Dynamic and Steady-State Characterization of the Liquid Spray Zone

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Dynamic and Steady-State Characterization of the Liquid Spray Zone in an Externally Heated Gas-Solid Fluidized Bed Jingyuan Sun, Zhengliang Huang, Dongfang Hu, Zuwei Liao, Yao Yang, Jingdai Wang, and Yongrong Yang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04047 • Publication Date (Web): 07 Feb 2018 Downloaded from http://pubs.acs.org on February 8, 2018

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Industrial & Engineering Chemistry Research

Dynamic and Steady-State Characterization of the Liquid Spray Zone in an Externally Heated Gas-Solid Fluidized Bed Jingyuan Sun†, Zhengliang Huang‡, Dongfang Hu†, Zuwei Liao†, Yao Yang†, Jingdai Wang†, Yongrong Yang*† †

State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China ‡

Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, Hangzhou 310027, P. R. China

ABSTRACT In industrial fluidized beds with liquid spray, dynamic and steady-state characteristics of the liquid spray zones are of significant importance for operation optimization and products control. In this study, a conductivity probe array, two thermocouple arrays, and a pressure sensing system are applied to an externally heated gas-solid fluidized bed with a side-wall liquid spray. Non-stationary and non-linear characteristics are exhibited in the Hilbert spectra of the conductivity probe signals, and the fluctuation energy distribution shifts to higher frequencies with the liquid spray velocity, related to the liquid-induced higher-frequency bubble motion. The variation coefficient analysis of temperature data is a reliable approach to characterizing the liquid spray zone boundary. The liquid spray zone is enlarged and extends downward along the wall with the liquid spray velocity, and shrinks with the gas velocity. Moreover, the liquid spray zone is enlarged and extends downward along the wall with the nozzle installation height.

Keywords:

fluidized bed; liquid spray zone, conductivity measurement;

temperature measurement, fluctuation analysis

1. INTRODUCTION Gas-solid fluidized beds with liquid spray or injection for catalytic and non-catalytic reactions and particle handling have been increasingly used in various

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

industrial processes, such as fluid catalytic cracking,1 Wurster coating,2,

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3

aniline

synthesis,4 granulation for agglomerate production,5 and super condensation process for olefin polymerization.6 Due to the strong heat removal capability by liquid temperature increase and evaporation, multiple-temperature zones commonly exist in the operation vessels.7-11 Taking the afore-mentioned polymerization process as an example, liquid condensing agent atomized through a nozzle is sprayed into a fluidized bed reactor from the side wall. Droplets then spread rapidly and collide with particles, forming a liquid spray zone composed of droplets, liquid-containing particles and evaporated liquid (vapor). The liquid amount, fluidization status, and reaction environment in such a low-temperature liquid spray zone are different from those in the high-temperature liquid-free zone in the fluidized bed. Therefore, the liquid spray zone is a relatively independent gas-liquid-solid system with dynamic variations of characteristic parameters and continuous heat and mass exchanges with the liquid-free zone. From the hydrodynamic perspective, the liquid spray zone characteristics are significantly affected by the dynamic and chaotic nature of the fluidized bed, while the coexistence of liquid spray zone and liquid-free zone also make the fluidization structures and patterns more complex. From the reaction perspective, when particles circulate between the liquid spray zone and liquid-free zone, polymer layers with high molecular weight and branching degree and those with low molecular weight and branching degree are alternatively generated, leading to a molecular chain-level mixing of different polymer structures and hence an excellent product performance. Therefore, it is of both theoretical and industrial significance to understand the dynamic and steady-state characteristics of the liquid spray zone, based on which the operation optimization and precise control of products will be achieved. Extensive work has been conducted in developing measurement techniques of liquid spray distribution in fluidized beds. McMillan et al.12 applied thermocouples to determine the liquid/solid distribution within the cross-sectional area of a gas-liquid jet sprayed into a fluidized bed of coke particles. Maronga and Wnukowski13 measured the temperature and humidity proﬁles in a top-spray coating bed through a thermocouple and a hygrometer, according to which the whole bed was roughly divided into a spray zone, a drying zone, a non-active zone, and a heat exchange zone. Zhou et al.14 also found obvious temperature differences between the spray zone and other zones in a fluidized bed, and studied the effects of operation conditions on the ACS Paragon Plus Environment

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temperature differences. Ariyapadi et al.15 also measured the liquid penetration length through a thermocouple array. Turchiuli et al.16 measured the bed volume fraction occupied by the wetting zone through thermocouple arrays in a fluidized granulator, based on which the evolution of particle size distribution was modelled. Fan et al.17 applied thermocouples, particle image velocimetry (PIV) and electric capacitance tomography (ECT) to determining the liquid jet boundary, penetration length, and individual phase motion under dilute and dense phase conditions. Despite a wide application in liquid spray characterization, thicker thermocouples are less sensitive to temperature fluctuations and hence more suitable for the measurement of time-averaged spray parameters. Conductivity and capacitance probes with more rapid response have also been extensively applied to determining the liquid spray distribution,18-20 spray boundary21 and quality of liquid-solid contact22 in fluidized beds. Capacitance probes were also used in combination with thermocouples to characterize the radial zones of a middle liquid spray in a high-density riser.20 In addition, a sampling and sieving method was used to estimate the effect of the interaction between attrition and spray jets on the agglomerate production in a hot fluidized bed with coke particles,23 yet suffers from a disadvantage of its off-line nature. X-ray imaging technique24 was also used by Ariyapadi et al. for estimating the jet expansion angles and penetration lengths of the gas, gas-liquid and liquid jets. However, the application of X-ray technique is still limited due to the sophisticated operation and the requirement of special protection devices. Although some characteristic parameters of liquid spray and jets have been measured through the aforementioned experimental approaches, the dynamic characteristics of a liquid spray zone in a fluidized bed are rarely considered, especially when the effects of heat and mass transfer are incorporated. In this work, a conductivity probe array, two thermocouple arrays, and a pressure sensing system are applied to a high-temperature fluidized bed with a side-wall liquid spray, respectively. Hilbert-Huang transform (HHT), power spectral analysis, and variation coefficient analysis are employed for fluctuation signal analysis. Both the dynamic and steady-state characteristics of the liquid spray zone and its complex interactions with the fluidized bed are studied.



2. EXPERIMENTAL SETUP Figure 1 shows the layout of the experimental apparatus used in this work. It consists of two main parts: a fluidized bed and a measurement system. The fluidized bed is made of stainless steel with an inner diameter of 100 mm and a height of 800 mm. A thermal-insulating jacket is mounted on the outer wall of the bed with circulating hot water of 85 °C inside. A 30 mm-wide glass window slot is embedded in the wall for the visualization of fluidization states. Two low-pressure atomization nozzles, with inner diameters of 0.2 mm and 0.5 mm, respectively, are used for liquid spray experiments. They are inserted into the side wall of the bed with a depth of 10 mm and at 170 mm (Hj=170 mm) above the gas distributor. The nozzle structure has been illustrated in our previous work.25 Linear low density polyethylene (LLDPE) particles (SINOPEC) with an average diameter of 0.65 mm and density of 920 kg/m3 are employed as the fluidization material. Compressed air is used as the fluidization gas and alcohol with a boiling point of 78 °C and density of 820 kg/m3 is used for the liquid phase, which is sprayed continuously into the bed through a metering pump. The air is preheated to 85 °C before it is introduced into the fluidized bed.

Figure 1. Layout of the experimental apparatus

The static bed height is 270 mm and the minimum fluidization velocity of the dry LLDPE particles, Umf0, at the air temperature of 85 °C is 0.11 m/s. The variation ranges of superficial gas velocity (Ug) and liquid spray velocity (Ul) are


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2.9Umf0~4.5Umf0 and 1.1 m/s~1.9 m/s, respectively. The superficial gas velocities are chosen to ensure a bubbling fluidization state in the bed, and the maximum liquid spray velocities are determined to prevent the defludization caused by liquid accumulation. In each experiment, liquid spray is started only after the fluidized bed has reached a hydrodynamic and thermal steady state, and is stopped when all the data acquisition has been accomplished. A hydrodynamic steady state is reached when the bed pressure fluctuates around a constant, and a thermal steady state is reached when the outlet gas temperature fluctuates within 2 ℃. After the liquid spraying, it typically takes about 20~30 mins for the system to reach a new steady state under all the conditions. Therefore, the measurement only starts after 30 mins from the liquid spraying. The measurement system consists of a conductivity probe array, two thermocouple arrays, and a pressure sensing system. The liquid distribution is determined through a conductivity probe array. Each conductivity probe consists of two unconnected copper electrodes with a gap of 0.3 mm. The two electrodes are fitted at the end of an elongated tube with an inner diameter of 3 mm. A 250 kΩ resistor, powered by a 20V DC power supply, is connected to the electrodes. When a liquid bridge is formed between the electrodes, the electric current flowing through the resistor is detected. The voltage signals are sampled at a frequency of 200 Hz with a duration of 120 s. The temperature axial distribution is measured through two axial arrays of resistance thermocouples (Pt-100) with an outer diameter of 2 mm, while the temperature distribution in the axial cross section of the bed is determined by moving the thermocouple arrays along the radial direction. The temperature sampling lasts for 300 s. Single conductivity probe and thermocouple are shown schematically in Figure 1, despite the sensor arrays employed. Figure 2 exhibits the installation locations of the conductivity probe array and thermocouple array. In addition, a pressure transducer (CYG 1219 type, Baoji Research Center of Transducer, China) with a measuring range of ±2 kPa and a relative accuracy of ±0.25% is used for the measurement of pressure fluctuations in the bed. Five steel pressure tubes with an inner diameter of 4 mm and a length of 80 mm are mounted flush with the inner wall at 40 mm, 120 mm, 270 mm, 330 mm and 390 mm above the gas distributor, respectively. The pressure signals are sampled at a frequency of 200 Hz with a duration of 180 s. After each experiment, particles are dried by the hot air to ensure that no particle agglomerates are left in the bed before the next experiment. The



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particle agglomerates mentioned here are those caused by liquid bridges, and their amount hence varies with the liquid hold-up in the bed. The pressure fluctuation is monitored to judge the presence of particle agglomerates left in the bed. When liquid is injected to the bed, the pressure starts to decrease significantly, and after the liquid injection is stopped, the pressure rises again to the normal value.

Figure 2. Installation locations of the conductivity probe array and thermocouple arrays

3. SIGNAL ANALYSIS METHODS 3.1. COEFFICIENT OF VARIATION The coefficient of variation is a standardized measurement of the dispersion of a data set26. Compared to the most commonly used measurement of variations, such as the variance and standard deviation, the coefficient of variation is more suitable for the comparison between the data sets with different mean values. The coefficient of variation of a time series signal, x ( n ) , is defined as,

V=

σ

(1)

x

where the standard deviation, σ , describes the degree to which the data spreads around a mean value and defined as, σ =

(

1 N ∑ x (n) − x N − 1 n =1

)

2

where the mean value, x , is evaluated from,


(2)

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1 N x = ∑ x ( n) N n=1

(3)

3.2. POWER SPECTRAL ANALYSIS The power spectrum of a signal describes the distribution of power into frequency components composing the signal27. The discrete Fourier transform (DFT) converts an equally-spaced signal of finite length into an equivalent-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The DFT is commonly implemented through the efficient fast Fourier transform (FFT) algorithm and defined as, N

−j

X ( k ) = ∑ x ( n)e

2π n N

k = 0,1,..., N −1

(4)

n=1

where x ( n ) is a time series signal, N is the length of the signal. 3.3. HILBERT-HUANG TRANSFORM HHT is suitable for multi-resolution analysis of non-linear and non-stationary signals. It consists of two steps named the empirical mode decomposition (EMD) and Hilbert transform28, 29. In the EMD process, a time series signal, x(t), is decomposed into a finite set of intrinsic mode functions (IMFs), ci(t) (i=1, 2, …, n), and the residual, rn(t). The original signal can be reconstructed through, n

x ( t ) = ∑ci ( t ) + rn ( t )

(5)

i =1

where n is the number of the IMFs, relying on the operation conditions, and t is the time. A complex representation of the IMF, yi(t), is obtained from the Hilbert transform,

ci ( t ' ) ' yi ( t ) = ∫ dt π −∞ t − t ' P

∞

(6)

where P is the Cauchy principal value. An analytical signal, zi(t), is thus defined from ci(t) and yi(t) as,

zi ( t ) = ci ( t ) + jyi ( t ) = ai ( t ) e jφi (t ) The amplitude ai(t) and phase angle φi ( t ) of each IMF are defined as,


(7)


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ai ( t) = ci2 ( t ) + yi2 ( t)

(8)

 yi ( t )    ci ( t ) 

(9)

φi ( t ) = arctan 

The instantaneous frequency of each IMF, fi(t), is calculated from,

fi ( t ) =

1 dφi ( t ) 2π dt

(10)

The original signal can be calculated by the instantaneous frequency and amplitude, j 2π fi ( t )dt  n x ( t ) = Re ∑ ai ( t )e ∫   i =1 

(11)

Both the amplitude and instantaneous frequency are hence represented as time functions, and the Hilbert spectrum is expressed as the frequency-time distribution of the squared amplitudes.

4. RESULTS AND DISCUSSION 4.1. DYNAMIC BEHAVIORS OF LIQUID SPRAY ZONE Voltage signals collected from the conductivity probes contain important information not only about the liquid distribution but also the three-phase motion in the liquid spray zone. For the sake of easy comparison, the original voltage signal collected at each position is divided by the corresponding maximum voltage value, resulting in a relative voltage signal for analysis. Figure 3 shows the relative voltage variations with the time at the nozzle installation height (h=Hj=170 mm) and different radial positions. The voltage increases when liquid bridges are formed due to the collisions between droplets or liquid-containing particles and the two electrodes, and decreases to zero with the evaporation or leaving of the droplets or liquid-containing particles. At Ul=1.1 m/s, weak peaks appear occasionally as continuous liquid bridges are seldom formed under such a small liquid amount. With the increase of Ul, the collision frequency between the liquid and electrodes increases, leading to stronger and more frequent voltage fluctuations. Because the nozzle outlet is close to the location of r=-40 mm, the intensity of voltage peaks decreases basically with the radial distance from r=-40 mm, which is mainly determined by the liquid distribution


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in the radial direction.

(a) Ul=1.1 m/s

(b) Ul=1.5 m/s

(c) Ul=1.9 m/s Figure 3. Relative voltage variations with the time at different radial positions and liquid spray velocities (Ug=3.7Umf0, h=Hj=170 mm, Dj=0.5 mm)

Figure 4 shows the corresponding time-averaged relative voltages at different radial positions and liquid spray velocities. The time-averaged voltages increase significantly with the liquid spray velocity due to the intensified liquid motion and liquid bridge formation, especially near the nozzle outlet (r=-40 mm). In addition, the time-average voltages basically decrease with the radial distance from the nozzle outlet and drop to zero at r=0 mm, which is hence considered as the farthest radial position that the liquid spray reaches at the liquid spray velocities under test.



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Figure 4. Time-averaged relative voltages at different radial positions and liquid spray velocities (Ug=3.7Umf0, h=Hj=170 mm, Dj=0.5 mm)

As voltage signals from the conductivity probes are typically non-linear and non-stationary, HHT is applied for further multi-resolution analysis of the signals. Figures 5 and 6 show the Hilbert spectra of the relative voltage signals at the nozzle installation height and r=-30 mm under different operation conditions as an example, describing the local characteristics and time-frequency energy distribution of the fluctuation signals. The Y axis represents the time-dependent instantaneous frequencies of the IMFs and each color bar, ranging from dark blue to dark red, indicates the fluctuation amplitude (energy) varying from the minimum to the maximum. Non-stationary and non-linear characteristics are reflected from the time dependence of frequency and the intermittent variation of fluctuation energy, determined

by

the

intermittent

collisions

between

the

liquid-containing

particles/droplets with the electrodes, the competition between the formation and breaking of liquid bridges, and the evaporation and motion of the liquid phase. Moreover, the energy distribution shifts to higher frequencies with the liquid spray velocity, which is related to the effects of liquid spray on bubble motion. Figure 7 gives the power spectra of pressure fluctuation signals at h=120 mm (near the nozzle position) under different operation conditions. The dominant frequency increases with the liquid spray velocity, despite slight changes based on the small liquid amount injected. This weak frequency shifts are comprehensive results caused by three reasons. First, the liquid addition enhances the particle-particle interactions and bubble breakage near the nozzle, leading to an increase of bubble frequency and


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hence the dominant frequency. Second, the minimum fluidization velocity is increased by liquid addition. According to the following Eq.(12) and Eq.(13) from Darton et al.30 and Davidson and Harrison31, respectively, the bubble size and rising velocity are decreased, leading to opposite effects on the bubble frequency. Third, the bubble size is increased by the vapor entering the bubble phase due to liquid evaporation, and the bubble rising velocity is hence increased, resulting in an increase of bubble frequency.

Db = 0.54 ( u − umf

) (H + 4 0.4

AD

)

0.8

g −0.2

(12)

where Db is the average bubble size, u the superficial gas velocity, u mf the minimum fluidization velocity, H the height, AD the influence area of each injection hole in the gas distributor, and g the gravitational acceleration. ub = u − u mf + 0.71 gDb

(13)

where ub is the bubble rising velocity. Moreover, liquid-containing particles and droplets near the nozzle are dragged by higher-frequency bubbles, colliding with and leaving the electrodes more frequently. Therefore, Figs. 5 and 6 show that the energy distribution shift to higher frequencies with the liquid spray velocity. 0

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(c) Ul=1.9 m/s Figure 5. Hilbert spectra of the relative voltage signals under different operation conditions (Ug=3.7Umf0, h=Hj=170 mm, r=-30 mm, Dj=0.5 mm)

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(b) Ul=1.5 m/s

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(c) Ul=1.9 m/s Figure 6. Hilbert spectra of the relative voltage signals under different operation conditions (Ug=4.1Umf0, h=Hj=170 mm, r=-30 mm, Dj=0.5 mm)

(a) Ug=3.7Umf0

(b) Ug=4.1Umf0

Figure 7. Power spectra of pressure fluctuation signals under different operation conditions


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(h=120 mm)

Figure 8 shows the relative voltage variations with the time at r=-30 mm and different heights. No obvious signal is detected above the nozzle installation height (h=Hj=170 mm), indicating that the liquid spray is mainly converted into liquid films covering the particles and hence follows the particles downward motion near the wall. Although the liquid film formation cannot be observed directly from our opaque apparatus, it is commonly considered in literature that liquid sprayed into the fluidized bed all adheres to particles to form liquid films, based on which the mass and heat transfer properties are calculated, and the results are reasonable and consistent well with the measured data.32, 33 In addition, the collision frequency between particles and liquid droplets in such a dense-phase fluidized bed is quite high (~105), droplets are difficult to exist separately and highly possible to collide with and adhere to particles. Therefore in this work, we employ the liquid film formation hypothesis and believe it reasonable. Moreover, the voltage fluctuations at and below h=170 mm are enhanced with the liquid spray velocity, due to the increased effects of liquid motion and evaporation on the liquid bridge formation and breakage at those locations.

(a) Ul=1.1 m/s

(b) Ul=1.5 m/s



(c) Ul=1.9 m/s Figure 8. Relative voltage variations at different heights and liquid spray velocities (Ug=3.7Umf0, r=-30 mm, Dj=0.5 mm)

4.2. ESTIMATION OF LIQUID PENETRATION LENGTH The liquid penetration length is an important steady-state parameter of the liquid spray zone. Figure 9 shows the temperature variations with the time at the nozzle installation height and different radial positions. The temperature fluctuates stronger at the positions near the nozzle outlet (r=-40 mm), ascribed to the intermittent liquid addition and evaporation under the effects of chaotic gas-solids flow at those positions. In addition, the temperature becomes almost constant at r=0 mm, indicating a consistent liquid penetration length with that obtained from the conductivity probe measurement. Therefore, the temperature measurement also allows the steady-state characterization of the liquid spray zone. It is known that conductivity probes allow the detection of liquid droplets and wet particles in the fluidized bed with water as the conductive compound, which determines the exact boundary of a liquid-present zone. While thermocouples probe the penetration boundary (length) through temperature variation, which is affected by both the liquid presence and liquid evaporation. It is hence expected that the liquid penetration length obtained from the conductivity probes is shorter than that from the thermocouples. However, due to the longer response time of thermocouples used in this work, the liquid penetration lengths obtained from the two measurement approaches are consistent with each other. Therefore, in this work, conductivity probes are used for dynamic behavior analysis of the liquid spray, and thermocouples are applied to the characterization of liquid spray zone boundaries as the vapor-influence area is also taken into account.


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(a) Ul=1.1 m/s

(b) Ul=1.5 m/s

(c) Ul=1.9 m/s Figure 9. Temperature variations with the time at different radial positions and liquid spray velocities (Ug=3.7Umf0, h=Hj=170 mm, Dj=0.5 mm)

Figure 10 shows the temperature variations with the time at r=-30 mm and different heights. Similar to Figure 8, temperature signals below the nozzle installation height are relatively stronger, indicating that the liquid spray is mainly converted into liquid films on particles and hence follows the particles downward motion near the wall. This conclusion is consistent well with that from the conductivity probe measurement. However, the temperature also fluctuates above the nozzle height, because the evaporated liquid (vapor) flow upwards and affects the bed temperature at those positions. Therefore, for the determination of the exact boundaries of a liquid spray zone, temperature measurement is prior to conductivity probe measurement as the vapor-influence area is also taken into account.



(a) Ul=1.1 m/s

(b) Ul=1.5 m/s

(c) Ul=1.9 m/s Figure 10. Temperature variations at different heights and liquid spray velocities (Ug=3.7Umf0, r=-30 mm, Dj=0.5 mm)

In order to quantitatively determine the liquid penetration length, a coefficient of variation method is applied to analyzing the temperature data. Figure 11 shows the coefficients of temperature variation at the nozzle installation height and different liquid spraying velocities. The coefficient of variation decreases with the radial distance from the nozzle outlet (r=-40 mm) and approaches a constant at r=0 mm, despite different liquid spraying velocities employed. Therefore, r=0 mm is considered as the farthest radial position that the liquid spray reaches, which is consistent well with that obtained from the conductivity probe measurement, as shown in Figure 4. The coefficient of variation method is hence a reliable approach to characterizing the liquid penetration length and spray zone boundaries. In addition, a sudden increase of temperature variation coefficient is exhibited at r=-30 mm and Ul=1.9 m/s due to two main reasons. First, the temperature fluctuation intensity


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basically increases with the liquid spray velocity, due to the stronger effects of evaporation and liquid motion on the local temperature. Second, the increased liquid amount present in the bed enhances the randomness of temperature fluctuation at different positions, and a sudden increase of temperature variation coefficient is more probably to occur.

Figure 11. Coefficients of temperature variation at different liquid spray velocities (Ug=3.7Umf0, h=Hj=170 mm, Dj=0.5 mm)

As the liquid spray is dynamic and its distribution fluctuates due to the chaotic gas-solids flow, an uncertainty analysis is conducted to quantify the fluctuation influence on the temperature measurement. The uncertainty of a temperature signal is represented by its standard deviation, as shown in Figure 12. The uncertainty is the highest at the liquid injection position (h=Hj=170 mm) and decreases with the distance to the nozzle, indicating that the liquid content is the main reason for the temperature fluctuation. However, the temperature uncertainty under all the conditions is lower than 2 ℃ , indicating the reliability of the temperature measurement employed.



(a) Ul=1.1 m/s

(b) Ul=1.5 m/s

(c) Ul=1.9 m/s Figure 12. Standard deviations of temperature signals under different positions and typical conditions (Ug=3.7Umf0, Hj=170 mm)

4.3. ESTIMATION OF SPRAY ZONE BOUNDARIES Based on the time-averaged temperature data obtained from the thermocouple arrays, extra temperature values are calculated through interpolation between the adjacent temperature data measured, resulting in a colored profile representing the temperature distribution in the axial cross section of the fluidized bed.13, 34 Although there may be temperature gradient in the fluidized bed, the temperature interpolation approach employed is applicable based on two reasons. First, the temperature data is sampled every 10 mm radially at the heights of 40 mm, 70 mm, 120 mm, 170 mm, 210 mm, 270 mm, 330 mm and 390 mm, respectively, totally 72 data series in the 100 mm×390 mm axial cross section. Such data density should be enough for an accurate interpolation. Second, an instantaneous sharp temperature change in a small area (high temperature gradient) only occurs when a bubble passes or a droplet evaporates.


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However, in a long-period temperature sampling, the influence of such high temperature gradient is smoothed and only the statistical feature is exhibited. Owing to the basis of time-averaged temperature data, the temperature interpolation should be reliable in this work. Figure 13 displays the temperature profiles under different operation conditions. When no liquid sprayed into the bed, as depicted in Figure 13(a), the temperature distribution is basically uniform attributed to the intense solids mixing and circulation driven by the rising bubbles. In addition, the temperature in the center of the bed is slightly higher than that near the wall, mainly due to the stronger bubble coalescence in the center.35 Figure 13(b)~(d) reveals that the temperature near the nozzle outlet is lower than that in the other regions due to the heat removal by liquid evaporation. In addition, the overall temperature in the bed decreases and the low-temperature region is enlarged with the liquid spray velocity. Although Figure 13 provides distinct temperature distributions under liquid spray conditions, it is still difficult to determine the exact spray zone boundaries. Coefficients of temperature variation are hence analyzed in the following. T /℃

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Figure 13. Temperature profiles in the bed under different operation conditions (Ug=3.7Umf0,

Dj=0.5 mm)

According to the conclusion in Section 4.2, the coefficients of temperature variation indicate the liquid penetration length in the radial direction. Figure 14 further shows the distribution of temperature variation coefficients in the axial cross section of the bed under different operation conditions. The coefficients of temperature variation are the highest near the nozzle outlet, and decrease gradually



with the radial distance from the nozzle outlet. This is because the liquid content is the highest near the nozzle outlet, leading to strong interactions between the liquid and particles and enhanced evaporation effects. Therefore, the temperature fluctuation in this region, represented by the coefficient of variation, is the strongest. The liquid sprayed then disperses in the bed while its effects on the bed temperature are weakened with the radial distance from the nozzle outlet. Moreover, compared to Figure 13, more distinct boundaries of the liquid spray zone are exhibited in Figure 14. The distribution of temperature variation coefficients is hence used for the estimation of spray zone boundaries, and the effects of operation conditions on the liquid spray zone area will be discussed in the following. V

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Figure 14. Distribution of temperature variation coefficients in the bed under different operation conditions (Ug=3.7Umf0, Dj=0.5 mm)

4.4. EFFECTS OF OPERATION CONDITIONS ON LIQUID SPRAY ZONE In order to distinguish the liquid spray zone more clearly, a threshold of 0.005 is used to binarize the distribution of temperature variation coefficients. Figure 15 shows the effects of operation conditions on the liquid spray zone (green) behaviors. At the same superficial gas velocity, the liquid spray zone extends towards the gas distributor along the wall with the liquid spray velocity. This is because when an injection-evaporation balance state is established, namely the liquid injection rate equaling the liquid evaporation rate, the liquid amount present in the bed is constant under a certain operation condition and increases with the liquid spray velocity. In addition, more liquid collides with particles and follows the particles circulation in the bed, represented by the liquid-containing particles flowing downward near the wall.


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At the same liquid spray velocity, the liquid spray zone shrinks with the superficial gas velocity due to the increased liquid evaporation rate. In addition to the liquid penetration length, the area is also an important steady-state parameter quantitatively describing the liquid spray zone behaviors. Figure 16 further provides the area ratios of the liquid spray zone in the axial cross section to the whole axial cross section. The spray zone area obviously increases with the liquid spray velocity and decreases with the superficial gas velocity.

(a1) Ug=2.9Umf0, Ul=1.1 m/s

(a2) Ug=2.9Umf0, Ul=1.5 m/s

(a3) Ug=2.9Umf0, Ul=1.9 m/s

(b1) Ug=3.3Umf0, Ul=1.1 m/s

(b2) Ug =3.3Umf0, Ul=1.5 m/s

(b3) Ug =3.3Umf0, Ul=1.9 m/s


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Figure 15. Liquid spray zones under different operation conditions


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Figure 16. Area ratios of the liquid spray zone in the axial cross section to the whole axial cross section under different operation conditions (Dj=0.5 mm)

Figure 17 shows the effects of nozzle installation height on the liquid spray zone behaviors. The extension of liquid spray zone with the nozzle installation height is attributed to two reasons. Firstly, bubbles grow up and accelerate with the height in the bed center. Particles entrained by the bubble wakes are hence accelerated upwards, leading to downward acceleration of particles near the wall with the height due to the internal solids circulation in the bed. Therefore, the downward velocity of liquid films carried by particles near the wall also increases, and the liquid spray zone is extended downward. Secondly, the temperature distribution at Ug=4.1Umf0 and Ul=1.1 m/s is similar to that shown in Figure 13(b), in which the temperature at the top is generally lower than that at the bottom. Therefore, the liquid evaporation is weakened with the height and the liquid spray zone is extended downward. Fig 18 shows the area ratios of the liquid spray zone in the axial cross section to the whole axial cross section. The liquid spray zone area increases with the nozzle installation height.


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Figure 17. Liquid spray zones under different nozzle installation heights (Ug=4.1Umf0, Ul=1.1 m/s, Dj=0.2 mm)

Figure 18. Area ratios of the liquid spray zone in the axial cross section to the whole axial cross section under different nozzle installation heights (Ug=4.1Umf0, Ul=1.1 m/s, Dj=0.2 mm)

In a real super-condensed olefin polymerization process, the industrial background of this experimental work, operation parameters such as liquid components, liquid spray rate, and pressure are different from those in this study, while the temperature is close (88 °C). For the conclusion extension, it is expected that non-stationary and non-linear characteristics will still be reflected from the Hilbert spectra of conductivity signals (if collected) in the industrial plant. Despite different liquid spray zone areas in the experimental and industrial beds, the variations of spray zone shape and area with the liquid spray velocity, superficial gas velocity and nozzle installation height should have similar tendencies.


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In addition, the effect of temperature on the vaporization rate can be described by an vaporization model, such as the non-equilibrium Langmuir–Knudsen model.36 According to the model analysis, the vaporization rate increases with the temperature. In addition, Zhou et al.33 has characterized the relationship between the droplet vaporization rate and emulsion-phase temperature. The droplet vaporization rate increases significantly with the temperature. Moreover, in an industrial bed, if the liquid vaporization rate increases due to the increase of liquid flow rate, the liquid amount present in the bed will increase and the spray zone area will be enlarged. More particles will hence be wetted with lower fluctuation activity and stronger liquid-bridge interaction, leading to more particle agglomerates and stronger fluidization unitability. If the liquid vaporization rate increases due to the increase of recycle gas inlet temperature, the liquid amount present in the bed will decrease and the spray zone area will be reduced. Less particles will hence be wetted with stronger fluctuation activity and weaker liquid-bridge interaction, further reducing particle agglomerates and increasing the fluidization stability. For the situations of liquid vaporization rate decrease, similar analysis can be correspondingly made.

5. CONCLUSIONS In this work, a conductivity probe array, two thermocouple arrays, and a pressure sensing system have been applied to characterizing the liquid spray zone in a high-temperature fluidized bed with a side-wall liquid spray, respectively. Hilbert-Huang transform (HHT), power spectral analysis, and variation coefficient analysis are employed for fluctuation signal analysis. Non-stationary and non-linear characteristics are reflected from the time dependence of frequency and the intermittent variation of fluctuation energy in the Hilbert spectra of the conductivity signals. The energy distribution shifts to higher frequencies with the liquid spray velocity, related to the enhanced activity of liquid-containing particles and droplets dragged by higher-frequency bubbles near the nozzle. For the determination of the exact boundaries of the liquid spray zone, temperature measurement is prior to conductivity measurement as the vapor-influence area is also taken into account. In addition, the variation coefficient analysis based on the temperature measurement is a reliable approach to characterizing the liquid penetration length and spray zone



boundaries. According to the two-dimensional profiles of the coefficients of temperature variation in the fluidized bed, the liquid spray zone extends downward along the wall with the liquid spray velocity, and the liquid spray zone shrinks with the superficial gas velocity. The spray zone area increases with the liquid spray velocity and decreases with the superficial gas velocity. Moreover, the liquid spray zone is enlarged and extends downward along the wall with the nozzle installation height.

AUTHOR INFORMATION Corresponding Author *

Email: [email protected]

ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support provided by the Project of National Natural Science Foundation of China (91434205), the National Natural Science Foundation for Young Scientists of China (21406194), the National Science Fund for Distinguished Young (21525627), the Natural Science Foundation of Zhejiang Province (LR14B060001) and the Natural Science Foundation of Zhejiang Province for Young (LQ18B060001).

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(6) Wu, W. Q.; Yang, Y. R.; Luo, G. H.; Wang, J. D.; Jiang, B. B.; Wang, S. F.; Han, G. D. A method for polymer preparation. China Patent Appl. 201110290783.8, 2011. (7) Becher, R. D.; Schlunder, E. U. Fluidized bed granulation - the importance of a drying zone for the particle growth mechanism. Chem. Eng. Process 1998, 37, 1-6. (8) Higman, C.; van der Burgt M. Gasiﬁcation. Gulf Professional Publishing: Burlington, MA, 2007. (9) Maronga, S. J.; Wnukowski, P. Establishing temperature and humidity profiles in fluidized bed particulate coating. Powder Technol. 1997, 94, 181-185. (10) Zhou, Y. F.; Wang, J. D.; Yang, Y. R.; Wu, W. Q. Modeling of the temperature profile in an ethylene polymerization fluidized-bed reactor in condensed-mode operation. Ind. Eng. Chem. Res. 2013, 52, 4455-4464. (11) Bruhns, S.; Werther, J. An investigation of the mechanism of liquid injection into fluidized beds. AIChE J. 2005, 51, 766-775. (12) McMillan, J.; Zhou, D.; Ariyapadi, S.; Briens, C.; Berruti, F.; Chan, E. Characterization of the contact between liquid spray droplets and particles in a fluidized bed. Ind. Eng. Chem. Res. 2005, 44, 4931-4939. (13) Maronga, S. J.; Wnukowski, P. The use of humidity and temperature profiles in optimizing the size of fluidized bed in a coating process. Chem. Eng. Process 1998, 37, 423-432. (14) Zhou, Y. F.; Shi, Q.; Huang, Z. L.; Liao, Z. W.; Wang, J. D.; Yang, Y. R. Realization and control of multiple temperature zones in liquid-containing gas-solid fluidized bed reactor. AIChE J. 2016, 62, 1454-1466. (15) Ariyapadi, S.; Berruti, F.; Briens, C.; McMillan, J.; Zhou, D. Horizontal penetration of gas-liquid spray jets in gas-solid fluidized beds. Int. J. Chem. React. Eng. 2004, 2. (16) Turchiuli, C.; Jimenèz, T.; Dumoulin, E. Identification of thermal zones and population balance modelling of fluidized bed spray granulation. Powder Technol. 2011, 208, 542-552. (17) Fan, L. S.; Lau, R.; Zhu, C.; Vuong, K.; Warsito, W.; Wang, X.; Liu, G. Evaporative liquid jets in gas-liquid-solid flow system. Chem. Eng. Sci. 2001, 56, 5871-5891. (18) Mohagheghi, M.; Hamidi, M.; Berruti, F.; Briens, C.; McMillan, J. Study of the effect of local hydrodynamics on liquid distribution in a gas-solid fluidized bed using a capacitance method. Fuel 2013, 107, 236-245. (19) Mohagheghi, M.; Hamidi, M.; Briens, C.; Berruti, F.; McMillan, J. The effects of liquid properties and bed hydrodynamics on the distribution of liquid on solid fluidized particles in a cold-model fluidized bed. Powder Technol. 2014, 256, 5-12. (20) Gehrke, S.; Wirth, K. E. Liquid feed injection in a high-density riser. Chem. Eng. Technol. 2008, 31, 1701 - 1705. (21) Börner, M.; Hagemeier, T.; Ganzer, G.; Peglow, M.; Tsotsas, E. Experimental spray zone characterization in top-spray fluidized bed granulation. Chem. Eng. Sci. 2014, 116, 317-330.



(22) Portoghese, F.; House, P.; Berruti, F.; Briens, C.; Adamiak, K.; Chan, E. Electric conductance method to study the contact of injected liquid with fluidized particles. AIChE J. 2008, 54, 1770-1781. (23) Jamaleddine, T. J.; Saha, M.; Berruti, F.; Briens, C. Effect of interaction between spray and attrition jets in a high temperature fluidized bed. Powder Technol. 2015, 278, 57-64. (24) Ariyapadi, S.; Holdsworth, D. W.; Norley, C. J. D.; Berruti, F.; Briens, C. Digital X-ray imaging technique to study the horizontal injection of gas-liquid jets into fluidized beds. Int. J. Chem. React. Eng. 2003, 1. (25) Hu, D. F.; Han, G. D.; Lungu, M.; Huang, Z. L.; Liao, Z. W.; Wang, J. D.; Yang, Y. R. Experimental investigation of bubble and particle motion behaviors in a gas-solid fluidized bed with side wall liquid spray. Adv. Powder Technol. 2017, 28, 2306-2316. (26) Liu, S. Confidence Interval Estimation for Coefficient of Variation. Georgia State University, 2012. (27) Stoica, P.; Moses, R. Spectral Analysis of Signals. Prentice Hall: New Jersey, 2005. (28) Huang, N. E.; Shen, Z..; Long, S. R.; Wu, M. C.; Shih, H. H.; Zheng, Q. N.; Yen, N. C.; Tung, C. C.; Liu, H. H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A 1998, 454, 903-995. (29) Xu, C.; Liang, C.; Zhou, B.; Wang, S. HHT analysis of electrostatic fluctuation signals in dense-phase pneumatic conveying of pulverized coal at high pressure. Chem. Eng. Sci. 2010, 65, 1334-1344. (30) Darton, R. C.; La Nauze, R. D.; Davidson, J. F.; Harrison, D. Bubble growth due to coalescence in fluidized beds. Trans. Inst. Chem. Eng. 1977, 55, 274-280. (31) Davidson, J. F.; Harrison, D. Fluidized Particles. Cambridge University Press: Cambridge, 1963. (32) Botros, K. K.; Price, G.; Ker, V.; Jiang, Y.; Goyal, S. K. Effects of hydrocarbon liquid feed in polyethylene polymerization process on particle surface temperature. Chem. Eng. Commun. 2006, 193, 1612-1634. (33) Zhou, Y. F.; Wang, J. D.; Yang, Y. R.; Wu, W. Q. Modeling of the temperature profile in an ethylene polymerization fluidized-bed reactor in condensed-mode operation. Ind. Eng. Chem. Res. 2013, 52, 4455-4464. (34) Jiménez, T.; Turchiuli, C.; Dumoulin, E. Particles agglomeration in a conical fluidized bed in relation with air temperature profiles. Chem. Eng. Sci. 2006, 61, 5954-5961. (35) Zhou, Y. F.; Shi, Q.; Huang, Z. L.; Wang, J. D.; Yang, Y. R. Effects of liquid action mechanisms on hydrodynamics in liquid-containing gas-solid fluidized bed reactor. Chem. Eng. J. 2016, 285, 121-127. (36) Kitano, T.; Nishio, J.; Kurose, R.; Komori, S. Effects of ambient pressure, gas temperature and combustion reaction on droplet evaporation. Combust. Flame 2014, 161, 551-564.


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FIGURE CAPTIONS Figure 1. Layout of the experimental apparatus Figure 2. Installation locations of the conductivity probe array and thermocouple arrays Figure 3. Relative voltage variations with the time at different radial positions and liquid spray velocities (Ug=3.7Umf0, h=Hj=170 mm, Dj=0.5 mm) (a) Ul=1.1 m/s, (b) Ul=1.5 m/s, (c) Ul=1.9 m/s Figure 4. Time-averaged relative voltages at different radial positions and liquid spray velocities (Ug=3.7Umf0, h=Hj=170 mm, Dj=0.5 mm) Figure 5. Hilbert spectra of the relative voltage signals under different operation conditions (Ug=3.7Umf0, h=170 mm, r=-30 mm, Dj=0.5 mm) (a) Ul=1.1 m/s, (b) Ul=1.5 m/s, (c) Ul=1.9 m/s Figure 6. Hilbert spectra of the relative voltage signals under different operation conditions (Ug=4.1Umf0, h=170 mm, r=-30 mm, Dj=0.5 mm) (a) Ul=1.1 m/s, (b) Ul=1.5 m/s, (c) Ul=1.9 m/s Figure 7. Power spectra of pressure fluctuation signals under different operation conditions (h=120 mm) (a) Ug=3.7Umf0, (a) Ug=4.1Umf0 Figure 8. Relative voltage variations at different heights and liquid spray velocities (Ug=3.7Umf0, r=-30 mm, Dj=0.5 mm) (a) Ul=1.1 m/s, (b) Ul=1.5 m/s, (c) Ul=1.9 m/s Figure 9. Temperature variations with the time at different radial positions and liquid spray velocities (Ug=3.7Umf0, h=170 mm, Dj=0.5 mm) (a) Ul=1.1 m/s, (b) Ul=1.5 m/s, (c) Ul=1.9 m/s Figure 10. Temperature variations at different heights and liquid spray velocities (Ug=3.7Umf0, r=-30 mm, Dj=0.5 mm) (a) Ul=1.1 m/s, (b) Ul=1.5 m/s, (c) Ul=1.9 m/s Figure 11. Coefficients of temperature variation at different liquid spray velocities (Ug=3.7Umf0, h=Hj=170 mm, Dj=0.5 mm) Figure 12. Standard deviations of temperature signals under different positions and typical conditions (Ug=3.7Umf0, Hj=170 mm) (a) Ul=1.1 m/s, (b) Ul=1.5 m/s, (c) Ul=1.9 m/s Figure 13. Temperature profiles in the bed under different operation conditions (Ug=3.7Umf0, Dj=0.5 mm) (a) Ul=0 m/s, (b) Ul=1.1 m/s, (c) Ul=1.5 m/s, (d) Ul=1.9 m/s Figure 14. Distribution of temperature variation coefficients in the bed under different operation conditions (Ug=3.7Umf0, Dj=0.5 mm) (a) Ul=1.1 m/s, (b) Ul=1.5 m/s, (c) Ul=1.9 m/s Figure 15. Liquid spray zones under different operation conditions (a1) Ug=2.9Umf0, Ul=1.1 m/s, (a2) Ug=2.9Umf0, Ul=1.5 m/s, (a3) Ug=2.9Umf0, Ul=1.9 m/s, (b1) Ug=3.3Umf0, Ul=1.1 m/s, (b2) Ug=3.3Umf0, Ul=1.5 m/s, (b3) Ug=3.3Umf0, Ul=1.9 m/s, (c1) Ug=3.7Umf0, Ul=1.1 m/s, (c2) Ug =3.7Umf0, Ul=1.5 m/s, (c3) Ug =3.7Umf0, Ul=1.9 m/s, (d1) Ug=4.1Umf0, Ul=1.1 m/s, (d2) Ug =4.1Umf0, Ul=1.5 m/s, (d3) Ug =4.1Umf0,



Ul=1.9 m/s, (e1) Ug=4.6Umf0, Ul=1.1 m/s, (e2) Ug =4.6Umf0, Ul=1.5 m/s, (e3) Ug =4.6Umf0, Ul=1.9 m/s Figure 16. Area ratios of the liquid spray zone in the axial cross section to the whole axial cross section under different operation conditions (Dj=0.5 mm) Figure 17. Liquid spray zones under different nozzle installation heights (Ug=4.1Umf0, Ul=1.1 m/s, Dj=0.2 mm) (a) Hj =70 mm, (b) Hj =120 mm, (c) Hj =170 mm, (d) Hj =210 mm, (e) Hj =270 mm Figure 18. Area ratios of the liquid spray zone in the axial cross section to the whole axial cross section under different nozzle installation heights (Ug=4.1Umf0, Ul=1.1 m/s, Dj=0.2 mm)


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264x237mm (96 x 96 DPI)


Dynamic and Steady-State Characterization of the Liquid Spray Zone

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