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A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

Petroleum Science 2024年第1期21卷 244-251页

作者： Ji-Lin Fan Feng Zhang Qian Chen Hao-Chen Song Lu-Yu Zhong Yue-Xiang Dai National Key Laboratory of Deep Oil and Gas School of GeosciencesChina University of Petroleum(East China)Qingdao 266580ShandongChina China National Logging Corporation Xi'an 710076ShaanxiChina Sinopec Matrix Corporation Qingdao 266001ShandongChina

Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.

关键词： Cement azimuthal density perturbation theory Casing eccentricity Spatial dynamic response function Regularized Newton iteration

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Characteristics of spectral-hole burning in Tm^(3+):YAG based on the perturbation theory

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Chinese Physics B 2014年第6期23卷 37-43页

作者：张世宇马秀荣张双根陈雷王夏洋穆宽林王松 Engineering Research Center on Communication Devices (Ministry of Education) School of Computer and Communication EngineeringTianjin University of Technology Tianjin Key Laboratory of Film Electronic and Communication Device School of Electronic Information EngineeringTianjin University of Technology

In this paper, the physical mechanism of the interaction between electromagnetic wave and spectral-hole burning crystal material is investigated in detail. In the small signal regime, a perturbation theory model is used to analyze the mechanism of spectral-hole burning. By solving the Liouville equation, three-order perturbation results are obtained. From the theoretic analysis, spectral-hole burning can be interpreted as a photon echo of the zero-order diffraction echo when the first optical pulse and the second optical pulse are overlapped in time. According to the model, the spectral-hole width is dependent on the chirp rate of the reading laser. When the chirp rate is slow with respect to the spectral features of interest, the spectral hole is closely mapped into time domain. For a fast chirp rate, distortions are observed. The results follow Maxwell-Bloch model and they are also in good agreement with the experimental results.

关键词： perturbation theory spectral-hole burning photon echo

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Derivation of Martin-Hou Equation of State from Hard-particle perturbation theory

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Chemical Research in Chinese Universities 2000年第1期16卷 49-56页

作者： ZHANG Bing-jian (Department of Chemistry, Zhejiang University, Hangzhou 310027, P. R. China) HOU Yu-chun (Department of Chemical Engineering, Zhejiang University, Hangzhou 310027, P. R. China) 浙江大学浙江杭州 310027

In this paper, the Martin-Hou equation of state is derived by using a power series representation of radial distribution function and an analytic representation of multi-section potential based on the Barker-Henderson hard-particle perturbation theory including high-order terms. In the derivation, a theoretical form of Martin-Hou equation was obtained. It had a similar form and the same capability to predict P-V-T properties as the Martin-Hou equation and no additional data were required for evaluating the constants. The characteristic constants of the theoretical expression have certain relationships with the molecular parameters.

关键词： perturbation theory Martin-Hou equation of state Theoretical expression P-V-T properties Molecular parameter

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Practical 0-stability of stochastic differential equations and corresponding stochastic perturbation theory

Practical 0-stability of stochastic differential equations...

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2009年中国智能自动化会议

作者：赵平康宇宗西举 School of Control Science and Engineering University of Jinan Department of Automation University of Science and Technology of China

The notions of practicalφ-stability were introduced for stochastic differential equations.Sufficient conditions on such practical properties were obtained by using the comparison principle and the cone-valued Lyapunov function methods.Based on an extended comparison theorem,a perturbation theory of stochastic differential systems was given.

关键词： practicalφ0-stability stochastic differential equation comparison principle perturbation theory

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A Thermodynamic Model for square-well Chain Fluid:theory and Monte Carlo Simulation

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Chemical Research in Chinese Universities 2001年第4期17卷 432-438页

作者： ZHANG Bing-jian LU Ying-hong HU Wen-xuan JIN Zhi-jun Department of Chemistry Zhejiang UniversityHangzhou 310027P.R.China Department of Earth Sciences Nanjing UniversityNanjing 210093P.R.China Basin and Reservoir Research Center China Petroleum UniversityBeijing 102200P.R.China

A thermodynamic model for the freely jointed square-well chain fluids was developed based on the thermodynamic perturbation theory of Barker-Henderson, Zhang and Wertheim. In this derivation Zhang’s expressions for square-well monomers improved from Barker-Henderson compressibility approximation were adopted as the reference fluid, and Wertheim’s polymerization method was used to obtain the free energy term due to the bond connectivity. An analytic expression for the Helmholtz free energy of the square-well chain fluids was obtained. The expression without adjustable parameters leads to the thermodynamic consistent predictions of the compressibility factors, residual internal energy and constant-volume heat capacity for dimer, 4-mer, 8-mer and 16-mer square-well fluids. The results are in good agreement with the Monte Carlo simulation. To obtain the MC data of residual internal energy and the constant-volume heat capacity needed, NVT MC simulations were performed for these square-well chain fluids.

关键词： Keywords Square-well chain perturbation theory Compressibility factor Internal energy

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Static and dynamic responses of a microcantilever with a T-shaped tip mass to an electrostatic actuation

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Acta Mechanica Sinica 2016年第6期32卷 1104-1122页

作者： B.Firouzi M.Zamanian S.A.A.Hosseini Department of Mechanical Engineering Faculty of Engineering Kharazmi University

In this study, nonlinear static and dynamic responses of a microcantilever with a T-shaped tip mass excited by electrostatic actuations are investigated. The electrostatic force is generated by applying an electric voltage between the horizontal part of?T-shaped tip mass and an opposite electrode plate. The cantilever microbeam is modeled as an Euler-Bernoulli beam. The T-shaped tip mass is assumed to be a rigid body and the nonlinear effect of electrostatic force is considered. An equation of motion and its associated boundary conditions are derived by the aid of combining the Hamilton principle and Newton’s method. An exact solution is obtained for static deflection and mode shape of vibration around the static position. The differential equation of nonlinear vibration around the static position is discretized using the Galerkin method. The system mode shapes are used as its related comparison functions. The discretized equations are solved by the perturbation theory in the neighborhood of primary and subharmonic resonances. In addition, effects of mass inertia, mass moment of inertia as well as rotation of the T-shaped mass, which were ignored in previous works, are considered in the analysis. It is shown that by increasing the length of the horizontal part of the T-shaped mass, the amount of static deflection increases, natural frequency decreases and nonlinear shift of the resonance frequency increases. It is concluded that attaching an electrode plate with a T-shaped configuration to the end of the cantilever microbeam results in a configuration with larger pull-in voltage and smaller nonlinear shift of the resonance frequency compared to the configuration in which the electrode plate is directly attached to it.

关键词： MEMS Electrostatic Static deflection Natural frequency Pull-in voltage perturbation theory T-shaped mass Primary and subharmonic resonances

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Peculiar features of the interaction potential between hydrogen and antihydrogen at intermediate separations

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Chinese Physics B 2008年第8期17卷 2897-2908页

作者：李德义黄卓然王礼贤 Physics Division Oak Ridge National Laboratory Oak Ridge Department of Physics and Astronomy University of Kentucky Lexington School of Physics & Optoelectronic Technology Dalian University of Technology Department of Physics Harvey Mudd College Claremont

This paper evaluates the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. It finds that the H-H interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ～ 6a.u. and a barrier rising at τ ≤5a.u.

关键词： few-body problems potential energy curve perturbation theory H-H interaction

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Research on mode localization of reticulated shell structures

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Earthquake Engineering and Engineering Vibration 2011年第1期10卷 75-84页

作者： Yan Weiming Wang Zhuo He Haoxiang Beijing Laboratory of Earthquake Engineering and Structural Retrofit Beijing University of Technology Beijing 100124 China The Open University of China Beijing 100031 China

Reticulated shell structures （RSSs） are characterized as cyclically periodic structures. Mistuning of RSSs will induce structural mode localization. Mode localization has the following two features： some modal vectors of the structure change remarkably when the values of its physical parameters （mass or stiffness） have a slight change; and the vibration of some modes is mainly restricted in some local areas of the structure. In this paper, two quantitative assessment indexes are introduced that correspond to these two features. The first feature is studied through a numerical example of a RSS, and its induced causes are analyzed by using the perturbation theory. The analysis showed that internally, mode localization is closely related to structural frequencies and externally, slight changes of the physical parameters of the structure cause instability to the RSS. A scaled model experiment to examine mode localization was carried out on a Kiewit single-layer spherical RSS, and both features of mode localization are studied. Eight tests that measured the changes of the physical parameters were carried out in the experiment. Since many modes make their contribution in structural dynamic response, six strong vibration modes were tested at random in the experimental analysis. The change and localization of the six modes are analyzed for each test. The results show that slight changes to the physical parameters are likely to induce remarkable changes and localization of some modal vectors in the RSSs.

关键词： reticulated shell structure mistuning mode localization perturbation theory seismic performance analysis damage identification

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perturbationAL SOLUTIONS FOR FUZZY-STOCHASTIC FINITE ELEMENT EQUILIBRIUM EQUATIONS (FSFEEE)

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Applied Mathematics and Mechanics(English Edition) 1997年第7期18卷 679-687页

作者：吕恩林 Department of Engineering Mechanics Chongqing University Chongqing P. R. China

In this paper, the random interval equilibrium equations (RIEE) is obtained by lambda-level cutting the fuzzy-stochastic finite element equilibrium equations (FSFEEE). Based on the relations between the variables of equilibrium equations, solving RIEE is transformed into solving two kinds of general random equilibrium equations (GREE). Then the recursive equations of evaluating the random interval displacement is derived from the small-parameter perturbation theory. The computational formulae of statistical characteristic of the fuzzy random displacements, the fuzzy random strains and the fuzzy random stresses are also deduced in detail.

关键词： fuzzy-stochastic finite element equations of interval numbers perturbation theory

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Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow

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Chinese Physics C 2021年第1期45卷 162-174页

作者：刘霄马滟青陶伟张鹏 School of Physics and State Key Laboratory of Nuclear Physics and Technology Peking UniversityBeijing 100871China Center for High Energy Physics Peking UniversityBeijing 100871China Collaborative Innovation Center of Quantum Matter Beijing 100871China

We extend the auxiliary-mass-flow(AMF) method originally developed for Feynman loop integration to calculate integrals which also involve phase-space integration.The flow of the auxiliary mass from the boundary(∞) to the physical point(0+) is obtained by numerically solving differential equations with respective to the auxiliary mass.For problems with two or more kinematical invariants,the AMF method can be combined with the traditional differential-equation method,providing systematic boundary conditions and a highly nontrivial self-consistency check.The method is described in detail using a pedagogical example of e+e-→γ*→tt+X at NNLO.We show that the AMF method can systematically and efficiently calculate integrals to high precision.

关键词： phase-space integration perturbation theory multi-loop

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