446
Ind. Eng. Chem. Process Des. Dev. 1980, 7 9 , 446-451
4 = Thiele parameter 7 = effectiveness factor Subscripts e = effective BT = benzothiophene H = hydrogen L i t e r a t u r e Cited Akhtar, S.,Sharkey, A. G., Shultz, J. L., Yavorsky, P. M.. Am. Chem. SOC. Div. Fuel Chem. Prepr., 19(1), 207 (1974). Bartsch, R., Tanielian D., J. Catal., 50, 35 (1977). Daly, F. P., J. Catal., 51, 221 (1978). Furimsky, E., Amberg, C. S.,Can. J. Chem., 54, 1507 (1976). Ghrens, E. N., Venuto, P. B., Am. Chem. SOC.Div. Pet. Chem. Prepr., 15(4), Ai63 (1970). Granoff, B., B a a , P. M., Sandia Laboratories Energy Report SAND-79-0505, (Aprll 1979). Guin, J. A., Tarrer, A. R., Prather, J. W., Johnson, D. R., Lee, J. M., Znd. Eng. Chem. Process Des. Dev., 17, 118 (1978).
Guin, J. A., Tarrer, A. R., Lee, J. M.. Lo, L., Curits. C. W., Znd. Eng. Chem. Process Des. Dev., 18, 371 (1979a). Guin, J. A,, Tarrer, A. R., Lee, J. M., Van Brackle, H. F., Curtis, C. W., Znd. Eng. Chem. Process Des. Dev., 18, 631 (1979b). Jackson, W. R., Larkins, F. P., Matshall, M., Rash, D., White, N., Fuel, 58, 281 (1979). Keisch, B., Gibbon, G. A., Akhtar, S . Fuel Process. Techno/., 1, 269 (1978). Lowell. S . . Karp, S.,Anal. Chem., 44, 1706 (1972). Morooka, S . , Hamrin, C. E., Jr., Chem. Eng. Sci., 32, 125 1977. Petersen. E. E.. "Chemical Reaction Analvsis", . .D 64. Prentice Hall, Enalewood Cliffs, N.J., 1965. Roberts, G.W., Satterfield, C. N., Znd. Eng. Chem. Fundam., 5, 317 (1966). Rollrnann, L. D., J. Catal., 46, 243 (1977). Schuit, G. C. A,, Gates, B. C., AZChE J., 19, 417 (1973). Shen. J.. Smith. J. M.. Ind. €no. Chem. Fundam.. 4. 293 (1965). Steniagen, E., Abrahamsson, S: McLafferty, F. W., "Registrybf Mass Spectral Data, Vol. I, Wiley, New York, 1974. Wright, C. H., Severson, D. E., Am. Chem. SOC.,Div. Fuel Chem. Prepr., 16(2), 68 (1972).
Received for review August 20, 1979 Accepted March 28, 1980
Process for Recovery of Solvent Vapors with Activated Carbon Phillip C. Wankat' and Lee R. Partln School
of Chemical Engineering, Purdue University, West Lafayette, Indiana 4 7907
A new process was developed for recovery of solvent vapors from air streams using activated carbon adsorption. The process consists of five steps: adsorb, desorb with desorbent vapor, steam to remove desorbent, dry, and cool. When the desorbent is selected so that it is easy to separate from both water and solvent, this scheme avoids the difficult downstream separations which often occur when the solvent forms an azeotrope with water. Experimental results are presented for the recovery of methyl ethyl ketone (MEK) from air using toluene as the desorbent and for the recovery of 2-propanol from air using ethylbenzene as the desorbent. These results show that with appropriate operating conditions the difficult methyl ethyl ketone-water and 2-propanol-water separations can be avoided.
Activated carbon processes for recovery of solvent vapors from air have been used commercially for many years. The standard process (e.g., Bowen, 1971; Fulker, 1964; Scamehorn, 1979; Turk, 1968) consists of the following fourstep cycle: (1)adsorb, (2) desorb, (3) dry (optional), and (4) cool (optional). The usual desorption step utilizes steam for desorption. The steam-air-solvent vapor mixture is then condensed and sent to appropriate separation devices. Water remaining in the bed can be exhausted to the atmosphere. The two optional steps are required if water is detrimental to the adsorption or if the hot carbon acts as a catalyst for the solvent. Two or more beds in parallel are commonly used. The conventional process is particularly inexpensive and convenient if the solvent is immiscible with water. Then a coalescer or settler can be used for the solvent-water separation. If the solvent is partially miscible or miscible with water, distillation is commonly employed to separate them. This rapidly increases capital and operating expenses for the process. When the solvent forms an azeotrope with water, the downstream separation can become complex. Common commercial examples are recovery of 2-propanol, MEK, tetrahydrofuran (THF), and MEKT H F mixtures. Alternatives to stream desorption include using heating coils inside the bed (Mantel, 1952), using hot gas for desorption (Smisek and Cerny, 1970, and Lovette and Cuniff, 19741, and vacuum regeneration (Lovett and Cuniff, 1974).
Because of very low heat transfer rates in a bed containing vapor and carbon, heating coils require a long time to heat the bed and desorb the solvent. Thus this method is rarely used. Hot gas desorption also tends to suffer from low rates of heat transfer. In addition, since gases generally have a low volumetric heat capacity it may require a long time to heat the bed. Vacuum regeneration is a common commercial method but it may require high capital and operating costs and excessively low condenser temperatures to condense the purged solvent. New Process A new process for solvent recovery by activated carbon was developed for recovery of solvents which are miscible or partially miscible with water. This process uses a desorbent, and then the desorbent is removed with steam. The process is illustrated in Figure 1 and now has five steps: (1) adsorb, (2) desorb with desorbent vapor, (3) steam to remove desorbent, (4) dry, and (5) cool. The vapors from steps 2 and 3 are sent to separate condensers so that water and solvent never mix. These streams are sent to different separation devices where desorbent and solvent are recovered. Two or more beds in parallel would be utilized for a continuous adsorption process. The purpose of the steaming step is to remove the desorbent so that it can be recovered and reused and to prevent exhausting desorbent into the air during the drying and cooling steps. The drying step removes water so that it
0196-4305/80/1119-0446$01.00/00 1980
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Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980 447
t
6 J?-TJYCLEAN
STEAM COOLING AND DRYING AIR
t AIR
Iesorbent
Y+
SEPARATOR
Solvtmnt
ADSORB
DESOFlB
Desorbent
Lci;el
cool Air
1'\
H
Water
STEAM
DRY
COOL
E X H A U S T AIR
Figure 1. New activated carbon solvent recovery process.
will not mix with solvent. This step does not have to be complete since additional water will be removed during the cooling and adsoription steps. The presence of some water on the carbon ait the start of the adsorption step is helpful since the water evaporation helps to keep the bed cool. The cooling step may be quite short or could be bypassed depending on the solvent which is being recovered. Other modifications such as aiding desorption by utilizing a vacuum or by auxiliary heating are possible. The success of this scheme hinges on the proper choice of desorbent. The desorbent should be easy to separate from both solvent and water. Ideally, it would be immiscible with either or both of these. In addition, the desorbent should be a good desorbent for the solvent and rapidly remove the solvent from the carbon. To rapidly heat the bed and rernove the solvent the desorbent's boiling point should be approximately the same as or above that of the solvent. Sinlce the carbon is at high temperature when the desorbent is present, little desorbent will be adsorbed and steam removal is relatively simple. Other desirable properties of the desorbent are that it should be nontoxic, noncorrosive, have low molecular weight, low viscosity, be chemically stable, readily available, and inexpensive. Naturally, no desorbent will satisfy all of these requirements. Although this process requires a more complex adsorption-desorption cycle, the overall process will be simpler since the downstream separations are much simpler. This is particularly true when the solvent forms an azeotrope with water, but neither the solvent-desorbent nor the desorbent-water pairs form azeotropes, and they both have large volatility differences.
Experimental Section The operation of the new cycle was tested in the small-scale apparatus which is shown schematically in Figure 2. The activated carbon, Columbia type SBV 416 mesh from Union Carbide was held between two copper screens in a Vycor glass tube. All experiments were done with a 5.15 cm i.d. bed and carbon bed lengths of 4.2, 5.4, and 12.0 cm. Two thermocouples were buried in the carbon and one thermocouple was placed in the gas space above the carbon. The column was then well insulated with asbestos cloth. The inlet air from the house compressed air system was filtered and dried with Drierite. The air stream was then split with the larger stream being heated in a heat exchanger consisting of tubing submerged in a constanttemperature bath. The smaller air stream flowed cocurrently with liquid solvent in a jacketed packed bed. This saturated air stream is then remixed with the other air stream. The combined air stream can either be exhausted or introduced into the adsorber. An electrically heated, three-neck flask was used as the desorbent boiler. The boiler was operated slightly above
TO F R A C T I O N
TO F R A C T I O N COLLECTOR
Figure 2. Schematic diagram of experimental apparatus.
atmospheric pressure. Boiler operation was at steady state with the vapor being circulated and then condensed when not required for desorption. After condensation, the separate desorbent-solvent and desorbent-water streams from the desorption and steaming steps were collected in fraction collectors for later analysis. A Carle No. 8515 gas chromatograph was used for analysis. Either an 8% G-E. SF 96 silicone or an 8% Carbowax 1540 column was used for the analysis. Complete details of the apparatus and analysis procedure are given by Partin (1977).
Results Preliminary runs with a formic acid, n-octane, steam system (Hitzeman, 1976) required a vacuum of -6 psig and external heating of the column during the desorption step since the desorbent boiler was malfunctioning. These runs showed that formic acid can be successfully adsorbed from air on activated carbon, desorbed with n-octane vapors, and the n-octane removed by steam. For the saturation runs from 12 to 14 mL of n-octane was required per milliliter of formic acid recovered for essentially complete regeneration of the carbon. Considerably less desorbent can be used if some residual formic acid can be left on the carbon. The steam removal of n-octane from the hot bed proved to be easy and was not carefully studied. After the preliminary experiments, the apparatus was redesigned and rebuilt as described previously. To illustrate the operation of the cycle complete results for a methyl ethyl ketone, toluene, steam run where the bed was first saturated with MEK will be presented, and then the results of a run where adsorption was stopped after MEK breakthrough will be discussed. Finally, the results for the 2-propanol, ethylbenzene, steam system will be presented briefly. Partin (1977) presents complete details of five experimental runs with MEK and five experimental runs with 2-propanol. Run 3 was an experimental run with MEK, toluene, steam where the adsorption step was run until the bed was essentially saturated. The experimental conditions and some of the results are tabulated in Table I. Air velocities in the tables are superficial air velocities. The run was started by steaming the bed, then running through a complete cycle without collecting data, and then collecting data starting with the drying and cooling step. The inlet and outlet concentration profiles during the adsorption step are shown in Figure 3. This figure shows that
448
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980
Table I. Experimental Conditions and Results for Run 3. MEK-Toluene Saturation Run bed height adsorption
5.4 cm; 44.7 g of carbon u h = 8.0 cm/s (upward); T& = 3 5 "C; P a = 1.10 atm; 8.30 min operating 0.8 vol % MEK in air (av) boiler T = 117 'C; downward flow; 76.1 g of toluene condensed; 8.2 g of MEK condensed, 1.1g of water condensed; first condensate recov ered a t 2.5 min; 17.0 rnin operation downward flow;toluene condensed, 20.7 g; MEK condensed, 0.3 g; water condensed, 123.3 g; 11.0 rnin operation u = 7.45 cm/s (downward); Th = 25 yC;P h = 1.02 atm; 30.0 min operation
desorption
-
steaming
drying and coo1in g
4-
1.0
I
a W
I
,
,
I
,
,
I
I
-
2-
-
LL
INLET
0.8-
E a
z Y W
Figure 5. Condensate from steaming step for run 3 (see Table I). 06
I L
TIME, MINUTES
Figure 3. Inlet and outlet concentrations for MEK adsorption for run 3 (see Table I).
TIME,-MINUTES
Figure 6. Bed temperatures for entire cycle for run 3 (see Table I): A, dry/cool; B, adsorb; C, desorb; D, steam.
TIME, MINUTES
Figure 4. Weight percent MEK in toluene during desorption for run 3 (see Table I).
breakthrough occurs very rapidly for this short bed and that the bed was essentially saturated at the end of the step. The results of the desorption step are shown in Figure 4. After a dead time of 2.5 min, condensate starts to appear. The bulk of the MEK comes out rapidly and then trails off. This is well illustrated in Figure 4 where the weight percent MEK in the condensate fraction is shown. Also, 1.1 total g of water was collected during the desorption step. Later runs showed that this amount of water can be reduced. The results of the condensate from the steaming step are shown in Figure 5 . The toluene is rapidly removed
from the bed and then the amount removed trails off. Since the bed is already hot, the rapid removal of the toluene is not surprising. For the entire cycle 1.2% of the toluene was unaccounted for; 0.3 g of MEK was stripped during this step and 0.26 g of this MEK remained in the toluene. This toluene would either be recycled to the desorbent boiler or sent to the MEK-toluene separation device. The bed temperature for the entire cycle is shown in Figure 6. The thermocouple was 4.1 cm above the bottom of the bed. The drop in bed temperature between steps was caused by cooling during a time delay (not shown in Figure 6) between each step. This time delay was required for operation of the non-automated experimental equipment, but would not occur in a full-sized plant. Since cool air was used for the drying and cooling step, the bed temperature drops rapidly and then more slowly. During the adsorption step, the bed temperature initially drops as more water is evaporated from the bed and then rises as the MEK is adsorbed. During the desorption step, the bed temperature rapidly rises and then levels off at the boiling temperature of toluene. The behavior during steaming is similar. This run was for a thin bed adsorber which was allowed to saturate. It also approximates the performance of a zone which becomes saturated within a larger bed. Thus a
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980
bed height adsorption desorption
steaming drying and cooling
12.0 c m ; 106.5 g of carbon uair = 7.67 cm/s (upward); Tab = 35 "C; P, = 1.12 atm; 60.0 rnin operation; 0.8 vol % MEK in air (av) boiler 'r = 118 "C; downward flow; 195.6 g of toluene condensed, 13.5 g of MEK condensed, 25.8 g of water condensed; first condensate recovered a t 4.8 min; 35.4 min operation downward flow; 75.7 g of toluene condensed, 277.0 g of water condensed, 0.7 g of MEK; 85.0 min operation v = 7.47 cm/s (downward); T,k = 26 qC;P,& = 1.02 atm; 60.0 min operation
,
80
Table 11. Experimental Conditions and Results for Run 6. MEK-Toluene Breakthrough Run
I
I
449
I
I
$ J4 0 1 1 3 0
I-
I1
I
30tI '0
I
40
80
I20
160
200
240
CONDENSED W A T E R , g
Figure 8. Condensate from steaming step for run 6 (see Table 11).
v)
W W D:
'0
20
40
60
80
100 120 140 160 180
90
200
CONDENSED TOLUENE, g
Figure 7. Condensate from desorption step for run 6 (see Table 11).
saturation run is helpful in the design of a larger bed. In addition, the results illustrate that the process works since MEK was desorbed by the toluene and the toluene was easily recovered by steaming the bed. An additional saturation experiment using a 12.0 cm bed length was also run (Pa.rtin, 1977). Experimental conditions were essentially the same as for run 3 except all of the cycle periods were correspondingly longer. The results are essentially the same as shown for run 3 except less water contaminated the MEK-toluene product because more water evaporated during the longer adsorption step. Run 6 was an MEK, .toluene, steam run where the adsorption step was stopped a t breakthrough which was arbitrarily set at an MEEC concentration of 10% of the inlet concentration. The experimental conditions and some of the results are tabulated in Table 11. Start-up procedures were the same as for previous runs. The desorption results for run 6 are shown in Figure 7. As expected, after a dead time toluene and MEK exit the bed. Again the MEK comes out rapidly and then trails off. Not shown in Figure 7 is the 26.8 g of water (11%of total condensate) which was collected during desorption. Drying for this run was not adequate and hot air should have been employed for drying (Scamehorn, 1979). The behavior during steaming is similar to that of run 3 and is shown in Figure 8. Again toluene is removed rapidly and then trails off. Although the point to stop steaming is not clear, neither toluene nor MEK was detected in the exhaust during the drying step which followed.
101 0
'
'
40
'
80
'
I
120
'
160
'
'
200
'
I
11
240
TIME, MINUTES
Figure 9. Bed temperatures for entire cycle for run 6 (see Table 11). A, dry/cool; B, adsorb; C, desorb; D, steam.
The bed temperatures measured by a thermocouple 4.2 cm above the bottom of the bed are shown in Figure 9. Note that during the drying/cooling step the bed gets below the inlet air temperature and below ambient. This is due to evaporative cooling of the air. When the adsorption step starts, the bed temperature initially rises because this air was hotter than the air used for cooling. Then the temperature again falls because of evaporative cooling. Since evaporation of water continues throughout the short adsorption step, the bed temperature never starts to rise again. The water remaining in the bed after the adsorption step later appeared in the condensate during desorption. During the desorption step the bed temperature rises rapidly, levels off, and then rises again. The leveling off period is a period when the water in the bed is being evaporated. Since a large portion of the toluene was condensed to evaporate water, the bed temperature never levels off at the boiling point of toluene as it did in run 3. During steaming the bed temperature rapidly rises and then levels off at the boiling temperature of the steam. Once again the discontinuities in the temperature profiles were caused by a time delay between steps. Saturation and breakthrough experiments were also conducted for the recovery of 2-propanol from air on activated carbon. The 2-propanol was desorbed with ethylbenzene which was then steamed off of the column.
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Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980
Table 111. Experimental Conditions and Results for Run 1. 2-Propanol-Ethylbenzene Saturation Run bed height adsorption desorption
steaming drying and cooling
'0
5.2 cm; 44.4 g of carbon v k = 8.56 cm/s (upward); T& = 38 " C ; Pair= 1.12 atm; 71.0 min operation, 1.1 vol % 2-propanol in air (av)
boiler T = 144 'C, downward flow; 113.5 g of ethylbenzene condensed, 5.9 g of 2-propanol condensed, less than 1 g of water condensed; first condensate recovered at 1.7 min; 1 5 . 0 min operation downward flow; 1 4 . 5 g of ethylbenzene condensed, 44.8 g of water condensed; 4 . 8 min operation u& = 8.5 cm/s (upward); T& = 38 " C ; P d = 1.03 atm; 4.5 min operation
25
50
75
103
I25
ETHY LBENZENE R E C O V E R E D , g
Figure 10. 2-Propanol recovery from desorption step for run 1 (see Table 111).
Ethylbenzene is not as efficient a desorbent as toluene since ethylbenzene has a lower latent heat per gram and a higher boiling point which will cause larger energy losses from the column than toluene. Also 2-propanol has a considerably higher latent heat than MEK. The experimental conditions and results for 2-propanol-ethylbenzene-steam run no. 1 are given in Table 111. The results for the desorption step are illustrated in Figure 10 where 2-propanol condensed is plotted vs. ethylbenzene condensed. The other experimental results for saturation and breakthrough runs are qualitatively similar to the MEK runs and are detailed by Partin (1977). Discussion The desorbent and steam usage in these experimental results is higher than that expected in large-scale plants. This occurred because energy losses are relatively much greater and the energy required to heat the column and rubber stoppers is relatively much greater for the small system with its high surface to volume ratio. The second of these factors was subtracted out and a preliminary design for an MEK recovery system was developed (Partin, 1977). As expected, the downstream separations required for this design are quite simple, consisting of a coalescer for the toluene-water separation and an ordinary distillation column for the MEK-toluene separation. The cycle for the adsorbers is more complex and a non-optimum system had to be designed since the experimental results were at low air velocities and good drying data were not obtained. However, by combining saturation and breakthrough runs the adsorbers could be designed. This design showed that the overall process is likely to be considerably simpler than conventional steam desorption with an ex-
tractive distillation to separate MEK from water. Safety considerations need to be explored. When the desorption step is first started, there is a time period when mixtures within the explosive range will occur if a flammable desorbent is used. This period is generally quite short and no problems occurred in our laboratory. Our experimental results for temperature changes within the column agree qualitatively with the results of El-Rifai et al. (1973) when little water is removed during the desorption step. When a large amount of water is evaporated during the desorption step, a temperature plateau appears before the plateau caused by the desorbent. This temperature plateau is caused by steam condensing to heat up the bed. Since there is air present, the partial pressure of the steam is low and condensation occurs below 100 "C. This steam was generated by water evaporated by the condensing desorbent. Because of its higher latent heat, the steam moves ahead of the desorbent. If the required equilibrium and mass transfer data are available, the breakthrough time for the adsorption step can be estimated if the temperature rise is not too large by using an average temperature for the adsorption step (Sherwood et al., 1975). The desorption and steaming steps are considerably more complicated. However, the thermal behavior during these steps can be approximately predicted with a differential energy balance which follows the movement of the condensing steam and desorbent fronts. This analysis qualitatively predicts the observed temperature behavior but does not predict the total time required for desorption and steaming. A complete analysis would be fairly complicated and would require numerical integration of the coupled, nonisothermal, multicomponent mass and energy balances. Desorbent selection is such an important topic that it is worth discussing again. No attempt was made in this study to optimize the desorbent used. For both MEK and 2-propanol a lower molecular weight desorbent with its higher latent heat per gram would result in a more concentrated solvent mixture. Obviously, the best desorbent will depend upon economics with separation costs for the solvent-desorbent and desorbent-water mixtures probably being the dominant factors. If a mixed solvent is being recovered where one of the chemicals is easy to separate from water but the other(s) are difficult to separate from water, use of the easy to separate solvent as the desorbent, if possible, has several advantages. No additional chemicals are added to the system, and probably only a stripping or enriching section of a distillation column will be needed for partial desorbent recovery from the recovered solvents. If the adsorber is being used for pollution control only and no attempt will be made to reuse the solvent, it may be possible to use a fuel such as kerosine as the desorbent and just burn the desorbent-solvent mixture for its heating value.
Conclusions The new activated carbon adsorption cycle utilizing separate desorption and steaming steps has been shown to work for three different chemical systems. For recovery of solvents which are difficult to separate from water the new process will be simpler than conventional steam desorption processes. Before scale-up additional research on the drying step and energy requirements is needed. Acknowledgment The preliminary experimentation of David Silarski and Dennis Hitzeman is gratefully acknowledged. Discussions with Alden Emery, Phillipe Jacob, and Daniel Tondeur were very helpful. The hospitality of ENSIC in Nancy,
Ind. Eng. Chem. Process Des. Dev. 1980, 79, 451-459
France (where the article was written), is gratefully acknowledged. This research was partially supported by NSF Grants ENG74-02002A01 and ENG77-21069. The paper was presented a t the ACS/CSJ Chemical Congress in Honolulu, Hawaii, in April 1979. Literature Cited Bowen, J. H., "Sorption Processes", J. M. Coulson and J. F. Richardson, Ed., "Chemical Engineering", Vol. 3, pp 475-574, Pergamon Press, Oxford, 1971. El-Rifai, M. A., Saleh, M. A., Youssef, H. A,, Chem. Eng. (London), No. 289, 36 (Jan 1973). Fuker, R. D., "Adsorptbn",in G. Nonhebel, Ed., pp 328-366, "Gas Purificatlon Processes", George Newnes Ltd.. London, 1964.
45 1
Hitzeman, D., Senior Research Project, Purdue University, 1976. Lovett, W. D.,Cunnlff, F. T., Chem. Eng. frog., 70(5), 43 (May 1974). Mantell, C. L., "Adsorption",2nd ed,pp 224-254, McGraw-Hill, New York, 1952. Partin, L. R., M.S. Thesis, Purdue University, Dec 1977. Scamehorn, J. F., Ind. Eng. Chem. Process Des. Dev., 18, 210 (1979). Sherwood, T. K., Pigford, R. L., Wilke, C. R., "Mass Transfer", Chapter 10, McGraw-Hill, New York, 1975. Smisek, M., Cerny, S., "Active Carbon", pp 163-180, Elsevier, New York, 1970. Turk, A,, "Source Control by Gas-Solid Adsorption and Related Processes", in A. C. Stern, Ed., "Air Pollution", 2nd ed, Vol. 111, pp 497-519, Academic Press, New York, 1968.
Receiued f o r review September 10, 1979 Accepted March 27, 1980
Prediction of Maximum Rate of Pressure Rise Due to Dust Explosion in Closed Spherical and Nonspherical Vessels Shin-ichiro Nomura and Tatsuo Tanaka" Deparfment of Chemical Process Engineering. Hokkaido University, Sapporo, Japan
Using a model of particles uniformly dispersed, the rate of pressure rise due to dust explosion in closed vessels is theoretically studied. As a result, an empirical relationship called "cubical law" for spherical vessels between maximum rate of pressure rise and volume of vessel, that is, dPldtl,, V01'3 = KG, is proved to be valid, and it is shown that KG is a constant depending upon particle size, dust cloud concentration, and kind of materials. Extension is also rnade to the rate of pressure rise in a cylinder, which is assumed as a representative of configurations other than sphere. Derivative results show that the cubical law still holds, in which the constant KG is modified in terms of the configuration factor specific for the similar shape of the vessels.
Introduction Most powder handling processes are always exposed to the risk due to dust explosion. Much experimental work has thus far been carriled out, but it is generally difficult to uniformly disperse the dust in a test apparatus, resulting in a considerable discrepancy in each investigation with respect to the dependence of explosive characteristics on the dust concentration (e.g., Ishihama and Enomoto, 1975a; Sakashita, et al., 1975). Assuming the dust cloud as the uniformly dispersed single-sized particles and ignoring the fluctuations of the concentration as to the time as well as the space, the authors (Mitsui and Tanaka, 1973; Nomura and Tanaka, 1978 and 1979) have aimed at theoretical predictions of some important items of dust explosion, i.e., ignition temperature, minimum explosible limit concentration, and flame propagation velocity. All of them agreed fairly well with reported experimental data. One of the important explosive characteristics is the rate of pressure rise due to dust explosion in a closed vessel; particularly, the maximum rate of pressure rise is of practical importance for the safety design of relief venting for a flammable powder handling apparatus. For this reason, it is necessary to clarify the scale-up effect of the vessel on the maximum rate of pressure rise. Experimentally, it has been reported by Bartknecht (1971) that in a spherical vessel there should be the relationship called "cubical law" between the vessel volume, V,, and the maximum rate of pressure rise, dP/dtlmax,as follows
wherein KGCis a constant depending upon the material 0196-4305/80/1119-0451$01.00/0
properties and the state of the dust cloud. However, there has been no theoretical background proved of this empirical law as yet. In addition, as to nonspherical vessels, we have had up until now no reliable scale-up laws relating the configuration of the vessels to the maximum rate of pressure rise and other variables concerned. This paper deals, first, with the theoretical rate of pressure rise in a closed spherical vessel, in which the ignition is initiated at the center, based on a model of uniformly dispersed single-sized particles. The relationship represented in eq 1 is proved to be valid, in which KGCis given as a definite function of the kind of material as well as the dust concentration and the particle size. Furthermore, a laboratory test apparatus used by each investigator in the past has a different configuration from sphere, e.g., Hartmann apparatus (Hartmann and Nagy, 1944), and to have their data converted and compared with the ones taken with any type of test apparatus or practical vessels, the cubical law should be modified in terms of the vessel configuration. Consideration is, therefore, also given in this paper to the theoretical form, which is confirmed by the past experimental data. Modeling a Closed Vessel Containing Dust Cloud Cubical law has been found with spherical vessels and the theoretical interest should naturally be focused on this shape because of its geometrical simplicity. However, the actual equipment handling powders as well as many of the conventional laboratory test apparatus (e.g., Hartmann's) differs much from sphere. To discuss the scale effect of dust explosion, it should be necessary and useful to involve the configuration of the vessel, which would make it possible to convert the test data obtained with a certain type of apparatus to any other type and scale of equip0 1980
American Chemical Society
