Dmitry Garagash

Dalhousie University | Dal · Department of Civil and Resource Engineering

This chapter considers a model for a radial hydraulic fracture propagation in a permeable, linear elastic rock formation driven by a point source fluid injection. The linear elastic fracture mechanics theory controls the quasi‐static propagation. The hydraulic fracturing fluid is slickwater − pure water solution with polymeric additives which allow...

We analyse the influence of fluid yield stress on the propagation of a radial (penny-shaped) hydraulic fracture in a permeable reservoir. In particular, the Herschel-Bulkley rheological model is adopted that includes yield stress and non-linearity of the shear stress. The rock is assumed to be linear elastic, and the fracture is driven by the point...

This chapter considers a model for a radial hydraulic fracture propagation in a permeable, linear elastic rock formation driven by a point source fluid injection. The linear elastic fracture mechanics theory controls the quasi-static propagation. The hydraulic fracturing fluid is slickwater -- pure water solution with polymeric additives which allo...

We analyse the influence of fluid yield stress on the propagation of a radial (penny-shaped) hydraulic fracture in a permeable reservoir. In particular, the Herschel-Bulkley rheological model is adopted that includes yield stress and non-linearity of the shear stress. The rock is assumed to be linear elastic, and the fracture is driven by the point...

Propagation of a slip transient on a fault with rate- and state-dependent friction resembles a fracture whose near tip region is characterized by large departure of the slip velocity and fault strength from the steady-state sliding. We develop a near tip solution to describe this unsteady dynamics, and obtain the fracture energy G c , dissipated in...

This work is devoted to an analysis of the near-tip region of a hydraulic fracture driven by slickwater in a permeable saturated rock. We consider a steady-state problem of a semi-infinite fracture propagating with constant velocity. The host rock is elastic and homogeneous, and fracture propagates according to linear elastic fracture mechanics. Th...

Propagation of a slip transient on a fault with rate-and-state dependent friction resembles a fracture which near tip region is characterized by large departure of the slip velocity and fault strength from the steady-state sliding. We develop a near tip solution to describe this unsteady dynamics, and obtain the fracture energy Gc, dissipated in ov...

This paper investigates the problem of a radial (or penny-shaped) hydraulic fracture propagating in a permeable reservoir. In particular, we consider the fluid exchange between the crack and ambient porous media as a pressure-dependent process. In most of the existing models, the fluid exchange process is represented as one-dimensional pressure-ind...

This work is devoted to an analysis of the near-tip region of a hydraulic fracture driven by slickwater in a permeable saturated rock. We consider a steady-state problem of a semi-infinite fracture propagating with constant velocity. The host rock is elastic and homogeneous, and fracture propagates according to linear elastic fracture mechanics. Th...

This paper investigates the problem of a radial (or penny-shaped) hydraulic fracture propagating in a permeable reservoir. In particular, we consider the fluid exchange between the crack and ambient porous media as a pressure-dependent process. In most of the existing models, the fluid exchange process is represented as one-dimensional pressure-ind...

In this paper we consider the near-tip region of a fluid-driven fracture propagating in permeable rock. We attempt to accurately resolve the coupling between the physical processes-rock breakage, fluid pressure drop in the viscous fluid flow in the fracture and fluid exchange between the fracture and the rock-that exert influence on the hydraulic f...

Hydraulic fracture presents an interesting case of crack elasticity and fracture propagation non-linearly coupled to fluid flow. Hydraulic fracture (HF) is often modeled using the Linear Elastic Fracture Mechanics (LEFM), which assumes that the damaged zone associated with the rock breakage near the advancing fracture front is small compared to the...

This paper is concerned with an analysis of the near tip region of a propagating fluid- driven fracture in a saturated permeable rock. The study attempts to accurately resolve the coupling between the physical processes - rock breakage, fluid pressure drop in the viscous fluid flow in the fracture, and fluid exchange between fracture and the rock -...

Models for hydraulic fracturing-induced earthquakes in shales typically ascribe fault activation to elevated pore pressure or increased shear stress; however, these mechanisms are incompatible with experiments and rate-state frictional models, which predict stable sliding (aseismic slip) on faults that penetrate rocks with high clay or total organi...

Hydraulic fracture presents an interesting case of crack elasticity and fracture propagation non-linearly coupled to fluid flow. Hydraulic fracture (HF) is often modeled using the Linear Elastic Fracture Mechan- ics (LEFM), which assumes that the damaged zone associated with the rock breakage near the advancing fracture front is small compared to t...

We investigate the growth of a hydraulic fracture assuming a power-law dependence of ma- terial toughness with fracture length for plane strain and radial geometries. Such a toughness fracture length dependence models in a simple manner a toughening mechanism for rocks. We develop an efficient numerical method for the hydraulic fracture growth prob...

Pulse-like ruptures arise spontaneously in many elastodynamic rupture simulations and seem to be the dominant rupture mode along crustal faults. Pulse-like ruptures propagating under steady-state conditions can be efficiently analysed theoretically, but it remains unclear how they can arise and how they evolve if perturbed. Using thermal pressurisa...

Pulse-like ruptures arise spontaneously in many elastodynamic rupture simulations and seem to be the dominant rupture mode along crustal faults. Pulse-like ruptures propagating under steady state conditions can be efficiently analyzed theoretically, but it remains unclear how they can arise and how they evolve if perturbed. Using thermal pressuriza...

Pulse-like ruptures arise spontaneously in many elastodynamic rupture simulations and seem to be the dominant rupture mode along several crustal faults. Pulse-like ruptures propagating under steady-state conditions can be efficiently analysed theoretically, but it remains unclear how they can arise and how they evolve if perturbed. Using thermal pr...

Models for hydraulic-fracturing induced earthquakes in shales typically ascribe fault activation to elevated pore pressure or increased shear stress. Seismicity up to Mw 4.1 has been correlated with hydraulic-fracturing operations targeting the Duvernay formation, western Canada. High resolution microseismic monitoring of treatments associated with...

Fluid-driven fracture presents an interesting case of crack elasticity and fracture propagation non- linearly coupled to fluid flow. With the exceptions of a few numerical studies, previous hydraulic fracture modeling efforts have been based on the premise of Linear Elastic Fracture Mechanics (LEFM): specifically, that the damage (aka cohesive) zon...

We consider numerical solutions in which the linear elastic response to an opening- or sliding- mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classi...

This work is concerned with the relationship between hydraulic fracturing injection into a fault and the possibility of a seismic slip. The results of this study show that the nucleation of dynamic slip on a fault with slip-weakening friction is only weakly dependent on the magnitude of the stress perturbation ahead of the propagating hydraulic fra...

This paper investigates the post fracture transient analysis of multi-fractured horizontal wells under the assumption of infinitely large fracture conductivity. Most of the existing studies of multi-fractured wells have considered finite fracture conductivity, when the dynamic fluid pressure drop in the flow within fractures is a part of the soluti...

This paper studies the transient pressurization of a pre-existing, fingerlike crack in a poroelastic, permeable rock due to a fluid injection, the problem previously considered in the nonporoelastic reservoir context in the companion paper [Sarvaramini and Garagash, J. Appl. Mech., 2015]. Large-scale fluid leak-off from the crack and the associated...

Current understanding suggests that the energy to propagate a hydraulic fracture is defined by the viscous fluid pressure drop along the fracture channel, while the energy dissipation in the immediate vicinity of the fracture front (i.e. fracture toughness) is negligible. This status quo relies on the assumption of Poiseuille flow in the fracture,...

Laboratory simulations of earthquakes show that at high slip rates, faults can weaken significantly, aiding rupture [1–3] . Various mechanisms, such as thermal pressurization and flash heating, have been proposed to cause this weakening during laboratory experiments [1,4–6], yet the processes that aid fault slip in nature remain unknown. Measuremen...

Geophysical observations suggest that mature faults weaken significantly at seismic slip rates. Thermal pressurization and thermal decomposition are two mechanisms commonly used to explain this dynamic weakening. Both rely on pore fluid pressurization with thermal pressurization achieving this through thermal expansion of native solids and pore flu...

This paper is concerned with the analysis of a low-viscosity fluid injection into a pre-existing, finger-like crack within a linear elastic, permeable rock, and of the conditions leading to the onset of the fracture propagation (i.e., the breakdown). The problem is of interest in reservoir waterflooding, supercritical CO2 injection for geological s...

We report here magnetic resonance imaging measurements performed on suspensions with a bulk solid volume fraction (φ0) up to 0.55 flowing in a pipe. We visualize and quantify spatial distributions of φ and velocity across the pipe at different axial positions. For dense suspensions (φ0 > 0.5), we found a different behavior compared to the known cas...

The problem of massive fluid injection into a pre-existing fracture has many applications in petroleum industry including underground liquid waste disposal and waterflooding to increase recovery from a hydrocarbon reservoir. Understanding the conditions leading to the re-activation of pre-existing fractures and ensuing propagation is critical for a...

This work is concerned with the relationship between hydraulic fracturing injection and induced seismicity on a fault. This is applicable to safety hazard assessment of the nucleation of dynamic slip along the fault as a result of hydraulic fracturing injection into or near the fault. The hydraulic fracture (HF) injection into the fault can be purp...

We investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al., 2011. The friction coefficient and solid volume fraction are taken as functions of the dimensionless viscous number I defined as the ratio between the f...

Seismological estimates of fracture energy show a scaling with the total slip of an earthquake. Potential sources for this scale dependency are coseismic fault strength reductions that continue with increasing slip or an increasing amount of off-fault inelastic deformation with dynamic rupture propagation. Here, we investigate the former mechanism...

Hydraulic fracturing has become ubiquitous in allowing to tap vast tight oil and gas reserves in North America and elsewhere in the world. In this method, fractures are initiated and propagated from a well into hydrocarbon-bearing strata by a high pressure fluid injection. Once created, the fractures provide a conductive pathway for hydrocarbons fr...

We benchmark a series of simulators against available reference solutions for propagating plane-strain and radial hydraulic fractures. In particular, we focus on the accuracy and convergence of the numerical solutions in the important practical case of viscosity dominated propagation. The simulators are based on different propagation criteria: line...

The aim of the present work is to investigate injection of a low-viscosity fluid into a pre-existing fracture within a linear elastic, permeable rock, as may occur in waterflooding and supercritical CO2 injection. In conventional hydraulic fracturing, high viscosity and cake building properties of injected fluid limit diffusion to a 1-D boundary la...

Elevated pore pressure can lead to reactivation of slip on pre-existing fractures and faults when the static Coulomb failure is reached locally. As the pressurized region spreads diffusively, slip can accumulate quasi-statically (paced by the pore fluid diffusion) or dynamically. In this work, we consider a prestressed fault with a locally peaked,...

There are several lines of evidence that suggest that thermal pressurization (TP) of pore fluid within a low-permeability fault core may play the key role in the development of earthquake slip. To elucidate effects of TP on spontaneous fault slip, we consider solutions for a steadily propagating slip pulse on a fault with a constant sliding frictio...

This paper investigates equilibrium of a pressurized plastic fluid invading a tensile wellbore crack in a linear elastic, permeable rock. The crack is initially filled by pore fluid at ambient pressure, that is immiscibly displaced by the plastic fluid invading from the wellbore. The plastic fluid comes to rest to form a “plug” within the elastical...

The present work investigates the injection of a low-viscosity fluid into a pre-existing fracture with constrained height (PKN), as in waterflooding or supercritical CO2 injection. Contrary to conventional hydraulic fracturing, where 'cake build up' limits diffusion to a small zone, the low viscosity fluid allows for diffusion over a wider range of...

High-resolution deformation and seismic observations are usually made only near the Earths' surface, kilometers away from where earthquake nucleate on active faults and are limited by inverse-cube-distance attenuation and ground noise. We have developed an experimental approach that aims at reactivating faults in-situ using thermal techniques and f...

Statically-strong faults that operate at low stress level require existence of strong dynamic weakening processes, of which the flash heating (FH) on asperities and the thermal pressurization (TP) are likely the most universal ones [e.g. Rice, JGR 2006]. The classical rate- and state-dependence of the fault friction inferred from laboratory observa...

This paper is concerned with an analysis of the near-tip region of a fluid-driven fracture propagating in a permeable saturated rock. The analysis is carried out by considering the stationary problem of a semi-infinite fracture moving at constant speed V. Two basic dissipative processes are taken into account: fracturing of the rock and viscous flo...

Faults are typically simulated in the laboratory at the cm-to-dm scale, and results are then up-scaled by orders of magnitude. We describe an experimental approach that aims to activate faults in-situ at scales of ~ 10–100 m using thermal techniques and fluid injection to modify in situ stresses and the fault strength to the point where the rock fa...

Fault-slip is typically simulated in the laboratory at the cm-to-dm scale. Laboratory results are then up-scaled by orders of magnitude to understand faulting and earthquakes processes. We suggest an experimental approach to reactivate faults in-situ at scales ~10-100 m using thermal techniques and fluid injection to modify in situ stresses and the...

A solution to the problem of a plane-strain fluid-driven crack propagation in elastic permeable rock with resistance to fracture is presented. The fracture is driven by injection of an incompressible Newtonian fluid at a constant rate. The solution, restricted to the case of zero lag between the fluid front and the fracture tip, evolves from the ea...

Fractures and fluids influence virtually all mechanical processes in the crust, but many aspects of these processes remain poorly understood largely because of a lack of controlled field experiments at appropriate scale. We have developed an in-situ experimental approach to create carefully controlled faults at scale of ~10 meters using thermal tec...

The presence of stress and material interfaces in hydrocarbon reservoirs may significantly complicate prediction of hydraulic fracture propagation, as the spatial resolution of numerical codes is usually insufficient to capture the details of the fracture-interface interaction at the early stages of the crossing. Thus, an explicit analytical and ex...

A particular class of fractures driven in a solid by pressurized viscous fluids is considered. These fractures could be either tens or hundreds meters long man-made hydraulic fractures in oil and gas reservoirs, or natural fractures, such as kilometers-long volcanic dikes driven by magma coming from upper mantle beneath the Earth’s crust. Different...

Most hydraulic fracturing treatments are in the viscosity-dominated regime. Hence, fracture growth does not depend on the rock toughness and it can be shown that the fracture aperture w near the fracture front, when viewed at the scale of the whole fracture, is not characterized by the classical square root behavior predicted by linear elastic frac...

This paper presents the results of an experimental study of the stress-strain behaviour of a normally-consolidated, saturated Kaolin clay in triaxial compression tests under undrained and drained conditions. Results of undrained tests have consistently shown existence of the softening part in the deviatoric stress-strain diagram at high strains. Th...

This paper analyses the problem of a fluid-driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power-law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibr...

This paper studies the propagation of a plane-strain fluid-driven fracture with a fluid lag in an elastic solid. The fracture is driven by a constant rate of injection of an incompressible viscous fluid at the fracture inlet. The leak-off of the fracturing fluid into the host solid is considered negligible. The viscous fluid flow is lagging behind...

This paper considers the problem of plane-strain fluid-driven fracture propagating in an impermeable elastic medium under condition of large toughness or, equivalently, of low fracturing fluid viscosity. We construct an explicit solution for a fracture propagating in the toughness-dominated regime when the energy dissipated in the viscous fluid flo...

The paper considers the problem of a plane-strain fluid-driven fracture propagating in an impermeable elastic solid, under condition of small (relative) solid toughness or high (relative) fracturing fluid viscosity. This condition typically applies in hydraulic fractur-ing treatments used to stimulate hydrocarbons-bearing rock layers, and in the tr...

This paper considers the problem of a hydraulic fracture in which an incompressible Newtonian fluid is injected at a constant rate to drive a fracture in a permeable, infinite, brittle elastic solid. The two cases of a plane strain and a penny-shaped fracture are considered. The fluid pressure is assumed to be uniform and thus the lag between the f...

This paper examines the effects of shear heating due to frictional slip in a simple model of a fluid saturated fault zone. The experimentally motivated friction law includes dependence on the rate of slip and a state variable. Inclusion of the rate and state dependence is shown to eliminate a non-uniqueness that occurs when shear heating is include...

The coupling between the pore fluid diffusion and deformation of geomaterials can alter the mechanical response and facilitate or delay material failure. Dilatant or contractive material behavior under conditions of limited drainage and/or of load-ing rate exceeding the pore fluid diffusion rate causes a reduction or increase in pore pressure, resp...

This paper is concerned with an analysis of the near-tip region of a fluid-driven fracture propagating in a permeable saturated rock. It focuses on the calculation of the pore fluid pressure in the tip cavity, the region corresponding to the lag between the front of the fracturing fluid and the fracture tip. In contrast to impermeable rocks where t...

This paper analyzes slip on a fluid-infiltrated dilatant fault for imposed (tectonic) strain rates much slower than the rate of fluid exchange between the gouge zone and the surroundings and for exchange of heat slower than of fluid, typical of interseismic or most laboratory loading conditions. The limiting solution, corresponding to the infinitel...

The one-dimensional model of Rudnicki and Chen [1988] for a slip-weakening dilating fault is extended to include shear heating. Because inertia is not included, instability (a seismic event) corresponds to an unbounded slip rate. Shear heating tends to increase pore pressure and decrease the effective compressive stress and the resistance to slip a...

The presence of pore fluids in geomaterials can alter deformation processes and facilitate or delay material failure. Dilation/contraction of geomaterials in the course of inelastic undrained deformation causes a reduction/increase in pore pressure altering the effective compressive stress. This results in an increase/decrease in shear stress that...

This paper is concerned with the near-tip analysis of a fluid-driven fracture propagating in a permeable saturated rock. The problem is characterized by existence of a tip cavity resulting from the lagging of the fracturing fluid behind the fracture tip. This cavity is filled by the pore fluid, which is drawn by suction at tip of the advancing frac...

We consider a Griffith fluid-driven fracture of half length ℓ (t) propagating in an impermeable linear elastic medium characterized by Young modulus E, Poisson ratio v, and toughness K Ic . An incompressible fluid of viscosity μ is injected at the center of the fracture at a given constant volumetric rate Q o (per unit fracture width). We choose a...