Evaluation of co-volume mixing rules for bitumen liquid density and bubble pressure estimation

The Peng–Robinson cubic equation of state (CEOS) is widely used to predict thermodynamic properties of pure fluids and mixtures. The usual implementation of this CEOS requires critical properties of each pure component and combining rules for mixtures. Determining critical properties for components of heavy asymmetric mixtures such as bitumen is a challenge due to thermolysis at elevated temperatures. Group contribution (GC) methods were applied for the determination of critical properties of molecular representations developed by Sheremata for Athabasca vacuum tower bottoms (VTB). In contrast to other GC methods evaluated, the Marrero–Gani GC method yielded estimated critical properties with realistic, non-negative values, followed more consistent trends with molar mass and yielded normal boiling points consistent with high temperature simulated distillation data. Application of classical mixing rules to a heavy asymmetric mixture such as bitumen yields saturated liquid density and bubble pressure estimates in qualitative agreement with experimental data. However the errors are too large for engineering calculations. In this work, new composite mixing rules for computing co-volumes of asymmetric mixtures are developed and evaluated. For example, composite mixing rules give improved bubble point predictions for the binary mixture ethane + n-tetratetracontane. For VTB and VTB + decane mixtures the new composite mixing rules showed encouraging results in predicting bubble point pressures and liquid phase densities.     

Fluid phase stability and equilibrium calculations in binary mixtures: Part I: Theoretical development for non-azeotropic mixtures

A framework is proposed for the solution of fluid phase equilibrium (P–T flash) for binary mixtures described by equations of state of general form. The framework is based on decomposing the phase equilibrium problem into sub-problems with more convenient and tractable mathematical and numerical properties. Systematic procedures are used to identify the mapping of the problem in the density and composition space, referred to as the density–composition pattern, at specified temperature and pressure. A series of stability tests is then carried out to explore the existence or non-existence of phases. Once the existence of a phase has been determined, the limits of stability and physical bounds on the problem are used to define the search area for that phase in the density–composition pattern. Finally, all available information from this detailed analysis is used for the solution of phase equilibrium between the phases identified in order to find the stable state at the specified conditions. The features of the proposed approach are exposed in detail through an algorithm for the fluid phase equilibria of the augmented van der Waals equation of state applied to non-azeotropic mixtures.     

甲烷晶体的晶格能和弹性性质: 不同方法及泛函的评估

通过对甲烷晶体进行结构、晶格能和弹性特性的研究, 评估了不包含和包含色散能量修正的密度泛函理论的性能. 我们分别利用不包含色散能量修正的密度泛函理论(DFT) (包含不同的标准泛函和杂化泛函)和包含色散能量修正的密度泛函理论(DFT-D)计算了甲烷晶体特性, 并与实验作对比. 尽管DFT-D 与传统密度泛函理论及杂化密度泛函理论相比, 修正了甲烷晶体中的范德华(vdW)相互作用, 但是一些修正方案过分修正了这种相互作用. 因此, 人们在使用DFT-D方法时务必谨慎.     

Construction of solutions for mixed hyperbolic elliptic Riemann initial value system of conservation laws

In this paper, we apply Adomian decomposition method (ADM) to develop a fast and accurate algorithm for systems of conservation laws of mixed hyperbolic elliptic type. The solutions of our model equations are calculated in the form of convergent power series with easily computable components. The results obtained are compared with our Modification of Adomian decomposition method (MADM) Az-Zo’bi and Al-Khaled (2010) [1]. The study outlines the significant features of the two methods. With application to van der Waals system, we obtain the stability of the approximate solutions graphically when the system changes type with more efficiency of the MADM.     

Models and numerical schemes for generalized van der Pol equations

This paper presents three generalizations of the van der Pol equation (VDPE) using newly proposed three new generalized K-, A- and B-operators. These operators allow kernel to be arbitrary. As a result, these operators provide a greater generalization of the VDPE than the fractional integral and differential operators do. Like the original VDPE, the generalized van der Pol equations (GVDPEs) are also nonlinear equations, and in most cases, they can not be solved analytically. Numerical algorithms are presented and used to solve the GVDPEs. Results for several examples are presented to demonstrate the effectiveness of the numerical algorithms, and to examine the behavior of the GVDPEs and the limit cycles associated with them. Although the numerical algorithms have been used to solve the GVDPEs only, they can also be used to solve many other generalized oscillators and generalized differential equations. This will be considered in the future.     

Trans-, cis-isomers of (1,1,1-trifluoro-2,4-pentandionato)Pt(II): Volatility, structure and crystal lattice energy

Trans-and cis-complexes of platinum(II) with trifluoroacetylacetone (Pt(tfa)₂) have been prepared and studied. The synthesis and the separation technique for the isomers are described. Temperature dependencies of saturated vapor pressure measured with a spoon gauge are reported for the cis-Pt(tfa)₂ and trans-Pt(tfa)₂ complexes. The isomers show a significant difference in volatility. The structural study of Pt(tfa)₂ isomers has been performed. Molecular packings in the crystal of each isomer are considered on the base of structural data. The calculation of van der Waals energy of the crystal lattice of cis-Pt(tfa)₂ and trans-Pt(tfa)₂ was made by the atom-atom potential technique, their values being compared with experimental ΔH _T ⁰ values of sublimation for the complexes.     

Rigorous van der Waals effect on vibration characteristics of multi-walled carbon nanotubes under a transverse magnetic field

An analytical method is presented to investigate rigorous van der Waals interaction effect on vibration characteristics of multi-walled carbon nanotubes embedded in matrix under a transverse magnetic field. Each of the concentric tubes of multiwall carbon nanotubes is considered as an individual elastic shell and coupled with any two walls through a rigorous van der Waals interaction being dependent on the change of interlayer spacing and the radii of tubes. Results show that the rigorous van der Waals interaction effect makes the lowest magneto-vibration frequency of multi-walled carbon nanotubes decrease and the highest magneto-vibration frequency increase. The effect of rigorous van der Waals interaction on magneto-elastic vibrations of multi-walled carbon nanotubes is dependent on the transverse magnetic strength and the matrix constrained stiffness.     

Dependence of the Interaction Potentials of Ar-HF and N2-HF on HF Bond Length

We explore in detail the nature of the intermolecular interactions in two HF containing complexes, ArHF and N₂ HF, at vibrationally excited HF stretching states using both high overtone spectroscopic and ab initio computational methods. By using an infrared intracavity laser-induced fluorescence technique, second overtone spectra of the two HF complexes have been obtained for the HF stretches and their combination modes with low-frequency van der Waals vibrations. The two complexes show the same trend that both van der Waals bond strength and rotational constant increase smoothly with v of the HF stretch. The investigation of the intermolecular potential above minimum provides a rigorous test of ab initio calculations. In particular for the ab initio calculations using an efficient basis set incorporating bond functions, the technique reproduces reasonably well the anisotropy of the interaction potential of Ar and HF. It is found that the intermolecular potential depends strongly upon the HF bond length only at the linear Ar-H-F geometry.     

等面积法则证明浅谈

本文对等面积法则证明过程中的佯谬问题进行了分析，认为该现象是由于等面积法则与范德瓦尔斯理论之间的不自洽造成的，并给出了一种在普物教学中适用的证明方法。