Modelling coal char gasification in a fluidized bed

Modelling coal char gasification in a fluidized bed J. F. Haggerty and A. H. Pulsifer Department of Cbemical Engineering and Engineering Research Institute, Iowa State University, Ames, Iowa 50010, USA (Received 30 July 197 1) (Revised 16 May 19721

Predictions obtained by using the accepted reaction model together with three different reactor models - plug-flow, complete-mixing and bubble-assemblage - are compared. In general, the three reactor models gave significantly different results. The bubbleassemblage model, therefore, represents a valid alternative when modelling fluidized-bed gasifiers. For small inverse space velocities, meaning high steam feed rates and shallow beds, the bubble-assemblage model predicts the lowest (among the three) steam conversions. For deep beds and low steam feed rates, the conversion predicted by the bubbleassemblage model becomes greater than that predicted by the completely mixed model and approaches, the values for the plug-flow model. However, this occurs only at very large height/diameter ratios which are not generally used in operating fluidized beds. Increase in the reaction rate constant associated with the partial pressure of water, kl, caused a marked increase in conversion. The effect of k2,-associated with the partial pressure of hydrogen, was not so great, conversion decreasing as k2 was increased. Inclusion of the water-gas shift reaction when calculating the gas composition in the kinetic rate expression may be of significance in predicting steam conversion by reactor model 3. However, varying the value of Ke, did not have a significant effect.

The design of a chemical reactor involves the combination of an appropriate rate expression and a reactor material balance. Owing to the complex gas flow and solid-particle movement within a fluidized bed, appropriate design procedures are not well established for these types of reactors. Recently, Kato and Wen’ proposed the bubble-assemblage model for predicting fluidized-bed operation. The advantage of this model is that it simulates the fluidized bed based only on the fundamental properties and conditions of the bed without the use of any adjustable parameters. The purpose of the present investigation was to apply this model to the gasification of carbon by steam, and to compare the results of using this model with those obtained by assuming plug flow and complete mixing in the gas phase. A comparison of the results of the calculations using these models would then give some guidance as to what information will be needed for designing larger reactors from laboratory data that are currently being collected2y3 and as to whether the bubble-assemblage model predicts conversions significantly different from the ideal models. Kato and Wen’ developed their model for fluidized-bed catalytic operation. This was applied to the gasification of carbon, a noncatalytic solid-gas reaction, by assuming that the kinetic constants were unaffected by the age and degree of conversion of the solid particle and that some average, constant diameter could be used to characterize the fluidization properties of the material.

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MODELS As noted above, three reactor models were used; plug flow, complete mixing, and bubble assemblage. Each of these was used with the accepted reaction model for the carbonsteam reaction.

Reaction model The previously reported work on the gasification of carbonaceous materials with steam is extensive and several reviews are available4v5. At 1 atm the primary reactions are c+H20=CO+H2

(1)

COtH20=C0,tH2

(2)

The rate of reaction (2), the water-gas shift reaction, is rapid above 870°C (16OO’F) and was assumed to be at equilibrium. The rate of the carbon-steam reaction (reaction (1)) follows a Langmuir-type rate equation of the form klPH,O

Rate =

(3) ’ + k$H2

+ kgH,O

where kl, k2, and k3 are kinetic rate constants, PH@ = partial pressure of steam, and PH2 = partial pressure of

J. F. Haggerty and A. H. Pulsifer: Modelling coal char gasification in a fluidized bed

hydrogen. Since k3 is small, it was assumed to be zero, a common assumption. Reactor models Equations describing steam conversion in the two ideal flow reactors, namely the plug-flow and complete-mixing cases, can be developed from a steam material balance6. For a plug-flow reactor (case l), the steam conversion can be calculated from the following equation: -1

W

__=-

F

hP

2(ln(l -x))

2at -

tx (

[

where a =

)

tln(1 -x))

1

l-%-q

1

-

F

klP

1 +x x-

X -

l-x

molar flow of gas into the nth compartment

-

w2

l-x

molar flow of gas out of the nth compartment

molar rate of depletion of steam reacting in the cloud

(7)

The volumes of the respective regions, the superficial gas velocity and the interchange coefficient, each dependent on the compartment location, are related to measurable or calculable parameters of the flunked bed. The parameters are particle size, particle density, minimum fluidizing velocity, gas distributor arrangement, column diameter, and incipient bed height. Hence, no adjustable parameters are required. Equations (6) and (7), therefore, represent two simultaneous equations with two unknowns, the concentration of gas in the bubble phase and the concentration of gas in the emulsion phase (the rate of reaction being expressed in terms of concentration). These equations, along with those for the plug-flow and complete-mixing cases, were programmed on an IBM 36G65 computer and the steam conversion in the reactor was calculated for various values of the system parameters.

-1 (5)

+

2(ax + 1)

where a has the same meaning. The bubble-assemblage model (case 3) which has been discussed in detail by Kato and Wen’, divides the reactor into three distinct regions, the emulsion phase, the bubble phase, and the cloud. The emulsion phase is composed of the fluidized solid reactant particles with the net gas velocity in this region assumed to be zero. The bubble phase, made up of spherical bubbles containing only a gaseous phase, is surrounded by the concentric cloud region that contains both solid particles and the gaseous compo nents. The fluidized bed is divided into n compartments, each equal to the size of the bubble at the corresponding bed height. The bubbles are considered to grow continuously while passing through the fluidized bed until they reach the maximum stable bubble size or the diameter of the column. At that point the bubble size is held constant until the top of the bed is reached. A steady-state material balance for steam can be written over both the bubble phase,

0=

Molar rate of depletion of steam reacting in the emulsion phase

(4)

With complete mixing of the gas in the reactor (case 2), the following equation is obtained:

w

_

0 = (Fo vb(Cb - Cc)), - (rc ve),

Xcq

_=

interchange of o = gas from the bubble to the emulsion

1

2a

-_ ,iZ ln(1 +x)+kflx

and the emulsion phase,

-

interchange of gas from the bubble to the emulsion

RESULTS Table 1 shows the values of kl, k2 and Keq used in the

reaction model, as a function of temperature. The values for the equilibrium constants for the water-gas shift reaction were taken from reference 4, while the values of the rate constants are typical of those reported in the literature’.

Table

1

Reaction

rate and equilibrium

constantsused

incalculations

Temp (“F) 1500 1600 1700 1800 1900

kl

(mol HnO/h

0.042 0.180 0.470 1.400 2.200

mol C atm)

kq

(atm-l)

1.7 2.0 2.3 2-9 3.7

Keq 1.00 O-84 0.71 0.62 0.54

In order to investigate the effect of each of the many parameters involved in the models, a constant value was assigned to each parameter which was used throughout the investigation, except when the parameter itself was varied. Table 2 presents the values used for each parameter which were selected because they were similar to those of Beeson’s reactor2.

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305

Modelling coal char gasification in a fluidized bed: J. F. Haggerty and A. H. Pulsifer Table 2 d

Operating

conditions

h

30.5 cm 0.0203 cm 0.0966 mol H p/s 38.1 cm

k,

0.18

k2

2.0 atm-1 0.84 8 1 .O atm 16OO’F (c.870°C) 12.4 cm/s 12.0 1248 mol C 0.6 0.0413

used in calculations

mol H&I

Kw

No P T u

&rl f W E

%O PC

f+W

h mol C atm

Inverse space velocity

Figure 2 (16ooOF) -model

Steam

conversion

fmol C.h/mol

H20)

versus inverse space velocity

at 870%

I.------model2,----model3

I.1 g/cm3 0.000189 g/cm3

In each of the graphs which follow, these standard operating conditions are used, exceptions being noted. No is the number of holes in the gas distributor plate, a parameter in the bubble-assemblage model, and variation of this number from 1 to 100 did not affect the calculated steam conversion’. Figure 1 shows the effect of temperature on steam conversion for each reactor model (cases 1, 2 and 3). The steam conversion predicted by each model increases with increasing temperature, and hence increasing kl, in much the same manner. The small difference in the shape of the curve for the bubble-assemblage model is caused by the effect of temperature on the gas density which is unaccounted for in the two idealized models.

interesting to note that the limiting conversion for the bubble-assemblage model is that approached by the plugflow model rather than that of the completely mixed model. The effects of variations in kl, k2 and Kq on the calculated results were tested to see how important was the correct choice of values of these. The effect of the kinetic constant kl on steam conversion is illustrated in Figure 3. The results are obviously very dependent on the value chosen for kl, particularly for smaller values of kl in which region most values reported in the literature lie.

Kinetic

Figure 3 -model

Temperature

f’F1

Figure 1 Steam conversion as a function of temperature _modefl,_______ model 2, - - - - - model 3

Figure 2 compares the effect of variation in inverse space velocity (W/fl on the reactor models at a temperature of 870°C (16OOOF). W/F is not a parameter of the bubble-assemblage model. However, when W/F is held constant while the bed height and superficial gas velocity are varied, the variation in conversion predicted by the bubble-assemblage model is smal18. Therefore Figure 2 represents a valid comparison of the three reactor models. As the inverse space velocity (or residence time) is increased, and therefore conversion increases, the bubble-assemblage model approaches the idealized case of plug flow. It is

306 FUEL, 1972, Vol 51, October

recction

constant

kt

(mol H201mol

Steam conversion as a function l,------model2,-----model3

C. h. atm

1

of the kinetic constant kl

The values of k2, the rate constant associated with the partial pressure of hydrogen, have been reported in the literature to range from unity to approximately 150 atm-l. The wide variation is primarily a result of the different carbon sources investigated. Figure 4 indicates that, as the rate constant k2 increases, the conversion decreases since hydrogen retards the carbon-steam reaction. The variation in conversion is not great, however, and the calculated results are not as strongly dependent upon k2 as they are on kl. The relation between conversion and variation in the water-gas shift equilibrium constant was also examined. Only at very low values of Kq, less than unity, is there any effect, and that only amounts to a 2 or 3% change in conversion. Additional calculations’ showed that inclusion of the water-gas shift reaction in the reaction model did not affect the predicted steam conversions for cases 1 and 2.

J. F. Haggerty and A. H. Pulsifer: Modelling coal char gasification in a fluidized bed

LIST OF SYMBOLS cb Ce d dP

F Fo

O, Figure 4

-model

I

I

1.5

I

I

I

1

I

I

3 5 7 10 2030 50 Kinetic reaction constant k2 (atm-‘1

Steam conversion

as a function

I

100 150

of the kinetic constant

h k %

kp

NO

l,------model2,-----model3 ::

;

For the bubble-assemblage model, the differences between the predicted conversion with and without the shift reaction ranged from 10 to 20%. Thus, consideration of the water-gas shift reaction may be significant for model 3; however, the value of Kq used is not critically important.

CONCLUSIONS The three reactor models predict different results and therefore represent valid alternatives. To test them, a given carbonaceous material would have to be gasified under well-recorded flow conditions to establish values for the kinetic rate constants. Then samples of the same material would need to be treated in a fluidized-bed gasifier to obtain data against which the models could be compared. Unfortunately, this has not been done; therefore, specific recommendations related to the models will have to await collection of the appropriate data.

ACKNOWLEDGEMENTS The work was supported in part by the Engineering Research Institute, Iowa State University, through funds made available by the Office of Coal Research, US Department of the Interior. One of the authors (JFH) held a fellowship provided by the Phillips Petroleum Company.

T u

umf vb Ve vc W x E P P *

steam concentration in the bubble phase (mol/cm3) steam concentration in the emulsion phase (mol/cms) column diameter (cm) particle diameter (cm) steam flow rate (cm3 HzO/h) gas interchange coefficient (s-l) distance from distributor (cm) kinetic rate constant water-gas shift equilibrium constant number of holes in gas distributor plate partial pressure (atm) total pressure (atm) reaction rate (mol/s) cross-sectional area of column (cm2) temperature superficial gas velocity (cm/s) minimum fluidizing velocity (cm/s) volume of the bubble phase (cm3) volume of the emulsion phase (cm3) volume of the cloud (cm3) weight of carbon in bed (g) steam conversion bed porosity viscosity (cP)* density (g/cm3)

lcP=lmNs/m2.

REFERENCES Kato, K. and Wen, C. Y. Chem. EngngSci. 1969,24,1351 Beeson, J. L., Pulsifer, A. H. and Wheelock, T. D. Znd. Engng Chem. - Process DesignDev. 1970, 9, 460. Pulsifer, A. H., Knowlton, T. M. and Wheelock, T. D. Znd. Engng Chem. -Process DesignDev. 1969,8,539. Von Fredersdorff, C. G. and Elliott, M. A., ‘Chemistry of Coal Utilization’ Supplementary Volume (Ed. H. H. Lowry), Wiley, New York, 1963, pp 892-1022 Walker, P. L. Jr, Rusinko, F. Jr and Austin, L. G. A&on. CutuZysis 1959, 11, 133-221 Levenspiel, 0. ‘Chemical Reaction Engineering’, Wiley, New York, 1962 May, W. G., Mueller, R. H. and Sweetser, S. B. Znd. Engng Chem 1958, 50, 1289 Haggerty, J. F. M.E.Thesis, Iowa State University, 1970

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