Andrea Parmigiani

Bubble accumulation and its role in the evolution of magma reservoirs in the upper crust

Volcanic eruptions transfer huge amounts of gas to the atmosphere. In particular, the sulfur released during large silicic explosive eruptions can induce global cooling. A fundamental goal in volcanology, therefore, is to assess the potential for eruption of the large volumes of crystal-poor, silicic magma that are stored at shallow depths in the crust, and to obtain theoretical bounds for the amount of volatiles that can be released during these eruptions. It is puzzling that highly evolved, crystal-poor silicic magmas are more likely to generate volcanic rocks than plutonic rocks. This observation suggests that such magmas are more prone to erupting than are their crystal-rich counterparts. Moreover, well studied examples of largely crystal-poor eruptions (for example, Katmai, Taupo and Minoan) often exhibit a release of sulfur that is 10 to 20 times higher than the amount of sulfur estimated to be stored in the melt. Here we argue that these two observations rest on how the magmatic volatile phase (MVP) behaves as it rises buoyantly in zoned magma reservoirs. By investigating the fluid dynamics that controls the transport of the MVP in crystal-rich and crystal-poor magmas, we show how the interplay between capillary stresses and the viscosity contrast between the MVP and the host melt results in a counterintuitive dynamics, whereby the MVP tends to migrate efficiently in crystal-rich parts of a magma reservoir and accumulate in crystal-poor regions. The accumulation of low-density bubbles of MVP in crystal-poor magmas has implications for the eruptive potential of such magmas, and is the likely source of the excess sulfur released during explosive eruptions.

Mush microphysics and the reactivation of crystal‐rich magma reservoirs

Reactivation and eruption of upper crustal crystal-rich magma reservoirs (“crystal mushes”) following recharge has recently been invoked in numerous volcanic systems worldwide. Over the last few years, several models have been proposed for the reactivation of such mushes prior to or during eruptions. These models vary significantly in terms of predicted timescales associated with reactivation, because they assume that different physical mechanisms control the dynamics of this process. A common limitation of all the proposed models is that they parameterize the complex nonlinear multiphase dynamics that govern the evolution of these magmas in their open system reservoirs and rely on simple empirical laws. We argue that microscale physical models are a necessity if one wants to better constrain the evolution of these complex systems and the conditions that lead to eruption. As petrological observations of erupted mushes strongly support a thermal and fluid input from wet magma recharges, we have developed a pore-scale multiphase heat and fluid transport model to understand the effect of a percolating fluid phase on the partial melting and reactivation of crystal mushes. Specifically, we use lattice Boltzmann calculations to reveal a counterintuitive feedback between volatile transport and melting in crystal-rich environments. We find that partial melting, even at a low degree, can significantly reduce the efficiency of the buoyant migration of exsolved volatiles in the mush and therefore negatively impact the heat transfer upward during reactivation. This negative feedback between melting and volatile transport is expected to significantly affect the distribution of exsolved volatiles in the reservoirs, as well as the transport of trace species carried by the volatile phase (e.g., S, metals). The presence of a disperse magmatic volatile phase (unconnected bubbles) will also affect the thermomechanical properties of the mush during reactivation, making it more compressible and thermally less conductive.

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurins law) and time-dependent (Washburns law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

Coupling Method for Building a Network of Irrigation Canals on a Distributed Computing Environment

An optimal management of an irrigation network is important to ensure an efficient water supply and to predict critical situations related to natural hazards. We present a multiscale coupling methodology to simulate numerically an entire irrigation canal over a distributed High Performance Computing (HPC) resource. We decompose the network into several segments that are coupled through junctions. Our coupling strategy, based on the concept of Complex Automata (CxA) and the Multiscale Modeling Language (MML), aims at coupling simple 1D model of canal sections with 3D complex ones. Our goal is to build a numerical model that can be run over a distributed grid infrastructure, thus offering a large amount of computing resources. We illustrate our approach by coupling two canal sections in 1D through a gate.

The mechanics of shallow magma reservoir outgassing

Magma degassing fundamentally controls the Earths volatile cycles. The large amount of gas expelled into the atmosphere during volcanic eruptions (i.e. volcanic outgassing) is the most obvious display of magmatic volatile release. However, owing to the large intrusive:extrusive ratio, and considering the paucity of volatiles left in intrusive rocks after final solidification, volcanic outgassing likely constitutes only a small fraction of the overall mass of magmatic volatiles released to the Earths surface. Therefore, as most magmas stall on their way to the surface, outgassing of uneruptible, crystal-rich magma storage regions will play a dominant role in closing the balance of volatile element cycling between the mantle and the surface. We use a numerical approach to study the migration of a magmatic volatile phase (MVP) in crystal-rich magma bodies (“mush zones”) at the pore-scale. Our results suggest that buoyancy driven outgassing is efficient over crystal volume fractions between 0.4 and 0.7 (for mm-sized crystals). We parameterize our pore-scale results for MVP migration in a thermo-mechanical magma reservoir model to study outgassing under dynamical conditions where cooling controls the evolution of the proportion of crystal, gas and melt phases and to investigate the role of the reservoir size and the temperature-dependent visco-elastic response of the crust on outgassing efficiency. We find that buoyancy-driven outgassing allows for a maximum of 40-50% volatiles to leave the reservoir over the 0.4-0.7 crystal volume fractions, implying that a significant amount of outgassing must occur at high crystal content (>0.7) through veining and/or capillary fracturing.

A LATTICE BOLTZMANN SIMULATION OF THE RHONE RIVER

We present a very detailed numerical simulation of the Rhone river in the Geneva area, using a Lattice Boltzmann (LB) modeling approach. The simulations of water ways are important to better predict and control their behavior when subject to exceptional event or new management strategies. Here, we investigate the current computing limits of using a three-dimensional (3D), free surface model to simulate a high resolution flow over a long section of the river, on a massively parallel computer. We argue that in a near future, computers will be powerful enough to tackle such a simulation. We also compare our results with a two-dimensional (2D) shallow water model to determine in which range a 3D free surface approach provides better insights. Finally, we discuss the advantage of a multi-scale approach for this type of problems.

A new bubble dynamics model to study bubble growth, deformation, and coalescence

We propose a new bubble dynamics model to study the evolution of a suspension of bubbles over a wide range of vesicularity, and that accounts for hydrodynamical interactions between bubbles while they grow, deform under shear flow conditions, and exchange mass by diffusion coarsening. The model is based on a lattice Boltzmann method for free surface flows. As such, it assumes an infinite viscosity contrast between the exsolved volatiles and the melt. Our model allows for coalescence when two bubbles approach each other because of growth or deformation. The parameter (disjoining pressure) that controls the coalescence efficiency, i.e., drainage time for the fluid film between the bubbles, can be set arbitrarily in our calculations. We calibrated this parameter by matching the measured time for the drainage of the melt film across a range of Bond numbers (ratio of buoyancy to surface tension stresses) with laboratory experiments of a bubble rising to a free surface. The model is then used successfully to model Ostwald ripening and bubble deformation under simple shear flow conditions. The results we obtain for the deformation of a single bubble are in excellent agreement with previous experimental and theoretical studies. For a suspension, we observe that the collective effect of bubbles is different depending on the relative magnitude of viscous and interfacial stresses (capillary number). At low capillary number, we find that bubbles deform more readily in a suspension than for the case of a single bubble, whereas the opposite is observed at high capillary number.

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear flow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scientific results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and suffers fewer limitations.

A physical model for three phase compaction in silicic magma reservoirs

We develop a model for phase separation in magma reservoirs containing a mixture of silicate melt, crystals and fluids (exsolved volatiles). The interplay between the three phases control the dynamics of phase separation and consequently the chemical and physical evolution of magma reservoirs. The model we propose is based on the 2-phase damage theory approach of Bercovici et al. [2001]; Bercovici and Ricard [2003] because it offers the leverage of considering interface (in the macroscopic limit) between phases that can deform depending on the mechanical work and phase changes taking place locally in the magma. Damage models also offer the advantage that pressure is defined uniquely to each phase and does not need to be equal among phases, which will enable us to consider, in future studies, the large capillary pressure at which fluids are mobilized in mature, crystal-rich, magma bodies. In this first analysis of three-phase compaction, we solve the 3-phase compaction equations numerically for a simple 1-D problem where we focus on the effect of fluids on the efficiency of melt-crystal separation considering the competition between viscous and buoyancy stresses only. We contrast three sets of simulations to explore the behavior of 3-phase compaction, a melt-crystal reference compaction scenario (2-phase compaction), a 3-phase scenario without phase changes and finally a 3-phase scenario with a parameterized second boiling (crystallization-induced exsolution). The simulations show a dramatic difference between two (melt-crystals) and three (melt-crystals-exsolved volatiles) compaction-driven phase separation. We find that the presence of a lighter, significantly less viscous fluid hinders melt-crystal separation.

Pore-scale simulations of concentration tails in heterogeneous porous media

The retention of contaminants in the finest and less-conductive regions of natural aquifer is known to strongly affect the decontamination of polluted aquifers. In fact, contaminant transfer from low to high mobility regions at the back end of a contaminant plume (i.e. back diffusion) is responsible for the long-term release of contaminants during remediation operation. In this paper, we perform pore-scale calculations for the transport of contaminant through heterogeneous porous media composed of low and high mobility regions with two objectives: (i) study the effect of permeability contrast and solute transport conditions on the exchange of solutes between mobile and immobile regions and (ii) estimate the mass of contaminants sequestered in low mobility regions based on concentration breakthrough curves.