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Estimation of uniaxial compressive strength of shale using indentation testing
Journal of Petroleum Science and Engineering 151 (2017) 24–30
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Estimation of uniaxial compressive strength of shale using indentation testing
MARK
⁎
Akbar Cheshomia, , Golnaz Hajipoura, Jafar Hassanpoura, Bahman Baga Dashtakib, Yavar Firouzeia, Ebrahim Ahmadi Sheshdea a b
Department of Structural and Engineering Geology, School of Geology, College of Science, University of Tehran, Enghelab Ave., Tehran, Iran NISOC Administrative Building, Fadaeeyane Islam St., Ahvaz, Iran
A R T I C L E I N F O
A BS T RAC T
Keywords: Uniaxial compressive strength Shale Indentation testing Critical transition force
A number of methods have been proposed to indirectly assess the uniaxial compressive strength (UCS) of intact rock in the drilling of oil wells and underground drilling. Indentation testing is a method in which an indentor of a specific diameter penetrates a particle of rock and the force-displacement curve is plotted to determine the critical transition force (CTF). In the present study, 10 shale block samples were collected from a cretaceous shale formation in Iran from which standard cores were prepared and subjected to UCS testing. Cubic particles 4, 5 and 7 mm3 in size were cut and entrenched in disks containing resin and a total of 300 indentation tests were conducted on them. Empirical relations for the relation between UCS and CTF were developed for each size. The highest correlation coefficient was recorded for the 7 mm3 particles and the lowest for the 4 mm3 particles. A simple method is proposed to determine the empirical relationship independent of particle dimensions between UCS and CTF that has a correlation coefficient of 0.78. Verification of the proposed equations show that they predicted UCS with 85% accuracy. A comparison of the proposed relationships and those from previous studies indicates that the empirical relationship between these two variables is influenced by variation in the uniaxial compressive strength and lithology of the different samples.
1. Introduction Determination of the uniaxial compressive strength (UCS) of rock is an essential step in oil exploration projects that study wellbore instability (Moos et al., 2003), sandification potential (Santarelli et al., 1989) and quantification of stress magnitude (Zoback et al., 2003). There are direct and indirect methods available to determine this parameter. The standard procedure recommended by ASTM (2002) and the International Society for Rock Mechanics (1981) is a direct method that requires standard cores with length-to-diameter ratios of 2.0–2.5 and diameters of 47 mm. Preparation of standard cores can be difficult, expensive and timeconsuming for deep exploration boreholes for oil and gas reservoirs in the presence of weak rock and joints and at great depth (Cheshomi et al., 2015). This has prompted researchers to propose indirect methods of estimating USC using drill cuttings. Santarelli et al. (1996) showed that drill cuttings are representative of a formation and can be a reliable source of information about its mechanical behavior. Indirect methods available for use on small rock fragments
(such as drill cuttings) are the continuous wave (Nes et al., 1998), lithological characteristics (Shakoor and Bonelli, 1991; Bell and Lindsay, 1999), reconstructed cores (Mehrabi et al., 2012), direct loading of single particles (Cheshomi and Ahmadi-Sheshde, 2013), and modified point load testing (Ahmadi-Sheshde and Cheshomi, 2015a) techniques. Indentation testing is an indirect method that allows measurement of the mechanical properties of rock. This test is simple, requires a comparatively short time for completion and is lower in cost than other mechanical tests (Garcia et al., 2008). Indentation testing uses a fat- tip indentor with a specific diameter (for example 1 mm; Mateus et al. (2007)) that penetrates small rock fragments at a steady velocity. The fragment to be tested is first inserted into a container of resin to provide support to the samples and allow measurement of the force required for penetration. This force is sufficient to demonstrate the elastic and plastic behavior of small rock fragments. The results are graphed in a force-displacement curve that is used to determine the critical transition force (CTF) and indentation modulus (Ringstad et al., 1998). Previous studies have proposed
⁎
Corresponding author. E-mail addresses: [email protected] (A. Cheshomi), [email protected] (G. Hajipour), [email protected] (J. Hassanpour), [email protected] (B.B. Dashtaki), Yavar.fi[email protected] (Y. Firouzei), [email protected] (E.A. Sheshde). http://dx.doi.org/10.1016/j.petrol.2017.01.030 Received 11 July 2016; Received in revised form 8 December 2016; Accepted 17 January 2017 Available online 24 January 2017 0920-4105/ © 2017 Elsevier B.V. All rights reserved.
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Table 1 Results of previous research on indentation testing. Author
Lithology
Particle shape
Size (mm)
Rate of penetration (mm/ Sec)
Proposed equation
Equation No.
Ringstad et al. (1998)
Shale, Sandstone and Limestone Sandstone Shale Limestone Limestone
Irregular
different size
–
UCS=0.149(CTF)
1
Irregular Irregular Irregular Cubic
4 <4 2, 5 2, 3, 4
0.3 0.3 0.01 0.01
UCS=91.97(CTF) UCS = −0.0083 CTF2 +33.08CTF UCS=0.48(CTF)n−19.36 UCS = 0.29 CTF – 41.28 D – 186.47 I + 317.63
2 3 4 5
Mateus et al. (2007) Garcia et al. (2008) Haftani et al. (2013) Ahmadi-Sheshde and Cheshomi (2015b)
CTF (Critical transition force In “N”), D (Particle diameters in “mm”), D*(Critical transition force per dimensionless parameter of surface in “N”), I (indenter diameter =1 mm), UCS (Mpa) Table 2 Results of indentation testing on cubic particles. SampleNo.
S−1 S−2 S−3 S−4 S−5 S−6 S−7 S−8 S−9 S−10
Measured
CTF (N)
UCS (MPa)
4 mm3
43.25 113.93 51.36 82.61 39.43 48.77 41.2 62.31 92.7 100.69
5 mm3
7 mm3
Min.
Max.
Ave.
Sd.
Min.
Max.
Ave.
Sd.
Min.
Max.
Ave.
Sd.
326.3 764.6 576.2 513.2 274.2 446.1 223.8 497.5 537.5 590.2
766.7 1114.4 1092.1 886.3 704.4 893.5 631.9 872.4 869.3 928.7
594.7 955 759.6 721.8 485.8 655.9 359.7 650.6 693 739.3
13.5 13.8 14.3 12.8 12.9 15.8 6.6 12.7 9.8 12.4
541.9 761.4 544 618.4 564.4 449.4 454.4 678.4 709.1 650.1
1002.5 1182.8 933.1 1161.8 800.9 1052.1 823 1050.1 954.7 1069
750.5 1005.2 723.3 911.2 664.7 666.7 638.8 835 844.1 826.7
13.7 12.7 11.8 17.6 8.7 17.3 14 13.5 8.2 12.5
712 1010.5 856.8 644.6 648.1 759.2 678.9 807.8 864.6 801.7
1292.5 1747.1 1290.3 1642.7 1337.7 1206.9 925.4 1154.3 1437.5 1519.5
950.6 1347.4 1029.4 1216 921.1 983.7 810.1 931.4 1135.4 1184.2
17.5 25 11.7 22.6 26.4 12.3 7.7 11.3 19 22.4
Fig. 1. Sample preparation: (a) cutting fragments to specified diameters; (b) entrenching cubic particles into disks containing resin; (c) samples prepared for testing.
Fig. 2. (a) Indentation testing apparatus and; ( b) load-displacement curve of sample S-7 (4, 5 and 7 mm3 in size).
25
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Sh-2
Sh-3
Sh-5
Sh-7
7 mm3
5 mm3
4 mm3
Fig. 4. Linear regression between UCS and CTF for particles 4, 5 and 7 mm3 in size.
• • • •
Fig. 3. Failure pattern for some particles (Sample No. Sh-2, Sh-3. Sh-5 and Sh-7 in cubic size 4, 5 and 7 mm3).
empirical relationships between CTF and UCS based on indentation testing of small rock fragments. Table 1 summarizes the most significant studies. The present study determined the UCS of 10 shale block samples from cretaceous formation outcrops in Iran. Small rock fragments were produced from natural blocks using a crushing machine and the CTF of 300 small rock fragments was determined. To assess the effect of particle size on CTF, particles of 4, 5 and 7 mm3 in size were prepared and the CTF was determined for each particle size. Empirical equations to determine the relationship between CTF and UCS were then developed. The proposed relationship was validated and the results of the present study were compared with those of previous studies.
The empirical equations were validated. The proposed empirical equations were compared with those from previous studies.
3. Sampling and laboratory testing Ten blocks (20×20×40 cm3) were obtained from cretaceous formation outcrops in the vicinity of Sanandaj, Iran and subjected to the following tests. 3.1. UCS NX cores (50.7 mm in diameter and 109.4 mm in length) were prepared from the blocks according to ASTM (2008) standards and subjected to UCS testing according to ASTM protocol (2002). Cores were drilled perpendicular to the direction of weakness surfaces so UCS tests were conducted perpendicular to the direction of cores weak surfaces. The results of the UCS testing are presented in Table 2. The UCS of the samples varied from 39.43 to 113.93 MPa.
2. Methodology Sample preparation and method of research are as follows:
• • • • •
support for the samples. Indentation testing was performed on each cubic particle and the CTF was measured. Empirical equations between UCS and CTF were developed.
Collection of 10 shale block samples. NX cores were drilled out of these blocks and UCS testing was conducted. Small rock fragments were prepared using a crushing machine.
3.2. Indentation test Small rock fragments were shaped into cubes 4, 5 and 7 mm3 in size. 3.2.1. Sample preparation After UCS testing, each core was crushed using a crushing machine and the fragments produced were cut in to cubic particles of 4, 5 and
The cubic particles were inserted into a container of resin to provide
Table 3 UCS–CTF equations for cubic shale particles 4, 5 and 7 mm3 in size (CTF in Newtons and UCS in MPa). Equation No.
Relation
Cube particle dimension (mm)
Empirical relationship
Correlation coefficient (R)
6 7 8
Linear
4 5 7
UCS=0.14 CTF−20.71 UCS=0.21 CTF−97.45 UCS=0.15CTF−89.73
0.78 0.91 0.92
9 10 11
Power
4 5 7
UCS=0.0286CTF1.196 UCS=0.000005CTF2.44 UCS=0.000008CTF2.285
0.77 0.91 0.91
12 13 14
Exponential
4 5 7
UCS=17.08e0.002CTF UCS=5.66e0.003CTF UCS=6.40e0.002CTF
0.79 0.91 0.92
15 16 17
logarithmic
4 5 7
UCS=80.19 Ln CTF- 448.27 UCS=167.31 Ln CTF – 1045.4 UCS=156.76 Ln CTF- 1018.7
0.75 0.91 0.91
26
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Fig. 5. Correlation between UCS and CTF/S.
Table 4 Measured UCS values and those estimated using Eqs. (6), (7), (8) and (19). Sample No.
Particle dimension (mm3)
Measured UCS (MPa)
CTF (N)
Equation 6,7,8
Eq. (19)
Estimated UCS
Similarity to measured UCS (%)
Estimated UCS
Similarity to measured UCS (%)
S−11 S−12 S−13
4
104.86 39.24 52.44
706.964 475.391 482.83
78.26 45.84 46.88
75 86 89
78.75 39.76 41.01
75 99 78
S−11 S−12 S−13
5
104.86 39.24 52.44
928.056 669.316 680.086
97.44 43.11 45.37
93 91 86
84.71 49.86 51.31
81 79 98
S−11 S−12 S−13
7
104.86 39.24 52.44
1194.44 812.456 897.37
89.44 32.14 44.88
85 82 86
74.62 37.88 46.05
71 96 88
Fig. 6. Comparison of measured and estimated UCS for cubic particles 4, 5 and 7 mm3.
Fig. 7. Correlation between measured and estimated UCS based on: (a) dependence on particle dimensions (Eqs. (6), (7), (8)) and; (b) independent of particle dimensions (19).
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Fig. 8. Similarity between measured and estimated UCS from Eqs. (6), (7), (8) and (19) for cubic particles 4, 5 and 7 mm in size. Table 5 Comparison of values obtained from present and previous studies. Sample no.
UCS
CTF
UCS values estimated from equation no. 1
S−1 S−2 S−3 S−4 S−5 S−6 S−7 S−8 S−9 S−10 S−11 S−12 S−13
(MPa)
(N)
(MPa)
43.25 113.93 51.36 82.61 39.43 48.77 41.2 62.31 92.7 100.69 104.86 39.24 52.44
594.72 955.06 759.67 721.8 485.86 655.92 359.78 650.60 693.02 739.93 706.96 475.39 482.83
88.61 142.3 113.19 107.55 72.39 97.73 53.61 96.94 103.26 110.25 105.34 70.83 71.94
2
3
4
5
19
54.7 78.84 69.86 66.38 44.68 60.33 33.09 59.84 63.74 68.05 65.02 43.72 44.41
113.82 163.35 138.31 132.96 95.97 123.26 73.63 122.46 128.78 135.54 130.82 94.18 95.45
123.37 209.85 162.96 153.87 97.25 138.06 66.99 136.78 146.96 158.22 150.31 94.73 96.52
138.51 243.01 186.34 175.36 106.94 156.26 70.38 154.71 167.02 180.62 171.06 103.9 106.06
60.16 121.02 88.02 81.62 41.77 70.49 20.48 69.59 76.76 84.68 79.11 40.01 41.26
Fig. 9. Comparison of measured and estimated UCS using different empirical relationships for 13 samples tested. Area "A" based on Eqs. 1, 2, 3 and (19) that related to sandstone and shale and area "B" based on equations 4 and 5 that related to limestone.
7 mm3 using a diamond slab saw. The cubic particles dimensions was measured with a caliper. Preparing cubic particles with smaller than 4 mm3 is very difficult, and particles bigger than 7 mm3 does not represent drill cuttings. Therefore in this research particles were prepared in this dimensions. Fig. 1 shows the preparation of the cubic particles. Preparing cubic particles with similar shape and diameter (in very small dimensions) requires significant accuracy and patience. The particles were first entrenched in disks containing ML-506 resin to restrain them from moving during testing. Previous researchers used resin as the surrounding material, thus boundary conditions in this research would be the same for all cubic particles as well as previous researches. Cubic particles of different sizes were prepared to eliminate
the influence of particle shape and to investigate the influence of fragment dimensions. 3.2.2. Testing procedure Indentation testing was carried out using a fat-tip indentor with a tip 1 mm in diameter at a constant peneteration rate of 0.01 mm/s as done in Mateus et al. (2007), Garcia et al. (2008), and Haftani et al. (2013 & 2014)). Fig. 2 shows the indentation test apparatus and the load-displacement curve for sample S-7. The CTF is the maximum force in load – displacment curve as is shown in Fig. 2b. Ten particles of each cubic particle size were tested. The cubic particles were 4, 5 and 7 mm3 in size, making a total of 300 indentation 28
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validity of this relationship falls into range of cubic particle dimensions tested. 5. Verification of empirical relationships In order to validate the proposed empirical relationship, three shale samples other than the original 10 used to propose the empirical relationship were selected. Standard core samples were prepared and the UCS values were determined according to standard testing procedure. The process in section 2.2 that then used to form cubic particles in 4, 5 and 7 mm3 in size. For each size, 10 indentation tests were conducted and the results were averaged to determine the CTF of each sample. Given the CTF, UCS was then estimated using Eqs. (6), (7), (8) and (19). Table 4 shows the measured UCS values and those calculated using the proposed relation. The data presented in Table 4 was used for comparison of the measured and estimated UCS as shown in Figs. 6 and 7 for the three samples. Fig. 6 shows that there is a slight difference between the measured and estimated UCS values. The proximity of points to line 1:1 in Fig. 7 indicates good correlation between the measured and estimated UCS values. Fig. 8 compares the percentage of similarity between the measured and estimated UCS. It can be said that the empirical relationships dependent and independent of dimensions can be used to estimate the UCS of the shale with more than 85% similarity.
Fig. 10. Measured USC range in present and previous studies. As can be seen measured UCS range for microcrystalline limestone is very different in comparison with sandstone and shale.
tests. Table 2 shows the minimum, maximum, average and standard deviation of the CTF values obtained from indentation testing. After the indentation test a photo was taken from each particle. In Fig. 3 failure pattern for some particles has been demonstrated. 4. Analysis and interpretation of results Laboratory testing was carried out to determine the relationship between UCS and CTF and investigate the effect of cubic particle diameter on CTF.
6. Discussion The relationship obtained in the present study (Eq. (19)) and empirical equations from previous studies (Eqs. (1), (2), (3), (4) and (5)) were compared. For this purpose, CTF values obtained from 4 mm3 samples from the 10 original blocks. The 3 validation samples were entered into Eqs. (1), (2), (3), (4) and (5) and the UCS values for each sample was estimated. The results are presented in Table 5. Fig. 9 shows the UCS values estimated using different equations versus values measured by standard testing. An obvious difference between the UCS values estimated by the different relationships can be observed. The equations proposed by Haftani et al. (2013) and Ahmadi-Sheshde and Cheshomi (2015b) related to microcrystalline limestone. Equations proposed by Ringstad et al. (1998), Mateus et al. (2007) and Garcia et al. (2008) related to sandstone and shale and equation proposed in this research related to shale. As can be seen in Fig. 9, UCS estimated by equations proposed for shale and sandston are closer to measured UCS and UCS estimated by equations proposed for limestone are further than measured UCS. So the reason for this variation is the difference in the lithology. On the other hand Fig. 10 shows measured UCS range in this research and previous research. Measured UCS range for microcrystalline limestone is very different in comparison with sandstone and shale. As can be seen in Fig. 10, measured UCS of sandstone and shale that studied in previous research are close to measured UCS that studied in this research. Therefore, the UCS estimated using these equations is close to those estimated in the present study.
4.1. Correlation between UCS and CTF To investigate the empirical relationship between UCS and CTF, a variation graph for the two variables was plotted using the results of the 10 samples of each size from Table 2 at linear, power, exponential and logarithmic scale. Table 3 shows the resulting empirical relationships. Table 3 shows that the correlation coefficients of the different models are acceptable; however, the simplicity of linear regression recommends this approach over the others. Fig. 4 shows the linear relationships between UCS and CTF for the cubic particles. The correlation coefficients of linear regression between CTF and UCS for cubic particles 4, 5 and 7 mm3 in size were 0.78, 0.91 and 0.92, respectively. The lowest correlation coefficient was for the 4 mm3 particles and the highest was for the 7 mm3 particles. This suggests that the correlation coefficient increased as the particle dimensions increased. 4.2. Empirical relationship independent of particle dimensions The equations in Table 3 are applicable to cubic particles 4, 5 and 7 mm3 in size and an indentor diameter of 1 mm. To eliminate the effect of particle dimensions, dimensionless parameter (S) is defined in Eq. (18) as:
S=
Ss Si
7. Conclusion
(18)
The present study evaluated the use of the indentation test to estimate the UCS of shale rock. Ten shale blocks were collected and their UCS values were determined in accordance with ASTM standards. More than 300 cubic particles 4, 5 and 7 mm3 in size were prepared and indentation testing was carried out. The CTF of each cubic particle was obtained from the related load–displacement diagrams. An empirical relationship between UCS and CTF using linear correlation was proposed that produced a correlation coefficient more than 0.87. To eliminate the effect of particle dimensions, a dimensionless parameter was defined and used for an empirical equation independent of particle dimensions that produced a correlation
In this equation, Ss is the particle surface and Si is the indentor surface. The CTF is divided into this dimensionless parameter (CTF/S) to eliminate the effect of particle dimension. Fig. 5 shows a graph of UCS-CTF/S. The graph was used to calculate the relationship between UCS and CTF as shown in Eq. (19).
UCS = 0.76(CTF / S )–40.28
R = 0.78
(19)
A correlation coefficient of 0.78 was achieved for Eq. (19) independent of particle dimensions. The correlation coefficient for Eq. (19) is lower than those for Eqs. (6), (7) and (8) and demonstrates the effect of particle dimensions on the correlation coefficient. Note that the 29
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experimental correlations between indentation parameters and unconfined compressive strength (UCS) values in shale samples. CTF-Cienc. Tecnol. Y. Futuro 3 (4), 61–81. International society for rock mechanic, 1981. In: Brown, E.T. (Ed.), Rock Characterization Testing and Monitoring. Pergam Press, Oxford. Haftani, M., Bohloli, B., Mosavi, M., Nouri, A., Moradi, M., MalekiJavan, M., 2013. A new method for correlating rock strength to indentation tests. J. Pet. Sci. Eng. 112, 24–31. Haftani, M., Bohloli, B., Nouri, A., MalekiJavan, M., Moradi, M., 2014. Size effect in strength assessment by indentation testing on rock fragments. In. J. Rock. Mech. MIn. Sci. 65, 141–148. Mateus, J., Saavedra, N.F., Calderó n, Z.H., Mateus, D., 2007. Correlation development between indentation parameters and unaxial compressive strength for Colombian sandstones. CTF-Cienc. Y. Futuro 3 (3), 125–135. Mehrabi mazidi, S., Haftani, M., Bohloli, B., Cheshomi, A, 2012. Measurement of uniaxial compressive strength of rocks using reconstructed cores from rock cuttings. J. Pet. Sci. Eng. 86–87, 39–43. Moos, D., Peska, P., Finkbiner, T., Zoback, M.D., 2003. Comprehensive wellbore stability analysis utilizing Quantitative Risk Assessment. J. Pet. Sci. Eng. 38, 97–110. Nes O.M., Horsrud P., Sonstebo E.F., Holt R.M., Ese A.M., Okland D., Kjorholt H., 1998. Rig-Site and laboratory use of CWT acoustic velocity measurements on cuttings. Paper SPE 36854 presented at the 1996 SPE European Petroleum Conference, Milan, Italy. Ringstad, C., Lofthus, E.B., Sonstebo, E.F., Fjæ r, E., Zausa, F.., & Giin-FaFuh, 1998. Prediction of Rock Parameters From Micro-indentation Measurements: The Effect of Sample Size. EUROCK ’98, Trondheim, Norway. July 8–10. SPE 47313. Santarelli, F.J., Detienne, J.L., Zundel, J.P., 1989. Determination of the mechanical properties of deep reservoir sandstones to assess the likelihood of sand production. In: aury.Fourmaintraux, D. (Ed.), Rockar Great Depth. A.A. Balkema, Brookfield, VT, 779–787. Santarelli, F.J., Marsala, A.F., Brignoli, M., Rossi, E., Bona, N., 1996. Formation evaluation from logging on cuttings. In: SPE, Proceedings of European Petroleum Conference. Milano, SPE36851. Shakoor, A., Bonelli, R.E., 1991. Relationship between petrographic characteristics, engineering index properties, and mechanical properties of selected sandstones. Bull. In. Ass. Eng. Geo 28, 55–71. Zoback, M.D., Barton, C.A., Brudy, M., Castillo, D.A., Finkbeiner, T., Grollimund, B.R., Moos, D.B., Peska, P., Ward, C.D., Wiprut, D.J., 2003. Determination of stress orientation and magnitude in deep wells. Int. J. Rock. Mech. Min. Sci. 40, 1049–1076.
coefficient more than 0.78. The proposed equation was validated by estimating the UCS values of 3 samples and comparing the results with the UCS values measured using standard procedures and showed a similarity of more than 85%. Comparison of the empirical relationship proposed in the present study with empirical equations proposed in previous studies indicated that the lithology and strength range of the rock are factors effecting the suggested relations. Acknowledgment The authors would like to thank the National Iranian South Oilfields Company (NISOC), for providing a part of the cost for this research. References Ahmadi-Sheshde, E., Cheshomi, A., 2015a. New method for estimating compressive strength (UCS) using small rock sample. J. Pet. Sci. Eng. 133, 367–375. Ahmadi-Sheshde, E., Cheshomi, A., 2015b. Estimation the uniaxial compressive strength of microcrystalline limestone using indentation test. J. Eng. Geol. 9 (3), 2891–2916, (In Persian language). American Society for Testing and Materials, 2002. Standard Test Method for Unconfined Compressive Strength of Intact Rock Core Specimens. ASTM D2938. American Society for Testing and Materials, 2008. Standard Practices for preparing Rock Cores as Cylinderical Test Speciments and Verifying Conformance to Dimensional and Shape Tolerances. ASTM D4543. Bell, F.G., Lindsay, P., 1999. The petrographic and geomechanical properties of some sandstones. Eng. Geol. 53, 57–81. Cheshomi, A., Ahmadi-Sheshde, E., 2013. Determination of uniaxial compressive strength of microcrystalline limestone using single particles load test. J. Pet. Sci. Eng. 11, 121–126. Cheshomi, A., Mousavi, E., Ahmadi-Sheshde, E., 2015. Evaluation of single particle loading test to estimate the uniaxial compressive strength of sandstone. J. Pet. Sci. Eng. 135, 421–428. Garcia, R.A., Saavedra, N.F., Caldero´n, Z.H., Mateus, D., 2008. Development of
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Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Estimation of uniaxial compressive strength of shale using indentation testing
MARK
⁎
Akbar Cheshomia, , Golnaz Hajipoura, Jafar Hassanpoura, Bahman Baga Dashtakib, Yavar Firouzeia, Ebrahim Ahmadi Sheshdea a b
Department of Structural and Engineering Geology, School of Geology, College of Science, University of Tehran, Enghelab Ave., Tehran, Iran NISOC Administrative Building, Fadaeeyane Islam St., Ahvaz, Iran
A R T I C L E I N F O
A BS T RAC T
Keywords: Uniaxial compressive strength Shale Indentation testing Critical transition force
A number of methods have been proposed to indirectly assess the uniaxial compressive strength (UCS) of intact rock in the drilling of oil wells and underground drilling. Indentation testing is a method in which an indentor of a specific diameter penetrates a particle of rock and the force-displacement curve is plotted to determine the critical transition force (CTF). In the present study, 10 shale block samples were collected from a cretaceous shale formation in Iran from which standard cores were prepared and subjected to UCS testing. Cubic particles 4, 5 and 7 mm3 in size were cut and entrenched in disks containing resin and a total of 300 indentation tests were conducted on them. Empirical relations for the relation between UCS and CTF were developed for each size. The highest correlation coefficient was recorded for the 7 mm3 particles and the lowest for the 4 mm3 particles. A simple method is proposed to determine the empirical relationship independent of particle dimensions between UCS and CTF that has a correlation coefficient of 0.78. Verification of the proposed equations show that they predicted UCS with 85% accuracy. A comparison of the proposed relationships and those from previous studies indicates that the empirical relationship between these two variables is influenced by variation in the uniaxial compressive strength and lithology of the different samples.
1. Introduction Determination of the uniaxial compressive strength (UCS) of rock is an essential step in oil exploration projects that study wellbore instability (Moos et al., 2003), sandification potential (Santarelli et al., 1989) and quantification of stress magnitude (Zoback et al., 2003). There are direct and indirect methods available to determine this parameter. The standard procedure recommended by ASTM (2002) and the International Society for Rock Mechanics (1981) is a direct method that requires standard cores with length-to-diameter ratios of 2.0–2.5 and diameters of 47 mm. Preparation of standard cores can be difficult, expensive and timeconsuming for deep exploration boreholes for oil and gas reservoirs in the presence of weak rock and joints and at great depth (Cheshomi et al., 2015). This has prompted researchers to propose indirect methods of estimating USC using drill cuttings. Santarelli et al. (1996) showed that drill cuttings are representative of a formation and can be a reliable source of information about its mechanical behavior. Indirect methods available for use on small rock fragments
(such as drill cuttings) are the continuous wave (Nes et al., 1998), lithological characteristics (Shakoor and Bonelli, 1991; Bell and Lindsay, 1999), reconstructed cores (Mehrabi et al., 2012), direct loading of single particles (Cheshomi and Ahmadi-Sheshde, 2013), and modified point load testing (Ahmadi-Sheshde and Cheshomi, 2015a) techniques. Indentation testing is an indirect method that allows measurement of the mechanical properties of rock. This test is simple, requires a comparatively short time for completion and is lower in cost than other mechanical tests (Garcia et al., 2008). Indentation testing uses a fat- tip indentor with a specific diameter (for example 1 mm; Mateus et al. (2007)) that penetrates small rock fragments at a steady velocity. The fragment to be tested is first inserted into a container of resin to provide support to the samples and allow measurement of the force required for penetration. This force is sufficient to demonstrate the elastic and plastic behavior of small rock fragments. The results are graphed in a force-displacement curve that is used to determine the critical transition force (CTF) and indentation modulus (Ringstad et al., 1998). Previous studies have proposed
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Corresponding author. E-mail addresses: [email protected] (A. Cheshomi), [email protected] (G. Hajipour), [email protected] (J. Hassanpour), [email protected] (B.B. Dashtaki), Yavar.fi[email protected] (Y. Firouzei), [email protected] (E.A. Sheshde). http://dx.doi.org/10.1016/j.petrol.2017.01.030 Received 11 July 2016; Received in revised form 8 December 2016; Accepted 17 January 2017 Available online 24 January 2017 0920-4105/ © 2017 Elsevier B.V. All rights reserved.
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Table 1 Results of previous research on indentation testing. Author
Lithology
Particle shape
Size (mm)
Rate of penetration (mm/ Sec)
Proposed equation
Equation No.
Ringstad et al. (1998)
Shale, Sandstone and Limestone Sandstone Shale Limestone Limestone
Irregular
different size
–
UCS=0.149(CTF)
1
Irregular Irregular Irregular Cubic
4 <4 2, 5 2, 3, 4
0.3 0.3 0.01 0.01
UCS=91.97(CTF) UCS = −0.0083 CTF2 +33.08CTF UCS=0.48(CTF)n−19.36 UCS = 0.29 CTF – 41.28 D – 186.47 I + 317.63
2 3 4 5
Mateus et al. (2007) Garcia et al. (2008) Haftani et al. (2013) Ahmadi-Sheshde and Cheshomi (2015b)
CTF (Critical transition force In “N”), D (Particle diameters in “mm”), D*(Critical transition force per dimensionless parameter of surface in “N”), I (indenter diameter =1 mm), UCS (Mpa) Table 2 Results of indentation testing on cubic particles. SampleNo.
S−1 S−2 S−3 S−4 S−5 S−6 S−7 S−8 S−9 S−10
Measured
CTF (N)
UCS (MPa)
4 mm3
43.25 113.93 51.36 82.61 39.43 48.77 41.2 62.31 92.7 100.69
5 mm3
7 mm3
Min.
Max.
Ave.
Sd.
Min.
Max.
Ave.
Sd.
Min.
Max.
Ave.
Sd.
326.3 764.6 576.2 513.2 274.2 446.1 223.8 497.5 537.5 590.2
766.7 1114.4 1092.1 886.3 704.4 893.5 631.9 872.4 869.3 928.7
594.7 955 759.6 721.8 485.8 655.9 359.7 650.6 693 739.3
13.5 13.8 14.3 12.8 12.9 15.8 6.6 12.7 9.8 12.4
541.9 761.4 544 618.4 564.4 449.4 454.4 678.4 709.1 650.1
1002.5 1182.8 933.1 1161.8 800.9 1052.1 823 1050.1 954.7 1069
750.5 1005.2 723.3 911.2 664.7 666.7 638.8 835 844.1 826.7
13.7 12.7 11.8 17.6 8.7 17.3 14 13.5 8.2 12.5
712 1010.5 856.8 644.6 648.1 759.2 678.9 807.8 864.6 801.7
1292.5 1747.1 1290.3 1642.7 1337.7 1206.9 925.4 1154.3 1437.5 1519.5
950.6 1347.4 1029.4 1216 921.1 983.7 810.1 931.4 1135.4 1184.2
17.5 25 11.7 22.6 26.4 12.3 7.7 11.3 19 22.4
Fig. 1. Sample preparation: (a) cutting fragments to specified diameters; (b) entrenching cubic particles into disks containing resin; (c) samples prepared for testing.
Fig. 2. (a) Indentation testing apparatus and; ( b) load-displacement curve of sample S-7 (4, 5 and 7 mm3 in size).
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Sh-2
Sh-3
Sh-5
Sh-7
7 mm3
5 mm3
4 mm3
Fig. 4. Linear regression between UCS and CTF for particles 4, 5 and 7 mm3 in size.
• • • •
Fig. 3. Failure pattern for some particles (Sample No. Sh-2, Sh-3. Sh-5 and Sh-7 in cubic size 4, 5 and 7 mm3).
empirical relationships between CTF and UCS based on indentation testing of small rock fragments. Table 1 summarizes the most significant studies. The present study determined the UCS of 10 shale block samples from cretaceous formation outcrops in Iran. Small rock fragments were produced from natural blocks using a crushing machine and the CTF of 300 small rock fragments was determined. To assess the effect of particle size on CTF, particles of 4, 5 and 7 mm3 in size were prepared and the CTF was determined for each particle size. Empirical equations to determine the relationship between CTF and UCS were then developed. The proposed relationship was validated and the results of the present study were compared with those of previous studies.
The empirical equations were validated. The proposed empirical equations were compared with those from previous studies.
3. Sampling and laboratory testing Ten blocks (20×20×40 cm3) were obtained from cretaceous formation outcrops in the vicinity of Sanandaj, Iran and subjected to the following tests. 3.1. UCS NX cores (50.7 mm in diameter and 109.4 mm in length) were prepared from the blocks according to ASTM (2008) standards and subjected to UCS testing according to ASTM protocol (2002). Cores were drilled perpendicular to the direction of weakness surfaces so UCS tests were conducted perpendicular to the direction of cores weak surfaces. The results of the UCS testing are presented in Table 2. The UCS of the samples varied from 39.43 to 113.93 MPa.
2. Methodology Sample preparation and method of research are as follows:
• • • • •
support for the samples. Indentation testing was performed on each cubic particle and the CTF was measured. Empirical equations between UCS and CTF were developed.
Collection of 10 shale block samples. NX cores were drilled out of these blocks and UCS testing was conducted. Small rock fragments were prepared using a crushing machine.
3.2. Indentation test Small rock fragments were shaped into cubes 4, 5 and 7 mm3 in size. 3.2.1. Sample preparation After UCS testing, each core was crushed using a crushing machine and the fragments produced were cut in to cubic particles of 4, 5 and
The cubic particles were inserted into a container of resin to provide
Table 3 UCS–CTF equations for cubic shale particles 4, 5 and 7 mm3 in size (CTF in Newtons and UCS in MPa). Equation No.
Relation
Cube particle dimension (mm)
Empirical relationship
Correlation coefficient (R)
6 7 8
Linear
4 5 7
UCS=0.14 CTF−20.71 UCS=0.21 CTF−97.45 UCS=0.15CTF−89.73
0.78 0.91 0.92
9 10 11
Power
4 5 7
UCS=0.0286CTF1.196 UCS=0.000005CTF2.44 UCS=0.000008CTF2.285
0.77 0.91 0.91
12 13 14
Exponential
4 5 7
UCS=17.08e0.002CTF UCS=5.66e0.003CTF UCS=6.40e0.002CTF
0.79 0.91 0.92
15 16 17
logarithmic
4 5 7
UCS=80.19 Ln CTF- 448.27 UCS=167.31 Ln CTF – 1045.4 UCS=156.76 Ln CTF- 1018.7
0.75 0.91 0.91
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Fig. 5. Correlation between UCS and CTF/S.
Table 4 Measured UCS values and those estimated using Eqs. (6), (7), (8) and (19). Sample No.
Particle dimension (mm3)
Measured UCS (MPa)
CTF (N)
Equation 6,7,8
Eq. (19)
Estimated UCS
Similarity to measured UCS (%)
Estimated UCS
Similarity to measured UCS (%)
S−11 S−12 S−13
4
104.86 39.24 52.44
706.964 475.391 482.83
78.26 45.84 46.88
75 86 89
78.75 39.76 41.01
75 99 78
S−11 S−12 S−13
5
104.86 39.24 52.44
928.056 669.316 680.086
97.44 43.11 45.37
93 91 86
84.71 49.86 51.31
81 79 98
S−11 S−12 S−13
7
104.86 39.24 52.44
1194.44 812.456 897.37
89.44 32.14 44.88
85 82 86
74.62 37.88 46.05
71 96 88
Fig. 6. Comparison of measured and estimated UCS for cubic particles 4, 5 and 7 mm3.
Fig. 7. Correlation between measured and estimated UCS based on: (a) dependence on particle dimensions (Eqs. (6), (7), (8)) and; (b) independent of particle dimensions (19).
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Fig. 8. Similarity between measured and estimated UCS from Eqs. (6), (7), (8) and (19) for cubic particles 4, 5 and 7 mm in size. Table 5 Comparison of values obtained from present and previous studies. Sample no.
UCS
CTF
UCS values estimated from equation no. 1
S−1 S−2 S−3 S−4 S−5 S−6 S−7 S−8 S−9 S−10 S−11 S−12 S−13
(MPa)
(N)
(MPa)
43.25 113.93 51.36 82.61 39.43 48.77 41.2 62.31 92.7 100.69 104.86 39.24 52.44
594.72 955.06 759.67 721.8 485.86 655.92 359.78 650.60 693.02 739.93 706.96 475.39 482.83
88.61 142.3 113.19 107.55 72.39 97.73 53.61 96.94 103.26 110.25 105.34 70.83 71.94
2
3
4
5
19
54.7 78.84 69.86 66.38 44.68 60.33 33.09 59.84 63.74 68.05 65.02 43.72 44.41
113.82 163.35 138.31 132.96 95.97 123.26 73.63 122.46 128.78 135.54 130.82 94.18 95.45
123.37 209.85 162.96 153.87 97.25 138.06 66.99 136.78 146.96 158.22 150.31 94.73 96.52
138.51 243.01 186.34 175.36 106.94 156.26 70.38 154.71 167.02 180.62 171.06 103.9 106.06
60.16 121.02 88.02 81.62 41.77 70.49 20.48 69.59 76.76 84.68 79.11 40.01 41.26
Fig. 9. Comparison of measured and estimated UCS using different empirical relationships for 13 samples tested. Area "A" based on Eqs. 1, 2, 3 and (19) that related to sandstone and shale and area "B" based on equations 4 and 5 that related to limestone.
7 mm3 using a diamond slab saw. The cubic particles dimensions was measured with a caliper. Preparing cubic particles with smaller than 4 mm3 is very difficult, and particles bigger than 7 mm3 does not represent drill cuttings. Therefore in this research particles were prepared in this dimensions. Fig. 1 shows the preparation of the cubic particles. Preparing cubic particles with similar shape and diameter (in very small dimensions) requires significant accuracy and patience. The particles were first entrenched in disks containing ML-506 resin to restrain them from moving during testing. Previous researchers used resin as the surrounding material, thus boundary conditions in this research would be the same for all cubic particles as well as previous researches. Cubic particles of different sizes were prepared to eliminate
the influence of particle shape and to investigate the influence of fragment dimensions. 3.2.2. Testing procedure Indentation testing was carried out using a fat-tip indentor with a tip 1 mm in diameter at a constant peneteration rate of 0.01 mm/s as done in Mateus et al. (2007), Garcia et al. (2008), and Haftani et al. (2013 & 2014)). Fig. 2 shows the indentation test apparatus and the load-displacement curve for sample S-7. The CTF is the maximum force in load – displacment curve as is shown in Fig. 2b. Ten particles of each cubic particle size were tested. The cubic particles were 4, 5 and 7 mm3 in size, making a total of 300 indentation 28
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validity of this relationship falls into range of cubic particle dimensions tested. 5. Verification of empirical relationships In order to validate the proposed empirical relationship, three shale samples other than the original 10 used to propose the empirical relationship were selected. Standard core samples were prepared and the UCS values were determined according to standard testing procedure. The process in section 2.2 that then used to form cubic particles in 4, 5 and 7 mm3 in size. For each size, 10 indentation tests were conducted and the results were averaged to determine the CTF of each sample. Given the CTF, UCS was then estimated using Eqs. (6), (7), (8) and (19). Table 4 shows the measured UCS values and those calculated using the proposed relation. The data presented in Table 4 was used for comparison of the measured and estimated UCS as shown in Figs. 6 and 7 for the three samples. Fig. 6 shows that there is a slight difference between the measured and estimated UCS values. The proximity of points to line 1:1 in Fig. 7 indicates good correlation between the measured and estimated UCS values. Fig. 8 compares the percentage of similarity between the measured and estimated UCS. It can be said that the empirical relationships dependent and independent of dimensions can be used to estimate the UCS of the shale with more than 85% similarity.
Fig. 10. Measured USC range in present and previous studies. As can be seen measured UCS range for microcrystalline limestone is very different in comparison with sandstone and shale.
tests. Table 2 shows the minimum, maximum, average and standard deviation of the CTF values obtained from indentation testing. After the indentation test a photo was taken from each particle. In Fig. 3 failure pattern for some particles has been demonstrated. 4. Analysis and interpretation of results Laboratory testing was carried out to determine the relationship between UCS and CTF and investigate the effect of cubic particle diameter on CTF.
6. Discussion The relationship obtained in the present study (Eq. (19)) and empirical equations from previous studies (Eqs. (1), (2), (3), (4) and (5)) were compared. For this purpose, CTF values obtained from 4 mm3 samples from the 10 original blocks. The 3 validation samples were entered into Eqs. (1), (2), (3), (4) and (5) and the UCS values for each sample was estimated. The results are presented in Table 5. Fig. 9 shows the UCS values estimated using different equations versus values measured by standard testing. An obvious difference between the UCS values estimated by the different relationships can be observed. The equations proposed by Haftani et al. (2013) and Ahmadi-Sheshde and Cheshomi (2015b) related to microcrystalline limestone. Equations proposed by Ringstad et al. (1998), Mateus et al. (2007) and Garcia et al. (2008) related to sandstone and shale and equation proposed in this research related to shale. As can be seen in Fig. 9, UCS estimated by equations proposed for shale and sandston are closer to measured UCS and UCS estimated by equations proposed for limestone are further than measured UCS. So the reason for this variation is the difference in the lithology. On the other hand Fig. 10 shows measured UCS range in this research and previous research. Measured UCS range for microcrystalline limestone is very different in comparison with sandstone and shale. As can be seen in Fig. 10, measured UCS of sandstone and shale that studied in previous research are close to measured UCS that studied in this research. Therefore, the UCS estimated using these equations is close to those estimated in the present study.
4.1. Correlation between UCS and CTF To investigate the empirical relationship between UCS and CTF, a variation graph for the two variables was plotted using the results of the 10 samples of each size from Table 2 at linear, power, exponential and logarithmic scale. Table 3 shows the resulting empirical relationships. Table 3 shows that the correlation coefficients of the different models are acceptable; however, the simplicity of linear regression recommends this approach over the others. Fig. 4 shows the linear relationships between UCS and CTF for the cubic particles. The correlation coefficients of linear regression between CTF and UCS for cubic particles 4, 5 and 7 mm3 in size were 0.78, 0.91 and 0.92, respectively. The lowest correlation coefficient was for the 4 mm3 particles and the highest was for the 7 mm3 particles. This suggests that the correlation coefficient increased as the particle dimensions increased. 4.2. Empirical relationship independent of particle dimensions The equations in Table 3 are applicable to cubic particles 4, 5 and 7 mm3 in size and an indentor diameter of 1 mm. To eliminate the effect of particle dimensions, dimensionless parameter (S) is defined in Eq. (18) as:
S=
Ss Si
7. Conclusion
(18)
The present study evaluated the use of the indentation test to estimate the UCS of shale rock. Ten shale blocks were collected and their UCS values were determined in accordance with ASTM standards. More than 300 cubic particles 4, 5 and 7 mm3 in size were prepared and indentation testing was carried out. The CTF of each cubic particle was obtained from the related load–displacement diagrams. An empirical relationship between UCS and CTF using linear correlation was proposed that produced a correlation coefficient more than 0.87. To eliminate the effect of particle dimensions, a dimensionless parameter was defined and used for an empirical equation independent of particle dimensions that produced a correlation
In this equation, Ss is the particle surface and Si is the indentor surface. The CTF is divided into this dimensionless parameter (CTF/S) to eliminate the effect of particle dimension. Fig. 5 shows a graph of UCS-CTF/S. The graph was used to calculate the relationship between UCS and CTF as shown in Eq. (19).
UCS = 0.76(CTF / S )–40.28
R = 0.78
(19)
A correlation coefficient of 0.78 was achieved for Eq. (19) independent of particle dimensions. The correlation coefficient for Eq. (19) is lower than those for Eqs. (6), (7) and (8) and demonstrates the effect of particle dimensions on the correlation coefficient. Note that the 29
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experimental correlations between indentation parameters and unconfined compressive strength (UCS) values in shale samples. CTF-Cienc. Tecnol. Y. Futuro 3 (4), 61–81. International society for rock mechanic, 1981. In: Brown, E.T. (Ed.), Rock Characterization Testing and Monitoring. Pergam Press, Oxford. Haftani, M., Bohloli, B., Mosavi, M., Nouri, A., Moradi, M., MalekiJavan, M., 2013. A new method for correlating rock strength to indentation tests. J. Pet. Sci. Eng. 112, 24–31. Haftani, M., Bohloli, B., Nouri, A., MalekiJavan, M., Moradi, M., 2014. Size effect in strength assessment by indentation testing on rock fragments. In. J. Rock. Mech. MIn. Sci. 65, 141–148. Mateus, J., Saavedra, N.F., Calderó n, Z.H., Mateus, D., 2007. Correlation development between indentation parameters and unaxial compressive strength for Colombian sandstones. CTF-Cienc. Y. Futuro 3 (3), 125–135. Mehrabi mazidi, S., Haftani, M., Bohloli, B., Cheshomi, A, 2012. Measurement of uniaxial compressive strength of rocks using reconstructed cores from rock cuttings. J. Pet. Sci. Eng. 86–87, 39–43. Moos, D., Peska, P., Finkbiner, T., Zoback, M.D., 2003. Comprehensive wellbore stability analysis utilizing Quantitative Risk Assessment. J. Pet. Sci. Eng. 38, 97–110. Nes O.M., Horsrud P., Sonstebo E.F., Holt R.M., Ese A.M., Okland D., Kjorholt H., 1998. Rig-Site and laboratory use of CWT acoustic velocity measurements on cuttings. Paper SPE 36854 presented at the 1996 SPE European Petroleum Conference, Milan, Italy. Ringstad, C., Lofthus, E.B., Sonstebo, E.F., Fjæ r, E., Zausa, F.., & Giin-FaFuh, 1998. Prediction of Rock Parameters From Micro-indentation Measurements: The Effect of Sample Size. EUROCK ’98, Trondheim, Norway. July 8–10. SPE 47313. Santarelli, F.J., Detienne, J.L., Zundel, J.P., 1989. Determination of the mechanical properties of deep reservoir sandstones to assess the likelihood of sand production. In: aury.Fourmaintraux, D. (Ed.), Rockar Great Depth. A.A. Balkema, Brookfield, VT, 779–787. Santarelli, F.J., Marsala, A.F., Brignoli, M., Rossi, E., Bona, N., 1996. Formation evaluation from logging on cuttings. In: SPE, Proceedings of European Petroleum Conference. Milano, SPE36851. Shakoor, A., Bonelli, R.E., 1991. Relationship between petrographic characteristics, engineering index properties, and mechanical properties of selected sandstones. Bull. In. Ass. Eng. Geo 28, 55–71. Zoback, M.D., Barton, C.A., Brudy, M., Castillo, D.A., Finkbeiner, T., Grollimund, B.R., Moos, D.B., Peska, P., Ward, C.D., Wiprut, D.J., 2003. Determination of stress orientation and magnitude in deep wells. Int. J. Rock. Mech. Min. Sci. 40, 1049–1076.
coefficient more than 0.78. The proposed equation was validated by estimating the UCS values of 3 samples and comparing the results with the UCS values measured using standard procedures and showed a similarity of more than 85%. Comparison of the empirical relationship proposed in the present study with empirical equations proposed in previous studies indicated that the lithology and strength range of the rock are factors effecting the suggested relations. Acknowledgment The authors would like to thank the National Iranian South Oilfields Company (NISOC), for providing a part of the cost for this research. References Ahmadi-Sheshde, E., Cheshomi, A., 2015a. New method for estimating compressive strength (UCS) using small rock sample. J. Pet. Sci. Eng. 133, 367–375. Ahmadi-Sheshde, E., Cheshomi, A., 2015b. Estimation the uniaxial compressive strength of microcrystalline limestone using indentation test. J. Eng. Geol. 9 (3), 2891–2916, (In Persian language). American Society for Testing and Materials, 2002. Standard Test Method for Unconfined Compressive Strength of Intact Rock Core Specimens. ASTM D2938. American Society for Testing and Materials, 2008. Standard Practices for preparing Rock Cores as Cylinderical Test Speciments and Verifying Conformance to Dimensional and Shape Tolerances. ASTM D4543. Bell, F.G., Lindsay, P., 1999. The petrographic and geomechanical properties of some sandstones. Eng. Geol. 53, 57–81. Cheshomi, A., Ahmadi-Sheshde, E., 2013. Determination of uniaxial compressive strength of microcrystalline limestone using single particles load test. J. Pet. Sci. Eng. 11, 121–126. Cheshomi, A., Mousavi, E., Ahmadi-Sheshde, E., 2015. Evaluation of single particle loading test to estimate the uniaxial compressive strength of sandstone. J. Pet. Sci. Eng. 135, 421–428. Garcia, R.A., Saavedra, N.F., Caldero´n, Z.H., Mateus, D., 2008. Development of
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