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Liquid-phase tracer responses in a cold-flow counter-current trayed bubble column from conductivity probe measurements
Chemical Engineering and Processing 45 (2006) 945–953
Liquid-phase tracer responses in a cold-flow counter-current trayed bubble column from conductivity probe measurements M.H. Al-Dahhan a,∗ , P.L. Mills b , P. Gupta a , L. Han a , M.P. Dudukovic a , T.M. Leib c , J.J. Lerou d a
b
Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Washington University, St. Louis, MO 63130-4899, USA Chemical Science and Engineering Laboratory, DuPont Central Research and Development, Experimental Station, E304/A204, Wilmington, DE 19880-0304, USA c Reaction Engineering Consultants, DuPont Engineering Technology, 1007 Market Street/B8458, Wilmington, DE 19898-0001, USA d Velocys, Inc., 7950 Corporate Boulevard, Plain City, OH 43064, USA Received 21 May 2004; received in revised form 17 January 2006; accepted 24 January 2006 Available online 24 May 2006
Abstract Liquid-phase mixing in a cold-flow counter-current-flow bubble column reactor with trays has been evaluated. A developed filtering technique [P. Gupta, M.H. Al-Dahhan, M.P. Dudukovic’, P.L. Mills, A novel signal filtering methodology for obtaining liquid-phase tracer responses from conductivity probes, Flow Meas. Instrum. 11 (2) (2000) 123–131.] was used to extract the liquid-phase concentration responses from the conductivity probe data in two phase gas–liquid flow with systematic corruption. Conductivity probe responses to a pulse input of KCl liquid tracer were measured at various point-wise locations in an 8 in. diameter clear acrylic column using air and water as the gas–liquid system. The superficial gas and liquid velocities were selected to span those encountered in a commercial unit using a pipe-type gas sparger with a number of laterals. Results from tracer experiments are presented along with a cross-correlation of signals to estimate the characteristic residence time of the liquid on a tray. The utility of the filtering algorithm for a broader range of gas–liquid flows is also discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Multiphase; Bubble columns; Conductivity; Tracer measurements; Filtering
1. Introduction Bubble columns are widely used in various industrial processes where mass transfer is accompanied by chemical reactions in a gas–liquid system [2–4]. Intense backmixing of the liquid-phase in bubble columns is usually encountered and represents one of its noticeable characteristics. The liquid backmixing intensity increases with the column diameter [5]. However, it has been shown that many industrial applications benefit from a reduction in the intensity of liquid backmixing [5–12]. Therefore, internals such as perforated plates are introduced into conventional bubble columns with the aim of reducing the overall backmixing of the phases so that plug flow can be approached [13,2]. In this case, staging of the bubble columns via partition perforated trays alters other various hydrodynamic and transport parameters that can potentially impact the reactor performance,
∗
Corresponding author. Tel.: +1 314 935 7187; fax: +1 314 935 7211. E-mail address: [email protected] (M.H. Al-Dahhan).
0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.01.011
such as holdups, pressure drop, phase distributions, local fluid mixing, phase residence time distribution, interphase mass transfer coefficients, interfacial areas, etc. [14]. The magnitude of the effects on these parameters depends on the staging configuration, perforated tray design, flow arrangement (i.e., cocurrent upward or downward, counter-current, batch liquid), and operating conditions. Although a large amount of literature exists on the hydrodynamic and transport parameters for staged mass transfer contactors [15,16], such studies for gas–liquid reactors are limited in the open literature [5,14,17–20]. In general, most knowledge of the use and design of internals in multiphase reactors, including perforated trays, is usually confined to either patents [21,22] or is kept as company proprietary technical information for a specific process. Hence, among other hydrodynamic and transport parameters, liquid-phase axial backmixing investigations are scarce in the open literature. Recently, Alvare [6] studied the overall liquid-phase mixing in a cocurrent upward flow trayed bubble column, while Dreher and Krishna [20] studied liquid-phase backmixing in a batch liquid trayed bubble column. Vinaya
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[17] studied the effects of perforated tray design, tray spacing, and superficial gas and liquid velocities on the liquid-phase backmixing in a counter-current trayed bubble column with downcomers, and proposed empirical correlations for the estimation of the Peclet number in bubbly and turbulent flow regimes. Magnussen et al. [23] and Ichikawa et al. [24] studied the effects of tray design, tray spacing and superficial gas and liquid velocities in trayed bubble columns without downcomers. They found that the axial dispersion coefficient decreases with the number of trays, and the suppression of backmixing due to the trays is stronger in columns with larger diameters, whereas backmixing increases with the trays open area. Superficial liquid velocity has a negligible effect on the axial dispersion coefficient (Ichikawa et al. [24]). While Vinaya [17] found no dependency of liquid backmixing on the superficial gas velocity, Ichikawa et al. [24] found significant effect of superficial gas velocity (Ug ) on axial dispersion coefficient when Ug > 7 cm/s, where the axial dispersion coefficient reaches a maximum at Ug = 18 cm/s. In all these studies, conductivity probes were used to measure overall or local liquid-phase tracer responses. In general, conductivity probes have been traditionally used in process applications to determine the concentrations of dissolved ionic species in solutions that are devoid of gas bubbles. However, these probes have also sometimes been used as diagnostic tools in reaction engineering research applications, to estimate local liquid-phase velocities and to evaluate local liquid mixing in both single and two-phase flow systems by measurement of liquid-phase electrolytic tracer concentrations [6,25–28]. When such measurements are used to obtain the overall liquid-phase residence time distribution (RTD) in a single-phase flow, little ambiguity is encountered in the interpretation of conductivity probe output signals. However, the use of conductivity probes for liquid-phase concentration measurements in two-phase gas–liquid flows introduces complications that are not present in single-phase flow measurements. In two-phase gas–liquid flows, the signals are corrupted due the significant reduction in the measured conductivity that occurs when a bubble contacts the probe. Since the conductivity of the gas phase is appreciably smaller than that of the electrolytic liquid tracer solution, frequent reductions in the conductivity signal are observed as bubbles pass over the probe measurement volume. This systematic bias in the measured conductance in gas–liquid flows has limited the use of such probes for liquid-phase tracer experiments. If standard filtering techniques are applied, such as the filters available in the Signal Processing Toolbox in [29], the resulting signal is always an underestimate of the actual signal. This is due to a reduction in the noise component where the actual signal has a non-zero mean. Hence, the filter tries to retain this mean in the filtered signal, which causes an under prediction in the output. A number of workers have proposed various experimental techniques and data processing methods in an attempt to extract liquid-phase concentration data from conductivity probes in various two-phase gas-liquid flows. Rustemeyer et al. [28] tried to avoid signal corruption due to bubble passage in a mechanical fashion, by screening the probe tips. However, the screening method was not perfect, and the resulting signals appeared to
contain some information due to bubble passage across the probe tips. Dreher and Krishna [20] used a slit of about 35 mm × 5 mm in the glass cover of the conductivity cells at the tip of the measuring device to achieve fast access of the liquid-phase. They claimed that such an arrangement prohibited an accumulation of gas bubbles inside the conductivity cell. However, this does not prevent the corruption of the obtained signal due to bubble passage. Other researchers have also tried to resolve the signal corruption due to bubble passage by using standard data filtering techniques [25]. Inspection of the filtered tracer responses suggests that some vital elements of the signal may have been removed for the reasons mentioned above. Application of standard filtering procedures also assumes that the noise component of the signal to be filtered has a zero mean. This is valid only with random noise, associated with either the measuring device or with fluctuations in the electrical signals. However, the interaction of the bubbles with the conductivity probes causes a systematic and not a random reduction in the measured signals. If this signal reduction were assumed to be noise, the mean of such a noise component would not be zero, and standard filtering algorithms would not be effective in filtering this component. In summary, interpretation of data from tracer experiments in gas–liquid flows is non-trivial, since standard filtering techniques are not applicable for removing biased noise having a non-zero mean from the conductivity probe signals. Recently, Gupta’s et al. [1] have developed a novel filtering technique for extracting liquid-phase tracer concentration responses from conductivity probe data in a two phase gas–liquid flow system. Implementation of the new filtering algorithm was performed by coupling it to a standard Butterworth filter. This technique was later used in a cocurrent flow trayed bubble column by [6] to measure its overall liquid-phase backmixing. The objective of this work focuses on evaluating the liquidphase backmixing by measuring the tracer response using Gupta’s et al. [1] filtering technique in a cold-flow countercurrent trayed bubble column reactor that was scaled-down from a DuPont commercial unit. The resulting tracer responses provide insight into the liquid-phase mixing that occurs in both the presence and absence of the trays over a range of gas and liquid superficial velocities and with gas spargers having two different sparger hole densities. 2. Cold-flow unit experimental system 2.1. Overall system set-up The experimental system consisted of the cold-flow test column along with various sub-systems for feeding and controlling the volumetric flow rates of air and water [14]. The liquid delivery system consisted of a 350-gallon feed tank that was connected to a centrifugal pump. A rotameter was used to control the liquid flow rate. The liquid was introduced at the top of the column through a shower-type distributor located about 51/4 in. above the top tray. The liquid exited the column bottom through a plenum, and then flowed into a surge tank having a total volume of about 50 gallons. A second centrifugal pump was used to recycle the liquid back to the main feed tank. The
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Fig. 2. Schematic of the tray design.
Fig. 1. Schematic diagram of the column used for the cold-flow studies. (all dimensions are given in cm).
air was supplied from the house supply system at a delivery pressure of about 120 psig. After flowing through a filter, it passed a rotameter and then went to the sparger. 2.2. Detailed column design
commercial-scale sparger design. Details of the scaled-down sparger design are shown in Fig. 3. The gas was introduced to the main sparger supply line through a 9.53 mm O.D. manifold. Ten laterals were welded to the manifold, with the lengths being selected so that the sparger formed a circle whose diameter was about 6.35–12.7 mm less than the inside diameter of the column. The laterals were drilled with either 40 or 200 holes having a diameter of 350 m. The hole locations on a lateral were off-
A schematic of the cold-flow column design is given in Fig. 1. Constructed of clear PlexiglasTM , it had a nominal diameter of 8 in. and an overall height of 94 1/2 in. The column was divided into four sections, with each section having an overall height of 20 1/2 in. Three sieve trays were used between the sections. The top and bottom trays were used to create entrance and exit effects. Several ports were installed in the middle stage and on each side of the tray so that liquid conductivity probes could be inserted for local measurement of liquid-phase tracer concentrations. The entire column was supported at the bottom by the plenum. A schematic of the tray design and hole layout is shown in Fig. 2. The trays were constructed of 6.35 mm thick acrylic sheet and contained 42 holes having a diameter of 6.35 mm and laid out on a triangular pitch. The down comer occupied about 10% of the total tray cross-sectional area. 2.3. Sparger design The spargers in the cold-flow unit were scaled down using operating conditions and mechanical data extracted from a
Fig. 3. Design of the gas sparger.
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Fig. 4. Details on the hole schedule for the gas sparger laterals.
set at an angle of 30◦ from the vertical, and the laterals were positioned so they pointed downward. To obtain overall gas mass velocities in the cold-flow unit that were in the same range as those used on a given tray in the DuPont commercial system, a gas jet velocity of 183–244 m/s was required from each respective sparger hole. As shown in Fig. 4, the number of holes in a lateral were varied to achieve this range of gas velocities at gas volumetric flow rates of 3.4 and 17 actual m3 /h, respectively. The spargers were mounted 40.64 cm below the first tray at the bottom of the column. 2.4. Probe location To characterize the behavior of the liquid mixing on a stage, tracer experiments were conducted at three operating conditions using four different locations for the liquid conductivity probes. The probes’ characteristic response time is about 75 ms [1]. The three sets of operating conditions that were investigated are summarized in Table 1. The effect of the sparger hole density, i.e., the number of sparger holes per unit column cross-sectional area, on the column hydrodynamics was also studied. The conductivity probe tips were positioned at various radial locations where differences in the liquid mixing and hence local liquid concentration were expected to occur, such as (1) adjacent to the acrylic column wall, (2) in the column centerline, (3) behind the down comer skirt, and (4) slightly above or below a particular tray. Ports that could accommodate a 6.35 mm male NPT were installed in the center acrylic test sections at various strategic points so that the conductivity probes could be inserted to any desired depth. The tracer response measurements were performed by simultaneously recording the output signal from two probes, which corresponds to a classical two-point method.
Fig. 5. Positions of the conductivity probes used in the tracer experiments.
Fig. 5 shows the specific locations of the two conductivity probes that were used for the various tracer experiments. In the first configuration (A), shown in the upper left of Fig. 5, the lower probe was located at the entrance to the down comer for the bottom tray, while the upper probe was positioned below the middle tray on the opposite side of the down comer. In the second configuration (B), shown in the upper right, both probe tips were positioned on the column centerline, with the lower probe slightly above the bottom tray and the upper probe slightly below the middle tray. The third configuration (C), in the lower left, had the lower probe positioned slightly above the bottom tray next to the wall and close to the middle tray down comer, while the tip of the upper probe was slightly below the middle tray, adjacent to the wall on the side opposite to the down comer. Initial experiments using sparger 1 (40 holes), sketched in Fig. 4, showed that on a time scale corresponding to the mean
Table 1 Range of operating conditions Experiment number
Qg (SCFH)
QL (GPM)
uSG (cm/s)
uSG (ft/s)
uSL (cm/s)
uSL (ft/s)
1 2 3
118 118 236
2.0 6.5 6.5
3.25 3.25 6.51
0.108 0.108 0.217
0.44 1.44 1.44
0.015 0.048 0.048
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residence time of the liquid in the column, the tracer responses for the two-point measurements on a single stage suggested that the liquid flow pattern approached complete back mixing. As a result, a fourth probe configuration was utilized with sparger 2 (200 holes), which is shown in the lower right of Fig. 5 (configuration D, position No. 4). Here, the lower probe was located slightly below the bottom tray on the column centerline, while the upper probe was positioned in the down comer of the middle tray. Due to the large volume of the section underneath the gas sparger filled with liquid (see Fig. 1), conductivity probe was not mounted at the exit of the liquid from the column to measure the overall tracer response with a mixing cup for the conditions studied. Unfortunately, such measurements were not obtained. 2.5. Experimental procedure For each run, 10 ml of an aqueous KCl solution containing 0.2 gm of KCl per ml was manually injected, via a plastic syringe, at the top of the column directly into the liquid distributor. The tracer injection time, based on repeated trials, was estimated to be 2.5 ± 0.5 s. The start of the injection was controlled to 0.1 s accuracy using a stopwatch. The data acquisition system used for sampling the continuous output signals from the two probes was initiated one minute before the tracer was injected. This was done to simplify filtering of the raw data and to establish an initial probe output signal baseline. The sampling frequency was 10 Hz for all the tracer experiments. The raw experimental tracer response data was then processed using the filtering algorithm described below.
Fig. 6. Performance of a standard Butterworth filter on the conductivity probe signal in the air–water system without tracer injection that has been corrupted due to bubble passage. QL = 6.5 GPM (uSL = 1.44 cm/s), QG = 118 SCFH (usg = 3.25 cm/s), sparger 2 (200 holes), position No. 4 (D, Fig. 5), lower probe.
probe). Inspection of Fig. 6 shows that in spite of such a low cut-off frequency, the filtered signal under-predicts the actual one. Thus, an alternative methodology is required. To overcome the difficulty associated with standard filtering techniques, an alternate approach was developed by Gupta et al. [1] so that the uncorrupted signal can be extracted from the noisy signal. This signal-filtering algorithm, described below, is implemented in this work. 3.2. Gupta et al.’s. signal filtering algorithm [1]
3. Signal filtering methods 3.1. Standard approach As mentioned earlier, difficulties are encountered when the local liquid-phase mixing is studied in a two-phase gas–liquid system by using conductivity probes to measure the local liquidphase tracer concentration at a point. Because the conductivity of the gas is appreciably smaller than that of the liquid containing an electrolyte as tracer, the conductivity signal undergoes a significant reduction as bubbles pass over the probe, which causes fluctuations (noises) with non-zero mean (i.e. non random noise). If a standard signal filtering technique is applied (which assumes the signal has a zero mean due to a random noise), our filtered signal would always underestimate the actual signal, because the noise component has a non-zero mean. Therefore, the filter tries to retain this mean in the filtered signal as well, which causes in this case the filtered signal to be under-predicted. This is illustrated in Fig. 6, where the solid line represents the filtered signal obtained after applying a second order Butterworth filter in [29] (i.e. a standard signal filtering technique) to the raw data, which is represented by the dashed lines. The cutoff frequency was 0.005 Hz, which corresponds to a normalized frequency of 0.001 with a 5 Hz normalizing frequency (Nyquist frequency). The raw data was acquired without tracer injection by mounting the conductivity probe just below the bottom tray close to the column centerline (position No. 4 in Fig. 5, lower
The following steps were followed as part of the algorithm to filter the conductivity-probe signals so that the biased noise due to bubble passage could be removed: (1) The raw signal was processed using a regular Butterworth filter, (2) at each time instant, if the filtered response was lower than the raw signal, the filtered response was made equal to the raw signal. Otherwise, no action was taken. The resulting signal is the filtered plus the threshold signal, (3) a sum of the squares of the differences between the raw and filtered plus threshold signals was calculated, (4) if this sum is less than a certain tolerance (5 × 10−5 V for this work), then the filtered plus threshold response was taken to be the final filtered response. Otherwise, the filtered plus the threshold signal replaced the raw signal and the process was repeated by returning to Step 1, and (5) this procedure was continued until the tolerance criterion was met. To demonstrate the difference between the new algorithm [1] and the standard one, an impulse tracer test was conducted using the same operating conditions and probe locations used in Fig. 6. The performance of the filtering algorithm on the signal obtained from this impulse tracer test is shown in Fig. 7 (dashed line). Visual observation shows that the new technique yields results that are an improvement when compared to those obtained with a standard Butterworth filter (solid line). A cutoff frequency of 0.05 was used for this case on the normalized scale, which corresponds to 0.05 × (10/2) = 0.25 Hz on the absolute scale. The above filtering plus threshold procedure retains
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Fig. 7. Performance comparison of a standard and the improved signal filtering algorithm using the tracer impulse response from a two-phase gas–liquid system. QL = 6.5 GPM (uSL = 1.44 cm/s), QG = 118 SCFH (usg = 3.25 cm/s, sparger 2 (200 holes), position No. 4 (D, Fig. 5), lower probe.
Fig. 8. Tracer concentrations versus time impulse response. Conditions: probes positioned in configuration D (position No. 4, Fig. 5); sparger 2 (200 holes), QL = 6.5 GPM (uSL = 1.44 cm/s); QG = 236 SCFH (usg = 6.51 cm/s).
frequencies less than or equal to 0.25 Hz as the successively filtered signal relaxes to the final filtered plus threshold signal. The sampling frequency used in the above data acquisition, as well as in all the experiments reported below, was 10 Hz. This frequency was chosen since the characteristic response time of the probes was about 75 ms, which corresponds approximately to a frequency of 13 Hz. A characteristic probe response time of ∼75 ms suggests that a process could be monitored having a characteristic response time of greater than ∼500 ms. In other words, any phenomenon having a characteristic frequency higher than 2–3 Hz could not be captured. The characteristic frequency of the tracer washout curves for all the experiments conducted for this study was in the range 5 × 10−3 –1 × 10−2 Hz. This range is two orders of magnitude lower than the highest frequencies that these probes can capture, implying that the use of these probes for the current work is well justified. Therefore, a sampling frequency between 3 and 5 times the highest characteristic frequency that can be captured with these probes would be approximately 10 Hz. Hence, 10 Hz was chosen as the final sampling frequency. 4. Results and discussion Some selected results are presented using the above mentioned signal filtering algorithm to process the conductivity probe tracer response data from the cold-flow trayed bubble column. Particular experimental variables that were investigated include the combined effects of sparger hole density, liquid-flow rate, and gas flow rate on the local liquid-phase tracer responses. Since the measured tracer responses are point measurements with open boundaries and vary with the radial positions of the two probe measurements (Figs. 8–10) in a single stage, unfortunately, quantification of the mixing flow pattern using reactor scale tracer modeling approach (e.g. tank-in-series model, axial dispersion model) was not considered in this work. As mentioned earlier, due to large volume of the section below the gas
Fig. 9. Effect of sparger hole density on tracer impulse responses. Conditions: probe positioned in configuration B at position No. 2, QL = 2 GPM (uSL = 0.44 cm/s); QG = 118 SCFH (usg = 3.26 cm/s).
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ever, this is not the case for the measured tracer responses in configuration B (position No. 2, Fig. 8), where the probes were mounted in the center of the column (see Figs. 9 and 10a). When the cross-correlation of the two signals (Fig. 8) was evaluated, the difference between the signal maximums for both probes was around 30.5 s. Since there was no port available to position lower probe in the down comer region of the bottom tray, it was positioned below the bottom tray in the column centerline. Thus, this time lag of 30.5 s is slightly greater than the mean residence time of liquid on the tray, which was estimated from the known liquid volume and liquid flow rate using the central volume principle. From overall holdup measurements [14], the average liquid holdup on the tray was ∼0.8. Since the tray spacing is 20.5 in. and the liquid superficial velocity is 1.44 cm/s, the mean residence time of the liquid is about 28.9 s. Thus, a reasonable estimate of the mean residence time of the liquid on the stage is obtained using the two independent methods. Similarly, the cross-correlations for all other pairs can be estimated. From these, the lag or lead-time can be found at which the cross-correlation is a maximum. Knowing the distance between the probes, the velocity between the two probes can be estimated by dividing the distance between the probes by the above time lag or lead. This is the design principle upon which the heat pulse anemometer (HPA) probe is based. However, the velocity estimated using this approach would yield a long-time average between the two points, and not a precise value for the liquid velocity at that particular set of probe coordinates. This aspect is considered in detail elsewhere [1]. 4.2. Effect of gas sparger design
Fig. 10. Effect of liquid flow rate on tracer impulse responses using sparger 2 (200 holes) at QG = 236 SCFH (usg = 6.51 cm/s), a. QL = 2 GPM (uSL = 0.44 cm/s), b. QL = 6.5 GPM (uSL = 1.44 cm/s).
sparger, overall reactor tracer response measured by mounting a probe in a mixing cup at the exit of the liquid stream from the reactor was also not possible. Hence, reactor mixing pattern and its variation with the studied conditions was not considered or quantified in this work. 4.1. Liquid mean residence time The liquid-phase tracer concentrations were calculated from the probe signals by using empirical calibration equations that were developed by relating signal response to salt concentration. Fig. 8 shows a typical concentration response to an impulse tracer injection when the probes are arranged according to configuration D in Fig. 5. The shapes of the tracer responses in Fig. 8 (configuration D, Fig. 5 position No. 4) suggest that the trays provide the desirable effect of staging, which results in reduced back-mixing. How-
The sparger seems to have the most significant effect on the local liquid-phase tracer responses as the liquid flow rate or equivalently, the liquid superficial velocity, is decreased. This is particularly noticeable at the lowest liquid flow rate used (2 GPM, 0.015 ft/s, 0.44 cm/s). Fig. 9 shows that with this liquid flow rate and with the probes positioned as shown in configuration B, the response curves with sparger 1 (40 holes) are noticeably broader than those obtained with sparger 2 (200 holes). However, when the probes are positioned as shown in configuration A, the responses have an almost opposite behavior (not shown). This finding suggests that at this flow rate, the liquid velocity is greater in the center of the column and also along the down comer when sparger 2 (200 holes) is used instead of sparger 1 (40 holes), whereas the opposite behavior occurs near the walls. This effect was not seen at the highest liquid flow rate used (6.5 GPM = 0.048 ft/s = 1.44 cm/s), irrespective of the gas flow rates that were used. 4.3. Effect of gas flow rate The effect of the gas flow rate was studied at a single value for the liquid flow rate, namely, 6.5 GPM, which corresponds to a liquid superficial velocity of 0.048 ft/s. By comparing the responses at a given location, it was concluded that there was no appreciable effect of gas flow rate on the tracer response
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curves, irrespective of the type of sparger that was used. This result was somewhat surprising, since the overall gas holdup was significantly affected by an increase in the superficial velocity of the gas. Despite the change in overall gas holdup, it does not seem to cause any appreciable change in the liquid tracer responses and hence the liquid mixing over the range of gas velocities employed in this study. This finding is consistent with the findings of [17]. 4.4. Effect of liquid flow rate Fig. 10 is a typical set of responses that show liquid flow rate has a noticeable effect on the shape of the tracer responses and also on the rate at which the liquid tracer elutes from the column. This behavior is expected, since according to the central volume principle, the mean residence time of the tracer is inversely proportional to the liquid flow rate. Hence, the mean residence time of the tracer at 2 GPM is approximately a factor of three less when compared to the mean residence time at a liquid flow rate of 6.5 GPM. Other results show that tracer washout is more pronounced in the center of the column when compared to the walls. This finding indicates that the higher liquid mass flux that exists in the column center enhances the radial mixing on the stage, so that the tracer is washed out almost uniformly throughout the stage.
5. Remarks The newly developed signal filtering methodology [1] was utilized to extract liquid-phase tracer responses from conductance measurements obtained in two-phase gas–liquid systems. By properly choosing a cut-off frequency and coupling this with an appropriate thresholding algorithm, the liquid-phase contribution to the corrupted signal can be extracted. This provides information on liquid macro mixing through experimental measurements characterizing liquid mixing in a trayed cold-flow bench-scale bubble column operated with counter-current flow of gas and liquid. The combined effects of the gas sparger, hole density, gas flow rate, and liquid flow rate have been investigated. It was shown that both sparger hole density and liquid-flow rate have the biggest impact on local liquid mixing between two trays. The new signal processing method has potential applications in various commercial systems where extraction of the liquid response in a two-phase gas-liquid medium is needed. Acknowledgement The authors acknowledge the financial support provided by DuPont.
4.5. Spatial distribution of the responses
References
Inspection of all the liquid-phase responses that were conducted at the three operating conditions using the two different spargers and various probe locations provides the basis for some general observation on the local liquid flow pattern in the trayed bubble column. The greatest flux of liquid and main flow path of the liquid-phase appears to be downward through the tray down comer, which acts as a feed point to the sieve tray located beneath the down comer. The liquid then flows across the sieve tray, with a fraction of this flow being recirculated upwards along the opposite walls, while the remaining fraction flows through the down comer into the next tray. This flow pattern has also been observed through flow visualization studies by injecting a blue dye into the middle stage. The differences in the liquid flux can also be inferred by comparing the tracer responses that were measured at the various liquid flow rates when the probes were positioned as shown in configuration C of Fig. 5. Comparisons between the local liquid tracer responses obtained using sparger 1 (40 holes) to those obtained using sparger 2 (200 holes) verify that the temporal response of the upper probe leads that of the lower probe, which implies that the liquid reaches the upper probe before it reaches the lower probe. The tracer responses for nearly all liquid flow rates and both spargers are essentially identical when the probes are positioned as shown in configuration B of Fig. 5, even though the probe tips are located in notably different spatial locations. This suggests that the axial liquid mixing in the center of the column, at least within the characteristic response time of the conductivity probes, is nearly instantaneous.
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[22] M.R. Resetarits, Multiphase Downcomer Contacting Tray with Fluid Directing Bottles, U.S. Patent 5,098,615, March 24, 1992. [23] P. Magnussen, V. Schumacher, Axial mixing of liquid in packed bubble columns and perforated plate columns of large diameter, Ger. ACS Symp. Ser. (1978) 337–347. [24] Y. Ichikawa, Y. Akachi, K. Makino, On the longitudinal mixing characteristics of gas bubble column with perforated plates, Kagaku Kogaku (abridged ed.) 5 (1967) 179–182. [25] K.H. Choi, Circulation liquid velocity in external-loop airlift reactors, Korean J. Chem. Eng. 13 (4) (1996) 379–383. [26] M. Boddem, D. Mewes, Two-phase flow in the upper plenum of a PWR during ECC, in: International Conference on Nuclear Engineering, 1, Part B, 813–823, ASME, 1996. [27] M. Sokolov, M. Mashaal, Velocity measurements in slow flow by the conductance-tracer method, Exp. Fluids 9 (1990) 252–256. [28] U. Rustemeyer, J. Pauli, T. Menzel, R. Buchholz, U. Onken, Liquidphase mixing model for hydrodynamics of bubble columns, Chem. Eng. Process 26 (1989) 165–172. [29] The MATH WORKS Inc., MATLAB Version 5, Boston, MA.
Liquid-phase tracer responses in a cold-flow counter-current trayed bubble column from conductivity probe measurements M.H. Al-Dahhan a,∗ , P.L. Mills b , P. Gupta a , L. Han a , M.P. Dudukovic a , T.M. Leib c , J.J. Lerou d a
b
Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Washington University, St. Louis, MO 63130-4899, USA Chemical Science and Engineering Laboratory, DuPont Central Research and Development, Experimental Station, E304/A204, Wilmington, DE 19880-0304, USA c Reaction Engineering Consultants, DuPont Engineering Technology, 1007 Market Street/B8458, Wilmington, DE 19898-0001, USA d Velocys, Inc., 7950 Corporate Boulevard, Plain City, OH 43064, USA Received 21 May 2004; received in revised form 17 January 2006; accepted 24 January 2006 Available online 24 May 2006
Abstract Liquid-phase mixing in a cold-flow counter-current-flow bubble column reactor with trays has been evaluated. A developed filtering technique [P. Gupta, M.H. Al-Dahhan, M.P. Dudukovic’, P.L. Mills, A novel signal filtering methodology for obtaining liquid-phase tracer responses from conductivity probes, Flow Meas. Instrum. 11 (2) (2000) 123–131.] was used to extract the liquid-phase concentration responses from the conductivity probe data in two phase gas–liquid flow with systematic corruption. Conductivity probe responses to a pulse input of KCl liquid tracer were measured at various point-wise locations in an 8 in. diameter clear acrylic column using air and water as the gas–liquid system. The superficial gas and liquid velocities were selected to span those encountered in a commercial unit using a pipe-type gas sparger with a number of laterals. Results from tracer experiments are presented along with a cross-correlation of signals to estimate the characteristic residence time of the liquid on a tray. The utility of the filtering algorithm for a broader range of gas–liquid flows is also discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Multiphase; Bubble columns; Conductivity; Tracer measurements; Filtering
1. Introduction Bubble columns are widely used in various industrial processes where mass transfer is accompanied by chemical reactions in a gas–liquid system [2–4]. Intense backmixing of the liquid-phase in bubble columns is usually encountered and represents one of its noticeable characteristics. The liquid backmixing intensity increases with the column diameter [5]. However, it has been shown that many industrial applications benefit from a reduction in the intensity of liquid backmixing [5–12]. Therefore, internals such as perforated plates are introduced into conventional bubble columns with the aim of reducing the overall backmixing of the phases so that plug flow can be approached [13,2]. In this case, staging of the bubble columns via partition perforated trays alters other various hydrodynamic and transport parameters that can potentially impact the reactor performance,
∗
Corresponding author. Tel.: +1 314 935 7187; fax: +1 314 935 7211. E-mail address: [email protected] (M.H. Al-Dahhan).
0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.01.011
such as holdups, pressure drop, phase distributions, local fluid mixing, phase residence time distribution, interphase mass transfer coefficients, interfacial areas, etc. [14]. The magnitude of the effects on these parameters depends on the staging configuration, perforated tray design, flow arrangement (i.e., cocurrent upward or downward, counter-current, batch liquid), and operating conditions. Although a large amount of literature exists on the hydrodynamic and transport parameters for staged mass transfer contactors [15,16], such studies for gas–liquid reactors are limited in the open literature [5,14,17–20]. In general, most knowledge of the use and design of internals in multiphase reactors, including perforated trays, is usually confined to either patents [21,22] or is kept as company proprietary technical information for a specific process. Hence, among other hydrodynamic and transport parameters, liquid-phase axial backmixing investigations are scarce in the open literature. Recently, Alvare [6] studied the overall liquid-phase mixing in a cocurrent upward flow trayed bubble column, while Dreher and Krishna [20] studied liquid-phase backmixing in a batch liquid trayed bubble column. Vinaya
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[17] studied the effects of perforated tray design, tray spacing, and superficial gas and liquid velocities on the liquid-phase backmixing in a counter-current trayed bubble column with downcomers, and proposed empirical correlations for the estimation of the Peclet number in bubbly and turbulent flow regimes. Magnussen et al. [23] and Ichikawa et al. [24] studied the effects of tray design, tray spacing and superficial gas and liquid velocities in trayed bubble columns without downcomers. They found that the axial dispersion coefficient decreases with the number of trays, and the suppression of backmixing due to the trays is stronger in columns with larger diameters, whereas backmixing increases with the trays open area. Superficial liquid velocity has a negligible effect on the axial dispersion coefficient (Ichikawa et al. [24]). While Vinaya [17] found no dependency of liquid backmixing on the superficial gas velocity, Ichikawa et al. [24] found significant effect of superficial gas velocity (Ug ) on axial dispersion coefficient when Ug > 7 cm/s, where the axial dispersion coefficient reaches a maximum at Ug = 18 cm/s. In all these studies, conductivity probes were used to measure overall or local liquid-phase tracer responses. In general, conductivity probes have been traditionally used in process applications to determine the concentrations of dissolved ionic species in solutions that are devoid of gas bubbles. However, these probes have also sometimes been used as diagnostic tools in reaction engineering research applications, to estimate local liquid-phase velocities and to evaluate local liquid mixing in both single and two-phase flow systems by measurement of liquid-phase electrolytic tracer concentrations [6,25–28]. When such measurements are used to obtain the overall liquid-phase residence time distribution (RTD) in a single-phase flow, little ambiguity is encountered in the interpretation of conductivity probe output signals. However, the use of conductivity probes for liquid-phase concentration measurements in two-phase gas–liquid flows introduces complications that are not present in single-phase flow measurements. In two-phase gas–liquid flows, the signals are corrupted due the significant reduction in the measured conductivity that occurs when a bubble contacts the probe. Since the conductivity of the gas phase is appreciably smaller than that of the electrolytic liquid tracer solution, frequent reductions in the conductivity signal are observed as bubbles pass over the probe measurement volume. This systematic bias in the measured conductance in gas–liquid flows has limited the use of such probes for liquid-phase tracer experiments. If standard filtering techniques are applied, such as the filters available in the Signal Processing Toolbox in [29], the resulting signal is always an underestimate of the actual signal. This is due to a reduction in the noise component where the actual signal has a non-zero mean. Hence, the filter tries to retain this mean in the filtered signal, which causes an under prediction in the output. A number of workers have proposed various experimental techniques and data processing methods in an attempt to extract liquid-phase concentration data from conductivity probes in various two-phase gas-liquid flows. Rustemeyer et al. [28] tried to avoid signal corruption due to bubble passage in a mechanical fashion, by screening the probe tips. However, the screening method was not perfect, and the resulting signals appeared to
contain some information due to bubble passage across the probe tips. Dreher and Krishna [20] used a slit of about 35 mm × 5 mm in the glass cover of the conductivity cells at the tip of the measuring device to achieve fast access of the liquid-phase. They claimed that such an arrangement prohibited an accumulation of gas bubbles inside the conductivity cell. However, this does not prevent the corruption of the obtained signal due to bubble passage. Other researchers have also tried to resolve the signal corruption due to bubble passage by using standard data filtering techniques [25]. Inspection of the filtered tracer responses suggests that some vital elements of the signal may have been removed for the reasons mentioned above. Application of standard filtering procedures also assumes that the noise component of the signal to be filtered has a zero mean. This is valid only with random noise, associated with either the measuring device or with fluctuations in the electrical signals. However, the interaction of the bubbles with the conductivity probes causes a systematic and not a random reduction in the measured signals. If this signal reduction were assumed to be noise, the mean of such a noise component would not be zero, and standard filtering algorithms would not be effective in filtering this component. In summary, interpretation of data from tracer experiments in gas–liquid flows is non-trivial, since standard filtering techniques are not applicable for removing biased noise having a non-zero mean from the conductivity probe signals. Recently, Gupta’s et al. [1] have developed a novel filtering technique for extracting liquid-phase tracer concentration responses from conductivity probe data in a two phase gas–liquid flow system. Implementation of the new filtering algorithm was performed by coupling it to a standard Butterworth filter. This technique was later used in a cocurrent flow trayed bubble column by [6] to measure its overall liquid-phase backmixing. The objective of this work focuses on evaluating the liquidphase backmixing by measuring the tracer response using Gupta’s et al. [1] filtering technique in a cold-flow countercurrent trayed bubble column reactor that was scaled-down from a DuPont commercial unit. The resulting tracer responses provide insight into the liquid-phase mixing that occurs in both the presence and absence of the trays over a range of gas and liquid superficial velocities and with gas spargers having two different sparger hole densities. 2. Cold-flow unit experimental system 2.1. Overall system set-up The experimental system consisted of the cold-flow test column along with various sub-systems for feeding and controlling the volumetric flow rates of air and water [14]. The liquid delivery system consisted of a 350-gallon feed tank that was connected to a centrifugal pump. A rotameter was used to control the liquid flow rate. The liquid was introduced at the top of the column through a shower-type distributor located about 51/4 in. above the top tray. The liquid exited the column bottom through a plenum, and then flowed into a surge tank having a total volume of about 50 gallons. A second centrifugal pump was used to recycle the liquid back to the main feed tank. The
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Fig. 2. Schematic of the tray design.
Fig. 1. Schematic diagram of the column used for the cold-flow studies. (all dimensions are given in cm).
air was supplied from the house supply system at a delivery pressure of about 120 psig. After flowing through a filter, it passed a rotameter and then went to the sparger. 2.2. Detailed column design
commercial-scale sparger design. Details of the scaled-down sparger design are shown in Fig. 3. The gas was introduced to the main sparger supply line through a 9.53 mm O.D. manifold. Ten laterals were welded to the manifold, with the lengths being selected so that the sparger formed a circle whose diameter was about 6.35–12.7 mm less than the inside diameter of the column. The laterals were drilled with either 40 or 200 holes having a diameter of 350 m. The hole locations on a lateral were off-
A schematic of the cold-flow column design is given in Fig. 1. Constructed of clear PlexiglasTM , it had a nominal diameter of 8 in. and an overall height of 94 1/2 in. The column was divided into four sections, with each section having an overall height of 20 1/2 in. Three sieve trays were used between the sections. The top and bottom trays were used to create entrance and exit effects. Several ports were installed in the middle stage and on each side of the tray so that liquid conductivity probes could be inserted for local measurement of liquid-phase tracer concentrations. The entire column was supported at the bottom by the plenum. A schematic of the tray design and hole layout is shown in Fig. 2. The trays were constructed of 6.35 mm thick acrylic sheet and contained 42 holes having a diameter of 6.35 mm and laid out on a triangular pitch. The down comer occupied about 10% of the total tray cross-sectional area. 2.3. Sparger design The spargers in the cold-flow unit were scaled down using operating conditions and mechanical data extracted from a
Fig. 3. Design of the gas sparger.
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Fig. 4. Details on the hole schedule for the gas sparger laterals.
set at an angle of 30◦ from the vertical, and the laterals were positioned so they pointed downward. To obtain overall gas mass velocities in the cold-flow unit that were in the same range as those used on a given tray in the DuPont commercial system, a gas jet velocity of 183–244 m/s was required from each respective sparger hole. As shown in Fig. 4, the number of holes in a lateral were varied to achieve this range of gas velocities at gas volumetric flow rates of 3.4 and 17 actual m3 /h, respectively. The spargers were mounted 40.64 cm below the first tray at the bottom of the column. 2.4. Probe location To characterize the behavior of the liquid mixing on a stage, tracer experiments were conducted at three operating conditions using four different locations for the liquid conductivity probes. The probes’ characteristic response time is about 75 ms [1]. The three sets of operating conditions that were investigated are summarized in Table 1. The effect of the sparger hole density, i.e., the number of sparger holes per unit column cross-sectional area, on the column hydrodynamics was also studied. The conductivity probe tips were positioned at various radial locations where differences in the liquid mixing and hence local liquid concentration were expected to occur, such as (1) adjacent to the acrylic column wall, (2) in the column centerline, (3) behind the down comer skirt, and (4) slightly above or below a particular tray. Ports that could accommodate a 6.35 mm male NPT were installed in the center acrylic test sections at various strategic points so that the conductivity probes could be inserted to any desired depth. The tracer response measurements were performed by simultaneously recording the output signal from two probes, which corresponds to a classical two-point method.
Fig. 5. Positions of the conductivity probes used in the tracer experiments.
Fig. 5 shows the specific locations of the two conductivity probes that were used for the various tracer experiments. In the first configuration (A), shown in the upper left of Fig. 5, the lower probe was located at the entrance to the down comer for the bottom tray, while the upper probe was positioned below the middle tray on the opposite side of the down comer. In the second configuration (B), shown in the upper right, both probe tips were positioned on the column centerline, with the lower probe slightly above the bottom tray and the upper probe slightly below the middle tray. The third configuration (C), in the lower left, had the lower probe positioned slightly above the bottom tray next to the wall and close to the middle tray down comer, while the tip of the upper probe was slightly below the middle tray, adjacent to the wall on the side opposite to the down comer. Initial experiments using sparger 1 (40 holes), sketched in Fig. 4, showed that on a time scale corresponding to the mean
Table 1 Range of operating conditions Experiment number
Qg (SCFH)
QL (GPM)
uSG (cm/s)
uSG (ft/s)
uSL (cm/s)
uSL (ft/s)
1 2 3
118 118 236
2.0 6.5 6.5
3.25 3.25 6.51
0.108 0.108 0.217
0.44 1.44 1.44
0.015 0.048 0.048
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residence time of the liquid in the column, the tracer responses for the two-point measurements on a single stage suggested that the liquid flow pattern approached complete back mixing. As a result, a fourth probe configuration was utilized with sparger 2 (200 holes), which is shown in the lower right of Fig. 5 (configuration D, position No. 4). Here, the lower probe was located slightly below the bottom tray on the column centerline, while the upper probe was positioned in the down comer of the middle tray. Due to the large volume of the section underneath the gas sparger filled with liquid (see Fig. 1), conductivity probe was not mounted at the exit of the liquid from the column to measure the overall tracer response with a mixing cup for the conditions studied. Unfortunately, such measurements were not obtained. 2.5. Experimental procedure For each run, 10 ml of an aqueous KCl solution containing 0.2 gm of KCl per ml was manually injected, via a plastic syringe, at the top of the column directly into the liquid distributor. The tracer injection time, based on repeated trials, was estimated to be 2.5 ± 0.5 s. The start of the injection was controlled to 0.1 s accuracy using a stopwatch. The data acquisition system used for sampling the continuous output signals from the two probes was initiated one minute before the tracer was injected. This was done to simplify filtering of the raw data and to establish an initial probe output signal baseline. The sampling frequency was 10 Hz for all the tracer experiments. The raw experimental tracer response data was then processed using the filtering algorithm described below.
Fig. 6. Performance of a standard Butterworth filter on the conductivity probe signal in the air–water system without tracer injection that has been corrupted due to bubble passage. QL = 6.5 GPM (uSL = 1.44 cm/s), QG = 118 SCFH (usg = 3.25 cm/s), sparger 2 (200 holes), position No. 4 (D, Fig. 5), lower probe.
probe). Inspection of Fig. 6 shows that in spite of such a low cut-off frequency, the filtered signal under-predicts the actual one. Thus, an alternative methodology is required. To overcome the difficulty associated with standard filtering techniques, an alternate approach was developed by Gupta et al. [1] so that the uncorrupted signal can be extracted from the noisy signal. This signal-filtering algorithm, described below, is implemented in this work. 3.2. Gupta et al.’s. signal filtering algorithm [1]
3. Signal filtering methods 3.1. Standard approach As mentioned earlier, difficulties are encountered when the local liquid-phase mixing is studied in a two-phase gas–liquid system by using conductivity probes to measure the local liquidphase tracer concentration at a point. Because the conductivity of the gas is appreciably smaller than that of the liquid containing an electrolyte as tracer, the conductivity signal undergoes a significant reduction as bubbles pass over the probe, which causes fluctuations (noises) with non-zero mean (i.e. non random noise). If a standard signal filtering technique is applied (which assumes the signal has a zero mean due to a random noise), our filtered signal would always underestimate the actual signal, because the noise component has a non-zero mean. Therefore, the filter tries to retain this mean in the filtered signal as well, which causes in this case the filtered signal to be under-predicted. This is illustrated in Fig. 6, where the solid line represents the filtered signal obtained after applying a second order Butterworth filter in [29] (i.e. a standard signal filtering technique) to the raw data, which is represented by the dashed lines. The cutoff frequency was 0.005 Hz, which corresponds to a normalized frequency of 0.001 with a 5 Hz normalizing frequency (Nyquist frequency). The raw data was acquired without tracer injection by mounting the conductivity probe just below the bottom tray close to the column centerline (position No. 4 in Fig. 5, lower
The following steps were followed as part of the algorithm to filter the conductivity-probe signals so that the biased noise due to bubble passage could be removed: (1) The raw signal was processed using a regular Butterworth filter, (2) at each time instant, if the filtered response was lower than the raw signal, the filtered response was made equal to the raw signal. Otherwise, no action was taken. The resulting signal is the filtered plus the threshold signal, (3) a sum of the squares of the differences between the raw and filtered plus threshold signals was calculated, (4) if this sum is less than a certain tolerance (5 × 10−5 V for this work), then the filtered plus threshold response was taken to be the final filtered response. Otherwise, the filtered plus the threshold signal replaced the raw signal and the process was repeated by returning to Step 1, and (5) this procedure was continued until the tolerance criterion was met. To demonstrate the difference between the new algorithm [1] and the standard one, an impulse tracer test was conducted using the same operating conditions and probe locations used in Fig. 6. The performance of the filtering algorithm on the signal obtained from this impulse tracer test is shown in Fig. 7 (dashed line). Visual observation shows that the new technique yields results that are an improvement when compared to those obtained with a standard Butterworth filter (solid line). A cutoff frequency of 0.05 was used for this case on the normalized scale, which corresponds to 0.05 × (10/2) = 0.25 Hz on the absolute scale. The above filtering plus threshold procedure retains
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Fig. 7. Performance comparison of a standard and the improved signal filtering algorithm using the tracer impulse response from a two-phase gas–liquid system. QL = 6.5 GPM (uSL = 1.44 cm/s), QG = 118 SCFH (usg = 3.25 cm/s, sparger 2 (200 holes), position No. 4 (D, Fig. 5), lower probe.
Fig. 8. Tracer concentrations versus time impulse response. Conditions: probes positioned in configuration D (position No. 4, Fig. 5); sparger 2 (200 holes), QL = 6.5 GPM (uSL = 1.44 cm/s); QG = 236 SCFH (usg = 6.51 cm/s).
frequencies less than or equal to 0.25 Hz as the successively filtered signal relaxes to the final filtered plus threshold signal. The sampling frequency used in the above data acquisition, as well as in all the experiments reported below, was 10 Hz. This frequency was chosen since the characteristic response time of the probes was about 75 ms, which corresponds approximately to a frequency of 13 Hz. A characteristic probe response time of ∼75 ms suggests that a process could be monitored having a characteristic response time of greater than ∼500 ms. In other words, any phenomenon having a characteristic frequency higher than 2–3 Hz could not be captured. The characteristic frequency of the tracer washout curves for all the experiments conducted for this study was in the range 5 × 10−3 –1 × 10−2 Hz. This range is two orders of magnitude lower than the highest frequencies that these probes can capture, implying that the use of these probes for the current work is well justified. Therefore, a sampling frequency between 3 and 5 times the highest characteristic frequency that can be captured with these probes would be approximately 10 Hz. Hence, 10 Hz was chosen as the final sampling frequency. 4. Results and discussion Some selected results are presented using the above mentioned signal filtering algorithm to process the conductivity probe tracer response data from the cold-flow trayed bubble column. Particular experimental variables that were investigated include the combined effects of sparger hole density, liquid-flow rate, and gas flow rate on the local liquid-phase tracer responses. Since the measured tracer responses are point measurements with open boundaries and vary with the radial positions of the two probe measurements (Figs. 8–10) in a single stage, unfortunately, quantification of the mixing flow pattern using reactor scale tracer modeling approach (e.g. tank-in-series model, axial dispersion model) was not considered in this work. As mentioned earlier, due to large volume of the section below the gas
Fig. 9. Effect of sparger hole density on tracer impulse responses. Conditions: probe positioned in configuration B at position No. 2, QL = 2 GPM (uSL = 0.44 cm/s); QG = 118 SCFH (usg = 3.26 cm/s).
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ever, this is not the case for the measured tracer responses in configuration B (position No. 2, Fig. 8), where the probes were mounted in the center of the column (see Figs. 9 and 10a). When the cross-correlation of the two signals (Fig. 8) was evaluated, the difference between the signal maximums for both probes was around 30.5 s. Since there was no port available to position lower probe in the down comer region of the bottom tray, it was positioned below the bottom tray in the column centerline. Thus, this time lag of 30.5 s is slightly greater than the mean residence time of liquid on the tray, which was estimated from the known liquid volume and liquid flow rate using the central volume principle. From overall holdup measurements [14], the average liquid holdup on the tray was ∼0.8. Since the tray spacing is 20.5 in. and the liquid superficial velocity is 1.44 cm/s, the mean residence time of the liquid is about 28.9 s. Thus, a reasonable estimate of the mean residence time of the liquid on the stage is obtained using the two independent methods. Similarly, the cross-correlations for all other pairs can be estimated. From these, the lag or lead-time can be found at which the cross-correlation is a maximum. Knowing the distance between the probes, the velocity between the two probes can be estimated by dividing the distance between the probes by the above time lag or lead. This is the design principle upon which the heat pulse anemometer (HPA) probe is based. However, the velocity estimated using this approach would yield a long-time average between the two points, and not a precise value for the liquid velocity at that particular set of probe coordinates. This aspect is considered in detail elsewhere [1]. 4.2. Effect of gas sparger design
Fig. 10. Effect of liquid flow rate on tracer impulse responses using sparger 2 (200 holes) at QG = 236 SCFH (usg = 6.51 cm/s), a. QL = 2 GPM (uSL = 0.44 cm/s), b. QL = 6.5 GPM (uSL = 1.44 cm/s).
sparger, overall reactor tracer response measured by mounting a probe in a mixing cup at the exit of the liquid stream from the reactor was also not possible. Hence, reactor mixing pattern and its variation with the studied conditions was not considered or quantified in this work. 4.1. Liquid mean residence time The liquid-phase tracer concentrations were calculated from the probe signals by using empirical calibration equations that were developed by relating signal response to salt concentration. Fig. 8 shows a typical concentration response to an impulse tracer injection when the probes are arranged according to configuration D in Fig. 5. The shapes of the tracer responses in Fig. 8 (configuration D, Fig. 5 position No. 4) suggest that the trays provide the desirable effect of staging, which results in reduced back-mixing. How-
The sparger seems to have the most significant effect on the local liquid-phase tracer responses as the liquid flow rate or equivalently, the liquid superficial velocity, is decreased. This is particularly noticeable at the lowest liquid flow rate used (2 GPM, 0.015 ft/s, 0.44 cm/s). Fig. 9 shows that with this liquid flow rate and with the probes positioned as shown in configuration B, the response curves with sparger 1 (40 holes) are noticeably broader than those obtained with sparger 2 (200 holes). However, when the probes are positioned as shown in configuration A, the responses have an almost opposite behavior (not shown). This finding suggests that at this flow rate, the liquid velocity is greater in the center of the column and also along the down comer when sparger 2 (200 holes) is used instead of sparger 1 (40 holes), whereas the opposite behavior occurs near the walls. This effect was not seen at the highest liquid flow rate used (6.5 GPM = 0.048 ft/s = 1.44 cm/s), irrespective of the gas flow rates that were used. 4.3. Effect of gas flow rate The effect of the gas flow rate was studied at a single value for the liquid flow rate, namely, 6.5 GPM, which corresponds to a liquid superficial velocity of 0.048 ft/s. By comparing the responses at a given location, it was concluded that there was no appreciable effect of gas flow rate on the tracer response
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curves, irrespective of the type of sparger that was used. This result was somewhat surprising, since the overall gas holdup was significantly affected by an increase in the superficial velocity of the gas. Despite the change in overall gas holdup, it does not seem to cause any appreciable change in the liquid tracer responses and hence the liquid mixing over the range of gas velocities employed in this study. This finding is consistent with the findings of [17]. 4.4. Effect of liquid flow rate Fig. 10 is a typical set of responses that show liquid flow rate has a noticeable effect on the shape of the tracer responses and also on the rate at which the liquid tracer elutes from the column. This behavior is expected, since according to the central volume principle, the mean residence time of the tracer is inversely proportional to the liquid flow rate. Hence, the mean residence time of the tracer at 2 GPM is approximately a factor of three less when compared to the mean residence time at a liquid flow rate of 6.5 GPM. Other results show that tracer washout is more pronounced in the center of the column when compared to the walls. This finding indicates that the higher liquid mass flux that exists in the column center enhances the radial mixing on the stage, so that the tracer is washed out almost uniformly throughout the stage.
5. Remarks The newly developed signal filtering methodology [1] was utilized to extract liquid-phase tracer responses from conductance measurements obtained in two-phase gas–liquid systems. By properly choosing a cut-off frequency and coupling this with an appropriate thresholding algorithm, the liquid-phase contribution to the corrupted signal can be extracted. This provides information on liquid macro mixing through experimental measurements characterizing liquid mixing in a trayed cold-flow bench-scale bubble column operated with counter-current flow of gas and liquid. The combined effects of the gas sparger, hole density, gas flow rate, and liquid flow rate have been investigated. It was shown that both sparger hole density and liquid-flow rate have the biggest impact on local liquid mixing between two trays. The new signal processing method has potential applications in various commercial systems where extraction of the liquid response in a two-phase gas-liquid medium is needed. Acknowledgement The authors acknowledge the financial support provided by DuPont.
4.5. Spatial distribution of the responses
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