Traveling wave front for the Fisher equation on an infinite band region

Instead of discussing the existence of a one-dimensional traveling wave front solution which connects two constant steady states, the present work deals with the case connecting a constant and a nonhomogeneous steady state on an infinite band region. The corresponding model is the well-known Fisher equation with variational coefficient and Dirichlet boundary condition. (c) 2006 Elsevier Ltd. All rights reserved.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

有源电磁扩散场克希霍夫积分偏移

As active electromagnetic method, field data of CSAMT method follow the equation of diffusion. Propagting in solid earth media, diffusion EM signal has strong attenuation and dispersion, otherwise seismic wave shows weak attenuation and dispersion, therefore the resolution power of CSAMT method is not better than seismic reflection method. However, there is consistence and similarity between EM signal and seismic wave in wave equation, we can apply Kirchhoff integral migration technique, a proven one in seismic method in time domain, to carry out seduo-seismic processing for CSAMT signal in frequency domain so that the attenuation and dispersion could be made compensated in some extent, and the resolution power and interpretation precision of active EM wave could be improved. Satisfying passive homogeneous Helmholtz quation, we proceed with Green theorem and combine the active inhomogenous Helmholtz quation, the Kirchhoff integral formula could be derived. Given practical problems, if we only consider the surface integral value, and assume that the intergral value in other interface is zero, combined with Green theorem in uniform half space, the expression could be simplified, and we can obtain frequency-domain Kirchhoff integral formula in surface, which is also called downward continuation of EM field in frequency domain. With image conditions and energy compensation considered, in order to get image conditions in time domain Fourier inverse transformation in frequency domain can be performed, so we can formulate the active Kirchhoff integral migration expression. At first, we construct relative stratified model, with different frequency series taken into account, then we change the distances between transmitter and reciever, the EM response can be obtained. Analyzing the EM properties, we can clarify near and far zone that can instruct us to carry out transmitter layout in practical application. Combined with field data surveyed in far zone, We perform Kirchhoff integral migration and compare the results with model to interpret. Secondly, with far field EM data, we apply TM mode to get EM response of given 2D model, then apply Kirchhoff integral migration on modelling data and interpret the results.

二氧化碳在孔隙咸水层中多相流动数值模拟研究

There has been a growing concern about the use of fossil fuels and its adverse effects on the atmospheric greenhouse and ecological environment. A reduction in the release rate of CO2 into the atmosphere poses a major challenge to the land ecology of China. The most promising way of achieving CO2 reduction is to dispose of CO2 in deep saline aquifers. Deep aquifers have a large potential for CO2 sequestration in geological medium in terms of volume and duration. Through the numerical simulation of multiphase flow in a porous media, the transformation and motion of CO2 in saline aquifers has been implemented under various temperature and hydrostatic pressure conditions, which plays an important role to the assessment of the reliability and safety of CO2 geological storage. As expected, the calculated results can provide meaningful and scientific information for management purposes. The key problem to the numerical simulation of multiphase flow in a porous media is to accurately capture the mass interface and to deal with the geological heterogeneity. In this study, the updated CE/SE (Space and time conservation element and solution element) method has been proposed, and the Hybrid Particle Level Set method (HPLS) has extended for multiphase flows in porous medium, which can accurately trace the transformation of the mass interface. The benchmark problems have been applied to evaluate and validate the proposed method. In this study, the reliability of CO2 storage in saline aquifers in Daqingzi oil field in Sunlong basin has been discussed. The simulation code developed in this study takes into account the state for CO2 covering the triple point temperature and pressure to the supercritical region. The geological heterogeneity has been implemented, using the well known geostatistical model (GSLIB) on the base of the hard data. The 2D and 3D model have been set up to simulate the CO2 multiphase flow in the porous saline aquifer, applying the CE/SE method and the HPLS method .The main contents and results are summarized as followings. (1) The 2D CE/SE method with first and second –order accuracy has been extended to simulate the multiphase flow in porous medium, which takes into account the contribution of source and sink in the momentum equation. The 3D CE/SE method with the first accuracy has been deduced. The accuracy and efficiency of the proposed CE/SE method have been investigated, using the benchmark problems. (2) The hybrid particle level set method has been made appropriate and extended for capturing the mass interface of multiphase flows in porous media, and the numerical method for level set function calculated has been formulated. (3) The closed equations for multiphase flow in porous medium has been developed, adept to both the Darcy flow and non-Darcy flow, getting over the limitation of Reynolds number to the calculation. It is found that Darcy number has a decisive influence on pressure as well as velocity given the Darcy number. (4) The new Euler scheme for numerical simulations of multiphase flows in porous medium has been proposed, which is efficient and can accurately capture the mass interface. The artificial compressibility method has been used to couple the velocities and pressure. It is found that the Darcy number has determinant effects on the numerical convergence and stability. In terms of the different Darcy numbers, the coefficient of artificial compressibility and the time step have been obtained. (5) The time scale of the critical instability for critical CO2 in the saline aquifer has been found, which is comparable with that of completely CO2 dissolved saline aquifer. (6) The concept model for CO2 multiphase flows in the saline aquifer has been configured, based on the temperature, pressure, porosity as well as permeability of the field site .Numerical simulation of CO2 hydrodynamic trapping in saline aquifers has been performed, applying the proposed CE/SE method. The state for CO2 has been employed to take into account realistic reservoir conditions for CO2 geological sequestration. The geological heterogeneity has been sufficiently treated , using the geostatistical model. (7) It is found that the Rayleigh-Taylor instability phenomenon, which is associated with the penetration of saline fluid into CO2 fluid in the direction of gravity, has been observed in CO2 multiphase flows in the saline aquifer. Development of a mushroom-type spike is a strong indication of the formation of Kelvin-Helmholtz instability due to the developed short wavelength perturbations present along the interface and parallel to the bulk flow. Additional key findings: the geological heterogeneity can distort the flow convection. The ascending of CO2 can induce the persistent flow cycling effects. The results show that boundary conditions of the field site have determinant effects on the transformation and motion of CO2 in saline aquifers. It is confirmed that the proposed method and numerical model has the reliability to simulate the process of the hydrodynamic trapping, which is the controlling mechanism for the initial period of CO2 storage at time scale of 100 years.

指数矩阵近似计算在地震波场延拓中的应用

Seismic wave field numerical modeling and seismic migration imaging based on wave equation have become useful and absolutely necessarily tools for imaging of complex geological objects. An important task for numerical modeling is to deal with the matrix exponential approximation in wave field extrapolation. For small value size matrix exponential, we can approximate the square root operator in exponential using different splitting algorithms. Splitting algorithms are usually used on the order or the dimension of one-way wave equation to reduce the complexity of the question. In this paper, we achieve approximate equation of 2-D Helmholtz operator inversion using multi-way splitting operation. Analysis on Gauss integral and coefficient of optimized partial fraction show that dispersion may accumulate by splitting algorithms for steep dipping imaging. High-order symplectic Pade approximation may deal with this problem, However, approximation of square root operator in exponential using splitting algorithm cannot solve dispersion problem during one-way wave field migration imaging. We try to implement exact approximation through eigenfunction expansion in matrix. Fast Fourier Transformation (FFT) method is selected because of its lowest computation. An 8-order Laplace matrix splitting is performed to achieve a assemblage of small matrixes using FFT method. Along with the introduction of Lie group and symplectic method into seismic wave-field extrapolation, accurate approximation of matrix exponential based on Lie group and symplectic method becomes the hot research field. To solve matrix exponential approximation problem, the Second-kind Coordinates (SKC) method and Generalized Polar Decompositions (GPD) method of Lie group are of choice. SKC method utilizes generalized Strang-splitting algorithm. While GPD method utilizes polar-type splitting and symmetric polar-type splitting algorithm. Comparing to Pade approximation, these two methods are less in computation, but they can both assure the Lie group structure. We think SKC and GPD methods are prospective and attractive in research and practice.

An empirical equation for the calculation of retention time with extrapolation of temperature in gas chromatography

An empirical equation is proposed to accurately correlate isothermal data over a wide range of temperature With the equation ln k = A* + B*/T-lambda the retention times of different solutes tested on OV-101, SE-54 and PEG 20M capillary columns have been achieved even when lambda is assigned a constant value of 1.7 Comparison with ln k = A + B/T and in k = c + d/T+ h/T-2, shows that the proposed equation is of higher accuracy and is applicable to extrapolation calculation, especially from data at high temperature to those at low temperature. Parameters A* and B* as well as A and B are also discussed. The linear correlation of A* and B* is weaker than that of A and B.