Analysis of minimum specific energy consumption and optimal transport concentration of slurry pipeline transport systems

Slurry pipeline transport is widely used in several industrial processes. Calculating the specific power consumption (SPC) and determining the best working conditions are important for the design and operation of transportation systems. Based on the Shanghai Jiao Tong University high-concentration multi-sized slurry pressure drop (SJTU-HMSPD) pipeline-resistance-calculation model, the SJTU-SPC model for calculating the power required to transport a unit volume of solid materials over a unit pipeline length is established for a slurry transport system. The said system demonstrates a uniformity coefficient in the 1.26–7.98 range, median particle size of 0.075–4 mm, particle volume concentration of 10–60%, and pipeline diameter of 0.203–0.8 m. The results obtained were successfully verified against existing experimental data. The influence of parameters, such as particle-gradation uniformity coefficient, median particle size, pipe diameter, and particle volume concentration, on the SPC were analysed. The results revealed that the greater is the uniformity coefficient, the smaller is the minimum specific energy consumption and the larger the optimal transport concentration for a constant, median particle size slurry. As observed, the optimal transport concentration for broad-graded sand equalled approximately 48%. These results supplement the conclusions of existing research, indicating that the optimal transport concentration is approximately 30% and provides theoretical support for high concentration transportation of broad graded slurry.     

Ethanol–CO2 two-phase flow in diverging and converging microchannels

The present study investigates experimentally two-phase flow patterns and pressure drop of ethanol and CO₂ in a converging or diverging rectangular microchannel. The two-phase flow pattern visualization is made possible using a high speed video camera. The increased superficial gas velocity due to the acceleration effect and the large pressure drop in a converging channel may result in the elongation of bubbles in slug flow, while the decreased superficial velocity owing to the deceleration effect and the possible pressure rise in the diverging channel may cause shortening of bubbles in slug flow significantly. For both types of channel, the collision and merger of two consecutive bubbles may take place and result in necking of bubbles. Two-phase flow pressure drop in the converging microchannel increases approximately linearly with the increasing liquid or gas flow rate with the frictional pressure drop being the major contributor to the channel pressure drop. In the diverging microchannel, the deceleration effect results in the pressure rise and counteracts the frictional pressure drop. Consequently, for low liquid flow rates the channel pressure drop increases only slightly with the gas flow rate while it is low and a reversed trend appears while it is high. For high liquid flow rates the effect of increasing gas flow rate on channel pressure drop is much more significant; a more significant reverse trend of the effect of gas flow rate is present in the region of high gas flow rates. The two-phase frictional multiplier in the converging or diverging microchannel is quite insensitive to the liquid flow rate and can be fitted very well within ±15% based on the Lockhart–Martinelli equation with a modified Chisholm parameter for the diverging microchannel and together with a modified coefficient for the X⁻² term for the converging microchannel.     

Characterization of countercurrent liquid-upward and solid-downward fluidized system

Acting as an operating mode of fluidization, the flow characteristics of a countercurrent liquid–solid fluidized bed (CCLSFB) were experimentally investigated using a Plexiglas column of 1.5 m in height. Countercurrent liquid-upward and solid-downward fluidization was achieved under a limited solid flowrate before flooding occurred.The “flooding” phenomena and the flooding velocity were identified by measuring the variations in pressure drop in the axial direction of the column. Two different methods were used to quantify the flooding point that led to the instability of the system. Axial solids holdup profiles were also obtained from the pressure drop data along the column and the influences of device structure and operating conditions on the solids holdup were also studied. Seven types of particles with different diameters and densities were used. An agreement was found between the experimental results and the mathematic prediction derived from the Richardson–Zaki equation on the data of the solids holdup.     

Low-velocity pneumatic conveying in horizontal pipe for coarse particles and fine powders

First,the characteristics of low-velocity conveying of particles having different hardness are experimentally investigated in a horizontal pipeline in terms of flow pattern and pressure drop to show that the slug flow can be classified into two types depending on the settling of particles along the pipeline,and the period is small for slug flow without the settled layer,which is called solitary slug flow.The pressure drop for soft particles is shown to be larger than that for hard particles.Then,experimental results are presented on horizontal fluidized-bed conveying of fine powders to show that air release from the top surface of the conveying channel is an important factor for high mass flow rate of particles.     

Low-velocity pneumatic conveying in horizontal pipe for coarse particles and fine powders

First, the characteristics of low-velocity conveying of particles having different hardness are experimentally investigated in a horizontal pipeline in terms of flow pattern and pressure drop to show that the slug flow can be classified into two types depending on the settling of particles along the pipeline, and the period is small for slug flow without the settled layer, which is called solitary slug flow. The pressure drop for soft particles is shown to be larger than that for hard particles. Then, experimental results are presented on horizontal fluidized-bed conveying of fine powders to show that air release from the top surface of the conveying channel is an imnortant factor for high mass flow rate of particles.     

Some hydrodynamic aspects of 3-phase inverse fluidized bed

Hydrodynamics of 3-phase inverse fluidized bed is studied experimentally using low density particles for different liquid and gas velocities. The hydrodynamic characteristics studied include pressure drop, minimum liquid and gas fluidization velocities and phase holdups. The minimum liquid fluidization velocity determined using the bed pressure gradient, decreases with increase in gas velocity. The axial profiles of phase holdups shows that the liquid holdup increases along the bed height, whereas the solid holdup decreases down the bed. However, the gas holdup is almost uniform in the bed.     

Non-uniform distribution of gas–solid flow through six parallel cyclones in a CFB system: An experimental study

In large-scale circulating fluidized bed (CFB) boilers, it is common to use multiple cyclones in parallel for the capture of solids, assuming that gas–solid flow to be the same in the cyclones. This article presents a study investigating gas–solid flow through six parallel cyclones in a CFB cold test rig. The six cyclones were located asymmetrically on the left and right walls of the riser. Solid volume fraction and particle velocity profiles at the riser outlets and in the horizontal ducts were measured using a fiber optical probe. Cyclone pressure drop and solid circulating rate were measured for each individual cyclone. Measurements showed good agreement as to the non-uniform distribution of the gas–solid flow, which occurred mainly across the three cyclones on one side: the middle cyclones on both sides had higher particle velocities. Conversely, the solid volume fractions, solid fluxes and solid circulating rates of the middle cyclones were lower than those of the other four cyclones. The apparent reason for the flow non-uniformity among the cyclones is the significant flow non-uniformity at the riser outlets. Under typical operating conditions, the solid volume fractions at the riser outlets had a deviation of up to 26% whereas the solid circulating rates at the stand pipes, 7%. These results are consistent with most other studies in the literature.     

Studies on two-phase co-current air/non-Newtonian shear-thinning fluid flows in inclined smooth pipes

In this work, co-current flow characteristics of air/non-Newtonian liquid systems in inclined smooth pipes are studied experimentally and theoretically using transparent tubes of 20, 40 and 60 mm in diameter. Each tube includes two 10 m long pipe branches connected by a U-bend that is capable of being inclined to any angle, from a completely horizontal to a fully vertical position. The flow rate of each phase is varied over a wide range. The studied flow phenomena are bubbly flow, stratified flow, plug flow, slug flow, churn flow and annular flow. These are observed and recorded by a high-speed camera over a wide range of operating conditions. The effects of the liquid phase properties, the inclination angle and the pipe diameter on two-phase flow characteristics are systematically studied. The Heywood–Charles model for horizontal flow was modified to accommodate stratified flow in inclined pipes, taking into account the average void fraction and pressure drop of the mixture flow of a gas/non-Newtonian liquid. The pressure drop gradient model of Taitel and Barnea for a gas/Newtonian liquid slug flow was extended to include liquids possessing shear-thinning flow behaviour in inclined pipes. The comparison of the predicted values with the experimental data shows that the models presented here provide a reasonable estimate of the average void fraction and the corresponding pressure drop for the mixture flow of a gas/non-Newtonian liquid.     

Experimental investigation of ice slurry flow pressure drop in horizontal tubes

Pressure drop behaviour of ice slurry based on ethanol–water mixture in circular horizontal tubes has been experimentally investigated. The secondary fluid was prepared by mixing ethyl alcohol and water to obtain initial alcohol concentration of 10.3% (initial freezing temperature ?4.4 °C). The pressure drop tests were conducted to cover laminar and slightly turbulent flow with ice mass fraction varying from 0% to 30% depending on test conditions. Results from flow tests reveal much higher pressure drop for higher ice concentrations and higher velocities in comparison to the single phase flow. However for ice concentrations of 15% and higher, certain velocity exists at which ice slurry pressure drop is same or even lower than for single phase flow. It seems that higher ice concentration delay flow pattern transition moment (from laminar to turbulent) toward higher velocities. In addition experimental results for pressure drop were compared to the analytical results, based on Poiseulle and Buckingham–Reiner models for laminar flow, Blasius, Darby and Melson, Dodge and Metzner, Steffe and Tomita for turbulent region and general correlation of Kitanovski which is valid for both flow regimes. For laminar flow and low buoyancy numbers Buckingham–Reiner method gives good agreement with experimental results while for turbulent flow best fit is provided with Dodge–Metzner and Tomita methods.Furthermore, for transport purposes it has been shown that ice mass fraction of 20% offers best ratio of ice slurry transport capability and required pumping power.     

Modeling the hydrodynamics of cocurrent gas–solid downers according to energy-minimization multi-scale theory

Cocurrent gas–solid downer reactors have many applications in industry because they possess the technological advantages of a lower pressure drop, shorter residence time, and less solid backmixing when compared with traditional circulating fluidized bed risers. By introducing the concept of particle clusters explicitly, a one-dimensional model with consideration of the interphase interactions between the fluid and particles at both microscale and mesoscale is formulated for concurrent downward gas–solid flow according to energy-minimization multi-scale (EMMS) theory. A unified stability condition is proposed for the differently developed sections of gas–solid flow according to the principle of the compromise in competition between dominant mechanisms. By optimizing the number density of particle clusters with respect to the stability condition, the formulated model can be numerically solved without introducing cluster-specific empirical correlations. The EMMS-based model predicts well the axial hydrodynamics of cocurrent gas–solid downers and is expected to have a wider range of applications than the existing cluster-based models.     

Statistical analysis of fluctuations of froth pressure on perforated plates without downcomers

Statistical properties of fluctuations of pressure drop across the gas–liquid dispersions on the tray were analyzed using a 215 mm dia. three plates column with different trays. Hydrodynamic regimes of the froth were characterized in terms of the statistical properties evaluated. It was proved that the on-line estimation of the flow behavior of the froth was possible on the basis of the pattern recognition of the power spectral density function of the pressure fluctuations. The time-domain stochastic models for fluctuations of the pressure drop were identified so as to be available for its forecast and simulation.     

Transportation characteristics of gas–solid two-phase flow in a long-distance pipeline

In this study, experiments on fly ash conveying were carried out with a home-made long-distance positive-pressure pneumatic conveying system equipped with a high performance electrical capacitance tomography system to observe the transient characteristics of gas–solid two-phase flow. The experimental results indicated that solids throughput increased with increasing solids–gas ratio when the conveying pipeline was not plugged. Moreover, the optimum operating state was determined for the 1000 m long conveying pipeline with a throttle plate of 26 orifices. At this state the solids throughput was about 12.97 t/h. Additionally, the transportation pattern of fly ash gradually changed from sparse–dense flow to partial and plug flows with increasing conveying distance because of the conveying pressure loss. These experimental results provide important reference data for the development of pneumatic conveying technology.     

Hydrodynamics and energy consumption studies in a three-phase liquid circulating three-phase fluid bed contactor

The hydrodynamics and energy consumption have been studied in a cold flow, bubbling and turbulent, pressurized gas–liquid–solid three-phase fluidized bed (0.15 m ID × 1 m height) with concurrent gas–liquid up flow is proposed with the intention of increasing the gas hold up. The hydrodynamic behaviour is described and characterised by some specific gas and liquid velocities. Particles are easily fluidized and can be uniformly distributed over the whole height of the column. The effect of parameters like liquid flow rate, gas flow rate, particle loading, particle size, and solid density on gas hold up and effect of gas flow rate, solid density and particle size on solid hold up, energy consumption and minimum fluidization velocity has been studied. At the elevated pressures a superior method for better prediction of minimum fluidization velocity and terminal settling velocities has been adopted. The results have been interpreted with Bernoulli’s theorem and Richardson–Zaki equation. Based on the assumption of the gas and liquid as a pretend fluid, a simplification has been made to predict the particle terminal settling velocities. The Richardson–Zaki parameter n′ was compared with Renzo’s results. A correlation has been proposed with the experimental results for the three-phase fluidization.     

Analysis and application of solid-gas flow inside a venturi with particle interaction

A two-phase one-dimensional solid—gas flow model which describes the flow inside a variable area duct has been developed. The model includes multiparticle equations and considers particle—particle interaction. Predictions have been compared with experimental data for the pressure drop and pressure recovery through two venturis at different solid to gas loading ratios. Accurate knowledge of the particle-size distribution is extremely important for good comparison. No meaningful single particle-size diameter is found that yields predictions to agree with the measurements. The venturi may be used as a measuring device for solid—gas flow rates for systems if the particle-size distribution is accurately known. However, the venturi-diffuser section loses its effectiveness in recovering the pressure as the solid loading increases.     

Bubble behaviors of geldart B particle in a pseudo two-dimensional pressurized fluidized bed

Pressurized fluidized beds have been developed in quite a few industrial applications because of intensified heat and mass transfer and chemical reaction. The bubble behaviors under elevated pressure, strongly influencing the fluidization and reaction conversion of the whole system, are of great research significance. In this work, the bubble behaviors of Geldart B particle in a pseudo two-dimensional (2D) pressurized fluidized bed were experimentally studied based on digital image analysis technique. The effects of pressure and fluidization gas velocity on the general bubble behaviors (i.e., size, shape and spatial distribution) and the dynamic characteristics, such as the time-evolution of voidage distribution and local flow regimes, were comprehensively investigated. Results show that increasing pressure reduces the stability of bubbles and facilitates gas passing through the emulsion phase, resulting in the “smoother” fluidization state with smaller bubbles and declined bubble fraction and standard deviation. The equivalent bubble diameter and bubble aspect ratio increase with the increasing gas velocity while decrease as pressure rises. The elevated pressure reduces bubbles extension in the vertical direction, prohibits the “short pass” of fluidization gas in large oblong bubbles/slugs and benefits the gas–solid interaction. The flow regimes variation with gas velocity is affected by the elevated pressure, and demonstrates different features in different local positions of the bed.     

Numerical simulation of a dense solid particle flow inside a cyclone separator using the hybrid Euler–Lagrange approach

This paper presents a numerical simulation of the flow inside a cyclone separator at high particle loads. The gas and gas–particle flows were analyzed using a commercial computational fluid dynamics code. The turbulence effects inside the separator were modeled using the Reynolds stress model. The two phase gas–solid particles flow was modeled using a hybrid Euler–Lagrange approach, which accounts for the four-way coupling between phases. The simulations were performed for three inlet velocities of the gaseous phase and several cyclone mass particle loadings. Moreover, the influences of several submodel parameters on the calculated results were investigated. The obtained results were compared against experimental data collected at the in-house experimental rig. The cyclone pressure drop evaluated numerically underpredicts the measured values. The possible reason of this discrepancies was disused.     

Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study, a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed. Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop. One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore, and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations. Predictions are compared with experimental data measured by Lali et al., where the computed porosities from model B are closer to the measured data than other models. Furthermore, the predicted pressure drop rises as liquid velocity increases, while it decreases with the increase of particle size. Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient, and particle concentration, granular temperature, granular pressure, and granular viscosity go down accordingly.     

深海采矿中试系统水力提升管道水击压力分析

深海采矿系统可能由于突然停泵、断电或机械故障等引起提升管道中流体速度瞬间变化, 导致管道内压力剧烈变化, 这种水击现象对管道破坏极大. 基于固液两相流体连续性原理和动量定理, 推导出含粗颗粒的固液两相流体管道水击压力的计算公式. 采用深海采矿中试系统参数, 模拟计算不同水体流速、不同流体浓度以及不同管径条件下的水击压力. 分析结果表明, 流速、体积浓度和管径是影响水击压力的重要因素, 其中, 流速影响最大. 研究结果可为深海采矿系统工程设计提供依据.     

MODELLING OF RELEASE OF GAS FROM HIGH-PRESSURE PIPELINES

The problem investigated is the break of a high-pressure pipeline carrying natural single-phase gas which may condensate (retrograde) when the pressure drops. Single-phase non-ideal gas is assumed using a general- ized equation of state. Taking advantage of the choked massflow condition, the break is split into a pipe flow problem and a dispersion flow problem, both solved using a finite difference control volume scheme. The transient flow field from the pipeline break location is expanded analytically, using an approximation of the governing equations, until ambient pressure is reached and matched to the corresponding gas dispersion flow field using as subgrid model a jet box with a time-varying equivalent nozzle area as an internal boundary of the dispersion domain. The turbulence models used for the pipe and dispersion flow fields are an empirical model of Reichard and the k–ϵ model for buoyant flow respectively. The pipe flow simulations indicate that the flow from the pipeline might include dispersed condensate which will affect quantitatively the mass flow rate from the pipeline and qualitatively the gas dispersion if the condensate rains out. The transient dispersion simulation shows that an entrainment flow field develops and mixes supersaturated gas with ambient warmer air to an unsaturated mixture. Because of the inertia of the ambient air, it takes time to develop the entrainment flow field. As a consequence of this and the decay of the mass flow with time, the lower flammability limit of the gas–air mixture reaches its most remote downstream position relatively early in the simulation (about 15 s) and withdraws closer to the break location.     

Pressure drop prediction with a modified frictional-kinetic model for alumina in bypass pneumatic conveying system

A new frictional-kinetic model is proposed and modified for pressure drop prediction of alumina in a bypass pneumatic conveying system. This new model is based on the conventional Johnson–Jackson frictional-kinetic model. The critical value of solids volume fraction and maximum packing limit are modified based on the fluidized bulk density and tapped bulk density, respectively. In addition, an offset solid volume fraction is introduced into the frictional pressure model as well as into the radial distribution functions which represents the correction factors to modify the probability of collisions between particles when solid phase becomes excessively dense. For the application of the model, computational fluid dynamics (CFD) simulations were conducted by using kinetic theory, conventional frictional-kinetic model and modified frictional-kinetic model. The simulation results were then compared with the experimental results. It was found that the modified frictional-kinetic model showed the largest improvement on pressure drop prediction results compared with results obtained from applying the kinetic theory and the conventional frictional-kinetic model, especially for denser flows with low air mass flow rates and high solid loading ratios (SLR). In addition, the solids volume investigation of CFD simulations shows a strong comparison to the actual flow conditions in the pipe, as transient slug type flow of alumina is observed.