热耦合空分流程变负荷特性分析与模拟方法

针对管网升压事件讨论低温空分三塔精馏热耦合流程的变负荷操作模拟问题。分析认为,此大规模变负荷问题的求解难点在于耦合流程操作变量的微小变化引起了精馏塔浓度波形的大幅度移动,某些变量在微小步长上产生数量级的变化,基于牛顿法及其改进算法的数值计算方法在梯度计算中难以获得正确的下降方向,导致收敛困难。利用工况变量构造同伦参数并采用回溯同伦法(HBM)进行自动搜索,可以有效解决考虑耦合换热器换热面积计算的变负荷问题,能够描述因粗氩塔顶换热温差减小引起的“氮塞”现象,对过程控制更有指导意义。     

模拟三相精馏过程的新算法

提出一种新算法Newton同伦-同时校正混合法模拟三相精馏过程,该算法将同时校正法有机地嵌入同伦法中,采用同伦弧长微分法求解,在保持同伦算法大范围收敛特性的同时,提高了计算效率.采用Michlesen稳定性判据作为液相稳定性判据.以正丙醇-正丁醇-水物系三相精馏塔为例,验证了算法的有效性.     

同伦函数法用于非理想物系分离的计算

在多组分非理想物系分离计算中，考查了牛顿同伦法、热力学同伦法，莫弗里板效率为参数的参数连续法。实例计算表明同伦函数法是一种对初值要求不高，对各种非理想物系分离计算效果较好的一种算法。     

大范围工况变化下联塔的严格机理模拟研究

建立基于严格机理的乙烯生产过程联塔系统开放式模型,采用大规模系统优化方法和自动微分方法,对此联塔系统进行大范围工况变化下的模拟.求解结果和收敛效率与Aspen Plus进行了对比.在初值相同、标度相同、建模和求解方式一致的情况下,本文联立求解方法的结果与Aspen Plus的EO模式的求解结果一致;对于进料工况大范围变化的情形,本文的联立求解方法收敛性明显优于Aspen Plus.采用大规模优化计算方法和稀疏自动微分方法对于提高求解效率、降低初值依赖性具有明显的效果.     

换热器动态参数模型的建立与计算分析

利用分布集中参数法建立了换热器(蒸发器和冷凝器)的动态参数模型,膨胀阀和压缩机采用稳态方程的形式作为动态模型的可移动边界,从而使模型方程封闭可解。模型针对水源热泵机组内的蒸发器和冷凝器在模拟工况下进行计算。求解基于MATLAB的偏微分方程组,利用PDEPE函数,输入初值函数、边界条件和问题描述函数,分别得出机组运行过程中换热器内制冷剂的温度、压力和换热系数随换热管长度的变化曲线。     

预测共沸物的同伦-牛顿联合方法

为了更有效地预测共沸系统,文内提出了同伦-牛顿联合算法,首先利用具有全局收敛性的同伦算法产生较好的初值,然后利用收敛速度快的牛顿算法求解共沸方程。应用联合方法预测了多个二元和三元非理想性物系的共沸点,结果表明,同伦-牛顿联合方法有较大的收敛范围,较高的迭代过程稳定性,较快的收敛速度。     

计算非线性方程组所有解的同伦连续法

在化工领域中，数学模拟导致非线性方程组的求解问题。介绍了一种同伦连续算法，可以不依赖于初值，求出非线性方程组的所有解。特别是经过映射变换，数学计算更为方便。     

聚酯酯交换塔的数学模型—反应精馏塔的模拟计算

本文用三对角矩阵法建立了聚酯（ＰＥＴ）酯交换塔的数学模型，并且通过移动参数的办法对这个数学模型进行了求解，讨论并验证了在用三对角矩阵法模拟反应精馏塔的过程中，选择初值、改善收敛性的几种常用方法。     

用同伦延拓算法模拟热偶精馏过程

讨论了考虑任意塔板可以存在交联流股的通用精馏过程的数学模型.以分离苯、甲苯、邻二甲苯物系的热偶精馏过程为计算实例,采用同伦延拓算法求解,在多种工况下均得到多解,并从中找出操作特性、经济效益均佳的设计条件.     

低浓度丙烯和苯催化精馏合成异丙苯过程非平衡级模拟

对苯与低浓度丙烯合成异丙苯的催化精馏过程建立非平衡级模型。针对模拟过程难以收敛的特点,在计算的开始阶段引入了模式搜索法（Hook-Jeeves method)求解。通过对变量的取值范围进行一定的约束,可比牛顿型法适用较宽的初值范围。计算中根据所用催化精馏塔的特点,对方程进行了一定程度的简化。得到了催化精馏塔内的温度及液相组成分布。模拟结果与试验数据吻合较好,可以为工艺设计提供参考。     

Reliable computation of solid solubility in dense gases through homotopy continuation approach

A method to reliably compute the solid solubility in supercritical fluids is described. The method is based on computing all the possible roots of equifugacity equation at given temperature and pressure through homotopy continuation. The equifugacity equation is reformulated through global fixed-point homotopy. The global fixed-point homotopy guarantees that all the solutions of a non-linear equation can be located on a single homotopy path when it is forced to start from a single starting point. The starting point is selected from a criterion which minimizes the number of real roots of the global fixed-point homotopy function. Homotopy continuation-based formulation of equifugacity equation is also used to directly generate the solubility-pressure and solubility-temperature bifurcation diagrams by selecting either pressure or temperature as continuation parameter. These bifurcation diagrams provide a direct pathway to locate the cross-over pressures. The effect of equation of state model parameters on solid solubility through homotopy continuation based sensitivity analysis is also analyzed. Peng Robinson Stryjek Vera equation of state with conventional and Wong-Sandler mixing rules are used.     

Controlled Picard Method for Solving Nonlinear Fractional Reaction–Diffusion Models in Porous Catalysts

This paper discusses the diffusion and reaction behaviors of catalyst pellets in the fractional-order domain as well as the case of nth-order reactions. Two generic models are studied to calculate the concentration of reactant in a porous catalyst in the case of a spherical geometric pellet and a flat-plate particle with different examples. A controlled Picard analytical method is introduced to obtain an approximated solution for these systems in both linear and nonlinear cases. This method can cover a wider range of problems due to the extra auxiliary parameter, which enhances the convergence and is suitable for higher-order differential equations. Moreover, the exact solution in the linear fractional-order system is obtained using the Mittag–Leffler function where the conventional solution is a special case. For nonlinear models, the proposed method gives matched responses with the homotopy analysis method (HAM) solutions for different fractional orders. The effect of fractional-order parameter on the dimensionless concentration of the reactant in a porous catalyst is analyzed graphically for different cases of order reactions and Thiele moduli. Moreover, the proposed method has been applied numerically for different cases to predict and calculate the dual solutions of a nonlinear fractional model when the reaction order n?=??1.     

Iterative identification of output error model for industrial processes with time delay subject to colored noise

To dealwith colored noise and unexpected load disturbance in identification of industrial processes with time delay, a bias-eliminated iterative least-squares (ILS) identification method is proposed in this paper to estimate the output error model parameters and time delay simultaneously. An extended observation vector is constructed to establish an ILS identification algorithm. Moreover, a variable forgetting factor is introduced to enhance the convergence rate of parameter estimation. For consistent estimation, an instrumental variable method is given to deal with the colored noise. The convergence and upper bound error of parameter estimation are analyzed. Two illustrative examples are used to show the effectiveness and merits of the proposed method.     

Analysis of a pH‐Based Potentiometric Biosensor Using the Homotopy Perturbation Method

A mathematical model of steady‐state and non‐steady‐state responses of a pH‐based potentiometric biosensor immobilizing organophosphorus hydrolase was developed. The model is based on non‐stationary diffusion equations containing a nonlinear term related to the Michaelis‐Menten kinetics of an enzymatic reaction. An analytical expression for the substrate concentration was obtained for all values of parameter a (Thiele modulus) using the homotopy perturbation method. From this result, the concentrations of the deprotonation products of an organophosphodiester (P_hH, ZH and AH) were obtained. Our analytical results were compared with available simulation results. A satisfactory agreement with the simulation data is noted.     

Homotopy continuation enhanced branch and bound algorithms for strongly nonconvex mixed-integer nonlinear optimization

Large-scale strongly nonlinear and nonconvex mixed-integer nonlinear programming (MINLP) models frequently appear in optimization-based process synthesis, integration, intensification, and process control. However, they are usually difficult to solve by existing algorithms within acceptable time. In this study, we propose two robust homotopy continuation enhanced branch and bound (HCBB) algorithms (denoted as HCBB-FP and HCBB-RB) where the homotopy continuation method is employed to gradually approach the optimum of the NLP subproblem at a node from the solution at its parent node. A variable step length is adapted to effectively balance feasibility and computational efficiency. The computational results from solving four existing process synthesis problems demonstrate that the proposed HCBB algorithms can find the same optimal solution from different initial points, while the existing MINLP algorithms fail or find much worse solutions. In addition, HCBB-RB is superior to HCBB-FP due to much lower computational effort required for the same locally optimal solution.     

Boundary layer flow of nanofluid over an exponentially stretching surface

The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically with the help of homotopy analysis method (HAM). The convergence of HAM solutions are obtained by plotting h-curve. The expressions for velocity, temperature and nanoparticle volume fraction are computed for some values of the parameters namely, suction injection parameter α, Lewis number Le, the Brownian motion parameter Nb and thermophoresis parameter Nt.     

氮化铝粉末制备方法研究进展

综述了AIN粉末制备方法的特点和研究进展,包括直接氮化法、碳热还原法、电弧熔炼法、气相反应法、等离子体法、裂解法、自蔓延高温合成法、高能球磨法和微波合成法。根据合成的原理及反应物的状态对这些方法进行了归类,重点论述了直接氮化法和碳热还原法的研究动态。     

过程系统变负荷下的数据校正与参数估计方法

过程系统的数据校正与参数估计是进行实时操作优化与过程控制的基础。过程系统变负荷下由于模型参数变化的非线性及显著误差的影响,导致数据校正与参数估计的结果不准确,从而影响实时操作优化与过程控制的效率。针对此问题,本文提出了一种用于变负荷下的数据校正与参数估计方法。此方法主要包括过程的稳态检测与数据采样,多工况下的数据聚类和基于多组测量的数据校正与参数估计。首先选择有效和可靠的过程测量数据,根据变负荷下工况的波动性与系统的非线性特征进行数据聚类,最后基于聚类结果调整模型参数使得模型输出与过程测量数据偏差最小。此方法可有效地减小模型参数变化的非线性及显著误差对数据校正与参数估计结果的影响。基于现场的测量数据,将此方法应用于空气分离流程系统中,结果显示了基于此方法的数据校正与参数估计结果更准确。