水平井多裂缝尖端应力干扰现象分析

致密砂岩储层具有低孔低渗的特征,水平井多裂缝压裂是致密砂岩储层油气增产的重要手段,合理预测裂缝扩展趋势是进行水力压裂开采的关键.为了准确认识水平井多裂缝压裂过程中尖端应力场变化,综合考虑地应力分布、井筒内压等因素,建立二维均质流固耦合有限元数值分析模型.模拟了致密砂岩储层不同裂缝半长、不同裂缝条数、不同裂缝间距及不同裂缝位置的应力场,进一步分析裂缝尖端应力干扰情况.结果表明,裂缝尖端附近存在明显的应力干扰现象,多裂缝同时压裂时,裂缝半长越长,裂缝条数越多,裂缝间距越小,应力干扰现象越明显.中间位置裂缝应力受附近裂缝的应力干扰,裂缝尖端应力集中值明显降低,不利于裂缝延伸和扩展,两侧裂缝尖端的应力集中有所增加.该研究深入认识水平井多裂缝压裂裂缝起裂和延伸机制,对制定压裂方案具有一定的指导意义.     

考虑应力阻隔和干扰效应的分段多簇压裂诱导应力计算模型

针对水平井分段多簇压裂过程中段内多条裂缝同步扩展的形成特点,考虑裂缝间存在的应力阻隔效应和应力干扰效应,分析了段内各条裂缝诱导应力的影响范围以及其相对于不同位置处的有效净压力,建立了水平井分段多簇压裂段内不同位置处诱导应力计算模型.通过研究得出如下认识:第N段压裂之前段内各点受到的诱导应力为之前各段最后一条裂缝产生的诱导应力的叠加,第N段压裂过程中段内各点受到的诱导应力是与其相邻的裂缝产生的;最小水平地应力方向的诱导应力抵消了一部分缝内净压力,应根据应力阻隔和应力干扰效应以及之前各段压裂诱导应力的分布计算每条裂缝相对于左右两侧地层的有效净压力以及诱导应力.考虑多条裂缝同步扩展时的应力阻隔和应力干扰效应以及有效净压力变化的分段多簇压裂诱导应力计算模型更为符合实际的工况情况,具有较高的精度,能够为水平井分段多簇压裂优化设计提供更为准确的理论指导.     

考虑基岩向井筒供气的气藏压裂水平井产能预测模型

基于等效井径模型,综合考虑各裂缝不同参数、裂缝变质量入流和井筒变质量流动等因素的影响,建立并求解了基岩和压裂缝同时向井筒供气的井筒与气藏耦合的压裂水平井产能预测模型.研究分析了压裂水平井产能敏感因素.结果表明:压裂水平井的产能随裂缝条数、裂缝半长、裂缝间距的增加而增加;为获得较高的产能,压裂时应尽可能保持裂缝与井筒垂直;压裂缝条数一定时,裂缝越长、间距越大,压裂缝产能贡献越大,而裂缝越短、间距越小时,基岩向井筒供气的贡献越大,压裂缝贡献相对较小.研究成果为气藏压裂水平井设计提供了科学依据.     

基于扩展有限元的页岩水力压裂数值模拟

考虑裂缝内流体流动和周围岩石应力变形,建立了页岩人工裂缝扩展的数学模型,分别采用有限元和扩展有限元求解裂缝流场和岩石应力场,并通过Picard迭代方法耦合求解,计算结果与经典模型结果吻合,验证了模型正确性.在此基础上,分析了岩石弹性模量、Poisson(泊松)比和注入速度对裂缝几何形态的影响以及水力裂缝任意角度逼近天然裂缝扩展动态.结果表明:弹性模量和注入速度对裂缝形态具有重要影响,而Poisson比对裂缝形态影响较小;随着页岩脆性增高,压裂裂缝趋于"长窄型"扩展;地应力差和逼近角越大,水力裂缝越易贯穿天然裂缝;水力裂缝与天然裂缝相交处裂缝宽度存在相对较大的降低;扩展有限元方法避免了计算过程中的网格重构与网格加密,减少了计算量,该模型可以为页岩压裂设计提供理论指导.     

固壁近旁Stokes流中粘性液滴的运动和变形

发展了一种模拟固壁近旁轴对称Stokes流中粘性液滴的运动和变形及直接计算固壁上应力的边界积分方法．用此方法对不同的液滴-固壁初始相对间距、粘度比、表面张力和浮力联合参数以及环境流动参数情况进行了数值实验．数值结果显示,由于环境流动和浮力的作用,随着时间的推进,液滴在轴向压缩,在径向拉伸．当环境流动的作用弱于浮力作用时,随着时间的推移,液滴上升并向上弯,固壁上由液滴运动所引起的应力不断减小．当环境流动的作用强于浮力作用时,随着时间的推移,液滴变得越来越扁．在这种情形,当大初始间距时,壁面上的应力随液滴的演变而增大;当小初始间距时,由环境流动、浮力及壁面对流动的较强作用的联合影响,此应力随液滴的演变而减小．由于液滴运动所引起的壁面应力的有效作用仅限于对称轴附近的一个小范围内,且此范围随液滴与固壁的初始间距增大而增大．应力的大小随初始间距增大而大为减小．表面张力对液滴变形有阻止作用．液滴粘性会减小液滴的变形和位置迁移．     

页岩压裂水平井增产改造体积的动态演化模型

页岩气藏开发实践表明,水平井分段压裂是实现页岩气藏经济有效开发的关键技术,其中增产改造体积(SRV)是控制页岩压后效果的核心参数,对SRV的准确计算和表征已成为页岩压裂研究领域的重点难点问题.基于目前SRV评价方法的局限性,考虑动态扩展裂缝与储层应力场和压力场的耦合作用,以及它们实时变化触发储层天然裂缝的破裂机制,建立了一种SRV动态演化计算模型,采用该模型可以计算和表征裂缝动态扩展形态、储层渗透率演化分布以及SRV的空间展布.由于模型与页岩压裂过程中储层SRV实际动态扩展物理机制较一致,采用该模型对SRV的评价计算更符合矿场实际.基于文中提出的计算方法,以威远页岩气开发示范区某压裂井段为例,验证了模型的可靠性,并计算分析了SRV随时间的动态演化过程及变化规律.该文研究对于提升页岩水平井分段分簇压裂SRV计算准确性,提高压裂优化设计以及压后效果评估具有重要的理论指导意义和矿场应用价值.     

基于正交灰关联法的气藏水平井体积压裂影响因素研究

影响苏里格气田致密砂岩气藏水平井段内多缝体积压裂效果的裂缝因素为裂缝条数、裂缝长度、裂缝导流能力、裂缝间距和缝宽.揭示裂缝参数对水平井段内多缝体积压裂效果的影响及影响程度的主次关系,优选合理压裂裂缝参数已成为必须解决的紧迫问题之一,它是制约水平井在苏里格致密砂岩气藏应用的技术瓶颈.针对苏里格气田致密砂岩气藏水平井段内多缝体积压裂效果多衡量指标、多影响因素的特点,运用正交试验设计结合灰关联分析法对水平井段内多缝体积压裂效果的各个影响因素进行了分析.应用结果表明,正交灰关联分析法能给出各指标影响权重大小、因素影响主次顺序及最优方案,该方法避免了仅通过单一评价指标来进行决策的不科学性,可为压裂方案的优化设计和施工提供可靠理论依据.     

基于正交灰关联法的气藏水平井体积压裂影响因素研究北大核心

影响苏里格气田致密砂岩气藏水平井段内多缝体积压裂效果的裂缝因素为裂缝条数、裂缝长度、裂缝导流能力、裂缝间距和缝宽.揭示裂缝参数对水平井段内多缝体积压裂效果的影响及影响程度的主次关系,优选合理压裂裂缝参数已成为必须解决的紧迫问题之一,它是制约水平井在苏里格致密砂岩气藏应用的技术瓶颈.针对苏里格气田致密砂岩气藏水平井段内多缝体积压裂效果多衡量指标、多影响因素的特点,运用正交试验设计结合灰关联分析法对水平井段内多缝体积压裂效果的各个影响因素进行了分析.应用结果表明,正交灰关联分析法能给出各指标影响权重大小、因素影响主次顺序及最优方案,该方法避免了仅通过单一评价指标来进行决策的不科学性,可为压裂方案的优化设计和施工提供可靠理论依据.     

煤岩体压裂裂缝演化混沌特征研究

准确地描述煤岩体压裂裂缝的形成与演化规律对煤层气井开采具有重要意义.本文以煤岩体压裂裂缝演化过程的微裂缝演化数目、裂缝尖端区域的径向应力与周向应力作为描述裂缝演化的特征指标,引入关联维数、最大Lyapunov指数和Ko1mogorov熵作为裂缝演化系统的混沌特征量,计算与描述煤岩体压裂裂缝的损伤演化过程.以黑龙江省某一煤岩开采区块岩体作为研究对象,计算分析煤岩体压裂裂缝的形成的混沌特征,为后续煤岩体压裂裂缝形成规律的研究提供了新的思路.     

基于灰色关联法的水平井压裂参数优化研究

针对低渗透薄互砂岩油藏A油田C9区块水平井井区储层物性差、非均质性强、开发难度大等问题,为改善水平井井区开发效果、提高水平井单井产能,应用灰色关联法,结合数值模拟软件,分析影响压裂水平井产能的主要因素,开展水平井压裂参数优化研究,结果表明裂缝半长和裂缝间距是影响压裂水平井产能的主要因素,优选出水平井压裂方案:裂缝半长为...     

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].