Ind. Eng. Chem. Process Des. Dev. 1904, 23, 479-482
0 = dimensionless gas temperature, T/T* u = Stefan-Boltzmann constant, W m2 K4 4 = dimensionless distance, ( w / a ) l /z p D = dome metal density p = gas density, P/RT, g-mol/m3 7 = dimensionless time, ut 7 ‘ = 7 + 7r/4 & = dimensionless concentration, Ci/Ci, w = frequency, 2 r / p
1
Literature Cited Abramowltz, M.; Stegun, I.,Ed. “Handbook of Mathematical Functlons”; Dover: New York, 1965; Chapter 7. AP-42 Supplement 12, 1981; p 4.3. API Bulletin 2512 “Tentative Methods of Measurlng Evaporatlon Loss from Petroleum Tanks and Transportation Equipment”; American Petroleum Institute: Washlngton, DC, 1957. API Bulletin 2513 “API Bulletln on Evaporation Loss In the Petroleum Industry--Causes and Control”: Amerlcan Petroleum Institute, DMslon of Reflnlng; Washlngton, DC, Feb 1959. API Bulletln 2516 “API Bulletin on Evaporatlon Loss from Flxed-Roof Tanks”;
479
American Petroleum Institute, NonDivlsional, Industry Affairs: Washing ton, DC, June 1962. Beckman, J. R.; Qllmer, J. R. Ind. Eng. Chem. Process Des. D e v . 1881, 20, 846. Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”: Wlley: New Yak, 1960: Chapter 18. Boardman, H. C. “Symposlum on Evaporatlon Loss”,Proceedings API 32 (1); 1952; pp 213-281. Bridgeman, 0. C. “Some Phases of the Problem of Evaluating Evaporation Losses from Petroleum Products by Means of Vapor Volume Measurements”; Phllllps Petroleum Co.: Bartlesvllle, OK, Phllllps Report 1288-55R (1955). Danlelson, J. A., Ed. Alr Pdlutlon Englneerlng Manual, U.S. Environmental Protection Agency, AP-40, 2nd ed, 1978; p 626. Duffie, J. A,: Beckman, W. A. ”Solar Englneerlng of Thermal Processes”; Wlley: New York; 1980; Chapter 1, 2, 3. Enghreerlng-Science Inc. Hydrocarbon Emissions from Flxed-Roof Petroleum Tanks, Arcadla, CA, July 1977. Harrer, R. D. 011 Gas J . Jan 2, 1878, 90-92, 97. Nayfeh, A. "Perturbation Methods”:Wlley: New York, 1973; Chapter 1.
Received for review November 11, 1982 Revised manuscript received August 22, 1983 Accepted September 12, 1983
Effect of Recycle on Cyclone Performance Pradeep R. Trasl and Wllllam Llcht’ Department of Chemical end Nuclear Engineering, University of Cincinnati, Cincinnati, Ohio 45221
The improvement in cyclone collection efficiency made possible by recycling a portion of the product stream is explored by the use of available performance models. As the recycle ratio is increased, significant improvement may occur in the overall efficiency prlmarlly because of enhanced collection of partlcles around the cut diameter size. The improvement comes at the expense of higher pressure drop and power consumption and increased cyclone size. A detailed numerical example is given relating performance to cyclone design and recycle ratlo and comparing the power consumption, overall efficiency, and outlet dust size dlstrlbutions at different recycle ratios.
Stricter particulate emission controls and renewed emphasis on a coal-based energy program have increased the importance of cyclonic particulate collectors. Cyclones are often used as primary collectors or precleaners. Improved cyclone performance in the collection of fine particles can reduce the performance demanded of complex and costly secondary collectors and decrease the shutdown and maintenance costs for these devices. One simple method of improving the collection efficiency of a cyclone system is the partial recycle of outlet gases. Although the authors are aware of instances where this mode of operation is used, they could find no published data nor theoretical developments relating to it. With the aid of recently developed performance models, however, the effect of recycle upon cyclone performance can be explored quantitatively. In the proposed recycle scheme, shown in Figure 1, a fraction r of the gas flow is recycled from the outlet back into the inlet. The derivation of the expression relating the increase in efficiency of the collection system (due to recycle) to the recycle ratio r is independent of the performance model for the cyclone itself. The model equations therefore will be taken up later in connection with a detailed numerical example. To obtain the efficiency of the collection system shown in Figure 1, consider particles of mean size di (microns) in the narrow size range di + Adi, which can be collected by the cyclone with an efficiency vi referred to hereafter as the grade efficiency. Let Ch and Coutdenote the inlet 0196-4305/84/ 1123-0479$01.50/0
and exit grain loading, respectively, of particles in this size range. A material balance at the point of mixing in the inlet gives QoCin + rQoCout = (1 + r)QoCrecycle or
Since the grade efficiency of particles in the above size range is vi, the exit grain loading Coutis given by (2) Cout = (1 - 7i)Crecycle Then, if Ei is defined as the effective grade efficiency of the collection system as a whole for collecting particles in this size range Gout = (1 - E& (3) These three equations, (l), (2), and (3), may be combined to give Ei/vi = (1 + r ) / ( l + rvi) or (4)
Note that in the absence of recycle, when r = 0 (as is the usual method of operation), eq 4 reduces to Ei = vi 0 1984 American Chemical Society
480
Ind. Eng. Chem. Process Des. Dev., Vol. 23,No. 3, 1984
-
qi CYCLONE GRADE EFFICIENCY, %
Figure 1. Recycle system for cyclone, showing flow rate and grain loading for recycle ratio r.
Figure 3. Net increase in grade efficiency (Ei - vi) vs. cyclone grade efficiency T~ for recycle ratios 0.5 and 1.
GRADE EFFICIENCY OF CYCLONE, q i X
Figure 2. Percent improvement in grade efficiency, [(Ei - T ~ ) / V { X] 100 vs.
T~ (eq
4) for recycle ratios 0.5 and 1.
Further, the net increase in grade efficiency, (Ei - 3 ,is given by
The basic nature of eq 4 is shown in Figure 2 for recycle ratios of 0.5 and 1. The percent increase in grade efficiency is larger for particles of smaller diameter which have lower values of vi. However, the net increase in grade efficiency (Ei- vi) given by eq 5 is largest for particles just below the cut diameter size for the cyclone (where qi = 0,5),as shown in Figure 3. The theoretical formula show that maximum (Ei - ai) is obtained when q i = [-1 + (1 + r)1/2]/r.Here qi 0.5 as P 0. This leads directly to a significant decrease in the effective cut-diameter d, for the collection system as a whole, defined as the diameter of the particle which is collected with an Ei of 50%. Figure 3 also shows that the net increase in efficiency is spread out over a rather wide range, from vj = 20% to qi = 80%. This results in a substantial increase in the overall collection efficiency of the recycle system, denoted by E. The overall collection efficiency E is determined by summing up the individual effective grade efficiencies, Ei, for the particles in each size range
-
-
1 Ei dGi = CE~AG, 1
E=
0
i
where Gi is the mass fraction of particles smaller than size
Figure 4. Reverse-flow tangential entry cyclone showing configuration ratios (see Table I). ( d i ) and AGi is the mass fraction of particles in the size range di f Adi/2. There is of course a price to be paid for this improvement in collection. This is reflected in increased energy cost and an increase in cyclone size. The increment in investment and operating costs due to larger cyclone size and greater power consumption has to be offset against the decrease in shutdown and maintenance costa for secondary cleaners (when cyclones are used as primary collectors) or the value of the collected particulate material and cleaner gas stream (when cyclones are the only collectors used). In some cases the secondary collector may even become unnecessary if the cyclone with recycle is by itself able to meet emission standards. The use and extent of recycle can be based on these considerations for an optimum approach. In using eq 4 and 5 to calculate the improvement in overall collection efficiency, another fador should be kept in mind. An increase in cyclone size is usually accompanied by a small decrease in grade efficiency ql,and also a small increase in pressure drop AP across the cyclone. I t is necessary to use a performance model for cyclone grade efficiency in order to take these factors into account and determine the actual improvement possible from the recycling of outlet gases. A cyclone is traditionally characterized, Licht (1980),by the seven configuration ratios shown in Figure 4. Some
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984 481
Table I. Cyclone Design Configurations “high efficiency” Stairmand Swift term
description body diameter inlet height inlet width outlet length outlet diameter cylinder height overall height dust outlet diameter configuration constant N H = 16KaKb/Ke2
(1951) 1.0 0.5 0.2 0.5 0.5 1.5 4.0 0.375 551.3 6.40
of the more commonly used seta of configuration ratios are shown in Table I. The grade efficiency of a cyclone for a given set of configuration ratios may be estimated by the grade efficiency model developed by Leith and Licht (1972) for vertical, reverse flow, tangential-entry cyclones
(l+n)QK ppd?
1/(2n+2)
(7)
In the above equation, K is a configuration constant calculated, as shown by Leith and Licht (1972), from the seven configuration ratios illustrated in Figure 4. The variable n is the empirical vortex constant calculated according to Alexander (1949) n = 1 - (1 - 0.670°.4)(T/283)0.3 (8) As shown by Koch and Licht (1977) the diameter D and inlet velocity uinmust be related, in order to obtain the optimum operation in regard to saltation as recommended by Kalen and Zenz (1974), according to
uin =
Q/ (K&tP2)
(10)
where K, and Kb are two of the configuration ratios. The pressure drop is calculated according to Shepherd and Lapple (1939) AP = 0.0049p,Ui,2(16KaKb/K,2) (11) where K, is another one of the seven configuration ratios. The effect of incorporating a recycle loop, such as shown in Figure 1, on these equations is to increase the gas flow Q through the cyclone by a factor of (1 + r). If the subscript r is used to denote recycle operation with a recycle ratio of r, and the subscript o indicates conventional operation without recycle, the following expressions can be derived to illustrate the changes occurring in Q, D , u,, and AP due to the recycle loop Q, = (1 + r)QO (12) D, = (1 r)0.4543D0 (13)
+ u ~= ~(1 +, r)0.0914 ~ AP, = (1 + r)o.1828APo &,o
(14) (15)
The grade efficiency of the cyclone is given by
where
n = 1 - [ l -O.67D,0.l4(1 + r)0.0636](T/283)0.3(17)
(1969) 1.0 0.44 0.21 0.5 0.4 1.4 3.9 0.4 699.2 9.24
“general purpose’’ Shepherd and Swift Peterson and Lapple (1939) (1969) Whitby (1965) 1.0 0.5 0.25 0.625 0.5 2.0 4.0 0.25 402.9 8.0
1.0 0.5 0.25 0.6 0.5 1.75 3.75 0.4 381.8 8.0
1.0 0.583 0.208 0.583 0.5 1.333 3.17 0.5 342.3 7.76
Table 11. Fine Dust,Stairmand (1970) 150 104 75 60 40 30 20 15 10 7.5 5.0 2.5 0
100 97 90 80 65 55 45 38 30 26 20 12 0
1 2 3 4 5 6 7 8 9 10 11 12
127 89.5 67.5 50 35 25 17.5 12.5 8.75 6.25 3.75 1.25
3 7 10 15 10 10 7 8 4 6 8 12
The grade efficiency Ei of the collection system as a whole is calculated from eq 4, and the overall efficiency E from eq 6 when the dust size distribution is known. In those cases where a cyclone is already available, it can be fitted with a recycle loop and set to operate at a recycle ratio such that eq 9 is satisfied. But in general, a cyclone system may be designed to operate at any desired value of r, and eq 7-11 can be used to calculate D , uin,AP, and t i after setting Q = Q, = (1 + r)Q,,. The following example, which uses the Leith and Licht (1972) performance model, will serve to highlight the advantages and disadvantages of recycling outlet gases in a cyclone. Illustration Compare the size, efficiency, pressure drop, power consumption, and outlet dust size distribution for a Swift (1969) configuration cyclone (see Table I) fitted with a recycle loop with recycle ratios of (a) 0.0, (b) 0.5, and (c) 1.0 for processing 9.44 m3/s of gases at 104.4 “C containing particulates (p, = 1.0 g/cm3) having fine dust size distribution, Stairmand (1970), given in Table 11. Solution: at 104.4 “C p, = 0.9135 kg/m3; pg = 2.177(10-5)kg/m-s
Q = Q, = 9.44(1 + r ) m3/s; pp = 1000 kg/m3 From Table I, for a Swift configuration, K = 699.2, K, = 0.44,Kb = 0.21, and K, = 0.4. The diameter of the cyclone can then be calculated from eq 9, the inlet velocity from eq 10, the pressure drop from eq 11, the grade efficiency from eq 16, and the effective grade efficiency and overall efficiency from eq 4 and 6. The expressions for grade efficiencies, obtained from eq 16, are: (a) vi = 1 - e ~ p ( 4 . 3 4 3 5 d P for ~ ~ r~=~ 0; ) (b) ti = 1 - exp(-0.3376dPMQ8) for r = 0.5; and (c) t i = 1 - exp(0.3340dPm) for r = 1.0. Cyclone size, inlet velocity, cut diameter, overall efficiency, pressure drop, and power consumption for the three cases are shown in Table 111. The effective grade efficiency for the collection system as a whole, Ei, is shown in Figure 5 for the recycle ratios
482
Process Des. Dev., Vol. 23, No. 3, 1984
Ind. Eng. Chem.
Table 111. Cyclone Size and Performance for Cases (a), (b), and (c) in Illustration term description units case (a) _ _ 0 r recycle ratio m 2.36 D cyclone diameter uin inlet velocity m/s 18.3 -_ 0.734 n empirical vortex constant cut diameter for collection system as a whole wn 3.38 dc E AP P
overall efficiency pressure drop power consumption
%
I
I
I
I
10
20
30
40
-
50
PARTICLE SIZE d,i, 10 - 6 m
Figure 5. Effective grade efficiency curve, for recycle ratio r = 0, 0.5, and 1.0 in example.
79.0
case ( b )
case (c)
0.5 2.84 19.0 0.755 2.07 82.8 0.150 20.83 27.92
1 3.23 19.5 0.771 1.41 85.4 0.158 29.21 39.21
m of water 0.139 kW 12.87 hP 17.25 four cyclones operating in parallel. Each of these would have only one-fourth of the total gas flow rate, and the cyclone diameter D would be reduced by a factor of (0.25)0.4543 = 0.533. The individual cyclone grade efficiency would increase (due to the term Q/D3)by a factor of 1.65 upon the term in brackets in eq 7. Inlet velocity would be lowered by a factor of 0.88 as given by eq 10, and consequently the pressure drop and power consumption would also be less. Nomenclature Ci, = grain loading in feed stream, kg/m3 of feed stream C, = grain loading in outlet stream, kg/m3 of outlet stream Creeyds= grain loading in inlet stream (in recycle system), kg/m3 of inlet stream d j = particle diameter, mean size, in the range (dif Adi/2), 10% m D = cyclone diameter, m Ei = effective grade efficiency for collection system with recycle, for particles of di E = overall efficiency of collection for the collection system with recycle Gi = mass fraction of particles of size less than ( d j ) AGi = mass fraction of particles contained in the size range (di f Adi/2)
K = configuration fador (see Table I, and eq 71, dimensionless K, = configuration ratio specifying inlet height (see Figure 4)
Kb = confiiation ratio specifying inlet width (see Figure 4)
2
J
1.5
' IO
5
l
'
l
s
'
'
t
'
20 40 60 SO 90 95 98 99 99.899.9 99.99 0. PERCENT FINER THAN dp, INLETBOUTLET
Figure 6. Dust size distribution for inlet stream and outlet stream (r = 0, 1.0) in examples.
of 0,0.5,and 1. The corresponding inlet and outlet dust size distributions are shown on a log-normal plot in Figure 6. It is noteworthy that the penetration, according to Table 111, decreases by as much as 30% as r is increased from 0 to 1. Also, the cut diameter decreases from 3.4 to 1.4 pm, a decrease of 59%. The cyclone size, however, is increased by 37% and the power consumption is more than doubled primarily because of the increased gas throughput. With reference to Figures 3 and 5, it will be observed that most of the improvement is due to enhanced collection of particles around the cyclone cubdiameter (i.e., at t i = 50%). The improvement is also spread out over a wide range, ti = 20% to 80%. Perhaps for this reason, there is hardly a perceptible change in the outlet dust size distribution (Figure 6) as the recycle ratio is increased from 0 to 1. The efficiency of Collection can be incrsaeed even further by replacing the large cyclone in the illustration by, say,
K, = configuration ratio specifying gas outlet diameter (see Figure 4) n = empirical vortex constant, eq 8 AP = pressure drop across the cyclone, m of water Q = gas flow rate at the cyclone inlet, m3/s r = recycle ratio (volume rate of gas recycle/volume rate of feed) T = temperature of gas stream, K uin = inlet gas velocity, m/s Subscripts
g = gas
L = in the size range (di i di/2), mean size di o = for system without recycle p = particle r = for system with recycle ratio r
Greek Letters p = viscosity, kg/m s p = density, kg/m3 7 = grade efficiency of
cyclone
Literature Cited Alexandet, R. McK. Roc. Aust. Inst. Mln. Met. ( N . S . ) 1949, 752/3,202. Kaien. B.; Zenz, F. A. AIChESynp. Ser. 1974, 70(137), 388. Koch, W. H.; Llcht, W. Chem. Eng. 1977. 84(24), 80. Lekh, D.; Llcht, W. AIChESymp. Ser. 1972, 68(126), 196. Licht, W. "Air Pdutkn Control Engineering: Bask Calndetlons for Particulate Coilectkn"; Marcel Dekker, Inc.: New York, 1980; p 235. Peterson, C. M.; WMtby, K. T. A S M A E J . 1086, 7(5), 42. Shepherd, C. B.; Lappb, C. E. Ind. Eng. Chem. 1930, 37,972. Stairmand, C. J. F h . Sep. 1970, 7(1). 202. Stairmand, C. J. Trans. Inst. Chem. Eng. 1911, 29, 356. Swift, P. Steam HeeHng Eng. 1969. 38, 453.
Received for review November 22, 1982 Accepted September 1, 1983
