Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs’ free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure [p_(co) = 11.5727(10)k_(B)T/σ^(3)] and the interfacial free energy [γ_({100}) = 0.636(11)k_(B)T/σ^(2)].

GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals

Phase equilibrium data regression is an unavoidable task necessary to obtain the appropriate values for any model to be used in separation equipment design for chemical process simulation and optimization. The accuracy of this process depends on different factors such as the experimental data quality, the selected model and the calculation algorithm. The present paper summarizes the results and conclusions achieved in our research on the capabilities and limitations of the existing GE models and about strategies that can be included in the correlation algorithms to improve the convergence and avoid inconsistencies. The NRTL model has been selected as a representative local composition model. New capabilities of this model, but also several relevant limitations, have been identified and some examples of the application of a modified NRTL equation have been discussed. Furthermore, a regression algorithm has been developed that allows for the advisable simultaneous regression of all the condensed phase equilibrium regions that are present in ternary systems at constant T and P. It includes specific strategies designed to avoid some of the pitfalls frequently found in commercial regression tools for phase equilibrium calculations. Most of the proposed strategies are based on the geometrical interpretation of the lowest common tangent plane equilibrium criterion, which allows an unambiguous comprehension of the behavior of the mixtures. The paper aims to show all the work as a whole in order to reveal the necessary efforts that must be devoted to overcome the difficulties that still exist in the phase equilibrium data regression problem.

Correlation of the liquid–liquid equilibrium data for specific ternary systems with one or two partially miscible binary subsystems

This paper presents the results of a liquid–liquid equilibrium data correlation for 11 ternary systems which have not been previously fitted using the NRTL model or, when they have, the results presented in the literature are inconsistent with the experimental behavior of the system. These ternary systems include mixtures with one or two partially miscible pairs. During the correlation process, new restrictions were imposed on the values for the NRTL binary parameters to ensure correct prediction of the total or partial miscibility for the binary pairs involved. In addition, topological concepts related to the Gibbs stability test have been applied in order to validate the results in the whole range of compositions.

Some examples of modeling in chemical engineering: thermal treatment of polymers, phase equilibrium calculations and process design

Presentation submitted to PSE Seminar, Chemical Engineering Department, Center for Advanced Process Design-making (CAPD), Carnegie Mellon University, Pittsburgh (USA), October 2012.

Geometrical study of the three-dimensional temperature–composition diagrams. An important aid to understand the behavior of the liquid–vapour equilibrium in ternary systems

In this work the usefulness of qualitatively studying and drawing three-dimensional temperature–composition diagrams for ternary systems is pointed out to understand and interpret the particular behavior of the liquid–vapour equilibrium of non-ideal ternary systems. Several examples have been used in order to highlight the interest and the possibilities of this tool, which should be an interesting support not only for lecturers, but also for researchers interested in experimental equilibrium data determination.

Liquid–Liquid, Vapor–Liquid, and Vapor–Liquid–Liquid Equilibrium Data for the Water–n-Butanol–Cyclohexane System at Atmospheric Pressure: Experimental Determination and Correlation

The temperature and the composition of the vapor–liquid–liquid equilibrium (VLLE) and the vapor–liquid equilibrium (VLE) of a ternary mixture of water–n-butanol–cyclohexane were measured at atmospheric pressure (101.32 kPa) in a modified dynamic recirculating still. As found in the literature, the experimental data obtained reveal a ternary azeotrope at 341.86 K with a mole fraction composition of 0.281, 0.034, and 0.685 water, n-butanol, and cyclohexane, respectively. The liquid–liquid equilibrium (LLE) compositions were measured at a constant temperature of 313.15 K and compared with data in the literature collected at other temperatures. Thermodynamic consistency of all the experimental data was demonstrated. The universal quasichemical (UNIQUAC) and the nonrandom two-liquid (NRTL) thermodynamic models were used to correlate the VLE and LLE data, while the original universal functional (UNIFAC) model was used to compare the predicted data.

Isothermal (liquid + liquid) equilibrium data at T = 313.15 K and isobaric (vapor + liquid + liquid) equilibrium data at 101.3 kPa for the ternary system (water + 1-butanol + p-xylene)

The (vapor + liquid), (liquid + liquid) and (vapor + liquid + liquid) equilibria of the ternary system (water + 1-butanol + p-xylene) have been determined. (Water + 1-butanol + p-xylene) is a type 2 heterogeneous ternary system with partially miscible (water + 1-butanol) and (water + p-xylene) pairs. By contrast, (1-butanol + p-xylene) is totally miscible under atmospheric conditions. This paper examines the (vapor + liquid) equilibrium in both heterogeneous and homogeneous regions at 101.3 kPa of pressure. (Liquid + liquid) equilibrium data at T = 313.15 K have also been determined, and for comparison, the obtained experimental data have been calculated by means of several thermodynamic models: UNIQUAC, UNIFAC and NRTL. Some discrepancies were found between the (vapor + liquid + liquid) correlations; however, the models reproduced the (liquid + liquid) equilibrium data well. The obtained data reveal a ternary heterogeneous azeotrope with mole fraction composition: 0.686 water, 0.146 1-butanol and 0.168 p-xylene.

New methodology for describing the equilibrium beach profile applied to the Valencia's beaches

Mathematical models used for the understanding of coastal seabed morphology play a key role in beach nourishment projects. These projects have become the fundamental strategy for coastal maintenance during the last few years. Accordingly, the accuracy of these models is vital to optimize the costs of coastal regeneration projects. Planning of such interventions requires methodologies that do not generate uncertainties in their interpretation. A study and comparison of mathematical simulation models of the coastline is carried out in this paper, as well as elements that are part of the model that are a source of uncertainty. The equilibrium profile (EP) and the offshore limit corresponding to the depth of closure (DoC) have been analyzed taking into account different timescale ranges. The results have thus been compared using data sets from three different periods which are identified as present, past and future. Accuracy in data collection for the beach profiles and the definition of the median grain size calculation using collected samples are the two main factors that have been taken into account in this paper. These data can generate high uncertainties and can produce a lack of accuracy in nourishment projects. Together they can generate excessive costs due to possible excess or shortage of sand used for the nourishment. The main goal of this paper is the development of a new methodology to increase the accuracy of the existing equilibrium beach profile models, providing an improvement to the inputs used in such models and in the fitting of the formulae used to obtain seabed shape. This new methodology has been applied and tested on Valencia's beaches.

Isobaric vapor–liquid–liquid–solid equilibrium of the water + NaCl + 1-butanol system at 101.3 kPa

A mixture of water + NaCl + 1-butanol at 101.3 kPa is studied in order to determine the influence of salt on its experimental vapor–liquid–liquid–solid equilibrium. A detailed analysis of the evolution with temperature of the different equilibrium regions is carried out. The study is conducted at a constant pressure of 101.3 kPa in a recirculating still that has been modified by our research group. The changes in the 1-butanol/water composition ratio in the vapor phase that are provoked by the salt are studied as a function of equilibrium region. In addition, the mutual solubility of 1-butanol and water is assessed in the liquid–liquid and solid–liquid regions.

The family Caseidae / [by] Everett C. Olson -- [Edited by Edward G. Nash, Patricia M. Williams]

v.17:no.3(1967)

The non-therapsid reptiles of the Lufeng Basin, Yunnan, China / David Jay Simmons -- [Edited by Edward G. Nash]

v.15:no.1(1965)

Factor Markets in Applied Equilibrium Models: The current state and planned extensions towards an improved presentation of factor markets in agriculture. Factor Markets Working Paper No. 23, February 2012

This paper describes how factor markets are presented in applied equilibrium models and how we plan to improve and to extend the presentation of factor markets in two specific models: MAGNET and ESIM. We do not argue that partial equilibrium models should become more ‘general’ in the sense of integrating all factor markets, but that the shift of agricultural income policies to decoupled payments linked to land in the EU necessitates the inclusion of land markets in policy-relevant modelling tools. To this end, this paper outlines options to integrate land markets in partial equilibrium models. A special feature of general equilibrium models is the inclusion of fully integrated factor markets in the system of equations to describe the functionality of a single country or a group of countries. Thus, this paper focuses on the implementation and improved representation of agricultural factor markets (land, labour and capital) in computable general equilibrium (CGE) models. This paper outlines the presentation of factor markets with an overview of currently applied CGE models and describes selected options to improve and extend the current factor market modelling in the MAGNET model, which also uses the results and empirical findings of our partners in this FP project.

Labour Supply Curves for EU Member and Candidate States: An applied general equilibrium analysis. Factor Markets Working Paper No. 26, June 2012

This paper introduces a more sophisticated modelling of the labour market functioning of the European member and candidate states through the introduction of labour supply curves in an applied general equilibrium model. A labour supply curve offers a middle way in labour supply modelling, sitting between the two commonly adopted extremes of spare capacity and full employment. The first part of the paper outlines the theoretical foundation of the labour supply curve. Real world data is then used to derive labour supply curves for each member state, along with Croatia and Turkey. Finally, the impact of the newly specified labour markets on the results of an illustrative scenario involving reform of the common agricultural policy is explored. The results of computable general equilibrium analysis with the labour supply curve confirm the theoretical expectation that modelling the labour supply through an upwards-sloping curve produces results that lie between the extremes of spare capacity of the labour factor and fully employed labour. This specification captures a greater degree of heterogeneity in the labour markets of the member and candidate states, allowing for a more nuanced modelling of the effects of policy reform, including welfare effects.

Factor Markets in General Computable Equilibrium Models. Factor Markets Working Document No. 47, May 2013

One objective of Computable general equilibrium (CGE) models is the analysis of economy-wide effects of policy measures. The focus of the Factor Markets project is to analyse the functioning of factor markets for agriculture in the EU-27, including the Candidate Countries. While agricultural and food markets are fully integrated in a European single market, subject to an EU-wide common policy, the Common Agricultural Policy (CAP), this is not the case for the agricultural factor markets capital, labour and land. There are partly serious differences with regard to member state regulations and institutions affecting land, labour and capital markets. The presentation of this heterogeneity of factor markets amongst EU Member States have been implemented in the CGE models to improve model-based analyses of the CAP and other policy measures affecting agricultural production. This final report comprises the outcome of a systematic extension and improvement of the Modular Applied GeNeral Equilibrium Tool (MAGNET) model starting from an overview of the current state of the art to represent factor markets in CGE models to a description of work on labour, land and capital in MAGNET.