Froth Heights on Dual-Flow Trays with a Heterogeneous Binary

Ind. Eng. Chem. Res. 2001, 40, 4951-4966

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Froth Heights on Dual-Flow Trays with a Heterogeneous Binary Azeotropic System and a Heterogeneous Ternary System with a Homogeneous Azeotrope Ian A. Furzer* Department of Chemical Engineering, University of Sydney, New South Wales 2006, Australia

Visual froth height measurements and the clear liquid heights on 20% free area dual-flow trays, operated at total reflux, have been obtained on the homogeneous system of water-steam, on the heterogeneous systems of ethyl acetate-water and ethyl acetate-ethanol-water, and in the homogeneous region near the homogeneous ternary azeotrope of that ternary system. The experimental results were obtained under distilling conditions at a total pressure of 101.3 kPa for a range of liquid and vapor densities and vapor velocities. The churn flow conditions on the dual-flow trays at total reflux were found to have the characteristic of constant volume fraction liquid in the froth for all systems investigated: ΦL ) 0.291; hf < 0.300. A correlating equation for the froth height that contains the impact pressure was found for all systems investigated to be hf ) 2.625(1/2FVu2)xFV/FL with hf < 0.300. A dimensionless correlating form, based on a modified Froude number, was found to be suitable for all systems: FrM ) 280.0 × 10-6(FV/FL)-1/2 with hf < 0.300. The clear liquid height was found for all systems to follow hCL ) ΦLhf with hf < 0.300. The dimensionless correlation for froth heights for all systems could be converted to a flooding vapor velocity relationship at total reflux for dual-flow trays by ufl ) 0.0283xZ(FV/ FL)-3/4 with Z < 0.300. Introduction A review1 has been completed of froth height measurements under distilling conditions on dual-flow trays at total reflux. That review included new experimental observations on froth heights on the single-component system (water-steam) and a ternary system with a ternary homogeneous azeotrope (ethyl acetate-ethanol-water). Attempts to correlate froth heights on sieve trays with downcomers and weirs with air-water simulators has led to empirical correlations that include the physical properties such as vapor density (FV) and liquid density (FL), tray characteristics such as weir height (hW), and operating conditions such as liquid (L) and vapor (V) flow rates. Churchill2 has shown the basic equations that describe the two-phase mixture on a sieve tray with downcomers and weirs has not been theoretically developed, when these empirical equations have been introduced. The formation of dimensionless groups, such as the Froude (Fr) number, may be inadequate if the basic theory is undeveloped:

Fr )

u2 ghf

(1)

The aim of this experimental work has been an attempt to identify the principal dimensional groups, and this may assist in developing a suitable mathematical model for the process. FRI3 (Fractionation Research International) data on the tray pressure drop on a column of 1.2 m diameter, containing sieve trays with downcomers and weirs, has been collected over a wide range of total pressure and with different binary systems. These data measurements effectively cover the change in vapor density from * E-mail: [email protected].

1.1 to 78 kg m-3 and the liquid density from 391 to 709 kg m-3. A plot of tray pressure drop at total reflux versus vapor velocity shows completely separated characteristics for different sets of FV and FL. For a constant tray pressure drop at total reflux, there is a lower vapor velocity at higher vapor density. If an attempt was made to correlate the tray pressure drops, then groups such as FVu, 1/2FVu2, and FV/FL may be important. Flooding was observed when the spray height equalled the tray spacing of 610 mm. Liquid entrainment4 rates from a tray to the tray above were observed to rise rapidly at vapor velocities near the flooding condition, resulting in reduced tray efficiencies. Two- and Three-Phase Flow Conditions The two-phase flow conditions on a tray under distilling conditions have been described as a froth, spray, emulsion, and foam. A macroscopic view of selected regions of the tray have seen developments in the analysis of vapor jets, bubble formation, droplets, spray, and Azbel’s5 treatment of a minimum energy condition, leading to a prediction of froth height. The two-phase flow conditions on the tray when froth is present can be described as churn flow. Liquid and vapor recirculation take place on the tray, combined with lateral oscillations from wall to wall. This description of the flow, as churn flow, has similarities to a churn flow description of two-phase flow in horizontal, inclined, and vertical tubes. An analysis of churn flow on a tray results in the basic describing equations, but the irregular geometry of mobile fluid volumes and the moving boundary conditions preclude any result at the present. The definition of froth height on a distillation tray has been attempted but is poorly defined. Azbel’s theory provides froth height as a limiting condition when the

10.1021/ie000874u CCC: $20.00 © 2001 American Chemical Society Published on Web 10/09/2001

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Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001

local liquid holdup is zero:

hF )

{ }

lim z h ΦL f 0 hCL CL

flow (ALV) provides

Experimental measurements of the vertical distribution of the liquid holdup above the tray floor have used the transmittance of light, X-rays, and γ-rays. The tail analysis of these distributions and a statistical test to verify if the distribution is at zero liquid holdup pose many numerical problems. The experimental measurements are unable to provide a well-described froth height measurement. Very few experimental results are available on froth heights under distilling conditions when two liquid phases are present and three-phase flow exists. Churn flow with two liquid phases can be described as the motion of irregular liquid volumes containing an emulsion. One liquid phase is dispersed in the other, continuous phase to form the emulsion. The intensity of the turbulence in the churn flow conditions controls the size of the irregular liquid volumes and the size distribution of the dispersed phase in the emulsion. The visual appearance of this three-phase distillation activity is a white milky emulsion. Froth height measurements in three-phase flow conditions are important for the design of columns operating under three-phase distillation conditions. Dual-flow trays are trays without downcomers and weirs, and the normal liquid cross-flow from downcomer to weir is absent. Churn flow is more active with dualflow trays in the absence of this liquid cross-flow. Threephase flow on dual-flow trays displays irregular liquid volumes with the two liquid phases contained within a mixed dispersed and continuous liquid volume. The froth height estimation on dual-flow trays with threephase flow is important for the design of columns operating under three-phase flow conditions. The froth height as observed, as the visual froth height, is a dynamic interface between the top of the froth regime and the base of the spray regime. Different observers will have different estimates of the visual froth height. The spray above the froth regime would appear to be considerably less important than the main bulk of liquid in the froth regime. Spray may be carried to the tray above as liquid entrainment. However, the visual observations indicate that flooding occurs when the visual froth height equals the tray spacing. The liquid downflow through the column results in a competition with the upflow of vapor for the free area of the dual-flow tray. Liquid passing through the free area is moving in a downward direction while entrained liquid from the tray below may be moving upward through the free area. The final liquid downflow through the free area is not entrained and interacts with the froth on the tray below and, most likely, reduces that froth height. Twoand three-phase froth on dual-flow trays in churn flow result in recirculating flows of liquid and vapor on the tray. Combined with this recirculating flow is an oscillatory motion traveling from wall to wall.

(4)

While the free area (AF) is a fixed constant for a tray, the values of AFV and AFL are mean or average values evaluated over a time ts, where ts is a sufficient time for the following integrals to converge:

AFV )

1 ts

∫0t AFV(t) dt

(5)

AFL )

1 ts

∫0t AFL(t) dt

(6)

s

s

A description of the vapor and liquid flows through the free area might consist of both flows occurring simultaneously through separate or combined holes, or there might be a pulsing type flow with all holes flowing vapor then liquid or a mixture of these flow patterns. The integrals given by eqs 5 and 6 ensure that an average free area is available for vapor and liquid flows and takes into account the complexity of these flow patterns. With three-phase flow, an emulsion flows through the liquid available free area (AFL). The vapor velocity (u) through the empty cross sectional area of the column is given by

u)

V ACSFV

(7)

The vapor velocity through the holes (uH) based on the full free area (AF) is

uH )

V ACSAFFV

(8)

u AF

(9)

uH )

The vapor velocity through the free area available for vapor flow (uFV) is

uFV )

t AFV(t)uFV(t) dt ∫ 0 AFVts

1

s

(10)

and the liquid velocity through the free area available for liquid flow (uFL) is

uFL )

1 AFLts

∫0t AFL(t)uFL(t) dt s

(11)

The full free area of a dual-flow tray is not available for vapor flow due to some of the free area being used for liquid flow. As a result

uFV > uH

(12)

At total reflux on a dual-flow tray

Correlating Variables The free area on a dual-flow tray is defined as

nAH AF ) ACS

AF ) AFV + AFL

(2)

(3)

The free area available for vapor flow (AFV) and liquid

AFL FL uFV ) uFL AFV FV

(13)

This introduces the density ratio term as a potential group for correlation. The volumetric liquid flow rate

Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 4953

(LVol; m3s-1) and the volumetric vapor flow rate (VVol; m3s-1) at total reflux provide

LVol FV ) VVol FL

The simple pressure balance giving

FrMFV ) 2 (14) Let a modified Froude number (FrM) be

This again introduces a density ratio term that may be important in correlation. The mass flow rate through the column is given by

V ) ACSFVu

(15)

V ) ACSAFVFVuFV

(16)

FrM )

FVu 2 FLghCL

u AFV

V ACSAFV

An important feature of the modified Froude numbers is the introduction of the density ratio term when a simple pressure balancing model is introduced.

(18)

Heterogeneous Azeotropic Systems

represents the mass flux (kg m-2 s-1) passing through the free area available for vapor flow on the dual-flow tray. This mass flux entering the froth above the dualflow tray drives the circulating flows in the churn flow regime. The mass flux in the empty cross sectional area of the column is given by

V ACS

(19)

1 F u AFV V FV

(20)

F Vu ) or

FV u )

The impact pressure of the vapor passing through the free area available for vapor flow on the dual-flow tray is given by

1 PIFV ) FVu2FV 2

(21)

The impact pressure of the vapor flowing in the empty cross section of the column is given by

1 PI ) FVu2 2

(22)

PI ) A2FVPIFV

(23)

or

It is tempting to propose a simple pressure balancing model with the equivalent hydrostatic pressure of a column of clear liquid (hCL) derived from the froth:

1 F u2 ) FLghCL 2 V FV

(24)

This could lead to a modified Froude number (FrMFV):

FrMFV )

FVu2FV FLghCL

(28)

(17)

The term

FVuFV )

(27)

where u is based on the empty cross sectional area of the column:

FrM ) A2FVFrMFV

or

uFV )

(26)

(25)

Visual froth heights on dual-flow trays under distilling conditions are affected by vapor velocity, liquid and vapor densities, and composition effects in binary and multicomponent systems. This composition effect can be described as being due to composition gradients in liquid films in the froth. These local composition gradients can result in changes in surface tension or dynamic surface tension and are grouped under the term Marangoni effect. Heterogeneous systems also have the additional complication of an interfacial tension or a dynamic interfacial tension between the two liquid phases in a froth consisting of dynamic irregular volumes of liquid. The composition effects can be eliminated by observing froth heights with a single-component system. There can be no composition gradients in this type of system. A column operated at total reflux will have a tray pressure drop, leading to a slight increase in temperature toward the reboiler. This may result in minor temperature gradients in the liquid in the froth, but the effect can be ignored. If water is selected as the single component, then the column operates at a temperature of 100 °C and a pressure of 101.3 kPa. The vapor density due to the low molecular weight of water is low and is readily available. The liquid density of water under the distilling conditions is also available. To ensure that only water is present in the column, it is necessary to flush the column several times to remove any residues from previous runs, which could have caused a surfactant effect. The composition effects can also be minimized through the use of binary and multicomponent azeotropes. All azeotropes, whether of homogeneous or heterogeneous form have the characteristics of equal vapor and liquid compositions of all components and equality of the bubble point and dew point temperatures. A column operated at total reflux and containing an azeotrope will have negligible composition gradients and hence a negligible Marangoni effect. The column will also exhibit very small temperature gradients and will operate at the bubble point temperature of the azeotrope, at the column pressure. Azeotropes have many characteristics that are similar to pure or single components in the column. When a heterogeneous azeotrope is present, the

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Figure 1. x-y diagram: ethyl acetate-water; P ) 101.3 kPa. Table 1. Binary Heterogeneous Azeotrope Ethyl Acetate-Water, P ) 101.3 kPa xI (EtAc)

xII (EtAc)

x (EtAc)

y (EtAc)

T (°C)

f

0.750

0.025

0.689

0.689

70.25

0.084

average liquid composition must be calculated from the composition of the individual phases, I and II:

xi )

LIxIi + LIIxII i LI + LII

i ) 1, 2, ..., nC

(29)

At the heteroazeotropic condition

yi ) xi i ) 1, 2, ..., nC

(30)

The fraction f (kg mol/kg mol) of the two-liquid-phase emulsion, often the aqueous phase, denoted by phase II, is given by

f)

LII LI + LII

(31)

The volumetric fraction fVol (m3/m3) of phase II is given by

fVol )

LII/FII ML LI/FIML + LII/FII ML

(32)

Figure 1 shows the phase equilibria, VLE (vaporliquid-equilibria) and VLLE (vapor-liquid-liquidequilibria) data at P ) 101.3 kPa for the binary system ethyl acetate-water, which forms a heterogeneous azeotrope. Details of the phase I and phase II compositions and f are given in Table 1. The binary heterogeneous azeotrope consists of an aqueous rich, phase II, that contains 0.084 (kg mol/kg mol) of the two-liquid-phase emulsion. This low value of f indicates that the aqueous phase is the dispersed phase in the emulsion. The phase diagram shows a wide range of liquid compositions from 0.025 to 0.750 mol frac (EtAc) that are in equilibrium with the vapor of composition 0.689 mol frac (EtAc).

Figure 2. Triangular diagram: ethyl acetate-ethanol-water; P ) 101.3 kPa.

A multitray distillation column that is initially charged with an ethyl acetate composition within that composition range and contains only one theoretical stage will lead to a reflux stream having a composition of the binary heterogeneous azeotrope. Figure 1 shows a multitray column charged with initially 0.400 mol frac (EtAc) and operated at total reflux with a 90% vapor tray efficiency. Only three actual trays are required for a very close approach to the azeotrope. All the experiments completed in this paper used an initial charge close to the heterogeneous azeotropic composition, thus ensuring that all trays in the column operated close to constant composition and temperature. This procedure ensured that there was a negligble Marangoni effect on the visual froth height measurements in this binary heterogeneous system. The phase equilibria for the ternary system ethyl acetate-ethanol-water is shown in Figure 2 as a part of a triangular diagram. The binary heterogeneous azeotrope between ethyl acetate-water is shown on the zero ethanol axis in Figure 2 and forms a node in the system. Another important, minimum bubble point temperature node is the ternary homogeneous azeotrope. An estimated distillation line connecting these two nodes is shown in Figure 2. Also shown in Figure 2 is the LLE data of Griswold et al.6 at T ) 70 °C, consisting of a number of LL tie-lines and the binodal curve. A distillation experiment at total reflux will follow the distillation line if the initial charge is close to the distillation line. When the tray compositions fall in the LL region, ternary heterogeneous behavior will be observed. The fraction (f) of the aqueous phase, phase II, is 0.084 (kg mol/kg mol) with the binary heterogeneous azeotrope ethyl acetate-water. As the tray compositions increase in ethanol to the first given LL tie-line shown in Figure 2 as the point L, the fraction f of the aqueous phase has decreased. The reduction in f continues until f is zero at the intersection of the distillation line with the binodal curve. All trays over this ethanol range will contain two liquid phases, and the emulsion will appear milky. Further extensions of


Figure 3. Experimental distillation column with 9 dual-flow trays.

the distillation line toward the ternary homogeneous azeotrope will result in normal VLE behavior with only one liquid phase on those trays. Those trays will have a clear liquid appearance, Recent7 distillation research has investigated the region of small temperature gradients surrounding this homogeneous ternary azeotrope. Experimental Equipment A glass column for visual observations of froth heights and the appearance of the froth had a diameter of 104 mm and contained nine dual-flow trays of 20% free area with a hole diameter of 8 mm on a 320-mm tray spacing. The column was operated at total reflux with a total pressure of 101.3 kPa. Figure 3 shows the special conditions for estimating the clear liquid holdup on a tray. Vapor (V) from a thermosiphon reboiler enters below tray 9 and after being condensed in the condenser is returned as reflux to tray 1. The liquid leaving tray 9 returns to the reboiler. Valves 1 and 2, as shown in Figure 3, could be closed simultaneously and the vapor supply quickly cut by turning off the steam supply to the reboiler. The liquid on all nine trays quickly dumped into the calibrated volume above valve 2 or for larger volumes into a second calibrated volume. The collected volume is the total liquid holdup (HT; m3). The average height of clear liquid on a tray is given by

hCL )

HT 9ACS

Figure 4. Series 1-3 experiments in the ternary system: ethyl acetate-ethanol-water; P ) 101.3 kPa.

water; and (iv) the ternary homogeneous region of the system, ethyl acetate-ethanol-water. The ternary system experiments were divided into three series according to the ethanol content on the trays. Figure 4 shows an expansion of the phase diagram for the system ethyl acetate-ethanol-water in a region near the distillation line. Series 1 experiments were confined to a completely ternary heterogeneous region at low ethanol compositions on all trays. All trays in the series 1 experiments showed a milky appearance, verifying that two liquid phases were present on all trays. Series 2 experiments were also in the ternary heterogeneous region, but due to the reduced value of f, the aqueous phase fraction on the tray resulted in a hazy appearance. Further increases in ethanol composition of the liquid on the trays resulted in the series 3 experiments, which were in the normal ternary VLE region with clear liquid on all trays. Visual Froth Heights and Clear Liquid Heights The volumetric liquid flow rate in the column could be determined accurately by closing valve 2, as shown in Figure 3, and measuring the time to fill a calibrated volume. At total reflux, the vapor velocity in the column is given by

(33)

The procedure by obtaining an average clear liquid height over nine trays provides a good estimate of hCL under distilling conditions. Visual froth height measurements were made on all nine trays. The appearance of the froth, whether clear or milky, was also observed on all nine trays. Both visual froth heights and clear liquid heights were observed over a wide range of vapor velocities. Froth heights, the appearance of the froth, and clear liquid heights were observed on (i) the single-component system, water-steam; (ii) the binary heterogeneous system, ethyl acetate-water; (iii) the ternary heterogeneous region of the system, ethyl acetate-ethanol-

u)

LVol FL ACS FV

(34)

These experimental arrangements permitted hf and hCL to be observed at a wide range of vapor velocities, u. The column was charged with a binary mixture of ethyl acetate-water near the heterogeneous azeotropic composition and operated at total reflux, at a total pressure of 101.3 kPa. All trays in the column were observed to have a milky appearance, confirming the presence of two liquid phases and that VLLE conditions existed. Experimental measurements were made to evaluate the visual froth height, clear liquid height, and vapor velocity. The nominal values of the physical

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Figure 5. Froth height; effect of vapor velocity on dual-flow tray 9. Binary heterogeneous system: ethyl acetate-Water. Total reflux, P ) 101.3 kPa.

Figure 7. Froth height; effect of clear liquid height on dual-flow tray 9. Binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

Figure 6. Clear liquid height; effect of vapor velocity on dualflow tray 9. Binary heterogeneous system: ethyl acetate-Water. Total reflux, P ) 101.3 kPa.

Figure 8. Froth height; effect of vapor velocity on dual-flow trays 2-9. Binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

Table 2. Nominal Physical Properties, P ) 101.3 kPa system

T (°C)

FL (kg m-3)

FV (kg m-3)

water-steam EtAc-W azeotrope EtAc-EtOH-W (all series 1-3)

100.0 70.0 70.0

1000.0 850.0 850.0

0.588 2.380 2.420

properties for the heterogeneous binary azeotrope are given in Table 2. Figure 5 shows the variation of froth height with vapor velocity for the heterogeneous binary system for tray 9. The froth height rises rapidly with vapor velocity, and there appears to be a considerable linear range. There is a minimum vapor velocity where no froth height was observed. The magnitude of the vapor velocities are reduced in this heterogeneous binary

system due principally to the high vapor density of 2.380 (kg m-3). Figure 6 shows the variation of clear liquid height with vapor velocity for the same runs in this heterogeneous system for tray 9. The experimental results show a smoother linear range. Figure 7 shows the variation of froth height with clear liquid height for tray 9. The figure indicates a strong relationship between these two variables for this binary heterogeneous system. Figure 8 shows the froth height and vapor velocity experimental results for trays 2-9 for the binary heterogeneous system. The minimum vapor velocity is clearly shown on this figure. Figure 9 shows the froth height and clear liquid height experimental results for


Figure 9. Froth height; effect of clear liquid height on dual-flow trays 2-9. Binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

Figure 11. Froth height; effect of clear liquid height on dualflow tray 9. Ternary heterogeneous system: ethyl acetateethanol-water. Total reflux, P ) 101.3 kPa.

Figure 10. Froth height; effect of vapor velocity on dual-flow tray 9. Ternary heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

Figure 12. Froth height; effect of vapor velocity on dual-flow trays 2-9. Ternary heterogeneous system: ethyl acetate-ethanolwater. Total reflux, P ) 101.3 kPa.

trays 2-9. Figure 9 confirms a strong relationship between these variables for this binary heterogeneous system.

nominal values of the physical properties of the ternary heterogeneous mixture are given in Table 2. Figure 10 shows the experimental results for this ternary heterogeneous system for the variation of froth height with vapor velocity for tray 9. Figure 11 shows the froth height and clear liquid height experimental results for tray 9 for this ternary heterogeneous system. There is a strong increase of froth height with vapor velocity and a strong relationship between froth height and clear liquid height in this ternary heterogeneous system. Figure 12 shows the experimental froth height and the variation with vapor velocity for trays 2-9 for the ternary heterogeneous system. There is a considerable range where a linear relationship could be applied.

Ternary Heterogeneous Froth Heights The ternary heterogeneous system ethyl acetateethanol-water was observed in the column with nine dual-flow trays. The ethanol composition could be described as very low and covers the range, shown in Figure 4, as series 1. The tray by tray composition profile followed the distillation line for series 1, as shown in Figure 4. All trays in the column were observed to have a milky appearance, confirming the presence of two liquid phases and that VLLE conditions existed. The

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Figure 13. Froth height; effect of clear liquid height on dualflow trays 2-9. Ternary heterogeneous system: ethyl acetateethanol-water. Total reflux, P ) 101.3 kPa.

Figure 15. Froth height; effect of clear liquid height on dualflow tray 9. Ternary moderately heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

Figure 14. Froth height; effect of vapor velocity on dual-flow tray 9. Ternary moderately heterogeneous system: ethyl acetateethanol-water. Total reflux, P ) 101.3 kPa.

Figure 16. Froth height; effect of vapor velocity on dual-flow trays 2-9. Ternary moderately heterogeneous system: ethyl acetateethanol-water. Total reflux, P ) 101.3 kPa.

Figure 13 shows the variation of froth height with clear liquid height for trays 2-9 for this ternary heterogeneous system. Further additions of ethanol resulted in the series 2 experiments that followed the distillation line in Figure 4. The ethanol compositions could be described as moderately low and cover the range shown as series 2 in Figure 4. All trays in the column were observed to have a hazy appearance, confirming the presence of two liquid phases and that VLLE conditions existed. The hazy rather than the milky appearance was due to the reduced fraction of the aqueous rich phase and the approach along the distillation line toward the binodal curve.

Figure 14 shows the experimental froth height and the variation with vapor velocity for tray 9 for this moderately ternary heterogeneous system. Figure 15 shows the variation of froth height with clear liquid height for tray 9 for this moderately ternary heterogeneous system. A linear relationship could be considered for both Figures 14 and 15. Figure 16 shows the experimental froth height variation with vapor velocity for trays 2-9 for this moderately ternary heterogeneous system. Figure 17 shows the variation of froth height with clear liquid height for trays 2-9 for this moderately ternary heterogeneous system. The linear relationship is further developed in Figures 16 and 17.


Figure 17. Froth height; effect of clear liquid height on dualflow trays 2-9. Ternary moderately heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

Figure 19. Froth height; effect of clear liquid height on dualflow tray 9. Ternary homogeneous system: ethyl acetate-ethanolwater. Total reflux, P ) 101.3 kPa.

Figure 18. Froth height; effect of vapor velocity on dual-flow tray 9. Ternary homogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

Figure 20. Froth height; effect of vapor velocity on dual-flow trays 2-9. Ternary homogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

Increased addition of ethanol resulted in series 3 experiments, which were in the homogeneous region of the ternary system ethyl acetate-ethanol-water. The series 3 experiments followed the distillation line shown as series 3 in Figure 4. The ethanol compositions could be described as low and cover the range shown in Figure 4. All trays in the column were observed to have a clear appearance, indicating that only one liquid phase was present and thatVLE conditions existed. Figure 18 shows the experimental froth height and the variation with vapor velocity for tray 9 for this ternary homogeneous region. Figure 19 shows the variation of froth height with clear liquid height for tray 9 for this ternary homogeneous region.

Figure 20 shows the experimental froth height variation with vapor velocity for trays 2-9 for this ternary homogeneous region. Figure 21 shows the variation of froth height with clear liquid height for trays 2-9 for this ternary homogeneous region. The linear relationship can be developed in Figures 20 and 21. Correlating Groups for Froth Heights Figure 22 shows a comparison of the froth height and vapor velocity characteristics for dual-flow tray 9 at total reflux for the homogeneous single-component system, water-steam, and the binary heterogeneous system, ethyl acetate-water. The results show quite clearly the complete separation of the characteristics between the

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Figure 21. Froth height; effect of clear liquid height on dualflow trays 2-9. Ternary homogeneous system: ethyl acetateethanol-water. Total reflux, P ) 101.3 kPa.

Figure 22. Froth height; effect of vapor velocity on dual-flow tray 9. Comparison of homogeneous system: water-steam and binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

froth heights for a homogeneous and a binary heterogeneous system. Table 2 shows that the ratio of vapor densities of the ethyl acetate-water system to the water-steam system is 4.050. The system with the low vapor density has the higher vapor velocity for the same froth height. Likewise the higher vapor density of the ethyl acetate-water system leads to lower vapor velocities for the same froth height. This separation of the characteristics with a difference in vapor density has many similarities to the FRI3 data on the separation of pressure drop characteristics for systems with different vapor densities. An important conclusion that can be reached from Figure 22 is that vapor velocity alone

Figure 23. Froth height; effect of clear liquid height on dualflow tray 9. Comparison of homogeneous system: water-steam and binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

Figure 24. Froth height; effect of vapor velocity on dual-flow tray 9. Comparison of homogeneous system: water-steam, ternary homogeneous system: ethyl acetate-ethanol-water, and ternary heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

cannot correlate froth height data on dual-flow trays at total reflux. Figure 23 shows a comparison of the froth height and clear liquid height characteristics for dual-flow tray 9 at total reflux for the homogeneous system, watersteam, and the binary heterogeneous system, ethyl acetate-water. The preliminary assessment indicates an almost overlap of the experimental data for the two systems. Vapor density would appear to be a minor component in any correlation of froth height with clear liquid height. Figure 23 shows a strong linear relation-


Figure 25. Froth height; effect of clear liquid height on dualflow tray 9. Comparison of homogeneous system: water-steam, binary heterogeneous system: ethyl acetate-Water, ternary homogeneous system: ethyl acetate-ethanol-water, and ternary heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

Figure 26. Froth height; effect of clear liquid height on dualflow trays 2-9. Comparison of homogeneous system: watersteam, binary heterogeneous system: ethyl acetate-water, ternary homogeneous system: ethyl acetate-ethanol-water, and ternary heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

ship between froth height and clear liquid height for both a homogeneous and a binary heterogeneous system. Figure 24 shows the froth height and vapor velocity characteristics for tray 9 at total reflux for the ternary heterogeneous system, ethyl acetate-ethanol-water, for series 1 and 2 runs plus series 3 runs for the ternary homogeneous region. The ternary homogeneous and heterogeneous runs almost overlap the characteristics for the binary heterogeneous system, ethyl acetate-

Figure 27. Froth height; effect of impact pressure on dual-flow tray 9. Comparison of homogeneous system: water-steam and binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

water. There is a clear and positive separation of the ternary homogeneous and heterogeneous characteristics from the homogeneous system, water-steam. Table 2 shows that the vapor density of series 1-3 runs has a nominal value of 2.420 kg m-3, which is similar to the vapor density of the ethyl acetate-water azeotrope. The vapor density ratio of the ternary system to the watersteam system is 4.160. A preliminary assessment of the ternary characteristics would indicate that vapor density is an important correlating variable and covers both homogeneous and heterogeneous systems. Figure 25 shows the froth height and clear liquid height characteristics for tray 9 at total reflux for the ternary heterogeneous system, ethyl acetate-ethanolwater, for series 1-3 runs. The ternary homogeneous and heterogeneous runs almost overlap the characteristics for the binary heterogeneous ethyl acetate-water runs and the homogeneous single-component watersteam runs. Figure 25 indicates a strong linear relationship between froth height and clear liquid height for tray 9 that covers both homogeneous and heterogeneous systems, Figure 26 shows the strong relationship between froth height and clear liquid height for trays 2-9 at total reflux for the binary heterogeneous system, ethyl acetate-water; for the ternary heterogeneous system, ethyl acetate-ethanol-water; and in the ternary homogeneous region of that ternary system. The experimental data can be correlated by the simple relationship

hf ) 3.730hCL - 0.019 hf < 0.300

(35)

A line passing through the origin is given by

hf ) 3.440hCL hf < 0.300

(36)

hCL ) 0.291hf hf < 0.300

(37)

or

From eq 36, the mean volume fraction of liquid in the

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Figure 28. Froth height; effect of impact pressure on dual-flow tray 9. Comparison of homogeneous system: water-steam, binary heterogeneous system: ethyl acetate-water, ternary homogeneous system: ethyl acetate-ethanol-water, and ternary heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

froth is given by

ΦL ) 0.291 hf < 0.300

(38)

It should be noted that the physical properties are absent in eqs 35-38. The effects of changes in physical properties are most likely to be equivalent with respect to both hf and hCL. Also it should be noted that the mean volume fraction of liquid in the froth, given by eq 38, is constant. That is the churn flow condition on a dualflow tray at total reflux is characterized by the value of ΦL of 29.1% when the froth height is below 0.300 m. Figures 25 and 26 show that the experimental results for both heterogeneous and homogeneous systems are characterized by a single correlating equation. The froth height correlations that have been published for distillation trays with downcomers and weirs have used the F number as a correlating variable:

F ) uxFV

(39)

It is useful to introduce in eq 39 the impact pressure PI given by

1 PI ) FVu2 2

(40)

1 PI ) F2 2

(41)

The impact pressure contains the vapor density and may be an important correlating variable for froth heights on dual-flow trays at total reflux. Figure 27 shows the froth height and impact pressure characteristic for dual-flow tray 9 at total reflux for the watersteam system and the binary heterogeneous system, ethyl acetate-water. There is a complete separation of the characteristics, indicating that the impact pressure, which contains FV, is inadequate to correlate the two

Figure 29. Froth height; effect of modified impact pressure on dual-flow tray 9. Comparison of homogeneous system: watersteam and binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

systems. Figure 28 shows a similar figure of froth height and impact pressure characteristics but includes the ternary heterogeneous system, ethyl acetate-ethanolwater for series 1 and 2 runs and a ternary homogeneous region, series 3, in this ternary system. There may be a mild separation of the characteristics between binary and ternary systems. However, the higher vapor densities in the binary and ternary systems show a completely separated characteristic from the lower vapor density system of water-steam. The vapor velocity in the area of the dual-flow tray available for vapor flow may play a significant part in the separation of the characteristics and also any differences in the ratio of the volumetric flow rates at total reflux. This introduces a function of the vapor to liquid densities as a dimensionless group that may correlate the variables in Figure 28. Assume that the following correlating form applies:

1 hf ) a FVu2 2

(

)xF

FV

(42)

L

where a is a constant to be determined and has the units of Pa-1 m. Figure 29 shows the modified characteristics for the water-steam system and the binary heterogeneous system, ethyl acetate-water, with hf graphed against the group:

(21F u )xF 2

FV

V

(43)

L

The square root function on the vapor to liquid density ratio appears satisfactory, and Figure 29 is a major improvement over the characteristics shown in Figure 27. Figure 30 shows the correlating effect of the term on trays 2-9 for both the homogeneous water-steam system and the heterogeneous ethyl acetate-ethanolwater system. Figure 31 extends that correlating effect


Figure 30. Froth height; effect of modified impact pressure on dual-flow trays 2-9. Comparison of homogeneous system: watersteam and binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

Figure 32. Froth height; effect of correlating group on dual-flow tray 9. Comparison of homogeneous system: water-steam and binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

Figure 31. Froth height; effect of modified impact pressure on dual-flow trays 2-9. Comparison of homogeneous system: watersteam, binary heterogeneous system: ethyl acetate-water, ternary homogeneous system: ethyl acetate-ethanol-water, and ternary heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

Figure 33. Froth height; effect of correlating group on dual-flow trays 2-9. Comparison of homogeneous system: water-steam and binary heterogeneous system: ethyl acetate-water. Total reflux, P ) 101.3 kPa.

for trays 2-9 for all systems: the homogeneous watersteam, the heterogeneous ethyl acetate-water and ethyl acetate-ethanol-water system, and the homogeneous region of that ternary system. The modified Froude number (FrM) given by eq 27 contains the liquid density FL, and this indicates a correlating group of the form

(21F u )F1 xF

FV

2

V

L

may be significant.

L

(44)

Figure 32 shows the adjusted characteristics for froth height for this new group for tray 9 for both the homogeneous water-steam system and the heterogeneous ethyl acetate-water system. There is an improved overlap of the experimental data for these two systems. Figure 33 is similar to Figure 32 but covers trays 2-9. The overlap of the experimental data is present for these trays. Figure 34 shows the froth height characteristics for the new group for all systems: the homogeneous water-steam, the heterogeneous ethyl acetate-water and ethyl acetate-ethanol-water system, and the homogeneous region of that ternary system. There is a good correlating effect between the variables.

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Figure 34. Froth height; effect of correlating group on dual-flow trays 2-9. Comparison of homogeneous system: water-steam, binary heterogeneous system: ethyl acetate-water, ternary homogeneous system: ethyl acetate-ethanol-water, and ternary heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

Figure 35. Froth height; linear correlation with modified impact pressure on dual-flow trays 2-9. Comparison of homogeneous system: water-steam, binary heterogeneous system: ethyl acetatewater, ternary homogeneous system: ethyl acetate-ethanolwater, and ternary heterogeneous system: ethyl acetate-ethanolwater. Total reflux, P ) 101.3 kPa.

Conclusions Figure 35 shows the correlation of all the experimental data points for trays 2-9 at total reflux with the group shown in eq 43. The correlating equation for all systems (the homogeneous water-steam, the heterogeneous ethyl acetate-water and ethyl acetate-ethanolwater system, and the homogeneous region of that ternary system) is given by

)x F

FV

1 hf ) 2.625 FVu2 2

(

hf < 0.300

(45)

L

Figure 36 shows the correlation of all the experimental data points for trays 2-9 at total reflux with the group shown in eq 44. The correlating equation for all systems (the homogeneous water-steam, the heterogeneous ethyl acetate-water and ethyl acetate-ethanolwater system, and the homogeneous region of that ternary system) is given by

1 1 hf ) 2500.0 FVu2 2 FL

(

)

x

FV hf < 0.300 FL

(46)

The modified Froude number includes the clear liquid height hCL in eq 27, and the experimental results for churn flow on dual-flow trays show a direct linear relationship with froth height given by eq 37. The modified Froude number in terms of hf becomes

Figure 36. Froth height; linear correlation with correlating group on dual-flow trays 2-9. Comparison of homogeneous system: water-steam, binary heterogeneous system: ethyl acetate-water, ternary homogeneous system: ethyl acetate-ethanol-water, and ternary heterogeneous system: ethyl acetate-ethanol-water. Total reflux, P ) 101.3 kPa.

be rewritten as

2

FrM )

FVu FLΦLghf

(47)

where the volume fraction of liquid in the froth φL was found to be a constant given by eq 38. Equation 46 can

()

(48)

()

(49)

FVu2 1 FV 2 ) FLΦLghf 2500 ΦLg FL

-1/2

or

FrM ) 280.0 × 10-6

FV FL

-1/2


area dual-flow trays at total reflux for both homogeneous and heterogeneous systems. Acknowledgment The experimental data was collected by M. Connolly and D. Garratt. Nomenclature

Figure 37. Flooding characteristics of dual-flow trays. 20% free area; total reflux.

The experimental results of all systems, including homogeneous and heterogeneous systems, are covered by the dimensionless correlating eq 49. The modified Froude number is only a simple function of the liquid and vapor densities for churn flow on 20% free area dual-flow trays at total reflux. It is useful to convert the correlating eq 49 into a flooding vapor velocity curve for 20% free area dualflow trays at total reflux. Let the froth height equal the tray spacing, Z at flooding, and the flooding vapor velocity is ufl:

ACS ) cross sectional area (m2) AF ) free area on the dual-flow tray (-) AFL ) free area available for liquid flow (-) AFV ) free area available for vapor flow (-) AH ) area of a hole on a dual-flow tray (m2) F ) F number defined by eq 39 (Pa0.5) Fr ) Froude number defined by eq 1 f ) liquid fraction in a two-liquid-phase mixture (kg mol/ kg mol) g ) gravitational constant (ms-2) HT ) total liquid holdup in the column (m3) hCL ) clear liquid height (m) hW ) weir height (m) L ) liquid flow rate (kg mol s-1) n ) number of holes PI ) impact pressure defined by eq 40 (Pa) T ) temperature (K) t ) time (s) ts ) sufficient time (s) u ) vapor velocity based on empty column cross sectional area (m2) V ) vapor flow rate (kg s-1) x ) liquid composition (mol frac) y ) vapor composition (mol frac) z ) z direction through froth Z ) dual-flow tray spacing (m) Greek Letters

Z ) hf

(50)

ufl ) u

(51)

ΦL ) volume fraction liquid in the froth F ) density (kgm-3) Superscripts I ) organic rich liquid phase II ) aqueous rich liquid phase

The flooding equation becomes

()

ufl ) 0.0283xZ

FV FL

-3/4

Z < 0.300

(52)

Figure 37 shows the graphical relationship between ufl and the ratio of the vapor to liquid density when Z varies from 0.100 to 0.300 m in steps of 0.050 m. An important conclusion of this examination of a wide range of experimental data of froth heights on 20% free area dual-flow trays at total reflux is that the significant dimensionless groups are the modified Froude number and the ratio of the vapor to liquid densities. The correlating equation covers a wide range of homogeneous and heterogeneous systems at the boiling point and bubble point temperatures. The froth can be described as being under churn flow conditions with a constant value for the volume fraction of liquid in the froth. This constant condition applies to a wide range of homogeneous and heterogeneous systems at the boiling point and bubble point temperatures. The correlation of the clear liquid height is simple under these conditions. Finally the correlating equation has been rearranged to give a new flooding curve for 20% free

Subscripts F ) free area FL ) free area available for liquid flow FV ) free area available for vapor flow f ) froth H ) hole i ) component identification M ) modified MFV ) modification based on free area available for vapor flow ML ) molar liquid Vol ) volumetric

Literature Cited (1) Furzer, I. A. Froth Heights on Dualflow Trays with a Ternary Azeotropic System of Ethyl Acetate-Ethanol-Water. Ind. Eng. Chem. Res. 2000, 39, 1430-1436. (2) Churchill, S. W. The Art of Correlation. Ind. Eng. Chem. Res. 2000, 32, 1850. (3) Sakata, M.; Yanagi, T. Performance of a Commercial Scale Sieve Tray. Ind. Chem. Eng. Symp. Ser. 1979, No. 56, 3.2/21-3.2/ 34.

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(4) Kister, H. Z. Distillation Design; McGraw-Hill: New York, 1992. (5) Azbel, D. Two-Phase Flows in Chemical Engingeering; Cambridge University Press: Cambridge, 1981. (6) Griswold, J.; Chu, P. L.; Winsauer, W. O. Phase Equilibria in Ethyl Alcohol-Ethyl Acetate-Water System. Ind. Eng. Chem. 1949, 41, 2352.

(7) Furzer, I. A. Critical Distillation Experiments in a Region Near the Homogeneous Ternary Azeotrope in the System: Ethyl Acetate-Ethanol-Water. Ind. Eng. Chem. Res. 2000, 40, 990.

Received for review October 11, 2000 Accepted August 1, 2001 IE000874U

Froth Heights on Dual-Flow Trays with a Heterogeneous Binary

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