Proppant embedment in coal and shale: Impacts of stress hardening and sorption

Asef, 2013, The effect of confining pressure on elastic wave velocities and dynamic to static Young’ s modulus ratio, Geophysics, 78, 10.1190/geo2012-0279.1 Bandara, 2019, Improved understanding of proppant embedment behavior under reservoir conditions : a review study, Powder Technol., 352, 170, 10.1016/j.powtec.2019.04.033 Chen, 2017, A permeability model for the hydraulic fracture fi lled with proppant packs under combined e ff ect of compaction and embedment, J. Pet. Sci. Eng., 149, 428, 10.1016/j.petrol.2016.10.045 Geng, 2015, Theory and technique of permeability enhancement and coal mine gas extraction by fracture network stimulation of surrounding beds and coal beds, Nat. Gas Ind. B, 1, 197, 10.1016/j.ngib.2014.11.012 Guo, 2017, Analytical analysis of fracture conductivity for sparse distribution of proppant packs, J. Geophys. Eng., 14, 599, 10.1088/1742-2140/aa6215 Hou, 2017, Experimental and theoretical study of fracture conductivity with heterogeneous proppant placement, J. Nat. Gas Sci. Eng., 37, 449, 10.1016/j.jngse.2016.11.059 Kogut, 2002, Elastic-plastic contact analysis of a sphere and a rigid flat, J. Appl. Mech., 69, 657, 10.1115/1.1490373 Kumar, 2015, Permeability evolution of propped artificial fractures in coal on injection of CO2, J. Pet. Sci. Eng., 133, 695, 10.1016/j.petrol.2015.07.008 Kumar, 2015, Permeability evolution of propped artificial fractures in coal on injection of CO2, J. Pet. Sci. Eng., 133, 695, 10.1016/j.petrol.2015.07.008 Lacy, 1998, Fracture width and embedment testing in soft reservoir sandstone, SPE Drill. Completion, 13, 25, 10.2118/36421-PA Lee, 2010, Experiment and modeling to evaluate the effects of proppant-pack diagenesis on fracture treatments, J. Pet. Sci. Eng., 74, 67, 10.1016/j.petrol.2010.08.007 Li, 2019, Controls of CO2–N2 gas fl ood ratios on enhanced shale gas recovery and ultimate CO2 sequestration, J. Pet. Sci. Eng., 179, 1037, 10.1016/j.petrol.2019.04.098 Li, 2009, An analytical solution for the unloading in spherical indentation of elastic – plastic solids, Int. J. Eng. Sci., 47, 452, 10.1016/j.ijengsci.2008.10.002 Li, 2015, New mathematical models for calculating proppant embedment and fracture conductivity, SPE J., 20, 496, 10.2118/155954-PA Li, 2018, The calculation of coal rock fracture conductivity with Different Arrangements of proppants, Geofluids, 2018, 10.1155/2018/4938294 Wu, 2011, A dual poroelastic model for CO2-enhanced coalbed methane recovery, Int. J. Coal Geol., 86, 177, 10.1016/j.coal.2011.01.004 Morcote, 2010, Dynamic elastic properties of coal, Geophysics, 75, 10.1190/1.3508874 Mueller, 2015 Pan, 2007, A theoretical model for gas adsorption-induced coal swelling, Int. J. Coal Geol., 69, 243, 10.1016/j.coal.2006.04.006 Penny, 1987, An evaluation of the effects of environmental conditions and fracturing fluids upon the long-term conductivity of proppants, SPE J., 229 Penny, 2012, Proppant and fluid selection to optimize performance of horizontal shale fracs, SPE J., 341 Sampath, 2017, CH 4 CO 2 gas exchange and supercritical CO 2 based hydraulic fracturing as CBM production-accelerating techniques: a review, J. CO2 Util., 22, 212, 10.1016/j.jcou.2017.10.004 Song, 2013, Mechanics of materials elastic – plastic spherical indentation: deformation regimes, evolution of plasticity, and hardening effect, Mech. Mater., 61, 91, 10.1016/j.mechmat.2013.01.003 Stoddard, 2011 Tang, 2018, An experimental and analytical study of the effects of shear displacement, fluid type, joint roughness, shear strength, friction angle and dilation angle on proppant embedment development in tight gas sandstone reservoirs, Int. J. Rock Mech. Min. Sci., 107, 94, 10.1016/j.ijrmms.2018.03.008 Volk, 1981, Embedment of high strength proppant into low-permeability reservoir rock, Proc. SPE Wang, 2011, Permeability evolution in fractured coal : the roles of fracture geometry and water-content, Int. J. Coal Geol., 87, 13, 10.1016/j.coal.2011.04.009 Wang, 2013, Mechanical behavior of methane infiltrated coal: the roles of gas desorption, stress level and loading rate, Rock Mech. Rock Eng., 945, 10.1007/s00603-012-0324-0 Wanniarachchi, 2017, Shale gas fracturing using foam-based fracturing fluid: a review, Environ. Earth Sci., 76, 1, 10.1007/s12665-017-6399-x Wu, 2018, Experimental study of permeability behaviour for proppant supported coal fracture, J. Nat. Gas Sci. Eng., 51, 18, 10.1016/j.jngse.2017.12.023 Zhang, 2016, Theoretical conductivity analysis of surface modification agent treated proppant II – Channel fracturing application, Fuel, 165, 28, 10.1016/j.fuel.2015.10.026 Zhao, 2000, An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow, J. Tribol., 122 Zhi, 2018, Hydraulic fracturing for improved nutrient delivery in microbially-enhanced coalbed-methane (MECBM ) production, J. Nat. Gas Sci. Eng., 60, 294, 10.1016/j.jngse.2018.10.012 Zhi, 2019, W-shaped permeability evolution of coal with supercritical CO 2 phase transition, Int. J. Coal Geol., 211, 103221, 10.1016/j.coal.2019.103221