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Characterization of Multiple Flow Morphologies within the Trickle Flow Regime Werner van der Merwe and Willie Nicol* Department of Chemical Engineering, University of Pretoria, Pretoria, South Africa
The existence of multiple hydrodynamic states in the trickle flow regime is a well documented, but as yet poorly quantified phenomenon. The prewetting procedure is known to drastically impact the hydrodynamic state and morphology of the liquid flow. In this work, three limiting cases for the case of no gas flow are identified: Nonprewetted, Levec-prewetted, and pseudoKan-prewetted. For the quiescent air-distilled water-3 mm glass spheres system, it is shown that bed-scale maldistribution exists in all three modes of operation, but is more severe in the Levec- and nonprewetted modes. The incorporation of a novel volumetric utilization coefficient into an existing momentum balance-based holdup model is sufficient to accurately model the holdup in all prewetted modes (AARE ) 9.2%). This results in the first holdup model that takes the prewetting procedure into account. Present results support the notion that Kan-type prewetting results in film flow, while Levec- and nonprewetted modes are dominated by rivulet flow. 1. Introduction The trickle flow regime is widely encountered throughout present day process industry. The term refers to the co-current flow of a gaseous phase and a gravity-driven liquid phase through a stationary bed of solids. Due to the many interacting phases a concise mathematical and fundamentally sound description of trickle flow has not yet been developed.1 Moreover, the ability of empirical and semiempirical correlations to predict macroscopic hydrodynamic parameters is unsatisfactory, largely due to the considerable amount of scatter in reported experimental data. This has created the need for more studies that are focused on the fundamental principles that govern trickle flow.1 The existence of multiple steady states in trickle flow is observed in the hysteretic behavior of pressure drop and liquid holdup. This phenomenon, although well reported, is typically not considered in the development of hydrodynamic models. Different hydrodynamic states correspond to differences in liquid morphology and distribution. These in turn influence a number of important hydrodynamic parameters, including the liquid holdup, two-phase pressure drop, mass transfer attributes, dispersion and wetting efficiency. A key factor in determining the morphology and distribution of the liquid is the prewetting procedure. Three cases have been identified: • Nonprewetted bed (a completely dry bed is irrigated at the desired flow rate)2-3 • Levec-prewetted bed (the bed is thoroughly prewetted and allowed to drain completely before irrigation at the desired flow rate starts)4-5 • Kan-prewetted bed (the fluid flow rates are increased until pulsing flow commences, after which they are reduced to the desired rates)6-7 There is substantial indication that the flow is more uniform in the prewetted beds than in the nonprewetted bed.8-12 Flow distribution differences between the Kan* To whom correspondence should be addressed. E-mail:
[email protected].
and Levec-prewetted modes have been attributed to differences in flow morphology.9,11 Christensen et al.12 visualized the Kan-prewetted mode to consist of predominantly film flow and the Levec-prewetted mode of pore-rivulets. Although this visualization succeeds in qualitatively explaining the observed hysteresis behavior, no attempt has been made to quantify the extent of liquid maldistribution as a result of the prewetted mode. In particular, the most commonly used holdup correlations13-18 do not take the prewetting procedure into account and can therefore not be expected to predict the differing holdups. In this study, we confirm quantitatively the differences in liquid distribution between the three modes of operation. From a fundamental point of departure, the study is limited to the case of distilled water flow through a packed bed of 3 mm glass spheres with no gas flow. It is desirable to first understand the underlying principles of such a simple system before the complexities of air flow and particle porosity are introduced. A volumetric utilization coefficient is defined in order to compensate for the effect that the different flow morphologies have on the bed-averaged holdup. This coefficient is defined as the volume fraction of the bed that receives liquid irrigation and has units m3 irrigated per m3 total bed. It is estimated by using the residual liquid holdup (RLH) in a novel procedure. RLH is the fraction of liquid remaining in the bed after it was allowed to drain. (Residual liquid holdup is often referred to as static liquid holdup, but we adopt the former semantic in order to clearly distinguish it from static holdup measurements inferred from residence time distribution studies.) RLH is known to form at particle contact points. Here, every contact point in the bed is treated as a binary indicator of whether irrigation had reached that point. The fraction of the total contact points that had received liquid irrigation is an indication of the volumetric utilization (some assumptions apply). Subsequently, the utilization coefficient is incorporated into a momentum balance-based holdup model.
10.1021/ie050216f CCC: $30.25 © 2005 American Chemical Society Published on Web 06/15/2005
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Figure 2. Contact points as binary indicators of liquid irrigation.
Figure 1. Experimental setup.
2. Experimental A schematic of the experimental setup is given in Figure 1. The objective is to measure total operating holdup and electrical conductivity. The setup consists of a 70 mm glass column mounted on an Ohaus Explorer Pro 220001 balance (accuracy: 0.5%). Note the column was open to the atmosphere at the top and the bottom (no air flow). The setup allows continuous monitoring of the weight (holdup) of the column. Conductivity is continuously measured over 4 orders of magnitude at both the inlet and outlet of the column with a dual channel Eutech PC5500 conductivity instrument (accuracy: 0.5%). No gas bubbles were entrained at the exit conductivity cell. The liquid distributor has a drip point density in excess of 15 000 per m2 and was tested with an annular collector to ensure the uniformity of its distribution. The 3 mm glass spheressdistilled waterslow-pressure air system is chosen because its generality in the literature facilitates easy comparison of the present data with those of previous investigations. 2.1. Prewetting Procedures. For the case of no gas flow, three modes of prewetting may be achieved as follows: • Nonprewetted: The column is packed with dried glass beads and the liquid is introduced at the desired flow rate through the distributor at the top of the column. • Levec-prewetted: The column is pre-flooded from the bottom (to ensure that no air bubbles are trapped) via the pre-flooding inlet. It is subsequently drained until only the residual liquid holdup remains. Liquid is then introduced through the distributor at the desired flow rate.
• Pseudo-Kan-prewetted: In the absence of gas flow pulsing flow cannot be achieved. A pseudo-Kan-prewetted mode may be achieved as follows: The column is pre-flooded as in the Levec-prewetted mode, but liquid is introduced through the distributor at the same moment that draining commences (i.e., the column drains while under irrigation). The resultant flow patern is believed to be similar to Kan-prewetted flow because in reducing the liquid flow rate from pulsing flow the liquid is not given time to drain. In each prewetted mode, the steady-state liquid holdup was determined by weighing. 2.2. Volumetric Utilization Coefficient. The volumetric utilization coefficient (χ) is defined as the volumetric fraction of the bed that receives liquid renewal over a long time of operation at steady state. Independent measurements of the utilization coefficient are not straightforward. In this study, the contact points between particles (that contains the residual liquid holdup) are used to estimate utilization. Every particle-particle contact point in the bed acts as a binary indicator of whether the flow had reached it. Contact points can be used in two different ways to estimate the utilization (illustrated schematically in Figure 2). In Figure 2 for the nonprewetted mode, there are two contact points (numbered 1 and 2). Liquid flow is introduced for at least 2 h after steady state is reached. Since the liquid reaches only point 1, RLH forms only there and point 2 remains dry. The bed is then flooded and RLH forms at all locations. The latter RLH is referred to as saturated RLH. The ratio of the trickle flow RLH to the saturated RLH is taken as the utilization. In Figure 2, it would be 50%. For the prewetted modes, the prewetting step makes the previous procedure impossible. In this case, the bed is prewetted with a salt solution of known concentration. For the Levec-mode, the salt solution is drained and RLH forms at all contact points (i.e., the saturated RLH). At this stage there is a known amount of salt in the bed (S0), as contained in the known amount of RLH. The liquid feed of distilled water is then introduced and operation continues for at least 2 h after steady state is reached. For irrigated points (point 1), the salt will wash out of the RLH until a RLH ring of distilled water remains. Nonirrigated points (point 2) on the other hand will still be made up of salt solution. Here, the ratio of salt left in the bed after irrigation (Sleft) to the original
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Figure 5. Effect of time irrigated on volumetric utilization coefficient estimation. Figure 3. Holdup in each prewetted mode.
Figure 4. Volumetric utilization as a function of liquid flux.
amount of salt in the bed is used to obtain the volumetric utilization. In the case of the pseudo-Kan-prewetted mode, the saturated RLH is determined separately for each packed bed before the experimental run. S0 is taken as the mass of salt that would be retained in the saturated RLH. For the Levec- and pseudo-Kan-prewetted cases, Sleft was determined by washing the bed repeatedly (5 or more times) with distilled water. The wash-water was collected, weighed and the conductivity thereof measured. A simple conductivity-concentration calibration allows one to determine the mass of salt that had remained in the column (Sleft). In summary, the volumetric utilization coefficient (χ) is estimated by the following equations:
Non-prewetted: χ )
RLHtrickle flow RLHsaturated
Levec-prewetted: χ ) 1 -
Sleft S0
Pseudo-Kan-prewetted: χ ) 1 -
Sleft S0
(1a)
(1b)
(1c)
3. Results 3.1. Holdup. Figure 3 shows the holdup as a function of the liquid flux in each prewetted mode of operation. There is clear indication that the holdup differs appreciably depending on the prewetted state. 3.2. Volumetric Utilization Coefficient. Figure 4 shows the volumetric utilization coefficient as estimated with the procedures above.
Figure 6. Holdup in comparison with the envelope of existence correlations.
This is striking evidence that severe liquid maldistribution takes place in the Levec-prewetted and the nonprewetted modes of operation. In these modes there are large fractions of the bed that are never irrigated. At low mass flux (L < 2 kg/m2s), bed-scale partial wetting exist even in the pseudo-Kan-prewetted mode. At low fluxes, the utilization coefficient increases sharply with liquid flux. Above the critical value (2 kg/m2s) the increase in utilization coefficient is nearly linear in the Levec- and nonprewetted modes. In the pseudo-Kanprewetted mode nearly the entire bed volume is irrigated. Barring the existence of temporally wandering rivulets, this indicates that the entire available solid surface was wet. The critical value of 2 kg/m2s was also observed in the tomographical studies of Sederman & Gladden.10 The rapid increase at low flux is attributed to the creation of new liquid rivulets. At higher fluxes an increased flux serves to fill up existing rivulets, hence the lower rate of increase in utilization. Estimation of the utilization coefficient by this procedure is dependent on the time that had been allowed for the distilled water to wash the salt from the column. Upon commencement of flow, the liquid flow pattern can be expected to take some time to reach a steady distribution. In addition, any transport processes such as those assumed by the cross-flow19 or the pistondispersion-exchange20 residence time distribution models would take some time to reduce the amount of salt in the “static” liquid to negligible amounts. In this study, it is assumed that such processes are completed once the exit conductivity had dropped to within 0.1% of the conductivity of distilled water. Confirmation of the adequacy of this allotted time is given in Figure 5. It is apparent that χ does not increase with time after
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approximately 2 h. This is in agreement with the procedure adopted by Ravindra et al.9
ratio), and this is equal to 1.6%.21 The final form of the extended model is as follows:
4. Holdup Prediction in the Three Prewetted States
vL2 χ3(1 - )2 vL χ2(1 - ) 150 µL + 1.75F L (L - RLH*)3 d2 (L - RLH*)2 d FL(L - RLH*)g ) 0 (3a) χ
4.1. Existing correlations. The ability of existing correlations to predict the holdup in each prewetted state is illustrated in Figure 6. The shaded area in Figure 6 is an envelope of the most commonly used holdup correlations applied to the present system. Interestingly, the experimental pseudo-Kan-prewetted mode values lie along the upper edge of this envelope (Boyer & Fanget18 and Larachi et. al.14 models). The Levec-prewetted mode holdup values lie almost exactly on the lower edge of this envelope (Holub et al.,13 Specchia & Baldi16 and Saez & Carbonell15-models). Note that none of these correlations takes the prewetting procedure into account or even mentions it. The prewetting condition (and flow history) may well account for some of the scatter observed in the literature. 4.2. Holdup Prediction. Boyer & Fanget18 presents the momentum balance for fully wetted film flow. Assuming the following:18 • Steady, one-dimensional, incompressible flow • No kinetic effects (i.e., holdup is independent of axial position) • No gas flow and negligible gas density • Parabolic velocity profile for expressing the laminar flow term of the drag force • The tortuosity factor in the laminar term is taken as 25/12 • The stress shear coefficient in the turbulent term is taken as 7/12 • The liquid-solid area is taken as the specific surface area (i.e., fully wetted solid) The resultant holdup model is as follows: 2
FLLg (1 - ) vL + 1.75FL ) (2) 2 2 d d
(1 - )2 vL
150 µL
L3
L
The present data can now be used to gauge the ability of eq 2 to predict the pseudo-Kan-prewetted holdup. Although there is a limited number of data points, an Average Absolute Relative Error (AARE) of 7.2% shows that the model succeeds very well, especially when taking into account that there are no fitted parameters, only the classical Ergun constants are used. The model can now be extended to predict the Levecand nonprewetted holdups as well, by assuming that only a fraction of the bed (χ) experiences liquid flow and that the model can be applied to this fraction only. Equation 2 is solved assuming that the same volumetric flow (i.e., LFLA) is flowing through χ times the volume of the bed. This yields #L, the holdup in the wetted volumes of the Levec- and nonprewetted modes (with units of [m3 liquid per m3 irrigated bed]). The bed volume based holdup (L) is equal to the product χ#L (with units of [m3 liquid per m3 total bed]). Volumetric utilization impacts the liquid-solid area (which is smaller) as well as the effective interstitial velocity (which is higher). In the case of the Levec-prewetted mode, the RLH of the nonirrigated zones (RLH*) still need to be added. By virtue of the wettability of the solid, the nonirrigated RLH may be assumed to be the RLH that lies in regions of high local porosity (small solid area to liquid volume
RLH* )
{
}
1.6 %, Levec - & pseudo-Kan-prewetted 0, Non-prewetted (3b)
The inclusion of the utilization factor and the nonirrigated RLH (RLH*) improves the pseudo-Kan-prewetted mode predictability to an AARE of 6.7%. The ability of eq 3 to predict the holdup in the various prewetted states is shown in Figure 7, where experimental values of χ had been used. Again considering that there are no fitted parameters, the total AARE of 9.2% is very satisfactory. The present findings seem to support the following flow visualization: • The pseudo-Kan-prewetted mode consists of liquid films that practically cover the entire solid surface (except at low liquid fluxes). The lower utilization coefficient at low liquid fluxes is due to the inability of the low liquid flux to sustain the film flow over all particles. Film breakage result in surface rivulet formation and a decrease in wetting. • The Levec-prewetted mode is characterized by porerivulet flow surrounded by localized film flow. Increased liquid flux at low fluxes results in the creation of new pore-rivulets, but at high fluxes the existing rivulets are expanded. • Severe channeling occurs in the nonprewetted mode. Moreover, increased liquid flux results in the expansion of these rivulets and not in the creation of new rivulets (complete utilization/wetting is never reached unless the column is flooded). Note that the holdups of the irrigated zones in the Levec- and nonprewetted modes are higher than the holdup of an equivalent volume of the pseudo-Kanprewetted mode (because of the higher interstitial velocity). Visually, these high holdup zones surrounded by low holdup zones will appear as rivulets. In Figures 3 and 4, the area between the nonprewetted curve and the pseudo-Kan-prewetted curve can be visualized as the boundaries of a continuum of possible steady states, in the sense that the operating point can be anywhere between these lines depending on the flow and prewetting history.
Figure 7. Holdup prediction in the three modes of prewetting.
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5. Conclusions In this study a novel use of the residual liquid holdup has served to quantify the extent of bed-averaged distribution in each of three limiting cases of prewetting. It was shown that severe liquid maldistribution occurs in Levec-prewetted and nonprewetted beds, while the entire bed volume is irrigated in the pseudo-Kanprewetted mode. This supports the visualizations of previous investigators that film flow is encountered in Kan-prewetted beds while Levec- and nonprewetted beds are dominated by rivulet flow. The definition of a volumetric utilization coefficient was shown to be sufficient to extend an existing holdup model to account for the prewetting procedure. A total AARE of 9.2% for 51 data points in all three prewetting modes for the air-water-glass system is highly satisfactory, especially considering the fact that no parameters were fitted to the data and only the classical Ergun constants appear in the final formulation. The present investigation has again highlighted the importance of the prewetting procedure on the hydrodynamic behavior of trickle flow units. Importantly, the effect of the prewetting procedure on the holdup has been quantified by extending a simple momentum balance-based model to include bed-scale maldistribution of liquid. Acknowledgment The authors gratefully acknowledge the support of Sasol R&D, and in particular the efforts of Arno de Klerk, toward the Hydrodynamics Focus Group at the University of Pretoria. Notation d ) particle diameter (m) g ) acceleration due to gravity (m/s2) L ) liquid flux (kg/m2s) S0 ) initial amount of salt (g) Sleft ) amount of salt left after irrigation (g) vL ) liquid superficial velocity (m/s) χ ) volumetric utilization coefficient (m3 irrigated/m3 bed) ) porosity (m3 void/m3 bed) L ) liquid holdup (m3 liquid/m3 bed) #L ) liquid holdup of the irrigated zones (m3 liquid/m3 irrigated bed) µL ) liquid viscosity (kg/ms) FL ) density (kg/m3) AARE ) Average Absolute Relative Error RLH ) Residual Liquid Holdup RLHtrickle flow ) RLH existing after trickle flow irrigation (nonprewetted mode) RLHsaturated ) RLH existing after complete flooding and draining of the bed
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(2) Lazzaroni, C. L.; Keselman, H. R.; Figoli, N. S. Colorimetric evaluation of the efficiency of liquid-solid contacting in trickle flow. Ind. Eng. Chem. Res. 1988, 27, 1132. (3) Lazzaroni, C. L.; Keselman, H. R.; Figoli, N. S. Trickle bed reactors. Multiplicity of hydrodynamic states. Relation between the pressure drop and the liquid holdup. Ind. Eng. Chem. Res. 1989, 28, 119. (4) Levec, J.; Grosser, K.; Carbonell, R. G. The hysteretic behaviour of pressure drop and liquid holdup in trickle beds. AIChE J. 1988, 34, 1027. (5) Levec, J.; Saez, A. E.; Carbonell, R. G. The hydrodynamics of trickling flow in packed beds, part I: Conduit models. AIChE J. 1986, 32, 515. (6) Kan, K. M.; Greenfield, P. F. Multiple hydrodynamic states in cocurrent two-phase down-flow through packed beds. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 482. (7) Kan, K. M.; Greenfield, P. F. Pressure drop and holdup in two-phase cocurrent trickle flows through packed beds. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 740. (8) Lutran, P. G.; Ng, K. M.; Delikat, E. P. Liquid distribution in trickle beds. An experimental study using computer-assisted tomography. Ind. Eng. Chem. Res. 1991, 30, 1270. (9) Ravindra, P. V.; Rao, D. P.; Rao, M. S. Liquid flow texture in trickle-bed reactors: an experimental study. Ind. Eng. Chem. Res. 1997, 36, 5133. (10) Sederman, A. J.; Gladden, L. F. Magnetic resonance imaging as a quantitative probe of gas-liquid distribution and wetting efficiency in trickle-bed reactors. Chem. Eng. Sci. 2001, 56, 2615. (11) Wang, R.; Mao, Z.; Chen, J. Experimental and theoretical studies of pressure drop hysteresis in trickle bed reactors. Chem. Eng. Sci. 1995, 50, 2321. (12) Christensen, G.; McGovern, S. J.; Sundaresan, S. Cocurrent downflow of air and water in a two-dimensional packed column. AIChE J. 1986, 32, 1677. (13) Holup, R. A.; Dudukovic, M. P.; Ramachandran, P. A. A phenomenological model for pressure drop, liquid hold-up and flow regime transition in gas-liquid trickle flow. Chem. Eng. Sci. 1992, 47, 2343. (14) Larachi, F.; Belfares, L.; Iliuta, I.; Grandjean, B. P. A. Liquid hold-up correlations for trickle beds without gas flow. Chem. Eng. Proc. 2004, 43, 85. (15) Saez, A. E.; Carbonell, R. G. Hydrodynamic parameters for gas-liquid cocurrent flow in packed beds. AIChE J. 1985, 31, 52. (16) Specchia, V.; Baldi, G. Pressure drop and liquid holdup for two phase concurrent flow in packed beds. Chem. Eng. Sci. 1977, 32, 515. (17) Wammes, W. J. A.; Mechielsen, S. J.; Westerterp, K. R. The influence of pressure on the liquid hold-up in a cocurrent gasliquid trickle-bed reactor operating at low gas velocities. Chem. Eng. Sci. 1991, 46, 409. (18) Boyer, C.; Fanget, B. Measurement of liquid flow distribution in trickle bed reactor of large diameter with a new gammaray tomographic system. Chem. Eng. Sci. 2002, 57, 1079. (19) Gianetto, A.; Baldi, G.; Specchia, V.; Sicardi, S. Hydrodynamics and the solid-liquid contacting effectiveness in tricklebed reactors. AIChE J. 1978, 24, 1087. (20) Van Swaaij, W. P. M.; Charpentier, J. C.; Villermaux, J. Residence time distribution in the liquid phase of trickle flow in packed columns I. Chem. Eng. Sci. 1969, 24, 1083. (21) Van der Merwe, W.; Maree, C.; Nicol, W. Nature of residual liquid holdup in packed beds of spherical particles. Ind. Eng. Chem. Res. 2004, 43, 8363.
Received for review February 21, 2005 Revised manuscript received May 5, 2005 Accepted May 12, 2005 IE050216F
