TY - GEN
T1 - Osmotic Ion Concentration Control of Steady-State Sub-critical Fracture Growth in Shale
AU - Nguyen, Hoang T.
AU - Bažant, Zdeněk P.
N1 - Publisher Copyright:
© 2022 ARMA, American Rock Mechanics Association.
PY - 2022
Y1 - 2022
N2 - The mechanism of formation of natural cracks in sedimentary rocks in the geologic past is an important problem in hydraulic fracturing. Why are the natural cracks roughly parallel and equidistant, and why is the spacing in the order of 10 cm rather than 1 cm or 100 cm? Fracture mechanics alone cannot answer these questions. Here it is proposed that fracture mechanics must be coupled with the diffusion of solute ions (Na+ and Cl− are considered here), driven by an osmotic pressure gradient. Parallel equidistant cracks are considered to be subcritical and governed by the Charles-Evans law. The evolution in solute concentration also affects the solvent pressure in the pores and cracks, altering the resistance to frictional sliding. Only steady-state propagation and periodic cracks are studied. An analytical solution of the crack spacing as a function of the properties of the rock as well as the solvent and solute, and the imposed far-field deformation is obtained. Finally, the stability of the growth of parallel cracks is proven by examining the second variation of free energy. Stability of the periodic growth state is also considered.
AB - The mechanism of formation of natural cracks in sedimentary rocks in the geologic past is an important problem in hydraulic fracturing. Why are the natural cracks roughly parallel and equidistant, and why is the spacing in the order of 10 cm rather than 1 cm or 100 cm? Fracture mechanics alone cannot answer these questions. Here it is proposed that fracture mechanics must be coupled with the diffusion of solute ions (Na+ and Cl− are considered here), driven by an osmotic pressure gradient. Parallel equidistant cracks are considered to be subcritical and governed by the Charles-Evans law. The evolution in solute concentration also affects the solvent pressure in the pores and cracks, altering the resistance to frictional sliding. Only steady-state propagation and periodic cracks are studied. An analytical solution of the crack spacing as a function of the properties of the rock as well as the solvent and solute, and the imposed far-field deformation is obtained. Finally, the stability of the growth of parallel cracks is proven by examining the second variation of free energy. Stability of the periodic growth state is also considered.
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M3 - Conference contribution
AN - SCOPUS:85149224848
T3 - 56th U.S. Rock Mechanics/Geomechanics Symposium
BT - 56th U.S. Rock Mechanics/Geomechanics Symposium
PB - American Rock Mechanics Association (ARMA)
T2 - 56th U.S. Rock Mechanics/Geomechanics Symposium
Y2 - 26 June 2022 through 29 June 2022
ER -