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1.
三孔单渗模型数值模拟研究   总被引:3,自引:2,他引:1       下载免费PDF全文
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。  相似文献   

2.
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   总被引:4,自引:0,他引:4  
王梅英  同登科 《力学季刊》2007,28(3):448-454
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.  相似文献   

3.
引入人工压力变量,将弹性本构方程以应力、应变和压力表达,建立求解不可压缩平面弹性问题的位移-压力方程和不可压缩条件方程的耦合偏微分方程组。利用张量积型重心Lagrange插值近似二元函数,得到计算插值节点处偏导数的偏微分矩阵。采用配点法离散不可压缩弹性控制方程,利用偏微分矩阵直接离散弹性力学控制方程为矩阵形式方程组。利用插值公式离散位移和应力边界条件,将离散边界条件与离散控制方程组合为新的方程组,得到求解弹性问题的过约束线性代数方程组;利用最小二乘法求解线性方程组,得到弹性力学问题位移数值解。数值算例验证了所提方法的数值计算精度为10-14~10-10。  相似文献   

4.
扁球壳在均布压力作用下的非线性弯曲问题   总被引:2,自引:0,他引:2  
本文应用逐步加裁法将圆底扁球壳在均布压力作用下的非线性微分方程组化为线性的微分方程组.然后以三次B样条函数为试函数,用配点法将此线性的微分方程组化成线性代数方程组.最后利用递推公式解此线性代数方程组,从而使问题得到解决.  相似文献   

5.
俯仰运动圆柱贮箱中液体的非线性晃动   总被引:9,自引:3,他引:6  
首次对储仰运动圆柱贮箱中液体的有限幅值晃动问题进行了解析研究。首先建立了描述俯仰和/或偏航运动贮箱中液体晃动的非线性偏微分方程组,而后提出了相应的变分原理,建立了压力体积分形式的Lagrange函数,通过变分方程,最终得到措述俯仰和/或偏航运动圆柱贮箱中液体晃动的非线性动力学微分方程组,该动力学方程组自然满足液体自由表面的运动学和动力学办界条件。而后动用多尺度法求解了所得的动力学方程组,对非线性液  相似文献   

6.
低渗透多孔介质渗流动边界模型的解析与数值解   总被引:1,自引:0,他引:1  
考虑启动压力梯度的低渗透多孔介质非达西渗流模型属于强非线性动边界问题, 分别利用相似变量变换方法和基于空间坐标变换的有限差分方法, 对内边界变压力情况下、考虑启动压力梯度的一维低渗透多孔介质非达西渗流动边界模型进行了精确解析与数值求解研究. 研究结果表明:该动边界模型存在唯一的精确解析解, 且所求得的精确解析解可严格验证数值解的正确性;且当启动压力梯度值趋于零时, 非达西渗流动边界模型的精确解析解将退化为达西渗流情况下的精确解析解. 由求解结果作出的非零无因次启动压力梯度下的地层压力分布曲线表现出紧支性特点, 其与达西渗流模型的有显著不同. 因此, 研究低渗透多孔介质中非稳态渗流问题时, 应该考虑动边界的影响. 研究内容完善了低渗透多孔介质的非达西渗流力学理论, 为低渗透油气藏开发的试井解释与油藏数值模拟技术提供了理论基础.  相似文献   

7.
液固混合介质隔振器基于一种全新的工作机理,具有优良的隔振系统动力学特性. 混合介质由一类几乎不可压缩液体和许多可压缩的固体单元混合而成. 当振动、冲击发生时, 液体将动压力瞬间传递到所有单元体上, 使它们同时参与变形,从而有效隔离振动,大幅度吸收、损耗冲击能量; 若设计得当,这类隔振器可同时具有卓越的隔振和缓冲性能. 以空心橡胶球作为固体单元体, 分析了该单元体在有限变形情况下的变形规律, 分析了隔振器的非线性刚度特性; 采用MTS液压伺服试验系统进行了测试验证, 理论分析和试验结果具有较好的一致性. 建立了系统的非线性动力学方程, 采用多尺度摄动法获得了系统的频响特性, 发现系统具有软弹簧非线性动力学特性, 并在试验中得到了证实; 因为弹性恢复力中存在位移平方项, 通过试验和数值仿真进一步验证了系统响应的非对称性.  相似文献   

8.
一类液固混合介质隔振器的动力学特性研究   总被引:2,自引:0,他引:2  
液固混合介质隔振器基于一种全新的工作机理,具有优良的隔振系统动力学特性.混合介质由一类几乎不可压缩液体和许多可压缩的固体单元混合而成.当振动、冲击发生时,液体将动压力瞬间传递到所有单元体上,使它们同时参与变形,从而有效隔离振动,大幅度吸收、损耗冲击能量;若设计得当,这类隔振器可同时具有卓越的隔振和缓冲性能.以空心橡胶球作为固体单元体,分析了该单元体在有限变形情况下的变形规律,分析了隔振器的非线性刚度特性;采用MTS液压伺服试验系统进行了测试验证,理论分析和试验结果具有较好的一致性.建立了系统的非线性动力学方程,采用多尺度摄动法获得了系统的频响特性,发现系统具有软弹簧非线性动力学特性,并在试验中得到了证实;因为弹性恢复力中存在位移平方项,通过试验和数值仿真进一步验证了系统响应的非对称性.  相似文献   

9.
二维定常不可压缩粘性流动N-S方程的数值流形方法   总被引:4,自引:4,他引:0  
将流形方法应用于定常不可压缩粘性流动N-S方程的直接数值求解,建立基于Galerkin加权余量法的N-S方程数值流形格式,有限覆盖系统采用混合覆盖形式,即速度分量取1阶和压力取0阶多项式覆盖函数,非线性流形方程组采用直接线性化交替迭代方法和Nowton-Raphson迭代方法进行求解.将混合覆盖的四节点矩形流形单元用于阶梯流和方腔驱动流动的数值算例,以较少单元获得的数值解与经典数值解十分吻合.数值实验证明,流形方法是求解定常不可压缩粘性流动N-S方程有效的高精度数值方法.  相似文献   

10.
多介质流体非守恒律欧拉方程组的数值计算方法   总被引:1,自引:0,他引:1  
对多介质流体在界面处满足的Euler方程进行了探讨,方程组中增加了描述材料参数间断性质的对流形式非守恒律方程组 .以波传播算法为基础,通过Roe方程近似求解Riemann问题,同时采用相同的数值差分格式求解流体动力学Euler方程组和界面方程组.该方法可以有效消除多介质流体在界面处压力、速度可能出现的非物理振荡.给出了部分典型一维和二维数值计算结果.  相似文献   

11.
The equations that describe weakly compressible fluid flows through a weakly deformable porous skeleton are analyzed for the nonlinear seepage law with a limiting (initial) pressure gradient. With reference to approximate and numerical solutions of the well and well-gallery start problems, it is shown that taking into account in the continuity equation the quadratic term usually discarded when obtaining the elastic regime equations may qualitatively change the behavior of large spatial scale solutions.  相似文献   

12.
In this paper we derive the Forchheimer law via the theory of homogenization. In particular, we study the nonlinear correction to Darcy's law due to inertial effects on the flow of a Newtonian fluid in rigid porous media. A general formula for this correction term is derived directly from the Navier–Stokes equation via homogenization. Unlike other studies based on the same approach that concluded for the nonlinear correction to be cubic in velocity for isotropic media, the present work shows that the nonlinear correction is quadratic. An example is constructed to illustrate our theory. In this example, the analytic solution to the Navier–Stokes equation is obtained and is utilized to show the validity of the quadratic correction. Both incompressible and compressible fluids are considered.  相似文献   

13.
The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform.Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.  相似文献   

14.
An expansion solution in the physical plane is developed for subsonic compressible fluid flow past an obstacle. Assuming that the stream is inviscid, isentropic, irrotational and steady, it is shown that the velocity potential may be expressed as a series of homogeneous Heun functions and radial distance terms. The basis of this analysis is Ludford's formal discussion of corresponding singularities in Bergman's Linear Integral Operator Method. A modification of these results permits reduction of the governing nonlinear partial differential equation to an ordinary, nonhomogeneous, linear differential equation. The expansion solution is compared with the Rayleigh-Janzen method and the Prandtl-Glauert theory. The comparison indicates that this expansion gives better results than other methods currently used. The simplicity and economy of this expansion solution facilitates direct practical application.  相似文献   

15.
A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy’s flow problem, the exact analytical solution for the case of Darcy’s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem.  相似文献   

16.
Separable solutions admitted by a nonlinear partial differential equation modeling the axisymmetric spreading under gravity of a thin power-law fluid on a horizontal plane are investigated. The model equation is reduced to a highly nonlinear second-order ordinary differential equation for the spatial variable. Using the techniques of Lie group analysis, the nonlinear ordinary differential equation is linearized and solved. As a consequence of this linearization, new results are obtained.  相似文献   

17.
Most of the developed models for fractured reservoirs assume ideal matrix block size distribution. This assumption may not be valid in reality for naturally fractured reservoirs and possibly lead to errors in prediction of production from the naturally fractured reservoirs especially during a transient period or early time production from the matrix blocks. In this study, we investigate the effect of variable block size distribution on one- dimensional flow of compressible fluids in fractured reservoirs. The effect of different matrix block size distributions on the single phase matrix-fracture transfer is studied using a recently developed semi-analytical approach. The proposed model is able to simulate fluid exchange between matrix and fracture for continuous or discrete block size distributions using probability density functions or structural information of a fractured formation. The presented semi-analytical model demonstrates a good accuracy compared to the numerical results. There have been recent attempts to consider the effect of variable block size distribution in naturally fractured reservoir modeling for slightly compressible fluids with a constant viscosity and compressibility. The main objective of this study is to consider the effect of variable block size distribution on a one-dimensional matrix-fracture transfer function for single-phase flow of a compressible fluid in fractured porous media. In the proposed semi-analytical model, the pressure variability of viscosity and isothermal compressibility is considered by solving the nonlinear partial differential equation of compressible fluid flow in the fractured media. The closed form solution provided can be applied to flow of compressible fluids with variable matrix block size distribution in naturally fractured gas reservoirs.  相似文献   

18.
A general theoretical solution of the boundary problem of aerodynamics of high subsonic velocities is presented. The solution of the partial differential equation for the velocity potential is carried out in the physical plane in streamline co-ordinates. The principle of the solution is the representation flow of a compressible fluid around a given profile to a hypothetical flow of an incompressible fluid around a different associated profile. In other words, the problem of compressible flow is transformed to the problem of incompressible flow, which can easily be solved. The results of this solution show very good agreement with solutions of other authors and with experiments.  相似文献   

19.
The transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied. A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory of one-dimensional flow of non-Newtonian fluids through porous media.  相似文献   

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