Cocurrent downflow in packed beds. Flow regimes and their acoustic

most distinctive signature was that of pulsing flow, namely, a single, high peak in the frequency range ... output was processed with a digital spectr...
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Ind. Eng. Chem. Res. 1990, 29, 2380-2389

2380

Cocurrent Downflow in Packed Beds. Flow Regimes and Their Acoustic Signatures William B. Kolb,? Tom6s R. Melli,l Juan M. de Santos, and L. E. Scriven* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455

T h e sound produced by the flow of water and air through a model packed column changes with the bed-scale regime. This paper reports acoustic sensing of pressure fluctuations together with flow visualization in an almost “two-dimensional” packed column. In the power spectra of sound detected at the outlet were found useful signatures of certain regimes and transitions between them. T h e most distinctive signature was that of pulsing flow, namely, a single, high peak in the frequency range of the liquid-rich slugs and of the gas-rich slugs that alternate with them, as seen in visualizations of the same flows.

Introduction Four main microscale flow regimes-trickling, bridged, flooded, and bubbling-are found in the passages of an almost “two-dimensional” packed column. These flow regimes combine in the two outlet passages of four-coordinated sites to give any one of 10 different flow states, all of them found in the experimental study reported by Melli et al. (1990). The macroscale flow regimes are described in terms of different combinations of microscale regimes, themselves outcomes of competitions of the gas and liquid for the “void space”. These flow regimes produce noise as the gas and liquid travel down the bed. Acoustic frequency analysis of the sound revealed that the pulsing regime and its transitions to continuous gas (trickling and spray) and bubbling regimes can be identified by the power spectrum of the sound: an acoustic signature of the flow regime. The signature of the pulsing regime is a single sharply defined peak at the characteristic frequency of the pulses; this peak varies markedly but systematically with liquid and gas flows. The frequency of the pulses increases when the liquid flow rate is raised at constant gas flow rate and does so too when the gas flow rate is raised at constant liquid flow rate. The peak gradually broadens and subsides in the transition from the pulsing regime to the bubbling regime and is absent in the bubbling regime. Multiple frequencies appear in the transition between either of gas-continuous regimes-trickling or spray-and the pulsing regime. Once the acoustic signatures and their evolution with changes in flow regimes have been identified by means of discrete Fourier frequency analysis and flow visualization, it is natural to use the acoustic signatures to refine flow regime maps and even to build them. The boundaries between the basic regimes are not sharp; rather, they span ranges of operating variables. Reducing surface tension moves the transition ranges and with them the pulsing regime to lower liquid and gas flow rates. Maldistributing the liquid to localized points of entry shifts the transition ranges to lower liquid flows and higher gas flows. Though flow regimes may vary down a contactor, acoustic frequency analysis may be useful in diagnosing and controlling operating conditions.

and are reported by Melli et al. (1990). A microphone, a spectrum analyzer, and a plotter were incorporated to capture and record the acoustic signal. Figure 1 indicates how an acoustic signal was captured. The liquid exiting the bed fell free for 25 mm before impinging on a plane that was inclined to avoid splattering. A cartridge-type condenser microphone (Model 4135, Briiel & Kjael, Denmark), was positioned 15 mm away from and directed toward the packed bed exit. The frequency range of the microphone was 6-20000 Hz. The microphone’s output was processed with a digital spectrum analyzer (Model HP3582a, Hewlett-Packard, Loveland, CO) which yielded the power spectrum. The frequency range of the spectrum analyzer was from 25.5 kHz down to as low as 20 mHz. Hann windowing was the choice for the sampling process (Stanley et al., 1984). The pressure in the chamber above the packed column ranged from slightly subatmospheric up to 2 atm. When the packed column operated in the pulsing regime, the chamber pressure oscillated with an amplitude as large as 10% of the average chamber pressure. The mainstay of flow visualization was a high-speed video camera (KodakSP2000 Motion Analyzer, San Diego, CAI, which can record up to 2000 frames/s. Backlighting was provided by a 500-W spotlight, 50 cm behind the model packed bed. Paraffin paper, positioned 20 cm behind the bed, served as the light diffuser. A camera placed 10 cm from the bottom of the bed, at the “intermediate test section” of the bed, spanned nine rows of the shallow cylinders, the “solid particles” of the bed, and the accompanying enlargements, or “sites”. Here, the velocity of a pulse was estimated from the time it took to travel down through the test section, i.e., the time elapsed from the moment at which the front of the pulse entered the test section to the moment at which the front of the pulse exited the test section. A camera located 15 mm from the top of the bed covered the “top test section” of the bed. Another camera 5 mm from the bottom of the bed covered the “bottom test section”. These two cameras were used to visualize, as reported by Melli et al. (1990), the formation of pulses in the transition between gas-continuous regimes and the pulsing regime.

Experimental Setup The experimental apparatus and the networks used are the same as those used for visualizations of flow regimes

Flow Regimes and Their Acoustic Spectra To study and describe the macroscale flow regimes in terms of their acoustic spectra, experiments were conducted at constant gas flow rate within the range of Rec between 0 and 3000 by raising the liquid flow rate from 0 up to ReL = 1800 and subsequently reducing it back to

Current address: University of Tulsa, Tulsa, OK 74104. of CONICET, Repfiblica Argentina.

3 Research Fellow

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Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990 2381 UQUID

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Figure 1. Pickup of the acoutic signature a t the exit of the packed bed. The microphone is positioned 15 mm away and directed to the exit of the bed. The output signal is sent to an HP3582a Hewlett-Packard spectrum analyzer.

0. The converse experiments, for which the gas flow rate was raised and lowered at constant liquid flow rate, were also conducted to validate the results and to study the effect of the history of gas and liquid flows (Le., hysteresis) on the acoustic spectra. No evidence of hysteresis was found in the acoustic spectra of the pulsing regime and its transitions. The Reynolds number of each phase is defined herein as Re, = 4Q,p,/(ag,d,n,), where Q, is the overall volumetric flow rate of the a-phase (water is the liquid phase and air is the gas phase), p a is the density of the a-phase (pL = 1.0 x lo3 kg/m3, pG = 1.2 kg/m3), g, is the viscosity of the a-phase (pL = 9.3 X lo-* kg/(m s), gG = 1.8 X kg/(m s)), d, = 4 A / P is the hydraulic diameter of the constricted passages, A is the cross-sectional area, P the wetted perimeter at the throat of the passages, and np is the number of passages along the width of the model packed bed. The results reported here were obtained with a rotated square, or diamond, network, described by Melli et al. (1990), with 17 constricted passages of rectangular cross section (2 mm X 1.2 mm). Thus, the hydraulic diameter was 1.5 mm. The effects of inertial, viscous, capillary, and gravitational forces are described in terms of three dimensionless numbers: the Reynolds number defined above, the Bond number (the ratio between gravitational and capillarity forces), Bo d?Apg/u, and the capillary number (the ratio between viscous and capillarity forces), Ca e ~ L U L / Here ~ . u is the surface tension, g is the gravitational acceleration, and uL is the superficial liquid velocity at the throat. At each pair of gas and liquid flow rates, the acoustic signal was recorded after the arithmetic average pressure in the distribution chamber and the amplitude of pressure fluctuations (around the average pressure) had become constant. The trickling regime a t the macroscale appears a t low gas and low liquid flow rates. In this regime, the gas Reynolds number ReGis less than 500, the liquid Reynolds number ReL is less than 300, and the capillary number Ca is less than 4 X The Bond number Bo, which is independent of gas and liquid rates, is constant, at 0.31 for the packed bed and fluids used.

The pulsing regime and its transition to gas-continuous regimes and to bubbling appear at intermediate values of gas and liquid flow rates, which correspond to ReLbetween 300 and 1200 and Rec between 500 and 1200; here the < Ca < 8 X capillary number is in the range 4 X The bubbling regime spans all gas flow rates where the liquid flow rate corresponds to ReL above 1200 and capillary number above 0.008 up to Ca = 0.016. The spray regime spans all gas flow rates that correspond to ReG above 2000 at low liquid rates. In what follows, references to “low”, “intermediate”, and “high” flows refer to the ranges of Reynolds numbers just given. Flow Regimes with Random Acoustic Spectra. It is shown by Melli et al. (1990) that at low gas and liquid flow rates, the macroscale regime is trickling, whereas the flow regimes at the pore level are mainly gas-continuous or bridged, although some local bubbling may appear in areas of tight pores. Pendant drops continually form on the undersides of the solid particles. They grow and tumble laterally, pushed by the incoming gas; sometimes they drip over the particle below, and sometimes they touch the neighboring particles, momentarily clogging the interparticle passages. This frequent local bridging process, accompanying as it does the continuous flow of gas at bed scale, produces small, virtually random flow fluctuations; thus, virtually random dripping and bubble bursting occur a t the column exit where the microphone senses pressure fluctuations. The acoustic spectra are of a random nature, as attested by the power spectrum (power versus frequency) shown in Figure 2a. A t low liquid flow rates and high gas flow rates, the macroscale regime is the spray regime; the flow of gas is so strong that it inhibits local bridging. Instead, the pendant drops are torn into droplets and carried off by the gas. The acoustic signal is again a random one, as the power spectrum in Figure 2b shows. A t high liquid flow rates and low gas flow rates, the macroscale regime is bubbling; the gas is dispersed as bubbles carried in a continuous liquid phase. In this regime, pressure fluctuations are negligible. The exit flow is smooth, the noise is weak, and the acoustic signal is a random one as the power spectrum in Figure 2c shows.

2382 Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990

1

FRKQUENCY

noise betrays an underlying regularity. The sound produced is of mixed (random and nonrandom) nature; the nonrandom part is periodic and its frequency corresponds to the frequency of alternation of gas-rich and liquid-rich slugs. Figure 2d shows the power spectrum of the sound at the exit during the pulsing regime. The appearance of a characteristic, single frequency peak that evolves in frequency and amplitude as the operating variables change provides an acoustic signature that can be used to refine flow regime maps.

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a - TRICKLING REGIME

b - SPRAY REGIME

Pulse Formation and Evolution of Gas-Continuous to Pulsing Transitions and Pulsing to Bubbling Transitions

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c - BUBBLING REGIME d - PULSING REGIME Figure 2. Random power spectra in trickling, spray, and bubbling regimes. In the power spectrum of the pulsing regime, there is a sharp peak at the frequency of the pulses.

Flow Regimes with Nonrandom Acoustic Spectra. A t intermediate liquid and gas flows, the macroscale regime is pulsing; slugs of enhanced liquid holdup and enhanced gas holdup descend in alternation. Melli et al. (1990) report that in the liquid-rich slugs the flow regime in the passages is local bubbling, whereas in the gas-rich slugs the flow regime is gas-continuous. Gas-rich and liquid-rich slugs are separated by regions where local bridging of passages dominates. The slugs span the entire cross section of the model packed column. The velocity and frequency of the slugs are well-defined and constant; the pressure fluctuations are strong, and the accompanying

FREQUENCY

-

Figure 3 shows how the spectra evolve as the liquid flow rate varies from 0 to that corresponding to ReL = 1360 at a fixed gas flow rate (Rec = 1100). Figure 3a shows the “white” noise spectrum characteristic of the gas-continuous regimes, trickIing in this case (ReL5 240). As the liquid flow rises and the transition to pulsing is approached, the spectrum becomes “colored” by a broad, low amplitude hump located at low frequencies, as shown in Figure 3b. Visualization shows small liquid clusters moving down the model packed bed at low velocities (0.5-0.7 m/s). In these clusters, the sites (enlargements) are gas-dominated, whereas the passages associated with them are flooded or bridged. The overall macroscale flow regime is still gascontinuous. The hump appears as the consequence of small pressure fluctuations produced by the liquid clusters reaching the bottom of the bed. The hump sharpens into a low frequency peak-see Figure 3c-as the liquid flow is raised to correspond to ReL

Re, = 1100

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TRANSITION FROM GAS-CONTINUOUS TO PULSING

TRANSITION FROM GAS-CONTINUOUS TO PULSING

Re~=970 PULSING REGIME

R e ~ = 1 2 4 0,

PULSING REGIME

1

TRANSITION FROM PULSING TO BUBBLING

BUBBLING REGIME

Figure 3. Power spectra a t constant gas Reynolds number while raising the liquid flow rate from the trickling regime (ReL < 230) to the bubbling regime (ReL > 1300). First a “hump” appears at low frequencies ( ~ 2 Hz, 0 a t ReL = 310). Multiple peaks appear in the transition from trickling regime to pulsing regime (ReL< 680). A single sharp peak characterizes the pulsing regime (730 < ReL < 970). The peak subsides in the transition from the pulsing regime to the bubbling regime (ReL < 1240).

Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990 2383 = 300. Visualization shows that in the bottom half of the bed, liquid-rich clusters invade not only passages but also the sites they interconnect. These liquid clusters do not span the entire width of the bed. Parts d and e of Figure 3 show power spectra characteristic of the transition region between either gas-continuous regime-trickling or spray-and the pulsing regime (350 IReL 5 700). Two or more peaks appear in the power spectra. The top test section of the bed operates in the trickling regime where small liquid clusters, or "protopulses", form in tight pore spaces. Further down the bed, liquid clusters as well as small pulses that span the bed width enter the bottom test section, pass through, and exit. In the intermediate and bottom test section, the merging of liquid clusters-the "overtaking mechanism" described by Melli et a1.(1990)-is noticeable. The peaks in the power spectra of this transition region cover a range that includes low to high frequencies (between 10-15 and 55-60 Hz). Frequency readings taken from direct visualizations are difficult and inaccurate because pulses of different sizes and velocities often coalesce within the test section. Parts f and g of Figure 3 show the acoustic signature of well-developed pulsing (700 IReL I1000). A single frequency peak appears and characterizes the f d y developed pulsing regime. Visualization shows that pulses extend across the entire bed width and span several rows of sites. The frequency and velocity of the pulses climb as the liquid flow rate is raised at constant gas flow rate. The liquid saturation, Le., the fraction of void space occupied by the liquid, jumps between the tail of the gas-rich slug and the front of the liquid-rich slug; the latter is trailed by a region of gradually falling saturation that merges into the front of the next gas-rich slug. Pulse frequency estimated by counting the number of pulses in a short time interval (around 4 s), which entails the counting of 240-280 pulses, agreed to within 5% with the peak frequency in the acoustic spectrum that sampled longer time intervals. Figure 3h shows the power spectrum of the acoustic signal in the transition between pulsing and bubbling regimes (1000 IReL 5 1300). Visualization shows that the front of a liquid-rich slug merges with the tail of the previous liquid-rich slug and the gas is confined to gas-rich pockets. The pressure oscillations diminish and so does the noise produced by the slugs reaching the bottom of the bed. The peak shifts to higher frequency in the acoustic signature, but its amplitude falls as the gas slugs wane. Figure 3i shows the power spectrum of the sound produced in the bubbling regime, ReL L 1300. The acoustic signature disappears. The pulse frequency in a fully developed pulsing regime increases with liquid and gas flow rates, as found by Blok and Drinkenburg (1982), Blok et al. (1983), and Rao and Drinkenburg (1983). Christensen et al. (1986) found a sharp increase of the pulse frequency with liquid flow, whereas they found only a weak dependence on the gas flow rate. Below is reported the evolution of the pulse frequency and velocity in the pulsing regime and at its transitions, in terms of gas and liquid rates. In the fully developed pulsing regime, when the liquid is uniformly distributed a t the top of the bed, the pulse frequency increases roughly twice as much with volumetric liquid flow rate as it does with the volumetric gas flow rate (the "weak" dependence found by Christensen et al. (1986) arose because superficial mass flow rates were used as the basis for comparison). Figure 4 shows the experimental contours of constant pulse frequency on the plane of gas and liquid Reynolds numbers. At intermediate gas and

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Figure 4. Experimental contour lines of pulse frequency in pulsing regime for a network 9 cm wide and 30 cm long packed with O-rings 7 mm in diameter. Here the Reynolds number of the liquid is defined as ReL = 2pLL/(7rnpr$J and the Reynolds number of the gas is ReG = 2&/(7npr&).

liquid flow rates (850 IReL I1200 and 800 IReG I1400), the pulse frequency varies linearly with flow rates. The constant frequency lines are equally spaced for frequencies between 56 and 71 Hz. A t higher gas and liquid rates, in the transition between the pulsing regime and the bubbling regime, the rate of increase of pulse frequency falls with an increase in either gas or liquid rate or both. Pulse frequencies tend asymptotically to maximum values in the transition between the pulsing regime and the spray regime-at high gas and low liquid rates-and in the transition between the pulsing regime and the bubbling regime-at high liquid rates and low gas rates. Figure 5 exemplifies the evolution of the pulsing regime signature with liquid flow a t constant gas flow that corresponds to ReG = 1395. The rate of increase of frequency is constant as the liquid flow rate is raised, C#J~ Av/AReL = 0.033, in the range of the liquid Reynolds number between 760 and 1000. Figure 6 exemplifies the evolution of the acoustic signature of the pulsing regime with gas flow at constant liquid flow rate corresponding to ReL = 760. In the range 1094 IReG I 1999, the rate of increase of the pulse frequency with the gas Reynolds number is also constant: @G E Av/ARec = 0.0133. Table I compares the rate of increase of the pulse frequency with the gas Reynolds number a t constant liquid Reynolds number, dG, and with the liquid Reynolds number at constant gas Reynolds number, $JL, as reported by Christensen et al. (1986) and as found here from acoustic frequency response. In the experiments of Christensen et al., the ratio between 4Land 4~ is { @L/& = 1.7 (this result is not shown explicitly in the paper of Christensen et al., but it can be immediately calculated from their Figure 17). In the present experiments, f = 2.5. Both results indicate a stronger dependence of the frequency on the liquid flow rate (of the order of twice the effect of

Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990

Re 1

1

G = 1395

Re L = 760 v

= 78 Hz

Re L = 1120

Figure 5. Pulse frequency a t constant gas flow rate while raising the liquid flow rate in a network 9 cm wide and 30 cm long packed with O-rings 7 mm in diameter. Table I. Comparison between the Results of Acoustic Frequency Analysis of the Pulsing Regime in This Work and Those Reported by Christensen et al. (1986) acoustic frequency Christensen anal. et al. (1986) range of ReL 760-1000, 60-82, ReG = 83 ReG = 1395 range of ReG 1090-2000, 31-67, ReL = 68; 82-118, ReL = 760 ReL = 89 4L= du/aReLa 0.0333 0.0381 4G = dv/dReGb 0.0133 0.0255, 0.0198; av = 0.0192 t=4~14~' 2.5 1.7 "Sensitivity of pulse frequency with liquid flow rate. bSensitivity of pulse frequency with gas flow rate. cRatio of sensitivities of pulse frequency with flow rates.

the gas flow rate). For the packed bed of Christensen et al., Re, = F,d,/p,, where Fais the superficial flow rate of the a-phase and d, is the nominal particle size (3-mm glass beads). In the transition region between either gas-continuous regime-trickling or spray-and the pulsing regime, more than one frequency peak appears in the acoustic signature. In these regions, the pulse frequency rises slowly with gas flow rate, whereas when the liquid flow rate is raised it rises sharply, from 10-15 Hz near the gas-continuous region to around 60 Hz near the fully developed pulsing regime, as Figure 7 shows.

Pulse Velocity The velocity of the pulses is calculated simply from the time elapsed during the movement of different pulses through the intermediate test section and is called the "pulse travel time, 7" here. The length of the test section is h = 9 cm. The motion analyzer equipment gives a

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1.

Figure 6. Pulse frequency at constant liquid flow rate while raising the gas flow rate in a network 9 cm wide and 30 cm long packed with O-rings 7 mm in diameter.

precision of 0.001 s for the 1000 frames/s recording rate used here. Figure 8 shows that 7 falls sharply in the transition between gas-continuous and pulse regimes (ReL 1700), but the standard deviation of the pulse travel time, ad, is high-another indication that pulses of different velocities and frequencies exist in this transition region. Moreover, the pulses of different sizes reach the bottom of the bed at different velocities. In the pulsing regime, ad diminishes sharply; there are well-defined pulses with constant frequency and velocity. The mean pulse velocity, vp = h/7,is shown in Figure 9. In the transition from either gas-continuousregime to the pulsing regime, the mean pulse velocity rises sharply, from 0.5 to 3 m/s. In the pulsing regime and in the transition from the pulsing to the bubbling regime, 7 falls slowly and therefore the velocity, v,, rises slowly, to a value between 3 and 3.5 m/s. These results agree with those of Blok and Drinkenburg (1982), Blok et al. (1983), and Rao and Drinkenburg (1983), all of whom found little effect of

Ind. Eng. Chem. Res., Vol. 29, NO. 12, 1990 2385 Or

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Figure 7. Pulse frequency versus gas and liquid Reynolds numbers. High frequencies correspond to the fully developed pulsing regime. Low and intermediate frequencies correspond to the transition between trickling and pulsing regimes; here the pulse frequency increases sharply as the liquid flow rate is raised. .

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F i g u r e 9. Pulse mean velocity from the experimentally measured pulse travel time. Pulse velocity tends to an asymptotic maximum value in the transition from pulsing to bubbling regimes.

the liquid flow rate on the pulse velocity in the transition from pulsing to bubbling. The velocities found in these

Figure 10. Dimensionless pressure drop (AP/(Apgl,) versus gas and liquid Reynolds numbers in a network 9 cm wide and 30 cm long packed with O-rings 7 mm in diameter. The transition to the pulsing regime is drawn where the pressure drop increases sharply.

experiments are higher than those found by Rao and Drinkenburg (1983), who employed quite different apparatus.

Flow Regime Maps and Pressure Drop Each flow regime shows distinct characteristics that can be used for the construction of flow maps. Most obvious are those seen in direct flow visualization of microscale flow regimes. Visualization with a high-speed video camera shows, in the gas-continuous regime, sites and passages that are gas-dominated; in the bubbling regime, sites and passages that are liquid-dominated; and in the pulsing regime, cyclic alternation of both states. In the transition from the gas-continuous to the pulsing regime, slugs of different sizes and velocities are seen, and in the transition from the pulsing to the bubbling regime, the gas slugs shrink to small gas-dominated pockets that disappear altogether in the bubbling regime. Another means of drawing the boundaries between flow regimes is pressure drop measurements. In the gas-continuous regime, the pressure drop is low. In the transition between the gas-continuous and pulsing regimes, the rate of change of pressure drop with both gas and liquid flow rate increases sharply. In the pulsing regime, the pressure drop and the rate of change of the pressure drop are both high and the pressure oscillations are noticeable. Figure 10 shows pressure drop in terms of gas and liquid Reynolds numbers. Here the pressure drop is measured in units of Apglt where 1, = 0.3 m is the total length of the packed bed. In this map, the onset of the transition between the main flow regimes is shown as a dashed line that, projected on the plane of flow rates, reproduces the shape of the curve that marks the transition between flow regimes in the common flow regime maps. Flow maps can be drawn-or refined-more accurately by using acoustic frequency response. Flow Regime Maps and Power Spectra Figure 11 is a map of the macroscale flow regime when the liquid is uniformly distributed at the top of the nearly two-dimensional bed. The curve that separates trickling and spray regimes from their transition to the pulsing regime is drawn where the low-frequency hump appears.

2386 Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990

Figure 11. Flow map for a "two-dimensional" network with uniform liquid distribution a t the entrance of the network. The transition between the pulsing and the trickling regimes is drawn where the "hump" appears. The pulsing regime is identified by a single sharp peak. The transition from the pulsing to the bubbling regime is drawn where the peak subsides.

Figure 12. Flow map for a "two-dimensional" network with liquid fed a t every other site a t the entrance of the bed. Compare with Figure 11, which shows a flow map for uniform liquid distribution. The pulsing regime shrinks and the transition from the trickling regime to the pulsing regime moves to higher gas flow rates and lower liquid flow rates.

The curve that separates pulsing from its transitions to the bubbling regime and to the gas-continuous regimes is

drawn here by following the boundary of the map region where the power spectra show a single, sharp, defined peak.

Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990 2387

1

1

;

.

I

POINTWISE DISTRIIIUTION LIQUID CHANNELING LESSENS PULSE DEFINITION Figure 13. Pulsing regime a t the bed scale in the network with liquid fed every other site a t the network entrance. The shape of the pulses loses definition. Liquid channels are noticeable in regions of heavier local liquid flow rate.

The transition between pulsing and bubbling regimes ends where the characteristic signature vanishes. The transition between either gas-continuous regime and the pulsing regime spans a broad range of liquid flow, whereas the transition between the pulsing regime and the bubbling regime spans a distinctly narrower range. Figure 12 is the flow regime map, over the same ranges of flow rates as Figure 11, when the liquid is deliberately maldistributed so that there is no feed at all to every other site a t the top of the bed. Comparison of the two maps shows that with such maldistribution the transitions, gas-continuous-to-pulsing and pulsing-to-bubbling span broader ranges of flow rates and appear a t higher gas flow rates and lower liquid flow rates. Moreover, the region of

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Conclusions In the power spectra of sound detected a t the outlet of an almost two-dimensional packed bed are found useful signatures of certain flow regimes and transitions between them. The most distinctive signature is that of pulsing flow, namely, a single, high peak in the frequency range of the liquid-rich slugs, and of the gas-rich slugs that alternate with them, as seen in visualizations of the same flows.

I

.

- - - - - - ;

well-developed pulsing flow is narrower. Channels of enhanced liquid holdup appear (see Figure 13), and the difference in saturation between the gas-rich and liquidrich slugs lessens. Thus, maldistribution of liquid a t the top of the bed inhibits the formation of fully developed pulses, a t least in the nearly two-dimensional model. Figure 14 shows the power spectra a t various combinations of gas and liquid flow rates, over the same ranges as in Figures 11 and 12, but instead when liquid is delivered solely a t the center of the bed entrance. A t all the combinations of flows set here, liquid channeling dominates, as Figure 15 illustrates: the pulsing regime is not attained. Figure 16 shows the flow regime map and power spectra when the liquid is an ethanol-water mixture of surface tension of 31 mN/m (as measured by the Du Nouy ring method) and when the liquid is uniformly fed a t the entrance of the bed. The air a t the inlet of the bed is not in equilibrium with the ethanol-water mixture; surface tension gradients may be induced by differential evaporation. The ethanol concentration at the interface is lower than in the liquid bulk, and therefore, the local surface tension is higher than that measured by the Du Nouy ring methods; also, differential expansion and contraction of the interfaces between the flowing air and flowing solution create surface tension gradients. The experiments are over the same range of fluxes as appear in the preceding maps. The pulsing region is narrower and displaced to lower flux values as found in other researches (e.g., Chou et al., 1977).

.--

- .. MALDISTRIL)VTION

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REMOVES PULSING REGIME !

-----"Figure 14. Flow map for the network with the same range of flow rates as in Figure 11. Here, liquid fed is localized in the two sites a t the center of the network entrance. Maldistribution removes the pulsing regime.

2388 Ind. Eng. Chem. Res., Vol. 29, No. 12, 1990

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CENTER :LOCAL BUBBLING REGIME SIDES :LOCAL GAS-CONTINUOUS REGIME Figure IS. Flow in the network a t the bed scale when liquid fed is concentrated in the two sites a t the center of the network entrance. Liquid flows through the center of the network, and gas flows through the sides. The pulsing regime is precluded.

At low gas and liquid rates, the flows of gas and liquid are steady everywhere except for local rippling and the power spectrum is low and flat. As the fluxes are raised, small liquid slugs travel downward; some of them coalesce and form larger liquid pulses. Multiple frequency peaks appear in the acoustic signature of the transition region between gas-continuous regimes and the pulsing regime. They correspond to liquid-rich slugs of different sizes. The pulse velocity increases sharply as the pulse size grows.

As coordinated pulses appear further and further up the column, a single, well-defined frequency peak emerges as the acoustic signature of the fully developed pulsing regime. As the liquid flow rate is raised further, the characteristic frequency peak widens and subsides in the transition from pulsing to bubbling. Visualization reveals that the tail of each liquid-rich slug blends with the following gas-rich slug in such a way that most of the gas travels downward as bubbles. The higher the liquid flow, the more intimate the blend and the smaller the bubbles. As a result, the flow a t the bed exit evolves from the sharp alternation of liquid and gas slugs to relatively placid outflow of bubbly liquid. Liquid distribution a t the top of the column has a tremendous influence on flow regime boundaries. Liquid maldistribution induces channeling and inhibits the formation of slugs that span the column width. Feeding all the liquid a t the center of the column so accentuates the channeling that the pulsing regime is never reached in the range of flow rates scanned in the rather short model column. Reduction of surface tension (or incitement of surface tension gradients) moves the pulsing regime boundary and transition regions to lower flow rates in the flow regime map, as well as shrinking the region of the pulsing regime. The combination of power spectrum analysis and flow visualization permits a fuller description of flow regimes and more refined definitions of transitions between them. When direct visualizations are not possible, as in opaque-walled industrial reactors, acoustic frequency analysis may be useful in diagnosing operating conditions and flow regimes a t different positions down the contactor, in comparing the effects of changes in operation conditions

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Figure 16. Flow map for the network when the liquid is a ethanol-water mixture with uniform liquid distribution a t the entrance of the network. Compare with Figure 11. The pulsing region shrinks. The transition from the trickling regime to the pulsing regime moves to lower gas and liquid flow rates.

2389

Ind. Eng. Chem. Res. 1990,29, 2389-2401

and even in controlling a trickle bed reactor.

Subscripts

G = gas L = liquid a = either gas or liquid (G or L)

Nomenclature A = cross-sectional area of constriction, m2 Bo = bond number, [d?(pL - p ~ ) g ] / udimensionless , Ca = capillary number, p V / u , dimensionless d , = nominal particle size, m d , = hydraulic diameter of constricted passage, 4 A / P , m F = superficial mass flow rate, kg/(s m2) g = acceleration of gravity, m/s2 h = length of test section, m 1, = total length of model packed bed, m n , = number of passages in the width of the model P = wetted perimeter of constriction, m Q = volumetric flow rate Re = Reynolds number, p V D / p , dimensionless v = superficial velocity, m/s up = pulse velocity, m/s & = rate of increase of pulse frequency with Reynolds number of phase CY, Au/ARe,, s-l u = frequency of pulses, s-l p = viscosity, kg/(m s) p = density, kg/m3 u = surface tension, kg/s2 ud = standard deviation T = pulse travel time, s { = d L / @ G , dimensionless

Literature Cited Blok, J. R.; Drinkenburg, A. A. H. Hydrodynamic Properties of Pulses in Two-Phase Downflow Operated Packed Columns. Chem. Eng. J . 1982,25, 89-99. Blok, J. R.; Varkevisser, J.; Drinkenburg, A. A. H. Transition to Pulsing Flow, Holdup and Pressure Drop in Packed Columns with Cocurrent Gas-Liquid Downflow. Chem. Eng. Sei. 1983, 38, 687-99. Christensen, G.; McGovern, S.J.; Sundaresan, S.Cocurrent Downflow of Air and Water in a Two-Dimensional Packed Column. AIChE J . 1986, 32, 1677-82. Chou. T. S.: Worlev. F. L.. Jr.: Luss. D. Transition to Pulsed Flow in MixedLPhase Cocurrent Downflow through a Fixed Bed. Ind. Eng. Chem. Process Des. Deu. 1977, 16, 424-27. Melli, T. R.; de Santos, J. M.; Kolb, W. B.; Scriven, L. E. Cocurrent Downflow in Networks of Passages. Microscale Roots of Macroscale Flow Regimes. Ind. Eng. Chem. Res. 1990, preceding paper in this issue. Rao, V. G.; Drinkenburg, A. A. H. Pressure Drop and Hydrodynamic Properties of Pulses in Two-Phase Gas-liquid Downflow through Packed Beds. Can. J. Chem. Eng. 1983,61, 158-67. Stanley, W. D.; Dougherty, G. R.; Dougherty, R. Digital Signal Processin,g;Restom Publishing Company, Inc.: Reston, VA, 1984.

Receiued for review November 2, 1989 Revised manuscript received May 10, 1990 Accepted May 23, 1990

Investigation of Acidulation and Coating of Saudi Phosphate Rocks. 1. Batch Acidulation Said S. Elnashaie,* Tariq F. Al-Fariss, Salah M. Abdel Razik, and Hazem A. Ibrahim Phosphoric Acid Group (PAG),Chemical Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

A mathematical model is used for the simulation of the acidulation of phosphate rock using both sulfuric acid and sulfuric acid/phosphoric acid mixtures. T h e attack on the rock by the acid and crystallization of the dihydrate are taking place in the same reactor vessel. T h e model has been tested by using a batch laboratory-scale reactor in a wide range of conditions. The matching between the model and the experimental results is used to obtain the effective diffusivity for the system. The effect of different parameters and the speed of acidulation on the coating of the rock particles is also investigated. 1. Introduction Sulfuric acid acidulation of phosphate rocks is already an old process for phosphoric acid production, and a broad experimental knowledge has been accumulated in the plants and in the laboratories. However, modeling the phosphoric acid reactor, which is the main stage of the process, remains a difficult and uncertain task, and design still relies to a great extent on empirical principles. Several reactions take place simultaneously in this reactor, and the effective rates of these reactions are very sensitive to the solution composition, agitation, temperature, and rock characteristics. As a result, very few papers in the literature use the physical modeling approach. Gioia et al. (1977) put forward a model that considers the two main reactions involved in the reactor: apatite acidulation through the action of H+ ions; calcium sulfate

* Author t o whom correspondence should be addressed.

crystallization in the hemihydrate state. However, no comparison between the experimental results and the computed data was presented; thus, Gioia et al.’s model remains purely theoretical. Shakourzadeh et al. (1980) put forward a model for the dihydrate system. The authors included a comparison between the experimental results and the computed data. Shakourzadeh et a1.k model was designed to study the influence of phosphate rock impurities using a continuous laboratory-scale reactor. The investigation covered only a very narrow range of sulfate ion concentration. Shakourzadeh et al.’s model did not consider the effect of the calcium sulfate layer, which forms around the rock surface, on the diffusion of ions to and from the rock surface and subsequently did not investigate thoroughly the coating phenomenon, which has a critical effect on the rate of the reaction. In Gioia et al.’s model, a diffusion coefficient was assumed to be on the order of magnitude of 7 X lo4 m2.h-’.

os8a-5aa5/90/2629-a~a9~02.50/0 0 1990 American Chemical Society