Experimental Investigation on the Pulse Flow Regime Transition of

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Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Experimental Investigation on the Pulse Flow Regime Transition of Gas−Liquid Concurrent Downward Flow through a Sieve Plate Packed Bed Min Qiao, Weixing Huang,* Junfeng Li, Yunxiang Xue, Anqi Zhang, and Hanlin Wang School of Chemical Engineering, Sichuan University, Chengdu 610065, China

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S Supporting Information *

ABSTRACT: Nine sets of packings were designed to study the pulse flow that occurs in gas−liquid concurrent flow downward through sieve plate packing. Through the observation of flow pattern and the analysis of the pressure fluctuation data acquired by pressure transducers, the mechanisms for the inception and the propagation of pulse flow in the plate packing were clarified, and a variation coefficient method was proposed to determine the boundary lines of the pulse flow. Accordingly, the pulse flow pattern maps were obtained and the effects of the geometric parameters and the installation method of the plate packing on the transition of the pulse flow were analyzed in detail, revealing that the hole diameter and plate quantity have the most evident effects. Finally, correlations for the onset and the disappearance lines of the pulse flow regime were developed, with the deviations from the experiments of ∼15% and 10%, respectively.

1. INTRODUCTION Gas−liquid two-phase concurrent downward flow is widely used in packed beds, because of its low pressure drop and high liquid throughput; furthermore, it does not lead to flooding.1,2 For example, in gas stripping columns, the heat and mass transfer occur under this flow mode. A gas stripping column consisting of three sections of sieve plate packed beds is an important piece of equipment in nuclear wastewater treatment.3 In this packed column, the gas vapor flows upward through the column while the liquid is fed from the top of the column; however, in each sieve plate packed bed, the gas and liquid flow concurrently downward through the bed, as shown in Figure 1. Compared with conventional packing, sieve plate packing is superior in many respects. First, because the packing consists of multiple sieve plates, it can significantly reduce manufacturing costs,4 and permit easier cleaning; further, it does not get blocked easily.5 Second, as the sieve plates are installed close together, good liquid distribution can be obtained, and the gas−liquid interface can be renewed frequently to improve the transport efficiency. However, although sieve plate packing has the potential for wide application, limited studies on this new type of packing have been performed to date.3−5 Despite its simple structure, the flow patterns in sieve plate packing are complex, which significantly affects the performance of the packed bed. Typically, several flow patterns can be identified in a sieve plate packed bed, including trickle flow, continuous flow, pulse flow, semidispersed flow, and dispersed flow.4 Of these flow patterns, pulse flow is a special type of flow that is commonly encountered in commercial-scale packed beds.6,7 Generally, pulse flow occurs above a certain liquid flow © XXXX American Chemical Society

Figure 1. Degassing unit of boron recycle system (TEP).

rate that maintains a relationship with the corresponding gas flow rate.4,8 The turbulent pulse flow regime can enhance the interaction between the gas and liquid phases, and thus it Received: Revised: Accepted: Published: A

January 11, 2019 April 29, 2019 May 9, 2019 May 9, 2019 DOI: 10.1021/acs.iecr.9b00180 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 2. Schematic diagram of the experimental apparatus.

provides good transport properties for chemical reactions.8−11 In addition, in the pulse flow regime, the alternating passage of gas-rich and liquid-rich columns continuously mobilizes the inactive liquid holdup,8 eliminates the hot spots that occur in fast exothermic catalytic reactions,11 increases the wetting efficiency and decreases axial backmixing,10 and reduces the occurrence of undesirable reactions.12 To take advantage of the pulse flow, most concurrent downward flow packed beds are operated under a pulse flow regime or at the transition between the pulse flow regime and trickle flow regime.6−8,13 Therefore, a good understanding of the pulse flow is a subject of long-standing interest for the design and application of packed columns. Most investigations of pulse flow are conducted in randomly packed beds and focus on the mechanism of the pulse flow. Ng14 proposed a theoretical model for the transition of the pulse flow and suggested that pulse flow begins when the channels are plugged by liquid. Zhao et al.8 applied electrical capacitance tomography to image the pulse flow in a trickle bed reactor and successfully visualized the liquid pulse structures. It was found that, with increasing liquid velocity, liquid blocking of the channels occasionally occurs. Subsequently, under the effect of the inertial force, the gas phase will break these blockages and push them downward to form local liquid pulses. With further increases in the liquid velocity, these local pulses may merge together to form large liquid pulses that block the cross-section of the bed, thus forming a visible pulse flow. Anadon et al.15 utilized ultrafast threedimensional (3-D) magnetic resonance imaging (MRI) to define the liquid velocity corresponding to the maximum number of isolated pulses as the inception velocity of the pulse flow. Attou and Ferschneider13 developed a model for the transition from trickle flow to pulse flow through linear stability analysis, which considered that pulse flow occurs when the parameters of the flow state do not satisfy the equilibrium state equation for trickle flow. As can be seen, the pulse flow mechanisms proposed in these previous investigations can be classified into two common viewpoints: the stability loss of a macroscale film16,17 and the microscale blockage of flow channels.8,18 The film stability concept ignores the effect of the packed bed diameter and considers an ideal homogeneous liquid distribution. Consequently, this concept does not

entirely reflect the actual situation in packed-bed devices.19 However, microscale occlusion does not readily occur in structured sieve plate packed beds, because the sieve holes are too large to be blocked easily by the liquid phase. Shi et al.4 introduced a new concept of gas obstruction by observing the pulse flow in sieve plate packed beds. However, this concept is not well understood and has not been studied comprehensively. Many researchers also investigated the effects of various parameters on the pulse flow, such as the column size, particle diameter, liquid viscosity, liquid surface tension, gas density, and operation pressure.8,13,20 Dashliborun and Larachi21 investigated the effects of the moving type and moving period of the porous packed bed on the pulse flow. However, all of these studies ignored the effect of the packing height on the pulse flow. Ng14 considered that pulse flow begins at the bottom of the packed bed, as a result of the Bernoulli Effect; however, this explanation does not seem appropriate, based on our experimental results. Although Boelhouwer et al.22 and Krieg et al.23 investigated the axial evolution of the pulse flow, the focus of those studies was mainly on the mechanism of the pulse flow. Many theoretical models for the trickle-to-pulse flow transition have been proposed,13,14,20 but all of these models are based on local pulses and ignore the axial evolution conditions of the pulse flow. Therefore, these theoretical models are incapable of fully describing the actual situation of a pulse flow in a packed bed. In fact, because pulse flow is a dynamic development process, it is difficult to propose a theoretical model for the transition of the pulse flow by considering the effect of the packing height. A simple and effective method is to propose empirical correlations based on the experimental data. In our previous study,4 pulse flow was observed as a special flow pattern in sieve plate packing that significantly affects the performance of the sieve plate packing. This provides a preliminary understanding of the pulse flow in this new type of packing and is the motivation of the present study. In this study, the pulse flow pattern is observed and the pressure drop fluctuation is measured experimentally with transducers, with the goal of elucidating the mechanism of the pulse flow and investigating the effects of the geometric characteristics of the B

DOI: 10.1021/acs.iecr.9b00180 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 3. Experimental setup with (a) sieve plate packing (observable), (b) sieve plate packing (unobservable), (c) the geometric dimension of adjacent sieve plates, (d1) the forward installation method of adjacent sieve plates, and (d2) the crossed installation method of adjacent sieve plates.

packing on the transition of the pulse flow. Finally, correlations are proposed for prediction of the pulse flow transition boundaries.

Water and air were used as liquid and gas phases, respectively. The gas was supplied by a gas blower and controlled by three gas float flow meters. A gas distributor is installed at the top of the packed bed. Beneath the gas distributor is a liquid distributor, which is a perforated pipe inserted in the packed column. Gas and liquid exits are located at the side and the bottom of the column, respectively. Two water tanks along

2. EXPERIMENTAL SETUP A schematic view of the experimental apparatus is shown in Figure 2. Experiments were conducted in a square column. C


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Industrial & Engineering Chemistry Research Table 1. Geometric Characteristics of Sieve Plate Packing Packing Label d0 (mm) W (mm) l (mm) h (mm) t (mm) free area ratio, α plate quantity, N hole distribution observation? installation method

A

B

C

D

E

F

G

H

I

14 190 30 25 1 0.115 21 square √ FI

10 190 20 18 1 0.110 21 square √ FI

6 190 14 11 1 0.093 21 square √ FI

6 290 14 10.5 1.5 0.115 24 square × FI

6 290 14 10.5 1.5 0.131 24 triangle × FI

10 290 20 16.5 1.5 0.146 24 square × FI

10 290 20 16.5 1.5 0.177 24 triangle × CI

14 290 30 23.5 1.5 0.132 24 square × FI

14 290 30 23.5 1.5 0.139 24 triangle × FI

with a pump and two liquid float flow meters are used for liquid circulation. Two types of plate packings were used in these experiments. One consisted of 21 stainless steel plates with a shell made of transparent acrylic resin, as shown in Figure 3a, which permits visual observation of the flow patterns. The other type consisted of 24 stainless steel plates with a shell made of stainless steel, as shown in Figure 3b. Each sieve plate has a side length of W. The holes are distributed evenly with a spacing of l and hole diameter of d0. Two distribution modes are employed for the holes: square distribution and regular triangular distribution. The sieve plates are spaced evenly along the packing bed with a spacing of h, as shown in Figure 3c, where t represents the thickness of the plate, and θ represents the turning angle between corresponding holes on two adjacent sieve plates. Two installation methods are applied for adjacent sieve plates: the forward installation method (FI) is shown in Figure 3d1 and the crossed installation method (CI) is shown in Figure 3d1, in which the dashed circles represent the downstream plate holes. The geometric characteristics of the nine sets of packings are summarized in Table 1. The packed column was equipped with four pressure taps separated by a spacing of 7 (or 8) sieve plates. Three differential pressure transducers were used to measure the instantaneous pressure drops across the upper 7 (or 8), the upper 14 (or 16), and the total 21 (or 24) sieve plates simultaneously. Experiments were performed under atmospheric pressure and at room temperature. During the experiments, the gas flow rate was increased steadily under a fixed liquid flow rate, and the gas flow rates at which pulse flow occurred and disappeared were recorded. The boundary lines of the pulse flow transition were thus obtained for packings B and C. In addition, at a fixed liquid flow rate, the gas flow rate was increased evenly and the pressure drop fluctuation was measured for all packings. The liquid superficial mass flux (Ls) ranged from 6.2 kg/m2/s to 118.8 kg/m2/s, and the gas superficial mass flux (Gs) ranged from 1.0 kg/m2/s to 14.2 kg/ m2/s. Before the experiments, the transducers were calibrated with a U-tube manometer, to ensure the reliability of the experimental data.

Figure 4. Pulse flow state in packing B at Ls = 88.4 kg/m2/s and Gs = 4.6 kg/m2/s.

present study is only focused on the pulse flow, and thus only the transition boundaries for the pulse flow will be presented in the flow pattern maps. Figure 4 shows the state of the pulse flow at one moment in the case with Ls = 88.4 kg/ m2/s and Gs = 4.6 kg/m2/s for packing B. To show the fluid state more clearly, this image was processed by increasing the exposure in the Photoshop computer program. It can be seen that liquid-rich and gas-rich zones are alternately distributed along the packed bed, particularly at the lower part of the bed. The corresponding video has been uploaded as Supporting Information for this study. During the experiments, it was noted that the pulse flow is always first observed at the bottom of the packed bed, and the range of the visible pulse coverage then expands upward with increasing Gs; however, it never reaches all the way to the top of the packed bed. In contrast, the upper part of the pulse flow is first dispersed with a further increase Gs, and after the pulse flow at the bottom of the packed bed is dispersed, there is no longer any pulse flow in the packed bed. Unlike for packings B and C, pulse flow was not observed with packing A. In these experiments, the onset of the pulse flow is defined as the occurrence of liquid-rich and gas-rich zones that are visible to the naked eye, and the disappearance of the pulse

3. RESULTS AND DISCUSSION 3.1. The Pulse Flow Regime and the Pressure Drop Fluctuation. During the gas−liquid concurrent downward flow through sieve plate packing, four flow patterns were identified in packings B and C: trickle flow, pulse flow, continuous flow, and semidispersed flow.4 However, the D


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Figure 5. Flow regime transition boundaries to pulse flow in (a) packing B and (b) packing C.

Figure 6. Variation of CV with Gs under fixed Ls for (a) packing A, (b) packing B, and (c) packing C.

the PDF initially decreases, then increases, and finally decreases again with increasing Gs, indicating that the amplitude of the pressure fluctuation initially increases, then decreases, and finally increases again. It is clear that the first increase in the amplitude is caused by the occurrence of pulse flow, while the final increase is caused by the increase of the gas disturbance; the decrease is mainly attributed to the disappearance of the pulse flow. This result reveals that the pulse flow is closely related to the geometric characteristics of the sieve plate packing and maintains some relationship with the gas and liquid flow rates. Figure S3 in the Supporting Information presents the variation in the pressure drop fluctuation, as a function of time with different sieve plate quantities N, for packing A (Figure S3a), packing B (Figure S3b), and packing C (Figure S3c). The corresponding PDFs are shown in Figure S4 in the Supporting Information. In packing A, it can be seen that the peak value of the PDF decreases slightly with increasing N, indicating that the amplitude of the pressure fluctuation

flow is defined as the complete dispersion of the visible pulses. Based on these criteria, pulse flow transition boundaries were obtained for packings B and C, as shown in Figure 5. For both packings, the experimental results show that, at low Ls, the pulse flow barely occurred. With increasing Ls, the onset of the pulse flow shifted to a lower Gs, while the disappearance of the pulse flow shifted to a higher Gs. Figure S1 in the Supporting Information presents the pressure drop fluctuations as a function of time at different Gs for (a) packing A, (b) packing B, and (c) packing C. To make the differences between these pressure drop fluctuations more easily observable, the time series data were analyzed statistically to obtain the probability density function (PDF), as shown in Figure S2 in the Supporting Information. Packing A shows that the peak value of the PDF gradually decreases as Gs increases, indicating that the amplitude of the pressure fluctuation increases with increasing Gs. This increase in the amplitude is primarily caused by an increase in the gas disturbance. However, in packings B and C, the peak value of E


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Figure 7. Variation of CV, as a function of Gs for packings D and H.

increases slightly with increasing N. However, in packings B and C, as N increases from 7 to 14 (or 21), the peak value of the PDF decreases significantly, indicating that the amplitude of the pressure fluctuation increases significantly as N increases. This result reveals that N significantly affects the behavior of the pulse flow. 3.2. The Identification of the Pulse Flow Transition Boundary Lines by CV. Besides observation, various statistical parameters are also available to identify the pulse flow regime transition in packed beds. Of these, the coefficient of variation (CV) has been used extensively,21,24,25 and is computed as follows: σ CV = (1) ΔP ̅ where ΔP̅ is the average pressure drop, and σ is the standard deviation, calculated as

therefore, there must be a point corresponding to the fastest increase in the CV curve. Based on the variation in the pressure drop fluctuation with the change in the Gs (see Figures S1b and S1c), it can be inferred that there must be a peak in the CV curve. After the CV peak, the pulses are gradually dispersed, which results in a decrease in C V . Approaching the disappearance of the pulse flow, the pressure drop still increases dramatically as Gs increases; consequently, there should be a point of rapid decrease in the CV curve corresponding to the disappearance of the pulse flow. These inferences will be verified by the experimental results for packings A, B, and C. Figure 6 shows the variation in the statistical parameter CV as a function of Gs for packings A, B, and C. It is clear that the trend in CV for packing A is different from that for packings B and C, and this difference is caused by the occurrence of pulse flow. For packing A, there is no pulse flow, and thus CV decreases with increasing Gs. For packings B and C, with increasing Gs, CV initially increases and then decreases, indicating that the intensity of the pulse flow initially increases and then decreases. Based on the inference discussed above, the beginning and ending of the pulse flow can be identified, as shown by the dashed lines in Figures 6b and 6c. The Gs parameters corresponding to the pulse flow transition boundaries are in good agreement with the experimental

n

σ=

∑i = 1 (ΔPi − ΔP ̅ )2 n−1

(2)

where ΔPi is the instantaneous pressure drop and n is the corresponding number of events in the observation window. The onset of pulse flow is defined as the appearance of liquid-rich and gas-rich zones that are visible to the naked eye. At this time, the pulse flow is enhanced with increasing Gs; F


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Figure 8. Pulse flow pattern map and the corresponding fluctuations in pressure drop for packing D.

Figure 9. Pulse flow pattern maps for packings E, F, and G.

G


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Figure 10. Typical pressure drop fluctuation under pulse flow regime for packing C at Ls = 44.5 kg/m2/s and Gs = 6.3 kg/m2/s. Figure 13. Fluid state at the disappearance of the pulse flow.

Figure 11. Fluid state at the onset of the pulse flow (the dashed lines represent the next position of the disturbance waves).

Figure 14. Comparison of the pulse flow scope between packings D and E.

Figure 15. Comparison of the pulse flow scope between packings F and G.

point and ending point of the pulse flow can also be found from the CV curve. The same results can also be obtained for packings E, F, and G, as shown in Figure S5 in the Supporting Information. However, the CV for packing H decreases continuously as Gs increases, and there is no significant change with varying Ls, as shown in Figure 7b, indicating that no pulse flow occurred with this packing. The same results can also be obtained for packing I, as shown in Figure S6 in the Supporting Information. Based on the identification criteria for the pulse flow transition boundaries using the CV curve as discussed above, the pulse flow regime transition boundary lines can be obtained for packings D, E, F, and G.

Figure 12. Breakup process of the disturbance wave.

data (see Figures 5a and 5b for Ls of 88.3 kg/m2/s and 89.2 kg/m2/s, respectively). Figure 7a shows the variation in CV, as a function of Gs, at different Ls for packing D. According to this figure, the following results can be obtained. First, the value of CV initially increases and then decreases as Gs increases, indicating that pulse flow occurred in this packing. Second, with increasing Ls, the Gs corresponding to the peak of the CV shifts to a lower value, indicating that pulse flow can be achieved more easily with increasing Ls. Similar to Figures 6b and 6c, the starting H


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Figure 16. Comparison of the pulse flow scope between (a) packings B and C, and (b) packings D and F.

Figure 17. Pressure drop fluctuations and the corresponding PDFs at different N for packing D.

Figure 18. Comparison of the pulse flow scope between (a) packings C and D, and (b) packings B and F.

Figure 8 shows the pulse flow transition map and the corresponding fluctuations in the pressure drop for packing D. For the convenience of proposing correlations to describe the transition lines of the pulse flow regime, the pulse flow pattern map is plotted as the superficial gas Reynolds number (ReG) versus the superficial liquid Reynolds number (ReL). It can be seen that the pressure drop fluctuations corresponding to the onset of the pulse flow exhibit a significant fluctuation amplitude. This is because at the point of the fastest increase in the CV, pulse flow is already occurring and will be enhanced

with increasing Gs. At the point of the disappearance of the pulse flow, the pressure drop is relatively high, and the amplitude of the pressure drop fluctuation decreases significantly, which corresponds to the point of rapid decrease in the CV curve. Taking ReL = 200 as an example, it can be seen that the amplitude of the pressure drop fluctuation initially increases and then decreases in the pulse flow regime, which is in agreement with the results in Figure S1 for packings B and C. The pulse flow pattern maps for packings E, F, and G are shown in Figure 9. I


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fluctuation.8,19 When local fluctuations propagate downward along the packed bed, they may be superposed and enlarged and finally develop into visible pulses. This flow pattern is referred to as pulse flow, which is driven by the overall gas flow.19 Figure 11 shows the fluid state at the onset of the pulse flow; the dashed lines represent the next position of the disturbance waves. Since increasing the gas flow rate will enhance the disturbance on the liquid film and promote the formation of disturbance waves, the distance the local fluctuations must travel before developing into a pulse flow will decrease with increasing Gs.22 This explains why the range of the visible pulse coverage was observed to expand upward with increasing Gs in the experiments in this study (see Section 3.1). However, this does not mean that the pulse flow begins at the bottom of the bed. The pulse flow should actually begin at some location in the upper section of the packing, where the pulse flow intensity is weak and cannot be identified visually by the naked eye. As gas and liquid flow downward, these weak pulses will be superposed and increasingly enlarged, thus increasing the intensity of the pulses. As a result, the pulse flow can be observed most easily at the bottom section of the packing. Although there is no pulse flow at the top of the packed bed, this section of the sieve plates is necessary to achieve the required superposition of the local fluctuations for pulse flow to occur. Thus, the quantity of the sieve plates plays an important role in the occurrence of pulse flow. Qiao et al.28 investigated the flow patterns of a gas−liquid concurrent downward flow through an orifice plate where pulse flow was not observed. One of the reasons why there was no pulse flow in that experiment may be that the superposing effect of multiple plates was not present. A detailed process of the rolling breakup of the liquid disturbance wave29 is presented in Figure 12. In the pulse flow regime, as Gs increases, the amplitude of the disturbance wave increases (see Figures 12a and 12b), thereby enhancing the intensity of the pulse flow. Subsequently, folding of the liquid disturbance wave from the gas/liquid interface appears29 (see Figures 12c and 12d). Finally, the liquid wave thins out to form lamella because of the intense disturbance of the gas phase, and these lamellae subsequently pinch off at the base,29 as shown in Figures 12e and 12f. The breakup of the liquid waves broadens the flow path of the gas phase, thus leading to the disappearance of the pulse flow. Figure 13 shows the fluid state at the disappearance of the pulse flow. According to the mechanism for the pulse flow discussed above, the reason that the onset of the pulse flow shifts to

Figure 19. Comparison of the predicted values with the experimental data for the pulse flow regime transition boundaries with packing D.

3.3. The Disturbance Wave Mechanism of the Pulse Flow. The amplitude of the pressure drop fluctuation reflects the intensity of the fluid turbulence in the packed bed, and thus the pressure drop fluctuation can be used to investigate the mechanism of the pulse flow. The mechanism of the pulse flow will be investigated based on the results presented in Section 3.1 and the characteristics of the pressure drop fluctuations. Figure 10 shows the typical pressure drop fluctuation under the pulse flow regime for packing C with Ls = 44.5 kg/m2/s and Gs = 6.3 kg/m2/s. It can be seen that there are many small and large oscillations. These two types of oscillations are herein referred to as ripple waves and pulses, respectively. As suggested by Almabrok,26 the ripple waves occur because the gas−liquid interface is always covered by small liquid film waves that are characterized by small wavelengths and amplitudes. The pulses are primarily caused by the disturbance waves that are characterized by large wavelengths and amplitudes.26,27 In gas−liquid concurrent downward flow through the sieve plate, the presence of the gas phase will obstruct the smooth flow of the liquid phase. Under the disturbance of the gas flow and the effect of gravity, the liquid phase will accumulate on the surface of the sieve plate, eventually forming liquid disturbance waves. When the disturbance wave flows through the sieve pore simultaneously with the gas phase, the presence of the disturbance wave will cause a temporary obstruction of the gas flow and thus produce an abrupt increase in the pressure drop. After the disturbance wave travels through the sieve plate, the pressure drop returns to a lower value; this is referred to as a local

Figure 20. Parity plot of the predicted and the experimental ReG with (a) the onset of the pulse flow and (b) the disappearance of the pulse flow. J


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Figure 21. Comparison of the calculated and the experimental values for the pulse flow transition boundaries with (a) packing B and (b) packing C.

Figure 22. Variation trends of the predicted transition boundaries for the pulse flow regime with the change of the packing geometric characteristics.

lower Gs with increasing Ls (see the lower limit in Figure 5) and the disappearance of the pulse flow shifts to higher Gs with increasing Ls (see the upper limit in Figure 5) can be explained as follows. With increasing Ls, the liquid holdup in the packed

bed will increase, and thus large disturbance waves are more easily formed. Accordingly, the pulse flow scope becomes broader with increasing Ls. In addition, because the pulse flow at the bottom section of the packing is always most evident, the K


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waves to be more easily broken at high gas flow rates, thereby making the disappearance of the pulse flow occur more easily. The hole spacing (l) mainly affects the change in the gas flow direction, and this effect is also related to the secant of the turning angle (θ). Therefore, the ratio of l/h in 1 + [l/(2h)]2 can be used to describe the effect of the hole spacing. A larger relative hole spacing (l/h) will lead to a more significant change in the flow direction of the fluids between two adjacent sieve plates.4,30 This will eventually lead to a more intense disturbance of the liquid flow, which facilitates the formation of the disturbance waves and thus causes the pulse flow to occur more readily. Similarly, a larger l/h will enhance the breakup of the liquid disturbance waves and cause the pulse flow to disappear more easily. 3.4.4. Effect of the Hole Diameter. Figure 16 shows a comparison of the pulse flow scope between packings B and C (Figure 16a) and packings D and F (Figure 16b). The most evident difference between packings B and C (or packings D and F) is the hole diameter (d0). Therefore, Figure 16 can be used to explore the effect of d0 on the pulse flow regime transition. Figure 16 shows that both the onset and disappearance boundary lines of the pulse flow shift to lower values with decreasing d0, especially the onset line. This is because the occurrence of the pulse flow is related to the blockage of the gas flow.4 A small d0 value more effectively causes blockage of the gas flow, and thus pulse flow can be achieved more easily with small d0 values. Nevertheless, small d0 values will also lead to more significant obstruction of the gas flow, thus resulting in the disturbance waves breaking up more easily. Another phenomenon that should be noted is that there is no pulse flow with packing H, but there is pulse flow with packing E. Comparing the geometric characteristics of these two packings, it can be seen that they differ in d0, d0/h, and l/h. The value of d0/h for packing H is larger than that for packing E, which contributes to the onset of pulse flow; therefore, the lack of pulse flow with packing H cannot be due to the difference in d0/h. The difference in d0 is significantly larger than that in l/h, and thus it can be considered that the large d0 value is primarily responsible for the lack of pulse flow with packing H. Based on these results, it can also be confirmed that a large d0 value is also responsible for the lack of pulse flow in packings A and I. Thus, it is clear that a small d0 value is important for the occurrence of pulse flow. In subsequent correlations, to describe the effect of d0 on the transition of the pulse flow, the ratio d0/W is defined, where W is the side length of the sieve plate. 3.4.5. Effect of the Sieve Plate Quantity. The difference in the sieve plate quantity (N) is expected to have a specific effect on the pulse flow inside the sieve plate packing. This effect can be captured from the variation in the pressure drop fluctuation and the probability density function (PDF). Figure 17 shows the variation in the instantaneous pressure drops and the corresponding PDFs at different N for packing D. As can be seen, as N increases, the amplitude of the pressure drop fluctuation increases significantly. Correspondingly, the PDF exhibits a single peak with a large amplitude at N = 8. As N increases, the amplitude of the PDF decreases while the pressure drop (ΔP) broadens. Furthermore, the PDF plot tends to show double peaks with very small amplitudes. This phenomenon indicates that as N increases, the intensity of the pulse flow becomes stronger. This is because the pulse flow is a dynamic transport process caused by the superposed enlarge-

upstream gas flow will be obstructed by this part of the pulse flow. Therefore, the pulses at the upper section of the packing will be dispersed first with increasing Gs, and the lower parts will then be dispersed successively until the pulse flow disappears entirely. 3.4. Effect of the Packing Geometric Characteristics on the Transition of the Pulse Flow Regime. 3.4.1. Effect of the Free Area Ratio. Figure 14 shows a comparison of the pulse flow scopes for packings D and E. The difference between these two packings is in the free area ratio (α). Therefore, Figure 14 can be used to explore the effect of α on the pulse flow regime transition. As can be seen, with decreasing α, the pulse flow regime becomes broader, indicating that a small α is more conductive to the occurrence of pulse flow. This result can be attributed to the fact that the liquid holdup increases as α decreases.13 A large liquid holdup contributes to the formation of disturbance waves, thus contributing to the broadening of the pulse flow scope. 3.4.2. Effect of the Installation Method for Two Adjacent Sieve Plates. Figure 15 shows a comparison of the pulse flow scopes for packings F and G. As can be seen, the lower limit of the pulse flow in packing F is significantly lower than that in packing G, while the upper limits are very similar. In addition to the difference in the free area ratio α, the installation method for adjacent sieve plates also differs in these two packings. Under forward installation, the impact of the gas stream on the next sieve plate and the effect of the abrupt change in the gas flow direction are significantly stronger than that under crossed installation. As a result, the disturbance of the gas flow on the liquid flow will be greater under forward installation than under crossed installation. Consequently, the onset of the pulse flow under forward installation shifts to a lower ReG than that under crossed installation. Similarly, because of the greater disturbance of the gas flow, liquid disturbance waves are more easily broken at large gas flow rates under the forward installation, and thus the ReG value corresponding to the pulse flow disappearance also shifts to a lower value. The change in the gas flow direction and the impact of the gas flow on the next plate are related to the secant of the turning angle, θ (see Figure 3c). For the forward installation (square distribution), the secant of θ can be calculated as follows: sec θ =

1+(

l 2 ) 2h

(3)

Therefore, the power function of 1 + [l/(2h)]2 can be used to describe the effect of the installation method on the transition of the pulse flow. For the crossed installation, only the exponent of 1 + [l/(2h)]2 is different. 3.4.3. Effects of the Relative Plate Spacing and the Relative Hole Spacing. Selecting d0 as the characteristic dimension, the effect of the plate spacing h can be described by the dimensionless parameter d0/h. Jiang et al.30 suggested that a larger relative plate spacing (d0/h) will lead to larger pressure drops. This occurs because a larger d0/h will lead to a more intense impact effect of the fluids on the next sieve plate.4 Accordingly, larger d0/h will lead to a more significant disturbance of the liquid flow, and thus will facilitate the onset of the pulse flow. However, the significant disturbance of the gas flow under larger d0/h also causes the disturbance L


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where m = −3.10. When this correlation is applied to crossed installation, only the parameter m has a different value. By fitting the experimental data of packing G, it finds m = −3.00. At the disappearance of the pulse flow, the effect of the gravity can be ignored, when compared to that of the inertia force. Therefore, the relevant dimensionless variables for the disappearance of pulse flow can be summarized as Ä É 2Ñ yz ij d d ÅÅÅ ij l yz ÑÑÑÑ 0 0 Å j Å j , , ÅÅ1 + jj zz ÑÑ, ReL zzzz ReG = f jjα , z j W h ÅÅÅ k 2h { ÑÑÑÖ (8) Ç { k

ment of the liquid disturbance waves. Thus, the greater the number of sieve plates, the more evident the superposition effect of the liquid disturbance waves will be. Figure 18 shows a comparison of the pulse flow scope between packings C and D (Figure 18a) and packings B and F (Figure 18b). Taking Figure 18a as an example, it can be seen that, compared to packing C, the pulse flow scope is broader in packing D. The parameters of packing C are N = 21, α = 0.093, l/h = 1.273, d0/h = 0.545, and d0/W = 0.030, while packing D has parameters of N = 24, α = 0.115, l/h = 1.333, d0/h = 0.571, and d0/W = 0.021. According to the above analysis, the pulse flow scope becomes narrower with increasing α. In addition, both the onset and disappearance boundaries of the pulse flow will shift to lower values as l/h and d0/h increase and d0/W decreases. Therefore, the broadening of the pulse flow scope in packing D can primarily attributed to the increase in N. As N increases, the pulses will be increasingly superposed and enlarged, and thus pulse flow will become easier to achieve. The same result can also be obtained from Figure 18b. 3.5. Correlations for Pulse Flow Regime Transition Boundary Lines. Although the effects of different factors on the transition of the pulse flow have been clarified, these effects are correlated to each other and are very complex, especially the effect of the plate quantity. In these experiments, there are two types of packings, in terms of the sieve plate quantity: one with 21 plates and the other with 24 plates. Considering that the packings with 24 plates have six specifications (packings D, E, F G, H, and I) and larger dimensions (closer to those of an industrial apparatus), correlations are presented for the packings with 24 plates. According to Section 3.4, the transition of the pulse flow is related to not only the geometric parameters of the plates, but also the installation method and the installation location (α, d0/h, d0/W, and 1 + [l/(2h)]2). In addition, at the onset of the pulse flow, the effect of the gravity cannot be ignored. Here, the liquid Froude number, FrL, is considered to account for this effect. Therefore, the relevant dimensionless variables for the onset of the pulse flow can be summarized as ÄÅ É 2Ñ ÑÑ jij d0 d0 ÅÅÅ zy i y l j z ReG = f jjjα , , , ÅÅÅ1 + jj zz ÑÑÑÑ, FrL , ReL zzzz j W h ÅÅÅ z k 2h { ÑÑÑÖ (4) Ç k {

Similar to eq 7, the correlation for the disappearance boundary line of pulse flow can be obtained as follows:

É ÄÅ ÉÑ ÅÄÅ −0.06 2 Ñk ÅÅ ÑÑ Å id y i l y ÑÑ i d y ReG = 2919.27 expÅÅÅÅ7.09jjjj 0 zzzz − 6.61α ÑÑÑÑ ÅÅÅÅ1 + jjj zzz ÑÑÑÑ jjjj 0 zzzz ÅÅÇ ÑÑÖ ÅÅÅÇ k 2h { ÑÑÑÖ k h { kW { 0.33 × [(1 − α)ReL ] (9)

where k = −3.55 for the forward installation, and k = −2.81 for the crossed installation. The test ranges of the parameters are as follows: 48.0 ≤ ReL ≤ 784.8, 0.001 ≤ FrL ≤ 0.068, 0.115 ≤ α ≤ 0.177, 0.021 ≤ d0/ W ≤ 0.034, 1.212 ≤ l/h ≤ 1.333, and 0.571 ≤ d0/h ≤ 0.606. Figure 19 shows a comparison of the predicted and experimental ReG for the pulse flow transition boundaries with packing D; the onset and disappearance ReG are calculated with eqs 7 and 9, respectively. It can be seen that the calculated values agree well with the experimental data. Similarly, the comparisons of the predicted and experimental ReG for packings E, F, and G can also be obtained, as shown in Figure S7 in the Supporting Information. The parity plot in Figure 20a shows a comparison between the calculated values (from eq 7) and the experimental data for the onset of the pulse flow; the average relative error is ∼15%. The ReG at the onset of the pulse flow are relatively low, and thus the discrepancies between the calculated results and the experimental data are relatively large. Figure 20b shows a comparison between the calculated values (from eq 9) and the experimental data for the disappearance of the pulse flow. The deviation of the calculated results from the experiments is ∼10%, indicating that the correlation provides good agreement. Figure 21 shows a comparison of the predicted and the experimental values for the transition boundaries of the pulse flow with (a) packing B and (b) packing C. The values of ReG for the onset of the pulse flow are calculated using eq 7 with m = −3.10, while those for the disappearance are calculated using eq 9 with k = −3.55. In agreement with the experimental results in Section 3.4, the correlations predict that, with increasing N, the pulse flow scope will become broader. Although the effect of plate quantity N is not included in the current correlations (more experiments are needed to correlate this effect), the above analysis, including the effect geometric characteristics of the packing on the transition of the pulse flow, has established a good basis for further study. Based on this study, further experiments with packings having different plate quantities will allow more general correlations to be developed, including the effect of the plate quantity. The predicted variation trends in the pulse flow transition boundaries, depending on the other packing characteristics, are presented in Figure 22. Figure 22a shows that the pulse flow scope becomes broader with decreasing α, indicating that a small α is more beneficial for the occurrence of pulse flow.

where FrL is the Froude number based on the liquid superficial velocity (uL), which is defined as FrL =

uL 2 , gd0

uL =

Ls ρL

(5)

ReG and ReL are the superficial gas and liquid Reynolds numbers, respectively, and they are defined as follows: ReG =

d0Gs , μG

ReL =

d0Ls μL

(6)

where ρL and μL are the liquid density and viscosity, respectively, and μG is the gas viscosity. For the forward installation, the correlation for the ReG of pulse flow onset can be obtained by fitting the experimental data of packings D, E, and F; that is, É −3.20 ÅÄÅ ÑÉÑ ÄÅÅÅ 2 Ñm ij d0 yz ÅÅ ÑÑ ÅÅ ij l yz ÑÑÑÑ ij d0 yz ReG = 523.16 expÅÅÅ39.03jjj zzz + 5α ÑÑÑ ÅÅ1 + jj zz ÑÑ jjj zzz ÅÅÇ ÑÑÖ ÅÅÅÇ k 2h { ÑÑÑÖ k h { kW { × (1 + ReL 0.03FrL 0.23)−5.61 (7)

M



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Figure 22b shows that both the onset and disappearance lines of the pulse flow shift to lower ReG when the installation method for adjacent sieve plates is changed from crossed installation to forward installation. This indicates that forward installation is more beneficial for the onset of the pulse flow, but it also makes the pulse flow disappear more easily. Figure 22c shows that both the onset and disappearance boundary lines of the pulse flow shift to lower ReG with decreasing d0/W, indicating that a small d0/W value is more beneficial for the onset of pulse flow, but it also causes the pulse flow to disappear more easily. Figures 22d and 22e show that the pulse flow transition boundaries shift to lower ReG with increasing d0/h and l/h, respectively, indicating that both large d0/h and l/h are more beneficial for the onset of pulse flow, but they also make the pulse flow disappear more easily. It is clear that the correlations can correctly predict the trends for the effects of the packing geometric characteristics of the packing on the transition boundaries of the pulse flow.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b00180.

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4. CONCLUSIONS Nine sets of packings were designed to investigate the pulse flow occurring when gas and liquid flow concurrently downward through the sieve plate packing. Through the systematic analysis of experimental data, the following conclusions can be obtained: • Through the observation of flow pattern and the analysis of the pressure fluctuation data, a method of variation coefficient (CV) was proposed to determine the onset and the disappearance points of the pulse flow. By this method, the upper and the lower boundary lines of the pulse flow regime for plate packings were successfully obtained, giving a clear map to show in what operation conditions the pulse flow begins and disappears. • Pulse flow is a dynamic transport process of the liquid disturbance waves. These liquid disturbance waves, resulting from the gas flow and gravity, will cause the flow to fluctuate locally. While traveling down the packed bed, these local fluctuations will be superposed and enlarged, and they will form a weak pulse flow at some upper location of the packing. Subsequently, these superposed local fluctuations will be enlarged to form a visible pulse flow. Therefore, the pulses are always observed most easily at the bottom section of the packing. • The effects of the packing geometric characteristics on the transition of pulse flow are complex and correlated to each other, among which the effects of the hole diameter and the plate quantity are most evident. With decreasing hole diameter, the blockage of the gas flow is enhanced and the pulse flow occurs more easily. As the plate quantity increases, the pulsing will be increasingly superposed and enlarged, and thus the strength of pulse flow will become stronger and the pulse flow scope will become broader. • The correlations for the boundary lines of pulse flow onset and disappearance were developed. The calculated values by the correlations for the upper and the lower boundary lines deviate from the experimental data by ∼15% and ∼10%, respectively. • To further investigate the pulse flow behaviors inside the packing, such as the position where the pulsing begins, the minimum plate quantity necessary for the occurrence of pulse flow, and so on, more experiments are required with packings of different plate quantities.

Pressure drop fluctuations at different Gs for packings A, B, and C (Figure S1); PDFs of the pressure fluctuations at different Gs for packings A, B, and C (Figure S2); pressure drop fluctuations at different N for packings A, B, and C (Figure S3); PDFs of the pressure fluctuations at different N for packings A, B, and C (Figure S4); variation of CV, as a function of Gs for packings E, F, and G (Figure S5); variation of CV, as a function of Gs for packing I (Figure S6); and comparison of the experimental and the predicted ReG for the pulse flow regime transition boundaries of packings E, F, and G (Figure S7) (PDF) Pulse flow in packings B and C (ZIP)

AUTHOR INFORMATION

Corresponding Author

*Tel.: 028-85408126. E-mail: [email protected]. ORCID

Weixing Huang: 0000-0001-7861-7498 Notes

The authors declare no competing financial interest.

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NOMENCLATURE

Latin Symbols

Gs = liquid superficial mass flux (kg/m2/s) Ls = gas superficial mass flux (kg/m2/s) ΔP = pressure drop (Pa) CV = coefficient of variation t = thickness of the orifice plate (mm) d0 = hole diameter (mm) h = spacing between two adjacent sieve plates (mm) l = distance between two adjacent orifices (mm) W = side length of the sieve plate (mm) N = sieve plate quantity ReG = gas superficial Reynolds number ReL = liquid superficial Reynolds number FrL = liquid Froude number uL = liquid superficial velocity (m/s) Greek Symbols

σ = standard deviation α = free area ratio ρL = liquid phase density (kg/m3) μG = gas phase viscosity (Pa s) μL = liquid phase viscosity (Pa s)

Subscripts

s = superficial L = liquid G = gas

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Experimental Investigation on the Pulse Flow Regime Transition of

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