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Theory and application of numerical simulation method of capillary force enhanced oil production

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Applied Mathematics and Mechanics(English Edition) 2015年第3期36卷 379-400页

作者： Yirang YUAN aijie cheng Danping YANG Changfeng LI Yunxin LIU Institute of Mathematics Shandong University

A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced （chemical） oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.

关键词： enhanced （chemical） oil production system on consideration ference optimal order l2 capillary force second-order three-dimensional porous coupled implicit upwind fractional step difestimate application in actual oilfield

Theory and Application of Numerical Simulation of Chemical Flooding in High Temperature and High Salt Reservoirs

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International Journal of Geosciences 2014年第9期5卷 956-970页

作者： Yirang Yuan aijie cheng Danping Yang Changfeng Li Institute of Mathematics Shandong University Jinan China

Applications, theoretical analysis and numerical methods are introduced for the simulation of mechanical models and principles of the porous flow in high temperature, high salt, complicated geology and large-scale reservoirs in this paper. Considering petroleum geology, geochemistry, computational permeation fluid mechanics and computer technology, we state the models of permeation fluid mechanics and put forward a sequence of implicit upwind difference iteration schemes based on refined fractional steps of the upstream, which can compute the pressures, the saturation and the concentrations of different chemistry components. A type of software applicable in major industries has been completed and carried out in numerical analysis and simulations of oil extraction in Shengli Oil-field, which brings huge economic benefits and social benefits. This software gives many characters: spatial steps are taken as ten meters, the number of nodes is up to hundreds of thousands and simulation time period can be tens of years and the high-order accuracy can be promised in numerical data. Precise analysis is present for simplified models of this type and that provides a tool to solve the international famous problem.

关键词： High Temperature and High Salt Complicated Chemical Flooding Computational Permeation Fluid Mechanics Numerical Method and Engineering Software Actual Application of Oil-Fields Theoretical Analysis

CHARACTERISTICS DIFFERENCE METHOD FOR INCOMPRESSIBLE MISCIBLE FLOW IN POROUS MEDIA

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Applied Mathematics(A Journal of Chinese Universities) 1999年第2期14卷 144-152页

作者： cheng aijie Dept. of Math. Shandong Univ. Jinan

Abstract Two phase,incompressible miscible flow in porous media is governed by a system of nonlinear partial differential equations.The pressure equation,which is elliptic in appearance,is discretized by a standard five points difference method.The concentration equation is treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms.A class of biquadratic interpolation is introduced for the method of characteristics.Convergence rate is proved to be O(Δt+h 2).

关键词： 1991 MR Subject Classification 65N15 65N30

GALERKIN METHOD FOR COMPLETELY COMPRESSIBLE DISPLACEMENT WITH MOLECULAR DIFFUSION AND DISPERSION

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Applied Mathematics(A Journal of Chinese Universities) 1998年第1期13卷 59-67页

作者： cheng aijie Department of Mathematics Shandong University Jinan

In this paper, the numerical approximation by Galerkin method for completely compressible miscible displacement with molecular diffusion and dispersion in porous media is considered. Continuous time procedure is introduced and analysed. Some new techniques are applied to the analysis. Optimal error estimates in L ∞(J;H 1(Ω)) are proved, which implies an essential improvement to existed results. MR Subject Classification: 65N15,65N30.

关键词： Compressible displacement molecular dispersion Galerkin method.

带溶质吸附的混溶驱动问题的Galerkin方法

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计算数学 1999年第1期21卷 45-58页

作者：程爱杰山东大学

A priori error estimates for Galerkin method for numerical approximation ofthe coupled quasilinear system for c = c(x, t), p = p(x, t), cr = c.(x, t) given byfor x E fl,t E (O,T] are considered. Equations of this type arise in model forthe miscible displacement of one compressible fiuid by another with adsorption ofor orsolute in a porous medium. The cofficient D, which is a function of x, c, X -reflects moleculer diffusion and dispersion. Colltinuous-time Galerkin procedureis analysed. A new technique is illtroduced to establish the evolution inequlity oferror. The optimal error estimates in Lco(J; H1(Ω)) are presented.

关键词：溶质吸附 Galerkin方法混溶驱动三次采油

含弥散平面两相渗流驱动问题有限元方法的误差分析

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系统科学与数学 1999年第4期19卷 478-483页

作者：程爱杰山东大学数学系济南250100

研究了平面两相渗流可压缩问题含弥散情形的矩形有限元格式．引进一类插值算子，通过插值函数证明了有限元解的最优误差估计．

关键词：可压缩渗流问题误差分析驱动问题有限元

多孔介质中两相不可压缩可混溶驱动问题的动态混合元方法及其特征修正格式

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系统科学与数学 2005年第1期25卷 118-128页

作者：刘保东程爱杰鲁统超山东大学数学与系统科学学院济南250100

许多依赖时间的问题涉及到局部化现象,如突出的前沿位置、激波、边界层等, 其位置随时间而变动.多孔介质中两相不可压缩可混溶驱动问题是一典型的、有代表性的"局部化现象"问题,其数学模型为耦合非线性偏微分方程组的初边值问题.为减轻... 详细信息

许多依赖时间的问题涉及到局部化现象,如突出的前沿位置、激波、边界层等, 其位置随时间而变动.多孔介质中两相不可压缩可混溶驱动问题是一典型的、有代表性的"局部化现象"问题,其数学模型为耦合非线性偏微分方程组的初边值问题.为减轻数值解在局部前沿位置的数值振荡,提高解的精确性,本文给出了该问题的动态混合元格式和沿特征线修正的动态混合元格式,证明了其收敛性,并给出了误差估计.

关键词：不可压缩非线性偏微分方程组初边值问题局部化收敛性误差估计前沿动态变动特征

乡村振兴综合能力评价及耦合协调度分析--以安徽黄山市三区四县为样本

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湖北工业大学学报 2022年第6期37卷 103-108页

作者：刘富勤程艾捷姜茂敏湖北工业大学土木建筑与环境学院湖北武汉430068 厦门大学公共事务学院福建厦门361005

乡村振兴战略是建设美丽中国的关键举措,构建乡村振兴评价指标体系可以为乡村地区的发展提供参考。以黄山市三区四县农村地区为研究对象,构建5个一级指标,26个三级指标,采用熵权TOPSIS结合灰色关联法具体分析黄山市三区四县乡村振兴发... 详细信息

乡村振兴战略是建设美丽中国的关键举措,构建乡村振兴评价指标体系可以为乡村地区的发展提供参考。以黄山市三区四县农村地区为研究对象,构建5个一级指标,26个三级指标,采用熵权TOPSIS结合灰色关联法具体分析黄山市三区四县乡村振兴发展水平测度,并选取权重占比前三的一级指标进行耦合协调度计算。结果表明,从指标权重看,产业振兴占比重较大;综合发展和协调性上,歙县灰色关联贴近度和耦合协调度分别为0.599和0.859,表现最好,其他各地区综合发展水平以及耦合协调度得分不理想,均有待完善。为了更好促进黄山市乡村可持续性建设,各地区要因地制宜补实地域短板,通过特色徽州产业带动其他产业协调同步发展,从而实现黄山市乡村振兴发展目标。

关键词：乡村振兴耦合协调度熵权TOPSIS 灰色关联分析黄山市

三维强化采油渗流耦合系统隐式迎风分数步差分方法的收敛性分析

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中国科学：数学 2014年第10期44卷 1035-1058页

作者：袁益让程爱杰羊丹平李长峰山东大学数学研究所济南250100

对强化(化学)采油数值模拟中的渗流耦合系统问题,本文提出隐式迎风分数步差分格式,利用变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到最佳阶l2模误差估计.该方法已成功应用到强... 详细信息

对强化(化学)采油数值模拟中的渗流耦合系统问题,本文提出隐式迎风分数步差分格式,利用变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到最佳阶l2模误差估计.该方法已成功应用到强化采油数值模拟的生产实践中,并且得到了很好的数值模拟效果.

关键词：强化(化学)采油三维渗流耦合系统隐式迎风分数步差分最佳阶l2估计能源数值模拟