Article pubs.acs.org/IECR
Monitoring Electrostatics and Hydrodynamics in Gas−Solid Bubbling Fluidized Beds Using Novel Electrostatic Probes Chuan He, Xiaotao T. Bi,* and John R. Grace Fluidization Research Centre Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, British Columbia, Canada V6T 1Z3 S Supporting Information *
ABSTRACT: The ability of recently developed novel electrostatic probes to monitor particle charge density and hydrodynamics in freely bubbling two- and three-dimensional fluidized beds of glass beads and polyethylene particles is demonstrated. Particle charge density and bubble properties in the beds were altered by abruptly changing superficial gas velocity or by impulsively adding antistatic agent to the bed. The probes were then utilized to quantitatively monitor the particle charge density and bubble rise velocity. The current signals from the probes responded quickly and significantly to abrupt changes in the superficial gas velocity. By analyzing time-series signals from the probes, the particle charge density and the bubble rise velocity deduced from the probes were found to be of similar order of magnitudes and changed consistently with those obtained from Faraday cup and video measurements. Charge densities from the Faraday cup decreased when an antistatic agent was added, as registered by the probe. Demirbas et al.12 analyzed the charge signals from an induction probe in a two-dimensional (2D) fluidized bed by standard deviation and attractor comparison methods. The standard deviation demonstrates the degree of local charge separation, which is represented by the difference between the minimum and maximum of the data points (as measured by an electrometer) at a specific location. The attractor of a system answers the question “where is the system if one waits long enough”; it is a fingerprint of the system, reflecting its hydrodynamic state.13 The attractor comparison method is based on the idea that the state of a fluidized bed at a given time can be determined by projecting all variables governing the system in a multidimensional space. The attractor comparison method statistically compares the attractors reconstructed from time series (for a selected reference period and evaluation period) and calculates a value, the S-value, which is defined as
1. INTRODUCTION Electrostatic phenomena in fluidized beds were first observed in the 1950s. They have recently received greater attention from both the academic and industrial communities. Because of repeated contacts and separations between particles and between particles and walls, charge generation in the bed is almost unavoidable. The charges result in a series of drawbacks, such as particle agglomeration and reactor wall fouling.1,2 Electrostatic generation of dielectric powders has been investigated in different setups,3−5 and several methods have been reported to mitigate bed electrification and reactor fouling, such as humidification, antistatic agents, or increasing the superficial gas velocity to clean the distributor plate.6−9 However, a reliable charge measurement tool that is capable of monitoring the charges is still missing. Commonly used electrostatic probes cannot detect changes of in-bed particle charge density, because cumulative charge signals from probes are affected by changes in both electrostatics and hydrodynamics. Also, there are currently no techniques to measure the charging of bulk powders, and no standardized methods are available to measure the electrostatics of pharmaceutical powders.10 A suitable charge density measurement tool could identify potential risks earlier and prevent hazards that are due to electrostatic discharges. It could also monitor the effectiveness of different strategies intended to reduce the charge density to provide safer operation for handling dielectric powders. Ideally, signal analysis should be neither time-consuming nor complicated, in order to be adapted for online monitoring in large commercial units. Bi et al.11 asserted that the standard deviations of current signals from a collision ball probe reflect changes in local hydrodynamics, as well as in particle charge density. Normalized by average values, the dimensionless standard deviation could be a good indicator of local hydrodynamics. © 2015 American Chemical Society
S=
Q̂ VC(Q̂ )
(1)
where Q̂ is the estimator of Q (Q is the squared distance between two attractors) and VC is the variance. For attractors generated by the same mechanism, S has an expected value of 0 and a standard deviation of 1. A value of S > 3 indicates, with >95% confidence, that two attractors were generated by different mechanisms.14 The authors compared the S-values of pressure and charge fluctuations while varying the relative humidity (RH) and found that the S-values of pressure and Received: Revised: Accepted: Published: 8333
April 21, 2015 June 30, 2015 August 10, 2015 August 10, 2015 DOI: 10.1021/acs.iecr.5b01512 Ind. Eng. Chem. Res. 2015, 54, 8333−8343
Article
Industrial & Engineering Chemistry Research
Figure 1. Schematics of (a) two-dimensional (2D) and (b) 0.30-m-ID three-dimensional (3D) columns, and (c) dual-tip electrostatic probe (not to scale).
charge fluctuations were insensitive to the RH in the first 150 min, and began to differ after the RH level decreased to I1̅ + ϕIsd,1 8335
Imin,1(i) < I1̅ − ϕIsd,1
(2)
DOI: 10.1021/acs.iecr.5b01512 Ind. Eng. Chem. Res. 2015, 54, 8333−8343
Article
Industrial & Engineering Chemistry Research Imax,2(i) > I2̅ + ϕIsd,2
Imin,2(i) < I2̅ − ϕIsd,2
glass beads and polyethylene particles of different size ranges were conducted with different particle charge density (qm) and bubble rise velocity (UB) in the freely bubbling bed. Single bubbles passing the probe in vertical alignment were selected from video recordings for analysis of the bubble rise velocity, and corresponding current peaks were selected from the synchronized probe signals. Many data were discarded, because of irregular bubble shapes or movement, such as coalescence, splitting, or nonvertical passages. Because of the complex flow pattern in the fluidized bed, only a small proportion (∼10%) of bubbles passed the local probe location vertically without splitting/coalescing. For the glass beads used in this study, parameters of αi = 0.21 kg/m, βi = 4.59 × 10−7 C s2/(kg m2), and γi = 2.95 × 10−6 C/kg were obtained from fitting measured data into eq 10. Both original and sieved polyethylene particles were tested. The original ones had a relatively wide size range of 100−1500 μm, whereas the sieved ones had a relatively narrow size range of 710−850 μm. Equation 10 was fitted to measured data (Ipeak,, qm, and UB) (see Table S1 in the Supporting Information) with ρp = 918 kg/m3 and εmf = 0.55 for the dense phase. Parameters of αi = 6.06 × 10−3 kg/m, βi = 1.80 × 10−7 C s2/(kg m2), and γi = 2.18 × 10−8 C/kg were obtained for original ones. Comparing fitted parameters for particles with narrow and relatively wide size distributions in this work and previous work,15 all the parameters were affected by particle size and distribution. The experimental data and values obtained from eq 10 with the fitted α, β, and γ values for polyethylene particles of narrow and wide size distributions are compared in a parity plot in Figure 2. It is likely that more
(3)
where I ̅ and Isd are the mean and standard deviations of the raw signal. The coefficient φ is set to 0.5 for the maximum peaks and 1 for the minimum peaks in the current study. For each tip, the time difference between adjacent maximum and minimum peaks represents the time for a single bubble to pass that tip, and this parameter is related to the bubble size by the expression ΔτBmax ≥ |tmax,1(j) − tmin,1(j)| ≥ ΔτBmin
(4)
ΔτBmax ≥ |tmax,2(j) − tmin,2(j)| ≥ ΔτBmin
(5)
where ΔτBmax and ΔτBmin are the maximum and minimum permissible time intervals for bubbles to pass the probe, based on the minimum and maximum credible bubble sizes, chosen as 0.01 and 0.2 m in the current system, based on visual observations of recorded videos. The times corresponding to the maximum and minimum peaks from the two tips (tmax,1, tmin,1, tmax,2, tmin,2) should follow the sequence tmax,2 < tmax,1 < tmin,2 < tmin,1. A ratio of time shift between maximum peaks from the two tips to the time shift between minimum peaks from the two tips, is within 0.8−1.2, allowing a reasonable range of deviations for bubbles passing the two tips vertically.15 tmax,2 < tmax,1 < tmin,2 < tmin,1⎫ ⎪ tmax,1 − tmax,2 ⎬ < 1.2 ⎪ 0.8 < tmin,1 − tmin,2 ⎭
(6)
All pairs of peaks that satisfy these criteria are selected and used for calculation. 2.2.2.2. Decoupling Methods. 2.2.2.2.1. Two-Tip CrossCorrelation Method. The time lag between the peaks from the two tips (denoted as Δt) can be obtained by crosscorrelating the time-series signals from the two tips: R I1I2(Δt ) =
1 lim H T →∞
∫0
H
I1(t )I2(t + Δt ) dt
(7)
where Δt is the time shift when the cross-correlation (coefficient) function reaches a maximum, indicating the time delay where two signals are best aligned, corresponding to the average time for bubble passage between the two tips. H is the cross-correlation integration time period. The time lag, Δt, is then used to estimate the bubble rise velocity (UB), in conjunction with the separation distance between the two tips (Δz): UB =
Δz Δt
Figure 2. Comparison of fitted data (from eq 10) and experimental data for different particle size ranges of PE powders.
(8)
The bubble size can be obtained from the time difference (Δτ) between the times corresponding to the arrival of the bubble nose and the wake from the signals of either tip.
DB = UBΔτ
experimental data could improve the coefficient of determination and measurement accuracy. With fitted α, β, and γ values from the 2-D bed for a give type of particles, UB and qm can then be predicted from eqs 7 and 10 using measured signals from the same electrostatic probe following three methods. 2.2.2.2.2. Two-Tip Peak-Times Method. Based on the time differences between peaks from the upper and lower tips and between adjacent maximum and minimum peaks from each tip, the time lag Δt and time difference Δτ could alternatively be calculated by using the expressions
(9)
Current peak values (Ipeak) can be related to the in-bed particle charge density (qm) and the bubble rise velocity (UB):15 Ipeak, i = αiqmUB + ρp (1 − εmf )UBA p(βi UB 2 + γi)
(10)
where αi, βi, and γi are fitted parameters; ρp is the particle density; εmf is the voidage at minimum fluidization; and Ap is the surface area of the probe tip. Following a similar procedure as described in previous work,15,16 calibration experiments with
Δt = 8336
(tmax,1 − tmax,2) + (tmin,1 − tmin,2) 2
(11) DOI: 10.1021/acs.iecr.5b01512 Ind. Eng. Chem. Res. 2015, 54, 8333−8343
Article
Industrial & Engineering Chemistry Research Δτ =
distance between the protruding and retracted tips is important. If this distance is too large, the signals from two tips may not be well correlated. The calculated value of UB, as shown in Figure 4, increased with increasing superficial gas velocity. The one-tip timedifference method gave more reasonable results than the other two methods. The effect of intrusive probe tips on the derived bubble size was also studied. Ratios of time differences (Δτ) for the lower and upper tips calculated for the selected bubbles at different Ug values fell into the range of 0.86−1.2, with an average of 1.0 and a standard deviation of 0.06. Again, this indicates that the pierced chord lengths of selected bubbles varied within a limited range while passing the probe. The relative differences between the decoupled average UB value from the upper and lower tips were
