Relations between single mineral equilibrium models and equilibrium models with a solid-solution of q end-members

Clay Minerals ◽  
1988 ◽  
Vol 23 (1) ◽  
pp. 69-80 ◽  
Author(s):  
J. Pages ◽  
P. Aurousseau

AbstractMinerals studied by an equilibrium model with a single mineral are similar to those studied in solid-solution models with q end-members. After discussing solid-solution models with q end-members where the limits of this kind of models are specified, the mathematical relations between the two kinds of models are developed. These relations show that the equilibrium model with a single mineral is compatible with the geochemical assumption of solid-solution. A method for estimation of equilibrium between a single mineral and a homogeneous set of aqueous solutions is proposed.

2015 ◽  
Vol 35 (3) ◽  
pp. 633-641 ◽  
Author(s):  
Mehdi Irannajad ◽  
Hossein Kamran Haghighi ◽  
Eshagh Safarzadeh

2021 ◽  
Author(s):  
◽  
Adolf Hermanus Stroombergen

<p>Whether a country gains or loses from dismantling protection is a question which has received much attention in overseas studies; studies which deal both with the relevant theory and with actual measurement. The topic has not been well analysed in the New Zealand context. Discussion amongst economists and other interested parties has certainly occurred but this has been based more on philosophical and political considerations than on applied economic research. Since questions of protection reform affect the whole economy it is inappropriate to study such problems in a partial or selective framework which cannot capture the interdependencies between each and every sector in the economy. A multi-sectoral general equilibrium model overcomes this deficiency. This thesis is concerned with the development and application of such a model. The model (named JULIANNE) is a medium term policy model designed to answer 'what if' type questions, particularly questions about trade and structure. It is not a forecasting model. Its role is rather like that of a laboratory in the natural sciences, where experiments can be conducted in a situation where certain aspects of the (economic) environment can be controlled by the researcher so that it is possible to measure the relationships between the variables of interest. The closer the environment is to the 'real world' the easier it is to apply deductions from the experiment to reality. But even quite artificial experiments can yield useful insights. The thesis comprises eleven chapters, the first three of which introduce and develop the model, examining some of the overseas general equilibrium models and assessing some of the problems which need to be addressed when constructing such a model for New Zealand; a model with an emphasis on trade and structure. The following three chapters present the JULIANNE model including its equations, a detailed explanation of its features and routines, and its method of solution, which for general equilibrium models is a most important consideration as it distinguishes the purely abstract Walrasian model from a model which is actually computable. Chapters 7 and 8 apply the model to various problems, especially to protection reform, but also to other interesting topics such as export subsidisation, relative occupational wage rates and medium term projections. The issue of model validation (in a general sense) is also covered. In Chapter 9 the model is extended from a single period snapshot model into a multi-period dynamic model, essentially introducing another variable; time, that can be controlled by the experimenter. Some of the results from Chapters 7 and 8 are then reassessed with the extended model, as described in Chapter 10. Results from the application of the model to questions about the effects of changes in protection enabled one to conclude that under flexible factor prices with fixed factor employment, the gains from freer trade vary directly with the values of the export price elasticities of demand, with the potential for economies of scale arising from specialization, and with the time horizon under consideration. They vary inversely with the values of the elasticities of substitution both between domestic and imported goods of a given type, and between goods of different types. Under a different labour market asumption, namely fixed real wage rates and flexible employment, the case for free trade is much stronger (that is, for a given set of parameter values). The profile of protection across sectors can also be important with the not improbable chance that a low uniform level of protection is superior to complete free trade, again depending on parameter values and the characteristics of the labour market. In this connection the observed uniformity of the current protection regime is very dependent on the degree of sectoral disaggregation identified in the model. As the degree of disaggregation increases, the potential for specialization also increases, as does the potential for substitution between different commodity types. Just how important these issues are, is a question for future research.</p>


2021 ◽  
Author(s):  
◽  
Adolf Hermanus Stroombergen

<p>Whether a country gains or loses from dismantling protection is a question which has received much attention in overseas studies; studies which deal both with the relevant theory and with actual measurement. The topic has not been well analysed in the New Zealand context. Discussion amongst economists and other interested parties has certainly occurred but this has been based more on philosophical and political considerations than on applied economic research. Since questions of protection reform affect the whole economy it is inappropriate to study such problems in a partial or selective framework which cannot capture the interdependencies between each and every sector in the economy. A multi-sectoral general equilibrium model overcomes this deficiency. This thesis is concerned with the development and application of such a model. The model (named JULIANNE) is a medium term policy model designed to answer 'what if' type questions, particularly questions about trade and structure. It is not a forecasting model. Its role is rather like that of a laboratory in the natural sciences, where experiments can be conducted in a situation where certain aspects of the (economic) environment can be controlled by the researcher so that it is possible to measure the relationships between the variables of interest. The closer the environment is to the 'real world' the easier it is to apply deductions from the experiment to reality. But even quite artificial experiments can yield useful insights. The thesis comprises eleven chapters, the first three of which introduce and develop the model, examining some of the overseas general equilibrium models and assessing some of the problems which need to be addressed when constructing such a model for New Zealand; a model with an emphasis on trade and structure. The following three chapters present the JULIANNE model including its equations, a detailed explanation of its features and routines, and its method of solution, which for general equilibrium models is a most important consideration as it distinguishes the purely abstract Walrasian model from a model which is actually computable. Chapters 7 and 8 apply the model to various problems, especially to protection reform, but also to other interesting topics such as export subsidisation, relative occupational wage rates and medium term projections. The issue of model validation (in a general sense) is also covered. In Chapter 9 the model is extended from a single period snapshot model into a multi-period dynamic model, essentially introducing another variable; time, that can be controlled by the experimenter. Some of the results from Chapters 7 and 8 are then reassessed with the extended model, as described in Chapter 10. Results from the application of the model to questions about the effects of changes in protection enabled one to conclude that under flexible factor prices with fixed factor employment, the gains from freer trade vary directly with the values of the export price elasticities of demand, with the potential for economies of scale arising from specialization, and with the time horizon under consideration. They vary inversely with the values of the elasticities of substitution both between domestic and imported goods of a given type, and between goods of different types. Under a different labour market asumption, namely fixed real wage rates and flexible employment, the case for free trade is much stronger (that is, for a given set of parameter values). The profile of protection across sectors can also be important with the not improbable chance that a low uniform level of protection is superior to complete free trade, again depending on parameter values and the characteristics of the labour market. In this connection the observed uniformity of the current protection regime is very dependent on the degree of sectoral disaggregation identified in the model. As the degree of disaggregation increases, the potential for specialization also increases, as does the potential for substitution between different commodity types. Just how important these issues are, is a question for future research.</p>


2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Thomas Gröbl ◽  
Heimo Walter

A large potential is contributed to the energetic utilization of biomass, whereby thermochemical gasification seems to be especially interesting. In order to contribute to a better understanding of the thermochemical conversion process in the gasifier, mathematical models are used. An intensive effort is made in development of mathematical models describing the gasification process and a large number of models, considerably differing in their degree of simplification, and their applications are reported in literature. In the present article, a brief review of models applied, mainly focused on equilibrium models, is provided and a robust and flexible modified stoichiometric equilibrium model, for modeling a novel gasifier, is presented.


Author(s):  
Lawrence A. Boland

This chapter examines Robert Clower’s 1959 article about the knowledge requirements for an equilibrium model of the supplier, and asks whether universal maximization is always an implication of equilibrium attainment. Clower’s article challenges Arrow’s suggestion of using an imperfect competitor. But the equilibrium reached by an ignorant monopolist may be an equilibrium state but unlike general equilibrium models, the equilibrium that Clower’s monopolist reaches is sub-optimal. The main reason for it being a sub-optimum is that the monopolist may not be maximizing profit even though the monopolist thinks so. The reason for his monopolist reaching a sub-optimal state is that the monopolist does not know the market’s demand curve and so must make possibly false assumptions about it.


1969 ◽  
Vol 13 ◽  
pp. 539-549
Author(s):  
Gerald G. Johnson ◽  
Frank L. Chan

Since for most real systems, solid solution effects influence the position and intensity of the x-ray powder diffraction pattern, it is desirable and necessary to have an automatic system which will identify standard reference phases regardless of the amount of solid solution. Using the system CdS-ZnS, where the lattice parameter a0 changes from 4.136 to 3.820Å, with complete solid solution over the entire range of composition, an illustrative study was made. This work presents the results obtained from a computer analysis of the powder pattern obtained. It has been found that if the starting chemistry is known and the end members of the series are in the ASTM Powder Diffraction File, that the solid solution can be identified. Once the phases present are identified, a plot following Vegard's law yields the approximate composition of the sample under consideration. These two methods of compositional determination agree quite well. Examples of the computer system and description of the program input and output with interpretation of the results will be discussed.


Minerals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 189 ◽  
Author(s):  
Pablo Forjanes ◽  
José Astilleros ◽  
Lurdes Fernández-Díaz

Barite (BaSO4) and celestite (SrSO4) are the end-members of a nearly ideal solid solution. Most of the exploitable deposits of celestite occur associated with evaporitic sediments which consist of gypsum (CaSO4·2H2O) or anhydrite (CaSO4). Barite, despite having a broader geological distribution is rarely present in these deposits. In this work, we present an experimental study of the interaction between gypsum crystals and aqueous solutions that bear Sr or Ba. This interaction leads to the development of dissolution-crystallization reactions that result in the pseudomorphic replacement of the gypsum crystals by aggregates of celestite or barite, respectively. The monitoring of both replacement reactions shows that they take place at very different rates. Millimeter-sized gypsum crystals in contact with a 0.5 M SrCl2 solution are completely replaced by celestite aggregates in less than 1 day. In contrast, only a thin barite rim replaces gypsum after seven days of interaction of the latter with a 0.5 M BaCl2 solution. We interpret that this marked difference in the kinetics of the two replacement reactions relates the different orientational relationship that exists between the crystals of the two replacing phases and the gypsum substrate. This influence is further modulated by the specific crystal habit of each secondary phase. Thus, the formation of a thin oriented layer of platy barite crystals effectively armors the gypsum surface and prevents its interaction with the Ba-bearing solution, thereby strongly hindering the progress of the replacement reaction. In contrast, the random orientation of celestite crystals with respect to gypsum guarantees that a significant volume of porosity contained in the celestite layer is interconnected, facilitating the continuous communication between the gypsum surface and the fluid phase and guaranteeing the progress of the gypsum-by-celestite replacement.


2010 ◽  
Vol 132 (12) ◽  
pp. 124507 ◽  
Author(s):  
Jacek Gliński ◽  
Andrzej Burakowski

2008 ◽  
Vol 80 (6) ◽  
pp. 1293-1302 ◽  
Author(s):  
Gunnar Eriksson ◽  
Erich Königsberger

The integrated thermochemical databank system FactSage enables the user to calculate equilibria and thermodynamic properties for a wide variety of multicomponent, multiphase systems and reactions. The Gibbs energy models and databases for condensed, gaseous, and aqueous solutions presently implemented in FactSage are of interest to chemical and physical metallurgy, chemical and corrosion engineering, inorganic and solution chemistry, geochemistry, environmental science, etc. Models for the aqueous phase include the Pitzer and Helgeson formalisms, but data and subroutines for concentrated aqueous solutions have also been provided by OLI Systems. ChemApp is a programmer's library for thermochemistry that also incorporates the Gibbs energy minimizer of FactSage. Applications of ChemApp include, for example, the handling of repetitive complex equilibrium calculations in application-specific programs and its linking to third-party process simulation packages. In this work, user-defined aqueous solution models in FactSage and ChemApp have been applied to the hydrometallurgical processing of aluminum ores in both caustic and acidic leach solutions.


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