Effect of dilatancy on the transition from aseismic to seismic slip due to fluid injection in a fault

Aseismic crack growth upon activation of fault slip due to fluid injection may or may not lead to the nucleation of a dynamic rupture depending on in-situ conditions, frictional properties of the fault and the value of overpressure. In particular, a fault is coined as unstable if its residual frictional strength $\tau_r$ is lower than the in-situ background shear stress $\tau_o$. We study here how fault dilatancy associated with slip affect shear crack propagation due to fluid injection. We use a planar bi-dimensional model with frictional weakening and assume that fluid flow only takes place along the fault (impermeable rock {/ immature fault}). Dilatancy induces an undrained pore-pressure drop locally strengthening the fault. We introduce an undrained residual fault shear strength $\tau_r^u$ (function of dilatancy) and show theoretically that under the assumption of small scale yielding, an otherwise unstable fault ($\tau_r<\tau_o$) is stabilized when $\tau_r^u$ is larger than $\tau_o$. We numerically solve the complete coupled hydro-mechanical problem and confirm this theoretical estimate. It is important to note that the undrained residual strength is fully activated only if residual friction is reached. Dilatancy stabilizes an otherwise unstable fault if the nucleation of an unabated dynamic rupture -without dilatancy- is affected by residual friction, which is the case for sufficiently large injection pressure. We also discuss the effect of fault permeability increase due to slip. Our numerical results show that permeability increases lead to faster aseismic growth but do not impact the stabilizing effect of dilatancy with respect to dynamic rupture

Effect of dilatancy on a frictional weakening fault subjected to fluid injection

Fluid injection at a pressure below the local minimum principal total stress in a fault may (re)activate shear crack propagation (hydroshearing). Because of the presence of asperities along the fault's surfaces, fault hydraulic width increase with slip. Scaled experiments in fact show that dilatancy (inelastic increment of hydraulic width) varies non linearly with the slip up to a constant value (for large values of shear displacements) [3]. Its effect on pore pressure diffusion along the fault is a local drop at the crack tip. Depending on the ability of the fluid to flow in the newly created void space, the local effective stresses increase and this leads to a stabilizing effect [2]. The questions we want to address in this contribution are the fol- lowing: does the increment of hydraulic width (dilatancy) always kill the dynamic instability associated with a frictional weakening fault subjected to fluid injection? does the change of fault permeability associated with dilatant hardening affect the shear crack propagation? Garagash & Germanovich [1] showed that the regime of propagation of pressurized faults can be ultimately stable or unstable depending on whether the initial shear stress state is greater or lower than the fault residual strength. In the former case the shear crack propagates with a moderate velocity (quasi-static) as it is induced by fluid pressure diffusion (but it might turns into a dynamic instability followed by an arrest). In the latter case, the shear crack initially propagates quasi-statically; then, as slip accumulate along the fault, the quasi-static crack growth become unstable and the shear crack runs away. The effect of dilatancy leads to a local reduction of pore-pressure at the shear crack tip. Notably, the local pore pressure drop and the consequent local increment of effective stress depends on the hydraulic diffusivity of the fault: we expect higher pressure drop for fault characterized by constant permeability (no change with fault dilatancy) than for fault whose permeability increase with dilatant hardening. So it is clear that there is an interplay be- tween pressure drop associated with dilatant hardening and fault permeability change. In this contribution we want to investigate such an interplay for both ultimately stable and unstable faults

Modelling of fluid injection into a frictional weakening dilatant fault

Understanding the mechanism of nucleation of dynamic rupture is an important issue in seismology. It is the key factor in determining the seismic potential of pre-existing faults under long-term loadings. Furthermore, the activation of Mode II fracture by means of fluid injection is the way to enhance the permeability of deep geothermal reservoirs (Enhanced Geothermal Systems) whose efficacy rely on the shear-induced dilation. Locally elevated pore pressure associated with fluid injection leads to a reduction of the fault frictional strength (product of the local normal effective stress and the slip-weakening friction coefficent) which may eventually falls below the background shear stress. As a result, a shear crack will start to propagate with an initially moderate velocity (quasi-static) as it is induced by fluid pressure diffusion. As slip accumulate, the quasi-static crack growth may become unstable due to the slip-weakening nature of friction, resulting in the nucleation of a dynamic rupture until residual frictional strength is reached (see Garagash & Germanovich, 2012). The size of such a dynamic rupture (associated with fluid injection) is intrinsically related to both the way the pore-pressure distribution evolves spatially and temporally along the fault and the initial background shear stress. Larger dynamic ruptures are actually obtained for lower overpressure that are spread over larger zones, while a dynamic rupture associated with larger (but more localized) peak overpressure reaches residual friction earlier. Moreover, for large values of overpressure (with respect to the initial effective stress state along the fault), the nucleation length is smaller for lower value of the background shear stress. In this contribution, we investigate the effect of the shear dilatancy of the fault on the diffusion of pore pressure. Dilatancy may locallly reduce pore-pressure depending on the ability of the fluid to flow in the newly created void space. Reduction in pore-pressure associated with dilatancy can result in increase of the fault shear resistance and thus can potentially arrest a dynamic rupture. We formulate a 2D model of fluid injection in a shear dilatant fault exhibiting slip weakening friction. The model couples elastic deformation, shear weakening Coulomb friction with dilatancy and fluid flow along the fault. We develop a numerical scheme based on boundary element (Displacement Discontinuity Method) for elastic deformation and a finite volume scheme for fluid flow. We verify our solver first on the non-dilatant case by comparing our results with the solution of Garagash & Germanovitch (2012). We then investigate the effect of shear-dilatancy and its feedback on the nucleation of dynamic rupture

Hydraulic stimulation of pre-existing discontinuities in tight rocks

Hydraulic stimulation is an engineering technique whose aim is to enhance the permeability of fractured rock masses at depths ranging from one to five kilometers. It consists in the injection of fluid at sufficiently high pressure in order to shear pre-existing fractures and/or to create new fractures. The local reduction of effective stresses can indeed result into localized inelastic deformations along pre-existing discontinuities which upon dilation increase the overall permeability of the rock mass. Although this technique is used to extract deep geothermal energy from crystalline rocks, some fundamental hydro-mechanical mechanisms are not yet fully understood, especially in regards to the transition between aseismic and seismic slip. In this context, the present thesis investigates the interplay between pore pressure diffusion within pre-existing discontinuities and induced deformations including the possible nucleation of a dynamic rupture. This is achieved via the development of specific numerical algorithms that are extensively verified against existing analytical and semi-analytical solutions of fracture growth. Thanks to the use of a boundary integral representation for elasticity, fluid driven deformations localized on pre-existing discontinuities can be efficiently modelled, without involving an intensive discretization of the whole domain. We first present an in-depth study on the effect of dilatancy on the propagation of a fluid driven crack along a frictional weakening planar fault. The numerical results reveal that shear-induced dilatancy can effectively stabilize an otherwise unstable fault with respect to the nucleation of an unabated dynamic rupture. Although counter-intuitive, this is valid only for sufficiently large injection over-pressure. This important result is confirmed theoretically using linear elastic fracture mechanics (LEFM) under small-scale yielding approximation. The simulations further show that this stabilization still hold even for large increase of fault permeability associated with shear deformations. In a second part of this manuscript, a new boundary element solver for localized inelastic deformations along a large set of pre-existing planes is proposed and described. Upon validation against several analytical and semi-analytical solutions, a series of problems are addressed in order to illustrate the capabilities, accuracy and performance of this algorithm. It is then used to model hydraulic stimulation of fractured rock masses in the extreme cases of critically stressed and marginally pressurized conditions

Fluid injection in a frictional weakening fracture

Understanding the mechanism of nucleation of dynamic rupture is an important issue in seismology since it is the key factor in determining the seismic potential of pre-existing faults under long-term loadings. Furthermore, the activation of Mode II crack by means of fluid injection in a fracture is one of the mechanisms that enhance the permeability in deep geothermal reservoirs (Enhanced Geothermal Systems) whose efficacy rely on the shear-induced dilation. Since we are interested in modelling a fracture network under hydraulic stimulation, a deep understanding of the shear crack propagation induced by fluid injection is needed. Locally elevated pore pressure associated with fluid injection leads to a reduction of the fault frictional strength (product of the local normal effective stress and the slip-weakening friction coefficient) which may eventually falls below the background shear stress. As a result, a shear crack will start to propagate with an initially moderate velocity (quasi-static) as it is induced by fluid pressure diffusion. As slip accumulate, the quasi-static crack growth may become unstable due to the slip-weakening nature of friction, resulting in the nucleation of a dynamic rupture (micro-seismicity) until residual frictional strength is reached. Theoretical and numerical models now exist to simulate shear fault/fracture under fluid injection for both quasi-static (QS) and quasi-dynamic (QD) crack growth. However, a comparison between the QS and QD approaches has not been done. Therefore the question that arises is how the inertial effects affect the dynamic instability and the rupture run-out distance

STIMDESIGN: Hydraulic stimulation design for deep geothermal reservoirs - a numerical approach

This report is the third intermediate report of the StimDesign project which will finish in June next year. The focus is here solely on our two dimensional numerical developments. We report advances on the different building blocks of our numerical model: fracture mechanics solver with frictional contacts and cohesive forces, finite volume discretization for fluid flow and fully coupled hydro-mechanical solvers. This reports documents in depth the mathematical formulation as well as the numerical discretization. Notably a new scheme to account for both frictional contact of shear crack as well as opening mode is presented and tested on a series of tests examples. Tests of our implementation of algorithms based on hierarchical matrices for the acceleration of the solution of linear systems arising in the boundary element methods is also documented. We report significant speedup and reduction in memory requirements. Finally, two studies which have or will soon be submitted for publication are put in appendix. The first study investigate the effect of shear induced dilatancy on the transition from aseismic to seismic in the context of fluid injection in a planar fault. The second study investigates the possibility of remote activation / nucleation (in a frictional weakening zone) due to the stress transfer associated with the propagation of a purely aseismic crack due to fluid injection in a friction neutral layer

Injection-Induced Aseismic Slip in Tight Fractured Rocks

We investigate the problem of fuid injection at constant pressure in a 2D Discrete Fracture Network (DFN) with randomly oriented and uniformly distributed frictionally-stable fractures. We show that this problem shares similarities with the simpler scenario of injection in a single planar shear fracture, investigated by Bhattacharya and Viesca (2019); Viesca (2021) and whose results are here extended to include closed form solutions for aseismic moment as function of injected volume Vinj. Notably, we demonstrate that the hydro-mechanical response of the fractured rock mass is at frst order governed by a single dimensionless parameter T associated with favourably oriented fractures: low values of T (critically stressed conditions) lead to fast migration of aseismic slip from injection point due to elastic stress transfer on critically stressed fractures. In this case, therefore, there is no efect of the DFN percolation number on the spatio-temporal evolution of aseismic slip. On the other hand, in marginally pressurized conditions (T ≳ 1), the slipping patch lags behind the pressurized region and hence the percolation number afects to a frst order the response of the medium. Furthermore, we show that the aseismic moment scales ∝ V2 inj in both limiting conditions, similarly to the case of a single planar fracture subjected to the same injection condition. The factor of proportionality, however, depends on the DFN characteristics in marginally pressurized conditions, while it appears to be only mildly dependent on the DFN properties in critically stressed conditions.ISSN:1434-453XISSN:0723-263

Impact of injection rate ramp-up on nucleation and arrest of dynamic fault slip

Fluid injection into underground formations reactivates preexisting geological discontinuities such as faults or fractures. In this work, we investigate the impact of injection rate ramp-up present in many standard injection protocols on the nucleation and potential arrest of dynamic slip along a planar pressurized fault. We assume a linear increasing function of injection rate with time, up to a given time t(c) after which a maximum value Q(m) is achieved. Under the assumption of negligible shear-induced dilatancy and impermeable host medium, we solve numerically the coupled hydro-mechanical model and explore the different slip regimes identified via scaling analysis. We show that in the limit when fluid diffusion time scale t(w) is much larger than the ramp-up time scale t(c), slip on an ultimately stable fault is essentially driven by pressurization at constant rate. Vice versa, in the limit when t(c)/t(w) >> 1, the pressurization rate, quantified by the dimensionless ratio Q(m)t(w)/t(c)Q* with Q* being a characteristic injection rate scale, does impact both nucleation time and arrest distance of dynamic slip. Indeed, for a given initial fault loading condition and frictional weakening property, lower pressurization rates delay the nucleation of a finite-sized dynamic event and increase the corresponding run-out distance approximately proportional to proportional to (Q(m)t(w)/t(c)Q*)^(-0.472). On critically stressed faults, instead, the ramp-up of injection rate activates quasi-static slip which quickly turn into a run-away dynamic rupture. Its nucleation time decreases non- linearly with increasing value of Q(m)t(w)/t(c)Q* and it may precede (or not) the one associated with fault pressurization at constant rate only.ISSN:2363-8427ISSN:2363-841

A fast boundary element based solver for localized inelastic deformations

We present a numerical method for the solution of nonlinear geomechanical problems involving localized deformation along shear bands and fractures. We leverage the boundary element method to solve for the quasi-static elastic deformation of the medium while rigid-plastic constitutive relations govern the behavior of displacement discontinuity (DD) segments capturing localized deformations. A fully implicit scheme is developed using a hierarchical approximation of the boundary element matrix. Combined with an adequate block preconditioner, this allows to tackle large problems via the use of an iterative solver for the solution of the tangent system. Several two-dimensional examples of the initiation and growth of shear-bands and tensile fractures illustrate the capabilities and accuracy of this technique. The method does not exhibit any mesh dependency associated with localization provided that (i) the softening length-scale is resolved and (ii) the plane of localized deformations is discretized a priori using DD segments

Impedance-based Rapid Diagnostic Tool for Single Malaria Parasite Detection

: This paper presents a custom, low-cost electronic system specifically designed for rapid and quantitative detection of the malaria parasite in a blood sample. The system exploits the paramagnetic properties of malaria-infected red blood cells (iRBCs) for their magnetophoretic capture on the surface of a silicon chip. A lattice of nickel magnetic micro-concentrators embedded in a silicon substrate concentrates the iRBCs above coplanar gold microelectrodes separated by 3 μm for their detection through an impedance measurement. The sensor is designed for a differential operation to remove the large contribution given by the blood sample. The electronic readout automatically balances the sensor before each experiment and reaches a resolution of 15 ppm in the impedance measurement at 1 MHz allowing a limit of detection of 40 parasite/μl with a capture time of 10 minutes. For better reliability of the results, four sensors are acquired during the same experiment. We demonstrate that the realized platform can also detect a single infected cell in real experimental conditions, measuring human blood infected by Plasmodium falciparum malaria specie