Photoelastic Observation of Toughness-Dominant Hydraulic Fracture Propagation Across an Orthogonal Discontinuity in Soft, Viscoelastic Layered Formations

International Journal of Rock Mechanics & Mining Sciences 134 (2020) 104438

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International Journal of Rock Mechanics and Mining Sciences

journal homepage: http://www.elsevier.com/locate/ijrmms

Photoelastic observation of toughness-dominant hydraulic fracture propagation across an orthogonal discontinuity in soft, viscoelastic layered formations

Soo-Min Ham, Tae-Hyuk Kwon *

Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, South Korea

ARTICLE INFO ABSTRACT

Keywords: Hydraulic fracture (HF) unavoidably encounters natural pre-existing discontinuities in geologic formations, Hydraulic fracture which complicates the propagation and containment behavior across a discontinuity. This study explored the HF Fracture visualization propagation across an orthogonal discontinuity in layered formations by exploiting the photoelastic, transparent, Photoelasticity soft (or deformable), and viscoelastic characteristics of gelatin. First, photoelastic HF experiments in homoge Stress intensity factor neous gelatin media were carried out while monitoring the fluidpressure and stress intensity factor (SIF). The SIF Fracture containment Discontinuity was observed to stay constant during steady-state HF propagation. Second, photoelastic HF experiments in layered gelatin media were conducted, in which biwing-type fractures encountered the bounding layers with different levels of stiffness. Two contrasting containment behaviors — crossing or dilation/arrested — were observed. The fracture crossed the discontinuity when it encountered the bounding layer with a lower toughness. By contrast, the fracture was arrested by the bounding layer and/or dilated the discontinuity, propagating along the discontinuity when the bounding layer had a greater toughness. In addition, competition between debonding of the layer interface and creating a fresh fracture in the bounding layer was found to play a significant role in fracture containment behavior. This study provides unique experimental data with photoelastic images that are comparable to analytical or numerical models. Furthermore, the results contribute to a better understanding of HF propagation and containment behaviors across a discontinuity in viscoelastic media.

1. Introduction discontinuity (or interface) — whether it will cross the interface (crossing or passing), be arrested by the interface (arrested or confined), Generation of fractures by fluid injection, also referred to as “hy or propagate along while dilating the interface (dilation).8,9 Various draulic fracturing”, enhances fluidtransport in geologic formations, and efforts using physical experimentation have attempted to answer this thus it is widely implemented in geo-engineering practices, including question and to identify the factors affecting such containment behavior enhanced hydrocarbon recovery,1,2 enhanced geothermal heat recov at a discontinuity. These include material properties, in situ stress con ery,3,4 and isolation of hazardous waste.5 Natural geologic formations ditions, discontinuity condition, and injecting-fluid properties. The contain innate discontinuity, such as stratification (layering), natural salient findings from previous experimental studies are summarized in faults and fractures, and tiny fissures and cracks. Previous mine-back Table 1. However, physical experimental results on HF propagation and experiments and microseismic fracture mapping studies at a field scale containment behavior in layered formations with discontinuity are still have reported the complex patterns of hydraulic fracture (HF) propa scarce, and experimental data that are interpretable and comparable to gation in fractured rocks or layered formations.6,7 Prediction of the analytical and numerical models are particularly limited. Moreover, generated HF geometry in natural geologic formations with layering and because the rock materials are opaque and the fracture propagation is a discontinuity is one of the important issues in safe and economic design fairly fast and dynamic process, observation of HF propagation patterns of hydraulic fracturing practices. at a discontinuity in physical experimentation still poses challenges. One of the intriguing questions concerns the containment behavior This hampers further advancement in the fundamental understanding of of a propagating fracture when it encounters a pre-existing natural HF containment behavior at a discontinuity.

* Corresponding author. E-mail addresses: [email protected] (S.-M. Ham), [email protected] (T.-H. Kwon). https://doi.org/10.1016/j.ijrmms.2020.104438 Received 22 January 2020; Received in revised form 27 May 2020; Accepted 7 July 2020 Available online 17 August 2020 1365-1609/© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). S.-M. Ham and T.-H. Kwon International Journal of Rock Mechanics and Mining Sciences 134 (2020) 104438

“Photoelasticity” refers to the optomechanical characteristics of 2. Materials and methods materials that become doubly refractive (or birefringent) when sub jected to stress. The resulting fringe pattern in a photoelastic material 2.1. Materials under stress makes possible the analysis of the stress distribution near a fracture tip and, hence, computation of the stress intensity factor (SIF) Gelatin was chosen as an analog to a rocklike medium because of the – (linear elastic fracture mechanics, or LEFM).10 12 Hence, the photo following advantages. (a) The gelatin is characterized with its visco- elasticity often has been used to calculate the SIF during fracture elasticity and it shows a remarkably wide elastic range, up to a verti – propagation in homogeneous media,13 16 although the majority of cal strain of ~30–50%.25,26 Therefore, the gelain can be a good analogy previous studies investigated the fractures driven by external mechani to soft rocks, such as shale.27,28 (b) The gelatin is optically transparent, cal loads. However, no photoelastic investigation on fluid-driven frac such that the fracture can be visualized during propagation. (c) Because ture propagation in homogeneous media or with the discontinuity has gelatin is known to become doubly refractive (or birefringent) when been reported to date. subjected to stress, this photoelasticity of gelatin makes possible the Furthermore, HF propagation behavior significantlydiffers with the analysis of the SIF and the stress distribution near a fracture tip.12 (d) material plasticity or viscosity with respect to, but not limited to, the fluid Finally, the specimen can be remolded into various shapes, and the injection pressure response, fracture geometry, and propagation veloc stiffness can be readily controlled with the gelatin concentration, which – ity.17 19 For instance, the pressure significantlydrops in hard and brittle provides a good control for physical experimentation. media with no or extremely low viscosity. However, in soft (or deform In this study, the gelatin stiffness was controlled to four different able) and viscous media, it gradually decreases as the fracture is initiated levels by varying the gelatin concentration in solution prior to gelation, and propagates. The fracture tip is sharp in brittle media, whereas it is following previous work.19 The gelatin concentration varied as follows: comet-shaped in deformable and viscous media. In brittle media, the HF 7.41 wt% for low stiffness (L), 12.28 wt% for medium stiffness (M), propagation velocity decreases with time, while it is kept at a steady state 13.79 wt% for high stiffness (H), and 16.7 wt% for very high stiffness in deformable, viscous media.19,20 There have been a few experimental (VH). Hereafter, the gelatin samples are named after their stiffness level: – studies on HF propagation in viscoelastic media19,21 23; however, no L-gelatin, M-gelatin, H-gelatin, and VH-gelatin. The Young’s modules attempt has been made to investigate the HF propagation across the and fracture toughness of these gelatin samples were determined using discontinuity in viscoelastic media. the indentation tests29 and the wire cutting method,30 and summarized Therefore, in this study, the HF propagation across discontinuities in in Table 2. Given the unique soft characteristics of gelatin, the values viscoelastic and layered plate media were investigated by employing a obtained herein provide good estimates on the elastic moduli and photoelastic experiment method. Previously, the steady-state HF prop toughness of gelatin, though the values may differ slightly from the ones agation in two-dimensional plate media made of transparent, visco from the ISRM-suggested standard methods, such as uniaxial compres elastic gelatin samples has been successfully visualized and sion test and Brazilian tensile test. The Poisson’s ratio was assumed to be – characterized.19 First, as a follow-up to that previous study, photoelastic 0.5 as the gelatin is an incompressible material.31 33 investigation in HF propagation in homogeneous, viscoelastic gelatin The photoelastic constant was determined by applying the loads onto media was carried out, in which the fracture geometry and photoelastic the disk-shaped gelatin samples with a thickness of 10 mm and a radius fringe patterns were visualized while monitoring the fluid injection of 9.3 mm. Fig. 1 shows the photoelastic images of L-, M , H-, and VH- pressure. Second, the effect of the bounding-layer stiffness on the HF and gelatin samples under a load. The photoelastic constant was calculated pre-existing fracture interactions was examined, because the elastic using the followed equation34 modulus of the bounding-layer formation plays a significant role in determining the fracture containment and fracture geometry.24 Four cases with different bounding-layer stiffnesses were tested, in which a Table 2 fracture was from a medium-stiffness material and propagated to a low-, Material properties of gelatin samples. medium-, high-, or very-high-stiffness material. Furthermore, the frac 0.5 Stiffness w% E (kPa) Kc (kPa⋅m ) fσ (N/m) ture geometry and the SIF variation at the fracture tip were analyzed and L 7.4 38 0.40 33 compared with the medium toughness and injection pressure. In this M 12.3 90 1.33 44 study, unique experimental test data on the HF propagation in visco H 13.8 110 1.53 54 elastic media and the HF containment behavior across a discontinuity VH 16.7 283 3.19 65 are presented.

Table 1 Previous observations on the factors affecting fracture containment behavior at discontinuity.

Factors Finding Material

Medium property From a stiff to a soft material: crossing Sand stone and shale zone70; Plaster (soft for Talc, stiff for From a soft to a stiff material: arrested or dilated hydrostone)73 In-situ stress HF crossed with a high normal stress orthogonal to interface: Cement and fine sand;36 crossing Sichuan shale;37 Low horizontal stress difference: dilation Raw coal block;38 Stacks of sandstone39 ◦ Interface Incident angle Close to 90 : crossing Colton sandstone;74 ◦ condition Less than 60 : dilation Concrete block;75 Eidsvold siltstone76 Discontinuity Thin discontinuity: crossing Cement block36; Gypsum plaster and hydrostone;77 thickness Thick discontinuity: dilation Marcellus shale78 Strength Strong bonding: crossing Sichuan shale79 Weak bonding: dilation Injecting fluid Injection rate High flow rate: crossing Raw coal block;38 Low flow rate: arrested or dilated Sichuan shale;79 Natural shale block80 Fluid viscosity High viscosity: crossing Stacks of sandstone39; Concrete block75 Low viscosity: arrested or dilated

2 S.-M. Ham and T.-H. Kwon International Journal of Rock Mechanics and Mining Sciences 134 (2020) 104438 ( )( ) 4 heff P was controlled to examine the effect of bounding-layer stiffness. In all fσ = , (1) πr h N layered samples, the middle layer was formed with the M-gelatin. Meanwhile, the gelatin stiffness of the top and bottom layers (or the where r is the disk radius, P is the applied load, N is the number of bounding layers) varied from L-to VH-stiffness gelatin. From a stiffness generated fringes (or fringe order), h is the specimen thickness, and heff is perspective, it was carefully designed that the initiated HF propagated the effective specimen thickness. In the transmission mode, the effective from M to L, M to M, M to H, and M to VH; these cases are referred to as specimen thickness heff is identical to the specimen thickness h. M2L, M2M, M2H, and M2VH, respectively. In total, seven gelatin plate Accordingly, the fringe constants of L-, M , H-, and VH-gelatin samples samples — three homogeneous samples and four layered samples — were determined as 33, 44, 54, and 65 N m0.5, as listed in Table 2. were prepared and tested in this study, as tabulated in Table 3. A sucrose solution with a viscosity of 10 cp was used as the fracturing Test setup and procedure. Upon preparation of a gelatin plate sample, fluid. Because the fluid viscosity can be controlled with the sucrose the plate sample was placed horizontally. A copper tube with an outer concentration, a sucrose concentration of 50 wt% produced a fluidwith diameter of 6.4 mm and an inner diameter of 3.8 mm was vertically a viscosity of 10 cp, i.e., 100 g of distilled water and 100 g of sugar.35 To inserted into the middle layer as a wellbore. At the tip of the copper tube, capture visually the fracture propagation behavior in the transparent two perforation holes with a diameter of 1.5 mm were made to inject the gelatin, the sucrose solution was dyed with blue ink. fracturing fluid. The perforation holes faced the layer interfaces at a right angle to induce the HF propagation orthogonal to the layer in terfaces. In addition, two initial cracks with a length of 5 mm were 2.2. Experimental setup and procedure created by scratching the gelatin and aligned with the perforation holes. These initial cracks facilitated the HF propagation in an orthogonal di Sample preparation. Fig. 2 shows the HF experimental setup, which rection to the layer interfaces. In this study, the incident angle was × × × ◦ ◦ used gelatin plate samples with a size of 200 200 10 mm (width strictly controlled to stay in the range of 80 –100 to minimize the effect × length thickness). For the homogeneous medium cases, gelatin plate of the incident angle. samples with three stiffness levels were prepared: L-, M , and H- The HF experiments were performed in a plain-strain condition with gelatin. Dry gelatin powder was thoroughly mixed with warm deionized ◦ no leak-off. Note that fractures were generated within the horizontally water at 55 C at a predetermined mass ratio, and the solution was ◦ placed gelatin plate samples cured in the mold while this rigid-wall poured into the acrylic mold and cured at 4 C for 20 h. acrylic mold was not removed. Thereby, the vertical deformation was For the layered-medium cases, the gelatin plate sample was designed not allowed by the rigid-wall mold, and the fracture height was to contain three layers and, hence, two discontinuities (or two in constraint to 10 mm during horizontal HF propagation. In addition, the terfaces, as in Fig. 2a). Once a warm gelatin solution was prepared, the gelatin itself is nearly impermeable for a given short time frame of gelatin solution was poured into the mold to a depth of 50 mm to form a ◦ fracture propagation, which lasted less than ~20 s. The discontinuity bottom layer, and, immediately, it was cured at 4 C for 2 h. A gelatin was perfectly closed with no aperture and no fluid left within the in solution was again poured onto the bottom layer to form a 100-mm-high ◦ terfaces upon complete curing. The fracture fluidswere invaded only to middle layer, and, in the same manner, cured at 4 C for 2 h. Thereafter, an open space when the fracture propagated and dilated the interface. the gelatin solution was poured to form a 50-mm-high top layer and then ◦ Thus, all the experiments were under no leak-off and no seepage kept at 4 C for 18 h. When each layer was prepared, the layer stiffness

Fig. 1. Digital image obtained from photoelastic constant measurement experiment for (a) L gelatin (loaded by 0.49 N), (b) M gelatin (loaded by 0.98 N), (c) H gelatin (loaded by 1.18 N), and (d) VH gelatin (loaded by 1.47 N): the images were taken using the transmission mode.

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Fig. 2. Experimental setup: (a) the acrylic mold filledwith layered medium, (b) a diagram of the polarizers and photoelastic material, and (c) a schematic drawing of the experimental setup.

λ Table 3 Intech-Optic) and two quarter-wave plates ( /4 Retarder Film, Edmund Experimental cases. Optics) were placed between the digital camera lens and the LED light for the transmission mode, as shown in Fig. 2b. The axes of the two Case Stiffness Symbol polarized filters were aligned parallel for the maximum brightness. Homogeneous Low stiffness L Upon the fluidinjection, time-lapsed photoelastic images were acquired Medium stiffness M High stiffness H at every 0.1 s (10 frames per second) using a digital camera Layered Medium to low stiffness M2L (UI–3360CP–C-HQ, IDS Corp.). Medium to medium stiffness M2M Medium to high stiffness M2H 2.3. Photoelastic analysis: calculation of the SIF value Medium to very high stiffness M2VH The isochromatic fringes at the fracture tip allows the photoelastic condition. Meanwhile, the stress condition also plays a significantrole in analysis of the SIF of the propagating HF. Fig. 3 shows a representative – fracture containment behaviors at an interface.36 39 It is worth pointing photoelastic fringe shape at an HF tip. In our HF tests, the generated out that our gelatin samples were not subjected to any external stress, fracture width ranges less than 10 mm and the fringe size is less than 20 which indicates zero external stress condition. Note that our study only mm. Given the plate size of 200 mm, it appears that the deformational considers the effect of stiffness contrast between layers. strain level is maintained in the elastic range, less than 30%, during The fracturing fluidwas injected through the copper tube, which was fracture propagation. Furthermore, when the fluid injection was connected to the transfer vessel and the syringe pump (Fig. 2c). In all HF stopped, the fractures were completely closed as the fluid pressure experiments, the flow rate was kept constant at 10 mL/min using the became zero, without leaving any permanent/plastic deformation but a syringe pump (500HP, ISCO Teledyne, Lincoln, NE, USA). The injection crack. This elastic characteristics of the gelatin enables to use of the 40 pressure was logged at 0.1 s intervals using a pressure transducer apogee method based on LEFM. The apogee is selected as the point (PX309-050A5V, Omega, Norwalk, CT, USA) and a data logger (34972A, where the radius from the crack tip becomes the maximum (Fig. 3), and 41 Agilent, Santa Rosa, CA, USA). the SIF can be calculated as follows, The photoelastic imaging required an additional setup to produce and analyze a polarized light. Therefore, two polarized filters(ESM-647,

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Fig. 3. General shape of fringes at the crack tip with the maximum radius from the crack tip to fringe, rm, and the angle of inclination corresponding to maximum radius, θm: (a) schematic drawing and (b) digital image of M gelatin sample. [ ] √̅̅̅̅̅̅̅̅̅̅ 19,42 2 tan(3θm/2) formation, the scaling factors can be mutually related, as follows: Nmf 2πrm 1 + σ 3 tan θm = √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ , SQ × Sμ SIF ( ) (2) = . 2 SE 3 (3) 2 Sr t sin θm 1 + 3 tan θm Given general reservoir-scale hydraulic fracturing practices, a vis cosity of 500 cp, a flowrate of 5 m3/min, and a wellbore radius of 40 mm where rm is the maximum radius from the crack tip to the outermost are chosen as the representative field-scalevalues. 43,44 Accordingly, the fringe, θm is the angle of inclination corresponding to the maximum scaling factors of the wellbore radius, flowrate, and fluidviscosity are Sr radius, Nm is the fringe order, fσ is the fringe constant, and t is the = 12.5, S = 500,000, and Sμ = 50, respectively. According to Eq (3), the specimen thickness. Q scaling factor of the elastic modulus is determined to be S = 12,800. The symmetric fringes at a tip and biwing fracture generation E Therefore, it is estimated that the gelatin media (L-, M , H-, and enabled the calculation of four SIF values in each HF test. Because the VH-gelatin) represent the model rocks having the elastic stiffness E = propagation behaviors of the upper and lower fractures were similar, the rock 0.48–3.6 GPa when up-scaled to a reservoir scale. This corresponds average SIF values were computed with the variance bar in the typical soft reservoir rocks, such as highly porous sandstones and shales homogeneous-medium cases. However, the SIF values of the upper and (E < 1 GPa, K < 1 MPa m0.5). lower fractures were plotted separately for the layered-medium cases. At IC The dimensionless toughness κ determines the regime of HF propa the early stage of HF propagation, the fringe was not sufficiently gation — viscosity-dominated or toughness-dominated hydraulic frac developed, which prevented reliable calculation of the SIF. Also, severe turing, and it is definedfor HF in a plane strain condition, as follows45: distortion in the fringe patterns by the interface prevented SIF calcula ′ tion near the interface. For the same reason, the SIF value could not be K κ = ) , (4) acquired when the fracture dilated along the interface. Only the cases ′ 3 ′ 1/4 E μ Q0 where the fracture crossed the interface were analyzed. ( ) 1/2 ′ ′ ′ = 2 = E μ = μ where K 4 π KIC, E 1 ν2 , and 12 . Herein, KIC is the 2.4. Gelatin as an analog to rock-like materials fracture toughness, E is Young’s modulus, ν is Poisson ratio, μ is fluid Our laboratory, scaled HF experiment setup and the gelatin media viscosity, and Q is the fluidinjection rate divided by the fracture height used in this study can be upscaled and compared to the field scale by as HF is developed in a plane strain condition, as in – – “ ” 45 using the scaling relations suggested by de Pater et al.42 The detailed Kristianovic Geerstma de Klerk model ( KGD model ). When the κ scaling procedure can be also found in Ham and Kwon.19 The scaling dimensionless toughness is less than 1, the majority of energy con principle is based on the basic assumption that the ratio between the sumption is associated with viscous drags in fluidflows during hydraulic elastic energy rate in medium deformation and the frictional dissipation fracturing, which is referred to as the viscosity-dominated hydraulic κ rate in fluidflows is kept constant at any scale, including the laboratory fracture. On the other hand, when the dimensionless toughness is and field scales. A scaling factor is defined as the ratio between a greater than 4, the most of energy is used to create new fracture surfaces in the medium, which is called the toughness-dominated hydraulic field-scale parameter and a lab-scale parameter, S = Xfield/Xlab. fracture. In this study, as the dimensionless fracture toughness κ ranges Accordingly, the scaling factors for injection flow rate SQ, wellbore 10–18, our HF experiments belong to the conditions where the tough radius Sr, elastic modulus SE, and fluid viscosity Sμ can be defined, ness is dominant over the fluidviscosity, i.e., the toughness-dominant HF respectively. By using the elastic deformation energy rate of the rock, 46,47 fluid frictional dissipation energy rate, and energy rate of crack behaviors.

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A fluidlag is expected during the HF propagation, associated with a propagated with the photoelastic fringes through a homogeneous tip cavity which is filled with inviscid vapors from the fracturing fluid. gelatin sample. The generated fractures were observed to be comet- Meanwhile, the fluid lag is exponentially small for large enough shaped, composed of a fracture head and a fracture body, because of dimensionless toughness.48 Therefore, the lag is assumed to be insig the viscoelastic characteristics of the gelatin. Generation of these comet- nificantin our HF conditions, less than 0.1% of the crack length, as the shaped fractures has been consistently reported in previous dimensionless toughness κ is much greater than 4. studies.19,49,50 From the commencing of the fluid injection, the pressure gradually 3. Results (I): homogeneous medium cases increased until the initiation and propagation of fractures. The pressure where a fracture was initiated was definedas the initiation pressure, as 3.1. HF test results denoted by the circle symbols in the pressure curves of Fig. 4. Even after the fracture initiation, the pressure continued to increase further, but at Fig. 4 shows the acquired digital images of the fracture tips with the a reduced rate for a while, as the initiated fracture opened wider and photoelastic fringes and the pressure responses during fluidinjection. In extended farther. Soon, once the fracture began to propagate steadily, all the cases with the homogeneous gelatin samples, two biwing-type the pressure reached the peak value and thereafter decreased in a fairly fractures were initiated along the direction of the perforation hole and slow and steady manner. This smooth pressure drop during the steady-

Fig. 4. Pressure responses and digital images of photoelastic fringe pattern denoting the maximum radius and the corresponding angle: (a) L gelatin, (b) M gelatin, and (c) H gelatin samples — the circle and triangle symbols in the pressure curves indicate the time when the fracture initiated and the test ended, respectively, and the digital images on the right side show the fracture tips with the photoelastic fringes at the end of the test, corresponding to the triangle symbol in the pres sure curves.

6 S.-M. Ham and T.-H. Kwon International Journal of Rock Mechanics and Mining Sciences 134 (2020) 104438 state fracture propagation was reported by Ham and Kwon,19 and it is shows the SIF values during HF propagation, superimposed with the possibly associated with the viscosity of the gelatin materials. By pressure response and fracture propagation velocity. contrast, upon reaching the peak pressure, a sudden pressure drop has For the L-, M , and H-gelatin samples, the SIF values were been widely observed in non-viscous materials.18,51 The HF test was approximately 0.42, 1.5, and 2 kPa m0.5, respectively. The SIF values halted when the fracture almost reached the sample boundary, as stayed remarkably consistent, with only a small variation of less than denoted by the triangle symbols in the pressure curves (Fig. 4). It was ~0.3 kPa m0.5 during HF propagation. This also corroborates the steady- also found that the initiation pressure increased with an increase in the state fracture propagation observed in viscoelastic media.19 An increase gelatin stiffness. The high-resolution, time-lapsed images of all the HF in the medium stiffness caused an increase in the fluid pressure and an tests of the homogeneous medium cases are available in the Supporting increase in the fringe size and radius, which led to an increase in the SIF Information (Movies S1-S3). values as well. There was a slight difference between the SIF values and the medium toughness values obtained from the wire-cutting method at 3.2. Photoelastic analysis results the rate of 50 mm/s (see Table 2) though the values are comparable. This can be attributable to the different ways of creating fractures and the The isochromatic fringe in the photoelastic images captured the different strain rate and fracture propagation velocity, associated with stress field created at the fracture tip, as shown in Fig. 4. The SIF was the energy loss of the viscoelastic gelatin media. obtained by using the apogee method40 — Equation (2) — in which a fringe order was assigned for each fringe in accordance with the 4. Results (II): layered medium Michel-Levy birefringence.52 As an example, for H-gelatin in Fig. 4c, the maximum radius was estimated as 5.9 mm, the corresponding angle as Fig. 6 through 11 show the results of HF propagation in the layered ◦ 115 , and the fringe order as 2, which yields an SIF of 2 kPa m0.5. Fig. 5 samples, where the pressure responses, time-lapsed images, and varia tions in the SIF values are shown. The high-resolution, time-lapsed im ages of all the HF experiments of the layered-medium cases are available in the Supporting Information (Movies S4–S9). In the same manner as in the homogeneous-medium cases, biwing fractures were initiated and propagated with the photoelastic fringes at the tips. The middle layer where the fracture was initiated was formed with the M-gelatin; there fore, the early HF propagation was similar to that observed in the ho mogeneous M case until the fracture approached the interfaces. The fracture initiation pressure and the initial SIF values were 55–70 kPa and ~1.5 kPa m0.5, respectively, and this was consistent with the homoge nous M case (Fig. 4b). However, the HF propagation behaviors, including the pressure and SIF responses, differed with the bounding- layer stiffness as the HF approached the interface and interacted with the bounding layers. Herein, the main observations are described with respect to the bounding-layer stiffness: (a) M2L case, (b) M2M case, and (c) M2H case and M2VH case.

4.1. M2L case: when the bounding layer has less stiffness than the propagating layer

In the M2L case, two fractures were initiated, and the upper fracture reached the interface faster than the lower fracture. Then, the upper fracture crossed the interface from the M-gelatin layer to the L-gelatin layer and continued to propagate in the L-gelatin (see Fig. 6b). A considerable pressure drop was noted immediately after the crossing of the interface, because the stiffness of the L-gelatin was less than that of the M-gelatin (Points B to C in Fig. 6a and c). Owing to this pressure drop, the propagation of the lower fracture in the M-gelatin almost stopped during the propagation of the upper fracture in the L-gelatin. Therefore, a stiffness contrast between geologic formation layers often caused preferential HF propagation in the less stiff medium. In addition, the reduced stiffness changed the fracture head geometry after crossing to a bigger fracture tip head with a wider width. As expected, the initial SIF values were consistent with the homo geneous M case, ~1.5–1.6 kPa m0.5, as shown in Fig. 6c. After crossing the interface, the SIF of the upper fracture was significantly reduced from ~1.6 to ~0.5 kPa m0.5. The SIF values after the crossing became close to the values obtained in the homogenous L case (i.e., 0.42 kPa m0.5, as in Fig. 5a). However, because the lower fracture stayed only in the M-gelatin, its SIF values were fairly constant. Fig. 6d details the photoelastic fringe patterns near the layer inter face. A fringe change around the fracture head was observed across the layer interface. Because of the stiffness difference between the L-gelatin Fig. 5. SIF values, fluid pressure responses, and HF velocity from the experi and M-gelatin, the fringe order and size in the L-gelatin layer were less mental cases of (a) L, (b) M, and (c) H: the upper and lower SIF values obtained and smaller than those in the M-gelatin layer (13.3 s in Fig. 6d). This from the fracture image are denoted with the variance bars. indicates that the strain field around one fracture differed with the

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Fig. 6. Result of M2L case: (a) pressure response, (b) time-lapsed digital images of the fractures, (c) SIF values and pressure responses, and (d) fringe shape passing the interface — the fracture images in (b) correspond to the circle symbols in (a), the initiation pressure is denoted with Point A, and the gap in the SIF value of the upper fracture is due to the severe distortion in the fringe pattern at the fracture tip by the interface. medium stiffness, although the fluidpressure within the fracture applies the homogeneous M case; thus, it was difficultto conclude whether this the same level of stress in every direction. After crossing the interface, pressure drop was caused by the interface. In this case, no or minimal the lower fringe order and the smaller fringe size were observed in the change in the fringe patterns was observed before and after crossing the bounding L-gelatin layer (13.62 s in Fig. 6d). interface, which resulted in the consistent SIF values of ~1.5–1.7 kPa m0.5, as in the homogeneous M case. 4.2. M2M case: when the bounding layer and propagating layer have the In the M2Mc case, both fractures dilated along the interface, as same stiffness shown in Fig. 9. The upper fracture reached the interface faster than the lower one. Thereafter, the upper fracture was dilated first to the left For the M2M case, the fracture behavior differed with the interfacial direction and then to the right direction. During this dilation, the pres bonding condition. Figs. 7 through 9 present the results from three sure significantly dropped (Points B to D in Fig. 9a). As the lower frac identical M2M samples (M2Ma, M2Mb, and M2Mc, respectively), but ture reached and was arrested by the interface, the pressure increased with different HF propagation behaviors. (Points D to E in Fig. 9a). In a sudden moment (Point E in Fig. 9a), the In the M2Ma case, the upper fracture dilated, and the lower fracture lower fracture began to dilate the interface, resulting in the pressure crossed the interface, as shown in Fig. 7. The upper one first dilated drop (Points E to F in Fig. 9a). along the interface before the lower one reached the interface. This The cases above clearly demonstrate that the bonding condition of caused the pressure drop (Points B to C in Fig. 7a). The lower fracture the interfaces plays a critical role in determining the HF propagation froze until the dilation of the upper one stopped, and then it propagated behavior across the interface when the stiffness between the layers is in a to the interface and crossed the interface. At this moment, the pressure similar range. slightly increased for fresh opening of the fracture in the bounding layer (Points C to D in Fig. 7a). From the SIF perspectives, when the lower 4.3. M2L case: M2H and M2VH cases: when the bounding layer has a fracture crossed the interface from the M-gelatin to the M-gelatin, the greater stiffness than the propagating layer SIF value hardly changed, remaining ~1.5–1.7 kPa m0.5 before and after crossing the interface (Fig. 7c). In the M2H and M2VH cases, a fracture was arrested for a while at In the M2Mb case, both fractures crossed the interfaces, as shown in the interface and then propagated along the interface with dilation, as Fig. 8. Only a minor pressure drop was observed, in a similar manner to shown in Figs. 10 and 11. In particular, for the moment when the

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Fig. 7. Result of M2Ma case: (a) pressure response, (b) time-lapsed digital images of the fractures, and (c) SIF values and pressure responses — the fracture images in (b) correspond to the circle symbols in (a), the initiation pressure is denoted with Point A, and the gap in the SIF value of the upper fracture is due to the severe distortion in the fringe pattern at the fracture tip by the interface.

Fig. 8. Result of M2Mb case: (a) pressure response, (b) time-lapsed digital images of the fractures, and (c) SIF values and pressure responses — the fracture images in (b) correspond to the circle symbols in (a), the initiation pressure is denoted with Point A, and the gap in the SIF value of the upper fracture is due to the severe distortion in the fringe pattern at the fracture tip by the interface.

9 S.-M. Ham and T.-H. Kwon International Journal of Rock Mechanics and Mining Sciences 134 (2020) 104438

Fig. 9. Result of M2Mc case: (a) pressure response and (b) time-lapsed digital images of the fractures — the fracture images in (b) correspond to the circle symbols in (a) and the initiation pressure is denoted with Point A.

Fig. 10. Result of M2H case: (a) pressure response and (b) time-lapsed digital images of the fractures — the fracture images in (b) correspond to the circle symbols in (a) and the initiation pressure is denoted with Point A. fracture was arrested, a pressure build-up was observed before the the fracture tip, while the HF was arrested for a few seconds at the dilation took place. Thereafter, the subsequent dilation caused a sig interface (from 16.1 to 22.1 s in Fig. 11c). This elevated stress at the nificant pressure drop. fracture tip caused the interfacial debonding and, consequently, facili In the M2H case, the lower fracture dilated along the interface to the tated the dilation of the layer interface and the propagation along the right direction (Point B in Fig. 10a), and the pressure dropped instantly. interface. During the propagation along the discontinuity with interface Thereafter, the fracture confinementtook place with a gradual pressure dilation, the fringe formed at the HF tip; however, the fringe shape was increase, and then the lower fracture again dilated toward the left di no longer symmetric and differed because of the stiffness contrast (from rection with a pressure drop (Points C to D in Fig. 10a). In the M2VH 24.9 to 25.1 s in Fig. 11c). case, the fracture confinementwas more clearly observed in association with pressure accumulation, which is possibly attributable to the greater 5. Discussions stiffness of the bounding layer (Points B to C in Fig. 11a). In fact, the upper and lower fractures in the M2VH case were arrested at the 5.1. SIF analysis in a homogeneous medium interface by the bounding layer for more than 7 s, which was accom panied by a significantincrease in the pressure from ~70 to ~100 kPa. The SIF represents the overall intensity of the stress distribution at Thereafter, dilation of the lower fracture took place and caused a pres the fracture tip, and the critical SIF, the minimum SIF value required for sure decrease (Points C to D in Fig. 11a). spontaneous growth, is defined as the fracture toughness of a material. Fig. 11c captures the changes of the fringe pattern when HF was Thus, the material fracture toughness can be considered as the resistance arrested and dilated in the M2VH case. During the period where the HF to crack growth. Based on the fracture energy balance,53 a fracture was arrested, the pressure accumulated. Therefore, the fringe pattern grows when the SIF exceeds the fracture toughness. In the following, and size became tighter and larger, indicating the stress accumulation at three salient observations are discussed in relation to the SIF.

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Fig. 11. Result of M2VH case: (a) pressure response, (b) time-lapsed digital images of the fractures, and (c) fringe shape passing the interface — the fracture images in (b) correspond to the circle symbols in (a) and the initiation pressure is denoted with Point A.

First, no or only a minimal variation in SIF was observed during the propagation. steady-state propagation of HF in all the homogeneous-medium cases Second, the photoelastic fringe analysis enabled the real-time (see Fig. 5). During quasi-static growth of hydraulic fracture, the steady- monitoring of SIF values during fracture propagation in the gelatin state SIF is a feature that can be found in a toughness-dominant HF media. It is worth noting that the SIF values were slightly greater than case.46,54 This also has relevance to the steady-state HF propagation the fracture toughness measured from the wire cutting method, and such velocity. difference became greater with an increase in the gelatin stiffness. Initiation and propagation of a HF in viscoelastic media can be Although the both are in similar ranges, the wire cutting method conceptualized, as shown in Fig. 12, although very weak fringe patterns appeared to have limited applicability to our HF propagation conditions. during the fracture initiation stage and the early propagation stage This is mainly attributable to different strain rate and fracture propa prevented the SIF computation. Before the fracture initiation, the SIF gation velocity, associated with the material viscosity, as the fracture increases with increasing fluidinjection pressure. When the SIF exceeds toughness of viscoelastic materials show strain rate-dependent – the material fracture toughness, a fracture is initiated and the propa characteristics.55 57 gation velocity gradually increases. When the velocity becomes stable Third, the SIF increased with an increase in the fluidpressure as the after the peak pressure, the SIF is kept consistent during the steady-state medium stiffness increased (see Fig. 5). This is corroborated by previous

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Fig. 13. Effect of the fluid pressure on the SIF.

M-gelatin layer near the interface was ~1.6 kPa m0.5. The required SIF of the bounding L-gelatin layer was ~0.42 kPa m0.5, less than that in the propagating layer. Thus, the HF passed the interface and propagated in the bounding layer. After the crossing, the injection pressure and the SIF value decrease while the fracture width becomes wider because of the Fig. 12. Conceptual figure for the fluid pressure, HF velocity, and SIF values from the experimental case of M: the fracture images in the figurecorrespond to reduced stiffness. In the M2L case, where two fractures (bi-wing frac the point in the pressure curve. tures) were initially generated, one fracture was contained in the propagating medium while the other fracture crossed the interface to the studies.19,58 For instance, the average fluid pressures during the softer bounding layer. This is mainly due to the reduced fluid pressure steady-state propagation were 29 kPa for L-gelatin, 65 kPa for M-gelatin, and SIF. Furthermore, we observed a reduction in the photoelastic fringe and 84 kPa for H-gelatin. According to the fluid pressure, the SIF value size at the contained fracture tip though it was little, while the other also increased to 0.42 kPa m0.5 for L-gelatin, 1.5 kPa m0.5 for M-gelatin, fracture crossing (Movie S4 in Supplementary Information). Therefore, and 2 kPa m0.5 for H-gelatin. The SIF is proportional to the stress level in the cases with multiple fracture growth, decreases in medium stiffness near the fracture tip, and the fluid pressure can be interpreted as an or fracture toughness across a discontinuity can cause preferential HF internal stress. Therefore, the SIF is expected to have a linear correlation propagation in the softer medium owing to the reduced SIF and fluid pressure. with the fluid pressure. To examine this, an additional experiment was 60 conducted with a greater injection rate of 40 mL/min for the M-gelatin In addition, the lower toughness implies the faster fracture growth. sample (Fig. S1 in the Supporting Information). The fluid pressure As the HF propagation regime is toughness-dominant, the M2L case during the steady-state propagation was approximately 100 kPa, greater confirms a rapid growth of the HF during the early stage of crossing, than that with a flow rate of 10 mL/min. As a result, the SIF also attributable to the reduced toughness (see Movie S4 in Supplementary increased to 2.5 kPa m0.5. As shown in Fig. 13, a linear correlation be Information). Thereafter, as HF propagation reaches a steady state, the tween the SIF and the fluid pressure was confirmed. HF propagation velocity is mostly controlled by the fracture geometry and injection flow rate. On the other hand, the reduced stiffness of the bounding layer plays a predominant role for the increased fracture 5.2. Effect of the contrasts in stiffness/fracture toughness on fracture width and the enlarged fracture tip size.61,62 containment behavior By contrast, the fracture is arrested by the bounding layer and/or dilating the discontinuity (or interface) while propagating along the The experiment results clearly demonstrate that the stiffness contrast interface when the fracture toughness increases from the propagating and the resulting toughness contrast between the propagating layer and layer to the bounding layer. For example, in the M2H case, the fracture the bounding layer have a profound effect on interactions between HF could not pass the interface, because the required SIF of the bounding H- and the pre-existing interface. Note that the fracture toughness increases gelatin layer was 2 kPa m0.5, greater than the concurrent SIF in the with an increase in elastic stiffness of rocks, thus the stiffer rocks propagating M-gelatin layer. At the moment at which HF is arrested, the 59 generally have the higher toughness. Two contrasting fracture fluid pressure increases owing to the constant flow rate applied. Given containment behaviors — crossing versus dilating/arrested — were the positive correlation between the SIF and fluidpressure, it is expected observed, depending on the toughness contrast from the propagating that the SIF also increases with the pressure increase. As soon as the HF layer to the bounding layer across the interface. These behaviors can be propagates along the interface, dilating the interface, the fluidpressure – predicted by comparing the SIF of the bounding layer required for drops. These trends are consistent with the previous researches.63 65 fracture growth and the concurrent SIF of the propagating layer. Herein, It is worth pointing out that in less-viscous, brittle materials, the the steady-state SIF values estimated in the homogeneous L-, M , and effect of medium stiffness on fracture propagation and containment H-gelatin cases are considered as the SIF values required for fracture behaviors across a discontinuity is consistent with our observations with – growth. viscoelastic gelatin media.66 68 Similar to the viscoelastic media, as The fracture crosses the interface between the layers when the shown in our study, when HF propagates from a low-stiffness brittle fracture toughness decreases from the propagating layer to the bounding medium to a high-stiffness brittle medium, the HF is either arrested or layer across the interface. It fulfills the fracture growth condition, dilates the interface. When HF propagates from a high-stiffness to a because the concurrent SIF is greater than the required SIF of the low-stiffness brittle medium, the HF crosses the interface. bounding layer. For instance, in the M2L case, the SIF in the propagating

12 S.-M. Ham and T.-H. Kwon International Journal of Rock Mechanics and Mining Sciences 134 (2020) 104438

However, it is found that the main differences of viscoelastic mate 6. Conclusions rials from brittle materials are the pressure response after breakdown (creating new fracture in a bounding layer) and the fracture width This study explored the HF propagation across discontinuities in change. When HF crosses the interface from a stiff layer to a soft layer, it viscoelastic layered media with the photoelastic analysis. can be considered as creation of a new fracture, which is associated with a pressure drop after the breakdown pressure. Tan et al.68 present the • The SIF was observed to be constant during the steady-state HF sudden and abrupt multiple pressure drops after breakdown pressures as propagation, which is a unique feature in viscoelastic media. Also, the the HF crosses the interfaces from tight sandstone layers to coal layers in fracture toughness of gelatin was directly computed from the real- the sandstone-coal interbedded formation. By contrast, in spite of the time SIF values by using photoelastic fringes. In addition, a linear large stiffness contrast in our study, the pressure drop is relatively gentle correlation between the SIF and the fluidpressure was confirmed. when crossing a discontinuity in viscoelastic media (see Fig. 6c), • The contrast of fracture toughness from the propagating layer to the compared to brittle materials, such as tight sandstones. bounding or encountering layer determined the HF containment On the other hand, Athavale and Miskimins66 and Afsar67 observed behavior across a discontinuity. The fracture crossed the disconti no significant changes in fracture width in brittle materials when the nuity when an HF encountered a bounding layer with a lower fracture crossed from a stiff layer to a soft layer, and this is consistent toughness. By contrast, the fracture was arrested by the bounding with the numerical simulation results by Guo et al.63 and Shan et al.64 By layer and/or dilating the discontinuity when an HF encountered a contrast, we observed an increase in fracture width when the fracture bounding layer with a higher toughness. crosses from a stiff layer to a soft layer, mainly attributable to the greater • The relative easiness between the debonding of a layer interface and stiffness contrast. However, caution is required here because it is not creating a fresh fracture in the bounding layer determined the frac clear whether this width difference is attributable to the viscoelastic ture containment behavior — whether HF dilated or crossed. When characteristic, different from brittle materials, or due to the large stiff the interfacial bonding was weak, the debonding between the layers ness contrast. was achieved, which caused the dilation. However, when the inter facial bonding was sufficiently strong, the fracture tended to cross 5.3. Debonding between the layers or creating a fresh fracture? the interface.

The layered-medium cases with no stiffness contrast show that the This study provided unique experimental data with high-quality interfacial bonding condition plays a significantrole in determining the photoelastic fringe images, and the data are comparable to analytical HF propagation behavior across the interface. Although the bounding or numerical models. Furthermore, the results contribute to a better and propagating layers have the same stiffness and toughness, a fracture understanding of the HF propagation behaviors in viscoelastic media can either dilate the interface (e.g., the M2Mc case) or cross the interface and the HF containment behaviors across a discontinuity. (e.g., the M2Mb case). It is presumed that the relative easiness of debonding the layer interface against creating a fresh fracture in the Declaration of competing interest bounding layer determines the fracture containment behavior. HF causes uneven deformation at the interface when approaching The authors declare that they have no known competing financial the interface, as can be seen in the distorted photoelastic fringe patterns interests or personal relationships that could have appeared to influence near the interface. When the interfacial bonding between the layers is the work reported in this paper. weak, HF can readily debond the layer interface and, therefore, generate a dilated, open space along which the fluid can preferentially flow. At Acknowledgement the moment when this dilation occurs, the pressure significantly de creases, because the debonded and dilated interface facilitates the fluid All of the video data, fluid pressure, SIF, and HF velocity values ac flow. quired during the experiment are archived in the website (kwon.kaist. By contrast, let us assume that the interfacial bonding is sufficiently ac.kr) and Mendeley Data (https://data.mendeley.com/) with the proj strong, such that debonding is not achievable with a given fluid pres ect name ‘Data of the hydraulic fracturing propagation across a sure. If the concurrent SIF is less than the fracture toughness of the discontinuity in layered formations’ (https://doi.org/10.17632/rhf bounding layer, HF is expected to be arrested by the interface for the 44kpmbn.1). These data can be also requested by e-mail (t.kwon@ka moment. However, the fluidpressure soon builds up, and the current SIF ist.ac.kr). This research was supported by the Basic Research Labora becomes greater than the fracture toughness of the bounding layer; tory Program through the National Research Foundation of Korea (NRF) therefore, HF is expected to cross the interface, creating a fresh fracture funded by the MSIT (NRF-2018R1A4A1025765) and by a grant in the bounding layer. In such a case, the pressure and SIF hardly change (19CTAP-C151917-01) from Technology Advancement Research Pro upon the crossing. gram (TARP) funded by Ministry of Land, Infrastructure and Transport Therefore, two competing factors are the debonding of the layer of Korean government. interface and the creating of a fresh fracture in the bounding layer across the interface. The relative easiness between them determines the frac Appendix A. Supplementary data ture behavior — whether it dilates or crosses. This is consistent with the 69 results by Fu et al., which shows that the bonding state affects the HF Supplementary data to this article can be found online at https://doi. propagation across the discontinuity. Furthermore, crossing and dilation org/10.1016/j.ijrmms.2020.104438. can take place simultaneously under a certain condition; particularly, Fu 69 et al. showed that HF crosses a partially bounded interface but with References some dilation while HF crosses a fully bonded interface with little dilation. Meanwhile, in some cases, it has been reported that the HFs can 1 Dusterhoft R, Chapman B. Fracturing high-permeability reservoirs increases – cross the interface and propagate to a stiffer bounding layer.70 72 This is productivity. Oil Gas J. 1994;92(25). 2 Li Q, Xing H, Liu J, Liu X. A review on hydraulic fracturing of unconventional because other factors can also have an effect on the behavior, such as the reservoir. Petrol Times. 2015;1(1):8–15. bonding strength of the interface, incident angle of the propagating HF 3 Rummel F, Kappelmeyer O. The Falkenberg geothermal frac project: concepts and to the interface, and in situ stress. experimental results. In: Nemat-Nasser S, Abe H, Hirakawa S, eds. Hydraulic Fracturing and Geothermal Energy. Dordrecht: Springer; 1983:59–74. 4 Li M, Lior N. Analysis of hydraulic fracturing and reservoir performance in enhanced geothermal systems. J Energy Resour Technol. 2015;137(4), 041203.

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