Case studies for selective agglomeration detection in fluidized beds: Application of a new screening methodology

Powder Technology 203 (2010) 148–166

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Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c

Case studies for selective agglomeration detection in fluidized beds: Application of a new screening methodology Malte Bartels, John Nijenhuis, Freek Kapteijn, J. Ruud van Ommen ⁎ Delft University of Technology, Department of Chemical Engineering, Delft Research Centre for Sustainable Energy, Julianalaan 136, 2628 BL Delft, The Netherlands

a r t i c l e

i n f o

Article history: Received 2 August 2008 Received in revised form 26 March 2010 Accepted 3 May 2010 Available online 7 May 2010 Keywords: Fluidized beds Selective agglomeration detection Signal analysis Screening methodology Data filtering Monitoring

a b s t r a c t We have recently presented a new methodology for screening different signal analysis methods in combination with signal pre-treatment methods with the goal to effectively identify those combinations that are highly selective towards a specific process change (Bartels et al., Ind. Chem. Eng. Res. 48 (2009) 3158– 3166). The main outcome of the methodology is visually represented in an overall result matrix with coloured tiles illustrating a measure for the suitability of each combination of analysis method and signal pre-treatment. Suitable methods can be visually identified very quickly. For the early detection of agglomeration in fluidized beds we illustrate this methodology by four different cases: two cases from a pilot-scale bubbling bed, one from an industrial scale bubbling bed and one case from a lab-scale circulating bed. With the result matrix for each case several suitable methods are identified. The data are also evaluated to identify methods that are more generally applicable for a range of different cases. The suitability of a positively identified method is subsequently analyzed for its temporal response to both agglomeration and other effects. The influence of the different data pre-treatment methods is also addressed. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Gas–solid fluidized beds are utilized for a variety of processes in the chemical industry, such as catalytic reactions, drying, coating and energy conversion (e.g. [1]). Knowledge of the bed hydrodynamics is of great importance not only for the safety of the process but also for its economics, operating at optimal conditions and avoiding unscheduled shutdowns. For example, unwanted agglomeration can be a major operational problem. Increased particle adhesiveness/stickiness, which can be caused by different mechanisms, can lead to permanent bonds between colliding particles. Relevant processes for this problem are found in the area of polyolefin production and energy conversion. In the gas-phase polymerization in fluidized beds for the production of polyethylene and polypropylene, the growing polymer particles can become sticky and form agglomerates within the bed and sheets on the reactor wall. Agglomeration also occurs in fluidized bed energy conversion process, where low-melting alkali silicates are responsible for agglomerate formation via increased particle stickiness (e.g. [2]). Ultimately, agglomeration can lead to partial or total defluidization when the agglomerates get too large to still be fluidized. Besides agglomeration the reverse process can occur, e.g. in the drying of powders, where particle size decreases during the

process. Here, the detection of the “end-point” of the drying process to avoid overheating is an important application (e.g. [3]). Ideally, a suitable early warning method is very sensitive to a specified process change, e.g. agglomeration. However, this is not the only requirement: a suitable method should also be as insensitive as possible towards other process changes to avoid false alarms. Unfortunately, the latter aspect is often neglected in the literature on monitoring multiphase reactors. This was the starting point for the development of our screening methodology, which has been presented in detail elsewhere [4]. The goal for this methodology is to screen different signal analysis methods and assess them for their suitability as a monitoring tool, i.e. being sensitive and selective. The goal of this paper is to identify signal analysis methods that are selectively sensitive to agglomeration and insensitive to other phenomena, applied to fluidized beds. We focus on method selectivity and sensitivity; the dynamics of the response of a method is not investigated explicitly, but based on the results we give some indication in this regard. We show how our newly developed screening methodology can be used to achieve this goal by four selected cases of agglomeration in fluidized beds. Although we only apply the methodology to pressure fluctuation data from fluidized beds in this paper, the methodology itself is more universally applicable, also outside the area of fluidization. 2. Methodology

⁎ Corresponding author. Tel.: +31 15 278 2133. E-mail addresses: [email protected] (M. Bartels), [email protected] (J.R. van Ommen). 0032-5910/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.05.003

The methodology applied here has been developed to screen different data analysis methods in combination with different pre-

M. Bartels et al. / Powder Technology 203 (2010) 148–166

treatment methods, to find methods that are selective towards specific process changes. In the following, we present a short summary of the methodology. A detailed description of the methodology can be found in [4]. The methodology consists of five steps: 1. Provision of pressure–fluctuation data sets with isolated process changes 2. Pre-treatment of the pressure–fluctuation data 3. Evaluation of the response of each combination of pre-treatment and signal analysis method 4. Calculation of the selectivity index f (a measure of the quality of the trend of the response of a method, and its selectivity compared to other effects) 5. Visualization of all selectivity indices in a matrix (each square represents a separate index value) First, suitable data sets have to be provided for the analysis. It is desired to detect a specific process change but no other process changes, i.e. to have an as high as possible sensitivity for the specified change and a low as possible cross-sensitivity for other process changes. For the analysis one therefore should ideally provide all considered process changes isolated from each other. Where this is not feasible, an alternative approach is to provide data containing typical process changes that occur during normal operation for the comparison (“normal process changes”). In the next step the data sets are pre-treated with one of the different methods. The pre-treatment, or filtering, extracts only specific components from the signal on which the subsequent analysis is based. Underlying motivation is that certain process changes can manifest themselves stronger in specific signal components and that sensitivity of an analysis method can therefore be enhanced. The subsequent and most time-consuming step is to evaluate the response of each combination of pre-treatment method and signal analysis method to the provided datasets. With a large number of pre-treatment and signal analysis methods the total number of combinations, the product of both, can be very large. In this case it is 33 × 40 = 1320. For this reason the evaluation is automated and is carried out in MatLab here. The evaluation is applied to consecutive time series of 3 min and the results are stored in individual files. After this, each individual calculated response has to be assessed in terms of sensitivity, i.e. overall change of the analysis variable upon the imposed change, and quality of the trend, i.e. a monotonically increasing or decreasing trend. For the evaluation of this trend quality the variation of the response is taken into account, i.e. the fluctuations around the mean of a block of data. This is done to avoid the rejection of an otherwise monotonic trend due to outliers and makes the assessment more robust. The response data are first divided into a number of blocks and for each block the average and the standard deviation is calculated. The selectivity index f is defined by the relative difference of the sensitivity towards the specified process change Δmaxzi,change type A relative to the sum of all process changes as expressed in the denominator (Eq. (1)). f =

Δmax zi;

change type A

Δmax zi; change type A + Δmax zi; change type B + Δmax zi;

ð1Þ change type C

The variable Δmaxzi indicates the maximum difference between the averages of all blocks. This normalization is necessary for a valid comparison between the responses of different methods given the fact that different analysis methods yield different quantitative results for the same physical phenomenon. In the chosen form, the equation is still generic; process changes of type A, B and C simply refer to different distinct process changes. For the subsequent cases 1 and 2, type A refers to agglomeration of the bed, type B refers to an increase in fluidization velocity and type C refers to an increase in bed mass. Where it was not possible to obtain all the relevant isolated process changes in a single fluidized bed, we chose to relate agglomeration

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to the natural variation within the common process operation, here called “normal process changes”. Eq. (1) then changes to: f =

Δmax zi;

Δmax zi; change type A + Δmax zi; normal

change type A

ð2Þ process changes

This common process condition has to contain a representative part of the normal process changes, which will contain several different physical effects occurring simultaneously. One also has to consider that in this case one cannot make any explicit choices on the magnitude of occurring process changes as with the previous approach with data sets containing isolated process changes. Where possible we quantitatively indicated the range of gas velocity changes and bed mass changes for the typical operation considered here (see the description of cases in the experimental section). For the subsequent cases 1 and 2 the process change A refers to bed agglomeration, B refers to bed mass increase and C refers to fluidizing gas velocity in Eq. (1). For cases 3 and 4 the alternative definition of the selectivity index as shown in Eq. (2) is taken, where process change A also refers to bed agglomeration. Finally, the selectivity index f for all combinations is visualized in a result matrix. The range of possible values between 0 and 1 is assigned a grey or color scale, so that by the color of the matrix elements one can quickly identify methods that perform well, i.e. which are much more sensitive to the effect to be detected than to the other effects. As a last step, one should inspect the actual temporal response of the method for the cases with high selectivity index to make sure the response is indeed suitable for on-line monitoring. For the cases 1, 2, and 4 the pressure measurement sampling frequency is 400 Hz, for case 3 it is 80 Hz (in both cases the signal is low-pass filtered at half the sampling frequency before sampling to avoid aliasing effects). The sample frequency of the pressure measurement is chosen such that the dominating low-frequency component of the power spectrum of the signal is retained, cutting off the higher frequency components that have negligible power. With respect to the block size for the calculation of the analysis variable (here in the range of 15–120 min) there will be an optimal size range: with too little time blocks the maximum difference decreases, with too many time blocks the higher the risk of rejection of a trend due to extreme values (no rigorous analysis was done). Most importantly, both the sampling frequency and block size are large as compared to the time scales of the fluidized bed. The implemented signal analysis methods consists of the following: Kolmogorov–Smirnov (KS) Test, Kuiper Test, Rescaled Range (R/S) Analysis, Diffusional Analysis, Probability Density Function (PDF) moments, Autocorrelation, Principal Component Analysis (PCA), Time–Frequency Analysis, Attractor Comparison (S-statistic), Correlation Dimension, Kolmogorov–Sinai (KS) Entropy, Average Cycle Time (ACT), Average Absolute Deviation (AAD), and W-statistic. The pretreatment methods incorporated here consist of three groups: frequency filtering using a 6th order Butterworth filter, wavelet-based filtering using a Daubechies 5 wavelet and principal component re-projection into a lower dimensionality. The choice of signal analysis methods and pre-treatment methods has been made based on their appearance within the relevant fluidization signal analysis literature and their common availability. A complete overview of all analysis methods and pre-treatment methods can be found in the Appendix A. 3. Experimental Four case studies are presented here that have been obtained from three different fluidized beds. The fluidized bed installations and their main operating conditions are further specified in Table 1. For details on the nature and quantity of the changes and length of the data sets see Tables 2 and 3. For all cases we have investigated the sensitivity to agglomeration. Moreover, we have chosen to investigate

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Table 1 Specifications and main operating conditions of the investigated installations. Properties

Pilot-scale (80 cm) cold-flow bubbling bed

80 MWth bubbling bed combustor [5,6]

Lab-scale circulating bed gasifier

Sampling frequency [Hz] Column diameter [cm] Particle size silica sand [µm] Bed inventory [kg] Gas velocity [m/s] Temperature [°C] Process Case

400 80 (cylindrical) 300–500 (range) ∼700 0.40 (∼ 3× Umf @ 25–30 °C) 25–30 Liquid-spraying onto top of the bed 1, 2

80 600 × 600 (square) ∼960 ∼32,000 ∼0.9 (∼3× Umf @ 850 °C) ∼850 Wood combustion 3

400 8.3 (riser, cylindrical) 500–800 (range) ∼ 10 ∼ 4.4 (riser) ∼ 750 Straw gasification 4

the cross-sensitivity to both gas velocity and bed mass in comparison to agglomeration, as these variables are most commonly varying in fluidized bed processes. The following four cases are investigated: 1. Case 1: Pilot-scale 80 cm cold-flow column: The pressure fluctuation data are measured at the wall at ∼ 40% fluidized bed height, using a wire gauze to prevent particles entering the measurement tube. Tap-water has been sprayed semi-continuously on top of the bed during operation (19 kg totally added), which temporarily increases the particle adhesiveness. Upon stopping the liquidspraying this process is reversed due to the continued evaporation of water. The total mass increase of the bed due to the injection of water is considered negligible in this case; depending on the evaporation rate it amounts to an increase between 0 and 2.7%. 2. Case 2: Pilot-scale 80 cm cold-flow column: In the second case carried out in the same setup as case 1 a 50 wt.% sugar (sucrose) solution has been sprayed semi-continuously on top of the bed (17 kg totally added). Also in this case the particle adhesiveness is increased. In contrast to the water spraying, the total particle surface covered by liquid in this case is considered to be smaller than in case 1 due to the smaller amount of liquid injected on the bed (both cases have very similar spraying rates on a mass basis). Moreover, in this case the formation of agglomerates is permanent as the sugar forms solid bonds in-between particles and remains in the bed; this has been confirmed by sampling both during operation and after the experiment. We carried out the spraying in two periods, where within the first period 28% of the total amount had been added already. The case considered here refers to the second spraying period and therefore simulates the presence of some agglomerates in the bed (not quantified). Such a scenario is considered valid for industrial practice, where also smaller amounts of agglomerates can already be present in the bed. The total mass increase of the bed due to the injection of sugar solution is considered negligible in this case. The sugar is assumed to remain in the bed and the water is partially evaporated; even without any evaporation (worst-case) the relative mass increase would only be 2.4% due to the spraying. Table 2 Experiments in the pilot-scale 80 cm cold-flow column. (# blocks refers to the number of blocks the total data set is divided into for assessment of the trend in the response of a method. In case of the gas velocity and bed mass changes those blocks correspond to the actual process changes.). Water spraying (Case 1) Agglomeration

Gas velocity

Bed mass

Relative change # blocks Length dataset [hh:mm] Relative change # blocks Length dataset [hh:mm] Relative change # blocks Length dataset [hh:mm]

n/a 6 02:20

3. Case 3: Industrial agglomeration case (80 MWth combustor): The pressure fluctuation data are measured within the dense bed at ∼50% fluidized bed height (∼ 30 cm above the air nozzles with total bed height ∼55–60 cm), using a purge flow to prevent particles entering the measurement tube. In this case, some gradual increase in the particle size fraction of 1.00–1.25 mm has been observed during production [6]. Shortly after, the installation had a regular maintenance stop and agglomerates were found in the bed, which agrees with the gradual increase in the larger particle size fraction. This size increase has been observed during the period of several days. For this case study, we have taken four fragments of approximately 2 h each from the whole period to limit calculation time. For the agglomeration dataset the first two fragments are for the constant (small) particle size, the third fragment is for an increased particle size and the fourth fragment for a further increased particle size. For the reference condition, four fragments from the period of constant (small) particle size were taken. The maximum range of gas velocity fluctuations is ∼ 12% for the agglomeration case and ∼ 9% for the normal process changes. Although the range is higher for the agglomeration case due to an overall slightly decreasing gas velocity, they are still comparable. The maximum range of fluctuations in bed mass was calculated based on pressure drop measurements and is about 3–4% for both cases. For this case the calculations were carried out for time windows of 6 min due to the longer dataset with a lower sampling frequency. 4. Case 4: Lab-scale circulating bed: This lab-scale circulating fluidized bed has an L-valve as solids return mechanism from downcomer to the riser. The pressure fluctuation data are measured at the wall of the horizontal return-leg, using a purge flow to prevent particles entering the measurement tube. Agglomeration has been forced by operating with a fuel with high-alkali content at operating temperatures slightly above 750 °C (typical onset of alkali silicates melting). The utilized data spans some stable operation in the beginning with subsequent agglomeration, until the point of defluidization. For the agglomeration case the total dataset is taken for the methodology; for the reference Table 3 Agglomeration cases for the industrial bubbling bed installation and the lab-scale circulating bed. (# blocks refers to the number of blocks the total data set is divided into for assessment of the trend in the response of a method). Lab-scale circulating Industrial agglomeration bed (Case 4) (Case 3)

Sugar solution spraying (Case 2)

n/a 6 02:15 0/+5/+10% 3 00:30 0/+4.5/+9% 3 01:30

Agglomeration

Relative change # blocks Length dataset [hh:mm] Normal process changes Relative change # blocks Length dataset [hh:mm]

n/a 4 08:11

n/a 6 01:33

n/a 4 08:11

n/a 3 00:43 (first part of data of agglomeration case)

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condition (“normal process changes”) only the first period of the dataset is taken. The observed range of gas velocity fluctuations for the normal process changes is ∼ 5% here. The range of fluctuations in bed mass could not be reliably estimated based on the existing pressure drop measurements. 4. Results and discussion For all four cases we will show the result matrix, in which a color scale is assigned to the calculated selectivity indices f. The color scale is slightly adapted to the individual cases to ensure that the most suitable methods can be identified well by contrast changes. From such a matrix often some basic trends can be extracted, i.e. whether there are groups of methods and/or pre-treatment methods that are generally suitable, i.e. have a high selectivity index. Subsequently a few combinations of signal pre-treatment and analysis methods are selected that we analyse in further detail. For the methods without any signal pre-treatment the criterion for our choice is a high selectivity index. For methods with pre-treatment we also consider the horizontal vicinity of the matrix element considered, and only choose an element that also has neighboring element with high selectivity indices, as this means that the pre-treatment is robust against some variation in the parameterization, e.g. the filter cut-off frequency. In cases where the pre-treatment did not yield any or only a slight improvement over the raw data, we chose the raw data as this would be simpler and faster in the implementation. In view of space limitations, we only present a limited number of methods. For each chosen method we will show its response to the three imposed phenomena (agglomeration, gas velocity change, and bed mass change). This procedure is illustrated in a flow-sheet in Fig. 1. The above mentioned procedure is carried out on a combined case, in which the selectivity index is defined as the average value of the three

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individual selectivity indices from cases 1, 2 and 3 (all bubbling bed cases, where case 4 concerns a circulating fluidized bed). The reason for analyzing this combined case, rather than only the individual cases, is that one ideally would like to have a method that is robust, i.e. universally applicable for several different agglomeration incidents. From this combined matrix we select a number of methods that perform well, according to the procedure in Fig. 1. The same methods are subsequently chosen for the individual cases, although they then do not necessarily perform well in all individual cases. In addition, we also show the results from one or more methods that perform well for the individual cases. It is remarked that for the purpose of monitoring agglomeration in a specific process the method(s) obtained from the combined case might not be optimal. In this case the screening methodology should be applied to that specific process. In the following, we first present the combined (averaged) result matrix and then the individual cases; the individual temporal responses of the selected methods are shown for each case. In view of space limitations, sometimes we only show the temporal response to agglomeration. 4.1. Combination of cases 1, 2, 3 (80 cm cold-flow agglomeration and industrial agglomeration) For the combined case the cases 1, 2 and 3 were chosen as they are all from bubbling beds; the circulating bed (case 4) was excluded due to its different operating principle. The combination has been carried out by averaging all three individual selectivity indices f and is shown in Fig. 2. From the averaged result matrix we decided to choose six combinations of signal analysis method (M, vertical) and pre-treatment (PT, horizontal) that perform well overall: • Kolmogorov–Smirnov Test of similarity hypothesis acceptance/ rejection, with a low-pass 15 Hz filter (M5/PT10) • Kuiper Test of similarity hypothesis acceptance/rejection, no pretreatment (M7/PT1) • Standard deviation, with a high-pass 10 Hz filter (M16/PT3) • S-statistic, no pre-treatment (M31/PT1) • Kolmogorov–Sinai entropy, no pre-treatment (M34/PT1) • Average cycle time, no pre-treatment (M36/PT1) 4.2. Case 1: 80 cm cold-flow unit with water spraying

Fig. 1. Flow-sheet for the selection process of suitable methods from a result matrix.

The case of agglomeration induced by water spraying is compared with both the gas velocity increase of 10% and the bed mass increase of 9%. The result matrix for this case is shown in Fig. 3. Often, the analysis method without any data pre-treatment (most left column) performs at least as good as with any pre-treatment. However, in some cases, the pre-treatment yields a higher selectivity index. For a specific method one can often observe isolated fields with high selectivity index, especially for wavelet filtering. This indicates that the choice of a suitable wavelet filter is crucial for the success of an analysis method, i.e. choosing the “wrong” decomposition level can make the method insensitive towards agglomeration or overly increase the cross-sensitivities for other effects. This phenomenon is due to the sharp filter characteristics of wavelet filters. For the different low- and high-pass frequency filters the selectivity index often changes more gradually, therefore their application seems more robust. In the result matrix occasional selectivity indices of unity (f = 1) are observed, represented by white fields; this phenomenon is also observed in other cases. According to the definition of the selectivity index (Eqs. (1) and (2)) such a high selectivity index can only occur when the cross-sensitivity is actually zero, independent of the absolute sensitivity to agglomeration. In the cases studied here, such a zero cross-sensitivity occurred for some of the pre-treated data, typically for high- and band-

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Fig. 2. Result matrix for the combination of all bubbling bed cases (cases 1 + 2 + 3).

pass filtering. This means that selectivity indices of unity have to be treated with care, as they are not necessarily suitable due to a potentially low sensitivity to agglomeration. For the choices of suitable methods in the individual case studies, we have taken this effect into account. In the following several methods are shown that appear suitable from the result matrix and are also visually confirmed by the temporal response of the analysis method to agglomeration, gas velocity increase and bed mass increase. The Kolmogorov–Smirnov (KS) Test and the Kuiper Test (e.g. [7]) are used to compare the similarity of two probability distributions by the maximum distance of the two cumulative distribution functions (CDF); they are applied to the pressure fluctuations (M2 and M4). In the result matrix both tests show a very clear trend for increasing agglomeration, with higher selectivity indices for the high-pass filtered data. Fig. 4 shows the outcome for the KS Test (M2) based on the raw data (PT1) as well as high-pass filtered data with a cut-off frequency of 5 Hz (PT2). Besides the very high sensitivity of the method towards agglomeration there is also some sensitivity towards gas velocity and bed mass, but they are relatively small. The analysis based on the 5 Hz high-pass filtered data is slightly better, as it yields a slight increase in agglomeration sensitivity and a slight decrease in bed mass sensitivity. The KS Test is also used to either accept (0) or reject (1) the nullhypothesis of both CDFs being similar, based on a 95% confidence level. In this case, the test is not applied to the overall data, but only to the distribution of the distances between consecutive crossings of the pressure fluctuation signal with its average (M5). For this reason here the KS Test is actually evaluating a change in the distribution of cycle times in the pressure fluctuation time series and therefore also related to the average cycle time. For the 15 Hz low-pass filtered data (PT10) a

high selectivity index is observed, which is confirmed by the response of the analysis variable (Fig. 5). Similar to the KS Test, the Kuiper Test to either accept (0) or reject (1) the null-hypothesis of both CDFs being similar, and applied to the distribution of the distances between consecutive crossings of the pressure fluctuation signal with its average (M7) reacts very similar to the previously shown KS Test (not shown). Both the KS Test and the Kuiper Test for the acceptance/rejection of the hypothesis of nonsimilarity have a “binary behaviour”, i.e. for a comparison with the reference case at the beginning of the data set the method either accepts (1) or rejects (0) the hypothesis that the underlying distributions are significantly different. This has to be taken into account when deciding whether such a test would be suitable for a given application or if more information on the intermediate state also is of interest. Also the KS Test for the CDF distance based on the mean crossings (M6) (not shown) shows a high selectivity index in the result matrix, with the CDF distance being sensitive towards agglomeration, whereas the cross-sensitivities are clearly smaller. However, its selectivity is less than the same method applied to the complete pressure signal (M2), as shown in Fig. 4. A very common method which has been proposed for agglomeration detection in the literature (e.g. [8]) is the standard deviation (M16). The standard deviation of the pressure fluctuations does not have a very high selectivity index f based on the raw data, but f clearly increases for high-pass filtered data. The standard deviation based on the raw data (PT1) and based on 10 Hz high-pass filtered data (PT3) are shown in Fig. 6. The standard deviation based on the raw data clearly decreases during agglomeration and it increases with increasing gas velocity, which agrees with previous findings [9]. The sensitivity to the bed

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Fig. 3. Result matrix for the 80 cm cold-flow bubbling column, in which particle stickiness/agglomeration has been introduced by spraying water on top of the bed surface (case 1).

mass increase is small. Notice an offset in the absolute standard deviation for the bed mass. The bed mass data come from a different measurement series with other measuring equipment (this holds also for the outcome of other methods). However, the relative changes within that data set are small. The high-pass filtering improves the sensitivity towards agglomeration as the decrease in standard deviation is stronger than for the raw data. More important, filtering also decreases the cross-sensitivity for gas velocity and bed mass changes, and therefore increases the selectivity for agglomeration. The power density of the signal at 25 Hz (M29) also shows a rather high selectivity index for this case. It is confirmed that a strong decrease in the power density is taking place for the agglomeration, whereas the cross-sensitivities are very small in comparison (Fig. 7). The S-statistic (M31) resulting from attractor comparison [10] also has a high selectivity index based on the raw data. From the response of the method one can observe a clear sensitivity of the S-value towards the agglomeration with S N 3, which is the statistical threshold-value for this test, whereas for the gas velocity increase and bed mass increase the S-value remains below 3 (Fig. 8). From the result matrix one can see that compared to the raw data selectivity index (f = 0.84) the pre-treatment can improve the sensitivity towards agglomeration somewhat, e.g. 5 Hz high-pass filtering (f = 0.88). However, also the data based on the wavelet decomposition (detail level 5) has a higher selectivity index (f = 0.95). The selectivity index f here is defined as follows:

f =

Δmax zi;

Agglomeration

Δmax zi; Agglomeration + Δmax zi; Gas velocity increase + Δmax zi;

Bed mass increase

ð3Þ

The high-pass filtered data is more sensitive towards agglomeration than the raw data, which explains the higher selectivity index. However, the level 5 wavelet decomposed data shows a lower maximal increase of the response to the agglomeration event (Δmaxzi, Agglomeration), despite the higher selectivity index f. Occasionally a situation like this can occur, in which for a specific pre-treatment method the response to agglomeration (Δmaxzi, Agglomeration) is only small, but the responses to gas velocity (Δmaxzi, Gas velocity increase) and/or bed mass changes (Δmaxzi, Bed mass increase) are incidentally even smaller. Such an effect will then result in a rather high selectivity index f. This phenomenon only occurred in very few cases. The above case was chosen to illustrate this effect and to emphasize that one should not only rely on the selectivity index, but also incorporate a final check of the actual temporal response of the method. To avoid such cases of artificially high selectivity indices, there is room for further improvement of the robustness of the selectivity index, e.g. by also considering the variance of the responses. The Kolmogorov–Sinai (KS) entropy (M34) (e.g. [11]) is a measure of the predictability of the pressure time series, expressed in bit/s. The entropy also has a high selectivity index here, and responds with a decreasing trend for the agglomeration, no significant sensitivity for gas velocity and a smaller sensitivity for the bed mass change (Fig. 9). The decrease in KS entropy means that the predictability of the system is increased; this can also be viewed as a decreased amount of information necessary to describe the behaviour of an attractor in time. The average cycle time (ACT) (M36) is defined as the average time between two consecutive crossings of the pressure fluctuation signal with its mean. For this case the ACT shows some sensitivity towards the agglomeration, no significant sensitivity towards gas velocity and some slight sensitivity towards bed mass changes (Fig. 9).

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Fig. 4. Response of KS Test applied to the cumulative distribution function (CDF) distance (M2), based on the raw data (PT1) and the 5 Hz high-pass filtered data (PT2), towards agglomeration induced by water, gas velocity changes and bed mass changes (process steps are indicated by vertical bars).

Fig. 5. Response of KS Test of the hypothesis acceptance/rejection applied to the mean crossings (M5) and pre-treated with a 15 Hz low-pass filter (PT10), towards agglomeration induced by water, gas velocity changes and bed mass changes (process steps are indicated by vertical bars).

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Fig. 6. Response of the standard deviation (M16), based on the raw data (PT1) and 10 Hz high-pass filtered data (PT3), towards agglomeration induced by water, gas velocity changes and bed mass changes (process steps are indicated by vertical bars). The absolute level for bed mass changes is different as it originates from a different measurement series, but exhibits only small relative differences.

Both the entropy and the average cycle time are represented in one figure here. It has been shown [12] that the entropy of fluidized bed pressure time series is linearly proportional to the average frequency obtained from the power spectral density function, and also linearly proportional to the inverse of the average cycle time. The trends of the

Fig. 7. Response of the power density at 25 Hz (M29), based on the raw data (PT1), towards agglomeration induced by water. The variation of the response to the gas velocity increase is ∼5% (slightly increasing trend) and for the bed mass increase it is ∼7.5% (no trend).

KS entropy and the average cycle time shown in Fig. 9 are in line with these findings. 4.3. Case 2: 80 cm cold-flow with sugar water spraying We carried out the sugar solution spraying in two periods, where in the first period 28% of the total amount had been added. The case considered here refers to the second spraying period and therefore simulates the presence of some agglomerates in the bed (amount not quantified). Such a scenario is considered valid for industrial practice, where also smaller amounts of agglomerates can already be present in the bed. The case of agglomeration by induced sugar water spraying is compared with both a gas velocity increase of 10% and a bed mass increase of 9%. The result matrix for this case is shown in Fig. 10. The result matrix for this case generally contains smaller values for the selectivity index than for the previous case with water spraying. The difference between the water spraying and this case is that the sugar–water solution sprayed onto the bed formed permanent agglomerates and that some agglomerates were still present due to the preceding, shorter spraying period. Similar to the case with water spraying (case 1), the binary KS Test to either accept (0) or reject (1) the null-hypothesis of both CDFs being similar (M5) based on 15 Hz low-pass filtered data (PT10) has a high selectivity index (not shown), but no significant response to increasing bed mass and gas velocity.

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Fig. 8. Response of the S-statistic from attractor comparison (M31), based on the raw data (PT1), 5 Hz high-pass filtered data (PT2) and detail level 4 wavelet decomposed data (PT21), towards agglomeration induced by water, gas velocity changes and bed mass changes (process steps are indicated by vertical bars).

The Kuiper Test of the hypothesis acceptance/rejection applied to the mean crossings (M7) based on the raw data (PT1) has also a high selectivity index, similar to the KS Test. It has been confirmed (not shown here) that the response of the Kuiper Test is very similar to the KS Test, which makes it also a viable method. The KS Test for the CDF based on the mean crossings (M6) still shows a higher sensitivity towards agglomeration as compared to the other effects (Fig. 11), but performs not as good as in case 1. The standard deviation of the pressure fluctuations also in this case is more sensitive to agglomeration than to other effects (Fig. 12), but does also perform less good as in case 1 (Fig. 6). The S-statistic (M31) from the attractor comparison has a relatively high selectivity index (Fig. 13). Here, the S-value for the agglomeration case just reaches the value of 3, which for this method corresponds to a 95% confidence level that the hydrodynamics have changed. It is remarked, however, that the sensitivity of the attractor comparison method depends on the window size for the analysis. A window size of 3 min has been used for all methods. With a larger window size (6 min) the sensitivity to agglomeration significantly increases, whereas the sensitivity to the other effects is not significantly influenced (S-values b1.5). In this case both the KS entropy (M34) and the average cycle (M36) also clearly respond to the agglomeration (Fig. 14). The response to gas velocity and bed mass increase is smaller (not shown). In general, the temporal responses of the various methods for this case of sugar solution spraying are smaller than in the first case of water spraying. It is surprising, however, that here the responses of some methods are also opposite to the case of water spraying: standard deviation is increasing, KS entropy is increasing and average cycle time is decreasing. The reason for this behaviour is not entirely clear. The total mass input is very similar for both the water and the 50 wt.% sugar solution spraying; the amount of water introduced in case of the sugar solution therefore is clearly smaller and can contribute less to the inter-

particle adhesive forces (“stickiness”). It is suspected that the shift in particle size due to a certain amount of agglomerates resulting from the first spraying period has become relatively large as compared to the increase in inter-particle adhesiveness here and is responsible for this phenomenon. It is confirmed that during the first spraying period with sugar solution that started with a clean bed, the responses were indeed qualitatively the same as for the water spraying (case 1). 4.4. Case 3: Agglomeration in an industrial unit The case of agglomeration during biomass combustion in an industrial unit is compared with a set of typical process fluctuations (“normal process changes”) from the same unit. The fluctuations in the gas velocity were ∼ 12% for the agglomeration case and ∼9% for the normal process changes, the fluctuations in bed mass were calculated based on pressure drop measurements and about 3–4% for both cases. The result matrix for this case is shown in Fig. 15. In the following, we will show the response of the previously selected analysis methods (M5/PT10; M7/PT1; M16/PT3; M31/PT1; M34/PT1; M36/PT1) to this agglomeration case and to the reference case of the “normal process changes”. For the agglomeration case the first two blocks refer to situations with ∼33–35 wt.% of the 1.00– 1.25 mm particle size fraction, whereas for the third and fourth block it increases to ∼ 38 wt.% and ∼ 42 wt.%, respectively. For all four segments of the “normal process changes” the 1.00–1.25 mm particle size fraction is similar to the one from the first two segments of the agglomeration case (∼ 33–35 wt.%). For this case, generally higher selectivity indices are observed than for the previous two cases. Pre-treatment normally does not yield any or no significant improvement as compared to the raw data in this case. For many methods the block of low-pass filtering looks very similar to the raw data; also within the low-pass filtering, there is mostly no difference seen. This indicates that the largest share of the

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Fig. 9. Response of the KS entropy (M34) and average cycle time (ACT) (M36), based on the raw data (PT1), towards agglomeration induced by water, gas velocity changes and bed mass changes (process steps are indicated by vertical bars).

relevant information in the pressure fluctuation signal often appears to be already contained in the region below 5 Hz, the lowest cut-off frequency applied here. The power spectrum of the raw data has shown to exhibit a relatively strong peak at 1 Hz. Wavelet filtering mostly performs worse than the raw data. More important, there are large differences between neighboring wavelet filters. This indicates that a practical implication of such a filter is difficult due to the sensitivity in the choice of the detail/approximation level. The principal component decomposition as pre-treatment also performs well in some cases, but normally is no improvement over the case without pre-treatment. One of the exceptions of a pre-treatment yielding an improvement in this case is the cumulative distribution function for both the KS Test (M2) and the Kuiper Test (M4). Here high-pass filtering as well as most wavelet filtering improves the outcome. The response of the cumulative distribution function (CDF) for the KS Test (M2) for the raw data (PT1) and 5 Hz high-pass filtered data (PT2) is shown in Fig. 16. The response based on the raw data does not show any significant trend, but based on the 5 Hz high-pass filtered data it clearly exhibits a difference between the second and third block, i.e. for increased particle size/agglomeration. The KS Test to either accept (0) or reject (1) the null-hypothesis of both CDFs being similar based on the mean crossings (M5) has a high selectivity index (not shown). The test based on the CDF distance of the mean crossings (M6) has a similarly high selectivity index (Fig. 17). In both cases the sensitivity of the method to the normal process changes is very low compared to the response to the agglomeration case. The response of the KS Test for acceptance/rejection has a “binary behaviour” of switching between 0 and 1, and clearly switches to 1 for

block 3 and 4 of the agglomeration case. For the normal process changes there is no trend, only occasional peaks. The KS Test for the CDF distance is different in nature and therefore also shows the intermediate steps, in which step 3 and 4 also can now be distinguished (Fig. 17). Depending on the specific application one can decide whether only accepting/rejecting the similarity hypothesis (M5) or the actual distance value (M6) would be better suitable. The Kuiper Test to either accept (0) or reject (1) the nullhypothesis of both CDFs being similar based on the mean crossings (M7) also has a high selectivity index. There is a response to the agglomeration (not shown), but virtually no response to the normal process changes, all evaluation blocks are accepted (0). This effect here actually results in a selectivity index of unity (f = 1). Nevertheless, the Kuiper Test is considered a worse choice in this case, as it already shows a response for the second block of the agglomeration case in which the 1.00–1.25 mm fraction still low, i.e. a false positive reaction. The standard deviation is slightly sensitive in this case (Fig. 18). A clear change can only be observed in the fourth block, whereas many other methods indicate the ongoing agglomeration already in the third block. A high-pass filter with 10 Hz cut-off frequency (PT3) does yield an improvement of the sensitivity towards agglomeration, especially in comparison with the response to the normal process changes. In contrast to the filtered data, the standard deviation of raw data slightly increases. Another block of methods that appears suitable from the result matrix is the variance contribution fraction of the difference principal components; the contribution for component 1, 2 and 5 is shown in Fig. 19.

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Fig. 10. Result matrix for the 80 cm cold-flow bubbling column, in which increased particle stickiness and agglomeration has been introduced by spraying 50 wt.% sugar solution on top of the bed surface (case 2).

The variance contribution of the first two principal components increases, i.e. the amount of variability that is described by the first principal components increases with agglomeration. For the first principal component, one can also see a difference between block 3 and 4. At the same time the variance contribution from the fifth component, and also higher components, decreases slightly. In general, more of the total variance of the signal can be described by fewer components, which would correspond to a decrease in the complexity (dimensionality) of the signal. The correlation dimension (M32/33), a

measure for the dimensionality of the attractor of the system, has also been investigated here, but it remains roughly constant. The S-statistic (M31) resulting from attractor comparison also performs well for this case; the S-value based on the raw data (PT1) is shown in Fig. 20. There is no significant reaction towards the normal process changes. The different pre-treatments do not yield any significant improvement of sensitivity towards agglomeration (not shown), which is consistent with the result matrix.

Fig. 11. Response of KS Test CDF based on the mean crossings (M6), based on the raw data (PT1), towards agglomeration induced by sugar solution. The range of the responses to changes in gas velocity and bed mass are both in the range of 0.02–0.07.

Fig. 12. Response of the standard deviation (M16), based on 10 Hz high-pass filtered data (PT3), towards agglomeration induced by sugar solution. The range of the responses to changes in gas velocity is 100–115 Pa and in bed mass is 55–65 Pa.

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Fig. 13. Response of the S-statistic from attractor comparison (M31) for 3 min and 6 min evaluation window size, based on the raw data (PT1), towards agglomeration induced by sugar water. The range of the responses to changes in gas velocity and bed mass are both below S = 1.5.

The KS entropy (M34) shows a clear decrease and the average cycle time (M36) shows a clear increase for the agglomeration/particle size increase, whereas for both only little variation can be seen for the process fluctuations during normal process changes (Fig. 21). 4.5. Case 4: Agglomeration in a lab-scale CFB The case of the agglomeration during biomass gasification in a labscale circulating fluidized bed is also compared with a set of typical process fluctuations (“normal process changes”). The result matrix for this case is shown in Fig. 22. For this case, the analysis based on the raw data and low-pass filtered data is optimal in many cases, i.e. they mostly have higher selectivity indices than other pre-treatment methods. In the following the responses of different methods are presented. For the agglomeration case the total agglomeration dataset is taken. As reference condition (“normal process changes”) only the first period of the agglomeration dataset is taken. Note that some agglomeration could already have taken place during this period. Putting the reference condition in the first part of the data is motivated by the fact that at least less agglomeration as compared to the second part has taken place. The KS Test for the CDF distance (M2) overall has high selectivity indices in the result matrix, its response without pre-treatment (PT1) and with Daubechies 5 wavelet decomposed data on detail level 2

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(PT18) is shown in Fig. 23. Despite the clear response, already some increasing trend is visible in the first part of the data. With most other methods, no increase can be observed there. It is not clear, however, if this effect is due to some non-agglomeration-related effect or that the analysis method is actually so sensitive that it indicates an agglomeration-related change in the hydrodynamics in such an early stage already. The analysis based on the wavelet-filtered data yields a slightly higher selectivity index in the result matrix. Although the absolute overall increase is smaller than for the raw data in this case, the higher selectivity index originates from the much more stable region in the first half, i.e. a clearer difference between the first and the second part of the dataset. The autocorrelation (e.g. [13]) of a signal is the cross-correlation of the signal with a time-shifted version of itself; the autocorrelation decay time is the time for the autocorrelation coefficient to drop to 37% (=1/e) (M20) and 63% (=1–1/e) (M22) of its starting value at zero lag, here for a maximum lag of 0.01 s. There is a clear response to the imposed agglomeration for the last part of the data (Fig. 24). The response is fluctuating considerably, which could be improved using a moving average filter or considering the variance, providing the temporal response does not become too slow for a successful early warning. The W-statistic [14] calculates the so-called small pressure fluctuations component, obtained by subtracting a wavelet-smoothed signal from the raw signal, in relation to the original signal. Here, it is calculated based on a wavelet decomposition up to level 5 and with the smallest 60% of the detail coefficients set to zero to obtain the smoothened version of the signal and yields a clear trend (Fig. 25). The other decomposition levels investigated (1 and 10), however, are not performing well (not shown). This indicates that there is an optimum in the threshold level for the W-statistic, which to our knowledge is not specifically addressed in the literature. It could be worthwhile to investigate the parameterization of this method in more detail to find the optimal decomposition level as well as the optimal level of omitting detail levels for the smoothed version of the signal. The S-statistic (M31) resulting from attractor comparison also in this case is clearly sensitive towards the occurring agglomeration (Fig. 26). Some of the methods that were identified as suitable for the bubbling bed cases perform worse for this circulating fluidized bed case, e.g. both the KS entropy (M34) and the average cycle time (M36) are less sensitive (Fig. 27). There is a slight increase in entropy observed as agglomeration proceeds. More important, the previously observed proportionality of the entropy to the inverse of the average cycle time is not observed here. This illustrates that the pressure fluctuation signal from the industrial bubbling bed and from the return-leg of the lab-scale circulating bed are–not surprisingly–rather different in nature; analysis methods can therefore also perform differently for such a system compared to bubbling beds. For the average cycle time, low-pass filtering can significantly decrease the sensitivity (not shown here), while it did not for the industrial agglomeration case. The variance contribution from the different principal components (M23–27) here shows no clear trends as opposed to the industrial bubbling bed agglomeration (not shown). 4.6. Final overview of the selected methods

Fig. 14. Response of the KS entropy (M34) and average cycle time (ACT) (M36), based on the raw data (PT1), towards agglomeration induced by sugar solution. The range of the responses to changes in gas velocity is 16.8–18.5 bit/s (entropy) and 0.33–0.36 s (ACT) and in bed mass is 19–22 bit/s (entropy) and 0.27–0.31 s (ACT).

To obtain a better picture on how a method performed in each of the four cases, a summarizing table is presented for the main methods investigated for all cases (Table 4). The presented methods have been selected based on the combined result matrix of the bubbling bed cases (1–3). For the circulating bed case most of the methods perform less well than for the bubbling bed cases (with some exceptions for case 2). This difference in performance is explained by the differing operating principles and hydrodynamics, which implies that the obtained pressure fluctuations in the return-leg are clearly different from a bubbling bed.

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Fig. 15. Result matrix for the industrial agglomeration case (case 3).

The Kuiper Test (M7) performs similar to the KS Test (M5) for the pilot-scale cases, but yields a false positive reaction for the industrial agglomeration case. Besides the six presented cases, some other suitable combinations of analysis method and pre-treatment method were found, that we omitted due to space limitations. This group comprises the Kolomogorov– Smirnov Test and Kuiper Test for the mean crossings data (M5–M8) based on the raw data (PT1) and most low-pass filtered data (PT8–PT13),

and also the kurtosis (M17) based on the raw data (PT1) and low-pass filtered data (PT8–PT13). It appears that generally speaking those methods that take all information in the data into account for the analysis (attractor comparison, KS Test based on raw data and Kuiper Test based on raw data) perform slightly better than methods that only take into account one distinct property of the distribution (standard deviation, entropy and average cycle time-entropy and cycle time could both be seen as a

Fig. 16. Response of KS Test applied to the cumulative distribution function (CDF) (M2), based on the raw data (PT1) and the 5 Hz high-pass filtered data (PT2), to the industrial agglomeration case (left) and the corresponding normal process changes (right).

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Fig. 17. Response of KS Test CDF based on the mean crossings (M6), based on the 15 Hz low-pass filtered data (PT10), to the industrial agglomeration case and the corresponding normal process changes.

Fig. 18. Response of the standard deviation (M16), based on the raw data (PT1) and the 10 Hz high-pass filtered data (PT3), to the industrial agglomeration case and the corresponding normal process changes.

distinct attractor property). Within the first group a similar effect can be observed: attractor comparison, which uses information on the total density of the distribution (the dimensionless distance between both attractors) and also retains the temporal information performs slightly better than the KS and Kuiper tests based on the raw data, which both only use a distance between distributions and also do not retain the temporal information of the data. For the cases with gradual agglomeration (cases 1, 2 and 4) it appears that the different methods generally respond at similar times, i.e. they

have similar early warning times, although sometimes differences are observed. Whether or not a method would be early enough to avoid shut-down by taking counteractions cannot be directly extracted from this investigation because a successful prevention of a shut-down depends not only on the time scales of the detection method, but also on the time scales of the counteraction strategy. Yet, with some knowledge or estimation on how quick a counteraction could be applied to positively affect the bed in a specific case, one can use the responses shown above to estimate whether or not any of the above listed methods would

Fig. 19. Response of the variance of principal components 1, 2 and 5 (M23–25), based on the raw data (PT1), to the industrial agglomeration case and the corresponding normal process changes.

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Fig. 20. Response of the S-statistic (M31) resulting from attractor comparison, based on the raw data (PT1), to the industrial agglomeration case and the corresponding normal process changes.

be early enough. All presented methods are suitable for the on-line monitoring of a single signal, i.e. the evaluation of the temporal response including any pre-treatment can be carried out within the time window of 3 min in this case (calculations were carried out on regular PCs with CPU speeds of at least 2 GHz). 4.7. Phenomenological description of the changes in bed pressure fluctuations during agglomeration The pressure fluctuations in most of the presented cases as well as other cases we studied earlier have often shown a shift during the agglomeration that can be described with the following characteristics: The amplitude decreases somewhat and the signal becomes somewhat more regular-sinusoidal in nature. In an exaggerated form this is illustrated in Fig. 28. The phenomenon of decreased signal amplitude for developing agglomeration in fluidized beds has been reported in the literature, e.g. expressed by the standard deviation [9] or the variance [8]. The relatively strongly decreased amplitude especially of the high-frequency components has been suggested by Briens et al. [14]. This simplified model view overall corresponds, with some exceptions, with the suitable methods that emerge from the combined matrix: • The standard deviation normally shows a decreasing response to agglomeration. However, the standard deviation is not directly suitable for agglomeration detection due to its sensitivity to gas velocity changes. The standard deviation of the high-frequent part

of the signal (obtained by high-pass filtering) generally also shows a response, but is less sensitive towards gas velocity changes. • The power spectrum of the pressure fluctuations confirms the proposed change in pressure fluctuations for the industrial agglomeration case: there is an increase in the dominating frequency around 2 Hz. The power at lower frequencies remains relatively constant, the power at higher frequency decreases with increasing frequency. For the water spraying the power decreased for all frequencies, however, the decrease was clearly less in the low-frequency region (about 0–5 Hz) compared to the higher frequencies. For the sugar solution spraying the power remained constant in the lowerfrequency region and decreased in the higher frequency regions. All these cases point towards the phenomenon that the high-frequency components are more strongly attenuated during agglomeration than low-frequency components of the pressure fluctuations. This phenomenon could relate to increased particle stickiness, which we expect to dampen higher frequency inter-particle collisions stronger as compared to the lower-frequency bubble movement and bed oscillations that are driven by the gas flow on larger length and time scales. • The average cycle time (ACT) is increasing, i.e. less crossings of zero occur as the high-frequency components decreases since additional crossings in the temporal vicinity a low-frequency crossing are removed, probably due to the previously described dampening effect in the high-frequency range. At the same time the KS entropy is decreasing. Van der Schaaf et al. [12] have shown that entropy and average cycle time are inversely proportional for fluidized bed systems.

Fig. 21. Response of the KS entropy (M34) and average cycle time (ACT) (M36), based on the raw data (PT1), to the industrial agglomeration case and the corresponding normal process changes.

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Fig. 22. Result matrix for the lab-scale circulating fluidized bed agglomeration case (case 4).

• The variance contribution of the different principal components shows a clear shift towards more variability of the signal being explained by the lower components for the industrial agglomeration case, but no clear shift for the other cases; the reason for this difference is not clear. The correlation dimension, a measure for the dimensionality or degrees of freedom of a system, decreases for the water spraying but shows no clear trend in the other cases. Both examples show that the signal complexity/dimensionality can decrease, as shown in our model illustration, but this is not necessarily always the case.

Fig. 23. Response of KS Test applied to the cumulative distribution function (CDF) (M2), based on the raw data (PT1) and the level 2 wavelet decomposed data (PT18), to the circulating bed agglomeration (the “normal process changes” here comprises the first part of the data before the vertical bar).

5. Conclusions Several case studies were presented that illustrate the use and benefit of a newly developed screening methodology [4]. The goal of this methodology is to efficiently identify suitable methods for monitoring multiphase reactor hydrodynamics. This is done by screening different signal analysis methods and assessing them for their sensitivity, but also selectivity to detect specific hydrodynamic changes. The case studies presented here focus on the detection of agglomeration in fluidized beds.

Fig. 24. Response of the autocorrelation decay time for 37% decay (M20) and 63% decay (M22), based on the raw data (PT1), to the circulating bed agglomeration (the “normal process changes” here comprises the first part of the data before the vertical bar).

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Fig. 25. Response of the W-statistic with a wavelet decomposition on level 5 (M39), based on the raw data (PT1), to the circulating bed agglomeration (the “normal process changes” here comprises the first part of the data before the vertical bar).

The overall result matrix illustrates the selectivity index f, a performance measure for each combination of signal pre-treatment and analysis method, with the help of coloured tiles. This matrix yields a convenient overview of the performance of combinations of pretreatment and analysis method, from which optimal combination were successfully identified for each specific case. Combinations are considered suitable if they have a high selectivity index and in case of pre-treatment also high selectivity indices in the horizontal vicinity; if pre-treatment is not yielding any clear advantage the raw data are preferred. The responses of the different pre-treatment/analysis methods to agglomeration as well as changes in gas velocity and bed mass are illustrated to show the characteristics of the method (step-change vs. gradual response character). Pre-treatment of the data often does not yield a big advantage; especially the analysis based on low-pass filtered data is often similar to the analysis based on the raw data. However, in some specific cases, pre-treatment significantly improves the response (e.g. high-pass filtering for the standard deviation). Moreover, wavelet filters are often only suitable for a specific decomposition level. Although they can improve the response, they bear the potential danger of choosing the “wrong” decomposition level with a significantly worse response, and therefore are considered less robust. The methodology can be applied to find methods suitable for one specific process. When searching for methods that are more universally applicable for different agglomeration processes and reactor scales, one can choose to combine the result-matrices from

Fig. 27. Response of the KS entropy (M34) and the average cycle time (ACT) (M36), based on the raw data (PT1), to the circulating bed agglomeration (the “normal process changes” here comprises the first part of the data before the vertical bar). Table 4 Summarized performance of the selected methods for all cases (+: sensitive, 0: slightly sensitive, –: not sensitive, *: including a false positive reaction). Method

Case 1 Case 2 Case 3 Case 4

KS Test of H0 acc./rej., LP 15 Hz filter (M5/PT10) Kuiper Test of H0 acc./rej., no pre-treatment (M7/PT1) Standard deviation, HP 10 Hz filter (M16/PT3) Attractor comparison, no pre-treatment (M31/PT1) KS entropy, no pre-treatment (M34/PT1) Average cycle time, no pre-treatment (M36/PT1)

+ +

+/0 +/0

+ +*

− −

+/0 +

0 0

+/0 +

+/0 +

+/0 +/0

0 0

+ +

0 0

different cases. Carrying out this combination by averaging we have identified several suitable methods for the given cases and have shown their temporal response to the individual cases. Specifically for agglomeration in bubbling beds we found several methods suitable, among which the Kolmogorov–Smirnov Test based on the mean crossing data with a 15 Hz low-pass filter, the Kuiper Test based on the mean crossing data, the standard deviation with a 10 Hz high-pass filter, attractor comparison, Kolmogorov–Sinai entropy, and average cycle time. A simplified phenomenological description of the changes in the pressure fluctuations for developing agglomeration in bubbling beds is proposed. The basic characteristics of this description comprise a reduction in amplitude, especially of the higher frequency components, an increase in average cycle time (and decreased entropy), and sometimes a decrease of dimensionality/complexity.

Acknowledgements Peter Verheijen (Delft University of Technology) is gratefully acknowledged for his helpful comments in the development of this work.

Fig. 26. Response of the S-statistic resulting from attractor comparison (M31), based on the raw data (PT1), to the circulating bed agglomeration (the “normal process changes” here comprises the first part of the data before the vertical bar).

Fig. 28. Exaggerated illustration of the development of pressure fluctuations during increased particle stickiness and agglomeration.

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Appendix A

Overview of applied pre-treatment methods. Index

Method

Parameter

1 2–7

No pre-treatment Frequency filtering, high-pass (Butterworth 6th order filter) Frequency filtering, low-pass (Butterworth 6th order filter) Frequency filtering, band-pass (Butterworth 6th order filter) Wavelet decomposition with Daubechies-5 wavelet Principal component decomposition filtering: projection of the data onto a new axis system, dimensionality = 20

– Cut-off frequencies: 5; 10; 15; 20; 30; and 50 Hz Cut-off frequencies: 5; 10; 15; 20; 30; and 50 Hz Lower/upper cut-off frequencies: 5/10; 5/30; and 15/30 Detail levels 1–10, approximation level 10 Axis systems for the re-projection defined by: each individual axis system; first block only; PC 1–10; PC 10–20; PC 1–5; and PC 15–20

8–13 14–16 17–27 28–33

Overview of all applied analysis methods and brief outline of each method. Index Method 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

Kolmogorov–Smirnov (KS) Test H0 rejection/acceptance (0/1), based on the distribution of the overall data KS Test Cumulative Distribution Function (CDF) distance Kuiper Test H0 rejection/acceptance (0/1) Kuiper Test CDF distance KS Test H0 rejection/acceptance (0/1), based on the Mean Crossings (MC) of the pressure fluctuations with zero KS Test CDF distance, based on MC Kuiper Test H0 rejection/acceptance (0/1), based on MC Kuiper Test CDF distance, based on MC Hurst exponent (HE) at small windows — rescaled range analysis HE at medium windows — rescaled range analysis HE at large windows — rescaled range analysis HE at 1000 point distances — diffusional analysis HE at 2500 point distances — diffusional analysis HE at 4999 point distances — diffusional analysis Mean Standard deviation Skewness Kurtosis Autocorrelation 63% decay time with 0.1 min maximum lag Autocorrelation 63% decay time with 0.01 min maximum lag Autocorrelation 37% decay time with 0.1 min maximum lag Autocorrelation 37% decay time with 0.01 min maximum lag PCA principal component 1 variance contribution fraction PCA principal component 2 variance contribution fraction PCA principal component 5 variance contribution fraction PCA principal component 10 variance contribution fraction PCA principal component 20 variance contribution fraction Power Spectral Density (PSD) power at 2 Hz PSD power at 25 Hz PSD power at 60 Hz Attractor comparsion (S-statistic) Correlation dimension — maximum likelihood Correlation dimension — best fit Kolmogorov–Sinai entropy — bits/s Kolmogorov–Sinai entropy — bits/cycle Average Cycle Time (ACT) Average Absolute Deviation (AAD) W-statistic, thresholding up to detail level 1 W-statistic, thresholding up to detail level 5 W-statistic, thresholding up to detail level 10

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1 and 5). The KS Test is applied to the distribution of the pressure fluctuation data (CDF distance — methods 1 and 2) as well as to the distribution of the lengths between consecutive crossings of the pressure fluctuation signal with zero (MC — methods 5 and 6). 3, 4, 7, and 8: The Kuiper Test (e.g. [7]) is analogous to the KS Test, but uses the sum of the maximum distances on both distribution sides for the probability calculation. 10–11: The Rescaled Range (R/S) analysis, e.g. [15], is a measure for the self-similarity of a dataset, as expressed by the Hurst exponent. 12–14: Diffusional analysis (e.g. [16]) monitors two different Hurst exponents over time, one related to long-term effects and one to short-term effects. 15–18: The first four Probability Density Function (PDF) moments describe different properties of the distribution of data: The mean, the standard deviation, the skewness (a measure for the asymmetry of a distribution) and the kurtosis (a measure for the peakedness of a distribution). 19–22: The autocorrelation (e.g. [13]) of a signal is the crosscorrelation of the signal with a time-shifted version of itself. The values of specific decay times for the cross-correlation coefficients to drop to 37% (1/e) and 63% (1–1/e) of the autocorrelation and for lagtimes of 0.1 and 0.01 min are monitored along time. 23–27: Principal Component Analysis (PCA) (e.g. [17]) describes the variation in a set of multivariate data in terms of a new set of uncorrelated variables. The data are consecutively re-projected onto the subspace defined by these uncorrelated variables. Here, the contribution of a specific component (1, 2, 5, 10, and 20) to the overall variability of all components of the data, i.e. the percentage of the total variability explained by that component, is calculated. 28–30: Within time–frequency analysis, the power spectral density in a power spectrum (obtained by Fourier transformation) at different frequencies is monitored. 31: In the Attractor Comparison method [10] the data is projected into a multidimensional state-space, yielding an attractor. Consecutively, this attractor compared to a reference attractor as obtained from a reference condition using a statistical test [18] which assesses the dimensionless distance S between both attractors. 32–33: The Correlation Dimension signifies the integral dimension of an object. It is therefore a measure for the complexity of the attractor. (General definition e.g. [11], calculation carried out here [19].) 34–35: The Kolmogorov–Sinai (KS) entropy is a measure for the predictability of an attractor, expressed in bit/s (34). Alternatively, it can be divided by the average cycle time and is then expressed in bit/ cycle (35). (General definition e.g. [11], calculation carried out here [20].) 36: The Average Cycle Time (ACT) is the average time for three subsequent crossings of the time series with its mean value. 37: The Average Absolute Deviation (AAD) is the average of the absolute deviations from the mean value. 38–40: The W-statistic [14] calculates the so-called small pressure fluctuations component (obtained by subtracting a waveletsmoothed signal from the raw signal) in relation to the original signal. The signal is first decomposed up to a certain level (1, 5 and 10 here), after which the smallest coefficients in the detail coefficient vectors (smallest 60% here) are set to zero and the smoothed version of the signal is reconstructed. Subsequently, the smoothened signal is subtracted from the original signal. References

1, 2, 5, and 6: The Kolmogorov–Smirnov (KS) Test (e.g. [7]) compares the similarity of two probability distributions by the maximum distance of two cumulative distribution functions (CDF). For once, the actual distance is calculated/monitored (methods 2 and 6). Moreover, a null-hypothesis of both CDFs being similar based on a 95% confidence interval is either rejected or accepted (0/1) (methods

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