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Here we evaluate the performance of bump arrays to separate large particles from non-Newtonian slurries with Bingham and Cross rheology. Bump arrays in deterministic lateral displacement devices separate large particles from small particles using arrays of staggered posts. Large particles, defined as those with radii larger than the distance between the edge of a post and the stagnation streamline from the next downstream post, must bump toward one side of the device, whereas particles smaller than this distance slalom from entrance to exit without net lateral displacement. Although these devices have been used to separate a wide variety of large particles from blood cells to sand, partition of large particles from non-Newtonian fluids remains unexplored. Yet, an important set of modestly concentrated slurries, including Hanford nuclear waste, displays non-Newtonian rheology. Here we evaluate the influence of non-Newtonian rheology on the large-small particle size cutoff in bump arrays using a model that explores the influence of yield stresses, ratios of zero and infinite shear viscosities, and Cross’s exponent under strictly laminar well-developed conditions. Surprisingly, we find that viscosity ratios and Cross’s exponent make no significant difference on the particle cutoffs between large particles that bump and small particles that slalom around the posts from entrance to exit. In contrast, we find that yield stresses do significantly affect the size cutoff. As the yield stress increases, velocity profiles become more plug like lowering the size cutoff. For nuclear waste separations where removing large particles is a priority, increasing yield stresses is conservative.

The prediction of frictional pressure loss in many oil wells drillings is of the utmost importance. Most studies in this area concerned fluid flow in pipes and annulus in order to predict friction losses. However, studies on the tool-joint effect in frictional pressure estimations were limited to only a few experimental and theoretical studies on water-based power-law drilling muds. (Tool-joint is the part in which two drill strings connect where the annulus has a gradual decrease and increase, respectively). The tool-joint plays an important role in extending the drill pipe, and its effect on pressure losses cannot be ignored. As of today, drilling muds must have certain qualities such as providing formation integrity, transporting the cuttings from bit to surface, drill pipe lubrication and heat transfer, and low-pressure loss to perform as a qualified and effective drilling fluid. Therefore, drilling muds have become more complex and expensive, and the process of choosing appropriate drilling muds is of great importance. For this reason, oil-based viscoplastic drilling muds are being used in more drilling operations, but for these drilling muds, almost no studies were conducted to predict the effect of the tool-joints on flow behavior and pressure loss. In this paper, the behavior of fluid flows and frictional pressure losses in weld-on tool-joints of different grades according to the IADC standard manual was studied using CFD simulations. The simulations were conducted using a drilling fluid with viscoplastic properties, following the Herschel–Bulkley model of Non-Newtonian fluids. And the characteristics of fluid flows in these tool-joints under different thermal boundary conditions were studied. The results show that tool-joints significantly affect the frictional pressure loss in the annulus. We also provided an accurate pressure loss prediction for the flow of oil-based viscoplastic muds passing through the tool-joint geometry. Furthermore, assuming the thixotropic behavior using the Moore-Cheng model for the drilling mud, the results showed that the flow behavior does not differ significantly from the Herschel-Bulkley drilling fluid in the range of study.

Slug flow is one of the most common flow patterns in non-Newtonian two-phase flow in pipes. It is a very common occurrence in gas-liquid two-phase flow in the pipe. Usually, it is an unfavorable flow pattern due to its unsteady nature, intermittency as well as high pressure drop. The differences between slug flow and elongated bubble flow are not clear because usually these two types of flow combined under one flow category. In general, these two-phase flow regimes are commonly defined as intermittent flow. In the present study, pressure gradient, and wave behavior in slug flow have been investigated depending on experimental work. In addition, void fraction has been estimated regarding available superficial liquid and gas velocities. The experimental records of superficial velocities of gas and liquid for slug flow and other flow patterns is used to create flow regime map for the gas non-Newtonian flow system. The effect of investigated flow regime velocities for non-Newtonian/gas flow on pressure drop and void fraction is reported. Pressure drop has been discovered to be reduced in slug flow more than other flow patterns due to high shear thinning behavior.

A directional drilling operation may include one or more bending sections along the drilling profile. These bend sections are the critical segments from the hole cleaning point of view. In this study, a computational fluid dynamic (CFD) method was used to investigate the hole cleaning behaviour in annulus bending section. Eulerian-Eulerian multiphase flow model was adopted in this study. The developed CFD model was validated with experimental data. Different non-Newtonian Herschel Bulkley fluids were used to simulate the drilling mud. Solid cuttings of different sizes (2 mm, 4 mm, and 5 mm) were used to replicate the drill cuttings. Different fluid flow rate (0.5 m/s, 1.0 m/s, 1.5 m/s and 2.0 m/s) were investigated to observe the solid settling tendency in the horizontal and bending section. Cuttings accumulation behaviour at different bending radius (10 inch. and 20 inch.) and bending angle (15°, 30°, and 60° from horizontal) were investigated. The simulation study shows that higher viscous fluid performs better hole cleaning at low mud velocity. Furthermore, a turbulent flow regime performs better solid transport in the bending section. Finally, this study summarizes the hole cleaning behaviour of a bend section for a range of fluid velocity, cuttings size and radius of curvature and inclination.

In-situ cutting transport measurement is essential to understand the hydrodynamics and operational parameters required for efficient annulus cleaning. Electrical resistance tomography (ERT) has been a promising method in many industrial applications. This study aimed to provide comprehensive information on the use of a non-invasive ERT method to examine the volume fraction of solids in the presence of non-Newtonian fluid (0.5 wt percent of Flowzan) in a directional drilling annulus (80–90° from vertical orientation). The experiments were performed in a horizontal flow loop system where the annulus segment was 240 (6.16 m) inch long with an inner and outer diameter of 2.5 inches (6.4 cm) and 4.5 inches (11.4 cm), respectively. The results obtained indicated that the ERT device could effectively detect the volume fraction of the solids in the presence of non-Newtonian fluid (Flowzan) under different drilling conditions. Results also showed that the annulus’ successful cleaning was observed with an increase in fluid mass flow rates indicated the relative increase in cuttings volumes (AVF = 7 to 9%). Besides, the rotation of the drill pipe often had a beneficial effect on cutting transport. Furthermore, it was observed that both (30%) eccentricity and inclination (80–85 °) cause a reduction in cutting volume fraction. Therefore, this study will provide an avenue for the industrial implementation of in situ ERT measurement technology in directional drilling operations, particularly in the case of non-Newtonian drilling fluids.

Plug and abandonment (P&A) of oil and gas wells is an essential process to prevent the oil and gas reservoir fluids migration over time and possibly contaminating other formations and also fresh water resources. In order to plug and abandon a well, a high quality cement plug placement is required. One of the most common methods of cement plug placement is the dump bailing method. In this method, a fixed volume of cement is dumped using a bailer on a mechanical plug in the wellbore. The cement slurry occupies the wellbore and also the annular region outside the dump bailer. In the processes of cement slurry placement, an extensive range of Newtonian or non-Newtonian fluids is used to remove the in-situ fluid (drilling fluid or water) in the wellbore. Based on the large number of parameters such as the density and viscosity differences between the fluids, the geometry type (pipe, annulus, etc.), the operation conditions (velocity, geometry inclination, dumping height), various kinds of placement and mixing flows can occur, and different flow regimes (e.g. inertial, viscous) can develop. In this paper, we experimentally study the placement of a heavy fluid to replace an in-situ light fluid in an inclined closed-end pipe (representative of the dump bailing method). The two fluids are Newtonian and miscible, and they have the same viscosity. We investigate the effects of some of the flow parameters such as the dumping height, the pipe inclination, and the inflow velocity of the heavy fluid on the degree of mixing and the placement quality and efficiency. Our results show that the the most efficient displacement happens with the shortest dumping height and at lower inclination from vertical. Also, a high inflow velocity displaces the light fluid promptly with more mixing in comparison with a low inflow rate. The results can help us to develop strategies for improving the dump bailing method in the P&A of the oil and gas wells.

Two-phase flow of gas/Newtonian and gas/non-Newtonian fluid through pipes occurs frequently in the chemical industry as well as in petroleum refining. Extensive experimental and theoretical research has been carried out on these systems in order to better understand their behaviour under different conditions regarding pressure, temperature and mixture concentrations. In this study, experimental apparatuses are used to investigate two-phase flow of gas/liquid systems through pipes. Air is used as the gas in the experiments, while water is used as the Newtonian fluid and Xanthan gum as the non-Newtonian fluid. The objectives of the study are to compare pressure drops when the same gas flows simultaneously with Newtonian and non-Newtonian fluids through tubes. The comparison here is between experimental pressure drops and estimated pressure drops, based on available empirical correlations for gas/Newtonian and gas/non-Newtonian flow. The trend exhibited by the pressure drops in both systems helps us to better understand the relationship between mixture flow pressure drops in Newtonian and non-Newtonian fluids and thereby develop a new experimental model. The tube diameter for the flow loop is 3/4 inch and the flow type ranges from transient to turbulent.

Static and dynamic performance parameters of two-lobe journal bearing, working with non-Newtonian lubricant has been obtained. Krieger-Dougherty model is used to obtain the effective viscosity of nano-lubricant for a given concentration of solid-particle in base lubricant. Modified Reynolds equation is solved to obtain bearing performance parameters for couple stress model and variable viscosity model. Dynamic coefficients are also determined for various couple stress parameter. Results reveal a noticeable increase in flow co-efficient and load carrying capacity while there is a decrease in friction variable. It also reveals a significant betterment in dynamic co-efficient of bearing.

Numerical simulation of human milk flow inside the breast ductal system is carried out to investigate the impact of milk flow properties, specifically viscosity, on the flow regime. The geometry of the ductal system is assumed as a rigid body with six bifurcation levels. The vacuum pressure, obtained from clinical investigations, is applied as boundary conditions for numerical analysis. The simulations are performed by considering both Newtonian and Non-Newtonian milk flow properties. The streamlines of velocity fluid, wall shear stress, and milk flow expression for these two models are discussed. The results show that the non-Newtonian fluid has a higher magnitude of velocity compared to the Newtonian fluid, which leads to a greater amount of milk expression.

In this paper, we have applied a recently-developed numerical technique to study the three-dimensional dynamics of a confined air bubble rising in shear thinning and shear-thickening power-law fluids. The method is a blend of Volume of Fluid and Level Set methods and incorporates a Sharp Surface Force Method (SSF) for surface tension forces by solving a second Pressure Poisson Equation (PPE). The gas-liquid interface is captured by an equation for the liquid volume fraction and advected using the geometry reconstruction method. The interface normal and curvature are computed using level-set and height function methods. The accurate representation of the interface and interfacial forces significantly suppressed the spurious velocities commonly observed with conventional volume of fluid method and the Continuum Surface Force (CSF). The algorithm is implemented in a in-house code called CUFLOW and runs on multiple GPUs platform. We explored the effects of fluid rheology, Bond number, and wall confinement on bubble’s transient shape, rise velocity, rise path, and generated vortex structures. The power-law index is varied from 0.25 to 1.50 covering shear-thinning and shear-thickening regimes. Three Bond numbers (Bo = 2, 10 and 50) and three confinement ratios (Cr = 4, 6 and 8) are considered, and their impacts on bubble’s dynamics are analyzed. For the range of parameters examined here, bubble motion in a shear-thinning fluid is seen to be unsteady with significant shape oscillations. The bubble rises with a secondary motion in the cross-sectional plane along with its primary vertical rise. However, in the Newtonian and shear-thickening fluids, the bubble’s shape is seen to reach a steady-state in a relatively short time and rise with only minor deviations from the vertical path.

A pressure driven electroosmotic flow (EOF) is numerically studied in a slit micro-channel with alternating hydrodynamic slip patches. The coupled Poisson-Boltzman-Navier Stokes equations dealt with external electric potential are solved for the flow enhancement of non-Newtonian fluids in microfluidic domain, which is a big challenge in the transportation and mixing of fluids in BioMEMS devices as the drag effect is very strong along the walls. This effect can be minimized with the use of slip boundary conditions by the coupling effects of liquid-liquid or gas-liquid interface positioning. In the present article, the fluid is considered to be a power-law fluids which is driven due to the coupling effects of two superimposed electric fields: the externally imposed electric field and the induced potential. An additional pressure gradient is created by the electrokinetic pumping to generate a higher velocity gradient in the presence of viscous dissipation and Joule heating effects. The analytical quantification of the electroosmotic flow velocity and temperature distribution is made and compared with the numerical results due to the staggered grid based finite volume method. The results are presented in terms of flow enhancement factor (Ef) (provides maximum species transport) and the average entropy generation due to fluid friction, viscous dissipation and Joule heating effect. The advantages and disadvantages of utilizing slip conditions are discussed which has large scale applications on drug delivery, DNA analysis and sequencing and especially biomedical applications, since cell damage due to pumping will be minimized compared to the micro pumps with moving valves, blades and pistons.

In this study, a computational examination of Taylor bubbles was performed for gas/non-Newtonian fluid two-phase flows developed in a minichannel T-junction mixer with a hydraulic diameter of 1 mm. The investigations employed three separate aqueous xanthan gum solutions at concentrations of 0.05, 0.1 and 0.15 w/w, which are referred to as non-Newtonian (yield power-law) fluids. The effective concentration of the xanthan gum solutions and superficial velocity of the inlet liquid phase on the length, velocity, and shape of the Taylor bubbles was studied using the ANSYS FLUENT 19 software package. The simulation results show an increase in bubble velocity with increasing film thickness, particularly in solutions of higher viscosity XG-0.15%. Furthermore, bubble lengths decreased as the xanthan gum concentrations increased, but bubble shapes underwent alterations when the concentrations increased. Another interesting result of the tests shows that when the liquid inlet velocity increases, bubble lengths decrease during lower liquid superficial velocity, whereas during higher velocities, they change only slightly after increases in concentration. Finally, with increasing XG concentration, the liquid film thickness around the bubble increased. The results show good agreement with correlations after modifying a capillary number (Ca*) for non-Newtonian liquids in all cases.

We present a numerical investigation of laminar miscible displacement flows in narrow, vertical, eccentric annuli. This study is motivated by the primary cementing stage of oil and gas well production, where successful displacement of drilling mud is crucial for the well integrity and zonal isolation. The large number of characterizing parameters makes a complete description of such flows challenging. In turn, this means that the design of effective strategies for primary cementing is a difficult task. As a result the existing literature is mostly based on non-inertial Hele-Shaw models and experiments in narrow annuli, where the dimensionality of the problem is reduced. In this preliminary study, we run a series of three-dimensional numerical simulations, using a Volume of Fluid (VOF) method to capture the interface between the fluids. Both Newtonian and non-Newtonian fluids are considered, and a variety of different phenomena are observed, e.g. dispersive spikes, static layers, instabilities and secondary flows. The range of flow parameters used in the simulations are similar to existing experimental data to allow for a preliminary comparison. The results show qualitative agreement with the experiments and gap-averaged models.

The determination of the slip velocity, or whether a solid particle will sediment, during its transport is of prime importance for hole cleaning evaluations during drilling operations. Yet, this task is complexified by the asymmetry of the annulus when the central pipe axis does not coincide with the borehole central line and when the inner string rotates, especially since drilling fluids typically follow a yield stress power law rheological behavior. This paper describes the modelling of the movement of a particle in such conditions yet with the following simplifications: the inner tube is eccentric but has a uniform movement, the shape of the particle is assimilated to a prolate, the change of shear rates in the fluid around the slipping particle is neglected and collisions between particles are not considered. Otherwise, gravitational effects are incorporated by accounting for the mass density difference between the particle and the surrounding fluid mixture and by considering the borehole inclination. The particle spin is also estimated as it plays an important role in the determination of the drag and lift forces. The solution to the differential equations that describe the time evolution of the position and orientation of the particle, depend largely upon the initial conditions. Therefore, an ensemble of boundary conditions is generated at a starting cross-section along the annulus and the resulting particle trajectories are estimated. It is then possible to estimate a probabilistic slip velocity for particles of the considered dimensions, far away from the entrance region. This probabilistic approach allows to define a critical transport fluid velocity as the lower limit of the bulk fluid velocity by which no particle risk to settle. Similarly, one can define a critical settling fluid velocity as the upper limit of the bulk fluid velocity where every particle will sediment regardless of the initial conditions. With the described modelling of the particle movement and its associated statistical methods, it is possible to quantitatively estimate the spatial distribution of particles in any cross-section. For those particles that get trapped between the tool-joint and the borehole, it is then possible to estimate their size reduction by grinding, resulting from the rotation of the tool-joint on the borehole wall. The grinding process impacts the particle size distribution passed a tool-joint. By applying this method iteratively up to the annulus outlet, it is possible to estimate the particle size distribution of the drill-cuttings when they arrive at the shale-shakers.

In this paper we present results from flow loop experiments with an oil-based drilling fluid with micronized barite as weight materials. The use of micronized barite allows using lower viscosity drilling fluid, providing non-laminar flow, which is advantageous for particle transport in near-horizontal sections. While transition to turbulence and turbulent flow of non-Newtonian fluids has been well studied both theoretically and experimentally, there are very few published results on the effect of wellbore wall properties on flow regime transition and turbulence. This is relevant because horizontal sections are often open-hole with less well-defined surfaces than a steel casing surface. We have conducted a series of flow experiments with and without cuttings size particles in a 10 m long annular test section using steel and concrete material to represent the wellbore wall of a cased and open hole section. In both cases the annulus was formed by a freely rotating steel pipe of 2” outer diameter inside a 4” diameter wellbore. Experiments were conducted at 48°, 60° and 90° wellbore inclination from vertical. The two materials result in different hydraulic behaviour without particles with stronger turbulence when using concrete wellbore wall material than when using steel casing. While there is negligible difference at low flow rates, at 0.8 m/s and below, there is an increasing difference as the flow rate increases and becomes transitional to turbulence. Hole cleaning is found to differ dependent on the wall material. However, the effect on hole cleaning is less clear than for the pressure loss.

Influence of the rheological model selection on the flow and mass transfer behavior of human blood in a separated and reattached flow region is investigated. Newtonian and non-Newtonian hemorheological models that account for the yield stress and shear-thinning characteristics of blood are used. The conservation of mass, momentum, and species equations as well as the Herschel-Bulkley constitutive equation are solved numerically using a finite-difference scheme. A parametric study is performed to reveal the impact of flow restriction and rheological modelling on blood-borne oxygen exchange with the confining walls. The wall mass transfer rates within the separated and reattached regions display a strong dependency on the used hemorheological model. Newtonian and non-Newtonian models result in a peak wall mass transfer rate within the recirculation region. However, non-Newtonian models that account for the yield stress and shear-thinning effects predict a substantial, highly localized, drop in the wall mass transfer rates of oxygen, at the reattachment point.

Wall shear stress (WSS) distribution in stenosed arteries has been known as an important hemodynamic factor to correlate with atherosclerosis and associated disturbances in blood flow. WSS depends on various factors such as geometric complexity and tortuosity of the artery, stenosis severity and morphology as well as blood rheological properties. We conducted a numerical simulation of blood flow using Ansys CFX software in 9 patient-specific coronary artery models with 3 classes of stenosis severity: mild, moderate and severe. For this purpose, we compared some numerical results between two non-Newtonian models and Newtonian blood flow viscosity using 9 patient-specific coronary artery models including the full range of real (physiological) stenosis, reconstructed from 3DQCA (quantities coronary angiography). Incompressible and steady state form of Navier-Stokes equations were used as governing equations. Flow was considered laminar and artery walls were assumed to be rigid. Results showed that the magnitude of WSS usually increases by decreasing the cross-section area of arteries. Despite the difference in the WSS magnitude between different models in each artery, the trend of variation of WSS along the artery was the same in all three models. The local peak point of WSS along the artery occurs at the stenosis location, same for all models.

In this study, capillary filling of diluted bitumen was evaluated using glass etched microchannel. Glass microchannel was treated using Trichloro(1H,1H,2H,2H-perfluorooctyl) silane that makes the microchannel lyophobic (not favorable for neither hydrophilic nor hydrophobic liquids). Water contact angle, as a degree of hydrophilicity, was changed from 15° for untreated microchannel to 115° for treated microchannel. Measured Capillary filling speed of bitumen in hexane (10% to 60%) was experimentally monitored using white light microscope and compared with Washburn theoretical model. For all samples, a linear relation between square of propagation distance and time was found. However, a deviation between experimental and theoretical values of penetration as a function of time was recorded. Experimental results indicated slower velocity compared to theoretical prediction due to simplifications of the Washburn model. Advancing dynamic contact angle of capillary-driven flow was measured and compared with static contact angle using MATLAB®. It was found that dynamic contact angle was increasing during the penetration in microchannel and application of a constant contact angle leads to higher deviation between experimental and theoretical results.

The mixing performance of a novel design propeller fixed at a position with the angle of −10° combine the inference of the variety of rotation speed and rheology properties were investigated using an ultrasonic Doppler anemometer (UDA) and CFD simulation to investigate the flow patterns and the power consumption in a mixing vessel. The fluids of interest in this research are CMC fluids, which is a type of Walocel CRT 40,000PA powder was added into water to prepare the solutions with the mass concentration which performed shear thinning non-Newtonian fluid properties. As the viscosity of the non-Newtonian fluids varies from the shear rate, rather than a constant value. Therefore, a non-Newtonian power-law model has been selected to describe the properties of the non-Newtonian fluids, and combine with six turbulence models (the standard k-ω model, RNG k-ε, standard k-ε, Realizable k-ε, SST k-ω and Reynolds stress model (RSM))for mechanical agitation of non-Newtonian fluids. Through comparing experiment results, the SST k-ω and Reynolds stress model (RSM) are found more physical than other turbulence models at the design operating point. Furthermore, the CFD simulation results from Reynolds stress model (RSM) and the SST models were validated with the experimental results over the range of rotation speed (small, design, and large rotation speeds), and show that the simulated propeller torque and flow patterns agreed very well with experimental measurements. The velocity field distribution with different operating conditions within selected planes also have been compared with each other and found that for different rheology concentrations and operating conditions, the turbulence model should be properly chosen. The model for simulating non-Newtonian fluid in a stirred vessel in this study can lay a foundation for further optimum research.

This study focuses on numerical simulation and evaluation of a hydraulically powered downhole Thruster. This device is numerically simulated and evaluated using ANSYS Fluent 17.2 to show its generation of pressure pulses that can induce downhole forces that magnify the downhole dynamic weight on bit (DWOB) using drilling mud. Such magnification of the DWOB can produce axial motion of the Thruster. Such axial motions, as proved by many publications can improve the drilling rate of penetration (ROP), release stuck pipes, and reduce frictions in non-vertical wells. The special inner design of the Thruster creates pressure pulses that can provide load impact on the drill bit leading to the increase of WOB that can enhance the drilling performance. The current stage of the study of the Thruster involves a mechanical design of the Thruster by the SolidWorks and an evaluation of the tool function and performance through pressure effect simulation by ANSYS Fluent 17.2. Initially, water is used as the fluid and the main parameters involved in the analysis are pressure and velocity. However, power-law as a non-Newtonian fluid is also used for comparison study in the section of pressure drop analysis. The results are analyzed based on velocity pressure profiles, pressure drops, pressure effects with applications of various back pressures at several planes using water and power-law fluids.

The objective of drilling a well is to prepare a clean hole without obstructions for further casing and production tubing running. Cuttings transport has always been important, but challenging process, especially when drilling long directional wells. Poor hole cleaning causes severe problems, as stuck pipe, extreme torque and drag, difficulties in casing landing, cementing, etc. Extensive studies of cuttings transport, both theoretical and experimental, have been performed to estimate, for example, cuttings concentration and cuttings slip velocity to determine optimal conditions for effective hole cleaning. This paper presents a dynamic analysis of cuttings transport in non-Newtonian fluids based on a transient drift-flux model and an associated numerical scheme AUSMV (advection upstream splitting method) developed by Evje and Fjelde 2002. In this paper, the scheme is modified to simulate cuttings transport dynamically taking into account effects related to pressure, temperature and cuttings slip. During drilling, the heat is transported from the formation into the wellbore and up to the surface. In this paper, the energy balance is enhanced by introducing an analytical temperature model into the AUSMV scheme. The temperature distribution along the well is calculated at the beginning of simulation and kept constant throughout the simulation. Additionally, the AUSMV scheme is improved by considering drilling fluid’s transport- and thermal properties. Transport properties of an oil-based mud, such as viscosity and density, are obtained from experiments. The experimental results were used to determine the coefficients in a linear density model used in the study to investigate the effect of non-Newtonian behavior on the heat transfer, cuttings transport and downhole pressure. Furthermore, a model to calculate the apparent viscosity at various pressures and temperatures was developed based on the experimental results and used to evaluate the impact of viscous forces on the cuttings distribution in the well. Presented numerical scheme solves dynamic cuttings transport problems taking into account the slip velocity variation with wellbore geometry, operational (controllable) parameters and formation properties. In comparison to the traditional steady-state models, the transient cuttings transport model with integrated depth-dependent parameters gives a possibility to achieve a more realistic simulation of cuttings transport, distribution and accumulation along the wellbore through the time.

Primary cementing is an important well construction process that should establish well control barriers and zonal isolation. Critical for primary cementing is the successful displacement of drilling fluid from the annulus between casing and formation by a sequence of spacer fluids and cement slurry. Failure to displace the drilling fluid may compromise the annular cement integrity and result in contaminated cement with degraded mechanical properties. Issues such as eccentricity, washouts and other geometric irregularities in the wellbore can complicate the displacement processes, and their effect on the quality of the cementing job and the final result is linked to uncertainty. We present numerical simulations of the displacement process between two viscoplastic fluids in the vicinity of a symmetric local hole enlargement. The study is limited to laminar flow regimes in the regular part of the annulus, and we focus on a near-horizontal section with significant eccentricity and small annular clearance. We vary the volumetric flow rate and the mass density difference between the fluids, and study how the irregularity affects the displacement efficiency and the presence of residual fluid in and after the irregularity. In the regular part of the geometry, eccentricity favors flow in the wider, upper part of the annulus, while density difference leads to azimuthal flow from the top to the low side of the annulus. The results support the assumption that increasing the mass density difference improves the displacement efficiency. In the laminar regime, lower flow rates can be favorable over higher ones in terms of efficiency measured as a function of volume that is pumped into the enlarged section. Displacement of drilling fluids for primary cementing is a rich flow problem involving different non-Newtonian fluids and possibly irregular geometry. Simulations of the displacement process can aid in optimizing fluid properties and injection rates for primary cementing operations, and assist cement log interpretation after the operation.

Drilling fluids experience a wide range of shear rates and oscillatory motion while circulating through the well and also during the operations for solids control. Therefore, it is important to investigate the influence of oscillatory fields on the velocity profiles, shear rate and resulting rheological condition of non-Newtonian polymers, which are additives in drilling fluids. In this paper, we present the dynamic velocity profiles within both Newtonian (deionized water) and non-Newtonian liquids (Polyanionic Cellulose – PAC) exposed to oscillatory motion. A 15 cm × 15 cm square cross-sectional liquid column was oscillated horizontally with very low frequencies (0.75–1.75 Hz) using a laboratory made oscillating table. The dynamic velocity profiles at the bulk of the oscillating liquid column were visualized by the Particle Image Velocimetry (PIV) method, where the motion of fluid is optically visualized using light scattering “seeding” particles. Increased frequency of oscillations lead to different dynamic patterns and ranges of velocity-shear magnitudes. The experiments are part of a comprehensive study aimed at investigating the influence of low frequency oscillations on particle settling in non-Newtonian drilling fluids. It is discussed, how such motion imposed on polymeric liquids influences both flow dynamics as well as local settling velocities of cuttings particles.

During drilling, the precipitation velocity of cuttings within an annulus depends on the density, configuration, and size of the cuttings, and on the density, viscosity, and rheological characteristics of the drilling fluid. In this study, in order to identify transfer features of cuttings, an experiment was performed under wide-ranging conditions by constructing a slim hole annulus (44 mm × 30 mm) device. In this experiment, the pressure loss and the particle transport ratio were measured in upward flow of Newtonian and non-Newtonian fluids. These quantities were influenced by particle concentration within the flow, pipe rotation, flow rate, and inclination of the annulus. For both water and CMC (carboxymethylcellulose) solutions, the higher the concentration of the solid particles is, the larger the pressure gradients become. The experimental uncertainty of this study varies from a minimum of 3% to a maximum of 9% depending on the experimental conditions.

Heat transfer enhancement in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers, Nu, higher than the fully developed value, in the downstream pipe, is observed only for Pr = 10 and 100. Higher Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane. Heat transfer augmentation for Pr = 10 and 100, is more dramatic for suddenly expanding annular flows, in comparison with suddenly expanding pipe flow. For a given annular diameter ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, for both Newtonian and shear-thinning non-Newtonian flows.

This paper proposes a novel approach to control the velocity of a piston using dilatant fluid. Commonly, a pressure compensated flow control valve is used for this purpose. It produces excellent results but is mechanically complex. A setup is proposed that makes use of the unique properties of dilatant (i.e. shear thickening) non-Newtonian fluids. A simple tube section filled with dilatant material can be used to achieve very low sensitivity of flow rate vs. pressure difference. A numerical study shows how the power law which relates the fluid shear rate to its viscosity results in this low sensitivity of flow to pressure difference. An experimental setup was build to validate the findings using a cheap and commercially available shear thickening fluid. It was found that the dilatant material used does not have a highly pronounced dilatant property and therefore the sensitivity of flow vs. pressure difference was not as low as desired. Nevertheless, the results support the practical applicability of this novel type of velocity control.

The impact of flow inertia on flow and heat transfer in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. The equations governing conservation of mass, momentum, and energy, along with the power-law constitutive model are numerically solved using a finite-difference numerical scheme. The influence of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5}; n = {1, 0.6}; and Pr = {1, 10, 100}. Heat transfer augmentation, downstream the plane of expansion, is only observed for Pr = 10 and 100. The extent and intensity of recirculation in the corner region, increases with inflow inertia. Higher Reynolds and Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane.

A twin-fluid atomizer configuration is predicted by means of the 2D weakly-compressible Smooth Particle Hydrodynamics (SPH) method and compared to experiments. The setup consists of an axial liquid jet fragmented by a co-flowing high-speed air stream (Ug ≈ 60 m/s) in a pressurized atmosphere up to 11 bar (abs.). Two types of liquid are investigated: a viscous Newtonian liquid (μl = 200 mPas) obtained with a glycerol/water mixture and a viscous non-Newtonian liquid (μl, apparent. ≈ 150 mPas) obtained with a carboxymethyl cellulose (CMC) solution. 3D effects are taken into account in the 2D code by introducing (i) a surface tension term, (ii) a cylindrical viscosity operator and (iii) a modified velocity accounting for the divergence of the volume in the radial direction. The numerical results at high pressure show a good qualitative agreement with experiment, i.e. a correct transition of the atomization regimes with regard to the pressure, and similar dynamics and length scales of the generated ligaments. The predicted frequency of the Kelvin-Helmholtz instability needs a correction factor of 2 to be globally well recovered with the Newtonian liquid. The simulation of the non-Newtonian liquid at high pressure shows a similar breakup regime with finer droplets compared to Newtonian liquids while the simulation at atmospheric pressure shows an apparent viscosity similar to the experiment.

For a particle on a wall or cuttings bed in a multiphase flow in confined geometries a condition for onset and lift-off is very important. In this case, a fundamental problem of hydrodynamic forces and torque acting on a particle moving near and on the wall in a viscous fluid needs to be solved. In this paper, systematical simulation of a flow was performed around a perfect rolling or sliding spherical particle near the wall. A shear flow of Newtonian and Herschel-Bulkley fluids was investigated. The simulation was conducted for Reynolds numbers up to 200 and the dimensionless positive particle velocity Vp < 1.4. The relative particle velocity was made dimensionless by dividing it by the incoming flow velocity in front of the particle. The simulation was performed using the open-source CFD package OpenFOAM. The simulation results for Newtonian fluid agree with data presented in the literature. For the particle’s low translational velocity the drag force coefficient in the non-Newtonian fluid is lower than in Newtonian fluid, but for increasing translational velocity the drag force coefficient increases. The lift force coefficient behavior is non-monotonic versus rheology parameters. Lift and drag force show a sudden drop for very small translational velocities. Our simulation shows that in the case of large Bingham numbers the particle’s lift force can be negative for steady perfect particle rolling. Thus, friction between particle and surface prevents particle’s take-off in some cases. Knowing the dependence of the lift force on Reynolds number and rheological parameters allows one to determine incipient motion and take-off conditions for a spherical particle.

Particle dynamics within Newtonian and viscoelastic shear thinning flows were investigated with a self-confined cloud of particles around an obstacle. Water and three aqueous Poly-Anionic Cellulose (PAC) solutions were test fluids. An experimental study of an upward vertical pipe was carried out using particle image velocimetry (PIV) techniques to measure the particle and liquid velocity profiles. The fluidized cloud height was measured for better assessing rheological and particle loading effects on particle interactions within liquid flows. It was observed that the dynamics of particles were closely associated with local shear rate, fluid rheology and particle loading. Additionally, it was noted that the slip velocity of particles was relative to the surrounding liquid and was high in regions with a high shear rate and depended significantly on the liquid rheological parameters. The experimental findings were compared against three-dimensional numerical CFD simulations. In the case of particle dynamics in the water sample, it was noted that the simulation results were comparable to the experimental observations. However, for PAC solutions, particles were completely flushed out from the computational domain. This was considered a consequence of inadequate drag and settling velocity formulation within the CFD model. These shortcomings of the drag model were rendered, as Newtonian drag laws were applied to a non-Newtonian fluid, and only used background shear rates of the fluid flow field in estimating the local viscosity experienced by these particles.

Stem cells in the bone marrow (BM) are used as regenerative treatment for leukemia. They are usually harvested by puncturing the cancellous bone in the ilium of the donor with a needle. However, this process can cause severe burden to the donor because of its inefficiency; the bone may require 50–100 punctures to obtain enough stem cells. Various factors affect the volume of BM harvested, and their influence can be estimated by observing the flow in the cancellous bone. Recent computational fluid dynamics (CFD) analyses of BM with 3-D reconstruction of the cancellous bone have profiled flow velocity or wall shear stress (WSS) and have shown that some parts on the surface of the cancellous bone have higher WSS and that this high WSS may tear cells from the surface of the bone. CFD analysis may therefore help determining a method for efficient stem cell harvest. However, it is difficult to validate CFD using BM structure because of its porosity. To improve the accuracy of WSS and flow pattern calculations, blood characteristics should be incorporated as key factors and the effects of non-Newtonian flow and viscosity on the flow patterns evaluated. Therefore, the purpose of this study was to evaluate CFD analyses of BM in the cancellous bone based on flow where viscosity depended on the shear rate. BM from porcine ilium bones was extracted, and the viscosities of samples, with or without anti-clotting medications, were measured at various shear rates. 3-D reconstruction of the cancellous bone was performed using micro-CT after removing BM and fat from the bone. The resolution of the reconstruction was 11.7 μm per pixel, which was sufficient to reconstruct the porous structure. The size of the bone sample was 2.5 × 2.5 × 3.5 mm. The number of mesh was approximately 4.3 million. CFD analyses were performed using 3-D reconstruction and viscosity profile at three pressure differences (5, 7, and 10 kPa). Constant pressure was applied in the outlet. The viscosity of BM could be divided into three shear rate ranges. The first corresponded with a shear rate over 100 1/s, where the viscosity was constant at less than 0.01 Pa·s. Transient curves were observed for shear rates 0.01–100 1/s. At lower shear rates, the viscosity was again constant, at over 105 Pa·s. These changes were higher than the changes in blood viscosity based on the shear rate. The CFD analyses showed that the results depended on the inlet pressure. When the pressure difference was 10 kPa, the viscosity change almost disappeared, and the velocity profile was similar to that of Newtonian flow. When the pressure difference was 5 or 7 kPa, changes in viscosity and completely changed flow patterns were observed. The WSS profile also changed with the velocity profile. Therefore, pressure can be a major factor in the velocity profile of BM in the cancellous bone. Effects of non-Newtonian flow on velocity and WSS profiles were observed under an appropriate pressure difference.

Human milk is a complex fluid suspension of many ingredients — such as fats, proteins, lactose, and minerals — that differs greatly from bovine and other mammalian milks. The rheological properties of human milk impact its flow inside the breast and when fed through artificial feeding methods. Past research concerning the flow characteristics of human milk is extremely limited and does not account for milks non-Newtonian behavior. In order to produce an accurate model of milk flow in the human breast, experimental work was performed on human milk donated by eight mothers at different stages of lactogenesis II. The results of this small study reveal the complexity of human milk flow characteristics and the challenges involved with modeling its flow, especially at low shear rates. Within the human breast, shear rates vary greatly from as low as 12 s−1 to as high as 2.5 × 1016 s−1 depending on the ductal system geometry and flow rate. For researchers involved in experimentation, the environmental conditions, handling methods, and age of milk are extremely important and must be reported if the data is to be of any value. Further experimentation is required to fully understand the mechanisms behind the time-dependence behavior of human milk.

Non-isothermal suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid are numerically studied within the steady laminar flow regime. The power-law constitutive equation is used to model the shear-thinning rheology of interest. A parametric study is performed to reveal the influence of annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers over the following range of parameters: k = {0, 0.5}; n = {1, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement, i.e., wall heat transfer rates higher than the fully developed ones downstream of the expansion plane, is observed only for Pr = 10 and 100. In the case of Pr = 1, wall heat transfer rates monotonically increase to the fully developed value. Higher Pr, k, and n values, in general, result in more significant heat transfer enhancement downstream of the expansion plane. Further, shear-thinning non-Newtonian flows display two local peak wall heat transfer rates, in comparison with only one peak value in the case of Newtonian flows.