ARTICLE pubs.acs.org/IECR
Modeling of Alkali Impregnation of Eucalyptus Wood Maria C. Inalbon,†,* Miguel C. Mussati,‡ Paulina Mocchiutti,† and Miguel A. Zanuttini† †
ITC Instituto de Tecnología Celulosica, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santiago del Estero 2654, S3000AOJ, Santa Fe, Argentina ‡ INGAR Instituto de Desarrollo y Dise~ no, CONICET-Universidad Tecnologica Nacional, Avellaneda 3657, S3002GJC, Santa Fe, Argentina ABSTRACT: In wood pulping processes, the quality of the impregnation stage has a significant influence on the final pulp properties. In this work, a refined version of a previously published model is used to analyze this operation stage. For liquor containing NaOH and Na2S, the study considers the reaction of wood acetyls and acidic groups. The Donnan effect is applied for analysis of ion concentrations in the wood-liquid interphase. The predicted concentration profiles are in acceptable agreement with the experimental results. The model is used afterward to simulate a batch or a cocurrent continuous kraft impregnation process. In the impregnating liquor, the alkali concentration is gradually reduced due to chemical reactions and alkali accumulation in the wood chips. The level of impregnation is finally analyzed considering different chip thickness values corresponding to an industrial chip stock sample.
1. INTRODUCTION In wood pulping processes, chips must be properly impregnated with chemical reagents prior to the cooking stage. For kraft pulping, the favorable effect of an adequate impregnation stage on the final pulp properties has been reported by several authors.1-5 A deeper knowledge of the impregnation stage can be useful for optimizing the kraft pulping process itself, and also for the analysis of innovations that consider the obtainment of byproduct or the reduction of the considerable carbon dioxide emission of the kraft process. Although emissions are associated with the chemical recovery cycle, they strongly depend on the efficiency of the pulping stage. A detailed alkali wood impregnation analysis should consider the penetration of liquids, diffusion of chemical reagents, and also chemical reactions and swelling. For the purpose of this work, the effect of the liquid penetration phenomenon can be ignored in the analysis. Industrial impregnation is normally performed after chip steaming. A proper steaming preheats the wood and displaces the air from the interior cavities. If the steaming stage is followed by a pressurized impregnation, the liquid saturation of the wood is reached. A complete liquid penetration is shown not only for hardwood6 but also for softwood.7 Under this condition, the alkali impregnation can be analyzed as a reacting nonconvective diffusion process. The deacetylation is the main reaction involved, and it is responsible for a considerable amount of alkali consumed.8 The kinetics of this reaction for eucalyptus wood impregnation under conditions close to real industrial practice has been reported by Inalbon and Zanuttini.9 Alkali dynamically modifies the local wood ion transport properties. The dependence of the effective capillary cross-sectional area on alkalinity, temperature, and chemical reaction degree has been experimentally determined for eucalyptus wood in a recent work.10 An ion concentration gap is established at the wood-liquid interphase. That is, the acid groups in wood that become ionized r 2011 American Chemical Society
by the action of sodium hydroxide establish a concentration difference between the outer solution phase and that associated with the solid phase. As the acid groups cannot move out of the gel, the solution within can be regarded as separated from the external solution by a semipermeable membrane, which confines the acid groups but allows transporting of water and all simple ions.11 The Donnan theory was originally developed to describe the distribution of ions between solutions on either side of a membrane.12 The concept was used to analyze the ion distribution between cellulose fibers and surrounding liquor in a pulp suspension,11,13,14 and also between wood and external liquor.15 This theory considers that the chemical potential of each mobile species is equal on both sides of the interphase, and it can be thus used to estimate the relationship between the concentrations at the equilibrium. Chip thickness (radial or tangential wood direction) is the critical dimension for the diffusion processes.1,16 Indeed, the importance of the chip thickness on the pulp uniformity obtained by a kraft pulping process has been shown by many authors.1,16-18 For this reason, a one-dimensional (1-D) balance along the transverse direction of the wood is a useful approach to understand and quantitatively analyze this phenomenon. In a previous paper,19 an isothermal dynamic 1-D model considering a rigorous mass balance for the main ions along the chip thickness direction was derived. The analysis took into account the relevant chemical reactions and the local dynamic diffusion coefficient. The model acceptably fitted the experimental concentration profiles of sodium and hydroxide ions and acetyl groups in wood. Received: September 20, 2010 Accepted: December 17, 2010 Revised: December 13, 2010 Published: January 24, 2011 2898
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Table 1. Donnan Effect: Concentration Distribution between the External Liquor and the Solution in the Internal Side of the Interphase (Wood) for 0.25 M NaOH and 25% Sulfidity Naþ
In this paper, the model is refined by considering the presence of sodium sulfide as well as the influence of the Donnan effect on the ion concentration at the wood-liquid interface. The model is experimentally validated from a batch impregnation of wood cubic blocks using constant liquor concentration. Then, the model is used to simulate a batch or a cocurrent continuous kraft impregnation process, whose impregnating liquor concentration is calculated from the evolution of the chemical reaction and alkali accumulation in the chips. The evolution of the impregnation level is analyzed for a chip thickness distribution corresponding to an industrial sample.
-COO- (acid groups)
0.285
0.25
0.035
-
0.19
0.027
0.156
Effective ion diffusion coefficients in the transverse direction of wood are expressed as the product of the wood effective capillary cross-sectional area ECCSA (dimensionless) in this direction and the ion diffusion coefficient in solution Di(in solution) (cm2/min), which in turn depends on the ion mobility λ0i (cm2/Ω 3 equiv), temperature, and the ion valence zi. Di ¼
RTλ0i ECCSA ºzi ßF 2
ð4Þ
The effective capillary dependence on temperature and reaction degree was previously obtained:20 ECCSA ¼ a þ bðCacetyls Þ - cðCacetyls Þ3 - dðCacetyls ÞT
2. MODEL DESCRIPTION 2.1. Departing Model. As mentioned above, a model that allows analyzing the one-dimensional isothermal alkali impregnation process along the chip thickness has been previously presented by Inalbon et al.19 Briefly, sodium, hydroxyl, and acetate as mobile ions and acetyls and acid groups as species fixed in the wood are considered. Figure 1 schematizes a wood chip and the main impregnation direction considered. The mobilities of the hemicelluloses and their alkaline degradation are neglected. The impregnation is considered as a reacting nonconvective diffusion process in a pseudohomogeneous solid. Then, the mass balance equation is ∂Ci ð1Þ þ rNi ¼ Ri ∂t
where Ci is the concentration of ion i (mol/L), t is the time (min), Ni is the net molar flux of ion i [mol 3 cm/(L 3 min)], and Ri is the chemical consumption or generation rate of ion i [mol/ (L 3 min)]. By assuming ideal solution behavior and expressing the net molar flux as a function of the ion electrochemical potential, the mass balance equation eq 1 becomes ∂Ci ∂Di ∂Ci ∂ 2 Ci F ∂Ci ∂Di ∂φ zi D i ¼ þ Di 2 þ þ zi C i RT ∂x ∂t ∂x ∂x ∂x ∂x ∂x ! F ∂2 φ þ zi Di Ci þ Ri Ri ð2Þ RT ∂x2 where φ is the electric potential (V), Di is the effective diffusion coefficient (cm2/min), x is the position in the direction of analysis, zi is the ion valence, T is the temperature (K), Ri is the stoichiometric coefficient, R is the universal gas constant (8.3143 J/mol 3 K), and F is the Faraday constant (96 487 J/mol 3 V). The condition of zero electric current is used to establish the electric potential as a function of concentrations and diffusion coefficients. The kinetic expression used for the deacetylation reaction is9 Ri ¼ Racetyls ¼ kðCacetyls Þn ðCOH Þm ðCNa Þp
HS-
internal solution (mol/L) 0.373
external liquor (mol/L)
Figure 1. Scheme of a wood chip and the main impregnation direction considered.
OH-
þ eðCacetyls Þ2 T þ fT
The values of the constants are a = -0.6349, b = 0.2998, c = -0.008 53, d = -0.001 62, e = 0.000 228, and f = 0.002 85. 2.2. Refined Model. In this paper, the model is refined taking into account the effect of the sodium sulfide presence in the liquor as well as the Donnan theory for a better representation of ions concentration at the interface between wood and external liquor. As the pK of S2-/HS- equilibrium (S2- þ Hþ T HS-) is 13.0 and the pK of HS-/H2S equilibrium (HS- þ Hþ T H2S(dis)) is 7.0, at the normal pH range of a kraft process, all the sulfide is in its hydrogen sulfide form: S2 - þ H2 O f HS - þ OH -
ð6Þ
It is assumed that hydrosulfide does not react under the range of conditions considered. The Donnan theory helps to analyze the difference between ion concentrations in wood and external liquors that takes place due to the existence of acid groups in wood. Assuming that the chemical potential and the activity coefficient of each mobile species are equal on both sides of the interphase, and discarding any osmotic pressure gradient, a constant ratio λ D between the concentrations inside and outside the wood (C I and CE, respectively) is obtained: λD ¼
CINa CE CE ¼ OH ¼ HS E I CNa COH CIHS
ð7Þ
By assuming an equilibrium condition, concentrations in wood can be estimated knowing the concentrations in the external liquor (CEi ) and the concentration of acid groups inside wood (CIAG). The electroneutrality condition leads to the following expressions for both sides:
ð3Þ
where k is the kinetic constant and n, m, and p are exponential factors.9 The reaction of acidic groups is considered to be coupled to the deacetylation one.
ð5Þ
CINa ¼ CIOH þ CIHS þ CIAG
ð8Þ
CENa ¼ CEOH þ CEHS
ð9Þ
Table 1 illustrates the ion distribution between the external liquor and the solution in the internal side of the interphase (wood) according to the Donnan effect for a 0.25 M NaOH 2899
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solution and a 25% sulfidity (sulfidity = 2[100C ENa2S/(CENaOH þ 2CENa2S)]). In this case, it can be observed that the hydroxyl concentration is reduced from 0.25 M outside to 0.19 M inside. Clearly, the Donnan effect has a negative influence on the impregnation rate. The concentration of acid groups in the wood is calculated as the content of acid groups (0.28 equiv/kg) divided by the water content (1.8 L of H2O/kg of wood). In the pulping liquor of a real pulping system, sodium carbonate and other ionic species can be found, which may partially reduce the Donnan effect. Nevertheless, it can be calculated that the effect always exists. The following assumptions are considered to set the initial and boundary conditions: Initial Conditions. The initial concentrations of hydroxyl and acetate ions in wood are 0. COH jðt ¼ 0, "xÞ ¼ Cacetate jðt ¼ 0, "xÞ ¼ 0
ð10Þ
The initial acetyl group and acid group contents in wood (CAcG and CAG, respectively) correspond to an untreated wood content. The initial sodium content is equal to the acid group content. wood CAcG jðt ¼ 0, "xÞ ¼ Cuntreated AcG
ð11Þ
wood CAG jðt ¼ 0, "xÞ ¼ Cuntreated AG
ð12Þ
CNa jðt ¼ 0, "xÞ ¼ CAG jðt ¼ 0, "xÞ
ð13Þ
Boundary Conditions. The species flux at the chip center (x = h/2) is 0, (h is the chip thickness): Niðx ¼ h=2;"tÞ ¼ 0
ð14Þ
External mass transfer restrictions are neglected. For all ions, the same relationship between concentrations in each side of the interface is considered, as derived from the Donnan theory. Then, eqs 7 are valid: CIOH jðx ¼ 0;"tÞ ¼
CEOH ; λD
CIHS jðx ¼ 0;"tÞ ¼
CEHS ; λD
CINa jðx ¼ 0;"tÞ ¼ CENa λD
3. EXPERIMENTAL PROTOCOL 3.1. Raw Materials. Green, fresh Eucalytpus grandis wood with an average density of 366 kg/m3 was used for the impregnation experience. Six-year-old logs were supplied by INTA-Concordia, Argentina. The acetyl content was 907 mequiv/kg (3.9% on wood), and the original and total acid group contents were 82.5 and 280 mequiv/kg, respectively. The analytical methods used for these determinations were previously described.9,20 Wood blocks of 35 mm sides were used to determine the experimental impregnation profiles for constant chemical concentration in the external liquor. 3.2. Experimental Impregnation Technique. In a closed reactor, wood blocks were steamed and then sunk in the thermostated impregnation liquor. The liquor to wood ratio was high enough (approximately 1000 L/kg) to consider constant chemical
Table 2. Experimental Conditions for Wood Block Impregnation
a
EAa (g of NaOH/L)
sulfidity (%)
temperature (C)
10/20
25/35
110
time (min) 15/30
EA, effective alkali. EA = CENaOH þ CNa2ES .
concentration in the external liquor during impregnation. Afterward, the system pressure was increased to 0.6 MPa. Blocks were kept under pressure and agitation. Once the treatment time was reached, the reactor was depressurized, and the blocks were taken off and immediately immersed into liquid nitrogen. Then, they were stored in a freezer at -10 C. The procedure is described in detail elsewhere.20 The adopted experimental conditions are shown in Table 2. The frozen blocks were sliced with a carpentry saw to remove the layers of impregnated wood, except for the block faces of interest (tangential faces). These faces were then cut into 200-μmthick serial slices. Slices were weighed, and their alkali and sulfide contents were determined by quantitative neutralization of 20 mL of water containing the slice, using SCAN N2:63.21 The sodium concentration in the liquid volume resulting from titration was determined by atomic absorption spectroscopy, and acetate concentration was determined by gas chromatography using the method proposed by Solar et al.22 The wood acetyl group content was estimated by diffuse Fourier transform infrared spectroscopy, directly applied on the dry slices. A published relation between the peak height at 1735 cm-1 normalized to the 1510 cm-1 band in the IR spectrum and the acetyl content determined by gas chromatography was used.23
4. COMPUTATIONAL ASPECTS The resulting model equations were implemented and numerically solved using general Process Modeling System gPROMS,24 from Process System Enterprise Ltd., which is a general-purpose computational environment for modeling, dynamic simulation, and optimization with both discrete and continuous as well as lumped and distributed characteristics. gPROMS is a high-level partial differential-algebraic equation (PDAE) package that allows symbolic specification. The PDAE system is numerically solved using the method-of-lines family of numerical method (MOL). This involves discretization of the distributed equations with respect to all spatial domains, which results in a mixed set of time-dependent DAEs. gPROMS allows the user to specify the type of the spatial approximation method (e.g., finite difference or finite elements) and the approximation order (e.g., first, second, etc.). Numerical discretization is applied automatically. The resulting DAE system is integrated over time by employing DASOLV code, which is integrated into gPROMS; it is based on the backward differentiation formulas (BDF) and automatically adjusts the time step size as well as the integration order to maintain the integration error within the user-specified tolerance. In this paper, the second-order centered finite difference method CFDM with 40 discretization intervals, and absolute and relative tolerances of 1 10-6, were used. All simulations were performed in approximately 120 s of CPU time on a 3.0 GHz Pentium IV processor with 512 MB RAM. 5. RESULTS AND DISCUSSION 5.1. Model Validation: Impregnation with Liquor of Constant Chemical Concentration. Figure 2 shows experimen-
tal and predicted sodium, acetyl, hydrosulfide, and hydroxyl 2900
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Figure 2. Experimental and model-predicted profiles (EA 9.6 g of NaOH/L, sulfidity 25%, 30 min, 110 C).
Figure 3. Comparison between experimental and predicted impregnation front positions for operating conditions given in Table 2. (a) Acetyl content becomes half the original content. (b) OH concentration becomes zero.
concentration profiles for the following set of conditions: 9.6 g of NaOH/L of effective alkali, 25% sulfidity, and 30 min of impregnation time at 110 C. As a chip thickness of 6 mm is considered here, and due to geometric symmetry, the simulation results are plotted for half the chip thickness, i.e., from the woodliquid interphase (x = 0) to the chip center (x = h/2). Species concentrations in the external liquor, which are kept essentially constant by setting a high liquor to wood ratio, are also indicated. It can be observed that the model predictions are satisfactory. In this case, a transition zone ranging from 1.6 to 2.2 mm can be defined, which is highlighted by dashed vertical lines. In the inner zone, there is no presence of alkali, and the acetyl content maintains the level of the untreated wood (0.5 N), which is calculated by dividing the content of acetyls (0.907 equiv/kg) by the water content (1.8 L of H2O/kg of wood). In the outer zone, there is no presence of acetyl groups. The transition zone can be considered as a moving impregnation front, whose position at different times allows determining the “pace” of impregnation. As consequence of the Donnan effect, Figure 2 shows that hydroxyl, hydrosulfide, and sodium concentrations in the internal side surface of the chip differ clearly from those in the external liquor. This is a novel result of the refined model presented here
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Figure 4. Predicted hydroxyl concentration profiles for impregnation at 110 C with effective alkali (EA) values of 10 and 20 g of NaOH/L and 20 and 40% sulfidity (S), at three impregnation times.
Figure 5. Scheme of a cocurrent impregnation system. Chips and liquor move at the same linear velocity along the reactor height.
as the original one was unable to explain those experimentally found differences. No difference can be observed between the advance of the predicted hydroxyl and hydrosulfide profiles, which is in agreement with what was experimentally found for all conditions. The model predictions adjust quite well the position of the reacting front. However, in some cases, the shape of the predicted profiles differs from that of the experimental results, especially for OH- concentration. The reason could be in the model hypothesis taken into account. Indeed, diffusion and deacetylation phenomena are considered, but the peeling reaction and the dissolution of hemicelluloses are not. In order to inspect the fit quality, results for all operation conditions can be grouped together in a unique graph plotting the reacting front position experimentally obtained for each condition set versus that one obtained by simulation. Specifically, Figure 3 shows the positions of the experimental versus predicted impregnation front positions for conditions given in Table 2 where (Figure 3a) the acetyl content becomes half the original content and (Figure 3b) the alkali concentration becomes zero. An acceptable agreement can be observed. 2901
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Industrial & Engineering Chemistry Research 5.2. Analysis of Sulfidity Effect. The model allows analyzing the sulfidity influence in the impregnation front position. Figure 4 shows the hydroxyl concentration profiles predicted for chips impregnated at 110 C with effective alkali of 10 and 20 g of NaOH/L, 20 and 40% sulfidity, at 10, 20, and 30 min. It can be observed that the sulfidity influence in the impregnation front position is not significant in the range of conditions investigated, which is usual in industrial operations. 5.3. Simulation of Chip Impregnation with Varying Liquor Concentration: Uniform Chip Thickness. The derived model has been used so far for simulating the impregnation phenomenon considering constant species concentrations in the external liquid. However, the model is also able to simulate the evolution of the reagent concentrations in the external liquid, i.e., their depletion across time (bath process) or along the reactor length (cocurrent process) when wood chips are impregnated. In a batch kraft impregnation process, the alkali concentration in the external liquor varies temporally due to two phenomena occurring inside chips: (i) the chemical reactions and (ii) the
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alkali accumulation. In a cocurrent continuous kraft impregnation process, this concentration varies spatially. If chips and liquor move together along the reactor length, i.e., at the same linear velocity (v), and the chip size is negligible compared to the reactor one, the liquor concentration can be considered homogeneous on the chip surface but varying with the axial position in the reactor. From a modeling point of view, a new variable ζ can be defined as follows: ζ = t for a batch process ζ = z/v for a continuous cocurrent process, where z is the reactor axial coordinate and v is the linear velocity of liquor and chips Thus, the liquor concentration in the external liquor can be considered as varying with either time t or reactor axial coordinate z for a batch or a cocurrent process, respectively. Figure 5 shows a scheme of a cocurrent impregnation system. Inlet and outlet process streams are indicated with their corresponding concentrations, keeping the same notation as above. The gray scale indicates the reagent consumption along the reactor height. The total alkali uptake by the chip U (mol/L 3 min) in a cocurrent or a batch reactor is equal to the alkali spent for chemical reactions Sch (mol/L 3 min) plus its accumulation in the chip A (mol/L 3 min). ð15Þ U ¼ Sch þ A 2 Sch ¼ h rlw 2 2
Z 0
h=2
wood BðCuntreated - CAcG Þ dx AcGðt ¼ 0Þ
2 A ¼ h rlw 2 2 Figure 6. Evolution of alkali concentration in the external liquor (CEOH) and in the internal side (wood) of the wood-liquid interphase (CIOH), and its consumption (%) for a 3.7 mm thick chip impregnated with EA of 20 g of NaOH/L, 30% sulfidity, and liquor to wood ratio 4.0 at 100 and 110 C.
Z 0
h=2
CIOH dx
ð16Þ
ð17Þ
wood where rlw is the liquor to wood ratio, Cuntreated is the initial AcG acetyl group concentration, and CAcG is the remaining acetyl group concentration. B is a stoichiometric constant that considers the alkali consumption produced by the acetyl and acid group reactions. The latter is considered coupled to the
Figure 7. Impregnation profiles in the thickness direction of a chip of 3.7 mm as a function of ζ for the following conditions: EA 20 g of NaOH/L, sulfidity 30%, and liquor to wood ratio 4.0 at 100 C. (a) Hydroxyl profile in wood and external liquor concentration. (b) Acetyl content profile. 2902
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Figure 8. Histogram and log-normal distribution of chip thickness (industrial sample).
Table 3. Critical Thickness Values % of area
thickness less than (mm)
10 25
2.43 2.92
50
3.7
75
4.4
90
5.29
deacetylation19 and represents an additional 20% of consumption (B = 1.20). The uptake is responsible for the variation of the liquor hydroxyl concentration, which can be computed considering the liquor - |0) minus the inlet hydroxyl concentration in the liquor (COH hydroxyl uptake of the chip. liquor
liquor
COH - ¼ COH - j0 - ðwcÞU
ð18Þ
where wc is the water content in the wood (1.8 g of H2O/g of wood), which is considered constant. The boundary conditions at the chip surface (x = 0) are given by eqs 7, 8, 9, and 18. The initial conditions look like eqs 10, 11, and 12 (subsection 2.2), but considering spatial coordinate z instead of time t. The impregnation of a 3.7 mm thick chip with a varying liquor concentration was simulated, for EA of 20 g of NaOH/L, 30% sulfidity, and 4.0 L of external liquor per kg of dry wood at 100 and 110 C. Figure 6 shows the evolution of the alkali concentration profile in the external liquor (CEOH) and in the internal side (wood) of the wood-liquid interphase (CIOH). Figure 6 also shows the percentage of consumed alkali related to its level in the inlet external liquor. Figure 7a shows the alkali profile as a function of ζ for a 3.7 mm chip thickness impregnated with EA of 20 g of NaOH/L, 30% sulfidity, and 4:1 external liquor to wood ratio (L/kg), at 100 C. It also shows the external liquor alkali concentration, which is always clearly higher than the interphase alkali concentration due to the Donnan effect. Figure 7b shows the acetyl group content profile as a function of ζ for the same conditions. At ζ = 30 min, 99% of acetyl groups are removed. 5.4. Simulation of Impregnation with Varying Liquor Concentration: Effect of Chip Thickness. A chip thickness distribution should be considered to analyze the impregnation in an industrial scenario. A thickness distribution determined in a 50-chip sample from an industrial chip stock is shown in Figure 8. The corresponding critical thickness values of this distribution are listed in Table 3. The model allows analyzing the uniformity of the impregnation considering a chip thickness distribution like that given in
Figure 9. Remnant acetyl group content in the chip for different thicknesses (EA 20 g/L, sulfidity 30%, liquor to wood ratio 4.0, 100 C). The variation of the external liquor concentration corresponding to a 3.7 mm thick chip was considered.
Table 3. The consumption of the liquor reagents is faster in thinner chips than in thicker chips, but an “average” consumption can be estimated considering chips of “medium” thickness. Figure 9 shows the remnant acetyl group content calculated for the critical values listed in Table 3 considering the variation of the external liquor concentration is that found when simulating the impregnation of an average thickness chip (3.7 mm). A 2.46, 2.92, and 3.7 mm thick chip requires 15, 20, and 30 min, respectively, for a completed deacetylation. If the chips are thicker (4.4 and 5.29 mm), deacetylation cannot be completed during a 30 min impregnation time.
6. CONCLUSIONS The model developed allows analyzing the effects of the main variables in a kraft impregnation process, such as alkali concentration, sulfidity, temperature, time, and chip thickness. For the impregnating liquor, not only a constant alkali concentration but also a concentration gradually reduced due to the alkali taken by chips can be considered. The model acceptably predicts the difference that is experimentally found between the liquor concentration and the woodliquid interphase concentration due to the Donnan effect. The profiles of hydrosulfide can be predicted. For the conditions analyzed here, the model clearly shows that the hydrosulfide concentration does not have a significant influence on the position of the impregnation front. The hydrosulfide and alkali impregnation is, generally, simultaneous. The level of impregnation can be assessed and compared for different chip thicknesses of an industrial chip stock. ’ AUTHOR INFORMATION Corresponding Author
*E-mail: cinalbon@fiq.unl.edu.ar. Tel./Fax: þ54-342-4520019.
’ ACKNOWLEDGMENT The authors wish to thank UNL, ANPCyT, and Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET) of Argentina for their financial support. 2903
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’ NOTATION a = constant of ECCSA correlation (eq 5) A = alkali accumulations in the chip (mol/L 3 min) AcG = acetyl groups AG (-COO-) = acid groups b = constant of ECCSA correlation (eq 5) c = constant of ECCSA correlation (eq 5) Ci = concentration of ion i (mol/L) d = constant of ECCSA correlation (eq 5) Di = effective diffusion coefficient (cm2/min) Di(in solution) = ion diffusion coefficient in solution (cm2/min) e = constant of ECCSA correlation (eq 5) EA = effective alkali ECCSA = effective capillary cross-sectional area (dimensionless) F = Faraday constant (96 487 J/mol 3 V) f = constant of ECCSA correlation (eq 5) h = chip thickness (cm) k = kinetic constant m = kinetic exponential factor n = kinetic exponential factor Na (Naþ) = sodium cation Ni = net molar flux of ion i [mol 3 cm/(L 3 min)] OH (OH-) = hydroxyl ion R = universal gas constant (8.3143 J/mol 3 K) Ri = reaction rate [mol/(L 3 min)] rlw = liquor to wood ratio Sch = alkali spent for chemical reactions (mol/L 3 min) SH (SH-) = hydrosulfide ion t = time (min) T = temperature (K) U = total alkali uptake (mol/L 3 min) v = linear velocity of liquor and chips in a cocurrent reactor. wc = water content in the wood (1.8 g of H2O/g of wood) x = position in the direction of analysis inside the chips z = reactor axial coordinate zi = ion valence Ri = stoichiometric coefficient φ = electric potential (V) λ0i = ion mobility (cm2/Ω 3 equiv) λD = constant ratio between the cation concentrations inside and outside the wood and between the anion concentrations outside and inside the wood ζ = time (for a batch process) or z/v (for a continuous cocurrent process)
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