Solid Volume Fraction Profiles Research Articles

Dispersion of solids in fracturing flows of yield stress fluids

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.

Triple Phase Simulation of Bubbling Fluidized Beds of Geldart “A” Particles with a Bubble-Based Drag Model

A triple-phase numerical model was developed for the simulations of gas-solid bubbling fluidized beds with Geldart “A” particles. In the model, the gas-solids suspension was modeled as a primary gas phase presented in the emulsion, a secondary gas phase presented in the bubble, and a third phase consisting of solids. A bubble-based drag model was derived taking into account of the heterogeneous flow structures of the emulsion phase. The KTGF model was used to describe the solid phase stresses. Simulations were conducted for two different scales bubbling fluidized beds of Group “A” particles. Mesh independences were confirmed up to a radial grid size of 200 times particle diameter, and the sensitivity of the transitional results on the time-steps was investigated. The predicted bed expansion and the voidage distribution, axial and radial solids volume fraction profiles, and the solids velocity vectors have been validated against literature data.

Influence of grid resolution, parcel size and drag models on bubbling fluidized bed simulation

In this paper, a bubbling fluidized bed is simulated with different numerical parameters, such as grid resolution and parcel size. We examined also the effect of using two homogeneous drag correlations and a heterogeneous drag based on the energy minimization method. A fast and reliable bubble detection algorithm was developed based on the connected component labeling. The radial and axial solids volume fraction profiles are compared with experiment data and previous simulation results. These results show a significant influence of drag models on bubble size and voidage distributions and a much less dependence on numerical parameters. With a heterogeneous drag model that accounts for sub-scale structures, the void fraction in the bubbling fluidized bed can be well captured with coarse grid and large computation parcels. Refining the CFD grid and reducing the parcel size can improve the simulation results but with a large increase in computation cost.

Comparisons of Eulerian-Eulerian and CFD-DEM simulations of mixing behaviors in bubbling fluidized beds

The Eulerian-Eulerian model and CFD-DEM have been applied extensively to investigate various aspects of fluidized bed systems. However, there have been very limited studies to date on comparisons of predictions made using these two fundamentally different approaches. To address this gap in the existing literature, both approaches were applied to perform simulations of solids mixing behaviors in gas fluidized beds with various inlet gas velocities. It was observed in both modeling approaches that bubbling had a significant influence on solids mixing behaviors. Higher gas velocities gave rise to larger and more plentiful bubbles throughout the bed which led to higher rates of mixing. All beds were observed to be well-mixed after 10s of fluidization. Both modeling approaches predicted similar fluidization behaviors and bubbling phenomena, while there were slight discrepancies in the solids volume fraction profiles possibly due to innate differences in the models and parameters used. When the amount of solids was increased by two times, deeper and more extensive bubbling was observed at all gas velocities due to the larger initial bed height. However, owing to the greater amount of solids, a longer fluidization time was needed to achieve the same extent of mixing. At low gas velocity, the rate of solids mixing predicted by CFD-DEM was higher than that by the Eulerian-Eulerian model. At high gas velocities, good agreement in extents of mixing at different instants of time during the fluidization processes between the two modeling approaches was achieved. However, a vigorous initial bed expansion process predicted by CFD-DEM was not observed in the Eulerian-Eulerian simulations and this might be another manifestation of the fundamental differences between the two modeling approaches.

Simulation of bubbling fluidized beds with cohesive particles by incorporating a novel structure‐Based drag model into the two‐fluid model

AbstractA novel structure‐based drag model was proposed to study the hydrodynamics of bubbling fluidized beds (BFBs) operated with ultrafine cohesive particles by considering local heterogeneous flow structures. Firstly, a local structure parameters model capturing the internal flow structures of the studied system was built by balance equations and empirical formulas and the solutions (i.e. local structure parameters) of this model solved by global search algorithm were evaluated in terms of hydrodynamics, energy consumption, and voidage. Then the local structure parameters were employed to derive the structure‐based drag model. Lastly, three drag models (i.e. the structure‐based drag model, Gidaspow model, and Syamlal‐O'Brien model) were investigated and incorporated separately into the two‐fluid model, where the simulation results were also separately compared with available experimental data. The comparison shows that Gidaspow and Syamlal‐O'Brien drag models failed to predict the solid volume fraction profiles. However, the error analysis results of the structure‐based drag model indicate the average absolute relative error of solid volume fraction in the radial direction is 7.04 % and 5.64 % at the height of 0.1 m and 0.2 m respectively, which exhibits promising predictions. Thus, it is feasible to simulate the BFBs with cohesive particles through the combination of the structure‐based drag model with the two‐fluid model.

Three-dimensional CFD study of conical spouted beds containing heavy particles: Design parameters

The flow behavior of conical spouted beds containing heavy particles that occurs in chemical vapor deposition (CVD) was investigated using the computational fluid dynamics (CFD) approach. A fully Eulerian description of solid and gas phases flows in 3D was used in these simulations. The hydrodynamics parameters including particle velocity, solid flux, and solid volume fraction profiles at different bed levels were evaluated, and the overall behavior of solid particles in the beds was studied. The results showed close agreement with the corresponding experimental data. The effects of cone angle, static bed height, and cone bottom diameter on the hydrodynamic behavior of heavy particles were analyzed and the results were presented. In addition, the effects of flat wall of semi-conical spouted bed (half-column) on the CFD results and performance of the spouted bed were investigated. The hydrodynamic results for the full bed were quite different from those for the half bed geometries. It was also found that the conical spouted bed with the angle of 45° leads to the roughly stable spouting compared to the 30° angle bed. The CFD model also showed that the conical-cylindrical spouted beds operating with heavy particles has the potential for periodic occurrence of choking in the spout zone.

Measurement of optical backscattering height scans from flocculated mineral sediments

This paper describes the calculation and interpretation of optical backscattering (OBS) signal values for the measurement of aggregation state within settled particulate suspensions. An OBS height scan method is applied to suspensions of kaolin prepared at two different solid concentrations and flocculated by varying dosages of a non-ionic polyacrylamide. It was found that the root-mean-square scattering, Frms, and mean scattering, Fmean, signal values correlate very well with changes in relative aggregation state as indicated by changes in the final sediment bed density and calculated index of aggregation values. Application of the measured signal value versus concentration data allows the calculation of the solid volume fraction versus height profile within the settled bed.

Numerical study of a fluid catalytic cracking regenerator hydrodynamics

Fluid catalytic cracking (FCC) is one of the most important conversion processes in petroleum refineries, and FCC regenerator is a key component of an FCC unit to recover the solid catalyst reactivity by burning off the deposited coke on the catalyst. In this paper, a three-dimensional multi-phase flow computational fluid dynamics (CFD) model was established to simulate the flow inside a commercial FCC regenerator. The two phases involved in the flow are gas phase and solid phase. The Eulerian-Eulerian approach, where the two phases are considered to be continuous and fully inter-penetrating, was employed. The effects of different drag models on the flow characteristics were firstly investigated. A modified drag force model was applied by using user define function (UDF) in ANSYS Fluent, which provides a better prediction on the solid volume fraction profile along the regenerator height. Particle clustering phenomena was taken into consideration through the adjustment of effective particle cluster diameters. The appropriate effective cluster diameters in the dense bed and the dilute phase are 300μm and 200μm, respectively. Catalyst solid volume fraction profile indicates that there are four zones in the computational domain: dense zone, sub-dense zone, dilute zone and sub-dilute zone. The developed CFD model was validated by plant data. The effect of air superficial velocity on the fluidization was also investigated and the results shown that the total flow rate of catalysts goes through the cyclone increases linearly with increasing air superficial velocity from a range of 0.6 to 1.03.

Effects of particle size and bubbling behavior on heat transfer in gas fluidized beds

The fluidization and heat transfer behaviors of a bubbling fluidized bed were studied using Computational Fluid Dynamics (CFD). The simulations were conducted with varying particle sizes and inlet gas superficial velocities. Solid volume fraction, solid temperature, air temperature, solid velocity vectors, and air velocity vectors distributions were analyzed and compared for the various operating conditions. Solid volume fraction profiles showed a symmetrical and non-uniform distribution during the initial phase of fluidization. The size of bubbles generated during the initial phase of fluidization increased with increasing inlet air superficial velocity and decreasing particle size. The coupled analysis of solid volume fraction and temperature profiles indicated that both conductive and convective heat transfer between the two phases were significant. The simulation results showed that rate of heat transfer from air to particles was dependent on the amount of interfacial surface area, which increased with increasing voidage within the bed. Voidage increased with decreasing particle size or increasing inlet air superficial velocity. However, based on the range of operating conditions studied, it could be deduced that there seemed to be an optimal set of operating conditions where heat transfer was most efficient. Over-fluidization led to poor heat transfer due to channeling which resulted in heat being unevenly distributed. Under-fluidization resulted in poorer convective heat transfer between the two phases but this was compensated partially by an increase in conductive particle-to-particle heat transfer due to high solid concentrations.

Impacts of solid-phase wall boundary condition on CFD simulation of conical spouted beds containing heavy zirconia particles

The gas–solid flow behavior of a conical spouted bed including heavy particles, zirconia, with density of 6050kg/m3 that typically encountered in chemical vapor deposition (CVD) was studied by the CFD technique. An Eulerian–Eulerian two-fluid model (TFM) in conjunction with the kinetic theory of granular flows (KTGF) was used in a full 3D computational framework. To reduce the computational time, while maintaining the accuracy of the results, polyhedral mesh structure was utilized. Parametric studies of the specularity coefficient and particle–wall restitution coefficient were also performed. The hydrodynamics parameters including particle velocity and solid volume fraction profiles at different bed levels were evaluated, and the overall behavior of particles in the bed was studied. The simulation results showed that the specularity coefficient significantly affects the CFD results, while the impact of small changes in the particle–wall restitution coefficient is not noticeable. Furthermore, a small specularity coefficient of 0.05 provides suitable predictions that are in agreement of the experimental data. Incoherent spouting was also properly predicted by the present CFD model, which was shown to be in agreement with the experimental observations. It was also found that both the no-slip boundary condition and the specularity of φ=1 wall boundary condition predict roughly the same results. Finally, the influences of the drag function and particle–particle restitution coefficient on the CFD results were studied, and the new findings were discussed.

Experimental and numerical study of pseudo-2D circulating fluidized beds

We present experimental investigations and numerical simulations of a pseudo-2D riser. Experiments were performed for various airflow rates, particle types/diameters, and particle size distributions. Pressure distributions along the wall of the riser were measured. Additional measurements from a smaller pseudo-2D riser (Kallio et al., 2009; Shah et al., 2012) were used to analyze horizontal solids volume fraction profiles. The experimental data were compared with simulation results carried out using an Euler–Euler approach. A mesh sensitivity study was conducted for numerical simulations and effects associated with simplifying real 3D geometry to a 2D model were examined. In addition, the effect of using an algebraic equation to represent the granular temperature versus a full partial differential equation also was examined for numerical simulations. Results showed small but significant near-wall sensitivity of the flow variables to mesh size. Substantial differences in mean pressure, solids distribution, and solid velocities were obtained, when 2D and 3D simulation results were compared. Finally, applying the simplified granular temperature equation for turbulent fluidization and for dilute-phase transport can lead to incorrect predictions in models.

Hydromagnetic flow and radiative heat transfer of nanofluid past a vertical plate

Hydromagnetic flow of an incompressible viscous nanofluid past a vertical plate in the presence of thermal radiation is investigated both analytically and numerically. The radiative heat flux is described by the Rosseland diffusion approximation in the energy equation. The governing non-linear partial differential equations are converted into a set of ordinary differential equations by suitable similarity transformations. The resulting ordinary differential equations are successfully solved analytically with the help of homotopy analysis method and numerically by the fourth order Runge–Kutta method with shooting technique. The effects of various physical parameters are analyzed and discussed in graphical and tabular forms. The effects of some physical parameters such as Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, radiation parameter and magnetic parameter are analyzed on the velocity, temperature and solid volume fraction profiles as well as on the reduced Nusselt number and the local Sherwood number. An excellent agreement is observed between present analytical and numerical results.

A minimal coupled fluid-discrete element model for bedload transport

A minimal Lagrangian two-phase model to study turbulent bedload transport focusing on the granular phase is presented and validated with experiments. The model intends to describe bedload transport of massive particles in fully rough flows at relatively low Shields numbers, for which no suspension occurs. A discrete element method for the granular phase is coupled with a one dimensional volume-averaged two-phase momentum equation for the fluid phase. The coupling between the discrete granular phase and the continuous fluid phase is discussed, and a consistent averaging formulation adapted to bedload transport is introduced. An original simple discrete random walk model is proposed to account for the fluid velocity fluctuations. The model is compared with experiments considering both classical sediment transport rate as a function of the Shields number, and depth profiles of solid velocity, volume fraction, and transport rate density, from existing bedload transport experiments in inclined flume. The results successfully reproduce the classical 3/2 power law, and more importantly describe well the depth profiles of the granular phase, showing that the model is able to reproduce the particle scale mechanisms. From a sensitivity analysis, it is shown that the fluctuation model allows to reproduce a realistic critical Shields number, and that the influence of the granular parameters on the macroscopic results is weak. Nevertheless, the analysis of the corresponding depth profiles reveals an evolution of the depth structure of the granular phase with varying restitution and friction coefficients, which denotes the non-trivial underlying physical mechanisms.

Numerical analysis of heat transfer and solid volume fraction profiles around a horizontal tube immersed in a supercritical water fluidized bed

In the present work, the heat transfer and solid volume fraction distribution characteristics in a supercritical water (SCW) fluidized bed with immersed tube are modeled with Two-Fluid model (TFM) incorporated with the Kinetic Theory of Granular Flow (KTGF). The Gidaspow drag model and Gunn heat transfer correlation are used to describe the interaction and heat transfer between different phases, respectively. A comparison between SCW and gas–solid fluidized bed was conducted. The results show that diameter and rising velocity of bubbles in the gas–solid fluidized bed are larger than that in the SCW fluidized bed when the corresponding fluidization numbers in both systems keep the same, and channeling is observed only in SCW fluidized bed. High particle concentration is always accompanied with high heat transfer coefficients around the tube in the gas–solid fluidized bed. In SCW fluidized bed, however, higher particle concentration will lead to lower heat transfer coefficients around the tube. Smaller fluctuations of solid volume fraction and heat transfer coefficients are also observed in the SCW fluidized bed than that in the gas–solid fluidized bed. In addition, the influence of fast fluid inlet velocity on solid volume fraction and heat transfer in SCW fluidized beds is considered.

Performance improvement of existing drag models in two-fluid modeling of gas–solid flows using a PR-DNS based drag model

This paper investigates a new drag model for the simulation of the fluidization of fluid catalytic cracking (FCC) particles with air in a fluidized bed using the two-fluid model (TFM) within the Multiphase Flow with Interphase Exchanges (MFIX) code. A cohesion index parameter based on the interparticle cohesive forces has been implemented in the MFIX-TFM code. This index is used as a switching criterion between a particle resolved drag model developed by Tenneti et al. (2011), and some of the drag models available in the MFIX for homogeneous particles, namely the Gidaspow, Syam–O'brien, and Wen–Yu models. The proposed drag correlation in this paper implements an indirect method of introducing interparticle cohesive forces to our TFM simulations. Significant improvement in the solid volume fraction profile along the riser was obtained for all of the drag law combinations, depending on the conditions set in the switching procedures. In the best case, the utilization of the Gidaspow and TGS models resulted in a 60% improvement in maximum deviation of numerical results from the available experimental data. The proposed model can be used in simulations of fluidized beds, where standard models fail to produce accurate results even on extremely refined computational grid, especially for Geldart A type particles that may exhibit strong clustering behavior.

A two-phase flow meter for determining water and solids volumetric flow rates in stratified, inclined solids-in-water flows

This paper describes the design and implementation of a two-phase flow meter which can be used in solids-in-water two phase pipe flows to measure the in-situ volume fraction distributions of both phases, the velocity profiles of both phases and the volumetric flow rates for both phases. The system contains an Impedance Cross Correlation (ICC) device which is used in conjunction with an Electromagnetic Velocity Profiler (EVP). Experimental results were obtained for the water and solids velocity and volume fraction profiles in upward inclined flow at 30° to the vertical, in which highly non-uniform velocity and volume fraction profiles occur.

A numerical study of gas–solid flow hydrodynamics in a riser under dense suspension upflow regime

The Eulerian–Eulerian two-fluid model coupled with the EMMS/Matrix drag model was employed to investigate the gas–solid flow hydrodynamics in the riser of high-density circulating fluidized bed using Geldart B particles under the dense suspension upflow (DSU) regime. Based on the 2D simulations of two test cases, the predicted axial and radial profiles of solid volume fraction agreed well with the experimental observations, and it could capture the key characteristics of the DSU regime. The transient solid flux and the power spectral density of pressure fluctuation were discussed. The 2D simulation results using the EMMS/Matrix and the Gidaspow drag models were compared in details, and the EMMS/Matrix drag model gave better radial distributions against experimental data, but the predicted radial profiles were improved by solving partial differential equation of granular temperature with the Gidaspow drag model. The 3D simulation with the EMMS/Matrix drag model was also performed, and the differences in the predicted axial and radial profiles of solid volume fraction between 2D and 3D simulations were not significant. The two-dimensional two-fluid model with the EMMS/Matrix drag model is applicable to the simulation of gas–solid flow in the riser under the DSU regime.

Computational fluid dynamics simulation and parametric study of coal gasification in a circulating fluidized bed reactor

AbstractA computational fluid dynamics model based on the Eulerian–Eulerian multiphase framework was implemented to simulate the coal gasification processes in a circulating fluidized bed gasifier. The standard k–ε turbulence model is used for gas phase, and the solid phases are modeled with kinetic theory of granular flow. A lumped chemical reaction model was compiled based on the chemical percolation devolatilization model and the METC Gasifier Advanced Simulation gasification model. The user‐defined functions are developed to calculate rates of chemical reactions and to recirculate solids from the riser exit to the solid recycle inlet. Sensitivity analysis was performed on char–steam gasification reaction to choose an appropriate kinetic rate in this study. The calculated gas composition out of the riser was first compared with experimental data; then, the flow fields such as solid volume fraction, solid velocity, and species profiles were analyzed, indicating that the model gave reasonable predictions. Furthermore, the effects of the operating temperature, the steam/coal ratio, and the air/coal ratio on the exiting gas composition were numerically studied, and the predicted trends vs these parameters are reasonable and consistent with the findings in the literature, which shows the applicability of the Eulerian multiphase model to simulate coal gasification processes in circulating fluidized bed gasifiers. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.

Wall adhesion and constitutive modeling of strong colloidal gels

Wall adhesion effects during batch sedimentation of strongly flocculated colloidal gels are commonly assumed to be negligible. In this study, in-situ measurements of gel rheology and solids volume fraction distribution suggest the contrary, where significant wall adhesion effects are observed in a 110 mm diameter settling column. We develop and validate a mathematical model for the equilibrium stress state in the presence of wall adhesion under both viscoplastic and viscoelastic constitutive models. These formulations highlight fundamental issues regarding the constitutive modeling of colloidal gels, specifically the relative utility and validity of viscoplastic and viscoelastic rheological models under arbitrary tensorial loadings. The developed model is validated against experimental data, which points toward a novel method to estimate the shear and compressive yield strength of strongly flocculated colloidal gels from a series of equilibrium solids volume fraction profiles over various column widths.

Riser simulation and radial porosity distribution characterization for gas-fluidized bed of cork particles

Numerical simulations are carried out for gas-solid fluidized bed of cork particles, using discrete element method. Results exhibit the existence of a so-called anti core-annular porosity profile with lower porosity in the core and higher porosity near the wall for non-slugging fluidization. The tendency to form this unfamiliar anti core-annular porosity profile is stronger when the solid flux is higher. There exist multiple inflection points in the simulated axial solid volume fraction profile for non-slugging fluidization. Results also show that the familiar core-annular porosity profile still appears for slugging fluidization. In addition, the classical choking phenomenon can be captured at the superficial gas velocity slightly lower than the correlated transport velocity.