Vapor-liquid Equilibrium Calculations Research Articles

Preliminary Evaluation of the SPUNG Equation of State for Modelling the Thermodynamic Properties of CO2-Water Mixtures

The accuracy of the extended corresponding state equation SPUNG is preliminary evaluated for the density, and Vapor Liquid Equilibrium (VLE) calculations of the CO2 -water mixtures. The evaluation is done by comparing the behavior of SPUNG to experimental data whenever possible, and three other state-of-the-art equations of state (EoS) of different classes. The three EoS are; the cubic equation Soave-Redlich-Kwong (SRK) with the van der Waals mixing rules, SRK with Huron Vidal mixing rules (SRK-HV), and the multi-parameter approach GERG-2004. The latter is used as a reference in the single phase region. The single phase studies for both liquid and vapor state are conducted at a mixture of 98% CO2 and 2% H2O. Recommendation for future work is highlighted.

Comparative study of eight cubic equations of state for predicting thermodynamic properties of alkanes

AbstractPrecise descriptions of the thermodynamic properties of pure fluids require accurate definition of vapour–pressure and phase volumes as well as residual volumes, enthalpies and entropies. While carefully fitted multi‐parameter equations of state (EOS), such as Benedict–Webb–Rubin–Starling fulfil these requirements, cubic EOSs usually do not. On the other hand, cubic EOSs are widely used in the oil industry, due to their simplicity and reliability in most vapour–liquid equilibrium calculations. For thermal oil recovery processes and the natural gas industry, the choice of EOS becomes important for predicting thermodynamic properties, such as isobaric and isochoric heat capacities, sound velocity and the Joule–Thomson coefficient. In this study, eight cubic EOSs which most of them are used in commercial reservoir simulators are selected for evaluation of their capability in the prediction of second‐order derivative thermodynamic properties at different temperatures and pressures, using pure components frequently found in petroleum and natural gas mixtures. It is shown that none of the cubic EOSs could accurately predict all of the stated parameters, especially below the critical point. All EOSs failed to show the extrema in the derivative properties. However, among these equations the Yu–Lu and Schmidt–Wenzel EOSs were found to have more reliable predictions in most of the cases. © 2011 Canadian Society for Chemical Engineering

Enhancement in Triethylene Glycol (TEG) Purity via Hydrocarbon Solvent Injection to a TEG + Water System in a Batch Distillation Column

Triethylene glycol (TEG) is one of the most important liquid desiccants in the natural gas dehydration industry. In enhanced TEG regeneration processes, liquid hydrocarbons such as toluene and isooctane are added to the stripping column of natural gas dehydration unit in order to boost water volatility and regenerate TEG to higher purity. In this study, isooctane and toluene were selected as liquid hydrocarbon solvents and the effect of these two solvents on TEG purity and the outlet water concentration from the reboiler of tray column were experimentally investigated and mathematically modeled. The vapor–liquid equilibrium calculations were performed using the NRTL activity coefficient model and ideal gas equation of state to represent the liquid and vapor phases, respectively. Moreover, a comprehensive model was used to determine the liquid molar flow rate on each tray where it changed with time and tray by tray. The impact of various concentrations of solvents and different operating conditions (total and no reflux) on the performance of the tray column was investigated. The modeling results were validated with the experimental data, and good agreement was observed between them. Results showed that the least water concentration in the reboiler and the highest TEG purity were achieved by adding 0.15 wt % isooctane under total reflux conditions. The achieved results can provide an initial insight into designing equipments in enhanced TEG regeneration processes with hydrocarbon solvent injection.

Development of a computational multiphase flow model for Fischer Tropsch synthesis in a slurry bubble column reactor

The Hybrid Energy Systems Testing (HYTEST) Laboratory at the Idaho National Laboratory was established to develop and test hybrid energy systems with the principal objective of reducing dependence on imported fossil fuels. A central component of the HYTEST is the slurry bubble column reactor (SBCR) in which the gas-to-liquid reactions are performed to synthesize transportation fuels using the Fischer Tropsch (FT) process. These SBCRs operate in the churn-turbulent flow regime, which is characterized by complex hydrodynamics, coupled with reacting flow chemistry and heat transfer. Results, our team is developing a research tool to aid in understanding the physicochemical processes occurring in the SBCR. A robust methodology to couple reaction kinetics and mass transfer into a four-field model (consisting of the bulk liquid, small bubbles, large bubbles and solid catalyst particles) consisting of thirteen species, which are CO reactant, H 2 reactant, hydrocarbon product, and H 2O product in small bubbles, large bubbles, and the bulk fluid plus catalyst is outlined. Mechanistic submodels for interfacial momentum transfer in the churn-turbulent flow regime are incorporated, along with bubble breakup/coalescence and two-phase turbulence submodels. The absorption and kinetic models, specifically changes in species concentrations, have been incorporated into the mass continuity equation. The reaction rate is based on the macrokinetic model for a cobalt catalyst developed by Yates and Satterfield. The model includes heat generation produced by the exothermic chemical reaction, as well as heat removal from a constant temperature heat exchanger. A property method approach is employed to incorporate vapor–liquid equilibrium (VLE) in a robust manner. Physical and thermodynamic properties as functions of changes in both pressure and temperature are obtained from VLE calculations performed external to the computational multiphase fluid dynamics (CMFD) solver. The novelty of this approach is in its simplicity, as well as its accuracy over a specified temperature and pressure range.

Modification of Peng Robinson EOS for modelling (vapour+liquid) equilibria with electrolyte solutions

► Extended PR-EOS was presented for VLE of H 2 O/Salt/CO 2 systems at high pressure. ► The proposed EPR-EOS is based upon contributions to the Helmholtz energy. ► Born, Margules, and Debye–Huckel or mean spherical approximation terms were used. ► Two different mixing rules Panagiotopoulos and Reid and Kwak and Mansoori (KM) were used. ► A combination of KM mixing rule with DH term results more accurate VLE results. A modification of the extended Peng–Robinson equation of state (PR-EOS) is presented to describe the (vapour + liquid) equilibria of systems containing water and salts. The modification employs three additional terms including a Born term, a Margules term and two terms separately used for estimation of the long-range electrostatic interactions (the Debye–Huckel (DH) or the mean spherical approximation (MSA) terms). Effects of two mixing rules, first, the Panagiotopoulos and Reid mixing rule (PR) and, second, the Kwak and Mansoori mixing rule (KM), on the final values of VLE calculations are also investigated. The results show that the KM mixing rule is more appropriate than the PR mixing rule. The proposed equation of state is used to calculate the (vapour + liquid) equilibrium (VLE) of the systems containing (water + sodium sulphate + carbon dioxide) and (water + sodium chloride + carbon dioxide) at high pressure. The comparison of calculated results with the experimental data shows that a combination of KM mixing rule with the DH term results a more accurate VLE values.

Applications of the Soave-Redlich-Kwong Equations of State Using Matlab

In this paper, using Matlab to solve Soave-Redlich-Kwong (SRK) EOS, as well as the estimation of pure component properties, plotting of vapor-liquid equilibrium (VLE) diagram and calculation of chemical equilibrium, is presented. First the SRK EOS is used to predict several pure-component properties, such as liquid and gas molar volumes for isobutane. The vapor-liquid isobaric diagram is then plotted for a binary mixture composed of n-pentane and n-hexane under the pressures of 1.5*10^5 and 7*10^5 Pa respectively. Finally, the extent of ammonia synthesis reaction under high pressure is calculated.

Co-evaporative multi-component fuel design for in-cylinder PLIF measurement and application in gasoline direct injection research

For in-cylinder fuel mixture distribution measurement, a method for designing a multi-component fuel for planar laser-induced fluorescence (PLIF) experiments is developed based on thermal gravity analysis and vapor–liquid equilibrium calculation. The goal is to create fuel that has a volatility similar to real gasoline and good co-evaporation ratios (near 1.0) with tracers. Acetone, toluene, and trimethylbenzene are chosen as tracers for light, medium, and heavy fractions, respectively, and a five-component test fuel is developed. The test fuel is used to study the influence of components and temperature on co-evaporation ratios. Any variation in tracer or fuel component proportions affects all co-evaporation ratios, but a variation within 5% is considered acceptable. Results show that acetone presents the most significant influence on co-evaporation ratios. Temperature is also a key factor. Saturated vapor pressure and activity coefficient of the tracer and components in a fraction group affect co-evaporation optimization substantially, indicating that these values are a primary consideration in tracer selection. Finally, the test fuel is applied to an in-cylinder gasoline direct injection fuel mixture distribution measurement using PLIF. Differences between light, medium, and heavy fraction groups are studied under different strategies. Cycle-to-cycle variation analysis shows that the influence of absorption attenuation of the aromatic is distinct in a typical stratified strategy. In the area near the spark plug, cycle-to-cycle variation decreases as injection is delayed.

Accounting for Vapor−Liquid Equilibrium in the Modeling and Simulation of a Commercial Hydrotreating Reactor

A one-dimensional, plug-flow, trickle-bed reactor model was developed to simulate a steady-state, adiabatic hydrotreating reactor with consideration of vapor−liquid equilibrium (VLE) effects. VLE calculations were simultaneously performed at each integration step of the model simulation. The thermophysical properties and mass flow rates of each fluid phase were updated as functions of local variables along the catalyst bed. Substantial differences in hydrodearomatization (HDA) and hydrodesulfurization (HDS) conversions were observed when the simulation was conducted with and without accounting for VLE, indicating the significance of VLE in the hydrotreater simulation. It was found that an increased inlet temperature increases HDS conversion but reduces HDA conversion. Increased pressure increases the reactor temperature and HDS and HDA conversions. Increased gas/oil ratio increases HDA conversion slightly, but does not change HDS conversion significantly. Polyaromatics are the most reactive for hydrogenat...

A New Modified van Laar Model for Associating Mixtures

In this study, a modification is presented for van Laar model (van der Waals mixture theory) for association mixtures. The molecular association effects are considered in van der Waals mixture theory by adding two new steps to van Laar cycle. The excess Gibbs free energy function and corresponding activity coefficient equations are derived for presented model. In addition to general case when both components are associating fluids, model simplified for two interesting cases: (i) only one fluid is associating, (ii) two fluids are associating but only self-associated species exist in the mixture. This model also is used for VLE calculations for 16 different binary mixtures in which one or both components are associating fluids. Results of the presented model show satisfactory improvement over the nonassociating case for vapor liquid equilibrium (VLE) prediction.

Quantification of Voltage Loss in the PEM Reactor for Electrolyzing Hydrogen Bromide to Produce Hydrogen

Simultaneous conversion of gaseous hydrogen bromide to bromine and hydrogen can be accomplished in a Proton Exchange Membrane (PEM) electrolyzer. The cell voltage required to carry out this conversion is a function of design and operating conditions. The cell voltage is composed of the equilibrium cell potential as well as individual potential losses in the cell (e.g. ohmic, activation, mass transfer etc). All these potential contributions are greatly influenced by the water content in the membrane and at the catalytic surface. Therefore, it is necessary to accurately predict the water transport across the cell to quantify the individual voltage losses. The equilibrium cell potential is predicted by Nernst equation coupled with vapor-liquid equilibrium (VLE) calculations for the Br2-HBr-H2O and H2-H2O system. The model for predicting the total cell potential shows good agreement to the data over a range of current densities.

Modeling of vapor-liquid equilibrium of gasoline-ethanol blended fuels for flash boiling simulations

Flash boiling is a physical phenomenon which governs the non-equilibrium phase change of a high temperature fluid as it is depressurized below its vapor pressure. The modeling of this process is of importance to a number of industrial applications and requires the vapor-liquid equilibrium properties of the fluid under consideration. The highly non-ideal nature of gasoline-ethanol fuel blends makes vapor-liquid equilibrium calculations extremely difficult for such fluids. A simple model known as GEFlash (Gasoline-Ethanol Flash), based on existing literature and fundamental chemical engineering thermodynamics is proposed to calculate the properties of gasoline-ethanol fuel blends that are required to perform flash boiling simulations. In addition, a second model based on the chemical engineering software Aspen Plus is also proposed and the predictions of the two models are validated against experimental data available in open literature. The results indicate that both models reproduce the trend in experimental data for vapor pressures and saturated liquid density for blends with different ethanol contents. The GEFlash model does not match the vapor mole fraction predictions of the Aspen Plus model for fuels with low ethanol content (E20 and E40). However, the vapor mole fractions for high ethanol content fuels (greater than E60) are accurate over the majority of the temperature range tested.

Effect of surface area parameters on the vapor–liquid equilibrium calculations using a lattice fluid equation of state with hydrogen bonding

Vapor–liquid equilibrium calculations at ambient and elevated pressures were performed using the lattice fluid equation of state with hydrogen bonding (NLF-HB EoS) proposed by You et al. [7,8] and Lee et al. [17]. Vapor–liquid equilibrium calculations composed of typical pure components were compared with electronic experimental database (Dortmund Data Bank). Special attention has been paid to the correction of surface area parameters. Bulkiness factors can be used to modify theoretical surface area parameters for molecules with nonlinear shapes. Empirical bulkiness factors were obtained from liquid density data and VLE data sets with n-hexane chosen as a reference component. Using empirical bulkiness factors, overall prediction performances without binary interaction parameters have been significantly improved. It is shown that the NLF-HB EoS have comparable prediction capability with UNIQUAC method or Peng–Robinson Equation of State only with pure component parameters and component-type-dependent hydrogen-bonding energy parameters for most systems considered in this study.

Vapor–liquid equilibrium calculations for refrigerant mixtures with the Mattedi–Tavares–Castier EOS

The present study uses the Mattedi–Tavares–Castier EOS to investigate VLE predictions for refrigerant binary mixtures. The refrigerant molecules are treated either by the associated-group or the uniform-molecular model. In the associated-group model, the refrigerant molecule is split into three groups: an electron-donor (α), an electron-acceptor (β), and a dispersion group (D). In the uniform-molecular model, the refrigerant molecule is represented as a single group. Results obtained with the MTC EOS are in agreement with experimental data reported in the literature. The EOS that treats refrigerant molecules with groups that can associate gives worse results than the uniform-molecular model.

An Applied and Efficient Model for Asphaltene Precipitation In Production and Miscible Gas Injection Processes

In this article the modeling results of asphaltene precipitation in some Iranian oil fields via a new and applicable polymer solution based model are presented. Application of polymer solution and lattice theory in this model leads to accurate prediction of the environmental parameters effects on asphaltene precipitation in oil fields. The involved parameters are pressure change through natural depletion; temperature change in fluid flow path during oil production; and composition change through either miscible gas injection or pressure and/or temperature variations. The adjustable parameters of the model are tuned via experimental data of asphaltene precipitation. The adjusted parameters can be used in the simulation section, which is the prediction of the effects of different parameters on amount of asphaltene deposition in oil mixtures. The experimental data in this work are the precipitation data in some Iranian live oils. The modified Flory-Huggins is re-modified by replacement of the entropy term in this model with the Miller's entropy term. The Peng-Robinson equation of state is also applied to vapor-liquid equilibrium calculations.

Soft-SAFT modeling of vapor–liquid equilibria of nitriles and their mixtures

Nitriles are strong polar compounds showing a highly non-ideal behavior, which makes them challenging systems from a modeling point of view; in spite of this, accurate predictions for the vapor–liquid equilibria of these systems are needed, as some of them, like acetonitrile (CH 3CN) and propionitrile (C 2H 5CN), play an important role as organic solvents in several industrial processes. This work deals with the calculation of the vapor–liquid equilibria (VLE) of nitriles and their mixtures by using the crossover soft-SAFT Equation of State (EoS). Both polar and associating interactions are taken into account in a single association term in the crossover soft-SAFT equation, while the crossover term allows for accurate calculations both far from and close to the critical point. Molecular parameters for acetonitrile, propionitrile and n-butyronitrile (C 3H 7CN) are regressed from experimental data. Their transferability is tested by the calculation of the VLE of heavier linear nitriles, namely, valeronitrile (C 4H 9CN) and hexanonitrile (C 5H 11CN), not included in the fitting procedure. Crossover soft-SAFT results are in excellent agreement with experimental data for the whole range of thermodynamic conditions investigated, proving the robustness of the approach. Parameters transferability has also been used to describe the isomers n-butyronitrile and i-butyronitrile. Finally, the nitriles soft-SAFT model is further tested in VLE calculation of mixtures with benzene, carbon tetrachloride and carbon dioxide, which proved to be satisfactory as well.

Comparison of activity coefficient models for electrolyte systems

AbstractThree activity coefficient models for electrolyte solutions were evaluated and compared. The activity coefficient models are: The electrolyte NRTL model (ElecNRTL) by Aspentech, the mixed solvent electrolyte model (MSE) by OLI Systems, and the Extended UNIQUAC model from the Technical University of Denmark (DTU). Test systems containing a single salt (NaCl), multiple salts, and mixed solvent aqueous electrolyte solutions were chosen. The performance of the activity coefficient models were compared regarding the accuracy of solid–liquid and vapor–liquid equilibrium calculations for the test systems. © 2009 American Institute of Chemical Engineers AIChE J, 2010

Application of the SAFT-VR equation of state to vapor–liquid equilibrium calculations for pure components and binary mixtures using the Sutherland potential

An equation of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) has been applied to model 35 pure associating and non-associating fluids and 15 binary mixtures. The pure components consist of alkanes, alcohols, water, aromatics and polar or multi-polar compounds like ammonia and H 2S. In contrast to other attempts which have used the SAFT-VR model for various thermodynamic calculations using the square-well or Yukawa potentials, the short-range dispersion interactions have been accounted for here using the Sutherland potential, while hydrogen bonding interactions are explicitly taken into account as in other versions of the SAFT approach. The Sutherland potential is particularly useful for modeling the interactions among multi-polar species. Model parameters for the pure components have been optimized by fitting available experimental data on vapor pressure, saturated vapor density and saturated liquid density for temperatures ranging from near the triple point up to reduced temperatures of 0.9. The effect of several simplifying assumptions aimed at reducing the number of model parameters has been investigated, and the resulting trends in parameters has been discussed. Binary interaction coefficients have been obtained for the binary systems by fitting experimental data on vapor–liquid equilibrium pressure and phase concentrations. Results have been compared to those obtained using other versions of the SAFT-VR model.

Hydrocracking of long chain linear paraffins

The hydrocracking reactivity of two model compounds, namely n-C 16H 34 ( n-C16) and n-C 28H 58 ( n-C28), was investigated on a Pt/SiO 2-Al 2O 3 catalyst. Conversion and products distribution have been determined under a wide range of operating conditions ( i.e. pressure: 20–80 bar; temperature: 270–330 °C; weight hourly space velocity: 0.33–1.0 h −1; H 2/ n-paraffin feeding ratio 0.05–0.15 wt/wt). The latter were changed according to a central composite design. The present paper summarises the results obtained on both the model paraffins, depending on the reaction conditions. A first, simple kinetic elaboration is also presented, based on an ideal PFR model and a first order kinetics. The reaction confirmed to be first order with respect to the n-paraffin. Experimental data showed that for both n-C16 and n-C28 conversion was affected by H 2/ n-paraffin ratio. The change of conversion was explained in terms of vapour liquid equilibrium (VLE), which in turn is affected by the H 2/n-paraffin ratio, so leading to a different vaporisation degree of reactant. In agreement with the VLE data, the effect of H 2/n-paraffin on conversion was lower for n-C28. VLE calculations have been carried out to estimate the H 2 partial pressure and degree of vaporisation of the normal paraffin. The reaction order for hydrogen was −1 and −0.5 for n-C16 an n-C28, respectively. However, in the case of n-C16 the data obtained at the lower bound of the pressure range examined displayed an increase of the reaction order. The apparent activation energy was calculated after correction of the contact time taking into account the liquid-vapour equilibrium: similar values have been estimated for n-C16 and n-C28, ca. 32 and 31 kcal/mol, respectively.

Use of normal boiling point correlations for predicting critical parameters of paraffins for vapour–liquid equilibrium calculations with the SRK equation of state

Correlations between normal boiling points and critical parameters (critical temperatures and critical pressures) and between normal boiling points and acentric factors of normal and branched paraffins in the range from C 7 to C 100 have been developed. These correlations can be used to quickly and easily compute critical properties that allow to reproduce closely, by means of the Soave–Redlich–Kwong (SRK) equation of state (EoS), the vapour pressure of pure compounds. In the range of 0.5–5 mmHg the values of vapour pressure calculated by means of the SRK EoS become less accurate and they can be improved using a different equation for the temperature-depending attractive parameter (i.e., the Mathias–Copeman alpha function) instead of the classical Soave function.

The effects of dissolved solids on the vapor-liquid equilibrium of DMS in black liquor

Researchers determined activity coefficients for use in vapor-liquid equilibrium (VLE) calculations using a headspace gas chromatographic method for dimethyl sulfide (DMS) in water, kraft pulp mill black liquor, and sodium salts and alkali lignin mixtures up to 6 wt%, for temperatures of 20°C to 90°C. Experimental data were regressed to determine DMS-water binary parameters for the nonrandom two-liquid (NRTL) equation. The effects of electrolytes were studied, and a strong correlation was observed between the activity coefficient and the sodium cation content of the solution. This suggested that the shift in vapor-liquid equilibrium in black liquor could be modeled based solely on the sodium concentration. Sodium salts solutions data were regressed to determine binary parameters for the eNRTL equation, an extended form of the NRTL equation used to describe electrolyte effects. We found that the eNRTL equation could be used to accurately predict activity coefficients of DMS in black liquor.