Critical fluid injection volumes for uncontrolled fracture ascent

Abstract

Hydro-fracturing is a routine industrial technique whose safety depends on fractures remaining confined within the target rock volume. Both observations and theoretical models show that pockets of fluid can propagate large distances in the Earth's crust, in a self-sustained, uncontrolled manner, providing that the fluid volume is large enough. Existing models that describe when self-sustaining ascent starts are difficult to use for predictions, as they are mostly twodimensional (2D) and depend on parameters (typically the fracture length) that are hard to assess, even a posteriori.Here we constrain, both analytically and numerically in three-dimensions (3D), scale-independent critical volumes as a function of only rock and fluid properties. We apply our model to laboratory, industrial and natural settings, showing that our critical volumes are consistent with observations and can be used as a conservative estimate in geological applications. We find typical injection volumes exceed the limit we define for the start of self-sustaining fracture ascent. We describe a number of other processes that may work to arrest fractures with volumes exceeding this limit.This appears to have resulted in a false sense of operational safety when working with large injection volumes. In Non-peer reviewed EarthArXiv preprint the context of our findings we outline the quantitative work that would be required to better elucidate the processes causing fracture arrest, which could help to assess more comprehensively the safety of such operations.

Stress Inversion in a Gelatin Box: Testing Eruptive Vent Location Forecasts With Analog Models

“…The more these assumptions are far from reality, the larger the mismatch between real and σ 3 ‐perpendicular trajectories. More complex dike trajectory models exist for simulations in 2D (Dahm, 2000; Maccaferri et al., 2011) and recently also in three dimensions (3D) (Davis et al., 2020). However, the predictive power of models increases if their complexity is reduced with regard to accurate explanatory dike trajectory models (see e.g., Forster & Sober, 1994).…”

Extreme curvature of shallow magma pathways controlled by competing stresses

“…Here we use a theoretically equivalent, but more flexible, approach based on the maximum stress intensity, K. In our analytical approach, we re-duce the sill geometry to that of a penny-shaped crack subject to stress gradients (Supplementary Information), with an opening that is compatible with the surface displacements observed along the short-axis of the sill (see Methods). At selected points along the sill's path, we calculate K, around the tip-line 9 , and assume the greatest tip-line advance occurs in the direction where K is largest (Paris fatigue law 10 ). In our numerical simulations, we discretise the sill into triangular elements 10,11 and update the tip-line at each step using the local value of K as compared to the critical rock strength, K c .…”

“…At selected points along the sill's path, we calculate K, around the tip-line 9 , and assume the greatest tip-line advance occurs in the direction where K is largest (Paris fatigue law 10 ). In our numerical simulations, we discretise the sill into triangular elements 10,11 and update the tip-line at each step using the local value of K as compared to the critical rock strength, K c .…”

“…Lastly, we run full 3D fracture propagation simulations 10 . Here the crack is neither constrained to be planar nor circular in shape, only such that it maintains a constant V .…”

Ascent rates of 3D fractures driven by a finite batch of buoyant fluid

“…This means that at the end of the injection, the crack tip-line is approximately circular and ṽ𝑉 should approximate the ascent velocity at this time. We expect that if the time scale of injection is much lower than the time scale of propagation, that once the crack has exceeded the critical radius of Davis et al (2020), it will begin to elongate in the direction of the stress gradient. In these cases, the upwards ascent speed should lie somewhere between the two limiting regimes; that predicted by equation ( 2 2𝑎 and the reported distance traversed by the batch of 24 km, we find that it is between 0.06 and 9.6 m s −1 .…”