Calculation of solution-vapor thermodynamic equilibria by the method of minimizing the Gibbs energy

An algorithm of direct numerical minimization of the Gibbs energy for calculating the liquid-vapor thermodynamic equilibrium in multicomponent systems is proposed. The method makes it possible to simultaneously determine the distributions of concentrations in the vapor and solution and the vapor mole fractionwhen the temperature, pressure, and initial mixture composition are given. The developed algorithm is distinguished from the existing equilibrium calculation methods by a higher stability and the capability of obtaining solutions in the range of parameters in which the conventional algorithms are not able to produce a physically meaningful result. The Peng-Robinson equation of state is used to simulate the Gibbs energy. The accuracy of the proposed algorithm is illustrated by comparison with experimental data.     

利用PR状态方程计算临界终点

In the design of chemical processes, such as catalytic cracking of bitumen and heavy oil, the knowledge of phase behavior at the critical endpoint is essential. Based on the PR equation of state, the algorithm developed by Heidemann and Khalil for calculating critical properties was used to compute critical points. An algorithm for determining the equilibrium phase of the critical point using the tangent plane criterion was developed, and was used to calculate the critical endpoints of different mixtures, including non-polar, polar and associating systems. The critical endpoint, representing the type of the phase behavior, was employed to fit the interaction parameter of mixtures in critical state at high pressure. Lines of critical endpoints for ternary mixtures were also determined with the algorithm.     

低温甲醇脱碳工艺热力学模型和过程模拟研究

为了进行含高压气体和强极性物质的体系的低温甲醇脱碳工艺的模拟研究,建立相应的热力学模型.采用Soave-Redlich-Kwong(SRK)立方型状态方程,结合Huron-Vidal混合规则和非随机双流体Non-Random-Two-Liquid(NRTL)活度系数模型建立的热力学模型,从气体溶解度和气液平衡数据拟合获...     

PSRK模型的修正混合规则及其应用于聚合物溶液汽液平衡的预测

To extend the PSRK(predictive Soave-Redlich-Kwong equation of state)model to vapor-liquid equilibria of polymer solutions,a new EOS-gE mixing rule is applied in which the term ∑ xi ln(b/bi)in the PSRK mixing rule for the parameter a,and the combinatorial part in the original universal functional activity coefficient(UNIFAC)model are cancelled.To take into account the free volume contribution to the excess Gibbs energy in polymer solution,a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied [b1/2 ij= 1/2(b1/2 i b1/2 j)].The literature reported Soave-Redlich-Kwong equation of state(SRK EOS)parameters of pure polymer are employed.The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium(VLE)of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.     

Calculating the Liquid–Gas Equilibrium in the Fischer–Tropsch Synthesis

The problem of determining the equilibrium composition of the gas phase from the known composition of the liquid phase is analyzed in terms of the Redlich–Kwong–Soave equation of state modified by Wang. An effective algorithm is suggested for solving this problem for systems with an arbitrary number of components. The molecular-weight distribution of the Fischer–Tropsch synthesis products can be estimated by calculating the composition of the gas phase from composition data for the liquid phase resulting from the reaction.     

Modified Soave-Redlich-Kwong equations of state applied to mixtures containing supercritical carbon dioxide

The well-known equation of state Soave-Redlich-Kwong and two of its modifications are applied to describe vapor-liquid equilibrium in binary asymmetric mixtures, which contain supercritical carbon dioxide and a heavy component. Several mixing rules including the classical van der Waals mixing rules with one and two interaction parameters, non-quadratic mixing rules, and the used of a Gibbs free energy model, are used with these equations. Seven mixtures containing supercritical carbon dioxide are considered in the study. The experimental data were obtained from literature sources and the adjustable parameters were found by minimizing the errors between predicted and experimental data of the concentration of the solute in the liquid phase. The work allows concluding on the advantages, disadvantages and expected accuracy of these equations of state and mixing rules for correlating vaporliquid equilibrium data in asymmetric systems as those studied.     

A simple and unified algorithm to solve fluid phase equilibria using either the gamma–phi or the phi–phi approach for binary and ternary mixtures

A new algorithm is proposed for calculating phase equilibria in binary systems at a fixed temperature and pressure. This algorithm is then extended to ternary systems (in which case, the mole fraction of one constituent in a given phase must be fixed in order to satisfy the Gibbs’ phase rule). The algorithm has the advantage of being very simple to implement and insensitive to the procedure used to initialize the unknowns. Most significantly, the algorithm allows the same solution procedure to be used regardless of the thermodynamic approach considered (γ–φ or φ–φ), the type of phase equilibrium (VLE, LLE, etc.) and the existence of singularities (azeotropy, criticality and so on).     

Melting temperature depression caused by high pressure gases. Effect of the gas on organic substances and on ionic liquids

The effect on the melting temperature depression (MTD) of organic substances and ionic liquids caused by different types of pressurizing gases is analyzed. A high pressure gas produces a combined effect between solubility and pressure that causes the melting temperature to decrease. The authors have previously used phase equilibrium relations to correlate MTD of organic substances and ionic liquids under high pressure carbon dioxide, but other gases were not considered. The Peng–Robinson equation of state with the Wong–Sandler mixing rules showed to be appropriate for correlating the phase equilibrium in these high pressurized systems and is the model used is in this work. Three organic substances (naphthalene, biphenyl and octacosane) under high pressure produced by three gases (ethane, ethylene and carbon dioxide) for which experimental data on MTD are available were considered in this study. Then extension to an ionic liquid under high pressure carbon dioxide and high pressure ethylene was done. The proposed thermodynamic method and the model used show to have the necessary flexibility to acceptably correlate the MTD produced in these systems.     

Application of PSRK for Process Design

A survey about the current status and potential of the predictive Soave-Redlich-Kwong (PSRK) group contribution equation of state (EoS) is given. The PSRK method combines the SRK EoS with the UNIFAC group contribution model by the PSRK mixing rule. The availability of a large number of interaction parameters between UNIFAC and new PSRK main groups allows calculating the phase equilibrium behavior and other thermodynamic quantities for various kinds of systems even with strong electrolytes. Different fields of application are discussed: the prediction of gas solubilities in asymmetric systems, the air solubility calculated for mixed solvents, the removal of H₂S from natural gas by predicting the physical absorption, and the calculation of the enthalpy effects of absorption processes with pressure and temperature.     

Application of PSRK for Process Design

A survey about the current status and potential of the predictive Soave-Redlich-Kwong (PSRK) group contribution equation of state (EoS) is given. The PSRK method combines the SRK EoS with the UNIFAC group contribution model by the PSRK mixing rule. The availability of a large number of interaction parameters between UNIFAC and new PSRK main groups allows calculating the phase equilibrium behavior and other thermodynamic quantities for various kinds of systems even with strong electrolytes. Different fields of application are discussed: the prediction of gas solubilities in asymmetric systems, the air solubility calculated for mixed solvents, the removal of H₂S from natural gas by predicting the physical absorption, and the calculation of the enthalpy effects of absorption processes with pressure and temperature.     

甲醇合成反应热力学分析及实验研究

比较了近年来文献中甲醇合成反应平衡常数的各种计算方法,采用固定反应器在反应温度为230－270℃和反应压力为5－8MPa的条件下对甲醇合成反应热力进行了实验研究。结果表明,不同计算方法的预测结果存在较大的差异,而采用Reid的热容 数据及SRK方程得到的计算结果与实验结果吻合很好,具有良好的预测能力。     

Calculation and Properties of the Inhomogeneity Function during the Phase Transformation of Multicomponent Systems

Theoretical Foundations of Chemical Engineering - An equation is derived for calculating the inhomogeneity function in the equilibrium liquid–vapor phase transition processes. In the...     

A RELIABLE METHOD FOR LIQUID-LIQUID PHASE EQUILIBRIUM CALCULATION AND GLOBAL STABILITY ANALYSIS

A new algorithm to determine liquid-liquid phase equilibrium at the global minimum of the Gibbs free energy is presented, the optimization results are then used by Newton-Raphson method to obtain the final accurale phase equilibrium compositions. The tangent plane distance function criterion is used as the sufficient and necessary condition for the global stability analysis, its global minimum is obtained by the simulated annealing algorithm in order to overcome the multiple local minimum problem. The Gibbs free energy functions for liquid-liquid equilibrium systems are formulated by NRTL or UNIQUAC activity coefficient equation. Aiming to overcome the nonconvex problem of the Gibbs free energy function the simulated annealing algorithm is used for achieving a near true equilibrium solution, this solution then is used as the initial values of the Newton-Raphson method. Our algorithm was implemented and tested for six examples with three components and up to three liquid phases. In all of the examples, results for liquid-liquid equilibrium calculations and global stability analysis were found to be reliable. The main advantage of our algorithm is its simplicity and that it is model independent.     

Calculation of Multiphase Liquid–Liquid Equilibrium and Automated Synthesis of the Structures of Phase Diagrams

A new method is suggested for calculating liquid–liquid equilibrium. The method requires the global structure of the phase diagram to be determined. An algorithm for the automated synthesis of diagram structures is developed.     

A MODEL FOR THE DISTRIBUTION OF ACID GASES BETWEEN AN AQUEOUS ALKANOLAMINE SOLUTION AND LPG

The model of Deshmukh and Mather (1981) is a popular method for correlating and predicting the vapor-liquid equilibria in systems containing acid gases (hydrogen sulfide and carbon dioxide) and aqueous solutions of alkanolamines. The model includes phase equilibrium between an aqueous liquid and a gas as well as chemical equilibrium in the aqueous phase. A recent review by Weiland et al. (1993) demonstrated the accuracy of the correlation. Presented here is a model based on that of Deshmukh and Mather (1981) for calculating the distribution of acid gases between two liquid phases - an aqueous phase and a non-aqueous liquid (typically a propane- or butane-rich liquid)

In the new model the phase equilibrium is modeled using a modified Henry's law approach. Fugacities of the components in the non-aqueous phase are calculated using the Peng and Robinson (1976a) equation of state. All of the parameters in the model are taken from the literature. Thus the model represents a prediction of the behavior. It is demonstrated that the predictions are in good agreement with the available experimental data     

Thermochemical Computations on Propellant Powder Gases at interior ballistic pressures and temperatures

The interaction of powder gas molecules in the interior ballistic pressure and temperature range does not allow the application of the Nobel-Abel equation of state. An equation of state which correlates the thermodynamic variables pressure, specific volume, and temperature, and which meets to a high extent the physical facts, is the virial equation. Using an additive combined theorem for the virial coefficients, the equations for equilibrium in a chemically reacting gas composition without solid phase are derived by virtue of the virial equation as an equation of state. The internal energy and the enthalpy of the powder gases are given for the computation of the explosion temperature and the adiabatic flame temperature. For a numerical solution of this non-linear system of equations, a combination of the gradient process and the Newton-Raphson process (Such-Weg-Verfahren) is applied. Furthermore, the numerical results for different propellant powders are stated and discussed.     

凝析气相态行为的模拟

针对含重质烃的多元混合物提出了PR模型参数新的关联方法.对多于7个碳的重烃,其状态方程参数a和b改为通过可由实测数据确定的T_B、(?)和T计算,避免了由不同经验关联式计算的临界参数T_c、P_c和(?)值不一致的缺点.作者将经上述改进的PR模型应用于凝析气相态行为的模拟计算(露点压力、恒质量膨胀和恒容衰竭等过程)取得了较满意的结果.     

An Efficient and Stable Algorithm for Calculating Fictive Temperatures

An algorithm is given for calculating the fictive temperature of glass based on the differential form of Narayanaswamy's equation. This algorithm is more convenient and much more efficient than direct solution of the integral equation and has been implemented in viscoelastic stress analysis using finite-difference and finite-element methods.     

气-液-液-水合物多相平衡闪蒸的新算法

有水合物存在的多相闪蒸计算对于水合物法分离技术非常重要.提出了一个进行气-液-液-水合物四相闪蒸计算的新算法.其中气-液（富烃相）-液（富水相）三相平衡闪蒸计算采用Patel-Teja状态方程,Chen-Guo水合物模型用于气相与水合物相平衡的计算.此算法避免了求解复杂的方程组,因此使计算简单化.通过气体与纯水体系和有抑制剂体系的计算检验表明,此算法有很好的计算稳定性.