Ind. Eng. Chem. Process Des. Dev. 1981, 20, 4 1 1-416
41 1
Modeling of Dynamic and Steady-State Shallow Fluidized Bed Coal Combustors. Effects of Feeder Distribution K. ToJo, C. C. Chang, and L. T. Fan* Department of Chemical Engineering, Kansas State University, Manhattan, Kansas 66506
The effects of the distribution of feeders on the dynamic and steady-state characteristics of a shallow fluidized bed coal combustor have been studied on the basis of the two-phase model of fluidization, in which both the lateral gas and solids mixing are taken into account. It has been found that there exists a critiil pRch between successive rows of the feeders, above which the average carbon concentration in the bed increases sharply. I t has also been found that an increase in the number of the rows of the feeders can remarkably reduce the carbon concentration gradient, and that it is a more effective way to render the lateral carbon concentration uniform than the intensification of solids mixing by an increase in the bubble size. The results of simulation also indicate that for a given fluidized bed combustor there exist a critical bubble size and a carbon feed rate above which the phenomenon of “concentration runaway” can occur and the combustor will never attain a steady state.
Introduction Dynamic simulation of a shallow fluidized bed coal combustor by means of the two-phase model, in which the radial solids mixing is taken into account, has shown that an appreciable radial gradient of coal concentration can occur in the combustor (Fan et al., 1979). The occurrence of such a gradient is likely to be detrimental to the performance of the combustor, especially when its scale is large. It appears that the use of multiple rows of feeders is an effective means of reducing the radial concentration gradient of coal. While such an arrangement of feeders has actually been employed (Holcomb, 1975; Hoy, 1975), its effect on dynamic and steady-state characteristics of a coal combustor is not well understood. In the present work, we examine numerically the effect of feeder distribution (the number of feeders) on the dynamic and steady-state radial carbon concentration profiles in both small and large scale fluidized bed coal combustors on the basis of the two-phase model of a shallow fluidized bed. In addition, the effect of bubble motion or bubble size and the gas disperison on the radial coal concentration profile is examined. Mathematical Formulation Let us consider a rectangular shallow fluidized bed combustor as shown in Figure 1. Coordinate x is in the direction of width, coordinate y in the direction of length, and coordinate z in the direction of height. The combustor is provided with one or more rows of feeders distributed symmetrically in the direction of x . For simplicity, the feeders are assumed to be closely distributed in the direction of y so that the concentration gradients of all components involved in the combustion process in the direction of y can be neglected. This eliminates the need to consider the y corrdinate. The air for the combustor is fed uniformily from the bottom of the combustor. The additional assumptions imposed are the following. (a) The flow of gas in excess of minimum fluidization velocity passes through the bed in the form of bubbles (see, e.g., Davidson and Harrison, 1963). This gives rise to the well-known assumption that two phases, the emulsion and bubble phases, exist in the bed. (b) The voidage of the emulsion phase remains constant and equals that at the incipient state of fluidization. (c) The emulsion phase is well mixed in the axial direction, and the coal is assumed to be instantaneously mixed throughout the total bed 0196-4305/81/1120-0411$01.25/0
volume covered by the feeder area. This is a valid assumption for a relatively shallow fluidized bed (Highley and Merrick, 1971). (d) The bubble is spherical, its size remains constant, and the flow of bubbles is of the plug flow. This assumption is valid since there is usually no sufficient time for the bubble to grow in a shallow fluidized bed. (e) The overall rate of the combustion reaction represented as c + 0 2 COZ is sufficiently high so that the oxygen transfer into coal particles is the rate-determining step (see, e.g., Avedesian and Davidson, 1973). (f) No elutriation occurs. (g) The bed is under isothermal operation. With these assumptions, we obtain the following governing equations for the combustor. oxygen in the bubble phase
-
oxygen in the emulsion phase
carbon in the emulsion phase
The appropriate initial and boundary ionditions are t = 0: Cab = Cae = c a o c 0 t > 0: at z = 0 (bed bottom) C a b = CaO d c = -scab ax ax
acae -=0
_ -- -aCab ac =--
ax
at x = 0 (center of the bed)
acae
- 0 a t x = R (wall of the bed) ax ax ax The feeding rate function, gf, is defined as
g f = - -F
NAfH -
F (within effective feeding area) Nxt(G)H gf = 0 (outside the feeding area) 0
1981 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981
Table I. Relationships Among Variables minimum fluidization velocity (Davidson and Harrison, 1971)
umf =
emf3
P
- Pg
.g 5(1- emf) (6/dp)”@
cm/s
bubble fraction bubble velocity gas interchange coefficient (Kunii and Levenspiel, 1969) umf
K , = 4.5 - + 5.85 dB
K , = 6.78(,)”’
D112g1/4 (dg5‘4 1
€mfDUb
dB cm * Is
lateral dispersion coefficient of solids particles (Kunii and Levenspiel, 1969)
Table 11. Numerical Values of Fixed Parameters Used in Computations CaO= 2.38 X mol/cm3 (air) dB = 4, 5, 6, 7.5 Cm d, = 0.05 cm D = 1.74 cmi/s (Bird e t al., 1960) D,, = lOOD,, D,, D,/lO cmz/s Dab = D/100 or 0 cm*/s F = 1.5, 7.5 gls H = 30cm A L = 1 0 cm R = 30,150 cm Sh = 2 ( k g= (Sh.D)/d,) (Avedesian and Davidson, 1973) temperature = 800 “C U, = 105 cm/s (20% excess air) xf = 4.0, 20.0 cm E m f = 0.5 P = 1.0 g/cm3 Figure 1. Fluidized bed coal combustor. I
TYPE I ( N = l ;
P
P-ZRI
b
f
L.
40 0
AL
FEEDER AREA
Figure 2. Feeder configurations. I
0
Kn
1000
IMW
TIME( sed
where Af is the effective cross-sectional area of a single feeder (see Figure 2).
Figure 3. Effect of the bubble size, dg, on the transient average carbon concentration; I = 60 cm.
Numerical Simulation Numerical simulation has been carried out to determine the effects of the feeder distribution on both dynamic and steady-state concentration profiles and the maximum concentration differences in fluidized bed combustors. A software interface for numerical calculation, which is implemented by the so-called “method of lines” (Sincovac and Madsen, 1975), has been employed. In this software interface, Gear’s backward difference formulas (1971) are used for the time integration, and a modified Newton method is utilized to solve the nonlinear equations given in the preceding section. Three feeder designs are shown in Figure 2. The relationships among the variables and the nominal values of parameters employed in numerical simulations are listed in Tables I and 11, respectively. The values of the parameters in Table I1 are within the ranges of those reported
in the technical as well as commercial literature on fluidized bed combustors (see, e.g., Virr, 1978;Goodstine et al., 1979; Comparato and Norcross, 1979). Results and Discussion In Figure 3, the average carbon concentration, C,in the emulsion phase is shown as a function of time with the bubble size as the parameter. It can be seen that the average carbon concentration at steady state is strongly influenced by the bubble size; it increases as the bubble diameter increases. In addition, the time required to reach steady state is strongly influenced by the bubble size. When the bubble size is 7.5 cm or greater, the bed never reaches steady state because the rate of oxygen transfer between the bubble and emulsion phases is remarkably reduced as the bubble size increases, and consequently the unreacted carbon particles accumulate in the bed. The
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 413
0‘0 1
o o q
hrameter, I c m
Icm
Parameter:
100
0.03
I
100
IO
lop00
I,OOO
TIME(sec1
Figure 6. Effect of the feeder pitch on the transient average carbon concentration; dB = 5 cm.
0.02-
c 0 DIYNSIO~ESS
-I
2
3
3
1
I
BISTANCE FROM CENTER
OF
THE BED
Figure 4. Effect of the feeder pitch on the steady-state carbon concentration profiles; dB = 5 cm.
- 0006.
“ l
Figure 7. Effect of the feeder pitch on the steady-state average carbon concentration, (3, and T,; dB = 5 cm.
3
oY
___. MINIMUM
CONCENTRATION
Parameter PNn cm *-
I
10
100
I
u)00
lorn
T~me(rec)
Figure 6. Effect of the feeder pitch on the transient minimum and maximum concentrations of carbon; dB = 5 cm.
phenomenon may be termed “concentration runaway” analogous to the well-known “thermal runaway” (see, e.g., Barkelew, 1959). It is known that the fluidized bed can be relatively easily controlled and rendered stable when the bed is operated in the condition of a low carbon concentration. As can be seen from Figure 3, however, the stability of the bed is critically affected by the bubble size. Figure 4 shows the effect of the feeder pitch, which is defined as the distance between two successive rows of feeders, on the steady-state carbon concentration profiles. Apparently, the carbon concentration gradient in the bed can be substantially reduced by reducing the feeder pitch. A feeder pitch of 100 cm is equivalent to three rows of feeders in a bed with a width of 300 cm. Notice that an increase in the number of row of feeders is a very effective way of rendering the lateral carbon concentration uniform. In Figure 5, the lateral maximum and minimum concentrations of carbon particles in the bed are shown as
functions of time by solid and dotted lines, respectively. Obviously, the difference between them decreases substantially with a decrease in the feeder pitch. I t can also be observed that the time required to reach steady state is almost independent of the feeder pitch for the particular operating conditions studied. The effect of the feeder pitch on the transient average carbon concentration, is shown in Figure 6 . It can be seen that the average carbon concentration decreases drastically with a decrease in the feeder pitch. This is due mainly to the lateral solids mixing; the coal particles fed into a bed with a smaller feeder pitch are distributed rapidly throughout the bed, and no significant gradient of carbon concentration is generated. On the other hand, when the feeder pitch is large the time required for the particles to disperse in a lateral direction is appreciable. This can also explain the larger carbon concentration in the bed and larger time constant to attain a steady state in the bed with a larger feeder pitch than in the bed with a smaller feeder pitch. Figure I shows the effect of the feeder pitch, 1, on the average carbon concentration C, and the time Tw,when the average concentration reaches 9Oy0of the steady state value. It is interesting to see that C and Tw are almost constant f q the pitches up to approximately 40 cm, and that both C and Tw sharply increase with an increase in the feeder pitch after it is approximately larger than 60 cm. This implies that we should recognize the existence of the optimum feeder pitch in designing or scaling up a
e,
414
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981
0.024
t
1
i
1x166
QW BUBBLE SIZE. $(cm)
'Ik.
0
Figure 8. Effect of the bubble size on the steady-state maximum concentration difference, AC-; qf = 6.25 X lo4 g/s-cm3.
0
i
$0
-2
!
I
3 .3 DIMENSIONLESS DISTPNCE FROM THE CENTER OF THE BED
Figure 10. Effect of the coal feed rate function, +f, on the steadystate carbon concentration profiles; dB = 5 cm.
.;
016 014
-
I
-
r -
IO
312
010
008
I/
I
1
10
20
xx)
1
zoo
-
-
Imo
FEEDER flTCH.l(cm)
Figure 9. Effect of the feeder pitch, 1, on the steady-state maximum carbon concentration difference, AC-; dB = 5 cm.
fluidized bed coal combustor. Figure 8 shows the effect of the bubble size on the maximum concentration difference, AC,,, which is defined as the difference between the steady-state maximum and minimum concentrations. It decreases only slightly with an increase in the bubble diameter. This indicates that the solids mixing induced by the bubble motion, which is intensified by the increase in the bubble size, has a smaller effect on equalizing the lateral carbon concentration than the feeder pitch. The maximum concentration difference, AC-, is shown in Figure 9 as a function of the feeder pitch. It can be seen that AC- is approximately proportional to the square of the feeder pitch. Parametric studies of the coal feed rate, in terms of the feed rate function, $bhave also been made. The steadystate carbon concentration profiles obtained at different coal feed rates are given in Figure 10. Note that all the profiles are similar, indicating that the coal feed rate has a negligible effect on the carbon concentration gradient; it only influences the average concentration of carbon in the combustor. Figure 11shows the effect of coal feed rate on the transient average carbon concentration. We see that the time required to reach steady state is approximately the same under stable operation conditions; however, the average carbon concentration at steady state is strongly influenced by the coal feed rate. It increases as $t in-
1 0
10
100
1000
!ooOO
TIME ( s e c )
Figure 11. Effect of the coal feed rate function, J.f, on the transient average carbon concentration; dB = 5 cm.
creases, and there exists a critical coal feed rate above which concentration runaway also occurs and the bed will never reach steady state. The cause for the existence of the critical $fis essentially the same as that for the critical bubble size; that is, as the coal feed rate or the bubble size increases, the oxygen transfer from the bubble phase to the emulsion phase becomes the limiting step of the combustion process. Above the critical values, the rate of oxygen transfer becomes excessively low so that a steady-state condition cannot be reached. The lateral gas (oxygen) mixing or dispersion becomes increasing important in determining the bed efficiency as the bed size increases. Figure 12 shows the effect of lateral gas dispersion on the oxygen concentration profile in the emulsion phase of a fluidized bed combustor. As can be expected, the oxygen concentration gradient increases as the dispersion coefficient decreases. Within the range of the dispersion coefficient examined, however, the efficiency of carbon combustion is almost independent of the gas dispersion coefficients under the conditions listed in Table 11. In reality, the coal particles in a fluidized bed combustor shrink in size and have different lengths of stay in the bed. In addition, the coal particles in the feed may have different sizes. All these fadors influence the size distribution of coal particles. The particle size distribution function,
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 415
M E W L E S S DISTANCE FROM M E CENTER OF THE BED
Figure 12. Effect of the gas dispersion coefficient on the oxygen concentration profile in the emulsion phase of a fluidized bed combustor; R = 30 cm.
P(d,), which is a function of both time and lateral distance, needs to be included in the governing equations. While the resultant governing equations are solvable, the time and efforts required become excessive. In the present work, it is assumed that the mean coal particle size can be used to characterize the behavior of a bed containing coal particles with a wide size distribution. Development and solution of a model without this assumption will be included in our future work. Since it is assumed that the oxygen transfer into the coal particles is the rate-determinng step of the combustion reaction, qualitatively, the larger the coal particle size, the smaller the combustion rate and, thus, the higher the average carbon concentration. However, if the bed is operated in the regions where the oxygen transfer from the bubble phase to the emulsion phase is the rate-controlling step of the combustion process, the effect of the coal particle size becomes negligible. Because of the vigorous solids mixing, an assumption of the isothermal condition does not lead to an appreciable error even if the carbon concentration is not uniform laterally. The assumption has been verified numerically by including the energy balance in the governing equations (Fan and Chang, 1980). Conclusion The effects of the number of rows of feeders or feeder pitch on the transient and steady-state carbon concentrations in a fluidized bed combustor have been investigated on the basis of the two-phase model of fluidization. The coal concentration gradient in the bed is remarkably reduced by increasing the number or rows of feeders or decreasing the feeder pitch. The maximum concentration difference has been found to be nearly proportional to the square of the feeder pitch. The time required to attain steady state and the average carbon concentration are nearly independent of the feeder pitch but are strongly dependent on the bubble size if the feeder pitch is small. A decrease in the feeder pitch can equalize the lateral carbon concentration more effectively than the intensification of solids mixing by an increase in the bubble size. The effect of carbon feed rate on the shape of the steady-state carbon concentration profiles is almost negligible. On the other hand, the average carbon concentration in the bed is a strong function of the carbon feed rate, and there exists a critical value of the carbon feed rate above which steady-state operation of the bed cannot be attained.
The effect of lateral dispersion of gas in the emulsion phase on the transient and steady-state carbon concentrations in the bed is almost negligible under the conditions of the present study. The feeder distribution becomes an increasingly important factor as the bed width increases; the transient and steady-state bed characteristics drastically change when the feeder pitch exceeds a critical value. When the pitch is beyond the critical value, a steep carbon concentration profile may be generated in the bed. Though the dynamic modeling of fluidized bed combustors is relatively simple, the numerical computations of the resultant model can be quite complicated. Thus, the model needs to be simplified so that simulation results could be obtained within reasonable computing time and effort. It is hoped that the present relatively simplified model can at least be used to study qualitatively the dynamic behavior of fluidized bed combustors, and the results of simulation can be useful for analyzing stability and controllability of the fluidized bed combustors.
Nomenclature C = carbon concentration in the emulsion phase, g/cm3 C, = oxygen concentration in the emulsion phase, mol/cm3 c a b = oxygen concentration in the bubble phase, mol cm3 Ca0= initial oxygen concentration (feed gas), mol/cm dB = bubble diameter, dm D = gas diffusivity in the solid-gas boundary, cm2/s D, = effective dispersion coefficient of oxygen in the emulsion phase, cm2/s D,= effective dispersion coefficient of solids, cm2/s F = feeding rate of coal particles, g/s g = gravitational constant, cm/s2 H = bed height, cm k, = oxygen mass transfer coefficient in the solid-gas boundary, cm/s K = gas interchange coefficient, l / s 1 = distance between successive rows of feeders, cm AL = some characteristic distances in the direction of bed length, cm N = number of rows of feeders R = half width of the bed, cm Sh = Sherwood number t = time, s ub = bubble velocity, cm Vo= superficial velocity of gas, cm/s U,, = incipient fluidization velocity, cm/s xf = width of the feeder, cm x = coordinate in the direction of bed width, cm y = coordinate in the direction of bed length, cm z = coordinate in the direction of bed height, cm tb = fraction of the bubble phase tmf = void fraction in the emulsion phase p = gas viscosity, g/cm-s p = particle density, g/cm3 = feeding rate function, g/cm3-s
l
+f
Literature Cited Avedeslan. M. M.; Davldson. J. F. Trans. Inst. Chem. Eng. 1973, 51. 121. Barkelew, C. H. Chem. Eng. hog. Symp. Ser. 1959, 55, No. 25, 37. Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”; W k y : New York, 1960; Chapter 16. Comparato, J. R.; Norcross, W. R., paper presented at Coal and Illinois Industry Conference, Chicago, M a y 9-10, 1979. Davidson, J. F.; Harrison, D. “FiuMized Particles”; Cambridge University Press: New York, 1963. Davidson, J. F.; Harrison, D. “FiuMIzatlon”; Academic Press: New York, 1971; Chapter 2. Fan, L. T.; Chang, C. C., paper presented at the Second Chemical Congress of the North American Continent, Las Vegas, Aug 24-29, 1980. Fan, L. T.; Tojo, K.; Chang, C. C. Ind. Eng. Chem. ffocess ms. Dev. 1979, 18, 333. Gear, C. W. “Numerical Initial Value Problems in Ordinary Differential Equations”; Prentlce-Hall: Englewood Cliffs, NJ. 1971; Chapter 9.
Ind. Eng. Chem. Process Des. Dev. 1981,20,416-424
416
Goodsthe, S. L.; Comparato. J. R.; Matthews, F. T., paper presented at Second International Coal Utilization Conference, Houston, Texas, Nov 6-8, 1979. Highley, J.; Merrick, D. AICM Symp. Ser. 1071, 67(116), 219. Holcomb, R. S. "Proceedlngs of the Fourth International Conference on Fluidized-Bed Combustion"; MITRE Corporation: McLean, VA, 1975; p
Vlrr, M. J. "The Industrial Fluidized Bed Boiler"; StonePlatt Fluidfire Limited, West Mldlands, Engiand, 1978.
Received for review January 23, 1979 Revised mhnuscript received August 4, 1980 Accepted April 20, 1981
171
hy,'H.' R. "Proceedings Of the Fourth htm"Onai Conference On FluklizedBed Combustbn"; MITRE Corporatlon: McLean, VA. 1975; p 93. Kunii, D.; Levenspiel, 0. J. Chem. fng. Jpn. 1869, 2 , 122. Slncovec. R. F.; Madsen, N. K. ACM Trans. Math. Software 1975, 1 , 232.
This work was conducted under the sponsorship of the Engineering Experiment Station (Energy Study Project) of Kansas State University.
A New Process for Production of Purified Phosphoric Acid and/or Fertilizer Grade Dicalcium Phosphate from Various Grades of Phosphatic MateriaIs Grover L. Brldger,' Carl B. Drees,* and Amltava H. Roy*3 School of Chemical Engineering, Georgia Instnute of Technokgy, Atlanta, Georgia 30332
new process for production of purified phosphoric acid and/or fertilizergrade dicalcium phosphate has been developed and tested with various grades of phosphatic materials as the source of P2O5. This new process is based on dissociation of monocalcium phosphate with an organic solvent. Phosphate concentrates, colloidal phosphates, phosphate slimes, and phosphate matrix containing 7.5-34.3% P2O5 have all been found amenable to treatment by the above process to produce phosphoric acid of much greater purity than that produced by current commercial wet-acid processes. Altematively or simultaneously, the process will produce fertilizergrade dcalcium phosphate using much less sulfuric or phosphoric acid than previous processes. A highly concentratgd phosphoric acid can be made directly, without vacuum evaporation. A
Introduction For production of high-purity phosphoric acid by the wet process, high-grade phosphate rocks or concentrates are desirable. However, the supply of high-grade phosphates is rapidly decreasing, and it would be highly desirable to be able to produce high-purity phosphoric acid from low-grade phosphatic materials. In 1974 the domestic production of marketable phosphate rock was 45 686 OW tons. On the average P205content of this production was 30.8% (67.4% Bone Phosphate of Lime [BPL]). The average grade of phosphate ore mined in the United States was 13.3% Pz05,and the average PZO5 recovery from the ore was 67.7 % . The grade distribution of the marketable phosphate rock consumed in the United States in 1974 was as follows: less than 60 BPL, 5.6%; 60-66 BPL, 20.8%; 66-70 BPL, 42.0%; 70-72 BPL, 12.2%; 72-74 BPL, 11.6%; and over 74 BPL, 7.8%. More than two-thirds of the phosphate rock marketed in 1974 was less than 70 BPL. When the lower grades of presently marketable phosphate rock are used for manufacture of phosphoric acid by the wet process, the product acid contains substantially more impurities than when high-grade rock is used. A process which could produce high-purity phosphoric acid from low-grade phosphatic materials would be very de'G. L. Bridger was Director and Professor of Chemical Engineering at Georgia Institute of Technology,Atlanta, Ga., before his death on Nov 3, 1978. 2Chevronh e a r c h CO.,P.0.BOX1627, Richmond, CA 94802. To whom correspondence should be addresses International Fertilizer Development Center, P.O. Box 2040, Muscle Shoals, AL 35660. 0196-4305/81/1120-0416$01.25/0
sirable. In particular, a process which could produce high-purity acid from raw phosphate ore (matrix) would have the added advantages of eliminating the ore beneficiation cost and increasing the Pz05recovery, since PzO5 losses in washing and flotation would be eliminated. Also, many phosphatic materials not now economical for production of phosphoric acid could be used, thus extending the life of phosphate reserves. It is well known that monocalcium phosphate undergoes dissociation under suitable conditions to form phosphoric acid and dicalcium phosphate Ca(H2P0J2 = H3P04+ CaHP04 (1) The conditions under which this reaction proceeds in an aqueous system were investigated by Elmore et al. (19401, who found that high concentration and high temperature favored the reaction. The dissociation in the presence of a number of organic solvents, including ethanol, acetone, dioxane, tetrahydrofuran, and pyridine, was investigated by B o d e et aL (1959). However, the dissociation has never been successfully used as a basis of a commerical process. A number of studies have been made in the past concerned with the extraction of phosphoric acid by organic solvents and the solubility of phosphoric acid in various organic liquids. A variety of patents exist for chemical processes that produce a purified orthophosphoric acid . based on the extraction of'crude wet-process phosphoric acid by organic solvents with the subsequent recovery of the purified acid product. Very extensive literature reviews of the Processes, papers, and patents are given by Drees (1972), ROY (19761, and McCulloUgh (1976). The production of fertilizer-grade dicalcium phosphate by direct acidulation of phosphate rock with mineral acids 0 1981 American Chemical Society
