SRK Equation Research Articles

Entrainer Effect of Ethanol on High-Pressure Vapor−Liquid Equilibria for Supercritical Carbon Dioxide + Limonene + Linalool System

The high-pressure vapor−liquid equilibria for supercritical CO2 + citrus oil component (limonene and linalool) + ethanol systems were measured to study an entrainer effect of ethanol. The measured systems were CO2 + limonene + ethanol at 313.2 K and 6.9 MPa; CO2 + linalool + ethanol at 313.2 K and 6.9 MPa and at 333.2 K and 10.0 MPa; and CO2 + limonene + linalool + ethanol at 313.2 K and 6.9 MPa. The experimental apparatus used was based on a circulation-type method for liquid-phase sampling and a flow-type method for vapor-phase sampling. The mole fractions of limonene and linalool in vapor phase are not affected by the addition of ethanol. However, the mole fraction of linalool in the liquid phase decreases with increasing the concentration of ethanol. As a result, the relative volatilities between limonene and linalool increase by factors of 1.2 to 1.5 with the addition of ethanol. The experimental data were correlated by the SRK equation of state with an exponent-type mixing rule. The correlated results are in good agreement with the experimental data.

Estimation of vapour liquid equilibria of binary systems, carbon dioxide–ethyl caproate, ethyl caprylate and ethyl caprate using artificial neural networks

Vapour liquid equilibrium (VLE) data are important for designing and modeling of process equipments. Since it is not always possible to carry out experiments at all possible temperatures and pressures, generally thermodynamic models based on equations of state are used for estimation of VLE. In this paper, an alternate tool, i.e. the artificial neural network technique has been applied for estimation of VLE for three binary systems viz. carbon dioxide–ethyl caproate, ethyl caprylate and ethyl caprate which are of importance in supercritical extraction. The temperature range in which these models are valid is 308.2–328.2 K and the pressure range is 1.6–9.2 MPa. The average absolute deviation for all the three systems in the estimation of liquid phase mole fraction was 3% or less and less than 0.02% for the vapour phase mole fraction. The error was less compared to that estimated by SRK or Peng Robinsons equation of state.

Vapor–liquid equilibrium prediction at high pressures using activity coefficients at infinite dilution from COSMO-type methods

Predictions of vapor–liquid equilibria at high temperatures and pressures were obtained by applying a modified procedure using the Huron–Vidal mixing rule based on available activity coefficients at infinite dilution and low pressures. These activity coefficients were calculated with so-called conductor-like screening model for real solvents (COSMO-RS) and with a variation of this model, known as segment activity coefficient (COSMO-SAC) model. In this work, the performances of the mixing rule (HVID model) coupled with the SRK equation of state and a reduced UNIQUAC model are presented for six binary systems and a ternary system, whose VLE data are available over a large temperature and pressure range.

Phase equilibria in the system nitrogen–ethane and their prediction using cubic equations of state with different types of mixing rules

The system nitrogen–ethane is of fundamental importance for the examination of nitrogen–alkane systems that exhibit miscibility gaps. The aim of this work is to compare the widely used SRK and PR cubic equation of state with different types of mixing rules with respect to their ability to represent the phase behaviour of this system. We investigated the performance of the van der Waals mixing rule, two composition depending mixing rules and some G E -mixing rules in combination with the NRTL and UNIQUAC model. The binary interaction parameters were obtained by fitting only experimental VLE data and then used to test the capability of the different mixing rules to predict the VLLE and to describe the saturation densities. New experimental results for the VLE below 140 K including densities supplement available data sets needed to validate the correlation results.

Measurement and Correlation of Phase Equilibria for Water + Decane + 2-Propanol, Water + Hexane + 2-Propanol, and Water + Decane + 2-Butanol Ternary Systems at 573 and 593 K and 15.0 and 20.0 MPa

The phase equilibria for the water + decane + 2-propanol system at (573 and 593) K and (15.0 and 20.0) MPa, the water + hexane + 2-propanol system at 573 K and 20.0 MPa, and the water + decane + 2-butanol system at 573 K and 20.0 MPa were measured with a flow type apparatus. The experimental results were correlated by a modified SRK equation of state. An exponent type mixing rule and a conventional mixing rule were applied for the energy and size parameters of the equation of state, respectively. The average deviation between the mole fractions of experiment and correlation is 0.006.

Application of an improved equation of state to reservoir fluids: computation of minimum miscibility pressure

This contribution consists of two parts. First, an equation of state (EOS) applicable to the PVT of oil and gas mixtures is introduced. Matching the second virial coefficient for the equation of state with the second virial coefficient for the square-well fluids, a new temperature dependence is found for the parameter α of the equation of state. Using this parameter, the equation of state is extended to heavy hydrocarbons up to n-octacosane. This equation of state not only is applied to hydrocarbons but to non-hydrocarbons as well. The average absolute error for predicting the vapor pressure and saturated liquid density of hydrocarbons, non-hydrocarbons, polar compounds and associating fluids were found to be 1.7% and 2.6%, respectively. Then, this modified equation of state is used to calculate the minimum miscibility pressure (MMP) for displacing two oil mixtures using two gas mixtures. Application of widely used PR and SRK equations of state for the same systems in calculating minimum miscibility pressure is also discussed.

Influence of temperature on the volumetric properties of ethanol + water + 1-pentanol

Knowledge of physical properties and phase equilibria is necessary for the design and optimization of the equipment for the production of distilled alcoholic beverages. In this paper the temperature dependence of the excess molar volumes of the ternary system ethanol + water + 1-pentanol in the temperature range 228.15 ? 323.15 K and atmospheric pressure, are presented due to the importance of 1-pentanol among the flavour compounds contained in this type of beverages. The excess molar volumes are negative over the whole homogeneous composition range, but tend to positive values towards the binaries ethanol + 1-pentanol and water + 1-pentanol. Because the design of current processes is strongly computer oriented, consideration was also given to how accurate the predictions of the SRK equations of state are. Different derived properties were computed due to their importance in the study of specific molecular interactions.

Heterogeneous modeling for fixed-bed Fischer–Tropsch synthesis: Reactor model and its applications

A comprehensive one-dimensional heterogeneous reactor model is developed to simulate the performance of fixed-bed Fischer–Tropsch reactors for hydrocarbon production. The detailed mechanistic kinetics is combined into the reactor model along with considering the fact that the catalyst pores are filled with liquid wax under realistic conditions. The equilibrium between the gases in the bulk and the wax in the catalyst pores is correlated by using a modified SRK equation of state (MSRK EOS). The model is solved by using Gear method to integrate the reactor model with the embedded pellet model discretized by orthogonal collocation on finite elements. The validity of the reactor model is tested against the measured data from different-scale demonstration processes. Satisfactory agreements between model predictions and experiment results are obtained. Detailed numerical simulations are performed to investigate the effect of major process parameters on the reaction behavior of fixed-bed FTS systems with recycle operation.

Measurement and Prediction of Liquid−Liquid Equilibria for Water + Hexane + Hexadecane, Water + Toluene + Decane, and Water + Toluene + Ethylbenzene Ternary Systems at High Temperatures and Pressures

An experimental apparatus based on a flow method was used to measure the liquid−liquid equilibria for three ternary systems: water + hexane + hexadecane at 573 K and 20 MPa, water + toluene + decane at 553 and 573 K and 20 MPa, and water + toluene + ethylbenzene at 553 K and 20 MPa. Furthermore, the phase equilibria for water + toluene + decane and water + toluene + ethylbenzene were predicted by the modified SRK equation of state. An exponent-type and conventional mixing rules were applied for the energy and size parameters of the equation of state, respectively. The predicted results are in good agreement with the experimental results.

Fluid phase equilibria of the reacting mixture in the dimethyl carbonate synthesis from supercritical CO 2

In order to investigate the dimethyl carbonate synthesis from methanol and supercritical CO 2, the thermodynamic behaviour of the reacting mixture, i.e. the quaternary methanol–CO 2–DMC–water mixture, has to be known. The SRK equation of state with MHV2 mixing rules has been chosen to predict fluid phase equilibria in the reactor. The first part of this work is dedicated to the determination of binary interaction parameters, needed in the use of this model. These parameters are deduced from the fitting of experimental data concerning binary or ternary sub-systems existing in the quaternary mixture. Literature data was used for most of the binary sub-systems, but for the DMC–CO 2 and DMC–water mixtures, specific experiments were carried out. The agreement between experimental and predicted fluid phase equilibria was found to be satisfactory. With a view to studying of the operating conditions for the reaction, the thermodynamic model was used to predict fluid phase equilibria in the reactor, by considering several hypothetical feed ratios and conversions. This work shows that CO 2 has to be used in large excess in order to be sure of running the reaction in a homogeneous fluid medium.

Modeling of Catalyst Pellets for Fischer−Tropsch Synthesis

The present work focuses on the transfer and reaction phenomenon in a catalyst pellet for Fischer−Tropsch synthesis. It is considered that the pores of catalyst pellets are filled with liquid wax under Fischer−Tropsch synthesis conditions. The reactants in the bulk gas phase dissolve in the wax at the external surface of the pellet, and the dissolved components diffuse through the wax inside the pellet and react on the internal surface of the pellet. The thermodynamic equilibrium between the gases in the bulk and the liquid wax in the pores is correlated by a modified SRK equation of sate (MSRK EOS). On the basis of the phenomena observed from experiments, a comprehensive pellet model is suggested for catalyst design simulation, in which detailed Fischer−Tropsch mechanistic kinetics is properly imbedded. The reaction and diffusion interaction in a catalyst pellet and its effect on the product selectivity are further investigated. The potential of using eggshell-type catalyst pellets is explored as a means of decoupling the severe transport restriction and, hence, enhancing the overall selectivity of desired products.

Dynamic modelling of a fractionation process for a liquid mixture using supercritical carbon dioxide

This work presents a simple dynamic modelling of a process of separation of a quaternary mixture using supercritical CO 2. Thermodynamic description is accomplished using efficient available models (SRK equation of state with MHV2 mixing rules). An approximate approach was compared to the rigorous resolution of the system of algebro-differential equations, and was shown to enable a correct description of the dynamic behaviour. The modelling was compared to experiments performed on a small pilot composed of one 200-ml contactor and a cascade of three cyclonic separators. Good results were obtained for the contactor, although they were not very satisfactory for the description of the fractionation in the cyclonic separators. Even if discrepancies between experimental and calculated results may probably originate from the experimental procedure, the hydrodynamic description of the separators here is likely to be oversimplified. The cyclonic separator cannot be regarded as a simple theoretical stage (TSM), and we have proposed an alternate description (EPSM), that, although more suitable, still needs to be improved.

An Extension of CEOS/AE Zero-Pressure Mixing Rules for an Optimum Two-Parameter Cubic Equation of State

Cubic equations of state are widely used in refinery and petroleum reservoir industries for the prediction of fluid-phase behavior. Two of the most well-known cubic equations of state broadly accepted in industry are the SRK and PR equations. However, neither the SRK nor the PR equation of state yields the best results for the prediction of liquid densities of polar components and heavy hydrocarbons. An approach is proposed to locate an optimum two-parameter cubic equation of state. A methodology is also proposed to modify Twu's CEOS/AE zero-pressure mixing rules to extend the range of application of these mixing rules. The mixing rule developed in this work is incorporated into our new cubic equation of state for the prediction of phase equilibria of highly nonideal chemical mixtures.

Measurement and Correlation of Liquid−Liquid Equilibria for Water + Aromatic Hydrocarbon Binary Systems at High Temperatures and Pressures

Liquid−liquid equilibria for water + aromatic hydrocarbon binary systems were measured by a flow method at high temperatures and pressures. The measured systems and conditions are as follows: water + toluene system, (573.2 and 583.2) K from (10.5 to 28.1) MPa; water + ethylbenzene system, (553.2 and 583.2) K from (10.4 to 26.4) MPa; water + p-xylene system, (553.2 and 583.2) K from (10.2 to 26.5) MPa. The experimental results were correlated by the SRK equation of state. An exponent-type mixing rule was used for the energy parameter. The experimental data are fitted well by the correlation.

Determination of compressibility factor and fugacity coefficient of hydrogen in studies of adsorptive storage

The compressibility factor ( z) of hydrogen was evaluated from the experimental p– V– T data and calculated from equations of state, such as the SRK equation and BWR equation as well. The effect of z on the adsorbed amount calculated was demonstrated by the adsorption of hydrogen on 5A-zeolite. The compressibility factor and the fugacity coefficient of hydrogen were formulated based on the experimental p– V– T data for 60–333 K and up to 25 MPa.

High-Pressure Vapor−Liquid Equilibria in the Systems Nitrogen + Dimethyl Ether, Methanol + Dimethyl Ether, Carbon Dioxide + Dimethyl Ether + Methanol, and Nitrogen + Dimethyl Ether + Methanol

Isothermal (P, T, x, y) data have been measured for the binary and ternary systems nitrogen + dimethyl ether at 15, 35, and 45 °C, dimethyl ether + methanol at 80 °C, carbon dioxide + dimethyl ether + methanol at 40 and 60 °C, and nitrogen + dimethyl ether + methanol at 40 and 15 °C. The pressure range under investigation was up to 9.5 MPa. The experimental data for the binary systems were correlated with the SRK equation of state using the MHV2 mixing rule combined with the UNIFAC or UNIQUAC model for the expression of the excess Gibbs energy. The experimental data for the ternary systems have been compared with those predicted by means of the same models, and the results are discussed by comparison. The binary system of nitrogen + dimethyl ether as well as the two ternary systems have not previously been studied.

One parameter friction theory models for viscosity

In this work the friction theory ( f-theory) for viscosity modeling is used in conjunction with the SRK, PR and PRSV cubic equations of state in order to develop three one parameter general models for viscosity prediction. The models are considered one parameter models because they only require a characteristic critical velocity, which is a parameter normally not tabulated. The models use these rather simple cubic equations of state as a basis to obtain accurate modeling of the viscosity of fluids for wide ranges of temperature and pressure. The general models presented in this work are based on the viscosity behavior of n-alkanes from methane to n-octadecane. Although best performance is obtained for the considered n-alkanes, a good model performance is also obtained for other systems. Thus, recommended characteristic critical viscosity values for several systems are also reported in this work. However, in the case of n-alkanes, an empirical equation for the characteristic critical viscosity is provided so that no additional parameters are required. In addition, with the use of simple mixing rules, the viscosity of several binary to quaternary n-alkane mixtures can also be predicted with a satisfactory accuracy.

Measurement and Correlation of Phase Equilibria for Water + Hydrocarbon Systems near the Critical Temperature and Pressure of Water

An experimental apparatus based on a flow method was constructed in order to measure the phase equilibria for water + hydrocarbon systems near and above the critical temperature of water in the high-pressure region. The phase equilibria were measured for the water + decane system at 573.2 K from 12.1 to 30.3 MPa and at 593.2 K from 15.4 to 25.1 MPa and for the water + toluene system at 553.2 K from 15.1 to 30.1 MPa and at 573.2 K from 17.2 to 30.5 MPa. The phase equilibria of the water + decane system at 573.2 and 593.2 K and of the water + toluene system at 553.2 and 573.2 K are correlated by a modified SRK (MSRK) equation of state, which is modified in the attractive term of the SRK equation of state to calculate well the saturated vapor pressures of many organic and inorganic compounds. An exponent-type mixing rule, which uses empirical exponential parameters showing deviations from random mixing, is applied to the energy parameter a, and a conventional mixing rule is applied to the size parameter b. Good correlation results are obtained.

Phase stability with cubic equations of state: Global optimization approach

AbstractCalculation of phase and chemical equilibria is of fundamental importance for the design and simulation of chemical processes. Methods of minimizing the Gibbs free energy provide equilibrium solutions that are candidates only for the true equilibrium solution, because the number and type of phases must be assumed before the Gibbs energy minimization problem can be formulated. The tangent plane stability criterion was used to determine the stability of a candidate equilibrium solution. The Gibbs energy minimization and tangent plane stability problems are challenging due to highly nonlinear thermodynamic functions. This work develops a global optimization approach for the tangent plane stability problem that provides a theoretical guarantee about the stability of the candidate equilibrium solution with computational efficiency. Cubic equations of state were used due to their ability to accurately predict the behavior of nonideal vapor and liquid phases across a broad range of pressures. The mathematical form of the stability problem was analyzed and nonlinear functions with special structure were identified to achieve faster convergence of the algorithm. This approach, when applied to the SRK, Peng‐Robinson, and van der Waals cubic equations of state, could address a variety of mixing rules. Computational results on problems with two‐eight components are presented.

Vapor−Liquid Equilibria of Systems Containing Dichloromethane and Gaseous Components

Isothermal pressure−composition data were measured for three binary systems: carbon monoxide + dichloromethane; propene + dichloromethane; 1-butene + dichloromethane. Each system was measured at three temperatures (30.0, 60.0, and 90.0 °C) and pressures up to 70 bar. The experimental data were correlated with the SRK equation of state using the MHV2 mixing rule and the UNIQUAC method for the expression of the excess Gibbs energy.