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39
UDC 553.9
The relationship of fracture toughness coefficients and geophysical characteristics of rocks of hydrocarbon deposits
Yurii A. KASHNIKOV, Sergei G. ASHIKHMIN, Artem E. KUKHTINSKII», Denis V. SHUSTOV
Perm National Research Polytechnic University, Perm, Russia
This paper contains the results of laboratory tests to determine the fracture toughness coefficient KIC of rocks for terrigenous and carbonate objects by three methods. The tests were carried out by different methods due to the lack of a standard method for determining the fracture toughness characteristics of rocks in Russia. We used the following methods for determining the KIC coefficient: the extension of core specimens with an annular fracture, the action of a concentrated load on a beam specimen with a fracture and the method of bending semi-circular samples with a fracture according to ISRM recommendations.
The paper presents the relationship of the fracture toughness coefficients with the P-wave velocity and porosity. The obtained dependencies characterize the general trend of changing for the studied parameter and can be used in the design of hydraulic fracturing in the fields for which tests were conducted.
Key words: fracture toughness coefficient; extension; bending; terrigenous and carbonate objects; rocks
How to cite this article: Kashnikov Yu.A., Ashikhmin S.G., Kukhtinskii A.E., Shustov D.V. The relationship of fracture toughness coefficients and geophysical characteristics of rocks of hydrocarbon deposits. Journal of Mining Institute. 2020. Vol. 241, p. 83-90. DOI: 10.31897/PML2020.1.83
Introduction. All theoretical models and software for hydraulic fracturing modeling, which is the main geotechnical measure aimed to increase well productivity, use the concepts of fracture mechanics and, therefore, the values of fracture toughness coefficients KIC [2, 3, 5].
The determination of this rock parameter of oil and gas fields productive objects was practically not carried out, although the KIC parameter is included in all service packages for hydraulic
1/2
fracturing design. Most often, the KIC coefficient is assumed to be 1 MPa m and it does not have any connection with the filtration-capacitive and geophysical rocks characteristics. Due to the importance of this parameter for the theoretical justification of the hydraulic fracturing design, of laboratory tests are presented for KIC values determination by three methods for terrigenous and carbonate objects. Also there was considered the relationship of this parameter with geophysical characteristics, primarily the P-wave velocity.
Currently, there are no methods for determining the rock fracture toughness coefficients in the RF standards. At the same time, there are methods for determining KIC recommended for use by the International Society for Rock Mechanics (ISRM). In total, four different methods for determining the static fracture toughness coefficient were proposed by ISRM at different times [8, 10, 11]. The first two were proposed by a group of scientists in 1988 [11]. The first method involves bending a cylindrical core with a V-shaped cut perpendicular to the axis of the cylinder. In the second method [11], it is recommended that special clamps disclose a short cylinder with a V-shaped cut along the core axis. The third method, proposed in 1995 [8], involves the extension of a cylindrical specimens with a V-shaped cut. The fourth method, proposed in 2013 [10], involves bending semi-circular specimens with a cut. The advantage of this method over others recommended by ISRM is that it uses standard equipment. Also specimens preparing for testing and the results processing are relatively simple.
During the tests conducting for the fracture toughness coefficients of composites, construction and other materials, it is a common practice to use standards developed for metals and alloys, in particular GOST 25.506-85. As a rule, they are based on the determination of the KIC coefficient when testing specimens in tensile or bending mode with the initial fatigue fracture. The growth
Fig. 1. Scheme of loading a specimen with an annular fracture to determine KIC according to [4] P - extension load; R - radius of the cylinder; a - cut depth, a = R - b; b - minimal radius at the place of cut
of the initial fracture on rock specimens seems problematic, since it is a brittle material, and an uncontrolled dynamic fracture growth can occur, up to the destruction of the sample.
According to [1], rock tests can be carried out in two ways: direct extension and bending. When extending, it is desirable to use specimens in the form of thin plates with a cut. Before testing with dynamic loads, a fatigue fracture is created at the tip of the cut. Then the specimen is statically extended and the failure is determined, by which Kic is calculated.
As follows from the data given in [1], Kic coefficients for rocks, which can lie in oil deposit formation (sandstones and siltstones) vary within 0.5-1.7 MPa-m1/2.
in this paper, the Kic coefficients were determined by three methods: by extending core specimens with an annular fracture [4], by the action of a concentrated force on a beam specimen with a fracture using a technique similar to that described in [1], and by bending semi-circular specimens with a fracture, according to iSRM recommendations [10]. The main goal of the tests is not only the determination of specific values of KiC coefficients by different methods for hydrocarbon deposits, but also the establishment of a relationship between this parameter and the geophysical characteristics of rocks. There is already such research data in the international literature [6, 7], however, such studies are not presented in the RF literature. There are many known equations that relate the elastic modulus, strength, and other characteristics to geophysical parameters. However, in this article for the first time ever the statistical dependences of fracture toughness coefficients on rock geophysical characteristics have been obtained.
Determination of fracture toughness coefficients on cylindrical core specimens. To determine the KiC value, there were studied the specimens with a diameter of 30 mm and a length of 60 mm, which were made of the core material of well N 118 (Enapaevskoye deposit of LTD LUKOIL-PERM) from the interval of terrigenous rocks 1538-1541 m. Before testing, for individual specimens, the static and dynamic elastic properties of the rocks were determined in formation conditions.
Cylindrical samples with an annular groove were used in the experiments to determine Kic (Fig. 1).
Extension tests of rock specimens were carried out on a biaxial electrodynamic test system Instron ElectroPuls E10000. A special tooling was developed and designed to fix the cylindrical specimen in the clamps of the testing machine for extension testing.
The extension test of the specimen was carried out at room temperature. During the test the constant displacement speed of the test machine clamps was set at 0.2 mm/min.
The stress intensity factor KIC was calculated using the formulas given in [4] for a cylindrical specimen with a surface annular fracture while extension (designations according to Fig. 1)
Kj = pV^/j (a) / a = b / R ;
(1)
/ = 0,5(l + 0.5a + 0.375a2 - 0.363a3 + 0.731a4)jî
-a
In total, 25 samples were tested according to the described scheme. The average KC value was 0.108 MPa-m1/2, with minimum and maximum values of 0.044 MPa-m1/2 and 0.168 MPa-m1/2,
respectively. The tensile strength of the tested specimens varies from 0.55 MPa to 2.34 MPa, which corresponds to the characteristic values for this type of rock.
Determination of fracture toughness coefficients on beam specimens. The determination of KIC coefficients on beam samples was carried out according to the scheme presented in Fig.2. Used core material was taken from terrigenous deposits in the Western Ural (Table 1), represented by mudstones, siltstones and sandstones from carbonate objects of gas condensate deposits of the Uzbekistan Republic (Table 2), and by gray organogenic massive porous strong limestones. Table 2 shows the average deposit values of the parameters.
Table 1
Characteristics of core material for the production of beam specimens and coefficients KIC
of the Western Ural oil deposits
Deposit Number of the well Specimen quantity Depth of the sampling, m Kic, MPa-m1/2
Olkhovkoye 164 3 2014.57-2014.72 0.795
Unvinskoye 365, 215 8 2221.76-2221.91 0.413
Kokuiskoye 582 2 1727.43-1727.54 0.462
Sofinskoye 338 3 2553.25-2553.40 0.380
Viktorinskoye 94 4 1649.31-1649.50 0.969
Weighted average 0.604
Table 2
Characteristics of core material for the production of beam specimens and coefficients KIC of the gas condensate deposits of the Uzbekistan Republic
Deposit Average depth of the sampling, m Specimen quantity Open porosity, % P-wave velocity Vp, m/s Density p, g/cm3 Kic, MPa-m 1/2
Akkum 2114.17 5 7.74 5117 2.46 1.460
Alat 2238.52 3 13.27 4490 2.35 0.984
Kandym 2167.12 10 6.87 5227 2.33 0.846
Parsankul 2173.20 5 2.41 5833 2.41 1.038
Khodzhi 2208.18 5 2.54 5814 2.55 1.356
Weighted average 1.137
From each core monolith there were made 2 to 8 specimens for the deposits of Western Ural and 3 to 10 specimens for the deposits of the Uzbekistan Republic. The dimensions of the beam specimens were: W = 2 cm; t = 1 cm; a = (0.3-0.4)W; 5 = 0.05W.
The tests were carried out on an Instron 5965 testing machine on specimens in the form of a beam of rectangular cross section with an initial undercut. The initial undercut was made in two stages. At the first stage, cut was applied with a diamond disk with a nominal thickness of 0.6 mm to a depth of 6 mm using a table with a guide. At the second stage, the top of the undercut was formed using two blades of different thicknesses, previously unidirectional teeth were applied on the blades with a pitch of 2-4 mm. The resulting length of the primary fracture was measured using a microscope.
The values of the intensity coefficients were calculated by the formulas (designations in accordance with Fig.2) [4]:
4 W
a
I
CO <r O
<rt ->
S = 4W
Fig.2. Design scheme of the specimen beam loading to determine KIC according to [1]
P - applied load; 8 - width of the cut; S -distance between supports; W - specimen height; t - specimen width; a - cut depth
3SP i_
K =--V^aFj(a) ; (2)
2tW
Fi(a) =
a = a / W ; 1.99 -a(1 -a)(2.15 - 3.93a + 2.7a2)
(1 + 2a)(1 -a)
3/2
The KIC values obtained by this method for terrigenous objects of the Western Ural are significantly different from the values obtained by extension of round-shaped specimens with a circular undercut. It is characteristic that even the minimum KIC value determined by the second method significantly exceeds the maximum KIC value determined by the first method. However, this may be due to both the methodology for determining this parameter and the characteristics of the specimens.
The KIC values of carbonate objects of gas condensate deposit of the Uzbekistan Republic, determined by the second method, turned out to be two times higher than the values of this parameter for terrigenous objects of the Western Ural, which can be explained by the difference in strength properties. This experiment does not allow the determination of uniaxial compression strength. However, experiments on other specimens give average values of this parameter - 40-60 MPa for terrigenous objects of the Western Ural and 80-120 MPa for carbonate objects of the Uzbekistan Republic deposits.
Determination of fracture resistance coefficients on semi-circular specimens according to ISRM recommendations. Specimens preparation for the determination of KIC by this method is described down below. A standard cylindrical core is cut in half along the longitudinal axis. In this case, the deviation of the diametrical plane should not exceed 0.2 mm. The thickness of specimen B should be 0.8R. A cut of length a is made in the middle of the sample, the width of which should not exceed 1.5 mm. The length must satisfy the condition 0.4 < a/R < 0.6. The surface of the cut, located in the direction along the axis of the specimen, must be flat with an accuracy of 0.01 mm. The cut plane should not deviate from the perpendicular direction to the planes along the edges of the specimen by more than 0.5°. The geometry of the prepared specimen and the loading scheme are shown in Fig.3.
The test was performed on standard equipment designed for three-point bending tests. The loading rate should not exceed 0.2 mm/min to avoid dynamic effects. The support points should be located at a distance s from each other, which must satisfy the condition 0.5 < s/2R < 0.8. The diameter of the supports should be 5 mm. The direction of the load must coincide with the plane of the cut.
After failure of the specimen, verification of the type of its failure is required. If the plane of the formed fracture deviates from the plane of the cut by more than 0.05D, then the results are invalid.
The fracture toughness coefficient is calculated by the formula (designations in accordance with Fig.3)
KIC = 7 ' Pmax^ , (3)
2 RB
where 7' = -1.297 + 9.516(s/2R)-(0.47 + 16.457(s/2R))p +(1.071 + 34.401(s/2R))p2; p = a /R.
The equation determines the fracture toughness coefficient calculated by the finite element method under conditions of plane deformation [9, 10, 12].
Figure 4 shows the position of the specimen in the clamp before testing. The fracture growth process was quasi-equilibrium. In some cases, dynamic areas of sample destruction were noted.
Monoliths up to 0.5 m in size were selected for specimens' production to conduct an experiment to determine the fracture toughness coefficient KIC of terrigenous objects.
C
R
<->
B
Section CC
Fig.3. Specimen geometry (a) and loading scheme (b) according to recommendation of ISRM [10]
P - applied load; s - distance between supports; a - cut height; R - specimen radius; B - specimen width
Fig.4. Semi-circular specimen in the clamp before test
b
Before starting the experiments to determine fracture toughness coefficient, all specimens were extracted, the open porosity and the P-wave velocity were determined under atmospheric conditions (Table 3).
Table 3
Characteristics of core material for the production of semi-circular specimens and coefficients KIC
of the Western Ural oil deposits
Deposit Number of the well Average depth of the sampling, m Specimen quantity Open porosity, % P-wave velocity Vp, m/s Kic, MPa-m1'2
Dorokhovskoye 711 1963.9 15 12.5 4143 1.317
Unvinskoye 531 2411.9 14 17.4 3927 0.852
Batyrbaiskoye 976 1521.7 12 24.0 3720 0.167
Kokuiskoye 976 1984.2 16 15.2 4015 0.865
Weighted average 0.774
A total of 57 specimens were tested, 22 specimens were rejected according to the criterion of
deviation of the fracture from the cut plane by more than 0.05D. According to the results of the
1 /2
tests, the fracture toughness coefficients vary over a very wide range: 0.05-1.47 MPa-m with a
1/2
test average of 0.774 MPa-m weighted by the number of specimens.
The average values of KIC coefficients determined by this method are close (with the exception of specimens of the Batyrbaiskoye deposit, characterized by high porosity) to the values of this parameter, determined for terrigenous objects using the test method on a beam specimen. At the same time, a feature is the presence of very low values of the KiC parameter for high values of porosity (24-26 %). Such low values of the fracture toughness coefficient were not noted in the experiments described in the domestic literature.
Relationship of fracture toughness coefficients with geomechanical and geophysical characteristics of the cut. The statistical dependences of the fracture toughness coefficients of KIC rocks on geomechanical parameters, such as elastic modulus, compressive strength, and others are practically not found in the scientific and technical literature, which is primarily due to the difficulty of simultaneously determining the fracture toughness parameter and other geomechani-cal parameters. In this paper, the porosity and P-wave velocity were previously determined on core specimens, and then either beam specimens or semi-circular specimens, and an experiment was carried out to determine KIC.
1.5 "I
cd Ph
O
0.5
KC = 170.4Kp~00101 - 164.
12 14 16 18 20
Kp, % • 1 O 2
Fig.5. Dependence of the fracture toughness coefficient KIC of oil fields terrigenous objects
in the Western Ural, determined according to the ISRM standard, from open porosity Kp
1 - specimen data; 2 - deposit average data
22 24 26
4300 4200 " 4100 " X 4000 -
C
o
J 3900 -
£
3800 -3700 -3600
^formation = Vpatm + 2991 R2 = 0.81
T
1500 2000
2500 3000
Vpatm, m/s
-1-1
3500 4000
Fig.6. Dependence of the P-wave velocity determined in formation conditions Vpformation, from velocity determined in atmosphere conditions Vpatm
1
0
1.5
0.5
0
Kc = 2.554e - 03 fa™ - 9.26 R2 = 0.
2 -i
KC = 0.000364 Vp - 0.682 R2 = 0.79
1.5 -
3600 3700
3800 3900 4000
Vpformation, m/s • 1 2
o
4100 4200
1 -
0.5
3500
4000
4500 5000
^formation m/s
5500
6000
Fig.7. Dependence of the fracture toughness coefficient KIC of oil fields terrigenous objects in the Western Ural, determined according to the ISRM standard, from the P-wave velocity in formation conditions Vpformation
1 - specimen data; 2 - deposit average data
Fig.8. Dependence of the fracture toughness coefficient
KIC of the specimens from carbonate gas condensate deposits of the Uzbekistan Republic identified on beam specimens [1] from the P-wave velocity in formation conditions Vpformation
1
^Yurii A. Kashnikov, Sergei G. Ashikhmin, Artem E. Kukhtinskii, Denis V. Shustov DOI: 10.31897/PMI.2020.1.83
The relationship of fracture toughness coefficients and geophysical characteristics...
The next step was the analysis of the dependence of the fracture toughness coefficient on porosity and P-wave velocity under formation conditions for terrigenous objects of the Western Ural. Dependences for porosity were obtained both for the entire sampling and for averaged values over monoliths (Fig.5). The P-wave velocity and porosity under atmospheric conditions were previously determined for the specimens. However, it is obvious that the P-wave velocity in atmospheric conditions is not equal to the wave velocity in formation conditions, and therefore a transition between these parameters is required. Fig.6 shows the relationship between the P-wave velocity determined in formation conditions and the wave velocity determined in atmospheric conditions also for terrigenous objects of deposits in the Western Ural. Based on this dependence, a relationship was obtained between the fracture toughness coefficient and the P-wave velocity in formation conditions (Fig.7).
A feature of the obtained dependences is the presence of very low values of the KIC parameter for high values of porosity (24-26 %), which were not observed in the experiments described in Russian literature. At the same time, the determination of this parameter was previously carried out mainly for rock massifs, and the results were not correlated with porosity or with any geophysical factors.
For comparison, Fig.8 shows the dependence of the fracture toughness coefficient on the P-wave velocity determined by the authors of this paper for carbonate gas condensate objects of the LLC LUKOIL-Uzbekistan Operating Company deposits. The KIC parameter was determined by the second method, i.e. on beam specimens [1]. A more reliable dependence is noted, which, however, is characterized by a significantly lower angle of inclination to the Vp axis.
Conclusion. The results of laboratory tests to determine the fracture toughness KIC of rocks by three methods for terrigenous and carbonate objects reveal its very different values even for the same productive objects. However, it becomes obvious that the determination of this parameter on core samples leads to a deliberately incorrect result - the values of fracture toughness coefficients are much underestimated. The determination of the KIC parameter on beam specimens and semicircular specimens according to the method recommended by ISRM for terrigenous objects of the Western Ural deposits gives approximately similar results. At the same time, the results of determinations according to the ISRM standard give a very high range of parameter values -0.05-1.47 MPa-m1/2, with a mean value of 0.774 MPa-m1/2 weighted by the number of specimens and types of tests. In general, the authors of this paper adhere to the method recommended by ISRM.
The relationship of this parameter with the geophysical characteristics of the productive zone is obtained, primarily with the porosity and P-wave velocity. The obtained dependencies cannot be considered completely reliable due to the limited number of tests and two oil and gas producing regions - terrigenous objects of the Western Ural deposits and carbonate objects of the Uzbekistan Republic. Nevertheless, they characterize the general tendency of this parameter to change depending on the porosity and P-wave velocity and can be used to model hydraulic fracturing based on the acoustic logging of a productive field.
Implementation of the developed methodology for determining fracture toughness coefficients based on correlation equations is planned at the terrigenous objects of the LUKOIL-PERM LLC deposits and at carbonate sites of the Uzbekistan Republic when designing the proppant and acid fracturing. When creating a database using the KIC parameter and its dependence on geome-chanical and geological-geophysical parameters, it is planned to use the standard recommended by ISRM.
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Authors: Yurii A. Kashnikov, Doctor of Engineering Sciences, Professor, geotech@pstu.ru (Perm National Research Polytechnic University, Perm, Russia), Sergei G. Ashikhmin, Doctor of Engineering Sciences, Professor, geotech@pstu.ru (Perm National Research Polytechnic University, Perm, Russia), Artem E. Kukhtinskii, Leading Engineer, artyom@pstu.ru (Perm National Research Polytechnic University, Perm, Russia), Denis V. Shustov, Candidate of Engineering Sciences, Associate Professor, geotech@pstu.ru (Perm National Research Polytechnic University, Perm, Russia).
The paper was received on 31 January, 2019.
The paper was accepted for publication on 21 February, 2019.
