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Practical Multiphase Models for Aqueous Process Solutions Pertti Koukkari,† Risto Pajarre,† Heikki Pakarinen,‡ and Justin Salminen*,† VTT Chemical Technology, P.O. Box 1404, FIN-02044 VTT, Finland, and UPM-Kymmene, Paper Divisions, FIN-37601 Valkeakoski, Finland
Multicomponent equilibrium models for aqueous salt solutions have been developed with the novel ChemSheet program. The calculations are based on the minimization of the Gibbs free energy of the reaction mixtures. For the excess Gibbs energies of the solute species, the Pitzer interaction model with temperature-dependent parameters was used. The results of the ChemSheet multiphase calculations have been verified with experimental or reference data. With the presented modeling technique, reaction kinetics can also be taken into account for specific systems using the Gibbs energy approach. These methods have been applied to the aqueous chemistry of calcium carbonate and sulfate in the wet-end solutions of papermaking. ChemSheet models are applicable in spreadsheets and can be customized for the needs of an industrial user. Introduction Knowledge of the calcite chemistry is important in environmental systems as well as in many industrial applications. The chemistry and the pH of the aqueous calcite systems are dominated by the ionic interactions in the solution. Yet these interactions are strongly influenced by both precipitated phases and dissolved gaseous species within the pH range of industrial interest. As the pH of the solution is the key measurable quantity to define its chemical state, it has become increasingly important to control the aqueous chemistry of calcite solutions at process temperatures. The description of solubilities and ionic concentrations in terms of pH are best available at 25 °C. However, for practical process conditions, data from 40 to 60 °C are needed. The complex chemical changes involve interactions between the solid calcium carbonate and the stock solution, with its major solute species and the ambient gas, where carbon dioxide plays an important role in the solute-solution equilibrium and in the reaction kinetics. The number of practical simulation applications for salt solutions is increasing rapidly due to well-organized data banks along with improved calculation methods.1-7 In the present work, these phenomena were described with a multiphase physicochemical model. A number of geochemical studies of the equilibrium solubilities of the different forms of calcium carbonate, including calcite, aragonite, and vaterite, have been published, and thus the thermodynamic data of the dominant chemical species should be fairly well-established. An extensive model for the system CaCO3-CO2-H2O has been published by Plummer and Busenberg.8 In that work, a comprehensive outlook on both experimental and theoretical results is given along with temperaturedependent correlations. The equilibrium constants are * Corresponding author present address: Laboratory of Physical Chemistry and Electrochemistry, Helsinki University of Technology, P.O. Box 6100, FIN-02015 HUT, Finland. E-mail:
[email protected]; Tel: +385 9 4512506; Fax: +358 9 451 2580. † VTT Chemical Technology. ‡ UPM-Kymmene.
given both for the solution of carbon dioxide and for the dissociated and associated species of the calcium carbonate. The multicomponent models could further be applied to model the wet-end chemistry of the paper machine. It includes the solid precipitate phases, the aqueous solution, and the air gases including carbon dioxide. As for papermaking, sulfuric acid remains the major acidic substance used for pH control, although the use of carbon dioxide has been recently introduced with success.9 Thus, it was regarded necessary to include sulfuric acid and its respective anions in the multiphase model. Marshall and Jones10 studied the CaSO4-H2SO4-H2O system, and their data could be used to confirm the thermodynamic data used for calcium sulfate species. Finally, to provide for the simulation of neutralization and for the use of common anion techniques in the model, sodium hydroxide was applied as the necessary base component. Thus, the precipitation of the less soluble compounds could be simulated, e.g., for situations where both Na and Ca cations were present in carbonaceous or sulfate solutions. The thermodynamic data for the respective aqueous sodium system are available, for example, in SGTE.11 For such an extensive model, it would be tedious to work out all the possible stoichiometric reaction equilibria. Additionally, the stoichiometric models are limited in that practical (measurable) quantities such as concentrations and pH values need to be solved separately from the equilibrium constants, usually given in terms of ion activities. Thus, the Gibbs energy minimization method was chosen as the modeling tool. The solution of the multicomponent model yields the intensive properties including activities, equilibrium concentrations, osmotic coefficient of water, and pH at given temperature and total pressure. Although the approach is somewhat more abstract (minimization of the Gibbs energy of the entire multiphase system), the reward is the possibility of working entirely with directly measurable quantities. Another advantage is, of course, the straightforward possibility of adding new substances to the multicomponent model, such as sulfuric acid and NaOH and their respective sulfate species. The advantages of the thermodynamic approach have
10.1021/ie010236r CCC: $20.00 © 2001 American Chemical Society Published on Web 10/09/2001
Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 5015 Table 1. Stoichiometric Matrix of the Multiphase Model system components phase gas
aqueous
Figure 1. Test equipment used in the kinetic experiments.18
recently led to its further adaptation for the modeling of a range of different process chemistries.12 Various simulation packages offer a choice of Gibbs energy minimizing for the interested model builder.4 As the comprehensive Gibbs energy data are more established in pyrometallurgy, many of the Gibbs energy programs have a metallurgical background.13,14 Yet with improving methods, aqueous databases and more systems of complex aqueous equilibrium have also been modeled.15-17 In this work, the existent data of the aqueous calcium chemistry were used to calculate a number of situations that are of interest to advanced wet-end chemistry. As the modeling tool, the novel ChemSheet12 program was used since it combines a flexible spreadsheet environment with rigorous Gibbs energy calculations for multiphase chemical processes. The ChemSheet models can also be easily customized for the practices of the industrial user. As the need for reliable simulation models for aqueous carbonate chemistry within different branches of the industry is increasing, the emphasis of the work was on developing practical models for the aqueous multiphase chemistry of calcium carbonate. It was assumed that these processes, for both static and dynamic situations, must be understood in order to control the dynamic behavior of the aqueous “white water” solution, although the presence of the low or medium consistency pulp necessarily complicates the wet-end behavior. The Gibbs energy approach can be further extended to take in to account the ion exchange between the solution and the fiber. Experimental Section In the experimental part of the work, bench-scale tests were performed for the dynamic measurements of temperature, pH, total calcium, and free calcium in the solution (Ca2+). The equipment consisted of a 6 dm3 open vessel equipped with a mixer and with a peristaltic pump with a flow rate of 100 mL/min. A closed circulation of the solution could be arranged with the piping combined with the vessel and the pump. The experimental setup is shown in Figure 1. The measurements made during the experiment were as follows: temperature with a standard thermometer, pH (Bailey TB556), and [Ca2+] ion-selective electrode (Orion M 97/20). The total calcium content of a slurry or a pulp solution could be detected with the X-ray fluorescence on-line analyzer (Metorex-Courier-10). The inlet of the vessel was combined to a closed circulation through the peristaltic
solid
component
C
O
Ca
H
N
S
Na
e-
CO CO2 H2O N2 O2 SO2 H2O CO2(aq) CO32-(aq) Ca2+(aq) CaOH+(aq) H+(aq) Na+(aq) HCO2-(aq) HCO3-(aq) HSO42-(aq) SO42-(aq) N2(aq) O2(aq) OH-(aq) CaSO4‚2H2O CaSO4 CaCO3 CaCO3(A) Ca(OH)2 NaOH H2SO4
1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0
1 2 1 0 2 2 1 2 3 0 1 0 0 2 3 4 4 0 2 1 6 4 3 3 2 1 4
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0
0 0 2 0 0 0 2 0 0 0 1 1 0 1 1 1 0 0 0 1 4 0 0 0 2 1 2
0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 2 -2 -1 -1 -1 1 1 2 2 0 0 1 0 0 0 0 0 0 0
pump and the cuvette of the Courier on-line analyzer. The pH electrode was mounted horizontally to the vessel. The ion-selective electrode (ISE) and the thermometer were adjusted to the vessel with supports. The pH electrode, ISE, and the Courier analyzer were connected to a computer, and data were processed with the LabView program. That allowed both on-line monitoring and saving of logbook data. The experiments were mainly performed to provide data from reaction rates and residence times for calcite dissolution and pH changes in the aqueous solutions. Use of Gibbs Energy Minimization to Evaluate Process Chemistry For most of the models, the numeric technique of Gibbs energy minimization was used to solve for the three-phase equilibrium (solid-aqueous-gas). In the strict thermodynamic meaning, the system necessarily was described as a general multiphase entity, with all the solids taken as separate invariant phases. For practical purposes and in the given temperature range of 25-60 °C, the expected solids are CaCO3, CaSO4, and CaSO4‚2H2O. The hemihydrate CaSO4‚0.5H2O is considered unstable at temperatures below 60 °C and thus was not included in the model. The equilibria for dissolved gases O2, N2, and CO2 were included as they are of interest for the paper mill operation. The sodium compounds were assumed present at soluble concentrations only, and thus only sodium hydroxide was introduced as a solid into the system. In Table 1, the species included in the original multicomponent model have been listed. When the Gibbs energy minimization method is used to calculate chemical equilibrium, one needs, rather than equilibrium constants, the original thermodynamic data to derive the chemical potentials (partial molar Gibbs energies) of the chemical species, which appear in the system described in the stoichiometric matrix of the model. These data may be systematically collected
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Figure 2. ChemSheet works as an add-in of general thermodynamics to an MS-Excel spreadsheet. Thus, the tabulated data are combined with worksheet calculation techniques in a practical fashion.12
from several available databases, and as for pure compounds such as precipitated solids, the supplementing of the matrix with any new compound is simple. For ionic species, the data must be presented in terms of the partial Gibbs energies of the ions, which in the aqueous solution are dependent on the activities of the ions. Thus, to introduce a new soluble species, one should make sure that there is an activity expression compatible with the rest of the system for this particular species and for its respective solute ions. While such ion interaction models as Pitzer19 have been widely adapted, there appear to be only a few practically oriented data sources for aqueous process solutions. Thus, in an introductory part of this work, data for the Pitzer interaction parameters of 90 aqueous ions were collected from the literature and compiled with computer database.6 The temperature dependence, when available, was parametrized in a uniform manner compatible with ChemSheet. ChemSheet is a spreadsheet stand-alone program based on the ChemApp program library12 that enables one to formulate and run one’s multiphase process chemistry to and from a spreadsheet (MS-Excel). One can produce active simulation workbooks for practical engineering needs. The workbook includes a particular problem of process chemistry with its solutions in the form of calculation inputs and respective results. Conventional and familiar spreadsheet cell structure is used for presentation. The workbook contains the necessary input for the chemical problem as well as the resulting data and their adjacent illustrations, figures, and charts, respectively. The result columns and charts may be totally or partially active to enable efficient visual simulation of process chemistry changes. The calculations are performed with a particular toolbar, which is embedded during the installation of the program to be a part of the spreadsheet menu. The use of ChemSheet is schematically shown in Figure 2. In what follows, a few examples of model workbooks will be presented. Calculation Examples with ChemSheet The calculated effects of temperature and pressure on the solubility of CaCO3 and the adjacent pH values in the aqueous calcite system are shown in Figure 3 for the CaCO3-CO2-H2O system. The solubility of CO2 is presented in a separate chart. The flexible choice of calculation range and respective parameters is an advantage of the multicomponent approach. The effect of temperature or pressure changes can be quantified and presented in both numerics and graphics. The changes of pH and CO2 solubility are given in terms of the mole fraction of the gas phase in low-pressure systems at 25 and 50 °C. The pH values calculated are in agreement with the proposition that as the solubility of CO2(aq) increases according to Henry’s law, the amount of dissociation products increases.
The pH values and the solubilities are both derived from a single calculation. The combination of the spreadsheet techniques with the thermodynamic model allows for reducing the number of calculation steps and yet receiving a representative chart. The simulation was performed using a stepwise increase in the mole fraction of carbon dioxide. The steps are defined as a simple formula in the spreadsheet, so as to decrease the step size in the steep pH-gradient area and to increase it in the more linear range. Thus, 11 steps in each calculation are sufficient to provide the necessary data. Even this produces an extensive number of data, including the concentrations and activities of both gaseous and aqueous species (not shown in the figure), all of which are practically saved in the Excel workbook and may be processed further by the spreadsheet techniques. The calculated solubility values were found consistent with low-pressure reference data.8,20 The practicality of the ChemSheet, multicomponent model is further seen from the chart of Figure 4, which shows experimental and calculated pH values in CaCO3-CO2-H2O solution at 25 °C and 0.968 bar partial pressure of carbon dioxide. The comparison of the results received with the multiphase model with the stoichiometric equilibrium constant data is straightforward. The model calculates the individual activities of the aqueous species, and the values for the appropriate equilibrium constants can be formed out of these data. In Figure 5, the calculated log K(CaCO3) and measurements by Plummer and Busenberg8 are shown. As sulfuric acid is the most common agent in the pH control of practical processes, it was regarded as necessary to incorporate sulfate anions and their respective interaction parameters in the ChemSheet model. The calculated solubility of CaSO4 as function of the molality of sulfuric acid is shown in Figure 6. The maximum solubility received for CaSO4 at 25 °C was 0.0205 mol kg-1; the respective values given by Marshall and Jones10 being 0.0197 mol kg-1. The solubility maximum occurs at the concentration of ca. 1 mol/kg of H2SO4. The discrepancy between the thermochemical model and the measured values is somewhat enlarged with increasing temperature, yet the agreement between model and experiment remains relevant for practical industrial purposes. The solubility of gypsum in the acidic solution becomes less dependent on temperature in the dilute systems, which characteristically occur in the wet-end chemistry. To allow for the simulation of the effects of neutralization, sodium hydroxide and the respective Na+ cation were introduced to the system. The parameters used in the aqueous sodium systems in carbonaceous and sulfate systems have been recently assessed by Ko¨nigsberger and Eriksson.3 The Pitzer parameters for sodium carbonate systems have been published by SGTE11 and were adapted to the ChemSheet white water model to allow for the simulation of Na+-containing solutions. Application of Worksheet Models The model for the air-H2O-CaSO4-CaCO3-NaOH system can be applied to evaluate various alternatives to white water chemistry. Such applications include the calculation of pH and solubility trends as well as dissociation constants, which can be calculated in terms of relevant process conditions. In the first place, the Gibbs energy approach is valuable in the evaluation of new process equilibrium in terms of new substances or
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Figure 3. Solubility-pH diagram for CaCO3 showing the effect of temperature and partial pressure of CO2 on the solubility of CaCO3, CO2, and pH. Calculations at 25 and 50 °C are presented.
Figure 4. Comparison of modeled and measured, liquid junction-corrected pH values obtained by Plummer and Busenberg8 of CaCO3CO2-H2O solution at 25 °C and 0.968 bar partial pressure of carbon dioxide. The maximum solubility at pH 6.04 was received by a separate target calculation. The chemical amount of CaCO3 is then reduced stepwise in the model input. The reference data are incorporated in a separate spreadsheet column (upper right).
Figure 5. Temperature dependence of equilibrium constant of calcite in aqueous CaCO3 system where K ) a(Ca2+)a(CO32-).
alternating process conditions. However, the combination of known reaction kinetics with the multiphase calculations is also possible, and thus even dynamic trends can be simulated. Evaluation of New Process Equilibria. The use of carbon dioxide as an alternative agent for controlling the pH of stock solutions has gained interest within the present day industry. In chemical pulp mills, dissolved
Figure 6. Solubility of CaSO4 in sulfuric acid as calculated from the multicomponent model and compared with the measured results of Marshall and Jones.10
CO2 has been successfully used in increasing the efficiency of pulp washing since the mid 1980s by acidifying the stock from pH 10 to pH 6.9 The solubility of carbon dioxide in water is 55 times the solubility of air at room temperature. Thus, while the introduction of gases in the papermaking process is generally to be avoided, the overall solubility of CO2 should not limit
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Figure 7. Concentration of bicarbonate (HCO3-) ions in the calcite system at 25 °C.
its use as a pH control. If carbon dioxide is dissolved properly, it should not cause foaming or deaeration problems.9 Carbon dioxide will also bring H+ ions to the system that inevitably dissolve CaCO3 according to the overall reaction:
CaCO3 + CO2V + H2O f Ca2+ + 2HCO3-
(1)
However, when an excess of carbonate ions is led to the system, the common ion mechanism will influence the opposite way so that the total effect results in a lower content of free calcium with CO2 than with H2SO4 acidification. By using the model described above, a number of pH and solubility charts were produced to evaluate the effects of the use of carbon dioxide in the process. The multicomponent model also results with the ionic concentrations of the system. Examples of HCO3- concentrations in different temperatures and pressures as a function of the mole fraction of CO2 in the gas phase are presented in Figure 7. The solubility models are utilized in evaluating the conditions of short circulation, where it is advantageous to dissolve inorganic material in the recirculating parts and to enhance precipitation of calcium in the input. To decrease the solubility of CaCO3, the concept of common anion can also flexibly be used, when carbon dioxide is chosen as the pH agent.9 In this case, sodium carbonate is selected as the source of the common ion. The solubility of CaCO3 is lower than sodium carbonate. The addition of Na2CO3 or NaHCO3 into the calcium carbonate system will then increase the ion product of Ca2+ and CO32- ions according to
Ksp < [Ca2+][CO32- + CO32-(added)]
Figure 8. Calculated relation of pH and the chemical amount of Ca2+ ions at 25 and 50 °C in CaCO3-CO2-H2O and in CaCO3NaHCO3-CO2-H2O systems. The small amount (1 g/kg) of additive NaHCO3 at constant CO2 partial pressure decreases the solubility of CaCO3 due to the common ion effect.
(2)
To simulate the effect, the highly soluble sodium compounds were introduced to the multicomponent model. In Figure 8, the effect of NaHCO3 addition on the CaCO3 solubility is presented at 50 °C. Whenever a new process concept is introduced, the composition of the chemical equilibrium under the new process conditions needs to be examined. Although the process would not reach equilibrium, the equilibrium calculation gives but the direction of the change and the maximum effect attainable. Thus, the composition of the new equilibrium is generally the foremost criteria when considering the benefits of a renewed process concept. The multicomponent models provide an efficient tool to evaluate the effects of these changes. Processes Leading to CaCO3 Dissolution. The kinetic experiments conducted in an earlier work were performed by using sulfuric acid as an acidifying agent
Figure 9. Dissolution of CaCO3 in the aqueous sulfuric acid solution. The major ions and compounds are shown. The equilibrium between gaseous carbon dioxide and water has a major effect on the pH of the solution and thus on the dissolution of calcite.
in systems containing nondissolved CaCO3.18,22 When calcium carbonate is present, the addition of the acid lowers the pH and increases the solubility of the carbonate, respectively. The addition of sulfuric acid brings about the rise in the concentrations of the hydrogen ions (H+) and bisulfate ions (HSO4-) in the solution. Both of the acidic ions may contribute to the formation of bicarbonate ions (HCO3-) that are formed when solid calcium carbonate becomes dissolved. Thus, the dissolution of calcium carbonate functions as a pH buffer. The released carbon dioxide becomes dissolved into the solution to its saturation level but is mainly released to the surrounding air. The multiphase reaction processes involved in the calcite dissolution are illustrated in Figure 9. Dynamic Model of CaCO3 Dissolution. The dynamic model of calcite dissolution was designed for a white water system containing nondissolved calcite particles. The model sequence was as follows: (i) Addition of sulfuric acid or carbon dioxide lowers the pH of the solution and brings about dissolution of the particles The reactions in solution will increase the pH. (ii) The reactions in solution, including the release of gaseous CO2, were assumed fast when compared to the dissolution. With this sequence, a simple reaction rate expression could be combined with the multiphase Gibbs energy model to follow the effect of subsequent acidification of the solution. The reaction kinetics of CaCO3 dissolution
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Figure 10. Results from the dynamic pH model for calcium carbonate dissolution.
has been assessed by Compton and Daly,23 who considering different rate models suggest that the flux of Ca2+ ions to the solution can be described with a twoparameter rate equation:
jCa2+ (mol cm-2 s-1) ) k1[H+] + k2
(3)
If the effect of change in particle size is neglected, a simple rate equation for the Ca2+ concentration is received:
d[Ca2+] ) {k1[H+] + k2}A dt
(4)
where [Ca2+] and [H+] are the concentrations of the Ca2+ and H+ ions, t is time, A is the average particle size, and k1 and k2 are the respective reaction rate parameters. In this form, the dissolution rate can be combined with the multiphase equilibrium model, which may then be solved, e.g., by using discrete increments of the soluble calcium carbonate. For the reactions in solution, no kinetic constraining was applied, and thus the assumption in the dynamic multicomponent model is
w fast equilibria for reactions in solution: min G(c, T, P) T, P ) temperature, pressure c ) {c1, c2, ..., cN} ) concentrations in different phases With this rather simple model, the pH pulses caused with the subsequent acid additions can be simulated with adequate accuracy between the measured and the calculated pH and Ca2+ concentration values (Figure 10). The use of thermodynamic states in the simulation is particularly useful to ensure the robust representation of the amplitude of the pH oscillations in the model. The increase of acid during different intervals brings the mixture to a low pH level, determined by the amount of the solution and the acid excess. Assuming fast acid dissociation to be compared with the calcite dissolution, the low pH is that of the dissolving solution, which is also the lowest attainable pH value. Respectively, in the upper end of the pH pulse, the simulated pH value approaches slowly the equilibrium pH, corresponding to the thermodynamic state whereby the dissolving carbonate has entirely consumed the excess acid. In Figure 10, the results of the simplified dynamic model are shown for three subsequent acidifications of CaCO3 containing white water. The parameter A in eq 4 was adjusted according to the measured dissolution
Figure 11. Results from the dynamic pH model for ion distributions and formation of CO2.
rates (measured Ca2+ values), and the corresponding pH values were compared with respective measured pH curves. In Figure 11, the respective ion distributions during the acidification are shown. The model shows the relation between the bisulfate (HSO4-) and bicarbonate (HCO3-) ions during the acidification pulses. The concentration gradients of these ions follow the pace of the pH change and are less instantaneous than the respective changes of the Ca2+ and SO42- ions. Also, the gradient of the HSO4- and HCO3- concentrations spans a wide concentration range, which could be detected with a suitable ion-specific measurement method, such as those based on the electrophoretic effect. Thus, if an ion-specific measurement method were used to monitor the chemical state of the process, the model would suggest that the anions of (-1) charge number would give a timely behavior similar to pH. One may conclude that, whereas the overall kinetics used in the model is somewhat simplified and does not agree with the detailed form of the measured pH curves, yet both the amplitude and the time constant of the dynamic model are sufficient to describe the overall pH variation. The model uses the thermodynamic functions to describe the state of the solution both in the beginning and in the end of each acidification period and thus ensures the correct range of the dynamic calculation. Conclusions The reaction processes between the solid, solution, and gas phases each have an effect on the equilibrium. In particular, the dissolution equilibrium is dependent on the partial pressure of carbon dioxide in the gas phase. The available thermodynamic data on the threephase system consisting of calcium carbonate, sulfuric acid, and air gases proved to be sufficient for the treatment of the equilibrium with a multiphase Gibbs energy model. With the model, a number of situations of interest in terms of the process conditions, including those where carbon dioxide is used as a pH-controlling agent, could be calculated. The thermochemical model allows for the calculation of interesting measurable
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quantities such as solubility trends for both solids and gases and the ionic concentrations in terms of temperature, pressure, and pH (acid inputs). Simple reaction kinetics can be combined with the thermodynamic model. Thus, the model can be utilized to evaluate the pH-dependent quantities in different stages of the white water circulation and in evaluating different process alternatives. If the pH of a white water solution has been determined, one may use the model to deduce quantitative estimates of such practical properties as gas solubilities and dissolved and total calcium and ionic concentrations. The model has been constructed with an easy-to-use ChemSheet interface, which can be operated in a spreadsheet. Literature Cited (1) Gmehling, J. In Chemical Thermodynamics (IUPACChemistry for the 21st Century); Letcher, T. M., Ed.; Blackwell Science: Oxford, 1999; p 1. (2) Barthel, J.; Kunz, W. In Chemical Thermodynamics (IUPAC-Chemistry for the 21st Century); Letcher, T. M., Ed.; Blackwell Science: Oxford, 1999; p 85. (3) Ko¨nigsberger, E.; Eriksson, G. Simulation of Industrial Processes Involving Concentrated Aqueous Solutions. J. Solution Chem. 1999, 28, 721. (4) Liu, Y.; Watanasiri, S. Successfully Simulate Electrolyte Systems. Chem. Eng. Prog. 1999, 10, 25. (5) Prausnitz, J.; Lichtenthaler, R.; Azevedo E. Molecular thermodynamics of fluid-phase equilibria, 3rd ed.; Prentice-Hall: Upper Saddle River, NJ, 1999. (6) Salminen, J.; Koukkari, P.; Pajarre, R.; Liukkonen, S. Multicomponent calculations and database-development with aqueous process solutions. Proceedings of Equifase 99, Vigo, Spain, June 20-24, 1999; Libro de Actas: Tomo II; 1999; p 433. (7) Eriksson, G.; Hack, K.; Petersen, S. ChemApp-A Programmable Thermodynamic Calculation Interface. Werkstoffswoche ‘96, Symposium 8: Simulation Modellierung; Informationsysteme: Frankfurt, Germany, 1997; p 47. (8) Plummer, L.; Busenberg, E. The Solubilities of Calsite, Argonite and Vaterite in CO2-H2O Solution Between 0 and 90 °C, and an Evaluation of the Aqueous Model for the System CaCO3-CO2-H2O. Geochim. Cosmochim. Acta 1982, 46, 1011. (9) Pakarinen, H.; Leino, H. Benefits of using carbon dioxide in the production of DIP containing newsprint. 9th PTS-CTP Deinking Symposium, Munich, Germany, May 9-12, 2000.
(10) Marshall, W. M.; Jones, E. V. J. Phys. Chem. 1966, 70, 4028. (11) Hack, K. The SGTE casebook, Thermodynamics at work; Materials Modeling Series; The Institute of Materials, Borne Press: Bournemouth, 1996. (12) Koukkari, P.; Penttila¨, K.; Hack, K.; Petersen, S. ChemSheet-an Efficient Worksheet Tool for Thermodynamic Process Simulation. In Microstructures, Mechanical properties and processcomputer simulation and modeling; Brechet, Y., Eds.; Euromat99, Vol. 3; Wiley-VCH: Berline, 2000; p 323. (13) Erikson, G.; Hack, K. Chemsage-a computer program for the calculation of complex chemical equilibria. Metall. Mater. Trans. B 1990, 21B, 1013. (14) Roine, A. HSC Chemistry for Windows, User’s guide, version 4.0; Outokumpu Research Oy: Pori, Finland, 1999. (15) Saunders, N.; Miodownik, A. CALPHAD, Calculation of phase diagrams; Pergamon: New York, 1998. (16) Kobylin, P.; Salminen, J.; Liukkonen, S. Measurements and modeling of aqueous process solutions. ICCT2000, Halifax, Canada, August 5-11, 2000; P8-TUE-1. (17) Koukkari, P.; Laukkanen, I.; Liukkonen, S. Combination of overall reaction rate with Gibbs energy minimization. Fluid Phase Equilib. 1997, 136, 345. (18) Komulainen, P. Modeling of the dynamic chemical state of de-inked pulp. Masters Thesis, Technical University of Helsinki, 2000. (19) Pitzer, K. S. Thermodynamics, 3rd ed.; McGraw-Hill: London, 1995; p 318. (20) Emmerich, W.; Battino, R.; Wilcock, R. Low-pressure solubility of gases in liquid water. Chem. Rev. 1977, 77, 219. (21) Reed, A. H. The fizz keeper, a case study in chemical education, equilibrium, and kinetics. J. Chem. Educ. 1999, 76, 208. (22) Koukkari, P.; Pajarre, R.; Penttila¨, K.; Salminen, J. Worksheet solutions for wet end chemistry. Annual Cactus SeminarTekes, Espoo, Finland, 1999. (23) Compton, R.; Daly, P. The dissolution/precipitation kinetics of calcium carbonate: An assessment of various kinetic equations using a rotating disk method. J. Colloid Interface Sci. 1987, 115, 493.
Received for review March 13, 2001 Revised manuscript received August 7, 2001 Accepted August 9, 2001 IE010236R
