Ind. Eng. Chem. Res. 2003, 42, 2219-2222
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SEPARATIONS New Method for Designing an Energy-Saving Tray and Its Hydrodynamic Aspects: Temperature Distribution and Efficiency of Deflected Tray-95 Zheng Zhou, Ying Chun Liang, and Zhi Bing Zhang* Department of Chemical Engineering, Nanjing University, Nanjing 210093, People’s Republic of China
A series of well-designed deflectors were placed on the tray-95 to improve the flow pattern. A phenomenon of multiple plug flow was observed in each liquid flow channel between two deflectors on the deflected tray-95. In compliance with the theoretical prediction, temperature profiles of the liquid layer on the tray were measured both vertically and horizontally by resistive thermal detectors. An oxygen desorption experiment was carried out, and the oxygen concentrations in the inlet and outlet liquids were detected by iodometry. Then the liquid-phase Murphree tray efficiencies (EML) were calculated. The results show that the well-designed and well-placed deflectors can obviously increase the tray efficiency by almost 30% under the same operating conditions. Introduction As the most important tower internal parts, trays are widely used in various fields. Research and development of new types of trays are being done continually. On the basis of the results of entropy generation rate analysis,1 an energy-saving tray, the tray-95,2 was designed and tested. It offers a lower pressure drop and permits larger flow rates than a conventional sieve tray. However, similar to all conventional trays, the tray-95 also has an eddy area on each side of the main liquid flow on the tray. In these two areas, there is a serious backmixing of liquid flow (see Figure 2 of ref 2). The mass transfer between the vapor and liquid phases is weakened by the nonideal flow so that the overall tray efficiency is decreased. The flow pattern plays an important role in the tray efficiency and affects other key properties such as capacity and flexibility. Many experiments have been carried out to study the flow pattern, and several methods have been developed to improve it. Tedder3 used a system of intermediate weirs, risers, and curtainpattern vapor holes on his T-By tray to set up a series of multiple vapor-liquid contacting cells (see Figure 2 of ref 3). These small mixing cells not only promote plug flow but also provide positive contact zones for mass transfer. It was reported that T-By trays can improve the tray performance, but its structure is somewhat more complex (it was rectangular) than that of the conventional trays. In addition, inappropriate hole patterns or cell dimensions may lead to excessive pressure drops per tray as well as reductions in tray capacities. Yu and Huang4 and Zhou et al.5 studied the flow patterns and liquid velocity distributions using tracer techniques on large-diameter (not less than 1 m) * To whom correspondence should be addressed. Tel.: +8625-3593772 and +86-25-3596665. Fax: +86-25-3317761. Email:
[email protected].
trays. Their experiments further verified that there exist highly nonideal flowing behaviors on the tray. Zhao et al.6 suggested that the ideal flow pattern could be approached by placing suitable inlet weirs of varying heights. Commercial applications have confirmed that this method can significantly improve the tray efficiency. However, this way cannot be applied to trays without inlet weirs, for example, the 95 trays. So, Li et al.2 recommended setting deflectors on these trays. As the continuation of Li’s work, this work is not only to improve the flow pattern with well-designed deflectors but also to measure the liquid layer temperatures and the overall tray efficiencies to evaluate the effectiveness of these deflectors. Experimental Section General Description of the Deflectors. The tray95 was described in a previous study.2 Specifications of the deflectors were presented in Table 1 of that paper. Deflector no. 3 was adopted in this test. Its height and form were kept unchanged. Also, its length was increased to about 1 m to achieve a “full-guide” from the inlet to the overflow weir, which was expected to eliminate the liquid maldistribution near the overflow weir. Deflectors were arranged like the meridians (this is because the meridians separate every parallel of latitude into isometric segments) of the globe on plane maps (see Figure 1; considering the tray as the earth, the dotted lines represent the parallels of latitudes, and then the deflectors are set along with the meridians), dividing the bubbling region of the tray into several long and narrow flow channels. Coming from the inlet, the liquid was evenly guided into these paths. The liquid vortex and backflow were almost eliminated because the velocity gradient of cross-flow was greatly reduced in each path to approximately zero. Thus, the plug flow, an ideal flow pattern, was almost approached, and the multiple-plug-flow pattern could be set up. The same
10.1021/ie020720+ CCC: $25.00 © 2003 American Chemical Society Published on Web 03/29/2003
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Figure 3. Vertical temperature profile of the liquid layer. Figure 1. Arrangement of the deflectors on tray-95.
Figure 4. Horizontal temperature profile of the liquid layer.
outlet of the tray at the same time. Oxygen contents were titrated7 by iodometry without delay. Then EML can be calculated through Figure 2. Settings of RTDs.
method can be applied to other round trays such as valve trays and all conventional sieve trays. Because all round trays can be regarded as the earth, it is easy to set up the meridians. Apparatus and Procedures. The schematic diagram of the experimental apparatus was shown in Figure 1 of that previous study.2 The test tray was the same except for the deflectors. (1) Temperature profiles. Sensitive platinum resistive thermal detectors (RTDs; accuracy up to 0.01 °C) were used to measure the temperatures of the liquid layer. Detectors were set in two ways: vertical and horizontal (see Figure 2). In the vertical setting, the detectors were suspended in the liquid layer of the central channel on the tray. The distance from the RTD head point to the tray surface can be adjusted continuously as desired. In the horizontal setting, nine RTDs were fixed in the middle flow channel on the tray, which separated this flowing path into 10 equal parts. Through a discrete collective system, the data of temperatures can be directly collected into the computer and then analyzed. (2) Tray efficiency. The water-enriched oxygen was pumped to the test rig. Desorption tests of oxygen from the water were carried out to measure EML (it is unadvisable to measure EMV because the oxygen desorption process is controlled by the liquid film). The oxygen-rich water was prepared by injecting oxygen into the water at the water source. Also enough time was needed to let oxygen dissolve sufficiently into the water so that an oxygen content of about 20 mg/L (O2/H2O) was obtained. When the testing system reached a steady state, liquid samples were collected from the inlet and
EML ) (Ci - Co)/(Ci - C*) × 100
(1)
where Ci and Co refer to the inlet and outlet oxygen contents, respectively. C* (also determined by tests) is the oxygen content of the water, which is in equilibrium with the outlet gas (air in this experiment) at the relevant temperature and pressure. Results and Discussion Flow Patterns on the Deflected Tray-95. Red ink was added into the liquid phase as the tracer to study the flow patterns on the tray with deflectors. It was observed that in each flow channel the liquid phase flows approximately like a plug-flow pattern, which has been traditionally considered as the ideal flow pattern for liquid flow on trays. Vortex, backmixing flow, stagnant flow, etc., which often happened on conventional trays, were not found in this experiment. Temperature Profile of the Liquid Layer. Test results are presented in Figures 3 and 4. Figure 3 shows the vertical temperature profile in the liquid layer on the tray. It shows that the temperature tends to decrease linearly as the liquid layer height increases. This result could be explained as follows. In the vertical direction, gas bubbles through the liquid layer. The liquid only flows (we suppose that it is plug flow) in the horizontal direction in each channel, shown in Figure 5. T1, T2, t1, and t2 are the temperature values of the inlet gas, outlet gas, bottom layer of the liquid, and top layer of the liquid, respectively. T and t are the temperatures of the gas and liquid at the height of h. H is the full height of the liquid layer. The differential heat transfer between the gas and the liquid
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pressed as a linear function of the liquid layer height:
Q ) Kh
(11)
where K is a constant number. Substituting eq 11 into eq 3a gives
T ) -mKh + n
(12)
Considering the heat balance
-QG ) QL and substituting eqs 2a and 2b into eq 13 give
Figure 5. Schematic diagram of the liquid and gas flow.
WGCpG(T - T1) ) WLCpL(t - t1)
according to heat balance is
dQ ) -WGCpG dT ) WLCpL dt
(13)
(2)
(14)
or
t ) (WGCpG/WLCpL)T - (WGCpG/WLCpL)T1 + t1 (15)
or
dQ/dT ) -WGCpG
(2a)
Introducing T of eq 12 into eq 15,
dQ/dt ) WLCpL
(2b)
t ) -mK(WGCpG/WLCpL)h + (WGCpG/WLCpL)(n - T1) + t1 (16)
The temperatures of the gas and liquid are relatively constant; thus, CpG and CpL can also be considered as constants. Then WG and WL are constants too. Therefore, Q is a linear function of T or t:
T ) -mQ + n
(3a)
t ) m′Q + n′
(3b)
(4)
This shows that ∆t is a linear function of Q and
d(∆t)/dQ ) (∆t2 - ∆t1)/Qtotal
(5)
According to the heat-transfer theory
dQ ) k∆t ds ) kAa∆t dh
(6)
Substituting eq 6 into eq 5, we get
d(∆t)/kAa∆t dh ) (∆t2 - ∆t1)/Qtotal
(7)
d(∆t)/∆t ) (kAa/Qtotal)(∆t2 - ∆t1) dh
(8)
or
Integrating eq 8
∫∆t∆t d(∆t)/∆t ) ∫0H(kAa/Qtotal)(∆t2 - ∆t1) dh 2
1
b ) mK(WGCpG/WLCpL)
(17)
b′ ) (WGCpG/WLCpL)(n - T1) + t1
(18)
Then eq 16 can be written as
t ) -bh + b′
where m, m′, n, and n′ are all constants. Subtracting eq 3a from eq 3b leads to
T - t ) (-m - m′)Q + (n - n′) ) ∆t
For simplification, introduce
(19)
Equation 19 explains theoretically that the liquid layer temperature decreases linearly as the height increases. Figure 4 shows the temperature profile along the liquid flow channel in the horizontal direction. At the same height of the liquid layer, the temperature increases linearly from the liquid inlet to the outlet. This result can be obtained in almost the same way as that stated above. The above theoretical deduction is based on the premise that the flow pattern is plug flow. Because the experimental results fulfilled the conditions, it can be shown that the flow pattern on the tray is plug flow. Murphree Tray Efficiencies. The ultimate purpose of setting the deflectors was to strengthen the mass transfer between the liquid and gas phases. Therefore, the tray efficiency is a macroscopic parameter more suitable than anything else to directly reflect the changes of interphase mass transfers between the tray95 and deflected tray-95. The efficiencies of the tray-95 and deflected tray-95 were compared (see Figure 6). The
(9)
Then we have
Qtotal ) kAaH(∆t2 - ∆t1)/(ln ∆t2 - ln ∆t1) ) kAaH∆tm (10) where k is the heat-transfer coefficient, A is the area of the tray bubbling region, and a is the contacting area of the gas and liquid per unit volume. They are all constants on a certain tray under a specific condition. Because ∆t is almost unvariable, ∆tm has little effect on Qtotal. Therefore, approximately heat can be ex-
Figure 6. Tray efficiencies of the tray-95 and deflected tray-95.
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following the flow directions of the gas and water, respectively. (3) The liquid-phase tray efficiency of the deflected tray-95 is about 30% higher than that of the tray-95 under the same operating conditions. (4) The deflected tray-95 offers advantages of a higher capacity and a larger operating flexibility than the tray-95 without sacrificing such good qualities as lower pressure and larger flow rates than those of a conventional sieve tray. Nomenclature Figure 7. Tray efficiencies of the tray-95 and deflected tray-95.
efficiency of the latter is about 30% higher than that of the former under the same operating conditions. It is also shown that, when the gas-phase F factor increases, EML of the tray-95 increases along with it at first, but after approaching a maximum point, it declines quickly; however, for the deflected tray-95, EML remains high and only declines slowly after the maximum point. This means that the deflected tray-95 has a higher capacity and operating flexibility than the tray-95. Figure 7 presents the efficiencies of the tray-95 and deflected tray-95 under different liquid flow rates. The efficiency of the deflected tray-95 is relatively stable and high, while the efficiency of the tray-95 decreases quickly as the flow rate increases because of the increasing weeping rates. All of these differences come from the changes of flow states. At the center of the tray-95, because of the influx effect of the downcomer, the liquid layer there is higher than the average height, causing serious weeping; at the same time, the liquid layer near the edge is relatively thin, and accordingly the high gas hole velocity causes high entrainment. Deflectors can change the maldistributed liquid and nonuniform flow into relatively well-distributed liquid and plug flow. The liquid layer near the edge of the tray becomes thick, and the gases distribute evenly. Hence, the weeping and gas entrainment can be cut down, and the time of the gas pass through the liquid layer is prolonged. All of these help improve the tray efficiency. What must be pointed out is that, compared with conventional trays, the advantages of the tray-95 such as lower pressure and larger flow rates are still maintained because deflectors do not change such structural parameters as perforating ratios, hole size, length of the flowing path, and height of the outlet wire. Concluding Remarks The following conclusions can be drawn from this study: (1) The flow pattern of the tray-95 can be improved into plug flow with deflectors that are exactly designed and arranged following the principles of separating globe meridians on plane maps. (2) On the basis of the ideal flow pattern, the temperature profiles of the liquid layer are all linear in the vertical and horizontal directions. The former decreases and the latter increases
a ) contacting area of gas and liquid per unit volume A ) bubbling region area of the tray Ci ) oxygen content of the inlet water Co ) oxygen content of the outlet water C* ) oxygen content of the water balanced with the outlet gas CpG, CpL ) specific heat capacities of the gas and liquid EML ) liquid-phase Murphree tray efficiency F ) F factor h ) height of a liquid layer H ) full height of the liquid layer k ) heat-transfer coefficient L ) liquid flow rate Q ) heat transferred in the liquid layer from the bottom to the height of h Qtotal ) heat transferred in the full height of the liquid layer t, t1, t2 ) temperatures of the liquid at the height of h, bottom, and top of the full liquid layer T, T1, T2 ) temperatures of the gases at the height of h, bottom, and top of the full liquid layer WG, WL ) flow of the gas and liquid
Literature Cited (1) Liu, Q. L.; Li, P.; Xiao, J.; Zhang, Z. B. A New Method for Designing an Energy-Saving Tray and Its Hydrodynamic Aspects: Model Development and Simulation. Ind. Eng. Chem. Res. 2002, 41, 285-292. (2) Li, P.; Liu, Q. L.; Xiao, J.; Zhang, Z. B. A New Method for Designing an Energy-Saving Tray and Its Hydrodynamic Aspects: Hydrodynamic Aspects of 95 trays. A Brief Research Note on the Previous Study. Ind. Eng. Chem. Res. 2002, 41, 293-296. (3) Tedder, D. W.; Bravo, J. L.; Parker, B. M.; Parker, T. J. Improving Hydraulics and Efficiencies with the T-By Sieve Tray. AIChE J. 1993, 39, 569-580. (4) Yu, K. T.; Huang, J. Simulation and Efficiency of Large Tray (I): Eddy Diffusion Model with Non-Uniform Liquid Velocity Field. J. Chem. Ind. Eng. (China) 1981, 1, 11-19. (5) Zhou, Y. F.; Ye, Y. H.; Yang, R. L. Study of Liquid Residence Time Distribution on Large Tray. Chem. Eng. 1982, 2, 35-42. (6) Zhao, L. T.; Zhong, S. Q.; Yu, M. J.; Liu, S. X.; Zhang, C. F. Study of Liquid Flow Distribution and Its Improvement on Column Tray. Petrochem. Technol. 2000, 29, 347-353. (7) Meites, L. Handbook of Analytical Chemistry, 1st ed.; McGraw-Hill: New York, 1964.
Received for review September 13, 2002 Revised manuscript received February 7, 2003 Accepted February 25, 2003 IE020720+
