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Ind. Eng. Chem. Res. 2002, 41, 3312-3316
Physicochemical Modeling of a Bleaching Solution and Reaction J. Salminen*,† and O. Antson‡ Laboratory of Physical Chemistry and Electrochemistry, Helsinki University of Technology, P.O. Box 6100, FIN-02015 HUT, Finland, and VTT Processes, P.O. Box 1404, FIN-02044 VTT, Finland
The thermodynamic model and experiments were used to study the peroxide-oxide bleaching solution. The solution properties such as pH have been measured and modeled both in a pure aqueous solution and with wood fibers. Further, the thermodynamic multicomponent model was used with kinetic constraints for pH calculations in a reactive solution. The knowledge of the pulp and solution properties along with the results of the model calculations could be used for optimization of the bleaching process with respect to reaction time and temperature. 1. Introduction Computer-aided multicomponent calculation methods for aqueous solutions have been developed in recent years and are increasingly applied to actual processes in order to solve practical problems. The extensive mechanistic models following reaction kinetics are traditionally used for chemical process simulations. The dynamic models that are based on the Gibbs energy change approach can further be used for calculations of equilibrium and kinetically constrained systems. These methods can be applied to industrial processes, which involve aqueous salt solutions including neutral components. The oxygen-pressurized alkaline peroxide (PO) stage is an important sequence of total chlorine free (TCF) bleaching. It was adopted to replace chlorine for environmental reasons. The kinetics and thermodynamics of the process solution and the changes on the kraft pulp properties are both needed for process optimization with respect to time, temperature, pressure, pulp consistency, and chemical charges.1,2 The thermodynamic properties of the bleaching solution were studied with appropriate models. The Gibbs energy calculations together with measured solution and pulp properties give valuable information of the bleaching process. 2. Thermochemical Calculations of an Alkaline Peroxide Solution Both improved calculation methods and critically evaluated databanks for pure substances increase the number of practical applications for thermochemical calculations. The calculation methods are based on the measured and partly predicted properties. Simulations should be, if possible, verified against independent data or measurements. In the calculations for the aqueous solutions, a temperature-dependent standard data and activity coefficient model is needed to describe the total Gibbs energy for the solution.3 The total Gibbs energy G(T,P,ni) of the multiphase system is the sum over the phases R to ξ that exist in the system.
G)
∑R ∑i niRµiR
(1)
* Corresponding author. E-mail:
[email protected]. Fax: +358 9 451 2580. † Helsinki University of Technology. ‡ VTT Processes. E-mail:
[email protected].
The Gibbs energy G of the mixture in different phases is made up of contributions of the pure components and of the mixing effects including nonideal terms. The determination of chemical equilibrium for those closed systems at constant T and P, which involve only work related to volume change, is the point of the global minimum of the total Gibbs energy, min(G) on the set of points (n1, n2, ..., nN) satisfying the material balance equations. Modern calculation techniques4-6 allow the user to choose the model for excess Gibbs energy. A recognized thermodynamic model and computer routine are needed in order to calculate multicomponent compositions accurately. The solution matrix of the minimum of G yields the intensive properties from which the familiar equilibrium constants can be obtained. Systems where nonequilibrium processes take place can additionally be calculated by the Gibbs energy approach. The question of how fast the reaction is cannot be answered by means of thermodynamics. That is the problem of chemical kinetics. If the reaction dynamics are known, the Gibbs energy minimum can be used to follow the time- dependent advancement of the reaction for specific systems. The system is then in a dynamic chemical state, which represents the local equilibrium of the reactive solution. Dynamic constraints as material restrictions can be included in the model according to the separately measured kinetic path. This can be applied to various problems where one or some of the constituents of the reactive system are kinetically constrained.7-12 The chemical as well as the energetic changes are then calculated simultaneously as a function of the extent of the reaction or according to changing chemical amounts. This methodology has been applied in many fields of industrial processes with chemical reactions in the gas, liquid, or solid phase. To study the alkaline peroxide bleaching solution, a multicomponent model was developed. The constituents used in the model are given in Table 1. An alkaline solution has been observed to stabilize hydrogen peroxide in a pure solution even at high temperatures.13,14 After some time, hydrogen peroxide will eventually decompose to water and oxygen. In practice, the peroxide first dissociates to hydrogen and perhydroxyl ions and will behave as a weak acid in the solution. At 298.15 K the calculation yields KP ) 2.105 × 10-12 for equilibrium constant (2)
KP )
a(H+)a(HO2-) a(H2O2)
10.1021/ie020027m CCC: $22.00 © 2002 American Chemical Society Published on Web 05/30/2002
(2)
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3313
which is in accordance with the NBS tables,15 which give the standard change of Gibbs energy ∆rG° ) 66 647.8 J/mol of the hydrogen peroxide dissociation reaction. In addition, the numerical value KP ) 2.4 × 10-12 (∆rG° ) 66 322.2 J/mol) has been reported16 at 25 °C. For the Gibbs excess energy Gex, the Pitzer’s virial model was used to derive the respective activity coefficients for solute species.
Gex RTnw
) f(I) +
Table 1. System Components Used in the Thermodynamic Model system components phase gas aqueous
∑i ∑j λij(I) mimj +
∑i ∑j ∑k τijk mimjmk + ...
(3)
solid a
component
O
Na
H
qa
H2O H2O2 O2 H2O2 O2 Na+ OHOOHH+ NaOH
1 2 2 2 2 0 1 2 0 1
0 0 0 0 0 1 0 0 0 1
2 2 0 2 0 0 1 1 1 1
0 0 0 0 0 -1 +1 +1 -1 0
q is negative value of elementary charge of the species.
where mi, mj, and mk are the molalities of the various ions or neutral solutes present. f(I) is the Debye-Hu¨ckel term. In terms of Gex, the activity coefficients yield
( )
∂Gex 1 νRTYnwMw ∂ni
ln γi )
(4)
T,P,nj*i
where γi is the activity coefficient of an ion, v is the sum of stoichiometric numbers of the dissociated ions, nw is the number of moles of water, Mw is the molar mass of water, T is the temperature, and R is the gas constant. Index i refers to ionic species. In the model used in this work, only binary interaction parameters λij were used and ternary parameters τijk were set to zero. This simplification yields the corresponding activity coefficients for ionic species. For the excess Gibbs energy, the Pitzer model was used. The binary interactions for the individual ions are presented in eqs 5-8
ln γNa ) f γ + 2mOHBNaOH + 2mOOHBNaOOH + mNamOHB′NaOH + mNaOOHB′NaOOH (5) ln γOH ) f γ + 2mNaBNaOH + mNamOHB′NaOH
(6)
ln γOOH ) f γ + 2mNaBNaOOH + mNamOOHB′NaOOH (7) ln γH ) f γ + mNamOHB′NaOH + mNaOOHB′NaOOH
(8)
where
f γ ) -Aφ
[
B( ) λij(I) ) βij0 + βij1 B′( )
]
2 I1/2 + ln(1 + bI1/2) 1/2 b 1 + bI
{
} ) ]
2 [1 - (1 + x)e-x] 2 x
[ (
dλij 2 x2 -x ) -βij1 2 1 - 1 + x + e dI 2 Ix x ) RxI I)
1 2
∑i mizi2
(9) (10)
(11) (12) (13)
3. Experiments and Modeling of an Alkaline Peroxide Solution Including Negatively Charged Wood Fibers The Henderson model was used for the approximation of the liquid-junction potential of the measured pH
Figure 1. Experimental and calculated pH values are shown as a function of H2O2 molality in four different NaOH molalities at 24 °C.
values described by Bates.17 The pH measurements were done by a tip point electrode, and the liquidjunction correction was made between the 3 mol/dm3 KCl solution and 0.0075, 0.017, 0.049, and 0.075 mol/ kg alkaline solutions. The calculated theoretical pH yield values which are higher than those measured if only the binary Pitzer ion interaction parameters for Na+ and OH- are used. This could be explained by interaction between Na+ and OOH- ions, which is expected to have a small effect on the pH of the solution. The liquid-junction-corrected pH values were used to fit empirical parameters βNaOOH(0) ) 0.040 and βNaOOH(1) ) -7.283. The contribution of the parameter CNaOOHφ is assumed to be zero in the dilute solution. pH measurements were carried out at ambient temperature by a tip point electrode. The calculated and experimental liquid-junction-corrected pH values for a NaOHH2O2 solution are shown in Figure 1. The calculations were further applied to simulate the chemical change in the heterogeneous system between the negatively charged fiber phase and the aqueous bulk phase. The potential difference φR - φβ in the fiber R-water β solution is defined as the Donnan potential. While charges in the fiber are considered point charges, free ions in the water phase are divided unevenly in space, which satisfies the Poisson-Boltzmann distribution.18 At constant temperature, the electrochemical equilibrium exists for those charged species that can cross the phase boundary.
µiR + ziFφR ) µiβ + ziFφβ
(14)
In macroscopic systems, the space charge density can
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Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 Table 2. Time-Dependent Functions for Alkali Consumption Based on Analyzed Concentrations Obtained from Bleaching Experimentsa T/°C
g of NaOH/kg of pulp
95 110 120
-0.039t + 0.4937 -13.57 + 5.283 exp(-0.0591t) + 17.16 exp(-0.00123t) 0.3246 + 3.581 exp(-0.0329t) + 3.521 exp(-0.0329t)
a The alkali feed was 13.6 g/kg of pulp in every experiment. The time t is in minutes.
Table 3. Functions for Peroxide Consumption Based on Analyzed Concentrations Obtained from Experimentsa
Figure 2. Measured pH values for bleached pulp as a function of pulp consistency at 25 °C. The fibers were first washed with ion-free water and with a 0.1 M HCl solution in order to change the functional groups into a hydrogen form. The concentration of bounded acidic groups (BAC) was defined as 35 mol/kg of fiber by conductometric titration.
T/°C
[H2O2]/(g/dm3)
95 110 120
0.4492 + 0.2247 exp(-0.04225t) + 0.4905 exp(-0.002878t) 0.3237 + 0.3352 exp(-0.1276t) + 0.4724 exp(-0.004818t) 0.649 + 0.5061 exp(-0.2318t)
a The peroxide feed was 1.15 g/dm3 in every experiment. The time t is in minutes.
Figure 4. Decrease of pH as a function of the κ reduction percentage. The end points of the curves represent a reaction of 120 min duration. The curves, which represent the reactions at 110 and 120 °C are identical to the point where the κ decrease is 31% and the corresponding pH is 10.7. Figure 3. Change of pH in a 5 wt % fiber mixture in an initial 0.0172 mol of NaOH/kg of H2O solution. For a fully bleached process sample pulp, the average change of pH was 0.13, and for brown pulp, it was 0.25.
be neglected and the electroneutrality condition is valid.
∑i zimi ) 0
(15)
The Donnan potential leads to alkaline adsorption and a noticeable pH change in the external solution, and the addition of pulp fibers decreases the pH of the external solution.19,20
∆pHR ) pH(pure) - pH(pulp)
(16)
∆pHR ) -log aH+R
(17)
The constant D is defined as the ratio of the activities:
D)
aH+R aH+β
)
aNa+R aNa+β
(18)
where the activity a is the product of activity coefficient γ and molality m of the ion, respectively. The superscript R denotes the internal fiber, and superscript β, the external solution concentration. In Figure 2, the pH decrease is shown as a function of the fully bleached pulp consistency in four NaOH
solutions. Adsorption of Na+ ions lowers the conductivity of the solution as the number of free charge carriers in the liquid phase decreases. The pH of the system decreases in a NaOH-water-pulp system as a function of added fiber consistency. An empirical equation for D was defined from the pH dependence on pulp consistency in four different ionic strengths
D ) 0.756I-0.711
(19)
where I is the initial ionic strength of the solution. To take account of the effect of the fiber on the multicomponent calculations, a mass balance constraint was used. The effect of the fully bleached and brown pulp on pH was taken into account in the model using separate pH target calculations. In the target calculation, the chemical amounts of one or some of the components (like salt MX) in the system are allowed to change to obtain the desired (measured) pH level. One still has to know the chemical amounts of the rest of the components in the solution which have an effect on the pH. It is not an independent variable; thus, it is possible to obtain the same pH value with different mixtures, compositions, and components. As the chemical amounts are changed in the model solution, the activity coefficient of the proton changes according to its functional composition dependence at constant T and P.
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3315
Figure 5. Effect on NaOH consumption and pH when changing the bleaching temperature from 95 to 110 °C and pressure from 12 to 2 bar during the bleaching reaction. Typical plots for 95 and 110 °C reactions at 0.5 MPa pressure are also shown. The twostage process yielded κ ) 4.9, which is between the average pulp properties of 2 h reactions at 95 and 110 °C.
The change of pH as a result of adding 5 wt % pulp can be seen clearly in Figure 3. For fully bleached (white) pulp, the pH change is assumed to be due to the neutralizing effect of bounded acid groups. In the brown pulp there is expected to be more carboxylic acid groups. In addition, also small amounts of precipitated acids and salts are dissolved in the solution. The pH change between the pure solution and the pulp mixture within 0-0.05 mol of H2O2/kg of H2O was found to be nearly constant for both white and brown pulp. The calculation can be further applied in such way that one can estimate the effect of the fiber on the pH and use it for pH control in dilute alkaline systems. 4. Changes of Chemical Amounts, K Number Properties, and pH during the Bleaching Reaction The bleaching reactions were performed at 95, 110, and 120 °C at 0.5 MPa oxygen pressure. The consistency of the pulp was set as 5 wt %, using κ ) 9.6 Finnish pine pulp in all experiments. The κ number is a dimensionless number that indicates the degree of lignification and the whiteness of the pulp. The measurements were carried out in a pressurized Parr 4522 autoclave. The experimental setup is given in detail in ref 2. The peroxide and alkali concentrations were determined by titration from the samples taken during the reaction. A nonlinear Levenberg-Marguardt algorithm was used to fit time-dependent functions for each set of experiments.21 The functions are given in Tables 2 and 3. The pulp properties and pH were also measured at timed intervals at ambient temperature. The bleaching reaction was found to become more rapid as the tem-
perature increased until a point was reached at each temperature where a further increase in the bleaching time had an undesired effect on the final pulp quality. The measured changes of the κ number and pH are plotted in Figure 4. The chemicals are then consumed only in nondesired neutralizing and surface reactions. In Figure 4, the measured change of pH in the bleaching solution is shown as a function of the κ reduction percentage. The end point of each curve represents a reaction of 120 min duration. At a temperature of 120 °C, the κ number reduces dramatically and stops completely after 25 min. The peroxide consumption was noticed to freeze, but the alkaline continues to be consumed by other neutralizing reactions. After this point, the alkaline is wasted and the quality of the fiber was found to decrease. The curves which represent the reactions at 110 and 120 °C are identical to the point where the κ decrease is 31% and the corresponding pH is 10.7. It takes 40 min for the 110 °C reaction to reach this point and 25 min for the 120 °C reaction. The effect of changing the temperature and pressure during the reaction was studied in order to simulate one- and two-stage processes. It was evident from the measurements taken that raising the temperature from 110 to 120 °C during the reaction has a detrimental effect on the residual pulp properties. The effect on NaOH consumption and pH was measured in variable conditions, whereby the bleaching temperature was changed from 95 to 113 °C and the pressure from 1.2 to 0.2 MPa during the 2 h reaction. Typical plots for 95 and 110 °C reactions at 0.5 MPa pressure are also shown in Figure 5. 5. Setting Kinetic Control for pH Calculations The addition of hydrogen peroxide into the alkaline solution containing 5 mass % of fibers initiates the bleaching reaction. The heterogeneous reactions then consume alkaline and peroxide in solution, and the pH of the solution decreases. The reactions in the liquid phase were assumed to be fast. With this sequence, an empirical reaction rate expression for chemical consumption could be combined with the multiphase Gibbs energy model by empirically determined mass balance conditions (Figure 6). The assumption in the dynamic multicomponent model is that an equilibrium point is rapidly reached for reactions in solution to obtain the minimum for the given chemical amounts and function G(mi,T, P). The changing chemical amounts of the reactants r in the aqueous phase were given in the model as frozen equilibrium amounts. By using the kinetic data in Tables 2 and 3, the pH was calculated. At each given time point, the pH is calculated and verified against measured values at ambient temperature. The measured and calculated pH sample values from 95, 110, and 120 °C experiments are shown in Figures 7 and 8.
Figure 6. Method for the calculation of reactive processes using the Gibbs energy approach.
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Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002
tions in the pulp and paper processes and natural and environmental sciences. Literature Cited
Figure 7. Modeled and measured pH changes in the oxygenpressurized peroxide bleaching reaction at 95 and 110 °C at 0.5 MPa oxygen partial pressure. The thermodynamic model could produce the pH of the reactive system up to ca. 70 min of reaction time in 110 °C and ca. 120 min of a 95 °C reaction.
Figure 8. Modeled and measured pH changes in the oxygenpressurized peroxide bleaching reaction at 120 °C at 0.5 MPa oxygen partial pressure.
6. Conclusions Thermodynamic modeling and measurements were applied in the alkaline peroxide solution that is relevant for TCF bleaching. Both physicochemical simulations and measurements of standard pulp properties are needed for understanding the behavior of the bleaching reaction. The use of kinetic control in the equilibrium calculations is useful for representation of the pH changes in the reactive systems. The calculated pH values were found to be in accordance with experimental values for the reaction taking place at 95 °C. At lower temperatures (80-100 °C), the reaction rates are relatively slow and κ reduction is small. In each temperature the decrease of κ numbers is more rapid in the beginning of the 2 h reaction but the slows after approximately 10-30 min. This can be noticed by a greater decrease of pH and alkaline consumption. In many industrial processes, the pH is used as an online control parameter in combination with pressure and temperature. The knowledge of the pulp properties and the results of the model calculations can be used to reduce heating costs and the chemical charges in the bleaching process. The combination of kinetics and thermodynamics can be used for specific systems and have many useful applica-
(1) Dence, C. V.; Reeve, D. W. Pulp Bleaching, Principles and Practice; TAPPI Press: Atlanta, GA, 1996. (2) Salminen, J.; Koukkari, P.; Ja¨ka¨ra¨, J.; Paren, A. Thermochemical experiments and modelling of the PO bleaching stage. J. Pulp Pap. Sci. 2000, 26, 441. (3) Pitzer, K. S. Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268. (4) Erikson, G.; Hack, K. Chemsagesa computer program for the calculation of complex chemical equilibria. Met. Trans. B 1990, 21B, 1013. (5) Koukkari, P.; Penttila¨, K.; Hack, K.; Petersen, S. ChemSheetsan efficient worksheet tool for thermodynamic process simulation. In Microstructures, Mechanical properties and processcomputer simulation and modelling; Brechet, Y., Ed.; Euromat99, Vol. 3; Wiley-VCH: Berlin, 2000; p 323. (6) Koukkari, P.; Laukkanen, I.; Liukkonen, S. Combination of overall reaction rate with Gibbs energy minimization. Fluid Phase Equilib. 1997, 136, 345. (7) Kondepudi, D.; Progogine, I. Modern Thermodynamics: From Heat Engines to Dissipative Structures; Wiley: Chichester, U.K., 1998. (8) Salminen, J. Some industrial applications of thermodynamics and kinetics with a NaOH-H2O2-H2O-O2 system. Licentiate’s Thesis, Helsinki University of Technology, Helsinki, Finland, 1998. (9) Pajarre, R. Modelling of equilibrium and nonequilibrium systems by Gibbs energy minimization. Master’s Thesis, Helsinki University of Technology, Helsinki, Finland, 2001. (10) Koukkari, P.; Pajarre, R.; Pakarinen, H.; Salminen, J. Practical multiphase models for aqueous process solutions. Ind. Eng. Chem. Res. 2001, 40, 5014. (11) Koukkari, P.; Pajarre, R.; Hack, K. Setting kinetic controls for complex equilibrium calculations. Z. Metallkd. 2001, 92, 1151. (12) Salminen, J.; Antson, O. Physico-chemical modelling and experiments involving reactive aqueous solution. Bunsen Discussion Meeting on Global Phase Diagrams, Walberberg, Germany, Aug 2001; Shaker Verlag: Aachen, Germany, 2001; ISBN 3-82659130-5. (13) Frederick, R.; Duke, R.; Haas, W. The homogenous basecatalysed decomposition of hydrogen peroxide. J. Phys. Chem. 1961, 65, 304. (14) Lachenal, D. The potential of H2O2 as delignifying and bleaching agent. Application to new bleaching sequences, PanPacific Pulp and Paper Technology Conference, Sept. 8-10, Japan Tappi: Tokyo, Japan, 1992; Part A, pp 33-38. (15) Wagman et al. The NBS tables of chemical thermodynamic properties. J. Phys. Chem. Ref. Data 1982, 11. (16) Freiser, I. Aqueous solutions, Data for inorganic and organic compounds; Walter de Gruyter: Hawthorne, NY, 1978; Vol. 2. (17) Bates, R. Determination of pHstheory and practice; Wiley: New York, 1973. (18) Haase, R. Thermodynamics of irreversible processes; Addison-Wesley: Reading, MA, 1969. (19) Been, J.; Oloman, C. Electrical conductivity of pulp suspensions using the Donnan equilibrium theory. J. Pulp Pap. Sci. 1995, 21, 80. (20) Scallan, A. The electrical conductance of pulp suspensions. Tappi J. 1989, 11, 157. (21) Bazaraa, M.; Shenah, H.; Shetty, C. Nonlinear programming: theory and algorithms, 2nd ed.; John Wiley & Sons Inc.: New York, 1993.
Received for review January 16, 2002 Revised manuscript received April 9, 2002 Accepted April 15, 2002 IE020027M
