多孔介质结构对渗流惯性效应的影响规律研究

本文通过局部展开算法研究了多孔介质中排列结构对非线性渗流规律的影响．计算结果表明：规则排列结构的渗流标度律和渗流方向相关,然而非规则排列结构的渗流标度律不依赖于渗流方向而只依赖于多孔介质的几何结构．伴随着排列结构的非规则程度增强,不同方向的渗流阻力变化规律的差异性减小．当流场输运区域较为复杂且不存在较宽直通道时,渗流阻力在较宽雷诺数范围内体现出较为明显的标度律特性．周期性强非规则排列结构中不同区域大小的模型却具有相似的渗流阻力的标度律特性,同时标度律特性与孔隙度的大小相关性不大．阻力非线性标度律由多孔介质结构的不同而取值为2至3之间．     

致密油储层毛细管力自发渗吸模型分析

部分致密油井压后关井一段时间,压裂液返排率普遍低于30%,但是致密油气井产量反而越高,这与压裂液毛细管力渗吸排驱原油有关。然而,致密油储层致密,物性差,渗流机理复杂,尚没有形成统一的自发渗吸模型。本文基于油水两相非活塞式渗流理论,建立了压后闷井期间压裂液在毛细管力作用下自发渗吸进入致密油储层的数学模型,采用数值差分方法进行求解,并分析了相关影响因素。结果显示渗吸体积、渗吸前缘移动距离与渗吸时间的平方根呈线性正相关关系,与经典Handy渗吸理论模型预测结果一致,说明毛细管力自发渗吸模型可靠性较高。数值计算结果表明毛细管水相扩散系数是致密储层自发渗吸速率的主控参数,毛细管水相扩散系数越高,自发渗吸速率越大。毛细管水相扩散系数随着含水饱和度先增加后减小;随着束缚水饱和度、油相和水相端点相对渗透率增加而增加;随着相渗特征指数、油水黏度比和残余油饱和度增加而减小。该研究有助于深入认识致密油储层压裂液渗吸机理,对优化返排制度、提高致密油井产量具有重要意义。     

SPONTANEOUS CAPILLARY IMBIBITION MODEL IN TIGHT OIL RESERVOIRS 1)

部分致密油井压后关井一段时间,压裂液返排率普遍低于30%,但是致密油气井产量反而越高,这与压裂液毛细管力渗吸排驱原油有关。然而,致密油储层致密,物性差,渗流机理复杂,尚没有形成统一的自发渗吸模型。本文基于油水两相非活塞式渗流理论,建立了压后闷井期间压裂液在毛细管力作用下自发渗吸进入致密油储层的数学模型,采用数值差分方法进行求解,并分析了相关影响因素。结果显示渗吸体积、渗吸前缘移动距离与渗吸时间的平方根呈线性正相关关系,与经典Handy渗吸理论模型预测结果一致,说明毛细管力自发渗吸模型可靠性较高。数值计算结果表明毛细管水相扩散系数是致密储层自发渗吸速率的主控参数,毛细管水相扩散系数越高,自发渗吸速率越大。毛细管水相扩散系数随着含水饱和度先增加后减小;随着束缚水饱和度、油相和水相端点相对渗透率增加而增加;随着相渗特征指数、油水黏度比和残余油饱和度增加而减小。该研究有助于深入认识致密油储层压裂液渗吸机理,对优化返排制度、提高致密油井产量具有重要意义。     

低渗透多孔介质渗流动边界模型的解析与数值解

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.      

基于核磁共振孔隙划分的致密油藏自发渗吸原油可动性研究

自发渗吸驱油是致密油藏提高采收率的有效手段,但不同的孔隙划分方法会导致原油可动性精细定量表征存在差异性.基于此,以鄂尔多斯盆地延长组致密油藏为研究对象,开展了四种典型致密岩心的自发渗吸驱油实验,利用基于核磁共振分形理论的流体分布孔隙精细划分方法,区分了致密砂岩岩心孔隙类型,明确了不同类型岩心孔隙结构对原油可动性和自发渗吸驱油速率的控制特征.研究结果表明不同类型岩心自发渗吸模拟油动用程度介于22.07%～33.26%,核磁共振T2谱双峰型岩心自发渗吸模拟油动用程度高于单峰型岩心;不同类型致密砂岩岩心中流体分布孔隙可初步划分出P1和P2两种类型, P1类型孔隙则可进一步划分出P1-1, P1-2和P1-3三种亚类型孔隙;致密砂岩岩心中P1和P2类孔隙中模拟油均有不同程度的动用, P1类孔隙作为致密岩心中主要孔隙,尤其是P1类孔隙中P1-2和P1-3类孔隙的数量决定了自发渗吸模拟油动用程度;P1-1, P1-2和P1-3类孔隙结构差异性对自发渗吸模拟油动用程度起决定性作用,较小尺寸孔径孔隙较大的孔隙结构差异性不仅提升了自发渗吸模拟油动用程度,而且提升了自发渗吸驱油速率;流体可动性指数较高的P...     

基于改进LBM的气液自发渗吸过程中动态润湿效应模拟

微通道内气液自发渗吸是广泛发生在自然界及诸多工业领域的物理现象,而动态接触角是影响整个渗吸过程的关键因素.针对该问题,本文使用改进的伪势多相流格子玻尔兹曼方法 (LBM),直接捕捉微通道内气液自发渗吸过程中的实时接触角,并分析接触角的动态变化特性及其对渗吸长度的影响.首先,本文在原始的伪势多相流LBM的基础上耦合Peng-Robinson (PR)状态方程,改进流体-流体作用力以及流-固作用力格式,并采用精确差分方法将外力添加至LBM框架中.然后,通过校准模型的热力学一致性,模拟测试界面张力,静态平衡接触角等界面现象验证了模型的准确性.最后,基于建立的模拟方法,在水平方向上模拟微通道内气液自发渗吸过程.结果表明:渗吸过程中的接触角呈现动态变化特征,在渗吸初期,因受到惯性力的影响存在较大波动;随着渗吸距离的增大,其逐渐减小并趋近于静态平衡接触角.渗吸过程中的接触角与微通道尺寸及静态接触角有关,随着微通道宽度增大,实时的动态接触角与静态接触角相差大;随着静态接触角增大,实时的动态接触角与静态接触角的相差增大.此外,忽略动态接触角的Lucas-Washburn (LW)方程所预测的弯液面位置...     

多孔介质输运性质的分形分析研究进展

首先对多孔介质输运性质的传统实验测量、解析分析和数值模拟计算研究进展作了扼要的评述.然后,着重综述采用分形理论和方法研究多孔介质输运性质分析解的理论、方法和所取得的进展.最后,指出采用分形理论和方法有可能解决其它尚未解决的有关多孔介质输运性质的若干课题和方向.      

非饱和土力学理论的研究进展

回顾了非饱和土有效应力的发展,目前普遍认同采用两个应力变量来建立本构模型,且对基质吸力中毛细和粘吸两部分作用进行了阐述。分析了非饱和土强度问题,包括抗剪强度和抗拉强度。讨论了非饱和土的本构模型问题,包括基于净应力和基质吸力的弹塑性模型,基于Bishop有效应力和基质吸力的水力力学耦合弹塑性模型,以及双孔隙结构的模型。最后探讨了热力学方法和多孔介质理论在非饱和土中的应用,基于多孔介质理论在多场耦合条件下土体复杂的行为是当前值得研究的问题。     

油藏多孔介质热质传递“三箱”分析模型研究

油藏多孔介质孔隙组成及结构变化多样,一些特性参数很难全部获得,精确描述和分析困难;另外,多孔介质内渗流过程水力条件和作用机理复杂,存在热流固耦合作用,目前的一些分析方法和研究模型具有一定的局限性.提出了油藏多孔介质的表征单元体（representative elementary volume,REV）描述表征方法;基于表征单元体建立了多孔介质的黑箱模型、灰箱模型和白箱模型,据此提出了多孔介质的“黑箱→灰箱→白箱”分析过程.基于黑箱模型和灰箱模型推导了REV导热系数计算公式、给出了REV热质传递过程的热平衡方程.结合中国油藏热采情况,对多孔介质导热系数变化规律和蒸汽驱热质传递特性进行了分析,得到了一些有意义的结果.该工作为多孔介质热质传递过程分析提供了新思路和新方法.      

STUDY ON ANALYSIS METHOD OF “THREE BOX” IN HEAT AND MASS TRANSFER PROCESS OF RESERVOIR MEDIA

油藏多孔介质孔隙组成及结构变化多样,一些特性参数很难全部获得,精确描述和分析困难;另外,多孔介质内渗流过程水力条件和作用机理复杂,存在热流固耦合作用,目前的一些分析方法和研究模型具有一定的局限性.提出了油藏多孔介质的表征单元体（representative elementary volume,REV）描述表征方法;基于表征单元体建立了多孔介质的黑箱模型、灰箱模型和白箱模型,据此提出了多孔介质的“黑箱→灰箱→白箱”分析过程.基于黑箱模型和灰箱模型推导了REV导热系数计算公式、给出了REV热质传递过程的热平衡方程.结合中国油藏热采情况,对多孔介质导热系数变化规律和蒸汽驱热质传递特性进行了分析,得到了一些有意义的结果.该工作为多孔介质热质传递过程分析提供了新思路和新方法.     

A Dynamic Network Model for Two-Phase Flow in Porous Media

We present a dynamic model of immiscible two-phase flow in a network representation of a porous medium. The model is based on the governing equations describing two-phase flow in porous media, and can handle both drainage, imbibition, and steady-state displacement. Dynamic wetting layers in corners of the pore space are incorporated, with focus on modeling resistivity measurements on saturated rocks at different capillary numbers. The flow simulations are performed on a realistic network of a sandpack which is perfectly water-wet. Our numerical results show saturation profiles for imbibition in agreement with experiments. For free spontaneous imbibition we find that the imbibition rate follows the Washburn relation, i.e., the water saturation increases proportionally to the square root of time. We also reproduce rate effects in the resistivity index for drainage and imbibition.     

Fractal Prediction Model of Spontaneous Imbibition Rate

By utilizing fractal dimension as one of the parameters to characterize rocks, a mathematical model was derived to predict the production rate by spontaneous imbibition. This fractal production model predicts a power law relationship between spontaneous imbibition rate and time. Fractal dimension can be estimated from the fractal production model using the experimental data of spontaneous imbibition in porous media. The experimental data of recovery in gas-water-rock and oil–water–rock systems were used to test the fractal production model. The rocks (Berea sandstone, chalk, and The Geysers graywacke) in which the spontaneous water imbibition experiments were conducted had different permeabilities ranging from 0.5 to over 1000 md. The results demonstrate that the fractal production model can match the experimental data satisfactorily in the cases studied. The fractal dimension data inferred from the model match were approximately equal to the values of fractal dimension measured using a different technique (mercury-intrusion capillary pressure) in Berea sandstone.     

Numerical Solution of Equation for Dynamic,Spontaneous Imbibition with Variable Inlet Saturation and Interfacial Coupling Effects

In the oil industry, dynamic spontaneous imbibition plays an important role in several flow processes in porous media. A numerical approach is developed to simulate dynamic spontaneous imbibition with variable inlet saturation and interfacial coupling. The inclusion of interfacial coupling effects invalidates the assumption that the interfaces (fluid/fluid and fluid/solid) act in the same way. The one-dimensional numerical simulation model is developed using a Lagrangian formulation discretized in time and saturation. The solution of the partial differential equations utilizes an iteration process that includes two material balance criteria to ensure the validity of the variable inlet saturation. Furthermore, an error analysis, the validation of the model and a sensitivity study on the optimal number of time steps and saturation grid cells are undertaken. The numerical simulation solution represents an accurate approach to investigate the effect of fluid and rock properties on dynamic spontaneous imbibition.     

A Semi-Analytical Model for Two Phase Immiscible Flow in Porous Media Honouring Capillary Pressure

This article describes a semi-analytical model for two-phase immiscible flow in porous media. The model incorporates the effect of capillary pressure gradient on fluid displacement. It also includes a correction to the capillarity-free Buckley–Leverett saturation profile for the stabilized-zone around the displacement front and the end-effects near the core outlet. The model is valid for both drainage and imbibition oil–water displacements in porous media with different wettability conditions. A stepwise procedure is presented to derive relative permeabilities from coreflood displacements using the proposed semi-analytical model. The procedure can be utilized for both before and after breakthrough data and hence is capable to generate a continuous relative permeability curve unlike other analytical/semi-analytical approaches. The model predictions are compared with numerical simulations and laboratory experiments. The comparison shows that the model predictions for drainage process agree well with the numerical simulations for different capillary numbers, whereas there is mismatch between the relative permeability derived using the Johnson–Bossler–Naumann (JBN) method and the simulations. The coreflood experiments carried out on a Berea sandstone core suggest that the proposed model works better than the JBN method for a drainage process in strongly wet rocks. Both methods give similar results for imbibition processes.     

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．     

A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

In the past decades, there was considerable controversy over the Lucas–Washburn (LW) equation widely applied in capillary imbibition kinetics. Many experimental results showed that the time exponent of the LW equation is less than 0.5. Based on the tortuous capillary model and fractal geometry, the effect of tortuosity on the capillary imbibition in wetting porous media is discussed in this article. The average height growth of wetting liquid in porous media driven by capillary force following the [`(L)] _s(t) ~ t^1/2D_T{\overline L _{\rm {s}}(t)\sim t^{1/{2D_{\rm {T}}}}} law is obtained (here D _T is the fractal dimension for tortuosity, which represents the heterogeneity of flow in porous media). The LW law turns out to be the special case when the straight capillary tube (D _T = 1) is assumed. The predictions by the present model for the time exponent for capillary imbibition in porous media are compared with available experimental data, and the present model can reproduce approximately the global trend of variation of the time exponent with porosity changing.     

Effect of fluids properties on non-equilibrium capillarity effects: Dynamic pore-network modeling

We have developed a Dynamic Pore-network model for Simulating Two-phase flow in porous media (DYPOSIT). The model is applicable to both drainage and imbibition processes. Employing improved numerical and geometrical features in the model facilitate a physically-based pore-scale simulator. This computational tool is employed to perform several numerical experiments (primary and main drainage, main imbibition) to investigate the current capillarity theory. Traditional two-phase flow formulations state that the pressure difference between the two phase is equal to the capillary pressure, which is assumed to be a function of saturation only. Many theoretical and experimental studies have shown that this assumption is invalid and the pressure difference between the two fluids is not only equal to the capillary pressure but is also related to the variation of saturation with time in the domain; this is referred to as the non-equilibrium capillarity effect. To date, non-equilibrium capillarity effect has been investigated mainly under drainage. In this study, we analyze the non-equilibrium capillarity theory under drainage and imbibition as a function of saturation, viscosity ratio, and effective viscosity. Other aspects of the dynamics of two-phase flow such as trapping and saturation profile are also studied.     

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.