三孔单渗模型数值模拟研究

保留了非线性偏微分方程中的所有项,没有忽略二次梯度项的影响。建立了由基岩、裂缝及溶洞系统组成的三孔单渗模型。采用有限差分的方法获得了无限大地层定产量生产、有界封闭地层定产量生产和有界封闭地层定压生产时的三孔单渗模型的差分方程,用解非线性方程组的Broyder迭代法求得了方程组的数值解。分别讨论了三重介质参数变化时的压力变化规律,并考虑了井筒储集和表皮效应对压力的影响,做出了典型压力曲线图。     

分形煤层气藏数值模拟研究——Douglas-Jones预估-校正法的应用

传统的煤层气动力学模型多建立在欧几里得基础上,难以描述煤层气孔隙结构的复杂性和形状的不规则性。为此,以分形理论为基础,通过引入煤层基质和裂缝的分形维数来刻画煤层气孔隙结构的复杂性和吸附特性,建立了双重分形介质渗流模型,采用Douglas-Jones预估-校正法对非线性方程组进行离散,获得了无限大地层和有限地层定产量生产时拟稳态吸附模型的差分方程,求得数值解。结果表明,Douglas-Jones预估-校正法可以有效解决这类非线性模型的求解问题,获得无限大地层定产量生产时变形双重分形介质模型的数值解;分析各种分形参数下的煤层压力动态,做出了典型压力曲线图。对无限大地层,初期分形维数对压力影响不大,后期分形维数越小,压力越高。对有限地层,初期分形维数的影响明显,且分形维数越大,压力越低。压力随分形指数的减小量呈现先增大后减小的趋势,在末期压力平稳趋向同一值。     

具有井简储集的变形介质双渗模型的压力分析

为更好地研究碳酸盐油藏和低渗油的渗流问题，引入渗透率模数，考虑应力敏感地层中介质的变形，介质的双孔隙度、双渗秀率特征，同时考虑井筒储集的影响，建立新的数学模型。渗透率依赖于孔隙压力变化的流动方程是强非线性的，模型采用Douglas—Jones预估-校正法获得了无限大地层及有界封闭地层的数值解，形成了新的理论图版，并利用这些图版对模型中的有关参数进行了敏感性分析。     

变形双重介质广义流动分析

对于碳酸盐油藏和低渗油藏的渗流问题，传统的研究方法都是假设地层渗透率是常数，这假设，对于地层渗透率是压力敏感的情况，对压力的空间变化和瞬时变化将导致较大的误差。本文研究了应力敏感地层中双重介质渗流问题的压力不稳定响应，不仅考虑了储层的双重介质特征，而且考虑了应力敏感地层中介质的变形，建立了应力敏感地层双重介质的数学模型，渗透率依赖于孔隙压力变化的流动方程是强非线性的，采用Douglas-Jones预估－校正法获得了只有裂缝发生形变定产量生产时无限大地层的数值解及定产量生产岩块与裂隙同时发生形变时无限大地层的数值解，并探讨了变形参数和双重介质参数变化时压力的变化规律，给出几种情况下典型压力曲线图版，这些结果可用于实际试井分析。     

具有井筒储集的变形介质双渗模型的压力分析

为更好地研究碳酸盐油藏和低渗油的渗流问题,引入渗透率模数,考虑应力敏感地层中介质的变形,介质的双孔隙度、双渗秀率特征,同时考虑井筒储集的影响,建立新的数学模型。渗透率依赖于孔隙压力变化的流动方程是强非线性的,模型采用Douglas-Jones预估-校正法获得了无限大地层及有界封闭地层的数值解,形成了新的理论图版,并利用这些图版对模型中的有关参数进行了敏感性分析。     

考虑井储和表皮效应的分形介质煤层气压力动态分析

考虑煤层的双重介质特征和介质的分形特征,建立了考虑井筒储存和表皮效应影响的分形介质煤储层非平衡吸附、非稳态条件下的气体流动数学模型,并分别求得了无限大地层条件下中心一口井定产量生产时无因次井底压力的Laplace空间解析解和实空间上的数值解.给出了无因次井底压力及其导数随分形参数、无因次井筒储存系数以及表皮系数等变化的双对数曲线图.     

动态裂纹扩展中的分形效应

假设裂纹顶端沿着分形轨迹运动，建立了裂纹扩展的分形弯折（ｋｉｎｋｉｎｇ）模型来描述裂纹的动态扩展。根据这个模型，我们推导了分形裂纹扩展对劝态应力强度和裂纹速度的影响．动态应力强度因子与表观应力强度因子之比Ｋ（ｌ（ｔ），Ｖ）／Ｋ（Ｌ（ｔ），Ｏ）是表观裂纹速度Ｖ＿Ｏ，材料微结构参数（ｄ／Δａ），分维Ｄ和裂纹扩展路径的弯折角θ的函数。本文研究结果表明：在分形裂纹扩展中，表观（或量测）的裂纹速度Ｖ＿Ｏ很难接近Ｒａｙｌｅｉｇｈ波速Ｃ＿ｒ．动态断裂实验中Ｖ＿Ｏ明显低于Ｃ＿ｒ的原因可能是分形裂纹扩展效应所致。材料的微结构，裂纹扩展路径的分维和弯折角均很强地影响动态应力强度因子和裂纹扩展速度。     

基于分形理论的煤层气非达西流动分析

在考虑了煤层的分形特征和启动压力梯度影响的基础上,建立了无限大煤层中气体低速非达西流动的数学模型,并求得了量纲为一的井底压力的Laplace空间解析解,并根据数值求解结果绘制了典型的井底压力动态曲线。研究结果表明:在定产量生产的情况下,分形维数和量纲为一的启动压力梯度对早期井底压力动态无显著影响;在生产的中后期,由于受二者的影响,压力导数曲线上的径向流水平直线段消失;量纲为一的井储系数的影响主要表现在续流阶段,而吸附系数则主要影响煤基质向裂隙扩散的过渡阶段。     

应用分形有限元方法于外域声场计算

 应用二级分形有限元方法计算了外域声场. 用一人工边界把外域声场分为两 部分，人工边界以内使用常规有限元方法，人工边界以外的无限大区域使用分形有限元方法. 使用分形有限元方法的优点是：一方面形成几何自相似网格使得相邻层之间的单元刚度矩阵 和质量矩阵具有非常简单的关系；另一方面引用自动满足无限远辐射条件的全域插值函数把 节点自由度变换为一组广义坐标，因而计算量可以大大减少. 数值算例表明：该方法对于计 算无限大外域声场是有效的.     

考虑二次梯度项及动边界的双重介质低渗透油藏流动分析

在传统试井模型的非线性偏微分方程中根据弱可压缩流体的假设,忽略了二次梯度项,对于低渗透油藏这种方法是有疑问的.低渗透问题一个显著的特点就是流体的流动边界随着时间不断向外扩展.为了更好地研究双重介质低渗透油藏中流体的流动问题,考虑了二次梯度项及活动边界的影响,同时考虑了低渗透油藏的非达西渗流特征,建立了双重介质低渗透油藏流动模型.采用Douglas-Jones预估-校正差分方法获得了无限大地层定产量生产时模型的数值解,分别讨论了不同参数变化时压力的变化规律及活动边界随时间的传播规律,还分析了考虑和忽略二次梯度项影响时模型数值解之间的差异随时间的变化规律,做出了典型压力曲线图版,这些结果可用于实际试井分析.     

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

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The Flow Problem of Fluids Flow in a Fractal Reservoir with Double Porosity

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The Transient Flow Analysis of Fluid in a Fractal, Double-Porosity Reservoir

The mathematical model for transient fluid flow in porous media is based in general on mass conservation principle. Because of the small compressibility of formation fluid, the quadratic term of pressure gradient is always ignored to linearize the non-linear diffusion equation. This may result in significant errors in model prediction, especially at large time scale. In order to solve this problem, it may be necessary to keep the quadratic term in the non-linear equations. In our study, the quadratic term is reserved to fully describe the transient fluid flow. Based on this rigorous treatment, the mathematical models are established to analyze the transient flow behavior in a double porosity, fractal reservoir with spherical and cylindrical matrix. In addition, Laplace transformation method is employed to solve these mathematical models and the type curves are provided to analyze the pressure transient characteristics. This study indicates that the relative errors in calculated pressure caused by ignoring the quadratic term may amount to 10?% in a fractal reservoir with double porosity, which can??t be neglected in general for fractal reservoirs with double porosity at large time scale.     

Generalized flow analysis of non-Newtonian visco-elastic fluid flow through fractal reservoir

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分形在油气田开发中的应用

分形用于测井资料分析，为油藏描述提供了新的工具，使得利用油藏数值模拟来模拟复杂结构的油气藏变得更加便利；分形油藏上的试井分析解决了一些以前难以解释的问题；用分形来描述裂缝和孔洞结构，提高了酸化压裂的设计水平；用分形理论来描述两相流，揭示了部分粘性指进的触发机理．总之，分形理论在油气田开发中的应用，促进了渗流力学基础理论的发展．     

Percolation theory approach to transport phenomena in porous media

The percolation theory approach to static and dynamic properties of the single- and two-phase fluid flow in porous media is described. Using percolation cluster scaling laws, one can obtain functional relations between the saturation fraction of a given phase and the capillary pressure, the relative permeability, and the dispersion coefficient, in drainage and imbibition processes. In addition, the scale dependency of the transport coefficient is shown to be an outcome of the fractal nature of pore space and of the random flow pattern of the fluids or contaminant.     

TRANSIENT WELL TEST MODEL FOR THE WELL WITH GAS AND WATER DISTRIBUTED IN COALBED

煤层气是一种高效清洁的非常规天然气资源,其开采过程是一个排水降压采气的过程. 由于煤层气主要是以吸附态的形式存在于煤层中,当煤层压力降低到临界解吸压力以下时煤层气从煤层中解吸出来并与水一起采出,因此煤层中流体是气水两相分布的. 本文根据煤层气藏排采过程中的解吸特征,通过考虑气水两相分布的渗透率关系,提出了一种与解吸区域大小相关的煤层气井不稳定试井模型. 该模型较好地描述了煤层气排采过程中煤层内气水的流动状态,采用分区模式对气水两相进行描述. 通过有限体积方法求解了所建立的试井模型,计算得到了煤层气井气水两相分布不稳定试井理论曲线,分析了煤层气解吸系数、解吸复合半径、气水饱和度分布等对试井理论曲线的影响.     

Numerical Estimation of the Degree of Reservoir Permeability Heterogeneity Using Pressure Drawdown Tests

This study aims to correlate the response of pressure transient test to permeability distribution type. For this purpose, correlated permeability distributions in x–y direction are generated using fractional Brownian motion (fBm) as it has been shown in literature that permeability in carbonate reservoirs exhibits an fBm type distribution horizontally. 2-D fBm permeability distributions created using mid point displacement method are employed as data to a black oil simulator. The intermittence exponent, H or fractal dimension of the distribution, D, as defined by D=2 – H, characterizes the distribution type. All permeability distributions are normalized to represent the same arithmetic mean (20, 100, and 500 mD) and uniform variance so that only their fractal dimension that underlies the smoothness of the distribution distinguishes them. Many different realizations of permeability distributions are generated based on the random number seeds used and pressure transient (drawdown) tests are simulated using a black oil simulator package (ECLIPSE 100). Pressure transient analysis is performed using PanSystem package. As a base case and for the comparison purpose, the same procedure is repeated for the totally homogeneous case (the same permeability for all grids) and a random (normally distributed) permeability distribution with the same mean and uniform variance. The effects of permeability distribution type on the pressure response are clarified. A strong impact of heterogeneity is observed as an increase in skin effect with increasing fractal dimension of permeability distribution. This additional (or pseudo) skin effect due to heterogeneity is correlated to the fractal dimension of the permeability distribution. As a further step, the procedure is repeated for different flow rates applied during the drawdown test. The correlation between the fractal dimension of permeability distribution and additional skin is improved by incorporating the rate into it. The methodology followed can be used in the assessment of reservoir heterogeneity quantitatively using pressure transient response.     

Flow of an electrorheological fluid between eccentric rotating cylinders

Electrorheological fluids have numerous potential applications in vibration dampers, brakes, valves, clutches, exercise equipment, etc. The flows in such applications are complex three-dimensional flows. Most models that have been developed to describe the flows of electrorheological fluids are one-dimensional models. Here, we discuss the behavior of two fully three-dimensional models for electrorheological fluids. The models are such that they reduce, in the case of simple shear flows with the intensity of the electric field perpendicular to the streamlines, to the same constitutive relation, but they would not be identical in more complicated three-dimensional settings. In order to show the difference between the two models, we study the flow of these fluids between eccentrically placed rotating cylinders kept at different potentials, in the setting that corresponds to technologically relevant problem of flow of electrorheological fluid in journal bearing. Even though the two models have quite a different constitutive structure, due to the assumed forms for the velocity and pressure fields, the models lead to the same velocity field but to different pressure fields. This finding illustrates the need for considering the flows of fluids described by three-dimensional constitutive models in complex geometries, and not restricting ourselves to flows of fluids described by one-dimensional models or simple shear flows of fluids characterized by three-dimensional models.