420
Ind. Eng. Chem. Process Des. Dev. 1988, 25, 420-426
Pyrolysis of Black Liquor Solids Prashant K. Bhattacharya, Vidyasekara Parthiban, and Deepak Kunzru Department of Chemical Engineering, Indian Institute of Technology, Kanpur, India
Black liquor solids of -30+60-, -60+80-, and -80+150-mesh sire were pyrolyzed in a fixed-bed reactor in an inert atmosphere of nitrogen at 863-1013 K and atmospheric pressure. The effect of reaction time, temperature, and feed particle size on the product yields and the composition of product gases was investigated. The main components of the product gases were hydrogen, methane, carbon monoxide, carbon dioxide, and hydrogen sulfide. A reaction model, in which the black liquor solids decomposed into gas, tar, and char by three parallel first-order reactions, was proposed, and the frequency factors and activation energies of the rate constants were determined.
The present energy crisis has revitalized the interest in converting waste to fuel. Production of fuel from wastes not only reduces the problem of waste disposal but also increases the supply of energy produced from nonfossil sources. Moreover, it is generally available at a negative cost. Black liquor, a spent liquor from the alkaline pulp and paper industry, is not a waste in the strict sense of the word. In fact, the present practice is to regenerate it to obtain valuable inorganic pulping chemicals by burning the organic content. The conventional black liquor regeneration process, an integral part of the kraft pulping process, also recovers energy and provides approximately 35% of the total energy requirements. The regeneration of black liquor as well as the process of deriving energy from the black liquor for the paper industry are cumbersome and costly. The big paper mills have the potential to do so, but smaller units simply discard the effluent, thus creating acute environmental problems. Pyrolysis, a well-known process for obtaining fuels from wood, cellulose, municipal, and bovine waste, etc., can also be employed for black liquor, because of its similar chemical nature. The implementation of such a process depends to a large extent on the reliable design of units, in which the pyrolysis reactor plays an important role. Proper design of such a reactor requires knowledge and understanding of the kinetics of black liquor pyrolysis. Not much information is available on the pyrolysis of black liquor. Methods of utilizing the spent liquor through pyrolytic gasification at atmospheric pressure have been demonstrated by Prahacs and Gravel (1967) and Prachacs (1967). Technical feasibility of producing H,-rich gas by pyrolytic gasification of black liquor was experimentally demonstrated by Liu et al. (1977). Hydropyrolysis of black liquor has been carried out by Timpe and Evers (1973). The black liquor after pretreatment was subjected to temperatures of 505-645 K and high pressure, producing a low-ash char and a water-immiscible organic fraction as the two main products. Oye and Okayama (1977) pyrolyzed Eucalyptus black liquor at 673 K under helium; more COz than CO and CHI was generated. Brink and Thomas (1975) have developed an experimental unit to pyrolyze and completely gasify the organic content of concentrated pulping liquors at rates of up to 1ton/day of kraft black liquor solids. It has been claimed that some of the problems of the conventional kraft recovery process have been eliminated in the AST and SCA Billerud processes as discussed by Bjorkman (1968). Raymond and Roscoe (1974) have converted the organic constituents of the black liquor to a solid char product * T o whom correspondence should be addressed.
which was found suitable for the production of activated carbon. In an earlier study of Shrinath (1981), the pyrolysis of black liquor was investigated in a semibatch reactor. However, due to the size of the reactor, a significant time was needed for heating the black liquor to the desired temperature, and thus the experiments were not conducted at isothermal conditions, rendering the analysis difficult. Moreover, water was the main liquid product, and the organic liquid fraction could not be accurately collected. The present study was aimed at overcoming the limitations of the previous work. To prevent the dilution of the liquid products with water and to reduce the heating time, black liquor solids, rather than black liquor, were pyrolyzed. The black liquor solids were obtained by evaporating the water from the black liquor. The objective of this study was to investigate the effect of time, temperature, and particle size of the black liquor solids on the gas, liquid, and solid yields during the pyrolysis of black liquor solids and to propose a kinetic model for the pyrolysis of black liquor solids. In addition, the effect of these parameters on the composition and heating value of the gaseous product was also investigated. Experimental Section Apparatus. The pyrolysis of black liquor solids was carried out in a fixed-bed reactor. The pyrolysis tube consisted of three sections, reactor, gas supply and gas collection, and the setup is shown in Figure 1. The system is a modification of the pyrolysis tube used by Thurner and Mann (1981). The reactor consisted of a reaction chamber, a cooler, and a condenser. The reaction chamber was made of a 45 cm long, 2.2 cm. i.d. stainless steel tube. This tube was heated in a manually controlled tubular furnace. A sample boat assembly was used to insert the black liquor solids samples into the reaction chamber and to withdraw these into the cooler at the end of the run. The arrangement was such that the sample boat assembly could be slid smoothly into or out of the reaction chamber through the inner tube of the cooler with the help of leak-proof gasket arrangement. The sample boat assembly consisted of a 63 cm long, 1 cm i.d. stainless steel tube to which a boat could be attached. The boat was made by cutting off the upper half of a 1 cm i.d. stainless steel tube of length 8.5 cm. The depth of the boat was 0.5 cm. The fused end of a chromel-alumel thermocouple insulated with a ceramic sheath was placed in the middle of the sample boat in order to measure the reaction temperature accurately inside the sample. The thermocouple was passed through the long hollow tube of the sample boat assembly, and the free end of the thermocouple was connected to an elec-
0196-4305/86/1125-0420$01.50/00 1986 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 2, 1986
brine solution 1 2 3
Reaction chamber Furnace Sample b o a t assembly
5 6 7
Chromel-alumel thermocwple Condenser Separating funnel Sampling bulb assembly
8
Figure 1. Experimental setup.
tronic temperature indicator. To prevent the reacting gases from flowing through the space between the thermocouple sheath and the tube, this space was sealed with a high-temperature refractory cement. Another thermocouple placed on the reaction chamber wall measured the temperature of the furnace. The cooler was used to maintain the sample at a low temperature before it was inserted into the reaction chamber and to quench the reaction at the end of the run. The cooler was constructed by inserting a 2.2 cm i.d., 34 cm long stainless steel tube inside a 4.53 cm i.d., 34 cm long stainless steel tube. For cooling, the sample boat assembly was slid into the center of the inner tube. Ice-cold water was circulated in the outer tube. The condensable and noncondensable products of pyrolysis were passed through the condenser. Further, the noncondensables from the condenser were passed through the sampling bulb assembly and then through a saturated brine solution to measure the production rate by downward displacement of brine solution. Nitrogen was used as the inert carrier gas, with an inlet provision in the cooler. Procedure. A run was initiated by heating the furnace to the desired steady-state temperature. During this period, the sample boat was kept inside the cooler. After the furnace had attained the desired temperature, a known amount of the solid was taken in the sample boat and placed in the cooler. For each run, approximately 2 g of the black liquor solids of a particular size was placed in the sample boat. Since the amount of tar produced was usually very small, it adhered to the condenser walls and could not be collected in the receiver. Therefore, prior to each run, the condenser wall was covered with weighed aluminium foils, and its interior space was loosely filled with weighed glass wool to ensure complete collection of the tar formed during pyrolysis. After this, nitrogen was passed through the system for approximately 15 min to flush out the air and any other impurities. Then, the nitrogen flow rate was set a t 60 mL/min and the sample boat assembly slid into the reaction chamber. The temperature of the sample was measured continuously by using the electronic digital indicator. The gas samples were collected as a function of reaction time for analysis. The volume of the gases collected at each time was also noted, At the end of the run, the sample boat was quickly withdrawn into the cooler and the residue allowed to cool. After each run, the gases in the sampling bulbs were analyzed on a gas chromatograph. The amount of condensables collected was determined by weighing the preweighed aluminium foils and glass wool. The residue a t the end of the run was also weighed. Samples of these solids were retained for the measurement of ash content.
421
Table I. Characterization of Black Liquor and Black Liquor Solids" mesh size of black liquor solids black characteristics liauor -30+60 -60+80 -80+150 1.1752 specific gravity 5.74 5.67 5.78 44.83 moisture content 94.22 94.26 94.33 55.17 total solids content 30.02 29.91 29.89 16.58 ash content 69.98 70.09 70.11 38.59 organic content 3.47 active alkali content as NazO 33.85 33.73 33.67 19.82 total alkali content as NazO 14.07 Na2C03as NazO 2.49 NaOH as Na20 1.84 NazS as NazO 1.42 other alkali as NazO (by difference) ultimate analysis (moisture-free) 31.60 30.50 31.40 32.00 carbon 4.15 4.26 4.70 4.08 hydrogen nil nil nil nil nitrogen 25.11 25.02 24.98 26.66 sodium 1.22 1.20 1.26 1.28 sulfur 37.92 39.02 35.36 38.28 oxygen (by difference) 3628 3675 3682 heat of combustion, cal/g "All the data are in percentages except the specific gravity and heat of combustion.
Analysis of Product Gases. The product gases, consisting mainly of H2, CHI, CO, COz, and H2S, were analyzed on a gas chromatograph (CIC, Baroda). For the analysis of these gases, two columns were required. A 0.32 cm i.d., 2 m long column (molecular sieve 5A, -80+100 mesh) was used for separating H2, CH,, and CO, while a 0.32 cm i.d., 2 m long column (Porapak Q, -80+100 mesh) separated COz, CH,, and H2S. H2 and CO emerged as a single peak in the Porapak Q column. For both of the columns, the operating conditions were the same. Nitrogen at a flow rate of 80 cm3/min was used as the carrier gas, whereas the column temperature was 323 K. Preparation and Analysis of Black Liquor Solids. The concentrated black liquor, obtained from Central Pulp Mills, Surat, was used for the experiments. The solids from the black liquor were recovered by vacuum distillation. The pyrolysis feed was prepared by further drying these solids in an oven at 378 K for 3 h, grinding, and sieving into three fractions of -30+60-, -60+80-, and -80+150mesh sizes. The original black liquor and black liquor solids feed of three different size fractions was analyzed for its constituents according to standard procedures (Tappi standards and provisional methods, Tappi loose leaf data, Atlanta). An ultimate analysis of black liquor was also carried out to determine carbon and hydrogen contents by using Coleman 29 carbon-hydrogen analyzer, while nitrogen content was determined by using a Coleman 29A nitrogen analyzer. The calorific value of the solids was determined by using an adiabatic bomb calorimeter (Toshniwal, Model CCO1). The characteristics of the black liquor and black liquor solids are given in Table I. Results and Discussion The pyrolysis of black liquor solids of different sizes was carried out at six different temperatures in the range 863-1013 K. A t each temperature, the variation of gas, liquid, and solid residue yields with run time was mea-
422
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 2, 1986 , "
09
Residue
Tar
o
Gas
___
08
/;/--
3L1
-
'32
0
U r
c 30-
9
2
$28-
c" $26-
24
22
-
c
0 0
20
0
10
5
983 1013
o
863
0
893 923 953 983 1013
15
Time.min
0
Figure 6. Effect of reaction time and temperature on the carbon monoxide concentration in the gaseous product.
% of the oxygen in the black liquor solid feed goes out as carbon oxides (CO and C 0 2 ) ,whereas a t 1013 K the carbon oxides account for 27 wt 7% of the feed oxygen. There was no appreciable effect of feed particle size on the gaseous composition. Since the trends in the composition of the product gases with time and temperature for the other two sizes were found to be similar, graphical plots have not been showr) for these fractions. Goheen et al. (1976) studied the indirect pyrolysis of black liquor solids in the temperature range of 623-773 K. A typical analysis reported for the product gases was CH, 5%, H2S 15%, CO 30%, and C 0 2 30% by volume. In this study, the range for these components was CH, 1-5%, H2S 8-20%, CO 25-45 % , and C 0 2 30-40 %. A similar trend for the effect of time and temperature on the composition of the product gases was also observed in an earlier study of black liquor pyrolysis in the temperature range 873-993 K (Bhattacharya et al., 1985). However, due to the difference in the feed condition and reactor configuration, the
0
0
5
10
15
Time, min
Figure 8. Effect of reaction time and temperature on the methane concentration in the gaseous product.
actual values were different. Since the main objective of this study was to maximize gas yields, experiments were conducted a t atmospheric pressure only. It is expected that at higher pressures, yields of the liquid product would increase, whereas gas yields would decrease (Timpe and Evers, 1973). There is not much information available on the reactions occurring during pyrolysis of black liquor solids. Presumably, until about 473 K, only the moisture is removed from the black liquor solids. At higher temperatures, depending on the structural groups present, several volatile organic compounds together with heavy organic liquids (tar) and char are formed. The organic liquids further decompose
424
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 2, 1986
I
211
1
0
l5I
1I
983
141
I
I
0
5
10
I I 15
Time. min
Figure 9. Effect of reaction time and temperature on the hydrogen sulfide concentration in the gaseous product.
to give additional char and gases. The overall pyrolysis of black liquor solids can be represented as black liquor solids gases (CH,, CO, C02, H2, H2S, etc.) + organic liquids (tar) + char (1)
-
tar
-
char
+ gases
(2) The solids consist mainly of organic carbon residue. In addition, the inorganic salts such as Na2C03which are initially present in black liquor are also left behind. Pyrolysis of complex organic compounds involves the rupture of various bonds. The effect of temperature and time on the product gas compositions can be qualitatively explained in terms of structural groups present in black liquor solids as has been done for coal pyrolysis (Solomon and Colket, 1978). The evolution of a species results from the thermal decomposition of particular structural elements a t a kinetic rate which depends on the types of element. The formation of pyrolysis product gases is mainly due to decarboxylation, decarbonylation, dealkylation, and aromatic ring rupture (Wen and Dutta, 1979). Considering the functional groups constituting the black liquor solids, the mercaptans and the carboxyl bonds are the weakest and are ruptured easily. This explains the high concentration of C 0 2 and H2Sin the initial stages of pyrolysis. As the reaction proceeds, the concentrations of structural groups yielding COz and H2S are depleted and the concentration of these gases decreases with time. At intermediate reaction times, the dealkylation reaction is predominant. During the final stages of pyrolysis, the main reaction is the breaking of ether linkages and aromatic ring rupture producing CO and H2. The actual reactions occurring during pyrolysis are very complex, and the observed variations in the yields of the different products will depend on the reaction temperature and the concentration of various functional groups. The gross heating value of the gaseous product was calculated by the summation of the product of the individual heats of combustion and respective weight percents. At a particular temperature, the heating value of the product gases varied with reaction time. An average value for each temperature was calculated by taking a weighted average of the product of the instantaneous yield and heating value. There was no significant effect of temperature on particle si?e of the feed solids on the average heating value. The average heating value for all the runs was 6.4 f 0.4 MJ/kg. Pyrolysis Model. Many models have been proposed
for the pyrolysis of complex feedstocks such as bark, wood, and cellulose (Tran and Rai, 1976; Thurner and Mann, 1981; Shafizadeh et al., 1979; Stamm, 1956; Akita and Kase, 1967; Roberts and Clough, 1963). These investigators point out that pyrolysis of cellulosic materials proceeds through a very complex series of parallel and consecutive reactions, the nature and extent of which are not properly understood. Most of the workers have modeled the pyrolysis of a wide variety of feedstocks such as wood, cellulose, and noncatalyzed bark by assuming the overall reaction to be first-order or pseudo-first-order. On the other hand, Barooah and Long (1976) in their study of thermal decomposition of various carbonaceous materials divided the pyrolysis reaction into two stages in order to fit the data. Shafizadeh and Chin (1977) have proposed a model for wood pyrolysis in which the different products are lumped into three groups: gas, tar, and char. In their model, the wood is pyrolyzed into gas, tar,and char from three parallel reactions and the tar further decomposes into gas and char by two secondary reactions. Thurner and Mann (1981) used a simplified form of this model to explain their data on wood pyrolysis. The major organic components present in black liquor solids, such as cellulose, hemicellulose, lignin, and levoglucosan, are similar in nature to the components present in wood; therefore, the model as proposed by Shafizadeh and Chin (1977) was used to model the pyrolysis of black liquor solids. This model can be represented as gas
black liquor solids
-.’b
tar
(3)
char
In the reactor used for this study, the primary gaseous and tar products are continuously flushed from the reaction zone with inert nitrogen, thus minimizing the extent of the secondary reactions. It was assumed that the secondary reactions were negligible and the black liquor solids pyrolysis could be modeled according to the three primary reactions. Moreover, if the secondary reactions of the tar were appreciable, a maximum would be observed in the tar yields with reaction time. In this study, a t all temperatures, the yield of tar increased continuously with time (refer Figures 2-4), further justifying the above assumption. Each of the three primary reactions was assumed to be firsborder. Since the molecular weights of the components are not well-defined, it is more convenient to express the rate of disappearance or formation of the components in terms of mass or mass fraction. Thus, we have (4)
(7) The initial condition is att=O wB,,
=1
wGO
=
WTO =
ujcO = 0
(8)
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 2, 1986 425
Table 11. Activation Energies and Frequency Factors for the Pyrolysis of Black Liquor Solids particle size of feed solids, mesh Ei (kJ/mol) or Ai (min-') -30+60 -60+80 -80+150 39.90 52.10 El 34.60 23.90 E2 16.70 19.40 '42
21.80 3.42 0.69
26.80 6.76 0.94
A3
1.94
3.14
E3
A1
30.90 31.32 1.70 5.05
wB(t)
=
wR(t) - W R ( t 1 - WR(t
-
m,
(11)
Equations 9-11 are valid only for isothermal pyrolysis. As already mentioned in this study, it took 30-60 s for the feed sample to reach the steady-state temperature compared to the maximum reaction time of approximately 15 min. Thus, except for small run times, the assumption of isothermality is justified. Using eq 9, k3/(k1 12,) can be easily determined by measuring the residue mass fraction a t complete conversion. For black liquor solids pyrolysis, k3/(k1+ k,) did not vary significantly with temperature and was assumed to be constant for each of the three fractions. This assumption is valid if wR(t m ) is the same at the different reaction temperatures. As the temperature was increased from 863 to 1013 K, wR(t a) decreased from 0.5 to 0.48 for the largest size fraction (-30+60 mesh). Similarly, for the same temperature range, wR(t m ) decreased from 0.5 to 0.41 and from 0.5 to 0.38 for the -60+80- and -80+150-mesh size fractions, respectively. Since the variation of wR(t m ) with temperature was not appreciable, corresponding average values were used for the three fractions. k l and k 2 can be determined from the experimental yield vs. time plots of gas and tar by
+
-
-
-
I
.ob
t
The above equations are similar to those used by Thurner and Mann (1981) to model wood pyrolysis, and these authors have discussed in detail the methodology to obtain the individual rate constants from the experimental data. In the pyrolysis experiments, it is not possible to measure the mass fraction of the unreacted black liquor solids and the char produced separately because both are collected together as solid residue. I t can be shown (Thurner and Mann, 1981) that for isothermal pyrolysis
and
-1
-
where wB(t) is calculated by eq 11. The reaction rate constants k,, kZ,and k3 were calculated for the six different reaction temperatures for the three feed sizes. The Arrhenius plot for the largest size fraction (-30+60 mesh) is shown in Figure 10, while the activation energies and frequency factors for k l , k2, and k 3 for each size are given in Table 11. Compared to the usual values of activation energies for chemical reactions, those obtained in this study are quite low. A plausible explanation for these low values could be the simplified nature of the
-5
ol 0975
I 10
1
1025
1
I
I
1 0 5 1075 11 lOOOlT ( K)-'
I
1125
I
115
1175
Figure 10. Arrhenius plot of reaction rate constants.
model. In reality, each of the numerous constituents of black liquor solids would be decomposing by parallel paths but for analytical convenience have been lumped together. Anthony and Howard (1976) have reported that it has been demonstrated theoretically that a set of independent, parallel, first-order reactions can be approximated by a single, first-order expression having both lower activation energy and frequency factor than any of the reactions in the set. For coal pyrolysis, an activation energy of 10 kcal for a single-step correlation was obtaned, whereas for the same data the activation energy for a multistep correlation was found to be 50 kcal (Anthony et al., 1975). To evaluate the accuracy of the model, the yields of the pyrolysis products were calculated by using the determined rate constants and compared with the experimental yields. The cumulative mass fraction of any component as a function of time was determined by analytically integrating eq 4-7. The comparison between the predicted and experimental product yields for the largest size (-30+60 mesh) at three different temperatures is shown in Figures 2-4. The predicted curves agree quite well with the experimental plots. The deviation between the predicted and experimental yields was higher for lower conversion and decreased a t long reaction periods. A reason for the lack of fit of this model is the assumption of first-order kinetics throughout the whole conversion range. Some investigators (Tang and Neill, 1964; Lipska and Parker, 1966) have correlated the weight loss data of cellulose by an initial zeroth-order reaction followed by a first-order reaction at high conversions. Such a model would give a better fit for this case also, but the complexity of the model would be increased. It is possible that non-first-order kinetics might give a better prediction; however, analytical solutions would not then be possible,and numerical trial and error would be required to determine the model parameters. It should be emphasized that this model should not be taken to represent a mechanism for the pyrolysis of black liquor solids, which is a very complex reaction involving hundreds of free-radical reactions. The utility of such a model is in the analysis and design of pyrolysis furnaces where the details of the exact reaction mechanism are not required; rather the interest is in predicting the product yields. Moreover, such overall pyrolysis models can be used to quantitatively compare the rates of pyrolysis of different black liquors. Conclusions. From the above study, it can be concluded that significant amounts of Hz, CH4, and CO can be produced during the pyrolysis of black liquor solids. The gaseous composition depends on both the reaction temperature and run time. The pyrolysis of black liquor solids can be satisfactorily represented by a model in which char, gases, and tar are formed by three parallel first-order reactions from the black liquor solids.
Ind. Eng. Chem. Process Des. Dev.
426
Nomenclature A, = frequency factor for the ith reaction, min-' E, = activation energy for the ith reaction, kJ/mol k , = reaction rate constant for the ith reaction, mi& t = reaction time, min w = mass fraction Subscripts B = black liquor solids C = char G = gas R = residue T = tar Registry No. Hydrogen, 1333-74-0;carbon monoxide, 630-0&0; carbon dioxide, 124-38-9;hydrogen sulfide, 7783-06-4;methane, 74-82-8.
Literature Cited Akita, K.; Kase, M. J . Po/ym. S d . 1967, 5 , 833. Anthony, D. B.; Howard, J. B.; Hottel, H. C.; Meissner, H. 0. 15th Symposlum (International) on Combustion, The Combustion Instltute, Pittsburgh, 1975, p 1303. Anthony, D. B.; Howard, J. 8. AIChE J . 1976, 22, 625. Barroah, J. N.; Long V. D. Fuel 1976, 55, 116. Bhattacharya, P. K.; Shrinath, A. S.; Kunzru, D. J . Chem. Techno/. Biotechno/ 1985, 35A, 223. Bjorkman, A. Proceedings of the Symposium on Recovery of Pulping Chemicals, Finnish Pulp and Paper Research Institute, Helsinki, 1968, p 235.
1986,25, 426-429
Brink, D. L.; Thomas, J. F. Tappi 1975, 5 6 , 142. Goheen, D. W.; Orie, J. V.: Wither, R. P. I n "Thermal Uses and Properties of Carbohydrates and Lignins"; Shafiadeh, F., Ed.; Academic Press: New York, 1976; pp 227-244. Lipska, A. E.; Parker, W. J. J . Appl. Polym. Sci. 1966, IO, 1437. Liu, K. T.; Stambaugh, E. P.; Nack, H.; Oxley, J. H. "Pyrolytic Gasification of Kraft Black Liquors" Fuels from Waste"; Anderson, L. L., Tillman, D. A,, Eds.; Academic Press: New York, 1977; p 161. Goye, R.; Okayama, T. Kami Pa Gikyoshi 1977, 3 1 , 404. Parthiban, V. M. Technology Thesis, I.I.T., Kanpur, 1983. Prahacs, S.;Gravel, J. J. 0. Ind. Eng. Chem. Process Des. Dev. 1967, 6 , 180. Prahacs, S.Adv. Chem. Ser, 1967, 6 9 , 230. Raymond, D. R.; Roscoe, R. W. AIChE Symp. Ser. 1974, No. 139, 45. Roberts, A. F.; Clough, G. 9th Symposium (International) on Combustion, 1963, p 158. Shaflzadeh. F.; Chin, P. P. S. ACS Symp. Ser. 1977, No. 4 3 , 57. Shafizadeh, F.; Cochran, T. G.; Sakai, Y. AIChE Symp. Ser. 1979, No, 184, 24. Shrlnath, A. S. M. Technology Thesis, I.I.T.. Kanpur, 1981. Solomon, P. R.; Colket. M. B. Fuel 1978, 57, 749. Stamm, A. J. Ind. Eng. Chem. 1956, 4 8 , 413. Tang, W. K.; Neill, W. K. J . Po/ym. Sci. 1964, 6 , 65. Timpe, W. G.;Evers, W. J. Tappi 1973, 56, 100. Thurner, F.; Mann, U. Ind. Eng. Chem. Process Des. Dev. 1981, 2 0 , 482. Tran, D. Q.;Rai, C. AIChE Symp. Ser. 1976, No. 157, 72, 100. Wen, C. Y.; Dutta, S. I n "Coal ConversionTechnoiogy", Wen, C. Y., Lee, E. S.,Eds.; Addison-Wesley: Reading, 1979.
Received for review December 28, 1984 Revised manuscript received July 11, 1985 Accepted August 1, 1985
Improved Equation for the Calculation of Minimum Fluidization Velocity Antoni Lucas, Josep Arnaldos, Joaqulm Casal, and Lluls Pulgjaner Chemical Engineering Deparfment, Universitat Politecnica de Catalunya, Barcelona -08026,
Spain
A certain number of equations have been suggested to calculate the minimum fluidization velocity without needing the knowledge of bed voidage and shape factor. Most of them, corresponding to the same general expression, introduce, however, an error when not applied to a restricted range of shape factors, due to the variation of the constants appearing in that expression with particle shape. I n the present work, particles have been classified in three categories, according to their shape, and optimum values of those constants have been determined for each category. Three equations have been thus obtained which minimize the error in the calculation of minimum fluidization velocity.
Minimum fluidization velocity calculation has been the subject of a number of publications, mainly concerned with empirical correlations restricted to concrete systems under specific operating conditions and working hypothesis. In some cases, the knowledge of difficult to determine parameters is implied, like shape factor and bed voidage at incipient fluidization, while others simply ignore the influence of such parameters to the expense of accuracy when applied to particular systems beyond the specific conditions that validate the correlation proposed. Some authors, trying to avoid the difficulty associated in finding the values of emf and 4, have developed different generalized equations through the correlation of experimental data taken from diverse sources. The accuracy of these equations has been recently reviewed (Casal, 1984). In this paper, substantially better equations are developed with improved accuracy in the calculation of minimum fluidization velocity; they have been obtained, not from experimental data correlations on Ar and Remf but from the intrinsic relationships between e and 4 for dif0196-4305/86/1125-0426$01.50/0
ferent bed densities following Brownell et al. (1950) (Figure 1).
Proposed Equations On the basis of Ergun's equation applied to incipient fluidization, the following expression can be obtained
Remf=
[(
42.85'72)2
+ L]1'2 1.75C1
- 42.857-CI
(1)
c2
where
Equations 2 have been represented in Figures 2 and 3, showing, respectively, the values of emf as a function of 4 at constant values of C1and C p . Some authors have tried to avoid the restrictive use of eq 1, subjected to the knowledge of 4 and emf. The procedure has always been the correlation of experimental 0 1986 American Chemical Society
