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Experimental investigation of hydraulic fracturing in random naturally fractured blocks
International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
Contents lists available at ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Technical Note
Experimental investigation of hydraulic fracturing in random naturally fractured blocks Jian Zhou n, Yan Jin, Mian Chen Faculty of Petroleum Engineering, China University of Petroleum, Beijing 102249, China
a r t i c l e in fo Article history: Received 13 April 2009 Received in revised form 10 May 2010 Accepted 5 July 2010 Available online 17 July 2010
1. Introduction Hydraulic fracturing has become a valuable technique for the stimulation of oil and gas reservoirs in a variety of reservoir rocks. In naturally fractured oil and gas reservoirs, the widely held assumption that the hydraulic fracture is an ideal, simple, straight, bi-wing, but planar feature is untenable because of pre-existing natural fractures. In naturally fractured reservoirs, due to interaction with pre-existing natural fractures, the fracture may propagate asymmetrically or in multiple strands or segments. Natural fractures are ubiquitous features whose effect on the hydraulic fractures depends on ancillary treatment and such reservoir parameters as the treating pressure, in-situ stresses, orientations of natural fractures and permeability. The presence of natural fractures alters the way the induced fracture propagates through the rock. Experimental investigation [1–3] has shown that the propagating fracture crosses the natural fracture, turns into the natural fracture, or in some cases, turns into the natural fracture for a short distance, then breaks out again to propagate in a mechanically more favorable direction, depending primarily on the orientation of the natural fracture relative to stress field. Recently, several field and lab experimental studies have been done in the past to investigate the effect of single natural fracture on the propagation of an induced hydraulic fracture. Blanton [4] found that hydraulic fractures are unperturbed and cross pre-existing fractures only under high differential stress conditions and high angle of approach. Warpinski and Teufel [5] conducted mineback experiments to study the effect of geologic discontinuities on the hydraulic fracture propagation. A fracture
n
Corresponding author. Tel.: +3115 278 3942. E-mail address: [email protected] (J. Zhou).
1365-1609/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2010.07.005
interaction criterion to predict whether the induced fracture causes a shear slippage on single natural fracture plane leading to arrest of the propagating fracture or dilates the single natural fracture causing excessive leak-off is promoted. As to multi-fractured medium, the effect of discontinuities on the hydraulic fracture propagation was analyzed through a series of experiments on Portland cement blocks [6–7]. Multiple factors are decided by a series of natural fractures’ parameters such as aperture, conditions of filled, and it also related to fracture transmissivity [8]. Many field studies [9–11] conducted in naturally fractured formations reveal that the effects of natural fractures on fracture propagation are enhanced fluid leak-off, premature screen-out, arrest of the fracture propagation, formation of multiple fractures, fracture offsets and high net pressures. Regarding far-field hydraulic fracture geometry: it would be more likely to have fractures with wings diverted at different angles or with truncated wings of different lengths [4]; stress ratios of horizontal maximum to minimum below approximately 1.5–1.0 showed proportionally increasing branching and fracture multiplicity with proportionally decreasing stress orientation [12]. The fracture follows the local path of least resistance, not the global path, and this leads to substantial branching, presence of extensive shear fractures, and a growth pattern that is dominated by conditions at the tip of the propagating fracture, thus making its growth haphazard and off balance in naturally fractured reservoir [13]. Mineback studies showed that fracture patterns can be readily divided into four categories. One of the categories is circular or ring fractures. The ring fractures were found over or close to the end of the packers [14]. Our objective here is to investigate the effect of random natural fractures on hydraulic fracture, relating the phenomena derived from a series of tri-axial experiments on observed fracture propagation behaviors. In addition, the possibility of using minifracturing to determine the minimum stress in random naturally fractured blocks is explored.
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J. Zhou et al. / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
2. Experimental setup and procedure 2.1. Experimental preparation In the past, scaling laws for performing proper hydraulic fracture experiments were derived [15]. These laws scale the experiments in terms of energy rates associated with fluid flow, fracture opening and rock separation. In view of the low injection rate in the laboratory, it is necessary to use highly viscous fluids. Also, we use a material with low fracture toughness for our experiments. When the block has conductive pre-existing fracture, another scale factor for the stresses appears, since the fracture aperture depends on the average stress level. For given fracture stiffness, the conductivity will be strongly influenced by the stress level. For instance in the Barton–Bandis joint model the aperture is given by [16] Un ¼
sn i ÞÞ Kn0 ð1 þðsn =Kn0m Um
ð1Þ
i is the maximum allowable in which sn is the confining stress, Um joint closure at the first load cycle and Kn0 is the initial normal stiffness of the discontinuity. From this relation we derive a characteristic stress sn,D that can be used for scaling of the stresses:
sn,D ¼
sn i K Um n0
The wellbores were drilled with a depth and a diameter, which are 140 and 10 mm, respectively. Then a mental tubing with an inside diameter of 6 mm was inserted into wellbores followed with a naked borehole completion, leaving a central 10 mm open borehole section in central of blocks for fracture initiation (Fig. 3). Guar fracturing fluid with a viscosity of 135 mPa s was employed during the tests. Meanwhile, a red agent was added into the fracturing fluid for better tracing of hydraulic fractures. In addition, a constant flow rate was adopted and its value is 4.2 10 9 m3/s. In this condition, the maximum injection fluid pressure observed in our tests is 19.28 MPa. One of a key point of the experiments of hydraulic fracturing is in-situ stresses simulation. We conducted our experiments in a normal-faulting stress regime. In this case, the maximum stress was vertical, and the constant value of vertical stress sv was 20 MPa. Meanwhile, we used two types of the horizontal stress difference, which was 5 and 10 MPa, respectively.
ð2Þ
In the absence of natural fractures, we perform tests at in-situ stress, but when we introduce joints, the stress level should also scale with the natural fracture stiffness. We chose the applied stress level to ensure open discontinuities in the model block. In that way, we will have the possibility for fluid flow into the natural fractures. We use now stresses that are much lower compared with fracture pressure. One should therefore be careful in extrapolating the test results to field conditions. The pertinence incarnated in establishing the interaction of hydraulic fractures with natural fractures in physical models. 2.2. Experimental set up and model block preparation The experiments were performed in a tri-axial pressure machine (Fig. 1). Cubic model blocks of 300 mm on a side were positioned in between the pressurised pistons for simulating insitu stress conditions. Meanwhile, the pressure platens were equipped with spherical sheets to ensure equal pressure distribution [17]. Between the model block and the pressure platen, we inserted a thin Teflon sheet covered on both sides with Vaseline for avoiding shear stress. The injection pressure is controlled by a servo hydraulic pump of MTS 816 and the maximum capacity of fluid injection pressure is 140 MPa. The blocks were prepared with a mixture of cement no. 325 and fine sand with constant mass ratio is 1:1. After being mixed with water homogeneously, the fluid of cement was stored into a mental mould with an inner space of a cubic of 300 mm and kept for two weeks. The following was heating process on purpose of making random fractures. These blocks were transferred to a large oven and heated there with a constant temperature 400 1C for three hours, then dealing with natural air cooling. Because of dehydration during the heating process, random shrinkage cracks formed both inside and outside of these blocks (Fig. 2). Before heating process, we sampled one of these blocks and did rock mechanic test and permeability test for investigating the following parameters (Table 1). With low permeability and porosity of matrix, it is easier to detect the impact of random natural factures on hydraulic fracture during our tests via pressure profiles.
3. Experimental results and interpretation 3.1. Influence of in-situ stress and natural fractures on geometry of hydraulic fractures Renshaw [18] found hydraulic fracture tends to be a single, straight fracture in conditions of high differential stress. The effect of the horizontal stress on the hydraulic fracture geometry was determined in our test with a different value for Kh, which is defined as Kh ¼
sH sh sh
ð3Þ
in which Kh is the horizontal stress difference (dimensionless), sH is the maximum horizontal principal stress (MPa) and sh is the minimum horizontal principal stress (MPa). Table 2 illustrated insitu stress condition during our experiments, in which sV is vertical stress, in MPa. In this situation, hydraulic fracture could be a vertical, straight, bi-wing, planar fracture if we did not make natural fractures according to previous research. The Kh value in our tests changed from 1 to 10. Three types of geometry were observed in our tests (Fig. 4). The first is a vertical dominating facture with multiple branches, which was created at high difference of horizontal stress (samples 1 and 2). In this case, dominating fracture still propagated close to the preferred direction, which is the direction of maximum horizontal stress (Fig. 5 and Fig. 6). The second is radial net-fractures around wellbore at low difference of horizontal stress (sample 6) and the net-natural fractures system dominated the geometry of hydraulic fracture (Fig. 7). The third is partly vertical fracture with random branches (samples 3–5). Here, only one wing of vertical, dominating fracture was created with small branches and propagated along the preferred direction, on the other wing, fracture geometry was dominated by random natural fractures. The results demonstrated that hydraulic fracture would propagate along the direction of maximum horizontal stress at a large differential stress and natural fractures could lead to lots of random branches. Different geometries could be reflected by their significant pressure profiles. Fig. 8 indicated two types of special pressure curves in our tests, which could interpret different propagations of hydraulic fractures. The solid line represents the pressure profile of sample 1, and it fluctuated with an extremely high frequency during the whole propagation. It means small cracks adjacent to dominating fracture opened and closing frequently due to injection pressure and fluids leak-off during the injecting time. The dash line represents another type of pressure profile (sample 6). In its injecting process, pressure changed very slowly
J. Zhou et al. / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
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Fig. 1. Schematic diagram of tri-axial hydraulic fracturing test system.
Hydraulic fluid injection
Unit: cm
Wellbore
O- ring
Open hole section Fig. 2. Random natural fractures on the surface of a block after heat and air cooling treatments. Table 1 Parameters of blocks before heat treatment.
Table 2 Summary of in-situ stress conditions.
Symbol
Parameter
Value
Units
E u
Young’s modulus Poisson’s ratio Unconfined compressive strength Permeability Porosity
8.402 0.23 28.34 0.1 1.85%
GPa
sc k
f
Fig. 3. Schematic of inside structure of a block. The length of open borehole is 10 mm.
MPa mD
or smoothly compared with sample 1. It was evident that fluid injection caused the opening of natural fracture system of the block and it reached a balance between fluids injection and fluid leak-off into random network of natural fractures. Both of in-situ stress and naturally fracture system controls geometry of hydraulic fracture, and sometimes one could dominate fracture geometry individually when the other was comparably weak.
Sample number
sV MPa
sH MPa
sh MPa
Kh (dimensionless)
1 2 3 4 5 6
20 20 20 20 20 20
11 6 10 15 8 10
1 1 3 5 3 5
10 5 2.3 2 1.7 1
3.2. The impact of random fractures on estimating the minimum stress Mini-fracturing test remains the most reliable method of determining the minimum (usually horizontal) in-situ stress of
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10 Vertical main fracture with multiple branches
Horizontal stress difference Kh
9 8
Partly Vertical fracture with random branches
7
Radial random net-fractures
6 5 4 3
Fig. 6. Partly vertical fracture with random branches (sample 4).
2 1
1
2 3 4 5 Sample number
6
Fig. 4. Relationship between geometry of hydraulic fractures and horizontal stress difference.
Fig. 7. Radial random net-fractures at low difference of horizontal stress (sample 6).
16
Pressure / MPa
14 12 10 Radial net-fractures (number 6)
8 6 4
Fig. 5. Dominating fracture with multiple branches at large difference of horizontal stress (sample 1).
Main fracture with multiple branches (number 1)
2 0
petroleum engineering [19]. In naturally fractured reservoirs, natural fractures could lead to negative effect on estimating the minimum horizontal stress when using mini-fracturing tests. We could pre-set the horizontal stresses in our tri-axial machine, then the negative effect of natural fractures on estimating minimum horizontal stress could be assessed by using minifracturing tests. Before that, a comparable sample was tested by minifracturing test. This block was made together with others except
0
200
400
600
800 1000 1200 1400 1600 Time / s
Fig. 8. Pressure signals of radial random net-fractures and dominating fracture with multiple branches.
the process of heating and air cooling so that it is just pure cement block without random natural fractures in it. With its results we could calibrate the effect of natural fractures. A coefficient of error
Sample
sV (MPa)
sH (MPa)
sh (MPa)
Kh
pc (MPa)
Zh
M-comp Min-1 Min-2 Min-3 Min-4 Min-4 Min-6 Min-7 Min-8 Min-9
20 20 20 20 20 20 20 20 20 20
15 10 15 10 15 10 10 11 11 11
5 5 5 5 5 3 3 1 1 1
2 1 2 1 2 2.3 2.3 10 10 10
6.49 5.83 6.00 5.77 5.81 3.50 3.47 1.32 1.29 1.35
0.298 0.166 0.200 0.154 0.162 0.167 0.157 0.320 0.290 0.350
for estimating the least stress was defined as
Zf ¼
pc sh
P/pump dP/dG GdP/dG
13 12 11 10 9 8 7 6 5 4 3 2 1 0
13 12 11 10 9 8 7 6 5 4 3 2 1 0
B
A
0.0
ð4Þ
sh
Pressure / MPa
Table 3 Summary of in-situ stress condition and results of mini-fracturing tests.
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0.5
1.0
1.5
GdP/ dG or dP / dG
J. Zhou et al. / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
2.0
G function Fig. 9. Analysis of closure pressure using G-function (sample Min-2).
in which Zf donates coefficient of error for estimating of the least stress (dimensionless), sh donates the minimum horizontal principal stress (MPa) and pc donates closure pressure (MPa). When designing the mini-fracturing tests, the influence of in-situ stress was also considered. Stress conditions and results of minifracturing tests are listed in Table 3. The G-function is widely used to estimate closure pressure of certain formation in petroleum industry [20], in which the pressure decline between the time of shut-in and re-injection is introduced to make an analysis: GðDtD Þ ¼
4
p
gðDtD Þg0
ð5Þ
where g(DtD) is the dimensionless fluid-loss volume function and g0 the value of g(DtD) at the moment of shut-in. For a wall-building fluid with a Newtonian filtrate, the value of area exponent a is in the range of 0.5 and 1. The lower bound of area exponent a is 0.5, corresponding for a low fluid efficiency, then the calculation is as follows:
Z-0 gðDtD Þ ¼ ð1þ DtD Þarcsinð1 þ DtD Þ1=2 þ DtD 1=2 g0 ¼ p=2 ð6Þ The upper bound of area exponent a is 1, corresponding for a high fluid efficiency, then as the following: h i Z-1 gðDtD Þ ¼ 43 ð1 þ DtD Þ3=2 DtD 3=2 g0 ¼ 4=3 ð7Þ where DtD is the dimensionless shut-in time, which is calculated by
DtD ¼
ttP Dt ¼ tP tP
ð8Þ
where t is the time, tP is the pumping time and Dt is the shut-in time. Finally, other intermediate values of g(DtD) and g0 at any other value of area exponent a can be obtained through simple interpolation between bounding values. Fig. 9 shows G-function curves of Min-2. An obvious dP/dG decline as well as an increasing of the value of GdP/dG to point A was observed between 0.0 and 1.0 of G-function and it demonstrated a dominating hydraulic fracture is closing due to shut-in of the injection pump. After that there is no obvious increase of GdP/dG, so that we could determine the corresponding point B is the closure pressure and its value is 6.0 MPa. After the closure of hydraulic fracture, some fluid leak-off continued, which led to small declines both of pressure and dP/dG from 1.25 to 2.0. With the in-situ stress listed in Table 3, hydraulic fracture could be a simple, vertical, planar fracture that opened against the least tress. Hydraulic fracture of Mini-compare included all above characters although it was a mini-fracturing test (Fig. 10). The closure pressure of min-compare was 6.49 MPa, which was more
Fig. 10. Simple, vertical and planar hydraulic fracture of Min-compare.
than actual the minimum stress, 5 MPa. Obviously, closure pressure is higher than constant confining pressure and the coefficient is 0.298. The coefficients of error from Min-2 to Min-6 were more close to real confining pressure compared with Mincompare because most of fracturing fluid came into random natural fractures and ideal hydraulic fractures did not exist in these blocks in the situation of the lower differential stresses. On the other hand, the coefficients of error of Min-7 to Min-9 were a little more than that of Min-compare. In the situation of the higher differential stresses, dominating fractures with multiple branches were created in these blocks. Natural fractures in these blocks lowered the value Zf for closure pressure estimation, which is 21.8% on average. There were some different pressure profiles between the tests with random natural fractures and the test without natural fractures during mini-fracturing tests. Fig. 11 is the pressure curves of Min-compare (without natural fractures) and Min-2 (with random natural fractures). Break-down pressure was very clear in those two pressure curves and it indicated that hydraulic fracture initiated and propagated from borehole of wellbore successfully. Shut-in of injection was carried out shortly after hydraulic fracture propagating from wellbore because of limited size of blocks. Instantaneous shut-in pressure could easily be recognized in pressure curve of Min-compare because it is a homogenous block and there was no natural fracture in it. And its
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J. Zhou et al. / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
18
but must be at least equal to the minimum confining stress sh. Thus the stress ratio is approximately (sH sh)/sh. This is equivalent to the parameter Kh defined by in eq. (3). Renshaw and Pollard showed that the critical value of the stress ratio required for the pre-existing fracture to arrest the propagating fracture depends on the coefficient of friction along the preexisting fracture. But for typical values of the coefficient of friction m for rock and cement ( 0.4 o m o 1.0), the critical stress ratio is about 1–2 (Fig. 7 of [22]). Thus, for Kh larger than about 2, we expect that the hydraulic fracture can propagate across the preexisting fractures and the hydraulic fracture geometry to be more or less planar. In contrast, for Kh value of about 2 or less, we can expect the pre-existing fractures to arrest the propagation of the hydraulic fracture and the hydraulic fracture geometry to be complex. These expectations agree well with our results.
Shut-in
16
Pressure / MPa
14 12 10 8 6 4 With natural fractures (Min-2)
2
Without natural fractures (Mincompare)
0 0
200
400
600
800
1000
1200
Times / s
5. Conclusion
Fig. 11. Pressure signals of Min-compare and Min-2.
leak-off fitted Carter leak-off model [21] because hydraulic fracture was an ideal bi-wing planar fracture here (Fig. 10). But from pressure curve of Min-2, it is difficult to determine the instantaneous shut-in pressure directly. Besides, after the test we found random natural fractures totally arrested hydraulic fracture. It means most of its leak-off depended on random natural fracture system. After restarting the injection, the frequency of pressure curve fluctuating in test of Min-2 is obviously higher than that of Min-compare and it indicated that random natural fractures opened and closed frequently during reinjection process.
4. Discussion Blanton [3] and Warpinski and Teufel [5] found that differential stresses and the angle of approach are most important factors to control fracture propagation behavior in this situation. They found that hydraulic fracture tends to cross pre-existing fractures only under high differential stresses and high angles of approach. At intermediate and low differential stresses and angles of approach pre-existing fractures tend either to open and divert fracturing fluid or arrest propagation of the hydraulic fracture. Their conclusions are based on the same assumption that fracture interaction is between hydraulic fracture and a single natural fracture. Based on their work, the systematic experiments in heated cements were designed and performed for investigating the influence of random natural fractures on hydraulic fracture. Renshaw and Pollard [22] proposed a simple criterion for the state of stress required for a pre-existing fracture to impact the propagation of a fracture. Consider a pre-existing fracture parallel to the least compressive stress sh and a growing fracture propagating parallel to the most compressive horizontal stress sH. Renshaw and Pollard proposed that whether or not the preexisting fracture would impact the growth of the propagating fracture depended on the stress ratio sH/(T0 + sh), where T0 is the tensile strength of the material (MPa). We assume that sh 5T0 (the tensile strength of concrete is often about an order of magnitude less than its compressive strength – much less for fractured concrete such as considered here). Also, the numerator of the stress ratio, which is related to the frictional strength of the unbonded interface, needs to be modified to account for the leakage of the injection fluid into the pre-existing fracture. Thus the stress ratio can be written as (sH P)/sh. The fluid pressure at the tip of the propagating fracture is less than that at the wellbore,
Laboratory experiments were performed to investigate the influence of random natural fracture system on geometry and propagation behaviors of hydraulic fractures. Both random natural fractures and differential in-situ stresses dominated geometry and propagating behaviors. Hydraulic fracture tended to be a dominating fracture with random multiple branches at high difference of horizontal stresses. On the other hand, it tended to be partly vertical, planar fracture with branches at low difference of horizontal stresses. Natural fracture system with a high strength of network could dominate geometry of hydraulic fracture also, where it was radial random net-fractures in our tests. Pressure profiles could reflect different characters of propagating behaviors. Random small natural fractures could lead to high frequency of pressure fluctuating during fracture propagation. Also, natural fractures with strong network could lead to more smooth pressure during injection. The closure pressure is higher than confining pressure estimated by mini-fracturing tests in our tight cement blocks. In presence of random natural fractures, this method is still reliable if fracture geometry is a vertical, dominating one (even partly). Because of these random natural factures, the value Zf for closure pressure estimation is on average lower than that of without natural fractures in our tests, which are 21.8 and 29.8%, respectively.
Acknowledgments This work is financially supported by the National Natural Science Foundation of China (Grant no. 90510005) and partly by ‘‘Innovation Group’’ Foundation of Ministry of Education of China (Authorized no. IRT0411). We also thank C.J. de Pater and the reviewers for their beneficial suggestions for improving the paper. References [1] Daneshy AA. Hydraulic fracture propagation in the presence of planes of weakness. In: Proceedings of the SPE European spring meeting, 29–30 May 1974, Amsterdam, paper SPE 4852. [2] Lamont N, Jessen F. The effects of existing fractures in rocks on the extension of hydraulic fractures. J Petrol Technol 1963:203–9. [3] Blanton TL. An experimental study of interaction between hydraulically induced and pre-existing fractures. In: Proceedings of the SPE/DOE symposium on unconventional gas, 16–18 May 1982, Pittsburgh, paper SPE 10847. [4] Blanton TL. Propagation of hydraulically and dynamically induced fractures in naturally fractured reservoirs. In: Proceedings of the SPE/DOE symposium on unconventional gas, 18–21 May 1986, Louisville, Kentucky, paper SPE 15261. [5] Warpinski N, Teufel LW. Influence of geologic discontinuities on hydraulic fracture propagation. J Petrol Technol 1987:209–20. [6] Beugelsdijk LJL, de Pater CJ, Sato K. Experimental hydraulic fracture propagation in multi-fractured medium. In: Proceedings of the SPE Asia
J. Zhou et al. / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
[7]
[8] [9]
[10]
[11]
[12] [13]
Pacific conference on integrated modeling, 25–26 April 2000, Yokohoma, paper SPE 59419. de Pater CJ, Beugelsdijk LJL. Experiments and numerical simulation of hydraulic fracturing in naturally fractured rock. In: Proceedings of the 40th US symposium on rock mechanics, Anchorage, 25–29 June 2005. Zimmerman RW, Bodvarsson GS. Hydraulic conductivity of rock fractures. Transp Porous Media 1996;23:1–30. Britt LK, Hager CJ. Hydraulic fracturing in a naturally fractured reservoir. In: Proceedings of the SPE international petroleum conference exhibition, 10–13 October 1994, Veracruz, Mexico, paper SPE 28717. Rodgerson JL. Impact of natural fractures in hydraulic fracturing of tight gas sands. In: Proceedings of the SPE Permian basin oil & gas recovery conference, 21–23 March 2000, Midland, Texas, SPE 59540. Azeemuddin M, Ghori SG, Saner S, Khan MN. Injection-induced hydraulic fracturing in a naturally fractured carbonate reservoir: a case study from Saudi Arabia. In: Proceedings of the SPE international symposium & exhibition on formation damage control, 20–21 February 2002, Lafayette, Louisiana, SPE 73784. Doe TW, Boyce G. Orientation of hydraulic fractures in salt under hydrostatic and non-hydrostatic stresses. Int J Rock Mech Min Sci 1989;26:605–11. Daneshy AA. Off-balance growth: a new concept in hydraulic fracturing. J Petrol Technol 2003:78–85.
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[14] Wawersik WR, Stone CM. A characterization of pressure records in inelastic rock demonstrated by hydraulic fracturing measurements in salt. Int J Rock Mech Min Sci 1989;26:613–27. [15] de Pater CJ, et al. Experimental verification of dimensional analysis for hydraulic fracturing. SPE Prod Facil 1994:230. [16] Bandis SC, et al. Application of a new numerical model of joint behavior to rock mechanics problems. In: Proceedings of the international conference on ˚ p. 345–56. rock joints, September 1985, Lulea, [17] Jian Z, et al. Analysis of fracture propagation behavior and fracture geometry using a tri-axial fracturing system in naturally fractured reservoirs. Int J Rock Mech Min Sci 2008;45:1143–52. [18] Renshaw CE. Are large differential stresses required for straight fracture propagation paths. J Struct Geol 1994;16(6):817–22. [19] de Bree P, Walters JV. Micro/Minifrac test procedures and interpretation for in situ stress determination. Int J Rock Mech Min Sci 1989;26(6):512–5. [20] Nolte KG, Smith MB. Interpretation of fracturing pressures. J Petrol Technol 1981:271. [21] Howard GC, Fast CR. Optimum fluid characteristics for fracture extension. Drill Prod Pract 1957;24:261–70. [22] Renshaw CE, Pollard DD. An experimentally verified criterion for propagation across unbonded frictional interfaces in brittle, linear elastic materials. Int J Rock Mech Min Sci 1995;32:237.
Contents lists available at ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Technical Note
Experimental investigation of hydraulic fracturing in random naturally fractured blocks Jian Zhou n, Yan Jin, Mian Chen Faculty of Petroleum Engineering, China University of Petroleum, Beijing 102249, China
a r t i c l e in fo Article history: Received 13 April 2009 Received in revised form 10 May 2010 Accepted 5 July 2010 Available online 17 July 2010
1. Introduction Hydraulic fracturing has become a valuable technique for the stimulation of oil and gas reservoirs in a variety of reservoir rocks. In naturally fractured oil and gas reservoirs, the widely held assumption that the hydraulic fracture is an ideal, simple, straight, bi-wing, but planar feature is untenable because of pre-existing natural fractures. In naturally fractured reservoirs, due to interaction with pre-existing natural fractures, the fracture may propagate asymmetrically or in multiple strands or segments. Natural fractures are ubiquitous features whose effect on the hydraulic fractures depends on ancillary treatment and such reservoir parameters as the treating pressure, in-situ stresses, orientations of natural fractures and permeability. The presence of natural fractures alters the way the induced fracture propagates through the rock. Experimental investigation [1–3] has shown that the propagating fracture crosses the natural fracture, turns into the natural fracture, or in some cases, turns into the natural fracture for a short distance, then breaks out again to propagate in a mechanically more favorable direction, depending primarily on the orientation of the natural fracture relative to stress field. Recently, several field and lab experimental studies have been done in the past to investigate the effect of single natural fracture on the propagation of an induced hydraulic fracture. Blanton [4] found that hydraulic fractures are unperturbed and cross pre-existing fractures only under high differential stress conditions and high angle of approach. Warpinski and Teufel [5] conducted mineback experiments to study the effect of geologic discontinuities on the hydraulic fracture propagation. A fracture
n
Corresponding author. Tel.: +3115 278 3942. E-mail address: [email protected] (J. Zhou).
1365-1609/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2010.07.005
interaction criterion to predict whether the induced fracture causes a shear slippage on single natural fracture plane leading to arrest of the propagating fracture or dilates the single natural fracture causing excessive leak-off is promoted. As to multi-fractured medium, the effect of discontinuities on the hydraulic fracture propagation was analyzed through a series of experiments on Portland cement blocks [6–7]. Multiple factors are decided by a series of natural fractures’ parameters such as aperture, conditions of filled, and it also related to fracture transmissivity [8]. Many field studies [9–11] conducted in naturally fractured formations reveal that the effects of natural fractures on fracture propagation are enhanced fluid leak-off, premature screen-out, arrest of the fracture propagation, formation of multiple fractures, fracture offsets and high net pressures. Regarding far-field hydraulic fracture geometry: it would be more likely to have fractures with wings diverted at different angles or with truncated wings of different lengths [4]; stress ratios of horizontal maximum to minimum below approximately 1.5–1.0 showed proportionally increasing branching and fracture multiplicity with proportionally decreasing stress orientation [12]. The fracture follows the local path of least resistance, not the global path, and this leads to substantial branching, presence of extensive shear fractures, and a growth pattern that is dominated by conditions at the tip of the propagating fracture, thus making its growth haphazard and off balance in naturally fractured reservoir [13]. Mineback studies showed that fracture patterns can be readily divided into four categories. One of the categories is circular or ring fractures. The ring fractures were found over or close to the end of the packers [14]. Our objective here is to investigate the effect of random natural fractures on hydraulic fracture, relating the phenomena derived from a series of tri-axial experiments on observed fracture propagation behaviors. In addition, the possibility of using minifracturing to determine the minimum stress in random naturally fractured blocks is explored.
1194
J. Zhou et al. / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
2. Experimental setup and procedure 2.1. Experimental preparation In the past, scaling laws for performing proper hydraulic fracture experiments were derived [15]. These laws scale the experiments in terms of energy rates associated with fluid flow, fracture opening and rock separation. In view of the low injection rate in the laboratory, it is necessary to use highly viscous fluids. Also, we use a material with low fracture toughness for our experiments. When the block has conductive pre-existing fracture, another scale factor for the stresses appears, since the fracture aperture depends on the average stress level. For given fracture stiffness, the conductivity will be strongly influenced by the stress level. For instance in the Barton–Bandis joint model the aperture is given by [16] Un ¼
sn i ÞÞ Kn0 ð1 þðsn =Kn0m Um
ð1Þ
i is the maximum allowable in which sn is the confining stress, Um joint closure at the first load cycle and Kn0 is the initial normal stiffness of the discontinuity. From this relation we derive a characteristic stress sn,D that can be used for scaling of the stresses:
sn,D ¼
sn i K Um n0
The wellbores were drilled with a depth and a diameter, which are 140 and 10 mm, respectively. Then a mental tubing with an inside diameter of 6 mm was inserted into wellbores followed with a naked borehole completion, leaving a central 10 mm open borehole section in central of blocks for fracture initiation (Fig. 3). Guar fracturing fluid with a viscosity of 135 mPa s was employed during the tests. Meanwhile, a red agent was added into the fracturing fluid for better tracing of hydraulic fractures. In addition, a constant flow rate was adopted and its value is 4.2 10 9 m3/s. In this condition, the maximum injection fluid pressure observed in our tests is 19.28 MPa. One of a key point of the experiments of hydraulic fracturing is in-situ stresses simulation. We conducted our experiments in a normal-faulting stress regime. In this case, the maximum stress was vertical, and the constant value of vertical stress sv was 20 MPa. Meanwhile, we used two types of the horizontal stress difference, which was 5 and 10 MPa, respectively.
ð2Þ
In the absence of natural fractures, we perform tests at in-situ stress, but when we introduce joints, the stress level should also scale with the natural fracture stiffness. We chose the applied stress level to ensure open discontinuities in the model block. In that way, we will have the possibility for fluid flow into the natural fractures. We use now stresses that are much lower compared with fracture pressure. One should therefore be careful in extrapolating the test results to field conditions. The pertinence incarnated in establishing the interaction of hydraulic fractures with natural fractures in physical models. 2.2. Experimental set up and model block preparation The experiments were performed in a tri-axial pressure machine (Fig. 1). Cubic model blocks of 300 mm on a side were positioned in between the pressurised pistons for simulating insitu stress conditions. Meanwhile, the pressure platens were equipped with spherical sheets to ensure equal pressure distribution [17]. Between the model block and the pressure platen, we inserted a thin Teflon sheet covered on both sides with Vaseline for avoiding shear stress. The injection pressure is controlled by a servo hydraulic pump of MTS 816 and the maximum capacity of fluid injection pressure is 140 MPa. The blocks were prepared with a mixture of cement no. 325 and fine sand with constant mass ratio is 1:1. After being mixed with water homogeneously, the fluid of cement was stored into a mental mould with an inner space of a cubic of 300 mm and kept for two weeks. The following was heating process on purpose of making random fractures. These blocks were transferred to a large oven and heated there with a constant temperature 400 1C for three hours, then dealing with natural air cooling. Because of dehydration during the heating process, random shrinkage cracks formed both inside and outside of these blocks (Fig. 2). Before heating process, we sampled one of these blocks and did rock mechanic test and permeability test for investigating the following parameters (Table 1). With low permeability and porosity of matrix, it is easier to detect the impact of random natural factures on hydraulic fracture during our tests via pressure profiles.
3. Experimental results and interpretation 3.1. Influence of in-situ stress and natural fractures on geometry of hydraulic fractures Renshaw [18] found hydraulic fracture tends to be a single, straight fracture in conditions of high differential stress. The effect of the horizontal stress on the hydraulic fracture geometry was determined in our test with a different value for Kh, which is defined as Kh ¼
sH sh sh
ð3Þ
in which Kh is the horizontal stress difference (dimensionless), sH is the maximum horizontal principal stress (MPa) and sh is the minimum horizontal principal stress (MPa). Table 2 illustrated insitu stress condition during our experiments, in which sV is vertical stress, in MPa. In this situation, hydraulic fracture could be a vertical, straight, bi-wing, planar fracture if we did not make natural fractures according to previous research. The Kh value in our tests changed from 1 to 10. Three types of geometry were observed in our tests (Fig. 4). The first is a vertical dominating facture with multiple branches, which was created at high difference of horizontal stress (samples 1 and 2). In this case, dominating fracture still propagated close to the preferred direction, which is the direction of maximum horizontal stress (Fig. 5 and Fig. 6). The second is radial net-fractures around wellbore at low difference of horizontal stress (sample 6) and the net-natural fractures system dominated the geometry of hydraulic fracture (Fig. 7). The third is partly vertical fracture with random branches (samples 3–5). Here, only one wing of vertical, dominating fracture was created with small branches and propagated along the preferred direction, on the other wing, fracture geometry was dominated by random natural fractures. The results demonstrated that hydraulic fracture would propagate along the direction of maximum horizontal stress at a large differential stress and natural fractures could lead to lots of random branches. Different geometries could be reflected by their significant pressure profiles. Fig. 8 indicated two types of special pressure curves in our tests, which could interpret different propagations of hydraulic fractures. The solid line represents the pressure profile of sample 1, and it fluctuated with an extremely high frequency during the whole propagation. It means small cracks adjacent to dominating fracture opened and closing frequently due to injection pressure and fluids leak-off during the injecting time. The dash line represents another type of pressure profile (sample 6). In its injecting process, pressure changed very slowly
J. Zhou et al. / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
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Fig. 1. Schematic diagram of tri-axial hydraulic fracturing test system.
Hydraulic fluid injection
Unit: cm
Wellbore
O- ring
Open hole section Fig. 2. Random natural fractures on the surface of a block after heat and air cooling treatments. Table 1 Parameters of blocks before heat treatment.
Table 2 Summary of in-situ stress conditions.
Symbol
Parameter
Value
Units
E u
Young’s modulus Poisson’s ratio Unconfined compressive strength Permeability Porosity
8.402 0.23 28.34 0.1 1.85%
GPa
sc k
f
Fig. 3. Schematic of inside structure of a block. The length of open borehole is 10 mm.
MPa mD
or smoothly compared with sample 1. It was evident that fluid injection caused the opening of natural fracture system of the block and it reached a balance between fluids injection and fluid leak-off into random network of natural fractures. Both of in-situ stress and naturally fracture system controls geometry of hydraulic fracture, and sometimes one could dominate fracture geometry individually when the other was comparably weak.
Sample number
sV MPa
sH MPa
sh MPa
Kh (dimensionless)
1 2 3 4 5 6
20 20 20 20 20 20
11 6 10 15 8 10
1 1 3 5 3 5
10 5 2.3 2 1.7 1
3.2. The impact of random fractures on estimating the minimum stress Mini-fracturing test remains the most reliable method of determining the minimum (usually horizontal) in-situ stress of
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10 Vertical main fracture with multiple branches
Horizontal stress difference Kh
9 8
Partly Vertical fracture with random branches
7
Radial random net-fractures
6 5 4 3
Fig. 6. Partly vertical fracture with random branches (sample 4).
2 1
1
2 3 4 5 Sample number
6
Fig. 4. Relationship between geometry of hydraulic fractures and horizontal stress difference.
Fig. 7. Radial random net-fractures at low difference of horizontal stress (sample 6).
16
Pressure / MPa
14 12 10 Radial net-fractures (number 6)
8 6 4
Fig. 5. Dominating fracture with multiple branches at large difference of horizontal stress (sample 1).
Main fracture with multiple branches (number 1)
2 0
petroleum engineering [19]. In naturally fractured reservoirs, natural fractures could lead to negative effect on estimating the minimum horizontal stress when using mini-fracturing tests. We could pre-set the horizontal stresses in our tri-axial machine, then the negative effect of natural fractures on estimating minimum horizontal stress could be assessed by using minifracturing tests. Before that, a comparable sample was tested by minifracturing test. This block was made together with others except
0
200
400
600
800 1000 1200 1400 1600 Time / s
Fig. 8. Pressure signals of radial random net-fractures and dominating fracture with multiple branches.
the process of heating and air cooling so that it is just pure cement block without random natural fractures in it. With its results we could calibrate the effect of natural fractures. A coefficient of error
Sample
sV (MPa)
sH (MPa)
sh (MPa)
Kh
pc (MPa)
Zh
M-comp Min-1 Min-2 Min-3 Min-4 Min-4 Min-6 Min-7 Min-8 Min-9
20 20 20 20 20 20 20 20 20 20
15 10 15 10 15 10 10 11 11 11
5 5 5 5 5 3 3 1 1 1
2 1 2 1 2 2.3 2.3 10 10 10
6.49 5.83 6.00 5.77 5.81 3.50 3.47 1.32 1.29 1.35
0.298 0.166 0.200 0.154 0.162 0.167 0.157 0.320 0.290 0.350
for estimating the least stress was defined as
Zf ¼
pc sh
P/pump dP/dG GdP/dG
13 12 11 10 9 8 7 6 5 4 3 2 1 0
13 12 11 10 9 8 7 6 5 4 3 2 1 0
B
A
0.0
ð4Þ
sh
Pressure / MPa
Table 3 Summary of in-situ stress condition and results of mini-fracturing tests.
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0.5
1.0
1.5
GdP/ dG or dP / dG
J. Zhou et al. / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 1193–1199
2.0
G function Fig. 9. Analysis of closure pressure using G-function (sample Min-2).
in which Zf donates coefficient of error for estimating of the least stress (dimensionless), sh donates the minimum horizontal principal stress (MPa) and pc donates closure pressure (MPa). When designing the mini-fracturing tests, the influence of in-situ stress was also considered. Stress conditions and results of minifracturing tests are listed in Table 3. The G-function is widely used to estimate closure pressure of certain formation in petroleum industry [20], in which the pressure decline between the time of shut-in and re-injection is introduced to make an analysis: GðDtD Þ ¼
4
p
gðDtD Þg0
ð5Þ
where g(DtD) is the dimensionless fluid-loss volume function and g0 the value of g(DtD) at the moment of shut-in. For a wall-building fluid with a Newtonian filtrate, the value of area exponent a is in the range of 0.5 and 1. The lower bound of area exponent a is 0.5, corresponding for a low fluid efficiency, then the calculation is as follows:
Z-0 gðDtD Þ ¼ ð1þ DtD Þarcsinð1 þ DtD Þ1=2 þ DtD 1=2 g0 ¼ p=2 ð6Þ The upper bound of area exponent a is 1, corresponding for a high fluid efficiency, then as the following: h i Z-1 gðDtD Þ ¼ 43 ð1 þ DtD Þ3=2 DtD 3=2 g0 ¼ 4=3 ð7Þ where DtD is the dimensionless shut-in time, which is calculated by
DtD ¼
ttP Dt ¼ tP tP
ð8Þ
where t is the time, tP is the pumping time and Dt is the shut-in time. Finally, other intermediate values of g(DtD) and g0 at any other value of area exponent a can be obtained through simple interpolation between bounding values. Fig. 9 shows G-function curves of Min-2. An obvious dP/dG decline as well as an increasing of the value of GdP/dG to point A was observed between 0.0 and 1.0 of G-function and it demonstrated a dominating hydraulic fracture is closing due to shut-in of the injection pump. After that there is no obvious increase of GdP/dG, so that we could determine the corresponding point B is the closure pressure and its value is 6.0 MPa. After the closure of hydraulic fracture, some fluid leak-off continued, which led to small declines both of pressure and dP/dG from 1.25 to 2.0. With the in-situ stress listed in Table 3, hydraulic fracture could be a simple, vertical, planar fracture that opened against the least tress. Hydraulic fracture of Mini-compare included all above characters although it was a mini-fracturing test (Fig. 10). The closure pressure of min-compare was 6.49 MPa, which was more
Fig. 10. Simple, vertical and planar hydraulic fracture of Min-compare.
than actual the minimum stress, 5 MPa. Obviously, closure pressure is higher than constant confining pressure and the coefficient is 0.298. The coefficients of error from Min-2 to Min-6 were more close to real confining pressure compared with Mincompare because most of fracturing fluid came into random natural fractures and ideal hydraulic fractures did not exist in these blocks in the situation of the lower differential stresses. On the other hand, the coefficients of error of Min-7 to Min-9 were a little more than that of Min-compare. In the situation of the higher differential stresses, dominating fractures with multiple branches were created in these blocks. Natural fractures in these blocks lowered the value Zf for closure pressure estimation, which is 21.8% on average. There were some different pressure profiles between the tests with random natural fractures and the test without natural fractures during mini-fracturing tests. Fig. 11 is the pressure curves of Min-compare (without natural fractures) and Min-2 (with random natural fractures). Break-down pressure was very clear in those two pressure curves and it indicated that hydraulic fracture initiated and propagated from borehole of wellbore successfully. Shut-in of injection was carried out shortly after hydraulic fracture propagating from wellbore because of limited size of blocks. Instantaneous shut-in pressure could easily be recognized in pressure curve of Min-compare because it is a homogenous block and there was no natural fracture in it. And its
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but must be at least equal to the minimum confining stress sh. Thus the stress ratio is approximately (sH sh)/sh. This is equivalent to the parameter Kh defined by in eq. (3). Renshaw and Pollard showed that the critical value of the stress ratio required for the pre-existing fracture to arrest the propagating fracture depends on the coefficient of friction along the preexisting fracture. But for typical values of the coefficient of friction m for rock and cement ( 0.4 o m o 1.0), the critical stress ratio is about 1–2 (Fig. 7 of [22]). Thus, for Kh larger than about 2, we expect that the hydraulic fracture can propagate across the preexisting fractures and the hydraulic fracture geometry to be more or less planar. In contrast, for Kh value of about 2 or less, we can expect the pre-existing fractures to arrest the propagation of the hydraulic fracture and the hydraulic fracture geometry to be complex. These expectations agree well with our results.
Shut-in
16
Pressure / MPa
14 12 10 8 6 4 With natural fractures (Min-2)
2
Without natural fractures (Mincompare)
0 0
200
400
600
800
1000
1200
Times / s
5. Conclusion
Fig. 11. Pressure signals of Min-compare and Min-2.
leak-off fitted Carter leak-off model [21] because hydraulic fracture was an ideal bi-wing planar fracture here (Fig. 10). But from pressure curve of Min-2, it is difficult to determine the instantaneous shut-in pressure directly. Besides, after the test we found random natural fractures totally arrested hydraulic fracture. It means most of its leak-off depended on random natural fracture system. After restarting the injection, the frequency of pressure curve fluctuating in test of Min-2 is obviously higher than that of Min-compare and it indicated that random natural fractures opened and closed frequently during reinjection process.
4. Discussion Blanton [3] and Warpinski and Teufel [5] found that differential stresses and the angle of approach are most important factors to control fracture propagation behavior in this situation. They found that hydraulic fracture tends to cross pre-existing fractures only under high differential stresses and high angles of approach. At intermediate and low differential stresses and angles of approach pre-existing fractures tend either to open and divert fracturing fluid or arrest propagation of the hydraulic fracture. Their conclusions are based on the same assumption that fracture interaction is between hydraulic fracture and a single natural fracture. Based on their work, the systematic experiments in heated cements were designed and performed for investigating the influence of random natural fractures on hydraulic fracture. Renshaw and Pollard [22] proposed a simple criterion for the state of stress required for a pre-existing fracture to impact the propagation of a fracture. Consider a pre-existing fracture parallel to the least compressive stress sh and a growing fracture propagating parallel to the most compressive horizontal stress sH. Renshaw and Pollard proposed that whether or not the preexisting fracture would impact the growth of the propagating fracture depended on the stress ratio sH/(T0 + sh), where T0 is the tensile strength of the material (MPa). We assume that sh 5T0 (the tensile strength of concrete is often about an order of magnitude less than its compressive strength – much less for fractured concrete such as considered here). Also, the numerator of the stress ratio, which is related to the frictional strength of the unbonded interface, needs to be modified to account for the leakage of the injection fluid into the pre-existing fracture. Thus the stress ratio can be written as (sH P)/sh. The fluid pressure at the tip of the propagating fracture is less than that at the wellbore,
Laboratory experiments were performed to investigate the influence of random natural fracture system on geometry and propagation behaviors of hydraulic fractures. Both random natural fractures and differential in-situ stresses dominated geometry and propagating behaviors. Hydraulic fracture tended to be a dominating fracture with random multiple branches at high difference of horizontal stresses. On the other hand, it tended to be partly vertical, planar fracture with branches at low difference of horizontal stresses. Natural fracture system with a high strength of network could dominate geometry of hydraulic fracture also, where it was radial random net-fractures in our tests. Pressure profiles could reflect different characters of propagating behaviors. Random small natural fractures could lead to high frequency of pressure fluctuating during fracture propagation. Also, natural fractures with strong network could lead to more smooth pressure during injection. The closure pressure is higher than confining pressure estimated by mini-fracturing tests in our tight cement blocks. In presence of random natural fractures, this method is still reliable if fracture geometry is a vertical, dominating one (even partly). Because of these random natural factures, the value Zf for closure pressure estimation is on average lower than that of without natural fractures in our tests, which are 21.8 and 29.8%, respectively.
Acknowledgments This work is financially supported by the National Natural Science Foundation of China (Grant no. 90510005) and partly by ‘‘Innovation Group’’ Foundation of Ministry of Education of China (Authorized no. IRT0411). We also thank C.J. de Pater and the reviewers for their beneficial suggestions for improving the paper. References [1] Daneshy AA. Hydraulic fracture propagation in the presence of planes of weakness. In: Proceedings of the SPE European spring meeting, 29–30 May 1974, Amsterdam, paper SPE 4852. [2] Lamont N, Jessen F. The effects of existing fractures in rocks on the extension of hydraulic fractures. J Petrol Technol 1963:203–9. [3] Blanton TL. An experimental study of interaction between hydraulically induced and pre-existing fractures. In: Proceedings of the SPE/DOE symposium on unconventional gas, 16–18 May 1982, Pittsburgh, paper SPE 10847. [4] Blanton TL. Propagation of hydraulically and dynamically induced fractures in naturally fractured reservoirs. In: Proceedings of the SPE/DOE symposium on unconventional gas, 18–21 May 1986, Louisville, Kentucky, paper SPE 15261. [5] Warpinski N, Teufel LW. Influence of geologic discontinuities on hydraulic fracture propagation. J Petrol Technol 1987:209–20. [6] Beugelsdijk LJL, de Pater CJ, Sato K. Experimental hydraulic fracture propagation in multi-fractured medium. In: Proceedings of the SPE Asia
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