气流床粉煤气化的Gibbs自由能最小化模拟

用Gibbs自由能最小化方法对粉煤气化过程进行了热力学平衡分析。对一混合煤种,在3.0 MPa和气化温度限制在1 200 ℃～1 450 ℃时,研究了氧-煤比、蒸气-煤比对气化炉出口气体组成、温度和有效气产率的影响,并由此确定了可行的操作域是氧-煤比545m3/t～605 m3/t、蒸气-煤比为152.64 kg/t～313.92 kg/t及其对应的工艺指标。从操作域中选择有代表性的工艺条件为氧-煤比578 m3/t、蒸气-煤比为187 kg/t,对应的气化炉出口温度1 358 ℃,CO+H2干基体积分数为91.5%,有效气产率为2.123(CO+H2)m3/kg。同时,研究了碳转化率和热损失对气化工艺指标的影响,其影响是显著的。     

The decisive role of calorimetric measurements in equilibrium phase diagram calculations

In this paper, examples are given of how calorimetric values can give greater certainty to phase equilibria calculated from thermodynamic data. Errors that may arise when phase diagram evaluations are carried out largely from the basis of Gibbs energy information only are illustrated by reference to recent evaluations of the Ti?Si system and the resulting calculated oxidation behaviour of titanium silicides. The importance of calorimetric values for calculation of metastable phase equilibria is demonstrated by results of work on the AlN?TiN hard-metal coating system. Finally, suggestions are made with regard to areas of work where calorimetric data are urgently needed.     

The Area method for pure fluids and an analysis of the two-phase region

The Area method, developed recently for solving multicomponent phase equilibrium problems, has been extended to pure fluids. The method is based on maximizing a single objective function in the Helmholtz-volume surface along any given isotherm, which reduces the number of independent variables to only two: the saturated liquid and vapour volumes. Two techniques are employed to find the maximum of the objective function, the integral and iterative. The integral always finds the thermodynamically stable solution without any prior assumptions about the values of the molar volumes. This factor distinguishes the integral from the iterative technique and also from methods based on the Maxwell equal-area principle. The method has been applied to a group of high accuracy non-cubic equations of state and some of the thermodynamic inconsistencies which occur inside the two-phase region are explored. A new inequality constraint which eliminates these inconsistencies during the development of new equations of state is proposed, and initial results with fitting a preliminary Helmholtz equation of state for benzene are encouraging.     

A comparative study of particle swarm optimization and its variants for phase stability and equilibrium calculations in multicomponent reactive and non-reactive systems

Particle swarm optimization is a novel evolutionary stochastic global optimization method that has gained popularity in the chemical engineering community. This optimization strategy has been successfully used for several applications including thermodynamic calculations. To the best of our knowledge, the performance of PSO in phase stability and equilibrium calculations for both multicomponent reactive and non-reactive mixtures has not yet been reported. This study introduces the application of particle swarm optimization and several of its variants for solving phase stability and equilibrium problems in multicomponent systems with or without chemical equilibrium. The reliability and efficiency of a number of particle swarm optimization algorithms are tested and compared using multicomponent systems with vapor–liquid and liquid–liquid equilibrium. Our results indicate that the classical particle swarm optimization with constant cognitive and social parameters is a reliable method and offers the best performance for global minimization of the tangent plane distance function and the Gibbs energy function in both reactive and non-reactive systems.     

Evaluation of repulsive particle swarm method for phase equilibrium and phase stability problems

Phase equilibrium and stability problems are of crucial importance in simulation, design and optimization of several separation processes. Recently, these problems have been solved using minimization of Gibbs free energy, using global optimization techniques. In this paper, repulsive particle swarm (RPS), a recent global optimization technique is explored for the solution of phase stability and phase equilibrium.     

Solid-liquid equilibrium using the SAFT-VR equation of state: Solubility of naphthalene and acetic acid in binary mixtures and calculation of phase diagrams

A solid-liquid equilibrium (SLE) thermodynamic model based on the SAFT-VR equation of state (EOS) is presented. The model allows for the calculation of solid-liquid phase equilibria in binary mixtures at atmospheric pressure. The fluid (liquid) phase is treated with the SAFT-VR approach, where molecules are modelled as associating chains of tangentially bonded spherical segments interacting via square-well potentials of variable range. The equilibrium between the liquid and solid phase is treated following a standard thermodynamic method that requires the experimental temperature and enthalpy of fusion of the solute. The model is used to calculate the solubilities of naphthalene and acetic acid in common associating and non-associating organic solvents and to determine the solid-liquid phase behaviour of binary mixtures with simple eutectics. The SAFT-VR pure component model parameters are determined by comparison to experimental vapour pressure and saturated liquid density data with the choice of association models according to the nature of the molecule; in addition, an unlike adjustable parameter (k_ij) is used to model the solutions. The solubility data of naphthalene and acetic acid in both associating and non-associating solvents are reproduced essentially within the accuracy of the experimental measurements. The phase boundaries and the position of the eutectic points in the binary mixtures considered are, in most cases, reproduced with the accuracy commensurate with the industrial applications. Overall, the results presented show that the SAFT-VR EOS can be used with confidence for the prediction of the SLE of binary systems at atmospheric pressure.     

Modelling of phase equilibria for associating mixtures using an equation of state

In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures.     

Use of GAMESS/COSMO program in support of COSMO-SAC model applications in phase equilibrium prediction calculations

Thermodynamic models based on conductor-like screening models (COSMO) offer viable alternatives to existing group-contribution methods for the prediction of phase equilibria. Normally a COSMO-based model requires input of the distribution of screening charges on the molecular surface, aka. the sigma profile, determined from a specific quantum chemistry program and settings. For example, the COSMO-SAC model requires input of DMol³ generated sigma profiles. In this paper, we investigate the proper settings for an open-source quantum chemistry package GAMESS in order to generate sigma profiles to be used directly in the COSMO-SAC model. The phase behaviors (VLE and VLLE) of 45 binary mixtures from 10 commonly used solvents and the solubilities of 4 complex drug compounds in these solvents calculated from DMol³ and GAMESS generated sigma profiles are compared. While noticeable fine structure differences are observed in the individual sigma profiles for the same chemical compound generated from the two packages, it is found that the accuracy in the VLE/VLLE and solubility predictions from the two packages are comparable. Based on the systems we studied here, the open-source GAMESS/COSMO program with proper program settings could be used as an alternative sigma profile generation source in support of COSMO-SAC model applications in phase equilibrium prediction calculations.     

Modeling of phase equilibria with CPA using the homomorph approach

For association models, like CPA and SAFT, a classical approach is often used for estimating pure-compound and mixture parameters. According to this approach, the pure-compound parameters are estimated from vapor pressure and liquid density data. Then, the binary interaction parameters, k_ij, are estimated from binary systems; one binary interaction parameter per system. No additional mixing rules are needed for cross-associating systems, but combining rules are required, e.g. the Elliott rule or the so-called CR-1 rule. There is a very large class of mixtures, e.g. water or glycols with aromatic hydrocarbons, chloroform-acetone, esters-water, CO₂-water, etc., which are classified as “solvating” or “induced associating”. The classical approach cannot be used and the cross-association interactions are difficult to be estimated a priori since usually no appropriate experimental data exist, while the aforementioned combining rules cannot capture the physical meaning of such interactions (as at least one of the compounds is non-self-associating). Consequently, very often one or more of the interaction parameters are optimized to experimental mixture data. For example, in the case of the CPA EoS, two interaction parameters are often used for solvating systems; one for the physical part (k_ij) and one for the association part (β^cross). This limits the predictive capabilities and possibilities of generalization of the model. In this work we present an approach to reduce the number of adjustable parameters in CPA for solvating systems. The so-called homomorph approach will be used, according to which the k_ij parameter can be obtained from a corresponding system (homomorph) which has similar physical interactions as the solvating system studied. This leaves only one adjustable parameter for solvating mixtures, the cross-association volume (β^cross). It is shown that the homomorph approach can be used with success for mixtures of water and glycols with aromatic hydrocarbons as well as for mixtures of acid gases (CO₂, H₂S) with alcohols and water. The homomorph approach is less satisfactory for mixtures with fluorocarbons as well as for aqueous mixtures with ethers and esters. In these cases, CPA can correlate liquid-liquid equilibria for solvating systems using two adjustable parameters. The capabilities and limitations of the homomorph approach are discussed.     

Prediction of vapor-liquid equilibrium data of the system MTBE + methanol + ethanol by PRSV2 EOS

The Stryjek and Vera (1986) [9] modification of Peng-Robinson (PRSV2) equation of state has been applied for modeling vapor-liquid equilibrium of the systems MTBE + methanol, MTBE + ethanol and methanol + ethanol. Binary interaction parameters for mixing rules have been estimated by using experimental data at the atmospheric pressure. The calculated binary interaction parameters were used for predicting azeotropic behavior at high pressure and also for isobaric equilibrium points which showed an excellent agreement with experimental data. In addition, estimated binary interaction parameters for binary systems were used for ternary system (MTBE + methanol + ethanol). The predictions deviated only slightly from the experimental data. The results show PRSV2 can be used for VLE prediction of polar systems.     

超临界CO2+CH3OH及C2H5OH二元系的气液平衡

在带有石英可视窗和内搅拌的可变体积高压釜内，测定了超临界CO2＋CH3OH及C2H5OH两个系统的相平衡数据，温度为50－200℃，压力4．0－16．0MPa，利用从硬球模型得出的适用于高压高温的状态方程，计算了这两个系统的临界曲线，并与实验值进行比较。     

Prediction of phase equilibria in hydrocarbon + near-critical solvent systems

In this paper the Hole Quasichemical Group-Contribution model (HM) is used to describe phase diagram peculiarities of multicomponent aqueous systems containing hydrocarbons and alcohols. The model correctly describes liquid-liquid (LL), liquid-liquid-vapour (LLV), liquid-vapour (LV) and vapour-vapour equilibria (VVE), and critical and azeotrope curves. The potential use of the HM in the prediction of the solubilities of hydrocarbons in near-critical water and the densities of coexisting phases in the critical region of the system n-hexane-water are presented.     

Application of stochastic algorithms for parameter estimation in the liquid–liquid phase equilibrium modeling

In this work the Simulated Annealing (SA) and Particle Swarm Optimization (PSO) algorithms were employed to modeling liquid–liquid phase equilibrium data. For this purpose, some strategies for stochastic algorithms were investigated from common test functions and used in LLE parameter estimation procedure. The strategy used for the flash calculation was based on the isoactivity criteria associated with phase stability test and interpolation function for the initial estimate to improve reliability of phase equilibria calculations. It is shown that both algorithms SA and PSO were capable of estimating the parameters in models describing liquid–liquid phase behavior of binary and multicomponent systems with a good representation of the experimental data.     

A simple method for evaluation of parameters of the Bender equation of state from experimental data

A simple numerical method for evaluation of parameters (constants) of Bender equation of state for pure fluids is proposed. The minimisation of the objective function leads to a set of linear equations. The method employs experimental data on state behaviour (p–ρ–T) of fluid phases, vapour–liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas–liquid critical point. Results of the tests using data for two fluids (methane and n-pentane) are presented.     

Analytic calculation of phase diagrams for solutions containing colloids or globular proteins

Second-order Barker–Henderson perturbation theory gives phase diagrams for colloid and protein solutions that include stable and metastable fluid–fluid, solid–fluid, and solid–solid phases. The potential of mean force is described by a hard-sphere interacting with a Yukawa potential. Calculations for different ranges of attraction show that, as expected, fluid–fluid coexistence becomes metastable when the potential becomes short-ranged. For a very short-ranged Yukawa potential, the phase diagram shows isostructural solid–solid equilibria with a critical point. To test more simplified models, phase diagrams from second-order Barker–Henderson perturbation theory are compared with those from the random-phase approximation for the fluid phase and the van der Waals theory for the solid phase; this comparison shows significantly different phase diagrams. Moreover, with a potential of mean force with primary and secondary minima, calculations using second-order perturbation theory identify conditions where colloidal and protein solutions can present two fluid–fluid regions, each with a critical point; however, the higher-density fluid–fluid region is likely to be metastable. The analytic calculations described here may be useful for interpretation of experimental phase diagrams and for guiding design of separation processes.     

An equation of state for hydrogen fluoride

Using a similar approach as Lencka and Anderko [AIChE J. 39 (1993) 533], we developed an equation of state for hydrogen fluoride (HF), which can correlate the vapor pressure, the saturated liquid and vapor densities of it from the triple point to critical point with good accuracy. We used an equilibrium model to account for hydrogen bonding that assumes the formation of dimer, hexamer, and octamer species as suggested by Schotte [Ind. Eng. Chem. Process Des. Dev. 19 (1980) 432]. The physical and chemical parameters are obtained directly from the regression of pure component properties by applying the critical constraints to the equation of state for hydrogen fluoride. This equation of state together with the Wong–Sandler mixing rule as well as the van der Waals one-fluid mixing rule are used to correlate the phase equilibria of binary hydrogen fluoride mixtures with HCl, HCFC-124, HFC-134a, HFC-152a, HCFC-22, and HFC-32. For these systems, new equation of state with the Wong–Sandler mixing rule gives good results.     

CO2与2-丁醇二元系统的高压相平衡模型

采用固定体积可视观察法测定了在323.2~353.2 K温度范围内2-丁醇在CO₂中高压相平衡数据. 运用Peng-Robinson状态方程(PR)和van der Waals-2混合规则建立了相平衡模型, 并运用Chrastil半经验方程建立了溶解度方程. 通过优化计算得到了状态方程中的模型参数, 同时得到的Chrastil溶解度方程为c=ρ^3.3617·exp(-2198.8193/T+6.5545). 二元体系的溶解热为-18.2809 kJ/mol.