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Brice Lecampion - One of the best experts on this subject based on the ideXlab platform.
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propagation of a plane strain hydraulic fracture accounting for a rough cohesive zone
Journal of The Mechanics and Physics of Solids, 2021Co-Authors: Dong Liu, Brice LecampionAbstract:Abstract The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): namely, linear elastic fracture mechanics and smooth parallel plates Lubrication Fluid flow inside the propagating fracture. We relax these hypotheses and investigate in details the growth of a plane-strain hydraulic fracture in an impermeable medium accounting for a rough cohesive zone and a Fluid lag. In addition to a dimensionless toughness and the time-scale t o m of coalescence of the Fluid and fracture fronts governing the fracture evolution in the LHFM case, the solution now also depends on the ratio between the in-situ stress and material peak cohesive stress σ o ∕ σ c and the intensity of the flow deviation induced by aperture roughness (captured by a dimensionless power exponent). We show that the solution is appropriately described by a nucleation time-scale t c m = t o m × ( σ o ∕ σ c ) 3 , which delineates the fracture growth into three distinct stages: a nucleation phase ( t ≪ t c m ), an intermediate stage ( t ∼ t c m ) and late time ( t ≫ t c m ) stage where convergence toward LHFM predictions finally occurs. A highly non-linear hydro-mechanical coupling takes place as the Fluid front enters the rough cohesive zone which itself evolves during the nucleation and intermediate stages of growth. This coupling leads to significant additional viscous flow dissipation. As a result, the fracture evolution deviates from LHFM predictions with shorter fracture lengths, larger widths and net pressures. These deviations from LHFM ultimately decrease at late times ( t ≫ t c m ) as the ratios of the lag and cohesive zone sizes with the fracture length both become smaller. The deviations increase with larger dimensionless toughness and larger σ o ∕ σ c ratio, as both have the effect of further localizing viscous dissipation near the Fluid front located in the small rough cohesive zone. The convergence toward LHFM can occur at very late time compared to the nucleation time-scale t c m (by a factor of hundred to thousand times) for realistic values of σ o ∕ σ c encountered at depth. The impact of a rough cohesive zone appears to be prominent for laboratory experiments and short in-situ injections in quasi-brittle rocks with ultimately a larger energy demand compared to LHFM predictions.
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Propagation of a plane-strain hydraulic fracture accounting for a rough cohesive zone.
arXiv: Fluid Dynamics, 2020Co-Authors: Dong Liu, Brice LecampionAbstract:The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): linear elastic fracture mechanics and smooth parallel plates Lubrication Fluid flow. We relax these hypotheses and investigate the growth of a plane-strain hydraulic fracture in an impermeable medium accounting for a rough cohesive zone and a Fluid lag. In addition to a dimensionless toughness and the time-scale of coalescence of the Fluid and fracture fronts as in the LHFM case, the solution now also depends on the in-situ-to-cohesive stress ratio and the intensity of the flow deviation induced by aperture roughness. The solution is appropriately described by a nucleation time-scale, which delineates the fracture growth into a nucleation phase, an intermediate stage and a late time stage where convergence toward LHFM predictions finally occurs. A highly non-linear hydro-mechanical coupling takes place as the Fluid front enters the rough cohesive zone which itself evolves during the nucleation and intermediate stages. This coupling leads to significant additional viscous flow dissipation. As a result, the fracture evolution deviates from LHFM solutions with shorter fracture lengths, larger widths and net pressures. These deviations ultimately decrease at late times as the lag and cohesive zone fractions both become smaller. The deviations increase with larger dimensionless toughness and in-situ-to-cohesive stress ratio, as both further localize viscous dissipation near the Fluid front located in the rough cohesive zone. The convergence toward LHFM can occur at very late time for realistic values of in-situ-to-cohesive stress ratio encountered at depth. The impact of a rough cohesive zone appears to be prominent for laboratory experiments and short in-situ injections in quasi-brittle rocks with ultimately a larger energy demand compared to LHFM predictions.
Dong Liu - One of the best experts on this subject based on the ideXlab platform.
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propagation of a plane strain hydraulic fracture accounting for a rough cohesive zone
Journal of The Mechanics and Physics of Solids, 2021Co-Authors: Dong Liu, Brice LecampionAbstract:Abstract The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): namely, linear elastic fracture mechanics and smooth parallel plates Lubrication Fluid flow inside the propagating fracture. We relax these hypotheses and investigate in details the growth of a plane-strain hydraulic fracture in an impermeable medium accounting for a rough cohesive zone and a Fluid lag. In addition to a dimensionless toughness and the time-scale t o m of coalescence of the Fluid and fracture fronts governing the fracture evolution in the LHFM case, the solution now also depends on the ratio between the in-situ stress and material peak cohesive stress σ o ∕ σ c and the intensity of the flow deviation induced by aperture roughness (captured by a dimensionless power exponent). We show that the solution is appropriately described by a nucleation time-scale t c m = t o m × ( σ o ∕ σ c ) 3 , which delineates the fracture growth into three distinct stages: a nucleation phase ( t ≪ t c m ), an intermediate stage ( t ∼ t c m ) and late time ( t ≫ t c m ) stage where convergence toward LHFM predictions finally occurs. A highly non-linear hydro-mechanical coupling takes place as the Fluid front enters the rough cohesive zone which itself evolves during the nucleation and intermediate stages of growth. This coupling leads to significant additional viscous flow dissipation. As a result, the fracture evolution deviates from LHFM predictions with shorter fracture lengths, larger widths and net pressures. These deviations from LHFM ultimately decrease at late times ( t ≫ t c m ) as the ratios of the lag and cohesive zone sizes with the fracture length both become smaller. The deviations increase with larger dimensionless toughness and larger σ o ∕ σ c ratio, as both have the effect of further localizing viscous dissipation near the Fluid front located in the small rough cohesive zone. The convergence toward LHFM can occur at very late time compared to the nucleation time-scale t c m (by a factor of hundred to thousand times) for realistic values of σ o ∕ σ c encountered at depth. The impact of a rough cohesive zone appears to be prominent for laboratory experiments and short in-situ injections in quasi-brittle rocks with ultimately a larger energy demand compared to LHFM predictions.
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Propagation of a plane-strain hydraulic fracture accounting for a rough cohesive zone.
arXiv: Fluid Dynamics, 2020Co-Authors: Dong Liu, Brice LecampionAbstract:The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): linear elastic fracture mechanics and smooth parallel plates Lubrication Fluid flow. We relax these hypotheses and investigate the growth of a plane-strain hydraulic fracture in an impermeable medium accounting for a rough cohesive zone and a Fluid lag. In addition to a dimensionless toughness and the time-scale of coalescence of the Fluid and fracture fronts as in the LHFM case, the solution now also depends on the in-situ-to-cohesive stress ratio and the intensity of the flow deviation induced by aperture roughness. The solution is appropriately described by a nucleation time-scale, which delineates the fracture growth into a nucleation phase, an intermediate stage and a late time stage where convergence toward LHFM predictions finally occurs. A highly non-linear hydro-mechanical coupling takes place as the Fluid front enters the rough cohesive zone which itself evolves during the nucleation and intermediate stages. This coupling leads to significant additional viscous flow dissipation. As a result, the fracture evolution deviates from LHFM solutions with shorter fracture lengths, larger widths and net pressures. These deviations ultimately decrease at late times as the lag and cohesive zone fractions both become smaller. The deviations increase with larger dimensionless toughness and in-situ-to-cohesive stress ratio, as both further localize viscous dissipation near the Fluid front located in the rough cohesive zone. The convergence toward LHFM can occur at very late time for realistic values of in-situ-to-cohesive stress ratio encountered at depth. The impact of a rough cohesive zone appears to be prominent for laboratory experiments and short in-situ injections in quasi-brittle rocks with ultimately a larger energy demand compared to LHFM predictions.
Tayfun E. Tezduyar - One of the best experts on this subject based on the ideXlab platform.
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space time isogeometric flow analysis with built in reynolds equation limit
Mathematical Models and Methods in Applied Sciences, 2019Co-Authors: Takashi Kuraishi, Kenji Takizawa, Tayfun E. TezduyarAbstract:We present a space–time (ST) computational flow analysis method with built-in Reynolds-equation limit. The method enables solution of Lubrication Fluid dynamics problems with a computational cost c...
Pietro De Palma - One of the best experts on this subject based on the ideXlab platform.
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hydrodynamic Lubrication of micro textured surfaces two dimensional cfd analysis
Tribology International, 2015Co-Authors: Giovanni Caramia, Giuseppe Carbone, Pietro De PalmaAbstract:Abstract This paper provides a numerical study of the hydrodynamic Lubrication between two parallel surfaces with micro-texturing. The two-dimensional Navier–Stokes equations for an isothermal incompressible steady flow have been considered as a suitable model. A wide variety of geometries characterised by different micro-cavity depth and width, and different gap values have been analysed in order to study the influence of these parameters on the drag force magnitude. A detailed analysis of flow velocity profiles and pressure distributions has been performed to study the forces acting on the textured surface, providing an explanation for the maximum drag reduction achievable with a single-phase Lubrication Fluid. Furthermore, results indicate that three regions exist, depending on the cavity depth, in which a different flow dynamics occurs and the cavities have a different influence on the drag force. Finally, an “optimal” value of the depth has been found, for which the pressure reaches a minimum value and the probability of cavitation is maximised.
Lecampion Brice - One of the best experts on this subject based on the ideXlab platform.
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Propagation of a plane-strain hydraulic fracture accounting for a rough cohesive zone
'Elsevier BV', 2020Co-Authors: Liu Dong, Lecampion BriceAbstract:The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): linear elastic fracture mechanics and smooth parallel plates Lubrication Fluid flow. We relax these hypotheses and investigate the growth of a plane-strain hydraulic fracture in an impermeable medium accounting for a rough cohesive zone and a Fluid lag. In addition to a dimensionless toughness and the time-scale of coalescence of the Fluid and fracture fronts as in the LHFM case, the solution now also depends on the in-situ-to-cohesive stress ratio and the intensity of the flow deviation induced by aperture roughness. The solution is appropriately described by a nucleation time-scale, which delineates the fracture growth into a nucleation phase, an intermediate stage and a late time stage where convergence toward LHFM predictions finally occurs. A highly non-linear hydro-mechanical coupling takes place as the Fluid front enters the rough cohesive zone which itself evolves during the nucleation and intermediate stages. This coupling leads to significant additional viscous flow dissipation. As a result, the fracture evolution deviates from LHFM solutions with shorter fracture lengths, larger widths and net pressures. These deviations ultimately decrease at late times as the lag and cohesive zone fractions both become smaller. The deviations increase with larger dimensionless toughness and in-situ-to-cohesive stress ratio, as both further localize viscous dissipation near the Fluid front located in the rough cohesive zone. The convergence toward LHFM can occur at very late time for realistic values of in-situ-to-cohesive stress ratio encountered at depth. The impact of a rough cohesive zone appears to be prominent for laboratory experiments and short in-situ injections in quasi-brittle rocks with ultimately a larger energy demand compared to LHFM predictions.Comment: submitted to J. Mech. Phys. So
