Chapter 21
Supercritical Fluid Science and Technology Downloaded from pubs.acs.org by UNIV OF MELBOURNE on 04/20/19. For personal use only.
Kinetic Model for Supercritical Delignification of Wood 1
2
Lixiong Li and Erdogan Kiran
Department of Chemical Engineering, University of Maine, Orono, ME 04469
A reaction-diffusion model for delignification of red spruce by supercritical methylamine-nitrous oxide mix tures has been developed. The overall model has the form: l.5
-d[X]/dt = k {[X][S] } - k {[X] -[X]} 1
2
0
where [X] and [ X ] are the weight fraction of lignin in wood at time 0 and t, [S] is the weight fraction of methylamine in the extraction fluid, k and k are the rate constants for chemical reaction and diffusional resistance, respectively. The model has been shown to predict the experimental data over a wide range of tem peratures (from 170 to 185°C), pressures (from 172 to 276 bars) and compositions (from 0 to 100% methylamine). The temperature and pressure dependence of the rate constants k and k have been determined and are discussed in terms of activation energies and volumes of activation. 0
1
1
2
2
Supercritical fluids display attractive solvent characteristics which can be manipulated by either the pressure or temperature. Using supercritical fluids as reaction media, simultaneous reaction and separation are also achievable. This methodology has recently been applied to the reactive separation of wood constituents, espe cially lignin, by supercritical fluids (1-4). Delignification processes using supercritical fluids are of potential industrial importance (5,6) and there is a need for the development of kinetic models which could permit a priori prediction of the rate of lignin removal. The present paper discusses such a model. 1
Current address: Center for Energy Studies, Separations Research Program, The University of Texas, 10100 Burnett Road, Austin, TX 78758 Address correspondence to this author.
2
0097-6156789/M06-O317$06.00/0 ο 1989 American Chemical Society
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Development of K i n e t i c Model General Considerations. Any k i n e t i c model that describes d e l l g n 1ficat1on of wood by s u p e r c r i t i c a l f l u i d s must take Into account the factors related to the structure of wood, the heterogeneous nature of the r e a c t i o n , and the factors associated with high pressure reaction k i n e t i c s . Wood 1s a porous material composed of elongated hollow c e l l s ( f i b e r s ) which are held together by the middle lamella (an I n t e r c e l l u l a r substance containing mostly H g n l n and pectlc substances). The c e l l wall displays a layered structure and contains d i f f e r e n t amounts of the major wood components, c e l l u l o s e , hem1eel l u i oses and l i g n i n . Even though middle lamella has the highest I1gn1n concentration, the majority of I1gn1n (about 70-80%) 1s located 1n the c e l l walls ( 7 , 8 ) . Thus, for complete H g n l n removal, chemicals must penetrate and react through the c e l l w a l l . From a consideration of typical c e l l dimensions for a softwood tracheld (3 mm length, 0.03 mm width, 4 urn c e l l wall thickness), 1t can be calculated that the Inner surface area of the c e l l wall 1s about 10,000 times larger than Its cross sectional area and hence provides the primary surface for reaction and d i f f u s i o n during delignification. D e l i g n i f i c a t i o n can be treated as a f l u i d - s o l i d reaction occurring at the c e l l wall Interface. It may be e n v i sioned to proceed through steps Involving (1) d i f f u s i o n of reactants from the bulk of the f l u i d phase to the c e l l wall Interface; (2) d i f f u s i o n of the f l u i d from the Interface to the bulk of the c e l l w a l l ; (3) chemical reaction between the reactants from the f l u i d phase and I1gn1n 1n the c e l l w a l l ; and (4) d i f f u s i o n of products within the c e l l wall and f i n a l l y out of the c e l l wall Into the bulk of the f l u i d phase. R e a l i s t i c models of d e l i g n i f i c a t i o n should also consider s t r u c tural changes, 1n p a r t i c u l a r changes 1n porosity of wood accompanying H g n l n removal. General k i n e t i c models which consider such changes for s o l i d reactions (9,10) require parameters such as the change 1n d i s t r i b u t i o n of pore sizes with reaction which are d i f f i c u l t to access. It turns out that often many complex heterogeneous reactions can be g l o b a l l y described by simpler models. For example, d e l i g n i f i c a t i o n reactions 1n conventional pulping such as kraft pulping (which Involves NaOH and Na2S as cooking chemicals) are usually treated by a simple relationship of the form: - d L / d t - kL
(1)
where L 1s the residual H g n i n content at time t (calculated on the o r i g i n a l wood weight, wt %), and k 1s the apparent rate constant (11-13). This 1s a pseudo-first-order rate equation with respect to H g n l n under the assumption that a l k a l i concentration 1n the cooking liquor does not change s u b s t a n t i a l l y . A l l the factors associated with any structural changes (such as porosity) have been combined 1n the apparent rate constant (k). C l e a r l y , such global relationships are of limited use for an understanding of the d e t a i l s of the actual reaction process, espe-
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Kinetic Modelfor Supercritical Delignification of Wood
LI A N D KIRAN
dally the dlffuslonal effects which may change significantly as the reaction proceeds. In the treatment of dlffuslonal factors 1n condensed phase reactions, the rate of reaction between reactants A and Β can be explicitly expressed by a chemical reaction term and a diffusion term (14), such as: -8CA/8t - K
2
A
2
- DA3 CA/9r
(2)
where C/\ 1s the concentration of A which 1s a function of the dis tance from the origin of coordinates 1n the direction of diffusion (r) and time (t). K/\ 1s the rate of change of CA caused by the chemical reaction and DA 1S the diffusion coefficient of A. If this rate equation were used to describe the conventional kraft delignification reaction, one could represent the I1gn1n 1n wood as reactant A and cooking liquor 1n lumen (cell cavities) as reactant B. Since the diffusion of lignin 1n wood can be neglected, DA would be zero. If the delignification reaction can be assumed to occur at the interface and follow a first-order kinetics with respect to I1gn1n, that 1s KA • kCA. then, 1t 1s easy to see that Equation 2 reduces to Equation 1. However, there is a subtle dif ference between the two rate equations. In Equation 1, L 1s the residual I1gn1n content based on Initial wood weight (wt %) which 1s an averaged value of the lignin throughout the cell wall (bulk solid phase). In Equation 2, CA 1S the I1gn1n concentration at the interface where delignification reaction takes place. Because of the experimental difficulty of obtaining positional and time dependent variation of I1gn1n concentration at the interface, Equation 2 can not be conveniently used for kinetic modeling of delignification. In the present model, our approach has been to take the simplicity of Equation 1 and combine 1t with the notion of Including a term which would represent dlffuslonal factors in a way similar to Equation 2, but involving more readily accessible quantities. Before discussing the present model, it 1s Instructive to exam ine also some aspects related to the pressure dependence of the reactions. As 1s well known, at low pressures, the rate constant k 1s considered to be a function of temperature only, and Its temper ature dependence 1s expressed by the Arrhenlus equation: Ink « InA - E/RT
(3)
or equlvalently, 2
dlnk/dT « E/RT
(4)
where A 1s the frequency or pre-exponent1al factor, Ε 1s the acti vation energy, R 1s the gas constant, and Τ 1s the absolute temperature. When a reaction takes place under high pressures, however, the effect of pressure on the reaction rate may not be neglected. The description of the pressure dependence of reaction rates (15) 1s based on the assumption that the reaction goes through a transition state Involving a volume change between reactants and the transi-
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tlon state complex. The pressure dependence of rate constants Is expressed 1n a form similar to the Arrhenlus relationship (16-19) which 1s given by: [dlnk/dP] - -AV*/RT
(5)
T
where ΔΥ* 1s the "volume of activation" and represents the volume change accompanying the formation of the transition state, (the difference between the partial molar volume of the transition state and the sum of the partial molar volume of the reactants): #
AV - ( Vtransltion state) - Σ( V ctant) rea
(6)
A task 1n high pressure kinetics 1s the determination of either volumes of activation or empirical relations of k as a function of pressure for specific reactions (20-23). Many functional forms relating k and Ρ have been used for specific systems (17,24). A common form 1s the second order polynomial relationship, I.e.: Ink - α + βΡ + γρ2
(7)
where α, 3, and γ are constants to be determined. From Equation 5 and Equation 7, one then obtains a linear relation of AV* with pressure: âV* - AV *-2YRTP 0
(8)
where ΔΥ * represents the volume of activation at Ρ « 0 and 1s Independent of pressure. 0
Formulation of the Present Kinetic Model. The starting point of our model for supercritical delignification 1s the assumption that the reaction 1s heterogeneous and occurs primarily at the surface of the cell wall. After the reactive supercritical fluid reaches the Interface (the surface of the cell wall), reactions with I1gn1n are assumed to occur at numerous locations on the surface of the cell wall. As the delignification reaction proceeds, the reaction areas are envisioned to develop as pores into the cell wall, lead ing to longer diffusion paths which can result 1n greater "diffusion resistance" for the fluid to penetrate further Into the cell wall to react with remaining lignin. The size, shape, and distribution of these pores would largely depend on the original distribution of I1gn1n in the cell wall, and the selectivity of the delignification reaction, i.e., the extent of removal of components other than I1gn1n from the cell wall. Unless the pore openings are excessively large, one would anticipate greater diffusion resis tance as delignification proceeds. Longer path length will also present a diffusion resistance for removal of the solubillzed lignin. To Include a diffusion resistance term 1n the rate equation, one can assume that the dlffuslonal resistance would be propor tional to the diffusion path which as discussed above would be related to the amount of lignin that has been removed from the cell
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Kinetic Moddfor Supercritical Delignification of Wood
LIANDKIRAN
wall matrix. We therefore propose the following form of the rate expression to describe rate of delignification: -d[L]/dt » ki[L]-k (CL]o-CL])
(9)
2
where [L] and [L] are the I1gn1n concentrations 1n wood at time 0 and t, respectively, kj 1s the rate constant for chemical reaction, and k 1s the overall rate constant for the change 1n the diffusion resistance. The first term 1n this rate equation accounts for the chemical reaction which Is assumed to be first-order Irreversible. The second term accounts for the diffusion resistance which makes a negative contribution to the overall rate. The observed delignification rate 1s thus regarded as the net result of reaction and diffusion processes. The rate constant for chemical reaction, k\ would be a function of temperature and pressure. The other constant (k may be a function of parameters such as d1ffus1v1ty and thickness of diffusion layer and encompasses the structural changes such as the porosity of wood cell wall which Increases with Increasing value of ([L] -[L]). It should be noted that because of the completely different nature of ki and k , the [L] terms cannot be combined and Equation 9 cannot be reduced to a simple first order relationship. I t should be further noted that the model considers the reaction and diffusion processes after the supercritical fluid reaches the cell wall surface. Thus, the Implication of Equation 9 that at time zero there 1s no dlffuslonal resistance should be Interpreted to mean that no pores 1n the cell wall (as a result of I1gn1n removal) have yet been generated and the fluid 1s simply reacting with the I1gn1n distributed on the outer surface layer of the cell wall. Since I1gn1n content 1n wood 1s normally expressed on weight basis, lignin concentration can be more appropriately expressed as: 0
2
9
2
0
2
[L]
- N /W - ( W / M ) / W L
0
L
L
0
- [X]/M
L
(10)
where NL 1S the number of moles of I1gn1n in wood at time t; W 1s the weight of Initial wood sample; W_ j and ML are the weight and average molecular weight of the residual lignin 1n wood sample at time t, respectively; and [X](=W|_/W) 1s the Hgnln weight fraction at time t based on initial wood. Since the molecular weight of native lignin 1n wood 1s not known (no method to Isolate native Hgnin from wood without degradation has yet been found) and since during the course of degradation ML 1s continuously changing, evaluation of [L] directly from Equation 10 1s difficult. Therefore, an Indirect approach is suggested to express [L]. Because lignin molecules are made from many phenylpropane units which are Inter-connected by aryl-ether bonds (about two thirds of total bonds) and carbon-carbon bonds, a del1gn1fy1ng agent can attack many sites of the same Hgnln molecule according to the distribution of a particular type of bond 1n the molecule. I t would appear that the concentration of the reactive sites available in Hgnin molecules 1s a more appropriate parameter than the concentration of Hgnin molecules as a whole. Thus a convenient way to express lignin concentration 1n wood would be: 0
0
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[L]rs
«
N
R S
/W
(11)
0
where N represents the total number of relative sites available 1n the Hgnln molecule and [ L ] 1s the concentration of Hgnln reactive sites available 1n the wood sample. The total number of reactive sites available 1n Hgnln molecules at time t can be estimated by the total weight (Wi ) of Hgnln at time t divided by the average molecular weight (M$) of the chain segment between two consecutive reactive sites 1n a Hgnln molecule. Thus [ L ] can be written as: rs
rs
rs
(12)
DJrs * CX]/Ms
where [ X ] 1s WL/W as before. Since the average molecular weight of the chain segment between two consecutive reactive sites may be considered to be a constant for Hgnln 1n a given wood species, M$ will not be affected by the extent of delignification. Therefore, after substitution for Hgnln concentration 1n Equation 9, M$ can be eliminated from both sides of the equation. Hence one obtains: 0
(13)
-d[X]/dt « ki[X]-k ([X] -[X]) 2
0
where [X] and [X] are the weight percent of Hgnln In the wood sample at time 0 and t, respectively, both expressed with respect to Initial weight of wood. 0
Evaluation of the Kinetic Model Experimental Data. The experimental system has been described prevlously (1,2). It Involves a tubular reactor for extraction and a separator trap for precipitation. In a typical run, about 3.5 grams of red spruce sawdust (16 mesh) was packed Into the reactor (19 cc) and delignification was carried out for different time periods 1n the temperature range from 170 to 185°C and the pressure range from 172 to 276 bar. Methylamine (99.8% purity from Alrco) and nitrous oxide (99.9% purity from L1nde) at selected compositions were continuously pumped into the system at a constant flow rate (1 g/min). Delignification conditions were all above the critical temperature and the pressure of the fluids used. [The critical properties of methylamine, nitrous oxide and their binary mixtures have been reported elsewhere (25)]. The reaction mixture was then released to the separator (35 cc) where the dissolved Hgnln was precipitated at atmospheric pressure. After a desired period of delignification time, the residue remaining 1n the reactor and the precipitate collected in the separator were taken out and analyzed. Lignin contents were determined as the acidInsoluble Hgnin (Klason Hgnin) using a modified procedure (26). Evaluation of the Kinetic Parameters. [X] 1n Equation 13 1s given by: [X] « ([X]
C
0
t
+ C /Ci)e~ l - C /Ci 2
2
The analytical solution for (14)
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Kinetic Modelfor Supercritical Delignification of Wood
LI A N D KIRAN
where: Ci « ki + k
2
(15)
C - -k [X]
0
(16)
2
2
In this study, the Hgnln content [X] 1n wood has been replaced by Klason Hgnln contents of the residues. It should be noted that Klason Hgnln only accounts for the ac1d-1nsoluble portion of the Hgnln 1n the wood residue and therefore represents the lower limit of the Hgnln that actually exist 1n the wood residue. The amount of soluble Hgnlns that may remain 1n the residue has not been further Investigated 1n this study. Figure 1 compares the experimental data (Klason Hgnln contents) for delignification of red spruce by methylamine at 185°C and 276 bar with the predictions from the reaction-diffusion model (Equation 13) and from n order homogeneous reaction models. For the reaction-diffusion model, the rate constants k\ and k have been calculated to be 0.5163 and 0.2012 [1/hr], respectively. The figure demonstrates that the reaction-diffusion model proposed 1n this work is capable of predicting the experimental data over a much wider range. The predictions from the first-order (n=l) homogeneous reaction model grossly deviates from the experimental data points. The second-order reaction model shows substantial improvement over the first-order but still underpredlcts the extent of delignification. Whereas the third-order reaction model overpredicts the extent of delignification. All four models seem to agree and converge at long extraction times. There 1s some deviation for the reaction-diffusion model 1n the prediction of lignin content at low extraction times (i.e., half hour data point). This may however be a consequence of the delay period In the start-up of extraction which introduces some uncertainty in total extraction time when extraction times are short. There 1s a time period over which the system pressure 1s Increased to the extraction conditions. t h
2
Effect of Temperature on Reaction Rate. The Klason Hgnln contents of red spruce residue extracted by methylamine at four different temperatures along with the predicted curves from the reactiondiffusion model are shown 1n Figure 2. The calculated (least square fit) values of kj and k according to Equation 13 are given 1n Table I. The standard deviations expressed as wt% Klason Hgnin refer to deviation between Hgnln predicted (using the Indicated values of k} and k and Equation 13) and the experimental data. The table shows that the rate constant k\ Increases with temperature as would be expected from the Arrhenlus relationship (Equation 3). However, the constant for diffusion (k ) 1s seen to decrease with Increasing temperature under the experimental conditions according to: 2
2
2
lnk » lnA* + E*/RT 2
(17)
where A* 1s a constant and E* 1s the activation energy for dlffu-
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40
-drxi/dt - ki[Xl - k2([X]o-[Xl) Reaction-diffusion model 30
-d[X3/dt = klXl" 1st order (n-1 ) 2nd order (n=2) 3rd order (n-3)
0
1
2 3 4 Extraction Time (hourD
5
6
Figure 1 . Comparison of the extent of delignification predicted by the homogeneous (first-order, second-order and third-order) models and by the reaction-diffusion kinetic model. The open circles are the measured Klason Hgnln contents 1n the residues obtained from methylamine extraction of red spruce at 276 bar, 185°C and 1 g/min solvent flow rate.
Extraction Time (hour)
Figure 2. Comparison of the extent of delignification predicted by the reaction-diffusion model with the measured Klason Hgnln contents 1n the residues obtained from supercritical methylamine extraction of red spruce at 276 bar, 1 g/m1n solvent flow rate, and four different temperatures (170, 175, 180, and 185°C).
21.
LI A N D KIRAN
Kinetic Modelfor Supercritical Delignification of Wood
Table I. The Rate Constants for Delignification of Red Spruce by Supercritical Methylamine at 276 bar and Four Different Temperatures
170°C 175°C 180°C 185°C
[l/hour]
*2 [l/hour]
Standard Deviation [wt% Klason Lignin]
0.3375 0.3769 0.4541 0.5163
0.2447 0.2322 0.2155 0.2012
0.3703 0.5028 0.9483 0.5921
slon process. The decrease 1n k with temperature Indicates that the second term 1n Equation 13 becomes smaller (a decrease 1n the diffusion resistance term) with temperature and hence lead to an increase 1n the overall rate of delignification. Factors that con tribute to this type of temperature dependence of the diffusion resistance term can be various. One of the factors that would Influence k 1s the viscosity of the solvent. A decrease 1n the solvent viscosity may facilitate diffusion. Even though there 1s no data 1n the literature on the viscosity of methylamine and methylamlne-nltrous oxide mixtures at the specific extraction conditions, 1n most cases the viscosity of fluids 1s found to be Inversely proportional to temperature (27). Another factor that may affect diffusion process 1s the density of the solvent. For example, self-diffusion coefficients of supercritical ethylene Increases drastically with decreasing density of ethylene (28). Since both the fluid viscosity and density would become more favor able for easier diffusion with Increasing temperature, the dlffus lonal resistance to delignification 1s expected to decrease with increasing temperature. If the level of Hgnln removal ([X] -tX]) is maintained constant, then k should decrease with Increasing temperature, which 1s In accord with the observed temperature dependence of this quantity. By a linear regression of Equation 3 using the data given in Table I, activation energy and frequency factors have been calcu lated and are given 1n Table II. (The standard deviation in this 2
2
0
2
Table II. The Activation Energy and Frequency Factor for Delignification Reactions 1n Supercritical Methylamine at 276 bar
Ink! lnk 2
InA
E/R [K]
A [l/hour]
12.30 -7.455
5935 2682
2.197x10 5.78x10"*
e
Ε [KJ/mol]
Corr. coeff.
Standard deviation
49.32 22.29
0.9946 0.9971
0.02398 0.00795
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table refers to the deviation between Ink calculated using the Ε and A values Indicated 1n the table and the values based on Table I). As shown, the activation energies are calculated to be 49 KJ/mol for the reaction term (kj) and 22 KJ/mol for the diffusion resistance term ( k ) . respectively. These values are 1n the lower range of reported activation energy values (40 - 150 KJ/mol) for kraft and high pressure delignification processes (11,13,29-31). In conventional pulping, three regions of delignification (which are often described by psuedo-flrst-order kinetic models) are observed (7,13). These regions, referred to as the I n i t i a l , bulk, and residual delignification stages, show different activation energies, the low values are often associated with the I n i t i a l delignification stage. It should be noted that the temperature dependence of k\ and k given 1n Table II 1s based on data obtained at 276 bar. To e s t i mate the rate constants at other pressure levels, one need to correlate the rate constants with pressure which 1s discussed 1n the following section. 2
2
Effect of Pressure on Reaction Rate. The variation of Klason Hgnln contents of red spruce residue with extraction pressure 1s shown 1n Figure 3. Based on these data points, the rate constants at different pressures have been estimated and are given 1n Table III. TABLE I I I . The Rate Constants for Delignification of Red Spruce by Supercritical Methylamine at 185°C and Four Different Pressures
172 207 241 276
bar bar bar bar
kl [l/hour]
*2 [l/hour]
Standard deviation [wt% Klason Hgnln]
0.3375 0.4691 0.5432 0.5163
0.1560 0.1994 0.2270 0.2012
0.5167 0.8235 0.6972 0.5921
They have been fitted with the parabolic relationship given by Equation 7 resulting 1n: 2
(18)
2
(19)
lnki « -4.057 + 0.02720P - 0.00005388P lnk2 * -5.968 + 0.03705P - 0.00007688P
where k\ and k are 1n units of [l/hour] and Ρ in [bar]. According to Equation 5, the volume of activation terms are expressed as: 2
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LI AND KIRAN
Kinetic Modelfor Supercritical Ddigmfication of Wood
c
c c O)
2 3 4 Extraction Time (hour)
Figure 3. Comparison of the extent of del1gn1f1cat1on predicted by the reaction-diffusion model with the measured Klason lignin contents in the residues from supercritical methylamine extraction of red spruce at 185°C, 1 g/m1n solvent flow rate, and four different pressures (172, 207, 241, and 276 bar).
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AVi* * -1036 + 4.105P
(20)
ΔΥ2* « -1411 + 5.857P
(21)
a r e
1 n
3
where ΔΥι* and LVz* [cm /mol] and Ρ 1s 1n [bar]. ΔΥι* and AV2^ show a sign change (and an accompanying decrease 1n k% and k2) above 252 and 241 bar, respectively. This reversal 1n sign 1s not unusual since volumes of both the reactants and the transition state change with pressure and since there 1s no a priori reason for their having similar compressibilities. The plots of Ink ver sus pressure are 1n general curved towards the pressure axis (23). Effect of Solvent Concentration on Reaction Rate. In the kinetic modeling of chemical (such as kraft) pulping, the effect of cooking Hquor on delignification rate 1s sometimes considered. For example, the alkali concentration [OH"] can be Included 1n the rate equation (12,13,32). Since the extraction experiments 1n this study have been conducted under constant solvent flow (1 g/m1n) and the solvent ratios 1n binary fluid extractions have been maintained at a constant, one can combine the solvent concentration factor into an effective rate constant (k ff). Therefore, Equation 13 can be rewritten as: e
-d[X]/dt « kieffCX] - k ff([X] -[X]) 2e
0
(22)
with k
s
kleff - l C ]
n
(23)
and 24
*2eff » k [Sp
2
where ki ff and k2eff are the effective rate constants for reaction and diffusion processes, respectively, [S] 1s the concentration of methylamine expressed as weight fraction 1n the binary extraction fluid, and η and m are some constants to be determined. If [S>1 (corresponding to pure methylamine solvent). Equation 22 reduces back to Equation 13. If 1t is a binary solvent (methylamlnenltrous oxide), ki ff and k2eff are expected to have different val ues for k\ and k2, respectively. Following similar procedure used for determination of rate con stants (ki and k2), ki ff and k eff for methylam1ne-n1trous oxide extraction at 60 wt% of methylamine ([S] * 0.6), 185°C, 276 bar and 1 g/min solvent flow rate have been found to be 0.2399 [l/hour] and 0.1997 [l/hour], respectively. Substituting these values along with the values of k\ and k Into Equation 23 and Equation 24, one solves η as 1.500 and m as 0.01465. A physical Interpretation of η and m 1s that nitrous oxide acts as an Inert which blocks the active reaction sites on the surface of the Inner cell wall, hence reducing the observed rate constant. On the other hand, the diffu sion process (transporting dissolved fractions Into bulk phase) should not be affected by an Inert as long as the Inert Is compatie
e
e
2
2
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Kinetic Moddfor Supercritical Delignification of Wood
LIANDKIRAN
ble with the active reagent and the dissolved materials. This explanation 1s supported by a near zero value of m, Indicating that nitrous oxide has Indeed no significant effect on the diffusion process. Hence the final expression of the kinetic model for delignification of red spruce by supercritical methylamine and methylam1ne-n1trous mixture 1s expressed as: -d[X]/dt » k [X][S]l-5-k ([X] -[X]) 1
2
0
(25)
where m has been set to zero for simplicity. Figure 4 shows the delignification curves predicted with Equation 25 at five compositions of methylamine-n1trous oxide mixture, along with the experimental data points. The standard deviation of the Klason Hgnln content of red spruce residue from methylamine (60 wt%)-n1trous oxide mixture extraction 1s 0.2103% as compared to 0.5921X from pure methylamine extraction. There 1s only one experimental data point for each of the other three compositions (20 wt%, 40 wt%, and 80 wt%). The data point from methylamine (80 wt%)-n1trous oxide extraction appears to be noticeably different from the predicted delignification curve. But based on the experimental data adjacent to this solvent composition—100 wt% methylamine (8 points) and 60 wt% methylamine (5 points), the predicted curve for 80 wt% methylamine 1s considered more reliable than the single data point.
Figure 4. Comparison of the extent of delignification predicted by the reaction-diffusion model with the measured Klason Hgnln contents 1n the residues from supercritical methylamine extraction of red spruce at 272 bar, 185°C, 1 g/m1n solvent flow rate, and five different solvent compositions (20, 40, 60, 80, and 100 wt% of methylamine).
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SUPERCRITICAL FLUID SCIENCE A N D T E C H N O L O G Y
CONCLUSIONS This study has shown that a reaction-diffusion model can effectively describe the supercritical delignification of wood, accounting for temperature, pressure, and solvent effects over a wide range. The residual Hgnln contents predicted by the model are 1n good agreement with the measured Klason Hgnln contents of the residues from supercritical methyl amine-nltrous oxide delignification of red spruce. ACKNOWLEDGMENT This research has In part been supported by the National Science Foundation (Grant No. CBT-84168875). LITERATURE CITED 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
L i , L . ; Kiran, E. Ind. Eng. Chem. Res. 1988, 27, 1301-1312. L i , L . ; Kiran, E. Tappi J. 1989 (in press). L i , L . ; Kiran, E. Paper presented at the 195th ACS National Meeting, Toronto, Canada, 1988. L i , L. Ph.D. Thesis, University of Maine, Orono, Maine, 1988. Kiran, E. Tappi 1987, 70(11), 23-24. Kiran, E. American Papermaker 1987 (November), 26-28. Sjostrom, E. Wood Chemistry—Fundamentals and Applications; Academic Press: New York, 1981; Chapter 4. Fengel, D.; Wegener, G. Wood-Chemistry, Ultrastructure, Reactions; Walter de Gruyter: London, 1983; Chapter 8. Szekely, J.; Evans, J.W.; Sohn, H.Y. Gas-Solid Reactions; Academic Press: New York, 1976. Doraiswamy, L.K.; Sharma, M.M. Heterogeneous Reactions: Analysis, Examples, and Reactor Design, Vol. 1: Gas-Solid and Solid-Solid Reactions; John Wiley & Sons: New York, 1984. Kleinert, T.N. Tappi 1966, 49(2), 53-57. Yan, J.F. Tappi 1980, 63(11), 154. Kondo, R.; Sarkanen, K.V. Holzforschung 1984, 38(1), 31-36. Eyrlng, H.; Lin, S.H.; Lin, S.M. Basic Chemical Kinetics; John Wiley & Sons: New York, 1980; Chapter 9. Evans, M.G.; Polanyi, M. Trans. Faraday Soc. 1935, 31, 875-895. Koch, E. Non-Isothermal Reaction Analysis; Academic Press: New York, 1977; Chapter 2. van Eldik, R. Inorganic High Pressure Chemistry--Kinetics and Mechanisms; Elsevier: New York, 1986. Whalley, E. Trans. Faraday Soc. 1958, 55, 798-808. Isaacs, N.S. Liquid Phase High Pressure Chemistry, John Wiley & Sons: New York, 1981; Chapter 4. Lohmuller, R.; Macdonald, D.D.; Mackinnon, M.; Hyne, J.B. Can. Chem. 1978 56, 1739-1745. Plamer, D.A.; Kelm, H. Coord. Chem. Rev. 1981, 36, 89-153. Asano, T.; Okada, T. J. Phys. Chem. 19577 88, 235-243. Tiltscher, H.; Hofmann, H. Chem. Eng. Sci. 1987, 42(5), 959-977.
21. LI AND KIRAN Kinetic Model for Supercritical Delignification of Wood 24. 25. 26. 27. 28. 29. 30. 31. 32.
Eckert, C.A. Ann. Rev. Phys. Chem. 1972, 239-264. L i , L.; Kiran, E. J. Chem. Eng. Data 1988, 33, 342-344. Effland, M.J. Tappi, 1977, 60(10), 43-144. Reid, R.C.; Prausnitz, J.M.; Poling, B.E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. Jonas, J.; Lamb, D.M. In Supercritical Fluids; Squires, T.G; Paulaitis, M.E., Eds; ACS Sumposium Series 329, 1987. Olm, L . ; Tistad, G.; Svensk Papperstidn. 1979, 82, 458-464. Beer, R.; Peter, S. in Supercritical Fluid Technology, Penninger, J.M.L.; Radosz, M.; McHugh, M.A.; Krukonis, V.J., Eds; Elsevier: New York, 1985. Norden, S.; Teder, A. Tappi 1979, 62(7), 49-51. Kleppe, P . J . , Tappi 1970, 53(1), 35-47.
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