Re-entrainment correlations for demisting cyclones acting at elevated pressures on a range of fluids

Transcription

1 Re-entrainment correlations for demisting cyclones acting at elevated pressures on a range of fluids Trond Austrheim and Lars H. Gjertsen Statoil ASA 7005 Trondheim, Norway and Alex C. Hoffmann Dept. of Physics and Technology, University of Bergen Allegt. 55, 5007 Bergen, Norway May 21, 2007 Key words: Gas scrubber; axial-flow cyclone; high pressure; re-entrainment; hydrocarbon fluids; Abstract In this paper separation efficiency results for three different demisters acting on three different fluid systems: Exxsol D60/nitrogen, a syn- 1

2 thetic natural gas and a real natural gas at a range of pressures up to 114 bara are brought together using two dimensionless parameters: 1) a re-entrainment parameter and 2) the Weber number. The fact that this can be achieved shows that demisting cyclones limited by re-entrainment can be modeled by adapting re-entrainment concepts derived for liquid films in a gravity film. 1 Introduction Much research literature has been dedicated over the years to predict the performance of cyclone dedusters and demisters acting on particles/droplets close to their cut size. Both analytical models and CFD models have been presented. While the former are still often superior in predicting the separation performance of a given cyclone, the latter can be valuable in revealing details of the flow pattern in the separator that would otherwise not be recognized. In CFD, a very exiting development is that of large eddy turbulence modelling (LES), which is very computationally intensive, but avoids much of the empiricism in other types of turbulence models (see e.g. the recent articles by Derksen et al. [1, 2]). However, CFD remains mainly useful for studying the flow of pure gas or for low solids or liquid loadings; for high loadings, with siginificant two-way coupling, CFD simulations becomes increasingly unreliable and inaccurate. However, in reality, for a separator acting at high liquid loading, the separation performance may well be dominated by re-entrainment of liquid rather than penetration of liquid droplets under the separator s cut size. 2

3 In particular in a commonly used gas scrubber configuration the last separation step, after an inlet vane and a mist mat, is a bank of axial-flow cyclones and re-entrainment from the cyclones may well limit the separation performance. Only little research literature on high liquid loading in, and re-entrainment from, demisting cyclones has been published. Ng et al. [3] studied flooding and re-entrainment phenomena in once-through swirl tubes with upflow. They installed and tested design improvements to the swirl vanes, using vanes with peripheral rather than axial inflow, to delay the onset of flooding and entrainment. This paper describes how re-entrainment from a cyclone bank, acting as the final separation internal in natural gas scrubbers, influences separation efficiency. 2 Re-entrainment mechanisms and two existing models In this section an outline of the two dominating re-entrainment mechanisms is given. 2.1 Mechanisms Different mechanisms of entrainment are dominant in different flow regimes. Ishii and Grolmes [4] summarize four basic mechanisms for entrainment from 3

4 a liquid film into a gas flowing co-currently above it. Two of these are relevant for this work, they are shown in Fig. 1. Gas flow F σ a F d λ Gas flow Figure 1: Two mechanisms [4] for entrainment from a liquid film into a gas flowing over it. Top: entrainment by droplets being sheared from the surface of a roll wave, which is dominant at higher film Reynolds numbers. Bottom: entrainment by the gas undercutting a wave crest, which dominates at low film Reynolds numbers Which entrainment mechanism is active depends on the film Reynolds number: Re l ρ lu l δ µ l = ρ lγ µ l (1) where δ is the thickness of the film, u l its mean velocity and ρ l and µ l the density and viscosity of the liquid, respectively. Γ is the liquid flow in the film per unit wetted perimeter, P w. Γ is sometimes called the liquid loading, but we reserve that term for the volumetric liquid concentration in the droplet-laden gas flow. We have defined Re l as Verlaan [5] did, this is four times lower than that used by Ishii and Grolmes [4]. 4

5 The paper of Ishii and Grolmes [4] states that there exists a lower limit of Re l, whereunder roll-wave entrainment will not take place no matter how high the gas velocity over the film. In the other extreme, at high Re l, where the film is fully turbulent, the gas velocity necessary for the inception of entrainment becomes independent of Re l. The two limits are not firmly quantified, but the lower limit may be from 2 to 160 dependent on whether the flow is upward or downward in the gravity field, and the upper limit may be in the range Higher liquid film Reynolds numbers, roll-wave entrainment Ishii and Grolmes derived a criterion for the onset of roll-wave entrainment by considering a force balance between the drag force F d, from the gas acting on a wave crest on the film, and the retaining force of the surface tension F σ as indicated in Fig. 1. They assumed that roll wave entrainment was possible when the drag forces exceeded the retaining force of the surface tension σ: F d F σ. (2) They derived as criterion for the inception of entrainment: µ l u g σ µ l u g σ ρg ρ l 11.78N 0.8 µ Re 1/3 l for N µ (3) ρg ρ l 1.35Re 1/3 l for N µ 1 15 In these equations, u g is the superficial gas velocity, µ l and ρ l the liquid viscosity and density, respectively, and ρ g the gas density. 5

6 N µ is a viscosity number, which originally was used by Hinze [6] to analyze the problem of droplet disintegration in a gas flow. This number compares the viscous force induced by an internal flow to the surface tension force, and, when used for droplet entrainment, is defined as: N µ µ l ρ l σ σ g ρ, (4) where ρ is the difference between the liquid and gas densities. The expression σ g ρ has the dimension of length and is proportional to the critical wavelength of a Taylor instability. The dependence on the acceleration of gravity, g, is explained by the stabilising effect of the gravity force on the wavy interface. 2.3 Low film Reynolds numbers, undercut entrainment When Re l becomes very low, the evidence is that the roll-wave entrainment no longer occurs. However, entrainment is still possible at high gas velocities, as found by van Rossum [7], through the undercut mechanism shown in the lower figure in Fig. 1. Van Rossum carried out entrainment experiments for nine different fluids with interfacial tension ranging from 30 to 78 mn/m. In his study, van Rossum analyzed the onset of entrainment in terms of two dimensionless numbers, the film Weber number, W e, with the liquid film thickness as length scale, and a correlation parameter, S: W e ρ gv 2 gδ σ S u gµ l σ. (5) 6

7 For velocities higher than 25 m/s he found that the critical Weber number for inception of entrainment was practically independent of S for S > 5, while it became dependent on S for lower S-values. 3 Experimental facilities We are in this paper analyzing the results from three different experimental rigs. The rigs and the results have been described in three other articles [8 10]. Each of the rigs have specific advantages and limitations. They are: A low-pressure rig. This rig could operate up to 7 bara, and two fluid systems were used: air/water and air/exxsol D60. A high-pressure rig, capable of operating up to 100 bara. Two fluid systems were used: nitrogen/exxsol D60 and a live natural gas synthesized from methane, ethane and N-pentane. A large-scale test installation at an on-shore gas processing facility. This rig could operate at pressures up to 150 bara. A real, live natural gas, obtained by recombining dry natural gas with natural gas condensates, was used as fluid system. The range of physical fluid properties are given in Table 1. Note that in the live natural gas systems in the high-pressure and large-scale rigs the physical properties of the liquid phase change so drastically with pressure due to their changing composition, governed by the phase equilibria at the 7

8 given pressures. The interfacial tensions were calculated using the simple method that Weinaug and Katz [11] used for methane-propane mixtures. Fig. 2 shows a 3-D diagram of the test scrubber in the large-scale rig. The configuration of the other two test scrubbers are similar, except that the cross-sectional areas and therefore the number of cyclones in the cyclone banks are different. There are 7 cyclones in the scrubber in the low-pressure rig, 2 in the high-pressure rig and 31 in the large-scale rig. Figure 2: The test scrubber configuration in the large-scale rig. Lowest is the inlet vane, in the middle the mist-mat and on top is the cyclone deck The drainpipes and manifolds under the cyclones were arranged such that they did not block the cyclones significantly. In the high-pressure and lowpressure rigs, where there were only a few cyclones in the decks, the drainpipes were positioned at the side of the deck and did not interfere with the cyclones at all. The arrangement in the large-scale rig is shown in Fig. 3. Although the pipes can be seen to block part of the cross-sectional area, they 8

9 Table 1: Overview of the physical fluid properties, where relevant the pressures in bara are given in parentheses Density (kg m 3 ) Low-pressure rig Viscosity (kg m 1 s 1 ) Interfacial tension (mn m 1 ) Air Exxsol D Water High-pressure rig, N 2 /Exxsol D60 Gas 1.14 (1) (100) (1) (100) Liquid (1) High-pressure rig, synthetic natural gas 16.0 (100) Gas 17.2 (20.1) 97.0 (92) Liquid (20.1) (92) Large-scale rig Gas 22.0 (28) (113) Liquid 704 (28) 640 (113) (20.1) (92) (20.1) (92) (28) (113) (28) (113) 11.4 (20.1) 2.2 (92) 14.5 (28) 5.0 (113) 9

10 are reasonably far below the cyclone deck, such that the flow to some extent redistributes over the cross-section above the pipes before reaching the deck. The liquid flowrate to the deck was measured as the sum of the overhead and captured liquid fractions. Figure 3: The drainage arrangement under the cyclone deck in the largescale rig The intention of the inlet vane is to distribute the mist-laden gas evenly over the scrubber cross-section, and separate bulk liquid. The mist-mat separates more droplets, or, when the scrubber is operated such that the mist-mat is flooded, may act as a coalescer for the cyclone bank. The final separation step is the cyclone bank, where a number of cylindrical axial flow cyclones with swirl vanes generating the swirling flow, work in parallel. The axial flow cyclones are the most important in this present context, and a diagram is shown in Fig. 4. This is the type and size of cyclone used in the cyclone banks of all three rigs. Table 2 gives an overview of the experimental facilities and the operating 10

11 4 cm Secondary outlet Vortex finder 25 cm 5 cm Figure 4: A diagram of an axial flow cyclone constructed in accordance with the cyclones used by Verlaan [5]. The cyclone is equipped with vertical drainage slits as shown, and, in contrast to that of Verlaan, with a vortex finder to reduce re-entrainment 11

12 conditions used for generating the results analyzed in this article. Figure 5 shows scaled drawings of the three test scrubbers used with the distances between the internals. Table 2: Overview of the experimental facilities, operating conditions and approximate fluid rates used Low-press. rig High-press. rig Large-scale rig Scrubber diameter [m] Cyclones in deck Pressures [bara] , 50 and and 114 Temperature Ambient Fluid systems Air/Exxsol N 2 /Exxsol Live natural D60 D60 gas Synthetic live natural gas Superficial gas velocity and 5.4 in cyclones [m/s] Liquid loadings [vol % ]

13 Low-pressure rig High-pressure rig Large-scale rig Figure 5: Scaled drawings of the three test scrubbers used for generating the results analyzed in this article. The distances in mm between the internals: lowest the vaned inlet, then the mist mat and highest the cyclone bank are given 4 Re-entrainment from cyclones in gas scrubbers and its modeling 4.1 Basic assumptions Some results obtained in the high-pressure test rig are shown in Fig. 6. Clearly the efficiency drops with increasing gas velocity through the cyclones. In general the results from the cyclone experiments in this rig show [9] that the efficiency drops off with increasing gas velocity and liquid load. They also 13

14 100 Separation efficiency [%] N 2/Exxsol 20 bar 50 bar 92 bar Natural gas 20 bar 50 bar 92 bar Superficial gas velocity [m/s] Figure 6: Cyclone efficiency in the high-pressure rig with a constant liquid flowrate to the cyclones of 45 l/hr per cyclone show that the liquid carry-over is much larger when the pressure is increased and a natural gas fluid is used instead of a N2/Exxsol D60 fluid. Table 1 show the density and viscosity of the liquid and gas phases to be somewhat similar for the two systems, but calcuations [12] showed, as indicated in the last column of Table 1 that the interfacial tension is much the lower in the natural gas system, perhaps explaining most of the difference in behaviour between the two fluid systems. Further on in this paper, we bring the results from the two systems onto one curve taking into account the differences in physical properties between them. All cyclone models, including the one we derived for axial flow cyclones in [8], predict that if the droplets are so small that the cyclone separation efficiency is determined by the droplet size, the efficiency should increase with increasing volumetric gas flow and probably with increasing liquid loading (the latter due to coalescence effects). 14

15 However, if re-entrainment is the determining factor, the efficiency would be expected to drop off with higher volumetric gas flow and liquid loadings. Since this is the case in the results from the three rigs, we assume that the liquid carry-over from the cyclones is dominated by re-entrainment of liquid that has already settled on the cyclone wall. We now attempt to derive a parameter that will unify the results on the basis of Ishii and Grolmes [4] work. While they were only focusing on the inception of re-entrainment, this study also focuses on the the rate of re-entrainment. Near the point of inception of droplet entrainment, the entrainment rate increases quite slowly with increasing gas velocity, but at relatively high entrainment fraction the entrainment rate increases faster and appears to be linearly correlated with the superficial gas velocity. Since the droplets that are re-entrained inside a cyclone are exposed to a centrifugal force one can think of liquid carry-over as a dynamic equilibrium between capture and re-entrainment at the inner wall or the outlet of the cyclone. We propose that this dynamic equilibrium can be described as a function of the ratio of the two forces used by Ishii and Grolmes, the drag force and the retaining force: η cycl = f ( Fd F σ ) when re-entrainment dominates. (6) We are aware that re-entrainment may well take place to a large extent from edges in the separator. For instance, Verlaan [5] states that rivulets formed at the edges of the slits in his separators, and that this limited the separation efficiency. However, he used liquids with higher interfacial tension, and generally lower liquid loading, which will give rise to different creep flows 15

16 than we are likely to encounter in our systems. We assume, moreover, that re-entrainment from edges in the equipment will be governed by the same physical parameters as from liquid films. We need, however, to adapt this theory to the present situation: a film moving on the wall of a cyclone in a strongly swirling flow. 4.2 Adaptation of the theory The first task is to determine Re l, the liquid film Reynolds number in Eq. (1). Under the influence of the upward swirling gas flow, the film moves upward on the cyclone wall at an an angle, α, to the horizontal. We can therefore take the wetted perimeter as P w = πd/ cos α, if we define the wetted perimeter as the width of the film measured normal to the direction of flow (a consequence is that the wetted area cannot be calculated as P w H, with H the cyclone height). The gas moves at an angle β to the horizontal, where β is the exit angle from the swirl vanes, and as an approximation we assume that the liquid moves at the same angle, i.e. α = β. If we further assume that the captured fraction η of the total liquid flow to the cyclone Q moves in the liquid film, i.e. that most of the droplets entering the cyclone are so large that they are slung to the wall almost immediately, we obtain for Re l : Re l = Q l ηρ l P w µ l. (7) Ishii and Grolmes found that the transition from low Reynolds number entrainment to transition regime entrainment occurred at approximately 16

17 Re l = 160 (their definition) for horizontal flow or vertical up-flow and Re l = 2 for vertical down-flow. The transition to a rough turbulent regime occurred when Re l exceeded When Re l is calculated for the experiments in the high-pressure rig, most of the N2/Exxsol D60 results are found to be in the low Reynolds number regime, while most of the natural gas experiments are found to be within the transition regime. If transition regime theory is used for experiments that are calculated to be within low Reynolds number regime, the results will become increasingly inaccurate as the velocity is decreased. However, on balance it was thought best to use the same theory for all the results avoiding an anomalous jump in prediction when changing from one theory to the other. All the results from the high-pressure rig are therefore treated as if they were within the transition regime in this analysis. The theory of Ishii and Grolmes is based on two fundamental assumptions: 1. The initiation of roll-wave entrainment depends on a balance between the gas drag force and the surface tension retaining force acting on the liquid in a wavelet. 2. To calculate the amplitude, a, of a wavelet, it was assumed that the flow in the wavelet is simple shear flow, while flow in the film as such may be turbulent, and that the shear stresses above and below the wave are the same as those for the rest of the film (the shear stress acting on the film from the gas and that acting on the wall from the film have to be equal, since the film is not accelerating). This paper is not discussing the merits of these assumptions but adapting this model, that has stood the test of time, to our system, which differs from 17

18 theirs in that it involves a centrifugal field rather than the gravitational one. We also note here that Verlaan [5] handles two criteria for re-entrainment to take place: that droplets are created by shear, and that these droplets are transported in the surrounding gas flow. Consistent with the work of Ishii and Grolmes, we focus on the creation of droplets here, but, as stated above, consider that a model must describe the dynamic equilibrium between re-entrainment and capture at the cyclone wall. The length scale chosen for N µ, σ g ρ is the critical wavelength of a Taylor instability, and therefore characteristic for the length of waves on the film. This length scale involves the gravitational constant, g. We replace this by the centrifugal force acting on the liquid film, u 2 l,θ /R, where u l,θ is the tangential component of the liquid velocity, and R the cyclone radius. This makes it necessary to find u l,θ = u l cos α, which we do in a way similar to Ishii and Grolmes, as follows. If we call the tangential components of the shear stresses acting on the film due to the gas and on the wall due to the film τ i,θ and τ w,θ, respectively, we can say: τ i,θ = f g,i ρ g u 2 r,θ 2 f g,i ρ g u 2 g,θ 2 τ w,θ = f l,w ρ l u 2 l,θ 2 = τ i,θ, (8) where u r is the relative velocity between the liquid and the gas, assumed to be approximately equal to the gas velocity, since u g u l. Solving these two equations for u l,θ gives: u l,θ = f g,i ρ g u 2 g,θ f l,w ρ l (9) 18

19 We need the friction factor for the gas flow over the liquid film, f g,i. Wallis [13] proposed for the rough wavy regime in a tube of diameter D: ( f g,i = δ ). D For the present case of flow swirling with an angle of about 45, we propose to replace D by R, the radius of the cyclone: ( f g,i = δ ). R The liquid friction factor, f l,w, can, following Ishii and Grolmes, be obtained from the empirical correlation for a liquid film given by Hughmark [14] K = 3.73; m = 0.47 for 2 < Re fl,w = K Re m l < 100 l where: K = 1.96; m = 1/3 for 100 < Re l < 1000 The gas friction factor requires information about the liquid film thickness. Obviously: δ = Q l P w u l = Q l cos α P w u l,θ = Q l cos 2 α πdu l,θ (10) We now have two expressions for the two unknown variables δ and u l,θ. u g,θ is the last parameter we need to find u l,θ from Eq. (9) in order to evaluate the centrifugal force acting on the rotating liquid film. Clearly: u g,θ = u z tan α. Measurements [15] have shown that the mean axial velocity in the cyclone u z is approximately 0.8 times that at the wall, and that the axial flowpattern is fairly uniform throughout the cyclone, so that: u g,θ = u z 0.8 tan α (11) 19

20 4.3 The re-entrainment number Based on the calculated Re l for the experiments in the high-pressure rig, most experiments seem to be within the transition regime, where entrainment depends on Re l as explained above. For all experiments in that rig, N µ < 1/15. Assuming that transition regime is the dominant liquid film regime on the inner cyclone wall, the top criterion in Eq. (3) can be used in the force ratio in Eq. (6) and, hence, we get the re-entrainment number: R ent (a) = µ l u g ρg σ ρ l N a µre 1/3 l (12) where, as discussed above, g is replaced by u 2 l,θ /R in Eq. (4) for the evaluation of N µ. The argument a signifies that the power of the viscosity number is as yet undetermined. We can thus say that the cyclone efficiency, η cycl is a function of R ent (a): η cycl (R ent (a)) = f µ l u g ρg σ ρ l N a µre 1/3 l. (13) Ishii and Grolmes adjusted the power, a, of the viscosity number, N µ, to fit their data for the inception of the entrainment. The power should therefore be adjusted to the cyclone experiments. The power of N µ is important when experiments with different physical fluid properties like natural gas and N2/Exxsol are scaled. The re-entrainment number for all experiments that have been carried out in the high-pressure rig have been calculated in accordance with Eq. (13) and 20

21 are plotted in Fig. 7. Since many of the experiments with low liquid loading showed increasing efficiency with increasing gas flow, it was assumed that droplet size played an essential role for the efficiency at these low loadings. Therefore only experiments were the liquid load exceeded 9 l/hr have been included in the plot. Separation efficiency [%] N 2 /Exxsol 20 bar 50 bar 92 bar Natural gas 20 bar 50 bar 92 bar Reentrainment Number [-] Figure 7: The cyclone efficiency in the high-pressure rig as function of the re-entrainment number ([µ l u g /σ][ρ g /ρ l ] 0.5 )/(N 0.4 µ Re 1/3 l ). The plot includes superficial gas velocities of 1 6 m/s, and liquid loads of vol% Although these results and the ones shown in the following figure cover a wide range of operating conditions and also different fluid systems, they are all obtained in one type of cyclone and may well be geometry dependent. However, the general mechanisms governing reentrainment in other types of cyclones are likely to be the same. The power a = 0.4 gives a good fit between the natural gas and Exxsol D60 data as seen in the figure. However, the pressure scaling, although good, could be even better. One may therefore think that the gas and liquid 21

22 densities could be accounted for more precisely. For this reason the power of the gas to liquid density ratio was subjected to regression and a good scaling was found with a power of 0.8, as seen in Fig. 8. Separation efficiency [%] N 2 /Exxsol 20 bar 50 bar 92 bar Natural gas 20 bar 50 bar 92 bar Reentrainment Number [-] Figure 8: The data from Fig. 7 plotted against the modified re-entrainment number ([µ l u g /σ][ρ g /ρ l ] 0.8 )/(N 0.4 µ Re 1/3 l ) The excellent correlation between the cyclone efficiency and the re-entrainment number confirms that the cyclone efficiency is dominated by liquid film reentrainment rather than the penetration of fine droplets. The plot in Fig. 8 can be regarded as the maximum achievable efficiency due to limitations caused by re-entrainment for this particular geometry. However, if a significant amount of droplets comparable to the cut size of the cyclone are present in the inlet liquid loading, an extra contribution will be added to the liquid carry-over of the cyclone. Experiments with such contributions will have lower efficiency than predicted by the re-entrainment number solely. There is still some scatter in the results in Fig. 8, but with all the simplifi- 22

23 cations done and the complex process of gas-liquid interactions involved, the correlation is still remarkably good. Some of the scatter might also be caused by liquid carry-over due to the presence of small droplets, especially for the high-pressure natural gas case. Some of the most important simplifications are: Gradual drainage of liquid film through the slits in the cyclone wall has not been accounted for The film is assumed to be evenly distributed on the wall Transition regime entrainment is assumed even though some of the experiments appear to have a liquid Reynolds number smaller than the limit given by Ishii and Grolmes Finally, it is possible that wavelet behaviour in a centrifugal field, where the centripetal acceleration varies with the radius, is somewhat different from that in a gravity field. 4.4 Re-entrainment at low pressures, the Weber number As in the high-pressure rig, the cyclone efficiency from the low-pressure rig shows a general tendency of decreasing efficiency with increasing gas and liquid flow, consistent with re-entrainment limitation. Figure 9 shows separation efficiency data from the low-pressure rig plotted against superficial velocity in the cyclones. The physical properties of the fluids are given in 23

24 Table 1. The pressure was not varied independently in this rig, but was always in the range 2 7 bara. 100 Efficiency [%] Exxsol: Water: Vol% Vol% Vol% Vol% Vol% Vol% Superficial gas velocity [m/s] Figure 9: Separation efficiency in the low-pressure rig plotted against the superficial velocity in the cyclones. The liquid loadings are given in the legends However, at low pressure the calculated values for Re l indicate that the liquid film is below the regime where roll-wave entrainment is possible. If these results are plotted against the re-entrainment number the decrease in performance is much faster than in the high-pressure rig, as seen in Fig. 10. However, the re-entrainment number appears to bring also the low-pressure rig results, which were obtained [8] under a wide range of gas and liquid flows, and with two different fluid systems, onto one curve. Since the velocity is considerably higher in the low-pressure rig, re-entrainment is still possible by the undercut mechanism. However, as we also mentioned above, at these low values of Re l, the film Weber number can better be used 24

25 100 Separation efficiency [%] N 2 /Exxsol Natural gas 20 bar 20 bar 50 bar 50 bar 92 bar 92 bar Results from low-pressure rig with Exxsol D Reentrainment Number [-] Figure 10: A comparison between the cyclone efficiency in the high-pressure and the low-pressure rigs in terms of the modified re-entrainment number ([µ l u g /σ][ρ g /ρ l ] 0.8 )/(N 0.4 µ Re 1/3 l ). The data from the low-pressure rig include cyclone superficial gas velocities in the range 6 30 m/s and liquid loads in the range vol% 25

26 for correlating the results [7]. ( ρg u 2 ) g,sδ η = f (W e l ) = f. (14) σ Figure 11 a) shows the low-pressure results plotted against W e l, where we have used Eq. (10) to calculate the film thickness, δ. Clearly the results are brought onto one curve. We note that since the liquid density and the interfacial tension are approximately constant in the low-pressure rig, the variation in the liquid film Weber number is near identical to the gas dynamic pressure times the liquid rate. When the results from the high-pressure rig are plotted onto the same coordinates, as in Fig. 11 b), they can be seen to globally form a cloud of points in the same area as the low-pressure results. This shows that W e l does account for important parameters governing re-entrainment. On the other hand, a closer inspection of the figure shows that W e l does not account sufficiently well for differences in the fluid properties with pressure. We have included this plot to show that W e l actually is able to bring results from the two rigs closer together, something that the re-entrainment number did not do. In experiments with kerosine, a liquid that is comparable to Exxsol D60, van Rossum [7] found that a Weber number of around 6 is a lower limit for the onset of re-entrainment. This result is in agreement with the plot in Fig. 11 a) where re-entrainment appears to become significant around W e l = 6. Once again, this criterion was originally used to determine the onset of entrainment, and not the entrained fraction. 26

27 Separation efficiency [%] a) We l [-] Separation efficiency [%] b) N2/Exxsol 20 bar 50 bar 92 bar Natural gas 20 bar 50 bar 92 bar Low-pressure rig results We l [-] Figure 11: a) The results from the low-pressure rig plotted against the liquid film Weber number, W e l. b) The results from the low-pressure and high-pressure rigs plotted against W e l 27

28 4.5 The influence of scale The efficiency in the high-pressure rig is totally dominated by re-entrainment, at least for liquid flows per cyclone above 9 l/hr. However, in the experiments at K-lab it was seen that outer cyclones in the cyclone deck handled up to 2.5 times the amount of liquid that the inner cyclones handled [10], due to crosssectionally uneven liquid distribution. Since the cyclone efficiency generally drops off with increasing liquid load the outer cyclones might suffer from poorer efficiency. If, in addition, some of the cyclones in the middle of the cyclone deck receive a small amount of liquid but distributed as a fine mist, this might also have a negative impact on the efficiency. Based on earlier experience [16] we believe that the uneven distribution to some extent is due to the vaned inlet not distributing the liquid and gas ideally over the column cross-section. In the small scale high-pressure rig only two cyclones where installed and obviously, little liquid mal-distribution could have occurred. Therefore, the efficiency in the this rig can be regarded as the maximum efficiency when the efficiency is limited by re-entrainment. In Figure 12 the measured cyclone efficiency at the large scale rig is compared to the maximum efficiency found in the high-pressure rig. The results are plotted as function of the re-entrainment number and the average liquid load per cyclone has been used as input in the calculations. The figure shows that the cyclone deck in the K-lab tests is very influenced by the poor liquid distribution. In fact, in one case the efficiency drops from an expected maximum efficiency of more than 80% down to approximately 28

29 Separartion efficiency [%] K-lab 55 barg 113 barg High-pressure rig N 2 /Exxsol Natural gas 20 bar 20 bar 50 bar 50 bar 92 bar 92 bar Maximum efficiency due to reentrainment Reentrainment Number [-] Figure 12: The cyclones in the large scale rig suffer from reduced efficiency compared to the results from the high-pressure rig. The maximum efficiency found in the high-pressure rig is indicated and extrapolated. The large-scale rig results include cyclone superficial gas velocities of 9 m/s and m/s (at 56 and 114 bara, respectively) and liquid loadings in the approximate range vol% 29

30 40%. This effect of severely reduced efficiency at larger scale has, to the authors knowledge, never before been documented. The result is very important, since it demonstrates how much the efficiency of a large scale scrubber can deviate from the efficiency found in a small scale lab even when the gas velocity, the liquid concentration and the fluid properties are identical. The re-entrainment number offers an analysis tool to quantify the impact of liquid mal-distribution. 5 Concluding Remarks A first step in the direction of modelling and scaling cyclone efficiency when this is limited by re-entrainment rather than by separation efficiency for small droplets has been outlined Results with different fluid systems and spanning wide ranges of pressures, gas flowrates and liquid loadings have been brought to collapse on one curve by plotting them against a modified re-entrainment number derived on basis of the theory for the onset of roll-wave re-entrainment of Ishii and Grolmes [4]. All the results were obtained under conditions such that the Reynolds number of the liquid film on the cyclone wall, Re l was moderate or high. Results generated at lower pressures, where Re l is lower, but also for two different fluid systems, and at a wide range of gas and liquid flows, were brought to collapse on one curve when plotted against the liq- 30

31 uid film Weber number, agreeing with the work on the onset of reentrainment at low Re l of van Rossum [7]. An important effect of scale in reducing the efficiency of cyclone banks, probably due to mal-distribution of liquid between the cyclones, has been documented. For further understanding of the phenomena taking place, measurements of the droplet sizes throughout the equipment are desirable, and achieving this will have a high priority in the future. Acknowledgment Financial support from the Research Council of Norway through the HiPGaS programme, and the industrial sponsors Statoil AS, ConocoPhillips, Norsk Hydro AS, Vetco, FMC Kongsberg Subsea and Aker-Kværner is highly appreciated. References [1] J. J. Derksen. Separation performance predictions of a Stairmand highefficiency cyclone. AIChE Journal, 49: , [2] J. J. Derksen, S. Sundaresan, and H. E. A. van den Akker. Simulation of mass-loading effects in gas-solid cyclone separators. Powder Technology, 163:59 68,

32 [3] S. Y. Ng, G. H. Priestman, and R. W. K. Allen. Investigation of flooding, re-entrainment and grade efficiency in axial flow cyclones. Chem. Eng. Res. & Des., 84: , [4] M. Ishii and M. A. Grolmes. Inception criteria for droplet entrainment in two-phase concurrent film flow. AIChE Journal, 21: , [5] C. C. J. Verlaan. Performance of novel mist eliminators. PhD thesis, Delft University of Technology, ISBN [6] J. O. Hinze. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE Journal, 1: , [7] J. J. van Rossum. Experimental investigation of horizontal liquid films : Wave formation, atomization, film thickness. Chem. Eng. Sci., 11:35 52, [8] T. Austrheim, L. H. Gjertsen, and A. C. Hoffmann. An experimental investigation of scrubber internals at conditions of low pressure, submitted. [9] T. Austrheim, L. H. Gjertsen, and A. C. Hoffmann. Experimental investigation of the performance of a large-scale scrubber operating at elevated pressure on live natural gas, submitted. [10] T. Austrheim, L. H. Gjertsen, and A. C. Hoffmann. Is the Souders- Brown equation sufficient for scrubber design? An experimental investigation at elevated pressure with hydrocarbon fluids, submitted. [11] C. F. Weinaug and D. L. Katz. Surface tension of methane-propane mixtures. Industrial & Engineering Chemistry, 35: ,

33 [12] T. Austrheim. Experimental characterization of high-pressure natural gas scrubbers. PhD thesis, University of Bergen, [13] G. B. Wallis. One-dimensional two-phase flow. McGraw-Hill, New York, [14] G. A. Hughmark. Film thickness, entrainment, and pressure-drop in upward annular and dispersed flow. AIChE Journal, 5: , [15] S. Jacobsson. Single-phase characterization of the verlaan cyclone. Master s thesis, University of Bergen, Dept. of Physics and Technology, [16] L. H. Gjertsen, K. V. Lokken, N. Marheim, and J. Ophaug. Separation efficiency of the Troll Kollsnes separators and the improvment in their perfomance. In GPA 82nd Annual Convention, New Orleans,