Vapour-liquid equilibrium studies at atmospheric to moderate pressures

A study of vapour-liquid equilibria is presented together with current developments. The theory of vapour-liquid equilibria is discussed. Both experimental and prediction methods for obtaining vapour-liquid equilibria data are critically reviewed. The development of a new family of equilibrium stills to measure experimental VLE data from sub-atmosphere to 35 bar pressure is described. Existing experimental techniques are reviewed, to highlight the needs for these new apparati and their major attributes. Details are provided of how apparatus may be further improved and how computer control may be implemented. To provide a rigorous test of the apparatus the stills have been commissioned using acetic acid-water mixture at one atmosphere pressure. A Barker-type consistency test computer program, which allows for association in both phases has been applied to the data generated and clearly shows that the stills produce data of a very high quality. Two high quality data sets, for the mixture acetone-chloroform, have been generated at one atmosphere and 64.3oC. These data are used to investigate the ability of the new novel technique, based on molecular parameters, to predict VLE data for highly polar mixtures. Eight, vapour-liquid equilibrium data sets have been produced for the cyclohexane-ethanol mixture at one atmosphere, 2, 4, 6, 8 and 11 bar, 90.9oC and 132.8oC. These data sets have been tested for thermodynamic consistency using a Barker-type fitting package and shown to be of high quality. The data have been used to investigate the dependence of UNIQUAC parameters with temperature. The data have in addition been used to compare directly the performance of the predictive methods - Original UNIFAC, a modified version of UNIFAC, and the new novel technique, based on molecular parameters developed from generalised London's potential (GLP) theory.

Models of gas-liquid solubilities

A recent method for phase equilibria, the AGAPE method, has been used to predict activity coefficients and excess Gibbs energy for binary mixtures with good accuracy. The theory, based on a generalised London potential (GLP), accounts for intermolecular attractive forces. Unlike existing prediction methods, for example UNIFAC, the AGAPE method uses only information derived from accessible experimental data and molecular information for pure components. Presently, the AGAPE method has some limitations, namely that the mixtures must consist of small, non-polar compounds with no hydrogen bonding, at low moderate pressures and at conditions below the critical conditions of the components. Distinction between vapour-liquid equilibria and gas-liquid solubility is rather arbitrary and it seems reasonable to extend these ideas to solubility. The AGAPE model uses a molecular lattice-based mixing rule. By judicious use of computer programs a methodology was created to examine a body of experimental gas-liquid solubility data for gases such as carbon dioxide, propane, n-butane or sulphur hexafluoride which all have critical temperatures a little above 298 K dissolved in benzene, cyclo-hexane and methanol. Within this methodology the value of the GLP as an ab initio combining rule for such solutes in very dilute solutions in a variety of liquids has been tested. Using the GLP as a mixing rule involves the computation of rotationally averaged interactions between the constituent atoms, and new calculations have had to be made to discover the magnitude of the unlike pair interactions. These numbers have been seen as significant in their own right in the context of the behaviour of infinitely-dilute solutions. A method for extending this treatment to "permanent" gases has also been developed. The findings from the GLP method and from the more general AGAPE approach have been examined in the context of other models for gas-liquid solubility, both "classical" and contemporary, in particular those derived from equations-of-state methods and from reference solvent methods.

BTX extraction by sulfolane in a mixer-settler cascade

The literature relating to the extraction of the aromatics, benzene, toluene and xylene (BTX) using different commercial solvents, and to mixer-settler design and performance, has been reviewed. Liquid-liquid equilibria of the ternary systems: hexane-benzene-sulfolane, n-heptane-toluene-sulfolane, and octane-xylene-sulfolane were determined experimentally at temperatures of 30oC, 35oC, and 40oC. The work was then extended to a multicomponent system. The data were correlated by using Hand's method and were found to be in a good agreement with theoretical predictions using the UNIFAC method. A study was made of the performance of a 10-stage laboratory mixer-settler cascade for the extraction of BTX from a synthetic reformate utilizing sulfolane as a solvent. Murphree stage efficiency decreased with stage number but 99% extraction was achievable within 4 stages. The effects of temperature, phase ratio, and agitator speed were investigated. The efficiency increased with agitator speed but > 1050 rpm resulted in secondary haze formation. An optimum temperature of 30oC was selected from the phase equilibria; the optimum solvent: feed ratio was 3:1 for 4 stages. The experimental overall mass transfer coefficients were compared with those predicted from single drop correlations and were in all cases greater, by a factor of 1.5 to 3, due to the surface renewal associated with drop break-up and coalescence promoted by agitation. A similar investigation was performed using real reformate from the Kuwait Oil Company. The phase ratios were in the range 0.5 to 1 to 3.25 to 1, the agitator speed 1050 rpm, and the operating temperature 30oC. A maximum recovery of 99% aromatics was achieved in 4 stages at a phase ratio of 3.25 to 1. A backflow model was extended to simulate conditions in the mixer-settler cascade with this multicomponent system. Overall mass transfer coefficients were estimated by obtaining the best fit between experimental and predicted concentration profiles. They were up to 10% greater than those with the synthetic feed but close agreement was not possible because the distribution coefficient and phase ratio varied with stage number. Sulfolane was demonstrated to be an excellent solvent for BTX recovery and a mixer-settler cascade was concluded to be a technically viable alternative to agitated columns for this process.

Phase equilibrium studies at moderate pressures

The theory of vapour-liquid equilibria is reviewed, as is the present status or prediction methods in this field. After discussion of the experimental methods available, development of a recirculating equilibrium still based on a previously successful design (the modified Raal, Code and Best still of O'Donnell and Jenkins) is described. This novel still is designed to work at pressures up to 35 bar and for the measurement of both isothermal and isobaric vapour-liquid equilibrium data. The equilibrium still was first commissioned by measuring the saturated vapour pressures of pure ethanol and cyclohexane in the temperature range 77-124°C and 80-142°C respectively. The data obtained were compared with available literature experimental values and with values derived from an extended form of the Antoine equation for which parameters were given in the literature. Commissioning continued with the study of the phase behaviour of mixtures of the two pure components as such mixtures are strongly non-ideal, showing azeotopic behaviour. Existing data did not exist above one atmosphere pressure. Isothermal measurements were made at 83.29°C and 106.54°C, whilst isobaric measurements were made at pressures of 1 bar, 3 bar and 5 bar respectively. The experimental vapour-liquid equilibrium data obtained are assessed by a standard literature method incorporating a themodynamic consistency test that minimises the errors in all the measured variables. This assessment showed that reasonable x-P-T data-sets had been measured, from which y-values could be deduced, but that the experimental y-values indicated the need for improvements in the design of the still. The final discussion sets out the improvements required and outlines how they might be attained.

Development of an enantiomer selective microsampling assay for the quantification of ketorolac suitable for paediatric pharmacokinetic studies

Background: Ketorolac, a potent nonsteroidal anti-inflammatory drug used for pain control in children, exists as a racemate of inactive R (+) and active S (-) enantiomers. Aim: To develop a microsampling assay for the enantioselective analysis of ketorolac in children. Methods: Ketorolac enantiomers were extracted from 50 µl of plasma by liquid–liquid extraction and separated on a ChiralPak AD-RH. Detection was by a TSQ quantum triple quadrupole mass spectrometer with an electrospray ionisation source operating in a positive ion mode. Five children (age 13.8 (1.6) years, weight 52.7 (7.2) kg), were administered intravenous ketorolac 0.5 mg/kg (maximum 10 mg) and blood samples were taken at 0, 0.25, 0.5, 1, 2, 4, 6, 8 and 12 h post administration. CL, VD and t1/2 were calculated based on non-compartmental methods. Results: The standard curves for R (+) and S (-) ketorolac were linear in the range 0–2000 ng/ml. The LLOQs of the method were 0.15 ng on column and 0.31 ng on column for R (+) and S (-) ketorolac, respectively. The median (range) VD and CL of R (+) and S (-) ketorolac were 0.12 l/kg (0.07–0.17), 0.017 l/h/kg (0.12–0.29) and 0.17 (0.09–0.31) l/kg, 0.049 (0.02–0.1) l/h/kg, p = 0.043), respectively. The median (range) elimination half-life (t1/2) of the R (+) and S (-) ketorolac was 5.0 h (2.5–5.8) and 3.1 h (1.8–4.4), p = 0.043), respectively. Conclusion: The development of a simple, rapid and reliable ketorolac assay suitable for paediatric PK studies is reported. Copyright © 2013 John Wiley & Sons, Ltd.

Elemental partitioning and microstructural development in duplex stainless steel weld metal

A thermodynamic analysis which is capable of estimating the austenite/ferrite equilibria in duplex stainless steels has been carried out using the sublattice thermodynamic model. The partitioning of alloying elements between the austenite and ferrite phases has been calculated as a function of temperature. The results showed that chromium partitioning was not influenced significantly by the temperature. The molybdenum, on the other hand, was found to partition preferentially into ferrite phase as the temperature decreases. A strong partitioning of nickel into the austenite was observed to decrease gradually with increasing temperature. Among the alloying elements, average nitrogen concentration was found to have the most profound effect on the phase balance and the partitioning of nitrogen into the austenite. The partitioning coefficient of nitrogen (the ratio of the mole fraction of nitrogen in the austenite to that in the ferrite) was found to be as high as 7.0 around 1300 K. Consequently, the volume fraction of austenite was influenced by relatively small additions of nitrogen. The results are compared with the experimentally observed data in a duplex stainless steel weld metal in conjunction with the solid state δ → δ + γ phase transformation. Particular attention was given to the morphological instability of grain boundary austenite allotriomorphs. A compariso between the experimental results and calculations indicated that the instability associated with irregular austenite perturbations results from the high degree of undercooling. The results suggest that the model can be used successfully to understand the development of the microstructure in duplex stainless steel weld metals.

PPD v1.0 - an integrated, web-accessible database of experimentally determined protein pKa values

The Protein pKa Database (PPD) v1.0 provides a compendium of protein residue-specific ionization equilibria (pKa values), as collated from the primary literature, in the form of a web-accessible postgreSQL relational database. Ionizable residues play key roles in the molecular mechanisms that underlie many biological phenomena, including protein folding and enzyme catalysis. The PPD serves as a general protein pKa archive and as a source of data that allows for the development and improvement of pKa prediction systems. The database is accessed through an HTML interface, which offers two fast, efficient search methods: an amino acid-based query and a Basic Local Alignment Search Tool search. Entries also give details of experimental techniques and links to other key databases, such as National Center for Biotechnology Information and the Protein Data Bank, providing the user with considerable background information.

A Countable Economy: An Example

Weiss (1981) established core equivalence and the existence of competitive equilibria in finitely additive exchange economies. To underline the relevance of finitely additive economies we present in this note an example with a close connection to finite exchange economies.

Price vs. quantity in oligopoly games

Price-setting and quantity-setting oligopoly games lead to extremely dierent outcomes in the market. One natural way to address this problem is to formulate a model in which some rms use price while the remaining rms use quantity as their decision variable. We introduce a mixed oligopoly game of this type and determine its equilibria. In addition, we consider an extension of this mixed oligopoly game through which the choice of the decision variables can be endogenized. We prove the emergence of the Cournot game.

A generalization of correlated equilibrium: A new protocol

A new correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is introduced for finite games. After randomization over the outcome space, players have the choice either to follow the recommendation of an umpire blindly or freely choose some other action except the one suggested. This scheme can lead to Pareto-better outcomes than the simple extension introduced by [Moulin, H., Vial, J.-P., 1978. Strategically zero-sum games: the class of games whose completely mixed equilibria cannot be improved upon. International Journal of Game Theory 7, 201–221]. The informational and interpretational aspects of soft correlated equilibria are also discussed in detail. The power of the generalization is illustrated in the prisoners’s dilemma and a congestion game.

Generalized correlated equilibrium for two-person games in extensive form with perfect information

A correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is applied for two-person finite games in extensive form with perfect information. Randomization by an umpire takes place over the leaves of the game tree. At every decision point players have the choice either to follow the recommendation of the umpire blindly or freely choose any other action except the one suggested. This scheme can lead to Pareto-improved outcomes of other correlated equilibria. Computational issues of maximizing a linear function over the set of soft correlated equilibria are considered and a linear-time algorithm in terms of the number of edges in the game tree is given for a special procedure called “subgame perfect optimization”.

A vállalati likviditáskezelés szerepe eszközfedezettel rendelkező hitelszerződésekben. Az alkun alapuló megközelítés eredményei (The role of corporate liquidity management under secured debt financing Results of the bargaining approach)

A szerző azt a kérdést vizsgálja, hogy a vállalat működése során a likvid eszközök mekkora arányát tartsa fenn. A kérdést a finanszírozás szemszögéből veti fel, mivel a hitelezés okozta korlátok jelentősen befolyásolják a likvid eszköz tartalékolásának motivációit. A cikk a vállalkozói-hitelezői információs kapcsolat háromféle esetében mutatja be az eszközfedezettel rendelkező hitelek adósságszolgálatát meghatározó tényezőket. Elsőként a teljes információs viszony melletti stratégiákkal meghatározott adósságszolgálatot vizsgálja, majd a második típusú információs kapcsolatban a nem megfigyelhető vállalkozói erőfeszítéseket feltételezve adja meg az adósságszolgálat fizetésének ex ante és ex post egyensúlyát. Harmadikként, a nem igazolható vállalati adatok feltevése mellett teljes és részleges eszközfedezetre is meghatározza az optimális vállalkozói likviditási politikát, és tárgyalja az itt fennálló ellentéteket. Megmutatja, hogy részleges eszközfedezet mellett 1. újratárgyalható a hitelszerződés, és a stratégiai adósságszolgálatot nem lehet elkerülni, 2. a likviditásoptimalizálásnak nincs ex post Pareto-egyensúlyi megoldása, ugyanis a hitelszerződésben részt vevő felek alkuereje határozza meg a vállalat likviditásának szintjét. / === / This paper investigates what the liquid asset ratio for firms should be. Financing constraints significantly influence motivations for liquidity hoarding. The article shows the determinants of secured debt services for three different information cases of a lender-borrower relationship. First, it examines the strategic debt service under full information, and then, assuming non-observable entrepreneurial efforts, it gives the ex ante and ex post equilibria of the strategic debt service. The third case supposes non-verifiable firm information; this provides the optimal corporate liquidity policy and explains the contrary propositions. It shows that under not fully secured collateral, 1. the debt contract is renegotiable; the lender cannot avoid the strategic debt service, 2. there is no ex post optimal Pareto efficient solution to liquidity policy, because the corporate liquidity ratio is determined by the bargaining power of the partners in the debt contract.

Invariance under type morphisms: the bayesian Nash equilibrium

Ely and Peski (2006) and Friedenberg and Meier (2010) provide examples when changing the type space behind a game, taking a "bigger" type space, induces changes of Bayesian Nash Equilibria, in other words, the Bayesian Nash Equilibrium is not invariant under type morphisms. In this paper we introduce the notion of strong type morphism. Strong type morphisms are stronger than ordinary and conditional type morphisms (Ely and Peski, 2006), and we show that Bayesian Nash Equilibria are not invariant under strong type morphisms either. We present our results in a very simple, finite setting, and conclude that there is no chance to get reasonable assumptions for Bayesian Nash Equilibria to be invariant under any kind of reasonable type morphisms.

Non-uniqueness through duality in the von Neumann growth models

Duality can be viewed as the soul of each von Neumann growth model. This is not at all surprising because von Neumann (1955), a mathematical genius, extensively studied quantum mechanics which involves a “dual nature” (electromagnetic waves and discrete corpuscules or light quanta). This may have had some influence on developing his own economic duality concept. The main object of this paper is to restore the spirit of economic duality in the investigations of the multiple von Neumann equilibria. By means of the (ir)reducibility taxonomy in Móczár (1995) the author transforms the primal canonical decomposition given by Bromek (1974) in the von Neumann growth model into the synergistic primal and dual canonical decomposition. This enables us to obtain all the information about the steadily maintainable states of growth sustained by the compatible price-constellations at each distinct expansion factor.

Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies

We determine the endogenous order of moves in which the firms set their prices in the framework of a capacity-constrained Bertrand-Edgeworth triopoly. A three-period timing game that determines the period in which the firms announce their prices precedes the price-setting stage. We show for the non-trivial case (in which the Bertrand-Edgeworth triopoly has only an equilibrium in non-degenerated mixed-strategies) that the firm with the largest capacity sets its price first, while the two other firms set their prices later. Our result extends a finding by Deneckere and Kovenock (1992) from duopolies to triopolies. This extension was made possible by Hirata's (2009) recent advancements on the mixed-strategy equilibria of Bertrand-Edgeworth games.