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RESEARCH NOTES New Technique for Measuring Fluid Flow Patterns on a Multiple Downcomer Tray Yumin Li, Lianghua Wang, and Kejian Yao* College of Chemical Engineering & Material Science, Zhejiang UniVersity of Technology, Hangzhou, 310032 China
Fluid flow patterns on a distillation tray played an important role in the tray efficiency. A new technique for measuring fluid flow patterns on a distillation tray was introduced. The new technique involved observing a step input of a liquid tracer of higher temperature while keeping a record with a thermal infrared camera, and the principle for measurement was also deduced. Experiments were carried out in a 1200-mm-diameter simulation column using two types of trays with one and two hanging downcomers. With the new technique, the detailed picture of the residence time distribution on a multiple downcomer tray was obtained. The results showed that the new technique was convenient, accurate, and not contaminated to measure the residence time distribution of the tray. A stagnant region existed in the multiple downcomer tray. The size of the stagnant region decreased with a decrease of the liquid rate and bubbling of air. The initial velocity of liquid entering the tray determined the flow pattern of the tray. 1. Introduction
2. New Technique
It is well-known that liquid flow pattern on large size trays is far from the uniform flow. The type of flow pattern includes liquid channeling, bypassing, and flow recirculation, which all result in losses of tray efficiency. For understanding more about the flow phenomena across large trays, many experiments have been carried out and a variety of techniques were developed. Simple techniques included floats dropped onto the surface of the froth1,2 and colored dye injection.1,3 Common methods included salt and fluorescein dye solution tracer injection.4-7 And, the use of the water cooling method gave temperature profiles of liquid on a tray analogous to concentration profiles.8,9 Additionally, the hydrogen bubble and flow vanes techniques gave liquid velocity distributions on the tray,10,11 and the cantilever strain gauge probe technique gave both direction and velocity directly.12 These studies have established a detailed picture of fluid flow patterns on the tray. However, those techniques had their limitations, and a simple, direct, and accurate indication of residence time distribution will be very useful. The fluid flow pattern of multiple downcomer trays is more complex than that of conventional trays, as the hanging downcomers of sequent trays are positioned perpendicularly to each other. The liquid in the downcomer flows downward onto the tray through the bottom orifices of the hanging downcomer. Zhu and Yu13 measured the liquid residence time distribution using a fiber optic technique, showing that the flow was not uniform and a low-rate pool was found in the tray center. However, the study was poor and a more detailed residence time distribution was necessary.
Ambient water flows on the tray in a simulator of a plate column. At a steady ambient water rate, the hot water at 90 °C is introduced into the inlet downcomer by a step input with the rate of 3% of the ambient water rate. The ambient and hot water are fully mixed in the inlet downcomer, and the warmer water with its temperature 2 °C higher than the ambient water is developed. That is, at time τ ) 0, the flowing water is switched from ambient water to warmer water. The warmer water is used as the tracer material of the step input. Therefore, the frontier curve between ambient and warmer water is formed and moves forward. The frontier curve represents the curve of constant residence time, and its movement is recorded by a ThermaCAM SC3000 infrared camera system. The ThermaCAM SC3000 measures the emitted infrared radiation from the liquid. The fact that the infrared radiation is a function of the liquid surface temperature makes the camera calculate and display this temperature with an accuracy up to 0.1 °C. The camera captures video movies at rate of 50 frames/ s. The isotherm function of the system software can highlight all spots which have the same temperature as the isotherm in the video image, so the frontier curve is indicated with the isotherm. The direction of water flow is perpendicular to the frontier curve, so a micro-component section perpendicular to the frontier curve is taken to indicate the temperature profile between warmer and ambient water, as shown in Figure 1. The water temperature, t, is plotted vs the position, z, of the direction of water flow in the micro-component section. At time τ ) 0 of the step input of warmer water, the temperature profile in the micro-component section is shown in Figure 1a, with the position of the step input being z ) 0. When the microcomponent section moves forward as the water flows, both heat transfer and mass-mixing diffusion occur between liquid
* To whom correspondence should be addressed. Tel.: 86-57188033009. Fax: 86-571-88033331. E-mail:
[email protected].
10.1021/ie060377z CCC: $37.00 © 2007 American Chemical Society Published on Web 03/30/2007
Ind. Eng. Chem. Res., Vol. 46, No. 9, 2007 2893
warmer and ambient water, we get
x)
t - t0 t1 - t0
(3)
Substituting eq 3 into eq 2 gives
∂t ∂2 t )D 2 ∂τ ∂z
(4)
Equation 4 holds for both a single phase of water and a biphase of water and air. 2.2. Differential Equation for Heat Transfer. With heat transfer and without mass-mixing diffusion between warmer and ambient water, according to Fourier’s law, the equation is
∂ 2t ∂t )R 2 ∂τ ∂z
(5)
where R is the thermal diffusivity coefficient. Equation 5 holds only for a single phase of water. For a biphase of water and air, air bubbles up through the water removing some heat of water evaporation, and then Figure 1. Temperature profile in one micro-component section of the frontier curve at time (a) τ ) 0 and (b) τ ) τ1: (1) temperature profile of warmer water; (2) position of z ) 0 of the step input of warmer water; (3) temperature profile of ambient water.
particles of warmer and ambient water and the temperature profile varies. At time τ ) τ1, the temperature profile is shown in Figure 1b. So, the temperature, t, is a function of z and τ, that is t ) t(z, τ). The frontier curve as the curve of constant residence time is represented by an isotherm in the region between ambient and warmer water. We want to determine a temperature, t′, of the temperature profile in Figure 1b to ensure that the position of z ) 0 is invariable in the micro-component section, when the temperature profile varies as the water flows. That is, we need to determine a temperature of t′ ) t(0, τ) which acts as the isotherm temperature. 2.1. Differential Equation for Mass-Mixing Diffusion. With mass-mixing diffusion and without heat transfer between warmer and ambient water, according to Fick’s law, the equation is
∂c1 ∂2c1 )D 2 ∂τ ∂z
(1)
where D is the eddy dispersion coefficient and c1 is the molar concentration of warmer water. Assuming that the total concentration, c, of warmer and ambient water is constant, we divide eq 1 by c, and then
∂x ∂2x )D 2 ∂τ ∂z
(2)
where x is the molar fraction of warmer water, and x ) c1/c. For the mixture of warmer and ambient water with a molar fraction of warmer water, x, and temperature, t, it is known that t is a function of x, that is t ) t(x) with x ) 0 at t ) t0 and x ) 1 at t ) t1. And, t0 and t1 are the temperatures of ambient and warmer water, respectively. Due to there being little difference in physical properties between the
Φ ∂t ∂2t )R 2∂τ F ∂z l‚cpl
(6)
where Φ is rate of heat transfer due to water evaporation when air is bubbling up through the water, Fl is the density of water, and cpl is the specific heat capacity of water. Neglecting the heat transfer from air to water because the temperature difference between them is small and the residence time of the air in the froth on the tray is very short, we get
Φ ) kH(Hw - H)rwa
(7)
where kH is the mass-transfer coefficient, Hw is saturation humidity, H is the humidity of air, rw is the latent heat of water, and a is the area of interface per unit froth volume on the tray. The mass-transfer coefficient, kH, depends on the Reynolds number, Re, and the Schmidt number, Sc, given by14
Sh ) 0.023Re0.81Sc0.44
(8)
And, the area of interface per unit forth volume, a, is15
a ) 10.72η-0.14
() us σ
2/3
(FgFlg)1/3
(9)
where η is the fractional hole area, us is the air velocity based on the total column cross-sectional area, and σ is the surface tension. 2.3. Differential Equation and Its Solution for Both MassMixing Diffusion and Heat Transfer. Both heat transfer and mass-mixing diffusion occur simultaneously, so the differential equation and boundary conditions (BCs) are
∂2t ∂t ) (D + R) 2 ∂τ ∂z
{
t , z0
(10)
{
t , z f -∞ BC2: at τ > 0, t ) t1, 0 z f +∞
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Figure 2. Sketch of test trays used in the experiments. (a) Tray with one hanging downcomer: (1) test tray; (2) outlet hanging downcomer; (3) inlet hanging downcomer; (4) hot water; (5) ambient water; (6) lens; (7) bottom orifice. (b) Tray with two hanging downcomers: (1) test tray; (2) outlet hanging downcomer; (3) inlet hanging downcomer; (4) hot water; (5) ambient water; (6) lens; (7) baffle; (8) bottom orifice; (9) segmental region. Table 1. Test Tray Dimensions
Solving the differential equation gives
(x
t1 + t0 t1 - t0 t(z,τ) ) erf 2 2
z
4(D + R)τ
)
(11)
where erf(x) is an error function which is symmetrical. So, a symmetrical curve for eq 11 is shown in Figure 1b, and then
t′ ) t(0, τ) ) 0.5(t1 + t0)
(12)
For a biphase of water and air, the differential equation is
∂2t Φ ∂t ) (D + R) 2 ∂τ F ∂z l‚cpl
(13)
The boundary conditions are identical to those of eq 10. Solving the differential equation gives
t(z,τ) )
(x [ ∫ (x
t1 + t0 t1 - t0 erf 2 2 Φ τFl‚cpl
τ
0
erf
z
4(D + R)τ z
)
-
4(D + R)(τ - ξ)
) ]
dξ (14)
And then
t′ ) t(0, τ) ) 0.5(t1 + t0) -
Φ τ Fl‚cpl
(15)
From eq 12 or 15, t′ is determined, so the isotherm as the frontier curve, that is, the curve of residence time distribution, is obtained. 3. Experimental Section The experiments were conducted in a plexiglass 1200-mmdiameter simulation column, using two types of trays with one and two hanging downcomers, respectively, shown schematically in Figure 2. There existed long rectangle bottom orifices
no. of hanging downcomers column diameter no. of trays width of downcomer weir height system sieve hole diameter fractional hole area no. of long rectangle bottom orifices of one downcomer area of one long rectangle bottom orifice
1 1200 mm 1 120 mm 50 mm water and air-water 8 mm 5.38% 6 orifices with 3 orifices for every side of downcomer 1850 mm
2 1200 mm 1 65 mm 50 mm water 7 orifices in the middle of downcomer 800 mm
in the bottom of the hanging downcomer for liquid leaving the downcomer. The system for the tray with one hanging downcomer was water and air-water, respectively, and the tray with two downcomers only had water. The tray with air-water was a sieve tray, whereas the tray with water was a smooth plate without any sieve holes. The tray parameters and operating ranges were given in Table 1. The baffles in Figure 2b prevented the water leaving inlet downcomer from entering the segmental region byside. The column only consisted of one tray as a test tray, and the inlet downcomer was fixed to the column wall without a tray so that the flow of water on the test tray could be recorded by the ThermaCAM SC3000 infrared camera. The lens of the camera was positioned above the test tray, as shown in Figure 2. The hot water of 90 °C was introduced into the inlet downcomer by a step input with the rate of 3% of the ambient water rate through a distributing device installed above the inlet downcomer, so the warmer water with its temperature, t1, 2 °C higher than that of ambient water, t0, left the inlet downcomer and entered the tray. When the water on the tray flowed toward the outlet weir, the frontier curve between ambient and warmer water moved across the tray. The movement of the frontier curve was recorded by the camera system.
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Figure 3. Frontier curves in one-quarter of the test tray captured by the ThermaCAM SC3000 infrared camera system: (1) warmer water; (2) inlet downcomer; (3) isotherm as frontier curve whose temperature is determined by eq 12 or 15; (4) ambient water.
The frontier curve was represented by the isotherm whose temperature of t′ was from eqs 12 and 15. For a biphase of water and air, the value of Φ/Flcpl was calculated to be 0.0693 °C/s according to eqs 7, 8, and 9, in the experimental conditions of a water temperature of 25 °C, an air temperature of 30 °C, an air humidity of 0.004 kg/kg, a liquid rate of 22.6 m3/h, and an Fs of 0.6 m/s(kg/m3)1/2. From eq 15, t′ is 0.5(t1 + t0) 0.0693τ, and then, t′ will reduce when the time of τ elapses. The frontier curve between warmer and ambient water in onequarter of the test tray was captured by the infrared camera, as shown in Figure 3. Video movies captured by the camera were transferred to a PC for analysis. Through processing the video images, the detailed picture of the residence time distribution was obtained. 4. Results and Discussions 4.1. Residence Time Distribution for Trays with One Hanging Downcomer. Figures 4 and 5 describe the liquid residence time distribution on one-quarter of the test tray, in which every curve of constant residence time is represented by the attached numbers in units of seconds. And, the attached numbers represent the value of the time of τ. The flow pattern, which is described by the residence time distribution, is determined by the magnitude and direction of the velocity of the liquid leaving the downcomer. 4.1.1. Using a Single Phase of Water. Figure 4a and b show the residence time distribution on the tray with one hanging downcomer using single phase of water. Liquid leaving the bottom orifices of the inlet downcomer is divided into three streams. The directions of two streams, with the same velocity, u1, are contrary to each other, parallel to the direction of the length of the long rectangle bottom orifices, whereas the direction of the third stream, with velocity u2, is perpendicular to the direction of the length of the bottom orifices. The liquid spends 0.5 s flowing across the distance from the position of the liquid entering the tray to the first curve of constant residence time. Through measuring the distance, u1 and u2 are obtained, and u1/u2 ) 2.5, as shown in Figure 4a. The two streams with velocity, u1, flow along the circular column wall, respectively. After arriving at the outlet downcomer, the two streams, by the obstruction of the weir, flow toward the middle of the weir along the weir as some liquid of the stream enters the downcomer over the weir. When they meet in the middle of the weir (as shown by number 12 in Figure 4a), the stagnant region is developed. The stream with velocity,
Figure 4. Residence time distribution on the tray with one hanging downcomer and a liquid rate of (a) 45.2, (b) 22.6, or (c) 22.6 m3/h and air at Fs ) 0.6 m/(s(kg/m3)1/2: (1) outlet downcomer; (2) weir; (3) active region; (4) path of the stream with velocity u1; (5) one of the two streams with velocity u1; (6) direction of the length of the long rectangle bottom orifices; (7) long rectangle bottom orifices; (8) third stream with velocity u2; (9) inlet downcomer; (10) path of the stream with velocity u2; (11) stagnant region; (12) middle of the weir.
u2, flows around the stagnant region, and enters the downcomer. Therefore, two regions, the active region and stagnant region, exist in the tray. The size of the stagnant region decreases with a decreasing liquid rate, as shown in Figure 4a and b. 4.1.2. Using a Biphase of Water and Air. Figure 4c shows the residence time distribution using a biphase of water and air with a liquid rate of 22.6 m3/h and an Fs of 0.6 m/s(kg/m3)1/2. And, the isotherm temperature of t′ is 0.5(t1 + t0) - 0.0693τ
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Initiating from the left inlet downcomer, the stream with velocity u1 flows towards the test tray center and joins with the opposite stream from right inlet downcomer at the tray center. And then, divided into two streams, the stream flows toward the middle of the weir (as shown by number 10 in Figure 5a) of the front and back of the outlet downcomer, respectively. After arriving at the outlet downcomer, the stream flows along the weir as some liquid of the stream enters the downcomer. The two streams with velocity u2 flow towards the front and back of the outlet downcomers along the baffle. After arriving at the outlet downcomer, the stream flows along the weir. Finally, the two streams from u1 and u2 meet, and then, the stagnant region is developed, as shown in Figure 5a. Two regions, the active region and stagnant region, also exist in the tray, and the size of the stagnant region also decreased with a decreasing liquid rate, as shown in Figure 5a and b. 4.3. New Technique for Measuring Residence Time Distribution. Using the new technique, the residence time distribution measured is reliable, and the residence time distribution in Figure 4c is similar to that of Zhu and Yu (see Figure 4 of ref 13). The new technique is convenient, similar to colored dye injection. The tracer of warmer water has the same physical properties as the liquid system of ambient water, due to having a 2 °C difference in temperature between warmer and ambient water; so, the tracer does not contaminate the system liquid, and the measurement is accurate and effective.
Figure 5. Residence time distribution on the tray with two hanging downcomers and a liquid rate of (a) 45.2 or (b) 22.6 m3/h: (1) direction of the length of the long rectangle bottom orifices; (2) third stream with velocity u1; (3) long rectangle bottom orifices; (4) one of the two streams with velocity u2; (5) left inlet downcomer; (6) path of the stream with velocity u2; (7) stagnant region; (8) weir; (9) front of the outlet downcomer; (10) middle of the weir; (11) path of the stream with velocity u1; (12) active region.
(see section 3). When the gas bubbles, the mixing action of the gas passing through the liquid superimposes a random movement of liquid particles onto the flow pattern of a single phase of liquid, which causes back-mixing in the active region and interchange of liquid between the active and stagnant regions. Hence, the stagnant region was nonexistent, but the flow still is not uniform. In Figure 4c, for the curve of constant residence time is associated with the number 8.0, and the time of τ is 8.0 s. So, t′ is 0.5(t1 + t0) - 0.0693 × 8.0, that is 0.5(t1 + t0) - 0.554. The temperature of 0.554 °C, due to the cooling effect of evaporation of water, is about 25% of the temperature difference of 2 °C. So, the cooling effect cannot be neglected. 4.2. Residence Time Distribution for Trays with Two Hanging Downcomers. Figure 5a and b shows the residence time distribution on the tray with two hanging downcomers using a single phase of water. The flow pattern is more complex. Liquid leaving the inlet downcomer is also divided into three streams. The directions of two streams with the same velocity, u2, are contrary to each other, perpendicular to the direction of the length of the long rectangle bottom orifices, whereas the direction of the third stream with velocity u1 is parallel to the direction of the length of the bottom orifices. And, u1/u2 ) 1.5, as shown in Figure 5a.
5. Conclusion The following conclusions can be drawn: (1) A new technique of using a step input of warmer water tracer is convenient, effective, accurate, and not contaminated to measure the residence time distribution of a tray. For a biphase, the cooling effect of the evaporation of water cannot be neglected. (2) The stagnant region exists in the multiple downcomer tray. The size of the stagnant region decreased with a decreasing liquid rate, and the bubbling of gas can reduce the size of the stagnant region because the bubbling of gas causes interchange of liquid between the active and stagnant regions. The initial magnitude and direction of the velocity of the liquid entering the tray determine the flow pattern of the tray. Nomenclature a ) area of interface per unit froth volume on the tray, m2/m3 c1 ) molar concentration of warmer water, kmol/m3 c ) total molar concentration of warmer and ambient water, kmol/m3 cpl ) specific heat capacity of water, kJ/(kg °C) Fs ) column F-factor ) usxFg, m/(s(kg/m3)1/2) Hw ) saturation humidity, mass of vapor per unit mass of vaporfree air H ) humidity of air, mass of vapor per unit mass of vapor-free air kH ) mass-transfer coefficient, kmol/(m2 s) rw ) latent heat of water, kJ/kmol t ) water temperature, °C t1 ) temperature of warmer water, °C t0 ) temperature of ambient water, °C t′ ) temperature ensuring that the position of the step input of warmer water is invariable in the micro-component section, °C u1 ) liquid velocity parallel to the direction of the length of the long rectangle bottom orifices, m/s
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u2 ) liquid velocity perpendicular to the direction of the length of the long rectangle bottom orifices, m/s us ) air velocity based on total column cross-sectional area, m/s x ) molar fraction of warmer water z ) coordinate of direction of water flow, m Re ) Reynolds number Sc ) Schmidt number Sh ) Sherwood number Greek Symbol R ) thermal diffusivity coefficient, m2/s τ ) time, s η ) fractional hole area σ ) surface tension, N/m Fl ) density of liquid, kg/m3 Fg ) density of gas, kg/m3 Φ ) rate of heat transfer due to water evaporation, kJ/(m3 s) Literature Cited (1) Porter, K. E. The effect of liquid channeling on distillation plate efficiency. Trans. Inst. Chem. Eng. 1972, 50, 91. (2) Lim, C. T. The effect of liquid channeling on two-pass distillation plate efficiency. Trans. Inst. Chem. Eng. 1974, 52, 193. (3) Weiler, D. W. Flow Hydraulics of large Diameter Trays. Chem. Eng. Progress 1973, 69, 10. (4) Richard, L. B. Experimental determination of residence time distributions on commercial scale distillation trays using a fiber optic technique. AIChE J. 1972, 18 (3), 491.
(5) Richard, L. B. Residence time and Fluid Mixing on commercial scale Sieve trays. AIChE J. 1972, 18 (3), 498. (6) Solar, R. B. Liquid flow patterns and velocity Distribution on commercial-scale sieve tray. AIChE J. 1986, 32 (4), 640. (7) Yu, K. T. Two-Dimensional Flow and Eddy diffusion on a sieve Tray. Chem. Eng. Sci. 1990, 45 (9), 2901. (8) Porter, K. E.; Davies, B.; Enjugu, B. A.; Ani, C. C. Investigating the effect of liquid flow pattern on sieve tray performance by means of water cooling technique. Inst. Chem. Eng. Symp. Ser. 1987, 104. (9) Porter, K. E.; Yu, K. T.; Chambers, S.; Zhang, M. Q. Flow patterns and temperature profiles on a 2.44 m diameter sieve tray. Trans. Inst. Chem. Eng. 1992, 70 (9), 489. (10) Hine, C. T. Effect of liquid flow patterns on distillation tray. Ph.D. Thesis, Aston University, UK, 1991 (11) Mu¨ller, E. A. Improving flow patterns in a distillation tray by modifying downcomer apron shape. Chem. Eng. Commun. 1988, 74 (2), 195. (12) Biddulph, M. W. Flow Characteristics of a small-holes sieve Tray. AIChE J. 1990, 36 (12), 1913. (13) Zhu, L. Y.; Yu, X. M. Promotions for Further Improvements in Multiple Downcomer Tray Performance. Ind. Eng. Chem. Res. 2004, 43 (20), 6484 (14) Mccabe, W. L.; Smith, J. C.; Harriott, P. Unit Operations of Chemical Engineering, 6th ed.; McGraw-Hill Companies, Inc: New York, 2001. (15) Song, H. H. Distillation Simulation; Tianjin University Press: Tianjin, China, 2005.
ReceiVed for reView March 27, 2006 ReVised manuscript receiVed October 26, 2006 Accepted February 26, 2007 IE060377Z
