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Ind. Eng. Chem. Res. 2005, 44, 6406-6413
Trickle-Bed Reactors: Porosity-Induced Hysteresis† Rabindranath Maiti, Rajesh Khanna, and K. D. P. Nigam* Department of Chemical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India
The role played by the porous nature of the packing material in the hysteretic behavior of tricklebed reactors (TBRs) is presented based on a new framework that incorporates the current understanding of fluid flow in TBRs, concepts of participating and nonparticipating particles, and principles of liquid spreading on porous and nonporous substrates. A method to characterize the extent of hysteresis is also presented. The framework is applied to reported experiments (Ravindra, P. V.; Rao, D. P.; Rao, M. S. Ind. Eng. Chem. Res. 1997, 36, 5133-45) and is shown to be able to explain the difference in the hysteretic behavior of porous packings and of nonporous packings (comparable particle size) under varying startup conditions and numbers of cycles. In addition to providing a basis for the general framework within which hysteresis in TBRs should be studied, it provides explanations to specific questions such as (1) the existence of hysteresis in porous packings and its absence in nonporous packings under similar conditions and (2) when to expect open-loop or closed-loop hystersis. It is also a good illustration of how a framework, which is based on pore levels, can explain reactor level complex phenomena like hysteresis. It is expected that this work will enhance our understanding about the variations of the hysteretic behavior as well as hydrodynamics in TBR. In the absence of a data bank in the literature, the proposed framework has been validated with available limited data. 1. Introduction A trickle-bed reactor (TBR) is a reactor in which a gas and a liquid flow cocurrently downward over solid packings. Its use is widespread in petroleum and chemical industries.2,3 The performance of a TBR depends mainly on two hydrodynamic parameters, viz., pressure drop across the reactor and liquid holdup inside the reactor. The performance of the reactor is mostly predicted by using experimentally developed empirical/semiempirical correlations for these parameters. Recently, a more fundamental approach was proposed to predict hydrodynamic parameters such as pressure drop, liquid holdup, and wetting efficiency considering gas-liquid-particle interaction and the tortuosity factor.4,5 These developments are chronicled in reviews of several authors.2,6,7,8-12 Predictions of these correlations and the actual performance of the TBR differ significantly in many cases. One of the major contributors to these differences has been the existence of hysteresis in pressure drop and liquid holdup at the same liquid and gas flow rates in the TBR.1,13-19 It has been reported that this hysteresis depends on three factors, viz., startup conditions, the mode of operation, and the type of packing material.1,17 The startup conditions refer to the state of the system with respect to the initial prewetting or nonprewetting of the solid packing by the liquid. The mode of operation refers to how the desired flow has been attained, whether by increasing the flow of fluid from a low value or decreasing it from a high value. The type of packing material refers to it being porous or nonporous. Among all of these studies, which are summarized in Table 1, only one study1 has looked at the influence of all three control parameters. † Dedicated to Professor Mike P. Dudukovic on his 60th birthday. * To whom correspondence should be addressed. Tel.: (011) 26591020. Fax: (011) 26591020. E-mail:
[email protected].
In all of these studies, hysteresis has been attributed to the difference between an advancing and receding contact angle in rivulet and film flow of liquid over the solid packing. The porous/nonporous nature of the packing, though being taken as one of the control parameters for study, has not been invoked to explain the observed hysteresis. This omission needs a relook in light of recent work by Khanna and Nigam20 and Maiti et al.,21 whereby porosity is shown to play a major role in the spreading and retraction of liquid. It is, therefore, expected that the porosity of the packing material is likely to play a major role in the hysteretic behavior of the TBR. In the present work, an attempt has been made to examine this role based on the framework proposed by Khanna and Nigam20 and the subsequent analysis of Maiti et al.21 2. Hysteresis in the TBR: Experimental Observations Most of the reported hysteresis studies have looked at a limited number of variables that affect the hysteresis especially in cycles following the initial cycle. Only Ravindra et al.1 have reported a hysteresis study, which includes all of the major controlling parameters such as porous/nonporous and wet/dry conditions of the bed. They studied the hysteresis in the TBR where water, the liquid phase, and air, the gas phase, flowed cocurrently downward through a packed bed of glass beads (nonporous) and alumina particles (porous) in a rectangular glass frame. The liquid and gas were distributed through a uniform inlet distributor at the top. The flow rate was in the trickle-flow regime as per the model of Larachi et al.22 The pressure drop across the bed was measured to examine the hysteretic behavior of the bed. Two types of startup procedures were used. In one, water was introduced in a packed bed of dry particles
10.1021/ie049347r CCC: $30.25 © 2005 American Chemical Society Published on Web 06/02/2005
Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 6407 Table 1. Studies on the Hysteresis in a TBR author(s)
system studied
Kan and Greenfield13,14
air-water, wet bed, P ) 1 atm
Levec et al.15,16
air-water, wet bed, P ) 1 atm
Christen et al.17
air-water, wet bed, P ) 1 atm
Lutran et al.19
water, water + ethanol; dry and wet beds; P ) 1 atm air-water; dry and wet beds; P ) 1 atm
Ravindra et al.1
Lazzaroni et al.18 Ravindra et al.1
air-water; dry and wet beds; P ) 1 atm air-water; dry and wet beds; P ) 1 atm
bed properties Studies with Nonporous Particles acrylic column; diameter/height (cm), 2.5/45-80; packing type/diameter (mm), spherical glass/0.5, 1.0, 1.8; D/dp, 14-50 plexiglas column; diameter/height (cm): 17.2/130; packing type/diameter (mm), spherical glass/3, 6; D/dp, 28-57 plexiglas column; diameter/height (cm), 5.1 × 45.7/183; packing type/diameter (mm), glass beads/3 (nominal diameter); D/dp, 107 plexiglas; diameter/height (cm), 6 × 6.03/30.48; packing type/diameter (mm), glass sphere/3, 6; D/dp, 13-26 plexiglas column; diameter/height (cm), 6 × 8/20; packing type/diameter (mm), glass beads/1.6, 3.5, 5.7; D/dp, 16-55 Studies with Porous Particles slass column; diameter/height (cm), 3.05/50; packing type/diameter (mm), γ-alumina/3.0; D/dp, 10.1 plexiglas column; diameter/height (cm), 6.0 × 8.0/20; packing diameter (mm) [particle], 1.9 (γ), 3.5 (γ), 6.3 (R); D/dp, 16-55
at a low flow rate, and then it was increased to the desired flow rate. Then air flow was initiated. This state of the bed was referred to as a dry bed. In the other, water was introduced at a low flow rate and allowed to fill the bed by closing of the outlets. Once the water flow reached the top of the packing, the water flow was set to the desired value and then outlets were gradually opened to drain the excess liquid. Then air flow was initiated, and the state of the bed was referred to as a wet bed. In each type of bed, the liquid flow rate was increased gradually step by step to a higher value. In each step, the pressure drop was measured after steady state had been reached. The cycle was completed by decreasing the liquid flow stepwise to the initial value. Then, without draining the liquid from the bed, subsequent cycles were studied and parameters were measured. The major observations were classified according to the two control parameters of the experiment, viz., dry/wet bed and porous/nonporous particle. Because comprehensive data from this study are available only with 3.5 mm particle size, it is chosen for the present analysis. To present the experimental observation in a more relevant manner, a method of estimating the extent of hysteresis is formulated. The extent of hysteresis can be characterized by the average pressure drop difference between the increasing and decreasing flow rate branches or paths of any given cycle. This has been estimated by measuring the area of the pressure drop loop from the figures (Figure 1, reproduced from Figures 18 and 20 of Ravindra et al.1). No normalization is required because the range of flow rates is the same for all cases. 2.1. Nonporous Particles. Figure 1 presents the hysteretic behavior of the nonporous glass beads for both wet and dry beds. In both cases, the first cycle started with a very low liquid mass flow rate of about 0.3 kg/ m2‚s, which was gradually increased (following path 1-i) to a much higher value of about 5.0 kg/m2‚s. The first cycle was completed by gradually decreasing the liquid flow rate to the starting value (following path 1-d). The
parameter studied ∆P, eL
∆P, eL ∆P, eL
flow features, X-ray tomography ∆P, exit liquid distribution
∆P, eL, η ∆P, exit liquid distribution
subsequent cycles, e.g., second (path 2-i f 2-d) and third (path 3-i f 3-d), also operated between these ranges of flow rates. In the case of a dry bed, the pressure drop in the beginning of the first cycle was very low (∼1.0 cmwc). As the liquid flow rate was gradually increased (following path 1-i), the pressure drop also increased and reached a value of about 2.0 cmwc at the end of the increasing liquid flow branch (∼5.0 kg/m2‚s). During the decreasing branch (path 1-d), the pressure drop decreased only marginally, thus exhibiting a pronounced hysteresis (∼291 × 10-2 cmwc‚kg/m2‚s by our characterization scheme). The first cycle did not close because the pressure drop at the end was significantly higher than that at the beginning of the cycle. No appreciable hysteresis was observed in the subsequent cycles (paths 2-i f 2-d and 3-i f 3-d). In the case of a wet bed, the pressure drop in the beginning of the first cycle was much higher than that
Figure 1. Hysteresis loops with packing sizes of 3.5 mm glass beads and 3.5 mm alumina extrudates. G ) 0.05 kg/m2‚s.
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Table 2. Hysteresis in the Pressure Drop: Deviation in the Starting Point in the First and Subsequent Cycles dry first cycle second cycle onward
hysteresis (cmwc‚kg/m2‚s) end point shifted from the starting point hysteresis (cmwc‚kg/m2‚s) deviation in the end point pressure drop variation (cmwc) in the flow range
in the case of a dry bed (3.2 cmwc for a wet bed and 1.0 cmwc for a dry bed). As the liquid flow was gradually increased (path 1-i), the pressure drop also increased and reached a value of 6.5 cmwc, which is again significantly higher than the corresponding value of 2 cmwc for a dry bed. During the decreasing branch (path 1-d), the pressure drop decreased along the path 1-d, with the higher pressure drop exhibiting a pronounced hysteresis (∼153 × 10-2 cmwc‚kg/m2‚s by our characterization). Unlike the case with the dry bed, the end point of the loop closes to the starting value. In the subsequent cycles (paths 2-i f 2-d and 3-i f 3-d), significant closed-loop hysteresis (∼91 × 10-2 cmwc‚kg/ m2‚s by our characterization) was observed. The pressure drop variation in the operating flow range of the liquid was 3.2-6.5 cmwc, which is much higher than that of a dry bed in the same flow range. 2.2. Porous Particles. Figure 1 presents the hysteretic behavior of the porous alumina particles for both wet and dry beds. In both cases, the first cycle started with a very low liquid flow of about 0.3 kg/m2‚s and was gradually increased (following path 1-i) to a higher value of about 5.0 kg/m2‚s, the same as with a nonporous particle. The flow rate was again gradually decreased (following path 1-d) to the starting flow rate in the decreasing branch. The subsequent cycles, e.g., second (path 2-i f 2-d) and third (path 3-i f 3-d), also operated between these ranges of flow rates. In the case of a dry bed, the pressure drop in the beginning of the first cycle was very low (∼1.7 cmwc). As the liquid flow rate was gradually increased (path 1-i), the pressure drop also increased and reached a value of about 3.8 cmwc at the end of the increasing liquid flow branch (∼5.0 kg/m2‚s). During the decreasing branch (path 1-d), the pressure drop decreased slowly and consistently maintained a higher value than that of path 1-i, exhibiting a pronounced hysteresis (∼240 × 10-2 cmwc‚kg/m2‚s by our characterization scheme; the loop does not close). At the end of the first cycle, the pressure drop was significantly higher than that in the beginning of the cycle; thus, the hysteresis loop did not close. In subsequent cycles of operation, an appreciable amount of closed hysteresis was found (79 × 10-2 cmwc‚kg/m2‚s). The pressure drop variation in the operating flow range of the liquid was 2.0-3.8 cmwc. The maximum deviation in the pressure drop between two paths was 0.3 cmwc. In the case of a wet bed, the pressure drop in the beginning of the first cycle was marginally higher than that in the case of a dry bed (2.2 cmwc as compared to 2 cmwc). As the liquid flow was gradually increased (path 1-i), the pressure drop also increased and reached a value of 4.5 cmwc, which is again slightly higher than the corresponding value of 3.8 cmwc for the dry case. Again, during the decreasing flow (path 1-d), the pressure showed a pronounced hysteresis (∼152 × 10-2 cmwc‚kg/m2‚s by our characterization). Unlike the case with the dry bed, the hysteresis loop was closed.
wet
nonporous
porous
nonporous
porous
291 × 10-2 yes 0 no 2.0-2.1
240 × 10-2 yes (negligible) 79 × 10-2 no 2.0-3.8
153 × 10-2 no 91 × 10-2 no 3.2-6.5
152 × 10-2 no 152 × 10-2 no 2.2-4.5
In subsequent cycles, the increasing branch (path 2-i f 3-i) follows the path of the first cycle (path 1-i), whereas the decreasing branch (path 2-d f 3-d) also follows the decreasing path of the first cycle (path 1-d); i.e., all of the cycles are identical. The closed-loop hysteresis in these subsequent cycles remains the same as that of the first cycle (∼152 × 10-2 cmwc‚kg/m2‚s by our characterization method). The pressure drop variation was 2.2-4.5 cmwc in the operating flow range of the liquid, which is not much different from that found in a nonprewetted bed. The maximum deviation in the pressure drop between paths was 0.63 cmwc, which is much higher than those observed with any other control parameter. The relevant features of the observations have been compiled in Table 2 to facilitate the comparison. For dry beds, both porous and nonporous particles show significant open-loop hysteresis in the first cycle. Nonporous particles do not show any hysteresis in subsequent cycles. In contrast, reduced but identical closed-loop hysteresis is shown by porous particles in subsequent cycles. Similarly for wet beds, significant (but less than that for dry beds) hysteresis is shown by both types of particles, with porous particles showing closed-loop hysteresis and nonporous showing open-loop hysteresis. In subsequent cycles, both particles showed significant closed-loop hysteresis. Here nonporous particles showed a reduced hysteresis, whereas no change was found in porous particles. 3. Major Anomalies and Issues It is now clear that significant differences exist between the hysteretic behavior of porous and nonporous particles. We first try to explain these observations and underlying differences within the framework of current perceptions of fluid flow in the TBR. This exercise will reveal major shortcomings, which will then be fulfilled using the framework proposed by Khanna and Nigam20 and the subsequent analysis of Maiti et al.21 3.1. Dry Bed: Current Perceptions and Shortcomings. The general perception is that, starting from a zero liquid flow rate in a dry bed, as the liquid flow is commenced, the liquid flows in rivulets or channels. The cross-sectional area or number of particles covered in a channel is small. At this stage, the pressure drop is equivalent to the pressure drop in the dry bed and the liquid flows as rivulets. With increasing liquid flow, the rivulet will grow in size; enlargement of existing channels or the formation of additional channels also takes place. Therefore, the pressure drop increases as a result of lower effective porosity and larger liquid-solid and liquid-gas interactions. Also, it is understood that, with an increase in the flow rate, a three-phase contact line has to advance over the dry surface and will spread less because of a higher contact angle; i.e., rivulet-type flow persists. The cross-sectional area of the channel remains unchanged even as the flow rate is decreased. The liquid
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retracts from the peripheral regions of the channel, leaving a thin film of liquid over the packings and gas flowing in the resultant voids. The central core of the channel remains in filament mode. Even though the actual liquid coverage of the solid remains about the same, the effective porosity is higher and the gas-liquid interfacial area becomes more because of the simultaneous presence of a central core and a surrounding film in place of a liquid filament. This combined effect of increased solid-liquid and gas-liquid interactions more than offsets the decrease due to increased voidage. This results in a higher pressure drop during the decreasing mode than during the increasing mode at the same flow rate and, consequently, a higher pressure drop toward the end of the cycle. Thus, significant hysteresis is expected for both porous and nonporous particles in the first cycle. The experimental observations also confirm this (Table 2). In subsequent cycles, the liquid will spread over the film already formed over the wetted particles and the three-phase contact line will also retract over the wetted surface, thus bringing the values of advancing and receding contact angles closer to each other. Thus, the voidage, gas-liquid, and solid-liquid interactions remain the same for increasing and decreasing branches. It is, therefore, expected that there should be negligible or no hysteresis in the pressure drop in subsequent cycles. This is confirmed in the case of the nonporous particles (Figure 1 and Table 2) but is in contrast to the behavior shown by the porous particles. An appreciable amount of hysteresis is shown by the porous particles in subsequent cycles, as shown in Figure 1 and Table 2. To reconcile these anomalies and get more focused, one should try to find answers to the following question: 1. How does one account for closed-loop hysteresis in subsequent cycles for the porous particle? 3.2. Wet Bed: Current Perceptions and Anomalies. In a wet bed, liquid pockets and a thin layer of film exist over the packing at the start of the first cycle. Thus, increased gas-liquid and solid-liquid interactions and a lower effective voidage will contribute to the increase in the pressure drop. Even at low liquid flow, more pressure drop is expected as compared to the dry bed. This is also observed experimentally (Figure 1). It should be noted that a wet bed would become similar to a dry bed of subsequent cycles. Therefore, along the lines of the argument presented for subsequent cycles for the dry case (section 3.1), hysteresis is not expected to be present in any of the cycles in the wet bed including the first one. However, both types of particles showed large amounts of hysteresis in the pressure drop (Figure 1 and Table 2) in the first cycle. Moreover, porous particles showed closed-loop hysteresis in the first cycle itself, in contrast to the nonporous particles. A large amount of constant closed-loop hysteresis with both types of particles is shown in subsequent cycles (Figure 1 and Table 2). Once again, the observations do not conform to the expectations, and to reconcile this, one needs to find answers to these additional questions: 2. Why should there be hysteresis (closed loop for porous particles and open loop for nonporous particles) in a wet bed for both porous and nonporous particles during the first cycle? 3. Why should there be constant closed-loop hysteresis for porous particles in the first cycle as well as in subsequent cycles?
Figure 2. Liquid flow in proposed favorable clusters: (a and a1) when flow started; (b and b1) at increased flow; (c and c1) decreased back to the initial flow.
4. Why should there be reduced hysteresis in subsequent cycles for nonporous particles? 4. Verifications and Resolution In this section, we try to reconcile the anomalies presented in the earlier section by using the framework proposed by Khanna and Nigam20 and the subsequent analysis of Maiti et al.21 First the current perceptions are enhanced by including components from the two studies, and then they will be used to resolve the various questions that have been raised in the earlier section. The general perception is that in a wet bed liquid scatters to form liquid pockets or wet regions at locations with favorable geometry (due to several particles in close contact19 or due to variation in the porosity distribution in the bed).23,24 This can be applied to a dry bed also, because with the introduction of flow, a liquid flow pattern is established through such favorable particle clusters or channels (parts a and a1 of Figure 2). With an increase of the flow, liquid spreads laterally, covering more particles in the periphery of the core channel; i.e., the channel diameter increases as seen in parts a and b of Figure 2 (also in parts a1 and b1 of Figure 2). During decreasing flow, the liquid-filled core or filaments retract, leaving the surrounding region with the film (parts c and c1 of Figure 2). Upon a further decrease in the flow, a stage will come when peripheral particles are dried up and the core of the channel reduces to film flow. Thus, peripheral particles of the channel are the major contributors to the hysteretic behavior. We will now focus on the behavior of these peripheral particles during the spreading and retraction of flow in increasing and decreasing flow modes to explain the major differences between porous and nonporous particles. Starting with a dry bed, the liquid will start to flow as a rivulet or film in the channel. With increasing flow, the rivulet will grow in size; enlargement of existing channels or the formation of additional channels takes place, covering more particles, or the thickness of the rivulets increases as per general perception. Liquid will spread more on a porous particle because of the combined effect of wettability and the capillary action of the pore20,21 and film flow will be there in peripheral particles. In contrast, the liquid will spread less on
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nonporous solids and mostly rivulet flow will dominate. During decreasing flow, liquid retracts over a previously wetted surface. For a nonporous surface, this retraction is contact angle guided, i.e., film flow due to a lower contact angle. For a porous surface, it will take a completely different route, as outlined in the model of Khanna and Nigam.20 A combination of the following scenarios is likely to happen, viz., (1) the retracting liquid is held up because of the pinning force provided by the pores, which will result in greater liquid coverage and higher pressure drops, (2) the retracting film breaks free of this pinning either by rupture or by drying up of the gas flow, which will result in lower liquid coverage and lower pressure drop. A combination of these antagonistic processes can give rise to many interesting hysteresis scenarios including a staircase pattern first shown by Khanna and Nigam.20 Eventually, with a decrease in the liquid flow rate, a state may be reached when the liquid supply is not enough to maintain all of the thin film in a channel and hence the film ruptures as a result of the presence of a pore as a nonhomogeneity25 and partly as a result of the presence of gas flow. Thus, dry particles appear. For nonporous particles at very low liquid flow rate, fewer particles may become dry as a result of the presence of gas flow. It should be noted that the extra nonhomogeneity present in porous particles is absent in them. This dry section may be at the particle in the periphery of the channel or part of the surface in a particle; we will call them participating particles or seasoned particles, as discussed earlier. We will now use this enhanced framework to analyze the present situation. 4.1. Dry Bed. After the first cycle is over, a larger number of dry particles or seasoned particles will reappear in channels of the porous particle because of rupture of the film than in the nonporous particle. In the subsequent cycles, the liquid will spread and retract over these particles in addition to the nonparticipating particles and constant closed-loop hysteresis will be observed. Because the participating particles remain the same, the descending branch of these cycles is expected to be the same as that of the first cycle. In contrast, the ascending branch of the first cycle is different because the participating particles are identified only after the first retraction. This is confirmed by the experimental observations also (Figure 1). Because of the presence of a much smaller number of drier or seasoned particles, the hysteresis effect is not pronounced in the nonporous particle. Also, the bed is likely to come back to the same state as the one after the end of the first cycle because of the loss of the residual film. This implies that the hysteresis loop should close. This answers our first question; i.e., how does one account for closed-loop hysteresis in subsequent cycles for a porous particle? 4.1.1. Explanation of Differences in the Hysteresis Behavior of the Smaller Particles. Ravindra et al.1 also studied the hysteresis behavior of smaller size porous and nonporous particles (Figure 3, reproduced from Figures 18 and 20 of Ravindra et al.1). The major observations are classified according to the two control parameters of the experiment, viz., dry/wet bed and porous/nonporous particle (Table 3). It may be considered that, in the bed of smaller size particle, the numbers of particles are more, so the chances of the number of favorable clusters also will be more compared to larger size particles. On the basis of the above intuitive arguments, we would like to examine
Figure 3. Hysteresis loops with packing sizes of 1.6 mm glass beads and 1.9 mm alumina extrudates. G ) 0.05 kg/m2‚s.
the hysteresis of smaller size (1.6-1.9 mm) porous and nonporous particles in a dry bed. First Cycle. (a) Porous vs Nonporous (Comparable Particle Size). In the first cycle starting with a dry bed, the pressure drop path will follow paths 1-i and 1-d for both porous and nonporous particles (Figure 3), which is similar to that in the case of larger particles. In the case of porous particles, there will be enhanced liquid spreading during the increasing mode.21 In the decreasing mode, there will be a pinning effect of pores and film rupturing. Both of these factors will give less hysteresis in porous particles compared to nonporous particles. This is also observed from experimental results, as shown in Table 3 (504 × 10-2 cmwc‚kg/m2‚s for nonporous particles as compared to 266 × 10-2 cmwc‚kg/m2‚s for porous particles). (b) 1.6-1.9 mm vs 3.5 mm Particle Size. Again, because the bed consists of smaller particle size, the number of favorable clusters and therefore participating particles will be more. So, more hysteresis is expected for smaller size particles compared to larger size particles. This is observed from Tables 2 and 3 for nonporous particles (504 × 10-2 cmwc‚kg/m2‚s for a 1.6 mm particle compared to 291 × 10-2 cmwc‚kg/m2‚s for a 3.5 mm particle) as well as for porous particles (266 × 10-2 cmwc‚kg/m2‚s for a 1.9 mm particle compared to 216 × 10-2 cmwc‚kg/m2‚s for a 3.5 mm particle). Second and Third Subsequent Cycles. (a) Porous vs Nonporous (Comparable Particle Size). After the first cycle is over, a larger number of dry particles or seasoned particles will reappear in channels of the porous particles because of rupture of the film than in the nonporous particles. In the subsequent cycles, the liquid will spread and retract over these particles, in addition to the nonparticipating particles, and a constant closed-loop hysteresis will be observed. Because of the presence of a smaller number of participating particles (identified after the first cycle) in the nonporous particles, the hysteresis effect is less, as shown in Table 3 (184 × 10-2 cmwc‚kg/m2‚s for nonporous particles compared to 216 × 10-2 cmwc‚kg/m2‚s for porous particles). Because the participating particles remain the same, the descending branch of these cycles is expected to be the same as that of the first cycle. In contrast, the ascending branch of the first cycle is different because the participating particles are identified only after the first retraction. This is confirmed by
Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 6411 Table 3. Hysteresis in the Pressure Drop: Deviation in the Starting Point in the First and Subsequent Cycles (dp ) 1.6-1.9 mm) dry first cycle second cycle onward
hysteresis (cmwc‚kg/m2‚s) end point shifted from the starting point hysteresis (cmwc‚kg/m2‚s) deviation in the end point pressure drop variation (cmwc) in the flow range
the experimental observations for both porous and nonporous particles (Figure 3). (b) 1.6-1.9 mm vs 3.5 mm Particle Size. In the case of larger size particles, numbers of identified particles, after the first cycle, were small because of the lower number of favorable clusters. So, hysteresis was found to be lower with increasing particle size, as shown in Tables 2 and 3 (porous, 216 × 10-2 cmwc‚kg/m2‚s for a 1.9 mm particle compared to 79 × 10-2 cmwc‚kg/m2‚s for a 3.5 mm particle; nonporous, 184 × 10-2 cmwc‚kg/ m2‚s for a 1.6 mm particle compared to negligible for a 3.5 mm particle). Because of the presence of close-loop hysteresis for a 1.6 mm particle compared to negligible close-loop hysteresis for a 3.5 mm nonporous particle, the ascending line 2,3-i and descending line 2,3-d (Figure 3) were different. 4.1.2. Explanation of Hysteresis at Different Gas Flow Rates. Lazzaroni et al.18 studied the hysteretic behavior of porous 3 mm γ-alumina particles with an air-water system at higher gas flow rate (G ) 0.08 kg/ m2‚s) in a trickle flow regime. Starting from a dried bed condition and after setting of the gas flow rate at the desired value, the liquid flow rate was gradually increased and then decreased, measuring the pressure drop as shown in Figure 4 (reproduced from Figure 1 of Lazzaroni et al.18). Path 1 was obtained, starting from a dried bed, by increasing the liquid flow rate. When the liquid flow was reduced after reaching a higher liquid flow Lmax1, higher pressure drops were observed in Path 2 compared to Path 1. When the liquid flow rate was increased again from this end point of the first cycle to a new higher liquid flow rate Lmax2, the pressure drop line initially followed Path 2 until Lmax1, and then it moved along Path 1. After reaching the point Lmax2, the pressure drop followed Path 3 with decreasing liquid flow the same way as with Lmax1. When the liquid flow rate was increased again from this end point of the second cycle, the pressure drop line followed Path 3 until Lmax2, and then it moved along Path 1, as shown in
Figure 4. Hysteresis loops with packing sizes of 3.0 mm alumina extrudates. G ) 0.08 kg/m2‚s.
wet
nonporous
porous
nonporous
porous
504 × 10-2 yes 184 × 10-2 no 4.5-8.0
266 × 10-2 yes (negligible) 216 × 10-2 no 2.5-7.0
634 × 10-2 no 634 × 10-2 no 6.0-16.0
682 × 10-2 no 661 × 10-2 no 3.5-10.2
Figure 4. The pressure drop for decreasing liquid flow rate followed Path 4 the same way as with the operating flow range Lmax1-Lmax2. The results show that within the operating flow range Lmax the bed shows open-loop hysteresis for the first cycle and negligible or no hysteresis for subsequent cycles. Now we attempt to explain the above phenomena within the framework proposed in section 4. Starting with a dry bed, the liquid will start to flow as a rivulet in the channel, as discussed in section 4. With increasing flow, the rivulet will grow in size, and enlargement of existing channels or the formation of additional channels takes place, covering more particles, or the thickness of the rivulets increases. During decreasing flow, the liquid retracts over the previously wetted surface, as outlined in section 4. The retracting liquid is held up because of a pinning force provided by the pores that will result in greater liquid coverage and higher pressure drops. At a lower liquid flow rate, the retracting film breaks free of the pinning (participating particles, as discussed in section 4) either by rupture or by drying up of the gas flow. At the end of the first cycle, a much smaller number of participating particles are identified because of the presence of a smaller number of favorable clusters and this shows the existence of open-loop hysteresis. In the subsequent cycles, the liquid will spread and retract over these participating particles and a constant closed-loop hysteresis is expected. Because of the presence of a much smaller number of drier or seasoned particles, the hysteresis effect is not pronounced in subsequent cycles. When the liquid flow was increased from the end of the first cycle or subsequent cycles, the pressure drop followed Path 2 and then Path 1 up to Lmax2. At this higher liquid flow rate, larger numbers of clusters were activated. Because of higher liquid coverage in decreasing flow, the return path will follow Path 3. Similarly, an open-loop hystresis behavior was observed with the next maximum liquid flow Lmax3 with activation of some more favorable clusters, and in the same way the pressure drop will follow Path 4. The variations in hysteresis in the first cycle for all of the operating liquid flow rates are comparable to the observation of Ravindra et al.1 for a 3.5 mm alumina particle. According to our proposed framework, some amount of hysteresis behavior should have been observed in the subsequent cycles also. However, the experimental data of Lazzaroni et al.18 does not confirm this. The probable reason for this discrepancy may be as follows. If we look closely, it is observed that the absolute pressure drop values for all of the data of Lazzaroni et al.18 are lower as compared to data of Ravindra et al. under the same liquid flow rate even though the gas flux is high. Lazzaroni’s data correspond to a D/dp ratio of 10.1 only, whereas it is reported in the literature that in order to neglect the effect of wall flow the value of the D/dp ratio should be g25.12 Therefore, it is expected
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that the experimental data are under the influence of wall flow. Because of this wall-flow effect, the number of favorable clusters (as discussed in section 4) activated through flow initiation is lower, even at high liquid flux (Lmax3, Figure 4). This lower number of favorable clusters identifies a much lower number of seasoned particles in the subsequent cycle, giving negligible or no hysteresis. 4.2. Wet Bed. Even though the bed is wet, there is a possibility of some dry particles for nonporous particles.15 These may be much less for porous particles because of enhanced liquid spreading.21 There will be a much larger number of favorable clusters or channels that will be generated in a wet bed than in a dry bed because the liquid has spread more in this case by way of prewetting. As stated earlier, each channel will consist of some nonparticipating and some participating particles. The total number of such participating particles will be much larger here as compared to a dry bed (identified during the descending branch of the first cycle) because of the larger number of favorable clusters. During the first cycle, these participating particles justify the existence of hysteresis even after prewetting of the bed. In nonporous particles, some of the dry particles that are present will be covered by liquid and may not be identified as participating particles during the descending branch. Thus, the hysteresis will be open loop for nonporous particles during the first cycle. It should be noted that hysteresis is expected to be closed loop for porous particles because these dry portions are expected to be much smaller because of enhanced spreading and the participating particles remain the same during the ascending and descending branches of all cycles. This answers our second and third questions. For nonporous particles, the ascending branch of the first cycle is affected by the presence of dry portions. Because these will not contribute to the hysteresis in subsequent cycles, the extent of hysteresis is expected to be less during subsequent cycles than during the first cycle. This answers our fourth question. It is also observed from Figure 1 and Table 2 that the difference in the pressure drop data for a wet bed condition at maximum operating liquid flow rate (L ) 5.0 kg/m2‚s) for nonporous glass beads is much higher (4.4 cmwc) compared to that for porous alumina particles (0.7 cmwc). As stated earlier in section 4, the liquid spreads more under a dry bed condition on porous alumina particles because of the combined effect of wettability and capillary action. So, a larger number of particles get wetted, which is otherwise obtained by wetting of the bed. Because the enhanced liquid spreading due to pores is absent with nonporous particles, the difference in wetting persists between wet and dry beds, giving a much larger difference in the pressure drop. 4.2.1. Explanation of Differences in the Hysteresis Behavior of the Smaller Particles. Hysteresis data for smaller particles in wet bed conditions were reproduced from the study of Ravindra et al.1 (Figure 3 and Table 3). It could be seen from Figure 3 and Table 3 that there are significant differences in the hysteresis behavior for smaller size porous/nonporous particles in a wet bed condition also. Because earlier it may be considered that, in the bed of a smaller size particle, the number of particles is greater, chances of the number of favorable clusters will also be more compared to larger size particles. On the basis of the above intuitive arguments, the hysteresis behaviors of smaller size
(1.6-1.9 mm) porous and nonporous particles in a wet bed condition were examined. First Cycle. (a) Porous vs Nonporous (Comparable Particle Size). Even though the bed is wet, there is a possibility of some dry particles for nonporous particles.15 The number of dry particles will be much smaller for porous particles because of enhanced spreading.21 There will be a much larger number of favorable clusters or channels that will be generated in a wet bed compared to a dry bed because the liquid has spread more in this case by way of prewetting. As stated earlier, each channel will consist of some nonparticipating and some participating particles. During the first cycle of operation, these participating particles justify the existence of hysteresis even after prewetting of the bed. Because participating particles are larger in number, hysteresis in porous particles will be higher compared to that of nonporous particles. This is also observed in Table 3 (682 × 10-2 cmwc‚kg/m2‚s for a porous particle compared to 634 × 10-2 cmwc‚kg/m2‚s for a nonporous particle). The small difference in values is due to different particle sizes. The value of 682 × 10-2 cmwc‚ kg/m2‚s was expected to be more had the size been 1.6 mm instead of the present 1.9 mm for the porous particle. Because the total number of favorable clusters or participating particles is much higher compared to that of the dry bed, hysteresis will be much higher compared to that of the dry bed for both types of particles. This is also observed from Table 3. It is to be remembered that hysteresis of the wet bed should be compared with hystersis of the dry bed after the first cycle because these participating particles are identified after wetting of favorable clusters. (b) 1.6-1.9 mm vs 3.5 mm Particle Size. As stated earlier, because of the smaller size of the particle, the number of favorable clusters is much higher compared to that of larger particles for both types of particles. So, hysteresis will be much higher with smaller particles under similar conditions. This is also observed in Tables 2 and 3 (porous, 682 × 10-2 cmwc‚kg/m2‚s for a 1.9 mm particle compared to 152 × 10-2 cmwc‚kg/m2‚s for a 3.5 mm particle; nonporous, 634 × 10-2 cmwc‚kg/m2‚s for a 1.6 mm particle compared to 153 cmwc‚kg/m2‚s for a 3.5 mm particle). Second and Third Subsequent Cycles. (a) Porous vs Nonporous (Comparable Particle Size). In porous particles, few dry particles, which are present, will be covered by liquid and may not be identified as participating particles during the descending branch. Thus, the hysteresis will be open loop during the first cycle. In larger particles, this may not be observed because of the presence of a negligible number of dry particles because the number of favorable clusters is much smaller. So, ascending path 2,3-i will not follow the same path of 1-i. In nonporous particles, the presence of the dry particles is expected to be greater compared to that in porous particles or larger particles. These will be covered by liquid and may not be identified as participating particles during the descending branch. So, ascending path 2,3-i will not follow the same path of 1-i. However, this was not observed in Figure 3. More data will help to verify this behavior. (b) 1.6-1.9 mm vs 3.5 mm Particle Size. As stated earlier, because of the smaller size of the particle, the number of favorable clusters is much higher compared to that of larger particles for both types of particles. So,
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hysteresis will be much higher with smaller particles under similar conditions. This is also observed in Tables 2 and 3 (porous, 661 × 10-2 cmwc‚kg/m2‚s for a 1.9 mm particle compared to 152 × 10-2 cmwc‚kg/m2‚s for a 3.5 mm particle; nonporous, 634 × 10-2 cmwc‚kg/m2‚s for a 1.6 mm particle compared to 91 cmwc‚kg/m2‚s for a 3.5 mm particle). 5. Conclusions In summary, we conclude that the hysteretic behavior of porous particles is much different from that of nonporous particles and was explained on a new framework that incorporates the current understanding of fluid flow in TBRs, concepts of participating and nonparticipating particles, and principles of liquid spreading on porous and nonporous substrates. The genesis of this difference lies in the different ways liquid spreads/retracts over porous and nonporous particles. This difference manifests itself in many ways depending upon the wet/dry nature of the bed and the number of cycles. The framework is applied to reported experiments by Ravindra et al.1 and is shown to be able to explain the differences in the hysteretic behavior of porous and nonporous packings of different sizes under varying startup conditions and numbers of cycles. It also explains the limited hysteresis data available for porous particles at other gas flow rates. However, more comprehensive data with respect to other control parameters such as different gas flow, packing with different material and size, and different liquid need to be obtained. It is expected that this pore level conceptual new framework will enhance our understanding to further demystify the hydrodynamic phenomena in TBRs. However, strengthening the applicability of the framework over a wide range of physical properties of the fluids and different particles will help in further exploiting the applicability. Nomenclature dp ) packing diameter, mm D ) diameter of the bed, cm G ) gas mass flux, kg/m2s H ) height of the packing, m L ) liquid mass flux, kg/m2s P ) operating pressure, atm ∆P ) pressure drop, cmwc or mmwc eL ) liquid holdup η ) wetting efficiency
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Received for review July 24, 2004 Revised manuscript received March 8, 2005 Accepted April 6, 2005 IE049347R
