scholarly journals Chemical heterogeneities in the mantle: progress towards a general quantitative description

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1409-1428 ◽  
Author(s):  
Massimiliano Tirone
Keyword(s):  
Mass Transfer ◽  
Chemical Equilibrium ◽  
Transport Model ◽  
Numerical Models ◽  
Quantitative Description ◽  
Transient State ◽  
Real Data ◽  
Initial State ◽  
Initial Size ◽  
Chemical Equilibration

Abstract. Chemical equilibration between two different assemblages (peridotite type and gabbro–eclogite type) has been determined using basic thermodynamic principles and certain constraints and assumptions regarding mass and reaction exchange. When the whole system (defined by the sum of the two subsystems) is in chemical equilibrium the two assemblages will not be homogenized, but they will preserve distinctive chemical and mineralogical differences. Furthermore, the mass transfer between the two subsystems defines two petrological assemblages that separately are also in local thermodynamic equilibrium. In addition, when two assemblages previously equilibrated as a whole in a certain initial mass ratio are held together assuming a different proportion, no mass transfer occurs and the two subsystems remain unmodified. By modeling the chemical equilibration results of several systems of variable initial size and different initial composition it is possible to provide a quantitative framework to determine the chemical and petrological evolution of two assemblages from an initial state, in which the two are separately in chemical equilibrium, to a state of equilibration of the whole system. Assuming that the local Gibbs energy variation follows a simple transport model with an energy source at the interface, a complete petrological description of the two systems can be determined over time and space. Since there are no data to constrain the kinetics of the processes involved, the temporal and spatial scale is arbitrary. The evolution model should be considered only a semiempirical tool that shows how the initial assemblages evolve while preserving distinct chemical and petrological features. Nevertheless, despite the necessary simplification, a 1-D model illustrates how chemical equilibration is controlled by the size of the two subsystems. By increasing the initial size of the first assemblage (peridotite like), the compositional differences between the initial and the final equilibrated stage become smaller, while on the eclogite-type side the differences tend to be larger. A simplified 2-D dynamic model in which one of the two subsystems is allowed to move with a prescribed velocity shows that after an initial transient state, the moving subsystem tends to preserve its original composition defined at the influx side. The composition of the static subsystem instead progressively diverges from the composition defining the starting assemblage. The observation appears to be consistent for various initial proportions of the two assemblages, which somehow simplify the development of potential tools for predicting the chemical equilibration process from real data and geodynamic applications. Four animation files and the data files of three 1-D and two 2-D numerical models are available following the instructions in the Supplement.

scholarly journals Chemical Heterogeneities in the Mantle: Progress Towards a General Quantitative Description

2018 ◽  
Author(s):  
Massimiliano Tirone
Keyword(s):  
Mass Transfer ◽  
Numerical Models ◽  
Quantitative Description ◽  
Transient State ◽  
Real Data ◽  
Initial State ◽  
Initial Size ◽  
Simple Diffusion ◽  
Chemical Equilibration ◽  
The Difference

Abstract. Chemical equilibration between two different assemblages (peridotite-type and gabbro/eclogite-type) of variable initial size assuming few different initial compositions has been determined using certain mass and reactions constraints and thermodynamic principles. The pattern that emerges suggests that mass transfer between the two sub-systems defines two petrological assemblages that separately are maintained in local thermodynamic equilibrium. In addition, when two assemblages previously equilibrated together in a certain mass ratio are rearranged assuming a different initial ratio, no mass transfer occurs and the two sub-systems remain unmodified. By modeling the chemical equilibration results of several systems it is possible to provide a quantitative framework to determine the chemical and petrological evolution of two assemblages from an initial state, in which the two are separately in chemical equilibrium, to a state of equilibration of the whole system (sum of the two sub-systems). Assuming that the local Gibbs energy variation follows a simple diffusion couple model, a complete petrological description of the two systems can be determined over time and space. Since there are no data to constrain the kinetic of the processes involved, the temporal and spatial scale is arbitrary. Nevertheless a 1-D static model shows how chemical equilibration is controlled by the size of the two sub-systems. As the initial size of the first assemblage (peridotite-like) increases, the differences between the initial and the final equilibrated stage becomes smaller, while on the opposite side the difference increases. A simplified 2-D dynamic model in which either one of the two sub-systems is allowed to move with a prescribed velocity, shows that after an initial transient state, the moving sub-system tends to preserve its original composition defined at the entry side. The other sub-system instead evolves towards a large compositional difference from the starting assemblage. The results appear to be the same varying the initial proportion of the two assemblages, which simplify somehow the development of potential tools for predicting the chemical equilibration process from real data and geodynamic applications. Four animations and data sets of three 1-D and two 2-D numerical models are available following the instructions in the supplementary material.

Melting of ice in a porous medium saturated with ice and gas while injecting warm water

2019 ◽  
Vol 13 (4) ◽  
pp. 112-117 ◽  
Author(s):  
V.Sh. Shagapov ◽  
M.N. Zapivakhina
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Low Temperature ◽  
Numerical Models ◽  
Warm Water ◽  
Temperature Fields ◽  
Initial State ◽  
Simplified Models ◽  
Frozen Soils ◽  
Porous Formation

The numerical models for the injection of warm water (in the temperature range from 300 to 340 K) into a cold porous formation are considered. Simplified models describing the processes of heat and mass transfer are proposed. The influence of the parameters determining the initial state of the porous medium, the boundary pressure, temperature and moisture content on the rate of propagation of hydrodynamic and temperature fields in the porous medium is investigated. It has been established that it is economically feasible to melt frozen soils saturated with ice and gas (air) at a sufficiently low temperature of the injected water (about 300 K).

Consolidating rock-physics classics: A practical take on granular effective medium models

2019 ◽  
Vol 38 (5) ◽  
pp. 334-340 ◽  
Author(s):  
Fabien Allo
Keyword(s):  
Numerical Models ◽  
Quantitative Description ◽  
Rock Physics ◽  
Real Data ◽  
Analytical Form ◽  
Effective Medium ◽  
Seismic Exploration ◽  
Stiffness Index ◽  
Rock Composition ◽  
Rock Types

Granular effective medium (GEM) models rely on the physics of a random packing of spheres. Although the relative simplicity of these models contrasts with the complex texture of most grain-based sedimentary rocks, their analytical form makes them easier to apply than numerical models designed to simulate more complex rock structures. Also, unlike empirical models, they do not rely on data acquired under specific physical conditions and can therefore be used to extrapolate beyond available observations. In addition to these practical considerations, the appeal of GEM models lies in their parameterization, which is suited for a quantitative description of the rock texture. As a result, they have significantly helped promote the use of rock physics in the context of seismic exploration for hydrocarbon resources by providing geoscientists with tools to infer rock composition and microstructure from sonic velocities. Over the years, several classic GEM models have emerged to address modeling needs for different rock types such as unconsolidated, cemented, and clay-rich sandstones. We describe how these rock-physics models, pivotal links between geology and seismic data, can be combined into extended models through the introduction of a few additional parameters (matrix stiffness index, cement cohesion coefficient, contact-cement fraction, and laminated clays fraction), each associated with a compositional or textural property of the rock. A variety of real data sets are used to illustrate how these parameters expand the realm of seismic rock-physics diagnostics by increasing the versatility of the extended models and facilitating the simulation of plausible geologic variations away from the wells.

scholarly journals Numerical modelling in the coastal aquifer between Burlamacca Canal and Bufalina Ditch, southern Versilia (Tuscany, Italy)

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Gioia Bravini ◽  
Matia Menichini ◽  
Marco Doveri
Keyword(s):  
Flow Model ◽  
Transport Model ◽  
Numerical Models ◽  
Salt Water ◽  
Monitoring Network ◽  
Transient State ◽  
Salt Water Intrusion ◽  
Visual Modflow ◽  
Hydrogeological Model ◽  
Definition Of

Groundwater numerical models are necessary instruments for management of water resources and for their protection, both in terms of quantity and quality. In this paper we present a study on an area located along the southern coastline of Versilia (Viareggio,LU) affected by marine intrusion. The main purpose of this work was to create a mathematical flow model based on a conceptual hydrogeological model defined by a multidisciplinary approach. For the realization of the numerical model the ModFlow code and the graphic interface Visual ModFlow was used. The procedure for defining the mathematical model involves a series of steps such as horizontal and vertical discretization of the space, the definition of the initial and boundary conditions, the assignment of the hydraulic properties of the cells and, finally, the definitions of external perturbations to the system (recharge, evapotranspiration, drainage and pumping wells). Implementation, development and calibration of the numerical flow model was performed both in steady and transient state. Both models were calibrated using the manual “trial and error adjustment” method using heads measurements. Moreover the model results gathered in transient state simulation were compared with the data continuously recorded by a piezometer of the monitoring network of the Regional Hydrological Service. There is a good correlation between the measured data and those calculated by the model which then turns out to be sufficiently representative and provides a solid basis for the development of a transport model that could be useful to control and manage the phenomenon of the salt water intrusion.

Principles of Metal Refining and Recycling

2021 ◽  
Author(s):  
Thorvald Abel Engh ◽  
Geoffrey K. Sigworth ◽  
Anne Kvithyld
Keyword(s):  
Mass Transfer ◽  
Transport Properties ◽  
Numerical Models ◽  
Impurity Elements

Covers the field of recycling and refining of metals. An important point the book stresses is that the principles are the same in the treatment of various different metals. The book answerd why it is important to have a clean and properly alloyed metal from recycling and refined metal? The text covers basic thermodynamics, physical and transport properties, mixing, mass transfer and numerical models. Further it identifies problems and described methods for removal of dissolved impurity elements, particles and inclusions, also during solidification. And lastly applications remelting and addition of alloys, recycling and challenges and specific processes for each metal are included. The book is self-contained.

A generalized settling approach in the numerical modeling of sedimentation tanks

1998 ◽  
Vol 38 (3) ◽  
pp. 95-102 ◽  
Author(s):  
G. Mazzolani ◽  
F. Pirozzi ◽  
G. d'Antonoi
Keyword(s):  
Transport Model ◽  
Numerical Models ◽  
Removal Rate ◽  
Total Concentration ◽  
Suspended Solid ◽  
Primary Concern ◽  
High Concentration ◽  
Hindered Settling ◽  
Low Concentration ◽  
Solid Distribution

Numerical models for the prediction of turbulent flow field and suspended solid distribution in sedimentation tanks are characterized by refined modeling of hydrodynamics, but apparently weak modeling of settling properties of suspensions. It is known that sedimentation tanks typically treat highly heterodisperse suspensions, whose concentrations range from relatively high to low values. However, settling is modeled either by considering one or more particle classes of different settling velocity, without accounting for hindered settling conditions, or by treating the suspension as monodisperse, even in regions of low concentration. A new generalized settling model is proposed to account for both discrete settling conditions in low concentration regions of the tanks and hindered settling conditions in high concentration regions. Settling velocities of heterodisperse suspensions are then determined as a function of particle velocities in isolation and their total concentration. The settling model is used in the framework of a transport model for the simulation of hydrodynamics and solid distribution in a rectangular sedimentation tank. Results show that solid distribution is mainly affected by particle interactions in the inlet region and by settling properties of individual particles in the outlet region. Comparison of the proposed settling model with other settling models suggests that a generalized approach of the modeling of settling properties of suspensions is a primary concern to obtain reliable predictions of the removal rate.

On the Determination of Age of Air Trends from Atmospheric Trace Species

2011 ◽  
Vol 68 (1) ◽  
pp. 139-154 ◽  
Author(s):  
Rolando R. Garcia ◽  
William J. Randel ◽  
Douglas E. Kinnison
Keyword(s):  
Climate Model ◽  
Meridional Circulation ◽  
Transport Model ◽  
Numerical Models ◽  
Chemical Species ◽  
Large Error ◽  
Atmospheric Concentration ◽  
Nonlinear Growth ◽  
Mean Meridional Circulation ◽  
The Mean

Abstract Trace chemical species have been used in numerical models to calculate the age of air (AOA), which is a measure of the strength of the mean meridional circulation. The trend in the AOA has also been computed and found to be negative in simulations where greenhouse gases increase with time, which is consistent with the acceleration of the mean meridional circulation calculated under these conditions. This modeling result has been tested recently using observations of SF6, a very long lived species whose atmospheric concentration has increased rapidly over the last half century, and of CO2, which is also very long lived and increasing with time. Surprisingly, the AOA estimated from these gases exhibits no significant trend over the period 1975–2005. Here the Whole Atmosphere Community Climate Model (WACCM) is used to derive estimates of the AOA from SF6 and CO2 over the period 1965–2006. The calculated AOA yields trends that are smaller than the trend derived from a synthetic, linearly growing tracer, even after accounting for the nonlinear growth rates of SF6 and CO2. A simplified global transport model and analytical arguments are used to show that this follows from the variable growth rate of these species. It is also shown that, when AOA is sampled sparsely as in the observations, the resulting trends have very large error bars and are statistically undistinguishable from zero. These results suggest that trends in the AOA are difficult to estimate unambiguously except for well-sampled tracers that increase linearly and uniformly. While such tracers can be defined in numerical models, there are no naturally occurring species that exhibit such idealized behavior.

scholarly journals Turbulent vertical diffusivity in the sub-tropical stratosphere

2007 ◽  
Vol 7 (3) ◽  
pp. 6603-6629 ◽  
Author(s):  
I. Pisso ◽  
B. Legras
Keyword(s):  
Transport Model ◽  
Numerical Models ◽  
Small Scale ◽  
Chemistry Transport Model ◽  
Weather Forecasts ◽  
Chemical Tracers ◽  
Vertical Diffusivity ◽  
Large Ensembles ◽  
Local Equivalent ◽  
Using Data

Abstract. Vertical (cross-isentropic) mixing is produced by small-scale turbulent processes which are still poorly understood and parametrized in numerical models. In this work we provide estimates of local equivalent diffusion in the lower stratosphere by comparing balloon borne high-resolution measurements of chemical tracers with reconstructed mixing ratio from large ensembles of random Lagrangian backward trajectories using European Center for Medium-range Weather Forecasts analysed winds and a chemistry-transport model (REPROBUS). We have investigated cases in subtropical latitudes using data from HIBISCUS campaign. Upper bound on the vertical diffusivity is found to be of the order of 0.5 m2 s−1 in the subtropical region, which is larger than the estimates at higher latitudes. The relation between diffusion and dispersion is studied by estimating Lyapunov exponents and studying their variation according to the presence of active dynamical structures.

scholarly journals Aeration / Stripping of n-Butyl Mercaptan in aqueous environment

2013 ◽  
Vol 8 (2) ◽  
pp. 103-112
Keyword(s):  
Experimental Data ◽  
Water Quality ◽  
Mass Transfer ◽  
Transfer Coefficient ◽  
Mass Transfer Coefficient ◽  
Chemical Equilibrium ◽  
Reaction Rate ◽  
Reaction Parameter ◽  
Ph Values ◽  
Neutral Compound

Μany applications in water quality management have a common key water quality parameter, dissolved oxygen, resulting to the critical role of aeration. On the other hand, in municipal and industrial wastewater, especially where aeration is applied, the presence of volatile organic compounds (VOCs) causes several concerns including a direct threat to humans, partly due to their emission from treatment tanks. pH, temperature and Henry’s Law govern VOCs’ speciation and consequently their emission characteristics. Limited data and simplifications of available mass-transfer models pose obstacles to a realistic approach, especially in the presence of a chemical equilibrium, for example in the case of mercaptans. In the present study the importance of oxygen transfer and stripping of a VOC (n-butyl mercaptan) on aeration’s overall effectiveness are examined separately. Clean water oxygenation and stripping of mercaptan to an inert gas (nitrogen) were studied aiming to consider mass transfer aspects and to investigate the influence of chemical equilibrium between ionic and neutral form of the target compound in neutral and alkaline solutions. Using appropriate mass transfer relationships (dynamic method), experimental data were analyzed for the determination of overall mass transfer coefficient ( kOL,O2α ) of oxygen. Correlating kOL,O2 α with the corresponding mass transfer coefficient of n-butyl mercaptan in neutral solutions (calculated according the model proposed by Matter-Muller et al. [1]), a value of ratio βy of 0.566 is found, close to the reported values of other VOCs with similar values of Henry’s constant. At alkaline pH however the conventional simplified model fails to predict realistic values of mass-transfer coefficients. A coupled differential algebraic equation system, based on mass balances, taking into account dissociation of the compound to be stripped and assuming chemical non-equilibrium conditions during stripping, was developed. Reaction parameter k2 was calculated with non-linear least-squares analysis. The model predicts satisfactorily the experimental data and it provides a useful tool for the semibatch stripper design in situations where a reversible reaction is involved. At pH values below 8.5 mercaptan concentration falls exponentially whereas above 10.5 it tends to linearity. The bubble equilibrates and mercaptan transferred depends upon solubility and not diffusivity. Especially after depletion of initial neutral compound, transport depends upon neutral/ionic form speciation. The effectiveness of stripping n-butyl mercaptan, at a given pH, is mainly determined by a proportionality constant considered as “fugacity capacity” (removal effect on the process) and by a reversible reaction rate constant k2 (kinetic effect on the process). The ‘’fugacity capacity” is determined by hydrophobicity (i.e. low solubility and high limiting activity coefficient) rather than pure-component volatility (i.e. vapor pressure or boiling point). High limiting activity coefficient promotes mercaptan emission due to established vapor-liquid equilibrium, while the low reaction parameter k2, controls neutral compound quantity. At high pH, where ionic form predominates, experimental data showed that stripping was almost independent of the gas flow rate applied. A strong sensitivity of the model to uncertainty of γ∞ was found: γ∞ controls emission rate and through this the dynamic variations of neutral/ionic concentration profiles whereas reaction rate law parameter k2 controls the neutral/ionic transformation and it is the crucial quantity which governs the process at high pH values.

scholarly journals Final state hadronic rescattering with UrQMD

2018 ◽  
Vol 171 ◽  
pp. 05003 ◽  
Author(s):  
J. Steinheimer ◽  
V. Vovchenko ◽  
J. Aichelin ◽  
M. Bleicher ◽  
H. Stöcker
Keyword(s):  
Momentum Distribution ◽  
Chemical Equilibrium ◽  
Transport Model ◽  
Local Equilibrium ◽  
High Energy ◽  
Final State ◽  
Nuclear Collisions ◽  
Unstable Particles ◽  
Realistic Description ◽  
Do So

In this talk we discuss the effects of the hadronic rescattering on final state observables in high energy nuclear collisions. We do so by employing the UrQMD transport model for a realistic description of the hadronic decoupling process. The rescattering of hadrons modifies every hadronic bulk observable. For example apparent multiplicity of resonances is suppressed as compared to a chemical equilibrium freeze-out model. Stable and unstable particles change their momentum distribution by more than 30% through rescattering. The hadronic rescattering also leads to a substantial decorrelation of the conserved charge distributions. These findings show that it is all but trivial to conclude from the final state observables on the properties of the system at an earlier time where it may have been in or close to local equilibrium.

Sign in / Sign up

Export Citation Format

Share Document