888
~nd.Eng. Chem.
FYOC~SS ms.
mv. 1981, 20, 686-692
Mathematical Model for the Fluid-Bed Gasitication of Biomass Materials. Application to Feedlot Manure Pattabhl Raman, Walter P. Walawender,' L. 1. Fan, and C. C. Chang Department of Chemical Engineering, Kansas State UniversHy, Manhattan, Kansas 66506
A mathematical model was developed to describe the gasification of biomass in a fluid-bed reactor. The model was simplified, applied to the gasification of feedlot manwe, and a preliminary attempt was made to compute the gas composition and yields of gas, liquid, and solid products assumlng that the water-gas shift reaction was the only gas-phase reaction. The governing equations were solved by using a soltware Interface. Althu& the predicted and experimental values agreed reasonably well, the comparkon suggested that cracking and reforming reactions involving the volatiis produced during devolatitlzation should be included in the model. An approximate calculation of the gas yields and liquid yields incorporating the thermal cracking reactions of the heavy volatlles compared more favorably with the data.
Introduction Fluidized bed gasification is an important process by which carbonaceous solids such as coal, municipal wastes, agricultural wastes, and other biomass materials can be converted into fuel gas. The technological development of a fluidized bed gasification process from bench scale to commercial scale generally involves several stages of pilot plant operation. The scale-up technique from the pilot plant to the commercial stage can be greatly improved if a suitable mathematical model can be developed for the process and applied to the full-scale plant. Mathematical modeling of a fluidized bed gasification process requires knowledge of the hydrodynamics and chemical phenomena that take place in the reactor. A lack of the key components of this information can make modeling efforts extremely difficult, Also, any mathematical model developed must be verified experimentally before it can be used in design applications. Unlike coal gasification, little has been done toward modeling the fluidized bed gasification of carbonaceous solid wastes. Huffman et al. (1977), in attempting to model the gasification of feedlot manure in a fluid bed,considered that the reactions in the gasifier take place in two steps feed char + liquid gas liquid gas
- -
+
Both reactions were assumed to be of first order. The gas yield was estimated by assuming that the behavior of a fluidized bed can be approximated by that of a completely mixed reactor. The model developed permitted prediction of the gas yield but did not permit the composition of the gas produced or the char and liquid yields to be determined. The individual reactions involving the gases as well as the char were not considered; neither were the hydrodynamics of the fluid bed taken into account. Howard et al. (1979) approached gasification modeling by focusing on the liquid (oil) production. They assumed that the primary volatile products from solid waste contain only gas and oil and that part of the oil is converted into char and gas by a secondary reaction, as depicted below. -efuse
< gas o,,
gas
t
char
It was further assumed that the primary and secondary reactions were first order, and the reactions involving the gas phase as well as char were neglected. The main aim of the model was to predict the liquid yield at different 0196-4305/81/1120-0686$01.25/0
operating temperatures. The hydrodynamics of the fluid bed were not included in deriving the model. Five kinetic parameters involved in developing the model were evaluated by fitting the model to the experimental data collected. Maa and Bailie (1978) modeled the pyrolysis of wood in a fluid bed reactor. Their model, based on the shrinking core pyrolysis of a single large particle of wood, was developed to evaluate the reaction time of solids in a fluidized bed. No attempt was made to study product yield or composition. Seemingly, up to the present time no attempt has been made to include the hydrodynamics of the fluid bed in the modeling of biomass gasification. The models developed so far do not attempt to predict the composition of the gases produced or the overall product yields for all products (Le., gas, liquid, and char). This work includes both of these factors. The objectives of the work reported here were: (1) to develop a mathematical model to describe the fluid-bed gasification of biomass; (2) to apply the model developed to the fluidized bed gasification of feedlot manure; (3) to verify the model by using experimental data obtained with feedlot manure in a pilot-scale, fluid-bed gasifier. Model Development Experimental investigations of biomass gasification by Antal et al. (1978) have shown that gasification occurs as follows: (1) pyrolysis or devolatilization, which produces volatile matter and char; (2) secondary reactions involving the evolved volatiles; (3) gasification of char by water (steam). Based on this sequence of steps, the following reaction scheme can be envisioned to represent the reactions that take place in the gasifier. devolatiliation
manure heavy volatiles + gas (CO, H2, C02, CHI, etc.) heavy volatiles
cracking, reforming, etc.
C + H20
liquid
A CO + H2
c + COZ --%2 c o ha C + 2Hz CH4 CO + HzO COP + Hz -*
k4
@ 1981 American Chemical Society
+ char
+ gas
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 4, 1981
687
Table I. The Effects of Time and Temperature on Devolatilization of Manure z
t. s 1
I
0.0100T- 6.93 0.0108T- 6.93 0.0114T- 6.93 0.01162'- 6.93
10 60 100
The devolatilization characteristics of biomass materials depend on the nature of the material gasified. For example, the devolatilization of feedlot manure starts around 450 K and is virtually complete around 800 K, whereas the devolatilization of hard wood takes place between 570 and 750 K (Antal et al., 1978). Hence, the kinetics of devolatilization can be expected to depend on the characteristics of the individual material. The kinetics of devolatilization of manure were discussed by Raman et al. (1981) and found to be described by the equation l - y = - -v*V* -v
-
Amexp[-ALkoe-E/RTdt] f(E)dE
where
f(E) =
exp[-(E - E,)2/2u2] u(27r)'/2
(2)
and y is the fraction of the biomass devolatilized. Since the heat transfer rate is very high in a fluidized bed reactor, the biomass particles are rapidly heated to the temperature of the reactor, which remains essentially constant. This fast response to temperature allows eq 1 to be integrated a t isothermal conditions. Thus 1-Y =
Amexp(-kote-EIRT)f(E) dE
(3)
The term exp(-kote-E/RT)in the integrand changes from 0 to 1 as a steep S-shaped curve which can be approximated by a step function at kgte-EIRT= 1, as suggested by Pitt (1962). Using this approximation, eq 3 can be integrated to give (4)
where Z=
RT In (hot)- E, U
(5)
Equation 4 is the standard normal distribution function. The average experimental values of the kinetic parameters obtained for manure are (Raman et al., 1981): E, = 41.78 kcal/mol, u = 6.03 kcal/mol, and ko = 1.67 X 1013 s-l. Equation 5 permits the evaluation of i as a function of solid residence time, t, and temperature. Expressions for z for manure at selected residence times are presented in Table I. In general, the gasification temperatures for the biomass are of the order of lo00 K and the residence time of the solid in a fluid-bed reactor is relatively high, compared with that of the gases. Keeping these features in mind, it can be deduced from Table I that temperature is the dominant variable influencing z and hence the extent of devolatilization in the reactor. Consequently, it can be assumed, in the present model, that the devolatilization step is instantaneous in a fluid-bed gasifier; therefore, it is practically independent of the residence time of the solid in the reactor. A similar observation was made by Kayihan and Reklaitis (1980) for the devolatilization of coal in a
Bubble
1
Emulsion
I I
T lnlot Gar Volocity : u, Concontrotion : C io
Figure 1. Schematic representation of the model.
fluid-bed reactor. This assumption simplifies the model substantially. The actual gasification process that takes place in the fluidized bed reactor is a combination of the chemical reactions cited earlier and mass transfer phenomena involved due to the hydrodynamics associated with the fluidized bed. The mathematical equations describing the gasification process can be developed by following procedures similar to those used in the development of the bubbling bed model (Kunii and Levenspiel, 1968a,b). The following assumptions were made: (1)The fluidized bed reactor consists of two phases; namely, bubble and emulsion phases, which are homogeneously distributed statistically. (2) The flow of gas in excess of the minimum fluidization velocity passes through the bed in the form of bubbles (Davidson and Harrison, 1963). (3) The voidage of the emulsion phase remains constant and is equal to that at incipient fluidization. (4) The bed can be characterized by an equivalent bubble size and the flow of gas in the bubbles is in plug flow. Also, the bubble is assumed to be free of solids. ( 5 ) The emulsion phase is well mixed. (6) No elutriation of the solids occurs. (7) The bed is under isothermal conditions. (8) No reactions take place in the freeboard of the reactor. (9) Reactions involving the cracking and reforming of heavy volatiles are not included in the model. However, an initial yield of heavy volatiles is considered. Assumption 7 was made because of the assumption on the initial devolatilizationand because a well-fluidized bed is nearly isothermal. Although assumption 8 does not appear to be realistic, it is appropriate for the preliminary application. This point will be discussed later. Assumption 9 was made because of lack of information on the composition and kinetics of the heavy volatiles. Derivation of the Governing Equations. In developing the governing equations, the convective terms describing the flow of gases were approximated by a plug flow term with an axial dispersion term. This was done to facilitate the numerical solution of the resulting parabolic partial differential equations. The numerical values of the axial dispersion coefficients, D1and D2,were chosen such that they represented nearly plug flow conditions in the bubble phase and nearly completely mixed conditions in the emulsion phase, respectively. A schematic representation of the model is shown in Figure 1. Consider an elemental volume of AbAx in the bubble phase of the reactor. The mass balance equation for a species i over the incremental height Ax is: (accumulation of i) = (rate of i in by convection) - (rate of i out by convection) - (rate of i out by exchange with the emulsion
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Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 4, 1981
phase)
+ (rate of production of i by chemical reaction)
-
Dividing both sides of this expression by AbAx and letting 0, we obtain Ax
Similarly, for the gas in the emulsion phase
a
- (AJE,AxCi,) = at
-
Dividing both sides of this expression by A&Ax 0, we obtain letting Ax
and
range of temperature (700-1200 K)under which biomass is generally gasified and at atmospheric pressure, only six species are thermodynamically very stable (Ovenston and Walls, 1979): CHI, CO, COz,Hz, HzO, and C as solid char. Also, these species are the gaseous components that have significant concentrations in the gase produced during gasification. Because it is assumed that the devolatktion reactions are instantaneous, the feed material will not be present as another solid species in the reactor. Thus, m = 1and n = 5 are the total number of species considered; they give rise to eleven partial differential equations. Furthermore, it is to be noted that the boundary conditions used in the model preclude any chemical reactions taking place in the freeboard of the reactor, as stated in the assumptions for the model. Hydrodynamic Relationships. Many variables involved in the model are closely interrelated through the hydrodynamics of the bubbling phenomenon. The relationships between the variables that depend on the hydrodynamics of the fluid-bed are given below. 1. The bubble diameter, Db, is estimated using the following correlation developed by Mori and Wen (1975) Db = DbM - (DbM - Dw) exp(-0.3x/D) DbM = 1.64[A(Uo - u&]o'4 Dw = O.871[A(Uo - Umf)/R70.4
Here, Rie includes the rate of production of species i by the devolatilization of the feed as well as by other chemical reactions in the emulsion phase. For the solids in the emulsion phase, C, is defined as the relative weight fraction of species j with respect to the inert solids in the bed and B is the total weight of the inerts in the bed. Because the gasification of biomass materials is frequently conducted in a fluid bed containing an inert matrix, the solid concentration is defined in this manner. In that the solids are completely mixed in the emulsion phase, the material balance on the entire bed yields
where D w is the initial bubble diameter, and DbM is the maximum bubble diameter. The equivalent bubble diameter, as defined by Kunii and Levenspiel (1969), is calculated at the middle of the total bed height, x = H/2. 2. The bubble velocity, u b , is calculated by using the correlation proposed by Davidson and Harrison (1963) ub = u o - umf+ 0.711(gDb)0.5 3. The volume fraction of the bubble phase, DEL, is calculated from DEL = (Vo - u&)/ub 4. The emulsion phase gas velocity, Ue,is calculated as Ue = Umf/(l -DEL)
which, on rearranging, becomes
5. The gas-exchange coefficient between bubble and emulsion phases, Fb, is calculated from the following correlation suggested by Kobayashi et al. (1967) F b = o.ll/Db
The appropriate initial and boundary conditions are: for the n gaseous species in the bubble phase and emulsion phase t = 0; Cib = CiO; Cie = CiO
6. The height of the expanded bed, H, is calculated iteratively from the material balance for the solid as
t>O,x=H,
acib acie - = 0; - = O ax ax
For the m solid species in the emulsion phase t = 0; c, = 0 t>O,x=O;
acsj
-- -0 ax
Here m and n represent the total number of solid and gaseous species, respectively, present in the reactor. In the
H=
Hmf
(1 - DEL)
Method of Solution In spite of the simplifying assumptions made in the model developed, there are eleven partial differential equations that need to be solved for the simulation of the gasifier. The simultaneous solution of these parabolic partial differential equations yields the transient concentration distribution of different species in the reactor. The numerical solution of these nonlinear partial differential equations is often tedious, complicated, and time consuming. Sincovec and Madsen (1975) have developed a software interface that overcomes the difficulties associated with solving stiff and nonstiff nonlinear parabolic partial differential equations. This interface, which uses a centered difference approximation for spatial discretization, converts the nonlinear partial differential equations into a semidiscrete system of time-dependent, nonlinear, or-
Ind. Eng. Chem. Process Des. Dev., Vol. 20,No. 4, 1981 689 Table 11. Devolatilization Product Distribution for Manure at 983 K
The bubble phase equations for the different species can be written as
data source char
19.0 (wt % DAF) . 81.0 (wt % DAF)
volatiles volatiles composition dry gas heavy volatiles including water dry gas composition
co co,
TGA experiments
MRI Report 1971) 40.6 (wt %) 59.4 (wt %) MRI Report 1971) 16.0 (vol. %) 38.9 8.6 12.9 0.3 1.8 10.9
Table 111. Kinetic Parameters for the Reactionsa activation reaction k c + co, -L, 2 c o k C + H , O & C O + H, k C + 2H, 4 CH4 k CO + H,O 4CO, t H, CO
+
k H,O&CO, k,
kJ/kmol 360065
frequency factor (ki"), m/h 0.2 X 10'
where R b = k&lbC& - k5C2bC3b. The emulsion phase equations are
121417 5.0
230 274 0.75 X 1 2 560
0.1 X
lo' lo8 (m3/kmol
h)
+ H,
Biba et al. (1978). (1978).
K , = k , / k , = 0.0265 x exp( 3955.7/T)C
h i = hi" e x p ( - E j / R T ) .
Yoon
dinary differential equations. The system of equations is then solved by using Gear's backward difference formula for time integration. A modified Newton's method with internally generated Jacobian Matrix is used for solving the nonlinear equations. This package was employed to solve numerically the governing equations of the model. Verification of the Model To apply the general model developed for biomass gasification to feedlot manure, additional assumptions were made to render the model amenable to numerical solution. 1. The fractions of char and total volatiles produced during devolatilization are the same as those obtained from thermogravimetric studies. Data obtained in this laboratory were used (Raman et al., 1981). 2. The fractions of liquid and gas in the total volatiles generated, as well as the initial composition of the gas, were taken from the results obtained by MRI (1971). These data were obtained under slow heating conditions in a packed bed of manure heated from ambient to 773 K. In that the secondary reactions involving the volatiles produced, as well as the char, are not very dominant under this low-temperature condition, it was assumed that the product distribution reported by MRI directly corresponds to the primary devolatilization reaction. The devolatilization product distribution and the initial gas composition used are presented in Table 11. 3. The kinetic parameters for reactions involving manure char are the same as those obtained for coal char by Biba et al. (1978). These values are listed in Table 111. 4. The kinetic parameters of the gas phase shift reaction have the values reported by Biba et al. (1978).
Fbe
DEL
Ef(1 -DEL)
(C5b - C5e)
+ R k + CgC5 (18)
where
cg= HA(1-feed DEL)EmI S= Rhe
BACCB1 HA(1- DEL)E,I
= k4CleC4e - k5C2eC3e
Rle = S( klCle
+
F)
- Rb.
Table IV. Experimental Variables Used in Computation A = 0.041 mz A , = 1313 mz/kg p = 2580 kg/m3
D = 0.2286 m D , = 0.001 m2/s D, = 100 mz/s N = 844 B = 52.3 kg
Em,= 0.42 Umf= 0.11m/s
The appropriate initial and boundary conditions are att=O Cib = Cio i = 1,2,3,4,5 c, = cio c,1 = 0
Operating Conditions temperature, K 983 feed rate, kg/s 0.00176 Uo,m/s 0.44 W,, kg/s 0.00039 Wout, kgls 0.0 composition of the fluidizing gas C,,, kg-mol/m3 0.00042 C,,, kg-mol/m3 0.00130 C,,, kg-mol/m3 0.00034 C,, , kg-mol/m3 0.00410 C,,, kg-mol/m3 0.0
869 0.00373 0.46 0.00082 0.0 0.00011
0.00130 0.00020 0.00440 0.0
Table V. Comparison of Calculated and Experimental Results
t>O;x=H
acib
-= 0
ax
i = 1,2,3,4,5
ac, -
=o
ax In eq 14-18 the devolatilizationproducts generated were incorporated in the emulsion phase as an additional term involving the rate of production of species i per kg of dry ash free feed (Ci)and the dry ash free feed rate per unit volume (C,). The production of char by devolatilization was incorporated as W, in eq 19. Because the solids were present only in the emulsion phase, the devolatilization reactions were assumed to take place in the emulsion phase only. Using the equations generated, gasification results were simulated and compared with experimental data obtained in a 0.23 m i.d. fluid-bed reactor (Raman et al., 1980). Two experimental runs that were at isothermal conditions were chosen for comparison. The details of the input parameters used for computation at the operating temperatures of 869 K and 983 K are presented in Table IV. The partial differential equations, eq 9 through 19, were solved with these parameters, using the computer package described previously. A flow diagram of the computational procedure is presented in Figure 2. The number of spatial meshes chosen for computation was 21 and the relative error bound for the time integration process was set at lov4. The devolatilization data obtained by the Midwest Research Institute (MRI) were incorporated in the computational scheme by assuming that the product distribution and the composition of the dry gas produced during devolatilization in the reactor were the same as those presented in Table 11. The steady-state values of the off-gas composition computed with the model are compared with the experimental data in Table V. The yields of gas, liquid, and char products from manure, as predicted by the model, were calculated by material balance by using the procedure described elsewhere (Raman et al., 1980). The predicted and experimental yields of gas, liquid and char as percentages of the dry ash free feed are also presented in Table V. Discussion As can be seen from Table V, the concentrations of H z , CO, C2H4, and CHI predicted by the model were lower than the experimental values, whereas the concentrations of N2, COz, and CzH, were higher. The predicted values
H, N2
3
CO, C,H, C,H, produced gas yield, % DAF liquid yield, % DAF char, % DAF operating temperature, K
calcd,
exptl,
calcd,
exptl,
%
%
%
%
8.27 65.0 1.51 2.8 22.01 0.06 0.34 56.3 24.5 19.0
5.97 9.91 14.96 56.87 68.36 59.92 2.75 2.46 3.21 7.83 1.35 8.59 15.02 21.19 16.19 1.25 0.10 1.2 0.21 0.58 0.39 65.0 22.7 31.6
20.2 14.8 983
55.3 22.0
PDESOL( Partial
Differential Equation Solver ) Integrator
output Results
Figure 2. Flow diagram of the computations.
50.7 17.7 869
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 4, 1981 891
Table VI. Modified Product Yields gas yield from heavy volatiles included product 15% 20% 25% exptl values Run at 983 K gas 60.2 61.4 62.6 65.0 liquid 20.8 19.6 18.4 20.2 char 19.0 19.0 19.0 14.8 gas liquid char
24.0 54.0 22.0
Run at 869 K 25.3 26.0 52.7 52.0 22.0 22.0
31.6 50.7 17.1
of the gas yields were lower by about 9%, whereas the char and liquid yields were higher by about 5%. Two major factors contributed to the differences observed between the predicted and experimental values. First, the model used does not take into consideration the cracking and reforming reactions involving the heavy and other volatiles. The reforming reactions involving the hydrocarbons and heavy volatiles become increasingly important at higher temperatures. Both the cracking and reforming reactions result in the production of hydrogen, which explains the higher concentration of H2observed in the experimental data than was predicted by the model. Second, the initial weight fractions of char were obtained by thermogravimetric analysis under slow heating rates (3 K/s), whereas the heating rates in the fluid bed were very rapid (1000 K/s). Anthony and Howard (1976) observed that the char produced from coal under rapid heating rates was significantly less than that produced under slow heating rates. A similar effect can be anticipated for manure, and that might be why the values of char yield predicted by the model were high compared with the experimental values. Because this work is a preliminary attempt to model the gasification of feedlot manure, we used an approximate approach to improve the prediction of gas and liquid yields by attempting to account for some cracking of the heavy volatiles. It was assumed that the characteristics of the heavy volatiles produced during devolatilization of manure would be similar to those of heavy gas oil obtained during crude petroleum distillation. The decomposition rates of heavy gas oil given by Nelson (1949) were used for this approximation. Sung et al. (1945) reported that 15-25% of the heavy gas oil decomposed by cracking results in gas. Using the first-order reaction rate constant specified by Nelson (1949) and the estimated residence time of the volatiles in the reactor, we estimated the additional gas yield by thermal decomposition of the heavy volatiles. The original computer values of the gas and liquid yields were then adjusted to include the influence of the cracking reactions. The modified values are presented for both operating temperatures in Table VI. It can be seen from the table that this adjustment gave some improvement. In order to account for the increased devolatilization at high heating rates, calculations were made by assuming that the char produced during devolatilization at rapid heating rates in a fluid bed could be approximated by the char produced at 1223 K in a TGA (15% DAF). The corresponding product distribution was assumed and utilized in the model calculations. The resulting char, gas, and liquid yields compared more favorably with the experimental results. Eariler it was mentioned that the assumption of no gas phase reactions in the freeboard zone was suitable for the preliminary application of the model, There are two reasons for this. First, for the temperatures considered, the char gasification reactions do not take place to an
appreciable extent and as a consequence the production of gaseous species by the char gasification reactions is negligible. Because of this, the water-gas shift reaction is the only gas reaction of practial concern. Second, inspection of the transient solution shows that the gas composition reaches steady state in about 20 s and the axial concentration profiles reach the equilibrium values before the bubble and emulsion gases exit the fluid bed to the freeboard. It is only because of the low temperatures used for comparison, the assumption of no reaction of the heavy volatiles and isothermal conditions that the assumption of no reaction in the freeboard is valid. A more realistic application of the model should include the cracking and reforming reactions involving the heavy volatiles. In this case the time-temperature history of the volatiles in both the fluid bed and the freeboard needs to be considered. Such a model would include additional equations to account for the heavy volatiles in the bubble and emulsion phases of the bed section coupled with equations accounting for the mixture of permanent gases and volatiles in the freeboard section. Because of the reactions of the volatiles, it is doubtful that equilibrium conditions would exist in the reactor or freeboard. In the preliminary work we used rate constants from coal to describe the char gasification reactions. This is acceptable for this case since these reactions are not important at the temperatures considered. Rensfelt et al. (1978) indicate that biomass char gasification is not important for temperatures less than about 1100 K. A more realistic model for application above this temperature should use rate constants specific for the biomass char being considered. The above discussion indicates the limitations of the present model. For the model to be used with confidence for design purposes several refinements must be made in four specific areas. The first involves the inclusion of reactions of the heavy volatiles. To do this the following information is required. (1) Knowledge of the molecular species present in the heavy volatiles and their distribution. (2) Kinetics of their cracking reactions. (3) Knowledge of the time-temperature history of the volatiles. (4) Consideration of steam reforming reactions of the heavy volatiles. The second involves a more reliable data base for the initial devolatilization. The following is required: (1) Knowledge of the initial product distribution commensurate with the heating rates experienced in the fluidized bed; (2) kinetic rate constants for the biomass char if temperatures are in excess of 1100 K. Third, the steam reforming and cracking reactions of the light volatiles (CHI, C2H6, etc.) needs to be considered. Fourth, provision for reactions in the freeboard needs to be incorporated into the model.
Conclusions A mathematical model was developed to describe the gasification of biomass materials in a fluidized bed reactor. Because the initial devolatilization was nearly instantaneous, only the secondary reactions were considered in the model. The secondary reactions considered included char gasification and the water gas shift reaction. The model was applied to the gasification of feedlot manure and an attempt was made to simulate the gasification results. The governing equations were solved by using a software interface and the results computer were compared with experimental data. The comparison suggested that cracking and reforming reactions involving the volatiles produced during devolatilization should be included in the model. An approximate calculation of the gas and liquid yields incorporating the thermal cracking reactions of the heavy
682
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 4, 1981
volatiles compared more favorably with the data. Computations indicated that the reactions involving char are not very dominant in the range of the operating conditions used and that the water-gas shift reaction is the significant reaction. Several refinements are suggested before application to design. These consist of: (1)inclusion of reactions involving the heavy volatiles; (2) securing a more reliable data base for the initial devolatilization; (3) consideration of reforming and cracking of the light volatiles; and (4) inclusion of reactions in the freeboard. Acknowledgment This is contribution No. 81-51-j, Department of Chemical Engineering, Kansas Agricultural Experiment Station, Kansas State University, Manhattan, Kansas 66506. Nomenclature A = cross-sectional area of the reactor, m2 A, = surface area of char, m2/kg B = weight of sand in the reactor, kg Ci = yield of the ith species by devolatilization, kg-mol/kg of feed C,% = concentration of the ith species in the bubble phase, kg-mol/m3 Ck = concentration of the ith species in the emulsion phase, kg-mol/m3 CiO = inlet concentration of the ith species Csj = concentration of the jth solid species in the emulsion phase D = diameter of the reactor, m D1 = axial dispersion coefficient depicting plug flow, m2/s Dz = axial dispersion coefficient depicting completely mixed flow, m2/s DAF = dry ash free feed Db = bubble diameter, m DW = initial bubble diameter, m D~M = maximum bubble diameter, m DEL = volume fraction of bubble phase E = activation energy, kcal/g-mol E, = mean activation energy, kcal/g-mol E d = void fraction at minimum fluidization F b = gas interchange coefficient, l/s feed = feedrate of manure, kg/s g = 9.81 m/s2 H = bed height, m Hd = bed height at minimum fluidization, m ko = frequency factor, l / s k . = rate constant for the jth reaction, l / s If, = equilibrium constant for the shift reaction M , = atomic weight of carbon, 12 kg/kg-mol N = number of holes in the distributor plate R = gas constant = 1.987 kcal/kg-mol K Rib = rate of generation of the ith species in bubble phase, kg-mol/s R,, = rate of generation of the ith species in emulsion phase, kg-mol/s
R , = rate of generation of the jth solid species in the emulsion phase, kg/s T = temperature, K t = time, s V , = bubble velocity, m/s U, = emulsion phase gas velocity, m/s U d = minimum fluidization velocity, m/s V = fraction of volatiles remaining V* = total fraction of volatiles present W , = rate of char into the reactor by devolatilization, kg/s W,,, = rate of char out of the reactor, kg/s x = axial distance from the distributor, m y = wt. fraction of manure devolatilized z = variable defined in the binomial integral 2 = variable defined by eq 5 Subscripts i = 1 = CO;2 = CO,; 3 = H,;4 = H,O; 5. = CH,;6 = char j = subscripts corresponding to the reactions Greek Letters p = density of solids in the reactor, kg/m3 u = standard deviation from mean activation energy, kcal/ g-mol Literature Cited Antai, M. J.; Edwards, W. E.; Friedman, H. L.; Rogers, F. E. “A Study of the Steam Gasification of Organic Wastes”; P r o m Report to €PA, W. W. Lberlck, Project OtRCer, 1978. Anthony, D. B.; Howard, J. B. AIChE J . 1978, 22, 625. Biba, V.; Ma&. J.; Klose, E.; Malecha, J. Ind. Eng. Chem. PrOcessDes. Dev. 1978, 17, 92. Davidron, J. F.; Harrison. D. ”Fiuldization”; Academic Press: New York, 1983; Chapter 2. Howard, J. B.; Stephens, R. H.; Kosetrui, H.; Ahmed, S. M. “Pilot Scale Conversion of Wed Waste to Fuel, Volume I”; Prom Report to €PA, W. W. Llberick, P r o m Officer. 1979. Huffman, W. J.; Un, C.; Beck, S. R.; Halligan, J. E. “Kinetk Analysls of Manure F’yrolyuws”; presented at SERI Technbi Seminar-Ther”)cel Conver8ion of Biomass Residues, (klden, CO, Nov 3 0 D e c 31, 1977. Kaylhan, F.; Reklaitis, G. V. Ind. Eng. Chem. Process Des. D e v . 1980, 31, 239. Kobayashi, H.; Arai, F.; Sunagawa. T. Ct”.Eng. (Japan), 1980, 31, 239. Kunii, D.; Levenspbl, 0. I d . Ew. Chsm. Fundem. l W a , 7,446. Kunii, D.; Levenspiel, 0. Ind. Eng. Chem. Process Des. Dev. 1968b, 7, 481. Kunii, D.; Levenspiel, 0. “FluMizatbn Engineering”; 1987, WHey: New York, 1969; Chapter 4. Maa, P. S.; Bab, R. C. “Experimental Fyrolysls of CeHuo8lc Materials”; presented at the AICK 84th National Meeting, Atlanta, GA, 1978. Mod, S.; Wen, C. Y. AI= J . 1975, 21, 109. MRI (Midwest Research Instltute) Repart on “The Disposal of Cattle Feedlot Wastes by Py~dysis”,December, 1971. Nelson, W. W. “Petroleum Refinery Engineering”; Mc(Lew-Hiil: New York. 1949; p 582. Ovenston, A. and Wails, J. R. Chem. Em. Scl. 1979. 35, 327. PM, 0. J. Fuel1982. 41, 267. Raman. K. P.; Walawender, W. P.: Fan, L. T. Ind. Ens. - Chem. ,%cess Des. Dev. 1880. 19, 823. Raman, K. P.; Walawender, W. P.; Fan, L. T.; Howell, J. A. Ind. Eng. Chem. Process Des. Dev. companion article, 1981. Slncovec, R. F.; Madsen. N. K. ACM Trans. Meth. Software 1975, 1, 232. Sung, H. C.; Brown, C. G.; White, R. R. Ind. Eng. Chem. 1945, 37, 1153. Yoon, H. Ph.D.Thesis, University of Delaware, 1978.
Received for review August 5, 1980
Accepted June 29, 1981
