Ind. Eng. Chem. Res. 2003, 42, 1827-1831
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Oxygen Solubility in Industrial Process Development Toni Kaskiala† and Justin Salminen*,‡ Laboratory of Materials Processing and Powder Metallurgy, Helsinki University of Technology, P.O. Box 6200, FIN-02015 HUT, Espoo, Finland, and Laboratory of Physical Chemistry and Electrochemistry, Helsinki University of Technology, P.O. Box 6100, FIN-02015 HUT, Espoo, Finland
Oxygen solubility in pure water and in dilute sulfuric acid solution has been studied as a part of atmospheric direct zinc leaching process development. The experimental results were compared with reference data and the Gibbs energy model. The dissolution dynamics of oxygen was further combined with the Gibbs energy minimization method. Together the experimental and model results give useful information and methodology for the developers of industrial processes related to gas solubility. The dynamic Gibbs energy calculation approach presented in this work extends the possibilities of evaluating changes in different process chemistries needed in process design. 1. Introduction Dissolved gases are commonly used as reactive chemical agents in processes in atmospheric conditions as well as in elevated pressures. The experimental and modeling results in gas solubility phenomena are important in many metallurgical and pulp and paper processes.1-3 The processes are commonly controlled by the partial pressure of the reactive gas, temperature, and chemical composition of the reactive solution. Both measurements and simulations are needed to yield sufficient information for practical applications.4-7 Modern computeraided calculation methods extend the possibilities of using chemical thermodynamics for industrially important systems, which often involve dynamic reactive multiphase and multicomponent solutions. The quantitative understanding of the effects of temperature, pressure, chemical interactions, and reactions is essential for designing and optimizing processes. The present annual world production of iron/steel, aluminum, copper, zinc, lead, nickel, and magnesium is close to 1 billion tonnes. On the basis of current trends, metals are likely to remain one of the primary materials of choice for several decades to come. Hydrometallurgy is a specialized branch of extractive metallurgy dealing with metal recovery from ores, concentrates, and other metallurgical intermediate products by aqueous methods at low temperatures. Comparing the advantages of pyro- and hydrometallurgical processes is complex, but if the gas emissions into the environment are the key factor, then the latter could be more favorable. When the production volumes are large, small improvements in the processes lead to a notable annual savings in chemicals and energy costs. 2. Gibbs Approach and Oxygen Solubility The calculations are carried out by means of the total Gibbs energy of the system where sound temperaturedependent standard-state enthalpy H, entropy S, and heat capacity C data as well as an activity coefficient * To whom correspondence should be addressed. Tel.: +358 9 4512506. Fax: +358 9 4512580. E-mail: justin.salminen@ hut.fi. † Laboratory of Materials Processing and Powder Metallurgy. ‡ Laboratory of Physical Chemistry and Electrochemistry.
model are needed. The resulting values of chemical potentials µi in multicomponent and multiphase mixtures are obtained as a sum of the ideal µid i and excess terms of the chemical potentials. The ideal term is µex i the contribution of the standard-state chemical potential and the ideal mixing term. The excess term is the result of the nonideal contribution that is expressed by means of the activity coefficient γi of an individual species i in the mixture phase. The total Gibbs energy of the multiphase system is the sum of individual chemical potentials of species i over all of the stable phases from R to ζ that exist in the system.
G)
∑R ∑i nRi µRi
(1)
The results of the Gibbs energy minimization yield the equilibrium compositions at given temperature and total pressure according to a functional description of the ideal and excess Gibbs energy terms. The modern calculation techniques allow the user to choose the model for excess Gibbs energy3,4 like the Debye-Hu¨ckel and Pitzer models for aqueous salt solutions. The selection of the activity coefficient model depends on the validity of the model in different temperature, pressure, and composition ranges. At a given temperature, total pressure, and feed amounts, the solution matrix yields simultaneously intensive and extensive thermodynamic properties including compositions and activities. The quality of both the standard-state data and the activity coefficient model is important. In this work, temperature and pressure dependences of the solubility of oxygen have been measured and simulated by Gibbs energy minimization calculations with a comparison against reference data. In Figure 1, the standard chemical potential change ∆µ°n for oxygen dissolved in water is shown within 293-323 K. The standard change of chemical potential ∆µ°n(T,P°) ) µLn - µ°n is defined as the difference between the hypothetical chemical potential of dissolved gas at liquid state µLn and the standard chemical potential of a gas in the gas phase µ°n. Because the input data in the Gibbs energy model include the standard-state data, the exactitude of the data should be checked independently and carefully. The calculated standard chemical potential data values
10.1021/ie020990s CCC: $25.00 © 2003 American Chemical Society Published on Web 03/22/2003
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Ind. Eng. Chem. Res., Vol. 42, No. 8, 2003 Table 1. Henry’s Law Constants kH for Oxygen Solubility in Pure Water Obtained from Reference Data and Gibbs Energy Calculations and by a Moderate-Pressure Morrison-Billett Apparatus20-23 kH/bar
Figure 1. Temperature dependence for a standard chemical potential change in the solution process for oxygen in pure water.
Figure 2. Oxygen solubility in pure water at elevated pressures between 80 and 120 °C. The model results are compared with the experimental values obtained by Broden and Simonson.12
at 20, 35, and 50 °C shown in the Figure 1 yield 0.71.0% average absolute deviation (AAD %) compared to other reference data solubilities.15-17 Henry’s law constant is obtained as a limiting value from the measurements as the mole fraction of dissolved gas xn approaches zero, i.e., xn f 0. For the dissolved gases, Henry’s law determines the ideal solubility, which can be related to ∆µ°n, which is the standard molar Gibbs energy change ∆Gm° of the gas in the dissolution process. The relation of Henry’s law constant kH is given as follows:
kH(T,P°) ) exp(∆µ°n/RT)
(2)
A wide selection of reference data sets and temperature-dependent correlations8-19 are available for oxygen solubility in water and Henry’s law constant. Henry’s constant increases with temperature, passes through a maximum, and then declines at higher temperatures. This is inversely proportional to the solubility, as shown in Figure 2. In Figure 2, the temperature and pressure ranges are in the region of the pulp-bleaching process conditions, where dissolved oxygen is commonly used as a chemical agent. Elevated gas pressures allow an increase in the temperature above 100 °C in a bleaching process and typically increase the chemical reaction rates.2 In Table 1, various data points are shown for Henry’s law constants kH for oxygen solubility in pure water. These include calculated values and experimental results by a moderate-pressure Morrison-Billett apparatus.
T/°C
ref 15
ref 16
ref 17
ref 8, min(G)
ref 20
20 35 50
40 630 51 372 59 580
41 289 52 216 61 453
41 105 51 183 60 326
40 312 50 880 59 688
41 350 54 770 62 670
The experimental procedure with a MorrisonBillett20-23 gas solubility apparatus is described briefly. The facility was tested with oxygen, nitrogen, and hydrogen solubility in pure water for further use with industrially interesting aqueous mixed solvents. The apparatus was designed for measurements in the range of 1.5-6 bar total pressure. All pressure and temperature sensors were calibrated. In experiments, the apparatus was set to the desired temperature and pressure. Degassed water was then pumped to the absorption spiral in order to obtain saturation between the gas and liquid. Two chambers, the absorption and equilibrium chambers, are connected with a U tube, and between them is a horizontal connecting pipe with a valve. A stationary state is obtained when the amount of collected saturated water at the bottom of the U tube is equal to the amount of pumped water. The middle valve is then closed. After a typical 2-h measurement time, the middle valve is opened and the change of the water level between the two tubes is defined by hydrostatic pressure. Gas solubility values could then be obtained by measuring the amount in grams of the collected saturated solvent and the volume difference. The measured solubility values were found to be systematically lower than expected. The accuracy of the facility depends mainly on the degassing of the water and the 1-3 mbar pressure decrease in the equilibrium chamber during the measurement. Both of these lower the measured solubility value. On the other hand, the pressure dependency at each temperature was found to be linear with an average correlation of R2 ) 0.9996 for oxygen, nitrogen, and hydrogen gases. The total accuracy of the apparatus was defined as (5%, including (1% of error factors related to control of the total pressure, temperature gradients, and evaporation of the collected saturated solvent. The modified MorrisonBillett apparatus was considered to be satisfactory for evaluating the gas solubility at moderate pressures. The presence of ions changes the solubility of gases. The activity coefficient of a dissolved gas n in an aqueous salt solution can be expressed by the Setschenow model.24-26
ln
( ) ()
m°n γn ) ln ) kn,MXmMX mn γ°n
(3)
m°n is the solubility of gas in pure solvent, mn is the solubility of gas in the salt solution, γ°n is the activity coefficient of dissolved gas in pure solvent, γn is the activity coefficient of dissolved gas in a salt solution, kn,MX is the Setschenow constant in kg/mol units, and mMX is the molality [mol/kg] of dissolved salt MX in the solvent. Setschenow’s model can be applied for dilute or moderately dilute liquids with respect to dissolved salt. For highly soluble salts, the model tends to overestimate the salting effect, and with high salt molalities, the
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Figure 3. Experimental11,13,29-32 and calculated values of oxygen solubility in pure water and in a sulfuric acid solution at 1 atm oxygen partial pressure. The calculated values shown as a dotted line represent m(H2SO4) ) 1 mol/kg of solution. Some experimental solubility data points by Narita in a 1 mol/dm3 solution and by Kaskiala in 1 mol/kg of solution are shown.
Figure 4. Mean activity coefficient and osmotic coefficient of sulfuric acid in water at 25 °C.34,35
Figure 5. Dissociation of sulfuric acid into sulfate and bisulfate ions in water at 25 °C.34,36-38
Figure 6. Kinetic measurements of the oxygen dissolution process followed by the dynamic Gibbs energy model.
3. Dissolution Measurements and Calculations effect becomes nonlinear. For mixed salts, the saltingout/salting-in coefficient is a sum of each ion’s contribution in the mixture. The individual interactions can be applied to mixed electrolytes, included in the Pitzer model,27,28 and furthermore used in the Gibbs energy minimization routine. The oxygen solubility measurements and calculations in pure water and in a sulfuric acid solution at atmospheric pressure are shown in Figure 3. The calculations were verified with reference data from Wilhelm et al.,11 Clever and Han,13 and Narita.32 The solubility of oxygen closely conforms to Henry’s law in pure water. The average deviation of the calculated values for pure water was found at 0.88% and maximum 2.0% within 273.15-430 K. At constant temperature the addition of sulfuric acid decreases the oxygen solubility, as shown by experiments and model results. According to the literature, the salting out of oxygen is linear up to 1.5 mol/dm3 sulfuric acid solutions.33 The Gibbs energy minimization routine yields the solubilities as well as the chemical speciation in the aqueous phase. In Figure 4 the mean activity coefficient and osmotic coefficient of sulfuric acid in water are shown at 25 °C. In Figure 5 the dissociation of sulfuric acid into sulfate and bisulfate ions in water is shown at 25 °C. In the calculations, four binary Pitzer parameters obtained from the literature were used.34
Temperature-dependent activity coefficient models are combined and used together with well-established multicomponent Gibbs free energy minimization routines. Because the parameters in the models are temperature- and pressure-dependent, it is possible to extend the model to estimate the gas solubility in experimental and process conditions. In the direct zinc leaching process, oxygen acts as a primary oxidizer. Zinc sulfide (ZnS) is oxidized to ZnSO4 in sulfuric acid media where iron couple Fe3+/Fe2+ acts as a catalytic intermediary between the atmospheric oxygen and the mineral. The dissolved oxygen in the leach is expected to have a significant role in the kinetics of the whole process. Finally, the dissolved zinc sulfate (ZnSO4) undergoes a purification, iron is precipitated as a complex jarosite compound, and elementary sulfur (S) is separated by flotation. There exist little data on the equilibrium and kinetics of oxygen solubility in reactive sulfuric acid solutions.1,30,39-41 In Figures 6 and 7, the dissolution kinetics of oxygen is shown. These measurements were carried out in an agitated vessel using a commonly used dynamic pressure method.30 The apparatus consisted of a closed decanter on top of a magnetic agitator with a heater (Kika Werke RCT basic). A known amount of liquid was introduced into the decanter. Dissolved oxygen in the liquid was initially eliminated by injecting pure nitrogen gas through a submerged porous nozzle in the vessel agitated at a
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process designer. The approach presented in this work is particularly useful because at a given temperature, total pressure, and feed amounts the intensive properties such as gas solubilities, ionic compositions, and activities are obtained simultaneously. These modeling techniques described will be used in further process development together with complementary measurements for mixed salt solutions in an oxygen atmosphere. Literature Cited
Figure 7. Experimental and calculated dissolution kinetics of oxygen in pure water and in 1 mol/kg of a sulfuric acid solution at 40 °C.
specified rotational speed. Simultaneously, the desired liquid temperature was adjusted. The nitrogen gas was changed to oxygen at a specified gas flow rate, and the increase in the oxygen concentration of the liquid was measured with an oxygen analyzer (Orbisphere model 26071). The analyzer is based on an electronic circuit with a membrane (2958A) of penetrated oxygen as a part of it. Oxygen undergoes a reaction at the cathode, causing a measurable electric current flow, which is proportional to the amount of oxygen entering the electrochemical cell and outside the membrane. The response time of the analyzer is a few seconds, which compared to the slow dissolution process was considered to be satisfactory. The time-dependent increase of the solubility of oxygen at given experimental conditions was repeated by a thermodynamic model by setting dynamic constraints. The measured time-dependent oxygen dissolution in pure water is used in the model. At each time point, all of the calculated state properties are assumed be valid in the reacting system considered. Even if the system is not strictly in equilibrium, the Gibbs energy approach can be used to describe the chemical dynamics42 through the time-dependent chemical compositions in the mixture. In Figure 7, the salting-out effect for oxygen in 1 mol/ kg of a sulfuric acid solution in the time-dependent system is shown. In the calculations, the sulfuric acidoxygen interaction31,33 was included in the Gibbs energy model and no additional parameter fitting is required. The dynamic Gibbs energy calculations give a reasonable estimation of the change of the oxygen solubility in the dissolution process. 4. Conclusions The thermodynamic approach shows the natural boundaries of the physical and chemical interactions in solution where the reactions take place. Together, experiment, theory, and simulation play complementary roles in the development of applied thermodynamic models. The knowledge of the solubility of gases in acidic solutions is a relevant step for studying the leaching process. The measurements of gas solubilities are not easy, and new experiments are still needed. Simulation methods based on the Gibbs energy approach provide a practical tool along with the experiments. The extension of chemical dynamics into the traditional phase equilibrium treatment gives additional information for the
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Received for review December 9, 2002 Accepted March 6, 2003 IE020990S
