Herschel-Bulkley Behavior Research Articles

Fully Coupled CFD–DEM Simulation of Oil Well Hole Cleaning: Effect of Mud Hydrodynamics on Cuttings Transport

This paper presents a coupled computational fluid dynamics–discrete element method (CFD–DEM) simulation to predict cuttings transport by the drilling fluid (mud) in different oil well drilling conditions. The mud rheology is expressed by the Herschel–Bulkley behaviour and modelled in a Eulerian framework (CFD), while the cuttings are modelled using the Lagrangian approach (DEM). In this work, the effects of drill string rotation, inclination angle, cutting size, mud rheology, and annular velocity on cleaning efficiency are investigated. It is found that increasing the well deviation from vertical to horizontal leads to a higher cuttings concentration. However, at low annular velocity, the cuttings concentration for the inclined (45-degree) annulus is found to be higher than the horizontal one due to the sliding motion of cuttings on the lower section of the annulus. Overall, the drill pipe rotation has little effect on decreasing the cuttings concentration, but the effect is more pronounced at low annular velocity.

Comparison of models for predicting cleaning of viscoplastic soil layers by impinging coherent turbulent water jets

Different approaches to model the cleaning of (i) very thin and (ii) thin soil layers by impinging water jets are compared to evaluate their predictive capabilities. Cleaning experiments were performed with coherent 2 mm and 3 mm diameter water jets (Re > 10,000) impinging on flat layers of an insoluble, viscoplastic petroleum jelly. The jelly exhibited creep below the yield stress and Herschel-Bulkley behaviour above it. A two-film shear-driven model for case (i) gave very poor predictive capability, partly due to the complex soil rheology. Case (ii) data were compared to modified versions of the phenomenological model of Fernandes and Wilson (2020), and a fully-coupled CFD model of the liquid and soil motion using the volume of fluid method. The modifications to the former did not improve its accuracy. The latter gave a good prediction of the initial cleaning behaviour for the case considered: the high computational cost precluded extensive testing.

Investigations of rheology and a link to microstructure of oil-based drilling fluids

Towards establishing a first-principles physical link between the field-behavior and microstructure of oil-based drilling fluid (OBDF), we study rheology of an OBDF and its variation with different contents of water, clay viscosifier, or barite weighting agent during steady and dynamic rheological phenomena, and develop a “cryo-preserved” experimental methodology towards in-situ microscopy. Rheological data was collected for shear rate ramps between 0.0001 s and 1 and 1000 s−1, under temperatures ranging from 10°C to 60 °C, with three water/oil ratios, and multiple OBDF compositions. Oscillatory and constant shear rate measurements showed elastic and loss modulus co-dominate when stress is below ~1 Pa, but above a ~1 Pa “apparent yield-stress” the fluid microstructure reorganizes, elasticity decreases, and the flow follows a viscosity-dominated shear-thinning Herschel–Bulkley behavior. Signs of thixotropy are seen in increasing vs. decreasing flow curves when in the elastic regime, and elasticity shows time-dependency. Clay particles created elasticity more so than the other ingredients. Elimination of water, clay, or barite caused an approximately equal reduction of viscosity. Elimination of water also led to elastic modulus dominating over viscous modulus for a longer range of strain in the linear-elastic pre-yield state, likely due to water droplets having a shorter length scale over which yield-stress is broken than does a water-free mixture. Elimination of barite had a similar but lesser effect on elasticity. Cryological scanning electron microscopy (Cryo-SEM) and cryological x-ray spectroscopy (Cryo-EDS) methods show promise for future work to identify the spatial microstructure of the OBDF at nanometer to micrometer scales in a “cryo-preserved” state that approximates an in-situ like state. Chemical identification of individual phases within the mixture components is achieved via a quantitative elemental method. Water droplets, base oil, and barite are identifiable and future methods for in-situ imaging of sheared OBDFs is proposed.

Assessment of numerical methods for estimating the wall shear stress in turbulent Herschel–Bulkley slurries in circular pipes

This article concerns the turbulent flow of Herschel–Bulkley slurries through circular horizontal pipes; in particular, that of concentrated domestic slurry obtained upon separation of domestic waste water and reduction in the use of water for domestic purposes. Experiments with a rheologically equivalent clay (kaolin) slurry indicated a non-Newtonian behaviour of the Herschel–Bulkley type. A modified wall function was developed to enable the Reynolds-averaged Navier–Stokes simulation of Herschel–Bulkley slurries to estimate the wall shear stress. Despite the accuracy achieved, the use of Reynolds-averaged Navier–Stokes models for an entire waste water system is impractical. Therefore, this article assesses the accuracy of semi-empirical models in estimating frictional losses. It also discusses possible modifications of existing models to encompass Herschel–Bulkley behaviour. An evaluation suggests that most existing models deliver estimates of comparable accuracy; however, the probability of these estimates being reliable, while accounting for experimental errors in quantifying the actual frictional losses, is rather low.

Hydraulics and rheology of natural hyperconcentrated flows from Draix-Bleone observatory, French Alps

We present an experimental study of natural hyperconcentrated flows of fine sediment from Draix-Bleone observatory. Suspensions of volumic concentration ranging from 29 to 44% were tested in a rheometer and exhibit a Herschel–Bulkley behaviour. Suspensions of volumic concentration ranging from 0 to 31% were tested in flume experiments with varying slope and discharge. Velocity profile measurements indicate a transition from turbulent Newtonian flows to laminar non-Newtonian flows as the concentration increases. Rheological data and flume velocity profiles consistently suggest that a yield stress appears for volumic concentrations higher than 26–29%. Finally, the relation between the Reynolds number and the friction coefficient computed for all flume experiments is found to follow a unique trend, independently of the concentration. This allows the laminar, transitional and turbulent regimes to be identified, and suggests that transitional to laminar conditions can be observed in the field during hyperconcentrated events.

Non-stoichiometric zinc-doped spinel ferrite nanoparticles with enhanced magnetic property and their magnetorheology

To improve the magnetorheological (MR) performance compared to typical ferrites, non-stoichiometric zinc-doped spinel ferrite (Zn0.417Fe2.583O4) nanoparticles with a high saturation magnetization value and a truncated octahedron-like shape were synthesized using a simple thermal decomposition process with benefits of monodisperse and high crystallinity. The Zn0.417Fe2.583O4 had a high saturation magnetization value of 106 A m2/kg, which is generally higher than the other ferrites. The MR characteristics of the Zn0.417Fe2.583O4 particles dispersed in silicone oil were measured using a rotational rheometer under various magnetic field strengths. The flow curves and dynamic yield stress for the different magnetic field strengths exhibited the Herschel-Bulkley behavior with a slope of 2.0 and typical MR behavior. The sedimentation stability was further examined using Turbiscan.

Effect of concentration, homogenization and stabilizing salts on heat stability and rheological properties of cow skim milk ultrafiltered retentate.

Ultrafiltration (UF) of skimmed milk altered the composition of UF retentate and decreased the heat stability. Heat stability further reduced upon its subsequent homogenization or diafiltration. Poor heat stability of UF retentate restricts its processing at elevated temperatures. Therefore, this study was aimed to investigate the effect of protein concentration, homogenization and addition of stabilizing salts on the heat stability and rheological properties of UF retentates. Changes in the heat stability of fivefold homogenized UF retentate (5× HUFR) was studied in the pH range of 6.1-7.0. Disodium phosphate and trisodium citrate significantly increased the heat coagulation time (HCT) from 1.45min (pH 6.41) to 120min (at pH 6.5, 6.6, 7.0) and 80min (pH 6.6), respectively. Significant reduction in ζ-potential of UF retentates was observed with an increase in calcium and reduction in pH during UF process. Rheological behaviour of retentates above threefold concentration exhibited Herschel-Bulkley behavior with linear increase in flow behavior index (n). Changes in the viscosity of the homogenized retentates were measured at the respective pH of maximum heat stability as a function of temperature (20-80°C). Promising approaches that might improve the heat stability, solubility and other functional properties of protein rich powders have been discussed in this article.

Flows of suspensions of particles in yield stress fluids

We study the rheological behavior of suspensions of noncolloidal spheres in yield stress fluids (concentrated emulsions). These are good model systems for understanding, e.g., the rheology of fresh concrete or debris flows, and more generally, the behavior of particles dispersed in any nonlinear material. We use magnetic resonance imaging techniques to investigate the flows of these yield stress suspensions in a concentric-cylinder Couette geometry. We extend the theoretical approach of Chateau et al. [J. Rheol. 52, 489–506 (2008)], valid for isotropic suspensions, to describe suspensions in simple shear flows, in which an anisotropic spatial distribution of particles is induced by flow. Theory and experiments show that the suspensions can be modeled by a Herschel–Bulkley behavior of same index as their interstitial fluid. We characterize the increase of their consistency and their yield stress with the particle volume fraction ϕ in the 0%–50% range. We observe a good agreement between the experimental va...

Comparative study of film forming behaviour of low and high amylose starches using glycerol and xylitol as plasticizers

In this study, the film forming behaviour of low amylose (LA) and high amylose (HA) starches was studied. The starch-alone and a blend of plasticizer (polyol)–starch films were developed by gelatinising at various temperatures and casting at 25°C. The starch–plasticizer films contained glycerol and xylitol either individually or in 1:1 combination. The concentration of plasticizer used was 15%, 20% and 30% for LA films while it was 20%, 30% and 40% for HA films on dry solid basis. The HA-glycerol films retained the highest moisture content among all the films. The HA films exhibited higher glass transition temperature, higher tensile strength, higher modulus of elasticity and lower elongation at break than those obtained from LA starch. The tensile strength and modulus of elasticity decreased and the elongation increased with increasing plasticizer concentrations above 15% on dry solid basis regardless the starch type. Low water vapour permeability was evident in LA and HA films plasticized by combined plasticizers at 20% plasticizer concentration. Rheological measurements showed that most of the suspensions exhibited Herschel–Bulkley behaviour and some of the HA suspensions exhibited Bingham plastic behaviour. At 15% (on dry solid basis) plasticizer concentration, the films obtained from both the starches were brittle due to the anti-plasticization behaviour.

Glass Transition Seen through Asymptotic Expansions

Soft glassy materials exhibit the so-called glassy transition, which means that the behavior of the model at a low shear rate changes when a certain parameter (which we call the glass parameter) crosses a critical value. This behavior goes from a Newtonian behavior to a Herschel–Bulkley behavior through a power-law-type behavior at the transition point. In a previous paper we rigorously proved that the Hébraud–Lequeux model, a Fokker–Planck-like description of soft glassy material, exhibits such a glass transition. But the method we used was very specific to the one-dimensional setting of the model, and as a preparation for generalizing this model to take into account multidimensional situations, we look for another technique to study the glass transition of this type of model. In this paper we shall use matched asymptotic expansions for such a study. The difficulties encountered when using asymptotic expansions for the Hébraud–Lequeux model are that multiple ansaetze have to be used, even though the initial model is unique, due to the glass transition. We shall delineate the various regimes and give a rigorous justification of the expansion by means of an implicit function argument. The use of a two parameter expansion plays a crucial role in elucidating the reasons for the scalings which occur.

From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids

Stress-induced fluidization of a simple yield stress fluid, namely a carbopol microgel, is addressed through extensive rheological measurements coupled to simultaneous temporally and spatially resolved velocimetry. These combined measurements allow us to rule out any bulk fracture-like scenario during the fluidization process such as that suggested in [Caton {\it et al., Rheol Acta}, 2008, {\bf 47}, 601-607]. On the contrary, we observe that the transient regime from solidlike to liquidlike behaviour under a constant shear stress $\sigma$ successively involves creep deformation, total wall slip, and shear banding before a homogeneous steady state is reached. Interestingly, the total duration $\tau_f$ of this fluidization process scales as $\tau_f \propto 1/(\sigma - \sigma_c)^{\beta}$, where $\sigma_c$ stands for the yield stress of the microgel, and $\beta$ is an exponent which only depends on the microgel properties and not on the gap width or on the boundary conditions. Together with recent experiments under imposed shear rate [Divoux {\it et al., Phys. Rev. Lett.}, 2010, {\bf 104}, 208301], this scaling law suggests a route to rationalize the phenomenological Herschel-Bulkley (HB) power-law classically used to describe the steady-state rheology of simple yield stress fluids. In particular, we show that the {\it steady-state} HB exponent appears as the ratio of the two fluidization exponents extracted separately from the {\it transient} fluidization processes respectively under controlled shear rate and under controlled shear stress.

Slip and Flow of Hard-Sphere Colloidal Glasses

We study the flow of concentrated hard-sphere colloidal suspensions along smooth, nonstick walls using cone-plate rheometry and simultaneous confocal microscopy. In the glass regime, the global flow shows a transition from Herschel-Bulkley behavior at large shear rate to a characteristic Bingham slip response at small rates, absent for ergodic colloidal fluids. Imaging reveals both the "solid" microstructure during full slip and the local nature of the "slip to shear" transition. Both the local and global flow are described by a phenomenological model, and the associated Bingham slip parameters exhibit characteristic scaling with size and concentration of the hard spheres.

Wide-gap Couette flows of dense emulsions: Local concentration measurements, and comparison between macroscopic and local constitutive law measurements through magnetic resonance imaging

Flows of dense emulsions show many complex features among which long range nonlocal effects pose a problem for macroscopic characterization. In order to get around this problem, we study the flows of several dense emulsions, with droplet size ranging from 0.3to40microm , in a wide-gap Couette geometry. We couple macroscopic rheometric experiments and local velocity measurements through magnetic resonance imaging (MRI) techniques. As concentration heterogeneities are expected in the wide-gap Couette flows of multiphase materials, we also designed a method to measure the local droplet concentration in emulsions with a MRI device. In contrast to dense suspensions of rigid particles where very fast migration occurs under shear in wide-gap Couette flows, we show that no migration takes place in dense emulsions even for strains as large as 100 000 in our systems. As a result of the absence of migration and of finite size effect, we are able to determine very precisely the local rheological behavior of several dense emulsions. As the materials are homogeneous, this behavior can also be inferred from purely macroscopic measurements. We thus suggest that properly analyzed purely macroscopic measurements in a wide-gap Couette geometry can be used as a tool to study the local constitutive laws of dense emulsions. All behaviors are basically consistent with Herschel-Bulkley laws of index 0.5. The existence of a constitutive law accounting for all flows contrasts with previous results obtained within a microchannel by Goyon [Nature (London) 454, 84 (2008)]: the use of a wide-gap Couette geometry is likely to prevent here from nonlocal finite size effects; it also contrasts with the observations of Bécu [Phys. Rev. Lett. 96, 138302 (2006)]. We also evidence the existence of discrepancies between a perfect Herschel-Bulkley behavior and the observed local behavior at the approach of the yield stress due to slow shear flows below the apparent yield stress in the case of a strongly adhesive emulsion.

Three-Dimensional Imaging of Colloidal Glasses under Steady Shear

Using fast confocal microscopy we image the three-dimensional dynamics of particles in a yielded hard-sphere colloidal glass under steady shear. The structural relaxation, observed in regions with uniform shear, is nearly isotropic but is distinctly different from that of quiescent metastable colloidal fluids. The inverse relaxation time tau(alpha)(-1) and diffusion constant D, as functions of the local shear rate gamma*, show marked shear thinning with tau(alpha)(-1) proportional to D proportional to gamma*(0.8) over more than two decades in gamma*. In contrast, the global rheology of the system displays Herschel-Bulkley behavior. We discuss the possible role of large scale shear localization and other mechanisms in generating this difference.

Gelation of water–bentonite suspensions at high temperatures and rheological control with lignite addition

The effectiveness of lignite addition to prevent gelation of 6.42% w/w water–bentonite suspensions exposed to high temperatures has been studied, using twenty six lignites from various basins in Greece with variable organic and inorganic contents at concentrations of 0.5% and 3.0%. The lignite-free bentonite suspensions thickened considerably when heated at 177 °C for 16 h, as was indicated by a two-fold increase of the yield stress, when compared to samples hydrated only at room temperature. However plastic viscosity did not change appreciably. Full flow curves showed a Herschel–Bulkley behavior of all suspensions. Addition of lignite maintained the stability of the suspensions exposed to high temperatures (177 °C) by keeping the yield stress low and did not affect plastic viscosity. Some of the Greek lignites performed equally well with a commercial lignite product and improvements of 80 to 100% of the stability of the suspensions, compared to lignite-free suspensions, have been found. Lignite addition also lowered yield stresses for the hydrated samples. No specific trends have been identified between the effectiveness of lignites to stabilize bentonite suspensions and their humic and fulvic acids and humins content. However, those lignites with highest humic and fulvic acid contents have maximum stabilization capacity. Similarly, no specific trends have been observed between the stabilization capacity of lignites and their inorganic components such as oxygen and ash content and also with the cation exchange capacity. The effectiveness of the Greek lignites to stabilize bentonite suspensions is very high and the minor differences in the efficiency of the different lignites cannot be attributed solely to any specific component.

Influence of Temperature and Clays/Emulsion Microstructure on Oil-Based Mud Low Shear Rate Rheology

SummaryOil-based muds (OBMs) are complex fluids composed of water, oil, organophilic clays, and various additives. Their very good filtration and lubricating properties make their use beneficial in numerous drilling operations. Deep offshore operations may present phases using OBMs as drilling fluids. In these operations, the mud will experience extremely low temperature (down to 0°C) and low shear rate when flowing through the riser. It is therefore of primary importance to control mud rheological properties under such conditions.This work presents a rigorous experimental study of OBM rheological properties using scientific rheometers. Temperature dependence and low shear rate behavior are specially studied. Because of their complex nature, OBM rheological properties will be extremely dependent on their microstructure. Characterization of this microstructure has therefore been sought during this study.Several OBM compositions have been investigated. Flow curves have been established with a precise and reproducible procedure at temperatures varying from 0 to 80°C. For an offshore designed composition, a specific behavior at low shear rate has been detected. Two different regimes can be seen: a Newtonian behavior at low shear rate and a Herschel-Bulkley behavior at higher shear rate. The limiting shear rate value between the two regimes is dependent on temperature. Experiments on partial compositions (partial muds with/without solids, with/without clays) have shown that the specific clay used in this composition is responsible for this particular behavior at low shear rate. Oscillatory rheometry measurements have confirmed the existence of these two different regimes. CryoMeb and microscopic observations have allowed us to estimate the size of the emulsion droplets and of the clay particles. A simple energetic and structural model is proposed that fits the data well. Finally, a comparison is made between these experiments and those obtained using a Fann 35 (Fann Instrument Co., Houston) rheometer, concluding that classical Fann 35 measurements induce large error for low-shear-rate rheology.

Growth of denuded zone by grain boundary fluid flow in Mg alloys

A new mechanism is proposed for the growth of denuded zone and superplasticity in general. This is the flow of grain boundary fluid that has a Herschel–Bulkley behavior. Such a mechanism could provide a power-law stress dependence, a threshold stress, a grain size effect and an activation energy comparable to grain boundary diffusion.

Vibrational flow of non-Newtonian fluids

Abstract The flow of a time-independent fluid through a vibrated tube is studied both numerically by CFD simulation and experimentally. The effects are studied for Newtonian and non-Newtonian fluids which obey Bingham plastic, power-law or Herschel–Bulkley behaviour. The superimposed mechanical oscillations have no effect on the flow of Newtonian fluids, but can greatly influence that of shear-dependent fluids. Flow enhancement is obtained with shear-thinning fluids whereas flow reduction occurs when a shear-thickening fluid is vibrated. The effects of the various rheological parameters are investigated, and the flow behaviour index emerges as the most influential. The enhancement is a function of both vibration frequency and amplitude, but the same enhancement is generated with different amplitude–frequency combinations that correspond to the same peak acceleration. The CFD predictions are in both qualitative and quantitative agreement with experimental measurements.

Lois d'écoulement des laves torrentielles boueuses

Debris flows are large masses of water, clay, silt, sand, pebbles and boulders which sometimes flow in mountain streams after long or intense rains and can cause much damages to inhabited areas. Muddy debris flows which are the most common in France exhibit a Herschel-Bulkley behaviour. Here we present theoretical tools for predicting steady free surface debris flows. We first show the fundamental feature of channelized debris flows : an unsheared zone (called plug) within the material. For flow on an infinitely wide plane one can easily compute flox characteristics. From these formulae we deduce an expression for the wall shear stress. We also propose other expressions, established empirically, which may be used for flow in rectangular or trapezoidal channels. We then show that global steady flow characteristics are similar to water flows (supercritical and subcritical regimes, hydraulic jump, rol waves). Nevertheless flow through singularities are somewhat different (dead zones formation).