96
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 1, 1979
Joint Meeting, Munich, Sept 17-20, 1974. Pyrcioch, E. J., Feldklrchner, H. L., Tsaros, C. L., Johnson, J. L., Blair, W. G., Lee, 6. S., Shora, F. C., Jr., Huebler, J., Linden, H. R., "Production of Pipeline Gas by Hydrogasification o f Coal", Research Bulletin No. 39, Vol. 1, Inst. Gas. Technol., Chicago, Ill., Dec 1972. Rossini, F. D.,Pitzer, K. S., Arnett, R. L., Braun, R. M., Pimental, G. C., "Selected Values of Physical and Thermodynamic Properties of wdrocarbons and Related Compounds", Carnegie Press, Pittsburgh, Pa., 1953. Rowe, P. N., Chem. Eng. Sci., 31, 285 (1976). Seglin, L., Friedman, L. D.. Sacks, M. E., A m . Chem. SOC.,Div. FuelChem., Prepr., 19,No. 4, 31 (1974). Squires, A. M., Trans. Inst. Chern. Eng., 39,3, IO, 16 (1961). T a m n , P., Punwani, D., Bush, M., Talwakar, A,, "Development of the Steam-Iron System for Production of Hydrogen for the Hygas Process", R & D Report No. 95,Interim Report No. 1. Period of operation May 1973-June 1974, to the Office of Coal Research. Van Heek, K. H., Juntgen, H., Peters, W., J. Inst. Fuel, 46,No. 387,249 (1973). Walker, P. L., Jr., Rusinko, F., Jr., Austin, L. G., Adv. Catal., 11. 133 (1959).
Wen, C. Y., "Optimization of Coal Gasification Processes", R & D Report No. 66,Interim Report No. 1 to the Office of Coal Research, 1972. Wen, C. Y., Mori, C. S., Gray, J. A., Yavorsky, P. M., Am. Chem. SOC., Div. Fuel Chem., Prepr., 20,No. 3, 155 (1975). Wen, C. Y., Yu, Y . H., AIChE J . , 12, 610 (1966). Werther, J., "The Hydrodynamics of Fluidization in a Large Diameter Fluidized Bed", presented at the GVClAIChE Joint Meeting, Munich, Sept 17-20,1974. Yoshida, K., Kunii, D., J . Chem. Eng. Jpn., 7 (l),34 (1974). Yoshida, K., Fujii, S.,Kunii, D., "Characteristics of Fluidized Beds at High Temperatures", presented at the International Fluidization Conference, Pacific Grove, Calif., 1975. Yoshida, K., Wen, C. Y . , AIChESymp. Ser. No. 716, 67, 151 (1971). Zahradnik, R. L., Glenn, R. A,, Fuel, 50, 77 (1971). Zielke, C. W., Gorin, E., Ind. Eng. Chem., 47, 820 (1955).
Receiued for reuieu: September 20, 1977 Accepted July 21, 1978
Fluidized Bed Gasification Reactor Modeling. 2. Effect of the Residence Time Distribution and Mixing of the Particles. Staged Beds Modeling Hugo S. Caram and Neal R. Amundson" Department of Chemical Engineering, University of Minnesota, Minneapolis, Minnesota 55955
The solution of the population balance equations for the char particles in the fluidized bed gasifier is used to define the correct average in the reaction rate expression. A simplified model is used to study the effect of the flow pattern of gas through the dense phase. It is shown that the good mixing of the particles is enough to minimize, in a wide range of parameters, the difference between the models. Staging of the beds in the adiabatic system results in a significant improvement in the carbon conversion by providing a pretreating system and favorable conditions for the methane formation. For a fixed total residence time there seems to be an optimum relation between the residence times in each of the beds.
and the value of the carbon conversion to be used is given by the average carbon conversion in the bed as calculated from Wk - MFC
Introduction Some basic results observed in a simple model of a fluidized bed char gasifier have been presented in part 1. It is of interest to study the effect of the distribution of conversion of the particles in the reactor and the effect of particle mixing on the reactor behavior. Of some importance too, is the effect of the staging of two beds as has been proposed in some of the processes under study (hygas, hydrane) in which methane formation is the primary aim. In those cases the rapid rate methanation becomes important and must be accounted for in the model. Only simplified models are being considered, but it is expected that their detailed consideration will provide some insight in the underlying characteristics of the system. The Average Reaction Rate In most of the calculations performed in part 1 we have assumed the rate of carbon conversion to be given by an equation of the form
where MFC is the mass fraction of carbon in the bed. We are interested, however, in-the true average F ( X ) as opposed to the value of F ( X ) used, and it is a relevant question to find the relation between these functions. We are looking for a distribution function p ( X , t ) such that p ( X , t )d X is the mass fraction of char with conversion between X and X + d X at time t. When the bed behaves from the point of view of the particles like a well-mixed reactor, the mass conversion equation can be written (Levenspiel et al. 1968/69)
dX = bF(X) dt
where B = B ( t ) is the total mass in the reactor, M and Ml are the flowrates of solids entering and leaving the reactor, and po is the conversion distribution in the feed. The last term on the right stands for the rate of consumption of carbon by chemical reaction with B p ( X ) representing the mass per unit change of x and w h / ( 1 - W b X ) correcting to the original amount of carbon in the char considered as shown in part 1. The total mass balance for the reactor will be
with
* Address correspondence to this author at the Department of Chemical Engineering, University of Houston, Houston, Texas 77004. 0019-7882/79/1118-0096$01.00/0
C
1978
American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 1, 1979
dB at
-=
M
-
MI- AM
97
(4)
where AM is the mass consumption rate in the reactor. Combining (3) and (4) we obtain
A
Under steady state conditions this equation reduces to
dX
dlnF dX
1 ++
r2F
- - -I. 1
a
-
X
1
= -po
71F
, ; ; ! 40
(6) O2
02
Bb
72
=
:
x,
= 5
i
where
04 06 08Ave Carbon Conv X
10
Figure 1. Relation between the correct average reaction rate and the reaction rate determined using the average conversion for well mixed solids and a shrinking core model with and without deactivation. Curve a, a = 0,x o = 0.0; curve b, a = 0, xo = 0.5.
=-
71
1
,I , , ,
xo
M
Bb M - AM ~
a=-
1
(9)
where e(r2,XO) indicates the expresssion between brackets. An ash balance yields
a - Xo M a-X M-AM
Wb
Equation 6 can be integrated by using the condition p(O-) = 0 to obtain
(10)
If all the particles enter with the same conversion X o , po(X) = 6(X - X,) and
72
(15)
r1
and from (14) and (15) we obtain
which is the practical equivalent of (12). The average conversion 8 will be given by (17)
(11)
The standard approach to relate the values of is to use the normalization condition
T]
and r 2
and does not depend in this case on the ash content of the feed. The relation between the average rate and the value of the rate obtained using the average conversion defined in (2) can now be found using (71, (81, and (15) to be
h =
given by Levenspiel et al. (1968). In this case, however, this condition is not satisfied by the conversion distribution given by (10). The reason is that all the particles that have reached complete conversion (and most of the kinetics allow that to occur in a finite amount of time) and have not left the bed are not accounted for in the distribution. The integral indicated in (12) will only give the mass fraction of particles still containing carbon. The apparent difficulty in determining r1 from r 2 is, however, easily solved by using an ash balance as will be shown below. The mass fraction of carbon in the bed will be given by
F(X) bB(a - X )
-
-___
Bb F ( X )
-
Equations 18 and 17 define a parametric relation between X and 6. If the particles entering the reactor have uniform conversion, 6 will be independent of the ash content of the original char. In a few simple cases the integral defined by c can be evaluated analytically, and obviously if F ( X ) = (1- X ) then 6 = 1. Some numerical results are presented in Figure 1 for the shrinking core model with deactivation proposed by Johnson (1975)
F(X) = (1- X)2/3exp(-aX2) Where (1- s ) / ( a - s ) is the mass of carbon per unit mass of carbon of conversion s. If all the particles enter with the same conversion X o , (13) reduces to
for the cases where cy = 1.8, 0.97, and 0, the latter corresponding to the regular shrinking core model. It can be seen that the approximation used can lead to fairly large differences in the evaluation of the char reactivity, although as shown in part l they are not strongly reflected in the final conversion obtained from the reactor model when the reactor is considered to be adiabatic and only the composition and characteristics of the entering streams are given. However, if the reactor temperature is assumed to be fixed, the correction is necessary as large differences
98
Ind. Eng. Chem. Process Des. Dev., Vol.
18,
No. 1,
1979
in conversion can be expected.
The Effect of the Particle Mixing The small effect of the flow pattern on the carbon conversion shown in part 1 was attributed to the assumption of good mixing of the particles. A simple example can provide some insight on the range of validity of these results. Suppose a simple reaction A (gas) + S (solid) product
-
is carried out in a fluidized bed reactor of height L. The solid does not change volume and the rate of reaction per mole of solid is given by
r ' = k "cAe
(19)
where cAe is the concentration of A in the emulsion phase. The rate of reaction per unit volume of dense phase is given by
r = h',l
-
emf)
Po
f, - (1 - X)C,, = k'CAe = h ( l Ms
-
X) (20)
The gas and solid feed to the reactor is UocA, and M (kmol/s m2). A simple mass balance relates the gas conversion W to the solid conversion X
x = alw
Do, = k L / t l o
Figure 2. Effect of assuming a stationary vs. a well mixed gas phase in the emulsion phase for different dimensionless space velocities and interphase resistances.
(21)
with the last two terms corresponding to the expressions that would be obtained if both phases were well mixed. The same result is obtained when D a I 0 or m . If we use a DH type model where the dense phase is well mixed, the equations can be written
- -
In the case of a simplified KL model (see part l),the mass convervation equations can be written
0=
after integration we obtain, using eq 20 and 21
"=,
k
The reactor behavior is then defined by three dimensionless parameters: the ratios between the reaction rate constant and the gas spatial velocity (DuI), the reaction rate constant and the exchange coefficient between phases (p), and the gas and solid feed flow rates (al). It can be easily seen that if the solid is in large excess ( a 1 0), the system will approach the behavior of a plug flow catalytic reactor with the rate of reaction per unit volume given by k ' C A / ( 1 + 6). According to the relative values of the reaction rate constant and interphase mass transfer coefficient we will have the two extremes of mass transfer control (6 m) or reaction control ( p 0). If the gas is in large excess (aI m) the gas conversion will be limited by the condition (1 - aIw) 2 0 or its equivalent W 5 l / a I . In that case the exponential term can be approximated by the first two terms of its series expansion to obtain
-
- -
-
h'CAe
After some manipulation, and using the same dimensionless variables previously defined, the equations can be written
W= where
k(?A - C A e ) -
~ a ~- (e -i ~ 3 ) ( 1 -waI)
+
1 - e-Da~'3 D q ( 1 - Wa,)
(27)
- --.
As before, eq 27 approaches eq 26 when DuI 0 or /3 m . Although not as evident, the same is true when a I m because it can easily be proven that for small gas conversions all the models predict the same behavior (Davidson and Harrison, 1963). These results are presented in Figure 2 where we have plotted the values of the gas conversion as a function of the Damkohler number DuI for three different values of the relation between reaction rate constant and exchange coefficient (0= 0.,1.,10.) and for different molar flow relations cyI. It can be seen that at low conversions (0.-0.15) the models predict similar conversions for all values of a and p. The agreement improves also as expected with increasing values of /3 and a. For a I 4 and all values of p or for S 2 10 and all values of a almost no differences can be observed between the two models, at least within the range of DuI being considered. A simple calculation will better illustrate the validity of these results, assuming a steam gasifier operating at known temperature (1270 K) with equimolar feeds of gas and solid. We will ignore the ash and use the kinetics given by Gibson and Euker (see part 1)for Wyoming coal. Using the data given in part 1 (hol= 1226.4 exp(-18780/T) atm-' s-l, po = 1200 kg m-3, P = 1 atm, Fo = 0.01 kmol m-* s-l, emf = 0.5, Lmf= 2.5 m, eb = 0.3, (K& = O.ll/db) we obtain
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 1, 1979 Solid Feed
Table I
dh,
P
m
W (well mixed dense phase)
W (station-
0.705 0.629 0.512
0.770 0.642 0.514
1 5 10
0.014 0.07 0.14
HYDROGASIFIER
,
I
X 2.39/(0.7 X 1.067) = 8,R = k / ( q , = 2.39db/(0.3 X 0.1) = 72.42dh. Even for very small
I
bubbles there will be little difference between the conversions predicted by both models as can be seen in Table I. T h e Staged Beds Case The ultimate purpose of many of the processes described is to produce methane to be used as a substitute for natural gas. Methane can be obtained after shifting of the synthesis gas produced in the gasifier by the reaction
+ 3H2
-
6
r=l
Product Char
+ Q H ~ o H ~ T+, )
(UA)H(Tc - Tk1) = 6
CFH,fL(TH)+ ( M o- 12(Z4 + Z5))HdTd ( 2 8 )
1=l
With the stoichiometric reduction 3
FHL = FGI = Z Z I +N~L J j=1
M - I ~ ( Z I + Z ~ + Y ~,TF O )
CH4 + H 2 0
The methanation reaction is, however, highly exothermic and must be carried out a t low temperatures. This introduces practical difficulties requiring special design of reactors that will allow the elimination of the large amount of heat produced. On the other hand, we are burning part of the char in the gasifier to provide heat for the endothermic steam gasification. This is inefficient from the thermodynamic point of view because we must introduce heat into the system a t a very high temperature and withdraw it a t a low temperature. Unfortunately, as we have already seen, steam gasification is too slow to be carried out a t a temperature that will favor the formation of methane but it is clear that it will be convenient to maximize the amount of methane formed by direct reaction of carbon and hydrogen. Therefore, it is of some interest to model a system of two staged beds, the lower one being a gasifier and the top one a hydrogasifier. The gas products of the gasifier will be fed to the hydrogasifier and the char produced in the latter will move down to the first. Methane formation is favored in the hydrogasifier by higher hydrogen partial pressures and lower temperatures than those found in the gasification stage. For highly reactive chars and since the char-hydrogen reaction is very exothermic, it may be convenient to withdraw some of the heat produced in order to maximize methane production. This can be accomplished by either introducing a heat exchange surface in the hydrogasifier and use the heat removed to produce steam or by injecting a quenching steam stream that will enhance methane formation by absorbing heat and producing additional hydrogen. Mass balances may be set up following the same scheme used for a single bed in part 1, and some of the new notation introduced is summarized in Figure 3. As we did in the gasifier (see part 1)the energy balance for the hydrogasifier can be written E:FG,Hr(T) + M&dTd
Product Gases
ary dense phase)
DaI = L k / L i , = 2.5
CO
99
~ ~ Z Q H ~ O
(29)
Gas Feed
Figure 3. Schematic diagram of the staged beds model.
and combining (28) and (29) with the enthalpy balance for the gasification (see part 1) we obtain TH = IA31 [(A37'o + Q + A 2 + Qext)/(A3 + A5211 + QH + Q H ~ o C P + ~T AdTs ~ + ( U A ) H T C ~ / ( [ A ~ I A ~+/ ('452)) A ~ + QH~oCPZ + A4 + (UA),} (30) with '431
=
6
3
r=1
d=l
C FGICPr; A4 = MoCps; Q4 = CZ,+,(-AH,O)
(31) where all the heat capacities are average values between the entrance temperature of the stream considered and the hydrogasifier temperature. The terms Ab2and A4 represent the heat capacities of the entering streams of gas and solid while QH indicates the heat released by the three reactions considered. T h e Rapid Rate M e t h a n a t i o n As we have mentioned earlier, the char will, in its initial stages, show a high reactivity toward hydrogen that will not appear if it has been preheated in an inert atmosphere or if the reaction is carried out in pure steam. According to Johnson (1974) above 1089 K(1500 O F ) the reaction may be assumed to be instantaneous and carbon conversion due to it will be given by the equation
where LY is a deactivation factor and f R is the relative reactivity factor for rapid rate methanation which was found by Johnson to be relatively independent of the type of char considered and approximately equal to 1. Equivalent expressions have been found by Moseley and Paterson (1965) and Zahradnik and Glenn (1971). The basic mechanism proposed by these authors is the formation of active sites during devolatilization. These active sites may either react with hydrogen, catalyze the carbon-hydrogen reaction, or transform to relatively inactive char. At high temperatures the process is fast enough so that the amount of methane formed becomes independent of the residence time in the reactor. At low temperatures (below 1089 K) the process is much slower. A quantitative model was proposed by Johnson (1975) in which intermediate solid active species disappear rapidly to form
100
Ind. Eng. Chern. Process Des. Dev., Vol. 18, No. 1, 1979
I
P :70atrn RRM= Rapid Rate Methanation NRRM =Nan II II
r = T . + T -= 2500 s n
---_ bed case -- staged single ARRM
u
'8
5
10
15
20 % 0,
In
25 Feed
(I
'8
30
u"E 14
35
70/
L
1
~
l
l
l
l
l
l
l
l
IO 30 50 70 90 Hydrogasifier Volume / Total Gasifier Volume
Figure 4. Effect of the staging with and without rapid rate methanation for T H = 0.0017 and 7H = 0.57 at P = 70 atm.
Figure 5. Effect of the relative size of gasifier and hydrogasifier at 70 atm.
methane or ethane or deactivate to produce a relatively inert char. The rate-controlling step in thf formation of active species while the relation between the carbon deactivated and the carbon gasified depends only on the hydrogen partial pressure. This is a critical difference from the model proposed by Zahradnik and Glenn (1971) in which methane formation is activated by the temperature and would indicate that the total amount of methane formed is independent of the temperature history of the particle. We will not, however, pursue these lines which may be a subject of future study. The char will therefore be assumed to have been either deactivated before, or the process of rapid rate methanation will be considered to be very fast with the amount of carbon gasified in it given by eq (4.6.1). It should be pointed out that heats of hydrogenation measured in an experimental calorimeter (Institute of Gas Technology, 1974) show an increase in the heat of reaction with the carbon conversion from values well below those for P-graphite to values well above for highly converted chars. We have used, however, the value corresponding to the P-graphite to conserve the thermodynamic consistency of the data. As methane formation is only important a t high pressures, we will limit the study to €' = 70 atm, and, as we are evaluating the staged bed concept vs. the single bed, we will conserve the total effective residence time. The advantages of the staged bed come about for two reasons. First, the upper bed provides a reactor a t lower temperatures thus favoring methane formation and, second, the first stage acts as a preheater and provides solid at a higher temperature to the lower gasifier. If the hydrogasifier is very small it will only act as a preheater unless the char undergoes rapid rate methanation. Assuming the total effective residence time to be fixed, any increase in size of the hydrogasifier will be a t the expense of the gasifier size. The reduction in the gasifier size will be justified only if an appreciable amount of methane is formed providing additional heat to the system and correspondingly increasing the total carbon conversion. In the limit as the gasifier becomes smaller the top bed will begin to play the role of the gasifier and the system will approach the condition of the single bed with two disadvantages: it will lose its preheating system which was provided by the top bed and the solid will leave the bottom gasifier a t a very high temperature, thus depriving the system of heat at its highest level. We can then expect that under certain conditions there will be an optimal relation between the sizes of the two vessels. Figure 4 presents typical results when no rapid rate methanation (NRRM) is expected for
an effective residence time of 2500 s. As expected, the lowest carbon conversion in the gasification reactions corresponds to the well mixed tank reactor. The preheating only case is obtained assuming the residence time in the hydrogasifier to be i H = 0.017 and with the gasifier taking the rest. It can be seen that a t low oxygen concentration in the feed and thus low temperatures, this system will provide the highest conversion. On the other hand, when the feed contains more than 15% of oxygen a higher conversion is obtained from the system where iH = iG = 712 because in this condition hydrogasification becomes important. When rapid rate methanation (RRM) is expected the results are somewhat different and the most efficient disposition seems to be given by a small preheating hydrogasifier ( i H = 0 . 0 1 ~in ) which only the RRM will be taking place (plus the corresponding adjustment to the equilibrium of the gas shift reaction at the hydrogasifier temperature). In Figure 5 we have presented the effect of the relative size of the two vessels for a fixed total residence time and oxygen mole fraction in the feed. As expected, a maximum in the carbon conversion occurs when the char shows no rapid rate methanation but in the case of rapid rate methanation the maximum corresponds to the smallest possible hydrogasifier. It should be noted however, that the curves in the case of the NRRM are relatively flat in spite of the large changes in the reactor temperature showing the intrinsic stability of the system. In the case of the RRM, carbon conversion will be more sensitive to the size of the hydrogasifier and decrease monotonically with the size of the gasifier. Comparison of the temperatures shows that although in the RRM case the gasifier temperature is similar to the NRRM case, the temperature of the hydrogasifier starts a t a much higher level than in the NRRM case to go through minimum and increase again when the gasifier becomes very small. The amount of methane produced per hundred moles of feed is presented in Figure 6 for both RRM and NRRM cases and is compared to the amounts produced by gasification in a single gasifier. In all the cases inspected the methane yield was higher when using staged beds. In the NRRM case the use of the preheating bed increases a t small values of yo:, the methane production with respect to that of the single bed just because the system is more thermally efficient and larger amounts are being converted. For high values of yo: and higher temperatures, conditions in the gasifier (where methane is being produced) will become unfavorable to methane formation and the amount of methane formed will approach the value corresponding to the single bed. We should point out, however, that a higher amount of methane is formed a t complete carbon
lnd. Eng. Chem. Process Des. Dev., Vol. 18, No. 1, 1979 T = T H t 7, i 2500 s single bed reoctor
---20 staged
R R M = Ropld Rote Methanofon NRRM = Non II
beds
(I
0
,
0
5
IO
15
20
25
r =2500s 2500
30
35
% 0, in Feed
Figure 6. Effect of the staging on the methane formation with and without rapid rate methanation a t 70 atm.
conversion than in the single bed with no preheater (points C and C’ in Figure 6). In the RRM case the methane yield is so much higher in the staged bed case that the use of a single bed would be difficult to justify. Some calculations were performed utilizing a simple bubble rnodel in both stages. The results show a steep decrease in both total conversion and methane formation with an increasing bubble size similar to that observed in t h e single bed. They are, however, still well above those of single bed. S u m m a r y a n d Conclusions The ratio between the average rate of conversion and t h e rate of conversion calculated fur the average carbon content in the bed was found in the case of a feed of uniform composition. The proper average was obtained by solving t h e corresponding steady-state population balance equations. An ash balance must be used to replace t h e original normalization condition proposed by Levenspiel et al. (1968/69) since it is not applicable to particles containing an inert residue and which have been consumed in a finite time. There are noticeable differences between the calculated rates, and their ratio shows an unexpected maximum in the case when deactivation is considered. T h e use of the correct average is important when the reactor temperature is fixed and a t low gaseous conversions but has been shown t o have negligible effect (part I) in the analysis of the adiabatic reactor. T h e small effect of the flow pattern in the dense phase on the carbon conversion observed in part 1 is studied in two simplified two-phase models which contain either a well mixed dense phase or a stationary dense phase, respectively. In each the conversion is found to be a function of only three dimensionless parameters. A generalized plot of the conversion shows a wide range of parameters where it is difficult to distinguish between the two models and justifies the results observed in part 1. Finally, a system composed of two staged beds, a hydrogasifier on top of a gasifier, is studied. Two models of char are considered in this case; in the first one the char is assumed to behave as studied before, while in the second case the char will go through what is considered an instantaneous methanation step. In all cases the staging results in a n appreciable improvement in carbon conversion due in part to the additional methane formed and in part to the better thermal efficiency resulting by preheating the solid in the hydrogasifier. In the case where there is no rapid rate methanation and for a fixed total residence time it is shown that there is an optimal relation between the sizes of the gasifier and hydrogasifier, while
101
if rapid rate methanation occurs, the best combination will correspond t o the smallest possible hydrogasifier. l n a single bed rapid rate methanation produces only a modest increase in carbon conversion and methane formation, with respect to the rapid methanation case with no rapid methanation. There is, however, a dramatic increase in both carbon conversion and methane formation, when etaged beds are considered. The foregoing considerations indicate that without minimizing the effect of the char reactivity the chemical factors are overshadowed in many circumstances by the thermal and contact characteristics of the system used and research efforts in that direction would be clearly justified. Nomenclature a , I / It, A2, heat liberated by combustion in the gasifier, kcal/s AB,average heat capacity of the gases entering the gasifier between the entrance temperature and the temperature of the gasifier As1, average heat capacity of the gases leaving the gasifier between the gasifier and hydrogasifier temperature A4, average heat capacity of the solids entering the hydrogasifier between the entrance temperature and the hydrogasifier temperature AS2,average heat capacity of the solids entering the gasifier between the entrance temperature and the gasifier temperature B = B ( t ) ,mass of char in the bed, kg cAe, concentration of reactant A in the enirilsion phase D a I , defined in eq 25a db, bubble diameter, m f,, volume fraction of the emulsion phase fu, relative char reactivity as defined in part 1 F,, gas flow into the gasifier, kniol/m2 s FFl, molar flow of the ith component entering the gasifier, kniol/m2 s FG,. molar flow of the ith component leaving the gasifier, kmol/m2 s FH,, molar flow of Ith component leaving the hydrogasifier, kmol/m2 s F = F ( X ) , functional dependence of the rate of conversion on the conversion hol, rate constant for steam gasification, atm-ls-l k.h’,h’’, first-order reaction rate constants defined in eq 19 and 20
exchange coefficient between bubble and emulsion phase per unit volume of bubble phase, l / s 1, axial coordinate in the bed, m L d , fluidized bed height at minimum fluidization conditions, m M , solid feed to the gasifier, kg/m2 s M,,solid feed to the hydrogasifier, kg/m2 s M,, solid withdrawal rate from the bed, kg/m2 s MFC, mass fraction of carbon in the bed M s , solid molecular weight used in eq 20, kg/kmol p o ( X , t ) ,conversion distribution in the feed (mass basis) p ( X , t ) , conversion distribution in the reactor (mass basis) P, total pressure, atm Q H * ~ ,quenching steam flow into the gasifier, kmol/m2 s Q,,,, heat introduced into the gasifier, kcal/s Q, heat liberated by reactions I, 11, and I11 in the gasifier, kcal/s QH, same for the hydrogasifier, kcal/s r , r’, reaction rates defined in eq 19 and 20 t , time, s T , gasifier temperature, K Ts, temperature of the solid entering the hydrogasifier, K T H ,hydrogasifier temperature, K Tc, temperature of the hydrogasifier coolant, K T temperature of the steam quench to the hydrogasifier, K ( ~ A ) Hoverall , heat-exchange coefficient for the hydrogasifier, kcal/s m2 K Go,feed gas superficial velocity W , gas conversion (Kbe)b,
102
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 1, 1979
Wb, fixed carbon weight fraction in original char mole fraction of the ith gaseous component X,carbon conversion = (carbon in original char - carbon left in char)/(carbon in original char) X , average carbon conversion on a mass basis Z,, total rate for the j t h reaction (i 5 3); for d > 3 it is the rate of the j - 3 reaction, kmol/s m2 xi,
Greek Letters cyl, defined in eq 22 /3, defined eq 25b 6,,, Kronecker 6 AM rate of mass consumption in the reactor, kg/s m2 tb, bubble volume fraction emf, void fraction in the dense phase at minimum fluidization conditions K , defined in eq 23 il,i2, defined in eq 7 and 8, s r G , iH, effective residence times in the gasifier and hydrogasifier, s
= TG + i n original char density, kg/m3 Subscripts 0 , initial values or feed conditions b, bubble phase Components i
po,
1, H2 2, H20
3, co 4, co, 5, CH4 6, N2
Reactions I, C + H 2 0 = CO + H2 11, C + 2Hz = CH, 111, CO + HzO = CO2 + H1 Superscripts
- average value along the reactor length -
average value for all residence times
0 , conditions at the feed
L i t e r a t u r e Cited Davidson, T. F.. Harrison, D., "Fluidized Particles", Cambridge University Press, Cambridge, 1963. Levenspiei, O., Kunii, D., Fitzgerald, T.. Powder Techno/., 2. 87 (1968/69). Johnson, T. L., Adv, Chem. Ser., No. 131, 145 (1974). Moseley, F., Paterson, D., T . Inst. Fuel, 38 13 (1965). Zahradnik, R. L., Glenn, R. A,, Fuel, 50, 77 (1971). Johnson, T. L., Am. Chem. SOC.Div. FUelChem. Prepr., 20, No. 3, 61 (1975). Institute of Gas Technology "Pipeline Gas from Coal: (IGT. Hydrogenation Process)", Interim Report No. 1. August 1972-June 1974. (NTIS FE 1221-1).
Receiised f o r review November 21, 1977 Accepted July 21, 1978
Kinetics of Sulfur Form Removal during Coal Hydrogenation Dennis D. Gertenbach, Robert M. Baldwin, Richard L. Bain," James H. Gary, and John 0. Golden Chemical and Petroleum Engineering Department, Colorado School of Mines, Golden, Colorado 8040 1
The kinetics of coal hydrodesulfurization for both total and sulfur forms removal has been studied in a stirred, batch reactor. The removal of organic, pyritic, and total sulfur and the formation of sulfide (FeS) sulfur at three temperatures were modeled as first order. An organic desulfurization activation energy of 21.4 kcal/g-mol was calculated from the temperature-dependent kinetic data. Total desulfurization was modeled as a combination of organic and pyritic desulfurization and sulfide formation. as well as a function of only organic and pyritic desulfurization.
In trod uction Proper design of industrial coal liquefaction reactors will require precise knowledge of the kinetics of organic sulfur removal. Many petroleum and coal fractions show first-order dependence for overall desulfurization where all sulfur compounds are lumped together. The catalytic hydrodesulfurization studies of Wilson et al. (1957) with naphtha and Schuit and Gates (1973) with petroleum feeds showed that sulfur removal was first order with respect to residual sulfur concentration. Qader et al. (1968) studied the catalytic hydrodesulfurization of coal tar and, likewise, modeled the data as first order. The data given by ElKaddah and Ezz (1973) on the thermal desulfurization of petroleum coke also shows first-order dependence. Koltz et al. (1976) modeled the noncatalytic hydrodesulfurization of coal in anthracene oil as second order, in a manner similar to that used by Hill et al. (1966) for dissolution data dx, - = k(1dt Little work has been done on determining desulfurization kinetics of sulfur forms in coal. Whitehurst et al. (1976) showed that oxygen removal was first order, then 0019-7882/79/1118-0102$01.00/0
showed that organic sulfur concentration was proportional to oxygen concentration, thus leading to the conclusion that organic sulfur removal was also first order. Pitts et al. (1976) modeled catalytic organic desulfurization as two simultaneous, first-order reactions, lumping organic sulfur into two different groups of pseudo-compounds. Using nonisothermal techniques, Vestal et al. (1970, 1974) passed hydrogen gas over powdered coal, evolving hydrogen sulfide and removing sulfur from the coal. They showed pyritic sulfur removal to be order and organic sulfur removal to be first order in residual sulfur concentration. However, there were undoubtably mass transfer effects in this system not found in donor solvent systems. In this investigation a detailed analysis of the rate of removal of sulfur from coal during batch hydrogenation, which includes the thermal decomposition and dissolution of the coal particles and consequent hydrogenation of the dissolved coal, is performed by studying the rate of removal of the pyritic and organic sulfur compounds, in addition to total sulfur removal. Kinetic models are developed for the removal of pyritic and organic sulfur and for FeS sulfur (sulfide sulfur) formation. The activation energy for organic sulfur removal is calculated. Two correlations for 0 1978 American Chemical Society
