Session G37: Minisymposium: Hydraulic Fracturing

An Experimental Study of Penny-shaped Fluid-driven Cracks in an Elastic Matrix

When a pressurized fluid is injected into an elastic matrix, the fluid generates a fracture that grows along a plane and forms a fluid-filled disc-like shape. For example, such problems occur in various natural and industrial applications involving the subsurface of Earth, such as hydraulic fracturing operations. We report a laboratory study of such a fluid-driven crack in a gelatin matrix, study the crack shape as a function of time, and investigate the influence of different experimental parameters such as the injection flow rate, Young's modulus of the matrix, and fluid viscosity. We find that the crack radius increases with time as a power law, which has been predicted both for the limit where viscous effects in the flow along the crack opening control the rate of crack propagation, as well as the limit where fracture toughness controls crack propagation. We vary experimental parameters to probe the physical limits and highlight that for our typical parameters both effects can be significant. Also, we measure the time evolution of crack shape, which has not been studied before. The rescaled crack shapes collapse at longer times, based on an appropriate scaling argument, and again we compare the scaling arguments in different physical limits. The gelatin system provides a useful laboratory model for further studies of fluid-driven cracks, some of which we will mention as they are inspired by the physics of hydraulic fracturing. This work is part of the PhD thesis of Ching-Yao Lai and is a collaboration with Drs. Zhong Zheng and Jason Wexler (Princeton University) and Professor Emilie Dressaire (NYU).   

Engineering Fracking Fluids with Computer Simulation

There are no comprehensive simulation-based tools for engineering the flows of viscoelastic fluid-particle suspensions in fully three-dimensional geometries. On the other hand, the need for such a tool in engineering applications is immense. Suspensions of rigid particles in viscoelastic fluids play key roles in many energy applications. For example, in oil drilling the ``drilling mud'' is a very viscous, viscoelastic fluid designed to shear-thin during drilling, but thicken at stoppage so that the ``cuttings'' can remain suspended. In a related application known as hydraulic fracturing suspensions of solids called ``proppant'' are used to prop open the fracture by pumping them into the well. It is well-known that particle flow and settling in a viscoelastic fluid can be quite different from that which is observed in Newtonian fluids. First, it is now well known that the ``fluid particle split'' at bifurcation cracks is controlled by fluid rheology in a manner that is not understood. Second, in Newtonian fluids, the presence of an imposed shear flow in the direction perpendicular to gravity (which we term \textit{a cross or orthogonal shear flow}) has no effect on the settling of a spherical particle in Stokes flow (i.e. at vanishingly small Reynolds number). By contrast, in a non-Newtonian liquid, the complex rheological properties induce a nonlinear coupling between the sedimentation and shear flow. Recent experimental data have shown both the shear thinning and the elasticity of the suspending polymeric solutions significantly affects the fluid-particle split at bifurcations, as well as the settling rate of the solids. In the present work, we use the Immersed Boundary Method to develop computer simulations of viscoelastic flow in suspensions of spheres to study these problems. These simulations allow us to understand the detailed physical mechanisms for the remarkable physical behavior seen in practice, and actually suggest design rules for creating new fluid recipes.   

Subcontinuum mass transport of hydrocarbons in nanoporous media and long-time kinetics of recovery from unconventional reservoirs

In this talk I will discuss the transport of hydrocarbons across nanoporous media and analyze how this transport impacts at larger scales the long-time kinetics of hydrocarbon recovery from unconventional reservoirs (the so-called shale gas). First I will establish, using molecular simulation and statistical mechanics, that the continuum description -- the so-called Darcy law -- fails to predict transport within a nanoscale organic matrix. The non-Darcy behavior arises from the strong adsorption of the alkanes in the nanoporous material and the breakdown of hydrodynamics at the nanoscale, which contradicts the assumption of viscous flow. Despite this complexity, all permeances collapse on a master curve with an unexpected dependence on alkane length, which can be described theoretically by a scaling law for the permeance. Then I will show that alkane recovery from such nanoporous reservoirs is dynamically retarded due to interfacial effects occuring at the material's interface. This occurs especially in the hydraulic fracking situation in which water is used to open fractures to reach the hydrocarbon reservoirs. Despite the pressure gradient used to trigger desorption, the alkanes remain trapped for long times until water desorbs from the external surface. The free energy barrier can be predicted in terms of an effective contact angle on the composite nanoporous surface. Using a statistical description of the alkane recovery, I will then demonstrate that this retarded dynamics leads to an overall slow -- algebraic -- decay of the hydrocarbon flux. Such a behavior is consistent with algebraic decays of shale gas flux from various wells reported in the literature. \\[4pt] [1] K. Falk, B. Coasne, R. Pellenq, F. Ulm, L. Bocquet, Nature Com (2015).\\[0pt] [2] T. Lee, B. Coasne, L. Bocquet, submitted (2015).   

Fracturing in granular media: the role of capillarity, wetting, and disorder

The advent of shale oil and shale gas into the energy landscape has relied on achieving vigorous stimulation of the rock by means of horizontal drilling and hydraulic fracturing. Traditionally, hydraulic fracturing is understood as a single-fluid-phase, pressure-driven process, in which the fluid (typically water with additives) is injected at a high-enough rate that the pressure builds up faster than it can dissipate by permeating into the rock, thereby fracturing it. However, the prevalent conditions for shale (ultra fine pore size, moderate overburden stress, and poor cementation) suggest that capillary forces could play an important role in the fracturing process. Here, we show the results of our recent experimental and theoretical studies on fracturing of granular media by means of injection of an immiscible fluid. We conduct carefully controlled injection experiments in a quasi-2D granular medium (a circular Hele-Shaw cell filled with glass beads), in an experimental set-up that allows us to systematically study the impact of capillarity (by varying injection rate, bead size, and fluid-fluid surface tension), wetting properties (by treating the beads and the cell plates by chemical vapor deposition of silane-based substances) and confinement (by varying the load on the cell). Our choice of defending and invading liquids and granular medium allows us to investigate a wide range of contact angles, from drainage to imbibition. We demonstrate that wettability exerts a powerful influence on the invasion/fracturing morphology of unfavorable mobility displacements. High time resolution imaging techniques and particle image velocimetry (PIV) allow us to quantify matrix displacement and fracture opening dynamics. Our results provide insights on fracture propagation, fracture length distribution and the fracture drainage area, parameters which are critically important to better understand long-term hydrocarbon production from shale.   

Particle laden fluids in hydraulic fracturing

The aim of hydraulic fracturing is to create a highly conductive pathway in the reservoir formation of interest. This is typically achieved by ``propping'' the created fracture with solid particles (i.e. proppant) in order to prevent complete closure of the created fracture due to in-situ stresses when pumping stops. The placement of proppant is therefore the main goal of any fracturing treatment. It involves a number of interesting fluid dynamics problem (suspensions flow with settling, complex rheologies of the base fluid, effect of the fracture roughness etc.). In this talk, we will review the different class of fluids used to achieve proppant placement in fracture particularly focusing on their widely varied rheological properties. We will also discuss the different flow regimes that are typically encountered during a hydraulic fracturing job. In particular, we will notably present in details how recent advances in our understanding of dense suspensions flow [1,2] can improve predictions of proppant placement in the Stokesian regime. \\[4pt] [1] Boyer, F.; Guazzelli, \'{E}. {\&} Pouliquen, O. Unifying suspension and granular rheology Phys. Rev. Lett., APS, 2011, 107, 188301\\[0pt] [2] Lecampion, B. {\&} Garagash, D. Confined flow of suspensions modeled by a frictional rheology J. Fluid Mech., 2014, 759, 197-235