scholarly journals Brine Formation and Mobilization in Submarine Hydrothermal Systems: Insights from a Novel Multiphase Hydrothermal Flow Model in the System H2O–NaCl

2020 ◽  
Author(s):  
F. Vehling ◽  
J. Hasenclever ◽  
L. Rüpke
Keyword(s):  
Multiphase Flow ◽  
Flow Model ◽  
Full Range ◽  
Hydrothermal Systems ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Bulk Fluid ◽  
Submarine Hydrothermal Systems ◽  
Brine Layer ◽  
Hydrothermal Flow

AbstractNumerical models have become indispensable tools for investigating submarine hydrothermal systems and for relating seafloor observations to physicochemical processes at depth. Particularly useful are multiphase models that account for phase separation phenomena, so that model predictions can be compared to observed variations in vent fluid salinity. Yet, the numerics of multiphase flow remain a challenge. Here we present a novel hydrothermal flow model for the system H2O–NaCl able to resolve multiphase flow over the full range of pressure, temperature, and salinity variations that are relevant to submarine hydrothermal systems. The method is based on a 2-D finite volume scheme that uses a Newton–Raphson algorithm to couple the governing conservation equations and to treat the non-linearity of the fluid properties. The method uses pressure, specific fluid enthalpy, and bulk fluid salt content as primary variables, is not bounded to the Courant time step size, and allows for a direct control of how accurately mass and energy conservation is ensured. In a first application of this new model, we investigate brine formation and mobilization in hydrothermal systems driven by a transient basal temperature boundary condition—analogue to seawater circulation systems found at mid-ocean ridges. We find that basal heating results in the rapid formation of a stable brine layer that thermally insulates the driving heat source. While this brine layer is stable under steady-state conditions, it can be mobilized as a consequence of variations in heat input leading to brine entrainment and the venting of highly saline fluids.

scholarly journals A relaxation scheme for a hyperbolic multiphase flow model

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1795 ◽  
Author(s):  
Khaled Saleh
Keyword(s):  
Multiphase Flow ◽  
Flow Model ◽  
Two Phase Flow ◽  
Equations Of State ◽  
Energy Inequality ◽  
Approximation Error ◽  
Finite Volume Scheme ◽  
Phase Flow ◽  
Two Phase ◽  
Relaxation Scheme

This article is the first of two in which we develop a relaxation finite volume scheme for the convective part of the multiphase flow models introduced in the series of papers (Hérard, C.R. Math. 354 (2016) 954–959; Hérard, Math. Comput. Modell. 45 (2007) 732–755; Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). In the present article we focus on barotropic flows where in each phase the pressure is a given function of the density. The case of general equations of state will be the purpose of the second article. We show how it is possible to extend the relaxation scheme designed in Coquel et al. (ESAIM: M2AN 48 (2013) 165–206) for the barotropic Baer–Nunziato two phase flow model to the multiphase flow model with N – where N is arbitrarily large – phases. The obtained scheme inherits the main properties of the relaxation scheme designed for the Baer–Nunziato two phase flow model. It applies to general barotropic equations of state. It is able to cope with arbitrarily small values of the statistical phase fractions. The approximated phase fractions and phase densities are proven to remain positive and a fully discrete energy inequality is also proven under a classical CFL condition. For N = 3, the relaxation scheme is compared with Rusanov’s scheme, which is the only numerical scheme presently available for the three phase flow model (see Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). For the same level of refinement, the relaxation scheme is shown to be much more accurate than Rusanov’s scheme, and for a given level of approximation error, the relaxation scheme is shown to perform much better in terms of computational cost than Rusanov’s scheme. Moreover, contrary to Rusanov’s scheme which develops strong oscillations when approximating vanishing phase solutions, the numerical results show that the relaxation scheme remains stable in such regimes.

scholarly journals A compressible multiphase flow model for violent aerated wave impact problems

2014 ◽  
Vol 470 (2172) ◽  
pp. 20140542 ◽  
Author(s):  
Z. H. Ma ◽  
D. M. Causon ◽  
L. Qian ◽  
C. G. Mingham ◽  
H. B. Gu ◽  
...  
Keyword(s):  
Multiphase Flow ◽  
Flow Model ◽  
Volume Fraction ◽  
Vertical Wall ◽  
Homogeneous Material ◽  
Finite Volume Scheme ◽  
Advection Equation ◽  
Wave Impact ◽  
Phase Volume Fraction ◽  
Compressible Multiphase Flow

This paper focuses on the numerical modelling of wave impact events under air entrapment and aeration effects. The underlying flow model treats the dispersed water wave as a compressible mixture of air and water with homogeneous material properties. The corresponding mathematical equations are based on a multiphase flow model which builds on the conservation laws of mass, momentum and energy as well as the gas-phase volume fraction advection equation. A high-order finite volume scheme based on monotone upstream-centred schemes for conservation law reconstruction is used to discretize the integral form of the governing equations. The numerical flux across a mesh cell face is estimated by means of the HLLC approximate Riemann solver. A third-order total variation diminishing Runge–Kutta scheme is adopted to obtain a time-accurate solution. The present model provides an effective way to deal with the compressibility of air and water–air mixtures. Several test cases have been calculated using the present approach, including a gravity-induced liquid piston, free drop of a water column in a closed tank, water–air shock tubes, slamming of a flat plate into still pure and aerated water and a plunging wave impact at a vertical wall. The obtained results agree well with experiments, exact solutions and other numerical computations. This demonstrates the potential of the current method to tackle more general wave–air–structure interaction problems.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

scholarly journals Comparison of Surface Tension Models for the Volume of Fluid Method

Processes ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 542 ◽  
Author(s):  
Kurian J. Vachaparambil ◽  
Kristian Etienne Einarsrud
Keyword(s):  
Surface Tension ◽  
Multiphase Flow ◽  
Capillary Rise ◽  
Surface Tension Force ◽  
Surface Force ◽  
Parallel Plates ◽  
Time Step ◽  
Mesh Resolution ◽  
Active Research ◽  
Spurious Currents

With the increasing use of Computational Fluid Dynamics to investigate multiphase flow scenarios, modelling surface tension effects has been a topic of active research. A well known associated problem is the generation of spurious velocities (or currents), arising due to inaccuracies in calculations of the surface tension force. These spurious currents cause nonphysical flows which can adversely affect the predictive capability of these simulations. In this paper, we implement the Continuum Surface Force (CSF), Smoothed CSF and Sharp Surface Force (SSF) models in OpenFOAM. The models were validated for various multiphase flow scenarios for Capillary numbers of 10 − 3 –10. All the surface tension models provide reasonable agreement with benchmarking data for rising bubble simulations. Both CSF and SSF models successfully predicted the capillary rise between two parallel plates, but Smoothed CSF could not provide reliable results. The evolution of spurious current were studied for millimetre-sized stationary bubbles. The results shows that SSF and CSF models generate the least and most spurious currents, respectively. We also show that maximum time step, mesh resolution and the under-relaxation factor used in the simulations affect the magnitude of spurious currents.

The role of mineral nanoparticles at a fluid-magnetite interface: Implications for trace-element uptake in hydrothermal systems

2019 ◽  
Vol 104 (8) ◽  
pp. 1180-1188 ◽  
Author(s):  
Shuo Yin ◽  
Richard Wirth ◽  
Changqian Ma ◽  
Jiannan Xu
Keyword(s):  
Solid Solution ◽  
Crystal Lattice ◽  
Trace Element ◽  
Hydrothermal Systems ◽  
Oscillatory Zoning ◽  
Bulk Fluid ◽  
Continuous Increase ◽  
Interfacial Fluid ◽  
Spinel Nanoparticles

Abstract The migrating fluid-mineral interface provides an opportunity for the uptake of trace elements as solid solutions in the newly formed crystal lattice during the non-equilibrium growth of the crystal. However, mineral nanoparticles could precipitate directly from the interfacial fluid when it evolves to a supersaturated situation. To better understand the role of mineral nanoparticles in this scenario, this study focuses on a well-documented magnetite with oscillatory zoning from a skarn deposit by using high-resolution transmission electron microscopy (TEM). Our results show that the Al concentration in magnetite measured on a micrometer-scale is caused by three different effects: Al solid solution, Al-rich nanometer-sized lamellae, and zinc spinel nanoparticles in the host magnetite. Here, we propose a genetic relationship among the three different phases mentioned above. At first, a continuous increase of the Al concentration in the interfacial fluid can be incorporated into the crystal lattice of magnetite forming a solid solution. During cooling in a later stage, aluminum in magnetite is oversaturated and exsolution of hercynite (Al-rich lamellae) occurs from the host magnetite. If the Al concentration at the fluid-magnetite interface still increases during further growth of magnetite, the substitution of Fe by Al has gradually reached saturation so that aluminum cannot be incorporated in the magnetite crystal structure any longer. Using the magnetite lattice as a template, nucleation of abundant zinc spinel nanoparticles occurs. This will, in turn, lead to a gradual depletion of Al concentration in the interfacial fluid until the available ions for zinc spinel nucleation and growth have been used up. As a result, the migrating fluid-magnetite interface will enrich the Al concentration in the interfacial fluid until the available ion concentration is sufficient for nucleation of zinc spinel phase again. The fluid-mineral interface in this mechanism has been repeatedly utilized during crystal growth, providing an efficient way for the uptake of trace element from a related undersaturated bulk fluid.

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