Evaluation of the thermodynamic models for the thermal diffusion factor

Over the years, several thermodynamic models for the thermal diffusion factors for binary mixtures have been proposed. The goal of this paper is to test some of these models in combination with different equations of state. We tested the following models: those proposed by Rutherford and Drickamer in 1954, by Dougherty and Drickamer in 1955, by Haase in 1969, by Kempers in 1989 and 2002, and by Shucla and Firoozabadi in 1998. The calculated values of thermal diffusion factors were compared with a few sets of experimental data for hydrocarbon mixtures. For calculation of the partial molar properties we applied different thermodynamic models, such as the Soave-Redlich-Kwong and the Peng-Robinson equations of state. The necessity to try different thermo-dynamic models is caused by the high sensitivity of the thermal diffusion factors to the values of the partial molar properties. Two different corrections for the determination of the partial molar volumes have been implemented; the Peneloux correction and the correction based on the principle of corresponding states.     

Gravity Effect on Two-Phase Immiscible Flows in Communicating Layered Reservoirs

An upscaling method is developed for two-phase immiscible incompressible flows in layered reservoirs with good communication between the layers. It takes the effect of gravity into consideration. Waterflooding of petroleum reservoirs is used as a basic example for application of this method. An asymptotic analysis is applied to a system of 2D flow equations for incompressible fluids at high-anisotropy ratios, but low to moderate gravity ratios, which corresponds to the most often found reservoir conditions. The 2D Buckley–Leverett problem is reduced to a system of 1D parabolic equations in a layered reservoir. For low-gravity ratios, it can further be reduced to a system of hyperbolic equations. The number of the 1D equations in the system is equal to the number of layers in the reservoir. The method is tested on different examples of displacement in a layer-cake reservoir. Different combinations of gravity-viscous and anisotropy ratios are tested. Solutions by our method are compared with the results of 2D simulations carried out by the COMSOL solver. The results are comparable, especially if the layers of the reservoirs are further subdivided into sublayers, in order to account better for gravity segregation. The effects of gravity are analyzed.     

循环图C(n,m)}的最小亏格

本文给出了所有循环图的可定向与不可定向最小亏格. 同时, 也给出了部分循环图的强最小亏格.     

联图的圈基

MacLane于1937年给出了圈基方面的重要定理: 图G是平面图, 当且仅当图G有2-重基. 连通图G_1和G_2的联图G_1\vee G_2指的是在它们的不交并G_1\bigcup G_2上添加边集(u,v)|u\in V(G_1), v\in V(G_2). 对G_1和G_2的联图G_1\vee G_2的圈基重数进行了研究, 得到了一个上界, 改进了Zare的结果. 并在此基础之上, 进一步得到特殊联图C_m\vee C_n的圈基重数的一个上界.     

Spectra of states,and asymptotically abelianC*-algebras

For each state of aC*-algebra its spectrum is defined and shown to coincide with the spectrum of the naturally associated modular operator. For strongly clustering states of asymptotically abelianC*-algebras the spectrum is minimal among the states in the same quasi-equivalence class, hence is a *-isomorphic invariant for the weak closure of the G.N.S.-representation. Furthermore, the non-zero elements in the spectrum of strongly clustering states form a multiplicative group.     

Comparison of Iterative Methods for Computing the Pressure Field in a Dynamic Network Model

In dynamic network models, the pressure map (the pressure in the pores) must be evaluated at each time step. This calculation involves the solution of a large number of nonlinear algebraic systems of equations and accounts for more than 80 of the total CPU–time. Each nonlinear system requires at least the partial solution of a sequence of linear systems. We present a comparative study of iterative methods for solving these systems, where we apply both standard routines from the public domain package ITPACK 2C and our own routines tailored to the network problem. The conjugate gradient method, preconditioned by symmetric successive overrelaxation, was found to be consistently faster and more robust than the other solvers tested. In particular, it was found to be much superior to the successive overrelaxation technique currently used by many researchers.     

Efficient integration of stiff kinetics with phase change detection for reactive reservoir processes

We propose the use of implicit one-step Explicit Singly Diagonal Implicit Runge–Kutta (ESDIRK) methods for integration of the stiff kinetics in reactive, compositional and thermal processes that are solved using operator-splitting type approaches. To facilitate the algorithmic development we construct a virtual kinetic cell model. The model serves both as a tool for the development and testing of tailored solvers as well as a testbed for studying the interactions between chemical kinetics and phase behavior. As case study, two chemical kinetics models with 6 and 14 components, respectively, are implemented for in situ combustion, a thermal oil recovery process. Through benchmark studies using the 14 component reaction model the new ESDIRK solvers are shown to improve computational speed when compared to the widely used multi-step BDF methods DASSL and LSODE. Phase changes are known to cause convergence problems for the integration method. We propose an algorithm for detection and location of phase changes based on discrete event system theory. Experiments show that the algorithm improves the robustness of the integration process near phase boundaries by lowering the number convergence and error test failures by more than 50% compared to direct integration without the new algorithm.