双重孔隙渗流作用井眼围岩损伤力学模型研究

考虑双重介质建立了井眼围岩力学模型,考虑井眼围岩岩体为孔隙、裂缝双重介质,将围岩区域分为破坏区、损伤区和弹性区,建立双重介质渗流作用下的井壁围岩不同区域的损伤力学计算模型和井眼损伤区域的计算方法,计算结果表明理论计算模型与有限元模拟结果吻合较好.     

有界封闭“裂缝-孔隙”介质弹性渗流问题的精确解及其在试井中的应用

本文全面求解和研究了有界封闭的“裂缝-孔隙”介质中的弹性渗流问题,进一步揭示和阐明了当忽略岩块系统中的流动时双重孔隙介质中弹性渗流的一些重要特性,并利用所得的解给出通过一系列试井确定有界封闭“裂缝-孔隙”介质地层的所有通常感兴趣的参数的方法.     

气体在双重孔隙介质中的渗流问题

本文将研究气体在双重孔隙介质中的渗流问题.所谓双重孔隙介质是指由两种不同性质的多孔材料均匀组合而成的介质,这种介质可以人工合成而且一些天然材料(例如裂缝-孔隙性油、气田的储集层)也可视为双重孔隙介质。设匀质气体的状态方程为γ=γ_0p~β,其中γ_0为气体常数,p是压力,γ是气体的密度,β=1(等温过程)或0<β<1(绝热过程).由质量守恒和Darcy定律得到     

双重孔隙介质渗流方程组的精确解

本文对未加任何简化的双重孔隙介质渗流的数学模型求解,在有界地层的普遍情形下指明了解的结构,从而奠定了用水动力学方法确定裂缝-孔隙地层储量的理论基础;对圆形均质地层中有一口圆心井的典型情形,则通过一类新的特殊函数获得了双重孔隙介质渗流方程组的精确解.     

三重介质弹性渗流方程组的精确解

本文用分解的方法求得了有限封闭地层中三重介质弹性渗流的精确解.它不仅概括了已有的双重介质弹性渗流的主要结果,而且给出各重介质弹性渗流的基本特征.     

油藏渗流问题的新模型及其精确解

本文在考虑到井筒储集和表皮效应情况下,利用双重介质渗流方程组建立了油藏渗流问题的新模型,并通过各种极限形式得到了外边界为无限大,有界封闭,有界定压三种情况下二类常见油藏(裂缝性油藏,均质油藏)内压力分布的精确解析表达式.     

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。     

双重介质油藏单相可压缩流动的特征差分格式及理论分析

双重介质油藏单相可压缩流动的特征差分格式及理论分析芮洪兴（山东大学数学系，济南２５０１００）１．引言研究裂缝－孔隙介质油藏流体流动的数值模拟，对于油田开发等许多工程技术问题具有十分重要的意义．解决这类问题的关键是如何处理裂缝与岩块间的流体交换．对比，...     

裂缝性储集层内渗流问题的精确解(Ⅱ)

为了描述石油在碳酸盐岩天然裂缝性储集层内的渗流规律,等人在文献[1,2]中提出均质微压缩液体在双重孔隙介质内的下列渗流方程组     

非线性双重介质模型的精确解及动态特征

考虑了二次梯度项的非线性双重介质模型．在模型中假设岩块和裂缝间的压力差作为初始未知量,在岩块中是拟先态的,从而避免了解联立方程组．利用广义Hankel变换求得了径向流动的解析解,由于解析解是无穷级数,无法得到具体的值．通过数值求解特征值问题,从而算得了窟体的压力值,并探讨了非线性参数和双重介质参数变化时压力的变化规律,给出了典型压力曲线图版,这些结果可用于实际的试井分析．     

Micropolar fluid flow through the membrane composed of impermeable cylindrical particles coated by porous layer under the effect of magnetic field

In the present work, the magnetohydrodynamic flow of a micropolar fluid through the membrane composed of impermeable cylindrical particles coated by porous layer is considered. The flow of a fluid is taken parallel to an axis of cylinder and a uniform magnetic field is applied in transverse direction of the flow. The problem is solved by using the cell model technique for the flow through assemblage of cylindrical particles. The solution of the problem has been obtained by using no-slip condition, continuity of velocity and stresses at interfaces along with Happle's no-couple stress condition as the boundary conditions. The expressions for the linear velocity, micro-rotational velocity, flow rate and hydrodynamic permeability of the membrane are achieved in this work. The obtained solution for velocities is used to plot the graph against various transport parameters such as, Hartmann number, coupling parameter, porosity, scaling parameter etc. The effect of these transport parameters on the flow velocity, micro-rotational velocity, and the hydrodynamic permeability of the membrane have been presented and discussed in this work.     

A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method

In this paper, a finite element method is proposed to investigate multiple solutions of the Navier-Stokes equations for an unsteady, laminar, incompressible flow in a porous expanding channel. Dual or triple solutions for the fixed values of the wall suction Reynolds number $R$ and the expansion ratio $α$ are obtained numerically. The computed multiple solutions for the symmetric flow are validated by comparing them with approximate analytic solutions obtained by the similarity transformation and homotopy analysis method. Unlike previous works, our method deals with the Navier-Stokes equations directly and thus has no similarity and other restrictions as in previous works. Finally we use the method to study multiple solutions for three cases of the asymmetric flow (which has not been studied before using the similarity-type techniques).     

双重介质分形油藏渗流问题

将油井有效半径引入双重介质分形油藏渗流问题的内边界之中,从而建立了双重介质分形油藏的一种渗流模型,并在考虑了井筒储集和表皮效应的情况求得了外边界为无限大、有界封闭和有界定压三种情况下双重介质分形油藏压力分布的精确解析表达式,利用拉氏数值反演Stehfest方法分析了双重介质分形油藏压力动态特征,讨论了各种参数对压力动态的影响。     

UNSTEADY BOUNDARY LAYER FLOW OF FRACTIONAL OLDROYD-B VISCOELASTIC FLUID PAST A MOVING PLATE IN A POROUS MEDIUM

This paper considers the unsteady boundary layer flow over a moving flat plate embedded in a porous medium with fractional Oldroyd-B viscoelastic fluid. The governing equations with mixed time-space fractional derivatives are solved numerically by using the finite difference method combined with an L1-algorithm. The effect of various physical parameters on the velocity and average skin friction are discussed and graphically illustrated in detail.Results show that the porosity € and fractional derivative α enhance the flow of Oldroyd-B viscoelastic fluid within porous medium, but fractional derivative βweakens the flow. Moreover, it is found that the average skin friction coefficient rises with the increase of fractional derivative β.     

A nonlinear two phase fluid flow through a porous medium in presence of a well

We study a flow of fresh and salt water in a two dimensional axially symmetric coastal aquifer with a well on the central axis. The flow is governed by a nonlinear Darcy's law. We also show the behaviour of the solution when the out flow of salt water at well goes to 0. Received May 1999     

Dynamic responses of shear flows over a deformable porous surface layer in a cylindrical tube

This paper investigates dynamic responses of a viscous fluid flow introduced under a time dependent pressure gradient in a rigid cylindrical tube that is lined with a deformable porous surface layer. With the Darcy’s law and a linear elasticity assumption, we have solved the coupling effect of the fluid movement and the deformation of the porous medium in the Laplace transform space. Governing equations are deduced for the solid displacement and the fluid velocity in the porous layer. Analytical solutions in the transformed domain are derived and the time dependent variables are inverted numerically using Durbin’s algorithm. Interaction between the solid and the fluid phases in the porous layer and its effects on fluid flow in tube are investigated under steady and unsteady flow conditions when the solid phase is either rigid or deformable. Examples are presented for flows driven by a Heaviside or a sinusoid pressure gradient. Significant effects of the porous surface layer on the flow in the tube are observed. The analytical solutions can be used to test more complicated numerical schemes.     

生物磁粘弹性流体的流动:应用动脉电磁过热评估血液的流动,癌症治疗进程

利用生物磁流体动力学(BFD)原理,在生物磁流体经由遭受磁场作用的多孔介质时,研究其流动的基本理论.所研究流体的磁化强度随温度而变化.流体被认为是非Newton流体,其流动由二阶梯度流体方程所控制,并考虑了流体的粘弹性效应.假设管道壁是能够伸展的,管壁表面的速度与到坐标原点的纵向距离成正比.首先将问题简化为包括7个参数的、耦合的非线性微分方程组的求解.将血液看作生物磁流体,并用上述方法分析,目的是计算某些血液的流动参数,并配以适当的数值方法,导数用差分格式近似.计算结果用图形给出,从而在磁场作用下,得到过热状态中关系血液的、血流动力学流动的理论预测.结果清楚地表明,在电磁过热治疗进程期间,磁偶极子对动脉中血液流动特征的影响起着重大作用.该研究引起了临床医学的关注,其结果有益于癌症病人采用电磁过热的治疗.     

Oberbeck convection through vertical porous stratum

Natural convection through a vertical porous stratum is investigated both analytically and numerically. Analytical solutions are obtained using a perturbation method valid for small values of buoyancy parameterN and the numerical solutions are obtained using Runge-Kutta-Gill method. It is shown that analytical solutions are valid forN < 1 and several features of the effect of large values ofN are reported. The combined effects of increase in the values of temperature difference between the plates and the permeability parameter on velocity, temperature, mass flow rate and the rate of heat transfer are reported. It is shown that higher temperature difference is required to achieve the mass flow rate in a porous medium equivalent to that of viscous flow.     

两相流体非线性渗流模型及其应用

基于三参数非线性渗流运动定律、质量守恒定律及椭圆渗流的概念,建立了低渗透介质中两相流体椭圆非线性渗流数学模型,运用有限差分法与外推法求得了其解,导出了两相流体椭圆非线性渗流条件下油井见水前后开发指标的计算公式,进行了实例分析。结果表明:非线性渗流对含水饱和度分布影响较大;非线性渗流使得水驱油推进速度比线性渗流的快,使油井见水时间提前,使得石油开发指标变差;非线性渗流使得同一时刻的压差比线性渗流的大,使石油开发难度加大。这为低渗油藏垂直裂缝井开发工程提供了科学依据。     

RECENT ADVANCES OF UPSCALING METHODS FOR THE SIMULATION OF FLOW TRANSPORT THROUGH HETEROGENEOUS POROUS MEDIA

We review some of our recent efforts in developing upscaling methods for simulatingthe flow transport through heterogeneous porous media. In particular, the steady flowtransport through highly heterogeneous porous media driven by extraction wells and theflow transport through unsaturated porous media will be considered.