Equilibrium and natural systems

Initially, we develop Matlab code and Excel spreadsheets for relatively simple systems that have explicit analytical solutions. The main thrust of this chapter is the development of a toolbox of methods for modelling equilibrium and kinetic systems of any complexity. The computations are all iterative processes where, starting from initial guesses, the algorithms converge toward the correct solutions. Computations of this nature are beyond the limits of straightforward Excel calculations. Matlab, on the other hand, is ideally suited for these tasks, as most of them can be formulated as matrix operations. Many readers will be surprised at the simplicity and compactness of well-written Matlab functions that resolve equilibrium systems of any complexity. 

Butcher, S.S., and Anthony, S.E. (2000) Equilibrium, rate, and natural systems. In Earth System Science, from Biogeochemical Cycles to Global Change (Jacobson, M.C., Charlson, R.J., Rodhe, H, and Orians, G.H., eds.), pp. 85-105, International Geophysics Series, Academic Press, New York. 

In the second half of the 20th century it is precisely the classical equilibrium thermodynamics that became a basis for the creation of numerous computing systems for analysis of irreversible processes in complex open technical and natural systems as applied to the solution of theoretical and applied problems in various fields. The methods of MP, i.e., the mathematical discipline that emerged from the Lagrange interpretation of the equilibrium state, were a main computational tool employed for the studies. 

Modelling calculations were performed for Crooks Gap and Bonanza to determine how much calcite could dissolve given sufficient time to reach equilibrium between calcite and the added CO2. The purpose of the calculations was to determine how far from equilibrium the natural systems were, and to assess the potential for using a thermodynamic equilibrium modelling program to predict well bore scale (discussed in the next section). 

Thermodynamics allows us to calculate the energy differences between equilibrium states of all kinds, stable and metastable, for all kinds of substances. If that is all it does, and natural systems are not at equilibrium, how can it be useful ... 

There has also been extensive discussion on the influence of EDTA on the equilibrium of natural systems and biological and medicinal consequences of chelation of metals in the body (cf. and references therein). 

The phase rule is one of the most impressive and, yes, beautiful, results in all of equilibrium thermodynamics. It has proven essential in the study of experimental and natural systems. 

The concept of partial and local chemical equilibrium in natural system has been proposed and developed by Thompson (1959) and Helgeson (1979). After that many application and computer simulations based on partial chemical equilibrium have been conducted (e.g., Wolery 1983 Reed 1983). The principle of this model will be briefly described and application of this model to hydrothermal system accompanied by hydrothermal alteration and formation of hydrothermal ore deposits will be given below. 

Chalykh, A. E., Avdav, N. N., Berlin, A. A., and Meshikovskii, S. M., Phase equilibrium and natural diffusion in the ohgomer-polymer systems, Dokl. Akad. Nauk. SSSR, 238, 893, 1978 (Russian). 

There are many examples in nature where a system is not in equilibrium and is evolving in time towards a thennodynamic equilibrium state. (There are also instances where non-equilibrium and time variation appear to be a persistent feature. These include chaos, oscillations and strange attractors. Such phenomena are not considered here.)... 

In spite of these limitations it is hoped that this chapter will provide an introduction to the unusual phenomena that chemically reacting systems exlribit when driven far from equilibrium and an indication of how these phenomena may be analysed. Although such systems were often regarded as curiosities in the past, it is now clear that they are the mle rather than the exception in nature and deserve our full attention. 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

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