Fluid-induced fracture into weakly consolidated sand: Impact of confining stress on initialization pressure

Paula A. Gago, Kuba Wieladek, and Peter King

Phys. Rev. E 101, 012907 – Published 29 January 2020

Abstract

This paper studies the process of fluid injection driven fractures in granular packs where particles are held together by external confining stresses and weak intergrain cohesion. We investigate the process of fracture formations in soft sand confined into a radial Hele-Shaw cell. Two main regimes are well known for fluid injection in soft sand. For low fluid injection pressures it behaves as a solid porous material while for high enough injection pressures grain rearrangement takes place. Grain rearrangements lead to the formation of fluid channels or “fractures,” the structure and geometry of which depend on the material and fluid properties. Due to macroscopic grain displacements and the predominant role of dissipative frictional forces in granular system dynamics, these materials do not behave as conventional brittle, linear elastic materials and the transition between these two regimes cannot usually be described using poroelastic models. In this work we investigate the change in the minimum fluid pressure required to start grain mobilization as a function of the confining stresses applied to the system using a spatially resolved computational fluid dynamics–discrete element method numerical model. We show that this change is proportional to the applied stress when the confining stresses can be regarded as uniformly distributed among the particles in the system. A preliminary analytical expression for this change is presented.

Received 21 October 2019

DOI:https://doi.org/10.1103/PhysRevE.101.012907

Physics Subject Headings (PhySH)

Emergence of patterns Fracture Granular materials

Nonlinear DynamicsPolymers & Soft Matter

Authors & Affiliations

Paula A. Gago ^*, Kuba Wieladek, and Peter King

Department of Earth Science and Engineering, Imperial College, London, SW7 2BP, United Kingdom

^*paulaalejandrayo@gmail.com

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 101, Iss. 1 — January 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic representation of the setup for the numerical simulations. (a) A Hele-Shaw cell of radius $R \sim 4.4 cm$ with central fluid injection inlet (radius $r_{0} = 3.5 mm$ ) filled with a dense granular pack of grains of mean diameter is $d = 1.363 mm$ . Cell thickness $t \sim 2.4 mm ≪ R$ . (b) Boundary conditions for the fluid injection; fluid is injected from the central inlet at a constant pressure $p_{i}$ while the external cell perimeter is considered open ( $p_{outlet} = 0$ ). Fluid flow is allowed through the outer perimeter but is not allowed through the upper and the lower walls. (c) The initial setup is obtained by compacting an initially loose pack of particles confined between two parallel plates separated a constant distance, using eight pistonlike walls applying a constant force $F_{wall}$ to the system. This step stops once a static configuration is reached. (d) Once a dense granular pack is created [as explained in (c)], a constant force $F_{load}$ is applied to the upper wall of the cell until a new equilibrium is obtained. All system walls remain fixed after this configuration is achieved. (e) Pressure profile as a function of the distance $r$ from the center of the injection inlet.
Reuse & Permissions
Figure 2
Final stationary state obtained with four different values of the fluid inlet pressure. These results correspond to $F_{load} = 30 N, F_{wall} = 2 N$ , and (a) $p i = 5 kPa$ , (b) $p i = 42 kPa$ , (c) $p i = 46 kPa$ , and (d) $p i = 48.5 kPa$ . (See Supplemental Material [17] for a higher resolution version of this figure.)
Reuse & Permissions
Figure 3
(a) Particle positions for the slice $z = 3$ of a lattice-based representation over a (482, 482, 6) square mesh of the system configuration shown in Fig. 2. The value of void fraction $v_{f}$ assigned to each block corresponds to the percentage of grid block occupied by fluid (or void). (b) Same as (a) but for the configuration in Fig. 2. Panels (c) and (d) show the detected clusters of grid blocks with $v_{f} > 0.8$ (almost just fluid) for systems in (a) and (b), respectively. (See Supplemental Material [17] for a higher resolution version of this figure.)
Reuse & Permissions
Figure 4
(a) Fracture area as a function of inlet pressure $p_{i}$ for different $F_{load}$ applied to the initial condition [see Fig. 1] and $F_{wall} = 2 N$ [see Fig. 1]. (b) Fracture area as a function of $p_{i}$ for different $F_{w a l l s}$ applied to create the initial condition and $F_{load} = 30 N$ .
Reuse & Permissions
Figure 5
(a) Same as Fig. 2 but as a function of the difference $p_{i} - 1.6 \times p_{c}$ , with $p_{c}$ obtained from Eq. (8). Red dashed line points to the position of $p_{i} - 1.6 \times p_{c} = 0$ . Inset corresponds to the same information but obtained with a system having a static friction coefficient $μ = 0.5$ (for the grain-grain and the grain-wall interaction). (b) Same as (a) for systems whose initial condition was created applying a different lateral stress $F_{wall}$ (see Fig. 1). (c) Same as (a) for a system composed of particles having a much more narrow size distribution, namely composed of three particle sizes ( $d_{1} = 1.4 mm, d_{2} = 1.3 mm$ , and $d_{3} = 1.2 mm$ ) homogeneously distributed.
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics