Abstract

A study was conducted to explore the applicability of recurrence and recurrence quantification analysis (RQA) to the detection of process failures in spouted bed reactor systems. Three different potential failure modes were examined in a transparent, cold flow slot-rectangular spouted bed. These being, a simulated air leak from a side wall of the reactor, a simulated gas leak from the top wall of the reactor, and simulated agglomeration of solids via introduction of larger “klinker” particles. Bed pressure drop time history data were collected and analyzed via generation of recurrence plots (RPs) and RQA parameters. In general, the simulated agglomeration case was quite easily detected via ever RQA Parameter examined, whereas the simulated air leaks were detected by only a single RQA parameter.

Introduction

Circulating fluidized bed (CFB) boilers are energy conversion systems that utilize fossil fuels to generate heat to convert water into steam at high pressure, which is then utilized to drive a turbine for electrical power generation [1]. The combustion of these fossil fuels (typically coal) tend to generate not only fly ash and corrosive gasses in the exhaust stream but can also experience particle agglomeration depending upon the fuel properties, moisture content, and operating conditions within the fluidized bed boiler [25]. The fly ash and corrosive sulphur gases can cause problems via fouling and corrosive failure of the heat transfer tubes of the plant economizers and air preheaters, as well as electrostatic precipitators [1,69]. Within the CFB boiler itself, the thermal cycling and corrosive slag depositions on the refractory walls can lead to refractory failures and spalling, which can result in sections of the refractory detaching from the wall and falling into the boiler, mixing in with the bed material and potentially affecting the bed dynamics [1,10,11].

Additionally, the coal particles undergoing combustion can become “sticky” at elevated temperatures and form larger agglomerations as the particles collide with one another. This formation of agglomerations is enhanced when there is high moisture content, as well as high alkali contents that form low melting point eutectics that flow over particles and form liquid bridges that bind particles together more strongly [4,5]. The growth of these agglomerations can lead to a loss fluidization of the bed because of changes in the particle size distribution of the solid fuel, as well as fouling of the air distributors at the bottom of the CFB riser [25]. The loss of fluidization, or defluidization, is characterized by a collapse of the dense bed of solids, decreased bed pressure drop, decreased solids mixing, large temperature variations in the axial direction, and gas bypass of the solids [25,1217].

Early detection of defluidization due to agglomeration of solids is highly desirable because the earlier the onset of defluidization is detected, the sooner corrective measures can be taken, potentially avoiding costly plant shutdown and repairs. Therefore, significant research efforts have been dedicated to the development of early defluidization detection methods in recent years [1318]. van Ommen et al. proposed using the standard deviation of pressure fluctuations of the boiler pressure fluctuations in a bubbling fluidized bed reactor to detect defluidization. Parise et al. [14] proposed using the Gaussian spectral pressure distribution and decreases in the central frequency to identify onset of defluidization. Briens et al. [15] introduced a W-statistic and “bogging index” that attempted to correlate the relative amplitude of small pressure fluctuations, isolated via wavelet analysis, to the likelihood of defluidization in a fluidized bed coker. Finally, Shabanian et al. [16,17] developed a method of detecting defluidization utilizing average axial pressure and temperature drops that compared current values with acceptable reference values to determine if the bed was undergoing defluidization in a bubbling fluidized bed. While all these methods were able to detect defluidization states, only Shabanian et al. [16,17] was able to provide early warning of incipient onset of defluidization but relied on significant changes in pressure and temperatures to do so.

Recently, in another study conducted at the National Energy Technology Center (NETL) in which recurrence quantification analysis (RQA) was being used for regime mapping and scaling in spouted beds, a process failure occurred in a high-temperature carbothermic reduction process in the form of the failure of a reactor pressure-regulating graphite rupture disc. This event was not observed while the tests were being conducted but was identified while post-processing the reactor pressure data after the conclusion of testing. This event led the researchers to the belief that this method for characterizing the underlying dynamics of complex systems could be used as a possible tool for detecting agglomeration of solids in a slot-rectangular spouted fluidized bed prior to the onset of defluidization. The details and findings of the resulting exploratory study are presented here. It is the belief of the researchers at NETL that recurrence analysis, introduced by Eckmann et al. [19] and detailed by Marwan et al. [20], will be able to provide a more sensitive tool for detection of agglomeration and defluidization.

Recurrence

Recurrence is a fundamental property of dynamic systems that can be used to characterize the system's behavior in phase space [20]. The recurrence of a time series is when a point in the trajectory repeats itself, within a suitably selected margin of error, or neighborhood parameter ɛ. Using this, a recurrence matrix, R(i,j) for the given set of time series data, x(i) can be developed as follows:
R(i,j)={1,ifx(i)x(j)ε0,otherwise}i,j=1,,N
(1)

Equation (1) produces an N × N matrix that represents the dynamic system's reconstructed phase space attractor. This matrix can then be used to generate a recurrence plot (RP) to provide a visual representation of that dynamic system, where values of 1 are represented by black dots, and values of 0 are represented by white dots. Examples of the resulting recurrence plots are shown in Fig. 1 [20]. In these recurrence plots, the black horizontal and vertical lines indicate that the state of the system is unchanging or changing slowly, whereas diagonal black lines show periodicity.

Fig. 1
Recurrence plots for (a) a periodic motion with one frequency, (b) a chaotic Rössler system, and (c) uniformly distributed noise (from Marwan et al. [20])
Fig. 1
Recurrence plots for (a) a periodic motion with one frequency, (b) a chaotic Rössler system, and (c) uniformly distributed noise (from Marwan et al. [20])
Close modal

As shown in Fig. 1(a), a simple periodic motion with a single frequency will result in a RP that is characterized by a set of equally spaced diagonal black lines. A chaotic system, such as shown in Fig. 1(b) will appear in the RP as a series of broken, unevenly spaced diagonal black lines that may or may not be mixed with single black dots. These broken diagonal line sections represent different orbits on the system's chaotic attractor. Finally, as shown in Fig. 1(c), uncorrelated noise is represented as patterns of single black dots.

Depending upon the complexity of the system being analyzed, these recurrence plots can become extremely difficult to interpret visually. In response, Zbilut and Webber [21] and Webber and Zbilut [21,22] developed RQA to quantify the morphology of recurrence plots. They studied the density of recurrent points, as well as the length of diagonal, vertical, and horizontal lines, and developed statistical parameters to assist in the interpretation of recurrence plots. A detailed discussion of these parameters can be found in Marwan et al. [20], but some of the more critical parameters are discussed below.

Recurrence rate.

The recurrence rate (RR) is defined as the percentage of recurrent points that fall within the specified margin of error or neighborhood ε and is given by Eq. (2) [20]. A recurrence rate of 0 means there are no matching points, whereas a recurrence rate of 1 means that all points in the time series fall within the specified value of ɛ
RR=1N2i,j=1NR(i,j)
(2)

Determinism.

Determinism (DET) is the percentage of recurrent points that form diagonal lines, given by Eq. (3) [20]. For periodic systems, DET will be high, while it will be low for more stochastic, non-periodic systems
DET=l=lminNlP(l)l=1NlP(l)
(3)
where l is the length of the diagonal line, lmin is a minimum line length (usually 2), and P(l) is the probability of a line of length l.

Divergence.

The divergence (DIV) is the inverse of maximum diagonal line length.

Laminarity.

The laminarity (LAM) is the percentage of recurrent points that form vertical lines, which represent a system that is currently a steady state or a state that is changing very slowly. The laminarity is given by [20]
LAM=v=vminNvP(v)v=1NvP(v)
(4)
where v is the vertical line length, vmin is a minimum vertical line length (typically 2), and P(v) is the probability of a line of length v.

Trapping Time.

Related to the laminarity, the trapping time (TT) is a measure of low long of a time period, in data points, a system remains “trapped” in a specific state. The larger the trapping time, the more stationary the system is. Trapping time is given by [20]
TT=v=vminNvP(v)v=vminNP(v)
(5)

Entropy.

The entropy (ENTR) is a measurement of the complexity and information stored within a system. Highly complex, structured systems will have high entropy values, whereas uncorrelated noise will exhibit very low entropy values. The entropy can be based upon either the diagonal or vertical lines and is given by [20]
ENTR=l=lminNP(l)lnP(l)
(6)

Note that Eq. (6) is given in terms of the diagonal line length l. To obtain the entropy of the vertical lines, replace the diagonal line length with the vertical line length.

Finally, as general observations regarding recurrence plots. (1) Recurrence plots will always have the main diagonal as a solid line, this is basically an identity line as each point is being compared with itself along this line. (2) Recurrence plots are typically symmetrical about this identify line, where lines that are vertical above this line will appear as horizontal lines below it. (3) A system whose dynamics is slowly changing over time will exhibit strong recurrence around the identity line but will show less recurrence (i.e., more white areas) in the top left and bottom right regions of the figure [20]. (4) Recurrence plots are extremely sensitive to the value of the neighborhood parameter, ɛ, and thus must be chosen with extreme care. A value that is too large will result in a recurrence plot that is a solid black box as every point fall within the selected neighborhood; whereas a parameter that is too small will have the opposite result. Marwan et al. [20] suggests several guidelines for correctly selecting a value for ɛ. The one used is this work was that the value should be a minimum of five times the inherent system noise, thus the results presented in this study are based upon ɛ = 0.2 in-H2O, which corresponds to five times the accuracy of the pressure transducers used to collect the bed pressure drop data.

Experimental System and Test Conditions

The rectangular spouted bed used in this study is shown in Fig. 2. The system incorporates clear acrylic front and back panels bolted onto an aluminum frame, with rubber gaskets between the frame and acrylic panels. The interior bed dimensions are 10.16 mm (4 in.) × 30.2 mm (1 3/16 in.), and the total height is 864 mm (34 in.). The conical portion of the unit is flanged to facilitate changing between cone sections of different angles. For this study, the cone angle used was 75 deg from horizontal, providing a 30 deg included angle. Spouting gas enters the system through an interchangeable 3D printed nozzle that allows for a variety of different nozzle sizes and configurations to be used.

Fig. 2
Cold flow slot-rectangular spouted bed unit
Fig. 2
Cold flow slot-rectangular spouted bed unit
Close modal

For this study, the rectangular slotted nozzle used was sized to match the internal area of a standard ½-in. schedule 40 pipe nipple, with dimensions of 19.1 mm by 6.6 mm. After entering the system through the inlet nozzle, the gas passes through the bed of materials and exits through a pair of outlet ports that are connected to modified ShopVac filter cartridges. Differential pressures are measured via a series of Setra 239 0-30 in-H2O differential pressure transducers. The signals from these transmitters are sampled and recorded at a sample rate of 50 Hz via Labview. Post-processing of total bed pressure drop was performed via python using the pyRQA module, as well as Microsoft Excel. A Sony RX10-II camera with a resolution of 1920 × 1080 pixels and 0.001 s shutter time is used to record video at 500 frames per second.

For this study, two 0.25-in. swage-lok hand valves were added to the spouted bed, as shown in Fig. 2. The purpose of these valves was to simulate vessel leaks by opening one or the other valve while the system is in operation. One such valve is located just above the conical bottom section of the bed, but still within the settled dense bed region, and the other was located on the top wall, between the two gas outlet ports.

For test conditions that were considered in this study, the first was the control or nominal condition. For this condition, both valves were closed, and only the primary bed material was loaded into the unit. The second and third conditions involved opening either the side or top valve, respectively. Finally, the fourth condition was conducted with both valves closed, and with approximately 10% (by volume) “klinker” material added to the bed. For all test conditions, the primary bed material was 14/40 mesh Duralum AB hollow alumina bubbles from Washington Mills, and the “klinker” material from the fourth test condition was 3.2 mm nylon balls. This “klinker” material was used to simulate particle agglomerations within the bed. The material properties for both the hollow alumina and larger nylon balls are provided in Table 1. Table 2 lists the four experimental conditions. For each of these conditions, pressure data were collected for approximately 3 min and 30 s of video was recorded. Each condition was repeated three times.

Table 1

Material properties

MaterialParticle diameter (µm)Particle density (g/cm3)
Hollow alumina (Duralam AB)7701.18
Nylon31901.13
MaterialParticle diameter (µm)Particle density (g/cm3)
Hollow alumina (Duralam AB)7701.18
Nylon31901.13
Table 2

Test matrix

Test nameGas velocity (m/s)Simulated failure condition
Nominal0.815No simulated failure
Side valve open0.815Side wall gas leak
Top valve open0.815Top wall gas leak
Klinker added0.815Presence of solid agglomerates
Test nameGas velocity (m/s)Simulated failure condition
Nominal0.815No simulated failure
Side valve open0.815Side wall gas leak
Top valve open0.815Top wall gas leak
Klinker added0.815Presence of solid agglomerates

Results and Discussion

As previously mentioned, the four experimental conditions were repeated three times. For each of these experimental runs, the bed was operated at the given test condition for a minimum of 5 min to allow the bed to reach a steady-state operating condition, after which three consecutive sets of 3 min duration pressure data were recorded. At the same time as the pressure data was being recorded, a 30 s video of the bed was filmed. During post-processing of the data, the total bed pressure drop was determined by summing the individual pressure drops from the three differential pressure transducers located along the height of the unit.

Pressure Time Series and Video Results.

Figure 3 shows typical total bed pressure drop time histories for all four cases. As can be seen, very little difference can be seen in the pressure time histories for the nominal, side valve open, and top valve open cases, while the klinker added case exhibits clearly different characteristics. This agrees with the visual observations of the bed, as shown in Fig. 4. For the nominal, side valve open, and top valve open cases, there is a clearly defined spouted core located centrally within the bed, as well as a well-defined fountain of particles above the bed surface. These are the defining characteristics of spouting beds. However, with the addition of the klinker materials, the bed appears to oscillate between the previously described spouting regime and slugging, as seen in Fig. 4(d).

Fig. 3
Time series pressure data for (from top to bottom) nominal, side valve open, top valve open, and klinker added cases
Fig. 3
Time series pressure data for (from top to bottom) nominal, side valve open, top valve open, and klinker added cases
Close modal
Fig. 4
Still image showing spouting in cases (a) nominal, (b) side valve open, (c) top valve open, and intermittent spouting/slugging in (d) klinker added case
Fig. 4
Still image showing spouting in cases (a) nominal, (b) side valve open, (c) top valve open, and intermittent spouting/slugging in (d) klinker added case
Close modal

Recurrence Plots.

The RPs shown in Fig. 5 shows a similar trend. When looking at the plots for the full 3 minutes of data, there is very little to visually distinguish between the RPs for the nominal case and the cases where either the side or top valve are open. However, the density of black dots is significantly reduced when comparing the Fig. 5(d) with Figs. 5(a)5(c). The differences between these conditions are more readily visible in the offset images, which depict approximately the first 5 s of data for each condition, as well as when one considers the RQA parameters shown in Figs. 611.

Fig. 5
Recurrence plots for (a: top left) nominal, (b: top right) side valve open, (c: bottom left) top valve open, and (d: bottom right) klinker added cases
Fig. 5
Recurrence plots for (a: top left) nominal, (b: top right) side valve open, (c: bottom left) top valve open, and (d: bottom right) klinker added cases
Close modal
Fig. 6
Recurrence rate comparison for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Fig. 6
Recurrence rate comparison for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Close modal
Fig. 7
Divergence comparison for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Fig. 7
Divergence comparison for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Close modal
Fig. 8
Determinism comparison for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Fig. 8
Determinism comparison for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Close modal
Fig. 9
Vertical line entropy comparison for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Fig. 9
Vertical line entropy comparison for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Close modal
Fig. 10
Comparison of the ratio of determinism and recurrence rate for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Fig. 10
Comparison of the ratio of determinism and recurrence rate for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Close modal
Fig. 11
Comparison of the ratio laminarity and determinism for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Fig. 11
Comparison of the ratio laminarity and determinism for the (a) nominal, (b) side valve open, (c) top valve open, and (d) klinker added cases. Values shown are the mean values for all runs, error bars are ±1 standard deviation.
Close modal

Recurrence Quantification Analysis Parameter Results.

Figure 6 shows that the recurrence rate (i.e., percentage of recurrent points, or those points falling within the specified neighborhood, ɛ) is significantly less for the case in which the larger nylon “klinkers” have been added to the bed material, than it is for either the nominal case or either of the open valve cases. This reflects the fact that the presence of these simulated agglomerates, or klinkers, leads to much larger fluctuations in pressure, so recorded data are spread over a much wider range.

Conversely, the divergence data shown in Fig. 7 shows that the klinker added case has significantly greater divergence. The divergence is the inverse of the average vertical line length, which was previously related to the time over which the system remains at a similar state. If the RP has short vertical lines, as indicated by larger divergence values, that suggests that the system is undergoing rapid changes in condition. This is evident in the rapidly fluctuating time series pressure data for that case.

Figure 8 shows the comparison of determinism for the four cases. While the general trend for all cases is that the value of the determinism is relatively low, suggesting a low level of periodicity in the data, there is still a clearly defined difference between the klinker added case and the remaining cases, suggesting that the system becomes more stochastic in nature when the simulated agglomerates are present. Similar trends for the differentiation of the klinker case from the other cases can also be seen in Figs. 911, which show the entropy of vertical lines, ratio of determinism to recurrence rate, and ratio of laminarity to determinism, respectively.

Interestingly, the pressure time histories, videos, recurrence plots, and the majority of the RQA parameters failed to differentiate between the nominal case and the two cases where one of the valves were opened in order to simulate a leaking reactor. The only parameter currently under consideration to be able to differentiate between these three cases was the entropy of the vertical lines, shown in Fig. 9. The vertical line entropy for the side valve open case, Fig. 9(b) is nearly double the entropy values for Figs. 9(a) and 9(c). While this sensitivity was not seen in the other RQA parameters, it does suggest that this RQA parameter may be useful for leak detection. It bears mentioning here that the simulated side wall leak, even with the valve fully open, resulted in airflows out of the valve that were barely detectable by placing one's hand over the opening. This is most likely due to the nature of spouted bed, where the gas is mostly confined to the core spout structure, with little gas dispersion through the annulus of downflowing solids toward the walls.

Conclusions

A study was conducted to explore the applicability of recurrence and RQA to the detection of process failures in spouted bed reactor systems. Three different potential failure modes were examined. These being, a simulated air leak from a side wall of the reactor, a simulated gas leak from the top wall of the reactor, and simulated agglomeration of solids via introduction of larger “klinker” particles.

Bed pressure drop time history data was collected and analyzed via generation of recurrence plots and RQA parameters. In general, the simulated agglomeration case was quite easily detected via every RQA parameter examined. In contrast, the simulated air leaks were much more difficult to detect. This is reasonable and to be expected because neither leak condition showed any appreciable effect on either the bed pressure drop data or the visually observed spouting conditions within the reactor itself. Despite this, simulated reactor side wall leak was detectable through examination of the entropy of vertical lines RQA parameter, making this a possible method for detecting such leaks in other systems.

While these results show that recurrence is able to detect changes in the spouting/fluidization conditions within a slot-rectangular spouted bed due to the presence or formation of agglomerations, more work needs to be done to explore the level of sensitivity of this method to the onset of agglomeration and defluidization.

Acknowledgment

This research was supported in part by an appointment to the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education.

Disclaimer

The U.S. Department of Energy and NETL contributions to this report were prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

The authors declare no competing financial interest.

Nomenclature

     
  • l =

    diagonal line length

  •  
  • v =

    vertical line length

  •  
  • lmin =

    minimum diagonal line length (normally two data points)

  •  
  • vmin =

    minimum vertical line length (normally two data points)

  •  
  • x(i) =

    time series data

  •  
  • P(x) =

    probability of the occurrence of generic parameter, X

  •  
  • R(i, j) =

    recurrence matrix

  •  
  • ɛ =

    distance/neighborhood parameter used in determining the recurrence matrix

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