Transient spherical flow of non-newtonian power-law fluids in porous media

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.     

非牛顿幂律流体球向不定常渗流

本文研究了弱压缩非牛顿幂律流体球向不定常渗流,导出了抛物型偏微分非线性方程.球向扩散方程是其特殊情况.用Laplace变换的方法,找到了线性化后方程的解析解和渐近解.用影响半径的概念和平均值方法求得了近似解.渐近解和近似解的结构是相似的,从而丰富了非牛顿流体一维不定常渗流的理论.     

Analytical solution of partial differential equations for radial transport of a solute in double porous media

The mathematical model for radial transport of a solute is summed up in this paper. The action of non-equilibrium linear adsorption, the double property of porous media and the decay of solute are considered. With the first kind of boundary condition, one finds the analytical solution of these equations by Laplace transform and calculates the dimensionless solution by FORTRAN program with DJS-040. The distribution and change of solute are evaluated and the solution under various limit cases is given. By numerical analysis, one obtains some valuable conclusions.     

地下水在粘弹性含水层系中不定常渗流

本文研究了地下水在粘弹性含水层系中不定常渗流动态。在前人工作的基础上导出了新的微分-积分方程组。已知的微分方程组是它的特殊情况。新的线性微分-积分方程组描写了弱压缩流体在粘弹性含水层系中流动。用Laplace变换的方法求得了微分-积分方程组的解析解。粘弹性增加了含水层系的非均质性,即具有延迟和补给的性质。数值反演解和解析解符合得较好。它们给出了地下水在这种非均质含水层系中水位变化动态。     

关于计算渗流力学问题

渗流力学能够较好地解决油、气、水田开发工程中提出的复杂而困难的力学问题,是与引用和研究新的数值方法分不开的。早在50年代初,G.H.Bruce,D.W.Peaceman,H.H.Rachford,Jr。就用有限差分方法在计算机上(IBM卡片程序计算机)求得了理想气体非线性非定常渗流的数值解。1959年,J.Douglas,D.W.Peaceman,H.H.Rachford,Jr。研究了水、油二相多维渗流非线性微分方程组的数值计算方法。1966年,Zienkiewicz把有限元方法用于二维定常渗流计算。1968年,Javendal,Witherspoon进一步用有限元方法解非定常渗流问题。渗流力学发展到现代,可以毫不夸张的说,离开了数值模拟将很难有新的突破和重大进展。由于计算渗流力学内容很丰富,限于水平,我们只就几个方面的较有代表性的问题作些不完全的综述。      

低渗透微尺度孔隙气体渗流规律

微尺度条件下气体流动特性的研究是现代渗流力学前沿领域之一．分析了低渗透岩石饱和气体渗流实验结果,探索了微尺度孔隙气体渗流规律,探讨了气体非线性渗流力学机理,发现了低渗透岩石微尺度孔隙气体与液体渗流遵循同一形式的运动定律,建立了气体与液体非线性运动定律统一模型．结果表明：新模型与实验结果吻合很好,为微尺度孔隙气体微流动特性研究提供了新的理论依据,对工程地质环境保护及地下流体资源开发有重要指导意义．     

各向异性双重介质垂直裂缝井两相流体渗流

建立了各向异性双重介质中垂直裂缝井两相渗流数学模型,用有限差分法求得了其解,进行了算例分析。得到了含水饱和度沿径向、最大及最小渗透率方向的分布和水驱油前缘等饱和度面随时间的变化,分别讨论了各向异性、吸渗作用对这种介质中两相流体渗流的影响。结果表明：渗透率较在的方向,前缘推进速度较快,油井见水较早;吸渗使前缘推进速度减慢,使油井见水晚。注水开发这种油藏时,见水前注入率不能太大以充分发挥吸渗作用,存在最佳注入率。这对于水力压裂垂直裂缝井注水开发碳酸盐岩裂缝性油藏有指导意义。     

Law of nonlinear flow in saturated clays and radial consolidation

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media.There is good agreement between the derived results and test ones.Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow.Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius.The interaction is an important reason why nonlinear flow in saturated clays occurs.An exact mathematical model was presented for nonlinear flow in micro-scaie pore of saturated clays.Dimension and physical meanings of parameters of it are definite.A new law of nonlinear flow in saturated clays was established.It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one.Darcy law is a special case of the new law.A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow.Equations of average mass conservation and moving boundary,and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer,a method of steady state in stead of transient state and a method of integral of an equation.Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained.Re- suits show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay.The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases.Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.     

New studying of Lattice Boltzmann method for two-phase driven in porous media

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煤层压裂裂缝三维延伸模拟及产量预测研究

针对煤层气井的压裂特点和产出机理,综合应用流体力学、线弹性断裂力学、传热学、计算数学和软件工程等方面的知识,提出了煤层压裂裂缝三维延伸模型和产量动态预测模型,其中裂缝三维延伸模型考虑了煤层、上下遮挡层之间的地应力和岩石力学参数变化的影响,产量动态预测模型考虑了煤层气先解吸扩散后渗流入井的产出机理。在此基础上研制了煤层气井三维压裂优化设计软件,并通过实例计算验证了其实用性和可靠性。