Abstract
Mechanical damage and resultant permeability evolution during compaction of highly porous reservoir rocks have strong implications on the extraction of mineral and energy resources. Laboratory Experiments can be performed to quantify this effect; however, the effect of size on these processes and the information they provide need to be evaluated before any conclusion can be drawn. As part of this study, conventional triaxial compression tests under different confining pressures were carried out on large samples (30 mm diameter and 60 mm length). These experiments were compared to the same setup for small samples with 12.7 mm diameter and 25.4 mm length which allowed monitoring of the pore structure changes through the use of an X-ray transparent triaxial cell at constant confining pressure. Both scales showed a similar mechanical response. The large-scale experiments were used to investigate the transition from brittle to ductile deformation, and the small-scale experiments allowed detailed investigation of the microstructural changes affecting the permeability evolution. The permeabilities of the specimens were continually measured during the triaxial loading at both scales. At defined increasing axial strain levels, the small sample was imaged using X-ray computed tomography (XRCT) and internal structural changes were mapped. A series of digital rock analysis techniques and Pore Network Modelling allowed accurate analysis of the evolution of the microstructure and its effect on permeability evolution using Pore Network Models. An XRCT-based, microstructurally enriched, continuum model successfully describes the permeability evolution measured during triaxial testing. Self-organized criticality of the propagating front of compaction was also shown by R2 values > 0.95 for a double Pareto fractal scaling law. Both approaches, as well as the macroscale experiments, confirmed a phase change in permeability at ~ 5% axial strain which provided a solid basis for microstructurally enriched assessment of the dynamic permeability.
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Abbreviations
- k g :
-
Gas permeability
- k l :
-
Liquid permeability
- Q :
-
Gas flow rate
- μ :
-
Dynamic viscosity coefficient of the gas
- L :
-
Length of the specimen
- A:
-
Cross-sectional area of the specimen
- P out :
-
Outlet pressure
- P in :
-
Inlet pressure
- q :
-
Differential stress
- p :
-
Effective mean stress
- \(\varepsilon_{a}\) :
-
Axial strain
- \(\varepsilon_{r}\) :
-
Radial strain
- \(\varepsilon_{v}\) :
-
Volumetric strain
- \(\sigma_{1}\) :
-
Maximum principle stress
- \(\sigma_{2} = \sigma_{3}\) :
-
Minimum principle stress
- \(P_{c}\) :
-
Confining pressure
- \(P_{p}\) :
-
Pore pressure
- \(V_{{{\text{solid}}}}\) :
-
Volume of the solid phase in the specimen
- r :
-
Radius of the specimen
- \(\phi_{i}\) :
-
Porosity of the undeformed specimen
- \(\phi_{d}\) :
-
Porosity of the deformed specimen at certain axial strain
- \(\phi_{r}\) :
-
Porosity reduction in the specimen
- k nc :
-
Pre-compaction permeability of the specimen
- k cb :
-
Permeability of a single compaction band
- T :
-
Thickness of a single compaction band
- T cb :
-
Total thickness of the compaction bands
- N :
-
Number of compaction bands in the specimen
- c 1,2 :
-
Experimental constants in double Pareto model
- m 1,2 :
-
Experimental constants in double Pareto model
References
Baud, P., Klein, E., Wong, T.: Compaction localization in porous sandstones: spatial evolution of damage and acoustic emission activity. J. Struct. Geol. 26, 603–624 (2004). https://doi.org/10.1016/j.jsg.2003.09.002
Baud, P., Meredith, P., Townend, E.: Permeability evolution during triaxial compaction of an anisotropic porous sandstone. J. Geophys. Res. Solid Earth 117, B05203 (2012). https://doi.org/10.1029/2012JB009176
Baud, P., Reuschlé, T., Ji, Y., Cheung, C.S.N., Wong, T.: Mechanical compaction and strain localization in Bleurswiller sandstone. J. Geophys. Res. Solid Earth 120, 6501–6522 (2015). https://doi.org/10.1002/2015JB012192
Baud, P., Schubnel, A., Heap, M., Rolland, A.: Inelastic compaction in high-porosity limestone monitored using acoustic emissions. J Geophys. Res. Solid Earth 122(9989–9910), 9009 (2017). https://doi.org/10.1002/2017JB014627
Baychev, T.G., Jivkov, A.P., Rabbani, A., Raeini, A.Q., Xiong, Q., Lowe, T., Withers, P.J.: Reliability of algorithms interpreting topological and geometric properties of porous media for pore network modelling. Transp. Porous Media 128, 271–301 (2019). https://doi.org/10.1007/s11242-019-01244-8
Bedford, J.D., Faulkner, D.R., Leclère, H., Wheeler, J.: High-resolution mapping of yield curve shape and evolution for porous rock: the effect of inelastic compaction on porous bassanite. J. Geophys. Res. Solid Earth 123, 1217–1234 (2018). https://doi.org/10.1002/2017JB015250
Bogdanov, I., Mourzenko, V., Thovert, J.-F., Adler, P.: Effective permeability of fractured porous media with power-law distribution of fracture sizes. Phys. Rev. E 76, 036309 (2007). https://doi.org/10.1103/PhysRevE.76.036309
Bultreys, T., Van Hoorebeke, L., Cnudde, V.: Multi-scale, micro-computed tomography-based pore network models to simulate drainage in heterogeneous rocks. Adv. Water Resour. 78, 36–49 (2015). https://doi.org/10.1016/j.advwatres.2015.02.003
Carmichael, R.S.: Practical Handbook of Physical Properties of Rocks and Minerals. CRC Press, Boca Raton (1988)
Chen, X., Roshan, H., Lv, A., Hu, M., Regenauer-Lieb, K.: The dynamic evolution of compaction bands in highly porous carbonates: the role of local heterogeneity for nucleation and propagation. Prog. Earth Planet. Sci. 7, 28 (2020). https://doi.org/10.1186/s40645-020-00344-0
Chen, X., Roshan, H., Regenauer-Lieb, K.: Permeability evolution of limestone during formation of compaction bands: a digital poro-mechanics approach. Paper presented at the 53rd U.S. Rock Mechanics/Geomechanics Symposium, New York City, New York (2019)
Chen, X., Yu, J., Li, H., Wang, S.: Experimental and numerical investigation of permeability evolution with damage of sandstone under triaxial compression. Rock Mech. Rock Eng. 50, 1529–1549 (2017). https://doi.org/10.1007/s00603-017-1169-3
Cieplak, M., Robbins, M.O.: Dynamical transition in quasistatic fluid invasion in porous media. Phys. Rev. Lett. 60, 2042 (1988). https://doi.org/10.1103/PhysRevLett.60.2042
De Boever, E., Varloteaux, C., Nader, F.H., Foubert, A., Békri, S., Youssef, S., Rosenberg, E.: Quantification and prediction of the 3D pore network evolution in carbonate reservoir rocks. Oil. Gas Sci. Technol. Rev. IFP Energies Nouvelles 67, 161–178 (2012). https://doi.org/10.2516/ogst/2011170
Deng, S., Zuo, L., Aydin, A., Dvorkin, J., Mukerji, T.: Permeability characterization of natural compaction bands using core flooding experiments and three-dimensional image-based analysis: Comparing and contrasting the results from two different methods. AAPG Bull. 99, 27–49 (2015). https://doi.org/10.1306/07071413211
Detournay, C.: Numerical modeling of the slit mode of cavity evolution associated with sand production. SPE J. 14, 797–804 (2009). https://doi.org/10.2118/116168-PA
Fortin, J., Schubnel, A., Guéguen, Y.: Elastic wave velocities and permeability evolution during compaction of Bleurswiller sandstone. Int. J. Rock Mech. Min. Sci. 42, 873–889 (2005). https://doi.org/10.1016/j.ijrmms.2005.05.002
Fortin, J., Stanchits, S., Dresen, G., Guéguen, Y.: Acoustic emission and velocities associated with the formation of compaction bands in sandstone. J. Geophys. Res. Solid Earth 111, B10203 (2006). https://doi.org/10.1029/2005JB003854
Gustafson, G., Fransson, Å.: The use of the Pareto distribution for fracture transmissivity assessment. Hydrogeol. J. 14, 15–20 (2006). https://doi.org/10.1007/s10040-005-0440-y
Haimson, B.: Fracture-like borehole breakouts in high-porosity sandstone: are they caused by compaction bands? Phys. Chem. Earth A 26, 15–20 (2001). https://doi.org/10.1016/S1464-1895(01)00016-3
Haimson, B., Kovacich, J.: Borehole instability in high-porosity Berea sandstone and factors affecting dimensions and shape of fracture-like breakouts. Eng. Geol. 69, 219–231 (2003). https://doi.org/10.1016/S0013-7952(02)00283-1
Han, G., Liu, X., Wang, E.: Experimental study on formation mechanism of compaction bands in weathered rocks with high porosity. Sci. China Technol. Sci. 56, 2563–2571 (2013). https://doi.org/10.1007/s11431-013-5322-2
Holcomb, D., Olsson, W.: Compaction localization and fluid flow. J. Geophys. Res. Solid Earth 108, 2290 (2003). https://doi.org/10.1029/2001JB000813
Holcomb, D., Rudnicki, J.W., Issen, K.A., Sternlof, K.: Compaction localization in the earth and the laboratory: state of the research and research directions. Acta Geotech. 2, 1–15 (2007). https://doi.org/10.1007/s11440-007-0027-y
Jasinski, L., Sangaré, D., Adler, P.M., Mourzenko, V.V., Thovert, J.F., Gland, N., Békri, S.: Transport properties of a Bentheim sandstone under deformation. Phys. Rev. E 91, 013304 (2015). https://doi.org/10.1103/PhysRevE.91.013304
Kandula, N., Cordonnier, B., Boller, E., Weiss, J., Dysthe, D.K., Renard, F.: Dynamics of microscale precursors during brittle compressive failure in Carrara marble. J. Geophys. Res. Solid Earth 124, 6121–6139 (2019). https://doi.org/10.1029/2019jb017381
Lee, T.-C., Kashyap, R.L., Chu, C.-N.: Building skeleton models via 3-D medial surface axis thinning algorithms. CVGIP Graph Models Image Process 56, 462–478 (1994). https://doi.org/10.1006/cgip.1994.1042
Li, B., Liu, R., Jiang, Y.: A multiple fractal model for estimating permeability of dual-porosity media. J. Hydrol. 540, 659–669 (2016). https://doi.org/10.1016/j.jhydrol.2016.06.059
Li, L., Papamichos, E., Cerasi, P.: Investigation of sand production mechanisms using DEM with fluid flow. In: Proceedings of the International Symposium of the International Society for Rock Mechanics: Eurock 2006, Liège, Belgium, pp. 241–247 (2006). https://doi.org/https://doi.org/10.1201/9781439833469.ch33
Louis, L., Wong, T., Baud, P., Tembe, S.: Imaging strain localization by X-ray computed tomography: discrete compaction bands in Diemelstadt sandstone. J. Struct. Geol. 28, 762–775 (2006). https://doi.org/10.1016/j.jsg.2006.02.006
Lv, A., Masoumi, H., Walsh, S.D., Roshan, H.: Elastic-softening-plasticity around a borehole: an analytical and experimental study. Rock Mech. Rock Eng. 52, 1149–1164 (2019). https://doi.org/10.1007/s00603-018-1650-7
Lv, A., Ramandi, H.L., Masoumi, H., Saadatfar, M., Regenauer-Lieb, K., Roshan, H.: Analytical and experimental investigation of pore pressure induced strain softening around boreholes. Int. J. Rock Mech. Min. Sci. 113, 1–10 (2019). https://doi.org/10.1016/j.ijrmms.2018.11.001
Mair, K., Main, I., Elphick, S.: Sequential growth of deformation bands in the laboratory. J. Struct. Geol. 22, 25–42 (2000). https://doi.org/10.1016/S0191-8141(99)00124-8
Meng, F., Baud, P., Ge, H., Wong, T.: The effect of stress on limestone permeability and effective stress behavior of damaged samples. J. Geophys. Res. Solid Earth 124, 376–399 (2019). https://doi.org/10.1029/2018jb016526
Mourzenko, V., Thovert, J.-F., Adler, P.: Macroscopic permeability of three-dimensional fracture networks with power-law size distribution. Phys. Rev. E 69, 066307 (2004). https://doi.org/10.1103/PhysRevE.69.066307
Mourzenko, V.V., Galamay, O., Thovert, J.F., Adler, P.M.: Fracture deformation and influence on permeability. Phys. Rev. E 56, 3167–3184 (1997). https://doi.org/10.1103/PhysRevE.56.3167
Olsson, W.A.: Theoretical and experimental investigation of compaction bands in porous rock. J. Geophys. Res. Solid Earth 104, 7219–7228 (1999). https://doi.org/10.1029/1998JB900120
Rahmati, H., Nouri, A., Chan, D., Vaziri, H.: Simulation of drilling-induced compaction bands using discrete element method. Int. J. Numer. Anal. Meth. Geomech. 38, 37–50 (2014). https://doi.org/10.1002/nag.2194
Renard, F., Weiss, J., Mathiesen, J., Ben-Zion, Y., Kandula, N., Cordonnier, B.: Critical evolution of damage toward system-size failure in crystalline rock. J. Geophys. Res. Solid Earth 123, 1969–1986 (2018). https://doi.org/10.1002/2017jb014964
Roshan, H., Andersen, M.S., Acworth, R.I.: Effect of solid–fluid thermal expansion on thermo-osmotic tests: an experimental and analytical study. J. Petrol. Sci. Eng. 126, 222–230 (2015). https://doi.org/10.1016/j.petrol.2014.12.005
Roshan, H., Chen, X., Pirzada, M.A., Regenauer-Lieb, K.: Permeability measurements during triaxial and direct shear loading using a novel X-ray transparent apparatus: fractured shale examples from Beetaloo basin, Australia. NDT&E Int. 107, 102129 (2019). https://doi.org/10.1016/j.ndteint.2019.102129
Roshan, H., Lv, A., Xu, Y., Masoumi, H., Regenauer-Lieb, K.: New generation of hoek cells. Geotech. Test. J. 42, 747–760 (2019). https://doi.org/10.1520/GTJ20170110
Sato, M., Panaghi, K., Takada, N., Takeda, M.: Effect of bedding planes on the permeability and diffusivity anisotropies of Berea sandstone. Transp. Porous Media 127, 587–603 (2019). https://doi.org/10.1007/s11242-018-1214-z
Sethna, J.P.: Course 6 Crackling noise and avalanches: scaling, critical phenomena, and the renormalization group. In: Bouchaud, J.-P., Mézard, M., Dalibard, J. (eds.) Les Houches, vol. 85. Elsevier, pp. 257–288 (2007). https://doi.org/https://doi.org/10.1016/S0924-8099(07)80013-8
Shahin, G., Papazoglou, A., Marinelli, F., Buscarnera, G.: Simulation of localized compaction in Tuffeau de Maastricht based on evidence from X-ray tomography. Int. J. Rock Mech. Min. Sci. 121, 104039 (2019). https://doi.org/10.1016/j.ijrmms.2019.05.005
Singh, A., Kennedy, G.C.: Compression of calcite to 40 KB. J. Geophys. Res. 79, 2615–2622 (1974)
Skoczylas, N.: Determining the gas permeability coefficient of a porous medium by means of the bubble-counting flow meter. Meas. Sci. Technol. 26, 085004 (2015). https://doi.org/10.1088/0957-0233/26/8/085004
Sternlof, K.R., Karimi-Fard, M., Pollard, D.D., Durlofsky, L.: Flow and transport effects of compaction bands in sandstone at scales relevant to aquifer and reservoir management. Water Resour. Res. (2006). https://doi.org/10.1029/2005WR004664
Tanikawa, W., Shimamoto, T.: Klinkenberg effect for gas permeability and its comparison to water permeability for porous sedimentary rocks. Hydrol. Earth Syst. Sci. Discuss. 3, 1315–1338 (2006). https://doi.org/10.5194/hessd-3-1315-2006
Townend, E., Thompson, B.D., Benson, P.M., Meredith, P.G., Baud, P., Young, R.P.: Imaging compaction band propagation in Diemelstadt sandstone using acoustic emission locations. Geophys. Res. Lett. (2008). https://doi.org/10.1029/2008GL034723
Vajdova, V., Baud, P., Wong, T.: Permeability evolution during localized deformation in Bentheim sandstone. J. Geophys. Res. Solid Earth 109, B10406 (2004). https://doi.org/10.1029/2003JB002942
Vajdova, V., Zhu, W., Chen, T.-M.N., Wong, T.: Micromechanics of brittle faulting and cataclastic flow in Tavel limestone. J. Struct. Geol. 32, 1158–1169 (2010). https://doi.org/10.1016/j.jsg.2010.07.007
Wong, T., David, C., Zhu, W.: The transition from brittle faulting to cataclastic flow in porous sandstones: mechanical deformation. J. Geophys. Res. Solid Earth 102, 3009–3025 (1997). https://doi.org/10.1029/96JB03281
Wong, T., Baud, P., Klein, E.: Localized failure modes in a compactant porous rock. Geophys. Res. Lett. 28, 2521–2524 (2001). https://doi.org/10.1029/2001GL012960
Yu, X., Hong, C., Peng, G., Lu, S.: Response of pore structures to long-term fertilization by a combination of synchrotron radiation X-ray microcomputed tomography and a pore network model. Eur. J. Soil Sci. 69, 290–302 (2018). https://doi.org/10.1111/ejss.12513
Zhu, W., Baud, P., Wong, T.: Micromechanics of cataclastic pore collapse in limestone. J. Geophys. Res. Solid Earth 115, B04405 (2010). https://doi.org/10.1029/2009JB006610
Acknowledgements
We would like to thank the three reviewers of the manuscript for the suggestion to include additional material in the manuscript. The project was financially supported by the Australian Research Council (ARC Discovery Grants No DP17104550, DP17104557). The first author would like to acknowledge the fellowship from the UNSW Tuition Fee Scholarship (TFS) and the China Scholarship Council (CSC). In addition to the ARC Discovery support, KRL also acknowledges strategic support from the UNSW through the SPF01 internal funding scheme.
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The project was financially supported by the Australian Research Council (ARC Discovery Grants No DP17104550, DP17104557).
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KRL and HR are project coordinators, proposed the topic, conceived the study and reviewed the final manuscript. XC conducted the experiments, analysed the data and composed the draft of the manuscript. AL helped in experiment set-up and data interpretation. MH collaborated with the first author in the construction of the manuscript. All authors read and approved the final manuscript.
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Chen, X., Regenauer-Lieb, K., Lv, A. et al. The Dynamic Evolution of Permeability in Compacting Carbonates: Phase Transition and Critical Points. Transp Porous Med 135, 687–711 (2020). https://doi.org/10.1007/s11242-020-01493-y
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DOI: https://doi.org/10.1007/s11242-020-01493-y