A FOUR-PARAMETER EXTENSION OF MODIFIED LEE-KESLER EQUATION OF STATE

A modified Lee-Kesler equation of state has been proposed to improve the accuracy for the subcooled and saturated liquid regions of normal fluids. It is further extended to polar fluids by the addition of a fourth parameter X. The extended equation has been found to be reliable over a wide vapor and liquid regions for polar fluids and it is easy for computer use. Fourteen kinds of normal fluids and twelve kinds of polar fluids have been tested. The total average absolute deviations for the normal fluids and polar fluids are 0.79% and 1.68% over the range of T_r = 0.3 to 4 and P_r - 0.01 to 10.     

A FOUR-PARAMETER EXTENSION OF MODIFIED LEE-KESLER EQUATION OF STATE

A modified Lee-Kesler equation of state has been proposed to improve the accuracy for the subcooled and saturated liquid regions of normal fluids. It is further extended to polar fluids by the addition of a fourth parameter X. The extended equation has been found to be reliable over a wide vapor and liquid regions for polar fluids and it is easy for computer use. Fourteen kinds of normal fluids and twelve kinds of polar fluids have been tested. The total average absolute deviations for the normal fluids and polar fluids are 0.79% and 1.68% over the range of T_r = 0.3 to 4 and P_r - 0.01 to 10.     

A MODIFIED LEE-KESLER EQUATION OF STATE FOR REFRIGERANTS

For calculation of the thermodynamic properties of refrigerants it is proposed that the extended corresponding states principle (ECSP) should be used using two specific reference fluids, CFC12 (CCI₂F₂) and HFC134a (CF₃CH₂F), in order to cover the field of interest for most refrigerants. The specific parameters of these refrigerants have been determined for the Lee-Kesler modification of the Benedict-Webb-Rubin equation of state. In the parameter estimation, it has been taken into accounl that all variables are subject to errors by using the so-called Error-in-Variables-Model (EVM). The parameters have been estimated from experimental pressure-volume-temperature data, vapour pressure and saturated liquid and vapour volume data for CFC12 and HFC134a.

The extended corresponding states principle proposed in this work with CFC12 and HFC134a as reference fluids has been used in calculations of the thermodynamic properties of a number of refrigerants. In comparison with the original Lee-Kesler equation this concept gives improved results in calculations of vapour pressure and liquid volume.     

EVALUATION OF THE ORIGINAL AND THE EXTENDED CORRESPONDING STATES PRINCIPLE FOR REFRIGERANTS

The corresponding states and extended corresponding states principles have been evaluated for refrigerants. In the two corresponding states techniques the Riedel and Wagner vapour pressure correlations have been used to express the vapour pressure for the reference fluids. As reference fluids CFC12 and HFC134a have been used. These two fluids cover the acentric factor interval wherein refrigerants are found. Parameters have been estimated for CFC12 and HFC134a according to the Reidel and Wagner vapour pressure correlations used in the extended corresponding states principle. Experimental vapour pressure data for CFC12 and HFC134a have been used to estimate parameters according to Riedel and Wagner used in the hypothetical fluid and deviation function used in the corresponding states principle.

The Riedel and Wagner correlations are of equal accuracy in vapour pressure calculations. The results from the corresponding states and extended corresponding states principle are comparable due to the conformity between the Riedel and Wagner correlation, but improved results are obtained in comparison with the Lee-Kesler vapour pressure correlation in acentric factor interval studied.     

THE MODIFIED PGR EQUATION OF STATE: PURE-FLUID PREDICTIONS

The Park-Gasem-Robinson (PGR) equation of state (EOS) has been modified to improve its volumetric and equilibrium predictions. Specifically, the attractive term of the PGR equation was modified to enhance the flexibility of the model, and a new expression was developed for the temperature dependence of the attractive term in this segment-segment interaction model.

The predictive capability of the modified PGR EOS for vapor pressure and saturated liquid and vapor densities was evaluated for selected normal paraffins, normal alkenes, cyclo-paraffins, light aromatics, argon, carbon dioxide, and water. The generalized EOS constants and substance-specific characteristic parameters in the modified PGR EOS were obtained from pure component vapor pressures and saturated liquid and vapor molar volumes. The calculated phase properties were compared with those of the Peng-Robinson (PR), the simplified-perturbed-hard-chain theory (SPHCT), and the original PGR equations. Generally, the performance of the proposed EOS (%AAD of 1.3, 2.8, and 3.7 for vapor pressure, saturated liquid, and vapor densities, respectively) was better than the SPHCT and original PGR equations in predicting the pure fluid properties.     

THE MODIFIED PGR EQUATION OF STATE: ASYMMETRIC MIXTURE VLE REPRESENTATIONS AND PREDICTIONS

A set of mixing rules was proposed for the modified Park-Gasem-Robinson (PGR) equation of state (EOS) to extend its predictions to mixtures. The phase behavior predictive capability of this segment-segment interaction model was evaluated for selected binary asymmetric mixtures involving ethane, carbon dioxide, and hydrogen in normal paraffins. The predicted bubble point pressures for the ethane + n-paraffin and carbon dioxide + n-paraffin binaries were compared to those of the Peng-Robinson (PR), simplified perturbed hard-chain theory (SPHCT), and original PGR equations. The a priori predictive capability of the modified PGR EOS is significantly better than that of the PR, SPHCT, and original PGR equations of state for ethane binaries with absolute-average percent deviation (%AAD) of 5%. However, this EOS produces comparable representations for ethane binaries (%AAD of 1.9%) and carbon dioxide binaries (%AAD of 2.0). For hydrogen binaries, the modified PGR EOS showed much better representations (%AAD of 1.7) than the original PGR equation and was comparable to the PR equation.     

THE MODIFIED PGR EQUATION OF STATE: ASYMMETRIC MIXTURE VLE REPRESENTATIONS AND PREDICTIONS

A set of mixing rules was proposed for the modified Park-Gasem-Robinson (PGR) equation of state (EOS) to extend its predictions to mixtures. The phase behavior predictive capability of this segment-segment interaction model was evaluated for selected binary asymmetric mixtures involving ethane, carbon dioxide, and hydrogen in normal paraffins. The predicted bubble point pressures for the ethane + n-paraffin and carbon dioxide + n-paraffin binaries were compared to those of the Peng-Robinson (PR), simplified perturbed hard-chain theory (SPHCT), and original PGR equations. The a priori predictive capability of the modified PGR EOS is significantly better than that of the PR, SPHCT, and original PGR equations of state for ethane binaries with absolute-average percent deviation (%AAD) of 5%. However, this EOS produces comparable representations for ethane binaries (%AAD of 1.9%) and carbon dioxide binaries (%AAD of 2.0). For hydrogen binaries, the modified PGR EOS showed much better representations (%AAD of 1.7) than the original PGR equation and was comparable to the PR equation.     

EQUATION OF STATE FOR POLAR AND NONPOLAR SUBSTANCES FROM CORRELATIONS OF PURE COMPONENT PROPERTIES

A cubic equation of state of the van der Waals type is presented which is suitable for polar and nonpolar fluids and fluid mixtures. The form is based on the three-parameter equation of lwai, Margerum and Lu. Problems in parameter generalization are avoided by calculating the parameters directly from existing pure component vapor pressure and saturated liquid molar volume correlations. The proposed approach yields excellent representation of pure component saturated and single-phase region properties. Excellent results are also obtained for mixtures.     

COMMENTS CONCERNING A SIMPLE EQUATION OF STATE OF THE VAN DER WAALS FORM

When the Carnahan-Starling equation of state for hard spheres is combined with a simple attractive term, the molecular size parameter b for argon (as obtained from critical data) is much closer to the “correct” value than that obtained from the empirical Redlich-Kwong equation

For the critical isotherm for argon, the best simple form of the attractive term lies between the two common forms, proposed by van der Waals and by Redlich. At constant temperature, the attractive contribution to the compressibility factor is proportional to (v + 0.2b)^?1 where v is the molar volume. This proportionality is in agreement with results for a square-well fluid recently reported by Sandier.     

COMMENTS CONCERNING A SIMPLE EQUATION OF STATE OF THE VAN DER WAALS FORM

When the Carnahan-Starling equation of state for hard spheres is combined with a simple attractive term, the molecular size parameter b for argon (as obtained from critical data) is much closer to the “correct” value than that obtained from the empirical Redlich-Kwong equation

For the critical isotherm for argon, the best simple form of the attractive term lies between the two common forms, proposed by van der Waals and by Redlich. At constant temperature, the attractive contribution to the compressibility factor is proportional to (v + 0.2b)^-1 where v is the molar volume. This proportionality is in agreement with results for a square-well fluid recently reported by Sandier.     

RATIONAL CONSTRUCTION OF AN AUGMENTED HARD CORE EQUATION OF STATE FOR PURE COMPOUNDS AND STUDY OF ITS APPLICATION TO MIXTURES

The Carnahan-Starling hard-sphere equation of state perturbed by attractive forces expressed in a virial expansion has been studied in the vicinity of the critical point. The three van der Waals conditions for the critical isotherm at the critical point were used to determine the minimum number of terms required in the perturbation series. P-v-T data at other temperatures were used for the determination of the temperature dependence of the virial terms. The equation has been tested for mixtures using the mixing rules of Arai et at.     

RATIONAL CONSTRUCTION OF AN AUGMENTED HARD CORE EQUATION OF STATE FOR PURE COMPOUNDS AND STUDY OF ITS APPLICATION TO MIXTURES

The Carnahan-Starling hard-sphere equation of state perturbed by attractive forces expressed in a virial expansion has been studied in the vicinity of the critical point. The three van der Waals conditions for the critical isotherm at the critical point were used to determine the minimum number of terms required in the perturbation series. P-v-T data at other temperatures were used for the determination of the temperature dependence of the virial terms. The equation has been tested for mixtures using the mixing rules of Arai et at.     

EVALUATION OF PENG ROBINSON EQUATION OF STATE IN CALCULATING THERMOPHYSICAL PROPERTIES OF COMBUSTION GASES

A set of simple equations of the thermodynamic and transport properties of the combustion gases of a gas turbine have been derived based upon the critically evaluated data and two equations of state: The virial equation of state and Peng-Robinson (PR) equation of state.

The properties which have been considered were, density, specific heat at constant pressure, enthalpy, entropy, viscosity and thermal conductivity.

The temperature range was (200-2600 K) theoretically while the pressure range was (0.3-1.2 MPa).

A computer program, to evaluate the departure of thermophysical properties using virial and PR equations of state, was used.

The Peng Robinson (PR) equation of state gave better estimated accuracy than the virial equation of state especially in evaluating the departure of thermodynamic properties.     

A GENERALIZED EQUATION OF STATE FOR POLAR AND NON-POLAR FLUIDS BASED ON FOUR-PARAMETER CORRESPONDING STATES THEOREM

A new generalized equation of state for polar and non-polar fluids based on the corresponding states theorem is developed, f n addition to two critical parameters, four parameters are required; two for the calculation of volumetric properties and two for the calculation of pressure and departure functions. Parameteres for more than 100 polar and non-polar fluids are given. Comparison with the existing generalized state equations showed that the new method, in general, shows a better agreement with the experimental data. The absolute average deviation is 0.48% for the vapor pressure and 0.32% for the saturated liquid volume.     

AN EMPIRICAL VIRIAL-LIKE CUBIC EQUATION OF STATE FOR PHASE EQUILIBRIUM CALCULATIONS

An empirical cubic equation of state(EOS) was obtained by truncating the virial expansion in reciprocal of molar volume after the third term. The constants of the EOS was generalized in terms of critical temperature, critical pressure and Pitzer's acentric factor.

In pure component applications the EOS exhibited a performance comparable to Peng-Robinson (1976) EOS in the reduced temperature range of 0.5 to 1. The present EOS tends to predict better saturation liquid volumes at reduced temperatures below 0.8, and better estimations for second virial coefficient at high reduced temperatures.

The EOS was successfully employed for vapor liquid equilibrium calculations for some mixtures of normal or slightly polar fluids with traditional one binary parameter mixing rule at moderately high pressures. At low reduced temperatures, where conventional one adjustable parameter applications of the cubic equations compare unfavorably with dual methods based on excess Gibbs energy functions for the liquid phase, a new two constant mixing rule introduced by Stryjek and Vera (1986) was employed for the present equation of state.     

IMPROVED LIQUID DENSITIES WITH MODIFIED PENG—ROBINSON EQUATION

The Peng-Robinson equation gives poor results when used to calculate liquid phase densities. In order to improve the calculated liquid phase densities, the b constant in the Peng-Robinson equation has been expressed as a linear function of temperatrue. Preliminary evaluation indicates that this modification significantly improves predicted liquid densities for pure components.     

A CRITICAL EVALUATION OF THREE EQUATIONS OF STATE FOR DENSE GASES AGAINST OBSERVED DATA

The van der Waals, the Benedict-Webb-Rubin, and a virial equation of state predictions for dense gases are evaluated against observed “integral” properties (p, ρ, T) and “slope” properties like the speed of sound [(∂p/∂p)^1/2₃], isothermal compressibility coefficient [(∂ In ρ /∂p)_T], and few other thermodynamic properties directly derived from the observed data. The documented procedure thus constitutes a stringent test methodology to evaluate the applicability of these equations of state to dense gases which may also be followed for appraising any other equation of state. The graphical comparisons between the predictions and the observed data are presented and discussed critically     

MODELLING OF A COMPLEX POLAR SYSTEM WITH A MODIFIED SOAVE-REDLICH-KWONG EQUATION

A phase equilibrium model which will allow vapor-liquid equilibrium and liquid-liquid equilibrium calculations to be made over a broad range of operating conditions has been developed. The base equation is a Soavc-Rcdlich-Kwong equation of slate. Modifications are introduced. Model predictions ar: compared to literature data for two binary pairs and three multicomponent systems. Examples will include: 1) the hydrogen-water binary pair, 2) the ammonia-water binary pair from below the critical of ammonia to above the critical of ammonia, and 3) three examples from an operating unit including one liquid-liquid system.     

改进SRK方程提高正构烷烃饱和蒸气压和液体体积预测精度

<正>引言 在化学工程和油藏工程的相平衡和其他热力学性质计算中,两参数立方型SRK方程应用最为广泛。然而,在某些情况下由SRK方程预测的饱和蒸气压出预测的液体体积偏差较大,无法满足工程计算的需要,必须改进方程,提高其预测精度。1 饱和蒸气压的改进 SRK方程可以写为 p=RT/（V-b）-(a(T)）/V(V+b) （1）     

双流体配位状态方程在共聚物及共混物体系中的应用

采用双流体配位模型状态方程,对三个共聚物体系P(VAC/E)、P(S/MMA)及P(EP),两个共混物体系PVME/PS、PPO/PS进行了关联,精度较好.提出了共聚物的共混物假设的新设想.在关联中发现共聚物及共混物体系的二元模型参数具有一定的加和性,本文采用一个较为简单的混合规则,用均聚物的模型参数估算二元模型参数,进行了pVT数据预测,并与实验数据比较,具有良好的预测效果.