Evaluation of the use of capillary numbers for quantifying the removal of DNAPL trapped in a porous medium by surfactant and surfactant foam floods

The capillary number is used to quantify the mobilization potential of organic phases trapped within porous media. The capillary number has been defined in three different forms, according to types of flow velocity and viscosity used in its definition. This study evaluated the suitability of the capillary number definitions representing surfactant and surfactant foam floods by constructing capillary number-TCE saturation relationships. The results implied that the capillary number should be correctly employed, according to scale and fluid flow behavior. This study suggests that the pore-scale capillary number should be used only for investigating the organic-phase mobilization at the pore scale because it is defined by the pore velocity and the dynamic viscosity. The Newtonian-fluid capillary number using the Darcy velocity and the dynamic viscosity may be suitable for quantifying flood systems representing Newtonian fluid behavior. For viscous-force modified flood systems such as surfactant-foam floods, the apparent capillary number definition employing macroscopic properties (permeability and potential gradient) may be used to appropriately represent the desaturation of organic phases from porous media.     

Rheological properties of surface-modified nanoparticles-stabilized CO2 foam

This study investigates the rheological properties of surface-modified nanoparticles-stabilized CO₂ foam in porous media for enhanced oil recovery (EOR) applications. Due to the foam pseudo-plastic behavior, the foam apparent viscosity was estimated based on the power law constitutive model. The results show that foam exhibit shear-thinning behavior. The presence of surface-modified silica nanoparticles enhanced the foam bulk apparent viscosity by 15%. Foam apparent viscosity in the capillary porous media was four times higher than that in capillary viscometer, and foam apparent viscosity increased as porous media permeability increases. The high apparent viscosity of the surface-modified nanoparticles-stabilized foam could result in effective fluid diversion and pore blocking processes and enhance their potential applications in heterogeneous reservoir.     

Heterogeneous/homogeneous and inclined magnetic aspect of infinite shear rate viscosity model of Carreau fluid with nanoscale heat transport

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.     

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.     

The rheology of pseudoplastic fluids in porous media using network modeling

This paper considers the rheology of pseudoplastic (shear thinning) fluids in porous media. The central problem studied is the relationship between the viscometric behavior of the polymer solution and its observed behavior in the porous matrix. In the past, a number of macroscopic approaches have been applied, usually based on capillary bundle models of the porous medium. These simplified models have been used along with constitutive equations describing the fluid behavior (usually of power law type) to establish semiempirical macroscopic equations describing the flow of non-Newtonian fluids in porous media. This procedure has been reasonably successful in correlating experimental results on the flow of polymer solutions through both consolidated and unconsolidated porous materials. However, it does not allow an interpretation of polymer flow in porous media in terms of the flows on a microscopic scale; nor does it allow us to predict changes in macroscopic behavior resulting from variations at a microscopic level in the characteristics of the porous medium such as pore size distribution. In this work, we use a network approach to the modeling of non-Newtonian rheology, in order to understand some of the more detailed features of polymjer flow in porous media. This approach provides a mathematical bridge between the behavior of the non-Newtonian fluid in a single capillary and the macroscopic behavior as deduced from the pressure drop-flow rate relation across the whole network model. It demonstrates the importance of flow redistribution within the elements of the capillary network as the overall pressure gradient varies. As an example of a pseudoplastic fluid in a porous medium, we consider the flow of xanthan biopolymer. This polymer is important as a displacing fluid viscosifier in enhanced oil recovery applications and, for that reason, a considerable amount of experimental data has been published on the flow of xanthan solutions in various porous media.     

Experimental study of the immiscible displacement of shear-thinning fluids in pore networks

The pore scale mechanisms and network scale transient pattern of the immiscible displacement of a shear-thinning nonwetting oil phase (NWP) by a Newtonian wetting aqueous phase (WP) are investigated. Visualization imbibition experiments are performed on transparent glass-etched pore networks at a constant unfavorable viscosity ratio and varying values of the capillary number (Ca), and equilibrium contact angle (theta(e)). Dispersions of ozokerite in paraffin oil are used as the shear-thinning NWP, and aqueous solutions of PEG colored with methylene blue are used as the Newtonian WP. At high Ca values, the tip splitting and lateral spreading of WP viscous fingers are suppressed; at intermediate Ca values, the primary viscous fingers expand laterally with the growth of smaller capillary fingers; at low Ca values, network spanning clusters of capillary fingers separated by hydraulically conductive noninvaded zones of NWP arise. The spatial distribution of the mobility of shear-thinning NWP over the pore network is very broad. Pore network regions of low NWP mobility are invaded through a precursor advancement/swelling mechanism even at relatively high Ca and theta(e) values; this mechanism leads to irregular interfacial configurations and retention of a substantial amount of NWP along pore walls; it becomes the dominant mechanism in displacements performed at low Ca and theta(e) values. The residual NWP saturation increases and the end WP relative permeability decreases as Ca increases and both become more sensitive to this parameter as the shear-thinning behavior strengthens. The shear-thinning NWP is primarily entrapped in individual pores of the network rather than in clusters of pores bypassed by the WP. At relatively high flow rates, the amplitude of the variations of pressure drop, caused by fluid redistribution in the pore network, increase with shear-thinning strengthening, whereas at low flow rates, the motion of stable and unstable menisci in pores is reflected in strong pressure drop fluctuations.     

微孔中简单流体粘度的分子动力学模拟及关联模型

用分子动力学模拟计算了微孔介质中流体氩在不同温度、不同密度和不同孔径下的剪切粘度.并根据Chapman-Enskog关于硬球流体传递性质的理论以及Heyes的关于Lennard-Jones流体粘度的表达式,提出了两个描述微孔介质中流体粘度的模型,该模型可以计算微孔中流体氩在不同状态下的粘度值.通过与计算机模拟值的比较,证明这两个微孔流体粘度模型是可用的.     

Experimental and modeling study of Newtonian and non-Newtonian fluid flow in pore network micromodels

The in situ rheology of polymeric solutions has been studied experimentally in etched silicon micromodels which are idealizations of porous media. The rectangular channels in these etched networks have dimensions typical of pore sizes in sandstone rocks. Pressure drop/flow rate relations have been measured for water and non-Newtonian hydrolyzed-polyacrylamide (HPAM) solutions in both individual straight rectangular capillaries and in networks of such capillaries. Results from these experiments have been analyzed using pore-scale network modeling incorporating the non-Newtonian fluid mechanics of a Carreau fluid. Quantitative agreement is seen between the experiments and the network calculations in the Newtonian and shear-thinning flow regions demonstrating that the 'shift factor,'alpha, can be calculated a priori. Shear-thickening behavior was observed at higher flow rates in the micromodel experiments as a result of elastic effects becoming important and this remains to be incorporated in the network model.     

Unsteady-State Flow of Flexible Polymers in Porous Media

In this paper we report an investigation of the unsteady-state flow of polymer solutions through granular porous media. The experiments were performed using high-molecular-weight nonionic and anionic polyacrylamides dissolved in water containing NaCl and model porous media obtained by packing silicon carbide (SiC) grains having a narrow grain size distribution. Before injection in porous media, the polymer solutions were carefully filtered according to a method that was proved to be efficient in removing any possibly remaining microgels. The SiC grain surface was passively oxidized by a controlled thermal treatment in order to obtain a surface partially covered by a thin silica layer having adsorption properties similar to those of quartzitic sand. By packing SiC grains of different sizes, porous media having identical adsorption properties and well-known pore throats sizes can be obtained with a good reproducibility. Parameters investigated include pore size, velocity gradient, polymer concentration, and adsorption energy. A striking unsteady-state flow behavior (pressure build-up at constant flow rate) is observed when three conditions are fulfilled: (a) the velocity gradient is larger than that known to be able to induce a coil-stretch transition, (b) the polymer adsorbs on the pore surfaces, and (c) the length of stretched macromolecules is larger than the effective pore throat diameter. When one of these conditions is not satisfied the flow remains steady. These observations are interpreted by a mechanism involving the adsorption and bridging across pore restrictions of elongated chains. We propose to refer to this peculiar mode of polymer adsorption as bridging adsorption. Copyright 2001 Academic Press.     

Determination of the pressure coefficient and pressure effects in capillary flow

General expressions for determining the pressure coefficient and axial distribution of the viscosity and pressure in capillary flow are derived for Newtonian and shear-thinning fluids. The pressure-dependent viscosity model is obtained from the WLF equation as derived from Doolittle's free volume theory. The model has also been derived from Eyring's hole theory for viscosity. Poiseuille's equation is modified to correct for the pressure effect on viscosity. A Newtonian, low-molecular-weight polystyrene and a shear-thinning, high-molecular-weight polystyrene were tested in an Instron capillary rheometer. The axial velocity distribution was found to be negligibly affected by pressure whereas the viscosity was shown to increase markedly with a decrease in volume. The resulting pressure effects on the viscosity of both samples were analyzed by using the derived expressions.     

Flow of non‐newtonian fluids in porous media

The study of flow of non‐Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield‐stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non‐Newtonian fluids are generally classified into three main categories: time‐independent whose strain rate solely depends on the instantaneous stress, time‐dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article, the key aspects of these fluids are reviewed with particular emphasis on single‐phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore‐scale network modeling. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Destabilizing effect of time-dependent oblique magnetic field on magnetic fluids streaming in porous media

The present work studies Kelvin-Helmholtz waves propagating between two magnetic fluids. The system is composed of two semi-infinite magnetic fluids streaming throughout porous media. The system is influenced by an oblique magnetic field. The solution of the linearized equations of motion under the boundary conditions leads to deriving the Mathieu equation governing the interfacial displacement and having complex coefficients. The stability criteria are discussed theoretically and numerically, from which stability diagrams are obtained. Regions of stability and instability are identified for the magnetic fields versus the wavenumber. It is found that the increase of the fluid density ratio, the fluid velocity ratio, the upper viscosity, and the lower porous permeability play a stabilizing role in the stability behavior in the presence of an oscillating vertical magnetic field or in the presence of an oscillating tangential magnetic field. The increase of the fluid viscosity plays a stabilizing role and can be used to retard the destabilizing influence for the vertical magnetic field. Dual roles are observed for the fluid velocity in the stability criteria. It is found that the field frequency plays against the constant part for the magnetic field.     

Viscoelastic Drag of Particles Settling in Wormlike Micellar Solutions of Varying Surfactant Concentration

Wormlike micellar octadecyl trimethyl ammonium chloride (OTAC) solution is a self-assembled fracturing fluid used to carry proppants into fractures in oil recovery. Slow settling velocity of proppant is desirably resulted from the viscoelastic drag with low viscosity of fracturing fluids for fracturing work. Steel spheres, as a substitute for proppants, fall into three semi-dilute OTAC solutions. The steady rheology demonstrates that OTAC solutions are divided into shear-thickening and shear-thinning regimes by the critical shear rate. The applied steel spheres always lie in the shear-thickening regime of the 2.8 wt% OTAC solution with aggregated micelles as their characteristic shear rates are less than the critical shear rate of the solution. Strong shear-thickening viscous drag results in lower settling velocity of steel spheres. Most of the applied steel spheres, on the other hand, lie in the shear-thinning regime of the 4 wt% OTAC solution with orientated micelles. Although the latter solution has small dissipation coefficient, high Weissenberg number, and consequently high elastic effect, the shear-thinning viscosity results in higher settling velocity of steel spheres.     

Analysis of electroosmotic flow of power-law fluids in a slit microchannel

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.     

漆酚基乳化剂对水包油型生漆乳液流变行为的影响

以漆酚基乳化剂(UE)和聚乙烯醇(PVA)为混合乳化剂制备了水包油(O/W)型生漆乳液(RLE),用RHEOMETER(R/S)对RLE的流变性进行了研究.讨论了UE10浓度(cUE10)、混合乳化剂浓度(cME)、UE的结构对RLE流变性的影响.结果表明,RLE的黏度随着cUE10的增加而增大,用不同cUE10制备的RLE都有剪切变稀的特性,表现出假塑性流体的行为;当cME≤6.7%,RLE表现出假塑性流体的行为,而当cME≥10.0%,RLE则表现出膨胀型流体的特征;用不同UE制备的RLE均表现出假塑性流体的特征,其流变行为符合Herschel-Bulkley模型,随着UE分子中聚氧乙烯链的增长,RLE的黏度增大,RLE粒子间所形成的某种静态空间网状结构强度增强.     

Onset conditions for bicontinuity of domain structure in polymeric fluids

Recent investigations have somewhat clarified a supermolecular organization of polymeric fluids. Specifically, it has been found that at certain conditions water solutions of poly(ethylene oxide) (PEO) are two-phase fluids. As molecular weight increases one of two phases—the phase rich in polymer—first separates out as scattered globules. Then it builds up a liquid–crystalline fibrillar network. This network produces characteristic properties of PEO solutions: shear-thinning, elasticity, dynamic birefringence, macromolecular destruction. Most likely, similar properties of other polymeric fluids are generated in an analogous way. In this work for the same system, experiments have been pursued to find a surface that separates in the “intrinsic viscosity, concentration, temperature” space regions of the globular and the network state. Two methods were used. The first one is based on the fact that scission of PEO molecules stops at transition from the network state to the globular state. The second method employs the fact that only the network solutions possess shear-thinning properties. Previously published results are also used. The action of temperature was not detected. With increasing the intrinsic viscosity, the boundary concentration decreases. Data reveal that by dilution one can always obtain a solution in which PEO is not susceptible to destruction. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3208–3216, 1999     

Wall Effects on Spheres Settling Through Non-Newtonian Fluid Media in Cylindrical Tubes

Experimental study is performed to understand and quantify the wall and eccentric retardation effects on spheres settling in shear thinning and shear-thinning viscoelastic fluids over a wide range of diameter ratios (0.02 < λ < 0.9). The four-parameter Carreau viscosity equation has been chosen to represent the apparent viscosity-shear rate of polyacrylamide solutions. Two new wall factor corrections are presented with excellent agreement compared to experimental data.

The terminal settling velocity of a sphere in bounded fluid is significantly reduced by the presence of confining boundaries, named wall retardation effect that decreases due to the shear-thinning behavior of power law fluids, which is weaken further by the elastic effect of viscoelastic fluids. The wall factors of spheres settling in viscoelastic fluids increase at low ξ up to 50, followed by a horizontal confidence region (0.7 ≤ f ≤ 1) at high ξ. In this region, the wall factor is mainly dominated by fluids’ elasticity, which is more distinguished for small spheres. As the settling spheres approach to the wall (b/R → 1), the neighboring wall exert more intensive retardation that reduce the terminal settling velocity greatly when b/R > 0.6 in pure shear-thinning fluids, and the extra retardation effect of nearby wall increases at high concentration due to the enhanced non-Newtonian property. In contrast, the eccentric effect on settling velocity in viscoelastic fluids is cut down greatly by the fluid's elasticity, which is negligible.     

Shear viscosity of simple fluids in porous media: molecular dynamic simulations and correlation models

Equilibrium molecular dynamic simulations have been used to calculate the shear viscosity of liquid argon in macrovolume system and in porous media at different temperatures, densities and pore widths. On the other hand, based on the Chapman–Enskog theory and Heyes relationships, two correlation models which can describe the viscosity of simple liquids in porous media are proposed as a function of the reduced temperature, density and pore width. The validity of the models is evaluated by comparing the calculated viscosity to simulation data.