Innov. Infrastruct. Solut. (2017) 2:41 DOI 10.1007/s41062-017-0096-1
PRACTICE-ORIENTED PAPER
Effects of different stress regimes on hydraulic fracture geometry: a particle flow code approach Sajjad Jalili1 • Kaveh Ahangari2
Received: 21 March 2017 / Accepted: 27 June 2017 / Published online: 5 July 2017 Ó Springer International Publishing AG 2017
Abstract Hydraulic fracturing decisions are closely tied to quantitative description of rock mechanical properties and in situ stresses in the subsurface. Geomechanics plays a critical role in successfully optimizing hydraulic fracturing, especially in different stress regimes. For those stress regimes that are not normal, the hydraulic fracture geometry is usually more complex and more difficult to predict and investigate. In this study, a particle flow code (PFC) has been developed to investigate and compare the hydraulic fracture geometry in different stress regimes. The results have demonstrated that hydraulic fracture geometry is closely tied to in situ stress conditions, whereas any change in a predominant stress regime from normal to reverse affects the hydraulic fracture geometry. Based on the developed PFC3D model, in a given fracturing pressure, the width and height of the induced hydraulic fracture in a normal stress regime is higher than a reverse stress regime, while the length of the hydraulic fracture in a reverse stress regime is greater than the normal stress regime. The results from this study can be applied in both planning and real-time decisions during hydraulic fracturing jobs to optimize the operation and prevent any job failure which will in turn affect the ultimate productivity.
& Kaveh Ahangari
[email protected] 1
Department of Petroleum Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2
Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Keywords Hydraulic fracturing Geomechanical analysis Particle flow code (PFC) Stress regimes
Introduction Hydraulic fracturing has been one of the most frequently implemented techniques for increasing the production of oil/gas reservoirs for several decades. Generally, hydraulic fracturing is the pumping of fluids at rates and pressures sufficient to break the rock, ideally forming a fracture with two wings of equal length on both sides of the borehole. In other words, when the pumping pressure exceeds the strength of the rock formation, fractures are induced and propagated into the formation. The fracturing fluid would gradually leak off into the formation, and pressure inside the fracture would fall affecting the geometry of the propagating hydraulic fracture. Then the propping agent is pumped into the fractures to keep them open after pumping. Therefore, a passage with high conductivity is constructed and hydrocarbon can flow into the well from the formation [4]. These induced hydraulic fractures will open in the direction of least principal stress and propagate perpendicular to this direction. One of the important factors that should be considered during hydraulic fracturing planning and real-time operation is hydraulic fracture geometry. In this way, the effect of different parameters such as natural discontinuities on fracture geometry and propagation behavior of hydraulic fracture has been discussed by various authors [1, 3, 10–13, 15–18]. However, the role of stress regime on hydraulic fracture geometry has not been fully investigated. Before planning to do any hydraulic fracturing job, it is very important to know the general orientation and geometry of the induced hydraulic fracture, since the hydraulic fracture design for horizontal and vertical fracture propagation is totally
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different. If the induced hydraulic fracture propagates horizontally, but the well performance calculations and the fracture propagation behavior are based on vertical fracture orientation and geometry, the results can be challenging. In other words, in a planning stage of a hydraulic fracturing job in a reverse stress regime, if the fractures are not considered to be horizontal and are assumed to be vertical, then the productivity and efficiency would be affected in both technical and economical points of view. Fracture geometry is usually described by fracture height, length and width (or aperture) as shown in Fig. 1. On the other hand, hydraulic fracture geometry will be considerably affected by the predominant stress regime. Three in situ stress regimes which are normal faulting, strike-slip faulting and reverse faulting stress regime can be considered to describe the stress states as represented in Fig. 2 [14]. In this way, in normal faulting stress regime, the vertical stress (rv) is greater than the maximum (rH) and minimum (rh) horizontal stress rh \ rH \ rv and in strike-slip faulting stress regime the order is rh \ rv \ rH, while in reverse faulting stress regime the vertical stress is the least principal stress. For those stress regimes that are not normal, the hydraulic fracture geometry is usually more complex and more difficult to predict. Therefore, applying numerical models can be beneficial in such cases. One of those efficient numerical approaches is particle flow code (PFC). The PFC is a distinct element code that represents a rock mass as an assemblage of spherical balls of specified stiffness bonded together with bonds of specified strength at contact points and each bond breakage is assumed to be a microcrack [19]. The main objective of this study was to investigate and compare the hydraulic fracture geometry in normal and reverse stress regimes through PFC.
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Particle flow code (PFC) PFC3D models are generally the movement and interaction of spherical particles by the distinct element method (DEM), as described by Cundall and Strack [2]. The original application of this method was as a tool to perform research into the behavior of granular material, which was through representative elements containing several hundred particles tested numerically. The particle model was used to understand element behavior (in which conditions are uniform), and a continuum method was used to solve real problems that involve complicated deformation patterns (with the element behavior derived from the particle model tests). The task of deriving general constitutive laws from test results on particle assemblies is very difficult, but with the spectacular increase in the power of small computers it is now possible to model entire problems with particles; the constitutive behavior is built into the model automatically. PFC3D is designed to be an efficient tool to model complicated problems in solid mechanics and granular flow. A physical problem that is concerned with the movement and interaction of spherical particles may be modeled directly by PFC3D. It is also possible to create particles of arbitrary shape by attaching two or more particles together, such that each group of particles acts as an autonomous object. PFC3D is also able to model a brittle solid by bonding every particle to its neighbor. The resulting assembly can be regarded as a solid that has elastic properties and can be fractured when bonds break in a progressive manner. PFC3D contains extensive logic to facilitate the modeling of solids as close packed assemblies of bonded particles where the solid may be homogeneous, or it may be divided into a number of discrete regions or blocks. This type of physical system may also be modeled by the distinct element programs UDEC [7] and 3DEC [8], which deal with angular blocks. However, PFC3D has three advantages. First, it is potentially more efficient, since contact detection between circular objects is much simpler than contact detection between angular objects. Second, there is essentially no limit to magnitude of displacement that can be modeled and, third, it is possible for the blocks to break (since they are composed of bonded particles), unlike blocks modeled with UDEC or 3DEC which cannot break [9].
Model construction
Fig. 1 Schematic view of a hydraulic fracture geometry described by height, length and width [5]
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To increase computing speed, we have modeled a part of a sandstone reservoir in such a way that the density of particles is 2.545 g/cm3. Parameters used in the PFC3D model are shown in Table 1.
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Fig. 2 Different faulting stress regimes: a normal fault regime; b strike-slip fault regime; c reverse fault regime [6]
The particles are kept in a reservoir with fixed walls (walls with zero displacement). It is necessary to mention that modeling fluid flow in PFC3D does not allow using circular boundaries. Since PFC3D is unable to build a model with a curved wall, to simulate the model, a polygonal inscribed on the curved walls has been considered. This circular surface includes 48 discrete walls with the same angles and size (Fig. 3). Each sector is 7.5 °. Also, the same method has been used for the wall of the well as well as the circular cap. For simulation of hydraulic fracturing, firstly the model is filled with particles until all particles are deposited under the weight forces. This job is carried out in several steps. At each step, the mean unbalanced force curve (red curve) is depicted. Convergence of the mean unbalanced force toward a constant value in each step indicates that the deposition is completed. Figures 4 and 5 represent the initial and final steps of the particle deposition process. Each peak of the curve represents a step of the deposition. Figure 6 shows the model and particles before fluid injection. As it can be seen from the shape of the contact force, the model is in a state of tranquility and the forces are distributed uniformly. Also, there is no unbalanced Table 1 The parameters used in the PFC3D model
Parameters
Value
Primary porosity
0.3
Normal stiffness
106 N/m
Shear stiffness
106 N/m
Particle density
2.545 g/cm3
Fluid density
1 g/cm3
Fig. 3 Schematic view of the constructed model
force in the system and the mean unbalanced force and maximum unbalanced force are zero.
Results and discussions To investigate the effects of different stress regimes on hydraulic fracture geometry, two PFC3D models were constructed: one in a normal stress regime and the other in a reverse stress regime. The hydraulic fracture geometry has been studied through three values of fracturing pressure (38.14, 39.81 and 40.52 MPa). So, in the first step to simulate a normal stress regime, the values for in situ stresses rv (‘Z’’ direction), rH (‘‘Y’’ direction) and rh (‘‘X’’ direction) were considered to be
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Fig. 4 The first step of particle deposition. The red curve shows the mean unbalanced force converging to zero
Fig. 5 The final step of particle deposition. The red curve shows the mean unbalanced force converging to zero
45, 40 and 30 MPa, respectively. The results of hydraulic fracture geometry in three different fracturing pressures are shown in Table 2. As presented in Table 2, any increase in fracturing pressure in a normal stress regime leads to increasing fracture width, length and height. Figure 7 shows the induced hydraulic fracture propagation in this case. As a matter of fact, the fracture would open in the direction of least resistance and would propagate perpendicular to that. Figure 7 represents the direction of hydraulic fracture opening and propagation which would be parallel to the minimum (along the X direction) and maximum horizontal stress (along the Y direction), respectively. In addition, since the direction of least
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Fig. 6 State of the model before the fluid injection (black lines indicate the contact forces between particles)
principal stress is horizontal, the hydraulic fracture will be vertical and axial. Also, a reverse stress regime has been modeled by PFC3D in such a way that the values for rv (‘Z’’ direction), rH (‘‘Y’’ direction) and rh (‘‘X’’ direction) would be 30, 45 and 40 MPa, respectively. Table 3 and Fig. 8 represent the results of hydraulic fracture geometry in a reverse stress regime. Based on Table 3, it is clearly observed that hydraulic fracture width, length and height will increase by increasing the fracturing pressure. As shown in Fig. 8, in a reverse stress regime, hydraulic fracture opening would be in the direction of rv (‘‘Z’’ direction) and propagation along rh (‘‘X’’ direction). Also, based on Fig. 8, in a reverse stress regime the hydraulic fracture would be horizontal and transverse, since the vertical stress is the least in magnitude. The difference between the two horizontal stresses, which are orthogonal to the wellbore axis, can be influential as well. By comparing the results of hydraulic fracture geometry in normal and reverse stress regime in Tables 2 and 3, one can easily see that the width and height of the induced hydraulic fracture decreased in a reverse stress regime compared to the normal stress regime, while the hydraulic fracture length increased in a reverse stress regime. In other words, since the width and height of the hydraulic fracture in a reverse stress regime are lower than the normal stress regime, proppant bridging and blocking of proppant transport are more challenging in a reverse stress regime. Also, based on Figs. 7 and 8, it is clearly observed that in a normal stress regime the hydraulic fracture is axial, but in a reverse stress regime it is transverse.
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Table 2 Hydraulic fracture geometry in a normal stress regime Fracturing pressure (MPa)
Fracture opening (along the ‘‘X’’ direction, mm)
Fracture length (along the ‘‘Y’’ direction, m)
Fracture height (along the ‘‘Z’’ direction, m)
38.14
20.16
21.82
44
39.81
23.67
30.05
51.36
40.52
30.41
34.86
62.2
Fig. 7 Top view of hydraulic fracture propagation in a normal stress regime
Fig. 8 Hydraulic fracture propagation in a reverse stress regime
Table 3 Hydraulic fracture geometry in a reverse stress regime Fracturing pressure (MPa)
Fracture width (along the ‘‘Z’’ direction, mm)
Fracture length (along the ‘‘X’’ direction, m)
Fracture height (along the ‘‘Y’’ direction, m)
38.14
12.32
28.35
39.62
39.81
17.95
33.27
43.2
40.52
24.12
40.24
51.23
Conclusions A new methodology based on PFC3D was introduced to account for hydraulic fracture geometry in different stress regimes. PFC3D is able to model the movement and interaction of spherical particles by the distinct element method (DEM) and it is a tool to perform research into the behavior of granular materials, like the lithotypes which are found in oil and gas reservoirs. It is clearly observed that the hydraulic fracture geometry will be affected by any change in stress regime, whereas hydraulic fracture width, length and height are not similar in normal and reverse stress regimes. Based on the developed PFC3D model, in a
given fracturing pressure, the width and height of the induced hydraulic fracture in a normal stress regime are higher than a reverse stress regime, while the length of the hydraulic fracture in a reverse stress regime is greater than the normal stress regime. This indirectly means that, in a reverse stress regime, proppant transport inside the induced hydraulic fracture is more crucial than normal stress regime. Also, in a normal stress regime, the induced hydraulic fracture propagates vertically, while in a reverse stress regime it propagates horizontally. The results from this study can be applied to optimize the hydraulic fracturing operation and prevent any job failure which would in turn affect the ultimate productivity.
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Acknowledgements The authors thank the National Iranian South Oil Company (NISOC) for the encouragement and continuous support to publish this paper and also we appreciate Mr. Reza Keshavarzi for his fabulous consultations.
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