Geochemical and Biogeochemical Reaction Modeling

2021 ◽  
Author(s):  
Craig M. Bethke
Keyword(s):  
Wide Spectrum ◽  
Worked Examples ◽  
Surface Complexation Modeling ◽  
Kinetic Rate ◽  
University Teachers ◽  
Rate Laws ◽  
Partial Pressures ◽  
Scientists And Engineers ◽  
Scientific Practical ◽  
Geochemical Reaction

An indispensable primer and reference textbook, the third edition of Geochemical and Biogeochemical Reaction Modeling carries the reader from the field's origins and theoretical underpinnings through to a collection of fully worked examples. A clear exposition of the underlying equations and calculation techniques is balanced by real-world example calculations. The book depicts geochemical reaction modeling as a vibrant field of study applicable to a wide spectrum of issues of scientific, practical, and societal concern. The new edition offers a thorough description of surface complexation modeling, including two- and three-layer methods; broader treatment of kinetic rate laws; the effect of stagnant zones on transport; and techniques for determining gas partial pressures. This handbook demystifies and makes broadly accessible an elegant technique for portraying chemical processes in the geosphere. It will again prove to be invaluable for geochemists, environmental scientists and engineers, aqueous and surface chemists, microbiologists, university teachers, and government regulators.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

A field versus laboratory study of blood oxygen status in normoxic crabs at different temperatures

1996 ◽  
Vol 74 (3) ◽  
pp. 423-430 ◽  
Author(s):  
J.-C. Massabuau ◽  
J. Forgue
Keyword(s):  
Wide Spectrum ◽  
Venous Blood ◽  
Carcinus Maenas ◽  
Blood Oxygen ◽  
Arterial Blood ◽  
Field Versus ◽  
Partial Pressures ◽  
Different Temperatures ◽  
Head Pressure ◽  
Oxygen Status

The blood oxygen status of two species of active crabs (Carcinus maenas and Necora puber) was studied in the field and compared with the results of previous laboratory experiments performed on a wide spectrum of physiologically different water-breathers. The aim was to determine whether, as in the laboratory, the functioning of the O2 supply system in the field could be based on maintaining the arterial [Formula: see text] in the low range, 1–3 kPa. The O2 partial pressures and concentrations in the arterial and venous blood, arterial blood pH, and blood respiratory pigment concentration were measured in normoxic water at various temperatures ranging from 10 to 20 °C and in various seasons. In the field, [Formula: see text] values in normoxic C. maenas and N. puber were in the low range, 1–3 kPa, independently of temperature, season, and blood haemocyanin concentration. It is concluded that in the field as in the laboratory, [Formula: see text] values mainly in the low range provide a head pressure sufficient to meet O2 needs. The changes that appear to occur in other respiratory variables are discussed in relation to field versus laboratory conditions and temperature differences. The consequences for analysing problems of hypoxaemia in hypoxic waters or situations are discussed.

Polythermal, Fixed, and Sliding Paths

1996 ◽  
Author(s):  
Craig M. Bethke
Keyword(s):  
Mass Transfer ◽  
Equilibrium System ◽  
Reaction Paths ◽  
Governing Equations ◽  
Kinetic Rate ◽  
Reaction Progress ◽  
Rate Laws ◽  
Reaction Models ◽  
Temperature Path

In this chapter we consider how to construct reaction models that are somewhat more sophisticated than those discussed in the previous chapter, including reaction paths over which temperature varies and those in which species activities and gas fugacities are buffered. The latter cases involve the transfer of mass between the equilibrium system and an external buffer. Mass transfer in these cases occurs at rates implicit in solving the governing equations, rather than at rates set explicitly by the modeler. In Chapter 14 we consider the use of kinetic rate laws, a final method for defining mass transfer in reaction models. Polythermal reactions paths are those in which temperature varies as a function of reaction progress, ξ. In the simplest case, the modeler prescribes the temperatures T0 and Tf at the beginning and end of the reaction path. The model then varies temperature linearly with reaction progress. This type of model is sometimes called a “sliding temperature” path. The calculation procedure for a sliding temperature path is straightforward. In taking a reaction step, the model evaluates the temperature to be attained at the step’s end.

Mass Transfer

1996 ◽  
Author(s):  
Craig M. Bethke
Keyword(s):  
Mass Transfer ◽  
Numerical Methods ◽  
Equilibrium State ◽  
Reaction Path ◽  
Mineral Precipitation ◽  
Kinetic Rate ◽  
Reaction Progress ◽  
Rate Laws ◽  
Species Activity ◽  
Aqueous Species

In previous chapters we have discussed the nature of the equilibrium state in geochemical systems: how we can define it mathematically, what numerical methods we can use to solve for it, and what it means conceptually. With this chapter we begin to consider questions of process rather than state. How does a fluid respond to changes in composition as minerals dissolve into it, or as it mixes with other fluids? How does a fluid evolve in response to changing temperature or variations in the fugacity of a coexisting gas? In short, we begin to consider reaction modeling. In this chapter we consider how to construct reactions paths that account for the effects of simple reactants, a name given to reactants that are added to or removed from a system at constant rates. We take on other types of mass transfer in later chapters. Chapter 12 treats the mass transfer implicit in setting a species’ activity or gas’ fugacity over a reaction path. In Chapter 14 we develop reaction models in which the rates of mineral precipitation and dissolution are governed by kinetic rate laws. Simple reactants are those added to (or removed from) the system at constant rates over the reaction path. As noted in Chapter 2, we commonly refer to such a path as a titration model, because at each step in the process, much like in a laboratory titration, the model adds an aliquot of reactant mass to the system. Each reactant Ar is added at a rate nr, expressed in moles per unit reaction progress, ξ. Negative values of nr, of course, describe the removal rather than the addition of the reactant. Since ξ is unitless and varies from zero at the start of the path to one at the end, we can just as well think of nr as the number of moles of the reactant to be added over the reaction path. A simple reactant may be an aqueous species (including water), a mineral, a gas, or any entity of known composition.

Kinetic Rate Laws of Cd, Pb, and Zn Vaporization during Municipal Solid Waste Incineration

2009 ◽  
Vol 43 (6) ◽  
pp. 2184-2189 ◽  
Author(s):  
Quentin Falcoz ◽  
Daniel Gauthier ◽  
Stéphane Abanades ◽  
Gilles Flamant ◽  
Fabrice Patisson
Keyword(s):  
Municipal Solid Waste ◽  
Solid Waste ◽  
Waste Incineration ◽  
Municipal Solid Waste Incineration ◽  
Kinetic Rate ◽  
Rate Laws

scholarly journals On Unsaturated Soil Mechanics – Personal Views on Current Research

2015 ◽  
Vol 37 (3) ◽  
pp. 73-84 ◽  
Author(s):  
G.N. Pande ◽  
S. Pietruszczak
Keyword(s):  
Wide Spectrum ◽  
Soil Mechanics ◽  
Research Groups ◽  
Broad Area ◽  
Empirical Relations ◽  
Unsaturated Soil Mechanics ◽  
Petroleum Chemical ◽  
Scientists And Engineers ◽  
Semi Empirical ◽  
Sound Theoretical Basis

Abstract This paper presents the authors’ personal views on current research being conducted by various research groups around the world in the broad area of mechanics of unsaturated geomaterials in general and soils in particular. The topic is of interest to a wide spectrum of scientists and engineers working in diverse areas such as geology and geophysics, powder technology, agricultural, petroleum, chemical, geotechnical, civil, environmental and nuclear engineering. Even if we restrict ourselves to civil, geotechnical and environmental engineering, it is noted that a plethora of hypotheses as well as a number of empirical and semi-empirical relations have been introduced for describing the mechanics of unsaturated porous media. However, many of these proposed advances as well as methods of testing may lack sound theoretical basis.

A Note on the Principle of Maximum Dissipation Rate

2006 ◽  
Vol 74 (5) ◽  
pp. 923-926 ◽  
Author(s):  
F. D. Fischer ◽  
J. Svoboda
Keyword(s):  
Convex Functions ◽  
Dissipation Rate ◽  
Direct Consequence ◽  
Dissipation Function ◽  
Internal Variables ◽  
Entropy Production Rate ◽  
Kinetic Rate ◽  
Rate Laws ◽  
Thermodynamic Forces ◽  
Principle Of Maximum

The Principle of Maximum Dissipation Rate (PMD) can be exploited to derive homogeneous kinetic rate laws for the internal variables. A “normality structure” expressing the rates of the internal variables as normal to convex functions (entropy production rate, dissipation function as flow potentials) in the space of the conjugate thermodynamic forces is a direct consequence of the PMD. This paper can be considered as a note to Yang et al., 2005, ASME J. Appl. Mech., 72, pp. 322–329.

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