摘要
指进是一种相界面不稳定现象。通常情况下,其诱发的主要原因是流体间的黏度差,故有时也称黏性指进。黏性指进现象是多相渗流的重要特征之一,在很多工程应用中起着至关重要的作用,如化工、石油开采以及地下水污染的治理等领域。以石油开采为例,该现象的过早出现会减少波及效率,造成驱替流体的窜流,降低石油采收率。非混相驱油过程中的黏性指进现象是一个涉及到相界面捕捉、多组分多相流理论以及复杂几何流场内流体流动的复杂流体动力学问题。其影响因素众多,涉及到多孔介质的孔隙结构、壁面润湿性以及流体的物性等。该问题的内在产生机理至今尚不明晰,因此对于黏性指进现象的研究有着重要的学术意义和应用价值。本文以黏性指进现象为主要研究对象,针对采用Shan-Chen (SC)模型模拟具有不同密度比和黏度比流体系统时存在的问题,进行了改进,提出了一种新的LBM多组分模型,并利用格子Boltzmann方法(Lattice Boltzmann Method, LBM)模拟单孔隙和多孔介质内的指进现象,综合考虑不同因素对于相界面形态以及驱替效率的影响,具体内容包括：
(1)基于SC模型,提出一个新的可以模拟具有不同密度比和黏度比流体系统的LBM多组分模型。新模型中,对SC模型施加作用力的方式进行改进,消除了原模型中由于作用力的施加方式引入的离散误差。不同组分粒子的格子速度和格子声速均不同,因此,在一个时间步内,不同组分粒子的迁移距离也不同,相互之间的比例关系由流体间的密度比确定。迁移后格子节点上的粒子分布函数由双线性插值格式确定。给出考虑固体边界的特殊处理方法。利用新的LBM多组分模型模拟了在不同管径的圆管内、不同体积流量下,水驱癸烷的非混相驱替过程,并与实验结果进行比较。模拟中的平均驱替速度和驱替完成时间与实验结果相比,相对误差在3.2%以内,证明了新模型的正确性。新模型具有良好的守恒性。通过适当地选取边界条件,并对流场进行适当地处理,该模型可以用于模拟流体速度远小于模型本身伪速度的低速驱替过程。
(2)详细地讨论了不同影响因素：毛细管数(Ca)、黏度比(M)、邦德数(Bo)以及固体壁面润湿性(用接触角θ表征)对单孔隙内非混相驱替过程中指进现象的影响。着重分析了是否考虑与流动方向相垂直的重力场对指进过程的影响。比较了不同情况下相界面形态的差别。并用突破时间和面积扫掠效率两个参数考察了不同条件下的驱替效率。结果表明：不考虑重力时,相界面关于孔隙的中心是对称的。考虑重力时,相界面是不对称的,相界面前缘与孔隙中心有一定的偏移,而且相界面与孔隙上下壁面的交点位置也有所不同。同等条件下,和不考虑重力相比,当M>1时,重力的影响使得驱替效率有所降低。研究发现,随着Ca、M和Bo的增加,指进现象更加明显。当驱替流体的接触角θ1>90°时,指进现象被强化,而当驱替流体的接触角θ1<90°时,指进现象被抑制。指进现象明显时,驱替效率低。因此,从工程效益的角度出发,为了达到更大的驱替效率,对于单孔隙内的非混相驱替过程而言,驱替过程中Ca越小越好,M越小越好,Bo越小越好,驱替流体的θ1越小越好。
(3)和单孔隙内非混相驱替过程相比,固体骨架的存在使得多孔介质内的指进现象更加复杂。不考虑重力时,相界面关于流场中心是对称的。考虑重力时,相界面是不对称的,相界面的指状前缘会朝斜下方倾斜,并且会有离散的被驱替流体小液滴附着在固体骨架上或者被夹带在驱替流体中。以交错形式排列的多孔介质骨架结构会抑制指进现象的发生。随着Ca的增加,并没有明显的指进现象出现。在有限的M范围内(M=1～5),由于驱替流体的注入速度恒定以及固体骨架的交错排列方式,当M≥3时,最终的相界面前缘的形态相差不多。随着Bo的增加,相界面前端沿斜下方的运动趋势更加明显,相界面的指状前缘细而长。在驱替结束时,当Bo=0.218～0.229时,相界面的指状前缘最为粗壮,被圈闭在固体骨架上被驱替流体的小液滴也较大。不考虑重力时,固体壁面润湿性对指进现象的影响规律和单孔隙内的影响规律相同(抑制作用或强化作用)。不同之处在于：有被圈闭的被驱替流体会附着在背向流体流动方向的固体骨架右侧,无法被驱替出来。考虑重力时,相界面的形态更加复杂,但是润湿性对指进现象的“抑制”和“强化”规律不变。对于不同的情况,指进现象越明显,驱替效率越低。同样条件下,重力的存在使得突破时间和面积扫掠效率有所降低。
Fingering refers to interface instability phenomenon. Generally, it is caused by the viscosity ratio between fluids; hence sometimes it is called viscous fingering. Viscous fingering phenomenon is an important feature of multiphase flow. In many engineering applications, such as chemical engineering, oil recovery field and remediation of underground water contamination, it plays a crucial role. For example, in the oil recovery field, the early occurrence of viscous fingering phenomenon will decrease sweep efficiency and result in the breakthrough of displacing fluid, therefore, the oil recovery is reduced. Viscous fingering phenomenon in immiscible displacement is a complex fluid dynamic problem related to the capture of phase interface, multi-component multi-phase flow theory and fluid flow in complex geometry. The various impact factors include the structure of porous media, surface wettability and fluid properties. So far, the intrinsic mechanism is not yet clear, so the study of viscous fingering phenomenon is quite important for both theory and application. In this paper, in order to solve the problem encountered in the simulation of fluids with various density ratio and viscosity ratio by the original Shan-Chen (SC) model, a new scheme of LBM model for multi-component is proposed. In addtion, viscous fingering phenomenon in immiscible displacement in a channel and porous media will be investigated by the lattice Boltzmann method, respectively. The effects of various factors on fingering pattern and displacement efficiency will be studied. The main contents are as follows:
(1) Based on the original SC model, a new model for modelling immiscible fluids with various density ratio and viscosity ratio is proposed. In the new model, the incorporation scheme of the force is improved to remove the discretization error. The lattice speeds and lattice speeds of sound for fluid components are different, hence, the streaming distances of fluid components during a time step are different, and they are related to the density ratio. The particle distribution functions at the lattice points are determined by bilinear extrapolation scheme. Besides, the strategy for solid boundary condition is specified. The new model has been validated by modelling the displacement of decane by water at various volume fluxes in a circular tube with various diameters. Compared with the experimental data, the relative errors of average displacing velocity and displacement time are within 3.2%. The new model has a good conservativeness. By choosing suitable boundary condition and properly handling the flow domain, this model can be used to simulate low velocity displacement in which the displacing velocity is smaller than the pseudo-velocity.
(2) The effect of various impact factors on fingering phenomenon in a channel are analysed detailly, such as capillary number (Ca), viscosity ratio (M), Bond number (Bo) as well as surface wettability (represented by contact angleθ). Specific focuses are put on the situations whether the effect of gravity is considered or not. The interface patterns are compared under different circumstances. The displacement efficiencies in various conditions are examined by the breakthrough time and areal sweep efficiency. Simulations show that the interface is symmetric to the channel center without consideration of gravity and it is asymmetric when the gravity is taken into account. There is an offset between the interface front and channel center, and the intersections between the interface and channel upper/lower boundaries are different. In the same condition, for M>1, the displacement efficiency decreases when the effect of gravity is incorporated. With the increasing of Ca, Bo and M, the fingering phenomenon becomes more and more obvious. When the contact angle of displacing fluidθ, is larger than 90°, the fingering phenomenon is enhanced, and when the contact angle of displacing fluidθ1 is smaller than 90°, the fingering phenomenon is suspended. The more significant the viscous fingering is, the lower the displacement efficiency is. In conclusion, from the economic benefit, in order to achieve higher displacement efficiency, as for the immiscible displacement in a channel, it is better to maintain small capillary number, small viscosity ratio, small Bond number and small contact angle of displacing fluid.
(3) Compared to the situation in a channel, the existence of solid materials makes fingering phenomenon in porous media more complicated. The interface is symmetric when the gravity is ignored, and it is asymmetric when the gravity is considered. The interface front has a tendency of moving along the direction of gravity. In some circumstances, there are isolated droplets of displaced fluid adhering to the solid materials or being trapped in the displacing fluid. The staggered arrangement of solid materials suspends the occurrence of fingering. There is no significant fingering as Ca increases. In the limited viscosity ratio range (M=1～5), due to the constant injecting velocity of displacing fluid and staggered arrangement of solid materials, final interface pattern is similar in the case of M≥3. As Bo increases, the moving downwards tendency of the interface becomes more obvious. The finger front is narrow and long. In the end of displacement, the finger is the most strongest for Bo=0.218～0.229. Accordingly, the isolated droplets of displaced fluid adhering to the solid materials are bigger. No matter the gravity is taken into account or not, the effect of surface wettability on viscous fingering is the same as that in the case of displacement in a channel (enhancing or suspending). The difference is that, when the gravity is considered, there are isolated droplets of displaced fluid adhering to the solid materials which cannot be displaced. For various conditions, the more significant the viscous fingering is, the lower the displacement efficiency is. In the same situation, the existence of gravity decreases displacement efficiency.
引文
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