Fuller, E. C., Crist, R. H., J. Amer. Chem. SOC.,63,1644 (1941). Hughmark, G. A., Ind. Eng. Chem., Process Des. Develop., 6, 218 (1967). Jackson, M. L., James D. R., Leber, B. P., "Oxygen Transfer in a 23Meter Bubble Column," preprinted for the Joint International AIChEVTG meeting, Munich, Sept 1974. Jackson, M. L.. Collins, W. D.. lnd. Enq. Chem., Process Des. Develop., 3,386 (1964). Landberg. G. G.. Graulich, B. P.. Kipple. W. H.. Water Res., 3, 445 (1969) Leber, B. P., Jr.. M. S. Thesis. Chemical Engineering, University of Idaho. Moscow. Idaho. 1974. Nagashio, I . J., Kurosawa, K., Chem. Techno/., 33,927 (1969) (in Japanese). Nogaj, R. J., Chem. Eng. (N.Y . ) , 95 (Apr 17, 1972). Oldshue, J. Y . . Chem. Eng. Progr. 66,73 (Nov 1970). Perry, R. H., Chilton. C. H., Kirkpatrick, S. D., "Perry's Chemical Engineers' Handbook." 4th ed, pp. 6-16, McGraw-Hill, New York, N. Y.. 1963. Sideman, S., Hortacsu, O., Fulton, J. W., lnd. Eng. Chem., 58, 32 (1966)
Tapleshay. J. A., in J. McCabe, W. W. Eckenfelder. Jr., ed., "Advances in Biological Waste Treatment," p 225, Reinhold, New York, N. Y., 1956. Urza. I. J.. M . S. Chem. Engr. Thesis, University of Idaho, Moscow, Idaho, 1972. Von der Emde, W., "Advances in Water Quality Improvement." E. F. Gloyna and W. W. Eckenfelder. Ed., p 237, University of Texas Press, Austin, Texas, 1968. Weber, W. J.. Jr., "Physicochemical Processes for Water Ouality Control," p 518, Wiley-lnterscience, New York, N. y . . 1972. Wells, P. A., Moyer, A. J., Stubbs. J. J.. Herrick. H. T.. May, 0. E . , Ind. Eng. Chem., 29, 653 (1937). Westerterp, K. R., Van Dierendock, L. L., de Kraa, J. A , Chem Eng. Sci., 18, 157 (1963). Yoshida, F.,Akita. K..A.l.Ch.E. J., 11,9 (1965).
Received for reuieu: November 9, 1973 Accepted October 16,1974
Simulation of the Comminution of a Heterogeneous Mixture of Brittle and Nonbrittle Materials in a Swing Hammermill D. M. Obeng' and G. J. Trezek* Department of Mechanical Engineering, University of California, Berkeley, California 94720
Four matrix models were used to study and mathematically simulate the comminution process in the swing hammermill. The feed material was domestic packer truck refuse, a mixture of approximately 25% brittle and 75% nonbrittle constituents. The validity of the analytical models was substantiated through comparison with experimental data generated in a 10 ton/hr swing hammermill size reduction facility operating under controlled conditions. The *-Breakage Model and the Repeated Breakage Cycle model are both suitable for predicting the product size distributions for primary, secondary, and tertiary grinding processes. However, the x-Breakage Model is in closer agreement for the three grinding conditions
Introduction Packer truck refuse is a material of unique properties and characteristics. In general, this material is a heterogeneous mixture of approximately 75% nonbrittle materials: newsprint, mixed paper waste, cardboard, plastics, organic constituents, etc., and 25% brittle materials: ferrous metals, aluminum, glass, etc. Contingent upon proper constituent recovery, refuse can be a valuable resource in terms of its material and energy content. Modern solid waste management technology, predicated on the premise of resource and energy recovery as a means of dealing with critical disposal problems, nearly always requires some size reduction of the incoming refuse stream as an initial step in processing. This holds whether the process ranges from the simple magnetic removal of the ferrous materials, to advanced processes dealing with the recovery of the predominant cellulose fibre constituents, or to other complex processes dealing with sophisticated combustion or pyrolysis. In some instances, the latter process may require several comminution stages. Control of the size distribution of the ground product is critical to the proper performance of the subsequent stages of processing which are often carried out with standard equipment items. Thus, the present work is motivated by '
African Graduate Fellow (AFGRAD)
the need for developing an understanding of heterogeneous material comminution and for developing an analytical technique capable of predicting the size distribution of the product for a specified size distribution of the feed, i.e., the heterogeneous refuse mixture being comminuted in a swing hammermill. A semiempirical analysis of the breakage process was conducted as a means of achieving the above objectives. The influence of two Comminution parameters, the feed rate and moisture content. as well as the effects of secondary and tertiary grinding on the product size distribution are reflected in the experimental data base. Because of the nature of refuse, an extrapolation of brittle material comminution results to refuse has not been feasible (Patrick, 1967). Further, the product size distribution for brittle materials can usually be described by various relations such as the Gaudin-Schuhmann (Gaudin, 1926; Schuhmann, 1940) or the Rosin-Rammler (1933) equations. In addition, Gaudin and Meloy (1962) give a theoretical size-distribution equation for single fracture, and other size distribution equations (Bergstroni. 1966; Harris, 1968, 1969, 1970) have been proposed with additional parameters, ostensibly for greater curve-fitting flexibility, as further generalizations of the above relations. Due to the fact that refuse is a heterogeneous material it is unlikely that a single breakage law can describe I n d . Eng. C h e m . , P r o c e s s D e s . Dev., Vol. 14, No. 2 , 1 9 7 5
113
all types of breakage. There are some difficulties to the applications of these various laws characterizing size distribution. One of the major deficiencies is that, although it seems natural to suppose that a breakage process operates according to some law, our experimental results indicate that the feed cannot be characterized by any of the previously derived size distribution relations. Thus, when the process is supplied with some unusual distribution of feed, like refuse, it seems that the product need not obey any of the usual laws. The analysis of a breakage process by matrix method offers an excellent approach to overcome this difficulty, especially in the case of the simulation of a breakage process whereby the feed and discharge size distributions can be obtained (Austin, 1971/1972; Broadbent and Callcott, 1956a; Callcott, 1960).
do not cover the same sizes and the size ranges differ considerably treats the breakage process in terms of a series of cycles of mild breakage and is given by (Callcott, 1960; Callcott and Lynch, 1964)
p
p
The parameter x then completely describes the process if B is assumed to be known; it is a useful measure of the breakage effected by the process. The techniques for backcalculating the value of x from known feed and product distributions have been indicated by Broadbent and Callcott (1956b, 1957). (b) T , K-Breakage Process. This is similar to the x breakage process except that the breakage matrix is replaced by BK,K 2 1, on the basis that some machines would cause more severe degradation on breakage than others, corresponding to repeated breakage on the products of a particle without these products moving away from the grinding action and having to wait for reselection for breakage. Thus, the equation governing this process is characterized by two parameters x and K , and the matrix equation is
p
= { r B K + (1 - tr)I)f
(2)
( c ) x,K,w-Breakage Process. Here probability of a particle being selected for breakage varies with some power Y of the particle size, so that the proportion of particles in the it,h size range selected for breakage is
si
=
SI(?.)-”’
(3)
If w = r r U and the probability is x for the first size range it is HW, x d , . . . , run-1 in the following ranges. If R is the matrix with 1, W , ~ 2 ., . . , un-l along the main diagonal and zeros elsewhere, the selection matrix is xR. The equation of the process is
11
= (TBR
+
I - nn)f
(4)
(d) Repeated Breakage Cycles. A relation dealing with the situation where the feed and product size distributions 114
Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 2 , 1975
I - S,)).f
where h = 1, 2, . . . , N refers to the hth cycle in which the probability of breakage is sh. I t has been shown (Callcott, 1960; Callcott and Lynch, 1964) that given only p , f, and B the evaluation of each sh and of N is not possible so that the following sequential model was adopted to simplify the analysis. If the probability of breakage Sh is assumed to be the same for all cycles eq 5 becomes
Breakage Process Models A matrix method similar to that employed by Callcott (1960) for the comminution of coal in a swing hammer mill was used to analyze the size reduction of refuse. Observations of refuse size reduction in the swing hammer mill (Trezek, 1972) indicate that, in general, items pass through the mill without being subjected to repeated fracture. Thus, in a manner similar to that used by Broadbent and Callcott (1956b, 1957), the swing hammer mill can be considered as a once-through grinder for the simulation of the comminution process of municipal refuse. The four simulation models tested are summarized below. (a) x-Breakage Process. Here the selection function Scv) = x for all sizes y, i.e., a proportion x of the particles, independerit of particle size, is broken according to the breakage function B ( x , y ) . In matrix terms, S = TI and the equation describing the process is
+
= {’(BS, h=N1
(BS
+
I - S)’”.f
(6)
where S is the selection matrix common to all the N cycles. Setting
D = (BS
+
I
-
S)
then
P
= DNf
The whole process in the mill is treated as a sequence of operations in which the product from the j t h cycle becomes the feed for the (j 1)th cycle. In order to ensure that the undersize from any cycle of the process is correctly described p and f are made ( n + 1)-column vectors with the last elements p n + l and f n + l describing the undersize for the product and feed, respectively. D is written as a (n + 1) square matrix with the (n + 1)th row describing the proportions of the various size ranges which end up as undersize. The number, N, of cycles has been associated with the “stages of grinding” (Austin, 1971/1972). In the present model, the number of cycles, N, is not identified with the grinding zones as it was in the case of Callcott (1960) but it is introduced artificially as a means of repeatedly applying the single matrix D to the feed vector f in order to obtain p , when the top sizes of the feed and product distributions differ considerably. If x1 is the maximum size of the initial feed and x m the maximum size of the final product (where x L = rx, 1, i = 1, 2, , n - l), , m, then N is estimated from ,Y = ( I / / - 1) (9)
+
Experimental Facility The data used in this study were obtained on a commercial 10 tons/hr Grundler Model 48-4 swing hammer mill adapted as a research tool in the size reduction laboratory. Feed and discharge is accomplished with piano hinge steel belt conveyors a t a rate of between 1 and 10 tons/hr. Instrumentation is available for continuous monitoring of power consumption and surges and also rotational speed of the grinder shaft. A complete description of this facility has been previously presented (Savage and Trezek, 1972). Packer truck refuse is loaded by means of a front end type tractor loader and the feed rate is determined by removing the size reduced refuse from a 3-ft section of the discharge conveyor (belt speed 10 ft/min) and weighing it. The actual measurements of size distribution were performed by shaking a sample in a series of Tyler Standard Screens using a Ro-Tap Testing Sieve Shaker. In general, for ground refuse materials the sample sizes were of the order of 100-200 g and a shaking time of 20 min was used. The size distribution used in the subsequent simulation studies was based on a dry sieve analysis; that is, the
n - 0-1
I
0 01
I
I
I
01
I
I
I
I
1
I
I
I
IO
IO
PARTICLE SIZE, INCHES
Figure I. Comparison between computed and experimental product size distributions for primary, secondary, and tertiary grinding using the a-BreakageProcess Model. samples were dried before sieving. Experimental accuracy was monitored by obtaining sample means, standard deviation, and coefficients of variation for the measured quantities which include particle size (size distribution), feed rate, and power consumption.
in
W
rJ ln
Simulation Results Due to the fact that present comminution theories are not sufficiently developed, selection and breakage functions particularly for a heterogeneous refuse material cannot be obtained from first principles. Thus, in order to use the previously described simulation models, these quantities were determined with an indirect estimation or semiempirical technique similar to that proposed by Broadbent and Callcott. Two forms of the breakage function were selected, namely (a) after a modified form of Broadbent -Callcott
where n is some positive index. Experimental results indicated that certain products of the size reduction conformed to the Rosin-Rammler distribution with an n index varying between 0.845 and unity. The second form was ( b ) after the Gaudin-Meloy distribution equation
B(x,
= B(x/4,) = 1
-
(1 - x/,i$r
(11)
This additional relation was necessary since, as will be shown, eq 10 did not simulate primary grinding. These relations (eq 10 and 11) were used to compute the elements of the breakage matrices. The selection functions were determined with the leastsquare procedure for the a-breakage, x,K-breakage and a,r,o-breakage processes for integer values of K from 1 to 5 and (L’ = 1, 0.9. 0.8, . . . , to 0.1 using the experimental feed and product size distributions. The “best” selection func-
q
I! 0
I
0 001 0 01
FEED, RAW PACKER TRUCK REFUSE
-0- EXPERIMENTAL,PRIMARY GRINDING
E 001
I
I
I
l
l
I
I
I
l
l
I
I
01
10 PARTICLE S I Z E , INCHES
I
1
10
Figure 2. Comparison between computed and experimental product size distributions for primary grinding using the a-ABreakage
Process Model. tions and the breakage matrices, i.e., those which yield least squared errors, are then used to calculate the product size distributions for the particular breakage model. For the Repeated Breakage Cycles Model values of T = 0.1, 0.2, . . . , to 1 are chosen and used together with the breakage matrices to compute product size distributions. The particular selection function which gives the leastsquared error is chosen as the parameter to represent the model. In all the above cases, computations were performed with a systematic variation of combinations of the Ind. Eng. Chem.. Process Des. Dev., Vol. 14, No. 2, 1975
115
W
N v, 0
w
I-
a +
v,
z a
I I-
LK
w
zLL
0
z
0 I-
O
a E
LL
W
> Ia -1
3
5 O n r
u
L,
0 01
01
IO
IO
PARTICLE S I Z E , INCHES Figure 3. Comparison between computed a n d experimental product size distributions for primary grinding using the Repeated Breakage Cycle Model.
selection breakage function, so that the reported simulation results are those which yield the least-squared errors. The actual results of the simulation can be summarized according to the following. ( 1 ) a-Breakage Process. Figure 1 shows the comparison between the computed and experimental product size distributions for primary, secondary, and tertiary grindings using the a-Breakage Model for various selection and breakage functions. Here the breakage function based on eq 11 with the index r = 7 predicts the primary product size distribution very well within experimental errors. Also the breakage functions obtained from eq 10 give better results for the secondary and tertiary grinding processes than the predictions from eq 11. (2) a,x-Breakage Process. Figure 2 shows the comparison between the computed and experimental product size distributions for primary grinding using this model. The results for h = 2 and 3 using the modified BroadbentCallcott equation represent the best among a host of other computed product size distributions and since the above results do not in any way predict the actual experimental product size distribution, the a,K-Breakage Process Model is rejected as a representation of the refuse size reduction process in the hammermill. With A = 1 (Le., *-Breakage Process). eq 10 does not come any closer in predicting the product size distribution. The computations based on the a,h-Breakage Process Model for the secondary and tertiary grinding conditions do not give any better results than those predicted with the simple *-Breakage Process Model. (3) n,K,w-Breakage Process. This model is also rejected as a mathematical representation of the breakage process in the mill. The values of TT for w I0.9 are found to be greater than unity. Values of T greater than unity cannot be accepted because they violate the definition of * as a probability of a particle of a certain size being broken in passing through a process. If the values of K greater than 116
Ind. Eng. Chern., Process Des. Dev., Vol. 14, No. 2, 1975
unity were accepted it would just mean that we were merely curve-fitting the computed results to the experimental data and the model would not be amenable to any physical interpretations. (4) The Repeated Breakage Cycle Model. Figure 3 shows the partial success of this model in computing product size distributions for primary, secondary, and tertiary grinding processes. Breakage functions based on eq 10 yield good results for the primary grinding process for sizes down to 0.2 in. (5080 F ) with about 32% passing stated size; below this size the computed and experimental values diverge. There is a considerable improvement in the results of this model for the secondary and tertiary grinding process. The computed results are close to the experimental ones down to sizes as low as 0.02 in. (508 p ) with about 12% passing the stated size. In all the above cases, the breakage functions based on the modified Broadbent-Callcott equation or normalized RosinRammler equation (10) give better results than those of the Gaudin-Meloy equation (11). The Gaudin-Meloy equation fails to predict well in the small size ranges. Conclusions In general, a good model will include the most important features of the process, will be mathematically simple (if possible), will provide a minimum of assumptions, and will be fruitful for purposes of prediction and theoretical speculation. In the simulation of the various results in this paper, the two models, a+-Breakage and *,K,o-Breakage Models are found to be untenable because they fail to predict the product size distributions within any reasonable accuracy. The R-Breakage Model and the Repeated Breakage Cycle Model, however. give very good results for the products of primary, secondary. and tertiary grinding processes. The *-Breakage Model is clearly superior to the Repeated Breakage Cycle Model because it gives better results for all the three grinding conditions.
Acknowledgments
Callcott, T. G . . Lynch, A. J., Proc. A u s t . lnst. Min. Met., 209, 109-131
This work was supported by an Environmental Protection A~~~~~ ~~~~~~~hGrant, ~~~~tN ~ EPA . ~801218, "Size Reduction in Solid Waste Processing." The financia1 aid of the African-American Institute in supporting Dennis Obeng's graduate studies is appreciated. P u ~ f e s sor Thomas Mika of the Material Science Department gave advice concerning some of the analytical aspects of this work.
Gaudin. A. M . , Trans. A I M € , 73,253 (1926). Gaudin, A. M . . Meloy. T. p., Trans. A I M € . 223,40-43 (19621. Harris, C. C., Trans. A I M € , 241,343-358 (1968). Harris, C. C . , Trans. A I M € , 244,187-190(1969) Harris. C. C . , Trans. Inst. Mlniflg Met.. 79,C157-158 (1970) Patrick, P. K . . "Waste Volume Reduction by Pulverization, Crushing. and Shearina," The institute of Public Ciearino 69th Annual Conference. 5th to 9tk,June 1967. Rosin. P., Rammler. E., lnst. Fuel, 7,29-36 (1933) Savage, G., Trezek, G. J . , "Size Reduction in Solid Waste ProcessingSize Reduction Facility," Report prepared for Environmental Protection Agency, Grant No. EPA R801218,May 1972 Schuhmann, R , Tech. Publ. A I M € , 7189, 1 1 (Juiy 1940) Trezek, G. J . , 'Refuse Comminution." Compost Sci.. 13 (4).13-15
Literature Cited Austin, L G., Power Techno/., 5, 1-17 (1971/1972). Bergstrom. B. H . , Trans. A I M € , 235,45 (1966) Broadbent, S.R.. Callcott. T. G., Phil. Trans. Roy. SOC.,249,99 (1956a). Broadbent, S.R . , Callcott, T. G., J . lnst. Fuel, 20. 524-539 (1956b):30,
(19.641
(1972).
Received f o r recielc ,January 29, 1974 Accepted November 27, 1974
21-25 (1957) _.
Callcott, ?. G:, j. lnst Fuel. 33,529-539 (1960)
Kinetics of the Hydrodealkylation of Methylnaphthalenes in a
Nonisother mal Flow Reactor Paolo Beltrarne,* Bruno Marongiu, Vincenzo Solinas, Sergio Torrazza Istituto Chimico. Universita. 09700 Cagiiari. lfaiy
Lucio Forni and Sandro Mori lstituto d! Chimica Fisica. Universita, 20133 Milano. ltaly
The thermal hydrodealkylation of 1-methylnaphthalene (AMN) and of 2-methylnaphthalene (BMN) has been studied in a tubular flow reactor markedly deviating from isothermal conditions. Complete temperature profiles in the reactor were recorded: maximum values of temperature were kept at ca. 630, 660. and 700°C for AMN runs and at ca. 700, 730, and 760°C for BMN. Total pressure ranged from 4.9 to 39.7 atm, and H2:hydrocarbon molar ratio in the feed was varied from 3 to ca. 9. Assuming the rate equation r = ~ . C M N ~ - C HArrhenius ,~, parameters and partial reaction orders were obtained by a nonlinear optimization procedure. Results are: (AMN) rn = 0.25; n = 0.8; A = 4.8 X l o 9 1,0~05/rno10~05 sec, E = 50800 cal/mol; (BMN) rn = 0.35; n = 0.75; A = 4.2 X l o 8 l.O.l/rnolo.' sec, E = 46900 cal/ mol. Experimental molar conversions are reproduced with relative mean square deviations of 12% (AMN) and 6% ( B M N ) .
Several kinetic measurements have been performed on toluene hydrodealkylation and their results have been critically examined in reviews (Asselin, 1964; Benson and Shaw, 1967). Few studies on the analogous reaction of methylnaphthalenes have been reported (Asselin, 1964; Gonikberg, e t al., 1964, 1965) and some discrepancies exist among published results, mainly concerning the form of the rate equation. Therefore further kinetic measurements about l-methylnaphthalene (AMN) and 2 methylnaphthalene (BMN) have been undertaken by using a tubular flow reactor. Isothermal conditions would have been difficult to a t tain all along the reactor a t the temperatures required for thermal hydrodealkylation (Amano and Uchiyama, 1963; Zimmerman and York. 1964; Shull and Hixson, 1966). On the other hand, with the present computing facilities, a problem of nonisothermal kinetics can be easily handled by nonlinear regression analysis.
Experimental Section Materials. Merck-Schuchardt 97% l-methylnaphthalene and 98% 2-methylnaphthalene (mp 35°C) and cylinder 99.99% hydrogen were employed. In the conditions of the glc analysis described below, both methglnaphthalenes gave a single peak. Apparatus and Procedure. A scheme of the apparatus is presented in Figure 1. The tubular flow reactor, made of stainless steel (Incoloy), was fitted with two contacting axial concentric thermowells: the annular reaction tube was 49 cm long, 1.2 cm o.d., and 0.6 cm i.d. A vaporizerpreheater was also provided. Reactor and preheater were heated by means of four electric furnaces. The hydrocarbon reservoir, the pump, and the connecting pipes were equipped with a heating jacket in order to avoid crystallization of BMN. Axial temperature profiles were measured by placing thin (1.6 mm 0.d.) iron-constantan thermocouples at variInd. Eng. C h e m . , Process Des. Dev., Vol. 14, No. 2, 1975
117
