面向方程联立求解的精馏塔模拟与优化一体化算法

在精馏塔机理模型的基础上,提出了面向方程联立求解的精馏塔模拟与优化一体化算法.精馏塔模型方程的特殊结构使得可以进行一定的变量分解和降维,采用面向方程联立求解的技术,使模拟计算和寻优搜索在同一层迭代中完成,避免了双层法每一步优化搜索都需进行模型收敛计算的缺点.从而大大提高了计算效率.同时,这样的联立法提供了一种开放式的统一框架.无论是模拟计算、操作优化还是设计优化都可以毫无困难地利用这个灵活的计算结构进行解算.文中用两个计算实例说明了这个方法的有效性.     

化工过程系统物料衡算的信号流图法(一)

在对化工过程系统进行设计或研究的过程中,特别是在对化工过程系统进行优化的过程中,往往要多次进行有关系统的物料衡算。实际上,物料衡算在化工过程系统的数学模拟中占有极其重要的地位。迄今为止,对化工过程系统的物料衡算问题的求解方法进行了大量的工作,提出了不少方法。这些方法大致有三类:直接法,线性模型法和模块化法。第一类方法是对系统的所有方程同时求解,所有变量进行迭代,计算时间长而内存需要大。第三类方法将单元过程的有关方程安排在相应的模块中,采用单元迭代,逐个模块进行计算,易于通用化和序列化。这     

精馏塔联立优化的简约空间SQP算法

引言采用面向开放式方程的联立算法求解精馏塔优化问题,可以使模拟计算和寻优搜索在同一层迭代中完成,避免了双层法每一步优化搜索都需进行模型收敛计算的缺点,从而可以大大提高计算效率．而且原则上可任意指定自由变量．无论是模拟计算、操作优化还是设计优化都可以利用这个灵活的计算结构进行解算.高效、可靠的非线性约束最优化算法是实现精馏塔联立优化的关键．在流程模拟和过程系统优化中,序贯二次规划法（SequentialQuadraticProgramming,SQP)因其较高的计算效率而被广泛应用．SQP算法中,每一个迭代步都需要求解一个QP子问题…     

TS法的改进及其在求解化工优化问题中的应用

TS算法属于现代优化算法,是局部领域搜索法的推广,常用于求解组合优化问题.利用TS法搜索过程的有向性和能够跳离局部最优解的特点,对其进行了改造,以适应求解连续变量化工优化问题.首先,根据化工优化问题变量的特性,提出了一种简便的邻域映射方案,并改进了迭代过程中自适应因子的下降函数;进一步分析对比了禁忌步数、自适应因子和初始解等参数对于优化结果的影响.然后通过算例和换热网络优化问题的求解,表明改造后的TS法在求解连续变量化工优化问题中的有效性,及其在化工优化领域的发展价值.     

环丙沙星冷却结晶动力学测定

依据粒数衡算方程,采用分离变量方法求解粒数密度函数表达式,依据该方法通过加晶种的间歇冷却结晶实验研究了环丙沙星在23％(体积)水/乙醇溶液中的结晶动力学数据,得到了结晶动力学方程,为工业结晶动力学的测定、结晶特性辨识、粒度分布预测和控制提供了新的方法.     

基于复变量求导法反演边坡岩土体强度参数初探

提出了弹塑性参数反演的一种新方法,即复变量求导法、优化计算方法以及弹塑性有限元法三者的结合.利用弹塑性有限元方法正演计算测点处位移(复数形式),采用复变量求导法求解灵敏度矩阵,通过迭代优化方法完成变量更新,直至最终得到符合要求的解.数值算例表明,该方法对岩土体抗剪强度参数反演有效可靠,解决了参数反演时位移对反演参数不敏...     

丁烯异构反应精馏动态模型和开车过程模拟

建立了以严格的相平衡计算为基础的2-丁烯反应精馏制1-丁烯的过程动态模型,其中各组分的逸度和活度用RKS方法和Scatchard-Hildebrand方程计算.在模拟计算时用差分方法求解塔板的能量衡算方程,用可变阶数Numerical Differentiation Formulas(NDFs)方法求解全塔的组分物料衡算方程.比较了开车时不同的阀门线性调节时间对过程变量的影响.结果表明,所建立的模型能很好地反映反应精馏过程的动态特性,开车时可先进行全回流操作,之后直接将进出料阀门瞬间开至设定值.     

工业结晶过程的多相流与粒数衡算的CFD耦合求解

考虑不同尺寸的晶体为不同的分散相,通过有限体积法差分不同尺寸组的晶体求解粒数衡算方程,建立了质量衡算与粒数衡算之间的联系,在考虑晶体成核和生长的条件下,建立了稳态结晶过程的粒数衡算方程与多相流方程的耦合求解方法,得到了工业结晶过程的计算流体力学模拟模型。使用商业软件ANSYS CFD,采用该模型对DTB 型工业结晶器中氯化钾-水体系的结晶过程进行了模拟,最终获得不同尺寸晶体的流场和固体含量的分布信息,从而实现结晶过程的仿真模拟。对部分模拟结果与实验值进行了比较,结果表明模拟结果与实验结果吻合较好。     

基于QUKF的随钻测斜仪姿态估计算法研究

针对煤矿井下随钻测斜仪测量钻孔姿态角时，传感器容易受到外界干扰，引起解算姿态角误差的问题，本文采用一种基于四元数无迹卡尔曼滤波（quaternion unscented Kalman filter,QUKF）的姿态估计算法减小误差。首先通过四元数微分方程结合陀螺仪输出以及噪声误差，构建无迹卡尔曼滤波（unscented Kalman filter,UKF）状态方程；然后利用加速度计和磁强计的输出结合噪声误差作为观测值，构建量测方程；最后将迭代得到的四元数通过姿态旋转矩阵解算姿态角。通过MATLAB仿真以及双轴转台实验验证该估计算法，实验中经过该算法解算的俯仰角和方位角最大绝对误差均小于0.7°。实验表明，该算法可以有效减小随钻测斜仪测量姿态角时受到外界干扰的影响，提高测量精度。     

塑料熔体在注塑模中的三维流动模拟

建立了非等温条件下黏性、不可压缩、非牛顿流体流动的控制方程.为了避免同时求解耦合的压力场、速度场,通过修改传统方法的变分方程导出了关于压力场的拟Poisson方程,用迭代法独立求解连续性方程、动量方程,并进行速度场-黏度迭代求出最终的压力场、温度场.这种方法可以减少内存,提高数值方法的稳定性,避免了Hele-Shaw模型中容易引起争议的“中面”概念,并能模拟中面方法不能模拟的一些物理现象.算例表明数值结果与实验结果吻合较好,这种方法可以成功地预测注射成型流动过程中的重要特征.     

Process control structure screening by steady-state multiple disturbance sensitivity analysis

Control structures with poor steady-state disturbance rejection characteristics are screened from further consideration in the control design stage using steady-state multiple disturbance sensitivity analysis of the nonlinear process models. The procedure deals with the general case where an unequal number of manipulated and controlled variables are employed. A quadratic objective function that defines the relative importance of the control objectives and the manipulated variables governs the behaviour of the system. Continuation methods trace the optimal solution set under the influence of multiple disturbances and parameter variations. The method handles saturation of manipulated variables, control loop failures and hard bounds on the controlled variables efficiently.     

Design of single-effect mechanical vapor compression

This paper presents a comprehensive design model of the single effect mechanical vapor compression process. Previous literature models focused on determination of the heat transfer area and compressor power consumption. Several new design features included in this study are the evaporator dimensions, demister dimensions, dimensions of the non-condensable gases venting orifice, and capacity of the vacuum system. The model equations include fundamental mass and energy equations; power consumption of the vapor compressor; and a well tested set of correlations for calculations of the physical properties of the vapor and liquid streams, heat transfer coefficients, and thermodynamic losses. Dependence of system variables on temperature and salinity makes the system equations nonlinear and requires an iterative solution. System performance is discussed as a function of the product flow rate, brine boiling temperature, temperature difference of the saturated boiling brine and compressed vapor, and length of the evaporator tube. Comparison of the design results against available field data shows good agreement for the predictions of specific power consumption and specific heat transfer area.     

A solution method for solving coupled nonlinear boundary-value problems

A Strum-Liouville integral transform technique is novelly applied to solve system of coupled nonlinear boundary-value problems approximately. The systems of differential equations consist of a linear differential operator and a nonlinear function of the dependent variables. To illustrate the potential of this technique we consider an example which comes from the modeling of diffusion and nonlinear chemical reaction systems in chemical engineering. The approximate solutions obtained by our technique agree surprising well with the numerically exact solutions obtained by the orthogonal collocation technique. To improve the approximation an iteration scheme in transform space is also defined.

Scope—Today, mathematical modeling of physical phenomena often produces (single or coupled) nonlinear differential equations. The true physical situation can, in many cases, be more closely described if the differential equations are allowed to be nonlinear. However, nonlinear differential equations are generally too difficult to be solved analytically apart from a few “tricks” or substitutions which apply only to a handful of equations [1]. An alternative approach is to look for a method which will reduce the problem, via analytical techniques, to a point where a “simple” computer program can solve the rest of the problem. The method introduced in this paper belongs to this class of solution techniques.

The method, which in this paper is applied to solving coupled nonlinear boundary-value problems, is a generalization of an idea in a paper by Do and Bailey [2] who apply it to a single nonlinear differential equation of boundary-value type. The equations, to which the technique is applied, arise from Fick's law diffusion into a porous solid and nonlinear reaction within the solid.

The solution method employs a Strum-Loiuville integral transform and to account for the nonlinear part an approximation is introduced. An iteration scheme is defined to improved the accuracy of the solution. The system of coupled nonlinear differential equations is reduced to a system of coupled nonlinear algebraic equations which is solved using a Newton-Raphson process. Finally, the solution is expressed as an infinite series, which is summed using a computer.

In response to papers by Do and Bailey [3] and Do and Weiland [4], Jerri [5] has tried to put this method on a more mathematical footing, and he shows that this method is a special case of a more general technique he has devised. Jerri uses the idea of Fourier transforms and convolution products to justify his method. The results for the example he considered are good, but he did not state how many iterations he required to obtain the solutions reported.

Conclusions and Significance—This paper has presented a very powerful method of solving boundary-value problems with linear operators and a nonlinear function of the dependent variable. The method works well for a single equation or coupled equations and can handle any kind of nonlinear function. We have shown through extensive numerical calculation the accuracy of this solution method, where the accuracy is measured in terms of a ratio of norms. In most cases an error of 4% can be achieved with just one iteration (Tables 2 and 3). Even though the present method has been applied to problems which have arisen from the modeling of chemical engineering problems, it would also be applicable to differential equations arising in other areas, provided they are of the same form.     

Design Optimization of Convective Driers by Using Spreadsheets

The optimal design of a convective drier is hereby considered by means of using a well-known spreadsheet: Microsoft Excel 5. OTm.The degree of freedom analysis enabled a non linear equations system to be set up, in such a way that it was possible for different design variables to be considered. The equations system was keyed in to provide a possible solution via the iterative procedure built in the spreadsheet. Other complementary variables were computed to provide a unit cost for the operation, thus occasioning the opportunity of considering an economic objective function.Constraint and design variables were identified in the program. By giving initial values to the design variables, and by using the optimization capabilities included in Microsoft Excel 5.0Tm, an optimal set of values for the design variables was determined.Finally, the influence of constraint and design variables was analyzed, where both the input air temperature and the relative humidity of exhaust air were binding factors.     

A model-based characterization of the long-term asymptotic behavior of nonlinear discrete-time processes using invariance functional equations

The present research work proposes a new approach to the problem of quantitatively characterizing the long-term dynamic behavior of nonlinear discrete-time processes. It is assumed that in order to analyze the process dynamic behavior and digitally simulate it for performance monitoring purposes, the discrete-time dynamic process model considered can be obtained: (i) either through the employment of efficient and accurate discretization methods for the original continuous-time process which is mathematically described by a system of nonlinear ordinary (ODEs) or partial differential equations (PDEs) or (ii) through direct identification methods. In particular, nonlinear processes are considered whose dynamics can be viewed as driven: (i) either by an external time-varying “forcing” input/disturbance term, (ii) by a set of time-varying process parameters or (iii) by the autonomous dynamics of an upstream process. The formulation of the problem of interest can be naturally realized through a system of nonlinear functional equations (NFEs), for which a rather general set of conditions for the existence and uniqueness of a solution is derived. The solution to the aforementioned system of NFEs is then proven to represent a locally analytic invariant manifold of the nonlinear discrete-time process under consideration. The local analyticity property of the invariant manifold map enables the development of a series solution method for the above system of NFEs, which can be easily implemented with the aid of a symbolic software package such as MAPLE. Under a certain set of conditions, it is shown that the invariant manifold computed attracts all system trajectories, and therefore, the asymptotic process response and long-term dynamic behavior are determined through the restriction of the discrete-time process dynamics on the invariant manifold.     

Structural analysis and solution of systems of algebraic design equations

A new method for expressing the structure of a system of equations is developed using a type of occurrence matrix entitled the functionality matrix. The functionality matrix indicates not only the occurrence of variables in equations but also the functional form in which they occur. Since the difficulty of solving an equation for a variable is related to its functional form, analysis of the functionality matrix provides explicit information on the difficulty of solution of the solution of the equation. A methodology for the solution of design problems by digital computers is described. This methodology operates on the functionality matrix which describes the set of design equations. Algorithms using this methodology interact and guide the designer in an efficient selection of design variables and redundant equations. Once design variables and redundant equations are selected, a computational method is presented for ordering and solving the equations.     

Efficient solution of sparse sets of design equations

A new algorithm is described which can help the engineer find efficient strategies for solving sets of equations of the sorts that arise in process design. The algorithm systematically exploits small subsets of equations that can be solved directly because they are linear in certain variables or can be reduced to solvable forms. Technically a combination of ‘partitioning’ and ‘indexing,’ it recognizes that ‘tearing’ to make the equation set ‘triangular’ for iteration may not minimize the number of variables which must be iterated, or ‘torn’. Requiring only simple matrix rearrangements, the algorithm has been implemented easily by hand for systems of 15 or more equations. It yields improvements in strategies published by Lee{et al.} and Christensen and thus makes plain the possibility of improving on published precedence-ordering and tearing algorithms for computer-aided design.     

Solution of reaction and heat flow problems by nonlinear estimation

Before the advent of nonlinear optimization algorithms, the solution of chemical reaction or heat transfer equations was attempted primarily by trial and error or linear approximation methods. In the method illustrated by the two examples in this paper, any set of nonlinear equations for a chemical or physical process are replaced by a single equation. The variables of interest are in the resulting functional equation treated as parameters whose optimum values are determined by a nonlinear estimation technique. These values are considered as nonlinear regression coefficients which are simultaneously adjusted by an optimization algorithm. The method gives an estimate of the standard deviation in the determination of the value of each variable and provides information concerning the errors associated with their interaction or pairwise correlations. Validity of the results is confirmed by comparison with solutions independently obtained through a matrix technique developed by Wu ⁽¹⁾. For each of the examples the magnitude of computed residual is provided as a measure of the precision of the solution set. The general method is applicable to a very wide class of physical and chemical problems described by one or more nonlinear equations.     

Design Optimization of Convective Driers by Using Spreadsheets

ABSTRACT

The optimal design of a convective drier is hereby considered by means of using a well–known spreadsheet: Microsoft Excel 5. OTm.The degree of freedom analysis enabled a non linear equations system to be set up, in such a way that it was possible for different design variables to be considered. The equations system was keyed in to provide a possible solution via the iterative procedure built in the spreadsheet. Other complementary variables were computed to provide a unit cost for the operation, thus occasioning the opportunity of considering an economic objective function.Constraint and design variables were identified in the program. By giving initial values to the design variables, and by using the optimization capabilities included in Microsoft Excel 5.0Tm, an optimal set of values for the design variables was determined.Finally, the influence of constraint and design variables was analyzed, where both the input air temperature and the relative humidity of exhaust air were binding factors.     

Fuzzy cognitive approach of a molecular distillation process

Takagi-Sugeno fuzzy model is presented as an alternative modeling tool for the molecular distillation process of heavy liquid petroleum residues. A nonlinear phenomenological model formed by partial differential equations involving temperature and composition is regarded as a virtual working plant for the generation of data required to build the fuzzy models. Furthermore, experimental data from the molecular distillation process of an atmospheric residue 673.15 K upward (673.15 K+) at different operating conditions were used to develop the fuzzy representations. In this work, the system was simulated through the development of software in Fortran 90/95 and the numerical solution by using the finite-difference method. In the fuzzy approaches, the distillation temperature and the feed flow rate are the input variables, while the liquid interface temperature, the film thickness, the concentration profiles, and the distillate flow rate were considered as the output responses. The fuzzy models obtained were compared with the results generated from the phenomenological model, showing an excellent agreement.