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НАУКИ о ЗЕМЛЕ. Геомеханика, разрушение горных пород / Of EARTH SCIENCES. Geomechanics, rock destruction
УДК 622.01
Hou Bing, Li Dandan, Chen Mian, Liang Chuan, Jin Yan
HOU BING, PhD, Associate professor, State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, China. E-mail: houbing9802@163.com
LI DANDAN, Master Candidate, State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, China. E-mail: wilber-will@163.com
CHEN MIAN, Professor, Dean, State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, China. Key Laboratory of Reservoir Stimulation, CNPC, Langfang, China. E-mail: chenmian@vip.sina.com
LIANG CHUAN, PhD Candidate, State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, China. E-mail: liangchuan@gmail.com
JIN YAN, Professor, State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, China. E-mail: 13701222683@vip.163.com
The sensibility of mechanical behavior to loading rate for shale gas reservoir with different weak planes
Triaxial compression tests are performed on shale samples from Longmaxi reservoir formation with GCTS RTR1500 mechanical testing system. The failure modes and mechanical parameter sensitivity characteristics of shale under different loading rates are investigated. Longmaxi shale gas reservoir is well-developed laminations, featured by matrix and fractures, which has been called "dual pore structure", and is dramatically sensitive to loading rates. The relationship between compressive strength and loading rate is generally linear under different conditions of weak plane angles (P), yet in the meanwhile, elastic modulus manifests obviously nonlinear. When the loading rate is increased from 0.05
© Hou Bing, Li Dandan, Chen Mian, Liang Chuan, Jin Yan, 2014
This article is based on reports and statements 4th Russian-Chinese Scientific Forum "Nonlinear geomechanics and geodynamics in deep level mining" take place at Far East Federal University (July, 27-31th, 2014, Vladivostok, Russia) with support School of Engineering FEFU, the Russian Fund of Fundamental researches and Programs of development FEFU. The conference participants prepared their reports specifically for our magazine. [79]
mm/min to 0.2 mm/min, specimens with the angle Pof 30° has the largest growth amplitude , reaching to 17.16%, while the P =70° group has the largest amplification in elastic modulus. Moreover, elastic modulus is most sensitive to the loading rate at 0.12 mm/min. Since then, this trend is beginning to stabilize. Specially, shear failure is in charge under the rate of 12 mm/min, while tensing cracks begin to increase as loading rates going up.
Key words: shale, weak plane, triaxial test, loading rate, dual pore structure.
Introduction
A substantial effort has been made towards investigating mechanical behaviors and failure modes of rock materials over a wide range of loading rates. It is found that different loading rates on rock samples may lead to considerable differences among the cumulative AE hit-stress curves [1]. Also lots of tests show that compressive and tensile failure strength of rocks notably increase with the rate of loading of specimens. Also, the strength ratio of compression-tension of rocks is not a constant. It increase slightly with the loading rate [2, 3]. What's more, M.S. Paterson & T.F. Wong [4] revealed that three typical failure phenomena can be observed during loading process, including shear failure, splitting failure and splitting-shear hybrid failure modes. In addition, Da Huang [5] and Xiaotao Yang [6] analyzed the influences of loading rates on rupture process, crack number and propagation, stress-strain curves, energy transformation based on a series of experiments.
From different sides of demonstration, these literatures demonstrate rocks present strong stress sensitivity. Different loading rates will affect the results of rock petrophysics experiments in laboratory. So far, most of the researches have concerned the effect of the loading rate on granite, marble, sandstone, however, the investigation of the loading rate's influence on shale is rarely involved. This paper is mainly focused on a qualitative investigation on the fracture characteristics of the section of Sichuan Longmaxi Shale. Taking into account of the dual pore structure in the matrix and in the fractures of shale, triaxial compression tests were carried out to record integrated stress-strain curves. According to the experiment data, we comparatively studied the deformation properties and rules of shale with different weak plane angles under different loading rates.
Experimental procedures
The GCTS Rapid Triaxial Rock Test System is used to perform triaxial compression tests on standard specimens under different loading rates and confining pressures. A closed-loop digitally servo controlled apparatus is developed for accurately performing triaxial tests on rock specimens. Its stiffness load frame reaches to 10 MN/mm, and axial load reaches up to 4000 KN. 140 MPa cell pressure and 200 °C optional temperature control is feasible. It can meet all the specifications of the ISRM and ASTM for triaxial testing of rock samples. In addition, the system is also capable of performing permeability, hydraulic fracturing, indirect tension, and many other advanced rock test.
Specimens come from lower Silurian Longmaxi formation of Sichuan basin, where develops shale with natural fractures and bedding surface ("weak plane"). Graph 2-1 shows the outcrop of this shale suite, while graph 2-2 shows the core from Longmaxi shale gas reservoir. It is clear observed that Longmaxi shale formation is well-developed fissures and laminations.
As shown in figure 2-3, assuming that P is the included angle between weak plane normal direction and maximum principal stress. In order to investigate the impact of shale's dual porosity structure on the mechanical properties, we selected three groups of shale specimens containing natural fractures (weak plane), and Pequals to 30°, 45°, 70°, respectively. The different weak plane angles can be picked up by changing coring angles. Specimens were cut into standard cylinders with length of 50 mm and diameter of 25 mm, and its two ends were polished to keep them smooth and parallel with each other but vertical to the axis, as shown in Figure 2-4.
Influence of loading rate on shale mechanics parameters
On the basis of samples' stratum depth, we calculate confining pressure value and simulate the stratum situation in laboratory. Displacement-static loading method is adopted. Axial loading is applied at diverse rates on shale specimens, where exist different weak plane angles. After recording integrated stress-strain curve, we get shale's compressive strength (o) ,which equals to the curve's highest point, and elastic modulus(E), which equals to the elastic segment of the curve (in this experiment, adopting 40% ~ 60% of the peak intensity). List experimental data of each group in table 2-1:
Table 2-1
(I) Experimental results for shale mechanical parameters with p=30°
No. Loading rate mm/min Compressive stress (MPa) Standard deviation Elastic modulus (GPa) Standard deviation
1 0.04 176.4132 2.1249 27.5409 0.87679
2 0.08 178.1954 2.37173 27.55331 0.65231
3 0.12 177.639 3.24679 27.77151 0.6918
4 0.16 178.7286 2.80407 28.7471 0.95479
5 0.2 179.5972 3.438 28.93848 0.76458
(II) Experimental results for shale mechanical parameters with p=45°
No. Loading rate mm/min Compressive stress (MPa) Standard deviation Elastic modulus (GPa) Standard deviation
1 0.04 168.29 1.5527 25.96583 2.570182
2 0.08 170.2274 1.89013 27.77513 1.604391
3 0.12 172.4746 1.73019 30.21793 3.092429
4 0.16 174.8342 2.26021 30.41298 2.423433
5 0.2 176.3778 1.80179 30.77396 3.10382
(III) Experimental results for shale mechanical parameters with p=70°
No. Loading rate mm/min Compressive stress (MPa) Standard deviation Elastic modulus (GPa) Standard deviation
1 0.04 158.4266 4.46516 25.88051 1.881707
2 0.08 165.317 4.31788 27.54398 3.541415
3 0.12 166.3478 2.59814 29.3042 2.544844
4 0.16 168.9092 3.15214 29.88176 1.628617
5 0.2 172.6006 4.30115 30.06908 0.64322
Loading Rate (mm/min) Loading Rate (mm/min)
Fig. 2-5. Influence of loading rate on compressive strength Fig. 2-6. Influence of loading rate on elastic modulus
Relaying on experimental data, the relational graph of loading rate and compressive strength is obtained and the error line is added according to the standard deviation, as shown in figure 2-5. We can see that three groups of experiments have the same rule that with the increase of loading rate, the compressive strength of shale increases. The compressive strength point of different weak plane angles is
linear fitted. When P is 30°, the correlation coefficient R is 0.9299; when P is 45°, the correlation
22 coefficient R is 0.8828; when P is 70°, the correlation coefficient R is 0.9644. Thus it can be seen that in
different weak plane angles, compressive strength and loading rate has a good linear correlation.
However, with the change of the weak plane angles, the slope of fitting straight line is different. When
loading rate increases from 0.05 mm/min to 0.2 mm/min and P=30°, the slope of fitting straight line is
167.9 and the compressive strength adds 17.16%; when P=45°, the slope of fitting straight line is 148.6
and the compressive strength adds 12.72%; when P=70°, the slope of fitting straight line is 78.2 and the
compressive strength adds 7.45%. Because of the difference of weak plane angles, the rate sensitivity of compressive strength of shale measured in experiment is different, which will be discussed after this part.
Similarly, depending on the experimental results, the relational graph of loading rate and elastic modulus are given in figure 2-6. As shown, with the increase of loading rate, the elastic modulus of shale increases. When the weak plane angle P is 70 the increase of elastic modulus is the maximum; when the weak plane angle P is 45 the increase of elastic modulus is the second largest; when the weak plane angle P is 35 the increase of elastic modulus is the minimum. In addition, it can be derived that with the increase of loading rate, the increase of elastic modulus is nonlinear. When the loading rate is less than 0.12 mm/min, the rate sensitivity of elastic modulus remains at a high level. As loading rate going up within certain realms, the increase of elastic modulus is obvious. However, with the increase of loading rate continually, the increase trend of elastic modulus starts to slow down.
Fig. 2-7. Relationship between compressive strength and p
In order to further explore the effects of weak plane angle on shale properties, the relationship between compressive strength and weak plane angle P is depicted in figure 2-7. The experimental data shows that for the shale specimens with the weak plane angle of 30°, the average compressive strength is 187.91468, the standard deviation is 5.85051; for the shale specimens with the weak plane angle of 45°, the average compressive strength is 173.0408, the standard deviation is 7.22254; for the shale specimens with the weak plane angle of 70°, the sample average compressive strength is 168.92024, and the standard deviation of 6.456. It is obvious that the specimens of 30° present the highest compressive strength, and is significantly higher than the two other groups. Yet the compressive strength of specimens with the weak plane angle of 45° equal approximately or slightly higher than the 70° group.
Influence of loading rate on shale failure modes
The strain loading rate has significant effects on the failure modes of shale. Table 2-2 contains specimens' photos and corresponding crack sketches after triaxial experiments under different loading rates. Shale failure modes mainly include: shear failure, splitting failure and splitting-shear hybrid failure modes. The failure mode of which shale samples expand perpendicular to the fracture surface, which is perpendicular to the direction of the minimum principal stress, is called tensional fracture. As for the shear fracture, the relative displacement of both fracture surfaces is parallel, which is a kind of shear slip along the failure surface. The angle between the fracture surface and the direction of the maximum compressive stress is about 45 °.
Table 2-2
Failure mode sketches of shale specimens under different loading rates
0.04mm/min 0.04mm/min 0.12mm/min 0.08mm/min 0.08mm/min 0.12mm/min 0.16mm/min 0.16mm/min0.2mm/min0.2mm/min
When the loading rate is lower than 0.12 mm/min, the fracture mode of shale is mainly shear failure, generating fewer fractures. When the loading rate increases gradually, the sample begins to split, the number of crack increases and fails more completely. The failure mode is transformed from shear failure with single crack into the splitting failure with multi-cracks. When the loading rate reaches at 0.16mm/min, tensional failure takes the dominant position and the phenomenon of volume expansion is more obvious. At the lower loading rate, shear failure plays a main role, and tensile fracture is hard to form due to the development of the bedding plane and micro fracture of the shale itself, while higher loading rate leads axial force to facilitate shale producing multi-cracks.
Analysis of failure mechanism of shale
Shale is featured by matrix and fractures, which has been called "dual pore structure", and gas will be contained in matrix pores and flowed by fracture. Both matrix and fractures have separate porosity and permeability and different mechanical characteristics. In structure presentation, it performed itself as the existence of fractures, in mechanical presentation; it is performed as the existence of weak plane. As a
result, it is necessary to take into account the characteristics of anisotropy and heterogeneous of rock. The mechanical model should be a weak body with anisotropy and heterogeneity of all weak planes.
Mohr-Coulomb Criterion is expressed by diagram shown in figure 3-1. The intersection point M of AB line and stress circle represents the mechanical state of weak plane. Line AB represents the stress magnitude of weak plane. While the point M is beneath the ultimate strength line, it will not break through the weak plane, otherwise, it will become new initiation point of shear-slip cracks under compression environment and finally cause the shale failed.
^ rock intrinsic strength ¡\frictional sliding strength I
-:—* P
0 pTnin ft max 9 A
Fig. 3-1. T-a plot for rock containing weak plane Fig. 3-2. Predicted strength as function of p
Figure 3-2 shows the relationship of and p. According to the law of Mohr-Coulomb Criterion, if weak plane exists previously in rock, then the compressive strength o is with changing of the included angle between its normal and the maximum principal stress direction (P), as shown in figure 3-2. When p is smaller than pmin or is large than pmax, failure may propagate through the weak plane, instead of frictional sliding along the weak surface. At this point, the compressive strength stayed at the higher value regardless of the existence of the weak plane. However, once the P angle values between pmin and pmax, rock fractures will slide along the weak plane, while compressive strength is less than rock mass itself. The closer p is to the angle of the most the critical position, the more easily the rock slide along the fracture and the rate sensitivity of shale strengthen. Combined with the experimental data, it can be deduced that the strength of the first shale specimen group (P=30°) is more close to that of the rock mass itself; and the other two groups (P=45°& p=70°) are more highly influenced by the weak plane, the values of compressive strength are lower due to friction sliding.
Therefore, shale mechanics parameters are determined by both matrix and natural fractures, the smaller the angle between the maximum principal stress direction and weak plane normal, the influence of natural fractures in shale on mechanical properties is bigger, shale's rate sensitivity is stronger.
Conclusion
(1) The Longmaxi shale gas reservoir is transverse isotropy stratum. Because of the development of weak bedding plane, the mechanical model should be a weak body with anisotropy and heterogeneity of all weak planes. When the track of horizontal well is in the shale gas reservoir with many thin interbred, the deviation angle between wellbore and bedding plane may lead to the instability of borehole wall during drilling and the large different fracture pressure of different perforation clusters during staged fracturing.
(2) The triaxial rock mechanics parameters of the shale gas reservoir with different weak plane angles are sensitive to the loading rate. Under the different weak lane angles, compressive strength and loading rate
conform to the linear correlation, while loading rate sensitivity of elastic modulus is of great diversity. The closer P is to the angle of the most the critical position, the more easily the rock slide along the fracture and the rate sensitivity of shale strengthens.
(3) Shale is a kind of dual porosity structure. The failure mode of shale is different under different loading rates. When the loading rate is lower than 0.12 mm/min, the fracture mode of shale is mainly shear failure, generating fewer fractures. When the loading rate increases gradually, the failure mode is transformed from shear failure with single crack into the splitting failure with multi-cracks and the phenomenon of volume expansion is more obvious.
Acknowledgement
The authors are grateful for the projects supported by the Foundation for Innovative Research Groups of the NSFC (No. 51221003), NSFC (No. 51204195 and No. 51234006), Beijing Youth Elite Project (No. YETP0672) and Science Foundation of China University of Petroleum, Beijing (No. 2462011KYJJ0207).
REFERENCES
1. Chen M., Zhang Y., Jin Y., et al. Experimental study of influence of loading rate on Kaiser effect of different lithological rocks. Chinese Journal of Rock Mechanics and Engineering. 2009;(1)28.
2. Xu J.Y., Liu S. Effect of impact velocity on dynamic mechanical behaviors of marble after high temperatures. Chinese Journal of Geotechnical Engineering, 2013;35(005): 879-883.
3. Wang H.L., Fan P.X. Influence of strain rate on progressive failure process and characteristic stresses of red sandstone [J]. Rock and Soil Mechanics. 2011;32(5):1340-1346.
4. Paterson M.S.,Wong T.F. Experimental rock deformation-the brittle field [M]. 2nd ed. New York, SpringerVerlag, 2005, p. 155-158.
5. Huang D., Huang R.Q., Zhang Y.X. Experimental investigations on static loading rate effects on mechanical properties and energy mechanism of coarse crystal grain marble under uniaxial compression. Chinese Journal of Rock Mechanics and Engineering. 2012;31(2):245-255.
6. Jin X.T., Ge R.X., Li C.G. et al. Influences of loading rates on mechanical behaviors of rock materials. Chinese Journal of Rock Mechanics and Engineering. 2010;29.
7. Zhang G.Q., Jin Y., Chen M. Measurement of in-situ stress by Kaiser effect under confining pressures. Chinese Journal of Rock Mechanics and Engineering. 2002;21(3):360-363.
8. Stavrogin A.N., Tarasov B.G. Experimental physics and rock mechanics : results of laboratory study [M]. Tokyo, A.A. Balkema, 2001, p. 204-220.
9. Liu S.J.,Wu L.X. et al. Remote sensing rock mechanics (VI)-features of rock fraction-sliding and analysis on its influence factors. Chinese Journal of Rock Mechanics and Engineering. 2004;23(8):1247-1251.
10. Mahmutoglu L. The effects of strain rate and saturation on a micro-cracked marble. Engineering Geology. 2006; 82(3): 137-144.
11. Zhou X.P., Yang H.Q., Zhang Y.X. Rate dependent critical strain energy density factor of Huanglong limestone [J]. Theoretical and Applied Fracture Mechanics. 2009;51(1):57-61.
