加载历程对配径碎煤渗透特性影响的试验研究

为了证实加载历程对破碎煤样渗透特性的影响,利用一套由齿轮泵、换向阀、溢流阀和渗透仪等组成的渗透回路,在CMT5305型电子万能试验机试验系统上测试了配径碎煤在两种不同试验方案下的渗透特性,得到了两种方案配径碎煤的渗流速度、渗透率、非Darcy流? 因子与孔隙度的关系。研究表明：①第1种试验方案的渗流速度和渗透率与孔隙度的关系用幂函数拟合,第2种试验方案的渗流速度和渗透率与孔隙度的关系可用指数函数拟合。②孔隙度较大时,渗透率和非Darcy流? 因子与加载历程有关;孔隙度较小时,渗透率和非Darcy流? 因子趋于稳定,与加载历程无关。③随着孔隙度的减小,方案1非Darcy流? 因子由负变正,配径碎煤的渗透性加强;方案2非Darcy流? 因子始终为负值,配径碎煤的渗透性减弱。④两种方案的非Darcy流? 因子与孔隙度均可采用三次多项式拟合,多项式的系数与加载历程有关。     

基于非牛顿指数描述的非达西渗流一维固结分析

基于非牛顿指数描述的非达西渗流定律,同时考虑地基内部竖向附加应力随深度线性变化以及变荷载的影响,建立了一维固结控制方程并应用有限差分法进行数值求解,同时对不同参数单级加荷下的固结性状进行分析。结果表明：基于非达西渗流比达西渗流下固结速率要慢,且渗流模型中非牛顿指数越大,土层的固结速率越慢;土层厚度越厚,固结速率越慢,因此,传统固结理论中室内土样与地基土层之间的相似关系不再成立;作用于土层的平均附加应力越大,土层的固结速率越快;在单面排水情况下,附加应力分布对土层固结速率有较大影响;相反,双面排水条件下土层固结速率与附加应力的分布是无关的;荷载的加荷速率越快,则土层的固结速率越快。最后,讨论了达西渗流计算固结变形的适用范围。     

A pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures

This paper aims at developing a pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures. A simple general relationship between the local hydraulic conductivity and the flow velocity is proposed. A new governing equation for non-Darcy fluid flow through rough-walled fractures is then derived by introducing this relationship into the Reynolds equation. Based on the non-linear finite element method, a self-developed code is used to simulate the non-Darcy fluid flow through fractures. It is found that the macroscopic results obtained by the numerical simulation agree well with the experimental results. Furthermore, some interesting experimental observations can be reproduced.     

考虑非Darcy渗流时循环荷载下饱和黏土一维固结分析

考虑到土体处于超固结状态下的压缩性一般要比正常固结状态下的低,引入描述非Darcy渗流的Hansbo方程,修正了Terzaghi饱和黏土一维固结方程,并将其推广到低频循环荷载作用的情况。采用有限体积法对该方程进行了求解,并讨论了非Darcy渗流参数、循环荷载周期以及超固结状态下土体压缩性对固结进程的影响。计算结果表明,在矩形波载作用下,按孔压定义和按变形定义的固结度都随时间增长而震荡增加,且按孔压定义的固结度的震荡幅度明显大于按变形定义的固结度。另外,非Darcy渗流减缓了地基的沉降速率,且循环荷载周期越短,或超固结状态下压缩性越高,地基的沉降速率就越慢。     

The settling of consecutive spheres in viscoplastic fluids

One of the factors contributing to the uncertainties involved in the estimation of particle settling velocity in viscoplastic fluids is the time-dependent effect where the viscous parameters of the fluid change as a particle flows through and shears the medium. These changes, particularly at low shear Reynolds numbers, are reflected in the settling velocity of a following sphere that is released some time after an initial one, with the following sphere having a significantly greater velocity. This study found that changes in both fall velocity and equivalent viscosity can be correlated satisfactorily by a power law equation to the dimensionless form of the time interval between releases, and the rheogram shape factor for the fluid. A collision of particles occurs in cases where the time interval between releases is small, after which the particles combine and travel at a terminal velocity. A new variable, β, which takes into account the different surficial stress of the combined spheres, was introduced to the correlation of Wilson et al. [Wilson, K.C., Horsley, R.R., Kealy, T., Reizes, J.A., Horsley, M.R., 2003. Direct prediction of fall velocities in non-Newtonian materials. Int. J. Miner. Process. 71, 17–30] β was found to depend on the rheogram shape factor for the fluid and the shear Reynolds number for the particle. The validity of this approach was supported by experimental data.     

软土地层浅埋圆形隧道非达西渗流场解析研究

软土在低水力坡降下的渗流会偏离达西定律,即为非达西渗流模式。假设孔隙水渗透服从指数渗流模式,采用镜像法原理推导了浅埋单孔和双孔圆形隧道非达西渗流场的解析解。结合算例,对浅埋圆形隧道非达西渗流解析解与达西渗流解析解进行了对比分析与验证,并对非达西渗流指数、隧道周围土体与衬砌渗流系数比值对隧道渗流场的影响进行了讨论。结果表明：非达西渗流指数、渗流系数比值对隧道渗流量和周围土体孔压均有较大的影响;随着渗流指数逐渐增大,土体内水头损失加快,隧道周围土体孔压及渗流量逐渐减小;随着土体与衬砌渗流系数比值逐渐增大,衬砌排水能力增强,隧道渗流量逐渐增大,隧道周围土体孔压减小更大。     

A new insight into onset of inertial flow in porous media using network modeling with converging/diverging pores

The network modeling approach is applied to provide a new insight into the onset of non-Darcy flow through porous media. The analytical solutions of one-dimensional Navier-Stokes equation in sinusoidal and conical converging/diverging throats are used to calculate the pressure drop/flow rate responses in the capillaries of the network. The analysis of flow in a single pore revealed that there are two different regions for the flow coefficient ratio as a function of the aspect ratio. It is found that the critical Reynolds number strongly depends on the pore geometrical properties including throat length, average aspect ratio, and average coordination number of the porous media, and an estimation of such properties is required to achieve more reliable predictions. New criteria for the onset of non-Darcy flow are also proposed to overcome the lack of geometrical data. Although the average aspect ratio is the main parameter which controls the inertia effects, the effect of tortuosity on the onset of non-Darcy flow increases when the coordination number of media decreases. In addition, the higher non-Darcy coefficient does not essentially accelerate the onset of inertial flow. The results of this work can help to better understand how the onset of inertial flow may be controlled/changed by the pore architecture of porous media.     

低渗透油藏非达西渗流地层压力计算方法及分析

低渗透油藏非达西渗流时,地层的压力分布与常规达西流动情况下不同,储层存在压力波及不到的区域,难以有效动用。为此,基于渗流理论中质量守恒和动量守恒方程,建立了考虑启动压力梯度存在的新的不稳定渗流数学模型,推导出非达西径向流解析解和产能方程,形成了低渗透油藏新的地层压力计算方法,为低渗透储层的油藏评价和开发设计提供了理论依据。计算分析表明：低渗透油藏非达西流动下压力分布不同于以往有激励即有响应的达西流动情况,近井地带能量递减远快于常规油藏达西流动的情况,储层波及范围小,井筒外围有很大一部分面积的油藏没能有效动用。     

三轴应力下不同粒径破碎砂岩渗透特性试验

地下工程中破碎岩体往往处于三向应力状态,此类岩体具有孔隙率大、渗透性高等特点,在地应力与高水头作用下易发生渗流失稳破坏,诱发突水灾害。为研究三轴应力下破碎砂岩的渗透特性,运用自主研发的破碎岩石三轴渗流试验系统,采用稳态渗透法进行5种粒径破碎砂岩的渗流试验,得到了三轴应力下破碎砂岩渗透特性变化规律,推导了有效应力与渗流速度之间的关系。试验结果表明：三轴应力下破碎砂岩的有效应力与渗流速度呈线性关系,且轴向位移越大时,随有效应力的增加渗流速度减小的幅度越小;三轴应力下5种粒径破碎砂岩的孔压梯度与渗流速度服从Forchheimer关系,两者之间的相关系数达0.95以上;轴向位移恒定时,随着围压的增大,破碎砂岩渗透率k减小,非Darcy流β因子增大,各级轴向位移下,破碎砂岩的渗透率与围压之间呈指数函数关系;随着孔隙率的减小,5种粒径的破碎砂岩渗透率呈减小趋势,非Darcy流β因子整体增大,且渗透率量级为10-14～10-11 m2,非Darcy流β因子的量级为106～1012 m-1。     

Experimental Investigation of Non-Darcy Flow in Sandstone

A study was conducted to investigate non-Darcy flow for sandstone using an experimental system designed and constructed by the research group. Non-Darcy flow was found to exist for both the pre-peak and post-peak strains; post-peak flow behavior showed a higher level of non-Darcy flow. In addition, the post peak permeability turned out to be about 2–3 times that of the pre-peak permeability. This sudden change in permeability that occurs when sedimentary rock masses around underground excavations develop new fractures may lead to water inrush in coal mines. All three non-Darcy permeability parameters showed significant changes between the pre-peak and post peak strains. The main reason for that is the formation of new cracks around and after the peak stress. Relations are developed among the three non-Darcy permeability parameters.     

类陷落柱介质渗流突变机制试验研究

岩溶陷落柱是内部结构杂乱无章的特殊地质构造,易成为隐伏于煤层底板下的垂向导水通道,是华北地区石炭二叠系煤田的重大安全隐患。在采动影响下,底板隐伏陷落柱的突水通道通常由底板破坏带和陷落柱共同组成,为了研究其渗流突变机制,利用自行研制的破碎岩体渗透性试验系统,对不同底板破坏带条件下,隐伏陷落柱的渗流特性进行了试验研究。研究结果表明：渗流突变发生的根本原因是大颗粒流失导致破碎岩体孔隙结构改变;发生渗流突变时,流速随渗流边界孔隙直径的增大而增大,同时试样的初始孔隙度均大于0.21;未发生渗流突变时,渗流边界对渗流无显著影响,并且试样的渗透率随孔隙度的增大而增大,渗透率比和孔隙度比存在幂函数关系;非Darcy流 因子为负是渗流突变发生的充分必要条件,非Darcy流 因子的大小决定渗流突变的剧烈程度。     

破碎砂岩渗透特性与孔隙率关系的试验研究

利用一种专利装置与MTS815.02型岩石力学试验系统,进行了破碎砂岩的稳态渗透试验,得到了不同孔隙率下破碎砂岩的渗透率和非Darcy流 因子。通过线性回归得到了渗透率、非Darcy流 因子与孔隙率之间的关系。认为破碎岩石的渗透特性主要是由孔隙率决定的,孔隙率不仅与当前的应力有关,更取决于加载历史。研究表明,水在破碎砂岩中的渗流一般不服从Darcy定律,而服从Forchheimer关系,特别是在小孔隙率下,非Darcy性更为突出;渗透率、非Darcy流 因子与孔隙率之间的关系可用幂函数拟合。     

Flow of non-Newtonian fluids in fractured porous media: Isogeometric vs standard finite element discretisation

A formulation has been derived for the flow of non-Newtonian (power-law) fluids in deformable, fractured porous media. The formulation is enhanced with a subgrid scale model to accurately represent the flow of the power-law fluids inside the cracks. The resulting equations have been discretised using standard (Lagrangian) finite element shape functions and with non-uniform rational B-splines (NURBS), which have been cast into a standard finite element datastructure using Bézier extraction. The effect of the power-law index on the velocity inside the fracture and on the total fluid flow through the porous medium has been analysed for a typical boundary-value problem. It is shown that large differences between non-Newtonian and linearised Newtonian fluids can occur for the fluid velocity inside the fracture. This can significantly influence the total fluid transport through the domain. A mesh sensitivity study has been carried out as well and shows that markedly smaller element sizes are required in order to obtain accurate results for the local flow inside the fracture, compared with the element sizes necessary for obtaining accurate results inside the porous medium away from the fracture. Moreover, a comparison has been made between the results obtained using standard Lagrange polynomials and those obtained using NURBS. It is shown that while both discretisation methods are able to accurately simulate the deformations and pressures in the porous medium, the higher interelement continuity of NURBS is mandatory for obtaining correct values of the fluid velocities inside the fracture, especially near the tips.     

Computation of the filtration laws through porous media for a non-Newtonian fluid obeying the power law

We consider a stationary flow of an incompressible non-Newtonian flow through a porous medium, induced by an injection velocity when inertial effects are negligible. At the pore scale, the governing equations are based on a nonlinear relation between the stress and the rate of deformation. In such a situation, the limit problem obtained when the pore size tends to zero, is called the homogenized problem that leads to the filtration law. This filtration law is given by a non-linear system coupling a local problem on a typical cell of the porous medium to a global problem at the scale of the whole porous medium. We propose, in this work, a numerical method to solve this homogenized problem and apply this method when the velocity dependent viscosity is given by the power law. Finally, we propose some numerical experiments to illustrate our approach.     

油气成藏条件下低渗透砂岩石油运移的渗流特征实验研究

在室内低速渗流实验的基础上,采用恒压测试法,对成藏条件下石油在低渗透砂岩中的运移渗流规律及影响因素进行了研究。结果表明：(1)石油在低渗透砂岩中低速渗流时存在着启动压力梯度,非达西渗流特征明显。(2)低渗透砂岩中石油非达西渗流曲线主要有两种基本类型,视流度≤1时,非达西渗流曲线表现为上凹型曲线;视流度＞1时,表现为变性达西流曲线。(3)低渗透砂岩的物性、石油性质以及它们的相互作用对渗流曲线的位置、非线性段的曲率和变化范围以及直线段在压力梯度轴的截距具有重要影响。(4)随着低渗透砂岩渗透率的降低和石油粘度的增加或视流度的减小,石油在低渗透砂岩储层的非达西渗流特征更加明显。     

Research advances in non-Darcy flow in low permeability media

More and more experimental results show that Darcy’s law is not fully applicable in low permeability media,and non-Darcy flow has been identified.In this paper we reviewed the research of non-Darcy flow experiments in low-permeability media in recent decades,discuss the existence of non-Darcy flow,and summarize its constitutive equations.The reasons for the threshold gradient were also discussed and summarized for the criterion of the critical point of non-Darcy flow.On this basis,the future development of non-Darcy flow experiments in the rock and clay media were discussed,in order to provide a certain reference for subsequent research on seepage laws in low permeability media.     

考虑非达西流的弱透水层固结计算

由于成岩作用的影响,深部弱透水层中的黏性土较为坚硬、致密,在这种黏土层中的孔隙渗流规律有偏离达西定律的现象,而在现有的地面沉降研究中,对深部弱透水层的固结变形计算始终沿用以达西定律为基础的固结方程进行,这显然是与实际情况不相符的。鉴于此,以孔隙渗流为非达西流为基础,对太沙基一维固结方程进行了重新推导,并采用半解析法对非达西流-太沙基一维固结方程进行了求解。分别采用达西流-太沙基固结方程和非达西流-太沙基固结方程对同一固结问题进行了计算,结果表明,考虑非达西流后土层达到某一固结度所需的固结时间较之不考虑非达西流时明显增加了,而且固结时间增长的趋势与实测的增长趋势较为一致。     

Numerical well model for non-Darcy flow through isotropic porous media[*]This work was supported in part by the EPA under grant # R 825207-01-1, by the State of Texas under ARP/ATP grant # 010366-168 and by a gift grant from Mobil Oil Corp.

Numerical simulation of fluid flow in a hydrocarbon reservoir has to account for the presence of wells. The pressure of a grid cell containing a well is different from the average pressure in that cell and different from the bottom-hole pressure for the well [17]. This paper presents a study of grid pressures obtained from the simulation of single phase flow through an isotropic porous medium using different numerical methods. Well equations are proposed for Darcy flow with Galerkin finite elements and mixed finite elements. Furthermore, high velocity (non-Darcy) flow well equations are developed for cell-centered finite difference, Galerkin finite element and mixed finite element techniques.     

Effects of concentration-dependent settling velocity on non-equilibrium transport of suspended sediment

In this study, non-equilibrium transport of suspended sediment from one equilibrium state to another is investigated. Based on a convective-diffusion equation, a numerical model for flow with suspended sediment is developed by considering the effect of concentration-dependent settling velocity. The numerical model is validated by comparing analytical solutions and experimental results. The concentration profiles, mean concentrations and distance necessary to reach a new equilibrium state are examined by comparing them with the results of constant settling velocity. For a high concentration flow, the results indicate that evident differences between the above three indicators can be determined with and without concentration-dependent settling velocity. Additionally, the effects of concentration-dependent settling velocity are sensitive to the sediment mobility parameter (or Rouse number), although they are nearly independent of the diffusion Reynolds number.     

Unstructured, Control-Volume Distributed, Full-Tensor Finite-Volume Schemes with Flow Based Grids

Locally conservative flux-continuous, full-tensor, discretization schemes are presented for general unstructured grids. The schemes are control-volume distributed, where flow variables and rock properties are assigned to the polygonal control-volumes derived from the primal grid. A relationship between these finite volume schemes and the mixed finite element method is established. An extension for unstructured grids is described that leads to a general symmetric positive definite discretization matrix for both quadrilateral and triangular grids. A novel flow based gridding approach for unstructured mesh generation is also proposed for heterogeneous reservoir domains. Results computed with the flux continuous schemes on unstructured flow-based grids demonstrate the advantages of the methods.