Kinetics and mass transfer for supercritical fluid extraction of wood

282 Ind. Eng. Chem. Res. 1990,29, 282-289

Registry No. NaC1, 7647-14-5.

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Cellulose Acetate Reverse Osmosis Membranes. Desalination 1975, 17, 145.

1985. Kesting, R. Synthetic Polymeric Membranes; Wiley: New York,

Meares, P. On the Mechanism of Desalination by Reversed Osmotic Flow through Cellulose Acetate Membranes. Eur. Polm. J . 1966, 2, 241.

Muldowney, G. P.; Punzi, V. L. A Comparison of Solute Rejection Models in Reverse Osmosis Membranes for the System Water- Sodium Chloride-Cellulose Acetate. Ind. Eng. Chem. Res. 1988, 12, 2341.

Osmonics, Inc. Verbal communications and product literature. Os- monics: Minnetonka, MN, 1988.

Punzi, V. L.; Muldowney, G. P.; Hunt, K. B. Study of Solute Re- jection Models for Thin Film Composite Polyamide RO Mem- branes. J. Membrane Sci. 1989, in review.

Punzi, V. L.; Hunt, K. B.; Muldowney, ,G. P. A Comparison of Solute Rejection Models in Reverse Osmosis Membranes. 2. System Water-Sodium Chloride-Asymmetric Polyamide. Ind. Eng. Chem. Res. 1990, another paper in this issue.

Soltanieh, M.; Gill, W. N. Review of Reverse Osmosis Membranes and Transport Models. Chem. Eng. Commun. 1981,12,279.

Sourirajan, S . Reverse Osmosis; Academic: New York, 1970.

Received for review May 9, 1989 Revised manuscript received October 6, 1989

Accepted October 20, 1989

Kinetics and Mass Transfer for Supercritical Fluid Extraction of Wood

Motonobu Goto,+ J. M. Smith, and Ben J. McCoy* Department of Chemical Engineering, University of California, Davis, California 95616

Rates of extraction of lignin from white fir sapwood with supercritical tert-butyl alcohol were measured dynamically in a continuous-flow system. The extraction rate increased with temperature and pressure but was independent of particle size and flow rate for our experimental conditions. A model is presented for the supercritical reaction-extraction process, accounting for the reaction of solid lignin in the particle, intraparticle diffusion, and external mass transfer of lignin derivatives. For the reaction in the particle, two parallel first-order reactions for the degradation of two lignin types satisfactorily represent the data. The kinetic parameters for the reaction were estimated from the model analysis. Model simulations supported the experimental results, which showed the extraction process was not affected by the mass transfer.

The extraction of wood constituents with supercritical fluid (SCF) has been receiving considerable attention for liquefaction or gasification of biomass. Potential industrial applications are extraction of lignocellulosic materials as a source of organic chemicals or fuels and delignification for the pulping process. Most recent studies are focused on the former problem.

Wood consists of lignocellulosic materials, such as cellulose, hemicellulose, and lignin. Since lignin is an aro- matic cross-linked polymer and constitutes about 20-30% of the wood, it is a promising source of chemicals and energy (Li and Kiran, 1989). Although pyrolysis has been used for gasification of lignocellulosic materials, the secondary reactions, which produce char, cannot be avoided. Supercritical extraction processes can overcome this problem because the extraction can be performed below the pyrolysis temperature and also the products of SCF are less degraded (Calimli and Olcay, 1982).

Prior studies show that SCF extraction of lignocellulosic materials increases with time, pressure, and strongly with temperature (Li and Kiran, 1987; Poirier et al., 1987). However, most of the work has not addressed the rates of extraction. Beer and Peter (1985) found that the reaction of lignin with a mixture of water and methylamine solu- tions obeyed a two-stage first-order reaction system. Li and Kiran (1988) applied a reaction-diffusion model to the extraction of lignin by supercritical methylamine-nitrous oxide mixtures. In their model, the rate of decomposition of lignin was expressed by first-order kinetics with respect to the fraction of lignin. In our previous work, the extent of extraction of lignin with tert-butyl alcohol (Reyes et al.,

* To whom correspondence should be addressed. On leave from Kumamoto University, Kumamoto 860, Japan.

1989) increased with pressure and strongly with temperature.

Our present objectives are (1) to develop a model for reaction and extraction of solid particles in a fixed bed contacted with a flowing solvent at supercritical conditions and (2) to investigate the effects of particle size and flow rate in order to determine the influence of mass transfer. We studied the degradation and extraction of lignin from wood chips with supercritical tert-butyl alcohol (P, = 3.97 MPa, T, = 506.2 K). The extraction rate was measured dynamically with a fixed-bed reactor. The overall rate of extraction was found to be controlled by the chemical reaction at the conditions of our experiments. Two kinds of lignin are assumed to degrade to derivatives simulta- neously, each with first-order kinetics. This model agreed well with the experimental data for reasonable values of the parameters.

Experimental Method The extraction of wood chips was carried out dynami-

cally using a fixed bed contacted with flowing supercritical tert-butyl alcohol. In each run, the mass flow rate and pressure are held constant while the temperature is first increased at a constant rate and then held constant a t a chosen level until the end of the run.

Apparatus. The apparatus shown in Figure 1 is almost the same as used by Triday and Smith (1988) for the extraction of kerogen from oil shale and by Reyes et al. (1989). A piston-type accumulator was used as a feed tank to reduce the dissolution of nitrogen into the solvent, which can cause bubbles in the effluent. The stainless steel reactor was a 0.45-m long tube, of 0.029-m i.d. tert-Butyl alcohol was used as a solvent because lignin is selectively extracted by alcohol (Koll et al., 1983).

0S88-5S85/90/2629-0282$02.50/0 0 1990 American Chemical Society

Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990 283

wall is very high, only 20-30% of the total lignin exists there (Hillis, 1985). The remainder is in the much thicker secondary walls, occupying about 90% of the volume of the cell tissue.

Since lignin is a cross-linked macromolecule, it can be dissolved only by degradation to derivatives of smaller molecular weight in the process of extraction. Since temperature significantly affects the concentration of extracted lignin derivatives, chemical reaction must be a principal concern in the overall process, as in the case of extraction of kerogen from oil shale (Triday and Smith, 1988). The reaction was assumed to proceed as lignin(s) + tert-butyl alcohol(1) -

lignin derivatives(so1ution) (1) As a first attempt of modeling the extraction, a single

first-order reaction in terms of lignin, which was uniformly distributed throughout the particles, was assumed. How- ever, this model did not fit the experimental data.

Therefore, a parallel first-order reaction model was de- veloped for which two kinds of lignin are supposed to react to derivatives by fmt-order processes. The reaction is only a function of lignin concentration because the solvent exists in excess in the pores of the particle. The lignin concentration is considered uniform within the particle during the extraction. After the lignin reacts, the derivatives diffuse out of the porous particle and into the bulk fluid phase.

General Model. In the parallel reaction model, each type of solid lignin is supposed to obey a first-order irreversible reaction. The mass rate of disappearance of lignin can be described by the intrinsic rate equation,

dCL,l dCL,2 % = - +-

dt dt

I , ' I I

U

Figure 1. Schematic diagram of the apparatus: 1, solvent supply tank; 2, pressure feed tank; 3, nitrogen cylinder; 4, pressure gauge; 5, electric furnace; 6, reactor; 7, filter; 8, thermocoupled connection; 9, temperature controller; 10, water-cooled heat exchanger; 11, collection vessel for pressure relief; 12, rotameter; 13, spectrophotometer; 14, collection vessel for effluent; 15, vacuum gauge; 16, surge tank; 17, vacuum pump; 18, voltage control for heating elements; A, B, D, E, G, K, L, M, shut-off valves; H, flow-control valve; F, needle valve; C, pressure-regulator valve; J, rupture disk. The heavy line indicates where low-voltage electrical heating elements are wrapped.

Sample Preparation. Wood samples were prepared by crushing white fir sapwood in a hammer mill and sieving. Two particle sizes of approximate parallelepiped shapes were used: 0.47-mm thickness X 1.13-mm width X 3.64-mm length and 1.03 X 1.96 X 6.62 mm. The equivalent diameters, calculated by equating the surface area to volume ratio to that of a spherical particle (Aris, 1957), were 0.908 and 1.84 mm.

Samples were dried for 24 h at 368 K. For most runs, 0.175 g of wood particles was used, which filled the reactor to a depth of 2 mm. Differential-reactor operation was approximated because of the small bed size. The porosity and apparent density of the particles were 0.71 and 450 kg/m3. The mass fraction of lignin in the wood was 29%, corresponding to an initial lignin concentration C L , ~ = 0.29 (450) or 131 kg/m3.

Operating Procedure. After the entire system is evacuated, about 3 X m3 of solvent is drawn into the feed tank. The piston of the tank is pressurized with nitrogen gas and the flow rate is adjusted to either 1.67 X lo-' m3/s or 4.17 X lo-' m3/s. The pressure in the reactor was maintained constant a t values in the range 4.17-6.76 MPa. The temperature of the reactor was increased at a heating rate of 0.14 K/s to the desired temperature in the range 458-548 K. The concentration of the extracted lignin derivatives is monitored continuously with the spectrophotometer (Perkin-Elmer Lambda 4B) at a wavelength of 280 nm. Since the dead space in the tubing between the reactor and the detector for our apparatus contributed only to the time delay (Triday and Smith, 1988), the measured absorbance was corrected for this time. Further details of the experimental procedure are provided in Reyes et al. (1989).

Reaction-Extraction Model The wood cell wall consists of three distinct layers: the

middle lamella, the primary wall, and the secondary wall. The secondary layer, which is the major portion of the fiber, contains only around 10% lignin, while the middle lamella and primary wall contain over 50%. Although the concentration of lignin in the middle lamella and primary

(2) where CL,l and CL,2 are the mass of the lignin per unit volume of particle and the initial conditions are

CL,l = CL,l,O, CL,2 = CL,2,0 at t = 0 (3) The intrinsic reaction rate is determined by the initial

solid concentration and the measured temperature history. Thus, the intrinsic reaction rate and solid lignin concentration are independent of mass-transfer processes.

The mass balance of lignin derivatives (of total concentration C ) within the particle may be written as

The initial and boundary conditions are C = 0

ac /a r = 0 for all r at t = 0 (5)

(6) at r = 0 for t > 0

(7) ac ar -De - = kf[Cr=Ro - cb] a t r = Ro

The mass balance in the differential reactor-is repre- sented in terms of the average concentration Cb by the expression

where C b = Ce/2. The bulk fluid temperature is uniform throughout the bed according to the differential-reactor approximation.

284 Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990

Simplified Model (Linear Driving Force Model). Much numerical effort is necessary in solving the general model because of the inclusion of intraparticle diffusion according to eq 4. Goto et al. (1990) showed that assuming a parabolic concentration profile within the particle is an excellent approximation for the cme of reaction-extraction, i.e., when the reactant is a solid and the product of the reaction diffuses out of the porous particle. With the parabolic profile assumption, intraparticle diffusion and external mass-transfer effects can be combined in an overall mass-transfer coefficient, k ,

(9)

As the porosity of the particle changed less than 10% (Reyes et al., 1989), the porosity (ep) was assumed to be independent of time. With this approach, eq 4 can be rewritten in terms of average concentrations C and Cb,

5kf 5 + kfRO/De

k , =

The average intraparticle concentration is defined by

In terms of average concentration, eq 8 becomes

for which the initial condition is ~ = C ’ , = O at t = 0 (13)

Since eqs 10 and 12 are ordiqary differential equations with two dependent variables, C and Cb, they can be solved numerically by the Runge-Kutta-Gill method. First, the intrinsic rate Yi! is eliminated from eq 10 by integrating eq 2, using the measured temperature history. For the parallel reaction system, this requires integrating two forms of eq 2, one for each type of lignin. Also required is the fraction of the original total lignin in each form. These fractions were determined by optimized fitting of the model to the experimental effluent concentration data. The result of these integrations gives CL,l and CL,2 and hence R as a function of time. An analytical solution of eq 10 and 12 is not feasible since the temperature and rate constants change with time.

The global rate of reaction-extraction Q, per unit initial mass of wood mot is obtained from a mass balance of lignin around the differential reactor:

where q is the flow rate a t the reactor temperature and pressure and V the reactor volume.

As a special case, when the extraction process is controlled by the chemical reaction (i.e., when mass-transport resistances are unimportant), the intrinsic reaction rate based upon the initial particle volume can be calculated from the observed global reaction-extraction rate by

Physical and Transport Properties of Supercritical tert-Butyl Alcohol

Density. The density of tert-butyl alcohol in the supercritical region was estimated from the generalized

I . .

I .

c I I I I I I I 1 5 . - I I

0 0 - - - 7

T, [-I Figure 2. Density and viscosity of tert-butyl alcohol.

correlation of Lee and Keslet (1975), which is based upon a three-parameter equation of state. Figure 2 shows the variation in density with temperature a t P, = 1.50. The concentration at the exit of the reactor, C,, calculated from the models is at supercritical conditions, while the measured concentration at the absorption cell is at 298 K and 0.1 MPa. The calculated concentration was corrected to 298 K and 0.1 MPa by the expression

Pa c, = rce Pe

The flow rate in the reactor was also corrected in the same manner:

Pa

P e u = -ua

where pa is the density at the ambient condition, equal to 787 kg/m3.

Viscosity. The viscosity of tert-butyl alcohol a t high pressures was calculated by the residual viscosity correlation of Stiel and Thodos (1964) using the low-pressure gas viscosity estimated by the Golubev (1959) method. The variation in viscosity with temperature a t P, = 1.50 is also shown in Figure 2.

Diffusivity. Sun and Chen (1986) have measured the molecular diffusivities up to the supercritical region for several hydrocarbons by using the Taylor-Aris dispersion method. Their correlation, based on the Stokes-Einstein equation, agreed with the data within 4% and can be expressed as

m 1 D = 1.23 x 10-14 o,,96v o.503

PL2 c1

where w2 and VCl are the viscosity of the solvent (in ns/mz) and the critical volume of the solute (in m3/kmol), respectively.

To estimate the diffusivity from this correlation, we need the critical volume of the solute molecule. The fragmen- tation and chemical conversion of lignin lead to the for- mation of various phenolic derivatives. As the result of hydrolysis of lignin, the major compound classes are phenols, xylenols, catechols, guaiacols, and syringols (Janshekar and Fiechter, 1983). Poirier et al. (1987) showed by GC/MS analysis that the oil extracted from wood with supercritical methanol consists of various guaiacol and syringol derivatives and their dimeric com- pounds, In our previous paper (Reyes e t al., 1989), we showed by GC/MS and direct-probe mass spectrometry analysis that the extract consists mainly of syringol derivatives.

Ind. Eng. Chem. Res., Vol. 29, No. 2,1990 285

Table I. Diffusivities in tert-Butyl Alcohol at the Critical Point

critical vol, 108D, solute m3/kmol m2/s

phenol 0.229 6.30 cresol (methylphenol) 0.318 5.35 xylenol (dimethylphenol) 0.372 4.94 catechol (hydroxyphenol) 0.226 5.84 guaiacol (methoxyphenol) 0.338 5.18 syringol (dimethoxyphenol) 0.412 4.69 average 0.316 * 0.076 5.30 * 0.059

i o I , l o

0 8

d 0

0 6 - X

s \

- o 4 E

Y

d 0 2

0 5 0 7 0 9 1 1 1 3 1 5

T, [-I Figure 3. Estimated molecular diffusivity and fluid-to-solid mass- transfer coefficient of lignin derivatives.

Table I shows the estimated values for the diffusivity of some conceivable solutes existing in the lignin derivatives in tert-butyl alcohol at the critical point. The critical volume of the solute was estimated by Lydersen's method (Reid et al., 1977), which employs contributions of struc- tural groups. We used the average critical volume to calculate a diffusion coefficient of 5.36 X lo4 m2/s for the mixture a t the critical point. This diffusivity is in good agreement with the average value in Table I. Figure 3 shows the variation in diffusivity with temperature at P, = 1.50, as calculated from Sun and Chen's (1986) correlation.

The effective diffusivity can be evaluated from the molecular diffusivity, if the particle porosity and the tortuosity factor are known. The relatively large macro- pores in wood suggest a lower tortuosity factor than for catalyst particles. Thus, the formulation of Chang (1982), which expresses the tortuosity factor as 2 - ep, was used. Then the effective diffusivity is given by

CP D,=D- 2 - €p

Mass-Transfer Coefficient. Fluid-to-solid mass- transfer coefficients were measured by Tan et al. (1988) for the extraction of 0-naphthol in supercritical carbon dioxide. Their data were correlated with an average error of 20% by the following equation:

Sh = 0 . 3 8 S ~ ' J ~ R e ~ . ~ ~ (20) Figure 3 also shows the mass-transfer coefficient calculated by this correlation. The decrease of the mass-transfer coefficient with temperature beyond the critical point may be due to the density decrease.

Results Experimental Runs. Figure 4 shows the global reac-

tion-extradion rate calculated from the experimental data

' [SI Figure 4. Effect of temperature on experimental extraction curves (P, = 1.50, q = 1.67 X lo-' m3/s, d, = 1.84 mm).

/ P,=1 70

0 6 k I I I I I o 1000 2000 3000 4000 5000 6000

t [SI

Figure 5. Effect of pressure on experimental extraction curves (T, = 1.04, q = 1.67 X lo-' m3/s, d, = 1.84 mm).

0 9 1 0 1 1

T, [ - I Figure 6. Effect of temperature on the amount of lignin extracted.

by eq 14 for various temperatures a t a reduced pressure of 1.50. Since the accumulation in the interparticle fluid (the second term in the right-hand side of eq 14) was negligible, the Late a t any time is proportional to the concentration (C,) at that time. Slight changes in temperature greatly increased the rate, suggesting that the intrinsic reaction plays an important role in the overall extraction process.

The effect of pressure on the global rate a t a reduced temperature of 1.04 is displayed in Figure 5. The rate increased as the pressure increased, but the effect is not as pronounced as that of temperature. Figures 6 and 7 give the effects of temperature and pressure on the fraction of lignin extracted at the end of the run (100 min). The extracted amount increases with both temperature and pressure.

Figure 8 shows that the effect of the particle size on the extraction rate is insignificant. Thus, intraparticle diffusion does not affect the extraction process for our particle


3 1 4

,- - 1

- E X D E r-er.2

P r e n i c e o _ _ - _ -

1 T, - 3 24 I

-

I I I 1 0 1 2 1 4 . E . e

pr [ - I Figure 7. Effect of pressure on the amount of lignin extracted.

"4

I

r ,

> ,,..:' , I I

sizes. Since this result is observed at the highest temperature, there must be no effect of intraparticle diffusion for the other conditions of this work. This is a reasonable result because the diffusivity of the supercritical fluid is much higher than that of liquid, as indicated by Koll et al. (1983).

Figure 9 shows the effect of flow rate on the extraction rate. There seems to be no significant difference between the extraction rates a t the two flow rates. This result is supported by the model computations described later for the effect of m a s transfer. It was not pcasible to reproduce exactly the temperature history, especially for experimental runs at different flow rate. Since the extraction rate is very sensitive to temperature, the slight differences of concentration histories in Figure 9 do not necessarily indicate an effect of flow rate. When the extraction rate is controlled only by the chemical reaction of lignin, the observed extraction rate is related to the intrinsic reaction rate by eq 15.

Table 11. Predictions of the Parallel First-Order Reaction Model Effect of Temperature (PI = 1.5, q = 1.67 X m3/s, d, = 1.84

mm) k03 Ed, Ea29

run T. l / s kJ/mol kJ/mol f 8 0.90 98.5 46.2 96.9 0.121

18 0.97 28.0 44.2 59.9 0.203 17 1.01 57.9 45.9 59.4 0.236 15 1.04 53.4 44.8 59.1 0.246 9 1.08 51.0 44.7 58.7 0.266

Effect of Pressure (T , = 1.04, q = 1.67 X lo-' m3/s, d, = 1.84 mm)

k09 Ed? Ed? run P, l / s kJ/mol kJ/mol f 22 1.06 66.9 39.2 52.7 0.173 20 1.30 69.6 38.4 53.0 0.201 15 1.50 53.4 44.8 59.1 0.246 12 1.70 50.7 45.2 57.7 0.304

Effect of Particle Size (TI = 1.08, PI = 1.50, q = 4.17 X lo-' m3/s)

d,, ko, Ed, Ea2, run mm l / s kJ/mol kJ/mol f 50 0.910 50.4 44.9 57.1 0.299 44 1.84 54.1 45.7 56.8 0.274

Effect of Flow Rate (T, = 1.08, P, = 1.50, d, = 1.84 mm) lo'q, ko, Ed, Ed,

run m3/s l / s kJ/mol kJ/mol f

"0 - 0 1 * t

0 0 4 1

=reo cted l s e c o r d reac'lo"

Figure 10. Comparison between experimental and predicted extraction curves by the parallel first-order reaction model (TI = 1.08, P, = 1.50, q = 1.67 X

Model Predictions. The rate constants for both parallel first-order reactions are assumed to have identical preexponential factors. This approach was also used by Boroson et al. (1989) as a reasonable simplification because activation energy is more influential on rate behavior than the preexponential factor. Then, the experimentally determined parameters for the simultaneous first-order reaction model are the preexponential factor k,, activation energies Ea,1 and Ea,2, and fraction of lignin of type 1, f.

These four parameters were evaluated by minimizing the sum of the squares of the difference between experimental and calculated extraction rates. Table I1 displays the resultant values at various conditions, and Figure 10 shows predicted and experimental curves at T, = 1.08 and P, = 1.50. Since the predicted curve consists of two parallel reactions, the extraction rates of each reaction are shown in the figure. As the lignin for the first reaction is con- sumed at an earlier time, the tailing part of the curve mainly consists of the extraction of the lignin for the

m3/s, d, = 1.84 mm).


0 1 4 I I 0 1 4 , I - E x p e r ~ m e n t a l I

0 12 c A r T , = 1 0 8 Predicted - _ _ _

X

m 0 - o r 3 -

- '0 0 0 8 - m t m 5 0 0 6 - Y VI

C 0 4 r

t [SI

Figure 11. Comparison between experimental and predicted extraction rates by parallel first-order reaction model for various temperatures (P, = 1.50, 9 = 1.67 X

second reaction. Figure 11 shows that the comparison between the predicted and experimental curves for different temperatures is generally satisfactory.

As shown in Table 11, the values of the fraction (f) estimated from the experimental data coincide with the fraction of lignin existing in the middle lamella, i.e., 20-30%. This suggests that the lignin in the middle lamella reacts according to the first reaction and the remainder reacts according to the second reaction. Differ- ences in reactivity of lignin in different parts of the wood could occur because of differences in the bond between lignin and hemicellulose.

We also applied an nth-order reaction model with the adjustable parameters preexponential factor (kd, activation energy (Ea), and reaction order (n). The estimated reaction order was in the range 3-6, which is high for a reasonable explanation. The calculated curves are similar to those of the parallel first-order reaction model.

m3/s, d, = 1.84 mm).

Discussion Effect of Temperature. As shown in Table 11, the

parameter values for the parallel fmst-order reaction model are nearly constant for the range of operating conditions in the supercritical region. For the subcritical region, the values are substantially different. At the temperature below the critical point, the observed reaction rate decreased more than predicted by the Arrhenius equation. The chemical kinetics for the supercritical region, therefore, are not applicable to the subcritical region.

As indicated by the curve for the near-critical temperature, T, = 1.01, in Figure 11, the fluctuation in the concentration curve is larger than predicted by the model. When the temperature changes from subcritical to supercritical, the physical properties such as density and viscosity change significantly. The sensitivity of these properties may affect the reaction rate as well as the mass-transfer behavior.

Effect of Pressure. The effect of pressure on the estimated parameters is apparent in the increase with pressure of the fraction of lignin for the first reaction (Table 11). A large increase in reaction rate with pressure was observed by Johnston and Haynes (1987) in the supercritical region. They explained that the pressure effect is due to the change in the solvent strength or to the ex- tremely small activation volume. Li and Kiran (1988) also interpreted their experimental results using the activation volume. Poirier et al. (1987) observed a pressure effect for supercritical extraction of wood with methanol. They reported that the increase in extraction yield with pressure

0 0 i o m 7-

7 0 0 8 1

0 02

O o ; 1 &,' I I I , j 1000 2000 3000 43C3 5000 600C

t [SI

Figure 12. Predicted effect of particle size on the extraction rate (TI = 1.08, PI = 1.50, 9 = 1.67 X

is associated with the extraction of higher molecular weight fragments. Presumably as the pressure is increased, the solubility of higher molecular weight molecules increases.

Effect of Mass Transfer. The experimental data indicate that intraparticle diffusion does not affect the extraction process over the range of operating conditions. This result supports the assumption of an irreversible reaction used in the model. Thus, the experimental extraction rates observed in Figure 8 are not affected by intraparticle diffusion even though a large concentration gradient exists within the particle, as shown in Table 111. If the reaction is reversible and concentration gradients exist, the extraction rate would be influenced by intraparticle diffusion.

Calculations for various particle sizes reveal interesting features of this particular model. Calculated rates are shown in Figure 12 for a wide range of particle sizes: 0.2-50 times the experimental d, of 1.84 mm. Table I11 shows concentrations and other results at the specific time of 1500 s. The second to fourth columns give the average intraparticle concentration, the concentration at the particle surface, and the bulk Concentration. The overall mass- transfer coefficient (k,) and the external mass-transfer coefficient (kf) are estimated fro? the correlations. The flux was calculated by (3/R0)k (C - Cb). Since the global reaction-extraction rate in T a b i 111 indicates a point value at a particular time during a dynamic process, an increase in the value does not always mean an increase in the fraction of lignin extracted but may be due to the delay of the peak in the extraction curve. The values of the Thiele modulus, C#J = (R0/3)(k/De)1/2, and Biot number, Bi = kfRo/De, are indexes of mass-transfer resistance.

The intrinsic reaction rate (2) can be obtained by integrating the two forms of eq 2 using the measured temperature history. In the separate integration for each form of lignin, the initial concentration is needed. As shown in Table I1 for run 9, CL,l,o = 0.29 (0.266)(450) = 34.7 kg/m3. Then CL,2,0 = 131 - 34.7 = 96.3. The resultant value of R is 5.50 X kg/(m3.s) a t t = 1500 s and is independent of the mass-transfer processes. When the mass-transfer resistance is negligible, the global reaction-extraction rate, Q, equivalent to the intrinsic rate is calculated to be 1.22 X kg/(kg.s) by eq 15. This value agrees well with the global reaction-extraction rate shown in Table I11 for particle sizes in the 0.2-2 dp/dp,ref range.

Although the extraction rates are unchanged for the 0.2-2-fold increase in particle size, a concentration gradient exists within the particle and in the external fluid film. This result reveals the unique feature of this reaction- extraction process. The situation is different from the normal catalytic reaction, because the diffusing component

m3/s).


Table 111. Concentration Gradients at t = 1500 s (T, = 1.08, P, = 1.50, qrer = 1.67 X lo-' mS/s, dp,ref = 1.84 mm). The First Column Gives the Ratio of the Parameter to Its Reference Value

Effect of Particle Size c, Clr-ROt cb, 1O4kp, 1O4kf, 3k,(C - Cb)/Ro, 1040,

dp/dp,ref k / m 3 k / m 3 kg/m3 m/s m/s kg/(m3.s) kg/(kg.s) d Bi 0.2 0.0458 0.0424 0.0210 1.36 1.58 0.0549 1.23 0.0160 1.21 1 0.248 0.163 0.0211 0.750 1.20 0.0554 1.23 0.0799 4.61 2 0.684 0.343 0.0212 0.517 1.07 0.0557 1.24 0.160 8.19 5 3.19 0.987 0.0217 0.279 0.912 0.0575 1.28 0.399 17.5

10 9.45 1.89 0.0185 0.161 0.810 0.0494 1.09 0.799 31.1 50 21.6 1.32 0.0164 0.0377 0.616 0.0530 0.0965 3.99 118

Effect of Flow Rate c, Clr=Ro' Cbr 1O4k,, lo'kf, 3kp(C - Cb)/R,, 1040,

q / q r e t k / m 3 kg/m3 k / m 3 m/s m/s kg/(m3-s) kg/(kg.s) d Bi 0.01 7.69 7.61 1.70 0.0259 0.0262 0.0505 1.00 0.0799 0.101 0.1 1.29 1.19 0.217 0.163 0.177 0.0569 1.27 0.0799 0.681 0.5 0.381 0.296 0.0422 0.505 0.674 0.0557 1.24 0.0799 2.59 1 0.248 0.163 0.0211 0.750 1.20 0.0554 1.23 0.0799 4.61 2 0.175 0.0904 0.0105 1.03 2.13 0.0551 1.23 0.0799 8.19

Effect of D

10 0.108 0.0230 0.00210 1.61 8.10 0.0555 1.23 0.0799 31.1

c, Clr-RO, cb? lo'k,, lO'kr, 3k,(C - Cb)/R,, 1040, DIDref k / m 3 k / m 3 k / m 3 m/s m/s kg/(m3.s) kg/ (kg.4 d Bi

0.1 1.61 0.715 0.0221 0.113 0.258 0.0584 1.30 0.2526 9.92 1 0.248 0.163 0.0211 0.750 1.20 0.0554 1.23 0.0799 4.61

10 0.0600 0.0514 0.0210 4.36 5.56 0.0553 1.23 0.0253 2.14 100 0.0283 0.0275 0.0209 22.9 25.8 0.0551 1.23 0.00799 0.993

Effect of kf c, C l r - R o , l e k , , 104kf, 3k,(C - Cb)/RO, 1040,

kf/kf,ref k / m 3 k / m 3 k / m 3 m/s m/s kg/(m3d kg/(kg.s) $ Bi 0.1 1.56 1.48 0.0214 0.113 0.120 0.0566 1.26 0.0799 0.461 1 0.248 0.163 0.0211 0.750 1.20 0.0554 1.23 0.0799 4.61

10 0.120 0.0351 0.0210 1.72 12.0 100 0.107 0.0224 0.0210 1.97 120

is not the reactant but the product of the reaction, and the rate of reaction is not affected by the product. The increase in particle size increases the concentration gradient, while decreasing the mass-transfer coefficient. Hence, the flux, given by the product of these values, is relatively constant. As a result, the extraction rate is not affected by the particle size in this range of particle sizes. When the particle size increases to 5-fold, however, the intraparticle effect is evident in the model predictions. As shown in the second column in Table 111, the average concentration in the particle is high for larger particles. Thus, intraparticle diffusion resistance is a significant contribution for these particles. Since particle size in the pulping industry is 50-100 times the size of the particles used here, the mass transfer would have a greater influence in an industrial extraction process.

A similar situation applies to external mass transfer. Curves based on the model were compared for different flow rates from 0.01-fold to 10-fold of the typical experimental condition (q = 1.67 X lo-' m3/s) in Figure 13 and Table 111. The curves for 0.5-10-fold increases coincide, while the curve for the 0.1-fold increase is slightly different. When the flow rate decreased to 0.1-fold, the effect of flow rate began to appear.

The molecular diffusivity and external mass-transfer coefficient are also considered in Table 111. The diffusivity only beings to affect the rate ( Q ) when molecular diffusivity (D) is 0.1-fold of the estimated value. The same situation is observed for the external mass-transfer coefficient. When the external mass-transfer coefficient is reduced to 0.1-fold, a small change in the rate (Q) is observed.

The values of 9 and Bi are 0.080 and 4.6, respectively, for the experimental condition of d, = 1.84 mm and q = 1.67 X lo-' m3/s. As discussed in our earlier paper (Goto

0.0554 1.23 0.0799 46.1 0.0551 1.23 0.0799 461

1

I ' '

0 I I I I LOO0 5CX ECC2 2030 3000 1 ccc

t [SI

Figure 13. Predicted effect on flow rate on the extraction rate (Tr = 1.08, P, = 1.50, d, = 1.84 mm).

et al., 1990), the parabolic profile assumption is an accurate approximation for the reaction extraction with these small parameters.

Conclusion

The extraction rate of lignin from wood with supercritical tert-butyl alcohol was investigated dynamically. The extraction rate increased with temperature and pressure. For the conditions of the experiments, changing the particle size or flow rate had no observable effect. A parallel first-order reaction model was applied to the reaction extraction process. The predicted extraction rate agreed well with the experimental data and was consistent with the structure of the wood.


Acknowledgment

tion Grant CBT-8700092 is gratefully acknowledged.

Nomenclature Bi = Biot number, kfRo/D, C = concentration in the pores of the particle, kg/m3 C = volume-averaged concentration in the particle, kg/m3 C, = concentration at the spectrophotometer at T = 298 K,

C b = bulk concentration in the reactor, kg/m3 Cb = arithmetic average of concentrations of feed and effluent

C, = concentration in the reactor effluent, kg/m3 CL = lignin concentration, kg/m3 of particle De = effective diffusivity of lignin derivatives in the porous

D = diffusivity of lignin derivatives in tert-butyl alcohol, m2/s d = particle diameter, m 4 = activation energy, kJ/mol f = fraction of lignin for the first reaction ko = preexponential factor, s-l kf = fluid-to-solid mass-transfer coefficient, m/s k, = overall mass-transfer coefficient, m/s L = length of bed of particles, m mo = initial mass of wood chips, kg P = pressure, Pa P, = critical pressure, Pa P, = P/Pc q = flow rate, m3/s R = intrinsic reaction rate of lignin, kg/(m3.s) Ro = particle radius, m Re = Reynolds number, dpup/p R, = gas constant, kJ/(mol.K) r = intraparticle radial position, m S c = Schmidt number, p/pD Sh = Sherwood number, k&,/D T = temperature, K T, = critical temperature, K T, = T / T c t = time, s u = superficial fluid velocity, m/s u, = fluid velocity at the spectrophotometer, m/s V = volume of the reactor bed, m3 Greek Le t t e r s tb = bed void fraction cp = particle porosity /I = viscosity, Pa-s p = density, kg/m3 pa = density at the spectrophotometer, kg/m3 pe = density at the reactor exit conditions, kg/m3 4 = Thiele-type modulus, Ro/3(k/D,)1/2 D = global reaction-extraction rate, kg/ (kg.s)

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P = 0.1 MPa, kg/m3

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Kinetics and mass transfer for supercritical fluid extraction of wood

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