Entrainment from Spray Distributors for Packed Columns - American

Ind. Eng. Chem. Res. 2000, 39, 1797-1808

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Entrainment from Spray Distributors for Packed Columns Carlos J. Trompiz† and James R. Fair* Separations Research Program, The University of Texas at Austin, Austin, Texas 78759

Spray nozzles are widely used to provide a uniform liquid distribution to packed distillation and absorption columns. A disadvantage of such distributors is, however, the tendency for the atomized drops to be entrained by the upflowing gas. In some instances it is not convenient or even possible to remove the entrained liquid from the gas. A theoretical model has been developed for estimating the total entrainment from spray nozzle distributors. The model is based on drop size distribution and drop bouyancy relationships and has been confirmed by measurements in a 11.5-in. diameter spray contactor, using four different solid-cone nozzles and the air-water system. The model has also been confirmed by measurements of others using an air-paraffinic oil system. The model takes into account orifice diameter, phase flow rates, and phase physical properties. It predicts total entrainment and does not allow for partial removal of entrainment by walls, adjacent sprays, or target devices used to collect the entrained liquid. Thus, the predictions are conservative for multiple spray nozzle assemblies. Spray nozzle distributors are widely used in distillation and absorption columns to provide a uniform liquid distribution to the top surface of packed beds. Compared to gravity-type distributors, spray nozzles provide a very low pressure drop in the gas phase and in general are less expensive. For fouling systems, spray nozzles permit observation of gradual plugging whereas a gravity distributor does not. Further, a properly designed spray nozzle distributor minimizes disruptions of plant operations resulting from fouled gravity distributors. On the other hand, use of spray nozzles can lead to serious liquid entrainment problems. Another possible shortcoming is that when multiple nozzles are used at the same elevation, underlap and overlap of spray patterns can lead to a nonuniform liquid distribution to the packed bed. Certain hydrocarbon systems at temperatures above 650 °F also require spray nozzle distributors to reduce the liquid residence time and the risk of plugging a gravity distributor with coke particles formed by thermal coking operations. An example of such a system is the wash section of a crude oil vacuum distillation column where a certain amount of liquid (wash oil) must be distributed uniformly above a packed bed to remove contaminants from the feed vapor or flash zone vapor from below. In this specific case, the liquid rate is relatively low (less than 1 GPM/ft2), and the vapor superficial velocity is very high (over 15 ft/s). A high percentage of liquid entrainment is likely to occur in such a situation. For any system, when a significant fraction of the entering liquid is entrained, the following can result: (1) Lower efficiency of the packed bed below the distributor. (2) Capacity problems resulting from liquid recirculation. (3) Contamination of the liquid in the column section above (if any). * To whom correspondence should be addressed. E-mail: [email protected]. † Present address: Petroleos de Venezuela S.A., Caracas, Venezuela.

To minimize the effects of liquid entrainment, a deentraining device is often installed immediately above the distributor. However, for fouling systems this leads to plugging of the device. At present, quantitative estimates of entrainment from spray distributors are not possible because of the lack of a predictive entrainment model that takes into account nozzle size, operating conditions, and properties of the gas and liquid. Normally, the number of spray nozzles in the distributor is fixed by the column diameter, the spray angle, and available height above the packing. On the other hand, the size of the spray nozzles is fixed by the amount of liquid required by the process and the planned number of nozzles. The objective of this study was to develop an entrainment estimation model that would depend on nozzle design, gas and liquid rates, and gas and liquid properties. The study would include experimental validation of the model, using the air/water system. Such a model, if successful, would greatly improve the reliability of spray distributor designs and might, in fact, lead to a wider application of sprays for heat- and mass-transfer operations involving gas-liquid contacting. Background Spray Generation. A spray is a liquid-in-gas dispersion in the form of a multitude of drops that is produced by the breakup of liquid filaments or sheets. A liquid filament issuing from an orifice is inherently unstable, as predicted by Rayleigh,1 who employed the method of small disturbances to determine conditions to cause the collapse of a liquid filament at low velocity. Rayleigh’s theory, which is valid for low-viscosity liquids, predicts a drop diameter equal to 1.89 times the orifice diameter of the nozzle. The frequency of formation of drops as a liquid filament disintegrates was measured by Tyler,2 who related it to the wavelength of the disturbance. On the basis of certain assumptions, he obtained a drop/orifice diameter ratio of 1.92, in close agreement with Rayleigh’s value. Tyler concluded that cylindrical jets do break up under the conditions required for maximum instability, as predicted by Rayleigh’s theory.

10.1021/ie9903902 CCC: $19.00 © 2000 American Chemical Society Published on Web 04/08/2000

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Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000

A more general theory for disintegration of liquid filaments, developed by Weber,3 extended Rayleigh’s analysis to include viscous liquids. Weber derived a general differential equation for the breakup motion of a liquid filament when both the viscous and inertial forces offer significant resistance to filament disintegration. The modified diameter ratio as proposed by Weber is

[

]

1/2 1/6

3WeL D ) 1.89 1 + do ReL

(1)

where D is the drop diameter, do is the orifice diameter, and the dimensionless Reynolds and Weber groups are defined in the Nomenclature section. Experimental evidence in support of Weber’s theoretical analysis has been provided by Haenlein.4 Using nozzles with a length-to-bore ratio of 10:1 and liquids of various viscosities and surface tensions, Haenlein showed that for viscous liquids the ratio of wavelength-to-filament diameter producing maximum instability could range from 30:1 to 40:1, in contrast to the value of 4.5:1 predicted by Rayleigh for low-viscosity liquids. Spray nozzles do not form liquid filaments, but rather conical liquid sheets. Fraser and Eisenklam,5 Fraser et al.,6 and Dombrowski and Johns7 made studies of the mechanisms of disintegration of these sheets. Dombrowski and Fraser8 provided useful insight into the manner of sheet breakup, using an improved photographic technique and a specially designed source of lighting that combined high intensity with very short duration. They established that filaments are formed by perforations in the liquid sheet. If the perforations are caused by air friction, the filaments break up rapidly. However, if the perforations are caused by the turbulence in the nozzle, the filaments break more slowly. From a series of tests Dombrowski and Fraser concluded that sheets of liquids with high surface tension and viscosity are most resistant to disruption and that the effect of liquid density on sheet disintegration is practically negligible. York et al.9 made a rough estimate of the size of drops produced by the disintegration of conical sheets from spray nozzles. Waves form near the nozzle and cause thickening of the liquid sheet in the direction normal to the flow. Rings break off from the conical sheet and then disintegrate into drops according to the RayleighWeber mechanism. Spray Nozzle Design. Applications of spray nozzles are numerous and varied, and consequently many different forms and designs are in use. All nozzles may be classified under one of the following types: (1) Pressure nozzles in which the liquid under pressure is broken up by its inherent instability and its impact on the atmosphere of the surrounding gas. (2) Rotating nozzles in which the liquid is broken up by centrifugal forces. (3) Gas-atomizing nozzles in which the liquid is subjected to the disrupting effect of a high-velocity gas jet. For distributing liquid to packed beds for mass or heat transfer, one or more pressure nozzles with full-cone (i.e., solid-cone) distribution are normally used.The internal design of the nozzle is critical in forming a conical liquid sheet and an axial liquid jet to produce the full-cone pattern. Inside the nozzle pressure energy is converted into kinetic energy with a resulting rotary

Figure 1. Variation of spray intensity vs angle from the centerline. Sprayco 5B solid cone nozzle. Data of Pigford and Pyle.10

motion of the liquid, to create the conical sheet. Methods for imparting rotary motion within the nozzle include the use of inclined slotted inserts, spiral grooved inserts, and swirl inserts. In addition to the rotary motion of the liquid, the inserts also create an axial liquid jet which strikes the rotating liquid just within the outlet orifice. The liquid breakup is largely a result of this impact and the resulting turbulence. To obtain a uniform spatial distribution of the liquid, the nozzle internals are designed so that a proper relation exists between the amount of liquid in the axial jet, the amount of liquid with rotary motion, and the orifice size. Normally, more of the fluid is given a rotary motion than is passed through the axial jet. In a classic work, Pigford and Pyle10 observed that a solid-cone nozzle does not distribute the liquid uniformly over the cross-sectional area of the spray. They reported the variation of spray intensity (GPM/ft2) versus the angle from the spray center line (Figure 1). A nozzle with a 60° spray was used, and the intensity was fairly uniform over the central 75% of the total pattern. The included angle of the solid-cone spray is a function of the design of the nozzle and is nearly independent of the pressure drop. Most commercial solid-cone nozzles produce sprays with included angles ranging from 30° to 120°. Drop Size Distributions of Sprays. Pressure spray nozzles produce a spectrum of drop sizes. The distribution of drop sizes may be expressed in terms of drop number or drop volume, and average drop sizes may be expressed in several ways. Basics of drop size distribution may be found in sources such as Lefebvre.11 Of interest here are mathematical drop size distribution functions, a number of which have been proposed, based either on probability or purely empirical considerations that allow for the mathematical representation of drop size distributions. Those in general use include normal, log-normal, Nukiyama-Tanasawa, Rosin-Rammler, upper-limit, and bimodal distribution functions. The last-two named are of special interest here and will be discussed below. Upper-Limit Distribution Function. Mugele and Evans12 analyzed the various functions used to represent drop size distribution data by computing mean diameters from experimental data and comparing them with mean values calculated from the distribution functions. The empirical constants used in the functions were determined from the experimental distributions. As a result of their analysis, Mugele and Evans proposed a so-called “upper-limit function” as being the

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et al. concluded that this bimodal distribution results from two types of flow, one with a rotary motion and the other as an axial jet. For representing this type of drop size distribution, they proposed a bimodal function expressed as a sum of the integrals of two logarithmic normal distribution functions:

F(D) )

x2π ln σg1

1-β Figure 2. Bimodal drop size distributions for different distances ()r) from the axis. Pressure drop ) 14.2 psi; 15.7 in. below the nozzle, air-water. From Sada et al.16

best way of representing the drop size distribution of sprays. This is a modified form of the log-probability equation with a maximum limit for the drop diameter. The volume distribution equation is given by

dV δ exp(-δ2y2) ) dy xπ

(2)

where

(

y ) ln

RD Dm - D

)

(3)

As y goes from -∞ to +∞, D goes from 0 to Dm (maximum drop diameter), while δ is related to the standard deviation of D and R is a dimensionless constant. A smaller value of δ implies a more uniform distribution. Lekic and co-workers13 found the best estimates for the parameters R and δ from various experimental data. For the isooctane/air system, they reported 0.8803 and 0.8739 for R and δ, respectively. The upper-limit distribution function assumes a realistic spray of a finite maximum drop size, but involves difficult integration that requires the use of a computer. Mugele14 developed a formula to estimate the maximum drop diameter Dm as a function of nozzle orifice diameter, physical properties of the liquid, and the relative velocity of the dispersed liquid phase with respect to the continuous gas phase:

( ) ( )

doFLur Dm ) 57do µL

-0.48

µL u r σ

-0.18

(4)

where do is the nozzle orifice diameter and ur is the relative velocity of the dispersed liquid with respect to the gas phase. For countercurrent flow, ur ) uL + uG, all velocities with respect to the column wall. The value of uL can be calculated from

( )

u L ) C0

2∆p FL

1/2

(5)

where C0 is the discharge coefficient and ∆p is the liquid pressure drop across the spray nozzle. For solid-cone nozzles, the value of C0 may be taken as 0.7. (Fair15). Bimodal Distribution Function. Sada and coworkers16 measured drop size distributions for sprays generated by a solid-cone nozzle. They found that at the center of the spray the drop size distribution has one peak, but away from the center the distribution has two peaks (bimodal distribution), as shown in Figure 2. Sada

x2π ln σg2

[

∫D∞ exp 0

[

∫0 exp ∞

β

]

[ln(D/Dng1)]2 2(ln σg1)2

d(ln D) +

]

{ln[(D - D0)/(Dng2 - D0)]}2

× 2(ln σg2)2 d[ln(D - D0)] (6)

where β is the ratio of the number of drops contained in the first peak distribution to the total number of drops, D is the drop diameter, D0 is the minimum drop diameter for the second peak distribution, Dng1 and Dng2 are the number geometric mean diameters for the first peak and second peak distributions, respectively, and σg1 and σg2 are the geometric standard deviations for the same two respective distributions. F(D) in eq 6 represents the cumulative number distribution function because the logarithmic normal distributions are in the integral form. On the basis of their experimental data, Sada et al. presented graphically the parameters β, D0, Dng1, Dng2, σg1, and σg2 as functions of position in the spray (horizontal distance from the axis of the spray and vertical distance from the nozzle tip) and the liquid pressure drop across the nozzle. The experimental data were obtained by injecting water into static air using a solid-cone nozzle with a spray angle of 30° and an orifice diameter of 0.0787 in. Drop Movement Characteristics. Drops emerging from spray nozzles are ejected with a high-velocity component in the direction of the nozzle axis. For drops moving relative to a gas phase, there is a resisting force due to friction between the gas and surface of the drops (friction drag force). At any given instant of a spherical drop travel in the vertical plane, the forces acting on the drop can be expressed as follows:

1 π 3 duL π 3 D ) D (FL - FG)g - CDFGur2A 6 dt 6 2

(7)

where CD is the drag coefficient, uL is the velocity of the drop, ur is the relative velocity of the drop with respect to the gas phase, and A is the drop projected area (equal to πD2/4). When the drag force equals the gravitational force, drop acceleration becomes zero and the drop velocity is constant. This constant velocity is termed the terminal settling velocity (ut). Under these conditions, duL/dt ) 0, uL ) ut, and from eq 7,

CD )

4 gD (FL - FG) 3u2 FG

(8)

r

The value of the drag coefficient is dependent upon the drop Reynolds number (ReD). The general relationship between the drag coefficient and the drop Reynolds number is shown graphically in many references, for example, Bird et al.17 or Perry and Green.18 Liquid Entrainment. Sieve Trays. Liquid entrainment from conventional cross-flow trays of distillation

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Table 1. Entrainment from Sprays Reported by Pigford and Pyle10 air flow rate (lb/h‚ft2)

air velocity (ft/s)

entrainment (lb of water/lb of air)

470 640 800 1000

1.74 2.37 2.96 3.70

0.0078 0.011 0.010 0.016

Figure 4. Entrainment from a G-Series 70° spray nozzle at different pressure drops. Air-water. From Lin et al.20

Figure 3. Entrainment from nozzles with different spray angles. Pressure drop ) 25 psi, air-water. From Lin et al.21

columns has been studied extensively. A summary of work before 1992 is provided by Kister.19 Accurate measurement of entrainment from operating trays, especially in larger columns, is difficult owing to the problem of getting a representative sample. Recourse has been made to the use of a target tray of the same geometry as the tray under observation. Accordingly, the measured entrainment (that which is collected by the target tray) is lower than the actual entrainment which includes drops intercepted by the target tray; these drops largely coalesce and fall back to the tray under study. Although the mechanism of liquid entrainment from sieve trays is different from that from spray distributors, some general findings regarding physical property effects may be extended to sprays. As the liquid density and surface tension increase, entrainment decreases. As the gas density and velocity increase, entrainment increases. For trays, the dominant variable is superficial gas velocity, with absolute entrainment often varying with velocity to a power of 2-5.19 Sprays. There is very little published information on liquid entrainment from sprays. Pigford and Pyle10 reported entrainment from a bank of six Spraco 5B nozzles for air-water in a 31.5-in. diameter column, with a constant liquid feed rate of 600 lb/h‚ft2. Their results are presented in Table 1. The entrainment values were obtained by measuring the difference between liquid feed and liquid drawoff flows, checked approximately by entrainment collected in an overhead receiver. Lin and co-workers20,21 reported entrainment from a spray nozzle for air-water and air-Isopar-M systems in a 36-in. diameter column. The liquid entrainment was collected in a chimney tray located above the spray nozzle. Figure 3 shows entrainment for air-water at a nozzle pressure drop of 25 psi for three types of nozzles with different spray angles (70°, 90°, and 120°). The entrainment is expressed as a percentage of the water flow to the nozzle. According to a personal communication (Lin22), the nozzles with spray angles of 90° and 120° were manufactured by Bete Fog Nozzle, Inc., while the 70° spray nozzle is a proprietary “G-series” type of Koch-Glitsch, Inc.

Figure 5. Entrainment from a G-Series 70° spray nozzle at different pressure drops. Air-Isopar-M. From Lin et al.21

In Figure 3 the abscissa values are given in terms of a “C-factor” (CF), which is a density-corrected gas superficial velocity:

{

CF ) uG

FG

}

1/2

(FL - FG)

(9)

where uG is the gas superficial velocity based on the cross-sectional area of the column and FG and FL are the gas and liquid densities. There is widespread use of the C-factor (sometimes called the “Souders-Brown capacity parameter”) as a means for correcting gas and liquid density effects to a common basis for correlation purposes. Entrainment values from a G-series nozzle for airwater at pressure drops of 6, 15, and 25 psi are shown in Figure 4. Entrainment from the G-series nozzle for air-Isopar-M at pressure drops of 7, 10, 17, and 20 psi across the nozzle is shown in Figure 5. The papers by Pigford and Pyle and by Lin and coworkers are the only ones on spray entrainment found in the literature. Additional entrainment data may have been developed through flue gas desulfurization studies but have not been formally reported. Model Development Drop Buoyancy Model. The entrainment of a drop by a countercurrent gas flow occurs when the relative velocity of the drop is reduced by the drag force to the value of the gas superficial velocity, that is, ur ) uG. Considering the drop as a rigid sphere, a relation between the drag coefficient and the drop Reynolds number can be derived from eq 8 as follows:

CD 4 gµG(FL - FG) ) Re 3 u 3F 2 r

G

(10)


For the drop entrainment condition (ur ) uG, Re ) Re′), eq 10 becomes

F(D3) )

CD 4 gµG(FL - FG) ) Re′ 3 u 3F 2 G

(11)

G

Using eq 11 and a general relation between the drag coefficient and the Reynolds number, the largest drop diameter that can be entrained may be determined:

D ) Re′µG/µGFG

(12)

Thus, for the same system there will be different values of entrainment Reynolds number for the different sizes of drops in the spray. Drop Size Distribution Model. The drop size distribution of a spray is a critical factor for determining the amount of liquid entrained by the upflowing gas. Because drop size distributions provided by nozzle vendors are generally based on water sprayed into still air, a theoretical model is required for predicting the distribution in sprays of any liquid, taking into account the effects of gas velocity and properties other than those of water and air. In the present study, two of the mathematical distribution functions described earlier were considered to be the best for representing drop size distributions for solid-cone spray nozzles. These two are the bimodal function proposed by Sada et al.16 specifically for solidcone nozzles and the upper-limit function developed by Mugele and Evans.12 Bimodal Function Model. Equation 6 represents the cumulative number or frequency distribution for the two peaks of the function. To use the distribution function for estimating the liquid volume entrained, it must be transformed to the cumulative volume distribution. Using eq 6, the number geometric mean diameters, Dng1 and Dng2, can be changed to the corresponding volume geometric mean diameters, Dvg1 and Dvg2, as follows:

ln Dvg1 ) ln Dng1 + 3(ln σg1)2

(13)

ln Dvg2 ) ln Dng2 + 3(ln σg2)2

(13a)

The parameter β in eq 6, which represents the ratio of the number of drops in the first peak to the total number of drops in the spray, must be replaced by another parameter, β′, representing the ratio of the volume of the drops in the first peak to the total volume of drops in the spray. The new parameter β′ can be expressed in terms of β and the volume mean diameters as follows:

Dvg13 β′ ) 1-β Dvg13 + Dvg23 β

(

)

x2π ln σg1 1 - β′

x2π ln σg2

When β, Dng1, and Dng2 are replaced by β′, Dvg1, and Dvg2, respectively, in eq 6, the cumulative frequency distribution, F(D), is transformed into the cumulative volume distribution function, F(D3), expressed as

[

∫D∞ exp 0

]

[ln(D/Dvg1)]2 2(ln σg1)2

d[ln(D)] +

]

{ln[(D - D0)/Dvg2 - D0]}2

× 2(ln σg2)2 d[ln(D - D0)] (15)

Sada et al.16 found values of β, Dng1, Dng2, D0, σg1, and σg2 for different positions in the spray at a nozzle pressure drop of 42.6 psi as well as for different nozzle pressure drops at a vertical distance of 19.7 in. from the nozzle and a horizontal distance of 7.9 in. from the spray axis. Because a nozzle pressure drop of 42.6 psi is beyond the typical maximum of 20 psi for spray distributors for packed beds, only the values of the parameters for different nozzle pressure drops at a fixed position in the spray can be useful for the purposes of the present work. Values of Dng1, Dng2, D0, β, σg1, and σg2, reported by Sada et al., are shown in Figure 6. From eq 13 and Figure 6, values for the volume geometric mean diameters, Dvg1 and Dvg2, are obtained as shown in Figure 7. Similarly, eq 14 and Figure 6 yield values of β′ for different pressure drops, as shown in Figure 8. With parameters from Figures 6-8, eq 15 can be solved to give the cumulative volume distribution for a given nozzle pressure drop at the fixed position in the spray used by Sada et al. (7.9 in. from the spray axis and 19.7 in. below the nozzle). Cumulative volume distributions corresponding to nozzle pressure drops of 5, 10, and 20 psi are shown in Figure 9. As mentioned earlier, data of the type shown in Figure 9 may be available from the spray nozzle vendor. However, such data are measured with water under still air conditions and may not apply to the design and analysis of a flow system. However, vendor-supplied data for the nozzles used in this study showed very close agreement with the values of the type shown in Figure 9, for equivalent conditions. The model described here is based on predicted distributions only. Because the values of the parameters are based on a fixed position in the spray from a specific nozzle, the application of the bimodal model is limited. Additional experimental work, using spray nozzles with different orifice diameters and spray angles, is needed. Upper-Limit Function Model. The cumulative volume distribution can be obtained directly by integrating eq 2:

F(D3) ) V )

δ xπ

∫-∞∞exp(-δ2y2) dy

(16)

When y is substituted into eq 16, according to eq 3, the following expression for the cumulative volume distribution in terms of the drop diameter can be derived:

F(D3) ) (14)

[

∫0 exp ∞

β′

δDm

xπ

∫0D

m

1 × (Dm - D)

{ [(

exp -δ2 ln

RD Dm - D

)] } 2

d(ln D) (17)

When the best estimates for the parameters R and δ (0.8803 and 0.8739, respectively) as found by Lekic et al.13 are used, eq 17 can be solved for a given value of the maximum stable drop diameter Dm. Thus, the

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Figure 8. Effect of pressure drop on the fraction of total volume of drops contained in the first peak (eqs 14 and 15).

Figure 9. Cumulative volume distributions obtained from the bimodal function. Nozzle pressure drops 5, 10, and 20 psi.

parameters. Accordingly, the upper-limit function has been adopted for predicting entrainment as a function of drop size distribution. The calculation of entrainment involves a combination of distribution data and the buoyancy model. Figure 6. Effect of nozzle pressure drop on parameters in eqs 14 and 15. (a) Mean diameters, 7.9 in. from the spray axis and 19.7 in. below the nozzle. (b) Fraction of number of total drops contained in the first peak, 7.9 in. from the spray axis and 19.7 in. below the nozzle. (c) Standard deviations.

Figure 7. Effect of pressure drop on the geometric mean diameters for the two peaks (eqs 14 and 15).

solution of eq 17 provides the cumulative volume distribution for a given value of Dm, as shown in Figure 10. Use of logarithmic scales may be more suitable for depicting drop diameters smaller than 500 µm. According to eq 4 the value of Dm depends on the nozzle orifice diameter, the physical properties of the liquid, and the velocities of the gas and liquid phases. Thus, the upper-limit function model takes into account the effect on drop size distribution of these same

Experimental Work Experiments were carried out in an air-water contacting column containing a single spray nozzle. Four different nozzles were used to evaluate the effect on entrainment of orifice diameter, spray angle, and internal design. A flow diagram of the experimental system is shown in Figure 11. Air-Water Contacting Column. The bottom and middle sections of the column have an inside diameter of 17 in. The spray zone is 11.5-in. i.d. and contains an observation section of clear plastic. Details of the spray zone are shown in Figure 12. The water level in the sump is controlled by a siphon pipe and is checked by a level gage. Air enters the column in the bottom section about 6 in. above the water level. A six-foot bed of 2 in. metal Pall rings is used to provide good air distribution and to saturate the air passing to the spray section. The bed also captures any entrainment from the sump water. In the spray section an annular ring collector is used to collect entrained water that coalesces on the column wall (and which is part of the total entrainment from the spray). The elevation of the nozzle is such that the outermost liquid in the cone impinges at the ring location. Nozzles. Four solid-cone spray nozzles of different designs were used. Their specifications and sources are shown in Table 2. Their flow capacities as a function of nozzle pressure drop were provided by the vendors and were checked by a mass flowmeter with the finding that


Figure 10. Cumulative volume distributions obtained from the upper-limit function for different values of the maximum stable drop diameter Dm.

Figure 12. Top section of the contacting column.

Figure 11. Experimental apparatus.

the vendor data were accurate to within (2.0%. Nozzles MP187N, MP250N, and MP250M (Bete Fog Nozzle Co.) have internals that provide a maximum free passage. Nozzle 1/2HH25 (Spraying Systems Co.) has the same orifice diameter as MP187N (0.187 in.), but has a different internal design. Nozzles MP250N and MP250M have the same orifice size (0.25 in.), but different spray angles (60° and 90°, respectively). Details of the nozzles may be obtained from the vendors. A coalescer drum was used to collect the water drops in the overhead air stream. The drum has a tangential inlet nozzle to induce centrifugal separation and coalescence of the drops. A 6-in. thick woven wire mesh pad plus a special device called a cocurrent vapor-liquid separator tray (Fair and Seibert23) was used for final removal of drops. The special device contains a series of inclined narrow channels which promote the coalescence of liquid drops and carry the liquid to a lateral draw-off box. The total entrainment was obtained when the entrainment collected by the coalescer drum was added

Table 2. Spray Nozzle Specifications

nozzle

manufacturer

MP187N Bete Fog Nozzles

orifice spray press. liquida rate Dmb diam. angle drop (in.) (deg) (psi) (GPM) (µm) 0.187

60

1/2HH25 Spraying Systems 0.187

60

MP250N Bete Fog Nozzles

0.250

60

MP250M Bete Fog Nozzles

0.250

90

5 10 20 5 10 20 5 10 20 5 10 20

2.12 2.87 3.9 1.8 2.5 3.5 3.8 5.16 7.0 3.8 5.16 7.0

1990 1760 1530 1990 1760 1530 2320 2050 1780 2320 2050 1780

a Manufacturer’s information. b D m ) maximum stable drop diameter at a gas velocity of 20 ft/s.

to the entrainment collected by the annular ring in the spray section. Air flow from the blower was measured by a tube-type anemometer connected to a DP-cell. Flow rate was adjusted by venting a portion of the discharge air. The air inlet and exit temperatures were measured

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Figure 13. Total entrainment from nozzles. Gallons per minute measured at 65 °F, air velocity is based on 11.5-in. diameter column spray zone. (a) Nozzle MP187N; (b) nozzle 1/2HH25; (c) nozzle MP250N; (d) nozzle MP250M.

by thermocouples. An additional thermocouple measured the temperature of the exit air from the coalescer drum. Liquid entrainment measurements were taken for a given spray nozzle, air flow rate, and nozzle pressure drop operating at steady-state conditions. Entrained water was captured by the annular ring and by the coalescer drum. Details of the equipment and experimental procedure may be found in the thesis by Trompiz.24 Experimental Observations and Results General Observations. Once the air-water contacting column was placed in operation, the inlet air temperature increased slowly to about 30 °F above the ambient air temperature as a result of the heat of compression. Steady-state conditions were achieved about 10 min after the water spray was turned on and the air flow started through the contacting column. After this time, inlet and outlet air temperatures remained constant. However, each time the air flow rate was changed, inlet air temperatures changed and 5-10 min were required to achieve steady-state conditions. For changes in water flow, only 1-2 min were needed to achieve a new steady-state condition. During the operation of the contacting column, a large number of entrained drops were observed to reach the column wall and coalesce to a falling film; the film was

collected by the annular ring (Figure 12). Because most of the entrained large drops hit the column wall, the amount of the overhead entrainment collected in the coalescer drum was considerably less than the amount of water collected by the annular ring in the spray zone. Thus, the liquid collected in the annular ring simulates the commercial case where walls and adjacent sprays remove the bulk of the liquid drops carried through the spray by the gas. The overhead entrainment, which may be designated net entrainment, may represent the carryover that is independent of a target device, such as that used by Lin et al.,20,21 and is commonly used for sieve tray entrainment measurements. The gross or total entrainment is more representative of the carryover from the spray itself because it includes entrained drops that impact surfaces and are coalesced and measured. The practical application of entrainment level, as it affects efficiency, pressure drop, and downstream contamination, will require knowledge of the target device geometry, and the entrainment level in that case will probably be intermediate to the net and gross values reported in the present work. For large columns with multiple nozzles there is the question of whether the drop hitting the wall of the column in this work would coalesce and drop back to the multiple spray. This situation will be discussed later.


Figure 14. Experimental values of total entrainment compared with model predictions. Air-water, 20 psi nozzle pressure drop. Air velocity is based on 11.5-in. diameter column spray zone. (a) Nozzle MP187N; (b) nozzle 1/2HH25; (c) nozzle MP250N; (d) nozzle MP250N.

Results Figure 13 shows experimental entrainment data for the four nozzles used, plotted as a function of air velocity (and C-factor). The percentage entrainment may be calculated from the data given, and the highest values represent essentially 100% entrainment, that is, complete flooding. The data shown are total entrainment; the liquid collected by the ring in the spray zone ranged from 95.7% to 99.3% of the total. Detailed data are available elsewhere.24 A comparison of the results shown in Figure 13 shows that, for the same flow rate, spray angle, and orifice size the nozzle containing an x-shaped swirl device (1/ 2HH25) has a slightly lower entrainment than its counterpart with an s-shaped device (MP187N), indicating a somewhat coarser atomization. Nozzles with the larger orifice (MP250N, MP250N) have a lower entrainment for the same flow rate than those with the smaller orifice (1/2HH25, MP187N), indicating a coarser atomization. Finally, the 60° cone angle nozzle (MP250N) has a slightly higher entrainment than the 90° cone angle nozzle (MP250M), probably because of the lower cone surface of the latter. Model Testing Air-Water. Experimental results were compared with predicted values using the model described earlier in the paper. Example fits of the model for all four

Figure 15. Parity plot, model vs observed entrainment in GPM. All runs.

nozzles and a ∆P ) 20 psi are shown in Figure 14. A summary of the total fit is given in the parity plot (Figure 15). Nozzles MP187N, MP250N, and MP250M are relatively close to the experimental results. However, for nozzle 1/2HH25, the model predicts values above the experimental results. Even though nozzle 1/2HH25 has the same orifice diameter as the MP187N, its internal design is different.

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Figure 17. Percent entrainment from spray nozzle MP250W of Lin et al.,21 compared with model predictions. Air-water. Nozzle pressure drop 25 psi. Air velocity based on cross section of a 36in. diameter column.

Figure 16. Entrainment from Sprayco 5B nozzle of Pigford and Pyle,10 compared with model predictions. Air-water. Nozzle pressure drop 50 psi. Air velocity based on cross section of a 31.5in. diameter column. (a) Mass basis; (b) percentage basis.

Entrainment results reported by Pigford and Pyle10 for a bank of six Sprayco 5B solid-cone nozzles, in a 31.5in. air-water column, are compared with the modelpredicted values in Figure 16. For the same data, percentage entrainment is shown in Figure 16b. These data correspond to one of the six spray nozzles. The experimental values of entrainment reported by Pigford and Pyle are below those predicted by the model, probably because of the coalescence of entrained drops on the column wall. In addition, the multiple nozzle arrangement is expected to reduce the entrainment collected because entrained drops from one spray nozzle can be caught by the spray of an adjacent nozzle. Entrainment data of Lin et al.,21 who used a conventional spray nozzle (Bete MP281W, 120° angle) in a 36in. column, are compared with model predictions in Figure 17. Nozzle pressure drop was 25 psi. The experimental values are lower than those predicted because a chimney tray was used as a collector and a portion of the total entrainment was returned to the spray by the collector. The authors also provided entrainment data for air-water based on a G-Series nozzle; details of the nozzle have not been disclosed. The model predictions are much greater than the experimental values. Lin et al. reported a lower entrainment from this type of nozzle compared to the conventional nozzles (Figure 3). The G-Series nozzle is known to have internals that are part of a special proprietary design, but evidently the spray is relatively coarse, that is, has a larger fraction of large drops. Most of the differences between the model predictions and the reported values clearly result from coalescence of en-

Figure 18. Percent entrainment from G-Series nozzle of Lin et al.,21 compared with model predictions. Air-IsoPar-M. Nozzle pressure drop 10 psi. Air velocity based on cross section of a 36in. diameter column.

trained drops on the column wall and on the underneath surface of the chimney tray used to collect the entrainment. Air-Isopar-M. Isopar-M is one of several functional oils, marketed by Exxon Chemical Co. under the name Isopar, which contain mostly isoparaffin hydrocarbons. Isopar-M has a density of 48.89 lb/ft3, viscosity of 3.36 cP, and surface tension of 26.6 dyn/cm, all at room temperature. This particular fluid is useful for experimental work because it simulates the properties of many hydrocarbon liquids and is appropriate because of its low volatility and high flash point. Entrainmental values reported by Lin et al.21 for airIsopar-M and the G-Series spray nozzle are compared with the predicted entrainment at a nozzle pressure drop of 10 psi, as shown in Figure 18. Similar results were found for pressure drops of 7, 17, and 20 psi. The model-predicted values are in reasonable agreement with the measured values. At a pressure drop of 20 psi, the predicted entrainment is above the experimental values. At these conditions, a greater number of entrained drops can coalesce on the column wall and the underneath surface of the chimney tray; thus, the net entrainment collected on the target tray is smaller than the total entrainment, as predicted by the model.


Use of Model Use of the model for new designs can follow these steps: (1) For the required liquid flow rate and the column diameter, determine the number and arrangement of the nozzles. This determination is based on the nozzle selected, its spray angle, and liquid flow capacity for the available pressure drop. (2) Determine the height of the nozzles above the top packing surface. This establishes the degree of overlap or underlap of the spray patterns. (3) From eq 4, calculate the maximum drop diameter in the spray. (4) From eqs 10-12 and the well-established relationship between the drag coefficient and drop Reynolds number (e.g., refs 17 or 18), calculate the diameter of the largest entrained drop. (5) From Figure 10 (or its equivalent) and the values from steps 3 and 4, calculate the percent or fraction of the spray liquid entrained. This is the total entrainment; correct for the amount of coalescence caused by the impact of adjacent sprays. Conclusions A model has been developed for estimating the total entrainment from spray nozzles used as liquid distributors in packed columns. It includes the following features: (1) The drop buoyancy concept based on the balance of forces acting upon drops and the relationship between the drag coefficient and the Reynolds number. (2) A mathematical representation of the drop size distribution in a spray based on the upper-limit distribution function of Mugele and Evans.12 (3) The concept of the maximum stable drop diameter based on the empirical correlation of Mugele.14 Entrainment values predicted by this model have been compared with the experimental results obtained in the present work for the air-water system at atmospheric pressure in a 12-in. diameter column with a single spray nozzle. Model predictions have been compared also with the limited amount of experimental data found in the published literature, for air-water and air-paraffinic oil (Isopar-M) systems. The model provides total entrainment whereas most applications of nozzle distributors are in large columns with multiple nozzles and, often, not contacting air and water. Thus, depending on devices in the downstream gas flow, actual entrainment is likely to be less than that predicted by the model. This is because some of the liquid drops entrained from a spray are coalesced by (a) impact with a wall, (b) impact with a collector device above the spray, or (c) impact with the spray from an adjacent nozzle. We recommend that the model be used directly to determine total entrainment of water spray drops by countercurrent air flow. This will give a conservative prediction of entrainment for design. For liquids other than water, the model predicts the effect of liquid properties. For gases other than air, the model may be used also because it accounts for variations in gas density and viscosity. For multiple spray nozzles, coalescence of some entrained drops can be captured by the spray from

adjacent sprays; thus, the expected entrainment will be lower than that predicted by the model. Acknowledgment This study was funded by Petroleos de Venezuela S. A. and the Separations Research Program (SRP) of The University of Texas at Austin; the authors are grateful for this support. Dr. Frank Seibert of the SRP was especially helpful with the experimental work. Nomenclature A ) drop projected area in eq 7 (ft2) CD ) drag coefficient (dimensionless) CF ) C-factor, eq 9 (ft/s) C0 ) discharge coefficient of the spray nozzle (dimensionless) do ) nozzle orifice diameter (ft) D ) drop diameter or diameter of largest entrained drop, eq 12 (ft) Dm ) maximum drop diameter in the spray, eq 4 (ft) Dng1 ) geometric number mean diameter in the first peak of the bimodal distribution function, eq 6 (ft) Dng2 ) geometric number mean diameter in the second peak of the bimodal distribution function, eq 6 (ft) Dvg1 ) geometric volume mean diameter in the first peak of the bimodal distribution function, eqs 13 and 15 (ft) Dvg2 ) geometric volume mean diameter in the second peak of the bimodal distribution function, eqs 13a and 15 (ft) D0 ) minimum drop diameter for the second peak of the bimodal distribution function, eq 6 (ft) f(D) ) number or frequency distribution function of drops in a spray F(D) ) cumulative frequency distribution function of drops in a spray, eq 6 F(D3) ) cumulative volume distribution function of drops in a spray, eqs 15-17 g ) gravitational constant (ft/s2) GPM ) gallons per minute Re ) drop Reynolds number ) (DurFG)/µG (dimensionless) Re′ ) drop Reynolds number at entrainment condition, eq 12 (dimensionless) ReL ) Reynolds number of liquid at nozzle orifice ) dou0FL/ µL (dimensionless) t ) time (s) uL ) velocity of liquid drops with respect to the column wall (ft/s) uG ) superficial velocity of the gas (ft/s) ur ) relative velocity of liquid with respect to the gas (ft/s) uo ) liquid velocity through the spray nozzle orifice (ft/s) V ) fraction of the total volume contained in drops of diameter less than D in eqs 2 and 16 (dimensionless) We ) drop Weber number ) uG2FGD/σ (dimensionless) WeL ) Weber number of liquid (dimensionless) y ) substitution variable in the upper-limit distribution function, eqs 2 and 3 (dimensionless) Greek Letters R ) constant in the upper-limit distribution function, eq 3 (dimensionless) β ) ratio of number of drops contained in the first peak to the total number of drops in the bimodal distribution function, eq 6 (dimensionless) β′ ) ratio of the volume of drops contained in the first peak to the total volume of drops in the bimodal distribution function, eq 14 (dimensionless) δ ) parameter in the upper-limit distribution function, eq 2 (dimensionless) ∆p ) pressure drop for liquid flow through the spray nozzle (psi)

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µG ) gas viscosity (lb/ft‚s) µL ) liquid viscosity (lb/ft‚s) FG ) gas density (lb/ft3) FL ) liquid density (lb/ft3) σ ) surface tension (lb/s2) σg1 ) geometric standard deviation for the first peak of the bimodal distribution function, eq 6 (dimensionless) σg2 ) geometric standard deviation for the second peak of the bimodal distribution function, eq 6 (dimensionless)

Literature Cited (1) Rayleigh, L. On the Instability of Jets. Proc. London Math. Soc. 1878, 10, 4. (2) Tyler, E. Instability of Liquid Jets. Philos. Mag. (London) 1933, 11, 136. (3) Weber, C. Disintegration of Liquid Jets. Z. Angew. Math. Mech. 1931, 16, 504. (4) Haenlein, A. Disintegration of a Liquid Jet. Natl. Advis. Comm. Aeronaut. Tech. Memo. 1932, 659. (5) Fraser, R. P.; Eisenklam, P. Research into the Performance of Atomizers for Liquids. Imp. Coll. Chem. Eng. Soc. J. 1953, 7, 52. (6) Fraser, R. P.; Eisenklam, P.; Dombrowski, N.; Hasson, D. Drop Formation from Rapidly Moving Sheets. AIChE J. 1962, 8, 672. (7) Dombrowski, N.; Johns, W. R. The Aerodynamic Instability and Disintegration of Viscous Liquid Sheets. Chem. Eng. Sci. 1963, 18, 203. (8) Dombrowski, N.; Fraser, R. P. A Photographic Investigation into the Disintegration of Viscous Liquid Sheets. Math. Phys. Sci. 1954, 247, (924) 101. (9) York, J. L.; Stubbs, H. F.; Tek, M. R. The Mechanism of Disintegration of Liquid Sheets. Trans. ASME 1953, 75, 1279. (10) Pigford, R. L.; Pyle, C. Performance Characteristics of Spray-Type Absorption Equipment. Ind. Eng. Chem. 1951, 43, 1649. (11) Lefebvre, A. H. Atomization and Sprays; Hemisphere: New York, 1989.

(12) Mugele, R. A.; Evans, H. D. Droplet Size Distribution in Sprays. Ind. Eng. Chem. 1951, 43, 1317. (13) Lekic, A.; Bajramovic, R.; Ford, J. D. Droplet Size Distribution: An Improved Method for Fitting Experimental Data. Can. J. Chem. Eng. 1976, 54, 399. (14) Mugele, R. A. Maximum Stable Droplets in Dispersoids. AIChE J. 1960, 6, 3. (15) Fair, J. R. Sprays. In Kirk-Othmer Encyclopedia of Chemical Technology, 3rd ed.; John Wiley: New York, 1983; Vol. 21, p 466. (16) Sada, E.; Takahasi, K.; Morikawa, K.; Ito, S. Drop Size Distribution for Spray by Full Cone Nozzle. Can. J. Chem. Eng. 1978, 56, 455. (17) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena.; John Wiley: New York, 1960; p 192. (18) Perry, R. H., Green, D., Eds. Perry’s Chemical Engineers’ Handbook, 7th ed.; McGraw-Hill: New York, 1997. (19) Kister, H. Z. Distillation-Design; McGraw-Hill: New York, 1992. (20) Lin, D.; Lee, A. T.; Williams, S. D.; Lee, J. N.; Poon, J. A Case Study of Crude Vacuum Unit Revamp. Presented at the Annual Meeting of AIChE, New Orleans, 1996. (21) Lin. D.; Wu, K.; Yanoma, A.; Costanzo, S. Entrainment Limits and Operating Capacity of Large-Size Structured Packing with Sprayed Type Distributor. Presented at the Spring National Meeting of AIChE, Houston, 1997. (22) Lin, D., personal communication, Koch-Glitsch, Inc., 1998. (23) Fair, J. R.; Seibert, A. F. Contacting Mechanisms on a Cocurrent Flow Tray. Presented at the Annual Meeting of AIChE, San Francisco, 1994. (24) Trompiz, C. J. Liquid Entrainment from Spray Distributors for Packed Columns. M. S. Thesis, The University of Texas at Austin, May 1999.

Received for review June 15, 1999 Revised manuscript received August 23, 1999 Accepted August 23, 1999 IE9903902

Entrainment from Spray Distributors for Packed Columns - American

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