Sensitivity Analysis of the Dimensionless Parameters in Scaling a Polymer Flooding Reservoir

A set of scaling criteria of a polymer flooding reservoir is derived from the governing equations, which involve gravity and capillary force, compressibility of water, oil, and rock, non-Newtonian behavior of the polymer solution, absorption, dispersion, and diffusion, etc. A numerical approach to quantify the dominance degree of each dimensionless parameter is proposed.With this approach, the sensitivity factor of each dimensionless parameter is evaluated. The results show that in polymer flooding, the order of the sensitivity factor ranges from 10⁻⁵ to 10⁰ and the dominant dimensionless parameters are generally the ratio of the oil permeability under the condition of the irreducible water saturation to water permeability under the condition of residual oil saturation, density, and viscosity ratios between water and oil, the reduced initial oleic phase saturation and the shear rate exponent of the polymer solution. It is also revealed that the dominant dimensionless parameters may be different from case to case. The effect of some physical variables, such as oil viscosity, injection rate, and permeability, on the dominance degree of the dimensionless parameters is analyzed and the dominant ones are determined for different cases.     

Microscopic Roles of “Viscoelasticity” in HPMA polymer flooding for EOR

A polymer solution with a transient network structure due to the entanglement of long chain molecules exhibits a viscoelastic behavior when it flows through a tortuous and diverging/converging channel in porous media. A constitutive equation is first developed to represent the viscoelastic behavior of polymer solutions in this article. Then a 3D viscoelastic polymer flooding model is established to examine the effect of elasticity of polymers on EOR (enhanced oil recovery). The model is validated in comparison with laboratorial coring data. The simulated results show that the oil recovery of viscoelastic polymer flooding can be enhanced by larger displacement efficiency due to its microscopic roles. In the meanwhile, the injection pressure required increases correspondingly if the elastic effect is significant. Relaxation time as a major characteristic parameter of viscoelastic polymer plays a decisive role, and therefore the HPAM (partially hydrolyzed polyacrylamide) with evident elastic property is recommended in chemical flooding.     

Analytical and Experimental Study to Predict the Residual Resistance Factor on Polymer Flooding Process in Fractured Medium

The major objectives of this study are to analytically and experimentally determine the residual resistance factor in the fractured medium based on the polymer solution properties and operational conditions. The parameters considered in this study are the polymer concentration, power law constitutive equation parameter, and salt concentration, sulfonation content of polymer, temperature, and molecular weight of the water soluble polymers which are used in polymer flooding for enhanced oil recovery. The results indicated that residual resistance factor in fractured medium is dependent on the coil overlap parameter and power law equation parameter of polymer. The coil overlap parameter is a dimensionless number consists of intrinsic viscosity and polymer concentration. Since intrinsic viscosity is a function of polymer diameter in medium conditions, to predict the residual resistance factor in fracture medium, an experimental correlation is generated for determination of the molecular diameter of polymer based on polymer molecular weight, temperature, salt concentration, and sulfonation content.     

Asymmetry in the turbulent flow of a viscoelastic liquid through an axisymmetric sudden expansion

This paper concerns the asymmetry in mean axial velocity distributions for the flow through an axisymmetric sudden expansion of a viscoelastic, shear-thinning aqueous solution of a polyacrylamide (PAA). The asymmetry manifests itself as an azimuthal variation in the length of the recirculation region of the separated flow downstream of the expansion inlet. For water, the flow is found to be axisymmetric. The asymmetry for the PAA flow, which remained unchanged despite alterations to the flow facility, is attributed to the high viscoelasticity of the polymer solution. The conclusion is drawn that the asymmetry is a purely physical feature of such a flow, and not the product of upstream or downstream flow conditions deriving from the flow facility, or the result of geometrical imperfections in the axisymmetric sudden expansion set-up.     

Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

The attenuation and dispersion of elastic waves in fluid-saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov’s exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long-wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The attenuation (dispersion) is controlled by the parameter which represents the ratio of Biot’s characteristic frequency to the viscoelastic characteristic frequency. If Biot’s characteristic frequency is small compared with the viscoelastic characteristic frequency, the solution is identical to that derived from an anisotropic version of the Frenkel–Biot theory of poroelasticity. In the opposite case when Biot’s characteristic frequency is greater than the viscoelastic characteristic frequency, the attenuation/dispersion is dominated by the classical viscoelastic absorption due to the shear stiffening effect of the viscous fluid layers. The product of these two characteristic frequencies is equal to the squared resonant frequency of the layered system, times a dimensionless proportionality constant of the order 1. This explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic (effective medium) theories, as these theories imply that frequency is small compared to the resonant (scattering) frequency of individual pores.     

利用三维网络模型研究滞留聚合物微观分布规律

再利用地下滞留聚合物是聚合物驱之后进一步提高原油采收率的新途径。基于油水两相流网络模拟模型,综合考虑聚合物渗流机理建立起聚合物驱微观模拟模型。用微观数值模拟手段研究了地下滞留聚合物分布规律及影响因素,为有效地开采聚合物驱后剩余油、合理利用滞留地下聚合物提供必要的依据。模拟结果表明,由于吸附和捕集作用将引起大量聚合物滞留在孔喉中,滞留聚合物占注入聚合物的61.7%。总体上看,大孔喉中聚合物滞留量较大,但滞留聚合物浓度较小。孔喉半径和形状因子为聚合物滞留的主要影响因素,孔喉滞留聚合物浓度与孔喉半径和形状因子平方根的乘积成反比。     

Constant heat flux solution for mixed convection boundary layer viscoelastic fluid

The mixed convection boundary layer of a viscoelastic fluid past a circular cylinder with constant heat flux is discussed. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing non-similar partial differential equations are transformed into dimensionless forms and then solved numerically using the Keller-box method by augmenting an extra boundary condition at infinity. Numerical results obtained in the form of velocity distributions and temperature profiles are presented for a range of values of the dimensionless viscoelastic fluid parameter. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the momentum boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point.     

Stretch-induced wrinkling of polyethylene thin sheets: Experiments and modeling

This paper presents a study on stretch-induced wrinkling of thin polyethylene sheets when subjected to uniaxial stretch with two clamped ends. Three-dimensional digital image correlation was used to measure the wrinkling deformation. It was observed that the wrinkle amplitude increased as the nominal strain increased up to around 10%, but then decreased at larger strain levels. This behavior is consistent with results of finite element simulations for a hyperelastic thin sheet reported previously (Nayyar et al., 2011). However, wrinkles in the polyethylene sheet were not fully flattened out at large strains (>30%) as predicted for the hyperelastic sheet, but exhibited a residual wrinkle whose amplitude depended on the loading rate. This is attributed to the viscoelastic response of the material. Two different viscoelastic models were adopted in finite element simulations to study the effects of viscoelasticity on wrinkling and to improve the agreement with the experiments, including residual wrinkles and rate dependence. It is found that a parallel network model of nonlinear viscoelasticity is suitable for simulating the constitutive behavior and stretch-induced wrinkling of the polyethylene sheets.     

热环境中黏弹性功能梯度材料及其结构的蠕变

基于经典的对应原理, 将 Mori-Tanaka 方法等细观力学结果推广于定常温度环境下的黏弹性情形. 根据泊松比与时间呈弱相关的特点, 给出 Laplace 象空间中功能梯度材料的松弛模量和热膨胀系数, 并直接建立耦合热应变的多维黏弹性本构关系. 在此基础上, 求解黏弹性功能梯度圆柱薄壳在热环境中的轴对称弯曲蠕变变形问题. 考虑材料热物参数的温度相关性, 首先确定稳态温度场, 导出相空间中轴对称弯曲变形的解析解, 采用数值反演得到蠕变变形. 算例表明, 蠕变初期, 热环境的影响明显, 随着时间增加, 热应力松弛, 影响逐渐消失. 当圆柱薄壳受轴压时, 相比于两端固支, 两端简支的端部变形更加明显. 通过圆柱薄壳的轴对称弯曲求解, 给出体积含量呈任意分布的黏弹性功能梯度结构在热机载荷下的蠕变分析途径.      

Modelling of length scale effects in viscoelastic materials

A length scale dependent linear viscoelastic constitutive model is developed. First, a generalized Maxwell model that can describe standard linear viscoelasticity is considered. The model is then generalized to include effects of viscous strain gradients. The formulation of additional boundary conditions resulting from the strain gradient terms is discussed. It is shown that the boundary conditions can be formulated in terms of a surface energy. As an example, the thermal expansion of a thin polymeric film on an elastic substrate is analyzed. It is shown that the relative thermal expansion in the thickness direction of the film decreases for sufficiently small film thicknesses, in accordance with experimental observations. This effect cannot be captured by a standard thermo-viscoelastic theory, which gives a constant thermal expansion independent of film thickness.     

非牛顿流体在非均质油藏渗流压力场实验

在非均质油藏模型上进行非牛顿流体流动物理模拟实验，对比研究水驱、聚合物驱和交联聚合物对提高石油采收率的影响．通过布置高精度的压差传感器测量不同驱替过程模型中的渗流压力场的动态变化，成胶后的交联聚合物封堵了高渗条区，改变了油藏内流体流动方向，驱替出低渗区内油，提高了采收率．     

Selective withdrawal of polymer solutions: Experiments

Selective withdrawal refers to the process of drawing one or both components of stratified fluids through a tube placed near their interface. This paper reports an experimental study of selective withdrawal of viscous and viscoelastic liquids under air. The key mechanism of interest is how the viscoelasticity in the bulk liquid affects the evolution of the free surface. This is investigated by comparing the interfacial behavior between a Newtonian silicone oil and two dilute polymer solutions. While the surface undergoes smooth and gradual deformation for Newtonian liquids, for the polymer solutions there is a critical transition where the surface forms a cusp from which an air jet emanates toward the suction tube. This transition shows a hysteresis when the flow rate or location of the tube is varied. In the subcritical state, the surface of polymer solutions deform much more than its Newtonian counterpart but the deformation is more localized. The interfacial behavior of the polymer solutions can be attributed to the large polymer stress that develops under the surface because of predominantly extensional deformation.     

Effects of residual stress and viscous and hysteretic dampings on the stability of a spinning micro-shaft

This study examines the effects of the residual stress and viscous and hysteretic dampings on the vibrational behavior and stability of a spinning Timoshenko micro-shaft.A modified couple stress theory(MCST) is used to elucidate the sizedependency of the micro-shaft spinning stability,and the equations of motion are derived by employing Hamilton's principle and a spatial beam for spinning micro-shafts.Moreover,a differential quadrature method(DQM) is presented,along with the exact solution for the forward and backward(FW-BW) complex frequencies and normal modes.The effects of the material length scale parameter(MLSP),the spinning speed,the viscous damping coefficient,the hysteretic damping,and the residual stress on the stability of the spinning micro-shafts are investigated.The results indicate that the MLSP,the internal dampings(viscous and hysteretic),and the residual stress have significant effects on the complex frequency and stability of the spinning micro-shafts.Therefore,it is crucial to take these factors into account while these systems are designed and analyzed.The results show that an increase in the MLSP leads to stiffening of the spinning micro-shaft,increases the FW-BW dimensionless complex frequencies of the system,and enhances the stability of the system.Additionally,a rise in the tensile residual stresses causes an increase in the FW-BW dimensionless complex frequencies and stability of the micro-shafts,while the opposite is true for the compressive residual stresses.The results of this research can be employed for designing spinning structures and controlling their vibrations,thus forestalling resonance.     

A Numerical Study of Instability Control for the Design of an Optimal Policy of Enhanced Oil Recovery by Tertiary Displacement Processes

In this paper, we consider the problem of control of hydrodynamic instability arising in the displacement processes during enhanced oil recovery by SP-flooding (Surfactant?CPolymer). In particular, we consider a flooding process involving displacement of a viscous fluid in porous media by a less viscous fluid containing polymer and surfactant over a finite length which in turn is displaced by a even less viscous fluid such as water. The maximum stabilization capacities of several monotonic and non-monotonic viscous profiles created by non-uniform polymer concentration are studied in the presence of interfacial tensions created by surfactants. The study has been carried out numerically to determine and characterize the most optimal viscous profiles of each family. Similarities in optimal monotonic viscous profiles of this constant-time injection policy and other injection policies by previous workers are noted. The presence of interfacial instability (due to viscosity jump) and layer instability (due to viscosity gradient) in appropriate proportions has been numerically demonstrated to be a necessary condition for monotonic as well as optimal non-monotonic profiles except in the limiting case of infinite time injection in which case maximum stabilization appears to result from pure layer instability. It has also been demonstrated numerically that the optimal non-monotonic viscous profiles can have better stabilization potential than the optimal monotonic profiles. Many other new features of this injection policy which have not been recognized before have been discussed.     

Pore Scale and Macroscopic Displacement Mechanisms in Emulsion Flooding

The flow properties of complex fluids through porous media give rise to multiphase flow displacement mechanisms that operate at different scales, from pore-level to Darcy scale. Experiments have shown that injection of oil-in-water emulsions can be used as an effective enhanced-oil recovery (EOR) method, leading to substantial increase in the volume of oil recovered. Pore-scale flow visualization as well as core flooding results available in the literature have demonstrated that the enhanced recovery factor is regulated by the capillary number of the flow. However, the mechanisms by which additional oil is displaced during emulsion injection are still not clear. In this work, we carried out two different experiments to evaluate the effect of emulsion flooding both at pore and macro scales. Visualization of the flow through sand packed between transparent plexiglass parallel plates shows that emulsion flooding improves the pore-level displacement efficiency, leading to lower residual oil saturation. Oil recovery results during emulsion flooding in tertiary mode (after waterflooding) in parallel sandstone cores with very different absolute permeability values prove that emulsion flooding also leads to enhancement of conformance or volumetric sweep efficiency. Combined, the results presented here show that injection of emulsion offers multiscale mechanisms resulting from capillary-driven mobility control.     

An investigation of non-newtonian flow past a sphere

Any experimental work on the flow of a polymer solution or any theoretical analysis on the basis of a visoelastic constitutive equation does not always bring out viscoelastic effects but may be showing a non-Newtonian viscosity effect. Therefore, in order to obtain a clear understanding about viscoelastic effects, it is desirable to have a sufficient knowledge of the non-Newtonian viscosity effect. To facilitate this, finite-difference numerical solutions of non-Newtonian flow were carried out using a non-Newtonian viscous model for the Reynolds numbers of 0.1, 1.0, 20 and 60.Drag force measurements and flow visualization experiments were also performed over a wide range of experimental conditions using polymer solutions. The present work appears to support the following idea: When compared with the Newtonian case on the basis of DV_∞P/η₀, where η₀ is the zero shear viscosity, it is on account of the non-Newtonian viscosity that the friction and pressure drags decrease, that the separating vortices behind the sphere become larger, and that no shift occurs in the streamlines. On the other hand, it is due to viscoelasticity that the normal force drag increases, that the separating vortices behind the sphere become smaller, and that an upstream shift occurs in the streamlines.     

Mathematical simulation of micellar-polymer displacement of oil from flooded strata

The micellar-polymer method of increasing the oil recovery from strata [1] is currently regarded as promising. The method consists of injecting into an oil stratum, which has previously undergone ordinary flooding, a relatively small amount, a slug, of micellar solution (5–10% of of the pore volume), which is propelled through the stratum by slugs of a highly viscous buffer fluid (aqueous solution of a polymer). In turn, the system of slugs is propelled from the injection points to the extraction wells by the water used for ordinary flooding. The displacement of the oil that remains after flooding in the stratum is achieved by a decrease in the coefficient of surface tension at the boundaries of the micellar solution with the oil and the water to the value 10^–2-10^–3 dyn/cm, which leads to a decrease in the amount of fixed oil and also to a control of the mobility of the fluids, which is achieved by varying the concentrations of the components of the micellar solution and the buffer fluid. The main components of micellar solutions are: a hydrocarbon fluid (oil or its fractions), water, surface-active substances. The relationships between the main components, and also the addition of salts and alcohol to the water component have a strong influence on the interaction between the solution and the stratal oil and water [2]. The micellar solution considered in the present paper dissolves oil but does not mix with water; the relationships between the components in it are characteristic of the solutions used to increase oil recovery from strata.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 84–93, November–December, 1982.     

线弹簧和转动弹簧支承粘弹性圆柱体的动力特性

对线、转动弹簧支承三参量模型粘弹性圆柱体轴向流动中的特征方程进行了推导,运用Matlab软件求解了其在轴向流动中的前三阶复频率.给出了当质量比β、量纲为一的延滞时间α和弹性系数比λ一定时,改变量纲为一的弹簧刚度a和转动弹簧b的情况下,三参量模型粘弹性圆柱体的前三阶模态量纲为一的复频率的实部及虚部与流速ν之间的关系曲线图;并分析了量纲为一的弹簧刚度对圆柱体动力特性的影响.研究结果表明:三参量模型粘弹性圆柱体分别处于两端固定和两端自由状态的两种特殊情况:两种情况下,第一阶模态的临界发散速度几乎相同,但当圆柱体两端自由时,第三阶模态发散的无量纲临界流速明显小于两端固定的圆柱体.且当ν=0时,两种情况下的前三阶复频率的虚部都相等.     

Oil–water flows through sudden contraction and expansion in a horizontal pipe – Phase distribution and pressure drop

In this paper, change of flow patterns during the simultaneous flow of high viscous oil and water through the sudden contraction and expansion in a horizontal conduit has been studied. It is noted that these sudden changes in cross-section have a significant influence on the downstream phase distribution of lube oil–water flow. The observation suggests a simple technique to establish core flow as well as a way to prevent pipe wall fouling during the transportation of such oil. A number of interesting differences have been noted during low viscous oil–water flow through the same test rigs. While several types of core annular flow are observed for the former case, a wider variety of interfacial distribution characterizes kerosene–water systems. The pressure profiles during the simultaneous flow of lube oil and water through the sudden contraction and expansion are also studied and compared with low viscous oil–water flows. The pressure profiles are found to be independent of liquid viscosity and the loss coefficients are observed to be independent of flow patterns in both the cases.