation, or bed transport as proposed by Kern, Perkins, and Wyant51, Blot52, Patankar53 and shown in recent laboratory videos by Stim-Lab61 and others54. Field validation of proppant transport is somewhat limited, but there is evidence of proppant being transported significant distances – even with low viscosity fluids.56,57 Estimating Proppant Concentration and Propped Fracture Area

With the application of fracture mapping technologies it is now possible to directly measure hydraulic fracture length, height, and network width. Therefore, proppant concentrations can be directly calculated for the three scenarios presented if reasonable ranges of fracture complexity can be estimated. Fracture area (one fracture face) for a simple planar fracture is given by Equation B1 and the average fracture width for a simple planar fracture is given by Equation B2.

fffp hxA 2= …………...……………….. (B1), fp

flfp A

Vw

ε= .........................(B2)

Fracture area for a complex fracture system is given by Equation B3 and the average width is given by Equation B4.

nfffs

fnffc xhxh

xhxx

A ++Δ

= 24

......(B3), fc

flfc A

Vw

ε= .........................(B4)

For simplicity equation B3 assumes that the fracture network consists of evenly spaced blocks (Δxs). The proppant concentrations for the three limiting scenarios presented above can be calculated using equations B1, B3 and B4, the fluid volume pumped, an estimate of the fluid efficiency, and the amount of proppant pumped using the follow equations.

Case 1: fc

pp A

MC =1 ...................(B5), Case 2:

fp

pp A

MC =2 ..............(B6), Case 3: pbfcp wC ρ=3 ...............(B7)

The percentage of the fracture that is propped for Case 3 can be calculated using Equation B8.

fcp

ppropped AC

MA

3

= ...................(B8)