Agglomeration and defluidisation analysis

Bed agglomeration and defluidisation are analysed using the pressure signals obtained from the bed using the piezoelectric pressure sensors (Kistler type) located in the bed.

The analysis techniques are divided in two different methods: time domain and fre-quency domain. The results from these two techniques are also compared with visual observations.

Time domain analysis

For a better determination of the defluidisation time and a better comparison of the results, the standard deviation of pressure fluctuations is used. This parameter remains in zero or very close to it until the onset of fluidization and, from this point, it increases

linearly with gas velocity (Puncochár et al., 1985). For this reason, this first approach has been widely used to identify a regime change or defluidisation time (van Ommen et al., 2011; Gómez-Hernández et al., 2012). The standard deviation is calculated for 30 s time periods along the time-series with a 15 s overlapping between periods. Using this result, a threshold can be defined in order to distinguish whether the bed is defluidised or not. The transition between fluidization and defluidisation state could be ambiguous depending on the bed material employed in the experiments. As a consequence, three different threshold values, 75, 50 and 25 % of the standard deviation for experiments at u/umf = 2, have been adopted to compare their effect on the value of the defluidisation time. The selection of this reference experiment is because fluidization is less intense and, therefore, it is the most restrictive air excess.

The pressure drop across the bed acquired using the absolute pressure sensor (P3cm) and temperature difference between the two thermocouples inside the bed (T3cm and T6cm) are also measured. Visual observation of the bed surface is used to confirm the defluidisation of the bed.

Frequency domain analysis

Changes in the fluidization regime can be detected using the dominant frequency of the bed (Gómez-Hernández et al., 2012). According to this, the power spectral density (PSD) is calculated for the frequency analysis. The PSD is calculated using Welch’s periodogram (Welch, 1967) with a Hanning window (Johnsson et al., 2000) for different segments along the signal, obtaining different PSD function along time (van Ommen et al., 2011). As a result, the frequency with the highest energy is chosen as the dominant frequency for each period of time. Figure 2.8a shows an example of the PSD of pressure fluctuations at two different instants, before and after the deluidization of the bed, where the dominant frequency for each spectrum is marked in the plot.

Wide band energy analysis

The wide band energy (Ewb) is obtained computing the energy contained within the PSD.

This variable is defined as the ratio between the energy in a frequency region and the energy of the whole frequency domain and can be used to detect changes in the fluidiza-tion behaviour (Johnsson et al., 2000). Gómez-Hernández et al. (2014) studied both the visual and the Student’s t-distribution approaches available for such a frequency division.

The visual frequency division approach showed that the frequency regions obtained were able to detect neither the change in the bed aspect ratio nor the start of the rotating distributor, preventing its use to compute the wide band energy. Therefore, in this PhD thesis the Student’s t-distribution approximation of the cumulative energy distribution

0 5 10 15 20

Figure 2.8: a) Example of the PSD of pressure fluctuations at fluidised and defluidised conditions (the dominant frequency of each spectrum is marked with a circle in the plot) and b) example of the cumulative energy distribution of the PSD.

(CE) of the PSD is employed to divide the frequency spectra. This methodology divides the frequency domain considering the difference between the CE and the Student’s t-cumulative density function. As a result, the CE frequency distribution can be divided in three regions: two regions of poor matching that correspond to the tails of the CE distribution, and a region of proper matching corresponding to the highest energy con-tent of the distribution. According to this approach, each region is related to different fluidization phenomena, which depends on the CE distribution as well as on the cut-off frequencies. In general, each region represents:

– Region 1 (∆f < f < fcI): contains the low frequencies, which are associated to the long term dynamics and the larger structures of the bed.

– Region 2 (fcI < f < fcII ): contains the dominant frequency of the bed, suggesting its relation to the bulk dynamics of the bed.

– Region 3 (fcII < f < fN): includes the high frequency region of the spectrum, and thus, it is related to fast fluidization phenomena such as the bubble eruption on the bed surface and the presence of channels.

Figure 2.8b shows an example of the CE distribution in which the energy of the spectrum is mainly distributed near the dominant frequency, while the tails of the dis-tributions represents around 20–25 % of the total energy.

The wide band energy is employed together with the Statistical Process Control (SPC) scheme in order to define a reference state. This control scheme determines a control

zone estimating the control limits of the process. In this way, the identification of the bed defluidisation is possible. The main parameters used to estimate the control limits are summarized in Table 2.7 and further details can be found in Gómez-Hernández (2014).

Table 2.7: Settings for the SPC monitoring.

Time series length [s] Time window [s] Fitting UAL LAL

240 30 Normal distribution X + 3σ X - 3σ

Attractor comparison

The attractor comparison tool is used to decide if two time series are produced by the same mechanism. Diks et al. (1996) proposed a statistical parameter, S, for testing the null hypothesis, which establishes that two multidimensional probability distributions are identical. On the basis of this approach, van Ommen et al. (2000) defined a monitoring method that gives an early warning of the onset of agglomeration in a fluidised bed.

The attractor of a reference time series of pressure fluctuations is compared with that of successive time series measured during the bed operation. In this way, for S-values larger than 3, the attractor of time series under evaluation is statistically different from the reference attractor, indicating that the fluid-dynamic conditions have changed in the fluidised bed. Therefore, it is possible to detect agglomeration at the very early stages for a given reference state (de Martín et al., 2011; Bartels et al., 2008).