The role of bubble injection characteristics at incipient fluidization condition on the mixing of particles in a gas-solid fluidized bed at high operating pressures: A CFD-DPM approach
Graphical abstract
Introduction
Gas–solid fluidized beds have been widely used as reactors in chemical and petrochemical industries [1]. In spite of its difficulties in operation and high construction costs, most of the fluidized bed reactors operate at high pressures such as the polymerization reactors [2] and the coal combustors [3]. The operating pressure at which the fluidized bed works has a profound influence on the fluidization behavior [4]. At elevated pressures, the conversion of reactants is enhanced and the rector volume decreases due to more gas processing.
To prevent hot spot formation and unwanted agglomeration, it is very important to have the particles well-mixed so that all particles cool, react, or dry homogenously [5].
Several experimental and numerical works [6], [7], [8], [9], [10], [11], [12], [13] are published on the pressurized fluidized beds (Chan et al. [6], Chitester et al. [7], Olowson & Almstedt [8], [9], [10], Wiman & Almstedt [11], Sidorenko & Rhodes [12]; Norouzi et al. [13]) and various pressure dependent correlations are suggested for bubble characteristics, drag force, minimum fluidization and minimum bubbling velocities and segregation.
It has been known for some time that higher operating pressures improve the fluidization quality and enhances the process in fluidized beds [14].
By increasing the inlet gas pressure in a fluidized bed, Olowson & Almstedt [8] found that the mean bubble frequency, the mean bubble rise velocity, the mean bubble volume fraction and the visible bubble flow rate increase at elevated pressures. Also their studies showed that the mean pierced length decreases with increasing pressure.
Piepers et al. [15] investigated the effects of operating pressure and gas type on the particle-particle interactions and their influences on gas-solid fluidization behavior. They reported that the quality of bed fluidization of fine cracking catalysts improves with pressure increase and also depends on the type of fluidization gas used.
Chan et al. [6] determined the effect of operating pressure on the bubble parameters (bubble frequency, velocity and size). They also studied the effect of particle size, particle density, gas velocity and bed height on the bubble characteristics. They found that the bubble size decreases and the bubble formation frequency increases at elevated pressures.
Cao et al. [16] investigated the influence of pressure on the bubble size and average bed voidage experimentally and computationally in a circular three-dimensional cold-flow model of a pressurized jetting fluidized bed. They used electrical capacitance tomography (ECT) technique to study the average pressurized bed voidage and bubble size in the jetting fluidized bed. They proposed that with the same gas velocity in the jetting fluidized bed and with the pressure increase, the average bed voidage increases and the bubbles become smaller because of splitting at higher pressures.
Schweinzer and Molerus [17] presented the measurements of bubble behavior in presence of three powders in a semi-industrial scale pressurized fluidized bed. They found that the mean bubble size is markedly reduced by increasing the pressure up to 2.5 MPa, but bubbles are still present. With increasing the pressure and remaining the superficial gas velocity constant, the visible bubble flow rate increases or remains unchanged depending on the particle size. In contrast to the expectation, although bubbles become smaller, mean bubble velocity increases with increasing pressure.
Mansourpour et al. [18] used DEM-CFD approach to investigate the influence of pressure on bubble dynamics in a gas–solid fluidized bed. Their study showed that increasing the pressure reduces the bubbles' growth and stability and enhances the bubble gyration through the bed, leading to a change in the bed flow structure.
The influence of pressure on regime transition in dense gas fluidized beds was studied by Li and Kuipers [19] using DEM approach. Zhang, Li, and Fan [20] studied bubble and particle motions in a three-phase fluidized bed at high pressures.
Despite many studies have investigated the effect of pressure on fluidized bed behavior, a very few works have addressed the effect of pressure on mixing.
Deen et al. [5] studied some mixing indices and investigated the effect of pressure on the particle mixing. According to their results, with increasing the pressure, the number of bubbles increases, leading to a more chaotic particle movement in the bed which consequently enhances the vertical (micro) mixing. Regarding the horizontal mixing, they indicated that:
- 1
Horizontal mixing occurs partially through the circular movement of particles in the bed. It decreases when a fluidized bed expands due to increasing pressure.
- 2
Direct horizontal motion and mixing of particles increase with increasing pressure because of the more chaotic particle movement in the bed and increasing space between the particles.
Although many studies have been done in the atmospheric condition [21], [22], [23], [24], the effect of bubble on mixing at high pressures is not sufficiently investigated.
In our previous work [24], we studied the effect of bubble characteristics on mixing behavior in atmospheric condition. In the present work, CFD-DPM technique is used to investigate the role of bubble characteristics such as injection velocity and injection time at high pressures. Moreover, the quality of mixing in two directions (vertical and horizontal) is compared at different operating pressures.
Section snippets
Governing equations
There are three main numerical methods to study and characterize a gas solid fluidized bed. One of these methods is two fluids model (TFM) that uses Eulerian-Eulerian approach which considers the gas and solid phases as fluid and employs the kinetic theory of granular flow (KTGF) to derive internal momentum transport equation for solid phase. The other method is discrete particle model (DPM) that utilizes Eulerian-Lagrangian approach in which each particle is tracked individually in the solid
Simulation conditions
In this work, a two-dimensional (0.3 m × 0.6 m) gas-solid fluidized bed consisting of 17,000 spherical glass particles with 2 mm diameter and 2700 kg/m3 density is studied to investigate the particle mixing in a gas-solid fluidized bed at 2, 4, 8, 16, 32 bar. The simulations are 2-dimansional and the bed thickness is assumed to be equal to a single particle diameter. In our simulations, we use a 2-D to 3-D mapping function to account for particle induced void fraction calculations, as described by
Mixing characterization
In the study of granular mixing, it is essential to describe the state of a granular mixture as how well the particles are mixed homogeneously – using some quantitative measurements [38].
One of the most important mixing indices for quantitative measures is Lacey Mixing Index (LMI). The Lacey index is based on statistical analysis and is developed by Lacey [39]. In this method, the bed is compartmented to N cells and the particles are virtually colored in two groups (e.g. white and black).
Validation and verification
It is very difficult and expensive to measure the mixing of particles at high pressures experimentally. Due to the complexity and high expenses of experimentally measuring of particles at high pressures, we have used two different methods by the aid of reported experimental data and famous correlations in the literature [30], [41], [42] for validation of our simulation results. Moreover, the trend of averaged porosity distribution in the fluidized bed at different pressures has been
Mixing at different pressures
To investigate the general effect of increasing operating pressure on the particle mixing, in the first step, Umf is calculated for 4, 8, 16 and 32 bar of the bed pressure. In the next step, these values are used as background velocity and the bubble jet is injected every 1 s into the bed by means of a nozzle placed in the center of the distributor. The results of mixing index versus time under different operating pressures are shown in Fig. 4. As Fig. 4 shows, with increasing the bed pressure,
Conclusions
This work is in the continuation of our previous works [24], [44]. In this work, the CFD-DPM simulation was used to study the role of bubble injection characteristics on the mixing of solid particles in a gas-solid fluidized bed at high pressures. The following results were found from this study:
- •
The effect of the injection time on the mixing index at low pressures is more remarkable than that of the high pressure. In the other word, constant gas flow rate as small bubbles results in a better
Symbols
- a, b
constant values of equation
- dp
particle diameter, m
- epp
restitution coefficient between particles with each other
- epw
restitution coefficient between particles and wall
contact force vector, N
drag force vector, N
Saffman lift force vector, N
Magnus lift force vector, N
fluid particle interaction force, N
gravity acceleration vector, m/s2
- h
height, m
- Ii
particle moment of inertia
- LMI
Lacey mixing index
- Mfit
fitting function of mixing index
- MWg
Gas molecular weight,
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