A Generalized Model for Field Assessment of Particle Settling Velocity in Viscoelastic Fluids

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.

Settling behavior of spherical particles in eccentric annulus filled with viscous inelastic fluid

The problems of oscillatory flow of a viscoelastic incompressible fluid in a plane channel are solved for a given harmonic oscillation of the fluid flow rate. The transfer function (amplitude–phase frequency response) is determined. Using this function, the effect of the acceleration oscillation frequency and the relaxation properties of fluid on the ratio of the tangential shear stress on channel wall to the velocity averaged over the channel cross-section (cross-sectional velocity) is determined. It is shown that the viscoelastic properties of fluid, as well as its acceleration, are the limiting factors for using the quasi-stationary approach. The found formulas for determining the transfer function for viscoelastic fluid flow in the case of non-stationary stream make it possible to determine the dissipations of mechanical energy in a non-stationary flow of the medium which are of importance for calculation of the control of hydraulic and pneumatic systems.

High-viscosity sweeps have long been used in the drilling industry as a tool to enhance hole cleaning. They have found application in vertical as well as high-angle / horizontal wellbores, with variable results. Sometimes they have been used in tandem pills or in two-part sweeps (e.g., a low-viscosity sweep followed by a high-viscosity sweep, a high-viscosity sweep followed by a high-density sweep, etc.). Determination of the efficiency of sweeps centers on accurately predicting the settling velocity of various sized particles by using equations valid for turbulent and laminar slip. However, nearly all of the previous studies of particle settling velocity have been carried out under static flow conditions, which are rarely present while drilling a wellbore. Recent efforts in the modeling of the hydraulic effects of drill pipe rotation now allow more advanced modeling of the effects of drill pipe rotation on particle settling velocities under dynamic conditions. These recent studies show that use of high-viscosity sweeps to improve hole cleaning is often not as efficient as use of high- density sweeps under the same conditions. This is especially true when larger-sized particles are resident in the wellbore, as when wellbore instability conditions persist. This paper presents data that shows the conditions under which viscous sweeps can be used and those conditions under which they should be supplanted by high-density sweeps for enhanced hole cleaning.

The electrohydrodynamic Kelvin–Helmholtz instability of the interface between two uniform superposed viscoelastic (B´ model) dielectric fluids streaming through a porous medium is investigated. The considered system is influenced by applied electric fields acting normally to the interface between the two media, at which there are no surface charges present. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by either streaming and applied electric fields for the potentially unstable configuration, or streaming only for the potentially stable configuration, as long as perturbations in the direction of streaming are ignored. For perturbations in all other directions, there exists instability for a certain wavenumber range. The instability of this system can be enhanced (increased) by normal electric fields. In the presence of surface tension, it is found also that the normal electric fields have destabilizing effects, and that the surface tension is able to suppress the Kelvin–Helmholtz instability for small wavelength perturbations, and the medium porosity reduces the stability range given in terms of the velocities difference and the electric fields effect. Finally, it is shown that the presence of surface tension enhances the stabilizing effect played by the fluid velocities, and that the kinematic viscoelasticity has a stabilizing as well as a destabilizing effect on the considered system under certain conditions. Graphics have been plotted by giving numerical values to the parameters, to depict the stability characteristics.

In this paper, the behaviors of single bubble in shear-thinning viscoelastic fluids were investigated using OpenFOAM. The volume-of-fluid method was used to capture the interface, and the Giesekus model was adopted for describing the rheological behaviors of shear-thinning viscoelastic fluids. The bubble cusp, negative wake, and velocity jump phenomenons in viscoelastic fluids were obtained, and the effects of wall effect, mobility factor α, and Weissenberg number (Wi) on bubble behaviors were investigated. The results showed that the viscoelastic stress is the main reason for the formation of bubble cusp, the relaxation of polymer macromolecules leads to the formation of negative wake, and the negative wake may be the main reason for the velocity jump. The open angle θ of the negative wake decreases and the distribution region in the vertical direction increases with the increasing Reynolds numbers (Re). In addition, the magnitude of the maximum negative velocity increases with Re and appears further away from the bubble cusp. Moreover, decreasing the wall effect can accelerate the formation of viscoelastic stress and make the bubble cusp appear earlier. As the mobility factor α increases, the viscosity and viscoelastic stress of the fluid near the bubble decrease; this causes the terminal velocity of the bubble to increase. As the Wi increases, both the maximum velocity and terminal velocity of the bubble increase, and the time lag occur. The viscoelastic stress τyy has a longer linear distribution at the tail of the bubble with the increase in Wi.

The settling rate of particles in a fracturing fluid is a major factor in determining the distribution of propping agent in a hydraulic fracture. It is important to know the shape of the prop pack as well as the distribution of prop slurry in a fracture in order to optimize fracturing treatment designs. Terminal settling velocities of prop particles in hydraulic fracturing treatments are governed by fluid viscosity, fluid velocity, frac width, particle size, and particle density. There are a number of equations, based on both theoretical ground and empirical results, that can be used to predict the settling rate and thus the prop distribution in a fracture. Not all of these equations yield the same values for the terminal settling velocity of a particle under the same conditions. In this paper a number of the accepted methods will be reviewed. Predicted terminal settling velocities for a number of different conditions prevalent during a fracturing treatment will be presented. When a particle falls through a liquid containing other particles, the terminal settling velocity of the particle is different than a single particle falling through the same liquid. This effect, termed hindered settling, can be handled in a number of different ways. Several of the equations used to treat hindered settling will be covered along with a critique of their applicability in prop transport calculations.

The settling process of suspended particles in the turbulent flow was investigated by analyzing the Lagrangian motion of a large number of particles in the ocean mixed layer simulated by large eddy simulation (LES), focusing on the role of Langmuir circulation (LC). At the beginning, particles released near the surface are swept down rapidly following the downward jets in the presence of LC, contrary to the case of the horizontally uniform downward propagation in the absence of it. The strong vertical mixing by LC keeps the particle concentration almost uniform after the initial period in the presence of LC, while its mean concentration continues to decrease through particle settling. Under the influence of turbulence in the ocean mixed layer, the particle settling velocity W is always smaller than ws, and W∕ws decreases with decreasing ws∕u∗, where ws is the terminal velocity of a particle in the still fluid and u∗ is the frictional velocity. The presence of LC causes a further decrease of W ultimately, and the difference between the cases with and without LC is the largest at ws∕u∗∼1. The analysis of LES data reveals that particles spend more time in upward flows and that more particles tend to accumulate in the high vorticity region in the presence of LC. It suggests that particle trapping is more likely when the length scale of vortices is larger, which may lead to the decrease of W in the presence of LC. It was also found that the preferential concentration occurs away from the regions of high horizontal vorticity and divergence when ws∕u∗∼1.

Summary Recent studies highlight the significant role of drilling fluid elasticity in particle suspension and hole cleaning during drilling operations. Traditional methods to quantify fluid elasticity require the use of advanced rheometers, which are not suitable for field applications. The main objectives of this study were to investigate the factors influencing drilling fluid viscoelasticity in the field and develop generalized models for determining the viscoelasticity of a drilling fluid using standard field testing equipment. Ninety-three fluid formulations used in this study included field samples of oil-based drilling fluids as well as laboratory samples of water-based, invert emulsion and other oil-based fluids. Basic rheological characterizations of these fluids were done by using a funnel viscometer and a rotational viscometer. Elastic properties of the drilling fluids (quantified in terms of the energy required to cause an irreversible deformation in the fluid’s structure) were obtained from oscillatory tests conducted by using a research-grade rheometer with double gap concentric cylinder geometry. Using an empirical approach, two noniterative models for quantifying drilling fluid elasticity were developed (one for unweighted and the other for weighted drilling fluids) by correlating test results from a funnel viscometer and a rotational viscometer to energy required to cause an irreversible deformation of the fluid’s elastic structure. The generalized models for the unweighted and weighted viscoelastic drilling fluids were able to predict the elasticity of drilling fluids with a mean absolute error of 4.67 and 5.28%, respectively. In addition, the models offer practical versatility by requiring only standard drilling fluid testing equipment to predict viscoelasticity. Experimental results showed that nonaqueous fluid viscoelasticity is inversely proportional to the oil-water ratio (OWR), and the presence of clay greatly debilitates the elasticity of the drilling fluids while enhancing their viscosity. In this paper, we present models for estimating unweighted and weighted drilling fluid elasticity using standard drilling fluid field testing equipment. Furthermore, we proposed a prudent approach for quantifying the viscoelastic property of a drilling fluid by measuring the amount of energy required to irreversibly deform a unit volume of viscoelastic fluid. The new models, combined with the recommended use of the energy dissipation (ED) concept, provide practical tools that can be used for developing optimum drilling fluid formulations and hydraulic programs for effective hole cleaning operations, improved equivalent circulating density (ECD) management, and mitigating barite sag problems.

An experimental study of the settling velocities of single particles in non-Newtonian fluids

SummaryThis paper presents results of an experimental study on how fluid viscoelastic properties would influence the particle removal from the sandbed deposited in horizontal annuli. Water and two different viscoelastic fluids were used for bed-erosion experiments. The particle-image-velocimetry (PIV) technique was used to measure the local fluid velocity at the fluid/sandbed interface, allowing for accurate estimation of the fluid-drag forces and the turbulence stresses.It was found that polymer fluids needed to exert higher level drag forces (than those of water) on the sandbed to start movement of the particles. Results have also shown that, at the critical flow rate of bed erosion, the polymer fluids yielded higher local fluid velocities and turbulent stresses than those of water. Moreover, the local velocity measurements by means of the PIV technique and the resultant bed-shear-stress calculations indicated that enhancing polymer concentration under the constant flow rate should also enhance the drag forces acting on the sandbed. However, these improved fluid hydrodynamic forces did not result in any improvement in the bed erosion. Therefore, the mechanism causing the delay in the bed erosion by polymer additives could not be explained by any decrease in the local fluid velocity and the turbulence.The primary reason for the delayed bed erosion by the polymer fluids was suggested to be linked to their viscoelastic properties. Two possible mechanisms arising from the elastic properties of the polymer fluids that hinder bed erosion were further discussed in the paper. The stress tensor of the viscoelastic-fluid flow was analyzed to determine the normal stress differences and the resultant normal fluid force acting on the particles at the fluid/sandbed interface. The normal force induced by the normal stress differences of the viscoelastic fluid was identified as one of the possible causes of the delayed bed erosion by these types of fluids.

We have studied the poorly understood process of flow-induced structure formation by colloids suspended in shear-thinning fluids. These viscoelastic fluids contain long flexible chains whose entanglements appear and disappear continuously as a result of brownian motion and the applied shear flow. Responsive particle dynamics simulates each chain as a single smooth brownian particle, with slowly evolving inter-particle degrees of freedom accounting for the entanglements. The colloids mixed homogeneously in all simulated quiescent dispersions and they remain dispersed under slow shear flow. Beyond a critical shear rate, which varies depending on the fluid, the colloids aggregate and form flow-aligned strings in the bulk of the fluid. In this work we explore the physical origins of this hitherto unexplained ordering phenomena, both by systematically varying the parameters of the simulated fluids and by analyzing the flow-induced effective colloidal interactions. We also present an expression for the critical shear rate of the studied fluids.

A deeper understanding of the transport processes and pathways of pollutants and plastic debris in aquatic environments, such as water bodies, riverine and coastal zones, is required to effectively understand, prevent, and mitigate marine pollution. In this study, we present an updated version of the high-performance, three-dimensional Canadian Microplastics Simulation (CaMPSim-3D) particle tracking model (PTM), focused on simulating microplastics transport in marine and riverine environments. CaMPSim-3D is an efficient tool that utilizes the principles of ray tracing to enhance the accuracy and performance of particle simulations. New features of the PTM include the implementation of free-slip boundary conditions, particle settling and resuspension mechanisms, and turbulent diffusion, which improve the solution of the diffusion equations. A novel method for computing gradients over triangular prism elements and a double ray casting approach to solve the diffusion equations are also proposed. Additionally, accurate particle settling velocity for circular and elliptical microplastic fibres has been incorporated into the model. Several test cases are presented to demonstrate the new features of the PTM. A sensitivity analysis is performed to investigate the effects of different boundary conditions, particle settling velocity, and turbulent diffusion on the transport and fate of microplastics at two sites: the Saguenay Fjord and the Ottawa River. A test case for model validation against field sampling is also presented for the Ottawa River. The results show that the PTM is efficient, and the use of turbulent diffusion and settling/resuspension mechanisms is necessary, particularly when simulating sinking particles with higher density than water. The findings of this study provide valuable insights into the transport processes of microplastics in aquatic environments and can be used to improve the accuracy of microplastics simulations as well as to identify microplastics accumulation areas.

This study is concerned with modeling of the loss of fine dust from storage piles and their dispersion in the atmosphere. The results of downwind particulate dispersion are tested by means of a two-dimensional wind tunnel model using tracer particles. The study shows that a wind barrier located two to three pile heights upstream will effectively reduce the wind blowing of fine particles from storage piles and the downwind particle density. The tracers used in the experiment are smoke, magnesia, latex, and glass particles. The particle sizes studied range from 15 μm to 75 μm. Experimental results indicate that the effects of particle settling due to gravity force will be negligible when the particle settling velocity is less than 0.03 m/s. If particle size is less than 15 μm, particles will most likely remain in a suspension state over a long distance. Finite difference techniques are used for steady state numerical simulation of particulate dispersion. The effects of the particle sizes, wind velo...

The challenges and risks relating to injectivity decline due to injection of particulate-laden water are well documented in the petroleum industry and elsewhere. Although different theories have been advanced to rationalize this problem, the modeling aspects remain largely unresolved, putting huge investments at risk. By combining the fractional-flow and deep-bed filtration (DBF) theories, this work formulates a new model for describing reservoir impairments due to suspension transport by injection water. The critical settling velocity of the suspended particulates is determined from fractional-flow theory and used to create a condition at which particle settling will occur, dependent on its size. The particle settling velocity as obtained from Stokes law for laminar flow (NRe ≪1) is compared to the critical settling velocity, which is a function of the residence time of the particles, to obtain the optimum transported particle size profile in the formation. Furthermore, the average size of transportable particulates and their total volumes are then obtained and used to determine the volume of deposits which is in turn used to develop a new injectivity decline model for predicting permeability impairment due to the deposition of suspended particles in the porous media. The resulting models are validated by analyzing reported dataset from two water injectors offshore Niger Delta. Overall, the results are reasonable as the impairment model rationalized available field dataset satisfactorily. The developed models should find relevance in the following field applications: (1) quantifying formation damage; (2) optimising water treatment facilities design; (3) implementing an effective and safe backflow operation.