应用灰色关联法和模糊评判法结合评价特高含水期水驱开发效果

针对目前油藏特高含水期水驱开发效果评价难度大、各评价方法评价指标单一等不足,以杏一~三区西部乙块地质特征和油田开发实际数据资料为基础,采用灰色关联法分析确定油田开发指标主要影响因素,筛选水驱储量控制程度、水驱采收率等10项参数作为评价指标,进而应用模糊综合评判法对该区块特高含水期水驱开发效果进行评价.结果表明,评价结果符合开发实际.方法计算方便简单,结果全面可靠,可为同类油藏的特高含水期开发效果评价提供参考.     

一种基于相渗资料与动态数据的裂缝和基质水驱动用程度计算方法

利用水驱油机理研究裂缝性油藏注水开发过程中裂缝系统、基质系统产量贡献与采收率变化规律,对制定油田开发技术政策具有重要意义.根据注采守恒原理和渗吸机理,利用Welge水驱方程,推导了水驱开发过程中裂缝系统、基质系统的产油量、采出程度计算方法.该方法基于相渗资料和动态数据,利用Welge水驱方程通过产出端含水率计算裂缝系统含水饱和度,采用注采守恒原理计算裂缝系统、基质系统的存水量,根据渗吸机理计算裂缝系统、基质系统水驱储量采出程度,最终计算得到水驱开发过程中裂缝系统、基质系统的含水饱和度、含水率、产油量与采出程度变化情况.实例计算表明,该方法能够表征裂缝性油藏水驱开发过程中裂缝系统、基质系统的含水变化特征与水驱开发规律,可为制定该类油田开发技术政策提供依据.     

基于模糊综合评判的宋芳屯油田南部水驱开发效果综合评价

以宋芳屯油田南部区块为例,采用层次分析和模糊综合评判相结合的方法,对该油藏的水驱储量控制程度、水驱储量动用程度、可采储量、能量保持水平、能量利用程度、即时含水采出比、累积注水量、剩余可采储量采油速度、井网密度和注采井数比10项指标进行了评价,形成了一套水驱开发效果综合评价体系.评价结果认为该区目前水驱开发效果差,有必要进行井网加密及挖潜措施调整.     

基于DEMATEL的高含水油田水驱开发效果评价影响因素识别研究——以杏西油田为例

在高含水油田水驱开发效果评价中影响因素的选取决定了评价效果的好坏.不同区块、不同专家、不同时间可能所选取的指标体系也不一样,如何在众多指标中客观的识别出关键指标(关键影响因素)是要解决的问题.统计了国内外学者在高含水油田水驱开发效果评价中所选用的指标,根据统计的各指标所出现的频率,选取出现频率大于10%的指标构建了高含水油田水驱开发效果评价体系,该体系分为三级,一级指标包含开发技术因素和人为控制因素,二级指标包含井网完善状况、注水状况、含水变化状况、产油量变化状况、产液量变化状况、储采状况、开采程度、工作效果状况、管理状况和经济状况,三级指标包含了水驱储量控制程度、存水率等的23个指标,然后运用DEMATEL方法对所建立的评价体系中的指标进行了识别选择,通过对处理结果的分析,剔除了水驱储量控制程度、水驱储量动用程度、井网密度等7个影响度、被影响度、中心度和原因度都比较差的因素,最终识别出了存水率、水驱指数、耗水比、含水率、含水上升率等16个影响因素.     

油水两相渗流对称性特征研究与应用

通过岩心相渗资料分析,发现在一定条件下,油水相对渗透率比值随归一化饱和度变化呈现对称性.针对这一现象,结合实际岩心驱替和数字岩心的实验结果,考虑水驱油过程中的优势相和弱势相的转换,构建了新的油水渗流关系,即油、水相对渗透率比与归一化弱势相饱和度的幂指函数关系.设计了不同条件下水驱油实验,探讨了水驱油时对称性特征产生条件,并分析了其对水驱特征曲线的影响.最后利用对应条件下的油藏实际数据,验证了对称性的存在及双对数水驱特征曲线的适应性.表明考虑弱势相转换的幂指关系较好的表征了凹型水驱特征全生命周期的变化,丰富了油水两相渗流基础理论,对水驱特征曲线的研究和应用具有一定借鉴意义.     

多层合注封闭油藏注水井压降试井分析

对于复杂断块油气藏而言,砂体往往小、连片性差,但纵向上层数多,常规的单层注水模型已经不能准确的描述油藏的动态特征.为解决上述油藏的渗流问题,建立了多层合注外边界封闭油藏注水井不稳定渗流数学模型,模型中每一层的物性和边界大小各不相同.通过拉普拉斯变换,利用Stehfest数值反演对数学模型进行了求解,获得了多层合注条件下的井底压力响应特征曲线,并将曲线划分为六个阶段.研究表明主力层的砂体边界大小对井底压力动态影响较大;受多层干扰影响,用常规理论方法计算的边界大小有可能与实际地质情况不一致.     

杏六区薄差储层有效动用界限研究

大庆长垣内部油田已进入高含水期,目前的水驱开发对象已由中高渗透层逐渐转变为薄差储层,这类储层油藏地质条件复杂,开发效益较差,已探明的储量中却有数亿吨储量主要存在于低渗透的薄差储层中.由于其微观孔隙结构和物性特征与厚油层存在差异,有些物性较差的储层甚至无法动用.以大庆油田杏六区的薄差储层为研究对象,运用压力数法和非线性渗流指数法确定有效动用的渗透率下限,利用双管并联实验确定级差上限,结合核磁共振技术与压汞实验结果给出孔喉动用的下限,得出:杏六区薄差储层有效动用的渗透率下限为1×10~(-3)μm~2;级差上限为5;流动孔喉半径下限为0.288μm,该结果为薄差储层的有效开发提供了一定的参考和借鉴.     

利用模糊综合分析法识别水驱砂岩油藏注采井间优势通道

砂岩油藏由于长期注水开发形成的优势通道导致注入水在注采井间低效、无效循环,严重影响水驱开发效果.有效识别优势通道是油藏提高水驱采收率必须解决的关键问题.采用模糊综合分析法,以地质静态因素为基础,结合动态监测结果,利用变异系数法对指标加权并计算优势通道综合判别参数,定量识别出水驱砂岩油藏优势通道并描述其发育程度.将方法应用于X3油区典型井组优势通道识别并利用吸水剖面法验证其结果准确性.方法可实现软件编程计算,方便快捷、结果准确可靠,能够为油田开发后期制定合理调整方案提供有力依据.     

基于分形理论的新型水驱特征曲线

水驱特征曲线法是一种简单、有效的油藏工程方法.本文结合分形理论,根据油水相对渗透率的分形表达形式,结合一维油水两相稳定渗流理论推导出了一种新型水驱特征曲线.该水驱特征曲线可以准确预测中、高及特高含水期油田的采出程度,并且可以直观解释水驱特征曲线在特高含水期上翘的根本原因.通过实例应用表明,该新型水驱特征曲线在油田开发的中、高及特高含水阶段都具有较高的可靠性,并能很好的将微观物性特征与宏观渗流规律紧密结合.     

胜利断块油藏细分注水技术界限研究

老油田进入特高含水期后,剩余油分布更加零散,各种地质因素也因长期注水开发而发生了一定的改变.此时稳油控水难度进一步加大,为了进一步挖掘剩余油,控制含水上升速度、减缓产量递减,必须对注水井采取进一步的细分调整.基于水湿油藏注水井注水层段吸水效果,从注入水受力分析入手,运用达西定律推导出了水驱油藏水驱油全过程中的单位体积注入水沿竖直、地层两个方向运移的渗流速度公式,明晰了水驱油藏注水层段不同开发阶段砂岩吸水机理.研究结果表明,水驱油藏细分注水效果与岩石绝对渗透率、水相相对渗透率、注入水黏度、水动力压力梯度、注水井启动压力梯度、含水饱和度、地层倾角、油水密度差等参数有关.结合胜利油田断块油藏地质特征及细分注水工艺要求,制定了一套适合胜利油田不同断块区的细分注水技术政策界限:层段内渗透率变异系数小于0.3,砂岩条带宽度极比小于2.5,且东辛油区断块油藏层段内砂岩厚度小于6m,小层数小于4个;现河油区断块油藏层段内砂岩厚度小于5m,小层数小于5个;临盘油区断块油藏层段内砂岩厚度小于6m,小层数小于6个.矿场试验证实,该细分注水技术政策界限是合理、实用的,其为胜利断块油藏注上水、注够水、注好水,实现多层断块油藏的高效开发提供了技术保障,对类似油藏细分注水技术界限研究具有一定的借鉴意义.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.