Dispersion of solids in fracturing flows of yield stress fluids

2017 ◽  
Vol 830 ◽  
pp. 93-137 ◽  
Author(s):  
S. Hormozi ◽  
I. A. Frigaard
Keyword(s):  
Yield Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Process Variations ◽  
Model Framework ◽  
Shear Rates ◽  
Low Viscosity ◽  
High Shear Rates ◽  
Solids Concentration

Solids dispersion is an important part of hydraulic fracturing, both in helping to understand phenomena such as tip screen-out and spreading of the pad, and in new process variations such as cyclic pumping of proppant. Whereas many frac fluids have low viscosity, e.g. slickwater, others transport proppant through increased viscosity. In this context, one method for influencing both dispersion and solids-carrying capacity is to use a yield stress fluid as the frac fluid. We propose a model framework for this scenario and analyse one of the simplifications. A key effect of including a yield stress is to focus high shear rates near the fracture walls. In typical fracturing flows this results in a large variation in shear rates across the fracture. In using shear-thinning viscous frac fluids, flows may vary significantly on the particle scale, from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop a model framework able to include this range of flows, while still representing a significant simplification over fully three-dimensional computations. In relatively straight fractures and for fluids of moderate rheology, this simplifies into a one-dimensional model that predicts the solids concentration along a streamline within the fracture. We use this model to make estimates of the streamwise dispersion in various relevant scenarios. This model framework also predicts the transverse distributions of the solid volume fraction and velocity profiles as well as their evolutions along the flow part.

scholarly journals Macroscopic rheology of non-Brownian suspensions at high shear rates: the influence of solid volume fraction and non-Newtonian behaviour of the liquid phase

2021 ◽  
Author(s):  
Patrick Wilms ◽  
Jörg Hinrichs ◽  
Reinhard Kohlus
Keyword(s):  
Liquid Phase ◽  
Shear Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Shear Thinning ◽  
High Shear ◽  
Rate Dependency ◽  
Shear Rates ◽  
Liquid Phases ◽  
High Shear Rates

AbstractModelling the macroscopic rheology of non-Brownian suspensions is complicated by the non-linear behaviour that originates from the interaction between solid particles and the liquid phase. In this contribution, a model is presented that describes suspension rheology as a function of solid volume fraction and shear rate dependency of both the liquid phase, as well as the suspension as a whole. It is experimentally validated using rotational rheometry ($$\varphi$$ φ ≤ 0.40) and capillary rheometry (0.55 ≤ $$\varphi$$ φ  ≤ 0.60) at shear rates > 50 s−1. A modified Krieger-Dougherty relation was used to describe the influence of solid volume fraction on the consistency coefficient, $$K$$ K , and was fitted to suspensions with a shear thinning liquid phase, i.e. having a flow index, $$n$$ n , of 0.50. With the calculated fit parameters, it was possible to predict the consistency coefficients of suspensions with a large variation in the shear rate dependency of the liquid phase ($$n$$ n = 0.20–1.00). With increasing solid volume fraction, the flow indices of the suspensions were found to decrease for Newtonian and mildly shear thinning liquid phases ($$n$$ n ≥0.50), whereas they were found to increase for strongly shear thinning liquid phases ($$n$$ n ≤0.27). It is hypothesized that this is related to interparticle friction and the relative contribution of friction forces to the viscosity of the suspension. The proposed model is a step towards the prediction of the flow curves of concentrated suspensions with non-Newtonian liquid phases at high shear rates.

scholarly journals L-Box Form Filling of Thixotropic Cementitious Paste and Mortar

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1760
Author(s):  
Mareike Thiedeitz ◽  
Nasime Habib ◽  
Thomas Kränkel ◽  
Christoph Gehlen
Keyword(s):  
Yield Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Rheological Parameters ◽  
Empirical Equations ◽  
Dynamic Yield Stress ◽  
Shear Rates ◽  
Flow Length ◽  
Dynamic Yield ◽  
Fast Flow

Rheological properties of cementitious pastes and mortar affect the casting, placement, and setting properties of fresh concrete. Fundamental rheological knowledge thus helps in predicting concrete flowability and workability. Empirical equations correlate actual rheological parameters based on physical material characteristics to workability tests. Still, these equations generally only take the dynamic yield stress of the material into account. This is not sufficient for thixotropic cementitious pastes or mortars, which possess structural buildup at rest. Workability predictions regarding the flow of concrete are thus more complicated with thixotropic materials. During form-filling in L-shaped formworks, the flow velocity of concrete slows down, wherefore rheological parameters change with time. At initial fast flow, high shear rates without structural buildup can be assumed. Dynamic yield stress and a steady state viscosity thus are proper parameters for empirical equations describing concrete flowability. During low shear rates, partial structural buildup takes place. Viscosity and yield stress increase due to agglomeration and affect the flowability of concrete tremendously. Rheological parameters of various cementitious pastes and mortars varying in their solid volume fraction and flowability were investigated in a vane-in-cup rheometer. The workability of the same mixtures was investigated by measuring the flow length in an L-shaped formwork. The effect of yield stress, viscosity, and thixotropic structural buildup on flow length was investigated. Subsequently correlations and discrepancies between flowability parameters and workability equations were analyzed.

Fluid flow and heat transfer of a stratified system during natural convection – influence of chamfered corners

2019 ◽  
Vol 29 (2) ◽  
pp. 470-486 ◽  
Author(s):  
Alireza Rahimi ◽  
Aravindhan Surendar ◽  
Aygul Z. Ibatova ◽  
Abbas Kasaeipoor ◽  
Emad Hasani Malekshah
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Natural Convection ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Immiscible Fluids ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose This paper aims to investigate the three-dimensional natural convection and entropy generation in the rectangular cuboid cavities included by chamfered triangular partition made by polypropylene. Design/methodology/approach The enclosure is filled by multi-walled carbon nanotubes (MWCNTs)-H2O nanofluid and air as two immiscible fluids. The finite volume approach is used for computation. The fluid flow and heat transfer are considered with combination of local entropy generation due to fluid friction and heat transfer. Moreover, a numerical method is developed based on three-dimensional solution of Navier–Stokes equations. Findings Effects of side ratio of triangular partitions (SR = 0.5, 1 and 2), Rayleigh number (103 < Ra < 105) and solid volume fraction (f = 0.002, 0.004 and 0.01 Vol.%) of nanofluid are investigated on both natural convection characteristic and volumetric entropy generation. The results show that the partitions can be a suitable method to control fluid flow and energy consumption, and three-dimensional solutions renders more accurate results. Originality/value The originality of this work is to study the three-dimensional natural convection and entropy generation of a stratified system.

Three-Dimensional Printed Dielectric Substrates for Radio Frequency Applications

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Vana Snigdha Tummala ◽  
Ahsan Mian ◽  
Nowrin H. Chamok ◽  
Dhruva Poduval ◽  
Mohammod Ali ◽  
...  
Keyword(s):  
Radio Frequency ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Acrylonitrile Butadiene Styrene ◽  
Volume Fractions ◽  
The Core ◽  
Sandwich Construction ◽  
3D Printed ◽  
Rf Antenna

Engineered porous structures are being used in many applications including aerospace, electronics, biomedical, and others. The objective of this paper is to study the effect of three-dimensional (3D)-printed porous microstructure on the dielectric characteristics for radio frequency (RF) antenna applications. In this study, a sandwich construction made of a porous acrylonitrile butadiene styrene (ABS) thermoplastic core between two solid face sheets has been investigated. The porosity of the core structure has been varied by changing the fill densities or percent solid volume fractions in the 3D printer. Three separate sets of samples with dimensions of 50 mm × 50 mm × 5 mm are created at three different machine preset fill densities each using LulzBot and Stratasys dimension 3D printers. The printed samples are examined using a 3D X-ray microscope to understand pore distribution within the core region and uniformity of solid volumes. The nondestructively acquired 3D microscopy images are then postprocessed to measure actual solid volume fractions within the samples. This measurement is important specifically for dimension-printed samples as the printer cannot be set for any specific fill density. The experimentally measured solid volume fractions are found to be different from the factory preset values for samples prepared using LulzBot printer. It is also observed that the resonant frequency for samples created using both the printers decreases with an increase in solid volume fraction, which is intuitively correct. The results clearly demonstrate the ability to control the dielectric properties of 3D-printed structures based on prescribed fill density.

scholarly journals Progress on numerical simulation of nanofluids: impact of an isothermal spherical partition on the mixed convection of nanofluids within cubic enclosures

2020 ◽  
Vol 307 ◽  
pp. 01016
Author(s):  
A. BOUTRA ◽  
K. RAGUI ◽  
N. LABSI ◽  
Y.K. BENKAHLA ◽  
R BENNACER
Keyword(s):  
Lattice Boltzmann ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Numerical Code ◽  
Three Dimensional Flow ◽  
Boltzmann Method ◽  
Do So

The main objective of our work is to light out the three-dimensional flow of an Ag-water nanofluid within a lid-driven cubical space which equipped with a spherical heater into its center. Due to its crucial role in the characterization of the main transfer within such configurations, impact of some parameters is widely inspected. It consists the Richardson value (0,05 to 50), the solid volume fraction (0% to 10%), as well as the heater geometry (10% ≤ d ≤ 25%). To do so, a numerical code based on the Lattice-Boltzmann method, coupled with a finite difference one, is used. The latter has been validated after comparison between the present results and those of the literature. It is to note that the three dimensions D3Q19 model is adopted based on a cubic Lattice, where each pattern of the latter is characterized by nineteen discrete speeds.

Squeeze Casting of Semi-Solid A356 Alloy

2014 ◽  
Vol 217-218 ◽  
pp. 436-441
Author(s):  
Xiang Jie Yang ◽  
Ming Wang ◽  
Liang Sheng Ding ◽  
Hong Min Guo ◽  
Xu Bo Liu
Keyword(s):  
Cross Section ◽  
Squeeze Casting ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
A356 Alloy ◽  
Equivalent Diameter ◽  
Squeeze Cast ◽  
Cast Product ◽  
Semi Solid

the rheo-squeeze casting (Rheo-SQC) combining the rheocasting and the SQC was developed, in which semi-solid slurry was produced by the low superheat pouring with a shearing field (LSPSF) process. The three dimensional morphology of the primary α-Al phase and the rest spacing of slurry prepared by LSPSF process have been reconstructed and visualized, and the microstructures of squeeze cast A356 alloy have been obtained. Based on the three dimensional microstructure reconstructed, their three dimensional characterizations such as solid volume fraction, equivalent diameter of the extracted primary α-Al phase were measured and calculated, and the microstructures of cross section of squeeze cast product were investigated.

SHEAR VISCOSITY OF STRONGLY-COUPLED TWO-DIMENSIONAL YUKAWA LIQUIDS: EXPERIMENT AND MODELING

2007 ◽  
Vol 21 (21) ◽  
pp. 1357-1376 ◽  
Author(s):  
Z. DONKÓ ◽  
P. HARTMANN ◽  
J. GOREE
Keyword(s):  
Shear Viscosity ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Simulation Studies ◽  
Strongly Coupled ◽  
Shear Rates ◽  
High Shear Rates ◽  
Wide Range ◽  
Computer Simulation Studies

This paper reviews experimental and modeling efforts aimed at the determination of the shear viscosity of strongly-coupled Yukawa liquids. After briefly reviewing prior work on three-dimensional (3D) systems, recent experimental and computer simulation studies of two-dimensional (2D) settings are presented in detail. In the experiments two counterpropagating laser beams were used to perturb a dusty plasma monolayer and monitoring of the velocity field reconstructed from particle trajectories allowed the determination of the shear viscosity with the aid of an analytical model. Subsequent computer simulations based on the molecular dynamics approach resulted in velocity profiles which are in very good agreement with the experimental ones. Further simulation studies of idealized 2D Yukawa liquids (in which gas friction is neglected) gave results for the shear viscosity over a wide range of system parameters and demonstrated the existence of the shear thinning effect (non-Newtonian behavior) of the liquid at high shear rates.

scholarly journals Three-Phase 3D Reconstruction of a LiCoO2 Cathode via FIB-SEM Tomography

2016 ◽  
Vol 22 (1) ◽  
pp. 140-148 ◽  
Author(s):  
Zhao Liu ◽  
Yu-chen K. Chen-Wiegart ◽  
Jun Wang ◽  
Scott A. Barnett ◽  
Katherine T. Faber
Keyword(s):  
Focused Ion Beam ◽  
Volume Fraction ◽  
Ion Beam ◽  
Three Dimensional ◽  
Lithium Ion ◽  
Silicone Resin ◽  
Phase Volume Fraction ◽  
Low Viscosity ◽  
Three Phase ◽  
Battery Degradation

AbstractThree-phase three-dimensional (3D) microstructural reconstructions of lithium-ion battery electrodes are critical input for 3D simulations of electrode lithiation/delithiation, which provide a detailed understanding of battery operation. In this report, 3D images of a LiCoO2 electrode are achieved using focused ion beam-scanning electron microscopy (FIB-SEM), with clear contrast among the three phases: LiCoO2 particles, carbonaceous phases (carbon and binder) and the electrolyte space. The good contrast was achieved by utilizing an improved FIB-SEM sample preparation method that combined infiltration of the electrolyte space with a low-viscosity silicone resin and triple ion-beam polishing. Morphological parameters quantified include phase volume fraction, surface area, feature size distribution, connectivity, and tortuosity. Electrolyte tortuosity was determined using two different geometric calculations that were in good agreement. The electrolyte tortuosity distribution versus position within the electrode was found to be highly inhomogeneous; this will lead to inhomogeneous electrode lithiation/delithiation at high C-rates that could potentially cause battery degradation.

scholarly journals Experimental study on the rheological behaviour of coal ash slurries

2015 ◽  
Vol 63 (4) ◽  
pp. 303-310 ◽  
Author(s):  
K.M. Assefa ◽  
D.R. Kaushal
Keyword(s):  
Yield Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Substantial Reduction ◽  
Relative Viscosity ◽  
Rheological Behaviour ◽  
Experimental Investigations ◽  
Solid Mass ◽  
Mixing Proportion ◽  
Mass Concentrations

Abstract Extensive experimental investigations were carried out to evaluate the rheological behaviour of fly ash (FA) slurry without and with the addition of bottom ash (BA) and BA slurry without and with the addition of FA. The FA slurries exhibited Bingham behaviour at solid mass concentrations ranging from 60–65% and mixing proportions from 10– 40%. A substantial reduction in yield stress was observed except for mixing proportion of 40% on which the yield stress and viscosity were increased drastically for all solid concentrations. Hence, it can be concluded that the yield stress and viscosity of FA slurry were very much influenced by adding BA up to the mixing proportion of 30%. The rheological behaviour of BA slurries with and without the addition of FA in proportions of 10–50% was investigated and exhibited Newtonian behaviours for solid mass concentrations ranging from 30–50% without and with the addition of FA. The viscosity increases with increasing the solid concentrations and proportion of FA. Based on these experimental data, a correlation was developed to predict the relative viscosity of BA slurries as a function of solid volume fraction and FA mass proportion of 0–50% and the RMSE and R2 values showed good agreement between the experimental and the predicted data.

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