混合整数非线性规划法求解多组分复杂体系相平衡问题

基于Gibbs自由能最小化原理,提出一种求解多组分复杂体系相平衡问题的混合整数非线性规划(MlNLP)方法.通过建立MlNLP模型,将相平衡计算问题转化为有约束的双层最优化问题,内层用来计算给定相组合结构下的平衡组成,外层则是搜索最优的相组合结构,整个求解过程通过遗传算法来实现.所建立的方法只需要求解最小化问题,就可以同时给出多相平衡时存在的相数、相态及各相组成.以苯-乙氰-水和甲醇合成两个体系的相平衡计算为例,结果表明该方法是可行和有效的.     

应用遗传算法求解含化学反应体系的相平衡

基于Gibbs自由能最小原理 ,提出一种求解含化学反应体系相平衡的方法。采用反应进度和相分率消去等式约束 ,将含化学反应体系的相平衡计算转化为无约束的最优化问题 ,并应用遗传算法求解。采用本文提出的方法 ,能够避免计算中负数的组分摩尔数或摩尔分数的出现 ,确保得到组分的摩尔数或摩尔分数为非负的全局最优解。以聚甲醛反应体系的汽液平衡计算为例 ,表明本文所提出的方法是可行和有效的     

含盐酸和盐的气液固三相平衡计算

利用亨利定律和溶解平衡方程,建立了气液固同时存在时体系总Gibbs自由能的数学模型,活度系数模型选用Pitzer模型,基于相平衡体系Gibbs自由能最小化原理,运用遗传算法求解,计算NaCl-KCl-HCl-H2O体系固液平衡和气液平衡,并和实验数据进行对比,进一步计算了该体系固液气三相平衡,实现了一步计算固相、液相和气相的组成。     

多相多组分体系相平衡计算的改进τ因子法

提出了一种多相平衡计算的改进τ因子法,该方法基于一种修正各相摩尔分数和的概念,研究模型的建立和用遗传算法计算多组分复杂体系的相平衡问题。首先通过建立数学模型,将相平衡计算问题转化为带线性约束的非线性规划(NLP)问题;其次用遗传算法对模型进行求解,并通过对优化变量采取动态边界的可行域编码方法保证了算法的有效实施;最后对2个体系的计算表明,结果与文献值相吻合,且此方法不仅可以求解不含化学反应体系的相平衡问题,也同样适用于含化学反应体系的相平衡计算,是一种比较可靠和通用的方法。     

多相多组分化学反应平衡和相平衡计算的遗传算法

引　言多相多组分化学反应平衡和相平衡的计算是热力学研究的基础问题 ,同时也是化工流程模拟的重要环节 ,建立快速、稳定的求解方法具有特别重要的理论和现实意义 早期的以及目前应用较多的平衡常数法 (K值法 )的缺点是要预先知道体系的组分数、相态和具体反应 ,不适用于相态和反应未知的复杂体系 .Gibbs自由能最小法虽然具有通用性 ,然而需要求解多变量和复杂约束的非线性规划问题 对于非理想体系 ,涉及逸度、逸度系数的计算 ,这还是一个含有大量局部最优解的非凸问题[1,2 ] ,所以传统的数学规划算法不能保证得到全局最优解 文献 [3]…     

非理想多相共存体系的平衡计算

对于给定温度和压力的系统，平衡状态时其吉布斯自由能最小。根据热力学基本关系式，在多组分体系中元素和电荷守恒的限制条件下，最小化吉布斯函数，通过SQP方法来求解此有约束的优化问题，通过迭代法求解反应后的温度。该方法可用于复杂的非理想、多相流体、电解液或非电解液混合物的相平衡计算，平衡计算结果包括温度、密度、组分浓度等。对于某新型热动力系统中使用的一种含铝火药，应用本文方法，获得了化学平衡计算结果。     

缩合法合成甲基苯基二氯硅烷反应热力学研究

本工作研究了氯苯和甲基二氯硅烷气相缩合生成甲基苯基二氯硅烷反应体系,指出在温度低于600℃时,反应体系可由一个主反应和两个副反应组成的反应网络描述,并给出了此三个反应的平衡常数和反应热.利用吉布斯自由能最小化原理计算了热力学平衡组成和产品的平衡收率.计算表明由于副反应的平衡移动,温度升高有利于提高甲基苯基二氯硅烷的平衡...     

甲醇-乙酸-丙酸多元体系汽液平衡

用新型泵式沸点仪测定了在100kPa下甲醇-乙酸、甲醇-丙酸、乙酸-丙酸3个二元体系以及甲醇-乙酸-丙酸三元系在不同液相组成时的沸点,并用间接法T-p-x(温度、压力和液相摩尔分数)推算了3个二元体系的汽相平衡组成。3个二元体系活度系数分别用Wilson模型、NRTL模型、Margules模型和van Laar模型进行关联,用最小二乘法求出了它们的液相活度系数模型参数,同时,用这些模型参数来计算它们的汽相摩尔分数。所得的液相活度系数来计算3个二元体系的过量吉布斯自由能函数,且所研究的所有体系中各组分之间不存在共沸点。用3个二元体系Wilson模型参数对所测的三元体系数据进行关联,建立该系统汽液平衡的热力学模型并计算平衡时的汽相摩尔分数和泡点温度。由面积积分法检验这些模型参数计算的3个二元体系相平衡数据,得到很好的热力学一致性。     

甲醇-乙酸、甲醇-丙酸和乙酸-丙酸二元体系汽液平衡

用新型泵式沸点仪测定了101.325 kPa下甲醇-乙酸、甲醇-丙酸和乙酸-丙酸3个二元系在不同液相组成时的沸点,用过量自由能函数Q,采用间接法由Tpx推算了3个二元体系的汽相平衡组成y。3个二元体系活度系数分别用Wilson模型、NRTL模型、Margules模型和Van Laar模型进行关联,用最小二乘法求出了它们的液相活度系数模型参数。用所得的液相活度系数来计算此二元体系的过量吉布斯自由能函数GE/(RT)。用3个二元系模型参数对所测的数据进行关联,建立该系统汽液平衡的热力学模型并计算平衡时的泡点温度。计算的泡点与实验的沸点吻合良好,经面积积分法检验,这些模型参数计算的3个二元体系相平衡数据具有很好的热力学一致性。     

七水硫酸锌热解过程的吉布斯自由能 最小原理及TG-DTA分析

利用吉布斯自由能最小原理计算了七水硫酸锌在25～1 100 ℃下的平衡组成,并结合TG-DTA研究了其热分解过程。七水硫酸锌的热解大致可以分为脱结晶水和无水物热分解两个阶段。脱水发生在室温～311 ℃时,无水物热分解则发生在687～1 050 ℃时。脱水段固相含有ZnSO4·6H2O、ZnSO4·H2O、ZnSO4·xH2O［x∈（0.8,0.9）］等,无水物分解段中间产物有ZnO2·ZnSO4,最终固相产物为ZnO。结果表明,吉布斯自由能最小原理和TG-DTA具有内在一致性。     

Customized minimization techniques for phase equilibrium computations in reservoir simulation

This paper discusses a minimization algorithm for the solution of the Gibbs free energy minimization problem involving at most two phases. There are three major aspects to this paper. The first is the selection of descent directions and step lengths in order to handle the poorly scaled phase equilibrium problems associated with mixtures near bubble points and critical points. The second is the prevention of convergence to trivial solutions in both the Gibbs free energy minimization problem for two-phase mixtures and the associated phase stability test for single-phase mixtures. The third is the use of effective convergence criteria to obtain either the desired level of accuracy in the solution or the maximum accuracy allowed by the problem and the computer.     

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.     

复杂体系化学平衡组成计算方法

The chaos-Monte Carlo algorithm (CMCA) was proposed for solving chemical equilibrium of complex system. By introducing random well-distributed points into the Monte Carlo algorithm, this new approach showed good convergent probability and high-speed. Equilibrium composition of some complex systems, such as methanol synthesis, ammonia oxidation, and Claus process were calculated. The results showed good agreement with Liu Xiaodi‘s and Xu Jinhuo‘s calculations. Compared with the gradient method, the genetic algorithm and the modified genetic algorithm, the CMCA is simple, general and insensitive to initial value. It is an efficient algorithm based on the theory of minimization of Gibbs free energy to solve chemical equilibrium of complex system.     

Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method

This paper presents a new method for multiphase equilibria calculation by direct minimization of the Gibbs free energy of multicomponent systems. The methods for multiphase equilibria calculation based on the equality of chemical potentials cannot guarantee the convergence to the correct solution since the problem is non-convex (with several local minima), and they can find only one for a given initial guess. The global optimization methods currently available are generally very expensive. A global optimization method called Tunneling, able to escape from local minima and saddle points is used here, and has shown to be able to find efficiently the global solution for all the hypothetical and real problems tested. The Tunneling method has two phases. In phase one, a local bounded optimization method is used to minimize the objective function. In phase two (tunnelization), either global optimality is ascertained, or a feasible initial estimate for a new minimization is generated. For the minimization step, a limited-memory quasi-Newton method is used. The calculation of multiphase equilibria is organized in a stepwise manner, combining phase stability analysis by minimization of the tangent plane distance function with phase splitting calculations. The problems addressed here are the vapor–liquid and liquid–liquid two-phase equilibria, three-phase vapor–liquid–liquid equilibria, and three-phase vapor–liquid–solid equilibria, for a variety of representative systems. The examples show the robustness of the proposed method even in the most difficult situations. The Tunneling method is found to be more efficient than other global optimization methods. The results showed the efficiency and reliability of the novel method for solving the multiphase equilibria and the global stability problems. Although we have used here a cubic equation of state model for Gibbs free energy, any other approach can be used, as the method is model independent.     

甲醇乙烯烷基化反应体系热力学分析

考察了甲醇乙烯烷基化反应体系各独立反应吉布斯自由能随温度变化情况,采用吉布斯自由能最小法计算得到不同反应条件下体系平衡组成。结果表明:该反应体系主要受动力学控制;适当升高温度有利于烯烃生成,且乙烯和丁烯的生成是丙烯生成反应的阻碍点;在只生成丙烯的极端情况下,单独考察生成丙烯的反应,为了提高丙烯产率,需要适当降低反应温度,若综合考虑设备和能耗等因素,体系存在最佳反应压力和进料比(乙烯与甲醇摩尔比)。     

Bilevel optimization formulation for parameter estimation in liquid-liquid phase equilibrium problems

Excess Gibbs free energy models contain parameters which for a given mixture are estimated from measurements of phase-splits. Local composition models are very flexible and can accurately predict complex phase behavior. However, in many cases it has been reported that use of local composition models leads to prediction of more phase splits or more phases than measured, modeling homogeneous azeotropes as heterogeneous, etc. Here, a formulation is proposed that addresses these limitations of current parameter estimation methods. The formulation is based on a bilevel program, i.e., an optimization problem embedded in another one. Minimizing the error between model predictions and measurements gives the upper-level program. The lower-level programs are given by the minimization of the Gibbs free energy, or equivalently the satisfaction of the Gibbs tangent plane criterion. Each of the experiments is cast as a separate lower-level program. Additional requirements on the phase behavior of the system, such as enforcing the correct number of phase splits and the correct number of phases in each phase split, are similarly formulated as additional lower-level programs. Global optimization techniques are necessary even to obtain a feasible point since the lower-level programs are nonconvex. The proposed formulation is applied to problems from the literature, in which inappropriate fitting of the parameters of the non-random two-liquid (NRTL) model to experimental data has been reported to result in significant model errors, such as the prediction of an additional spurious phase split. The discussion is restricted to binary mixtures, however, the formulation can in principle be applied also to multicomponent mixtures.     

等离子体裂解煤制乙炔碳-氢体系的热力学平衡分析

碳-氢多相多组份体系的化学反应平衡组成可用Gibbs自由能极小化法求得. 计算表明：把C-H体系视为单相体系是不合理的，只有在多相体系下的计算结果才是真正意义上的热力学平衡组成，两种体系在生成乙炔的最佳温度范围和平衡组成两方面都有较大的差别. 得出C-H体系中生成乙炔的最佳温度范围是3400~3800 K的高温区域.