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1. Numerical Analysis of Time‐Dependent Conduit Magma Flow in Dome‐Forming Eruptions With Application to Mount St. Helens 2004–2008

   https://doi.org/10.1029/2019JB017585  

   Wong, Ying‐Qi ; Segall, Paul ( November 2019 , Journal of Geophysical Research: Solid Earth)

   Conduit models of volcanic eruptions simulate magma evolution through phase transitions and material changes during ascent. We present a time‐dependent one‐dimensional model of a chamber‐conduit system to examine the temporal evolution of dome‐forming eruptions. As magma ascends, volatiles exsolve and may escape vertically through the column or laterally through the conduit walls. Magma solidifies which increases viscosity, leading to a natural transition from viscous flow at depth to frictional sliding along the conduit walls near the surface, resulting in the extrusion of a semisolid plug. The model evaluates time‐ and depth‐dependent pressure, velocity, porosity, and relative amounts of exsolved water to carbon dioxide. Transient effects arise when magma outflux from the chamber appreciably decreases pressure over the magma ascent timescale. For low magma permeability, transient effects increase porosity and velocity relative to steady‐state solutions. For high magma permeability, efficient vertical and lateral gas escape depresses porosity and velocity at later times. We use the model to predict three time series data sets from the 2004–2008 eruption of Mount St. Helens: extruded volume, ground deformation, and carbon dioxide emissions. We quantify sensitivity of model predictions to input parameters using the distance‐based generalized sensitivity analysis. Chamber volatile content, volume, and excess pressure influence the amplitude of observables, while conduit radius, frictional rate dependence and magma permeability influence temporal evolution. High magma permeability can cause marked departures from exponentially decaying flux and may explain the unique temporal evolution of deformation observed at the only nearby continuous GPS station in operation at the eruption onset.

    

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2. The Transition from Darcy to Nonlinear Flow in Heterogeneous Porous Media: I—Single-Phase Flow

   https://doi.org/10.1007/s11242-024-02070-3  

   Arbabi, Sepehr ; Sahimi, Muhammad ( March 2024 , Transport in Porous Media)

   Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient$${\varvec{\nabla }}P$$$\nabla P$and the fluid velocityv. The results indicate that when the Reynolds number Re is low enough that the Darcy’s law holds, the magnitude$$\omega _z$$${\omega }_z$of the vorticity is nearly zero. As Re increases, however, so also does$$\omega _z$$${\omega }_z$, and its rise from nearly zero begins at the same Re at which the Darcy’s law breaks down. We also show that a nonlinear relation between the macroscopic pressure gradient and the fluid velocityv, given by,$$-{\varvec{\nabla }}P=(\mu /K_e)\textbf{v}+\beta _n\rho |\textbf{v}|^2\textbf{v}$$$-\nabla P=(\mu /K_e)v+{\beta }_n\rho {\left|v\right|}^{2}v$, provides accurate representation of the numerical data, where$$\mu$$$\mu$and$$\rho$$$\rho$are the fluid’s viscosity and density,$$K_e$$$K_e$is the effective Darcy permeability in the linear regime, and$$\beta _n$$${\beta }_n$is a generalized nonlinear resistance. Theoretical justification for the relation is presented, and its predictions are also compared with those of the Forchheimer’s equation.

    

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3. A Computational Analysis of Bubble-Structure Interaction in Near-Field Underwater Explosion

   https://doi.org/10.1115/IMECE2021-72854  

   Ma, Wentao ; Ozenkoski, Timothy ; Wang, Kevin ( November 2021 , Proceedings of ASME 2021 International Mechanical Engineering Congress and Exposition)

   Underwater explosion poses a significant threat to the structural integrity of ocean vehicles and platforms. Accurate prediction of the dynamic loads from an explosion and the resulting structural response is crucial to ensuring safety without overconservative design. When the distance between the explosive charge and the structure is relatively small (i.e., near-field explosion), the dynamics of the gaseous explosion product, i.e., the “bubble”, comes into play, rendering a multiphysics problem that features the interaction of the bubble, the surrounding liquid water, and the solid structure. The problem is highly nonlinear, as it involves shock waves, large deformation, yielding, contact, and possibly fracture. This paper investigates the two-way interaction between the cyclic expansion and collapse of an explosion bubble and the deformation of a thin-walled elastoplastic cylindrical shell in its vicinity. Intuitively, when a shock wave impinges on a thin cylindrical shell, the shell would collapse in the direction of shock propagation. However, some recent laboratory experiments have shown that under certain conditions the shell collapsed in a counter-intuitive mode in which the direction of collapse is perpendicular to that of shock propagation. In other words, the nearest point on the structural surface moved towards the explosion charge, despite being impacted by a compressive shock. This paper focuses on replicating this phenomenon through numerical simulation and elucidating the underlying mechanisms. A recently developed computational framework (“FIVER”) coupling a nonlinear finite element structural dynamics solver and a finite volume compressible fluid dynamics solver is used to complete this study. The solver utilizes an embedded boundary method to track the wetted surface of the structure (i.e. the fluid-structure interface), which is capable of handling large structural deformation and topological changes (e.g., fracture). The solver also adopts the level set method for tracking the bubble surface (i.e. the liquid-gas interface). The fluid-structure and liquid-gas interface conditions are enforced by constructing and solving one-dimensional multi-material Riemann problems, which naturally accommodates the propagation of shock waves across the interfaces. In this paper, mesh refinement study is made to examine the sensitivity of the results to various meshing parameters. The results show that the intermediate level of refinement is appropriate in terms of both the accuracy and the computation costs. Next, the deformation history of both the bubble and the structure are presented and analyzed to provide a detailed view of the counter-intuitive collapse mode mentioned above. We show that timewise, the structural collapse spans multiple cycles of bubble oscillation. Additional details about the time-histories of fluid pressure, structure displacement, and bubble size are presented to elucidate this dynamic bubble-structure interaction and the resulting structural failure. 

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4. Natural Gas Flow Equations: Uniqueness and an MI-SOCP Solver

   https://doi.org/10.23919/ACC.2019.8814704  

   Singh, Manish K. ; Kekatos, Vassilis ( July 2019 , 2019 American Control Conference (ACC))

   The critical role of gas fired-plants to compensate renewable generation has increased the operational variability in natural gas networks (GN). Towards developing more reliable and efficient computational tools for GN monitoring, control, and planning, this work considers the task of solving the nonlinear equations governing steady-state flows and pressures in GNs. It is first shown that if the gas flow equations are feasible, they enjoy a unique solution. To the best of our knowledge, this is the first result proving uniqueness of the steady-state gas flow solution over the entire feasible domain of gas injections. To find this solution, we put forth a mixed-integer second-order cone program (MI-SOCP)-based solver relying on a relaxation of the gas flow equations. This relaxation is provably exact under specific network topologies. Unlike existing alternatives, the devised solver does not need proper initialization or knowing the gas flow directions beforehand, and can handle gas networks with compressors. Numerical tests on tree and meshed networks indicate that the relaxation is exact even when the derived conditions are not met. 

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5. Expedition 366 Preliminary Report: Mariana Convergent Margin and South Chamorro Seamount

   https://doi.org/10.14379/iodp.pr.366.2017  

   Fryer, P. ; Wheat, G. ; Williams, T. ( November 2017 , Preliminary report)

   null (Ed.)

   Geologic processes at convergent plate margins control geochemical cycling, seismicity, and deep biosphere activity in subduction zones and suprasubduction zone lithosphere. International Ocean Discovery Program (IODP) Expedition 366 was designed to address the nature of these processes in the shallow to intermediate depth of the Mariana subduction channel. Although no technology is available to permit direct sampling of the subduction channel of an intraoceanic convergent margin at depths up to 18 km, the Mariana forearc region (between the trench and the active volcanic arc) provides a means to access this zone. Active conduits, resulting from fractures in the forearc, are prompted by along- and across-strike extension that allows slab-derived fluids and materials to ascend to the seafloor along associated faults, resulting in the formation of serpentinite mud volcanoes. Serpentinite mud volcanoes of the Mariana forearc are the largest mud volcanoes on Earth. Their positions adjacent to or atop fault scarps on the forearc are likely related to the regional extension and vertical tectonic deformation in the forearc. Serpentinite mudflows at these volcanoes include serpentinized forearc mantle clasts, crustal and subducted Pacific plate materials, a matrix of serpentinite muds, and deep-sourced formation fluid. Mud volcanism on the Mariana forearc occurs within 100 km of the trench, representing a range of depths and temperatures to the downgoing plate and the subduction channel. These processes have likely been active for tens of millions of years at this site and for billions of years on Earth. At least 10 active serpentinite mud volcanoes have been located in the Mariana forearc. Two of these mud volcanoes are Conical and South Chamorro Seamounts, which are the furthest from the Mariana Trench at 86 and 78 km, respectively. Both seamounts were cored during Ocean Drilling Program (ODP) Legs 125 and 195, respectively. Data from these two seamounts represent deeper, warmer examples of the continuum of slab-derived materials as the Pacific plate subducts, providing a snapshot of how slab subduction affects fluid release, the composition of ascending fluids, mantle hydration, and the metamorphic paragenesis of subducted oceanic lithosphere. Data from the study of these two mud volcanoes constrain the pressure, temperature, and composition of fluids and materials within the subduction channel at depths of about 18 to 19 km. Understanding such processes is necessary for elucidating factors that control seismicity in convergent margins, tectonic and magma genesis processes in the forearc and volcanic arc, fluid and material fluxes, and the nature and variability of environmental conditions that impact subseafloor microbial communities. Expedition 366 centered on data collection from cores recovered from three serpentinite mud volcanoes that define a continuum of subduction-channel processes defined by the two previously cored serpentinite mud volcanoes and the trench. Three serpentinite mud volcanoes (Yinazao, Fantangisña, and Asùt Tesoro) were chosen at distances 55 to 72 km from the Mariana Trench. Cores were recovered from active sites of eruption on their summit regions and on the flanks where ancient flows are overlain by more recent ones. Recovered materials show the effects of dynamic processes that are active at these sites, bringing a range of materials to the seafloor, including materials from the lithosphere of the Pacific plate and from subducted seamounts (including corals). Most of the recovered material consists of serpentinite mud containing lithic clasts, which are derived from the underlying forearc crust and mantle and the subducting Pacific plate. Cores from each of the three seamounts drilled during Expedition 366, as well as those from Legs 125 and 195, include material from the underlying Pacific plate. A thin cover of pelagic sediment was recovered at many Expedition 366 sites, and at Site U1498 we cored through serpentinite flows to the underlying pelagic sediment and volcanic ash deposits. Recovered serpentinites are largely uniform in major element composition, with serpentinized ultramafic rocks and serpentinite muds spanning a limited range in SiO2 , MgO, and Fe2 O3 compositions. However, variation in trace element composition reflects pore fluid composition, which differs as a function of the temperature and pressure of the underlying subduction channel. Dissolved gases H2 , CH4 , and C2 H6 are highest at the site furthest from the trench, which also has the most active fluid discharge of the Expedition 366 serpentinite mud volcanoes. These dissolved gases and their active discharge from depth likely support active microbial communities, which were the focus of in-depth subsampling and preservation for shore-based analytical and culturing procedures. The effects of fluid discharge were also registered in the porosity and GRA density data indicated by higher than expected values at some of the summit sites. These higher values are consistent with overpressured fluids that minimize compaction of serpentinite mud deposits. In contrast, flank sites have significantly greater decreases in porosity with depth, suggesting that processes in addition to compaction are required to achieve the observed data. Thermal measurements reveal higher heat flow values on the flanks (~31 mW/m2) than on the summits (~17 mW/m2) of the seamounts. The new 2G Enterprises superconducting rock magnetometer (liquid helium free) revealed relatively high values of both magnetization and bulk magnetic susceptibility of discrete samples related to ultramafic rocks, particularly in dunite. Magnetite, a product of serpentinization, and authigenic carbonates were observed in the mudflow matrix materials. In addition to coring operations, Expedition 366 focused on the deployment and remediation of borehole casings for future observatories and set the framework for in situ experimentation. Borehole work commenced at South Chamorro Seamount, where the original-style CORK was partially removed. Work then continued at each of the three summit sites following coring operations. Cased boreholes with at least three joints of screened casing were deployed, and a plug of cement was placed at the bottom of each hole. Water samples were collected from two of the three boreholes, revealing significant inputs of formation fluids. This suggests that each of the boreholes tapped a hydrologic zone, making these boreholes suitable for experimentation with the future deployment of a CORK-lite. An active education and outreach program connected with many classrooms on shore and with the general public through social media. 

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