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We present a distributed fiber optic sensing scheme to image 3D strain fields inside concrete blocks during laboratory-scale hydraulic fracturing. Strain fields were measured by optical fibers embedded during casting of the concrete blocks. The axial strain profile along the optical fiber was interrogated by the in-fiber Rayleigh backscattering with 1-cm spatial resolution using optical frequency domain reflectometry (OFDR). The 3D strain fields inside the cubes under various driving pressures and pumping schedules were measured and used to characterize the location, shape, and growth rate of the hydraulic fractures. The fiber optic sensor detection method presented in this paper provides scientists and engineers an unique laboratory tool to understand the hydraulic fracturing processes via internal, 3D strain measurements with the potential to ascertain mechanisms related to crack growth and its associated damage of the surrounding material as well as poromechanically-coupled mechanisms driven by fluid diffusion from the crack into the permeable matrix of concrete specimens.
© 2016 Optical Society of America
1. Introduction
The technology of hydraulic fracturing for stimulating production from oil and gas wells was first developed in the early 1950’s [1]. As an unconventional oil and gas extraction technique, high pressure water-sand slurries are pumped into wells to fracture rock with low permeability to extract oil and gas [2]. Over the last decade, the use of hydraulic fracturing has been undergoing a major period of growth with the proliferation of horizontal drilling. During this period, the success of the hydraulic fracturing stimulations that entail pumping water-sand slurries with relatively low sand concentrations has led to high volume treatments whereby horizontal wells in excess of 2500 m in length are stimulated in 30 or more individual locations with each location often entailing injection through 3-5 clusters of wellbore perforations (holes) spaced at roughly 10-30 m intervals [3].
This latter innovation raises the issue of how to effectively, yet economically track how uniformly fluid is partitioned among the perforation clusters, both as a diagnostic of treatment effectiveness and as a predictor of well performance. The drive for these innovations in turn drives development of laboratory experiments to understand how hydraulic pressure induced fractures occur and develop in various scenarios and rock formations. Key importance is therefore attributed to basic mechanisms of hydraulic fracture growth such as hydraulic fracture initiation and hydraulic fracture interaction with natural fractures [4, 5]. These mechanisms can be investigated in laboratory settings using analogues constructed from quasi-brittle, castable materials such as concrete or hydrostone. Knowledge gained from these laboratory investigations can in turn be used to develop more efficient fracturing schemes. Probably more importantly, though, this experience can also lead to field deployment of new sensing technologies developed and proven in the course of these laboratory experiments. Such embeddable technologies have the potential to uniquely characterize hydraulic fracture growth and help us to prognose the retention, permeation, inter-mixing, and back flows of hydraulic fluid, hydraulic chemical, and brine in both short and long periods of times.
Fiber optic sensors are well-known for their capability to withstand harsh environments. One of the unique traits of fiber optic sensors is its capability to perform high spatial resolution measurements using distributed sensing schemes such as Rayleigh [6–11], Raman [12, 13], and Brillouin scatters [14, 15]. In this paper, a distributed fiber optic sensing method is used to monitor laboratory scale hydraulic fracture growth. The method uses Rayleigh backscattering Optical Frequency Domain Reflectometry (OFDR) to measure fracturing-induced strain due to its higher spatial resolution, in comparison with Raman and Brillouin scattering methods. By embedding optical fiber in concrete during its fabrication process, 3D strain fields induced by hydraulic fracturing are imaged, thus offering a novel and useful tool for engineers and scientists to understand the hydraulic fracturing process.
2. Experiment setup and test procedure
2.1 Sensor embedding
To achieve the 3D strain field imaging for hydraulic fracturing studies, a conventional single mode optical fiber (SMF-28) was embedded into the concrete cube during its casting process. Since the Rayleigh OFDR is only sensitive to axial strain along the optical fiber, a helix shape was created to provide 3D strain information inside the cube. As shown in Fig. 1, the optical fiber with a total length of ~130 cm was embedded into a 5.7 cm × 7.5 cm × 7.5 cm (H × W × L) concrete cube. It comprised of 6 rings of optical fiber with a length of ~120 cm to form the helix and also a section of optical fiber link for 6 cm running from the top of the cube to its bottom. The total number of rings needed was determined to assure a 1-cm spatial resolution along the vertical direction, which matches the strain measurement resolution in the horizontal direction.
Fig. 1 (a) Photograph of concrete cubes during the casting process, (b) the schematic sketch of the optical fiber embedded in a concrete cube, and (c) photograph of the fiber-embedded concrete cube after the curing.
The optical fiber embedding process commenced along with the concrete deposition layer by layer in a bottom-to-up fashion. In total, six layers of the optical fiber and seven layers of concrete were deposited alternatively such that every layer of the optical fiber was positioned between two layers of concrete. The circumferences of the six loops of optical fiber were controlled to be ~20 cm with 1-cm accuracy. The centers of the helix fiber loops were placed to the central axis of the cube. To confirm locations of optical fibers after the curing of the concrete, the concrete cubes were dissected after the hydraulic fracturing tests to identify the vertical location of every loop in the fiber helix. After the fiber embedding and concrete casting, the cured concrete cube was drilled at the center. A stainless steel tube with an outer diameter of 0.95 cm and inner diameter of 0.70 cm was inserted into the cube. Spacing between the inserted tube and the wall of the drilled concrete was back filled with 1-cm deep epoxy and sealing O-rings on both ends. The completed concrete samples with embedded optical fibers are shown in Figs. 1(b) and 1(c). A pair of perforations (holes) at the middle of the inserted stainless steel tube was used to exert hydraulic pressure on the concrete block. The perforations were placed opposite to each other on the tube. As indicated in Fig. 1(b), one side of the tube was capped, and the hydraulic fluid (glycerin) was injected from the other end of the tube to apply hydraulic pressure. The hydraulic system employed in this experiment is able to precisely control the hydraulic pressure inside the cube from 500 psi up to over 3000 psi with 10-psi accuracy. The fully prepared concrete cubes were then left to cure for 1 week before the hydraulic fracturing tests.
2.1 Sensor interrogation
The OFDR system, OBR 4600 from Luna Technologies, was used for the experiment. The tunable laser source from the instrument was butt coupled to the optical fiber embedded in the concrete cube. The principle of in-fiber Rayleigh scattering measurement for distributed fiber sensing has been extensively reported [16–18]. Using a scanning range of 43.09 nm centered at 1550 nm and group delay mismatch τd = 800 ns, the maximum interrogating length for the Rayleigh backscattered signals during our studies was collected for ~41-m fiber with a spatial resolution of ~20 µm according to
where n refers to the effective refractive index of the optical fiber, Δfsweep is the scan range of the tunable laser in the frequency domain and c is equal to the speed of light. For the system setting used in our experiments, the total time taken for one measurement is ~5 seconds, during which the system assumes the strains are static. The OFDR system presents the Rayleigh backscattered signal in the time domain where the embedded section of optical fibers can be easily identified by calculating the optical fiber length. Once the embedded section of the optical fiber is identified, the OFDR instrument will perform piecewise strain/temperature measurements in frequency domain along the optical fiber length with increments of Δz, which is the actual spatial resolution of the distributed measurement and equal to 1 cm in this study. The 1-cm spatial resolution is the minimum value where 1-µε strain measurement resolution can be maintained. Such level of resolution turns out to be indispensable to detect small strain changes at the earliest stage of hydraulic fracturing processes. The strain change is interrogated in frequency domain where Eq. (2) below is followed to relate the spectral shift Δν to the strain or temperature to be measured,where KT = 6.45 × 10−6 °C−1 is the thermal-optic coefficient, Kε = 0.78 is the strain coefficient, ν is the mean optical frequency, and ΔT and Δε represent the temperature and strain changes under interrogation. In this study, ΔT was controlled to be zero in a constant temperature environment.2.1 Test procedure for the hydraulic fracturing
For the hydraulic fracturing test, two fiber-embedded concrete samples were prepared with the same fabrication procedure as mentioned before. They were tested with different hydraulic fracturing conditions. The hydraulic breakdown of Sample 1 was directly induced by stepwise increase of the hydraulic pressure with 250 psi per step before 1300 psi and then the step size was reduced to ~100 psi. Sample 1 was observed to break down by hydraulic fracturing at 1550 psi in less than 2 minutes. A typical hydraulic breakdown is featured by sudden release of hydraulic pressure and visible structural damage of the sample, where hydraulic fluid spill-out occurs. Each pressure setting was held for 3 minutes as three strain measurements were made with 1-minute intervals. For Sample 2, the hydraulic pressure was also increased stepwise with the same pressure steps as Sample 1 until it reached a critical pressure while the hydraulic breakdown started to occur instead of taking place momentarily. Before the onset of the critical pressure, three consecutive measurements yield consistent strain profiles. At the critical pressure, the Rayleigh OFDR measurements will produce increased strain profiles over a course of 3 minutes. Using this approach, the critical pressure point was experimentally identified as 1441 psi for Sample 2. Once the critical pressure was reached for Sample 2, the strain profiles were taken every minute at 1441 psi until the total breakdown of the sample. In addition, during the hydraulic fracturing tests, both samples were placed on a test bench with flat surface and free of vibration. No further containment was used to limit the movement of the sample during the fracturing. The ambient temperature was also kept constant. The non-vibrational environment and negligible ambient temperature change are essential to obtain valid strain measurements.
3. Distributed axial strain measurements and 3D strain field imaging
Figure 2 shows the distributed axial strain measurements for two concrete cubes, Sample 1 and Sample 2, tested in this experiment. The total lengths of the two embedded optical fibers shown in the Fig. 2 are both ~130 cm which correspond to the actual lengths of optical fibers embedded inside the cubes. Two arrows in both plots are also provided to represent the relative locations of the optical fiber in the samples. In Fig. 2(a), the pressure induced strain increase along the embedded optical fiber was clearly observed. The overall baseline strain along the embedded optical fiber increased from ~8 με with the applied hydraulic pressure of 560 psi to ~42 με when the hydraulic pressure increased to 1550 psi, which is direct indications of the overall structural deformation of the cube. Equally important, the strain profile also yields a periodic strain peak pattern with 20-cm period, which is consistent with the circumference of the fiber helix in Fig. 1(b). This is a telltale sign of a line defect induced by the hydraulic pressure based on the fact that in both concrete samples single-wing fractures were observed. Although the peak strain of the line defect increased with the hydraulic pressure, the length of the line defect remained largely unchanged. Test results for Sample 2, however, present a different scenario. Before the critical pressure point, strain profiles with the hydraulic pressures of 580 psi, 834 psi, 1082 psi, and 1330 psi are presented in Fig. 2(b). At low hydraulic pressures, 580 psi and 834 psi, periodic strain peaks with 20-cm period are only evident for part of the fibers embedded in the upper half of the cube. When the hydraulic pressure increased further, the line defect grew and extended to the entire cube at the critical pressure point of 1441 psi.
Fig. 2 Distributed axial strain evolution of the embedded optical fibers in two concrete cubes. Different methods to induce the breakdown were employed: (a) directly induced breakdown, and (b) delayed breakdown.
At 1441 psi, the hydraulic pressure was held. Strain measurements at the critical pressure point were carried out every minute until the breakdown. The first and the last measurements in this period are shown in the Fig. 2(b) labeled as curve 1441 psi-1 min and 1441 psi-22 min. They are the measurements taken at 1 and 22 minutes after the hydraulic pressure was stabilized at 1441 psi. The catastrophic breakdown was observed in 5 seconds after the last measurement was taken, while the hydraulic liquid leaked out from the cracked concrete. To further characterize the dynamics of strain growth, the strain evolution versus time curve obtained at the strongest strain peak at the critical pressure of 1441 psi in Fig. 2(b) is presented in Fig. 3. The peak strain grew slowly at the initial stage of the critical pressure from 0 to 15 minutes and then increased exponentially to reach the catastrophic breakdown with a time constant τ = 1.4 min.
Fig. 3 The strain evolution with time at a selected local point before the breakdown. The final stage of the strain growth is fitted by an exponential curve in red.
To better understand the physical meaning of the periodic strain peaks observed in the tests for both samples. The 3D strain field images were generated based on the distributed strain measurements. Given that the total length of the optical fiber in the helix structure is ~120 cm and the spatial resolution of the measurement is 1 cm, the helix structure consists of ~120 strain data points in total. Those points can be mapped to 3D domain by converting their linear coordinates on the optical fiber to the corresponding spatial coordinates in the helix. To achieve this, the circumference of every loop in the helix structure was taken as exactly 20 cm and the height information for each loop of the optical fiber in the helix was measured in dissection of the concrete cube carried out at the end of the test. The strain field images in 2D format are also provided to fully demonstrate the strain field information around the helix structure.
The reconstructed strain fields in 2D and 3D formats for Sample 1 are presented in Figs. 4 and 5. The x, y and z axis in the shown 3D images form the spatial coordinate system of the concrete cube. The center of the bottom side of the cube is set as the origin of the 3D coordinate system. To practically generate those 3D images of the strain fields, the 2D-format images were obtained first based on the linear strain measurement of the OBR system by coordinate conversion. Once the 2D images were produced, the 2D-format images were wrapped around a cylinder with a circumference of 20 cm to form the 3D strain images as shown in Figs. 4 and 5. The reconstructed 2D strain field does not result in a perfect parallelogram shape. This is because the spacing between different helix loops is not uniform.
Fig. 4 Reconstructed strain fields of Sample 1 in 2D (a-c) and 3D (d-f) formats under different pressure conditions: 810 psi (a and d), 1306 psi (b and e), and 1550 psi (c and f). Color bar indicates the axial strain (µε) in the optical fiber and localized strong strain regions are approximately highlighted with dashed lines.
Fig. 5 Reconstructed strain fields of Sample 2 in 2D (a-c) and 3D (d-f) formats under different pressure conditions: 1330 psi (a and d), 1441 psi-1min (b and e), and 1441 psi-22 min (c and f). Color bar indicates the axial strain (µε) in the optical fiber and localized strong strain regions are approximately highlighted with dashed lines.
The hydraulic pressure induced strain profile for Sample 1 is shown in Fig. 4. At a low hydraulic pressure of 810 psi in Figs. 4(a) and 4(d), a high strain region emerged at a location toward the top of the concrete block. The periodic strain peaks shown in Fig. 2(a) lead to a localized strong strain band running from the top of the concrete cube to the bottom, which is also evidenced in Figs. 4(a)-4(c) with localized strain regions highlighted. This is indicative that line cracks formed internally, parallel to the stainless tube used for the liquid injection. The higher hydraulic pressure of 1306 psi leads to a strong strain profile as shown in Figs. 4(b) and 4(e). However, the overall size and shape of the high strain fields prone to fracture remain largely unchanged. The further increase of the hydraulic pressure to 1550 psi finally fractured the concrete cube. It is clear the location that sustained highest strain is located at the top part of the cube in Figs. 4(c) and 4(f), which was also where the actual breakdown of the specimen initially occurred as shown in Fig. 6.
Fig. 6 Strain field images in 2D (a) and 3D (b) format, and (c) the photo of the actual concrete Sample 1 after the breakdown. The angle of view for 3D image is not the same as Fig. 4 for better demonstration of the fracturing feature. Color bar indicates the axial strain (µε) in the optical fiber.
The strain field images in 2D and 3D formats for Sample 2 are presented in Fig. 5. The most apparent difference from Sample 1 is that high strain region expanded with the increase of the hydraulic pressure. When the concrete cube sustained the hydraulic pressure of 1330 psi that is below the critical point (1441 psi) in Figs. 5(a) and 5(d), the high strain region appeared to be localized in a central region of the sample. This could suggest that a small crack or defect was produced internally. Unlike Sample 1, the high strain region expanded significantly at the critical pressure of 1441 psi along both directions of the concrete cube as shown in Figs. 5(b) and 5(e) and Figs. 5(c) and 5(f). Before its critical pressure the strain was also distributed more evenly on all directions in Sample 2, as evidenced by Figs. 2(a) and 2(b). That is probably why Sample 2 was observed to withstand higher hydraulic pressure. In Sample 1, evident line defect that goes from the top of the specimen to its bottom was formed at the starting pressure level of 560 psi. However, in Sample 2, the completed line defect is only evident by the last stage of its fracturing process. It is believed that in Sample 1 the prematurely formed internal defect line would provide a potential path of fracture propagation and therefore accelerated the fracturing process as hydraulic pressure was further increased.
After the hydraulic-induced breakdowns, the optical fibers embedded in the concrete cubes were still functional except the significantly increased axial strains. Figures 6 and 7 show strain field images along with photos taken for the samples after the breakdowns. It is important to realize that strain fields shown in Figs. 6 and 7 are due to permanent structure damages. This is different from results shown in Figs. 4 and 5, while strain fields induced by the hydraulic pressure are largely reversible.
Fig. 7 Strain field images in 2D (a) and 3D (b) format, and (c) the photo of the actual concrete Sample 2 after the breakdown. The angle of view for 3D image is the same as Fig. 5. Color bar indicates the axial strain (µε) in the optical fiber.
For Sample 1, the breakdown occurred when the hydraulic pressure were held at 1550 psi for about 110 seconds, while the instrument took the first measurement as shown in Figs. 4(c) and 4(f) at 1 min after the pressurization. During this 50 seconds of time after the measurement, it is highly possible that the internal strain field eventually increased to a value that is much larger than the peak strain (~60 με) measured in Figs. 4(c) and 4(f) to trigger the total breakdown and also developed a horizontally shifted line crack as shown in Figs. 6(a) and 6(b). Such continuous buildup of internal strain under hydraulic pressure has already been observed in Fig. 3, when the critical pressure of the sample has been reached. The region with the peak strain located close to the top surface of the concrete cube, which is consistent with the location of initial crack and spilling of the hydraulic fluid as shown in Fig. 6(c). In addition, distributed fiber sensors also reveals internal region with strain similar to where the breakdown is visible. It is reasonable to speculate the shape of the internal cracks accordingly although they cannot be revealed through visual inspection. This highlights usefulness of the distributed fiber sensor approach demonstrated in this paper.
Figure 7 shows the strain field and photograph when the fracturing occurred for Sample 2. Since the hydraulic pressure was held at the critical point of 1441 psi, the internal strain developed much slower for Sample 2 than that of Sample 1. The breakdown in this situation resulted in a much lower deformation value (~7000 µε), which, however, is over 70 times larger than the peak strain value before the breakdown occurs. The location of crack where the hydraulic fluid leaked out in Fig. 7(c) is consistent with the location of peak strain measured by the fiber sensor in Figs. 7(a) and 7(b). Strain images shown in Fig. 7 also reveal a vertical “offset” of the fracture feature. This off-set is probably due to the layer-by-layer concrete casting process while the internal natural defects were not aligned across all layers. Given that fracture at this center region is not aligned vertically, strain measured by the helix fiber only reflects the component of the deformation parallel to axial direction of the embedded optical fiber. This is probably why the strain field measured in the central region is weaker than other fractured region where the defects align along the vertical direction. This shows the limitation of the current fiber configuration, which could be improved by other fiber winding patterns.
4. Conclusion
This paper presents a proof of concept demonstration using distributed fiber sensing as a laboratory tool to measure the strain field evolution associated with hydraulic fracture initiation and growth. Taking advantage of high spatial resolution measurement capability enabled by the Rayleigh OFDR technique, evolution of 3D internal strain fields of concrete under hydraulic pressure can be imaged in real time to reveal defect origin, size, formation, propagation, and breakdown. As a robust sensing platform, this paper shows that distributed optical fiber sensors survive the entire hydraulic fracturing process including the complete loss of integrity of the specimen. Although this paper studies hydraulic fracturing events occurring in a relatively short time span (< 1 hour), the robust fiber sensors are also fully amendable to perform high spatial resolution measurements over longer periods of time. This will expand applicability of distributed fiber sensors for geologic studies such as oil/gas permeation through rock structures, impacts and processes of hydraulic fluids to the surrounding geological formation, and other issues important to oil/gas exploration and environment protections. The novel applications of fiber optical sensing techniques will provide new tools and capability to geophysicist, environmental scientists, and oil/gas engineers.
Acknowledgements
This work was supported by the National Science Foundation (IIP-0810429 and CMMI-0826286) and the Department of Energy (DE-FE0003859).
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