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1、Modeling of flow of oil-in-water emulsions through porous media 通过多孔介质的水包油乳化建模Ajay Mandal 1. Achinta Bera2Pet. Sci. (2015)12:273-281. DOI10.1007/s 12182-015-0025-xAbstract 摘要Formation and flow of emulsions in porous media are common in all enhanced oil recovery techniques. In most cases, oil-in-wate
2、r (O/W) emulsions are formed in porous media due to oilwater interaction. Even now, detailed flow mechanisms of emulsions through porous media are not well understood. In this study, variation of rate of flow of O/W emulsions with pressure drop was studied experimentally, and rheological parameters
3、were calculated. The pressure drop increases with an increase in oil concentration in the O/W emulsion due to high viscosity. The effective viscosity of the emulsion was calculated from the derived model and expressed as a function of shear rate while flowing through porous media. Flow of O/W emulsi
4、ons of different concentrations was evaluated in sand packs of different sand sizes. Emulsions were characterized by analyzing their stability, rheological properties, and temperature effects on rheological properties.多孔介质中乳化形成和流动常见于所有强化采用技术。大多数情况下，由于油-水相互 作用，在多孔介质中形成水包油(O/W)乳化。即使是现在，依然没有充分认识通过多孔介 质
5、的乳化流动详细机理。在这项研究中，实验研究了 O/W乳化流量随压降的变化，并计 算了流变参数。由于高粘度，压降随着O/W乳化中油浓度增加而增加。乳化的有效粘度 由导出模型计算，且表示流过多孔介质时的剪切速率的函数。评估了不同大小的沙填料中 不同浓度的O/W乳化流动。通过分析其稳定性、流变性质和温度对流变性质的影响，分 析乳化。Keywords Emulsion Porous media Rheology Modeling Pressure drop1 Introduction 弓 | 言Emulsion flow through porous media is an important phe
6、nomenon in oil production operations and is also a topic of special interest in many applications of science and engineering, especially petroleum industries (Soo and Radke 1984; Soma and Papadopoulos 1995; Vidrine et al. 2000; Arhuoma et al. 2009; Cobos et al. 2009). It has been suggested that oil
7、migrates through其中t是剪切应力，dynes/cm2； K和n是特定流体的常数，n值小于1。常数K 称为流体的稠度指数Pa s K值越高，流体越粘稠。常数n称为流动指数，用于衡量 偏离牛顿特性的程度。采用标准流变仪，评估了三种不同乳化的详细流变性质，发现乳化 的粘度随着剪切速率增加而降低，表现出非牛顿特性。在本研究中，流变学由 Ostwald-Dewaele模型或之前研究中包括的幕律模型描述。In order to develop an expression for the effective viscosity, p.eff fbr pseudo-plastic flow t
8、hrough a porous media let us consider the general equation (Mandal 2010),为了建立有效粘度的表达式，通过多孔介质的拟0-塑性流动也ff考虑为通用方程where v is the velocity of fluid. For fluid flowing through a porous media, a force balance on a cylindrical fluid element of radius r (imaginary) gives,其中V是流体流速。对于流过多孔介质的流体，半径为r (假想)的圆柱形流体单
9、元 上的力平衡给出，and that at the wall of the core holder and also at the surface of the particle where velocity is zero, tw can be written as且在岩芯支架壁以及速度为零的颗粒外表处，Tw可以写作Tw rHwhere L is the length of the core holder, cm; tw is the shear stress at the wall, dynes/cm2.其中L为岩芯支架长度，cm； tw是壁面处的剪切应力，dynecs/cm2oThere
10、fore,因此，r = 31Z(8)The volumetric flow rate Q through the porous media is given by通过多孔介质的体积流量Q由下式给出2 兀n,dr.z0where v is the average velocity, cm/s; Q is the volumetric flow rate of the emulsion through porous media, cm3/s.其中v是平均硫酸，cm/s； Q通过多孔介质的乳化体积流量，cm3/s。On integration by parts, and applying the c
11、ondition, at r = th, v = 0, and substitution of Eq. (9) leads to,局部积分，并采用r =H处v = 0条件，且替换式(9),得出，1/刃丸0Since for pseudo-plastic fluids,由于对于拟-塑性流体，/=therefore,因此(10)(H)q=1/%)&， 0which on integration gives,积分给出，(12)v _/w(3 + 1) /C /Rearranging one gets, 重新排列得到，(13)Tw = K(2u/)h) (), or,或，(14)Tw = K(8u/O
12、h)”,(15)where DH is the hydraulic diameter of the sand particles, cm.式中DH为砂粒的水力直径，cm。From the definition of根据Reff的定义，(16)(17)(16)(17).=蒜=K的，H)1(假设Neff = 8-1/To；TK,with 和K = KK = K(七)Therefore, the value of |icff can be evaluated if K and n are known. It is clear from Eq. (15) that if a logarithmic p
13、lot is made between tw and 8v/DH, a linear relationship will obtained and the slope of the line should give the value of n and the intercept因此，如果K和n，那么可以评估(leff的值。从式(15)可以清楚地看出，如果 在绘出TW和8v/DH之间对数图，那么取得线性关系，线的斜率应给出n和截距值。4 Results and discussion结果和讨论Characterization of emulsions 乳化分析Emulsions are char
14、acterized by analyzing their stability, rheological properties, temperature effects on rheological properties, etc. Figure 2 shows the variation of viscosity with shear rate at different temperatures. Viscosity of emulsions decreases with an increase in the shear rate at lower shear rates, showing n
15、on-Newtonian behavior of emulsions. On the other hand, at higher shear rates emulsions show Newtonian behavior. It is also observed from figure that with an increase in temperature the viscosity of the O/W emulsion decreases. This is due to the fact that with an increase in te mperature the average
16、speed of the molecules in a liquid increases and the amount of time they spend “ in contact“ with their nearest neighbors decreases. Thus, as the temperature increases, the average inter molecular forces decrease and hence the viscosity decreases. The variation of viscosity of emulsions of different
17、 concentrations is presented in Fig. 3. It may be found that at low shear rates the viscosity of emulsions with higher oil concentration is higher though the variation is only marginal.d。SFSOOSS00100200 1o70 006 o 50 004 o 30Shear rate, s*1不同温度下15 % O/W乳化的粘度(cP)与剪切速率(t)Fig. 2 Viscosity versus shear
18、rate at 30 for different O/W emulsion concentration。 下 不同O/W乳化浓度的粘度与剪切速率关系通过分析其稳定性、流变性质、温度对流变性质的影响，表征乳化。图2显示不同温 度下粘度随剪切速率的变化。在较低剪切速率下，乳化的粘度随着剪切速率的增加而降低, 表现出乳化的非牛顿特性。另一方面，在较高剪切速率下，乳化表现出牛顿特性。从图中 液可以看出，随着温度升高，O/W乳化粘度降低。这是由于随着温度升高，液体中分子的 平均速度增加，且与最近的分子“接触”的时间减少。因此，随着温度升高，分子间平均作 用力降低，因此，粘度降低。不同浓度乳化的粘度变化见
19、图3所示。可以看出，在低剪 切速率下，油浓度较高的如的粘度较高，但变化很小。Microscopic images of O/W emulsions were taken with a polarizing microscope. A typical microscopic image of 10 % O/W emulsion is shown in Fig. 4. The particle size distribution (PSD) of oil in the emulsion was studied using a particle size analyzer. The PSD curv
20、e of 10 % O/W emulsion is shown in Fig. 5 and it shows maximum intensity at 466.1 nm.采用偏光显微镜，拍摄O/W乳化的显微图像。10% O/W乳化的典型显微图像见图 4 o采用粒度分析仪，研究乳化中油的粒度分布(PSD)。10% O/W乳化的PSD曲线见图 5, 466.1 nm处显示最大强度。Fig. 3 Microscopic image of the 10 % O/W emulsionlO% O/W 乳化的显微图像Fig. 4 Particle size distribution of 10 % O/W
21、emulsion 10% O/W 乳化的粒径分布 4.2 Pressure drop of emulsion through a porous media 通过多孔介质的压降The emulsion concentration significantly affects the flow rate of emulsions through porous media. In Figs. 6, 7, 8, pressure drop versus flow rate curves are depicted for sand packs A, B and C at different emulsio
22、ns of varying concentrations.乳化浓度显著影响通过多孔介质乳化流量。在图6、7、8,描述砂层A、B和C在不 同浓度乳化的压降与流量曲线。In addition, the rate of brine flow was also measured. In all cases, the flow rate decreases with increasing emulsion concentration. This is due to the differences in viscosity between the different concentrations of i
23、njected emulsions. Brine has a higher flow rate compared to emulsions. For a particular pressure gradient, the flow rate decreases with an increase in emulsion concentration.另外，也测量了盐水流量。在所有情况下，流量都随着乳化浓度增加而降低。这是由 于不同浓度的注入乳化之间的粘度差异。与乳化相比，盐水具有更高的流量。对于特定的 压力梯度，流量随着乳化浓度的增加而降低。10- o o o o o 6 5 4 3 2 一sdC
24、L-V dop amssaid0.00.20.40.60.81.01.2Flow rate Q, cm3/so o o o o O 6 5 4 3 2 1 一 sd!E q MOLL20Fig. 13 Rheological parameters (flow index, n and consistency constant, K) as a function of emulsion concentration流变参数(流动指数n和稠度常数K)与乳化浓度的关系Fig. 14 Effective viscosity of emulsions calculated from the derived
25、 model at different shear rates (sand pack B)根据导出模型计算不同剪切速率下乳化有效粘度(砂层B)5 Conclusions结论Oil-in-water emulsions are characterized in terms of their rheological behavior and sizes of the dispersed oil globules in water. It has been found that the viscosity of emulsions decreases with an increase in shea
26、r rate at lower shear rates, showing non-Newtonian behavior. At low shear rates, the emulsions of higher oil concentration show higher viscosity though the viscosity variation is only marginal. The flow characteristics of different emulsions through porous media have been studied. The pressure drop
27、fbr emulsions flowing through porous media depends significantly on the oil concentration in the O/W emulsion and the average particle size of the medium. A mathematical model has been developed to analyze the experimental data of flow of emulsions through porous media. The shear stress-shear rate b
28、ehavior of different emulsionsthrough porous media shows non-Newtonian behavior and follows the power-law model. The variation of rheological parameters (flow index and consistency constant) as a function of emulsion concentration has also been presented. The effective viscosity of the emulsion calc
29、ulated from the derived model equation has been presented as a function of shear rate for different sand packs.水包油乳化的特征是其流变特性和分散在水中的油滴大小。发现在较低的剪切速率下, 乳化的粘度随着剪切速率增加而降低，表现为非牛顿特性。在低剪切速率下，较高油浓度 的乳化显示较高的粘度，但是粘度度变化很小。研究了不同如通过多孔介质的流动特性。 流过多孔介质的乳化压降很大程度上取决于O/W乳化中的油浓度和介质的平均粒径。建 立一个数学模型，分析乳化通过多孔介质流动的实验数据。通过多孔
30、介质的不同乳化的剪 切应力-剪切速率特性显示非牛顿特性，且符合幕律模型。也描述了流变参数(流动指数和 稠度常数)随乳化浓度的变化。根据导出模型方程计算的乳化有效粘度描述为不同砂层的 剪切速率函数。reservoir sands in the form of a fine, dispersed emulsion of oil in water, and that oil accumulations occur where the stream enters finer-grained rock such as silt or shale. Flow behavior of emulsions i
31、n both pipelines and reservoirs can be properly described based on emulsion properties and physical laws controlling their flow through porous media. Emulsions are generally liquid-liquid dispersions, in which the dispersed phase interferes with the flow of the continuous phase through the pore spac
32、e, as they can partially block the already swept, more permeable paths. Thus, the flow of injected water diverts to unswept regions, leading to more efficient reservoir sweep and higher recovery factor (Thomas and Ali 1989; Seright and Liang 1995; Babadagli 2005). These researchers reported that emu
33、lsions would have good displacement properties similar to those of a low-viscosity gel. In petroleum production, heavy crude oils are often produced from natural oil reservoirs in the form of water-in-oil (W/O) or oil-in-water (O/W) emulsion with water (Steinhauff 1962). In enhanced oil recovery (EO
34、R) methods a variety of emulsions are observed (Mandal et al. 2010a). During waterfloods fbr secondary recovery of oil from reservoirs, there is rapid channeling of water from injection to producing wells through the more permeable portions of reservoirs, resulting in low oil recovery. As water flow
35、s through tortuous paths in reservoirs in presence of oil, O/W emulsions are often formed. When the O/W emulsion flows through a heterogeneous reservoir, a great amount of emulsion enters the more permeable zones, so water begins to flow into less permeable zones, resulting in higher sweep efficienc
36、y. In this study the flow behavior of O/W emulsions through porous media has been discussed.通过多孔介质的乳化流动是石油生产作业中的一个重要现象，也是很多科学和工程应 用特别关注的课题，尤其是石油工业。提出了油以细、分散的水包油乳化形态通过储层砂 迁移，且在油流入细颗粒岩石的地方发生油聚集，如粉砂或页岩。可以基于乳化性质和控 制其在多孔介质中流动的物理定律，正确描述管道和油藏中乳化流动特性。乳化通常为液 -液分散，由于局部阻塞涉及后、更易渗透的路径，其中分散相会干扰通过孔隙空间的连续 相流动。因此，注入
37、水流转向到未涉及区域，导致更有效的储层涉及和更高的采收率。这 些研究人员报告了乳化具有与低粘度凝胶相似的良好驱替性质。在石油生产中，重质原油 通常以油包水(W/O)或水包油(O/W)乳化形态从天然油藏中采出。在强化采油(EOR) 方法中，观察到各种乳化。在储层二次采油的水驱过程中，存在通过更为渗透储层局部的 注如到生产井的快速窜流，导致低采收率。水流过存在油的储层中曲折路径时，通常形成0/W乳化。o/w乳化流经非均质储层时，大量乳乳化进入渗透率较高的区域，因此，水 开始流入渗透率较低区域，导致更高的涉及效率。在这项研究中，讨论了通过多孔介质的 0/W乳化的流动特性。Different typical configu