Mechanics of two interacting magma‐driven fractures: A numerical study

Abstract

To understand magma focusing from broad melting zones in the crust, propagation in brittle rocks of two interacting dikes ascending from a single deep source has been modeled using a time-dependent plane strain hydraulic fracturing model. The source is assumed to generate a constant influx rate to feed the dike growth, which is also aided by buoyancy effects. In contrast to uncoupled model results, the simultaneous parallel growth of two dikes to a certain distance is found to occur provided that the two dikes are initially of different heights, which might be produced either by previous magma intrusion or during nucleation. The shorter dike will chase the longer one and they can either progressively merge or continue subparallel growth at a reduced spacing, depending on the deviator stress between the vertical and horizontal stresses and the initial lateral separation, with parameters given in dimensionless forms. Numerical results reveal the mechanics for simultaneous ascents of two subparallel dikes, in that dike interaction can produce a low-stress field, which is just above the tip of the shorter dike, favorable to growth of the shorter dike. The energy analysis indicates that the energy required for two subparallel dikes is less than that for a single dike during the late-time buoyancy-viscosity propagation stage where considerable ascent occurs. This growth behavior might provide the mechanism for simultaneous, instead of sequential, growth of various dikes in a single set.

Numerical Simulation of Simultaneous Hydraulic Fracture Growth Within a Rock Layer: Implications for Stimulation of Low‐Permeability Reservoirs

“…The width in the counterpart segment of the shorter fracture is less affected by the stress shadow effect and instead is enlarged. This is attributed to the fracture interaction and self‐organization of internal pressure, as reported previously by Zhang and Jeffrey () and (Zhang et al, ) for plane‐strain cases. Due to the fluid‐solid coupling, stress interference does not look like in the same way as the commonly used stress shadow effect predicts based on LEFM.…”

“…One should note that the shorter fracture will curve to connect the longer one under some conditions such as nearly equal stress fields and very small spacing, which have not been studied here. If the differential stress is not large enough to restrain the curving at early time, the coalescence of closely spaced fractures may occur as discussed by (Ito & Martel, ; Zhang et al, ).…”

“…One can note that, in industrial hydraulic fracturing, the fluid‐driven fractures typically propagate symmetrically with respect to the source (wellbore) to form a so‐called bi‐wing geometry. By contrast, some natural fluid‐driven fractures tend to grow unilaterally away from the source, leading to a nearly single‐wing geometry as bedding plane‐abutted fractures (Zhang & Jeffrey, ), dikes (Zhang et al, ), and splay fractures (Zhang & Jeffrey, ). So far, how the distinct fracture geometries affect the growth behavior is not completely exploited, especially in a 3‐D form.…”

Numerical modeling of the simultaneous propagation of multiple hydraulic fractures with fluid lags

“…The fluid flow in the wellbore was incorporated in Lecampion and Desroches (2015) and Wu and Olson (2015) with DDM to simulate fracture propagation. The simultaneous propagation of two magma-drive fractures was modeled in Zhang et al (2014) to investigate their interaction effect. Chau et al (2016) adopted a damage model to simulate the branching phenomenon during the process of hydraulic fracturing.…”

A two‐step model for dynamical dike propagation in two dimensions: Application to the July 2001 Etna eruption

“…Two‐dimensional models able to account simultaneously for the dynamics of the viscous fluid (Navier‐Stokes equations) and the fracturing process at the dike tip are still a challenge from a theoretical and numerical point of view and limited to a few attempts that still assume straight propagation [ Dahm , ; Roper and Lister , ]. An interesting approach has recently been provided by Zhang et al [], who included dike interaction with both the local stress field and the magma flow. However, they did not include the effect of magma buoyancy on the magma pathway.…”