Effective shear and bulk viscosity of partially molten rock based on elastic moduli theory of a fluid filled poroelastic medium

Schmeling, Harro; Kruse, Jan Philipp; Richard, Guillaume

doi:10.1111/j.1365-246x.2012.05596.x

Cited by 74 publications

(67 citation statements)

References 29 publications

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“…This is expected, as our formulation only addresses the increase of ξ as the porosity φ → 0. However, this sensitivity to ξ/η might not be problematic for realistic applications, as this ratio is expected to be on the order of 1-100 (Hewitt & Fowler 2008;Takei & Holtzman 2009;Simpson et al 2010;Katz 2010;Schmeling et al 2012;Alisic et al 2014).…”

Section: Influence Of Materials Propertiesmentioning

confidence: 99%

A new formulation for coupled magma/mantle dynamics

Dannberg

Gassmöller

Grove

et al. 2019

Geophysical Journal International

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Many open problems in the Earth sciences can only be understood by modelling the porous flow of melt through a viscously deforming solid rock matrix. However, the system of equations describing this process becomes mathematically degenerate in the limit of vanishing melt fraction. Numerical methods that do not consider this degeneracy or avoid it solely by regularising specific material properties generally become computationally expensive as soon as the melt fraction approaches zero in some part of the domain.Here, we present a new formulation of the equations for coupled magma/mantle dynamics that addresses this problem, and allows it to accurately compute large-scale 3-D magma/mantle dynamics simulations with extensive regions of zero melt fraction. We achieve this by rescaling one of the solution variables, the compaction pressure, which ensures that for vanishing melt fraction, the equation causing the degeneracy becomes an identity and the other two equations revert to the Stokes system. This allows us to split the domain into two parts: In mesh cells where melt is present, we solve the coupled system of magma/mantle dynamics. In cells without melt, we solve the Stokes system as it is done for mantle convection without melt transport and constrain the remaining degrees of freedom.We have implemented this formulation in the open source geodynamic modelling code arXiv:1810.10105v1 [physics.geo-ph] 23 Oct 2018 2 J. Dannberg, R. Gassmöller, R. Grove, T. Heister ASPECT and illustrate the improved performance compared to the previous three-field formulation, showing numerically that the new formulation is optimal in terms of problem size and only minimally sensitive to model parameters. Beyond that, we demonstrate the applicability to realistic problems by showing large-scale 2-D and 3-D models of midocean ridges with complex rheology. Hence, we believe that our new formulation and its implementation in ASPECT will prove a valuable tool for studying the interaction of melt segregating through and interacting with a solid host rock in the Earth and other planetary bodies using high-resolution, three-dimensional simulations.

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Section: Influence Of Materials Propertiesmentioning

confidence: 99%

A new formulation for coupled magma/mantle dynamics

Dannberg

Gassmöller

Grove

et al. 2019

Geophysical Journal International

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“…Recently, Schmeling et al . [] numerically derived effective shear and bulk viscosities in purely viscous rocks with singular cavities of various geometries. They showed that spherical and ellipsoidal inclusions lead to

η_{b} = c_{1} η_{s} \frac{{((), c_{2} - φ)}^{k}}{φ}

where parameters c 1 , c 2 , and k depend on the melt geometry.…”

Section: Comparison To the Previous Modelsmentioning

confidence: 99%

(De)compaction of porous viscoelastoplastic media: Model formulation

2015

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A nonlinear viscoelastoplastic theory is developed for porous rate-dependent materials filled with a fluid in the presence of gravity. The theory is based on a rigorous thermodynamic formalism suitable for path-dependent and irreversible processes. Incremental evolution equations for porosity, Darcy's flux, and volumetric deformation of the matrix represent the simplest generalization of Biot's equations. Expressions for pore compressibility and effective bulk viscosity are given for idealized cylindrical and spherical pore geometries in an elastic-viscoplastic material with low pore concentration. We show that plastic yielding around pores leads to decompaction weakening and an exponential creep law. Viscous and plastic end-members of our model are consistent with experimentally verified models. In the poroelastic limit, our constitutive equations reproduce the exact Gassmann's relations, Biot's theory, and Terzaghi's effective stress law. The nature of the discrepancy between Biot's model and the True Porous Media theory is clarified. Our model provides a unified and consistent formulation for the elastic, viscous, and plastic cases that have previously been described by separate "end-member" models.

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“…Effects of nonconstant fluid/solid densities in triggering porosity waves and fluid networks during metamorphism are investigated in two recent studies (Malvoisin et al, 2015;Pl€ umper et al, 2017); this study, however, focuses on advective heat transport after porosity waves are triggered and evolve into channels. In addition, shear deformation is neglected as in previous studies to focus on volumetric compaction/decompaction (Connolly & Podladchikov, 2007;Spiegelman et al, 2001), but shear viscosity is considered because bulk viscosity depends on it via equation (6) (Hier-Majumder et al, 2006;Schmeling et al, 2012;Simpson et al, 2010). Notations for symbols are given in Table 1.…”

Section: Governing Equationsmentioning

confidence: 99%

The Potential for Metamorphic Thermal Pulses to Develop During Compaction‐Driven Fluid Flow

Tian

Ague

Chu

et al. 2018

Geochem Geophys Geosyst

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Compaction‐driven fluid flow below the brittle‐ductile transition may be a means of transporting fluids during metamorphism. In particular, when a decompaction weakening mechanism is introduced to account for the rock viscosity reduction due to fluid overpressures, channeling instabilities evolve into high‐porosity/permeability fluid conduits that focus mass and energy transfer. In this study, we consider a crustal rheology that accounts simultaneously for upward‐increasing viscosity and decompaction weakening to examine the nucleation and evolution of fluid channelization in two dimensions (2‐D). The model shows that plume‐shaped flow patterns can develop on time scales as short as 104 years, during which the plume tails act as fluid conduits and the plume heads act as fluid dispersion zones near the brittle‐ductile transition. Collection of fluids into conduits is accomplished by a basal fluid catchment zone characterized by strong lateral fluid pressure gradients but low porosity/permeability. Relatively narrow ranges of viscous activation energy (∼100 kJ mol−1) and decompaction weakening factor (∼10−4) are constrained if the fluid conduits are of kilometer scale in width. Significant thermal excursions (∼65 °C) can be induced if a high flow rate, potentially from rapid intermittent dehydration, is realized within channels. Moreover, if the focused fluids emanate from external anomalously hot sources (e.g., magma intrusion), thermal pulses (>100°C), and steep lateral temperature gradients (>50°C km−1) can be generated. Given the focusing efficiency estimated from our 2‐D compaction model, simple 3‐D modeling further shows that tubular conduits have the potential to cause thermal pulses >200°C within 104 years.

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Effective shear and bulk viscosity of partially molten rock based on elastic moduli theory of a fluid filled poroelastic medium

Cited by 74 publications

References 29 publications

A new formulation for coupled magma/mantle dynamics

A new formulation for coupled magma/mantle dynamics

(De)compaction of porous viscoelastoplastic media: Model formulation

The Potential for Metamorphic Thermal Pulses to Develop During Compaction‐Driven Fluid Flow

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