Magmatic Intrusions From a Hydraulic Fracture Modeling Perspective
Authors: Möri Andreas , Lecampion Brice 
Published: February 2023

The emplacement of magmatic intrusions in the earth&#8217;s crust has been investigated for decades. The driving mechanism is the density difference between the fluid and the rock. In the absence of heterogeneities, this difference creates a constant buoyancy force. This buoyancy governs the internal fluid pressure in excess of the background stress (magmatic overpressure) and creates a self-sustained hydraulic fracture (HF).
From early on, HF was investigated under a 2D plane-strain assumption, revealing a head-tail structure [1, 2, 3]. In this configuration, the propagating head has a constant volume, and viscous fluid flow in the tail dominates the ascent rate. Garagash and Germanovich (2022) [4] extended this approach to a late-time toughness-dominated 3D solution, confirming the head-tail structure and emphasizing a finger-like in-plane shape of such three-dimensional cracks.
Using PyFrac, a planar 3D solver for HF propagation, we compare 3D solutions to the 2D approximations. Considering a homogeneous medium and a continuous point source release of fluid, a family of solutions emerges, ranging from the solution of Garagash and Germanovich (2022) [4] to a zero-toughness limit [5]. These findings serve as a basis to derive the behaviour of buoyant hydraulic fractures produced by a finite volume release.
A recent body of work studied this problem, focusing on the limiting volume necessary for buoyant propagation as well as their ascent rate (see i. e. [6]). Using scaling analysis and numerical simulations, we clarify the entire parametric space. Similarly to the ongoing release case, a family of solutions exists as a function of two dimensionless parameters: A dimensionless viscosity (same as in the continuous release case) and a volume ratio (or, alternatively, a dimensionless buoyancy).
The knowledge of the entire parametric space of 3D finite volume buoyant cracks should help to interpret field emplacement data in a different light, design relevant experiments, study the effects of heterogeneities, and possibly build more computationally efficient, simplified models.

References:
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