Activity Coefficient Approach Research Articles

Application of the PC‐SAFT Equation of State to the Prediction of Vapor Solubility in Semicrystalline Polyethylenes

AbstractThis paper builds on the theoretical framework of the previous articles on the solubility of vapors in semicrystalline polyethylenes produced in the gas phase process. The present article clarifies the theoretical basis for an activity coefficient approach, which results from a constraint on the amorphous phase within semicrystalline polymers. This concept is coupled to an advanced equation of state for use in polyolefin reaction engineering, and presented in a modular way the procedure for computing the requisite thermodynamic quantities. A temperature dependence on polymer crystallinity is also introduced. In the interest of developing a more predictive model for solubility, the model using single pure gas isotherms are parameterized. The results demonstrate the ability to predict single and mixed gas absorption, including new data published herein. The validity of the model is further demonstrated through comparisons with literature studies on batch scale ethylene polymerization. Finally, how a simple correlation to standard polymer characteristics yields accurate predictions in the absence of measured data for parametrization is demonstrated.

CO2 absorption mechanism in aqueous ternary solutions of alkanolamines: Experimental and thermodynamic modeling approaches

The absorption mechanism of CO2 in an aqueous solution containing three alkanolamines was analyzed experimentally and theoretically. The vapor–liquid equilibrium of a CO2–monoethanolamine (MEA)–diisopropanolamine (DIPA)–2-amino-2-methyl-propanol (AMP)–H2O system was evaluated experimentally over a wide temperature range (323.15–393.15 K) at several MEA:DIPA:AMP:H2O blending ratios (15:10:5:70, 10:10:10:70, 7.5:7.5:15:70, and 5:15:10:70 wt%). The successive substitution method was used to calculate the concentrations of five molecules (CO2, MEA, DIPA, AMP, and H2O) and nine electrolytes (four cations and five anions) in the liquid phase by solving eight equilibrium equations, four mass balance equations, and one charge balance equation. The Deshmukh–Mather model, which is based on an activity coefficient approach, and the fugacity coefficient model were used to evaluate the nonideality of the liquid and vapor phases, respectively. Thereafter, the effect of the MEA:DIPA:AMP blending ratio was evaluated using the triangular diagrams of the carbamate, bicarbonate and carbonate molar fractions in liquid phase, CO2 loading ratio, CO2 cyclic capacity, and heat of CO2 absorption.

Thermodynamic Modeling of Calcium Sulfate Hydrates in a CaSO4-H2SO4-H2O System from 273.15 to 473.15 K up to 5 m Sulfuric Acid.

To prevent scaling and to recycle aqueous solutions in industrial processes, the thermodynamic properties of the CaSO4–H2SO4–H2O system are studied by thermodynamic modeling with the Pitzer model. The published solubility data of calcium sulfate hydrates in sulfuric acid solutions were collected and reviewed critically. Then, the CaSO4–H2SO4–H2O system was modeled using the Pitzer activity coefficient approach from critically selected experimental data to obtain optimized parameters. The model reproduces the solubility data with good accuracy up to 5 m sulfuric acid at temperatures of 283.15–368.15, 283.15–473.15, and 298.15–398.15 K for gypsum (CaSO4·2H2O), anhydrite (CaSO4), and hemihydrate (CaSO4·0.5H2O), respectively. However, at temperatures above 398.15 K and sulfuric acid concentration above 0.5 mol/kg, the solubility of anhydrite predicted by our model deviates significantly from the literature data. Our model predicts that the solubility of anhydrite would first increase but then decrease in more concentrated sulfuric acid solutions, which is in disagreement with the experimental data showing constantly increasing solubilities as a function of increasing sulfuric acid concentration. This discrepancy has been discussed. The transformations of gypsum to anhydrite and hemihydrate were predicted in sulfuric acid solutions. With increasing H2SO4 concentration, the transformation temperatures of gypsum to anhydrite and hemihydrate will decrease. Thus, gypsum is stable at low temperatures in solutions of low H2SO4 concentrations and transforms to anhydrite at high temperatures and in concentrated H2SO4 solutions, while hemihydrate is always a metastable phase. Furthermore, the predicted results were compared with previous experimental studies to verify the accuracy of the model.

Extending the Modified Regular Solution Model To Predict Component Partitioning to the Asphaltene-Rich Phase

The modified regular solution (MRS) model is an activity coefficient approach previously developed to predict the onset and amount of asphaltene precipitation from n-paraffin-diluted crude oils. Th...

A method for characterization of bitumen

Characterization of bitumen is a necessary step to perform phase equilibrium computations involved in bitumen production and processing. This study presents a methodology for bitumen characterization using a residue curve map. A fugacity–activity coefficient approach is applied to model the thermodynamic equilibrium of the species in the gas and liquid phases. The Peng–Robinson equation of state (PR-EoS) and NRTL activity model are utilized to calculate the fugacity and activity coefficients in the gas and liquid phases, respectively. The proposed model was evaluated using experimental simulated distillation (SD) data as well as experimental solubility data of light hydrocarbon (CH4, C2H6) and non-hydrocarbon gases (CO2, N2) in bitumen. The molecular weight, specific gravity, and SD curves were represented using defined pseudo-components. The tuned EoS was able to regenerate the solubility data with an acceptable accuracy (AARD less than 5.6% and 4.5% for hydrocarbon and non-hydrocarbon solvents, respectively). The proposed method can be applied for bitumen characterization and to predict the solubility of the light gases in bitumen.

Series approach to modeling of amino acid and electrolyte mixtures in the aqueous media

In this work, the electrolyte, amino acid and water solutions are modeled using activity coefficient (AC) approach. Two different models, modified Pitzer ion interaction equation proposed by Esteso (PE) and the Pitzer–Simonson–Clegg model (PSC) are used in their original and modified forms to correlate the activity coefficient and osmotic coefficient data for binary and ternary systems containing water, amino acid/peptide and electrolytes. The considered aqueous systems contain one of the eight amino acids: alanine, glycine, serine, threonine, β-alanine, methionine, α-amino n-butyric acid and α-amino butyric acid. Also, glycylglycine is used as one peptide. The salts are NaCl, NaBr, NaNO3, KCl and KBr.The results obtained from the studied models are compared to those of experimental data. The comparison shows that the PE model can correlate the experimental AC data of ternary systems more accurate than the other PSC. The equations are tested against the large number (30) of available experimental data sets.

Thermodynamic modelling of aqueous Mn(II) sulfate solutions

The H2O–MnSO4 system has been modelled using the Pitzer activity coefficient approach over a temperature interval of −11–175°C and in concentrations from pure water to the solubility limit of manganese sulfate hydrates, the maximum MnSO4 molality being 4.26mol/kg at the MnSO4·5H2O(s) to MnSO4·H2O(s) transition temperature of 23.9°C. The thermodynamic properties of MnSO4 hydrates were refined. The model in this work presents all the experimental data available, including the solubilities, mean activity coefficients, activities of water, enthalpy and heat capacity of solution and hydrate dissociation pressure, with good accuracy and consistently up to 175°C, but the model has limitations at higher than 100°C due to lack of experimental data.

Thermodynamic modelling of aqueous Fe(II) sulfate solutions

The H2O–FeSO4 system has been modelled using the Pitzer activity coefficient approach over a temperature interval of −2–220 °C and in concentrations from pure water to the solubility limit of ferrous sulfate hydrates, the maximum FeSO4 molality being 3.58 mol/kg at the FeSO4⋅7H2O(s) to FeSO4⋅H2O(s) transition temperature of 56.5 °C. The thermodynamic properties of FeSO4 hydrates were refined and FeSO4⋅4H2O(s) was found to be a metastable phase in the whole temperature range. The model in this work presents all the experimental data available, including the solubilities, mean activity coefficients, activities of water, enthalpy and heat capacity of solution, and hydrate dissociation pressure, with good accuracy and consistently up to 220 °C, but the model has limitations at temperatures higher than 100 °C due to lack of experimental data.

Liquid−Liquid and Solid−Liquid Equilibria in Systems Containing n-Eicosane, n-Tetracosane, Ethanol, and Water

The partitioning of n-eicosane (C20) and n-tetracosane (C24) between a melt phase (L1) and an aqueous ethanol phase (L2) at 333.2 K, and between a solid phase (S) and an aqueous ethanol phase (L) at 293.2 K was measured. The wax content of aqueous ethanol solutions was greater when the solutions were in equilibrium with a melt wax phase (liquid−liquid equilibrium) than when they were in equilibrium with a solid wax phase (solid−liquid equilibrium). The distribution coefficients of C20 and C24 between the aqueous phase and a wax phase were also significantly higher in the case of liquid−liquid equilibrium than in the case of solid−liquid equilibrium. The data could be modeled satisfactorily using simple thermodynamic expressions based on the UNIFAC activity coefficient approach.

A simplified CEOS/ AE mixing rule and its applications for vapor–liquid and liquid–liquid equilibrium predictions

The new CEOS/ A E mixing rule recently developed by Twu et al. [Fluid Phase Equilib. 158–160 (1999) 271] is simplified and tested for high-pressure vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE) predictions. This mixing rule has some significant features such as: (1) it is density dependent, (2) it is based on no reference-pressure, and (3) it automatically reduces to van der Waals mixing rule for normal mixtures. The mixing rule is used with any G E activity coefficient model such as NRTL, UNIQUAC, and UNIFAC. This approach can employ the available binary interaction parameters from those activity coefficient models without requiring any additional parameters or causing any thermodynamic inconsistency. It extends the predictive capability of the cubic type equation of state (CEOS) to highly nonideal mixtures, which have traditionally been handled using an activity coefficient approach. This work has tested various binary VLE/LLE systems including nonpolar, polar, and associating compounds. Overall, the accuracy of the mixing rule with a CEOS (with a modified alpha-function for each component) is comparable with that of the activity coefficient approach. For LLE, the mixing rule can predict the three different types of phase diagrams (with UCST, LCST, or both). This work also shows that the CEOS/ A E mixing rule can be applied to high-pressure systems for which the activity coefficient models have limited success.

Temperature and evaporation dynamics of saline solutions

An analytic procedure is presented to investigate the response of temperature in and evaporation from saline solutions whose activity coefficients are subject to dynamic changes. The temperature change ( γ) with respect to changes in the activity coefficient is found to be a strong function of the saturation vapor pressure at the temperature of the saline solution and the transfer coefficients for water vapor and sensible heat. Results show that γ increases appreciably as the activity coefficient ( β) departs further from unity. As the activity coefficient approaches unity, γ becomes quite small particularly when both the saline solution temperature and the transfer coefficients decrease. For a given change in the activity coefficient, the largest temperature response is experienced during the summer months. The procedure developed in this paper is applied to the current chemical composition of the Dead Sea to examine the sensitivities of its temperature and evaporation rate due to the alteration of its activity coefficient during the past 40 years. Results show that currently evaporation from the Dead Sea ( β≈0.67) is about 175 mm year −1 less than the values prior to 1960 ( β≈0.75).

A fluorescence spectroscopy study of the interaction of monocationic quinine with phospholipid vesicles Effect of the ionic strength and lipid composition

The interaction of monocationic quinine with zwitterionic dimyristoyl phosphatidylcholine (DMPC) and mixed negatively-charged dimyristoylphosphatidyl glycerol (DMPG) DMPC small unilamellar vesicles in the liquid-crystalline phase was investigated by steady-state fluorescence spectroscopy at pH 7 and 37°C. The maximum fluorescence emission peak at 383 nm, upon excitation at 335 nm, shifts to lower wavelength and decreases its intensity as the ratio between the total lipid and quinine concentrations increases. This indicates that in the membrane-bound state quinine is in an environment of low polarity, more deeply buried when anionic DMPG is present in the vesicle. For monoprotonated quinine/DMPC system the corresponding association isotherms show that the extension of binding is slightly enhanced as the ionic strength decreases, whereas for mixed DMPG DMPC vesicles at low ionic strength, the association of the drug is favoured as the percentage of anionic DMPG increases. The binding curves have been quantitatively analyzed by the binding and the partition models including in this latter an activity coefficient, γ, to account for non ideal quinine interactions. It is demonstrated for both neutral and anionic membranes that the activity coefficient approaches the unity and that the deviation from ideality is mainly due to electrostatic forces.

The activity coefficient at extremely low concentrations

It is suggested that the activity coefficient of a component approaches unity only in the range of reasonably high dilutions; at extremely low concentration the activity coefficient approaches zero with dilution.

Study of ternary liquid—liquid equilibria and of multiphase equilibria

In this study, we have calculated LLE and LLVE in ternary systems, using the PT equation of state with the mixing rules of Kurihara et al. Only two interaction parameters per binary system are used to correlate VLE and LLE data simultaneously and the results appear to be comparable with the activity coefficient approach using the same number of adjustable parameters. A wide range of systems has been studied. The multiphase P—T diagram for the system H 2SCO 2CH 4 is also plotted and compared with the experimental data.

A new mixing rule for the Patel-Teja equation of state. study of vapor-liquid equilibria

The Patel-Teja equation of state (PT EOS), coupled with the new mixing rule for the energy parameter ( a) developed by Kurihara et al. (1987), has been successfully applied to vapor-liquid equilibrium (VLE) calculations for strongly non-ideal mixtures. Three excess Gibbs energy ( g E) models—Wilson, NRTL and UNIQUAC—were used to represent the residual part of excess Gibbs energy at infinite pressure ( g E∞) in the new mixing rule. The UNIQUAC model is recommended. Fourteen sets of low pressure and eight sets of high pressure binary/ternary VLE data were examined. For low pressure VLE calculations, comparable results were obtained using the activity coefficient approach, the EOS density dependent local composition mixing rule approach, and the proposed new model. The chief advantages of the new model lie in its applicability to high pressure VLE calculations, its improved liquid density predictions, its capacity to describe liquid-liquid equilibria, and its retention of the simple cubic EOS form.

An acidity scale, [H+]hv, for proton quenching of excited states in aqueous perchloric acid

An acidity scale for excited state protonation kinetics in aqueous perchloric acid has been developed using 1-cyanonaph-thalene as a fluorescent indicator. A comparison of the quenching rate constants obtained using this scale is made with both the more general excess acidity function, X, and the transition state activity coefficient approach. A variety of chromophores were studied including 1- and 2-cyanonaphthalenes, 1- and 2-methoxynaphthalenes, benzyl alcohols, toluenes, benzonitriles, and 2-vinylnaphthalene. Keywords: acidity scale, proton fluorescence quenching.

Phase equilibria in natural gas, crude oil and coal liquid mixtures

The phase behavior of undefined and complex fluid mixtures has been investigated using the methods of continuous thermodynamics. In particular, an equation of state model using the boiling point and specific gravity as two continuously distributed characterization variables has been developed for high pressure phase equilibrium calculations. Dew points and phase densities of natural gas condensates, crude oils and coal liquids were predicted with excellent results. The results were compared with those obtained using a semi-continuous activity coefficient approach based on the regular solution theory.

The kinetics and mechanism of acid catalysed hydrolysis of lactams

The acid-catalysed hydrolysis of lactams of ring size 4–7, and of N-ethylacetamide, has been studied at various temperatures in 0–70% aqueous sulfuric acids. The kinetics have been analysed by means of the r-hydration parameter treatment and the transition-state activity coefficient (TSAC) approach. Except for the β-lactam, all substrates show a strong positive rate dependence on water activity, indicating a tetrahedral intermediate type of mechanism [Formula: see text], similar to that found for simple (acyclic) amide hydrolyses; only the β-lactam shows a negative rate – water activity dependence, which is interpreted in terms of a unimolecular [Formula: see text] mechanism, involving rate-determining acylium ion formation. Similarly, all substrates except the β-lactam show a pronounced destabilization of the transition-state as acidity is increased, typical of oxonium ion species. The behaviour of the β-lactam resembles that of methyl mesitoate hydrolysis. Basicity constants for lactams of ring size 4–9 show a definite dependence on ring size, with the δ-lactam being unusually basic. Both rate and pK dependence on ring size are discussed in terms of ring strain and steric effects. The activation parameters, particularly ΔS≠, are fully consistent with the conclusions drawn concerning transition-state hydration.

Oxygen exchange in methanol in acid solutions. Transition state activity coefficients

Rate constants for oxygen exchange of methanol in sulfuric acid and perchloric acid solutions are reported, along with activity coefficients of methanol in sulfuric acid. Transition state activity coefficients (f≠*) for methanol exchange and tert-butanol exchange have been calculated. Values of f≠* for the latter behave very similarly to those for tert-butyl acetate hydrolysis, consistent with a carbonium ion-like transition state. Values for methanol exchange show considerably more salting-out, consistent with an oxonium ion-like transition state. A significant difference with the AAc2 hydrolyses of esters and amides is noted. For the latter the transition state is salted-out relative to its protonated precursor, whereas for methanol exchange, there is little difference between the activity coefficient of the protonated alcohol and the transition state, with the latter actually being somewhat salted-in. It is pointed out that the transition state activity coefficient approach can be rigorously applied even in the absence of protonation data.

On the Rational Description of Mixtures

AbstractThe rational activity of a solute becomes equal to the mole fraction of the solute as the mixture becomes infinitely dilute. Simultaneously, the corresponding rational activity coefficient approaches unity. A rational description of a mixture is such that the activity coefficient of each solute component is rational. It is shown for a binary mixture that a description is rational if and only if the solvent osmotic coefficient approaches unity as the solvent mole fraction approaches unity. When the description is not rational, the limiting value of the osmotic coefficient is the van't Hoff number. For multicomponent mixtures, the limiting behavior of the osmotic coefficient is related to the composite extent of association and/or dissociation of all the solutes. It is further shown how the extent of aggregation of individual solutes at infinite dilution can be determined from the limiting behavior of individual activity coefficients.