CREC Optical-Fibre Sensors for Hydrodynamic Studies in Gas−Solid Fluidized Beds

Abstract

Optical probes can be employed in dense and dilute fluidized beds. Their application is useful to determine particle volume fraction, bubble velocity, bubble size, and solid segregation in dense-phase fluidized-bed reactors, as well as particle-cluster velocity, size, and shape, in downer/riser units. The CREC-UWO team has developed a unique and miniaturized CREC Optiprobes System (CREC-GS-OPS) equipped with a GRIN (graded refraction index) lens. The GRIN lens creates a small volume of high light irradiation by focusing a laser a few millimetres away from the front of the probe tip. This design minimizes sensor intrusiveness and, as a result, provides trustworthy measurements of hydrodynamic parameters. Through the application of the CREC-GS-OPS, advances have been achieved, leading to (a) the development of a “Y-back” unit with graphite ferrules that protects the optiprobes from fibre-optic stresses and prevents the loss of sensor calibration and (b) the establishment of statistically-based data analysis. It is envisioned that through the introduction of a few design changes, the CREC Optiprobes will be made suitable for high-temperature applications. This will allow the measurement of catalyst flow recirculation (among other measurements), in industrial-scale fluidized-bed catalytic cracking units involving fluidized riser crackers and catalyst regenerators.

1. Introduction

Fluidized beds (FB) are used to carry out important steps in many types of industrial processes [1]. Their efficacy and efficiency depend on operational conditions that have a close correlation with hydrodynamic parameters such as the bubble gas flow in the dense-phase fluidized beds and particle flow in dilute circulating fluidized beds [2,3,4].

Given the wide variety of possible configurations and operational conditions of FBs, involving a diversity of gas velocities, gas compositions, temperatures, size distributions of solids, pressures, and internal configurations, among others, as well as the fact that the size of a unit can range from a few cubic centimetres [5] to hundreds of cubic metres, obtaining hydrodynamic information in situ is a complicated task that must be approached with multiple tools. In controlled environments such as lab-scale and bench-scale units, pressure differentials, magnetic imaging, optical probes, capacitance measurements, and tracers are commonly used to obtain hydrodynamic data. However, in more complicated environments such as industrial-scale units, most of these tools cannot be applied. Thus, in these scenarios, optical probes are a viable option.

A common technique used to research fluidized-bed hydrodynamics is an experimental mock-up known as a “two-dimensional fluidized bed”. This 2D bed is built using transparent walls with a thin fluidized-bed column configuration. Bubbles are see-through and can be easily recorded via photographs or videos. The problem with this type of unit is that its walls severely constrain the flow and imprecisely represent the dynamics of three-dimensional fluidized beds. Thus, the data obtained are tainted excessively by wall effects [6].

Furthermore, in the case of industrial-scale high-temperature fluidized-bed units, establishing the bed hydrodynamics includes monitoring the bubble size, the bubble velocity, and the bubble hold-up. This requires special optical-probe sensors such as CREC-GS-Optiprobes [7,8,9,10]. Caloz [11] discussed the need to use optical probes for the evaluation of parameters in fluidized beds operating in harsh environments, such as the 250 MWe CFB boiler in Gardanne, France. Caloz proposed an optical design using a water-cooling jacket surrounding the optical probe and a sapphire window to allow the capture of the laser reflections. This design involved a flat-ended fibre-optic cable with the sensing volume placed at its tip. As a result, there were major anticipated intrusion effects in this design.

Thus, it is expected that adequate optical-probe designs can be helpful in monitoring key fluidized-bed parameters under a wide range of pressures and temperatures, with such parameters including a) particle concentration, cluster size, and particle velocity in dilute systems such as risers and downers and b) particle volume fraction, bubble size, bubble speed, bubble distribution, and solid segregation in dense-phase applications, such as biomass gasifiers.

Driven by the significant opportunities for using sensing probes as evaluation tools in fluidized beds, in 1998, de Lasa et al. [12] invented CREC-GS-Optical probes with GRIN (Graded Refraction Index) lenses. The present study reviews the design principles of the CREC-GS-Optiprobes, as well as their application to support the full development of a Phenomenological Probabilistic Predictive Model (PPPM). The PPPM applies to both dense-phase fluidized beds, such as biomass gasifiers, and to dilute beds, such as downers and riser units.

2. CREC Gas−Solid Optical-Probe System

The principle by which the CREC-GS-Optical Probe System works is a simple and effective one. A laser source is directed at a strand of optical fibre (emitter fibre) that carries its light through the tip of a probe. The light interacts with a GRIN lens, which focuses the beam, creating a volume of high light-irradiation density in front of the probe tip, which is called the “measurement volume”. A secondary optical fibre (receiver fibre), designated as the “receiver fibre”, is located under the GRIN lens. Within the “measurement volume”, the concentrated photon beam interacts with moving particles. The “measurement volume” is placed away from the tip of the probe to minimize intrusion effects. Moving particles falling within that volume reflect the rays back to the tip of the “receiver fibre”. The “receiver fibre” accepts the photons reflected from the particles within the “measurement volume”, depending on the fibre’s acceptance angle. Once the “receiver optical fibre” has captured the reflected rays, the beam travels to a silicon-based sensor that emits a voltage signal proportional to the photon flux.

In addition to the probe array, the CREC Gas−Solid Optical Probe System (CREC-GS-OPS) contains a laser box and a photodetector capture system. In order to develop experiments with the CREC-GS Optiprobes, two of them are vertically stacked at a set distance, typically 0.54 cm. This distance can be changed to control the delay between the sensors’ responses to address the detection of smaller particles or larger bubbles. Both probes are introduced into the fluidized-bed column though a wall port equipped with a device that aids in probe positioning. The positioning of the CREC-GS-OPS can change depending on the phase one would like to observe. Furthermore, by employing an aligned pair of CREC-GS-OPS, one above the other, the system gains the capacity to capture two signals simultaneously. The signals correspond to the axial-velocity component of a particle, a particle cluster, or a bubble at two different bed-residence times as they evolve in the fluidized bed.

2.1. Probe Design and Construction

To accomplish their function, the CREC-GS-OPS have to be designed and built following a number of technical considerations.

2.1.1. Optical Fibre

An optical fibre is a strand of flexible material in a series of encasings that has the ability to transmit light very efficiently. The optical fibre used in the CREC-GS-OPS consists of a 400 μm diameter silica core with a 550 μm diameter polymer cladding and an 850 μm diameter polymer jacket, as shown in Figure 1. Other important properties of the optical fibre used in the CREC-GS-OPS are listed in

Table 1. Properties of the optical fibre (note: “m” stands for metres).

Optical Fibre Property	Value
Numerical Aperture (NA)	0.37 (up to 2 m), 0.23 (greater than 50 m)
Full Acceptance Angle ($2{\theta }_h$)	43° (up to 2 m), 27° (greater than 50 m)
Average Half Acceptance Angle (${\theta }_h$)	17.5°
Fibre Core Diameter	400 ± 2% μm
Fibre Cladding Diameter	550 ± 2% μm
Fibre Jacket Diameter	850 ± 5% μm
Operation Temperature Range	−40 °C to 200 °C

.

2.1.2. GRIN Lens

Graded refraction-index lenses or gradient-index lenses are small cylindrical glass rods. The graded refraction index allows them to bend the trajectory of light rays, with this property being independent of lens shape, as is the case with GRIN lenses. GRIN lenses are made with controlled radial variations of refraction index. As a result, the rays evolve in the GRIN lens, converging on a focal region (the “measurement volume”) located at a set distance (“$l_1$”) from the back face of the GRIN lens (e.g., 5 mm), as described in Figure 2. One should note that the “$l_1$” focal distance depends on the type of refractive-index variation in the GRIN lens and on the GRIN lens length. Thus, careful selection of the GRIN lens is required for proper measurements to be obtained with minimum probe-intrusion effects.

The l₁ parameter depends on the $L$ and the $l_0$ parameters. In the case of the CREC-GS Optiprobe, L, the length of the GRIN lens, is set to $2.062\pm 0.02 \mathrm{m}\mathrm{m}$, while the space between the optical fibre carrying the laser beam and the frontal face of the lens is 8 mm [14]. This leads to a “measurement volume” located a few millimetres away from the “back face” of the GRIN lens or the probe tip. Therefore, if all the distances remain as described, the “measurement volume” is placed at a distance of 5 mm from the tip of the probe.

Therefore, the addition of a GRIN lens at the tip of the CREC-GS-OPS is important to creating a “measurement volume” away from the tip of the probe and reducing optical-probe intrusiveness in the gas-particle phases to be studied.

2.2. The Brass Housing of the CREC-GS-OP Probe Tip

A brass housing for every CREC-GS-OP has been engineered with the following four components, as shown in Figure 3: (a) one “emitter fibre” bringing the laser beam from the source, (b) one “receiver” fibre returning the detected light to the photodetector, (c) one calibration screw, and (d) one GRIN lens. A CREC-GS calibration device allows one to set the desired distance from the emitter fibre to the front face of the GRIN lens, thus ensuring the optimal operation of the CREC-GS-OPS, as described in Figure 2.

Furthermore, the design of the receiver optical fibre and its positioning at the CREC-GS-OPS tip take into consideration the optical acceptance angle of the receiver fibre to capture the reflections of ray particle from the fluidized media only.

$l_0$ is a theoretical value that was initially determined by Nova et al. in 2004 [14]. It was later confirmed by Ashraful et al. in 2011 [15], who used a laser-profiler device that directly measured the intensity of the laser beam at the “measurement volume”. This procedure determined that the best $l_0$ distance from the end of the transmitting fibre to the receiving face of the GRIN lens is 8 mm.

2.3. Y-Shaped Fibre Block Support

Optical fibres are fragile components of the CREC-GS-OPS. Their handling requires care and experience. One downside of their use is the potential for fibre breakage in zones where fibres bend or alternatively where they are repeatedly manipulated. To address this issue, a Y-shaped block holder was designed to immobilize the optical fibres of the CREC-GS-OPS as described in Figure 4. The Y-shaped block allows one to secure the optical fibres into position via the addition of graphite ferrules at the back end of the probes to keep them in place, preventing possible displacement and stresses. This permits the user to manipulate the fibres safely, with less risk of breaking or modifying the probe calibration.

2.4. Measurements in the Dilute Phase

Dilute phases, typically found in downers and risers, employ column diameters that are relatively small compared to the ones used for dense-phase applications. The “measurement volume” for dilute phases is, in many cases, in the range of a few to several centimetres away from the walls of the column. Therefore, this allows the use of the CREC-GS-OP system directly and without a vibration shield, a component that is often required for measurements in dense-phase fluidized beds.

Figure 5 shows a typical and adequate array of hardware in a dilute-phase configuration. It consists of the following: (a) a port, (b) a radial-positioning screw, (c) clamping blocks, and (d) two CREC Optiprobes.

2.5. Measurements in Dense Phase

In a dense-phase environment, like that of an industrial-scale FCC cracking unit or a gasifier, the unit diameters are expected to be much greater than those usually used in laboratory-scale downers and risers. This means that the distance between the walls of the column and the “measurement volume” of the Optiprobe will be larger than 20–50 cm and that, therefore, additional protection against probe vibrations induced by the flow of air or steam is necessary. In order to address this issue, the CREC team designed a shield (Figure 6) into which the two probes can be inserted. This shield adds support to the probes, allowing them to reach farther into the bed without becoming unstable.

2.6. Laser Box

The term “laser box” refers to a metallic box containing an array of lasers and sensors. The use of a laser box is a requirement to both protect the researchers against an accident while using lasers and eliminate any noise from the laboratory-room lights while measurements are being taken. Thus, inside the laser box, lasers are set so that beams first pass through “primary” emitting optical fibres. As previously explained, in a later step, a secondary receiving optical fibre carries reflected laser rays into a photodetector, producing a voltage signal, which us captured by the A/D data acquisition system for further data treatment.

The number of lasers placed in the laser box should always correspond to the number of sensor pairs to be used. Thus, the laser box should always accommodate an even number of CREC-GS-OPS (e.g., 2, 4, or 6). This is the case since every CREC-GS-OP system requires, as previously explained, a pair of sensors to determine the discontinuous phase velocity at selected locations inside the bed. For instance, if measurements must be taken at 5 different locations in the column simultaneously, then 10 lasers beams and 10 sensors are needed for velocity measurements.

2.7. Data Capture

The voltage-signal output of the silicon-based sensor is collected by using a BNC-2110 connector block that brings it to a PC capture card (NI PCI-6143). This setup, as configured in the studies by our research team [14,15,16,17], allows one to measure up to 10 signals using 5 pairs of CREC-GS-OPS that simultaneously record particle or bubble information at 5 different locations in a column.

3. Data Analysis

The digital voltage signals obtained by the CREC-GS Optiprobe System can be employed to determine different critical parameters of the hydrodynamics of the fluidized bed. The resulting pair of signals are shifted by a certain amount of time. By comparing the time shift of this pair of signals, one can determine the bubble-rise velocity in dense fluidized beds ($v_{rb}$). Alternatively, the time shift of this pair of signals can be employed to establish the particle-cluster velocity in downer or riser units. Furthermore, these velocities, in combination with the probe axial separation, can provide insights into the axial dimensions of the discontinuous phase (e.g., bubbles in dense-phase fluidized beds or particle clusters in dilute fluid beds).

One can consider the data obtained by the CREC-GS OPS as signals resulting from an “ON” and “OFF” switch (Figure 7). For instance, in downers, when laser rays interact with particles in front of the probe, the CREC-GS-OP signal is “ON”. However, when there is no particle−ray interaction in front of the probe, the signal is “OFF”. Based on this principle, one can expect, for a dilute phase, voltage values close to constant zero, with positive voltage peaks resulting from reflected rays from particles crossing the “measurement volume.” On the other hand, in a dense-phase fluidized bed, “ON” values should be obtained nearly constantly at the times when a CREC-GS-OP is immersed in the dense phase, with significant “OFF” voltage depressions or valleys observed when bubbles evolve in front of the probe.

While these ideal sudden “ON” and “OFF” peaks and valleys are the ones one can expect based on the above-described principles, experimental data display noise as well, and in many cases, data include a progressive voltage increase or decrease. This is attributed to the gas−solid phase heterogeneity, with loose particle clusters detected in downers or bubbles containing particles causing the obtained signal to be less steady than expected. Thus, the obtained data require both numerical filtering and statistical analysis.

3.1. Signal Filtering and Initial Peak Finding

Figure 8a reports a typical untreated CREC-GS-OPS output voltage signal obtained in a dense-phase fluidized bed. The first challenge is to clean the high level of noise from the output voltage signal. This is done via a MATLAB code by finding a signal average. All data surpassing this value (for a dense phase) or below this level (for a dilute phase) are deleted, as described in Figure 8b. Following this step, the remaining signal is normalized, creating a new dataset of values ranging from 0 volts to 1 volt. The results of this step are reported in Figure 8c.

Following this step, a MATLAB code searches for peaks (for a dilute phase) or valleys (for a dense phase) in the signal trains. With this process, one eliminates all small peaks and valleys that do not correlate with measurable events. The selection of which peaks to disregard and which peaks to retain for further analysis is a process that requires careful consideration in order to improve detection without eliminating valuable data.

To accomplish this, a “Signal-Intensity Condition” in the data series is considered as follows: (a) all signals surpassing a calculated average voltage level in dilute-phase experiments are considered to be possible particle clusters; and (b) all signals below a calculated voltage level in a dense-phase bed runs are considered likely to be bubbles. For instance, a usual minimum voltage depth at and below which signals are considered to represent bubbles is a voltage intensity below 50% of the dimensionless average voltage.

Furthermore, in order for the voltage signals of the data series to be retained, they also have to comply with a second Signal-Width Condition. This means that all signals considered have to display a minimum width of 30 timesteps, which is equivalent to 0.030 s.

Figure 8d reports a typical example of a selected bubble signal complying with the “Signal-Intensity Condition” and “Signal-Width Condition”, surpassing the 50% of the dimensionless average voltage, and exceeding the minimum time of contact between the bubble and the CREC-GS-OP of 30 milliseconds. For dilute phases, similar conditions can be considered to retain dimensionless particle-cluster voltage signals, as advised by Medina Pedraza [19].

Once this process is completed and signals closely resemble the ideal theoretical on−off voltage changes, a MATLAB code is used to count bubbles (dense phase) or particle clusters (dilute phase). Time delays between corresponding signals in the upper and lower CREC-GC-OP are calculated using a cross-correlation function.

Thus, the discontinuous phase velocity ($v_{ri}$), either the bubble or the particle cluster velocity, and the discontinuous-phase axial chord, that being the bubble axial chord ($BAC$) or the cluster axial chord ($CAC$), are calculated with Equations (1) and (2), respectively, as follows:

$$v_{ri}={\displaystyle \frac{inter sensor distance on the vertical stack}{crosscorrelation or time delay between signals}}$$

(1)

$$BAC or CAC=v_{ri}(peak width)$$

(2)

with the subscript “i” representing either the system dilute phase or the dense phase.

After the initial $v_{rb}$ and $BAC$ values have been calculated for bubbles, or, alternatively after the initial $v_{rc}$ and $CAC$ values have been calculated for particle clusters, a second step can be conducted to adjust the baseline of each valley and recalculate the size and velocity of each bubble, as explained in the following section.

3.2. Calibration of the Optiprobe System for the Dense Phase

Bubbles evolving in fluidized beds are 3D entities. In 2020, Torres Brauer et al. [18] proposed a geometrical model to represent the three-dimensional shape of a bubble and to correlate its axial chord to its volume. This was designated the “hybrid experimental-spherical cap bubble model” [20]. This model was later used to determine the expected $BAC$ for a series of single cap-shaped bubbles of a known volume that were produced in a fluidized bed and measured with the CREC-GS-OPS. From this study, it was concluded that a calibration curve involving baseline levels and BACs and established using single injected bubbles of a known volume is always needed.

Thus, the initial step in the data treatment involved the removal of noise, as already described in Section 3.1 of this article. Due to the trapezoidal nature of the bubble signal peaks, the selected average voltage level used during the noise-deletion process affected the resulting signal width, as shown in Figure 9. Furthermore, one can observe that the maximum heights of different measured signals were not identical and that, as a consequence, the resulting valley widths were different as well, affecting the calculated $BACs$, as per Equation (2). To address this issue, it is good practice to check how the measured $BACs$ compare with the theoretically expected $BACs$ for single injected bubbles in order to establish a calibration curve.

The BAC-calibration-curve method was established by Torres Brauer in 2020 [20]. It is an important procedure in which one tries to match the average experimental BACs with the theoretical ones. It was found, that the level at which the baselines are set changes almost linearly with the bubble size. Larger bubbles require lower baselines (lower voltage values).

Thus, to accomplish this, a MATLAB script was used in conjunction with the $BAC$ calibration curve. This allowed a baseline adjustment for every bubble that was recorded. As a result, there was a recalculation of both $BAC$ and $v_{rb}$ parameters when Equations (1) and (2) were used.

3.3. Statistical Treatment of the Results for the Dense Phase

Once all detected phase discontinuities (e.g., bubbles, particle cluster) are identified and their signal widths and heights, as well as their velocities and sizes, are calculated, a statistical treatment is required. This data treatment, which is described here for bubbles, can be extended to particle clusters.

Initially, statistical parameters such as the median, the average, the standard deviation, and quartiles are calculated for both the $BAC$ and the $v_{rb}$. After this, a search for outliers is performed using Equations (3)–(5), as follows:

$$IQR=Q_1-Q_3$$

(3)

$$Lower Limit=Q_1-IQR$$

(4)

$$Upper Limit=Q_3+IQR$$

(5)

where $IQR$ stands for the interquartile range, $Q_1$ and $Q_3$ are the 1st and 3rd statistical quartiles, respectively, and the lower and upper limits refer to the minimum and maximum BACs and $v_{rb}$ values in the dataset. Outside this range, every data point is considered an outlier.

Outliers are removed from the dataset, and then p-plots are generated for $BAC$ and $v_{rb}$, to look for normality and skewness in the distribution. Finally, the data are plotted to determine the correlation between the size of a bubble and its velocity.

Once the $BAC$ versus $v_{rb}$ scatterplots have been drawn, the distributions of bubble size and bubble velocity can be established. On this basis, operational parameters can be adjusted, design aspects can be improved, and scale-ups can be simulated to establish whether the $BAC$-versus-$v_{rb}$ model matches the experimental results.

The radial distribution of the bubbles at various bed heights is also an important factor to determine since it can serve as an important tracer to ascertain the direction of the flow within the bed. This is because, depending on its diameter, a fluidized bed can have different currents or patterns of movement of solids, ranging from an upstream flow in the centre of the column and a downstream current close to the walls, to an upstream flow near the walls and a downstream current in the centre of the column [21].

4. Data Treatment for the Dilute Phase

Given the characteristics of dilute phases, such as those in a riser or a downer, where the continuous phase is the fluid and the discontinuous phase is the solid, voltage signals associated with particle clusters become positive deviations. Thus, the process of data analysis, while being quite similar, has to account for these important distinctions.

In this regard, in Figure 10A, one can see that the CREC-GS-OPS can be introduced at different heights in a downer or a riser column in order to evaluate the speed and size of the formed particle clusters evolving in the unit.

Figure 10B shows a typical signal obtained using the CREC-GS-OPS in a downer unit, displaying positive voltage peaks. The reported signals were obtained from a pair of Optiprobes. This is the case because, as described above, the system requires two probes in order to be able to obtain the particle-cluster velocity via an assessment of the delays between the upper and lower probe peaks. The other valuable piece of information obtained with the CREC-GS-OPS is the width of the peak, which is related to the vertical size of the cluster of particles. Due to the particle-size distribution of the solids in the column, measurement of the vertical size of each cluster crossing the “measuring volume” does not yield the number of particles in a cluster.

As reported by Medina-Pedraza and de Lasa in 2020 [17], the first step in the data-treatment process is to establish the baselines ($V$) for both the upper and the lower signals. This is done with the average of the voltage signal ($\overline{x}$) and its standard deviation (${\sigma }_x$), as follows:

$$V=\overline{x}+n{\sigma }_x$$

(6)

with the factor $n$ in Equation (6) being established for every experiment. This allows one to establish the baseline by adjusting the baseline up or down the peak as required for the experimental conditions studied.

After the correct V baseline has been selected, the peak duration (width of the peak signal at its base) is recorded and used to determine the particle holdup by using Equation (7), as follows:

$${\epsilon }_s={\displaystyle \frac{\sum t_i}{t}}$$

(7)

with $t_i$ representing the particle-cluster residence time in the “measurement volume” and $t$ being the total sampling time.

Furthermore, the particle-cluster velocity is calculated by considering the time delay ($\tau$) between the upper and lower signals and by using a cross-correlation function. The maximum cross-correlation value, calculated with Equation (8), provides the most probable time-shift between particle clusters detected by the pair of CREC-GS-OPS, designated as $\tau$, as follows:

$$R_{xy}\left(\tau \right)=\underset{t\to \infty }{\lim }{\displaystyle \frac{1}{t}}{\int }_0^{t}x\left(t\right) y\left(t+\tau \right)dt$$

(8)

Then, once the $\tau$ value has been established, as described in Figure 11, the cluster velocity can be calculated by using Equation (9), as follows:

$$u_c={\displaystyle \frac{d}{\tau }}$$

(9)

One should note that the cross-correlation coefficient ($R_{xy}$) can be used as a parameter to establish whether the two peaks recorded correspond to the same cluster as it evolves from the upper to the lower probe. In this respect, in 2015, Lanza [22] proposed using a minimum coefficient value of 0.4 to ascertain that the two peaks recorded correspond to the same particle cluster.

Finally, in order to calculate the cluster axial size, designated as the “Cluster Axial Chord” ($CAC$), the size of a number of average-sized particles ($N$) that fit in the determined axial-cluster dimension can be calculated by using Equation (10), as follows:

$$N={\displaystyle \frac{t_i{u}_c-L+d_p}{d_p}}$$

(10)

where $L$ is the CREC-GS-OPS’s “measuring volume” transversal length, $t_i$ is the width of the peak (time) at the signal baseline, $u_c$ is the cluster velocity, and $d_p$ is the average particle diameter.

Furthermore, it was shown by Lanza et al., in 2016, and by Medina-Pedraza and de Lasa, in 2020 [17,23], as described in Figure 12, that a methodology can be used to determine the various possible stacked particle configurations in a given set axial dimension ($CAC$).

These possible stacked particle configurations can be established by using a randomized particle selection obtained from a given particle-size distribution and reaching a set $CAC$ distance (L). As a result, stacked particle clusters can be formed with various sizes of leading particles and trailing particles. Furthermore, various cluster drag coefficients that are strongly affected by the leading particle can be confirmed, yielding a band of possible $v_{rc}$ values for a given $CAC$ value.

Finally, regarding the CREC-GS-OPS in dilute gas−solid systems, one can cite a study by Lanza et al. [24], which showed that the consistency of particle fluxes in a downer unit, as calculated via the radial integration of measured cluster axial velocities and particle volume fractions, compared with those that were measured independently using a particle-collection system, could be used to validate the chosen signal baseline for the CREC-GS-OPS.

5. The Phenomenological Probabilistic Predictive Model (PPPM)

With the information gathered using the CREC-GS-OPS, in 2023, Torres Brauer et al. [25] proposed a Phenomenological Probabilistic Predictive Model (PPPM) for dense-phase fluidized beds that provides bubble velocities and $BAC$ values as a band of possible correlated values.

This band of correlated values can be validated given that the data obtained with the CREC-GS-OPS allows one to establish a $BAC$ and $v_{rb}$ equation with probabilistic factors included. It is considered in this regard that the shape, size, and velocity of gas bubbles formed in a dense-phase fluidized bed are affected by the intrinsic randomness of the local bed state. In this respect, Torres Brauer et al. [25] proposed that the fluid-dynamic randomness can be attributed to the rapid local changes in particle volume fraction that are constantly occurring inside the fluidized bed. These local environmental variations influence the characteristics of the bubbles that move through the bed. Thus, it is expected that in addition to random changes in bubble velocity and $BAC$, bubbles in high-particle-volume-fraction zones will become slower and flatter, while bubbles in low-particle-volume-fraction zones will be faster and more elongated.

One should note that the ability to predict probability bands of bubble sizes and their corresponding bubble velocities is critical, particularly in fluidized bed reactors such as biomass gasifiers. It is in these cases that there is a critical need to determine the impact of operational conditions on correlations between $v_{rb}$ and $BAC$ probabilistic bands.

Figure 13 reports a typical example of the correlation between $BAC$ and $v_{rb}$, in the PPPM prediction band.

While PPPM methodology has to date been applied to bubbles evolving in a dense fluidized bed, it is anticipated the PPPM model can also be extended to particle clusters in downer or riser units. This is the case given the intrinsic randomness of particle-cluster formation, which leads, as described in Figure 14, to band-correlated slip velocity and $CAC$ values.

One can thus see that for downer units, the best possible estimation of particle-cluster slip velocity and its changes with the particle-cluster size requires a probabilistic approach with band-value correlations. This requirement makes the PPPM model, as reported for bubbles in fluidized beds, a potentially very useful tool for the determination of $CAC$ and $v_{rc}$ band correlations in both downer and riser units.

6. Conclusions

(a)

The CREC-GS-OPS can be used for a wide range of applications in fluidized bed units, ranging from dense-phase fluidized beds such as those of biomass gasifiers to dilute-phase beds such as those of downers and risers.

(b)

The CREC-GS-OPS have the ability to measure critical hydrodynamic parameters in fluidized beds with minimum intrusion effects, given the placement of the “measurement volume” several millimetres away from the tip of the probe.

(c)

The CREC-GS-OPS have been engineered to take measurements in fluidized bed units of various dimensions. For large-scale applications, auxiliary components protect the sensors from the convection and turbulence of the gas−particle media. These include a shield and a Y-shaped block designed to protect the CREC-GS-OPS form vibrations and mechanical stresses, respectively.

(d)

The CREC-GS-OPS provide large datasets, confirming the need for probability-based models, such as the proposed Phenomenological Probabilistic Predictive Model (PPPM), that establish hydrodynamic parameters using behavioural bands.

7. Future Perspectives

As shown in the present article, the CREC-GS-OPS is a valuable tool that can be used to establish the hydrodynamics of fluidized bed reactors. This “non-intrusive” optical-probe design can be employed to monitor key fluidized-bed parameters under a wide range of pressures and temperatures, such as (a) particle concentration, cluster size, and particle velocity in dilute systems such as risers and downers and (b) particle volume fraction, bubble size, bubble speed, bubble distribution, and solid segregation in dense-phase applications, such as biomass gasifiers. While all this is beneficial, the CREC-GC-OPs may require adaptations and redesigns for their extended operation in large-scale fluidized-bed units, where bed particles may induce probe attrition and formed coke (solid deposits) may lead to significant decreases in probe performance.