Ind. Eng. Chem. Fundam.
1981, 20, 113-122
113
Model of Coal Pyrolysis. 1. Qualitative Development George R. Gavalas,’ Paul How-Kei Cheong, and Ravl Jaln Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 9 1 125
Coal is represented as a collection of 14 functional groups including aromatic rings, aliphatic chains and bridges, and oxygen-carrying groups. A procedure is developed for determining the concentrations of these groups from elemental analysis and nuclear magnetic resonance data. The chemical changes taking place during pyrolysis are described by a set of elementary reactions selected on the bask of chemical theory and information from model compound studies. The kinetic parameters of these reactions are estimated using the methods of thermochemical kinetics. Product formation is discussed qualitatively in terms of the elementary reactions.
Introduction Pyrolysis of coal signifies thermal decomposition in an inert atmosphere or in a vacuum. In coke production (carbonization), the traditional application of coal pyrolysis, large lumps of coal are subjected to slow heating such that the hindered product removal results in a relatively small amount of liquids (-10%) and a roughly equal amount of gases (-10%). More recently, rapid or “flash” pyrolysis has been investigated as a possible commercial route to gaseous and liquid fuels. Much of the practical importance of pyrolysis, however, derives from its relationship to other processes. Closely related to pyrolysis is “hydropyrolysis”, the rapid heating of coal in a stream of hydrogen. The products consist of tars, lighter liquids including single ring aromatics, and gaseous hydrocarbons-mainly methane. The liquid phase hydrogenation of coal, suspended in a solvent, is also closely related to pyrolysis. A significant difference between thermal decomposition in the gas phase and in a solvent lies in the size of the fragments removed from the coal matrix. The size of the fragments produced in the gas phase is limited by their volatility, while in a solvent the escaping fragments can be substantially larger. In spite of this difference, pyrolysis and liquid phase hydrogenation largely share the same free radical mechanisms. As the first step in coal combustion, pyrolysis influences the ignition characteristics and the evolution of pollutant gases. Certain undesirable phenomena such as caking and agglomeration encountered in diverse gasification processes are also intimately related to the thermal reactions of coal. Carried out a t conditions that restrict secondary reactions, pyrolysis entails relatively limited chemical change and constitutes a useful technique for investigating the structure of coal. For example, spectroscopic studies on pyrolysis tars have provided considerable structural information. Likewise, the composition of the gaseous products has yielded useful albeit indirect information. The dual role of pyrolysis, as a ubiquitous process in coal conversion and as a probe in structural studies, has sustained research interest over the years. The early experimental work concerned with coke formation or carbonization, has been reviewed in the wellknown volume of Lowry (1963). More recent experimental and modeling studies, emphasizing rapid or flash pyrolysis, have been reviewed by Anthony and Howard (1976), Juntgen and van Heek (1977), and Kobayashi et al. (1977). The earlier models were not adequate in describing the temperature-time dependence of pyrolysis rate and the ultimate weight loss. To better describe the temperature
dependence, Pitt (1962),Anthony and Howard (19761, and Anthony et al. (1976) used a series of parallel reactions with common A factor and distributed activation energies. The model described well the weight loss of a bituminous coal and a lignite for various heating rates and final temperatures. Suuberg (1977) and Suuberg et al. (1978) described the evolution of individual species by independent parallel reactions with certain products formed by more than one reaction. The nature of the chemical reactions was not specified but by adjusting the kinetic parameters good agreement was achieved with data from a lignite and a bituminous coal. Kinetic models of competing reactions have also been used to describe pyrolysis yields. One such model, Reidelbach and Summerfield (1975), is formulated in terms of pseudocompounds such as “activated coal”, “primary gases”, etc. and describes the yields of tar and total gases. Although it includes a relatively large number of adjustable parameters, this model has not shown any advantage over the simpler independent reaction models. The independent reaction models have been successful in correlating experimental results and in modeling combustion furnaces and gasifiers, e.g., Sarofim and Beer (1979). Such applications require the total rate of volatile evolution rather than the detailed pyrolysis chemistry. Processes such as hydropyrolysis and liquefaction aim at intermediate products and pose a more challenging modeliig problem. The product distribution in such processes is intimately related to the structure of coal and the details of its thermal reactions. Some subtler aspects of coal combustion, e.g., the evolution of NO,, might also be better understood if a detailed chemical model were available. The structural, mechanistic, and kinetic data base needed to develop a fundamental model of the thermal reactions of coal has been very limited until very recently. In the past few years, however, the accumulation of structural information by spectroscopic means and wet chemistry has accelerated. At the same time, considerable progress has been made in the application of group additivity methods and transition-state theory to the functional groups of coal and their thermal reactions. Based on the progress in these two directions, a fundamental model now appears to be a meaningful if complicated undertaking. A few years ago the authors reported their initial efforts on a model based on functional groups and their reactions (Cheong et al., 1975; Cheong, 1976). More recently, Solomon and Colket (1979) proposed a simple model relating the evolution of pyrolysis products to specific functional
0196-4313/81/1020-0113$01.25/00 1981 American Chemical Society
114
Ind. Eng. Chem. Fundarn., Vol. 20, No. 2, 1981
form the model is useful mainly as a theoretical framework for planning experiments and formulating simpler and more specialized models. Part 1is self-contained and can serve as a source of mechanistic and kinetic information. Part 2 develops mathematical modeling techniques for complex reaction systems. Such techniques can be applied to the pyrolysis of other organic materials like lignin.
Figure 1. Structure of the coal pyrolysis model.
groups. In this model the initial composition of coal is characterized by the fraction of certain functional groups including a potentially tar-forming fraction. The evolving tar is assumed to have the instantaneous composition of the remaining solid and hence to remove a corresponding amount of functional groups. Fourier transformed infrared spectra obtained by Solomon (1979) and elemental and NMR spectroscopic data, Solomon and Colket (1979), indicate that the composition of tar ahd char are closely related. Tar formation and other overall reactions used in Solomon’s model are not kinetically linked to elementary free radical steps, a fact which is reflected in the low activation energies reported. This model represents a conceptual advance in emphasizing the role of functional groups and describing, at least partially, the competition between gas and tar-forming reactions. In this paper we present a chemical model of coal pyrolysis which represents a more systematic and comprehensive version of the earlier model of Cheong (1976) and which rests on the following general principles: (i) Coals belonging to a broad range of rank, such as subbituminous and bituminous coals, can be characterized by a common set of functional groups, different coals differing by the concentrations of these functional groups. (ii) At high temperatures the functional groups of coal react by wellknown free radical reaction mechanisms. The reactions of coal will be described as reactions of functional groups and not of coal molecules. (iii) Many reaction rate parameters can be estimated by the methods of thermochemical kinetics. (iv) To describe the evolution of the solid coal and the formation of products, one needs in addition to the concentrations of functional groups the concentrations of reactive configurations. These depend on the spatial arrangement among the functional groups; in the absence of other information this arrangement is assumed to be random, subject to a few chemical constraints. By using functional groups the pyrolysis process can be described in terms of fewer than 20 state variables. The alternate description in terms of “coal molecules” would have required hundreds of variables. The description in terms of functional groups is also in keeping with the nature of experimental information about coal structure. The advantage of using functional groups and assuming their random arrangement is partly offset by the complicated nature of the resulting reaction rate expressions. Using the above principles (i)-(iv), the pyrolysis model has been organized as shown in Figure 1. The qualitative aspects of the model represented by blocks 1-5 are presented in part 1 (this paper) while the quantitative material, blocks 6-11, is presented in part 2 (following article in this issue). As presented in parts 1 and 2, the model is not suitable for process design and other such engineering applications. Considerable simplification and adjustment of kinetic parameters would be required. In its present
Characterization of Coals and Chars: Functional Groups and State Variables The chemical characterization of coals, chars, and coal-derived products has an extensive literature which is rapidly expanding with the resurgence of interest in coal chemistry. Much of the earlier work has been reviewed in the well-known volume (Lowry, 1963),while more recent reviews include Tingey and Morrey (1972), Larsen and Kuemmerle (1976),Suuberg (1977), and Whitehurst (1978). Chemical characterization has utilized wet chemical methods, i.e., various classes of reactions, and spectroscopic methods. Wet chemical methods have been used to determine the presence and amounts of various functionalities, for example, the amount of phenolic hydroxyl groups (Friedman et al., 1961),ether bonds (Ignasiak and Gawlak, 1977; Wachowska et al., 19791, or the nature of aliphatic structures (Deno et al., 1978). Infrared spectroscopy has been applied extensively to coals and chars to obtain useful, albeit qualitative results regarding the presence of various functional groups such as phenolic OH and carbonyl (Retcofsky and Friedel, 1968; Speight, 1971; Painter and Coleman, 1979). The most useful results, qualitative and quantitative, concerning the carbon-hydrogen skeleton of coal has been proton and 13C NMR spectroscopy. Until very recently these studies were conducted on coal liquids derived by extraction, pyrolysis, or hydrogenation. Therefore they gave only indirect information about the structure of solid coal (e.g., Heredy et al., 1966; Bartle et al., 1975; Yokohama et al., 1979). During the past 2 years, several groups have obtained I3C and proton NMR spectra of solid coals using special instruments (Maciel et al., 1979; Gerstein et al., 1979). From the information provided by these and other similar studies, there energes a structural view which is tentative but continues to improve with the accumulation of experimental data. The organic portion of coal consists of a variety of similar units linked covalently to form coal molecules with molecular weight in the range 1000-5000, although some smaller molecules are also present. The coal molecules are held together by weaker forces due to hydrogen bonds or weak ionic bonds, e.g., acid-base interactions. Each unit consists of an aromatic nucleus and an aliphatic peripheral part. The aromatic nucleus consists of 1-5 condensed rings. Medium and lower rank bituminous and subbituminous coals have mostly two and three rings while higher rank bituminous coals and anthracites contain a larger number of condensed rings. Some of the aromatic rings contain oxygen, sulfur, or nitrogen. In principle, a unit can be separated from other units by a succession of bond dissociation reactions or can sustain changes in ita aliphatic part. However, it cannot be separated into two segments each of which contains an aromatic nucleus. The aliphatic portion of each unit contains short aliphatic chains and bridges connected to the aromatic carbons. In addition, some ring structures are partially hydrogenated, constituting what are known as hydroaromatic structures. Phenolic hydroxyl groups, carboxyl groups, and smaller amounts of sulfur-containing chains are other substituents on the aromatic carbons. Of particular sig-
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
CH3
I
CH2 OH
I
115
The chain double bonds Y, and the /3 radicals Y12are allocated among Yz,Y3,Y6using the simple proportionality assumption
I
tPh---C=CHzI Y?
I I
+
r,
t Y3 t Y ,
r,
+
r,
21
C Ph-C-6H
Figure 2. Segment of a coal molecule illustrating the definition of state variables.
5
Y,
E?
y12
Table I. Definition of State Variables
nificance to pyrolysis are the bridges that connect the various units. These are mainly methylene, ethylene, and ether groups. One of the gaps in our structural knowledge involves the relative amounts of these three types of bridges and the possible presence of other types (Given, 1960, 1961; Brown and Ladner, 1960; Heredy and Neuworth, 1962; Heredy et al., 1965; Bartle et al., 1975). Similar uncertainties presist as to the relative abundance of various types of chains plnd hydroaromatic structures. In the model presented below, the ratio of ethylene and methylene bridges remains an important adjustable parameter. To reduce the complexity of the model, it was necessary to restrict the number of functional groups without losing the ability to describe the important chemical processes. Thus, each unit is assumed to consist of the same (average) aromatic nucleus which contains, in addition to carbon and hydrogen, heteroatoms 0, S, N in amounts representative of the elemental composition. Only one type of hydroaromatic structure was used, as shown below, while it is known that several structures may be present (Bartle et al., 1975; Farcasiu, 1977). Oxygen functionalities were limited to phenolic hydroxyl groups and ether bridges. Heteroatom oxygen was implicity included in the average aromatic nucleus contained in each unit. Keto and quinonic structures have not been included. We now proceed to define the functional groups or state variables needed to characterize the initial and instantaneous state of coal (or char) at any time during pyrolysis. To illustrate the selection of state variables, consider the unit shown in Figure 2. We recognize an aromatic nucleus, naphthalene, a phenolic hydroxyl group, a -CHz- group 1 that links with another unit, a methyl substituent 2, and a hydroaromatic ring containing an ethyl substituent. Other than the -OHgroup, all groups include a-carbons. Most of the state variables can, therefore, be defined as substituents t o a-carbons rather than substituents to the aromatic rings. Thus the a-carbon 1 in Figure 2 contains 2 substituent H, and a bridge. The a-carbon 2 contains 3 H. The a-carbon 3 contains 2 H and a hydroaromatic CH2 (see definition below). The a-carbon 4 contains 1 H, 1 CH2CH3,and one hydroaromatic CH2. Using a-carbons as pivots affords a flexible and concise description because structures such as those in the figure can be included without defining functional groups beyond ethyl. This definition is also appropriate in relation to the distinguished role of a carbons in chemical reactions by virtue of the resonance stabilization of benzyl radicals. The definition of the state variables is given in Table I. In each case, Ph represents a peripheral aromatic carbon (or an aromatic nucleus) and the state variable Yi (i = 1, ..., 14) represents the concentration of the encircled group or bond.
state variable, gmol/L
name
structure
Yl
a-hydrogen
Ph-i-ti
Y,
methyl chainf
Ph-C-CHa
y 3
ethyl chainf
0.5Y4
ethylene bridgea
0.5 Y,
hydroaromatic structure f
0.5Y6
double bond bridgesC
y,
chain double bonds
y,
ring-a carbon bonds
y 9
a radicals
I I I I
Ph-r-CH I I I I
Ph-C-C.-Ph’
I I I I
Ph-C=C-Ph’
Ph-C-
I
I I
?h-i‘
phenolic hydroxyls ether bridges
YlO O.5Yl1
Ph-OH Ph-0-Ph’
I I
radicals
Yl,
Ph-C-tH
I
ph-r CHZ-CH2
Yl,
CY
I
carbons -p ”
aromatic nuclei volume of remaininge coal matrix from an initial sample of unit weight
‘14
Yl s
Ph
a 0.5Y4 is the concentration of the bridge; therefore, Y, is the concentration of C, bonds (half-bridge) used in such bridges. 0.5Y, is the concentration of the overall structure; therefore, Y, is the concentration of -CH,groups (P-carbon). Y, is the concentration of the half double bond belonging to each C,. Y,, is the concentration of a-carbon-oxygen bonds. e This is the “subunit volume”; Le., it includes the micropores (< 12 A in diam-
eter) but excludes larger pores. Ph-l-bHZ;
I
y, includes
Y, includes / IP
CHRCH
II
\CHzCCH
Y, includes
I I
Ph--C--CH=CHZ,
and
m/CHZ-‘H I \CH;CHZ.
I I
I
Ph-c=cHz
Ph-C-CH2-CH2.
,
116 Ind. Eng.
Chem. Fundam., Vol. 20, No. 2, 1981
with similar relations for the double bonds and /3 radicals included in Y3and Y5. Initial Values of State Variables In this section we discuss the determination of the initial values of state variables from experimental data. Initially, the variables Y6,Y7 (double bonds), Y9,Ylz(CYand @ radicals) are assumed to be zero. The data required to specify the remaining variables are as follows. (a) Elemental Analysis. This includes percentages of carbon, hydrogen, oxygen, nitrogen, sulfur, and mineral matter. We will not get into the subtleties of oxygen and mineral matter determination but will assume that the mineral matter can be estimated from the ash, and the oxygen (other than the oxygen in the mineral matter) can also be estimated. (b) Density of coal (excluding volume of pores above 10 A diameter) can be measured by Nz displacement. (c) ‘Hand ‘3c NMR Data. Ideally, data for solid coal are required. In their absence, estimates can be made from coal derived liquids, pyrolyzates or extracts. 13C NMR provides mainly the aromaticity, i.e., the ratio of aromatic to total carbon. Proton NMR provides fractions of aromatic, a , and @ hydrogen. Usually the aromatic and phenolic-OH hydrogen are determined together and the phenolic hydrogen must be determined or estimated by other means. In some cases (Heredy et al., 1966))several types of CY and @-hydrogenwere individually determined. In view of these possibilities, we will not present a general procedure, but give, as an example, the procedure used for the calculations of part 2. We start with the determination of the volume per unit (initial) weight. The volume excluding pores above 10 A in diameter is simply the inverse of the nitrogen density, l/p. From this we must subtract the volume of the mineral matter WMM/pMM, where the density pMM can be estimated from the composition of mineral water.
WMM y15= -1 - P
PMM
Let Wc, WH, Wo, Ws, WNbe the weight fractions of the indicated elements in the coal. Carbon is divided into aromatic and aliphatic fractions, xCu, xed, and hydrogen , xm, i.e. aromatic, alpha CY and /3. Note that into x H ~ xHa, WC + WH + Wo + Ws + WN + W M M = 1
+ XCd = I XHar + XHa + XH@ Xcar
1
We now have the concentration of CY hydrogen Yi = P X H ~ W H and the concentration of aliphatic carbon
(1)
C d = (P/12)XCdWC
The concentrational Cd includes carbon atoms in carboxylic and ketone groups. The carboxylic groups have not been included in the state variables because they decompose to produce COPwithout significantly influencing the other reactions. To determine the various carbon-hydrogen groups, the concentration of carboxylic carbon Co must be estimated, e.g., from pyrolysis data, and deducted from the pool of aliphatic carbon to obtain the adjusted concentration =
cal- co
The adjusted aliphatic carbon Cl,, needs to be further divided into CY and /3 types. The concentration of beta ~ consists of conhydrogens is given by H, = p W H X and
tributions from Yz, Y3,and Y5 3Yz + 5Y3 + 2Y5 = H ,
(2)
We now consider the two ratios of aliphatic groups a = YZ/Y3; b = Y 2 / Y 5 (3)
For any given coal, these ratios can be crudely estimated from pyrolysis data, namely the relative amounts of methane, ethane and ethylene produced. From ( 1 ) and (2), we obtain Yz = H p / [ 3 + 5 / + ~ 2/b] (4) Y3 = H,/[a(3 + 5 / a
+ 2/b)]
(5)
+ 5 / +~ 2 / b ) ] (6) Now, the @ carbon (including @+carbon) can be computed Y5 = H , / [ b ( 3
from the atomic balance 1 3
C, = Yz + 2Y3 + Y5 = H B The concentration of
LY
+ 2/a + l / b + 3/a + 2 / b
(7)
carbons is given by
Each LY carbon is connected to a peripheral aromatic carbon while the remaining three bonds are taken by various chains or bridges; hence Y1 + Yz + Y3 + Y4 + Y5 + Ys = 4Y1, (9) In this equation, all state variables other then Y4and Ya have already been determined. Y4is the concentration of ethylene bridges while Ye is related to the concentration of the methylene bridges (= Ys - Y13).As will be seen in the following section, the activation energy for the dissociation of ethylene and methylene bridges is approximately 50 and 70 kcal/mol, respectively. Hence, the distinction between these two types of bridges is very important kinetically. In the absence of specific information, the ratio Y4/ Ys can be treated as an adjustable parameter. Having assumed a value for Y4/Ys we can use (9) to determine Y4 and Y8 individually. The concentration Ylo of phenolic hydroxyls can be roughly estimated, as has been suggested by some authors, by assigning a fraction of about 0.5 to 0.6 of the total oxygen to phenolic groups. Alternatively, it can be estimated from experimental data on the amount of “chemical” water produced in pyrolysis. The concentration Y14 of aromatic nuclei is yet to be specified. Presently available techniques do not provide direct information; hence this concentration is best treated as an adjustable parameter. However, the range of possible values of Y14 is constrained by the characteristics of the average unit and by the degree of cross-linking of coal. (i) The aromatic units have been assumed to be identical and have an average composition, including heteroatoms. The concentration of aromatic carbons is given by already specified quantities
Likewise, the concentration of peripheral aromatic carbons is also known, being the sum of phenolic hydroxyls, carboxyl groups, aromatic carbon to a-carbon bonds, and aromatic hydrogens Therefore the ratio of peripheral to total aromatic carbons is specified: u = C,,/C,. The value of the parameter u
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981 117
allows a rough estimate of the ring size by comparison with known compounds. For benzene, naphthalene, and phenanthrene, u = 1,0.8, and 0.714. Intermediate values of u can be interpreted as corresponding to mixtures or can be attributed to other aromatic rings such as indene, or to the presence of heteroatoms. Once the range of possible ring size has been established by u, one can find a corresponding range for Y14 via the number of aromatic carbons per nucleus, C,/ Y14.The two structural parameters u and C,/Y14 increase with increasing coal rank. (ii) The number of bridges per unit, nb = ( Y 4 / 2+ Ys Y 1 J /Y14, has a very important effect on the amount of tar formed in pyrolysis. Hence, the value of YI4 should be chosen such that nb is in a reasonable range. Numerical calculations discussed later indicate that in bituminous coals, nb is in the range 1.5-3. Summarizing the above procedure, we have estimated the initial values of 11state variables (the remaining four are zero) from seven analytical measurements and four assumed values, for Yz/Y3,Yz/Ys, Y4/Ye, Y14.These four quantities can be treated as adjustable parameters or estimated, very crudely, from kinetic data. If additional analytical data are available, e.g., more detailed NMR data, the number of assumptions can be accordingly reduced.
Reaction Mechanisms and Kinetics Having chosen a set of functional groups to represent the structure of coals, we need to specify the thermal reactions of these groups in the temperature range 400-700 “C. Several sources provide valuable information for this purpose. Textbooks and monographs in organic chemistry, especially the chemistry of free radicals (Kochi, 1973; Nonhebel and Walton, 1974; Williams, 1960) discuss reaction mechanisms and provide limited kinetic information. While aliphatic radicals have been studied at high temperatures, benzylic and phenoxy radicals, believed important in coal chemistry, have been studied largely in solution at quite modest temperatures. Investigations of the thermal degradation of polymers (Parker and Winkler, 1967; Fitzer and Schaffer, 1970; van Krevelen, 1975) provide data of some relevance to coal pyrolysis. Finally, model compound studies (Jones and Neuworth, 1952; Lang and Buffleb, 1958; Heredy and Neuworth, 1962; Braekman-Danheux et al., 1977; Benjamin et al., 1978; Kamiya et al., 1979) have yielded important information about the dissociation of methylene, ethylene, and ether bridges and about the activating role of phenolic or alkyl substituents. Based on these sources of information, we have selected the set of reactions listed in Table 11. Although extensive, the adopted set of reactions is by no means exhaustive. Certain reactions have been omitted because they appear unimportant in the temperature range 400-700 “ C , but they should probably be considered at higher temperatures. These include the formation of hydrogen and carbon monoxide accompanied by fusion or rearrangement of aromatic rings. Carbon monoxide is known to evolve from phenolic, ring, or ether oxygen, although the reaction mechanism has not been delineated. Two other classes of reactions were omitted for the sake of simplicity, although they are known to occur in the temperature range 400-700 “C. One class is the addition of small radicals H, CH3, C2H6to aliphatic double bonds. While such double bonds are absent in the parent coal, they are formed during pyrolysis. The second class of reactions involves the dissociation of ether bonds such as Ph-0-Ph’, Ph-0-CH2-Ph’, and Ph-O-CH3. The importance of ether bonds has been documented by Whitehurst (1978), Imuta and Ouchi (1973), and Wachowska (1979) among others. The first type of such bonds has been
included as a state variable, but the other two should also be included along with the phenoxy radicals produced from the dissociation reactions Ph-0-Ph’ Ph-0. Ph’. Ph--O. + Ph’--CHy Ph-0-CHZ-Ph’ Ph-0. + CH3. Ph-O-CHS
-
+
+
4
These three reactions have activation energies comparable to 6,5, and 1-3, respectively, on account of the resonance stabilization of the phenoxy radical. Thermodynamic and kinetic information about phenoxy radicals in solution has been reviewed by Mahoney and DaRooge (1975). Clearly, such reactions are more important in coals of high oxygen content. In any case, the addition to double bonds and the reactions of ether bonds and phenoxy radicals should be included in future applications of the model. Proceeding to reaction kinetics, we note that direct experimental data for the elementary reactions of interest are generally unavailable and recourse must be made to the thermochemical estimation methods developed over the years by Benson and co-workers (Benson and ONeal, 1970; Benson, 1976). These thermochemical estimation methods utilize group additivity and comparison with similar compounds for molecules and transition states. Such estimates, of course, are subject to considerable uncertainty but provide, at the minimum, a plausible range for the kinetic parameters. In the case of bimolecular reactions, an additional uncertainty exists due to the condensed nature of the reaction medium, in view of the fact that the estimated parameters refer to gas-phase kinetics. Two phenomena in the condensed phase are of particular importance, the cage effect (Herkes et al., 1969; Walling and Lepley, 1971) and the gel effect (Cardenas and ODriscoll, 1976). When free radicals are produced in pairs, a large probability exists that they will recombine before diffusing apart. This “cage effect” will be most pronounced in the dissociation of bridges, e.g.
I I I 1
Ph-C-C-Ph‘
-C
Ph-C*
I + Ph’-C* I I
I
Low mobility of the a radicals produced will result in recombination-almost a negligible probability in the gas phase. To take into account the cage effect in a simple manner, we have assumed that all bond dissociations that do not produce a volatile fragment have zero rate while dissociations that produce a volatile fragment have the rate given by gas phase kinetics, since the removal of the volatile fragment will effectively prevent recombination. The gel effect refers to the reduced probability of a bimolecular reaction in condensed phase due to limitations of proximity, orientation, alignment, etc. Thus, in the combination of two a radicals to form an ethylene-type bridge, the two groups should come to close proximity and attain proper orientation. These requirements amount to substantial restrictions on the reaction rate, considering that both groups are attached to bulky molecules. Similar restrictions apply to other reactions as hydrogen abstraction when both groups are in the solid phase. The gel effect has been approximately taken into account by using an activation energy characteristic of diffusion in the coal phase (the acd5vation energy for gas phase recombination is zero). Using the values reported in the literature and making some simple thermochemical calculations as needed, we have arrived a t a set of estimated values for the kinetic parameters, listed in Table 111. Detailed comments and examples of such calculations are given in the Appendix.
118
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
Table 11. Elementary Reactions of Coal Pyrolysis no. X reaction 1
2
no.
Bond Dissociation Producing Two Radicals H CH3
-
I I
Ph-
C -X
+
Ph-1.
X. (Y
22
I
5 6
reaction
21
'ZH5
4
X
\CNCH~ I I I Ph-C-C-Ph I I I Ph-C-Ph' I
I
I I
Ph-C.
- P h - 4 .I I
-
Ph-C-CH3
8
Ph-C-CHzCH3
9
Ph-C-CHZCH3
I
I .C-Ph' I
t
t *Ph'
I
4
I
Ph--C=CH2
t CHJ
I
Ph-C=CH&Hj
I
I
*C-Ph'
Ph-C-
-Ph'
H CH, CZH, H CH3 C,H.
30
H
31
CH3
Ph-C-
+
32
C,H,
(substituents on a carbon can be H, CH,, C P , )
X. t H,
---+
X. t Hp
XH
+
(Y
radical
XH t P radical
>CH t H, (P radical)
>CH, t a radical
Addition-Displacement
t H.
Ph-C=CH?
-
- 'I CI
/ /
t
23 24 25 26 27 28 29
Bond Dissociation Producing One Radical and One Double Bond
7
I I
Hydrogen Abstraction
\b-cHZiH2
-
Ph-C.
I
- Ph/Y'
ph/F-y2
Radical Recombination
H.
I 1
+
X.
-
t
PhX
I
.C-
I
I
I &CHZ I P h \ d ~CHZ I
10 33
H
11 X
12
-
Ph-i-i-ph'
I I
13 14
ph-r/ \
I I I CHZ-CHZ-CC
C-Ph'
*
B
15 16 17
Ph-C-X
I
I
Ph-C
I I
Ph-C-C-Ph'
I I
-
B
19
/I I
I Ph-C-Ph' I
-- Ph-C
Ph-C
36
H
37
CH3
Ph-C-Ph'
38
C,H,
(substituents on a carbon can be H,CH,, CZH,)
39
I/ I
I I
40
t *C-Ph'
II + *Ph' I
B
CHI
I
CH. C,&
t X.
(0 represents -CH, or >CH of) hydroaromatic structure R
18
-
T b
Ph+
34 35
~~
(substituents on c1 carbon can be H, CH3, CZH, 1
Ph-C=C-Ph
c&&'
x-
tx.-
41
I I
X.
-
I I
P h X t C-Ph'
Phenolic Condensation Ph-OH t HO-Ph' HZO t
Ph-OH
I I
H C 4 h '
-
-
Ph-0-Ph'
---f
I I
Ph-C-Ph'
t
t H$
Formation of Carbon Oxides Ph-COOH PhH t CO, 0
42
t
II
Ph-C-bl2
-
PhbiZ t CO
20
The values for the activation energies apply to single ring aromatics. Several of these activation energies, e.g., those for the dissociation reactions 1-6 should be reduced by 2-4 kcd (Stein et al., 1976) to account for the additional free radical stabilization due to condensed ring structures and by 2-5 kcal to account for phenolic, ether, and other activating substituents. The role of phenolic-OH in reducing the activation energy for H dissociation in 0- and p-cresol has been documented in the experimental studies of Jones and Neuworth (1952). The exact amount by which the activation energies of dissociation reactions need to be adjusted depends on the type of coal considered, especially
on its oxygen content. In Table I11 of part 2 we provide a set of recommended adjusted values for a high volatile C bituminous coal as well as the set actually used in the numerical calculations. Product Formation Before developing the quantitative aspects of the model, it is useful to discuss qualitatively the role of the reactions listed in Table I1 in the formation of various pyrolysis products. A concise representation of the interaction among the reactions and the pathways to product formation is given in Figure 3. Starting with bond dissociation,
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981 119
Table 111. Kinetic Parameters of Elementary Reactions at 800 K estimated values iog ( ~ i s - 1L)
no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
14.9 15.3 15.4 15.4 13.9 14.3 15.1 14.4 15.1 15.1 12.8 12.1 12.1 12.1 12.8 12.1 12.1 13.0 13.0 12.1 14.2 8.4 10.0 7.5 7.0 10.3 7.8 7.3
E , kcal/gmol 85.3 72.4 69.0 69.0 56.4 80.7 51.7 45.0 52.0 51.7 50.2 43.5 43.4 43.4 34.3 23.6 20.8 7.0 57.6 20.8 9.6 O 2.3 8.0 8.9 9.7 10.8 13.4 8.9 2.0 7.0 9.0 2.0 7.0 9.0 2.0 7.0 9.0
BON BON BON BON E E E E
E E E E E B B
z
7.0 E 10.4 M 7.8 M 7.3 M 10.4 M 7.8 7.3 10.4 7.8 7.3
'-1 I
I
t
1
I Double Bonds I
51 I
I I
kT I
El I ~
I
I I
I
Y
I
Alpha and Beta R a d i c a l s (Coal Phase)
FCJ
Figure 3. Mechanism of product formation.
we note that reactions 1-3 and 7-18, 21 provide the mechanisms for the formation of hydrogen and lower paraffins. The contributions of these two groups are comparable, for while (7-18, 21) have larger rate constants, their rates are proportional to concentrations of free radicals. Reactions 5 and 6 constitute the main mechanism of tar formation, 5 being significantly faster than 6. A smaller amount of tar is formed by reactions 19 and-36-38. Not all dissociations lead to tar formation since the fragments produced may or may not be volatile. If not, the pair of radicals most likely recombines because of the cage effect. The probability that a dissociation results in a free unit
E E E
reference or estimation method BON: Benson and O'Neal(l970) E: estimated by group additivity by analogy with 3
E E E E E
A factor assumed same as in 7 same parameters as in 7
E
E E E E E E E E Z
z
E B B Z E M M M
by analogy with 7 , 8 A factor assumed same as 12 assumed same as 13 A factor by analogy with 11-13 A factor by analogy with 11-13 A factor by analogy with 11-13 A factor by analogy with 5, 15 A factor by analogy with 4, 15 by analogy with 17 Z : Zavitsas and Mellikian (1975) B: Benson (1976)
M: miscellaneous sources by by by by by by
analogy with analogy with analogy with analogy with analogy with analogy with
30 31 32 30 31 32
depends on the number of bridges present and therefore declines with the progress of pyrolysis. Once a volatile fragment is formed, its removal from the coal particle depends on the rate of transport relative to the rate of recombination with sites in the condensed phase. A qualitative discussion of transport processes is given in the next section. If we stoichiometrically combine reactions 1-21 and 23-38, we find that the formation of a small molecule (H2, CHI, etc.) is accompanied by the formation of two free radicals in the condensed phase, or a double bond. The free radicals could recombine by reaction 22 to form a new bridge. The double bonds formed are located either on ethylene bridges, rendering them unbreakable, or on the hydroaromatic groups. The resulting increase in the number of bridges, especially the unbreakable bridges, decreases the potential for tar formation. However, the double bonds formed on the hydroaromatic groups do not contribute to this increase is cross-linking. These considerations underline the importance of hydroaromatic structures in donating hydrogen to various radicals, without a simultaneous increase in cross-linking. Another set of reactions that contributes to cross-linking and hence suppresses tar function is phenolic condensation (40,41). These reactions account to some extent for the small yield of tars from coals having a high oxygen content. Summarizing the above mechanisms, we can view the pyrolysis process as a collection of bond-breaking and bond-making reactions, along with an incessant internal hydrogen transfer. Volatile products and residue char arise from the same original structure. Hence, the traditional
120
Ind. Eng. Chem. Fundam., Vol. 20,No. 2, 1981
ill)
i
DCH3+ 'D 0
0
Figure 4. Mechanism of addition-displacement reactions.
distinction between volatile and nonvolatile parts of coal is of little chemical significance.
The Role of Transport Processes The main question relative to heat transfer is whether or not the temperature is uniform within a single coal particle. The situation clearly depends on particle size and final temperature and to a smaller extent on the heat of pyrolysis which may vary with the type of coal. According to some calculations reported by Anthony and Howard (1976), particles below 500 pm do not sustain significant internal temperature gradients at heating rates of 1000 OC/s or lower. These conditions are sufficiently broad for our purposes so that the particles will be assumed isothermal. Intraparticle mass transfer influences the course of pyrolysis under a wide range of conditions, as manifested by the dependence of product distribution on pressure and particle size. Coal possesses a wide pore size distribution includin micropores (4-12 A diameter), transitional pores (12-300 ), and macropores (>300 A). In a previous paper (Gavalas and Wiks, 19801, we examined the effect of mass transfer in the transitional pores and macropores. This effect is relatively modest, but its quantitative description is very difficult in the framework of a detailed chemical model. The mathematical model that we formulate in part 2 neglects the effect of mass transfer limitations in the transitional pores and macropores. The volume of the coal that does not belong to macropores or transitional pores constitutes the condensed phase proper. This volume is penetrated by micropores in which diffusion is activated and depends very strongly on the molecular size of the diffusing molecule. Products formed in the condensed phase can be removed only by diffusing to the surface of transitional pores and macropores. During this activated diffusion process, the volatiles are subject to reaction with the coal matrix with a probability that depends on the relative rates of diffusion and recombination. Small radicals like H, CH3, and C2H5 are highly reactive and will almost surely react by addition or hydrogen abstraction. Small permanent molecules such as HP, CH4, CO, and H 2 0 have low reactivity but relatively large diffusion coefficient, due to their small size. It will be consequently assumed that their rate of formation is not subject to diffusional limitations. The last class of molecules includes the aromatic nuclei with their peripheral groups that became free following a dissociation reaction. These "tar" molecules have a size around or in excess of 10 A. In the form of free radicals, they can react by recombination with free radical sites on or by addition to aromatic clusters on the condensed phase. As saturated molecules they can also react by an addition reaction. The tar molecules are therefore subject to strong diffusional limitations on account of both their size and reactivity. To account for the detailed diffusion and reaction of tar molecules in the condensed phase requires the introduction
1
of concentration gradients which would severely complicate a quantitative description. Clearly, however, a tar molecule can escape to the pore space only if it is produced in close proximity to the surface of transitional pores and macropores. If produced in the interior of the condensed phase, these molecules will quickly recombine. Based on these considerations, we propose to use an empirical factor X, treated as an adjustable parameter, such that if r is the rate of generation of undissociated tar molecules in the condensed phase, Xr is their actual rate of production. The exact way that X is used in the formulation of the differential equations is described in part 2. Acknowledgment This work was supported by the National Science Foundation under Grant No. AER 74-12161. Appendix. Estimation of Kinetic Parameters Most of the parameter values in Table I11 were estimated; the remaining ones were taken from various sources as indicated. The estimation of E and A was made by group additivity and transition state theory, respectively, by use of the techniques and the data of Benson (1976). The calculations for several reactions were simplified by comparison with related reactions. We provide three examples of the estimation techniques used. Reaction 2. Our estimates assume gas-phaee conditions. The activation energies of the reaction and ita reverse are related by E - E' = AH. Since the reverse (free-radical recombination) has zero activation energy, E = AH. The heat of the reaction can be estimated by group additivity. Considering Ph-CH2CH3 --* PH-CH2CH3 + CHy and using the notation of Benson (19761, we have AH = [CH,*] -I-[C*-(H),(CB)]- [C-(H)&C)I [C-(H)2(C)(CdI where brackets indicate the heat of formation at 300 K. Substituting the values given by Benson (1976), we obtain AH = 34.3 + 23.0 - (-10.2) - (-4.9) = 72.4 The difference in heat capacities for these dissociation reactions is very small, therefore, we can take E = 72.4 kcal at 800 K. The A fador is given by the transition theory expression kBT A = eexp(ASo*/R) h where ASo* is the activation entropy, Le., the entropy difference between the transition state and the reactant. This difference can be decomposed to contributions from various degrees of freedom. At 800 K these are estimated as follows. translation rotation internal rotation about Ph-CH, bond (barrier 15 --3 2 kcal) internal rotation about CH,-CH, bond (barrier 3 -+ 0 kcal) C-C stretching mode 1000 cm'' -+ reaction coordinate four bending modes 700 cm-' --+ 220 cm-'
0 negligible -2.1 0.4
-1.1
10.4 AS"+ =
7.6
logA = 15.3
-
Reaction 7. Ph-CH-CH3 Ph-CHECHz + H* Again, E - E' = AH. The heat of reaction can be estimated by group additivity
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
+ [Cd-(H)21 + [cd-(H)(c~)I[C-(H)3(C*)I- [c*-(H)(c)(c~)l= 52.1 + 6.26 6.78 - (-10.08) - 24.7 = 50.5 kcal
= [Hal
+
The activation energy E’ must be sought from experimental data. For the aliphatic analogue H. + CH&H&H=CH2 CH3CHZCHCH3 Kerr and Parsonage (1972) list the experimental value E’ = 1.2 kcal. For lack of other information we assume the same value for the reverse of reaction 2. The resulting E is 50.5 + 1.2 = 51.7 kcal. The entropy of activation can be estimated by analogy with the aliphatic analogue CHB-CH-CH3 CH3-CH CH2 H +
+
0..
for which the experimental value of Benson and O’Neal (1970) is log A = 14.3 at 500 K. The essential difference between the activation entropies of reaction 7 and its aliphatic analogue is due to the difference in the internal rotations about the bonds Ph-CH and CH3-CH, respectively. Making an adjustment for this difference we estimate for reaction 7 log A = 14.8 at 500 K and log A = 15.1 a t 800 K. Reaction 23. Ph-CH3 H. Ph-CH2. + CHd
+
+
The value for E listed in Table 111was taken from the data listed by Zavitsas and Melikian (1975). The A factor for a bimolecular reaction is given by
T A = $ - -R T ~ B exp(ASos/R) Po h where p o is 1 atm. The entropy of activation is by definition ASo = So’ - SO(PhCH3) - So(H.) where So*is the entropy of the transition state Ph-CH2-. H H. The difference So* - So(Ph-CH3) is analyzed to various components as follows.
...
rotation negligible spin ( 2 + 1) R In 2 internal rotation about Ph-C -1.3 bond (barrier 0 + 7.5 kcal) loss of a symmetry factor of 3 R In 3 C-H stretch + -0.1 reaction coordinate new H . * H stretch (2800 cm“) 0.1 two new H . . . H . . . C bends 2.2 (1000 cm-’) two H-C-H bends (1400 cm-’ ) 1.0 --fH.C-H bends (1000 cm-’) S o * -S”(Ph-CH,)= 5.5 9
From the tables So(H.) = 32.3 so that ASos= -26.8 and log A = 10.0. An introduction to the limited literature on additiondisplacement reactions (30)-(38) can be bound in the work of Szwarc and Binks (1958) and Williams (1960). The mechanism of these reactions involves a cyclodiene intermediate as shown in Figure 4. Hydrogen addition has not been studied as such because of difficulties in producing protons in solution, but the reaction should be quite rapid. Although such reactions have not been previously considered in connection with coal pyrolysis, they are energetically favorable and very likely to proceed quite readily, in competition with hydrogen abstraction reactions. Reaction (i) has the interesting effect of producing a C3 hydrocarbon which could not be produced by any of the previous reactions from the postulated structure (-CzH5 is the largest substituent on (Y carbon). Likewise,
121
(ii) is important as a low activation route for the dissociation of methylene bridges. Most of the kinetic information available concerns relative rates. It is well established, for example, that the rate of addition increases with the size of the aromatic cluster (benzene:phenanthrene:anthracene = 1:27:820, Szwarc and Bink, 1958). Benson (1976) estimates that the activation energies are in the range 0-8, probably close to 8 for CH3, C2H5and smaller for H. No information has been provided about A factors. Szwarc (1948) observed that the ratio of methane to hydrogen in the products of toluene pyrolysis at 750 OC was 0.67. The primary step in this reaction is the dissociation of an H atom from the methyl group. The H atom can produce H2 by H abstraction or add to the ring to form CH3, which in turn abstracts an H to form CHI. Thus, k d d / k a k = 0.67. Taking log Aabb = 11.1,Eebb = 10 and End& = 5 we find log And&= 9.9. To take into account the larger rings, this number is multiplied by 20. For the addition of CH3., C2H5. we very crudely estimate E = 8 and log A = 8.2, whence the values of Table 111. Literature Cited Anthony, D. B.; Howard, J. B. AIChE J. 1878, 79, 625-656. Anthony, D. B.; Howard, J. B.; Hottei, H. C.; Meissner, H. P. “Fifteenth Symposium (Internatlonai) on Combustion”, The Combustion Institute: Pittsburgh, PA, 1975, p 1303. Bartie, K. D.; Martin, T. G.; Williams, D. F. Fuel1875, 5 4 , 226-235. Benjamin, B. M.; Raaen, V. F.; Maupln. P. H.; Brown, L. L.; Collins, C. J. Fuel, 1878, 57, 269-272. Benson, S. W. “Thermochemical Kinetics”, Wiley: New York, 1976. Benson, S. W.; ONeal, H. E. “Kinetic Data on Gas phase Unimolecular Reactions”, NSRDSNBS 21, 1970. Braekman-Danheux, C.; Delanois, C.; Quyen, N. C. Fuel Process Technol. 1877, 1 , 57-64. Brown, J. K.; Ladner, W. R. Fuell880, 39, 87-96. Cardenas, J. N.; ODriscoil, K. F. J. Polym. Scl. 1878, 74, 883-897. Cheong. P. H., Ph.D. Thesis, California Institute of Technology, 1976. Cheong. P. H.; Oka, M.; Gavalas, 0. R., paper presented at the NSF workshop on the Fundamental Organic Chemistry of Coal, Knoxville, 1975. Deno, N. C.; Greigger, B. A.; Stroud,S. 0. Fuel1878, 5 7 , 455-459. Farcasiu, M. Fuel 1877, 56, 9-14. Fitzer, E.; Schafer, W. Carbon 1870, 6,353-364. Friedman, S.; Kaufman, M. L.; Steiner, W. A.; Wender, I.Fuel 1881, 40, 33-45. Gavalas, G. R.; Wiiks, K. A. AIChE J. 1880, 26. 201-212. Gerstein, B. C.; Chow, C.; Pembieton, R. G.; Wilson, R. C. J. phys. Chem. 1877, 8 7 , 565-570. Given, P. H. Fuel 1860,39, 147-153. Given, P. H. Fuel 1881,40, 427-431. Heredy, L. A.; Neuworth, M. B. FueI1882, 47, 221-231. Heredy, L. A.; Kostyo, A. E.; Neuworth, M. B. Fuel1885, 44, 125-133. Heredy, L. A.; Kostyo. A. E.; Neuworth, M. B. ACS Mnogr. 1888, No. 5 5 . Herkes, F. E.; Friedman, J.; Bartieft, P. D. Int. J. Chem. Klnet. 1988, 1, 193-207. Ignasiak, B. S.; Gawlak, M. Fuel 1877, 5 6 , 218-222. Imuta, K.; Ouchi, K. FueIl873, 5 2 , 174-180. Jones, B. W.; Neuworth, M. B. Ind. Eng. Chem. 1852, 44, 2872-2876. Juntgen, H.; van Heek, K. H., paper presented to the meeting on coal fundamentals, Stoke Orchard, 1977. Kerr, J. A.; Parsonage, M. J. “Evaluated Kinetic Data on Gas Phase Addition Reactions”, Butterworths: London, 1972. Kobayashi, H.; Howard, J. B.; Sarofim, A. F. “Sixteenth Symposium (International) on Combustion”, The Combustion Institute: Pittsbwgh, PA, 1977; p 411. Kochi, J. K., Ed. “Free Radicals”, Voi. 1 and 2, Wiiey: New York, 1973. Lang, K. F.; Buffieb, H. Chem. Ber. 1858, 9 7 , 2866-2870. Larsen, J. W.; Kuemmerle, E. W. Fuel1878, 5 5 , 162-169. Lowry, H. H., Ed. “Chemistry of Coal Utilization”, Wiiey: New York, 1963. Maciei, G. E.; Bartuska, V. J.; Miknis. F. P. Fuel1978, 58. 391-394. Mahoney, L. R.; De Rooge, M. A. J. Am. Chem. SOC. 1875, 9 7 , 4722-4731. Nonhebel, D. C.; Waiton, J. C. “Free Radical Chemistry”, Cambridge University Press, 1974. Painter, P. C.; Coleman, M. M. FueIl879, 58, 301-308. Parker, J. A.; Winkier, E. L. “The Effects of Molecular Structure on the Thermochemical Properties of Phenolics and Related Polymers”, NASA Report NO. TR R-276, 1967. Pitt, G. J. F ~ e l 1 8 8 2 ,4 7 , 267-274. Reideibach, H.; Summerfield, M. Prepr. Dlv. FuelChem., Am. Chem. Soc. 1875. 20(1), 161-202. Retcofsky, H. L.; Friedei, R. A . 6 ~ u e / 1 8 8 848, , 487-498. Sarofim, A. F.; Beer, J. M.. Seventeenth Symposium (International) on Combustion”, The Combustion Institute: Pittsburgh. PA, 1979, p 189. Solomon, P. R. Prepr., D/v. Fuel Chem., Am. Chem. Soc. 1878, 24(3), 154- 159. Solomon, P. R.; Coiket. M. B. “Seventeenth Symposium (International) on Combustion”, The Combustion Institute: Pittsburgh, PA, 1979. p 131. Speight, J. G. Appl. Spec. Rev. 1871, 5 , 211-264.
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Ind. Eng. Chem. Fundam. 1981, 20, 122-132
Stein, S.; Golden, D.; Benson, S.; Shaw, R., paper presented at the Coal Chemistry Workshop, Stanford Research Institute, Aug 1976. Suuberg, E. M. sc.D. Thesis, Massachusetts Institute of Technology, 1977. Suuberg, E. M.; Peters, W. A.; Howard, J. B. Ind. Eng. Chem. Process Des. Dw. 1978, 17. 37-46. Szwarc, M. J . Chem. fhys. 1048, 16, 128-136. Tingey, G. L.; Morrey, J. R. Batteiie Energy Program Report, Battelle, Pacific Northwest Laboratories, 1972. van Krevelen, D. W. f o @ m r 1975, 76, 615-620. Walling, C.; Lepley, A. R. Inf. J. Chem. Kinet. 1971, 3 , 97-104.
Wachowska, H. Fuel1979, 58, 00-108. Whltehurst, D. D. ACS Synp. Ser. 1978, No. 71. William, G. H. "Homolytic Aromatic Substhution”, P w ~ m W York, 1960. Yokohama. S.; BOdiiy, D. M.; Wiscw. W. H. FUel1979, 58, 162-170. Zavksas, A. A.; Meliklan, A. A. J. Am. Chem. Soc. 1975, 97. 2757-2763.
Received for review May 27, 1980 Accepted January 5,1981
Model of Coal Pyrolysis. 2. Quantitative Formulation and Results George R. Gavalas,’ Ravl Jaln, and Paul How-Kel Cheong Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, Callfomla 91 125
The reaction rates are expressed in terms of concentrations of reactive conflgurations whlch are calculated by randomly distributing the functional groups among the a carbons. The probability of formation of a free unit (tar molecule) following a bridge dissociation is ca!culated by a similar random placement technique. The rates of change of the state variables and the rates of product formation are expressed in termq of the various reaction rates and the rate of loss of free units. Computer simulations are carried out for an hvc bituminous coal and a subbituminous coal and the results are compared with limited experimental data. A sensitivity analysis is carried out to study the importance of various structural and kinetic parameters relative to the yield of various products.
Introduction In part 1, we proposed a representation of coal as a collection of functional groups and suggested a set of free radical reactions to describe chemical change during pyrolysis. The mechanism of formation of gases, tar,and char was explained in terms of these reactions. In this part, we formulate a mathematical model for quantitative description of the kinetics of coal pyrolysis. Following the general formulation, simulation results will be presented for the pyrolysis of two coals. Compared to modeling other free radical reaction systems (e.g., pyrolysis of hydrocarbons), the modeling of coal pyrolysis involves three additional complications: (i) rate expressions for the reactions are complicated because the reactants are not individual molecules but combinations of functional groups on the coal matrix (Table 11, part 1); (ii) the concentrations of functional groups change due to reactions and due to loss with departing volatile products; (iii) complications arise due to the fact that reactions occur in the condensed phase; for example, products of dissociation may undergo recombination before escaping the condensed phase. In the following sections we present methods developed to deal with the above difficulties. Then we proceed to formulate the differential equations and obtain numerical results for two coals. Reactive Configurations and Reaction Rates In part 1we defined a set of state variables representing the concentrations of various functional groups and certain reIated quantities and developed a procedure for calculating the initial values of the state variables from analytical data. In this section we first illustrate the difficulty in relating the state variables to reaction rates and then proceed to develop techniques to overcome this difficulty. Consider the methyl group in the two molecules PhCH2CH3,Ph-CHCH,. Only the first molecule can dissociate to produce a CH3-radical (reaction 2 in part 1). The 0196-4313/81/1020-0122$01.25/0
carbon-carbon bond in the second molecule cannot dissociate because of the unpaired electron on the a carbon. Dissociation is also impossible when the a carbon po&sesses a double bond. To calculate the rate of production of methyl radicals by dissociation, we need to determine the fraction of methyl groups which are attached to a carbons which have no radicals or double bonds. The total concentration Yz of methyl groups cannot be used directly in the rate expression. Similarly, to compute the rate of double bond formation, reaction 7, the concentration of CY carbons with a methyl group and an unpaired electron has to he computed. Yet another example is bridge dissociation, reaction 5, where we need the number of combinations of two a carbms, each of which participates in an ethylene bridge but has no radical or double bond. Evidently, a scheme is needed to distribute functional groups, including radicals and double bonds, to a carbons in order to compute the concentrations of various combinations of functional groups. These combinations, termed reactive configurations, will be the “molecules” participating in reactions. The scheme developed here is based on random distribution. In the absence of information on any naturally preferred arrangement of functional groups, random distribution is a reasonable approach. Moreover, the initial distribution derived from the coalification process will tend to become randomized by successive dissociation, recombination, and addition reactions. Under the scheme proposed, the functional groups are first classified into five categories and then randomly distributed in groups of two’s or three’s to a carbons. The five categories are represented by the following auxiliary variables: MR,concentration of a radicals; MD,concentration of double bonds-double bonds on chains and double bonds on bridges; Mp,concentration of methylene bridges; MH,concentration of hydroaromatic structures, including those bearing radicals; and MG,sum of concentrations of CY hydrogens, methyl and ethyl groups (including 0 1981 American Chemical Societv
