High-Field Nuclear Magnetic Resonance Observation of Gas Shale

Apr 23, 2014 - This helps us understand the fundamental relation between the newly created pathways and the enhanced gas transport. The ability to mak...
1 downloads 0 Views 4MB Size
Article pubs.acs.org/EF

High-Field Nuclear Magnetic Resonance Observation of Gas Shale Fracturing by Methane Gas Hai-Jing Wang,†,‡ Albina Mutina,§ and Ravinath Kausik*,† †

Schlumberger-Doll Research Center, 1 Hampshire Street, Cambridge, Massachusetts 02139 United States Schlumberger, Carretera Nacional Caripito km 1, Maturin, Monagas, Venezuela

§

ABSTRACT: We monitor the fracturing of gas shale using high-pressure methane gas, by studying the changes in gas transport using high-field nuclear magnetic resonance (NMR). This helps us understand the fundamental relation between the newly created pathways and the enhanced gas transport. The ability to make such correlations is challenging, partially because of the difficulty in monitoring the gas transport during the transient fracturing process. Here, we demonstrate a methodology for fracturing gas shale core samples inside a high-pressure, high-field NMR sample tube and studying its effect on gas transport kinetics by tracking the time-dependent NMR signal intensity. The ultralow permeability of shale makes the transient gas transport slow enough to be monitored by a series of NMR signals. The time constant that characterizes the transient process toward equilibrium is directly related to the permeability of core samples. The signatures of permanent fractures in the shale core plugs created by a sudden pressure release are identified by the shorter equilibrium time constant. Although these permanent fractures are not visible to the naked eye, they are ex-situ-verified by microcomputed tomography (microCT). These results demonstrate a NMR methodology to characterize the gas transport and fracturing property of gas shale, promising a better understanding of their relationships.

1. INTRODUCTION

Nuclear magnetic resonance (NMR) is a versatile and noninvasive analytical technique widely used in characterizing porous media9,10 and for well-logging11,12 and has also been successfully applied for the understanding of gas and bound water dynamics in gas shale at high pressures and low magnetic fields as applicable to the oilfield industry.13 NMR signal intensity can be quantitatively calibrated to measure the adsorption isotherms of gas and vapor on porous media,14 which are critical to understand the storage and adsorption mechanism of natural gas in gas shale. Conventional isotherm measurement methods, such as gravimetric and volumetric methods, can only quantify the total adsorption of one adsorbate at a time. NMR has unique advantages over conventional methods in several ways. First, NMR has a higher sensitivity than conventional methods; therefore, only a few milligrams of the gas shale sample are needed for the experiment. Second, NMR-measured isotherms do not depend upon the adsorption history, as opposed to the volumetric methods that need to accumulate the stepwise adsorption data over the whole adsorption process. This is because the NMR measurements at each pressure are carried out independently and are therefore not influenced by the errors in the previous pressure steps. Most importantly, there are a number of NMR spectroscopic and relaxation parameters that can reveal the dynamics and local environment of adsorbed molecules. For instance, NMR measurements of spin−lattice (T1) and spin− spin (T2) relaxation times have been shown to provide contrast between adsorbed gas on the surface, gas confined in the nanoporous media, and bulk gas in between large grains,

Recent breakthroughs in technologies, such as hydraulic fracturing, have made it possible to produce economic quantities of hydrocarbons from unconventional resources, such as gas shale.1 The gas shale reservoirs are termed “unconventional” because the hydrocarbons are sealed in the source rock and need stimulation (such as fracturing) to be produced.2 While hydraulic fracturing is the most commonly used method to fracture these rocks, other methods, including the use of liquid CO2 with sand3 and liquefied petroleum gas (LPG), which is mainly propane with a little butane,4 have also being investigated. The advantage of using LPG is that it mixes with the hydrocarbons downhole and returns to the surface along with the oil and gas unlike water. Laboratory characterizations have revealed that gas shales have low porosity (4T1) is used to capture the total amount of methane,18,19 where T1 < 2.5 s for the bulk gas within the pressure range of this study (P ≤ 3 kpsi).20 However, such a long recycle delay reduces the time resolution between consecutive FIDs to observe fast transport kinetics during the pressure release and reloading of the fractured core plugs. A shorter recycle delay of 0.5 s was therefore used as a T1 filter for selective observation of methane inside the core plugs (T1 ∼ 0.1 s) such that the fast kinetics can be captured. The absolute amount of methane was calibrated by comparing to the NMR signal intensity from the methane gas at a certain pressure within an empty NMR tube of known volume. 2.4. MicroCT Scans. The microCT images of gas shale core plugs were obtained by a SkyScan 1172 scanner (Bruker MicroCT, Kontich, Belgium). The scanner employs a cone-beam approach and contains a microfocus X-ray source tube with a tungsten target, which is characterized by stable operating peak energies of emitted X-ray

spectra in the range of 20−100 keV and the maximum power of 10 W. A set of filters (Al, Cu, and Al + Cu) of different thicknesses were applied to filter out the low X-ray energy part of the spectra to minimize the beam hardening effect. An 11 megapixel charge-coupled device (CCD) camera was used as a detector, with a scintillator converting the X-rays into light photons and fiber optics serving as a scaling-down media. MicroCT experiments on the shale samples were performed with a resolution of 600−700 nm/pixel. A micropositioning stage was used for precise sample alignment, and a 180° + α angular projection range with a 0.1° rotation step was used for data acquisition. A thermal correction procedure was applied to correct for source thermal drift caused by long scanning time (about 18 h for each sample, with 8 time frame averaging). The three-dimensional (3D) image of the internal structure of the object was reconstructed using a modified version of the Feldkamp algorithm for cone-beam acquisition geometry.21 The result of the reconstruction of raw acquired data (angular projections) in the microCT experiment is usually addressed as “a microCT image” and represents the spatial distribution of a linear attenuation coefficient of X-rays in matter in gray scale. Such an attenuation coefficient depends upon the material density and atomic number, often roughly approximated as μ ∼ ρ⟨Z⟩3, where ρ is the density of the matter and Z is the average atomic number. Thus, the microCT image of a geological sample reflects volumetric information about pore space morphology, mineral matrix properties, and saturating fluid distributions and can be used for qualitative/quantitate core analysis and simulation/modeling.22−25

3. RESULTS AND DISCUSSION 3.1. Methane Transport upon Stepwise Pressure Loading. Figure 2 shows the transient increase in the methane gas signal upon stepwise pressure loading from the time of injection into the system to reaching equilibrium with the gas shale core. The pressure was further increased after the system reaches equilibrium at each pressure step up to 3 kpsi. Once the gas valve is open, the high-pressure methane gas flows into the NMR sample tube within a few seconds and is therefore within the measurement time (∼10 s) of the first FID data point. Such a short pressure loading time is monitored by a pressure gauge and also confirmed by the huge change in the NMR signal 3640

dx.doi.org/10.1021/ef5002937 | Energy Fuels 2014, 28, 3638−3644

Energy & Fuels

Article

Figure 3. Signature of fracturing from transport kinetics of methane gas in GS plug 1. (a) Pressure loading from vacuum to 1 kpsi on GS plug 1 has a long characteristic time of ∼3.8 ks. (b) Sudden pressure release from 3 kpsi to vacuum creates fractures with a short characteristic time of ∼189 s. (c) Pressure reloading process reveals a short characteristic time of ∼60 s. Note the different time scale between panel a and panels b and c. The standard deviation is shown in the parentheses.

For core plugs with identical geometry experiencing the same pressure steps, the characteristic time should be inversely proportional to the permeability, τ ∝ 1/κ.30 This provides an easy methodology for the direct comparison of the gas transport properties for different plugs. For the same gas shale core plug, small variations of the characteristic time have been found at different pressures. The characteristic time remains comparable at 1 and 2 kpsi for the different samples but becomes slightly shorter at 3 kpsi for all three samples. If the characteristic times are solely dependent upon the permeability and viscosity, the characteristic time should become longer as the permeability decreases because of the slippage30 or increase in stress31 or viscosity32 at higher pressures. This may suggest that the pore structure has been deformed at 3 kpsi such that it takes much less time to reach equilibrium. Further investigations are needed to study these pressure-dependent characteristic times. The characteristic time is fundamentally connected to the mineralogy of the gas shale samples. The gas permeability is determined by transport in both the inorganic matrix and the organic porosity. Because adsorption equilibrium times are very short, the transport time constants constitute the rate-limiting step in this process. The differences in the characteristic times are connected to the mineralogical differences of the different samples. Because the samples have decreasing TOC and gas capacities from GS plug 1 to GS plug 3, they also have decreasing characteristic times to equilibrium. This can be understood from the lower permeability to methane gas of the organic fraction. Although this trend is clear from the samples used in this study, in reality, the characteristic times are also a function of the natural fractures and the permeability of the inorganic matrices. Some of the challenges for the accuracy and reproducibility of these experiments are the signal-to-noise ratio of the NMR experiment and possible changes to the core samples when they are exposed to high-pressure gas. The error in the experiments from the fit of the data is given in the figure, and the error is 4− 16% of the characteristic time. The differences in the

intensity. The origin of the time axis in Figure 2 has been shifted to coincide with the moment of pressure loading. A much slower increase in the methane gas signal takes place over the next few hours until equilibrium. The pressure remains stable during this slow process, because the amount of adsorbed methane (∼millimoles) is much less than that of methane in the high-pressure system (∼moles). The time-limiting step for this equilibrium process comes from the transport of methane gas into core plugs because of the ultralow permeability of gas shale.26 Once the gas molecules reach the pores, the gas adsorption/desorption equilibrium with the nanopore surface is established instantaneously.27 Therefore, the long time needed to reach equilibrium reveals the slow transport kinetics of methane gas in gas shale core plugs. The NMR signal intensity change as a function of time was fitted into a single exponential function to extrapolate a characteristic time τ, as shown in Figure 2. The characteristic time, on the order of magnitude of thousands of seconds, was observed in all three of the gas shale samples. The characteristic time is determined by the geometry of the core plugs, the permeability (κ) of methane gas in gas shale, and the intrinsic properties of methane gas, such as the viscosity (μ) and compressibility.26,28 In this experiment, a large pressure step (Δp = 1 kpsi) is applied to help accumulate a sufficient amount of methane molecules for NMR detection. The methane within core plugs experiences a large pressure variation during the equilibrium process. Because of the changing viscosity and compressibility along with the pressure, it is challenging to establish an explicit expression between the characteristic time and the permeability. An order of magnitude estimation of the permeability can be made based on κ ∼ μ(r0/ τ)(r0/Δp), where μ ∼ 10−5 Pa s, such that the characteristic time of τ1GSkpsi 2 = 2.4 ks corresponds to ∼1.6 nanodarcy, in agreement with the often encountered low permeability of gas shale.29 This also provides evidence that fractures have not been induced in the gas shale core plugs used in our experiments during drilling. 3641

dx.doi.org/10.1021/ef5002937 | Energy Fuels 2014, 28, 3638−3644

Energy & Fuels

Article

Figure 4. XY slices of microCT images of gas shale core plugs (r0 ∼ 1.4 mm) that (a) has not and (b) has already (GS plug 1.F) been subjected to gas fracturing. A zoom in onto the fracture of panel b is shown in panel c.

characteristic times between the different samples are reproducible. The samples that were fractured are irreparably changed from their initial states, and therefore, reproducibility tests are not feasible. 3.2. Pressure Release and Gas Fracturing. After the gas shale is equilibrated with methane gas at 3 kpsi, the pressure was rapidly released and the transient gas transport out of the core plugs was measured. A much shorter characteristic time was observed during the pressure release process. A shorter NMR sequence (∼32 s) with a recycle delay of 0.5 s was used to capture this faster transport. The evacuation removes the bulk gas within the NMR sample tube almost instantaneously such that the NMR signal from bulk gas is negligible. The characteristic time of τ3GSkpsi 1 |release = 189 s during the pressure release (Figure 3b) is significantly shorter than the characteristic time during the pressure loading τ3GSkpsi 1 |loading = 2.5 ks (Figure 2c). The order of magnitude shorter characteristic time seems to indicate that fractures were created during the sudden pressure release. To confirm this, pressure loading to 1 kpsi was repeated on the same sample after all methane had been evacuated. The characteristic time during this second pressure reloading step was found to be τ1GSkpsi 1 |reloading = 60 s, significantly shorter than the initial loading time of τ1GSkpsi 1 |loading = 3.8 ks. These observations from the gas transport property confirm that the sudden pressure release has created a permanent structural change to the paths through which the methane flows. The sudden pressure release is equivalent to an insideout gas fracturing process. Here, we introduce the nomenclature of GS plug 1 and GS plug 1.F to differentiate the gas shale plug before and after the fracturing process. 3.3. Direct Evidence of Fracturing from MicroCT Scans. The direct and ex situ evidence of the permanent fractures is visualized by the non-invasive high-resolution microCT technique. Panels a and b of Figure 4 show the cross-sections of two gas shale core plugs, namely, the gas shale core plug that has not been subjected to gas fracturing by pressure drop (Figure 4a) and the plug that has been subjected to gas fracturing (GS plug 1.F; Figure 4b). Black areas on the microCT image represent low signal attenuation zones (pore space), and bright white areas represent the highest attenuation zones (metals, heavy elements, etc.). Permanent fractures (black) are clearly seen in the GS plug 1.F, as shown in Figure 4c. It should be noted that multiple fractures of different openings (up to 7 μm) have been observed. They have been found to have near parallel orientation to each other in the Z axis and were distributed

all of the way along the length of the shale plug, providing large additional pathways for methane gas. Thus, microCT examination of the internal structure of shale plugs supports the conclusion from the NMR study, providing direct evidence of fractures caused by sudden pressure release. The absence of the fractures on the shale plug presented in Figure 4a also confirms that the drilling procedure to cut cores does not affect the internal shale structure. 3.4. Mechanism of the Inside-out Gas Fracturing. The permanent fractures were created after the sudden pressure release in the pressurization chamber. This can be understood by observing the relation between the confining stress and pore pressure, as shown in Figure 5.33−35 Gas shales can be approximated to be isotropic and homogeneous materials, obeying Hooke’s law to the first order. The tangential (σθ) and radial (σr) components of the horizontal stress (σh) are created instantaneously by the gas injected at high pressure, pw, because of the small size of the core plug (r0 ∼ 1.4 mm). The gas shale is kept in this state of stress for a long duration of time. This allows the pore pressure, pf, to equilibrate with the applied confining pressure, pw.35 Therefore, during pressure loading, the stress σθ increases to pw instantaneously, while it takes hours for pf to equilibrate with pw (Figure 2). This leads to the condition σθ − pf > 0, suggesting that no fracturing would occur. The applied pressure is then suddenly reduced to zero, i.e., vacuum. This creates a condition where the pore pressure becomes higher than the confining stress. This allows the condition σθ′ − pf < −T0 to be temporarily met, where T0 is the tensile strength of gas shale core plugs. When the pore pressure is more than the tensile strength of the rock, it results in the creation of microcracks (fractures) in the shale samples. As this condition is met in our samples, it indicates that the tensile strength T0 is smaller than 3 kpsi for the shale samples investigated here. An estimate of the tensile strength, T0, which is an intrinsic mechanical property essential for downhole fracturing of the gas shale, can therefore be obtained by such inside-out gas fracturing experiments. The stress tensor, which characterizes the anisotropy of the gas shale mechanical property, can be determined in a similar way using gas shale core plugs prepared by drilling along three different directions relative to the bedding planes. The gas fracturing demonstrated here is stimulated by the sudden pressure release, instead of pressure injection as during hydraulic fracturing. This is because the geometry of the cylindrical samples is opposite that of formation with a bore hole drilled out from inside. The mechanical response of the 3642

dx.doi.org/10.1021/ef5002937 | Energy Fuels 2014, 28, 3638−3644

Energy & Fuels

Article

Figure 5. (a) Illustration of the gas shale core plug within the NMR sample tube, and (b) pressure stress relation upon sudden pressure release. The stress changes immediately after the sudden pressure release from pw to pw′, while the pore pressure pf changes slowly toward pw′, allowing the fracturing condition σθ′− pf < −T0 to be met temporarily.



ACKNOWLEDGMENTS Hai-Jing Wang acknowledges the support of Schlumberger-Doll Research through the internship program during which this work was performed. The authors are grateful to Lukasz Zielinski, Yi-Qiao Song, Martin D. Hürlimann, Safdar Abbas, and Robert L. Kleinberg for the fruitful discussions and Schlumberger for permitting us to publish the results.

gas shale core plug is similar for the fracturing achieved within the NMR tube and the stimulated hydraulic fracturing process. We can therefore better understand the mechanical properties of gas shale in this sense and improve the exploration and production approaches. The presence of the natural fracture on the other hand would play a role in the gas transport characteristic times during injection, and this can be used to differentiate different shales. Furthermore, these natural fractures can be monitored through the difference in their relaxation time, which is a topic currently under investigation.



(1) Osborn, S. G.; Vengosh, A.; Warner, N. R.; Jackson, R. B. Methane contamination of drinking water accompanying gas-well drilling and hydraulic fracturing. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 8172−8176. (2) Rogers, H. Shale gasThe unfolding story. Oxford Rev. Econ. Policy 2011, 27, 117−143. (3) Campbell, S. M.; Fairchild, N. R., Jr.; Arnold, D. L. Liquid CO2 and sand stimulations in the Lewis shale, San Juan Basin, New Mexico: A case study. Proceedings of the SPE Rocky Mountain Regional/LowPermeability Reservoirs Symposium and Exhibition; Denver, CO, March 12−15, 2000; SPE 60317. (4) Tudor, E. H.; Nevison, G. W.; Allen, S.; Pike, B. 100% gelled LPG fracturing process: An alternative to conventional water-based fracturing techniques. Proceedings of the SPE Eastern Regional Meeting; Charleston, WV, Sept 23−25, 2009; SPE 124495. (5) Vandenbroucke, M.; Largeau, C. Kerogen origin, evolution and structure. Org. Geochem. 2007, 38, 719−833. (6) Curtis, M. E.; Sondergeld, C. H.; Ambrose, R. J.; Rai, C. S. Microstructural investigation of gas shales in two and three dimensions using nanometer-scale resolution imaging. AAPG Bull. 2012, 96, 665− 677. (7) Chalmers, G. R.; Bustin, R. M.; Power, I. M. Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy image analyses: Examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig units. AAPG Bull. 2012, 96, 1099− 1119. (8) Boyer, C.; Kieschnick, J.; Suarez-Rivera, R.; Lewis, R. E.; Waters, G. Producing gas from its source. Oilfield Rev. 2006, 18, 36−49. (9) Song, Y. Q.; Ryu, S. G.; Sen, P. N. Determining multiple length scales in rocks. Nature 2000, 406, 178−181. (10) Kimmich, R. Strange kinetics, porous media, and NMR. Chem. Phys. 2002, 284, 253−285. (11) Kleinberg, R. L.; Jackson, J. A. An introduction to the history of NMR well logging. Concepts Magn. Reson. 2001, 13, 340−342.

4. CONCLUSION In conclusion, we demonstrate an in situ characterization method for monitoring gas transport and the effects of fracturing as observed by high-field NMR equipped with a high-pressure methane gas loading system. The equilibrium time constant upon pressure change provides information on gas transport. The sudden release of pressure creates permanent fractures in gas shale core plugs, resulting in enhanced gas transport. These permanent fractures are directly verified by microCT images. The in situ gas fracturing enables the study of the mechanical properties of gas shale. These methods expand the capability of NMR for in situ and noninvasive gas shale studies, in addition to the adsorption isotherm measured by NMR signal intensity and the dynamics that are inferred by the spin−lattice and spin−spin relaxation. These results provide not only critical insights on the mechanism of gas transport and fracture creation and propagation but also important laboratory testing methodology for future development of more economical exploration and recovery techniques.



REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ‡

Materials Sciences Division, Lawrence Berkeley National Laboratory, and Department of Chemistry, University of California, Berkeley, California 94720, United States. Notes

The authors declare no competing financial interest. 3643

dx.doi.org/10.1021/ef5002937 | Energy Fuels 2014, 28, 3638−3644

Energy & Fuels

Article

(12) Kleinberg, R. L. Well logging. In Encyclopedia of Nuclear Magnetic Resonance, Grant, D. M., Harris, R. K., Eds.; John Wiley and Sons: Hoboken, NJ, 1996; p 4960. (13) Kausik, R.; Minh, C. C.; Zielinski, L.; Vissapragada, B.; Akkurt, R.; Song, Y. Q.; Liu, C.; Jones, S. Characterization of gas dynamics in kerogen nanopores by NMR. Proceedings of the SPE Annual Technical Conference and Exhibition; Denver, CO, Oct 30−Nov 2, 2011. (14) Wang, H.-J.; Kleinhammes, A.; McNicholas, T. P.; Liu, J.; Wu, Y. Water adsorption in nanoporous carbon characterized by in situ NMR: Measurements of pore size and pore size distribution. J. Phys. Chem. C 2014, 118, 8474−8480. (15) Peterson, R. W.; Wand, A. J. Self-contained high-pressure cell, apparatus, and procedure for the preparation of encapsulated proteins dissolved in low viscosity fluids for nuclear magnetic resonance spectroscopy. Rev. Sci. Instrum. 2005, 76, 094101. (16) Wang, H. J.; Xi, X. K.; Kleinhammes, A.; Wu, Y. Temperatureinduced hydrophobic−hydrophilic transition observed by water adsorption. Science 2008, 322, 80−83. (17) Anderson, R. J.; McNicholas, T. P.; Kleinhammes, A.; Wang, A. M.; Liu, J.; Wu, Y. NMR methods for characterizing the pore structures and hydrogen storage properties of microporous carbons. J. Am. Chem. Soc. 2010, 132, 8618−8626. (18) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, U.K., 1961. (19) Slichter, C. P. Principles of Magnetic Resonance; Springer-Verlag: New York, 1990. (20) Gerritsm, C. J.; Oosting, P. H.; Trappeni, N. J. Proton-spinlattice relaxation and self-diffusion in methanes. 2. Experimental results for proton-spin-lattice relaxation times. Physica 1971, 51, 381−394. (21) Feldkamp, L. A.; Davis, L. C.; Kress, J. W. Practical cone-beam algorithm. J. Opt. Soc. Am. A 1984, 1, 612−619. (22) Ketcham, R. A.; Iturrino, G. J. Nondestructive high-resolution visualization and measurement of anisotropic effective porosity in complex lithologies using high-resolution X-ray computed tomography. J. Hydrol. 2005, 302, 92−106. (23) Van Geet, M.; Swennen, R.; Wevers, M. Quantitative analysis of reservoir rocks by microfocus X-ray computerised tomography. Sediment. Geol. 2000, 132, 25−36. (24) Arns, J. Y.; Arns, C. H.; Sheppard, A. P.; Sok, R. M.; Knackstedt, M. A.; Pinczewski, W. V. Relative permeability from tomographic images; effect of correlated heterogeneity. J. Pet. Sci. Eng. 2003, 39, 247−259. (25) Grader, A. S.; Clark, A. B. S.; Al-Dayyani, T.; Nur, A. Computations of porosity and permeability of sparic carbonate using multi-scale CT images. Proceedings of the International Symposium of the Society of Core Analysts; Noordwijk, Netherlands, Sept 27−30, 2009. (26) Bird, R. B. Transport Phenomena; John Wiley and Sons: Hoboken, NJ, 2002. (27) de Boer, J. H. The Dynamical Character of Adsorption, 2nd ed.; Clarendon Press: Oxford, U.K., 1968. (28) Brace, W. F.; Walsh, J. B.; Frangos, W. T. Permeability of granite under high pressure. J. Geophys. Res. 1968, 73, 2225−2236. (29) Soeder, D. J. Porosity and permeability of eastern Devonian gas shale. SPE Form. Eval. 1988, 3, 116−124. (30) Klinkenberg, L. J. The permeability of porous media to liquids and gases. Drilling and Production Practice; American Petroleum Institute (API): Washington, D.C., 1941. (31) Vermylen, J. P.; Zoback, M. D. Hydraulic fracturing, microseismic magnitudes, and stress evolution in the Barnett shale, Texas, USA. Proceedings of the SPE Hydraulic Fracturing Technology Conference; Woodlands, TX, Jan 24−26, 2011. (32) Vandergulik, P. S.; Mostert, R.; Vandenberg, H. R. The viscosity of methane at 25 °C up to 10 kbar. Phys. A 1988, 151, 153−166. (33) Yew, C. H. Mechanics of Hydraulic Fracturing; Gulf Publishing: Houston, TX, 1997. (34) Valko, P. Hydraulic Fracture Mechanics; John Wiley and Sons: Hoboken, NJ, 1995.

(35) Fjaer, E.; Holt, R. M.; Raaen, A. M.; Risnes, R.; Horsrud, P. Petroleum Related Rock Mechanics; Elsevier: Amsterdam, Netherlands, 2008.

3644

dx.doi.org/10.1021/ef5002937 | Energy Fuels 2014, 28, 3638−3644