Arrest Mechanisms of Buoyant Hydraulic Fractures
Authors: Möri A. , Peruzzo C. , Lecampion B. , Garagash D. I. 
Published: September 2023

ABSTRACT
Hydraulic fracturing (HF) treatments can form widespread fractures. Understanding their containment at depth is critical, given the positive buoyancy contrast between the fracturing fluid and the surrounding rock, promoting upward growth. We study arrest mechanisms for established buoyant HF, restricting our investigation to fully planar fractures. We show that changes in the fracturing toughness (KIc) (E, and v remain unchanged) are inefficient in arresting buoyant HFs. A fracture size-dependent, apparent KIc can only prevent buoyant fractures from emerging but not stop their ascent. Sudden changes of KIc between layers need to be significant to arrest a buoyant HF KIc−2/KIc−1 ≥ 2 − 3. Contrary, a stress barrier efficiently arrests buoyant fractures for stress contrasts as little as Δσ ≥ 1.00 (MPa). We further demonstrate that the interaction with a high-leak-off layer is more efficient in arresting fracture ascent than an equivalent uniform leak-off value. Moderate to high leak-off arrests fractures before they become buoyant or without significant uprise. All considered arrest mechanisms can stop the propagation of a buoyant HF, implying that combining several mechanisms likely prevents buoyant HFs from reaching shallow formations or even the surface.

INTRODUCTION
Hydraulic fractures (HF) created through industrial treatments can show significant extents. Ensuring a safe operation and efficient exploitation of the targeted formation is only possible if the fracture becomes contained at depth. In the absence of any heterogeneity, assuming a Newtonian fluid, an impermeable medium subjected to linear background stress, and a block injection, Möri and Lecampion (2023) have shown that the containment depends on a single, dimensionless buoyancy (Equation) (see their Eq. (9)). It is possible to define a limiting volume, determining if the fracture arrests at depth or becomes buoyant (Davis et al., 2020; Salimzadeh et al., 2020). This limit for buoyant propagation is equivalent to (Equation). Here we investigate cases of buoyant fractures with (Equation) (see Tab. 1) and will explore what effects changes in the apparent fracturing toughness, stress barriers, and fluid leak-off will have on buoyant HF. Following Möri and Lecampion (2023), we consider a block injection of a fluid with a viscosity μ at a constant rate Qo until shut-in of the injection at ts, giving a total injected volume of Vo = Qots. The medium is considered linear-elastic with a given value of the plain-strain modulus E′ = E/(1 − v2), with E the materials Young's modulus and v its Poisson's coefficient. We consider a linearly varying background stress with depth (e.g. σ (z) μ z) and use constant values for the rock and fluid density. A buoyant force, caused by the difference of the two Δγ = Δρg = (ρsolid − ρfluid)g, with g = 9.81 (m·s−2) the earth gravitational acceleration, emerges, driving buoyant propagation. Note that we do not consider any density variation. The effect of any heterogeneity will be related to the dominating energy dissipation mechanism (viscosity- vs toughness-dominated) when the fracture becomes buoyant and/or encounters heterogeneity. For a change in properties at a given distance from the injection point, the interaction will differ if the fracture reaches the jump during an ongoing injection or when shut-in has already occurred. All these possible interactions depend on an additional set of two dimensionless coefficients. The first is the dimensionless viscosity (Equation) describing the dominant energy dissipation mechanism at the transition from radial to buoyant propagation (see Eq. (3.9) of Möri and Lecampion (2022)). This parameter alone governs the case of a constant rate, continuous release (Möri and Lecampion, 2022) and characterizes together with (Equation) the release of a finite volume of fluid. Combining these two coefficients is sufficient to describe any possible state of a buoyant fracture. Notably, values of (Equation) indicate viscosity-dominated and (Equation) toughness-dominated fractures at the transition from radial to buoyant. Finally, the case of a change in properties at a distance d (distance from the injection point to the change of properties, see Fig. 1) requires a dimensionless form of this distance. We achieve the dimensionless form using the buoyancy length scale ℓb = (KIc/Δγ)2/3 (Lister and Kerr, 1991) to obtain (Equation) (see Tab. 1). According to Möri and Lecampion (2023), we must ensure (Equation) to have fully developed buoyant fractures.