基于应力敏感的天然裂缝性页岩气藏双孔模型解的结构

针对天然裂缝性页岩气藏,研究了3种外边界条件（无穷大、定压、封闭）及内边界条件下的定产量生产问题,并建立了考虑应力敏感性和解析吸附的不稳定渗流的试井分析模型.先对此模型作线性化处理;然后通过摄动法以及利用Laplace变换,求得线性化后的无因次储层压力的Laplace空间精确解;最后根据解的相似结构理论,给出了求解该模型解结构的步骤,并且定义了3种外边界条件下的相似核函数,发现了此模型在3种外边界条件下精确解之间的相似结构.这项研究不仅为编制试井分析软件提供便利, 提高计算效率,而且对页岩气藏渗流理论的研究具有重要意义,也为页岩气藏渗流模型的求解提供了一种新的方法.     

边部注水时裂缝性油藏中水平井两相渗流

本文在流线不变的假定下研究边部注水时裂缝性油藏中水平井两相渗流问题,建立了双重孔隙介质中水平井两相流体垂直二维渗流的数学模型,并用特征线方法进行了精确求解,给出了裂缝系统和岩块系统中的饱和度分布以及水平井见水时间公式,从而为边部注水开发裂缝性油藏提供了必要的理论基础和工程计算方法。     

考虑毛管力/流变性/相渗作用的聚表二元驱前缘位置预测

油气田开发过程中,驱替相的前缘位置对评价驱替效果、判断储层特性等具有十分重要的意义.然而,由于储层渗流规律的复杂性,使得该问题较为难解.基于表达界面张力的拉普拉斯方程,来表示毛管力的大小,建立了考虑毛管力影响时的二元驱分流方程和前缘推进位置的微分方程.在微分方程的求解过程中,又考虑了聚合物的幂律指数、稠度系数两个流变性参数,和二元驱过程中储层渗透率、相渗曲线的变化.应用该方程计算锦州9-3油田注二元井的见二元时间,计算结果与实际矿场测试结果一致,对提高区块聚表二元驱的驱替效率有重要的指导意义.     

基于模糊综合评判法的优势渗流通道定量识别方法研究

目前我国大多数油田已进入高含水期,油水井间的优势渗流通道普遍发育,严重制约了油田采收率的提高.如何有效识别优势渗流通道已成为改善注入水驱油效果的关键.基于模糊综合评判法,将油水井动静态资料相结合建立评价模型,利用综合评判指数对优势渗流通道进行识别,并建立出量化标准.应用注采动态关联分析法对所建立的评价模型及标准进行验证,并对某区块油藏进行优势渗流通道识别判断,识别效果较好.评价方法资料获取难度低,计算方便,易于操作和推广,能够为油田后期深度调驱或井网调整提供理论依据.     

真实气体在均质气藏内流动的新模型及其应用

本文用新方法描述了气藏开采中的井筒边界条件,从而建立了均质气藏内真实气体渗流问题的新模型;并在无限大、有界封闭、有界定压三种典型外边界条件下,得出了均质气藏中拟压力函数的精确解析表达式;最后给出了本文的拟压力表达式在气井试井分析中的应用.     

基于聚合物驱渗流解的相似结构分析

研究聚合物驱注聚井和采油井井底压力变化对于评价聚合物驱油时储层物性变化具有重要的意义.基于渗流力学基本原理,针对不同的井建立非牛顿-牛顿以及牛顿-非牛顿双区复合油藏试井解释数学模型,利用Laplace积分变换等数学方法获得Laplace空间解析解,根据这两种模型解结构的相似性,采用高斯消元求得不同模型的井底压力,再利用Stehfest数值反演绘制双对数曲线.根据压力导数曲线特征该模型分为五个阶段.幂律指数越大,非牛顿幂律流体径向流阶段压力导数曲线斜率越小.方法可以方便的求解聚合物驱所形成的复合油藏压力解.     

关于求解二相渗流的平面问题的一类新方法

本文提出一类求解二相平面渗流问题的新方法:用有限元法求解关于压力分布的椭圆型方程,然后利用所得的对压力梯度的半解析解,根据已有的饱和度沿流线传播的精确公式求得饱和度场.其主要特点和优点是能克服通常的数值模拟方法所具有的数值弥散,给出准确清晰的水驱油前沿饱和度间断面的位置,并且完全避免了通常必须与压力方程联立求解或交替求解的饱和度方程,从而使计算工作量大大减少.     

多层合采注入液劈分机理研究

基于理论计算与物理模拟实验,明确水驱油合采层间干扰的实质.通过水驱油渗流阻力求解模型,得到渗透率-含水率-渗流阻力关系图版;进而建立水驱油合采注入液动态劈分模型,该模型能够定量表征合采过程任意时刻各层之间的相互干扰状况以及预判干扰发生与加剧的节点.研究表明:注入液体优先劈分至渗流阻力低的小层,渗流阻力不均衡是发生层间干扰的实质;层间干扰主要由储层先天静态差异渗透率、有效厚度以及后天动态含水差异共同作用;层间阻力差异越大,注入液劈分越剧烈,甚至注入液仅在高渗层进行无效循环,合层采油效率极低.     

低渗透非均质油藏油水两相渗流敏感系数理论模型

本文研究了低渗透油藏低速非达西油水两相渗流的反问题，建立了基于动态信息的油藏敏感系数计算模型，给出了井底压力和水油比关于渗透率和孔隙度的敏感系数的有效算法，为油藏数值模自动拟合和油藏精细描述算法提供了理论基础。     

推广的半绝对离差和动态投资组合选择

在标准的Black－Scholes型金融市场下，建立了以推广的半绝对离差（Extended Semi－Absolute Deviation；ESAD）度量风险的动态均值-ESAD投资组合选择模型，研究了模型的求解方法，得到了最优投资组合策略和均值-ESAD有效前沿的解析表达式．同时，与动态均值-方差模型作了比较分析．最后，结合实例说明了模型的求解方法．     

多孔介质中两相不可压混溶驱替的差分流线扩散法及其误差分析

多孔介质中两相不可压混熔驱替问题可描述为椭圆和抛物耦合的非线性偏微分方程组，对椭圆方程采用混合元方法，而对抛物方程采用差分流线扩散法，本文构造了求解该问题的差分流线扩散-混合元格式，最后，给出所构造格式按L^∞(L^2）模的拟最优误差阶估计。     

Exact analytical solution of a generalized multiple moving boundary model of one-dimensional non-Darcy flow in heterogeneous multilayered low-permeability porous media with a threshold pressure gradient

A nonlinear generalized multiple moving boundary model of one-dimensional non-Darcy flow in heterogeneous multilayered low-permeability porous media with a threshold pressure gradient is constructed, in which the total rate of fluid injection into the porous media remains constant. The number of layers in the model can be arbitrary, and thus the generalized model will be very suitable for describing the one-dimensional non-Darcy flow characteristics in low-permeability reservoirs with strong heterogeneity. Through the similarity transformation method, the exact analytical solution of the multiple moving boundary model is obtained, and the formula for the subrate of fluid injection into every layer is provided. Moreover, it is strictly proved that the exact analytical solution can reduce to the solution of Darcy flow as the threshold pressure gradient in different layers simultaneously tends to zero. Through the exact analytical solution, the effects of the layer threshold pressure gradient, the layer permeability ratio, and the layer elastic storage ratio on the moving boundaries, the spatial pressure distributions, the transient pressure, and the layer subrate in low-permeability porous media are discussed. Through comparison of the exact analytical solutions, it is also demonstrated that incorporation of the multiple moving boundary conditions is very necessary in the modeling of non-Darcy flow in heterogeneous multilayered porous media with a threshold pressure gradient, especially when the threshold pressure gradient is large. In particular, an explicit formula is presented for estimating the relative error of the transient pressure introduced by ignoring the moving boundaries in the modeling. All in all, solid theoretical foundations are provided for non-Darcy flow problems in stratified reservoirs with a threshold pressure gradient. They can be very useful for strictly verifying numerical simulation results, and for giving some guidance for project design and optimization of layer production or injection during the development of heterogeneous low-permeability reservoirs and heavy oil reservoirs so as to enhance oil recovery.     

Momentum-dominated orifice flow in hydraulic buffers

A study has been made of the orifice flow that occurs in a hydraulicbuffer. A technique was needed to explain phenomena that wereoccurring in some extreme situations and to provide an estimatefor parameters in a dynamic simulation model of the buffer.It has been shown that finite-element calculations of steady-statelaminar flow, with mass-conserving elements and streamline upwinding,can be used to estimate the flow within the orifice. In particular,the technique is sufficient to predict a cavitation bubble justbeyond the orifice entrance. An iterative inviscid potentialflow has been utilized to redesign the orifice boundary shapeto give a more streamlined flow. This model also confirmed thatthe ‘vena contracta’ parameter was close to thevalue of 0.9 which is needed for dynamic simulation models.Experiments confirm that the method developed suggests new orificedesigns with significantly improved performance.     

多孔介质二相驱动问题一种修正特征有限元方法的迭代解法及其收敛性分析

0 引言 多孔介质二相驱动问题的数学模型是由压力方程与浓度方程组成的偏微分方程组的初边值问题.关于该问题的数值解问题,已有大量的文献.为了得到最优的L~2-模误差估计,好多方法用混合元方法解压力方程.我们知道,混合元法得到的方程组系数矩阵是非正定的,从而解混合元比解标准元要困难得多,虽然许多人研究了混合元方法的求解问题,但到目前为止,还没有看到令人满意的好的算法.为了避开对混合元的求解,著名学者T.F.Russell考虑了用标准有限元方法解压力方程,用特征有限元方法解浓度方程的求解方法及其迭代解法,对只有分子扩散的二相驱动问题得到了最优的L~2模误差估计,对有机械弥散的一般二相驱动问题得不到最优的L~2模误差估计,同时在收敛性证明中要求压力有限元空间的指数至少是二.     

可变形孔隙介质中热、水耦合力学问题的代数多格子分析方法

研究了孔隙介质中包括热和质量传递的全耦合多相流问题的代数多格子分析方法。数学模型包括质量、线性矩、能量平衡方程和本构方程,以位移、毛细压力、汽压和温度为基本变量,模型中采用了考虑毛细压力关系的修正有效应力概念,并考虑相变、热传导、对流和潜热交换(汽化-冷凝),气相是由易混合的干空气和水蒸气组成,视为理想气体。考题显示出较高的计算效率。     

Block‐centered upwind multistep difference method and convergence analysis for numerical simulation of oil reservoir

The three‐dimensional displacement of two‐phase flow in porous media is a preliminary problem of numerical simulation of energy science and mathematics. The mathematical model is formulated by a nonlinear system of partial differential equations to describe incompressible miscible case. The pressure is defined by an elliptic equation, and the concentration is defined by a convection‐dominated diffusion equation. The pressure generates Darcy velocity and controls the dynamic change of concentration. We adopt a conservative block‐centered scheme to approximate the pressure and Darcy velocity, and the accuracy of Darcy velocity is improved one order. We use a block‐centered upwind multistep method to solve the concentration, where the time derivative is approximated by multistep method, and the diffusion term and convection term are treated by a block‐centered scheme and an upwind scheme, respectively. The composite algorithm is effective to solve such a convection‐dominated problem, since numerical oscillation and dispersion are avoided and computational accuracy is improved. Block‐centered method is conservative, and the concentration and the adjoint function are computed simultaneously. This physical nature is important in numerical simulation of seepage fluid. Using the convergence theory and techniques of priori estimates, we derive optimal estimate error. Numerical experiments and data show the support and consistency of theoretical result. The argument in the present paper shows a powerful tool to solve the well‐known model problem.     

Global Weak Solutions for a Parabolic System Modeling a One-Dimensional Miscible Flow in Porous Media

We consider an initial boundary value problem for a nonlinear differential system of two equations. Such a system is formed by the equations of compressible miscible flow in a one-dimensional porous medium. No assumption about the mobility ratio is involved. Under some reasonable assumptions on the data, we prove the existence of a global weak solution. Our basic approach is the semi-Galerkin method. We use the technique of renormalized solutions for parabolic equations in the derivation ofa prioriestimates.     

Modelling and simulation of wave transformation in porous structures using VOF based two-phase flow model

This paper represents the results of wave transformation in porous structures and hydraulic performance of a vertical porous seawall. The study was carried out using a VOF based two-phase numerical hydrodynamic model. The model was developed by coupling an ordinary porous flow model based on extended Navier–Stokes equations for porous media, and a two-phase flow model. A unique solution domain was established with proper treatment of the interface boundary between water, air and the structure. The VOF method with an improved fluid advection algorithm was used to trace the interface between water and air. The resistance to flow caused by the presence of structural material was modeled in terms of drag and inertia forces. The parameters that govern resistance to flow in a porous media were calibrated for a typical structural setup and then the computational efficacy of the model was evaluated for several wave and structural conditions other than the calibrated setup. A set of comparisons of wave properties in and around the structure showed that the model reproduced reasonably good agreement between computed results and measured data. The model was then applied to investigate wave transformation in a vertical porous structure. The role of porosity and width of a structure in reducing wave reflection and increasing energy dissipation was investigated. It is confirmed that there exists an optimum value of structure width and porosity that can maximize hydraulic performances of a porous seawall.     

榆树林油田CO_2吞吐采油目标井优选方法研究

CO_2吞吐是开发低渗透油田的有效方法之一,但进行CO_2吞吐前目标井的优选是关键步骤,它直接关系到CO_2吞吐措施的成败.首先分析了剩余油饱和度、油井含水率、油层厚度、渗透率、孔隙度、井底流压各因素对CO_2吞吐效果的影响,从而建立评价指标,然后利用层次分析方法确定各单因素的合理权重,最后根据模糊综合评判法优选出树11Y68-57和树11Y67-611两口油井适宜CO_2吞吐.优选出的油井具有良好的的油效果,表明该方法是正确可行的,具有一定的推广价值.     

Numerical solution of steady-state porous flow free boundary problems

Summary A new numerical method is used to solve stationary free boundary problems for fluid flow through porous media. The method also applies to inhomogeneous media, and to cases with a partial unsaturated flow.