基于变量分离的修正有限元数值计算

采用有限元方法直接求解粘性不可压缩流动N—S耦合方程，本文从离散化的动量方程和连续方程出发，得到了替代连续方程的压力简化统一方程，将各个求解变量分离开来，建立起直接从方程中求解压力场的有限元数值计算方法，有效地消除了压力场的伪震荡。通过对层流和紊流典型算例的分析比较，证明了本文方法是令人满意的。     

低充水液舱晃荡气垫效应的数值分析

为了研究空气可压缩性对液仓晃荡和流体动力载荷的影响,建立了基于NS方程和VOF方法的自由表面流动数学模型,其中气相可作为可压缩介质。通过单涡演化、溃坝和受迫晃荡三个典型算例的计算,验证了数值方法的有效性。与现有的实验结果对比发现,考虑气相可压缩的两相流模型能合理地反映液仓侧壁的压力振荡过程,而基于气相不可压缩假定的数值模型则无法给出合理的结果。采用空气可压缩的两相流模型,给出了不同背景压强作用下液舱晃荡形态及液体对壁面的拍击力。通过比较壁面监测点的压力时间过程线的计算结果和现有的实验数据,表明考虑空气可压缩性的两相流模型可以很好地预报最大压力峰值,并较合理地给出压力振荡过程,因此有必要在液仓晃荡与流动动力预报中考虑空气的气垫效应。     

轴对称体内外流全流场统一计算求解

本文推广了建立在半交错网格基础上的连续性方程压力联系方程方法来计算不可压缩粘性轴对称体内外流问题，整个内外流流场分块生成结构化网格，统一求解。并与建立在交错网格上的有限体积方法计算进行了比较，都得到了令人满意的结果，证明这两种方法在求解包含内外流流场的问题时是高效的。     

柱形容器内液体的强非线性自振

本文考虑了柱形容器内轴对称，有表面张力情形下理想，不可压缩液体的强非线笥自振。对自由面上的非线性条件不作任何近似。用优化的办法求解此强非线性问题，得到了一些有意义的结果，发现在非线性和表面张力共同作用下，液面运动有“反弹”现象。     

地下岩体裂隙蠕变渗流耦合分析

震后断层区岩体裂隙的愈合对于地震水力响应研究具有重要的作用.为研究裂隙岩体愈合对深部断层区渗透率时空演化规律的影响,在离散裂隙网络耦合模型基础上加入裂隙蠕变效应,建立裂隙岩体流固耦合时空演化模型,并利用COMSOL Multiphysics对建立的耦合方程进行求解.结果表明:封堵之前,常规的耦合渗流达到稳定状态,由于具有完整的通道,任意时刻的流固耦合并不能改变流体的压力;随着封堵发生,在蠕变效应下,裂隙开度减小,单元体渗透率降低,流体压力增大.该研究成果为震后破裂带岩体的愈合机理及渗透率演化分析提供了理论依据.     

任意形状复合油藏压力动态的边界元分析

油气藏形状对井底压力动态响应有着显著的影响，常规的解析方法只能计算规则形状油气藏的井底压力响应。该文建立了任意形状复合油藏不稳定渗流的数学模型，并将区域分割法与边界元方法相结合，研究了任意形状复合油藏不稳定压力响应的计算方法，应用杜哈美原理考虑了表皮效应与井储系数对井底压力动态响应的影响。绘制并分析了复合油藏的典型曲线，通过分析指出油藏的边界性质会影响典型曲线后期形态，而内区形状的也可能掩盖复合油藏典型曲线的特点。     

带启动压力梯度的双孔压敏介质压力动态及其应用研究

通过在流动方程中加入启动压力梯度,并考虑地层渗透率随压力的变化发生变化,建立了带启动压力梯度的双孔压敏介质油藏试井解释模型;通过隐式格式对所形成的非线性抛物型方程进行了线性化,采用追赶法进行了求解;通过对参数的敏感性分析表明:启动压力梯度和渗透率变化模数都对压力及压力导数有着很大的影响,导致径向流段不复存在,压力及压力导数曲线在后期上翘;将形成的方法在胜利油田的低渗透潜山油藏进行了应用,解释结果更加符合地质实际,表明了该方法的正确性和实用性。     

变形多孔介质流固耦合非线性渗流模型及解析

渗流的流固耦合问题在理论上与实践中都十分重要。考虑可变形多孔介质的渗透系数和孔隙率的变化依赖于压强变化,由渗透系数与渗透率的关系,结合非线性渗流流体质量守恒方程和连续性方程等基本微分方程建立了一维流固耦合非线性渗流问题的数学模型,推导了可变形介质非稳定渗流场微分方程。利用分离变量法推导出孔隙水压随时间和空间的变化关系的解析解,分析了渗流方程中的控制参数对渗流的非线性程度的影响。通过引入物理参数的方法处理渗流随时间的变化,并阐明了非线性渗流机理,最后定性分析了影响流体渗流压强分布的因素。     

建筑物地基动力液化的两相介质动力有限元分析

应用饱和多孔介质动力学原理分析了建筑物地基的地震液化问题。将地基视为两相介质体系，水是可压缩的。根据土力学模型，采用双曲线非线性动力本构，考虑了砂土的剪胀性，刚度退化，滞回特性和土水相对运动等因素，建立了动力方程 组。基于是否考虑渗流问题，建立了两种离散形式：(1) 以土骨架位移和水位移为未知量的矩阵方程；(2) 以土骨架位移、水位移和孔隙水压力为未知量的矩阵方程。用 显式差分法求解，通过计算发现地基下液化有明显的分区现象。     

计算各向异性岩心渗透率的方法研究

由于地质上的原因，储油气层岩石往往表现出渗透率的各向异性，正确认识渗透率的各向异性是油气田勘探与开发中的一项基础工作。根据改进的全岩心分析装置的测试数据，建立了描述流体在各向异性介质中三维不稳定渗流的数学模型和计算各向异性储油气层岩石渗透率张量的自动拟合模型，并采用逐步二次规划法进行了求解，从而为室内测量和解释各向异性岩心渗透率张量提供了可行的方法。最后，通过算例说明了方法的可行性和可靠性。     

内、外边界定压条件下地层压力的解

本文在内、外边界定压的条件下得到了平面单向流和平面径向流两种渗流形式在拉氏空间的解析解，利用Stehfest数值反演方法给出了地层各点的压力分布曲线，由这些曲线可以清楚地看到流体的流动由不稳态流向稳态流过渡以及最后达到稳态流的过程。本文给出的压力解可用于准确预测油井(或水井)由开井达到稳定生产所需要的最小时间，同时也是对油藏渗流力学基础理论的一个有意义的补充。     

THE PRESSURE TRANSIENT ANALYSIS OF DEFORMATION OF FRACTAL MEDIUM

The assumption of constant rock properties in pressure-transient analysis of stress-sensitive reservoirs can cause significant errors in the estimation of temporal and spatial variation of pressure. In this article, the pressure transient response of the fractal medium in stress-sensitive reservoirs was studied by using the self-similarity solution method and the regular perturbation method. The dependence of permeability on pore pressure makes the flow equation strongly nonlinear. The nonlinearities associated with the governing equation become weaker by using the logarithm transformation. The perturbation solutions for a constant pressure production and a constant rate production of a linear-source well were obtained by using the self-similarity solution method and the regular perturbation method in an infinitely large system, and inquire into the changing rule of pressure when the fractal and deformation parameters change. The plots of typical pressure curves were given in a few cases, and the results can be applied to well test analysis.     

INVESTIGATION OF THE FLOW IN FRACTAL RESERVOIR INCLUDING THE EFFECTS OF QUADRATIC GRADIENT TERM

According to the assumption of slightly compressible fluid, the quadratic gradient term in the nonlinear partial differential equations for the traditional well-test model is usually neglected. The linear partial differential equation is thus established. It is known that neglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flow model for fractal medium is constructed and the quadratic gradient term is considered. The exact solutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in a constant-rate and constant-pressure production for an infinitely large system. This paper addresses the variation of pressure with fluid compressibility coefficient and fractal reservoir parameters. The plots of the typical pressure curves are constructed, and the results can be applied to well-test analysis.     

EFFECT OF A MOVING BOUNDARY ON THE FLUID TRANSIENT FLOW IN LOW PERMEABILITY RESERVOIRS

In a low permeability reservoir, the existence of a moving boundary is considered in the study of the transient porous flow with threshold pressure gradient. The transmission of the moving boundary directly indicates the size of the drainage area as well as the apparent influences on the pressure behavior. The nonlinear transient flow mathematical model in which the threshold pressure gradient and the moving boundary are incorporated is solved by advanced mathematical methods. This paper presents some new analytical solutions describing the pressure distribution at a constant rate and the production decline in a constant pressure production with the boundary propagation. It is shown that the greater the threshold pressure gradient, the slower the transmission of the moving boundary, the larger the pressure loss will be, and there is no radial flow in the middle and later phases of the wellface pressure for a well at a constant rate. We have the the maximum moving boundary at a specific drawdown pressure for a low permeability reservoir. The greater the threshold pressure gradient, the smaller the maximum moving boundary distance, the quicker the production decline for a well in a constant pressure production will be. The type curve charts for the modern well test analysis and the rate transient analysis with a moving boundary are obtained and the field test and the production data are interpreted as examples to illustrate how to use our new results.     

承压含水层中非达西径向稳定流动抽水模拟试验

为分析抽水井附近水流的非达西流动,采用装填均质河砂的扇形密闭水槽模拟承压含水层,开展了外边界水头恒定条件下的定流量抽水试验,获得到了水流稳定流动时的水头降深曲线。通过比较试测水头降深与达西流动理论水头降深,以及比较相邻两压力传感器之间的平均水力梯度与相同流速下的达西水力梯度,进行了非达西流动的判别,比较结果发现本试验条件下存在明显的非达西流动现象。同时,应用基于Izbash方程的非达西稳定流动水头降深解析解,对不同流量下的试验数据进行了拟合分析,发现抽水流量对非达西稳定流动的Izbash方程系数值影响较小。通过不同平均方法获得了描述本试验中非达西流动的Izbash方程系数的适宜取值为k=7.17×10-7,n=1.65,此时不同抽水流量下拟合水头降深曲线与试测水头降深曲线吻合良好,表明基于Izbash方程的非达西稳定流动水头降深解析解可较好地描述抽水井附近的非达西径向稳定流动。     

承压含水层中非达西径向稳定流动抽水模拟实验

为分析抽水井附近水流的非达西流动，本文采用装填均质河砂的扇形密闭水槽模拟承压含水层，开展了外边界水头恒定条件下的定流量抽水实验。通过安装在扇形水槽侧壁的压力传感器测量压力水头，得到了水流稳定流动时的水头降深曲线。通过比较实测水头降深与达西流动理论水头降深，以及比较相邻两压力传感器之间的平均水力梯度与相同流速下的达西水力梯度，进行了非达西流动的判别，比较结果发现本实验条件下存在明显的非达西流动现象。同时，应用基于Izbash方程的非达西稳定流动水头降深解析解，对不同流量下的实验数据进行了拟合分析，研究发现抽水流量对非达西稳定流动的Izbash方程系数值影响较小。通过不同平均方法获得了描述本实验中非达西流动的Izbash方程系数的适宜取值为k=7.17×10-7，n=1.65，此时不同抽水流量下拟合水头降深曲线与实测水头降深曲线吻合良好。这说明基于Izbash方程的非达西稳定流动水头降深解析解可较好地描述抽水井附近的非达西径向稳定流动。     

Transient flow model and pressure dynamic features of tree-shaped fractal reservoirs

A transient flow model of tree-shaped fractal reservoirs is built by embedding a fracture network simulated by a tree-shaped fractal network into a matrix system. The model can be solved using the Laplace conversion method. The dimensionless bottom hole pressure can be obtained using the Stehfest numerical inversion method. The bi-logarithmic type curves for the trce-shaped fractal reservoirs are thus obtained. The pressure transient responses under different fractal factors are discussed. The factors with a primary effect on the inter-porosity flow regime include the initial branch number N, the length ratio α, and the branch angle θ. The diameter ratio β has a significant effect on the fracture radial flow, the inter-porosity and the total system radial flow regimes. The total branch level M of the network mainly influences the total system radial flow regime. The model presented in this paper provides a new methodology for analyzing and predicting the pressure dynamic characteristics of naturally fractured reservoirs.     

MODIFIED INTEGRAL-FACTOR METHOD FOR STEADY CONVECTION-DIFFUSION EQUATIONS

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NUMERICAL SIMULATION OF STEADY FLOW FOR VISCOELASTIC FLUID IN AN ECCENTRIC ANNULUS WITH INNER ROD MOVING AXIALLY

1. INTRODUCTION Compared with water-flood, polymer-flood has increased the recovery ratio by 12 %in Daqing oil field,and it’s economic profit is very promi- nent ,but severe well rod eccentric wear appears in the polymer-flood well , and rod breaking occurs someti mes , whichis a new problemthat should be solvedi mmediately in the polymer-flood well pro- duction. Experi ment[1]shows that the inner rod moving in polymer-water solution in the eccentric annulus will lean to outer pipe , whic…