Solids Concentration Profiles Research Articles

ANALYTICAL AND COMPARATIVE INVESTIGATION OF PARTICULATE SIZE EFFECT ON SLURRY FLOW CHARACTERISTICS USING COMPUTATIONAL FLUID DYNAMICS

The key issue associated with the industries is the transportation and dumping of solids particulates in the form of slurry at the desired place using long length pipelines. In this perspective, numerical simulation of three-dimensional horizontal slurry pipeline of 0.0549 m diameter using Eulerian two-phase model with RNG k-ɛ turbulence closure is carried out. The glass - beads solid particulates having density ( = 2470 kg/m3) and slurry concentration varies as 10% to 50% (by volume) for velocity ranges of 3-5 ms-1. The computational modeling is done using available commercial software ANSYS Fluent for 125µm and 440 µm particulate size at different velocity and concentration range to know their effect on slurry flow characteristics. It is observed that for chosen particulate size pressure drop increases with increase in velocity at all solid concentration range. The pressure drop in slurry for 440 µm solid particulates is found higher as compared to the pressure drop of 125 µm solid particulates slurry. The percentage change in pressure drop is also reported in the paper due to particulate size effect at all velocity and solid concentration. The obtained results of predicted pressure drop are analytically compared with the available experimental results of literature and are in synchronism with that. A parametric study is carried out with the aim of visualizing and understanding the solid particulate size effect on slurry flow characteristics. Finally, the results of settling solid concentration contour, velocity contour, concentration profiles, velocity profiles and vector representation of concentration/velocity were also predicted for chosen particulates sized slurry.

Numerical investigation on mixing characteristics of floating and sinking particles in a stirred tank with fractal impellers

The hydrodynamics of floating and sinking particles mixing process in a stirred tank with four pitched-blade impellers and fractal impellers were investigated employing computational fluid dynamics (CFD) simulation. Axial solid concentration profile, solid concentration distribution, power consumption, trailing vortex, cloud height, water integrated velocity, just suspension speed (Njs) and just drawdown speed (Njd) in the stirred tank were predicted. Results showed that the mixing quality of floating and sinking particles increased with the increase of impeller speed. Smaller density difference between solid-liquid two phases and smaller particle diameter resulted in higher suspension degree. Fractal impeller can enhance water integrated velocity and improve suspension quality compared with four pitched-blade impeller under the constant power consumption, and increasingly so with fractal iteration number. Meanwhile, fractal impeller can reduce the size of trailing vortex and decrease the power consumption based on four pitched-blade impeller at the same impeller speed. In addition, the just suspension speed (Njs), just drawdown speed (Njd) and correlation equation for Njs and Njd in the three different impeller systems were obtained. Fractal impeller could decrease the Njs and Njd on the basis of four pitched-blade impeller, and decreasingly so with the fractal iteration number.

Numerical simulation and comparative analysis of pressure drop estimation in horizontal and vertical slurry pipeline

Transportation of solids with water as a carrier in the form of slurry through long length pipelines is widely used by many industries and power plants. The transportation of slurry through vertical pipeline is a challenging task and require modification to overcome the pressure loss and power consumption requirements. In this perspective, numerical simulation of three-dimensional horizontal slurry pipeline (HSPL) and vertical slurry pipeline (VSPL) carrying glass beads solid particulates of spherical diameter 440 µm and density 2,470 kg/m3 is carried out. The 3D computational model for horizontal and vertical slurry pipeline is developed for a pipe of 0.0549 m diameter and analyzed in available commercial software ANSYS Fluent 16. The simulation is conducted by using Eulerian multiphase model with RNG k-ɛ turbulence closure at solid concentration range 10 – 20% (by volume) for mean flow velocities ranging from 1-4 ms-1. It is found that the pressure drop rises for both HSPL and VSPL with escalation in mean flow velocity and solid concentration. The predicted pressure drop in VSPL is found to follow the same pattern as with HSPL but higher in magnitude for all chosen velocity and solid concentration range. The obtained results of predicted pressure drop in HSPL are validated with the available experimental data in the literature. A parametric study is conducted with the aim of visualizing and understanding the slurry flow behavior in HSPL and VSPL. Finally, the results of solid concentration contour, velocity contour, solid concentration profiles, velocity profiles and pressure drop are predicted for both the slurry pipelines.

Design of a sensor based on neural networks to determine sludge level of industrial thickeners

In copper mining, there are two main separation processes: leaching for oxidized minerals and flotation for sulfide minerals. In Chile, the increase of sulfide minerals in the deposits and the decrease of oxidized minerals have led to an increase in the investigation of flotation processes and the optimization of their associated operations. One of the concentration processes is the use of thickeners, whose main objective is to treat the tailings that leave the plants in pulp form with approximately 30% solids and obtain a pulp with a concentration greater than 50% with clear water flow. The recovery of water is the main goal, so knowing the concentration profiles of solids and sedimentation is crucial. However, the characteristics of the pulp and the operation of the thickeners are complex because a great variety of forms can be found in the concentration profile of said pulp. This limits conventional measurement techniques and makes it difficult to apply deterministic models to the solids profile, given the high nonlinearities and variability of the system. In this article, a solution is proposed by developing a sensor that allows the online estimation of sludge level and concentration of solids, based on a model of neural networks (with the model of Maxwell for dispersions), allowing to measure the solids profile regardless of the operating conditions. The structure selected has nine inputs with a hidden layer, two neurons, and two outputs being trained with tailings from Chuquicamata, obtaining the information from a 50 L pilot with 10-electrode bar of 60 cm of length, resulting in an estimation error of 0.8 cm with a network of 26 parameters.

Intensification on drawdown process of floating particles by circle package fractal impellers

Abstract The floating particle drawdown and dispersion characteristics in a stirred tank with four pitched-blade impellers, fractal impellers, and circle package fractal impellers were studied using computational fluid dynamics (CFD) simulation. The effects of impeller type, impeller speed, impeller spacing, impeller submergence, initial floating particle concentration, and floating particle diameter on the floating particle dispersion quality were investigated. Results showed that the floating particle dispersion degree was improved with an increment in the impeller speed, in term of axial solid concentration profile, solid concentration distribution, and cloud height. The impeller spacing of T2/3 and impeller submergence of T/6 were appropriate for the floating particle drawdown process in this work. Higher initial floating particle concentration was easier to achieve a higher floating particle dispersion degree. Smaller particle diameter resulted in smaller buoyancy and more uniform distribution. Meanwhile, circle package fractal impeller can reduce the power consumption compared with four pitched-blade impeller and fractal impeller at the same impeller speed, and enhance the solid integrated velocity and the level of homogeneity for floating particle dispersion process under the constant power consumption. In addition, the just drawdown speed (Njd) and correlation equation for Njd in the three different impeller systems were obtained.

Settling of weighting agents in non-Newtonian fluids to off-shore drilling wells: Modeling, parameter estimation and analysis of constitutive equations

High-density solids such as barite and hematite are generally added to drilling fluids to increase their density, allowing the control of subsurface pressures. However, a variety of problems in drilling wells has been related to the gravitational settling of particulate materials. In this work, the dynamic behavior of barite settling in a synthetic paraffin-based drilling fluid was evaluated experimentally by monitoring the solid concentration as a function of time and height. The tests were conducted in a gravitational settling bench-scale rig using a gamma-ray attenuation technique. Following the standard approach of continuum mechanics, a mathematical model was developed to yield a single set of partial differential equations capable of describing all settling zones inherent in a batch sedimentation process. Further, by means of the predicted solid concentration profiles, it was possible to obtain the height of bottom piled up solids. The mathematical model takes particles compressibility under their own weight and permeability of the sediment into consideration. The parameters of the proposed constitutive equations for the effective pressure on solids and porous matrix permeability were estimated and statistically analyzed from the experimental profiles of solid concentration. In particular, the results obtained in this work indicated a good agreement between the model predictions and the experimental data.

Investigation of the Segregation of Binary Mixtures with Iron-Based Particles in a Bubbling Fluidized Bed.

The characterization of the segregation phenomena in binary mixtures of solids with very different densities and/or particle sizes is highly relevant in many industrial processes. As a recent example, some advanced CO2 capture systems using fluidized beds include the separation by segregation of the functional materials. In this work, we have conducted mixing-segregation experiments with particles of iron ore (a typical oxygen carrier in chemical looping combustion systems) acting as jetsam, and glass beads (representing a lower density solid present in the bed) acting as flotsam, to measure solid concentration profiles at different fluidizing gas velocities and mixture compositions of different-sized particles. The experimental concentration profiles have been interpreted using a modified version of the model proposed by Gibilaro and Rowe. A relatively simple correlation is included in the model to calculate the segregation model parameters, which depend on the physical properties of the fluidized solids. The model fits reasonably well with all experimental data, especially for mixtures with a low fraction of oxygen carriers, which are the most relevant for the design of future continuous separation of solids by segregation.

RANS-based predictions of dense solid–liquid suspensions in turbulent stirred tanks

This work is aimed at investigating the impact of different meso-scale models and constitutive equations for the RANS-based two-fluid model simulations of a turbulent solid–liquid stirred vessel with high solids loading. The model assessment is preceded with a grid convergence study, which confirms the variability of the discretization requirements depending on the observed variable. The simulation results demonstrate that for the investigated system the high solids loading contribution modelled by the kinetic theory of granular flows is negligible, both in incomplete and complete suspension conditions. Instead, the particle concentration fluctuations contribution included in the momentum equations dramatically affect the predictions, particularly in incomplete suspension conditions. The evaluation of the models is completed by the comparison of the predicted solids concentration profiles with experimental data measured by Electrical Resistance Tomography. The computational strategy for achieving realistic predictions of the solid distribution both in complete and incomplete suspension conditions is outlined.

Study of Axial Solid Concentration Distribution in Slurry Bubble Columns

The axial distribution of solid concentration was studied in semibatch slurry bubble columns. Tapered slurry bubble column (TSBC) and cylindrical slurry bubble column (CSBC) have been used in this study. Air, sodium chloride (NaCl) aqueous solution of concentration 0.15 M, and quartz sand, were represented gas, liquid and solid phases, respectively. The superficial velocity of gas was varied from 2.5 to 10 cm/s. Quartz sands with a mean diameter of 120 µm were used in the concentrations of 3,5,10 & 20 vol. %. Influences of gas velocity and solid loading on longitudinal profile of solid concentration were investigated. It was observed that the longitudinal distribution of solid concentration tends to be more uniform as superficial velocity of gas or solid loading increased. Under the same operation conditions, experimental results showed that TSBC offered more uniform distribution of solids along the column. The observed axial concentration distribution of solid particles in tapered slurry bubble column was analyzed on the basis of precipitation-dispersion model. The model successfully predicts the axial concentration distribution for narrow-sized range of solids systems in TSBC. Empirical correlation for the solid dispersion coefficient for solid particles in tapered slurry bubble column was proposed.

Calibration of a sedimentation model through a continuous genetic algorithm

ABSTRACTIn this contribution we consider the problem of flux identification in a scalar conservation law modelling the phenomenon of sedimentation. The experimental observation data used for the calibration consist of a solid concentration profile at a fixed time. The identification problem is formulated as an optimization one, where the distance between the profiles of the model simulation and observation data is minimized by a least squares cost function. The direct problem is approximated by a monotone finite volume scheme. The numerical solution of the calibration problem is obtained by a continuous genetic algorithm. Numerical results are presented in order to validate the efficiency of the proposed algorithm.

Determination of the solid concentration in a binary mixture from pressure drop measurements

A new and simple method to estimate the concentration of solids in a binary solids mixture is proposed and experimentally tested in a small fluidized bed set up. In the proposed method, it is necessary to measure the pressure drop in different sections of the bed at different gas velocities so as to be able to determine local minimum fluidization velocities using the Ergun equation. Because the minimum fluidization velocity of a solids mixture is known to be dependent on its weight fraction, a calibration curve can be derived by means of the Cheung equation and this is shown to be sufficient to obtain reasonably good estimates of the axial solids concentration profiles inside the bed. This methodology has been applied to three different mixtures of iron oxide ore of varying size with limestone or glass spheres. Satisfactory agreement between the experimental and calculated concentrations as well as pooled relative standard deviations lower than ±7%, are obtained in all three cases. This technique could facilitate future experimental research on solids mixing and segregation phenomena in fluidized beds, as it is a very low-cost, non-destructive and very fast method to determine solids concentration bed profiles.

Hydrodynamics and bubble behaviour in a three-phase two-stage internal loop airlift reactor

Abstract Local hydrodynamics of a gas–liquid–solid system, such as bubble circulation regime, gas holdup, liquid velocity and axial profile of solid concentration, are studied in a two-stage internal loop airlift reactor. Empirical correlations for gas holdup and liquid velocity are proposed to ease the reactor design and scale-up. Different bubble circulation regimes were displayed in the first (lower) and second (upper) stages. Increasing superficial gas velocity and solid loading can promote regime transition of the second stage, and the gas holdup of the second stage is higher than that of the lower stage. In addition, the effects of solid loading on bubble behaviour are experimentally investigated for each stage. It is found that bubble size in the downcomer decreases with the presence of solid particles, and bubble size distribution widens under higher superficial gas velocity and lower solid loading.

Coarse grid simulation of the hydrodynamics of binary gas‐solid flow in CFB risers

AbstractCFD simulation has become an effective way to study the mixing and segregation characteristics of gas‐solid flow in CFB risers, which is important for the proper operation and design of such reactors. In this study, the numerical solution of a recently developed EMMS drag model for binary gas‐solid flow which considers the effect of particle clustering structures on the interphase drag forces was first improved, it was then coupled with a multifluid model to perform extensive 3D simulations of the mixing and segregation pattern of binary gas‐solid flow in CFB risers. It was shown that the experimental data of axial solid concentration profiles and radial solid mass flux distributions can be captured reasonably by the combined EMMS‐multifluid model, indicating that the model is able to reproduce the hydrodynamics of complex gas‐solid flow with particle size distribution.

Importance of spinel reaction kinetics in packed-bed chemical looping combustion using a CuO/Al2O3 oxygen carrier

Chemical looping combustion is especially competitive for electrical power generation with integrated CO2 capture when it is operated at high temperatures (1000–1200 °C) and high pressures (15 bar or higher). For these demanding conditions, dynamically operated packed bed reactors have been proposed, providing a good alternative to fluidized bed technology. This work addresses the importance of including the formation and reduction kinetics of spinel compounds to proper predict the packed bed reactor performance by validating a pseudo-homogeneous packed-bed reactor model to describe the redox kinetics of a CuO/Al2O3 oxygen carrier with experiments in a lab-scale packed bed reactor setup. A grain model describing the reaction kinetics of all solid species, including both spinel compounds (CuAl2O4 and CuAlO2), was included in a particle model and used to develop correlations for the effectiveness factor as a function of the particle conversion in order to account for internal solids concentration profiles and mass transfer limitations. The particle effectiveness factors were subsequently included in the source terms of the component mass balances of the reactor model accounting for all the reactions of the spinel compounds. Cyclic experiments (oxidation with air and reduction with a H2-N2 mixture) have been carried out in a lab-scale packed bed reactor with a 12.5 wt% CuO/Al2O3 oxygen carrier at different temperatures ranging from 600 to 1000 °C. The experimental results are well described by the packed bed reactor model, only when including the developed particle effectiveness factors to fully account for the kinetics of the formation and reduction of the spinel compounds. The results confirm that it is neccesary to include a detailed description of the redox kinetics at the particle level to be able to accurately estimate the breakthrough time, cycle time, final amount of Cu present in the bed and the temperature rise in the reactor after reduction/oxidation reactions for packed-bed chemical looping combustion with a CuO/Al2O3 oxygen carrier.

Two-fluid Modeling of Geldart A Particles in Gas-solid Bubbling Fluidized Bed: Assessment of Drag Models and Solid Viscosity Correlations

Abstract In this work the influences of solid viscosity and the way to scale-down traditional drag models on the predicted hydrodynamics of Geldart A particles in a lab-scale gas-solid bubbling fluidized bed are investigated. To evaluate the effects of drag models, the modified Gibilaro et al. drag model (constant correction factor) and the EMMS drag model (non-constant correction factor) are tested. And the influences of solid viscosity are assessed by considering the empirical model proposed by Gidaspow et al. (1997, Turbulence, Viscosity and Numerical Simulation of FCC Particles in CFB. Fluidization and Fluid-particle Systems, AIChE Annual Meeting, Los Angeles, 58–62) and the models based on kinetic theory of granular flow (KTGF) with or without frictional stress. The resulting hydrodynamics by incorporating the different combinations of the drag model and solid viscosity model into two-fluid model (TFM) simulations are compared with the experimental data of Zhu et al. (2008, Detailed Measurements of Flow Structure inside a Dense Gas-Solids Fluidized Bed.” Powder Technological 180:339–349). The simulation results show that the predicted hydrodynamics closely depends on the setting of solid viscosity. When solid viscosity is calculated from the empirical model of Gidaspow et al., both drag models can reasonably predict the radial solid concentration profiles and particle velocity profiles. When the KTGF viscosity model without frictional stress is adopted, the EMMS drag model significantly over-estimates the bed expansion, whereas the modified Gibilaro et al. drag model can still give acceptable radial solid concentration profiles but over-estimate particle upwards and downwards velocity. When KTGF viscosity model with frictional stress is chosen, both drag models predict the occurrence of slugging. At this time, the particle velocity profiles predicted by EMMS drag model are still in well agreement with the experimental data, but the bed expansion is under-estimated.

Polynomial approximation pseudo-two-dimensional battery model for online application in embedded battery management system

Physics-based model has been regarded as a promising alternative to equivalent circuit model due to its ability to describe internal electrochemical states of battery. However, the rigorous physics-based model, namely pseudo-two-dimensional (P2D) model, is too complicated for online application in embedded battery management system. In this paper, to simplify the P2D model, a series of polynomial functions are employed to approximate the electrolyte phase concentration profile, solid phase concentration profile, and non-uniform reaction flux profile, respectively. Especially, the accuracy of 2nd-order and 3rd-order polynomial approximations for reaction flux is compared, and the higher-order is validated with more strength. Benefit from the acquisition of above variables, the electrolyte potential is derived directly according to the conservation of charge at electrolyte phase; the accuracy of activation overpotential is also improved by using the non-uniform reaction flux rather than assuming the uniform current density in single particle (SP) model. Finally, the developed model is simulated by different constant current rates, hybrid pulse and driving cycles, and its outputs are compared with P2D model and original SP model. The results demonstrate that the model proposed in this paper could capture the battery characteristics efficiently, and also significantly reduce the computation complexity.

The relationship between fluidization velocity and segregation in two-component gas fluidized beds: Density- or size-segregating mixtures

A model is proposed to predict the axial profile of solid concentration obtained by slowly defluidizing a binary mixture from the complete gas fluidized condition down to the fixed state. The model predictions are compared with experiments on beds of two solids differing either in density or size. The initial and final fluidization velocities of these mixtures as well as the concentration profiles at various overall composition are determined. It is shown that the theoretical equations used to predict the fluidization velocity interval of the two-solid system can also be used to calculate the axial distribution of its components at the end of the defluidization process. This is achieved by inferring an equilibrium relationship between the fluidized and the fixed region of the bed during defluidization. Despite the simplicity of the approach, an encouraging level of agreement between predictions and experiments is obtained, demonstrating that the extent of segregation is strongly related to the progress of binary fluidization.

Experimental study on the rheological behavior of ultra-fine cemented backfill

Ultra-fine cemented backfill (UCB) materials display distinctive rheological characteristics. This paper examines the rheological behaviors of UCB composited with cement and tailings that have a 80% cumulative passing size (d(80)) of 9.72µm. The findings were that UCB samples exhibit time-dependent non-Newtonian behaviors with a shear thinning characteristic, and both thixotropy and rheopexy properties are observed under long periods of steady-state shearing (300s−1 shear rate). The results indicate that samples sheared at higher rates display lower apparent viscosities compared to the samples sheared at lower rates. At low shear rates (≤0.5s−1), apparent viscosity increased until it reached a local peak (or two peaks) before behaving similarly to samples tested at higher shear rates. It was also found that the apparent viscosity of UCB increased consistently as the solids content was increased. Moreover, as cement content was increased, the apparent viscosity rose until it reached a peak at a cement content of 6%. The results also confirmed effects of solids concentration profiles changing over time and the cement hydration on the rheological behavior of UCB.

The influence of granular segregation on gravity-driven particle-fluid flows

We phrase and solve boundary-value problems for the segregation of spheres with either equal density and different sizes, or the same size and different densities in flows of a clear fluid driven by gravity over an inclined, erodible bed in a wide channel. We assume that the flow is steady and uniform, collisions between particles dissipate little energy, and the sizes and masses of the particles are not too different. For particles of the same material with diameters that differ by as little as ten per cent, we find that the flow features, such as velocity, granular temperature and solid concentration profiles, are significantly different from those for a flow of a single species with a diameter equal to the average of the two diameters. In particular, the total particle flux of the mixture is significantly larger.

Investigation of rope formation in gas–solid flows through a 90° pipe bend using high-speed video and CFD simulations

A study of rope formation in gas–solid flows through abrupt turns has been conducted. Experiments in which high-speed video was recorded and analyzed for solid concentration profiles were compared ...