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Jun 19, 2012 - State Key Laboratory of Chemical Engineering and Department of ... Agglomeration occurring in horizontal stirred bed reactors (HSBR) fo...
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Agglomeration Detection in Horizontal Stirred Bed Reactor Based on Autoregression Model by Acoustic Emission Signals Yefeng Zhou, Zhengliang Huang, Congjing Ren, Jingdai Wang,* and Yongrong Yang State Key Laboratory of Chemical Engineering and Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, P. R. China ABSTRACT: Agglomeration occurring in horizontal stirred bed reactors (HSBR) for polyolefin production has negative impacts on the efficiency of the reactor operation and may sometimes lead to unscheduled shutdown of the plant. In this paper, an autoregression (AR) model based on acoustic emission (AE) technique has been proposed to establish the qualitative relationship between AE signals and agglomeration in the HSBR. In this method, the frequency of AE signal varies with particles of different sizes striking the reactor walls. From the cold model experiments, it was found that AR power spectrum became fluctuant after the addition of agglomerations into laboratorial scale HSBR, and meanwhile the low frequency band energy ratio and the variance of AE signals kept rising. Furthermore, this AE-based AR model was also successfully applied to detect the agglomeration in an industrial HSBR unit, showing that the method could monitor agglomerations in an environmentally friendly manner and with fairly good accuracy. polymer products. 4 Figure 2 shows a photograph of agglomerations inside an industrial HSBR. The agglomerations

1. INTRODUCTION As a typical axial powder mixing reactor, horizontal stirred bed reactors (HSBRs) have been extensively used in gas-phase polypropylene (PP) production process and developed rapidly in recent years.1,2 A typical HSBR polymerization section of the Innovene process is shown in Figure 1. In this process, most of

Figure 2. Photography of agglomerations in an industrial HSBR.

Figure 1. Schematic diagram of polymerization section of the Innovene process.

are irregular in shape with a size range of 2−5 cm. The hydrodynamic behavior within the reactor will vary with size of agglomerations. For example, small agglomerates would lead to partial blockage of discharging pipelines, and then cause some defluidization zones within the reactor. As the agglomerations gather into larger lumps, these lumps would take up most of the effective volume of the stirred reactor, which results in complete blockage of the pipelines. At this moment, the deterioration of the entire reactor bed will lead to an unscheduled shutdown, causing tremendous economic losses. To improve HSBR technology and enhance its production efficiency, it is necessary to develop an effective technique for detection of agglomeration.

the reaction heat is removed by vaporizing condensed monomers (referred to as quench liquid in the Figure 1) distributed on the particles in the HSBR. The evaporated and unreacted gas monomers are recycled back to the reactor after cooling and phase-separation. In contrast to traditional gas-phase fluidized beds, HSBR technology is more likely to produce agglomerations due to the presence of liquid and low capacity of heat exchange.3 In HSBR PP production process, “hotspots” are likely to be formed inside the reactor owing to uneven distribution of quench liquid or catalysts. Further, the “hotspots” would expand rapidly and thus cause agglomeration formation. Agglomeration has been regarded as one of the toughest problems that needs to be solved in plant operations. Agglomeration will affect reactors’ normal operation in the long run as well as the quality of © 2012 American Chemical Society

Received: Revised: Accepted: Published: 11629

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So far, many popular techniques5 have been used to detect agglomerations in fluidized bed reactors, including electrostatic,6,7 temperature,8,9 pressure,10,11 radiation, and optical measurements.12 Since electrostatic effect is regarded as one of the causes of agglomerations in fluidized bed reactors, electrostatic measurement technique can be used to detect agglomeration. Besides, agglomeration may affect movement of bubbles in fluidized beds, further leading to variation of pressure fluctuation in the bed, thus pressure measurements has been used to monitor agglomeration. However, both measurements have their own drawbacks. For instance, invasive characteristics of measurement probes may affect flow behavior within the reactor and thus cause inconvenience for the users. Although some satisfactory results have been obtained from temperature measurement, there are still some unavoidable limitations. The measurement displays a hysteresis nature in time and could only reflect local agglomeration, rather than overall temperature which could reflect agglomeration information. The radiation measuring technique is now being replaced by other methods because of its harm to human health. Optical measurements are not fit for unfavorable industrial environments though they may offer accurate information about shape and size of agglomeration in laboratory experiments. At present, only one paper has discussed agglomeration detection using the attractor comparison method in HSBR.13 However this method is available only on the lab-scale and has not been used in industrial HSBR. Therefore, it is very urgent to develop a noninvasive, reliable, environmentally friendly technique for agglomeration detection in industrial HSBR. In recent years, the acoustic emission (AE) measurement technique has been developed to monitor equipment operation and physicochemical changes in chemical engineering processes.14,15 As a noninvasive technique, it can be used in rigorous industrial environments. Since AE signals are capable of reflecting random movement of particles and are sensitive to changes in particle size distribution, it is possible to apply AE technique to detect agglomeration.15−19 Cody et.al20−22 first defined the physics of acoustic measurement and applied it to lab and industrial gas solid fluidized bed units, which serve as an enlightenment to our study. Besides, several related application models for agglomeration detection by use of AE signals in fluidized beds have been reported by our group.13,16,18,23,24 Based on the previous studies, this work attempts to detect agglomerations in HSBR by use of AE signals generated by collisions between particles and reactor wall. Before conducting experiments, selecting an effective analysis method is crucial for establishing a qualitative relationship between AE signals and agglomeration. As is known to all, chaos analysis and multiscale analysis are complex in algorithm, and frequency spectrum analysis has its limitation.25 Compared with these mentioned analysis methods, autoregression (AR) analysis possesses a series of advantages26−28 and is popular at present. For example, the power spectrum estimation based on AR model shows great simplicity and integrity in signal processing. As one of the most widely used models, AR model can effectively characterize signal frequency spectrum and energy distribution variation under different conditions. Therefore, AR model has been applied in several measuring fields, such as fault diagnosis of rolling bearing, detection of hydraulic field signal of naval, and classification and discrimination of earthquake signal.

In this study, a noninvasive, reliable, sensitive, secure AE technique was used to collect signals caused by particle collisions within HSBR. AR model was then applied to analyze these collected AE signals. In this way, AR power spectrum density could be obtained and then variance of AE signal could be calculated so as to obtain accurate and real-time information about agglomeration. At first, a number of cold model experiments were carried out to verify the effectiveness of AE technique and AR model. Furthermore, the verified AR model was then utilized to detect agglomeration in industrial-scale HSBR. Through lab-scale experiment and industrial practice, the proposed method has proven to be suitable for monitoring agglomerations in HSBR. More details will be further discussed in the following parts.

2. THEORY AND METHODOLOGY 2.1. Fundamentals. As a passive detection method, AE technique can reflect signal changes in the reactor. Since the AE signal is generated mainly by collisions between particles and the wall, energy of the signal can be used to show the intensity of particles struck on the wall. Not only ordinary particles but also agglomerations may hit the reactor wall. Due to their different physical properties (including quality, shape, and elastic modulus, etc.), the signal produced by agglomerations hitting the wall is very different from that generated by ordinary particles.18 The difference can be reflected by energy distribution of the AE signal in various frequency ranges. To be specific, AE signal of agglomeration is relatively “dull” because its energy is mainly distributed in low frequency range, while AE signal of ordinary particles is “sharp” because most of the energy concentrates in high frequency range. In addition to the above brief introduction, it is necessary to understand the basic principles of AE detection for agglomeration. The study of this paper is conducted on the premise that materials with different physical properties generate different AE signals. Based on this precondition, by analyzing AE signals under different conditions, energy distribution in different frequency ranges could be revealed. Through analyzing the distribution, signal characteristic differences could be obtained and agglomeration detection could be achieved by analyzing obtained differences. The AE signals of agglomeration hitting the reactor wall are not continuous but in the form of episodic pulses. Since these signals are likely to be mixed with those produced by ordinary particle movement, it is difficult to distinguish the two kinds of signals just from their original form. Figure 3 shows an original AE signal in a HSBR. For discrete pulse signal, the frequency spectrum can be gained by applying fast Fourier transform (FFT) algorithm to handle collected data. Due to wide band frequency distribution of agglomeration-existing AE signals, AR

Figure 3. Typical acoustic signal of the HSBR. 11630

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A (z ) = 1 + H (z ) =

p

x(n) = − ∑ ak x(n − k) + u(n)

H (z ) =

1 1 = p A (z ) 1 + ∑k = 1 ak z −k

|1 +

p ∑k = 1 ak e−jωk|2

(7)

The model given by these three equations is called AR model which is an all-pole model. In this model, “autoregression” means that the output is a weighted sum of one current input and p past outputs. By multiplying x(n+m) to both sides of eq 5 and averaging them, autocorrelation function rx(m) can be thus obtained as follows: ⎧ −∑ p a r (m − k) k=1 k x rx(m) = ⎨ p 2 ⎩ −∑k = 1 ak rx(k) + σ

m≥1 m=0

(8)

During the derivation, the relationship of the autocorrelation function, rx(m) = rx(−m) is applied. Equation 8 can also be written as follows: ⎛ rx(0) rx(1) rx(2)··· rx(p) ⎞⎛ 1 ⎞ ⎛ 2 ⎞ ⎜ ⎟ σ ⎜ rx(1) rx(0) rx(1)··· rx(p − 1)⎟⎜ a1 ⎟ ⎜ 0 ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ rx(2) rx(1) rx(0)··· rx(p − 2)⎟⎜ a 2 ⎟ = ⎜ 0 ⎟ ⎜ ⎟⎜ ⋮ ⎟ ⎜ ⋮ ⎟ ⋮ ⋮ ⋮ ⎜ ⋮ ⎟⎜⎜ ⎟⎟ ⎜⎜ ⎟⎟ ⎜ ⎟⎝ ap ⎠ ⎝ 0 ⎠ rx(0) ⎠ ⎝ rx(p) rx(p − 1) rx(p − 2)··· (9)

The above two eqs 8 and 9 are called normal equations or Yule−Walker equations. From eq 9, it is obtained that the coefficient matrix is not only symmetric, but also the components of each diagonal line parallel to the main diagonal line present the same value. This coefficient matrix can be also used to denote the properties of x(n). The above eq 9 provides a way to estimate parameters of one specific AR model. These parameters, a1, a2, ..., ap, σ2 can be determined by eqs 8 and 9 and σ2 is the variance of u(n). By inserting these parameter values into eqs 5−7, AR power spectrum can be obtained. In this way, power spectrum

q

(2)

∞

∑ h(k)u(n − k) k=0

(6)

σ2

Px(e jω) =

(2) The parameters of H(z) can be obtained through the known x(n) or its autocorrelation function rx(m). (3) The power spectrum of x(n) can be estimated from the parameters of H(z). For a certain linear system shown in Figure 4, if u(n) is a white noise sequence with a variance (σ2) and AE sequence is shown as x(n), the relationship between them can be expressed as follows:

x(n) =

(5)

k=1

Figure 4. Basic mathematical principle of parametric model.

k=0

(4)

In this way, provided that the variance σ and parameters a1, a2, ..., ap,b1,b2, ...,bq are known, the power spectrum of x(n) can be obtained by the eq 4. By setting different values for these a and b, different parametric models can be generated, such as AR model, moving average (MA) model, and autoregression moving average (ARMA) model. To be specific, when b1, b2, ...,bk are all set as 0, the above equations become:

(1)

∑ bku(n − k)

∑ hkz−k

2

⎪

k=1

k=1

σ 2 |B(e jw)|2 |A(e jw)|2

Px(e jw) =

⎪

x(n) = − ∑ ak x(n − k) +

∑ bkz−k ,

According to linear system theory, Px(ejw) = Pu(ejw)|H(ejw)|2 is applied to the random AE sequence x(n), and thus the power spectrum can be shown as follows:

2.3. Autoregression (AR) model. Time series analysis is carried out on the premise that data have their own order and correlation. And then, by analyzing internal correlation of signals, change law of the system can be found so as to be used for signal prediction and process control. Classical power spectrum estimating methods do not have desirable variance performance and resolution, so the emergence of parametric model estimating methods work for improving resolution as well as smoothness of spectrogram.30 The main steps of the parametric model methods are as follows: (1) Assume x(n) is the output sequence excited by an input sequence u(n) on H(z) which is a linear and shift invariant discrete system. The relationship is shown in Figure 4.

p

B (z ) = 1 +

k=0

∑ x(n)e−j2πnf n=1

∑ akz−k ,

k=1 ∞

N

F (f ) =

q

p

model, which can fully display the main frequency of signals and adapt to continuous operation in industrial environment, was used to deal with these signals in this study. The model parameters of signals under agglomeration-existing condition (evaluated time series) and normal operating conditions (reference time series) were used for comparison. By combining these differences between the two states and power spectrum analysis of AR model, fault diagnosis for agglomeration can be achieved in the HSBR. 2.2. Spectrum Analysis. Spectrum analysis is the most widely used signal processing method in acoustics.29 Among spectrum analysis methods, discrete Fourier Transform (DFT) is a commonly used one. FFT is a highly efficient algorithm for DFT calculation. It transforms signal from time domain to frequency domain and focuses on signal characteristics in frequency domain. Frequency characteristics of the signal are reflected by its energy distribution in frequency domain. The DFT of a sampled signal x(n) can be expressed as follows:

(3)

By applying Z-transformations to both sides of eqs 2 and 3 and assuming b0 = 1, the relationship H(z) = (B(z)/A(z)) can be obtained, in which 11631

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Figure 5. Schematic diagram of cold model experimental apparatus.

The preamplifier (PXPA IV, 2−500 kHz, China) supplies sufficient gain to AE signals so as to make them capable of being transmitted via cables of 200 m length. PXMA signal conditioning equipment is applied as signal conditioning system in the experiments. It can filter signals by using a high-pass cutoff frequency of 50 kHz and at the same time provide sufficient gain to signals. The data acquisition system consists of a data acquisition card (NI PCI-6071E, National Instruments, USA) and a personal computer. AE signals generated by the piezoelectric accelerometer are amplified and conditioned, and then transferred to the data acquisition card which is connected to the computer and controlled by the software package LABVIEW. According to Shannon sampling theorem, sampling frequency must be twice higher than the highest frequency component of the signal. Thus the sampling frequency was controlled as 10 kHz and its sampling time was 10 s. Two different methods were used to create agglomeration. For cold model experiments in the HSBR lab-scale unit, spherical agglomerations with diameter of 25 mm from an industrial plant were used. For the industrial unit test, excessive catalyst was fed to the reactor to generate bigger agglomerations.

estimation for acoustic signal could be also obtained with help of autocorrelation calculation and selection of rational order p.

3. EXPERIMENTAL APPARATUS AND MATERIAL Figure 5 shows a schematic diagram of cold model experimental apparatus used in this study. It consists of two main parts: a HSBR and an AE measurement system. The HSBR, made of Plexiglas, is 1530 mm long and has inner diameter (i.d.) of 475 mm. There are four agitator paddles installed in the HSBR. The agitation speed is controlled at 20 rpm by an inverter (FangH F66-B IGBT, China). Compressed air is supplied to the bottom of the reactor through four pipelines each with a dedicated flow meter (0−10 m3/h). All laboratory experiments were carried out in this cold model reactor at room temperature. PP particles produced by industrial HSBR were used in cold model experiments. Table 1 shows particle size distribution and physical properties of PP particles. Table 1. Particle Size Distribution and Physical Properties of PP Particles d (mm)

weight fraction (%)

ρp ( kg·m−3)

MI (g(10 min)−1)

average diameter (mm)

0.850 0.563 0.355 0.273 0.231 0.180 0.150

0.1 13.4 58.5 9.9 5.3 11.2 1.6

900

2.0

312

4. RESULTS AND DISCUSSION 4.1. Cold Model Experimental Results of the LabScale HSBR. To establish an AR model of AE signals under normal operating conditions, AE signals were collected as reference time series (without any agglomeration) before the experiments were conducted. Besides, background noise is randomly distributed in time and frequency domain, thus a relatively high signal-to-noise ratio was achieved by reducing the noise through averaged multiple sampling of signals. In this way, the signals could be strengthened. In cold model experiments, forty AE signal samples under different conditions were collected for power spectrum estimation of the AR model. The first ten samples were collected under normal operating conditions at the beginning of experiments. After running the experiment for 11 min, the other thirty sampling signals were collected after the addition of agglomerated particles into the HSBR. By analyzing all these sample signals, their corresponding AR power spectra were obtained. The obtained AR power spectra results were compared with those of reference time series and variance of sample signals under different conditions was calculated. The

The AE signal online collection and analysis system was developed by the UNILAB Research Center of Chemical Engineering of Zhejiang University, China. It consists of an AE sensor, a preamplifier, a main amplifier, a signal conditioning system, and a data acquisition system. The transducer used in this study is a piezoelectric resonant accelerometer, which is extensively used to collect acceleration of vibration without noise transferred via air (PXR15, 150 kHz, 100−300 kHz, 65 dB, China). The transducer is attached noninvasively to the HSBR surface at 1/4 D above the bottom of reactor. It collects signals by a specific sampling frequency. An acoustic coupling agent is used to transfer AE signals produced in the reactor to the transducer. For temporary installations, silicone grease is used to fix the transducer. For permanent installations, adhesive grease is used instead of silicone grease to fix the transducer. 11632

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Figure 6. AR power spectrum density for AE signals at different times: (a) normal operating condition; (b) 11 min; (c) 16 min; (d) 32 min.

variance demonstrates the difference of hydrodynamic behavior within HSBR under two different conditions and it, therefore, could be applied to judge whether or not agglomerations occurred in the HSBR. To be specific, if variance of sample signal is larger than the maximum variance of AE signal under normal operating conditions, it indicates that both hydrodynamic behavior and AE signal in the HSBR undergo dramatic changes, which may be caused by agglomerations in the reactor. On the contrary, if the variance of sample signal shows no appreciable difference with the reference, it indicates that the reactor is under normal operating conditions without any agglomeration formed. Figure 6 shows AR power spectra estimation of AE signals at different operating times (normal operating condition, 11 min, 16 min, 32 min). Figure 6a shows power spectrum density under normal operating condition. It is obtained by averaging the AR frequency spectra of the first ten sampling signals (without agglomeration). Figure 6b, c, and d show power spectra density of AE signals at different delay times after the addition of agglomerations. From Figure 6, we can see that the energy spectrum distribution under normal operating conditions shows a relatively even distribution pattern and fluctuates in a narrow range, indicating that AE signals in this state were generated by collisions of particles with a regular size distribution. However, after addition of agglomerations, the spectra witnesses significant changes, especially in the frequency range of 500−1000 Hz. According to the latest literature,16,18 it can be easily obtained that relative high frequency signal reflects mainly movement of small particles, while low frequency signal stands for motion of large particles. Therefore, we can assume that the increase of low frequency energy was caused by addition of large agglomerations. Figure 7 shows the calculated variance based on AR power spectrum of sample signals at different operating times. It can be deduced from Figure 7 that the variance of the first ten sampling signals in the early period remains relatively small, indicating that the reactor was in a normal operating state (initial model-establishing stage). However, the variance of the other thirty sampling signals in the remaining time of the experiment was larger than that of the first ten signals and fluctuated greatly and repeatedly, indicating that the reactor was

Figure 7. Variance of AE signals based on AR model at different time in lab-scale HSBR.

in an abnormal state. This is because the added agglomerations hit the reactor wall at a certain frequency. This frequency is closely related with the rotational speed of agitator impeller. From the above discussion, we can see that the AE detection results were consistent with results from practical operation, which indicates that AE technique in combination with AR model could be used to judge whether an abnormal situation occurred. Further, this method could be applied to detect agglomerations in the cold model HSBR. The successful establishment of AR model based on AE technique in the laboratory provides a basis for its industrial application, which will be discussed in detail in the next section. 4.2. Application of AR Model Based on AE Technique in Industrial-Scale HSBR. To test and verify the detection effect of AE technique based on AR model in industry, AE measurement equipment was installed on the surface of an industrial HSBR to collect signals. Experiments were also carried out for agglomeration monitoring. Figure 8 shows variance of AE signals based on AR model at different time in the industrial HSBR. It can be seen from Figure 8 that in the time period of 1000−1500 min, the variance undergoes a dramatic change and reaches high value for several minutes, which indicates that the reactor was in an abnormal condition during this period. From this information, it can be deduced that agglomerations may form inside the reactor. Based on above inference, potential operating conditions which are likely to cause agglomerations have been analyzed, including the changes in catalyst feeding rate and quench liquid flow rate. 11633

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same period. All the above changes together led to an insufficient heat removal capacity and unstable operation conditions of the reactor, making the polymerization reactor operate in an abnormal state. Thus, the polymerization temperature in the industrial-scale HSBR increased with dramatic fluctuations. Meanwhile, the discharging pipeline was blocked by agglomerations and several agglomerations were discovered at the bottom of cyclone separator, causing ejector blockage. All these visual observations coupled with the analysis of the results verified our inference that during the time period of 1000−1500 min, the industrial-scale HSBR was in an unstable polymerization state, thus leading to the occurrence of agglomerations in the reactor. According to the agglomeration detection results based on AE technique, measures were taken immediately to ensure normal operation of the reactor, such as control of catalyst feeding rate and quench flow rate were restored. By taking these corrective measures, the variance of AE signal became steady with minor fluctuations, indicating that the reactor system returned back to a relatively normal operation condition. Therefore, agglomeration monitoring based on AE technique and AR model can be realized in the industrial HSBR. In conclusion, experiments conducted both in lab-scale and industrial-scale HSBR prove that online agglomeration detection can be achieved based on AR model by using AE measurement technique.

Figure 8. Variance of AE signals based on AR model at different time in industrial HSBR.

Figure 9a and b show the variation curves of catalyst feeding rate and flow rate of quench liquid, respectively, during the

5. CONCLUSIONS In this study, a new analysis method based on AR model was proposed to establish the qualitative relationship between AE signals and agglomeration in HSBR. In this method, power spectra and variance of AE signals were calculated and then compared for agglomeration detection. To be specific, agglomeration could be detected when the variance of AE signal under operating conditions was much larger than that in normal operating state. This method was at first applied in a lab-scale cold model HSBR with satisfactory results obtained. Based on these results, it was further used in an industrial PP production HSBR reactor and proved to be also suitable for agglomeration detection. Moreover, a quantitative relationship between AE signals and motion of different-sized agglomerations is also of great significance, which deserves further study. Overall, AE technique enjoys a promising future in industrial application. What’s more, accurate agglomeration diagnosis can help process plant operators earn more time to take measures against ongoing agglomeration production. The real-time diagnosis can prevent unscheduled shutdown of the reactor and in so doing avoid economic losses for the corporation.

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Figure 9. Changes of Fcat and QG/QL and QL in the industrial HSBR. (a) Fcat mass feed rate of catalyst, kg*min−1; (b) QGflow rate of gas, L*h−1; QLflow rate of quench liquid, L*h−1.

AUTHOR INFORMATION

Corresponding Author

*Tel.:+86-571-87951227. Fax: +86-571-87951227. E-mail: [email protected]. Notes

same time period. From Figure 9a, it can be seen that catalyst feeding rate starts to increase continuously around 1000 min. At that moment, the polymerization reaction rate increased greatly because of the increase in the amount of catalyst, causing a local heat production rise in the reactor. Therefore, a higher heat removal capacity for the reactor system was required. However, as shown in Figure 9b, the flow rate of the quench liquid (QL) decreased slightly and the gas/liquid flow rate ratio (QG/QL) underwent a small fluctuation during the

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS It is a pleasure to acknowledge the following scientists and students at Zhejiang University: Yijia Cao, Wei Liu. The field data presented here could not have been accomplished without their assistance. This work was supported by National Natural Science Foundation of China (Grant 21076180), National 11634

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Horizontal Stirred Bed Reactors by Acoustic Emission Sensors. AIChE J. 2009, 55 (12), 3099−3108. (14) Esbensen, K. H.; Halstensen, M.; Lied, T. T.; Saudland, A.; Svalestuen, J.; de Silva, S.; Hope, B. Acoustic chemometrics - from noise to information. Chemom. Intell. Lab. Syst. 1998, 44 (1−2), 61− 76. (15) Boyd, J. W. R.; Varley, J. The uses of passive measurement of acoustic emissions from chemical engineering processes. Chem. Eng. Sci. 2001, 56 (5), 1749−1767. (16) Ren, C. J.; Wang, J. D.; Song, D.; Jiang, B. B.; Liao, Z. W.; Yang, Y. R. Determination of particle size distribution by multi-scale analysis of acoustic emission signals in gas-solid fluidized bed. J. Zhejiang Univ., Sci., A 2011, 12 (4), 260−267. (17) Leach, M.; Rubin, G.; Williams, J. Particle size distribution characterization from acoustic emissions. Powder Technol. 1978, 19 (2), 157−167. (18) Jiang, X. J.; Wang, J. D.; Jiang, B. B.; Yang, Y. R.; Hou, L. X. Study of the power spectrum of acoustic emission (AE) by accelerometers in fluidized beds. Ind. Eng. Chem. Res. 2007, 46 (21), 6904−6909. (19) Matero, S.; Poutiainen, S.; Leskinen, J.; Järvinen, K.; Ketolainen, J.; Reinikainen, S.-P.; Hakulinen, M.; Lappalainen, R.; Poso, A. The feasibility of using acoustic emissions for monitoring of fluidized bed granulation. Chemom. Intell. Lab. Syst. 2009, 97 (1), 75−81. (20) Cody, G. D.; Goldfarb, D. J.; Storch, G. V.; Norris, A. N. Particle granular temperature in gas fluidized beds. Powder Technol. 1996, 87 (3), 211−232. (21) Cody, G. D.; Bellows, R. J.; Goldfarb, D. J.; Wolf, H. A.; Storch, G. V. A novel non-intrusive probe of particle motion and gas generation in the feed injection zone of the feed riser of a fluidized bed catalytic cracking unit. Powder Technol. 2000, 110 (1−2), 128−142. (22) Cody, G. D.; Johri, J.; Goldfarb, D. Dependence of particle fluctuation velocity on gas flow, and particle diameter in gas fluidized beds for monodispersed spheres in the Geldart B and A fluidization regimes. Powder Technol. 2008, 182 (2), 146−170. (23) Zhou, Y. F.; Dong, K. Z.; Zhengliang, H.; Wang, J. D.; Yang, Y. R. Fault Detection Based on Acoustic Emission-Early Agglomeration Recognition System in Fluidized Bed Reactor. Ind. Eng. Chem. Res. 2011, 50 (14), 8476−8484. (24) He, Y. J.; Wang, J. D.; Cao, Y. J.; Yang, Y. R. Resolution of Structure Characteristics of AE Signals in Multiphase Flow SystemFrom Data to Information. AIChE J. 2009, 55 (10), 2563−2577. (25) van der Schaaf, J.; van Ommen, J. R.; Takens, F.; Schouten, J. C.; van den Bleek, C. M. Similarity between chaos analysis and frequency analysis of pressure fluctuations in fluidized beds. Chem. Eng. Sci. 2004, 59 (8−9), 1829−1840. (26) Jiang, X. Q.; Kitagawa, G. A Time-varying Coefficient Vectoer AR Modeling of Nonstationary Covariance Time-series. Signal Process. 1993, 33 (3), 315−331. (27) Arnold, M.; Miltner, W. H. R.; Witte, H.; Bauer, R.; Braun, C. Adaptive AR modeling of nonstationary time series by means of Kalman filtering. IEEE Trans. Biomed. Eng. 1998, 45 (5), 553−562. (28) Kishida, K.; Yamada, S.; Bekki, K. Application of AR Model to Reactor Noise-Analysis. Progr. Nucl. Energy 1985, 15 (1−3), 841−848. (29) Havelock, D.; Kuwano, S.; Vorlander, M. Handbook of Signal Processing in Acoustics; Spring Science & Business Media: New York, 2008. (30) Hu, G. S. Digital Signal Processing; Tsinghua University Press: Beijing, 2003.

Basic Research Program of China (2012CB720500), Specialized Research Fund for the Doctoral Program of Higher Education (20110101120020), and Fundamental Research Funds for Central Universities (2011QNA4032).

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NOMENCLATURE

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REFERENCES

d = particle diameter, mm f = frequency, Hz Fcat = mass feed rate of catalyst, kg*min−1 F( f) = Discrete Fourier Transform H(z) = linear incentive system function of AR model L = length of cold model HSBR, mm MI = melting index, g·(10 min)−1 n = counter N = length of the time series p = order of AR model QG = gas velocity of HSBR, L*h−1 QL = flow rate of quench liquid, L*h−1 x(n) = original signal sequence, V2 rx(m) = autoregression function Φ = internal diameter of cold model HSBR, mm ρp = density of solid particles, kg·m−3

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dx.doi.org/10.1021/ie202497f | Ind. Eng. Chem. Res. 2012, 51, 11629−11635