甲醇在加压条件下脱水生成二甲醚的动力学研究

在压力3.0 MPa～5.0 MPa、反应温度260℃-380℃、液空速(2.5～8.0)ml/(g·h)条件下,在等温积分反应器内,采用0.154 mm～0.198 mm的CM-3催化剂,考察操作条件对甲醇转化率的影响,测定甲醇气相脱水生成二甲醚的反应动力学实验数据.实验结果表明,随着压力的增加,甲醇转化率下降;加压条件下,温度提高甲醇转化率提高,在380℃左右接近平衡;甲醇转化率随着空速的增加而降低.以Langmiur均匀吸附双曲型动力学方程式建立以各组分逸度表示的本征动力学模型,根据实验数据用参数估值方法获得动力学模型中的参数.残差分析和统计检验表明,动力学模型是适宜的.     

氯乙烯装置苯氯化脱低沸物的反应动力学研究

氯乙烯装置中的少量苯等低沸物不易从装置中除去,并严重影响装置的稳定运行.针对氯乙烯装置中少量苯进行了苯的 .氯化反应研究,基于幂函数型动力学模型,提出了宏观反应动力学方程.对文献中的实验数据进行了整理,针对文献中实验数据少的缺点,对实验数据进行了补充.利用补充后的实验数据对动力学参数进行了回归.得到苯氯化反应动力学方程的指前因子k0为59.466 5,反应活化能E为24.295 4 kJ·kmol-1,氯的浓度项指数为1.194 5,苯的浓度项指数为0.479 6.使用得到的动力学模型对实际氯乙烯装置苯氯化反应器进行了结构参数的计算,与实际反应器结构参数进行了对比,结果表明计算值与实际值吻合度较高,说明得到的反应动力学方程对氯乙烯装置中的苯氯化反应适用性较高.     

甲醇-环己酮二元体系汽液平衡的测定与关联

用改进的Ellis汽液平衡釜测定甲醇-环己酮二元体系常压汽液平衡数据,并校验实验数据的Herington热力学一致性,结果表明实验数据满足热力学一致性要求.以汽相组成的误差平方和作为目标函数,分别用Willson和NRTL方程关联实验数据,得两热力学方程的模型参数.汽相组成的模型计算值与实验值的平均相对偏差分别为0.56%和1.10%.     

盐酸-水-盐体系的汽液平衡预测

电解质溶液汽液平衡的预测和计算是加盐萃取精馏模拟的基础,准确计算电解质溶液的汽液平衡有重要的理论和实际意义。本文应用Chen的电解质溶液NRTL模型,根据电解质-水二元体系的汽液平衡数据回归的二元参数．对盐酸-水-氯化钙与盐酸-水-氯化镁两种体系的汽液平衡进行了预测,温度的平均绝对误差分别为0．32(K)和0．39(K),汽相摩尔分数的平均绝对误差分别为0．0080和0．0070。计算结果与文献数据比较一致。     

甲酸-水-N-甲基吡咯烷酮体系等压汽液平衡的研究

在常压下测试甲酸-水、甲酸-N-甲基吡咯烷酮、水-甲酸-N-甲基吡咯烷酮的汽液平衡数据。考虑甲酸在汽相中的缔合效应,用维里方程和Hayden-O'connell关联式修正了汽相的非理想性,并用非线性最小二乘法关联前2对二元体系的汽液平衡数据,得NRTL和Wilson方程的模型参数。以NRTL模型参数预测三元体系汽液平衡数据,温度平均偏差为1.76℃,甲酸的汽相平均偏差为0.032 2,水的汽相平均偏差为0.040 4;以Wilson模型参数预测三元体系汽液平衡数据,温度平均偏差为1.66℃,甲酸的汽相平均偏差为0.027 5,水的汽相平均偏差0.011 6,可见2个模型预测值均与实验值吻合良好,而Wilson模型的关联精度较高。     

常压下丙醛-水-甘油体系汽液平衡测定与关联

采用单循环汽液平衡釜测定了常压条件下丙醛-水的二元以及丙醛-水-甘油三元汽液平衡数据。运用MATLAB中求解非线性最小二乘法问题的函数Lsqnonli,结合丙醛-水的二元汽液平衡实验据,迭代出了Margules、Vanlaar、Wilson和UNIQAC四个方程的二元模型参数。通过计算值和实验值的比较,Wilson方程的相对误差均小于5%,故选择Wilson方程为本体系的适合模型。将测定的丙醛-水-甘油三元汽液平衡数据与模型参数带入Wilson方程求得的三元汽液平衡数据相比较,相对误差均小于5%,由此验证了本文Wilson模型参数的可靠性。本文的测定结果和计算结果为丙醛-水-甘油体系的萃取精馏模拟选择了合适的模型,关联得到的Wilson模型参数,为萃取精馏过程的模拟计算打下基础,同时也为丙醛和水混合液的有效分离提供了一定基础数据。     

盐-水-乙醇-乙二醇体系汽液平衡的预测

电解质溶液汽液平衡的预测和计算是是热力学的一个重要研究领域,是加盐萃取精馏模拟计算的重要基础,精 确的推算电解质溶液的汽液平衡数据有着十分重要的理论和实际意义。本文改进了计算电解质溶液汽液平衡的LI- QUAC模型,用计算水-乙醇-乙二醇体系汽液平衡更为精确的NRTL模型代替lIQUAC模型中的UNIFAC模型来计 算溶剂分子间相互作用对超额Gibbs自由能的影响,并据此推算出两种盐-水-乙醇-乙二醇体系的汽液平衡数据, 与本文实验数据及文献数据比较,结果比较满意。该模型对电解质溶液汽液平衡的进一步研究以及加盐萃取精馏的工 程计算均具有一定的指导意义。     

碳酸二乙酯-草酸二乙酯二元体系汽液平衡数据的测定与关联

测定了碳酸二乙酯草酸二乙酯二元体系常压汽液平衡数据，利用二元体系的汽液平衡实验数据，运用Visual Basic计算机语言，采用EOS γ法分别用Wilson和NRTL方程模拟计算了碳酸二乙酯-草酸二乙酯二元体系在常压下的汽液平衡并进行了关联，其平均偏差分别为0．0309和0．0201，并进行了热力学一致性检验，两种不同模型的计算结果与实验值都较为吻合，其中以NRTL拟合结果为更好。     

无实验参数模型的汽液平衡模拟

在无实验参数的条件下模拟汽液平衡,计算量大,计算过程复杂,对一些特殊的混合物计算误差较大,限制了模拟计算的应用范围,本文采用改进的UNIFAC计算活度系数模型和修正的拉乌尔定律模拟汽液平衡,再用构造饱和蒸汽压计算误差函数迭代计算汽液平衡温度,用试位法克服迭代计算中的收敛问题.改进了试位法的终止条件,通过调整迭代的初始温度,大大降低了迭代次数,有效提高了计算速度,对一些特殊的混合物也具有较好的模拟结果,在5 931 mmHg压力下,对水-乙酸混合物模拟计算的平均迭代次数仪19次,在Visual C++环境中,用面向对象的方法,实现了无实验参数模型模拟汽液平衡,数据处理用独立的类完成,并采用了动态分配内存的方法处理数据,使计算模块具有较好的独立性和复用性,最后在不同的压力下,模拟计算了乙醇-水、水-醋酸和苯-甲苯等混合物,证明该法可模拟实际过程,计算速度较快,模拟效果较好.     

基于非线性最小二乘法的Van Laar常数计算

以汽液平衡实验数据或以基于UNIFAC模型计算获得的汽液平衡数据为基础,采用非线性最小二乘法与数值计算的方法相结合计算VanLaar常数,对计算的过程和方法进行了详细的分析,并利用计算得到的VanLaar常数对20余个二元混合物进行模拟计算,其中包含了恒温和恒压条件下的数据计算,也包含了不同温度和不同压力条件下的汽液平衡数据计算,并应用计算结果进行验算,与相应的实验结果或通过UNIFAC模型计算获得的结果进行对比,计算所获得数据与实验数据相比,平均误差小于3%。同时,对不同的物系进行误差分析,非理想物系和强极性物系的误差较大,一般物系的平均误差小于1%,并使用计算获得的VanLaar常数进行汽液平衡曲线模拟,与实际汽液平衡曲线对比,效果理想。结果表明,采用非线性最小二乘法结合数值计算方法获得的VanLaar常数误差较小,可用于相关汽液平衡的模拟和计算。     

A Class of Sparse Spectral Operators for Inversion of Powers of the Laplacian in N Dimensions

For inversion of the Laplacian subject to Dirichlet boundary conditions and, more generally, for the kth power of the Laplacian subject to boundary conditions on the function and its first k – 1 derivatives in the normal coordinate, there is a sparse symmetric, well-conditioned, projection of the operator that results from an expansion in associated Legendre polynomials.     

Zakai equation of nonlinear filtering with unbounded coefficients. The case of dependent noises

In this paper, we prove that the unnormalized filter associated with nonlinear filtering problems with dependent noises and a one-dimensional observations process the coefficients of which are unbounded solves a parabolic stochastic partial differential equation, the Zakai equation. The robust form of the Zakai equation is also computed.     

Numerical solution of GRLW equation using Sinc-collocation method

In this paper, we present a meshfree technique for the numerical solution of the generalized regularized long wave (GRLW) equation. This approach is based on a global collocation method using Sinc basis functions. The propagation of single solitons and the interaction of two solitary waves are used to validate the method which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the method.     

求一类非线性偏微分方程解析解的简洁构造算法

通过引入一个变换,利用齐次平衡原理和选准一个待定函数来构造求解一类非线性偏微分方程解析解的算法.作为实例,我们将该算法应用到了mKdV方程,KdV-Burgers方程和KdV-Burgers-Kuramoto方程.借助符号计算软件Mathematica获得了这些方程的解析解.不难看出,该方法不仅简洁,而且有望进一步扩展.     

Perturbation of solutions of ordinary linear homogeneous differential equations of the second order

In this paper we give a method for peturbation of solutions of linear homogeneous differential equation of the second order.     

On exponential stability of linear non-autonomous functional differential equations of neutral type

General linear non-autonomous functional differential equations of neutral type are considered. A novel approach to exponential stability of neutral functional differential equations is presented. Consequently, explicit criteria are derived for exponential stability of linear non-autonomous functional differential equations of neutral type. A brief discussion to the obtained results and illustrative examples are given.     

非线性演化方程的新Jacobi椭圆函数解

基于sinh-Gordon方程的椭圆函数解,构造新的试探解来扩展sinh-Gordon方程展开法.利用该方法研究了KdV-mKdV方程,双sine-Gordon方程和BBM方程,获得了这些方程的新Jacobi椭圆函数解.该方法也能用来求解其他数学物理中的非线性演化方程.     

Bounds for the eigenvalues of the solution of the unified algebraic Riccati matrix equation

In recent years, several eigenvalues bounds have been investigated separately for the solutions of the continuous and the discrete Riccati and Lyapunov matrix equations. In this paper, lower bounds for the eigenvalues of the solution of the unified Riccati equation (relatively to continuous and discrete cases), are presented. In the limiting cases, the results reduce to some new bounds for both the continuous and discrete Riccati equation.     

The Unified Frame of Alternating Direction Method of Multipliers for Three Classes of Matrix Equations Arising in Control Theory

In this paper, the unified frame of alternating direction method of multipliers (ADMM) is proposed for solving three classes of matrix equations arising in control theory including the linear matrix equation, the generalized Sylvester matrix equation and the quadratic matrix equation. The convergence properties of ADMM and numerical results are presented. The numerical results show that ADMM tends to deliver higher quality solutions with less computing time on the tested problems.     

An analytic algorithm of Lane-Emden type equations arising in astrophysics using modified Homotopy analysis method

Lane-Emden type equation models many phenomena in mathematical physics and astrophysics. It is a nonlinear differential equation which describes the equilibrium density distribution in self-gravitating sphere of polytropic isothermal gas, has a singularity at the origin, and is of fundamental importance in the field of stellar structure, radiative cooling, modeling of clusters of galaxies. An efficient analytic algorithm is provided for Lane-Emden type equations using modified homotopy analysis method, which is different from other analytic techniques as it itself provides us with a convenient way to adjust convergence regions even without Pade technique. Some examples are given to show its validity.