Stimlab Proppant Consortium. Halliburton. Cundall, P.A. 1971. A computer model for simulating progressive large scale movements in blocky rock systems.
SPE 151647 Experiment and Simulation Study of Proppant Pack Compression X. Ye, SPE, N. Tonmukayakul, SPE, J.D. Weaver, SPE, Halliburton; J.F. Morris, City College of New York
Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE International Symposium and Exhibition on Formation Damage Control held in Lafayette, Louisiana, USA, 15–17 February 2012. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract Realistic laboratory simulation of fractures propped with sand, engineered ceramic proppants, and resin-coated proppants to determine the impact of temperature, stress, and stress cycling on proppant-pack structure and pack permeability is both difficult and expensive. Large, specialized testing equipment and long testing times are required, which can lead to high testing costs. This paper presents a new dynamic compression device (DCD) that permits rapid proppant-pack analysis to optimize proppant selection. Understanding the mechanical and fluid dynamics of hard granular particle packs subjected to high closure stress and cyclic stress is important for understanding fracture conductivity and the impact of production operations. Few experimental studies have been reported where the compression of proppant with variable stress rates was used that also includes simultaneous direct visualization of the proppant structure. The DCD imposes a controlled strain on the proppant pack while measuring the stress response, up to a compressive loading of 7,100 psi. Simultaneously, the liquid permeability and a detailed visualization of the proppant-pack structure are acquired. The stress loading and unloading process, performed in either a single or repeated (cycling) protocol, can be performed with precise measurement of the resulting system-level strain. Permeability results obtained using the DCD were comparable to those obtained using standard API linear conductivity determinations. Particle rearrangement by direct visualization during stress cycling was comparable to that predicted by use of a popular, commercial, three-dimensional particle-flow numeric simulator. The DCD is a small, bench-top device that uses a small proppant sample. It has been demonstrated to be an efficient tool to experimentally determine the impact of closure stress, stress-change rate, proppant-packing properties, and the effect of multiple stress cycles on liquid permeability, while providing direct proppant-pack structure visualization. This new device enables rapid testing to determine the impact of expected downhole production conditions on proppant-pack permeability and permit selection of optimum proppant and proppant coatings. Introduction As a tool to enhance the rate of hydrocarbon recovery from subsurface rock formations, hydraulic fracturing has been widely used in the oil industry. This process involves injecting fracturing fluid at high rate and high pressure, followed by placing proppant into the growing fracture to prevent the fracture from closing after discontinuing the high-pressure injection process. Quartz sand, resin-coated sand, and spherical ceramic particles are the most commonly used proppants. Typically, sand is suitable for closure stresses of less than 6,000 psi, resin-coated sand up to 8,000 psi, and intermediate-strength and high-strength ceramic proppant can be used up to 10,000 to 14,000 psi. If the proppant strength is not adequate, the closure stress will crush the proppant and generate fines that will significantly reduce the proppant permeability, and thus the well productivity. Extensive work has been performed to modify the proppant surface to enhance proppant strength and to provide stability to the proppant pack, as well as to reduce loss of conductivity caused by the formation of fines and to prevent fines migration within the proppant pack (Nguyen et al. 1998; Dewprashad et al. 1999; Weaver et al. 1999; Nguyen et al. 2000; Nguyen and Weaver et al. 2010). Recently, another mechanism has been proposed to explain the challenges of sustaining the proppant-pack conductivity under stress (i.e., loss of proppant-pack porosity as a result of proppant scaling and diagenesis; Weaver et al. 2005 and Weaver et al. 2007). Since the earliest days of hydraulic-fracturing stimulation, basic studies have been conducted on proppant characteristics, such as the Krumbein shape factor, mineral content, acid solubility, etc. Currently, the API conductivity cell measurement is primarily used to mimic proppant-conductivity performance in a propped fracture. Two new standards have been developed to evaluate and compare proppant characteristics under specific test procedures and conditions (Kaufman et al. 2007).
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However, it is labor intensive to prepare and conduct such tests, and high testing costs can limit their application. Thus, a laboratory bench-top device with the capability for rapid proppant evaluation in terms of permeability under varied stresses would be of benefit for practical quality control, proppant selection, and the evaluation of new chemical coatings. Moreover, some operators are required to periodically shut-in wells that have been subjected to hydraulic fracture. This is a common occurrence, especially for gas wells where gas deliverability often exceeds gas demand. Other reasons for well shut-in include pressure-buildup testing, well workovers, and/or equipment repair. On well shut-in, the net closure stress on the proppant pack inside the fracture decreases. As the well is brought back to production, the closure stress will again increase. In these circumstances, the proppant pack inside the fracture is subjected to cyclic-stress loading, which can lead to fatigue failure (Holditch and Blakeley 1992), and thus decrease productivity. It is extremely important to investigate the performance of proppant under cyclic-stress loading. Several studies of this phenomenon are available in literature. These include the study of cyclic deformation-failure (Kawamoto et al. 1981), the effects of stress cycles on proppant permeability (Kim and Willingham 1987; Malone et al. 1989), and the effects of numerous stress cycles on proppant permeability (Holditch and Blakeley 1992). Other studies on the behavior of proppant under cyclic stress focus on proppant size distribution (Stephens et al. 2006, 2007). All of these studies showed that repeated stress cycles can significantly reduce the proppant-pack permeability. However, not much is available in the literature to address how coated proppants behave under cyclic-stress loading. This is another goal of the current work. Experimental Work The Apparatus. A DCD was designed and built to investigate the cyclic loading of proppant packs, which was reported in a previous work (Ye et al. 2009). This bench-top apparatus has several unique features—it generates cyclic-stress loading on the proppant pack up to 7,100 psi, allows continuous measurement of permeability with simultaneous measurement of stresses in three directions of the proppant pack, and enables direct visualization through a window to determine local particle rearrangement. Fig. 1 is a schematic illustration of the overall setup. A servomotor is used to drive a rectangular piston to compress the proppant pack, while other faces are confined with aircraft-grade aluminum, except the top window, which is polycarbonate and used for visualization purposes. A digital camera is used to monitor the particle rearrangement through the top window during cyclic loading. An overflow water reservoir provides constant-pressure water flow through the pack perpendicular to the main compression direction. The accumulated water mass is monitored with a balance to provide flow rate values for permeability measurement. Concurrently, stresses are measured with load cells on the three faces of the pack: axial stress σA, rear stress σR, and transverse stress σT. Details of the setup are presented in other literature (Ye et al. 2009).
Fig. 1—Schematic illustration of the DCD setup.
The cross-section of the pack along the compression direction is 1.5 × 1.5 cm2. The flow direction is perpendicular to the compression direction, with a 1.5-cm flow-path length. The width of the proppant pack, w, can vary from 1.5 to 2.5 cm (Fig. 2), depending on the amount of proppant used. The proppant used in this study was a 20/40-mesh high-strength ceramic commercial proppant. The amount of proppant in this study was 9.2 g, which gives a proppant concentration of 8.4 lbm/ft2. The corresponding proppant pack width was about 2.1 cm. The loading/unloading rate depended on the servomotor, which has a velocity range of 0.034 to 102 mm/min. However, a constant rate of 0.34 mm/min was used for both loading and
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unloading processes. Note that the temperature study is out of the scope of this work, and all experiments were conducted at room temperature.
Fig. 2—Dimension of the proppant pack and three measured stresses.
Test Procedure. The test procedure is described as follows: 1. The overflow, constant head device provides a constant pressure variation between the inlet and outlet of the DCD. In this study, it was kept at 6.5 cm of water head. 2. The piston is moved to a fully open condition to provide a maximum cavity space. 3. The cell is submerged in water and the inlet and outlet lines are flushed to help ensure the system is air-bubble free. This is critical, especially for this small-volume proppant pack. Tiny air bubbles trapped in the cell will create additional flow resistance and thus affect the permeability measurement. 4. The cell is placed in testing position and carefully connected to the water-flow lines, helping to ensure no bubbles are introduced into the system. 5. For the system resistance test, the top window is sealed and water is run through the system for at least 10 min. The data recorded are the flow rate and system resistance. 6. The preweighed proppant (9.2 g in this study) is transferred into the cavity, and the proppant is stirred gently to help prevent possible air bubbles from becoming trapped in the pack. Then, the polycarbonate window and the top cover with gasket are fixed in place using eight evenly spaced screws to provide firm confinement. 7. The flow through the system is then started. At the same time, the piston is driven at a constant speed of 3.4 mm/min until the axial stress reaches 120 psi. This stress level is used in all tests as the initial stress condition. 8. The proppant pack is then compressed at a constant rate of 5.6 μm/sec until the axial stress reaches 7,100 psi. The piston is then withdrawn at the same rate until it reaches an axial stress of 1,000 psi, which completes the first cycle. During this cycle, photos are taken every 10 seconds for analysis using particle imaging velocimetry (PIV). Cyclic loading/unloading continues between 1,000 and 7,100 psi for five cycles. Results and Discussion System Characterization. The system has been characterized in terms of the piston friction, system resistance, and fluid inertia, as well as the apparatus deformation. These have been taken into account for the results presented in this study. Details can be seen in previous work (Ye et al. 2009). The system resistance should be checked every time before the cyclic-
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loading test. This is conducted without proppant in the cell and will help ensure that the calculated permeability is for the proppant pack itself. More specifically, Darcy’s law is applied to obtain the permeability, which is given by Eq. 1: ∆
................................................................................................................................................ (1)
where u is the volumetric flow rate, L is the length of the proppant pack in the flow direction, A is the test-specific crosssectional area (which accounts for the change of packing width because of loading), and Δp is pressure drop across the proppant-pack length L. The dynamic viscosity, µ, used herein was 1 cp for water at room temperature. Eq. 1 can be rewritten as ∆
....................................................................................................................................................... (2)
where the total resistance, , is the sum of the system resistance, permeability of the proppant pack can be written as ·
, and the proppant-pack resistance,
. Thus, the
................................................................................................................................................. (3)
Permeability. Fig. 3 shows a typical system-resistance test before the cyclic-loading study, where the accumulated water mass is plotted as a function of time. The slope, obtained by the linear fitting, is about 1.37 g/sec for this case, at a constant water head of 6.5 cm. This also confirms that the fluid inertia is negligible in this study. Note that the flow rate might vary from one test to another because of the possibility of remnant coating materials from the previous tests. Thus, the systemresistance test should be conducted before each cyclic-loading test of proppant pack.
Fig. 3—System-resistance test with accumulated water as a function of time at a constant water head of 6.5 cm. The solid line is linear fit with a slope of 1.37 g/sec.
A comparison of the permeability obtained from the DCD and API measurements for the same proppant. Fig. 4 shows the permeability of uncoated 20/40-mesh high-strength ceramic proppant as a function of axial stress. The API conductivity data (Conway and Abney 2003) are about 15% lower than the data obtained from the DCD. This is expected because of the
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significant difference in the apparatus’ aspect ratio, where the difference in the wall effect is expected to play an important role. For this consideration, the API permeability measurement is adjusted based on the same dimension of the DCD, and the data are shown as open cycles in Fig. 4. Clearly, the permeability obtained from both techniques are within reasonable agreement.
Fig. 4—Comparison of permeability obtained from the DCD and API measurements for uncoated 20/40-mesh high-strength ceramic proppant.
A typical permeability profile is shown in Fig. 5 for uncoated 20/40-mesh high-strength ceramic proppant after five stress cycles. During the first compression, the permeability decreases dramatically with increasing axial stress. This is directly related to the loss of porosity of the proppant pack under stress as the pack rearranges. In addition, fines are generated from proppant crushing, which is more pronounced at higher stress levels. The permeability continually decreases with each stress cycle. While this permeability loss is not large for this high-strength proppant, it does continue to decline with each stress cycle. This might be caused by the creation of fines.
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Fig. 5—Permeability of uncoated 20/40-mesh high-strength ceramic proppant under cyclic stress.
Effects of Proppant Surface Treatment. In this section, examples of how this device can be used to study the effects of surface modification agent (SMA) coatings on permeability of the proppant pack under cyclic stress are presented. This type of additive will coat the proppant grains instantaneously and does not cure or harden (Nguyen et al. 1998 and 2000). As mentioned in the previous section, only the commercial 20/40-mesh high-strength ceramic proppant was used as received in this study. The permeability profile is similar to those shown in Fig. 5. A good reproducibility can be observed in Fig. 6, where two independent experiments using 3 wt% SMA-coated proppant after hydrothermal exposure to 550°F for 30 days show similar results. Comparison of two proppant-surface treatments is shown in Fig. 7, where water-based SMAs (WBSMAs) are used (Nguyen and Weaver 2010). The data shown are taken from the raw permeability versus stress data at an intermediate stress of 3,000 psi. This resulted in a simple graph showing that uncoated proppant permeability continues to decline with each stress cycle, while the coated proppants do not. Results with 2 and 3 wt% WBSMA show that, after the initial compaction of the proppant pack, little permeability loss was caused by the repeated stress cycle, while the uncoated proppant resulted in more than 10% additional loss. This system was used to evaluate the effect of separately applied hydrothermal conditions (550°F in formation water for 30 days) on proppant by comparing 20/40-mesh high-strength ceramic proppant coated with WBSMA. As can be seen in Fig. 8, the exposure to high temperature caused the uncoated proppant to lose significant permeability after applying stress cycling. However, the WBSMA-coated proppant significantly improved the proppant-pack performance, with 26% permeability improvement in the first cycle, compared to the same coated proppant without exposure to high-temperature treatment. Similar comparison can be seen in Fig. 9 for proppant coated with WBSMA and SMA, along with the data for uncoated proppant. These samples had not been previously exposed to hydrothermal conditions. The permeability of both coated proppants leveled off after the second stress cycle, while the uncoated proppant-pack permeability continued to decrease with each stress cycle. In addition, it seems that the SMA was consistently better than WBSMA in terms of permeability improvement without hydrothermal aging.
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Fig. 6—Reproducibility of permeability measurement under cyclic stress.
Fig. 7—Comparison of permeability at 3,000 psi for WBSMA-coated proppant with uncoated sample.
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Fig. 8—Comparison of permeability at 3,000 psi for coated and uncoated proppant with and without exposure to temperature treatment.
Fig. 9—Comparison of permeability at 3,000 psi for uncoated proppant and with different coatings.
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Cyclic Stress and Simulation. As mentioned in the previous section, three stresses are simultaneously measured during cyclic-loading experiments—axial stress, rear stress, and transverse stress. For clarity, it should be noted that the axial stress and rear stress would be the same if it were not a granular pack, where the friction between particles can partially dissipate some of the energy. The transverse stress is measured to better understand how the stress distribution occurs within the proppant pack. Figs. 10 through 12 show typical stress profiles for 2 wt% WBSMA-coated proppant for five cycles. After the first cycle, all stresses approached reversible status during the loading and unloading process, especially for transverse stress. This indicates that the proppant particles formed an internal structure, which helped maintain constant permeability, as seen in Fig. 7. Indeed, significant stress remained in both rear and transverse stresses when the axial stress had been totally removed. Similar results were seen for uncoated samples. To capture the granular particle behavior under stress, the distinct element method (DEM) was used in a preliminary simulation study. This method, introduced by Cundall (1971), uses a time-stepping algorithm to calculate each particle’s contact by continually applying the law of motion and a force-displacement law. A simple contact force law is used for this simulation: .............................................................................................................................................. (4) where the normal contact force is propotional to the local deformation by the material’s stiffness and is the shear by the friction coefficient. In this study, the number of particles is component of the contact force that can be related to the same as that used in the experiment, and it was assumed that they were spherical with a diameter normally distributed with the 20/40-mesh size. The 9.2 g of 20/40-mesh high-strength ceramic proppant used in the simulation corresponded to about 11,000 particles (see Fig. 13 for the assembly). The stiffness of the proppant can be experimentally obtained by crushing a single 20/40-mesh high-strength ceramic proppant particle, giving a representative value of about 7×106 N/m dependent on the exact size of a particle used for a measurement. It is challenging to accurately obtain the friction coefficient from this experiment; however, a common value of 1 was used for this preliminary study (Ruina and Pratap 2002). To obtain a quasi-steady state for the simulation, the time step should be sufficiently small and was 10-6 sec in this study. It can be seen in Fig. 14 that this simulation matched fairly well with the axial-stress profile from the experiment. This promising preliminary simulation result enables one to further examine the stress distribution through the granular particles under cyclic loading. The porosity of the proppant pack can be calculated from the simulation and related to its permeability (theoretical porosity is directly related to decreases of the chamber volume). In addition, fluid coupling can be incorporated into this simulation by taking into account the fluid/particle interaction, and thus a direct simulation can be made of the permeability changing at various stresses. These additions are planned for future work.
Fig. 10—Axial stress as a function of displacement for 2 wt% WBSMA-coated proppant.
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Fig. 11—Rear stress as a function of displacement for 2 wt% WBSMA-coated proppant.
Fig. 12—Transverse stress as a function of displacement for 2 wt% WBSMA-coated proppant.
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Fig. 13—Visualization of assembly of 11,000 particles of 20/40-mesh high-strength ceramic proppant for simulation.
Fig. 14—Comparison of simulation and experimental data of the axial stress for 11,000 20/40-mesh proppant grains.
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Conclusions The following conclusions are a result of this work. • The bench-top DCD has the ability to compress proppants up to 7,100 psi at a controlled strain rate mode (constant speed). • Cyclic-stress experiments on proppant can be easily achieved with this apparatus, which permits rapid proppantpack analysis. • Permeability obtained from both the DCD and API conductivity cell measurements match fairly well for uncoated commercial 20/40-mesh high-strength ceramic proppant. • WBSMA and SMA coating on the proppant improves the proppant performance in terms of permeability, particularly after the second cyclic loading. Significant improvement can be observed for WBSMA-coated proppants after hydrothermal exposure at 550°F for 30 days. • Preliminary simulation using DEM provides good prediction of the axial stress growth of the proppant pack, which serves as an alternative tool to examine the stress distribution of proppant pack under cyclic loading. It also has potential to provide useful information for permeability simulation by incorporating fluid/particle interaction.
Acknowledgments The authors thank Halliburton management for their support and permission to publish this work. References Conway, M. and Abney, K. 2003. Stimlab Proppant Consortium. Halliburton. Cundall, P.A. 1971. A computer model for simulating progressive large scale movements in blocky rock systems. Paper No. II-8 presented at the Proceeding of the Symposium of the International Society of Rock Mechanics, Nancy, France. Dewprashad, B.T., Weaver, J.D., Nguyen, P.D., and Parker, M. 1999. Modifying Proppant Surface to Enhance Fracture Conductivity. Paper SPE 50733 presented at the International Symposium on Oilfield Chemistry, Houston, Texas, USA, 16–19 February. doi: 10.2118/50733-MS. Holditch, S.A. and Blakeley, D.M. 1992. Flow Characteristics of Hydraulic Fracture Proppants Subjected to Repeated Production Cycles. SPE Prod. Eng. 7 (1): 15–20. doi: 10.2118/19091-PA. Kaufman, P.B., Brannon, H.D., Anderson, R.W., Ziegler, M., Neves, A.R., Parker, M., Abney, K., de Paiva Cortes, G., Joyce, S., Mining, B., and Penny, G.S. 2007. Introducing New API/ISO Procedures for Proppant Testing. Paper SPE 110697 presented at the Annual Technical Conference and Exhibition, Anaheim, California, USA, 11–14. doi: 10.2118/110697-PA. Kawamoto, T., Obara, Y., and Tokashiki, N. 1981. Characteristics of Deformation and Permeability of Fractured Rock. Proceedings of the International Symposium on Weak Rock, Tokyo, Japan, 21–24. Kim, C.M. and Willingham, J.R. 1987. Flow Response of Propped Fracture to Repeated Production Cycles. Paper SPE 16912 presented at the Annual Technical Conference and Exhibition, Dallas, Texas, USA, 27–30. doi: 10.2118/16912-MS. Malone, D.R., Gall, B.L. and Raible, C.J. 1989. Non-Darcy Gas Flow through Propped Fractures: Effects of Partial Saturation, Gel Damage, and Stress. SPE Prod. Eng. 4 (4): 417–422. doi: 10.2118/16899-PA. Nguyen, P.D., Weaver, J.D., and Dewprashad, B.T. 1998. Surface-Modification System for Fracture-Conductivity Enhancement. Paper SPE 48897 presented at the International Conference and Exhibition, Beijing, China, 2–6 November. doi: 10.2118/48897-MS. Nguyen, P.D., Dewprashad, B.T., and Weaver, J.D. 2000. New Approach for Enhancing Fracture Conductivity. SPE Prod. & Facilities 15 (2): 83–89. Nguyen, P.D. and Weaver, J.D. 2010. Enhancing Well Productivity in a Tight-Gas Formation with an Aqueous-Based, SurfaceModification Agent: Laboratory Study. Paper SPE 137136 presented at the Tight Gas Completions Conference, San Antonio, Texas, USA, 2–3 November. doi: 10.2118/137136-MS. Ruina, A. and Pratap, R. 2002. Introduction to Statics and Dynamics. New York: Oxford University Press. Stephens, W.T., Schubarth, S.K., Rivera, D.I., and Herndon, D.C. 2006. Statistical Study of the Crush Resistance Measurement for Ceramic Proppants. Paper SPE 102645 presented at the Annual Meeting, San Antonio, Texas, USA, 24–27. doi: 10.2118/102645-PA. Stephens, W.T., Schubarth, S.K., and Dickson, K.R. 2007. Behavior of Proppants under Cyclic Stress. Paper SPE 106365 presented at the SPE Hydraulic Fracturing Technology Conference, College Station, Texas, USA, 29–31. doi: 10.2118/106365-PA. Weaver, J.D., Baker, J.D., and Parker, M. 1999. Application of Surface Modification Agent in Wells with High Flow Rates. Paper SPE 54645 presented at the Western Regional Meeting, Anchorage, Alaska, USA, 26–27. doi: 10.2118/54645-MS. Weaver, J.D., Nguyen, P.D., Parker, M., and van Batenburg, D. 2005. Sustaining Fracture Conductivity. Paper SPE 94666 presented at the European Formation Damage Conference, Scheveningen, The Netherlands, 25–27 May. doi: 10.2118/94666-MS. Weaver, J.D., Parker, M., van Batenburg, D., and Nguyen, P.D. 2007. Fracture-Related Diagenesis may Impact Conductivity. SPE J. 12 (3): 272–281. doi: 10.2118/98236-PA. Ye, X., Ganley, T., Morris, J.F., Tonmukayakul, N., and Parker, M.A. 2009. Uniaxial Compression of Dense Granular Materials: Stress Distribution and Permeability. J. Petro. Sci. and Eng. 65 (3-4): 193–207. doi: 10.1016/j.petrol.2008.12.034.
