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Register a new userA Model for Tracking Fronts of Stress-Induced Permeability Enhancement
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Using an analogy to the classical Stefan problem, we construct evolution equations for the fluid pore pressure on both sides of a propagating stress-induced damage front. Closed form expressions are derived for the position of the damage front as a function of time for the cases of thermally-induced damage as well as damage induced by over-pressure. We derive expressions for the flow rate during constant pressure fluid injection from the surface corresponding to a spherically shaped subsurface damage front. Finally, our model results suggest an interpretation of field data obtained during constant pressure fluid injection over the course of 16 days at an injection site near Desert Peak, NV.
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In an interesting recent paper [1] (A. Acharya, Stress of a spatially uniform dislocation density field, J. Elasticity 137 (2019), 151--155), Acharya proved that the stress produced by a spatially uniform dislocation density field in a body comprising a nonlinear elastic material may fail to vanish under no loads. The class of counterexamples constructed in [1] is essentially $2$-dimensional: it works with the subgroup $mathcal{O}(2) oplus langle{bf Id}rangle subset mathcal{O}(3)$. The objective of this note is to extend Acharyas result in [1] to $mathcal{O}(3)$, subject to an additional structural assumption and less regularity requirements.
The stress-dilatancy relation is of critical importance for constitutive modelling of sand. A new fractional-order stress-dilatancy equation is analytically developed in this study, based on stress-fractional operators. An apparent linear response of the stress-dilatancy behaviour of soil after sufficient shearing is obtained. As the fractional order varies, the derived stress-dilatancy curve and the associated phase transformation state stress ratio shift. But, unlike existing researches, no other specific parameters, except the fractional order, concerning such shift and the state-dependence are required. The developed stress-dilatancy equation is then incorporated into an existing constitutive model for validation. Test results of different sands are simulated and compared, where a good model performance is observed.
We present a model for the effect of stress on thin amorphous films that develop atop ion-irradiated silicon, based on the mechanism of ion-induced anisotropic plastic flow. Using only parameters directly measured or known to high accuracy, the model exhibits remarkably good agreement with the wavelengths of experimentally-observed patterns, and agrees qualitatively with limited data on ripple propagation speed. The predictions of the model are discussed in the context of other mechanisms recently theorized to explain the wavelengths, including extensive comparison with an alternate model of stress.
Permeability is the key parameter for quantifying fluid flow in porous rocks. Knowledge of the spatial distribution of the connected pore space allows, in principle, to predict the permeability of a rock sample. However, limitations in feature resolution and approximations at microscopic scales have so far precluded systematic upscaling of permeability predictions. Here, we report fluid flow simulations in capillary network representations designed to overcome such limitations. Performed with an unprecedented level of accuracy in geometric approximation at microscale, the pore scale flow simulations predict experimental permeabilities measured at lab scale in the same rock sample without the need for calibration or correction. By applying the method to a broader class of representative geological samples, with permeability values covering two orders of magnitude, we obtain scaling relationships that reveal how mesoscale permeability emerges from microscopic capillary diameter and fluid velocity distributions.
Seeing the Earth crust as crisscrossed by faults filled with fluid at close to lithostatic pressures, we develop a model in which its elastic modulii are different in net tension versus compression. In constrast with standard nonlinear effects, this ``threshold nonlinearity is non-perturbative and occurs for infinitesimal perturbations around the lithostatic pressure taken as the reference. For a given earthquake source, such nonlinear elasticity is shown to (i) rotate, widen or narrow the different lobes of stress transfer, (ii) to modify the $1/r^2$ 2D-decay of elastic stress Green functions into the generalized power law $1/r^{gamma}$ where $gamma$ depends on the azimuth and on the amplitude of the modulii asymmetry. Using reasonable estimates, this implies an enhancement of the range of interaction between earthquakes by a factor up to 5-10 at distances of several tens of rupture length. This may explain certain long-range earthquake triggering and hydrological anomalies in wells and suggest to revisit the standard stress transfer calculations which use linear elasticity. We also show that the standard double-couple of forces representing an earthquake source leads to an opening of the corresponding fault plane, which suggests a mechanism for the non-zero isotropic component of the seismic moment tensor observed for some events.
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