1396
Ind. Eng. Chem. Res. 1993,32, 1396-1410
Modeling of a Fluidized-Bed Coal Carbonizer Ani1 Goyal' a n d Amir Rehmat Institute of Gas Technology, 3424 South State Street, Chicago, Illinois 60616
A computer model has been developed, based on data currently available in the literature, to simulate air-blown pyrolysis of coal in a carbonizer. A calcium-based sorbent (limestone or dolomite) can
also be fed simultaneously with coal to the carbonizer to capture in-situ sulfur released into the gas. In addition to capturing the sulfur, the sorbent also influences the product yields by cracking some tar to gases and soot. Empirical correlations have been derived for the yields (tar, gas, and char) obtained from the carbonization of bituminous coals as well as lignites. These correlations have been incorporated into the computer model; the model predicts the char, soot, tar, spent sorbent, air feed, and product gas flow rates and their compositions, and sulfur capture. This model has been used to predict the carbonizer performance for two feedstocks, Pittsburgh No. 8 bituminous coal and Texas lignite, at pressures of 14 and 10 atm. Also, the effects of feedstock moisture content and operating temperature on the carbonizer performance have been studied for each feedstock and pressure. A coal-water slurry feed has also been considered for the bituminous coal. Introduction There has been a significant increase in developing coalbased advanced technologies for power generation. A team of companies, led by Foster Wheeler Development Corp. and consisting of GilbertlCommonwealth, the Institute of Gas Technology (IGT), the Combustion Turbine Operations Division of Westinghouse Electric Corp., and the Research and DevelopmentDivision of Westinghouse Electric Corp., has been developing an advanced secondgeneration pressurized fluidized-bed (PFB) combustion system. The targeted goals of this second-generation PFB combustion plant are a 45% efficiency and a cost of electricity that is at least 20% lower than conventional pulverized-coal-fired plants with stack gas scrubbers. In addition, the plant emissions are to be within New Source Performance Standards, and the plant should have high availability, be able to process different ranks of coal, and incorporate modular construction technologies. These goals are achieved by shifting power generation to the more efficient gas turbine cycle and away from the steam cycle, while maintaining sulfur capture by the sorbent and by providing significantly higher gas turbine inlet temperatures without increasing the bed temperature through the incorporation of a topping combustor in the system (Robertson et al., 1988). In this arrangement (Figure 11, a carbonizer generates a coal-derivedlow-Btu fuel gas from carbonization of coal at approximately 1500-1700 OF. This is mixed with flue gases from a PFB combustor operating at 1500-1700 OF and is burned in a topping combustor to increase the gas turbine inlet temperature to approximately 2200-2400 OF. The combustion air to the topping combustor is provided by high excess air present in the flue gas from the PFB combustor. Therefore, the carbonizer is an essential element of this system. The coal is primarily fed to the carbonizer. The coal char residue from the carbonizer is burned in the PFB combustor along with the balance of the plant coal, if there is any left. A calciumbased sorbent is injected into the carbonizer and PFB combustor to minimize carbonizer tar yield and to desulfurize the gases from both units. The efficiency is largely dependent upon the performance of the carbonizer. The coal carbonizer, depending on the coal properties, can be designed as a bubbling or a fast fluidized-bed
* Author to whom correspondence is to be addressed.
SORBENT AIR
4
1
FLUE GASES + EXCESS AIR
I CHAR AIR
A
COMBUSTOR
WATER
SOLID WASTE
STEAM
Figure 1. Advanced pressurized fluidized-bed combustion system.
reactor, each having its own characteristics with respect to the coal and air injection and product recovery. These constraints associated with the carbonizer design were recognized and, therefore, a highly generalized model was developed to accommodate various coal carbonizer configurations. The model can simulate a bubbling or a fast fluidized-bedreactor with or without fines recycle in which the coal and sorbent can be introduced into the fluidizedbed region and/or into the freeboard region of the carbonizer. Later, the model was tailored specifically for the three most practical configurations of the carbonizer. An extensive literature search was conducted, and correlations were developed for yields of various species as a function of coal properties and carbonizer operating parameters. Although there are a lot of data available on the subject of pyrolysis, only a small amount of this information was applicable for the type of coal processing used here. Much of the data for coal pyrolysis were obtained in a heated grid reactor where the coal was subjected to the desired temperature from a fraction of a second to about 2 s, usually yielding only a fraction of the pyrolysis product. On the other hand, in a fluidized-bed reactor, coal is subjected to a sufficiently long residence time (a gas residence time of over 5 s and a solids residence time of several minutes), so the maximum yield is typically obtained. The data available in this category were used to develop the correlations for the coal carbonization product yields and their compositions. These correlations have been developed for bituminous coals as well as for lignites to cover a wide range of feedstock properties. The correlations used in the model have been summarizedhere; the details of the development of these correlations have been given by Rehmat and Goyal(1987)in the DOE Final Report.
0888-5885/93/2632-1396$04.00/0 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1397 Table I. Bituminous Coals Used by Various Investinators for Coal Pyrolysis Study reference
coal
Xu and Tomita (1987) Yeboah (1979);Yeboah et al. (1980) Desypris (1982) Tyler (1980) Tyler (1980) Tyler (1980) Tyler (1980) Suuberg et al. (1978) Graff et al. (1986) Freihaut and Seery (1981) CSRIO (1958) Xu and Tomita (1987)
Lindell Illinois No. 6 Blachall Singles (Durham) Millmerran Pittsburgh No. 8 Lindell B Blair Athol Pittsburgh No. 8 Illinois No. 6
0
Utah Portland, Australian Hunter Valley
83.5 76.9 86.0 78.4 77.7 80.3 81.6 77.7 78.8 78.2 85.5 80.3
5.4 5.9 5.7 6.4 5.6 5.8 4.7 5.5 5.9 5.5 5.5 5.0
8.4 11.7 5.6
2.1 1.2 1.8 1.2
0.6 4.4 1.0
2.0 1.9 1.5 1.3 1.7 1.7 2.0
9.3 10.5 13.9 6.7 12.2
6.0 3.4 0.7 0.6 0.4
7.7 8.4 4.0 13.3 12.2 18.7 6.3 11.3 12.0
3.7 2.7 2.1 4.6 2.0 2.6 7.0 1.4 2.3
9.1 9.0
4.4 4.4
0.77 0.93 0.79 0.98 0.86 0.87 0.69 0.84 0.89 0.84 0.77 0.74
0.755 0.114 0.048
0.089 0.099 0.133 0.058 0.113
DAF = dry, ash-free.
Data Correlations for Bituminous Coals The correlations for the product yields from bituminous coals have been developed from the literature at the following four conditions: (1) correlations for the temperature effects on product yields and their compositions during coal pyrolysis in the absence of oxygen at atmospheric pressure; (2) correlations for the pressure effects on product yields and their compositions in the absence of oxygen; (3) correlations for the lime effects on product yields and their compositions in the absence of oxygen at atmospheric pressure; (4) correlations for the oxygen effects on product yields and their compositions at atmospheric pressure. Temperature Effects on Yields at Atmospheric Pressure. The sources of data and the coals used to develop the correlations for the coal carbonization product yields and their compositions in the absence of air are shown in Table I. Tar Yield. The tar yield, based on the studies of Graff et al. (19861, Freihaut and Seery (1981), Yeboah (19791, Tyler (1980), Suuberg et al. (1978), and Xu and Tomita (1987), obtained at various temperatures in the range of 1300-1600 O F was plotted against the coal property represented by H/C atomic ratio. For an H/C ratio greater than 0.75, the tar yield at a given temperature attains a constant value and hence becomes independent of the H/C ratio. Therefore, for all coals that have an H/C ratio in excess of 0.75, the tar yield appears to be a function of temperature only. For an H/C ratio of less than 0.75, the literature lacks sufficient data to draw any meaningful conclusions. Furthermore, a plot of the tar yield vs temperature showedthat the tar yield increases up to about 1250 OF, after which it decreases because of the increased activity of the secondary reactions of tar cracking (Rehmat and Goyal, 1987). In the temperature range of 1300-1600 O F , the taryield was found to be linear and can be expressed as
these elements present in the coal to the tar were correlated as follows:
X, -2.75 X 10"T + 64.75 X (1) where Xt, = fraction of feed carbon converted to tar,
where YH~o, YCO, and Ycoz= fraction of feed coal oxygen converted to H20, CO, and C02, lb-atom O/lb-atom 0 in feed coal, and O/C = atomic ratio of 0 to C in feed coal. The methane and ethylene yields are functions of temperature and available hydrogen, where available hydrogen is the excess over what is required for water formation (eq 8) and can be expressed as
lb-atom C/lb-atom C in feed, and T = temperature, OF. The composition of tar can be represented as CH,O,N,S,Cl, (2) The amount of hydrogen, oxygen, nitrogen, sulfur, and chlorine present in the tar depends upon their respective quantities present in the parent coal as well as upon the temperature. Depending upon the conversion of these elements into tar and knowing the amount of carbon conversion to tar, the atomic ratios x , y, z , w ,and u for the tar composition can be determined. The conversions of
XH = -1.34
X
10"T
+ 34.08 X 1200 O F IT I1600 O
Xo -1.25
X
10"T
Xo = 6.5 X XN = -0.84 X 10"T
+ 25.0 X 1400 O
F
(3)
T 5 1400 O F (4) F
< T I 1600 O F
(5)
+ 24.58 X 1200 O F IT I 1600 O F (6)
X s= -1.50
X
10"T
+ 30.50 X lo-'
1200 O F I T I 1600 O F (7) where X H = conversion of feed hydrogen to tar, lb-atom H/lb-atom H in feed; Xo = conversion of feed oxygen to tar, lb-atom O/lb-atom 0 in feed; X N = conversion of feed nitrogen to tar, lb-atom N/lb-atom N in feed; Xs = conversion of feed sulfur to tar, lb-atom S/lb-atom S in feed; and T = temperature, O F . The literature lacks data about chlorine in tar. For calculation purposes, the conversion of chlorine is assumed to be the same as that of nitrogen. Gas Yields.In the temperature range of 1400-1600 O F , the limiting yields of HzO, CO, and C02 were found to be independent of temperature but depend upon the oxygen present in the coal (Rehmat and Goyal, 1987). The total coal oxygen conversion to HzO, CO, and C02 for all coals equals approximately 80 % This oxygen conversion can be expressed as
.
YHlo= 0.375
(8)
Yco 0.283
(9)
Yco,= 0.167 - O.O017/(O/C)
(10)
HaV,i, = (H/C) - 2(H2O/C)
(11)
where H/C = atomic ratio of H to C in coal, lb-atom H/lbatom C in coal, and H20/C = water yield, lb-mol H20/ lb-atom C in coal. The correlations for methane and ethylene yields are as follows:
1398 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993
YCH, = 0.085Havd,+ 4.25 X 10"T
- 0.0957
Yca, = 0.212Havd + 1.35 X 104T - 0.33
(12)
(13)
where YCH, and YQH,= fraction of feed coal carbon converted to CH4 and C2H4, lb-atom C/lb-atom C in feed, and T = temperature, O F . Yields of other C2+are independent of temperature and Havail in the temperature range of 1400-1600 O F and the Havailrange of 0.7-0.85. These yields can be expressed as YC,H,
= 9.2 x 10-~
YC,%= 1.04 X
(14)
(15)
YC,H,
= 2.8 x 10-~
YC,H,
2.2 x 10-~
(17)
where Yi = fraction of feed coal carbon converted to species i, lb-atom C/lb-atom C in feed coal. Some data pertaining to the quantities of benzene, toluene, xylene (BTX),and phenols produced during coal pyrolysis have appeared recently (Xu and Tomita, 1987). In the temperature range of interest, 1300-1600 O F , these yields are linear and can be expressed as follows:
YCEH, = 9.0 x 1O4T - 0.01
(18)
YC,H, 2.5 X 104T Yc,H,, = 3.0 X YC,H,OH
lo3
= 3.7 x 10-~
(21)
where Yi = fraction of feed carbon converted to species i, lb-atom C/lb-atom C in feed coal, and T = temperature, OF. The yields of "3, H2S, and COS have been expressed in terms of nitrogen conversion to NH3 and sulfur conversion to HzS and COS. The correlations for "3, H2S, and COS yields are
Y", = 0.19 YH8
2.17 X 10"T- 6.0 X
(23)
ycOs= 5.0 x 10-~ (24) where Y N H=~fraction of feed coal nitrogen converted to "3, lb-atom N/lb-atom N in feed coal; Y H ~ sYcos , = fraction of feed coal sulfur converted to H2S and COS, lb-atom S/lb-atom S in feed coal; and T = temperature, OF.
The literature lacks data on ammonia yield. The above yield of ammonia is based on a single literature datum by CSIRO (1958). The hydrogen in the gas can be determined by hydrogen balance around the system. Similarly, the nitrogen in the gas can be computed by nitrogen balance among the feed coal, tar, "3, and char. Char Yield. Char composition, like tar, can be represented as CH,O,N,S,Cl, (25) The conversion of feed carbon to char, which constitutes a major species in the char, can be determined by carbon balance around the system. The data available in the literature on char yields have been correlated as a function of temperature (Rehmat and Goyal, 1987) to provide a check on the balance. This correlation is given by the
following equation: X,,
= -1.79 X 104T
+ 0.879
(26)
where X c h = fraction of feed coal carbon converted to char, lb-atom C/lb-atom C in feed coal, and T = temperature, O F . The conversion of coal hydrogen and nitrogen to char was correlated from the data of Yeboah (1979). The correlations for these species in terms of H/C and N/C ratios in the char are given by RHC = -3.0
X
104T + 0.97
(27)
RNC = -3.34 X 104T + 0.015 (28) where RHC = hydrogen to carbon ratio in char, lb-atom H/lb-atom C; RNC = nitrogen to carbon ratio in char, lb-atom N/lb-atom C; and T = temperature, O F . The amount of coal oxygen and sulfur present in the char can be determined by elemental balance. Pressure Effects on Yields. Despite the abundant literature on high-pressure hydropyrolysis, the number of sources on the effect of pressure on coal pyrolysis in inert atmosphere is limited. The effect of pressure on pyrolysis reactions generally is either an intrinsic effect on the reaction rate or an effect through its influence on the residence time of the volatile8 within the particles, and it is manifested by different amounts of tar and gas formed. Tar Yield. Suuberg et al. (1978) and Arendt and van Heek (1981) conducted experiments with bituminous coals at 1832 OF and reported a considerable reduction in the carbon conversion to tar with an increase in pressure from 1 to 100 atm. The data indicated that the tar yield decreases logarithmically with pressure (Rehmat and Goyal, 1987). A similar effect on the tar yield has been shown by Eklund and Wanzl(1981) with a subbituminous coal at 1472 O F . The correlation for the tar yield as a function of temperature in the temperature range of 13001600 O F at the atmospheric pressure given earlier can be combined with the effect of pressure to obtain the tar yield at any pressure. This can be expressed as Xk(P)/Xk(l) = -0.258 log(P) + 1 (29) where X & ' ) = fraction of feed carbon converted to tar at pressure of P atm, lb-atom C/lb-atom C in feed coal; XW(1) = fraction of feed carbon converted to tar at pressure of 1atm (eq 11, lb-atm C/lb-atom C in feed coal; and P = pressure, atm. The tar composition does not appear to change with pressure. Gas Yields. The effect of pressure on gas yields other than methane is either nonexistent or minimal in the literature. According to Steinberg et al. (1982), at a temperature of 1650 O F in an entrained-bed reactor with a nitrogen atmosphere, C02 did not vary with pressure in the range of 1-70 atm. Tran (1981) observed a similar lack of pressure effect on CO, CO2, and H2O yields in the temperature range of 1400-16OO O F and the pressure range of 2-70 atm. The experiments conducted by Suuberg et al. (1978),Arendt and van Heek (1981),and Eklund and Wanzl (1981) indicate a logarithmic increase in the methane yield due to an increase in pressure. Similar results for the effect of pressure on methane yield have been reported by Steinberg et al. (1982). The methane yield at atmospheric pressure as a function of temperature and available hydrogen, where available hydrogen is the excess over what is required for water formation, was correlated per eq 12. The increase in CH4 yield at higher pressure can be expressed as
Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 1399
+
= 0.148 lOg(P) 1 (30) where YcH,(P) = fraction of feed carbon converted to CH4 at P-atm pressure, lb-atom C/lb-atom C in feed coal; Ych(1) = fraction of feed carbon converted to CH4 at l-atm pressure (eq 121, lb-atom C/lb-atom C in feed coal; and P = pressure, atm. Yields of ethylene and other C2+hydrocarbons are either not affected or slightly affected by an increase in the pressure, as reported by Suuberg et al. (1978) and Arendt and van Heek (1981). The literature lacks data on the effects of pressure on "3, H2S, and COS. Thus, in the present model, it is assumed that an increase in the pressure does not alter the yields of these species. According to Arendt and van Heek (1981), hydrogen gas yield is not affected appreciably by pressure variation at a temperature of 1832 O F and pressure range of 1-100 atm. However, the literature lacks data on the effect of pressure on hydrogen gas yield at lower temperatures. The nitrogen in the gas is also assumed not to be affected by pressure. The literature lacks data in this area also. The quantity of nitrogen in the gas phase a t atmospheric pressure was previouslyobtained from the nitrogen balance among the feed coal, tar, "3, and char, and it can be similarly determined at elevated pressure. Char Yield. The char yield is expected to increase with pressure because of the tar that is retained in the char at elevated pressure. The char yield and its composition are computed by elemental balance. The conversion of hydrogen and nitrogen to the char are assumed to be independent of pressure. Lime Effects on Yields. Most of the work reported on the effect of adding limestone or dolomite on the products of pyrolysis (Yeboah, 1979; Yeboah et al., 1980; Longwell et al., 1985; Floess et al., 1985) was performed at atmospheric pressure, and consequently the limestone or dolomite was calcined to CaO because of the low partial pressure of C02 in the system. At higher pressures, it is conceivable that there is sufficiently high partial pressure of CO2 in the system to prevent calcination of limestone to CaO. Data on the effect of limestone under the latter condition are not available. Because the mechanism of the effect of limestone on coal pyrolysis is also not known, it is assumed here that both CaO and CaC03 produce a similar effect on the coal pyrolysis. Yeboah (1980) and Longwell et al. (1985) have reported an appreciable decrease in the tar yield when limestone or dolomite was added during the pyrolysis of coal. A simultaneous increase in the hydrocarbon gases was noticed with some soot formation on the surface of the limestone. The effect of CaO on the char yield and other gases was very little. These observations led to a conclusion that the addition of limestone or dolomite during coal pyrolysis causes some of the evolved tar to crack into hydrocarbon gases and soot. The fraction of tar that cracks upon the addition of limestone can be obtained by comparing the respective quantities of the tar produced with and without the addition of the limestone. As stated earlier, the tar yield in the absence of limestone is given by the following correlation: YCH,(P)/YcH,(l)
X, -2.75 X 10aT + 64.75 X (1) The tar yield in the presence of CaO was correlated as follows: X,(Ca) = -0.9 X 1O4T + 23.50 X (31) Using above equations, the fraction of the tar cracked
in the presence of limestone as a function of temperature can be obtained as follows: FTC=l--
X,(Ca)
(32)
x,
where X, = fraction of feed carbon converted to tar in the absence of limestone, lb-atom C/lb-atom C in feed; X,(Ca) = fraction of feed carbon converted to tar in the presence of limestone, lb-atom C/lb-atom C in feed; FTC = fraction of tar cracked upon limestone addition, dimensionless; and T = temperature, O F . It is also assumed that the tar cracks uniformly, and as a result the composition of the remaining tar does not change. Also, because the data of tar cracking with limestone are lacking at elevated pressure, it is assumed that the relationship for the tar cracking developed for l-atm pressure holds true a t all other pressures. Yeboah (1979) has reported an increase in CH4 and C2+ yields with temperature due to the limestone addition. This increased yield is due to the tar cracking as explained above. These data have been analyzed, and the fraction of cracked tar resulting in CH4 and C2+has been correlated as a function of temperature as follows (Rehmat and Goyal, 1987): YCH,
= 9.5 X 10aT - 1.18
Yc,+ = 20.15 X 10"T - 2.564
T I 1600 O
(33)
F
T I1600 O
F
(34)
where YCH,= fraction of cracked tar carbon yielding CH4, lb-atom C/lb-atom C in cracked tar; Yc2+= fraction of cracked tar carbon yielding C2+, lb-atom C/lb-atom C in cracked tar; and T = temperature, O F . For the model, C2+ is assumed to consist of 20% C2Hs and 80% C2H4. The balance of the cracked tar carbon forms soot. The quantity of oxygen present in the cracked tar, which does not appear in the soot, will react with H2 to produce H20. Similarly, sulfur will produce H2S. The balance of the hydrogen and the nitrogen will appear as H2 and N2. The data related to the soot composition are generally not found in the literature. The amount of soot formed from the cracked tar is obtained by carbon balance. Carbon forms the major component of the soot; all other elements are present in very small quantities. For the model, the soot composition has been assumed to be as follows: (35) Oxygen Effects on Yields. It has been shown by various investigators (Howard and Essenhigh, 1967;Boley and Fegley, 1977; Landers et al., 1965; Saito et al., 1987) that when oxygen is introduced into the carbonizer, both tar and char combustion occur. Tar also cracks to hydrocarbon gases. From the data of cod pyrolysis in the absence of oxygen and in the presence of oxygen, we have estimated the fraction of tar and char that combusts with oxygen. Similarly, by comparison of the respective data for CH4 and Ca+ yields, we have also determined the fraction of cracked tar resulting in these species. Similarly, the fractional conversion of combusting carbon to CO and C02 has also been determined. Table I1 shows the reduction in tar and char yields as a function of temperature in the presence of oxygen. It can be seen that the reduction is only slightly affected by temperature. Basically, the oxygen reacts with carbon in tar and carbon in char. The split between the tar and char carbon CH0.040900.~7N0.0027S0.0025
1400 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 Table 11. Reduction in Tar and Char Yields due to Oxygen Feed for Bituminous Coals reduction in tar yield, % 58 56 54
temp, O F 1400 1500 1600
reduction in char yield. % 5 3 3
Table 111. Split between Tar and Char Carbon Reacting with Oxygen Feed for Bituminous Coals temp, OF 1400 1500 1600
tar 83 85 83
char 17 15 17
Table IV. Product Distribution from Tar/Char Secondary Reactions in the Presence of Oxygen for Bituminous Coals temp, O F 1400 1450 1500 1550
co/c02 mole ratio 0.73 0.76 0.78 0.73
tar carbon yield to CHI, % 6.0 6.8 7.9 9.1
tar carbon yield to C2+, % 9.0 9.1 9.2 7.6
reacting with the oxygen is given in Table 111. The table shows that at atmospheric pressure approximately 83 5% of the carbon that reacts with oxygen comes from the tar. In contrast to this, the data of lignites that appear in the latter section indicate that only 40% of the tar carbon is attacked by oxygen. Therefore, the combustion of 83 % of tar carbon obtained from the limited data appears to be rather high. Thus, until more data in this area become available, for the model purposes, a conservative value of 70 % of the tar carbon combustion at atmospheric pressure is used here. The literature lacks such data about the pressure effect. As indicated earlier, at higher pressure, the tar yield decreases, which results in less tar available for reacting with oxygen. In the absence of literature information, it is assumed that the effect of pressure on the tar carbon reacting with oxygen is similar to that on the tar yield (eq 29). Thus
R , = (0.70)(-0.258 log(P) + 1) (36) where Rt, = (tar carbon reacted)/(tar carbon reacted + char carbon reacted), and P = pressure, atm. If all the tar is burned with oxygen and additional carbon combustion is needed to satisfy energy balance, then this additional carbon comes from the char. Table IV shows the product distribution obtained from the tar and char reaction with oxygen. In the temperature range of 1400-1500 O F , the ratio of CO to COZproduced from this reaction increases slightly, whereas the fraction of tar carbon cracking to CH4 increases significantly. The yields of CH4 and CZ+produced from the cracking of tar carbon due to the secondary reactions can be represented by (Rehmat and Goyal, 1987) FTM = 2.075 X 10"'T - 0.2313 (37) FTCB = 2.0 X 105T + 0.062 (38) where FTM = fraction of reacting tar carbon yielding methane, lb-atom C/lb-atom C in reacting tar; and FTCB = fraction of reacting tar carbon yielding CZ+species, lbatom C/lb-atom C in the reacting tar; and T = temperature, OF.
For the empirical model, CZ+is assumed to consist of 20% CzHs and 80% C Z H ~ . The relative amounts of CO and COZproduced as a result of the tar and char carbon combustion with oxygen
have been correlated as follows: RCOCO, = 4.9333 X 10"'T + 4.267 X lo-' (39) where RCOCOz = mole ratio of CO to COZproduced as a result of tar and char carbon combustion with oxygen, and T = temperature, OF. Data Correlations for Lignites The following correlations for lignite have been developed, as done above for bituminous coals, in order to estimate product yields from the carbonizer: (1)correlations for the temperature effect on the product yields and their compositions during lignite pyrolysis in the absence of air at atmospheric pressure; (2) correlations for the oxygen effects on the product yields and their compositions at atmospheric pressure. For the estimation of product yields at pressure and to incorporate the effects of lime addition, the correlations developed for the bituminous coals have been utilized because no such data are available for lignites. The correlations used in the model have been summarized here; the details of the development of these correlations have been given by Rehmat and Goyal(l987) in a DOE Final Report. Temperature Effects on Yields at Atmottpheric Pressure. The sources of lignites and their analyses used by various investigators for lignite pyrolysisa t atmospheric pressure in inert atmosphere are shown in Table V. These data have primarily been used to develop the following correlations. Tar Yield. On the basis of the studies of Suuberg et al. (1978),Torrest and Van Meum (19801, Floess et al. (1985), and Scott and Piskorz (1986), the tar yield was plotted as a function of temperature and H/C atomic ratio in lignite. The tar yield clearly seemed to be dependent upon the coal property expressed as H/C, as well as on the temperature. A larger quantity of tar is formed for a larger H/C ratio; the quantity of the tar is decreased as temperature is increased due to secondary cracking. The data for the tar yield have been correlated as follows in the temperature range of 1400-1600 OF and the H/C range of 0.71-0.96 (Rehmat and Goyal, 1987).
X, = -1.18 X 103(H/C)T + 2.24(H/C) + 8.545 X 104T - 1.541 (40) where Xt, = fraction of feed carbon converted to tar, lbatom C/lb-atom C in feed; H/C = atomic ratio of H to C in feed, lb-atom H/lb-atom C; and T = temperature, O F . The tar can be represented as CH,O,,N,S,Cl, (41) The amount of hydrogen, oxygen, nitrogen, sulfur, and chlorine present in the tar depends upon the coal composition, as well as upon the temperature of pyrolysis. Depending on the conversion of these elements into tar and knowing the amount of carbon conversion to tar,the atomic ratios x , y, z, w , and u for the tar composition in eq 41 can be determined. The temperature dependence of hydrogen, oxygen, and nitrogen conversion of the feed lignite to tar can be expressed by the followingcorrelations:
X,
= 5.32 X 10"T(H/C) - 7.60 X 10"'T - 0.348(H/C)
Xo = -2.34 X 104T + 0.392 X, = -8.0 X 1O5T + 0.216
+
0.892 (42) (43)
(44) where XH = conversion of feed hydrogen to tar, lb-atom H/lb-atom H in feed; Xo = conversion of feed oxygen to
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1401 Table V. Lignites Used by Various Investigators for Pyrolysis Study ultimate analysis (DAFbasisa), w t %
reference Torrest and Van Meurs (1980) Scott and Piskorz (1986) Scott and Piskon (1986) Suuberg et al. (1978) Floess et al. (1985) a
lignite source Texas lignite Estevan lignite Forestburg Montana lignite Texas lignite
c
H 5.63 4.24 4.51 4.56 5.49
70.02 71.21 71.42 71.18 69.75
0 21.52 22.23 21.89 21.84 22.22
ash,
moisture,
N
S
wt %
wt%
H/C
atomic ratio
O/C
1.33 1.63 1.56 1.08 1.26
1.47 0.69 0.62 1.32 1.26
11.3 6.3 6.7 9.9 12.7
7.9 10.0 6.8
0.96 0.71 0.75 0.76 0.94
0.231 0.234 0.230 0.230 0.239
DAF = dry, ash-free.
tar, lb-atom O/lb-atom 0 in feed; XN = conversion of feed nitrogen to tar,lb-atom N/lb-atom N in feed; and T = temperature, O F . The literature (Suuberg, 1978; Torrest and Van Meurs, 1980)lacks data for sulfur conversion to tar. The literature has, however, addressed conversion of sulfur to char. The conversion of the balance of sulfur from feed has been distributed between gas and tar; conversion of sulfur to gas is maintained the same as that for the bituminous coals. The conversion to the tar is then obtained by difference, which is correlated as follows:
X, = -6 X 1O"T + 0.229 1200 O F I T I 1600 O F (45) where XS= conversion of feed sulfur to tar,lb-atom S/lbatom S in feed, and T = temperature, O F . The literature lacks data about chlorine in tar. For modeling purposes, the conversion of chlorine is assumed to be same as that of nitrogen. Gas Yields. In the temperature range of 1400-1600 O F , the yields of H2O and COz are independent of temperature but dependent upon the oxygen present in the lignite. The yield of CO depends on both the temperature and the quantity of oxygen in the feed. Because oxygen will be the limiting factor for the production of these three species, the correlation for their yields have been tied to the feed oxygen. These yields can be represented as follows:
YH,o = 0.37 Yco = 6.75 X 10"T - 0.81 Yco = 0.28 Yco, = 0.30
T 1 1200 O
F
(46)
1300 O F I T I 1600 O F (47) T 1 1600 OF (48) T L 1400 O F (49)
where Y ~ f=ifraction of lignite oxygen converted to H20, lb-atom O/lb-atom 0 in feed; Yco = fraction of lignite oxygen converted to CO, lb-atom O/lb-atom 0 in feed; Ycop = fraction of lignite oxygen converted to C02, lbatom O/lb-atom 0 in feed; and T = temperature, O F . The methane and ethylene yields are functions of temperature and the available hydrogen, where available hydrogen is the excess over what is required for water formation (see eq 46) and can be expressed as follows: Havd = (H/C) - 2(H2O/C) (11) where H/C = atomic ratio of H to C in feed lignite, lbatom H/lb-atom C in lignite, and H20/C = water yield, lb-mol H2O/lb-atom C in feed lignite. The correlations for methane and ethylene yields in the temperature range of 1100-1600 O F are as follows:
YCH, = 1.42 X 1O4HaVdT- 5.34 X 10dT - 0.1544Hav,,
Yea, = 6.34 X 10"Hav~T- 1.34 X
+
6.70 X (50) 104T - 0.043Havd-
9.75 X lo4 (51) where YCH,= fraction of feed carbon converted to CH4,
lb-atom C/lb-atom C in feed; Y C ~ = Hfraction , of feed carbon converted to CZH4, lb-atom C/lb-atom C in feed; and T = temperature, O F . The yields of C2H6 and C3's are independent of Havail, but depend on the operating temperature. The yields of these species can be represented as follows:
YC,%= 0.35 X lo-' Yc, = 2.5 X 10"T - 0.025
1100 OF I T I 1600 O
F
1100 O F I T I 1600 O
(52) F
(53) where Y c , =~fraction of feed carbon converted to C2H6, lb-atom C/lb-atom C in feed; Yc, = fraction of feed carbon converted to Cis, lb-atom C/lb-atom C in feed; and T = temperature, OF. For modeling purposes, all C3's will be considered as C3H6, because it is the major component of C3's. The BTX yield can be expressed as follows:
YBTX= 2.5
104T + 3.65 X lo3
T I1200 O F (54) where YBTX= fraction of feed carbon converted to BTX, lb-atom C/lb-atom C in feed, and T = temperature, O F . For modeling purposes, the entire BTX yield will be assigned to benzene, because the breakdown for BTX is not found in the literature. The literature lacks data for phenols. However, phenols are expected to be formed during lignite pyrolysis. The amount of phenols will be assumed to be the same as those for the bituminous coals (see eq 21). The yields of "3, HzS, and COS are not available in the literature. As an approximation, the values obtained for bituminous coals will be employed (see eqs 22-24). The hydrogen in the gas can be computed from an elemental hydrogen balance. Furthermore, the nitrogen in the gas can be computed by nitrogen balance among the feed coal, tar, "3, and char. Char Yield. The composition of char, like tar, can be represented as follows: X
CH,O,N,S,Cl, (55) Again, the conversionsof feed carbon, hydrogen, oxygen, nitrogen, sulfur, and chlorine to char determine the values of a, b, c, d, and e. In the model, the carbon conversion to char is determined by a balance between feed carbon, carbon in the tar yield, and the carbon in the gas yield. However, data exist in the literature to determine this quantity; the carbon conversion to char is generally a function of temperature, which can be represented as follows:
X,, = -1.1 X 104T + 0.852 (56) where X C h m = fraction of feed carbon converted to char, lb-atom C/lb-atom C in feed, and T = temperature, OF. The conversion of lignite hydrogen and nitrogen to char was correlated from the data of Torrest and Van Meurs (1980) and Suuberg et al. (1978). The correlations for these conversions can be expressed in terms of
1402 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 Table VI. Reduction in Tar and Char Yields due to Oxygen Feed for Lignites ______~ reduction reduction temp, O F in tar yield, % in char yield, % 15.4 1400 70.2 17.7 1450 77.8 20.1 1500 85.8 22.5 1550 94.2
temp, O F 1400 1450 1500 1550
char 0.59 0.61 0.62 0.63
tar 0.41 0.39 0.38 0.37
Table VIII. Product Distribution from Tar/Char Secondary Reactions in the Presence of Oxygen for Lignites
temperature as follows:
X, = -6.27
Table VII. Split between Tar and Char Carbon Reacting with Oxygen Feed for Lignites
X
10"'T
+ 1.127
(57)
XN = -3.95 X 104T + 1.238 (58) where X H = fraction of feed hydrogen converted to char, lb-atom H/lb-atom H in feed; XN = fraction of feed nitrogen converted to char, lb-atom N/lb-atom N in feed; and T = temperature, O F . The amount of oxygen and sulfur present in the char is determined by elemental balance. Pressure Effects on Yields. Because very little data about the effect of pressure on yields from lignite are available, it is assumed that the correlations developed for the bituminous coals for pressure effect also hold true for the lignites. Lime Effects on Yields. Lime effects on yields from lignites are assumed to be the same as those for the yields from the bituminous coals. For modeling purposes, the soot composition has been assumed to be as follows: (59) Oxygen Effects on Yields. I t has been shown by Boley and Fegley (1977) that when oxygen is introduced into the carbonizer, both tar and char combustion occur. Tar also cracks to hydrocarbon gases. From the data of lignite pyrolysis in the absence of oxygen and in the presence of oxygen, we have estimated the fraction of tar and char that combusts with oxygen. Similarly, by comparison of the respective data for CH4 and CZ+yields, we have also determined the fraction of cracked tar resulting in these species. In the same way, the fractional conversion of combusting carbon to CO and C02 has also been determined. It should be noted that the experimental data are available only up to 1200OF and the following information is based on the extrapolation of these limited data. The data for the additional CHI produced from the fraction of tar carbon that reacts with oxygen has been correlated as a function of temperature as follows: ~~o.oz,~o.,,,~o.,,,~,.~~z
FTM = -6.9 X 10"T + 0.1432 (60) where FTM = fraction of reacting tar carbon yielding methane, lb-atom C/lb-atom C in reacting tar, and T = temperature, O F . The ratio of CO to C02 produced as a result of the tar and char combustion with oxygen has been correlated as follows: RCOCO, = -4.7 X 10"T + 1.107 (61) where RCOCO2 = ratio of CO to C02 produced as a result of tar and char carbon combustion with oxygen, and T = temperature, O F . Table VI shows the computed reduction in the tar and char yields as a function of temperature in the presence of oxygen. The table shows that as the temperature is increased, more char reacts with oxygen. Basically, the oxygen reacts with carbon in tar and carbon in char. The split between the tar and char carbon
co/co2 temD. O F 1400 1450 1500 1550
mole ratio 0.449 0.426 0.402 0.379
tar carbon vield to CfL.% 4.6 4.3 4.0 3.6
reacting with the oxygen is given in Table VII. This table shows that at atmospheric pressure approximately 40 % of the carbon that reacts with oxygen comes from tar. The literature lacks data about the pressure effect. As indicated earlier, a t higher pressure, the tar yield decreases, which results in less tar available for reacting with oxygen. In the absence of literature information, it is assumed the effect of pressure on the tar carbon reacting with oxygen is similar to that on the tar yield (see eq 29). Thus
R, = (0.40)(-0.258 log(P) + 1)
(62)
where Rt, = (tar carbon reacted)/(tar carbon reacted + char carbon reacted), and P = pressure, atm. If all the tar is burnt with oxygen and additional carbon combustion is needed to satisfy energy balance, then this additional carbon comes from the char. Table VI11gives the product distribution obtained from the tar and char reaction with oxygen as calculated from eqs 60 and 61. The table shows that the ratio of CO to COZproduced from this reaction and the fraction of tar carbon cracking to CHI decrease slightly with temperature. Carbonizer Model Description The primary function of the model developed is to make an estimate for a given coal of the product yields from a coal carbonizer operating at a specified temperature and pressure. In addition, sorbent (limestone or dolomite) may be added to capture in-situ sulfur released into the gas. In addition to reacting with sulfur, the sorbent also influences the product yields from the coal carbonization and hence, like temperature and pressure, forms a distinctly independent parameter of the system. The coal carbonizer, depending upon the coal properties, can take many forms from a bubbling fluidized bed to an entrainedflow reactor, each having its own peculiarities associated with the coal and air introduction and product recovery. These constrainb were recognized,and as a result, a highly generalized model has been developed to accommodate different features that may be found in a coal carbonizer. Later, the model was tailored specifically to consider three practical configurations of the carbonizer. For modeling purposes, and to accommodate various carbonizer configurations, the reactor has been divided into two sections, namely, the upper zone and the lower zone. The various streams leaving and entering these zones are shown in Figure 2. The coal (stream S1) and sorbent (stream S2) are fed into the upper zone along with the transport gas (stream G4). The transport gas could be an inert gas, recycled gas, and/or air. Two additional gas streams (secondary gas streams G2 and G3)can also enter
Ind. Eng. Chem. Res., Vol. 32,No.7, 1993 1403 SOOT
-4
Figure 2. Schematic drawing for general model for carbonizer. 'Includes tars.
this zone, if needed. The product gas stream from the lower zone (stream G9) also enters this upper zone. Basically, the coal devolatilization takes place in the upper zone. If the air is fed to this zone (stream G1 or G4),then the oxygen present in the air will also react in this zone. The combustion in the upper zone and the sensible heat of the solids/gas from the lower zone provide the heat required for the coal devolatilization. The sulfur in the gas is captured by the sorbent present in this zone. The solids elutriated from this zone (stream 58) are captured by a cyclone and returned to the solids splitter (stream S7). The gas leaving this zone (stream G8)is the gas yield from the carbonizer. The carbonizer product gas also contains some chadsorbent fines (stream S4)and evolved tars (stream Tl). The coal devolatilization temperature could be specified differently from the exit product gas temperature. Furthermore, tar cracking occurs when the sorbent is added to the system, producing soot and hydrocarbon gases. The soot formed in the carbonizer leaves the upper zone (stream S13)and enters the cyclone. The soot produced in the carbonizer may deposit on the char and sorbent particles and thus leave the gasification system along with various solids discharge streams (such as streams 54,S5,S6, and S12). However, for modeling purposes, this stream is assumed to be withdrawn from the cyclone (stream S14)along with the cyclone fines. The composition and flow rate of streams ,913 and S14 are identical; however, they may differ in temperature. The combustion air (stream G5)enters the lower zone along with the recycled char and reacted sorbent (stream S9) from the upper zone. The primary reaction in the lower zone is the char combustion reaction. If the temperature of this zone is high enough, then some slow rate gasification reactions will also take place. However, at present no such gasification reactions have been considered in the model. The solids stream containing char and spent sorbent (stream S5)can leave the carbonizer system from this zone. Alternatively, a part of the solids stream captured by the cyclone, which contains char and spent sorbent (stream S7), may be removed from the system (stream S6). The sorbent (stream S3)can also be fed into this lower zone along with the transport gas (stream G7).For modeling purposes, it is assumed that the sorbent fed to the lower zone is calcined, if thermodynamically permitted, in this zone and transferred into the upper zone (stream Sll). An additional gas stream (secondary gas stream G6) may also enter this zone, if needed. The
gas produced in this lower zone enters the upper zone (stream G9). The sorbent can be fed into the upper or lower zone or into both zones simultaneously. This will depend upon i h sulfur capture capability and the system energy balance requirements for each zone. Furthermore, the temperature in each zone is assumed to be uniform, but not necessarily the same as the gas leaving the zone. As shown in Figure 2,there are 14 solids streams, 10 of which are unknown (each solids stream can contain up to 15 species); 9 gas streams, 4 of which are unknown (each gas stream can contain up to 22 species); and 1 tar stream which is unknown (this stream is actually part of the product gas; however, for modeling purposes, it has been represented separately). The above two-zone model is an appropriate description of a fluidized-bed reactor or a fast fluidized-bed reactor in which the coal is fed into the reactor above the bed, that is, in the freeboard region. The model would also accommodate a carbonizer in which coal, sorbent, and air are fed in a single zone. Computational Methodology
The computer model has been kept as general as possible to accommodate various possible carbonizer conflgurations. The three most practical configurations for the carbonizer are discussed below. Case 1. The various streams entering and leaving the system for case 1 are shown in Figure 3. In this case, coal and sorbent (limestone or dolomite) are fed into the fluidized bed, and the fines captured by the cyclone are not recycled to the reactor; instead they are directed to the combustor. The bed is fluidized primarily using air. A model representation for this case is also given in the figure. Basically, this is represented by a single-stage (upper zone) configuration. The solids stretun 57 is equal to the solids stream S6, while the solids streams S3,S5, S9, S10,and ,911are zero. Furthermore, the gas stream G9 is also equal to zero. All the model predictions given later in this paper are based on this case 1 carbonizer configuration. Case 2. Case 2 (Figure 4)is similar to case 1 except the fines captured by the cyclone are recycled to the ctirbonizer bed, and a part of the fines recycle stream can also leave the system. A model representation for this case is also provided in the figure. For this case, the solids stream S10 is equal to stream S9,while the solids streams S3,S5, and S11 are zero. Furthermore, the gas stream G9 is also equal to zero. Case 3. The various streams entering and leaving the system for case 3 are shown in Figure 5. In this case, coal and sorbent (limestone or dolomite) are fed into the freeboard region of the carbonizer. The fines captured by the cyclone are recycled to the reactor, arid a part of the fines recycle stream can also leave the system. A model representation for this case is also given in the figure. For this case, the freeboard region is represented by the upper zone, while the fluidized-bed region is represented by the lower zone. The solids stream S12is zero because no solids are withdrawn from the upper zone (freeboard region). If no sorbent is fed into the fluidized bed, then the streams 53 and S11 are also zero. Yields Determination. Figure 6 illustrates the methodology employed for the determination of the product yields from the carbonizer. Basically, complete information is available for the coal pyrolysis as a function of temperature at l-atm pressure in an inert atmosphere. The individual effects of pressure, sorbent (limestone or
1404 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 OAS/TAR
7 + FINES
COAL+-
SORBENT
CASE 1
-
FINES TO COMBUSTOR
FLU1D IZED
BED
@COAL-
@
-
SORBEM@AIR
UPPER ZONE
QAS/TAR + FINES
CASE 2 0
COAL, SORBENT AND
AIR ARE
FED INTO THE FLUIDIZED BED
0 FINES ARE RECYCLED TO THE
FLUIDIZED BED
0 FRACTION OF ELUTRIATED FINES
ARE WITHDRAWN FROM TM: SYSTEM (Optional)
CHAR+
SPENT SORBENT TO COMBUSTOR
SPENT SORBENT CHAR+ SPENT SORBMT
Figure 4. Carbonizer configuration for case 2. *Optional.
dolomite), and oxygen on these product yields are also available. However,the literature lacks informationabout the combined effects of these factors on the product yields. The model has been constructed by superimposingeffects of these factors (Figure 6) to yield information about the products of coal pyrolysis as a function of temperature, pressure, sorbent, and oxygen. The product yields are determined in four steps, as illustrated in Figure 6. In the first step, a complete product slate is determined for coal carbonization a t 1-atmpressure in an inert atmosphere and at specified carbonizer
temperature. In the second step, the yields are adjusted for pressure. In the third step, using the information derived for the effect of oxygen on pyrolysis yield at 1-atm pressure, and assuming the same effect to hold a t pressure, the yields obtained in the second step are adjusted for the effect of oxygen feed. Finally, in the fourth step, the effect of sorbent is integrated into the third step above. When doing so, it is again assumed that the relationships derived at 1-atm pressure between products of pyrolysis with and without the addition of sorbent in the inert atmosphere are also valid at elevated pressure in the presence of oxygen.
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1405 GAS/TAR + FINES
COAL
+
SORBEM
CASE 3 0 COAL AND SORBEM ARE FED I N T I E FREEBOARD
-
0 AIR I S FED INTO T N FLUIDIZED
FLUI DIZED B€D
0 0
FINES TO C(X.BUSTOR*
I
CHAR +
SPENT SORBENT
@COAL
TO CGt-8USTOR
@
BED TO REACT WITH CHAR FINES ARE RECYCLED TO THE FLUIDIZED BED FRACTION OF FINES I S WITWRAWN FROM THE SYSTEM (Optlonai)
SOOT
UPPER
ZONE
SORBENT-
SPENT SORBENT
Figure 5. Carbonizer configuration for case 3. *Optional.
log(Pc0,) = -8799.7/TK
WITmWT AIR, WITH SORBENT
I@ -b =----b
EXTRAPOLATION (For Modrl)
Figure 6. Methodology for carbonizer product yield determination.
The yields and compositions obtained in the fourth step are thus considered to have accounted for all the process parameters-namely, temperature, pressure, sorbent, and oxygen. Depending on the partial pressure of C02 in the carbonizer, the CaC03 in the sorbent will either exist as CaC03 or get calcined to CaO. This will also determine whether the H2S will react with CaC03 or CaO. The extent of the sulfur capture by sorbent will be determined by its approach to the appropriate reaction equilibrium. The following reactions show the calcination of CaC03, the reaction of H2S with CaO, and the reaction of H2S with CaC03, respectively. CaO + CO,
CaO + H,S =,Cas + H 2 0 CaCO,
+ H,S ==, Cas + H,O + CO,
(64)
log[(H,O)(CO2)(P)/(H2S)] = 7.253 - 5280.5/TK (65) where P = total system pressure, atm; (HzO) = mole
AVAILABLE LITERATURE INFOFWATION
-
(63)
where Pco2= equilibrium decomposition partial pressure of C02 in gas, atm, and TK = temperature, K. The equilibrium for the above reactions B and C are given by the following equations (Squires et al., 1971): log[(H,O)/(H,S)] = 3519.2/TK - 0.268
i
CaCO,
+ 7.521
(A)
(B) (C)
Determining equilibrium decomposition pressures of calcite (reaction A) has proved to be a durable problem, and dubious values have appeared in the literature. The following correlation (Squires, 1967) has been used here:
fraction of H2O in gas; (C02) = mole fraction of CO2 in gas; (HzS)= mole fraction of H2S ingas;andTK =temperature, K. The product gas is also considered to be a t water-gas shift equilibrium at the carbonizer exit temperature. The shift reaction is given by CO
+ H,O =,CO, + H,
(D) The equilibrium relationship for this reaction is given by the following equation:
~O~[[(CO~)(H~)~/[(CO)(H~~)]I = 18ll/TK - 1.6780 (66) where (CO) = mole fraction of CO in gas, (C02) = mole fraction of C02 in gas, (H2) = mole fraction of H2 in gas, (HzO) = mole fraction of H2O in gas; and TK = temperature, K. The feed oxygen can also react with the Cas present in the system as follows: Cas + 2 0 ,
-
CaSO,
(E)
Model Predictions The computer model has been kept as general as possible to accommodate various possible carbonizer configurations. However, for the current study, the carbonizer configuration shown in Figure 3 (case 1) is considered. The carbonizer performance has been predicted at two pressure levels (14and 10atm) for two different feedstocks,
1406 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 Table IX. Summary of Carbonizer Material Balances for Pittsburgh No. 8 Coal at 14-atm Pressure (Basis: 1000 lb of Moisture-FreeCoal Feed) 1600 OF 30% slurry base case 6% moisture case description 1600 1500 1500 1500 carbonizer temperature, OF lo00 lo00 lo00 1000 coal feed (moisture-free), lb 2.5 6.0 2.5 30.73" moisture in coal feed, % 1443.6 1063.8 1025.6 1025.6 coal feed (as-fed),lb 307.9 307.9 307.9 307.9 sorbent (dolomite) feed, lb 1069.5 1102.0 1002.4 1765.8 air feed, lb 605.1 598.5 558.4 char in solids discharged from carbonizer, lb 609.6 226.4 225.0 226.1 228.9 spent sorbent in solids discharged from carbonizer, lb 10.7 2.8 10.0 0.0 soot leaving carbonizer system, lb 1460.7 1572.8 1592.7 2719.6 product gas (tar-free) leaving carbonizer, lb 28.7 7.6 26.9 19.3 tars leaving carbonizer, lb 2917 2896 1685 2709 product gas (tar-free) HHV, Btu/lb 15485 15485 15462 15485 tars HHV, Btu/lb 13244 13244 13244 13244 feedstock HHV, Btu/lb (MF) 35.3 35.3 total (product gas + tars) HHV/feedstock HHV, % 35.5 37.3 34.0 33.9 33.6 total (product gas + tars) LHV/feedstock LHV, % 35.9 224.2 212.8 146.7 227.5 product gas (tar-free) HHV, Btu/SCF 32.25 33.14 feedstock carbon conversion to gas, % 42.31 35.93 35.84 43.26 36.49 38.33 feedstock carbon conversion to gas + tars, % 39.24 48.21 40.03 42.74 MAF coal conversion to gas, % 42.45 49.06 43.03 44.89 MAF coal conversion to gas + tars, % 1.75 1.75 1.75 1.75 Ca/S feed mole ratio 92.0 92.0 92.0 92.0 approach to H&sorbent reaction equilibrium, % 39.73 29.51 38.85 sulfur captured by sorbent, % of coal sulfur 43.82 5.40 6.79 sulfur appearing in product gas + tars, % of coal sulfur 3.42 21.34 88.0 85.1 92.8 sulfur captured by sorbent, % of sulfur released 58.0 0
Includes slurry water.
Table X. Summary of Carbonizer Material Balances for Pittsburgh No. 8 Coal at 10-atm Pressure (Basis: 1000 lb of Moisture-Free Coal Feed) case description carbonizer temperature, OF coal feed (moisture-free), lb moisture in coal feed, 7% coal feed (as-fed), lb sorbent (dolomite) feed, lb air feed, lb char in solids discharged from carbonizer, lb spent sorbent in solids discharged from carbonizer, lb soot leaving carbonizer system, lb product gas (tar-free) leaving carbonizer, lb tars leaving carbonizer, lb product gas (tar-free) HHV, Btu/lb tars HHV, Btu/lb feedstock HHV, Btu/lb (MF) total (product gas + tars) HHV/feedstock HHV, % total (product gas tars) LHV/feedstock LHV, % product gas (tar-free) HHV, Btu/SCF feedstock carbon conversion to gas, % feedstock carbon conversion to gas + tars, % MAF coal conversion to gas, % MAF coal conversion to gas + tars, % Ca/S feed mole ratio approach to H&sorbent reaction equilibrium, % sulfur captured by sorbent, % of coal sulfur sulfur appearing in product gas + tars, % of coal sulfur sulfur captured by sorbent, % of sulfur released
+
0
2.5% moisture 1500 1000 2.5 1025.6 307.9 1000.8 606.4 225.9 11.3 1460.7 30.1 2907 15485 13244 35.6 34.3 225.4 32.42 36.18 39.38 42.76 1.75 92.0 40.70 4.42 90.2
6% moisture 1500 lo00 6.0 1063.8 307.9 1068.2 602.1 226.0 10.5 1573.2 28.2 2718 15485 13244 35.6 34.2 213.8 33.30 36.81 40.17 43.32 1.75 92.0 40.22 5.39 88.2
1600 OF 1600 lo00 2.5 1025.6 307.9 1100.3 596.5 224.9 0.0 1592.2 20.2 2927 15462 13244 37.6 36.2 228.6 36.08 38.59 42.86 45.12 1.75 92.0 44.31 2.84 94.0
30% slurry 1500
lo00 30.730 1443.6 307.9 1767.9 557.4 227.4 2.9 2724.2 7.7 1682 15485 13244 35.5 33.6 146.6 42.44 43.40 48.32 49.17 1.75 92.0 35.07 15.58 69.2
Includes slurry water.
namely, Pittsburgh No. 8 bituminous coal containing 3.07% sulfur and Texas lignite containing 1.47% sulfur. The char, soot, spent dolomite, tar, air feed, and product gas flow rates and their compositions are determined by the computer model. The air feed requirement is based on the energy balance around the carbonizer. The heat losses from the carbonizer are assumed to be negligible. The relative humidity of the air is 50% at 70 O F , which is equivalent to 1.235mol % moisture in the air. The H2S in the product gas is based on 92% approach to the equilibrium concentration, that is, the ratio of calculated equilibrium H2S content in the product gas (using eq 64 or 65) to the actual H2S content in the product gas is 0.92.
The dolomite feed rate to the carbonizer is based on feed Ca/S mole ratio of 1.75 and 1.0 for Pittsburgh coal and Texas lignite, respectively. It is also assumed that Cas04 formation does not take place in the carbonizer. The product gas is in water-gas shift at the carbonizer exit gas temperature. The fines leaving the carbonizer have been included in the discharged solids stream. The computer model allows the formation of acetylene (CZH~), naphthalene (CloHs),and hydrogen cyanide (HCN). However, due to the lack of literature information on this subject, amounts of these species have been assumed to be zero in all the balances. Carbonizer Performance with Pittsburgh No. 8
Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 1407 Fuel Gas Plow (lb/h) "V (Btu/lb) L W (Btu/lb) LHV (Btu/SCF)
1489.42 3139 2917 207.2 (Gas Only)
4 Tar
Hydrogen Sulfur Nitrogen Oxygen Mol s t ure Ash Total "V (Btu/lb)
462.89
10.58
63.73
7.67
0.04
129.73
16.77 8.34
0.07
27.45
0.03
5.23
8.25
0.01
--
GAS'
/ F l o w Rate = 28.71 lb/hl
--Carbon
I
I
Char-Sorbent (Flow = 846.9 lb/h) Spent Char Soot Dolomite
lFlou Rate = 1460.71 lb/h, 54.54 mol/h)
HW = 13.0449 ~~
Atomic Composition:
MgO
CHO. 46 2'0.
CaC03 Cas" Inerts
1 ENO. 0076s0.005 3
W V (Btu/lb)
15485
L W (Btu/lb)
15147
ut 8
co
11.26
10.77
co2
20.47
12.46
820
5.80
8.63
82
0.54
7.20
--
--
3.60
6.00
105.70
--
0.957
0.852
609.62
10.73
2.975
2.840
0.204
0.321
cos
0.020
0.003
C3,S
0.787
0.435
C4'S
0.134
0.062
0.192
0.066
---\ 11830
226.14
14568
CARBONIZER 14 a t m 15OOOF
C7% C6R50H 7OoF
0.374
0.109
0.244
0.069
HRV (Btu/lb)
711OF Pittsburgh Coal / F l o w Rate = 1025.64 lb/hl 737.90
Hydrogen
48.10
Nitrogen
17.90
Oxygen Uoist ur et Ash
Air
\
25.64 105.70
(Btu/lb)
wt 8
lb/h
CACOJ
54.5
167.81
M9CO3
43.3
133.32
02
231.65 lb/h
Moisture
0.5
1.54
N2
762.95
Inerts
1.7
5.23
100.0
307.90
Mo i I t u re gAv
2677
Plum Run Dolomite (Flow Rate = 307.9 lb/h; Ca/S = 1.75)
(Relative Humidity: 509 at 7 0 D F )
64.70
7.77
12913
a
2896
L W (Btu/lb)
Carbon
mol
Total
1002.37
L W (Btu/lb)
12469
Figure 7. Carbonizer balance for Pittaburgh coal at 14 atm, 1600 O F , and 2.5% moisture (base case). *Excludes tar. **92% approach to H&sorbent reaction equilibrium. +Afterdrying.
Bituminous Coal. The carbonizer performance was predicted at 14-atm pressure for several cases. Besides the base case at 14-atm pressure and 1500 O F temperature for the coal containing 2.5% moisture, the other cases accounted for the effect of using as-received coal without drying (6% moisture), operating the carbonizer at the increased temperature of 1600 O F , and using a nominal 30 % coal/water slurry instead of dried feed. The dolomite feed rate to the carbonizer was based on a feed Ca/S mole ratio of 1.75. The operating conditions and the results of the model predictions are summarized in Table IX. This table is based on lo00 lb of moisture-free coal feed to the carbonizer. The results on the moisture-free coal feed basis provide a better comparison of yields at different operating conditions. A detailed material balance for the base case at 14-atm pressure and 1500 O F temperature is given in Figure 7.
To determine the effect of pressure on the carbonizer performance, four balances were prepared under conditions identical to those of 14-atm-pressure cases given above, except the pressure was reduced to 10 atm. The operating conditions and the results of the model predictions are summarized in Table X. Carbonizer Performance with Texas Lignite. The carbonizer performance was predicted a t 14-atm pressure for three cases. Besides the base case at 14-atm pressure and 1500 O F temperature for the lignite containing 15% moisture, the other cases accounted for the effect of using higher moisture (25.8%)feed and operating the carbonizer at the reduced temperature of 1400 O F . The dolomite feed rate to the carbonizer is based on the feed Ca/S mole ratio of 1.0. The operating conditions and the results of the model predictions are summarized in Table XI. This table is based on lo00 lb of moisture-free lignite feed to
1408 Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 Table XI. Summary of Carbonizer Material Balances for Texas Lignite at 14-atm Pressure (Basis: lo00 lb of Moisture-Free Lignite Feed) base case 26% moisture 1400 OF case description 1500 1500 1400 carbonizer temperature, O F 1000 lo00 lo00 lignite feed (moisture-free), lb 15.0 25.8 15.0 moisture in lignite feed, % 1176.5 1347.7 1176.5 lignite feed (as-fed), lb 84.2 84.2 84.2 sorbent (dolomite) feed, lb 1108.1 1408.4 975.2 air feed, lb 608.4 581.9 641.3 char in solids discharged from carbonizer, lb spent sorbent in solids discharged from carbonizer, lb 61.4 62.9 64.5 1.0 0.0 3.7 soot leaving carbonizer system, lb product gas (tar-free) leaving carbonizer, lb 1694.9 2195.6 1520.6 3.1 0.0 5.7 tars leaving carbonizer, lb 1511 1210 1466 product gas (tar-free) HHV, Btu/lb 14223 0 13954 tars HHV, Btu/lb 9531 9531 9531 feedstock HHV, Btu/lb (MF) total (product gas tars) HHV/feedstock HHV, % 27.3 27.9 24.2 total (product gas + tars) LHV/feedstock LHV, % 25.9 26.3 22.9 128.9 109.0 126.9 product gas (tar-free) HHV, Btu/SCF feedstock carbon conversion to gas, % 34.62 39.54 30.15 35.06 39.54 30.91 feedstock carbon conversion to gas + tars, % 49.03 52.90 44.20 MAF coal conversion to gas, % 49.42 52.90 44.92 MAF coal conversion to gas + tars, % 1.00 1.00 1.00 Ca/S feed mole ratio approach to HzWsorbent reaction equilibrium, % 92.0 92.0 92.0 26.18 14.87 1.73 sulfur captured by sorbent, % of coal sulfur sulfur appearing in product gas + tars, % of coal sulfur 26.41 40.90 47.99 sulfur captured by sorbent, % of sulfur released 49.8 26.7 3.5
+
Table XII. Summary of Carbonizer Material Balances for Texas Lignite at 10-atm Pressure (Basis: 1000 lb of Moisture-Free Lignite Feed) 15% moisture case description 26% moisture 1400 OF carbonizer temperature, OF 1500 1500 1400 lignite feed (moisture-free), lb lo00 lo00 lo00 moisture in lignite feed, % 15.0 25.8 15.0 1176.5 1347.7 1176.5 lignite feed (as-fed), lb 84.2 84.2 sorbent (dolomite) feed, lb 84.2 1110.6 1411.9 978.7 air feed, lb 608.0 581.5 char in solids discharned from carbonizer. lb 640.3 60.5 61.4 spent sorbent in soli& discharged from cbbonizer, lb 62.9 1.0 soot leaving carbonizer system, lb 0.0 3.8 1698.6 2201.0 1526.4 product gas (tar-free) leaving carbonizer, lb 3.2 tars leaving carbonizer, lb 0.0 6.0 1502 1201 1449 product gas (tar-free) HHV, Btu/lb 14223 13954 tars HHV, Btu/lb 0 9531 9531 9531 feedstock HHV, Btu/lb (MF) 27.3 27.7 24.1 total (product gas + tars) HHV/feedstock HHV, % 25.9 26.1 22.8 total (product gas + tars) LHV/feedstock LHV, % 128.2 125.7 product gas (tar-free) HHV, Btu/SCF 108.2 34.65 feedstock carbon conversion to gas, % 39.57 30.21 35.10 39.57 feedstock carbon conversion to gas + tars, % 31.00 44.27 49.07 52.95 MAF coal conversion to gas, % 49.47 52.95 MAF coal conversion to gas + tars, % 45.03 1.00 1.00 1.00 Ca/S feed mole ratio 92.0 92.0 92.0 approach to HzS/sorbent reaction equilibrium, % 14.87 26.48 33.54 sulfur captured by sorbent, % of coal sulfur 19.33 sulfur appearing in product gas tars, % of coal sulfur 29.55 35.19 47.3 63.4 sulfur captured by sorbent, % of sulfur released 29.7
+
the carbonizer. The results on the moisture-free feed basis provide a better comparison of yields at different operating conditions. A detailed material balance for the base case at 14-atm pressure and 1500 O F temperature is given in Figure 8. To determine the effect of pressure on the carbonizer performance, three balances were prepared under conditions identical to those of the 14-atm-pressure cases given above, except the pressure was reduced to 10 atm. The operating conditions and the results of the model predictions are summarized in Table XII. The sulfur captured by the sorbent relative to the sulfur released from the feedstock is quite less for Texas lignite cases compared to the Pittsburgh coal cases. The reasons are as follows: 1. The Pittsburgh coal contained 3.07% sulfur, while
the Texas lignite contained 1.47 % sulfur. The lower sulfur content of the lignite results in a reduced amount of total sulfur released into the gas and tars. 2. The higher moisture content in the lignite feed relative to the Pittsburgh coal (15% vs 2.5%)results in higher moisture content in the product gas. This allows higher HzS content in the product gas leaving the carbonizer at equilibrium (see eqs 64 and 65). Other observations based on these balances are summarized under conclusions. Conclusions An extensive analysis of literature data has been conducted, and correlations have been developed for yields of various species as a function of coal properties and
Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 1409 F u e l Gas F l a w ( l b / h ) RRV (Btu/lb) LHV ( B t u / l b ) LHV (Btu/SCF)
1697.96 1534 1403 117.7
( C a s Only)
I I
-
Char-Sorbent ( F l w Rate 670.85 l b / h ) Spent Char Soot Dolomite
Hw =
--
14.798
372.29
0.998
17.43
HgO
Hydrogen
5.00
0.002
33.88
CaC03
q. 702'0
Sulfur
6.97
0.003
8.66
Cast
HHV ( B t u / l b )
2.17
0.002
1.43
Inerts
LKV ( B t u / l b )
12.31
0.002
Nitrogen Oxygen
-
Ho is t u r e Ash
Total
209.70 --
-
608.44
61.40
1.007
HHV ( B t u / l b )
9298
14532
LHV ( B t u l l b )
9221
14513
-
Gas* (Flov R a t e 1694.89 l b / h , 66.56 mol/h) wt X m o l f:
(Flow Rate = 3.07 l b l h )
- -
Carbon
I
Tar
co
Atomic Composition:
7.04
6.40
"2
23.64
13.68
14223
"
14.96
21.15
13758
H2
0.76
9.56
.090N0. 0 1 1'0.0 14
20
t CARBONIZER
1.33
2.11
0.171
0.145
5%
0.854
0.775
"3
0.100
0.149
0.233
0.174
N2
49.98
45.43
cos
0.008
0.003
1 4 atm
C3'S
0.495
0.300
lSOO'F
C4'S
0.000
0.000
C6H6
0.272 0.000
0.089 0.000
L
C7"8 CgH50H
7 O*F
\
0.164
HHV ( B t d l b ) LKV ( B t u l l b )
71 l o p
-
Texas L i g n i t e (Flov Rate 1176.47 l b / h ) Carbon
36.20
Sulfur
14.70
Nitrogen Oxygen
1381
Plm Run D o l o m i t e
(Flow R a t e = 84.20 l b / h ; Ca/S = 1 . 0 0 ) s
57 4.80
Hydrogen
0.044 1511
Air
CaC03
wt Z lb/h -
54.5
45.89
7.30 157.30
no is t u r e l
176.47
Ash
209.70
HHV ( B t u / l b ) 8101 LHV ( B t u / l b ) 7810 Figure 8. Carbonizer balance for Texas lignite at 14 atm, 1500 O F , and 15% moisture (base case). "Excludes tar. t92% approach to H& sorbent reaction equilibrium. #If based on sulfur releaee-Ca/S = 1.90. 'Dried to 15% moisture.
carbonizeroperating parameters. These correlations have been developed for bituminous coals as well as for lignites to cover a wide range of feedstock properties. The individual effects of pressure, sorbent feed, and oxygen feed on the product yields are available in the literature; however, the literature lacks information about the combined effects of these factors on the product yields. A carbonizer model has been constructedby superimposing effects of these factors in a logical fashion to yield information about the products of coal pyrolysis ae a function of temperature, pressure,sorbent feed, and oxygen feed. The model has been used to predict carbonizer performance for Pittsburgh No. 8 bituminous coal and Texas lignite at different operating conditions. The following conclusions are derived from this study: 1. An increase in pressure results in a decrease in the amount of tar and soot, but somewhat reduced sulfur capture at a specified temperature.
2. An increase in temperature results in a reduction in the amount of tar and soot, as well as an improvement in the sulfur capture at a specified pressure. 3. An increase in feedstock moisture or the use of slurry requires additional air, which in turn results in reduced amounts of tar and soot and lower quality product gas. Also, the sulfur capture is reduced due to higher steam partial pressure in the product gas. 4. The tar,as well as soot, produced from Texas lignite is less than that produced from Pittsburgh coal for a specified temperature and pressure.
Acknowledgment The authors thank the U.S.Department of Energy, Morgantown Energy Technology Center, for their support of this work under Contract No. DE-AC21-86MC21023.
1410 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993
Literature Cited Arendt, P.; van Heek, K. H. Comparative Investigations of Coal Pyrolysis Under Inert Gas and Hz at Low and High Heating Rates and Pressures Up to 10 MPa. Fuel 1981,60, 779. Boley,C. C.; Fegley, M. M. 'Design and Operation of Two RefractoryLined, Internally Heated, Entrained-Bed Carbonizers"; Grand Forks Energy Research Center: Grand Forks, ND, 1977; Report GFERC/R1/77/1. CSIRO. "Combustion and CarbonizationCharacteristics of Coal From Portland No. 1Seam Globe Mine, MaryboroughDistrict, Southern Queensland"; Commonwealth Scientific and Industrial Research Organization, Coal Research Section, England, Reference M. 142, September 1958. Despyris, J.; Murdoch, P.; Williams, A. Investigation of the Flash Pyrolysis of Some Coals. Fuel 1982, 61, 807. Eklund, H.; Wanzl, W. Pyrolysis and Hydropyrolysis of Solid Fuels at High Heating Rates (10' K/s) Using Curie-Point Technique. In Proceedings of the International Conference on Coal Science, Dusseldorf, Germany, Verlag GliickauE Essen, Germany, D18; 1981; p 701. Floess, J. K.; Plawsky, J.; Longwell, J. P.; Peters, W. A. Effects of Calcined Dolomite on the Fluidized-Bed Pyrolysis of a Colorado Oil Shale and a Texas Lignite. Znd. Eng. Chem. Process Des. Dev. 1985, 24, 730. Freihaut, J. D.; Seery, D. J. An Investigation of Yields and Characteristics of Tars Released During the Thermal Decomposition of Coal. Prepr. Pap.-Am. Chem. SOC.,Diu. Fuel Chem. 1981,26 (2), 133. Graff, R. A.; Zhou, P.; Brandes, S. D. Conditioning Techniques for Mild Gasificationto Produce Coproducts. InProceedings of Sixth Annual GasificationContractors Meeting;DOE/METC-86/6043, US. Dept of Energy, Morgantown Energy Technology Center: Morgantown, WV, 1986; p 144. Howard, J. B.; Essenhigh, R. H. Pyrolysis of Coal Particles in Pulverized Fuel Flames. Znd. Eng. Chem. Process Des. Dev. 1967, 6, 74. Landers, W. S.; Wagner, E. 0.;Gomez, M.; Boley, C. C.; Goodman, J. B. "Entrained-Bed Carbonization of Bituminous Coal"; U.S. Bureau of Mines, RI6608, 1965. Longwell, J. P.; Chang, C. S.; Peters, W. A. 'Coal Gasification and Tar Conversion Reactions Over Calcium Oxide"; Final Technical Report for the Period August 7,1981-August 6,1984; DOE/MC/ 16026-1839 (DE85011734); Massachusetts Institute of Technology: Cambridge, MA, May 1985. Rehmat, A,; Goyal, A. 'Pressurized Fluidized-Bed Combustion (PFBC): Second Generation Systems Research and Development, Subtask: Carbonizer Model"; Final Report; Institute of Gas Technology: Chicago, November 1987.
Robertson, A.; Garland, R.; Newby, R.; Patel, J.; Rubow, L. SecondGeneration PFB Combustion Plant Performance and Economics. Paper presented at the 1988Seminar on Fluidized-BedCombustion Technologyfor Utility Applications, Palo Alto, CA;May 3-5,1988. Saito, M.; Sadakata, M.; Sato, M.; Sakai, T. Devolatilization Characteristics of Single Coal Particles for Combustion in Air and Pyrolysis in Nitrogen. Fuel 1987, 66, 717. Scott, D. S.; Piskorz, J. Pyrolysis of Low-Rank Canadian Coals. Fuel Process. Technol. 1986, 13, 157. Squires, A. M. Cyclic Use of Calcined Dolomite to Desulfurize Fuels Undergoing Gasification. In Advances in Chemistry Series: Fuel Gasification;American Chemical Society: Washington, DC, 1967; Vol. 69. Squires, A. M.; Graff, R. A.; Pell, M. Desulfurization of Fuels With CalcinedDolomite. Part 1. IntroductionandFirst Kinetichults. Chemical Engineering Progress Symposium Series: Important Chemical Reactions in Air Pollution Control;American Institute of Chemical Engineers: New York, 1971; Vol. 67, No. 115, p 23. Steinberg, M.; Fallon, P. T.; Sundaram, M. S. "Flash Pyrolysis of Coalwith Reactive and Non-ReactiveGases";DOE Annual Report, Contract No. DOE/CH/0001601402;Chicago, 1982. Suuberg, E. M.; Peters, W. A,; Howard, J. B. Product Composition and Formation Kinetics in Rapid Pyrolysis of Pulverized Coal-Implication for Combustion. Proc. Symp. (Znt.)Combust. 1978,17th, p 117. Torrest, R. S.; Van Meurs, P. Laboratory Studies of the Rapid Pyrolysis and Desulfurization of a Texas Lignite. Fuel 1980,59, 458. Tran, D. Q. 'Rapid-Rate Bituminous Coal Gasification";Final Report; Institute of Gas Technology: Chicago, August 1981. Tyler, R. J. Flash Pyrolysis of Coals. Devolatilization of Bituminous Coals in a Small Fluidized-Bed Reactor. Fuel 1980,59, 218. Xu, W.; Tomita, A. Effect of Coal Type on the Flash Pyrolysis of Various Coals. Fuel 1987,66,629. Yeboah, Y. D. The Fluidized-Bed Pyrolysis of Coal in Both the Presence and the Absence of Dolomite Compounds. DSC Dissertation, Massachusetta Institute of Technology,Cambridge,MA, 1979. Yeboah, Y. D.; Longwell, J. P.; Howard, J. B.; Peters, W. A. Effect of Calcined Dolomite on the Fluidized-Bed Pyrolysisof Coal. Znd. Eng. Chem. Process Des. Dev. 1980, 19, 646. Yeboah, Y. D.; Longwell,J. P.; Howard, J. B.; Peters, W. A. Pyrolytic Desulfurization of Coal in Fluidized Beds of Calcined Dolomite. Znd. Eng. Chem. Process Des. Deu. 1982,21, 324.
Received f o r review April 23, 1992 Revised manuscript received March 3, 1993 Accepted March 26,1993
