The Investigation of Proppant Particle-Fluid Flow in the Vertical Fracture with a Contracted Aperture

SPE Journal ◽  
2021 ◽  
pp. 1-18
Author(s):  
Hai Qu ◽  
Rui Wang ◽  
Xiang Ao ◽  
Ling Xue ◽  
Zhonghua Liu ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Volume Fraction ◽  
Particle Density ◽  
Particle Volume Fraction ◽  
Experimental Results ◽  
Fluid Viscosity ◽  
Flow Conditions ◽  
Particle Volume ◽  
Proppant Transport ◽  
Bed Height

Summary Proppant placement plays a crucial role in maintaining the conductivity of fractures after a hydraulic fracturing treatment. The process involves the transport of particles by fluid flow in complex fractures. Many studies have focused on proppant transport and distribution in the fracture with a constant aperture, but relatively few studies have investigated the proppant-fluid flow in a vertical fracture with a contracted aperture. In this work, we examine experimentally proppant transport in a fracture with a contracted aperture. The objective is to evaluate the distribution of particle beds in the contracted fracture at different flow conditions. In this paper, particle-fluid flow in the contracted fracture is studied experimentally by a laboratory size slot. A planar slot with a constant width is used to benchmark the experimental results, and a published correlation validates the bed equilibrium heights in the planar slot. Six types of particles are chosen to simulate the effects of particle density and size. The proppant distribution is evaluated by the bed height when the bed reaches the equilibrium states. The effects of fluid velocity, fluid viscosity, particle density, particle size, and particle volume fraction on particle distribution are investigated. The results confirm that the proppant particle-fluid flow in the contracted slot is more complicated than that in the planar slot. The phenomena of particle vortices and resuspension were observed at the contraction of the cross-section. The shape on the top of the bed is like a descending stair in which the height gradually decreases in the length direction. The bed height in the contracted slot is lower and more irregular than that in the planar slot at the same flow conditions. Smaller sands injected at a high flow rate and fluid viscosity can form a lower bed. The trend would be reversed by using denser particles and high particle volume fraction. A reliable model expressed by four dimensionless numbers is developed by the linear regression method for predicting the bed equilibrium height. The model and experimental results provide directions to quantitatively evaluate the particle transport and distribution in a fracture with a contracted aperture.

Effects of Particle Concentration on the Partitioning of Suspensions at Small Divergent Bifurcations

1996 ◽  
Vol 118 (3) ◽  
pp. 287-294 ◽  
Author(s):  
R. Ditchfield ◽  
W. L. Olbricht
Keyword(s):  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Diameter ◽  
Circular Cross Section ◽  
Experimental Results ◽  
Hydrodynamic Interactions ◽  
Spherical Particles ◽  
Straight Tube ◽  
Particle Volume ◽  
Reynolds Number Flow

Experimental results are reported for the low Reynolds number flow of a suspension of spherical particles through a divergent capillary bifurcation consisting of a straight tube of circular cross-section that splits to form two tubes of equal diameter. The partitioning of particles between the downstream branches of the bifurcation is measured as a function of the partitioning of total volume (particles + suspending fluid) between the branches. Two bifurcation geometries are examined: a symmetric Y-shaped bifurcation and a nonsymmetric T-shaped bifurcation. This experiment focuses on the role of hydrodynamic interactions between particles on the partitioning of particles at the bifurcation. The particle diameter, made dimensionless with respect to the diameter of the branch tubes, ranges from 0.4 to 0.8. Results show that hydrodynamic interactions among the particles are significant at the bifurcation, even for conditions where interactions are unimportant in the straight branches away from the bifurcation. As a result of hydrodynamic interactions among particles at the bifurcation, the partitioning of particles between the branches is affected for particle volume fractions as small as 2 percent. The experimental results show that the effect of particle volume fraction is to diminish the inhomogeneity of particle partitioning at the bifurcation. However, the magnitude of this effect depends strongly on the overall shape of the bifurcation geometry, and, in particular on the angles between the branches.

The motion of Brownian particles and sediment on an inclined plate

1997 ◽  
Vol 337 ◽  
pp. 25-47 ◽  
Author(s):  
A. A. DAHLKILD
Keyword(s):  
Volume Fraction ◽  
Particle Density ◽  
Particle Volume Fraction ◽  
Present Theory ◽  
Brownian Diffusion ◽  
Inclined Plate ◽  
Particle Volume ◽  
Hindered Settling ◽  
Brownian Particles ◽  
And Migration

The gravitational settling of a homogeneous suspension of Brownian particles on an inclined plate is considered. The hindered settling towards the wall and the viscous, buoyancy-driven bulk motion of the sediment are considered assuming steady conditions and accounting for the effects of Brownian diffusion, shear-induced diffusion and migration of particles due to a gradient in shear stress. Generally, the results show the development of a sediment boundary layer where the settling towards the wall is balanced by Brownian diffusion at the beginning of the plate and by shear-induced diffusion further downstream. Compared to previous results in the literature, the present theory allows steady-state solutions for extended values of the plate inclination and particle volume fraction above the sediment; upon reconsidering the case with non-Brownian particles, a new similarity solution, with a stable shock in particle density, is developed.

Nanoscale Strain Measurements in Polymer Nanocomposites

2006 ◽  
Vol 977 ◽  
Author(s):  
Qi Chen ◽  
Ioannis Chasiotis ◽  
Chenggang Chen ◽  
Ajit Roy
Keyword(s):  
Mechanical Behavior ◽  
Polymer Nanocomposites ◽  
Volume Fraction ◽  
Particle Density ◽  
Particle Volume Fraction ◽  
Volume Ratio ◽  
Local Strain ◽  
Fused Silica ◽  
Particle Volume ◽  
Strain Measurements

AbstractThe paper describes a multiscale experimental investigation of the mechanical behavior of polymer nanocomposites with nanoscale fused silica inclusions with the objective to shed light into the effect of the hard nanoparticles on the quasistatic mechanical behavior of epoxy matrix and the implications of the latter to the effective composite properties. The main variable in this study was the nanofiller volume fraction while the particle size was either 15 nm or 100 nm. Local strain measurements indicated strain field localization in the vicinity of the nanofillers at strains that macroscopically fall in the linearly elastic regime. The matrix strains were as high as three times the applied far field strain at applied effective strains of ∼ 1%. At larger stresses the local strain fields evolved to maxima that were considerably higher than the applied strain, and they were affected by local particle density and distribution. In composites with the largest particle volume fraction, 5 vol.%, 100 nm fillers, neighboring particles located in small proximities behaved as single large particles and often resulted in matrix strain shielding thus decreasing the benefit of the large surface-to-volume ratio and the associated efficiency in load transfer. On the other hand the 15 nm fillers resulted in more uniformly distributed deformation compared to composites with 100 nm particles.

scholarly journals Magnetohydrodynamic Effects in Mixed Convection Copper-Water Nano Fluid Flow at Lower Stagnation Point on a Sliced Sphere

CFD Letters ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 21-31
Author(s):  
Basuki Widodo ◽  
Adhi Surya Nugraha ◽  
Dieky Adzkiya ◽  
Mohd Zuki Salleh
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Copper Particle ◽  
Particle Volume ◽  
Nano Fluid ◽  
Determining Factors

The study of simulation and applications of mathematics in fluid dynamics continues to grow along with the development of computer science and technology. One of them is Magnetohydrodynamics (MHD) which is closely related to its implementation in engineering and industry. And given the importance of magnetic fluid flow has attracted researchers to study and explore its benefits and uses in the industrial field, especially in convective flow and heat transfer processes. This paper therefore considers mathematical modeling on mixed convection MHD viscous fluid flow on the lower stagnation point of a magnetic sliced sphere. The study began with transforming the governing equations which are in dimensional partial differential equations to non-dimensional ordinary differential equations by using the similarity variable. The resulting similarity equations are then solved by the Keller-Box scheme. The characteristics and effects of the Prandtl number, the sliced angle, the magnetic parameter, and the mixed convection parameter are analyzed and discussed. The results depicted that the uniform magnetic field produced by Lorentz force and slicing on the sphere act as determining factors for the trend of nano fluid movement and controlling the cooling rate of the sphere surface. In addition, the viscosity depends on the copper particle volume fraction.

Numerical Investigation of Proppant Transport and Placement Along Opened Bedding Interfaces

2021 ◽  
Author(s):  
Jun Xie ◽  
Jizhou Tang ◽  
Sijie Sun ◽  
Yuwei Li ◽  
Yi Song ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Volume Fraction ◽  
Transport Model ◽  
Fluid Velocity ◽  
Fracture Propagation ◽  
Propagation Model ◽  
Fluid Viscosity ◽  
Fracture Width ◽  
Proppant Transport ◽  
Penny Shaped Crack

Abstract Slurry, as a proppant-laden fluid for hydraulic fracturing, is pumped into initial perforated cracks to generate a conductive pathway for hydrocarbon movement. Recently, numerous studies have been done to investigate mechanisms of proppant transport within vertical fractures. However, the distribution of proppant during stimulation becomes much more complicated if bedding planes (BPs), natural fractures (NFs) or other discontinuities pervasively distributed throughout the formation. Thus, how to capture the transport and placement mechanisms of proppant particles in the opened BPs becomes a significant issue. In this paper, we propose a closed-form continuous proppant transport model based on the conservation of total proppant volume and sedimentation of proppant particles. This model enables to integrate with the fluid flow section of a 3-D hydro-mechanical coupled fracture propagation model and then predict the distribution of proppant velocity and slurry volume fraction within a dynamic fracture network. Stokes’ law is applied to determine the sedimentation velocity. In the fracture propagation model, rock deformation is governed by the analytical solution of penny-shaped crack to determine fracture width. Fluid flow is characterized by finite differentiation scheme and then the fluid velocity is obtained. These two parameters above are inputs for the proppant transport model and both slurry viscosity and density are updated in this step. Afterwards, both fracture width and fluid velocity would be altered in the fracture model. Analysis of the proppant distribution within crossing-shaped fracture is conducted to study mechanisms of proppant transport along opened BPs. From our numerical analysis, we find that the distribution of proppant concentration is independent with the fluid viscosity, but highly dependent on the volume fraction of pumping slurry, under a given pumping pressure. Due to the difference of viscosity and proppant volume fraction at locations of upper and lower BPs, we observe that two symmetric BPs are unevenly opened, with different channel length along BP. Moreover, the width of opened upper BP is much smaller than that of opened lower BP as a result of discrepancy of proppant sedimentation. Last but not the least, a criterion of flow bed mobilization is established for dynamically tracking the sedimentation along the BP. Then the effect of different parameters (such as proppant size, proppant density, fluid viscosity, injection rate) on proppant distribution along opened BPs is also studied. Our model fully considers the proppant transport and settlement, proppant bed formation and interaction between fracture and proppant, which helps to predict the influence of proppant during fracturing treatment. Additionally, our model is also capable of dynamically tracking the settlement of proppant along opened BPs.

Full Factorial Design to Study Material Parameters of Magnetorheological Fluid

2013 ◽  
Vol 543 ◽  
pp. 511-514
Author(s):  
Izwan Ismail ◽  
Saiful Amri Mazlan ◽  
Syarifah Nur Aqida ◽  
A.G. Olabi
Keyword(s):  
Volume Fraction ◽  
Silicone Oil ◽  
Particle Volume Fraction ◽  
Testing Machine ◽  
Vertical Direction ◽  
Statistical Investigation ◽  
Fluid Viscosity ◽  
Particle Volume ◽  
Mr Fluid ◽  
Carrier Fluid

This paper presents the effects of magnetorheological (MR) fluid parameters, bidisperse ratio, carrier fluid viscosity and particle volume fraction, on its mechanical behaviour using statistical investigation. Silicone oil-based MR fluid samples were compressed using universal testing machine (UTM) in a vertical direction. A set of eight experiments was designed by Design Expert 7 software in which was conducted at two levels for each factor. Stress-strain curves that obtained from the compression test were then analysed by testXpert analyser software. The responses in terms of maximum stresses at 0.75 of strain were extracted from the curves. The result indicated that a combination of high bidisperse ratio and particle volume fraction, and a low carrier fluid viscosity could produce a high compressive stress. The findings are important to be considered in designing squeeze mode MR fluid actuators.

scholarly journals Performance improvement of double-tube gas cooler in CO2 refrigeration system using nanofluids

2015 ◽  
Vol 19 (1) ◽  
pp. 109-118 ◽  
Author(s):  
Jahar Sarkar
Keyword(s):  
Performance Improvement ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Cooling Capacity ◽  
Inlet Temperature ◽  
Refrigeration Cycle ◽  
Particle Volume ◽  
Transcritical Carbon Dioxide ◽  
The Given ◽  
Theoretical Analyses

The theoretical analyses of the double-tube gas cooler in transcritical carbon dioxide refrigeration cycle have been performed to study the performance improvement of gas cooler as well as CO2 cycle using Al2O3, TiO2, CuO and Cu nanofluids as coolants. Effects of various operating parameters (nanofluid inlet temperature and mass flow rate, CO2 pressure and particle volume fraction) are studied as well. Use of nanofluid as coolant in double-tube gas cooler of CO2 cycle improves the gas cooler effectiveness, cooling capacity and COP without penalty of pumping power. The CO2 cycle yields best performance using Al2O3-H2O as a coolant in double-tube gas cooler followed by TiO2-H2O, CuO-H2O and Cu-H2O. The maximum cooling COP improvement of transcritical CO2 cycle for Al2O3-H2O is 25.4%, whereas that for TiO2-H2O is 23.8%, for CuO-H2O is 20.2% and for Cu-H2O is 16.2% for the given ranges of study. Study shows that the nanofluid may effectively use as coolant in double-tube gas cooler to improve the performance of transcritical CO2 refrigeration cycle.

A simulation and experimental study on particle volume fraction of PMMA suspension in centrifugal fields

2021 ◽  
Author(s):  
Yosephus Ardean Kurnianto Prayitno ◽  
Tong Zhao ◽  
Yoshiyuki Iso ◽  
Masahiro Takei
Keyword(s):  
Experimental Study ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Volume
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