幂律流体在单根弯曲毛细管中的毛细上升

基于分形理论和数值模拟的方法, 给出了幂律流体在单根弯曲毛细管的上升高 度和上升累积质量随时间的变化关系曲线. 研究结果表明: 在上升初期阶段, 重力因素可以 忽略; 但随着时间增加, 重力因素的影响越来越大; 幂律流体上升的最大高度只与毛细管直 径$\lambda$、幂律流体密度$\rho $有关, 与毛细管弯曲程度$\tau _0 $和幂指数$n$无关; 幂指数$n$越小, 上升初期上升速度越快; 迂曲度分形维数$D_T $越大, 平衡时吸入的幂律流体质量也越大.     

多孔介质渗透率的一种新分形模型

多孔介质的渗流特性是油气藏工程、地下水资源利用、高放废物深地质处置等实际工程领域的热门研究问题．基于分形理论及多孔介质由一束面积大小不等的椭圆形毛细管组成的假设,本文建立了流体在分形多孔介质中渗流时的绝对渗透率及相对渗透率的分形渗透率模型．结果表明,绝对渗透率是最大和最小孔隙面积、分形维数、形状因子ε的函数,且当ε =1时,本文模型可以简化成Yu与Cheng模型;而非饱和多孔介质的相对渗透率与饱和度和多孔介质微结构参数有关．将本文提出的渗透率分形模型预测与实验测量数据及其他模型结果进行对比,显示它们整体吻合很好．     

变开度岩体裂隙多相渗流实验与有效渗透率模型

岩体裂隙的有效渗透率是描述岩体非饱和或多相渗流的关键参数,而裂隙开度是影响有效渗透率的重要因素.通过自主研发的粗糙裂隙多相渗流可视化实验平台,针对天然岩体裂隙复制而成的裂隙模型开展变开度条件下的多相渗流可视化实验,研究开度变化对多相渗流流动结构以及有效渗透率的影响.研究表明:非湿润相流体运动通道,在低流量比条件下呈现出气泡流流动结构,而在高流量比条件下呈现较为稳定的通道流流动结构.随着开度的增加,非湿润相流动通道的分支变少、等效宽度增加,两相流体的有效渗透率均增大,流动结构趋于稳定.可视化结果还阐明了柱塞流流动结构下,两相流体交替占据裂隙空间的竞争机制:当非湿润相流体通道由连续转变为不连续时,裂隙进出口压差显著增加;反之,当该通道由不连续转变为连续时,压差显著减小.最后,基于分形理论以及渗透率统计建模方法,建立了考虑开度效应的岩体裂隙多相渗流有效渗透率理论模型,并通过实验测定的有效渗透率数据验证了该模型的正确性与有效性.     

光弹模拟岩石分形节理的抗剪强度

本文用分形维数人为地制成具有分形曲线的节理面以模拟岩石节理粗糙度特征，利用光弹技术测定了分形节理最大剪应力随维数变化的过程．研究表明，岩石分形节理的抗剪强度不会随分维的增加而无限制地增大     

考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析

为建立更完善和精确的结合面接触刚度模型,本文根据分形理论和摩擦学原理,从微观角度建立了考虑摩擦因素的结合面切向接触刚度分形预估模型.通过数值仿真分析研究了接触载荷、分形维数、摩擦系数和接触面积等因素对结合面切向接触刚度的影响.分析结果表明:结合面切向接触刚度随法向载荷和分形维数的增加而增大,而随分形尺度参数的增大而减小;摩擦系数对结合面切向接触刚度的影响较大,不同实际接触面积下的切向刚度相差较大;当分形维数较小时,摩擦系数对结合面切向刚度的影响将降低.这些研究对于进一步开展结合面的动力学特性研究具有重要意义.     

结合面静摩擦因数分形模型的建立与仿真

提出一个确定分形维数和分形粗糙度参数(G')的分形函数,并用分形函数逼近结合面的表面粗糙度.根据分形理论和改进后的尺寸分布,推导了静摩擦因数f的解析解.数字仿真结果表明,f随量纲为一的总法向载荷(P')增加而增加.当D较小或较大时,f与(P')之间存在不同的微凸和微凹弧非线性关系,D=1.2时f与(P')的关系基本上是线性的;当D较小时,f随D增加而增加;当D较大时,f随D增加而减小;f随分形粗糙度参数(G')增加而减小,随相关系数K增加而增加,随材料特性(φ)增加而增加.     

大理岩微孔隙演化的分形特征

本文利用压汞技术测定了大理岩随应力变化的微孔隙演化过程，根据孔隙介质的分形模型，计算了大理岩微孔隙演化过程中的分维变化。研究表明：孔隙岩体确实是一个分形结构，孔隙体积分维随外载增加而增大。     

摩擦信号分形维数与载荷和速度的关系研究

在立式万能摩擦磨损试验机上对GCr15/45#钢摩擦副进行不同接触载荷和滑动速度下的摩擦磨损试验,对初始滑动距离1 000 m内的摩擦系数信号进行数据采集,运用结构函数测度方法对摩擦系数信号进行分形表征,计算不同载荷和速度下的分形维数,研究摩擦信号的分形维数随载荷和速度的变化规律.结果表明,摩擦系数信号具有显著的分形特征,其分形维数随载荷和速度而变化.在相同载荷下,分形维数随滑动速度增加而增大;在相同速度下,分形维数随着接触载荷增加而增大.磨损率与摩擦系数信号的分形维数正相关.     

掺稀采油管内稠油流速径向分布特性研究

考虑稠油(幂律流体)与稀油(牛顿流体)层间扩散、相间作用力、掺混粘度等参数,建立了掺稀采油管内牛顿-幂律流体的流速计算模型对其编程求解;从掺稀前及掺稀后两种工况着手,对稠油掺稀采油管内流速的径向分布规律进行了详细分析。结果表明:流速在油管中的分布呈现轴对称性;随采油管外径增大、稠油稠度系数增大及采油管压力降的减小,采油管径向上稠油流速呈现减小趋势;稠油掺稀过程中,与层流的流动对比分析发现,稠油和稀油掺混时紊流流动过程中的过渡段出现增大趋势,此时的掺混速度以及均匀程度都有所提高。     

有效应力升降过程中不同饱和度水合物沉积物渗透率实验研究

为了研究天然气水合物开采过程中水合物饱和度和有效应力变化对含水合物沉积层渗透率变化规律的影响,利用自主研制的水合物沉积物合成与三轴渗流实验一体化装置,进行了有效应力升降过程中不同饱和度水合物沉积物渗透性实验。结果表明:有效应力升降过程中,不同饱和度水合物沉积物的渗透率与有效应力均呈负指数规律变化,并表现出在低有效应力阶段渗透率变化的幅度大于高有效应力阶段;有效应力升降过程中,试样产生的不可恢复变形使渗透率不能完全恢复,造成渗透率永久损失;有效应力不变时,水合物沉积物的渗透率与水合物饱和度呈负指数规律变化,且曲线的斜率随饱和度增加由大变小;水合物的饱和度越大,最大渗透率损害率越大,渗透率恢复的程度越差。     

A Fractal Model for Oil Transport in Tight Porous Media

Tight porous media are mainly composed of micro/nano-pores and throats, which leads to obvious microscale effect and nonlinear seepage characteristics. Based on the capillary bundle model and the fractal theory, a new nonlinear seepage equation was deduced, and a further fractal permeability model was obtained for oil transport in tight porous media by considering the effect of the boundary layer. The predictions of the model were then compared with experimental data to demonstrate that the model is valid. This model clarifies the oil transport mechanisms in tight porous media: the effective permeability is no longer a constant value and is governed by properties of tight porous media and oil. Furthermore, parameters influencing effective permeability were analyzed. The model can accurately present the seepage characteristics of the oil in tight porous media and provide a reliable basis for the development of unconventional reservoirs.     

Study of the effect of capillary pressure on the permeability of porous media embedded with a fractal-like tree network

In this paper, the analytical expressions for permeability of (both saturated and unsaturated) porous media embedded with a fractal-like tree network are presented based on fractal theory and technique when the capillary pressure is taken into account. Both the dimensionless effective permeability and the relative permeability of the composites, which are defined as porous media embedded with a fractal-like tree network in this work, are derived and found to be a function of saturation, the capillary pressure and microstructural parameters of the networks. The relative permeabilities predicted by the present fractal model are compared with the available experimental data and a fair agreement between them is found.     

The use of standard deviation and skewness for estimating apparent permeability in a two-dimensional,heterogeneous medium

In this theoretical study, characteristic or effective permeabilities (referred to as ‘apparent permeability’) of a radial/parallel flow system in a heterogeneous medium are calculated by the Monte Carlo method and the finite element method. The permeability distribution in the radial and parallel flow systems are not the same, as going from Cartesian to cylindrical coordinates changes the probability measure. The Bernoulli trials, the normal distribution or the log-normal distribution, is assumed to be the probability density function of permeability. The results are summarized as follows: (1) when the skewness of the distribution function is equal to zero or nearly equal to zero (that is, when the permeability distribution is regarded to be symmetric), the apparent permeability depends on the standard deviation, but not on the kind of distribution function, (2) when the skewness is not equal to zero, the apparent permeability depends not only on the standard deviation, but also on the skewness, (3) the above facts appeared in the radial and the parallel flow systems.     

Stress-Dependent Porosity and Permeability of Porous Rocks Represented by a Mechanistic Elastic Cylindrical Pore-Shell Model

The stress dependency of the porosity and permeability of porous rocks is described theoretically by representing the preferential flow paths in heterogeneous porous rocks by a bundle of tortuous cylindrical elastic tubes. A Lamé-type equation is applied to relate the radial displacement of the internal wall of the cylindrical elastic tubes and the porosity to the variation of the pore fluid pressure. The variation of the permeability of porous rocks by effective stress is determined by incorporating the radial displacement of the internal wall of the cylindrical elastic tubes into the Kozeny–Carman relationship. The fully analytical solutions of the mechanistic elastic pore-shell model developed by combining the Lamé and Kozeny–Carman equations are shown to lead to very accurate correlations of the stress dependency of both the porosity and the permeability of porous rocks.

     

开裂孔隙材料渗透率的细观力学模型研究

采用细观力学方法对含随机裂纹网络的孔隙材料渗透性进行研究.开裂孔隙材料渗透性的影响因素包括裂纹网络的密度、连通度、裂纹的开度以及孔隙材料基体渗透性.对于不连通的裂纹网络,该文采用已有的相互作用直推法(interaction direct derivative,IDD)的理论框架,引入裂纹的密度$\rho$和裂纹开度比$b$,提出了裂纹夹杂$\!$-$\!$-$\!$基体两相复合材料渗透率的IDD理论解.对于部分连通裂纹网络,考虑局部裂纹团内部各个裂纹对有效渗透率的相互放大作用,引入裂纹网络的连通度$f$,定义与连通度相关的水平裂纹密度$\rho^{h}$,按照增量法将表征连通特征的水平裂纹嵌入有效基体中,以此方式来考虑裂纹夹杂间的相互搭接,提出了考虑裂纹连通特征的扩展IDD理论解,分别考虑了基体材料渗透率$K_{m}$、裂纹密度$\rho $、裂纹开度比$b$以及与连通度$f$相关的$\rho ^{\rm h}$.最后通过对有限区域内含随机裂纹网络孔隙材料渗透过程的有限元模拟分别验证了不连通和部分连通裂纹网络扩展IDD模型的适用性:(1)当裂纹不连通时,由于基体对流体渗透的阻隔作用,裂纹的开度对有效渗透率影响不大;(2)当裂纹部分连通时,裂纹密度分别小于1.1(无关联裂纹网络,分形维数为2.0)、1.2(关联裂纹网络,分形维数为1.75)时,扩展IDD模型能够很好地估计开裂孔隙材料的有效渗透率,但是随着裂纹进一步扩展,最大裂纹团主导作用凸显,扩展IDD模型不再适用.      

A Fractal Model for Gas–Water Relative Permeability in Inorganic Shale with Nanoscale Pores

A reliable gas–water relative permeability model in shale is extremely important for the accurate numerical simulation of gas–water two-phase flow (e.g., fracturing fluid flowback) in gas-shale reservoirs, which has important implication for the economic development of gas-shale reservoir. A gas–water relative permeability model in inorganic shale with nanoscale pores at laboratory condition and reservoir condition was proposed based on the fractal scaling theory and modified non-slip boundary of continuity equation in the nanotube. The model not only considers the gas slippage in the entire Knudsen regime, multilayer sticking (near-wall high-viscosity water) and the quantified thickness of water film, but also combines the real gas effect and stress dependence effect. The presented model has been validated by various experiments data of sandstone with microscale pores and bulk shale with nanoscale pores. The results show that: (1) The Knudsen diffusion and slippage effects enhance the gas relative permeability dramatically; however, it is not obviously affected at high pressure. (2) The multilayer sticking effect and water film should not be neglected: the multilayer sticking would reduce the water relative permeability as well as slightly decrease gas relative permeability, and the film flow has a negative impact on both of the gas and water relative permeability. (3) The increased fractal dimension for pore size distribution or tortuosity would increase gas relative permeability but decrease the water relative permeability for a given saturation; however, the effect on relative permeability is not that notable. (4) The real gas effect is beneficial for the gas relative permeability, and the influence is considerable when the pressure is high enough and when the nanopores of bulk shale are mostly with smaller size. For the stress dependence, not like the intrinsic permeability, none of the gas or water relative permeability is sensitive to the net pressure and it can be ignored completely.     

On shear thinning fluid flow induced by continuous mass injection in porous media with variable conductivity

A new formulation is proposed to examine the propagation of the pressure disturbance induced by the injection of a time-variable mass of a weakly compressible shear thinning fluid in a porous domain with generalized geometry (plane, radial, or spherical). Medium heterogeneity along the flow direction is conceptualized as a monotonic power-law permeability variation. The resulting nonlinear differential problem admits a similarity solution in dimensionless form which provides the velocity of the pressure front and describes the pressure field within the domain as a function of geometry, fluid flow behavior index, injection rate, and exponent of the permeability variation. The problem has a closed-form solution for an instantaneous injection, generalizing earlier results for constant permeability. A parameter-dependent upper bound to the permeability increase in the flow direction needs to be imposed for the expression of the front velocity to retain its physical meaning. An example application to the radial injection of a remediation agent in a subsurface environment demonstrates the impact of permeability spatial variations and of their interplay with uncertainties in flow behavior index on model predictions.     

Numerical Estimation of the Degree of Reservoir Permeability Heterogeneity Using Pressure Drawdown Tests

This study aims to correlate the response of pressure transient test to permeability distribution type. For this purpose, correlated permeability distributions in x–y direction are generated using fractional Brownian motion (fBm) as it has been shown in literature that permeability in carbonate reservoirs exhibits an fBm type distribution horizontally. 2-D fBm permeability distributions created using mid point displacement method are employed as data to a black oil simulator. The intermittence exponent, H or fractal dimension of the distribution, D, as defined by D=2 – H, characterizes the distribution type. All permeability distributions are normalized to represent the same arithmetic mean (20, 100, and 500 mD) and uniform variance so that only their fractal dimension that underlies the smoothness of the distribution distinguishes them. Many different realizations of permeability distributions are generated based on the random number seeds used and pressure transient (drawdown) tests are simulated using a black oil simulator package (ECLIPSE 100). Pressure transient analysis is performed using PanSystem package. As a base case and for the comparison purpose, the same procedure is repeated for the totally homogeneous case (the same permeability for all grids) and a random (normally distributed) permeability distribution with the same mean and uniform variance. The effects of permeability distribution type on the pressure response are clarified. A strong impact of heterogeneity is observed as an increase in skin effect with increasing fractal dimension of permeability distribution. This additional (or pseudo) skin effect due to heterogeneity is correlated to the fractal dimension of the permeability distribution. As a further step, the procedure is repeated for different flow rates applied during the drawdown test. The correlation between the fractal dimension of permeability distribution and additional skin is improved by incorporating the rate into it. The methodology followed can be used in the assessment of reservoir heterogeneity quantitatively using pressure transient response.