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1. Effects of fluid diffusivity on hydraulic fracturing processes using visual analysis

   Baptista-Pereira, C; Goncalves da Silva, B (January 2019, US Rock Mechanics/Geomechanics Symposium)

   Hydraulic fracturing arises as a method to enhance oil and gas production, and also as a way to recover geothermal energy. It is, therefore, essential to understand how injecting a fluid inside a rock reservoir will affect its surroundings. Hydraulic fracturing processes can be strongly affected by the interaction between two mechanisms: the elastic effects caused by the hydraulic pressure applied inside fractures and the poro-mechanical effects caused by the fluid infiltration inside the porous media (i.e. fluid diffusivity); this, in turn, is affected by the injection rate used. The interaction between poro-elastic mechanisms, particularly the effect of the fluid diffusivity, in the hydraulic fracturing processes is not well-understood and is investigated in this paper. This study aims to experimentally and theoretically comprehend the effects of the injection rate on crack propagation and on pore pressures, when flaws pre-fabricated in prismatic gypsum specimens are hydraulically pressurized. In order to accomplish this, laboratory experiments were performed using two injection rates (2 and 20 ml/min), applied by an apparatus consisting of a pressure enclosure with an impermeable membrane in both faces of the specimen, which allowed one to observe the growth of a fluid front from the pre-fabricated flaws to the unsaturated porous media (i.e. rock), before fracturing took place. It was observed that the fracturing pressures and patterns are injection-rate-dependent. This was interpreted to be caused by the different pore pressures that developed in the rock matrix, which resulted from the significantly distinct fluid fronts observed for the two injection rates tested. 

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2. Osmotic Ion Concentration Control of Steady-State Subcritical Fracture Growth in Shale

   https://doi.org/10.56952/ARMA-2022-0830  

   Nguyen, Hoang T; Bažant, P Zdenek (June 2022, ARMA)

   ABSTRACT: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. 1 INTRODUCTIONThe deep layers of sedimentary rocks such as shale and sandstone are usually intersected by systems of nearly parallel natural cracks either filled by mineral deposits or closed by creep over a million year life span. Their spacing is roughly uniform and is on the order of 0.1 m (rather than 1 m or 0.01m). These cracks likely play an important role in hydraulic fracturing for gas or oil recovery (aka fracking, fraccing or frac) (Rahimi-Aghdam et al., 2019, e.g.). Therefore, understanding the mechanism of their formation in the distant geologic past is of interest.What controls the spacing of the nearly parallel cracks in shale? According to the fracture mechanics alone, the crack spacing is arbitrary. If propagating parallel equidistant cracks are in a critical state, stability analysis shows that many cracks would have to stop growing, causing a great increase of their average spacing, which was obviously not the case (Bažant et al., 2014). 

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3. Hydraulic Crack Propagation and Rock Permeability Under Osmotic Pressure Gradients with Implications for Deep CO2 Sequestration and Fraccing

   https://doi.org/10.56952/ARMA-2024-0264  

   Bažant, Zdenek P; Nguyen, Anh Tay; Xu, Houlin; Asem, Pouyan; Labuz, Joseph F (June 2024, ARMA)

   ABSTRACT:Long-term deep sequestration of CO2-rich brine in deep formations of ultramafic rock (e.g. Oman serpentinized harzburgite) will be feasible only if a network of hydraulic cracks could be produced and made to grow for years and decades. Fraccing of gas- or oil-bearing shales has a similar objective. The following points are planned to be made in the presentation in Golden. 1) A branching of fracture can be analyzed only if the fracture is modeled by a band with triaxial tensorial damage, for which the new smooth Lagrangian crack band model is effective. 2) To achieve a progressive growth of the fracture network one will need to manipulate the osmotic pressure gradients by changing alkali metal ion concentration in pore fluid. 3) A standardized experimental framework to measure rock permeability at various ion concentrations and various osmotic pressure gradients is needed, and will be presented. 1 INTRODUCTIONCarbon dioxide (CO2) emissions by human activities is the largest contributor to global warming; therefore, effective carbon sequestration technologies attract great amount of interest. One emerging and promising technology for storing CO2 in the subsurface permanently is through carbon mineralization in mafic and ultramafic rock (Kelemen and Matter, 2008). Despite the abundance of these types of rock in the Earth's upper crust (Matter et al., 2016), the rate of this process in nature is too slow to reduce CO2 emissions effectively (Seifritz, 1990). One of the key challenges to achieve a sustainable and large-scale storage of CO2 by mineralization is to engineer a progressive growth of a fracture network conveying water with dissolved CO2 to reach a gradually increasing volume of the mafic rock formation. The CO2 rich water often cannot penetrate the tight matrix of silica-rich serpentinized harzburgites because under high concentrations of CO2, the wetting angle of CO2 -bearing water-rock-rock interface exceeds the critical value of 60 degrees. Therefore, the presence of a family of cracks is the only means by which CO2 -bearing fluids can interact with matrix of ultramafic rock (Bruce Watson and Brenan, 1987). Lateral fracture branching from a major fracture provides a sustainable fluid pathway and therefore is essential for continued rock-water geochemical reactions that lead to mineralization of carbonate minerals. Realistic computational modeling of hydraulic fractures in peridotite or basalt must involve lateral fracture branching and account for stress distribution changes between solid and fluid phases under constant tectonic stress, triggered by pore exposure to fluid pressure in hydraulic cracks. 

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4. Impact of differential stress on fracture due to volume increasing hydration

   https://doi.org/10.5194/se-17-537-2026  

   McElwee, Jeremiah J; Wada, Ikuko; Yoshida, Kazuki; Shimizu, Hiroyuki; Okamoto, Atsushi (January 2026, Solid Earth)

   Abstract. The volume increase that accompanies many hydration reactions can stress and fracture the surrounding rock, a process commonly called reaction-induced fracturing. Reaction-induced fracturing accelerates the rate of hydration by creating new pathways for fluids to migrate into reactive rock and by generating new reactive surface areas. The evolution of reaction-induced fractures also depends on the background stress state, which varies among different tectonic environments. We investigate the impact of tectonic stresses on reaction-induced fracturing using 2-D hydraulic-chemical-mechanical distinct element models. The results indicate that the general pattern of reaction-induced fractures depends on the orientation of background tectonic stresses relative to fluid-supplying channels. A spalling fracture pattern characterized by short cracks parallel to and along fluid-supplying channels occurs when the maximum principal tectonic stress is parallel to the channels whereas a branching fracture pattern characterized by long tensile cracks that propagate in a hierarchical manner into unreacted parts of the rock is expected when the tectonic stress is hydrostatic or when the maximum principal tectonic stress is normal to fluid-supplying channels. Spalling localizes hydration and fluid flow along the channels whereas branching promotes spatially extensive hydration and fluid flow away from the fluid supply. The results indicate tectonic stresses may guide the hydration distribution in the oceanic lithosphere at mid-ocean ridges and outer rises and in the cold mantle wedge corner in subduction zones. 

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5. Tuning crack-inclusion interaction with an applied T-stress

   https://doi.org/10.1007/s10704-020-00423-9  

   Kai Guo, Bo Ni (February 2020, International journal of fracture)

   The interaction between cracks and inclusions plays an important role in the fracture behavior of particulate composites. It is commonly recognized that an inclusion stiffer than the matrix tends to deflect an approaching crack away while a softer inclusion attracts the crack. Here, we demonstrate by analytical modeling and numerical simulations that the crack-inclusion interaction can be tuned by an applied T-stress. Under a sufficiently large compressive applied T-stress, cracks can be attracted to stiffer inclusions while repelled by softer ones, thus reversing the conventional trend. Potential applications of this work include composite electrodes in lithium-ion batteries and hydraulic fracturing. 

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