Abstract
A quantitative method for evaluating brittleness is pivotal in optimizing hydraulic fracturing of shale. Shale reservoirs are characterized by diverse components and complex diagenetic environment, resulting in multiple factors influencing the brittleness feature, which makes the traditional brittleness index hardly applied widely. This study proposes a new quantitative brittleness model for shale based on the significance assignment of the brittle-sensitive index (BSI) at different stage during the loading. This study divides the complete stress–strain curve into three stages and acquires corresponding BSI based on the brittle failure evolution. Then, a fuzzy analytic hierarchy process (FAHP) is proposed to determine the contribution weight coefficients of BSI at each stage to the brittle behavior of shale, where a comparison matrix is constructed based on the evolution of energy accumulating and releasing during the loading to avoid the experience lacking and consistency issues. Experimental evaluations of two sets of reservoir shale show that the new model can effectively indicate the variation of brittleness with affecting factors, such as brittle–plastic mineral content, porosity, burial depth, and confining pressure, which demonstrate its accuracy and superiorities. Comparative analysis of the published models reveals that the new model has stronger sensitivity to the buried depth. The procedure of weight determination can effectively explain the prediction of brittle variation under confining pressure. Furthermore, the proposed model, combined with the controlled artificial shale, indicates that the brittleness decreases with the kerogen content. The results are of great importance in optimizing hydraulic fracturing of shale gas reservoirs.
Highlights
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A new quantitative brittleness model for shale is proposed based on the energy evolution-based fuzzy analytic hierarchy process.
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The new model can effectively indicate the variation of brittleness with brittle–plastic mineral content, porosity, burial depth, and confining pressure.
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The brittleness of shale is verified to be decreasing with the kerogen content by combining with the controlled artificial organic-rich shale and the proposed model.
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Abbreviations
- E :
-
Young’s modulus
- \({\varepsilon }_{\mathrm{i}}\) :
-
Ductile strain
- \({\sigma }_{\mathrm{p}}\) :
-
Peak strength
- \({\varepsilon }_{\mathrm{r}}\) :
-
Residual strain
- S2:
-
The plastic energy
- \({r}_{ik}\) :
-
Value of the i-th row and k-column in the optimal matrix
- \({f}_{ij}\) :
-
Value of row i and column j in the fuzzy consistent matrix
- \({r}_{i}\) :
-
Matrix obtained by summing the optimal matrix by row i
- BEn 1, BEn 2, BEn 3 :
-
Normalized brittleness indexes
- BM:
-
Brittle minerals
- Q + C:
-
Quartz + calcium
- TOC:
-
Total organic content
- ν :
-
Poisson’s ratio
- \({\varepsilon }_{\mathrm{p}}\) :
-
Total strain at failure
- \({\sigma }_{\mathrm{r}}\) :
-
Residual stress
- S1:
-
Elastic energy accumulated before the peak
- S5:
-
Additional energy provided outside the peak
- m :
-
Number of evaluation indicators
- BSI:
-
Brittle-sensitive index
- a, b and c :
-
Weight coefficients of BSI
- NBM:
-
Non-brittle minerals
- Cl + T + E:
-
Clay + TOC + else minerals
References
Ai C, Zhang J, Li YW, Zeng J, Yang XL, Wang JG (2016) Estimation criteria for rock brittleness based on energy analysis during the rupturing process. Rock Mech Rock Eng 49(12):4681–4698. https://doi.org/10.1007/s00603-016-1078-x
Allaby A, Allaby M (1990) The concise Oxford dictionary of earth sciences. Oxford University Press, Oxford. https://doi.org/10.1180/minmag.1990.054.377.26
Altindag R (2010) Assessment of some brittleness indexes in rock-drilling efficiency. Rock Mech Rock Eng 43(3):361–370. https://doi.org/10.1007/s00603-009-0057-x
Altindag, R. (2003). Correlation of specific energy with rock brittleness concepts on rock cutting. Journal of the Southern African Institute of Mining and Metallurgy, 103(3), 163-171.
Alzahabi A, Al Qahtani G, Soliman MY et al (2015) Fracturability index is a mineralogical index: a new approach for fracturing decision. In: SPE Saudi Arabia Section Annual Technical Symposium and Exhibition. OnePetro. https://doi.org/10.2118/178033-MS
Bishop AW (1967) Progressive failure with special reference to the mechanism causingit. In: Proceedings of the geotechnical conference, Oslo, pp 142–150
Buller D, Hughes S, Market J et al (2010) Petrophysical evaluation for enhancing hydraulic stimulation in horizontal shale gas wells. In: SPE Annual Technical Conference and Exhibition. OnePetro. https://doi.org/10.2118/132990-MS
Chen G, Jiang W, Sun X et al (2019) Quantitative evaluation of rock brittleness based on crack initiation stress and complete stress–strain curves. Bull Eng Geol Env 78(8):5919–5936. https://doi.org/10.1007/s10064-019-01486-2
Emrouznejad A, Ho W (2017) Fuzzy analytic hierarchy process. CRC Press, Hoboken
Feng T, Xie XB, Wang WX, Pan CL (2000) Brittleness of rock and brittleness coefficient describing rockburst tendency. Min Metall Eng 20:18–19. https://doi.org/10.1016/j.jrmge.2020.06.008
Feng R, Zhang Y, Rezagholilou A et al (2020) Brittleness Index: from conventional to hydraulic fracturing energy model. Rock Mech Rock Eng 53(2):739–753. https://doi.org/10.1007/s00603-019-01942-1
Gale JFW, Reed RM, Holder J (2007) Natural fractures in the Barnett Shale and their importance for hydraulic fracture treatments. AAPG Bull 91(4):603–622. https://doi.org/10.1306/11010606061
Glorioso J C, Rattia A. (2012) Unconventional reservoirs: basic petrophysical concepts for shale gas. In: SPE/EAGE European unconventional resources conference & exhibition-from potential to production. European Association of Geoscientists & Engineers cp-285-00058. https://doi.org/10.2118/153004-MS
Hajiabdolmajid V, Kaiser P (2003) Brittleness of rock and stability assessment in hard rock tunneling. Tunn Undergr Space Eng 18:35–48. https://doi.org/10.1016/S0886-7798(02)00100-1
Hatefi AAH, Ekhtesasi MR (2016) Groundwater potentiality through analytic hierarchy process (AHP) using remote sensing and geographic information system (GIS). Geopersia 6(1):75–88. https://doi.org/10.22059/jgeope.2016.57823
Heard HC (1960) "Chapter 7: Transition from Brittle Fracture to Ductile Flow in Solenhofen Limestone as a Function of Temperature, Confining Pressure, and Interstitial Fluid Pressure", Rock Deformation (A Symposium), David Griggs, John Handin. https://doi.org/10.1130/MEM79-p193
Heidari M, Khanlari GR, TorabiKaveh M et al (2014) Effect of porosity on rock brittleness. Rock Mech Rock Eng 47(2):785–790. https://doi.org/10.1007/s00603-013-0400-0
Hetényi M (1950) Handbook of experimental stress analysis. Wiley, New York
Honda H, Sanada Y (1956) Hardness of coal. Fuel 35:451–461
Hou ZK, Yang CH, Wei X et al (2016) Experimental study on the brittle characteristics of Longmaxi formation shale. J China Coal Soc 41(5):1188–1196. https://doi.org/10.13225/j.cnki.jccs.2015.0957
Howell JV (1960) Glossary of geology and related sciences. American Geological Institute, Washington, D.C. https://doi.org/10.1086/348782
Hucka V, Das B (1974) Brittleness determination of rocks by different methods. Int J Rock Mech Min Sci Geomech Abstr 11:389–392. https://doi.org/10.1016/0148-9062(74)91109-7
Jarvie DM, Hill RJ, Ruble TE, Pollastro RM (2007) Unconventional shale-gas systems: the Mississippian Barnett Shale of North-Central Texas as one model for thermogenic shale-gas assessment; American Association of Petroleum Geologists: Tulsa, vol 91, pp 475–499. https://doi.org/10.1306/12190606068
Jin X, Shah SN, Roegiers JC et al (2014) Fracability evaluation in shale reservoirs-an integrated petrophysics and geomechanics approach. In: SPE hydraulic fracturing technology conference. OnePetro. https://doi.org/10.2118/168589-MS
KimWang TS, Jang S (2017) Petrophysical approach for S-wave velocity prediction based on brittleness index and total organic carbon of shale gas reservoir: a case study from Horn River Basin, Canada. J Appl Geophys 136:513–520. https://doi.org/10.1016/j.jappgeo.2016.12.003
Kivi IR, Ameri M, Molladavoodi H (2018) Shale brittleness evaluation based on energy balance analysis of stress-strain curves. J Petrol Sci Eng 167:1–19. https://doi.org/10.1016/j.petrol.2018.03.061
Lawal LO, Mahmoud M, Adebayo A et al (2021) Brittleness and microcracks: a new approach of brittleness characterization for shale fracking. J Natural Gas Sci Eng 87:10379. https://doi.org/10.1016/j.jngse.2020.103793
Lawn B, Marshall D (1979) Hardness, toughness, and brittleness: an indentation analysis. J Am Ceram Soc 62:347–350. https://doi.org/10.1111/j.1151-2916.1979.tb19075.x
Li QH, Chen M, Jin Y et al (2012) Indoor evaluation method for shale brittleness and improvement. Chin J Rock Mech Eng 31(8):1680–1685.
Li L, Zhai M, Zhang L et al (2019) Brittleness evaluation of glutenite based on energy balance and damage evolution. Energies 12(18):3421. https://doi.org/10.3390/en12183421
Liu JX, Li JR, Yin BR (2022) New brittleness index based on energy balance and analysis of failure mechanism of shale. Chin J Rock Mech Eng 41(4):734–747. https://doi.org/10.13722/j.cnki.jrme.2021.0732
Luan X, Di B, Wei J, Li X, Qian K, Xie J, Ding P (2014) Laboratory Measurements of brittleness anisotropy in synthetic shale with different cementation. In: Proceedings of the 2014 SEG Annual Meeting. Denver, Society of Exploration Geophysicists, pp 3005–3009. https://doi.org/10.1190/segam2014-0432.1
Martin CD (1996) Brittle failure of rock materials: test results and constitutive models. Can Geotech J 33(2):378–378. https://doi.org/10.1139/t96-901
Mews KS, Alhubail MM, Barati RG (2019) A review of brittleness index correlations for unconventional tight and ultra-tight reservoirs. Geosciences 9(7):319. https://doi.org/10.3390/geosciences9070319
Morley A (1944) Strength of materials. Longmans, Green and Company, New York
Munoz H, Taheri A, Chanda EK (2016) Fracture energy-based brittleness index development and brittleness quantification by pre-peak strength parameters in rock uniaxial compression. Rock Mech Rock Eng 49(12):4587–4606. https://doi.org/10.1007/s00603-016-1071-4
Obert L, Duvall WI (1967) Rock mechanics and the design of structures in rock. Wiley, New York, pp 78–82
Paddock D (2012) Seismic reservoir characterization of U.S. Shales: an update, AAPG eSymposium
Papanastasiou P (1997) The influence of plasticity in hydraulic fracturing. Int J Fract 84:61–79
Papanastasiou P (1999) The effective fracture toughness in hydraulic fracturing. Int J Fract 96:127
Papanastasiou P, Papamichos E, Atkinson C (2016) On the risk of hydraulic fracturing in CO2 geological storage. Int J Numer Anal Methods Geomech 40:1472–1484
Papanastasiou P, Atkinson C (2015) The brittleness index in hydraulic fracturing. In: 49th US rock mechanics/geomechanics symposium. American Rock Mechanics Association
Paterson MS, Wong TF (2005) Experimental rock deformation: the brittle field. Springer, Berlin-Heidelberg, pp 65–66. https://doi.org/10.1007/b137431
Quinn JB, Quinn DG (1997) Indentation brittleness of ceramics: a fresh approach. J Mater Sci 32:4331–4346. https://doi.org/10.1023/A:1018671823059
Ramsay JG (1967) Folding and fracturing of rocks. Mc Graw Hill Book Company, London, pp 44–47
Rickman R, Mullen M, Petre E, Grieser B, Kundert DA (2008) Practical use of shale petrophysics for stimulation design optimization: all shale plays are not clones of the Barnett Shale; Society of Petroleum Engineers: Richardson. https://doi.org/10.2118/115258-MS
Rybacki E, Meier T, Dresen G (2016) What controls the mechanical properties of shale rocks? Part II: brittleness. J Pet Sci Eng 144:39–58. https://doi.org/10.1016/j.petrol.2016.02.022
Saaty T (1980) The analytic hierarchy process. McGraw-Hill, New York
Saaty TL (2008) Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy/network process. Rev Real Acad Cienc Exact Fisic Natur Ser A Mate 102(2):251–318
Sharma RK, Chopra S (2012) New attribute for determination of lithology and brittleness; society of exploration geophysicists: Tulsa, pp 1–7. https://doi.org/10.1190/segam2012-1389.1
Singh K, Kumar V (2018) Hazard assessment of landslide disaster using information value method and analytical hierarchy process in highly tectonic Chamba region in bosom of Himalaya. J Mt Sci 15(4):808–824. https://doi.org/10.1007/s11629-017-4634-2
Song HQ, Zuo JP, Chen Y et al (2019) Revised energy drop coefficient based on energy characteristics in the whole process of rock failure. Rock Soil Mech 40(1):1–9. https://doi.org/10.16285/j.rsm.2017.2275
Sui L, Ju Y, Yang Y et al (2016) A quantification method for shale fracability based on analytic hierarchy process. Energy 115:637–645. https://doi.org/10.1016/j.energy.2016.09.035
Tarasov Boris, Potvin Yves (2013) Universal criteria for rock brittleness estimation under triaxial compression. International Journal of Rock Mechanics and Mining Sciences 5957-69 S1365160912002390 10.1016/j.ijrmms.2012.12.011
Verma S, Zhao T, Marfurt KJ et al (2016) Estimation of total organic carbon and brittleness volume. Interpretation 4(3):T373–T385. https://doi.org/10.1190/INT-2015-0166.1
Wang FP, Gale JFW (2009) Screening criteria for shale-gas systems. Gulf Coast Assoc Geol Soc Trans 59:779–793
Wang S, Li XY, Di B et al (2010) Reservoir fluid substitution effects on seismic profile interpretation: a physical modeling experiment. Geophys Res Lett 37:10. https://doi.org/10.1029/2010GL043090
Wang Y, Li X, Wu Y et al (2014) Research on relationship between crack initiation stress level and brittleness indices for brittle rocks. Chin J Rock Mech Eng 33(2):264–275. https://doi.org/10.13722/j.cnki.jrme.2014.02.003
Xia YJ, Li LC, Tang CA et al (2017) A new method to evaluate rock mass brittleness based on stress-strain curves of class I. Rock Mech Rock Eng 50(5):1123–1139. https://doi.org/10.1007/s00603-017-1174-6
Xie HP, Ju Y, Li LY (2005) Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles. Chin J Rock Mech Eng 24(17):3003–3010. https://doi.org/10.1007/s11769-005-0030-x
Xie J, Cao J, Schmitt DR et al (2019) Effects of kerogen content on elastic properties-based on artificial organic-rich shale (AORS). J Geophys Res Solid Earth 124(12):12660–12678. https://doi.org/10.1029/2019JB017595
Xu Z, Liao H (2014) Intuitionistic Fuzzy analytic hierarchy process. IEEE Trans Fuzzy Syst 22:749–761
Yilmaz NG, Karaca Z, Goktan RM, Akal C (2009) Relative brittleness characterization of some selected granitic building stones: influence of mineral grain size. Constr Build Mater 23(1):370–375. https://doi.org/10.1016/j.conbuildmat.2007.11.014
Zhang J, Ai C, Li Y et al (2018) Energy-based brittleness index and acoustic emission characteristics of anisotropic coal under triaxial stress condition. Rock Mech Rock Eng 51(11):3343–3360. https://doi.org/10.1007/s00603-018-1535-9
Zhang Y, Feng XT, Yang C et al (2021) Evaluation method of rock brittleness under true triaxial stress states based on pre-peak deformation characteristic and post-peak energy evolution. Rock Mech Rock Eng 54(3):1277–1291. https://doi.org/10.1007/s00603-020-02330-w
Zhou X, Liu H, Guo Y et al (2019) An evaluation method of brittleness characteristics of shale based on the unloading experiment. Energies 12(9):1779. https://doi.org/10.3390/en12091779
Acknowledgements
This research is supported National Natural Science Foundation of China (42274175, 42004112, 42030812, 41974160), Natural Science Foundation of Sichuan Province (23NSFSC5311), and the Open Fund (PLC2020002) of the State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Chengdu University of Technology). The data or code relating to this work is available by contacting the corresponding author.
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All the authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by JX, JZ, JC and JD. The first draft of the manuscript was written by JX and JZ, and all the authors commented on previous versions of the manuscript. All the authors read and approve tdhe final manuscript.
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Xie, J., Zhang, J., Fang, Y. et al. Quantitative Evaluation of Shale Brittleness Based on Brittle-Sensitive Index and Energy Evolution-Based Fuzzy Analytic Hierarchy Process. Rock Mech Rock Eng 56, 3003–3021 (2023). https://doi.org/10.1007/s00603-022-03213-y
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DOI: https://doi.org/10.1007/s00603-022-03213-y