Solvation and chemical engineering thermodynamics

With the continued advances in computational chemistry, solvation calculation from first principle methods is becoming a promising route for phase equilibrium modeling. However, except in a few instances, such an approach has not been widely adopted, which may be a consequence of the abstractness of solvation itself and also of the lack of a simple bridge between solvation and other thermodynamic properties. Here, we establish and summarize the relationship between solvation and other properties frequently used in phase equilibrium modeling. An important quantity, called the total solvation free energy, is introduced so that one can easily derive engineering thermodynamic models (such as an equation of state) from solvation models, or vice versa. The equations presented here are of general validity and would be useful for obtaining existing model parameters from solvation calculations and for developing new models stemming from the ideas of molecular solvation.     

Unified equation of state based on the lattice fluid theory for phase equilibria of complex mixtures part II. Application to complex mixtures

In part I of the present article [Yoo et al., 1995], new rigorous and simplified lattice-fluid equations of state (EOS) were derived and their characteristic features of the molecular thermodynamic foundation were discussed by applying to pure fluids. In this part II, both EOSs were extended to various phase equilibrium properties of mixtures. Comparison of the models with experimental mixture data ranges from density, to equilibria of vaporliquid, vapor-solid and liquid-liquid phases for nonpolar/nonpolar, nonpolar/polar, polar/polar mixtures. Both models were also applied to supercritical fluid phase equilibria and activities of solvents in polymer solutions. With two temperature dependent parameters for pure compounds and one temperature-independent binary interaction energy parameter for a binary mixtures, results obtained to date illustrated that both EOSs are quantitatively applicable to versatile phase equilibria of mixtures over a wide range of temperatures, pressures and compositions.     

Limits in the evaluation of closely spaced chemical relaxation processes

Earlier studies on fundamental errors in the evaluation of chemical relaxation parameters from curves of closely spaced relaxation processes are reinvestigated with rigorous mathematical tools. Very precise data referring to two neighboring relaxation processes are produced by non-linear equations and subsequently evaluated by non-linear least squares analysis, assuming two exponential terms. Previously, linear equations were used in the generation of precise data and then evaluated by graphical means. Relaxation processes are evaluated with ratios of two consecutive relaxation times of up to 2/3. The enzyme catalyzed isomerization is used as underlying chemical mechanism with most thermodynamic parameters fixed. The analyses showed that derived signal amplitudes should be used with great care, if relaxation times exceed ratios of around 1/10. If these amplitudes have the same sign, the relaxation times are generally quite precise, as long as the overall amplitudes are sufficiently large. If amplitudes become comparatively small in selected regions, evaluated amplitudes may deviate considerably from computed (theoretical) ones. The experimentalist has to be aware of this problem even if high signal-to-noise ratios are maintained (S/N ? 1000).     

Equation of state model for metals with ionization effectively taken into account. Equation of state of tantalum, tungsten, aluminum, and beryllium

A model of a wide-range semi-empirical equation of state for metals is presented. The specific heat and Grüneisen coefficients of ions and electrons are functions of temperature and density. At low temperatures, the heat capacity varies according to Debye theory. The removal of the degeneration of the electron gas with increasing temperature is taken into account. The effect of ionization on the thermodynamic functions is effectively taken into account. The equation of state allows the calculation of states in a two-phase liquid-vapor region. This model was used to develop the equations of state for Ta, W, Al, and Be. For its range of applicability, the equation of state contains a relatively small number of free parameters, most of which have a physical meaning. Comparison of calculations of various isolines using equations of state with experimental data and calculations based on other models show that the equations of state for Ta, W, Al, and Be, describe most experimental data for these substances. At ultrahigh pressures and temperatures, calculations using the equations of state are in good agreement with calculations using the Thomas-Fermi model with corrections.     

An evaluation of the thermodynamic properties and the P,T phase diagram of carbon

A new evaluation of the thermodynamic properties of carbon has been made. A set of parameter values describing the Gibbs energy of each individual phase as a function of temperature and pressure is given. The experimental information on the P, T phase diagram and the thermodynamical data are compared with calculations made using the presented set of parameters. The experimental information is well reproduced.     

Energetics of protein thermodynamic cooperativity: contributions of local and nonlocal interactions

The respective roles of local and nonlocal interactions in the thermodynamic cooperativity of proteins are investigated using continuum (off-lattice) native-centric Gō-like models with a coarse-grained C_α chain representation. We study a series of models in which the (local) bond- and torsion-angle terms have different strengths relative to the (nonlocal) pairwise contact energy terms. Conformational distributions in these models are sampled by Langevin dynamics. Thermodynamic cooperativity is characterized by the experimental criteria requiring the van't Hoff to calorimetric enthalpy ratio ΔH_vH/ΔH_cal≈1 (the calorimetric criterion), as well as a two-state-like variation of the average radius of gyration upon denaturation. We find that both local and nonlocal interactions are critical for thermodynamic cooperativity. Chain models with either much weakened local conformational propensities or much weakened favorable nonlocal interactions are significantly less cooperative than chain models with both strong local propensities and strong favorable nonlocal interactions. These findings are compared with results from a recently proposed lattice model with a local-nonlocal coupling mechanism; their relationship with experimental measurements of protein cooperativity and chain compactness is discussed.     

Crossover Equation of State for Selected Hydrocarbons (C4–C7)

The organic Rankine cycle (ORC) has attracted attention for waste heat recovery and renewable energy systems. An accurate prediction for thermodynamic properties of working fluids is of great importance for cycle performance evaluations and system design. Particularly, hydrocarbons are promising for their good performance and low global warming potentials. Moreover, the thermal efficiency of the ORC is higher when the evaporation temperature is closer to the critical temperature, which makes the properties in the critical region rather important. Recent research has shown that using mixture as working fluid can achieve better temperature matches. Therefore, an equation of state (EoS) that can be extended to mixture calculations is more attractive. Specific EoS for selected hydrocarbons is precise, but very complex. Cubic EoSs, such as widely used Peng–Robinson EoS and Soave–Redlich–Kwong (SRK) EoS, fail to accurately predict liquid densities over wide pressure ranges or pressure–density–temperature (pρT) properties in the near-critical region. This work combines the volume translation approach and the crossover method to provide better prediction for thermodynamic properties in the critical region and in regions far from the critical point. A crossover volume translation SRK EoS is developed and used for n-butane, i-butane, n-pentane, i-pentane, n-hexane, i-hexane and n-heptane. The volume translation term is set as a constant to ensure the accuracy of the saturated liquid density at low reduced temperatures. Then, the crossover method is introduced into the volume translation EoS to improve the predictions of thermodynamic properties in the critical region. Six crossover parameters are used, which are constants or functions of acentric factor and critical parameters. Therefore, none of the parameters in the crossover volume translation SRK EoS is adjustable, which makes the crossover EoS totally predictive and easily extend to mixtures. Comparisons show that the crossover EoS is in much better agreement with experimental data than the original SRK EoS.     

Thermodynamic modeling of solubilities of various solid compounds in supercritical carbon dioxide: Effects of equations of state and mixing rules

No one can ever deny the significance of calculations of solubilities of industrial solid compounds in supercritical CO₂ in separation processes. In this work, the Peng-Robinson (PR) and the Esmaeilzadeh-Roshanfekr (ER) equations of state (EoS) along with several mixing rules including the Wong-Sandler (WS), the covolume dependent (CVD) and the van der Waals one (VDW1) and two (VDW2) fluid mixing rules are applied to evaluate the solubilities of 52 mostly used solid compounds in supercritical carbon dioxide. Besides, the Van-Laar excess Gibbs energy (G^ex) model is applied in phase behavior calculations by the WS mixing rule. The optimal values of the proposed thermodynamic model parameters are evaluated using the DE (differential evolution) optimization strategy. The absolute average deviations of the model results from 1776 experimental data points and the optimal values of the adjustable parameters of the model are reported to investigate the capabilities of combinations of each equation of state with different mixing rules in calculations of the solubilities. The results indicate that the combination of the ER EoS with the WS mixing rule leads to more accurate results (AAD = 9.0%) compared with other ones.     

QUASI-CHEMICAL LOCAL COMPOSITION MODEL AND ITS EXAMINATION USING ADHESIVE HARD SPHERE MIXTURES

A local composition expression has been derived from the Guggenheim′s quasi-chemicalequation.On this basic a thermodynamic model,the quasi-chemical local composition model(QCLC)was established.To examine its capability for correlation and prediction,Baxter′s adhesivehard sphere mixtures were used,and an improved numerical method was proposed to estimate theirthermodynamic properties.By means of this method the excess properties of the mixtures composedof four kinds of adhesive hard spheres were calculated,The activity coefficients from QCLC modelwere compared with those from the Wilson,NRTL and UNIQUAC equations.Results show thatamong these models,the QCLC model is the best one for correlation and prediction.     

Phasengleichgewichtsmodelle zur Synthese und Auslegung von Trennprozessen

Phase Equilibrium Models in the Synthesis and Design of Separation Processes. While approximately 20 years ago the design of separation processes required expensive and time consuming experiments, modern thermodynamic models nowadays allow a reliable prediction of the phase equilibrium behavior of multicomponent systems using binary data alone. If binary data are not available, group contribution methods can be applied to predict the real behavior. These methods have been developed for the prediction of vapor-liquid equilibria. The range of application and the reliability of these models were improved by modification of the model, definition of new main groups and introduction of temperature dependent parameters. Especially promising models arise on utilising g^E-mixing rules in cubic equations of state. These models can be applied for the calculation and prediction of phase equilibria of strongly polar systems, including supercritical compounds. At the same time these models allow the calculation of densities, thermodynamic properties, etc.     

A note on approximation techniques used for process optimization

The need for increasingly complex models for process simulation has led several researchers to develop more efficient steady-state simulation strategies. In a common approach, rigorous physical property calculations are replaced by simplified ones which approximate locally the behavior of the rigorous ones. Periodically the rigorous models are executed to check if the simplified ones are still accurate enough, and, if not, parameters for the simplified ones are adjusted so both the rigorous and simplified models again predict the same values locally. Convergence is assumed when no adjustments are needed for these parameters and the simplified model is converged.This approach works well for phase equilibrium and even general process simulation problems. Some researchers have extended this approach to optimization problems as well. In this note we discuss problems which arise when adapting this approach for process optimization problems. We also present three examples where the use of simplified models can lead to detection of false optima or convergence failures.     

Phase equilibria and defect chemistry of the La-Sr-Co-O system

Strontium doped lanthanum cobaltite (LSC, La_1−xSr_xCoO_3−δ) is a promising oxygen electrode material for intermediate temperature solid oxide cells (SOCs) and oxygen membranes. Its application in service is however impeded by its thermodynamic instability. The present work is aiming to identify the phase stability of LSC by thermodynamic modeling of the La-Sr-Co-O system using the CALculation of PHAse Diagrams (CALPHAD) method coupled with experiments. The calculated results based on the developed database are validated using experimental data both from literature and the present work. General agreement is achieved between model predictions and experimental results. Other properties of the LSC perovskite, such as oxygen non-stoichiometry and cation distribution, are also calculated and predicted based on the developed La-Sr-Co-O database. These calculations can provide important guidance in designing LSC-based materials for various applications and the established thermodynamic functions can serve as input for further thermodynamic calculations on altered and even more complex perovskites.     

A novel approach for describing mixing effects in homogeneous reactors

The Liapunov–Schmidt technique of classical bifurcation theory is used to spatially average the convection–diffusion–reaction (CDR) equations over smaller time/length scales to obtain low-dimensional two-mode models for describing mixing effects due to local diffusion, velocity gradients and reactions. For the cases of isothermal homogeneous tubular, loop/recycle and tank reactors, the two-mode models are described by a pair of coupled balance equations for the mixing-cup (C_m) and spatial average (〈C〉) concentrations. The global equation describes the variation of C_m with residence time (or position) in the reactor, while the local equation expresses the coupling between local diffusion, velocity gradients and reaction at the local scales, in terms of the difference between C_m and 〈C〉. It is shown that the two-mode models have many similarities with the classical two-phase models of heterogeneous catalytic reactors with the concept of transfer between phases being replaced by that of exchange between the two-modes. It is also shown that when the local Damköhler number (ratio of local diffusion to reaction time) is small, the solution of two-mode models approaches the exact solution of full CDR equations, while for fast reactions the two-mode models retain all the qualitative features of the latter. Examples are provided to illustrate the usefulness of these two-mode models in predicting micromixing effects on homogeneous reactions.     

Optimal design of distillation systems with less than N − 1 columns for a class of four component mixtures

The optimal design of complex distillation systems is a highly non-linear and multivariable problem, with several local optimums and subject to different constraints. In addition, some attributes for the design of these separation schemes are often conflicting objectives, and the design problem should be represented from a multiple objective perspective. As a result, solving with traditional optimization methods is not reliable because they generally converge to local optimums, and often fail to capture the full Pareto optimal front. In this paper, a method for the multiobjective optimization of distillation systems, conventional and thermally coupled, with less than N − 1 columns is presented. We use a multiobjective genetic algorithm with restrictions coupled to AspenONE Aspen Plus; so, the complete MESH equations and rigorous phase equilibrium calculations are used. Results show some tendencies in the design of intensified sequences, according to the nature of the mixture and feed compositions.     

Thermodynamic Modeling of the FeO–Fe2O3–MgO–SiO2 System

The liquid and solid phases in the FeO–Fe₂O₃–MgO–SiO₂ system are of importance in ceramics, metallurgy, and petrology. A complete critical evaluation and thermodynamic modeling of the phase diagrams and thermodynamic properties of this system are presented. Optimized equations for the thermodynamic properties of all phases are obtained that reproduce all available thermodynamic and phase equilibrium data within experimental error limits from 25°C to above the liquidus temperatures at all compositions and oxygen partial pressures. The optimized thermodynamic properties and phase diagrams are believed to be the best estimates presently available. The database of the model parameters can be used with software for Gibbs energy minimization to calculate any type of phase diagram section.     

CALCULATION OF THE BINARY INTERACTION AND NONRANDOMNESS PARAMETERS OF NRTL,NRTL1, AND NRTL2 MODELS USING GENETIC ALGORITHM FOR TERNARY IONIC LIQUID SYSTEMS

One of the most important applications of thermodynamics is the accurate prediction of fluid phase equilibria problems related to real chemical engineering processes. Various equations of state as well as activity coefficient models have been developed for such calculations with many interaction, size, and randomness parameters, which should be optimized based on powerful and effective computational methods. Leading to globally optimal values, genetic algorithm (GA) as a powerful and effective tool can be used for prediction of the interaction parameters of thermodynamic models in complex liquid-liquid equilibrium (LLE) systems. It requires only lower and upper bounds for the interaction parameters and the necessary initial guesses are produced automatically. In the present work, based on the GA method, a global optimization procedure is introduced for calculation of the binary interaction and nonrandomness parameters of NRTL, NRTL1, and NRTL2 activity coefficient models for 20 ternary aromatic extraction systems containing 16 different ionic liquids at various temperatures. The values of the parameters along with the root-mean-square deviations (rmsd) are reported. The results, in terms of rmsd for NRTL, NRTL1, and NRTL2 models, are very satisfactory, with global values of 0.0031, 0.0020, and 0.0053 for 187 tie-lines respectively. The obtained rmsd values for the NRTL model using the GA method are better than those reported in the literature. The rmsd results for the three studied models show that NRTL1 can handle the LLE calculations with more accuracy than the original NRTL and NRTL2 activity coefficient models.