DOE/ER/14691
Spectroscopy, Modeling and Computation of Metal ChelateVolubility in Supercritical COZ
Final Report
J. F. BrenneckeM. A. StadtherrJ. E. Chateauneuf
September 1999
Work Performed Under Contract No. DE-FG07-96ER14691
ForU.S. Department of EnergyAssistant Secretary forEnergy ResearchWashington, DC
ByUniversity of Notre DameNotre Dame, IN
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DOE/ER/14691
SPECTROSCOPY, MODELING AND COMPUTATION OF METALCHELATE VOLUBILITY IN SUPERCRITICAL CO,
FINAL REPORT
J. F. BrenneckeM, A. Stadtherr
J. E. Chateauneuf
September 1999
Work Performed Under Contract No. DE-FG07-96ER14691
Prepared for theU.S. Department of Energy
Assistant Secretary forEnergy ResearchWashington, DC
Prepared byUniversity of Notre Dame
Notre Dame, IN
Final Report
DE-FG07-96ER14691Spectroscopy, Modeling and Computation of Metal Chelate
Volubility in Supercritical COZ
9/15/96-9/14/99
Joan F. Brennecke and Mark A. Stadthem John E. ChateauneufDepartment of Chemical Engineering Department of ChemistryUniversity of Notre Dame Western Michigan University .Notre Dame, IN 46556 Kakunazoo, MI 49008
This final report for DE-FG07-96ER14691, entitled “Spectroscopy, Modeling andComputation of Metal Chelate Volubility in Supercritical COz,” contains 1) a statement of theoriginal objectives of the overall project, 2) an executive summary of the accomplishmentsrealized, 3) background, 4) a detailed discussion of the results for the three year grant period, 5) alist of publications andinvolved in the project.
1. Objectives
presentations that resulted from this grant, and 6) a list of the personnelThis is followed by the literature cited and the pertinent figures.
The overall objectives of this project were to gain a fundamental understanding of thevolubility and phase behavior of metal chelates in supercritical COZ. Extraction with C02 is aexcellent way to remove organic compounds from soils, sludges and aqueous solutions andrecent research has demonstrated that together with chelating agents it is a viable way to removemetals, as well. In this project we sought to gain fimdamental knowledge that is vitid tocomputing phase behavior, and modeling and designing processes using COZ to separate organicsand metal compounds from DOE mixed wastes. Our overall program was a comprehensive oneto measure, model and compute the volubility of metal chelate complexes in supercritical COZand COz/cosolvent mixtures. One aspect of this work was the measurement of local solvation ofmetal chelates using UV-visible spectroscopy, which provided information on the solutionmicrostructure. We also focused on the measurement of the volubility of metal chelates insupercritical C02 and COz/cosolvent mixtures, as well as the phase behavior of the chelatingagents themselves in COZ. The purpose of these measurements was to provide information withwhich we could evaluate and develop thermodynamic models of the volubility behavior. Finally,we focused on the implementation of a more reliable computational technique, based on intervalmathematics, to c~mpute the phase equilibria using the thermodynamic models. These studieswere undertaken because fundamental information about metal chelate volubility in supercriticalC02 is important in the design of processes using COZ to extract components from mixed wastesand in determining the optimum operating conditions.
2
2. Executive Summary
The major accomplishments from this project are as follows.We have shown that Regular Solution Theory, which is the model used by essentially allprevious researchers to estimate the volubility of metal chelate complexes in supercriticalCOZ, is totally inadequate. It gives both quantitatively and qualitatively incorrect predictions.Its use for process design purposes would have catastrophic consequences. Rather, we haveshown that equation of state models provide a much superior representation of the phasebehavior with just one parameter fit to limited metal chelate/COZ volubility measurements, aslong as some minimal thermodynamic data is available.From new volubility measurements, we show for the first time that over a wide range ofpressures and temperatures the presence of organic co-contaminants would actually increasethe volubility of metal chelates in supercritical COZ.We have demonstrated that on a microscopic level organic co-contaminants that aredissolved in the COZ will enrich the immediate area around a solubilized metal chelatecomplex. However, in determining the extent to which the metal chelate volubility increaseswith the addition of co-contaminant, this microscopic behavior is secondary to the solutions’bulk density increase.We have developed a completely reliable computational technique, based on intervalanalysis, to compute the phase behavior of COZ mixtures that contain metai chelates and’chelating agents using cubic equations of state. Unlike any conventional method (that maybe prone to error through failure to converge or convergence to an incorrect solution), thenew method that we have developed is guaranteed to provide the correct phase behavior forany particukir cubic equation of state model.
Through a combination of phase behavior measurements, spectroscopy and the development of anew computational technique, we have achieved a completely reliable way to model metalchelate volubility in supercritical COZ and C02/co-contarninant mixtures. Thus, we can nowdesign and optimize processes to extract metals from solid matrices using supercritical COZ, asan alternative to hazardous organic solvents that create their own environmental problems, evenwhile helping in metals decontamination.
3. Background
Extraction with supercritical COZ is an attractive possibility for the separation of DOE mixedwastes. Carbon dioxide is nontoxic and nonflammable and extraction with COZ ‘has beensuccessful for the decaffeination of coffee and te% recovery of hops, edible oils and other naturalproducts, the regeneration of activated carbon, the separation of organic solutions, and thefractionation of polymers. Supercritical COZ has also been used for the selective extraction ofcompounds from’ ~soils and other solid matrices (McHugh and Krukonis, 1990). Based onpreliminary investigations at Rocky Flats and the University of Colorado, extraction with COZhas been proposed as a way to separate organics from DOE low-level mixed wastes at Hanfordand Rocky Flats. However, an important issue is the fate of the metal compounds. The seminalwork of several research groups over the last decade has shown not only that some metal chelatesare sufficiently soluble in C02 or COz/cosolvent mixtures, but that metals can be successfullyextracted from aqueous solutions and solid matrices with COZ. Although not reviewed here,there have, in particular, been significant contributions in the form of numerous publications
3
from the groups of Professor Chen Wai at the University of Idaho, and Professor Robert Sieversat the University of Colorado.
An alternative to extraction of metals from solid matrices with chelating agents dissolved inC02 is the use of conventional organic solvents. Although it would require higher capitalinvestment for the high pressure vessels, there are some significant advantages to the use of COZ.Using chelating agents in conventional organic solvents is effective in removing metalcontaminants but it leaves residual organic solvent in the solid matrix. Moreover, the effluentfrom the extractor presents a complicated separation problem, where metal chelates and organicco-contaminants must be separated from the organic solventichelating agent mixture that onewould like to recycle. The residual organics in the solid matrix generally must be steam stripped,which produces an aqueous waste stream that is contaminated with organics. Thus, the clean-upeffort would produce a waste of its own. Conversely, supercritical COZ leaves no residualsolvent in the solid matrix, has higher diffusivity so it is more effective in permeating the matrix,and the solutes can be separated from the COZby simple depressurization.
Since metal chelates have significantly lower solubilities in COZ than most liquid organics,one could devise a two-step extraction of solid matrices in which the organics were removed firstand then the metals were removed by adding the chelating agent to the COl solvent stream.Conversely, one can envision a process in which both organics and metals are extracted at arelatively high pressure (e.g., 200-400 bar). As our data will show below, there may be somesignificant process advantages to this configuration. The metal chelates and organics could beselectively separated by partial depressurizations. If the chelating agent was less volatile thanthe organic co-contaminants then excess chelating agent could be separated and re-added to theC02 recycle stream, as shown in F@u-e 1. Conversely, if the chelating agent was more volatilethan the organic co-contaminants then the metal chelates and organics could be separated out bypartial depressurizations, and the excess chelating that remained in solution could be directlyrecycled with the COZ, as shown in Figure 2.
Although the feasibility of such a process has been demonstrated by previous researchers,what has been lacking is a quantitative and reliable method to model and compute the volubilityof metal chelates in supercritical COZ and COz/co-contarninant mixtures, as well as the fullmulticomponent high pressure phase behavior of the process systems necessary for C02extraction of metals from solid matrices. This is exactly what has been accomplished under thesponsorship of this grant, and the results are presented below.
4. Results and Dhcussion
The accompli~ments realized under the sponsorship of this grant fall into four categories:A) Modeling, B) Volubility Measurements, C) Local Composition Measurements, and D)Computational Methods.
A) Modeling
Essentially all previous modeling of metal chelate solubilities in supercritical COZ had beendone with Regular Solution Theory (Lagalante et al., 1995; Wai et af., 1996). The main
4
advantages of this model are that for solutions of components that are all liquids at thetemperature of interest, the only information needed to predict the phase behavior is each
components’ liquid molar volume, v~, and volubility parameter, & The volubility parameter is
defined as (AU/ v~)in, where AU is the internal energy of vaporization. If the component ofinterest is a solid then one requires the enthalpy change on melting, and the triple pointtemperature (which can generally be approximated by the normal melting point). If moreaccuracy is needed then the heat capacities of the solute as ,a liquid and a solid are needed.Although these properties are not always known for metal chelates, Regular Solution Theory(RST) has been used quite successfully to predict the volubility of metal chelates in liquids(Koshimura, 1978). However, this model is an excess Gibbs free energy (GE) model developedby Scatchard and Hildebrand for liquid solutions only and it explicitly assumes no volumechange on mixing. Clearly, this assumption is violated by su ercritical fluid (SCF) mixtures,
8where large volume changes are expected to occur. In fact, G models are general not used forSCF mixtures because they do not explicitly include any SCMof pressure dependence; clearly,pressure is an important varjable for SCF mixtures. Thus, one would not expect RST toaccurately model the volubility of metal chelates in SCFS, which is, in fact, the case.
In Figure 3, we show the RST predictions for the volubility of Fe(acetylacetonate)~ insupercritical C02 at 40°C and 60”C. The data are new measurements taken in our laboratory andthese will be discussed below. As shown in the figure, RST underpredicts the volubility byseveral orders of magnitude – note the logarithmic scale on the y-axis. The problem is worst inthe low pressure region, where the predictions are off by as much as fourteen orders ofmagnitude ! Also’ shown on the graph are the predictions for ideal volubility, i.e., assuming anactivity coefficient of one. Another interesting feature of RST is that it gives the incorrecttemperature dependence. RST predicts that the volubility of Fe(acetylacetonate)3 in SC C02should be greater at 40°C than at 60”C over the entire pressure range. In reality, solubilities ofmost solids in SC C02 exhibit a “crossover” pressure. At low pressures the volubility at a givenpressure is greater at lower temperatures but at higher pressures the volubility is greater at highertemperatures. This is due to the competing effects of temperature that raises the sublimationpressure and density. At a given pressure the solution density will be lower at the highertemperature, and lower density generally means lower volubility of solutes. The density effectdominates at low pressures and the temperature effect on the sublimation pressure dominates athigher pressures. Not surprisingly, these entire trends are missed by RST. Thus, we concludethat RST is inadequate in modeling metal chelate solubilities in SCFS and that its use wouldprovide gross errors in design calculations. For these calculations, the 6 for C02 was taken from
Giddings et al. (1968), who gave 3 as a function of the reduced density. The molar volumes forC02, vL, for C02 were calculated from the equation of state developed by Span and Wagner(1996). The 6. and v~ for Fe(acetylacetonate)3 of 23.80942 MPa”2 and 271 cm3/mol,respectively, were’ taken from Koshimura (1978). The enthalpy of fusion and normal meltingpoint temperature (used as an approximation of the triple point temperature) ofFe(acetylacetonate)3 were 34.10 kJ/mol and 181.5K, respectively (Ribeiro da Silva et af., 1996;Beech and Lintonbon, 1971).
Conversely, equations of state have been used to model solid solubilities in SCFS withsubstantial success (Johnston et al., 1989). The solid/tluid equilibrium requirement is:
5
,
1+(P-1’:’ (n) = YJ%WXY) = Rwhere f2sis the fugacity of the solute in the pure solid phase, }.F is the fugacity of the solute inthe fluid phase solution, P~b (T) is the sublimation pressure of pure solute, v; is the moku
volume of pure solute, and ~~ (T, P, y) is the fugacity coefficient of the solute in a fluid phase of
composition y = (Y1,yz, . . .. yc)T. A cubic equation of state, such as the Peng-Robinson equation(Peng and Robinson 1976), can be used to calculate the fugacity coefficient.
RT a
(v-b) [V(v+l?)+b(v-b)]
where,
0.45724R2~2a =
~[1+ (0.3764+
and w is the acentric factor.T
)54226w - 0.2699w2)(1- ~“’)]2
T=and ~ are the critical temperature and pressure of the compound,
respectively, and T, = ~. To extend this equation to mixtures, the conventional van der Waals
mixing rules can be use;:nn n
a = xx xixjai, b = ~ xibi, and ai = (ai,aj )05(1– $)+1 j=l i=l
where the sums extend over all components, and aii and bi indicate the pure component valuesfor component i.
As shown in Figure 4-6, which now shows the data for Fe(acetylacetonate)3 on a linearaxis. The Peng-Robinson equation gives both qualitatively and quaiititatively correctrepresentation of the phase behavior. However, this model does require some unknownparameters and the differences in the three graphs are the way those parameters were fit orestimated. In Figure 4, the T., P., w of Fe(acetylacetonate)3 and the binary interactionparameter, ko, between Fe(acetylacetonate)3 and CO? were all fit to the experimental volubilitydata. While T=,Pc, and w are available for many organic compounds, they are not available foressentially any of the metal chelates of interest. In Figure 5, we estimate Tc and P=from a groupcontribution method developed by Joback (Prausnitz et al., 1999) and fit w and kti to theexperimental volubility data. in Figure 6, the only fit parameter is k+ The acentric factor was
0
pvvdetermined from its definition, o =-10 ~ -1.000. For this equation, the vapor pressures
/&=.7
were determined from the literature value of the enthalpy of vaporization (Beech and Lintonbon,
6
197 1) and the vapor pressure at the triplet point. This was determined by extrapolatingsublimation pressure data (Ribeiro da Silva et aL, 1996) to the triple point, where the sublimation
pressure and the vapor pressure are equal. The critical pressure and temperature were estimatedfrom Joback’s method (Prausnitz et al., 1999), which requires the normal boiling point. This, ofcourse, could be determined from the vapor pressure equation evaluated at 1 atm. It gave aboiling point for Fe(acetylacetonate)3 of 343”C, which is close to published values of other trisacetylacetonates. All of these methods to calculate the volubility of the Fe(acetylacetonate)3 inC02 using the Peng-Robinson equation of state require the solid density (Roof, 1956) and thesublimation pressure (Fedotova et af., 1992). As you can see, all three methods giveequivalently good results. Thus, using minimal pure component thermodynamic data andstandard estimation techniques, we are able to obtain quantitative estimates of the volubility ofFe(acetylacetonate)3 in supercritical C02 with only one interaction parameter fit to a fewvolubility measurements.
B) Volubility Measurements
To aid in the development of a new modeling technique based on cubic equations of state formetal chelates in supercritical COZ, we measured the volubility of a representative metal chelatecomplex, Fe(acetylacetonate)3 in supercritical COZ and COz/co-contaminant mixtures. Previousdata for most compounds has only given a couple pressures or temperatures and we needed somecomplete isotherms with which to compare the modeling. These data were taken using w ISCO220SX extractor that has been modified to use a variable micrometering restrictor valve (309-505 series) from Supercritical Fluid Technologies, Inc., along with an imovative flush systemthat we developed in our laboratory. We found that when studying this high melting metalchelate, the standard heated restrictor from ISCO plugged dependably, but the new system givesgood results.
The data for the volubility of Fe(acetylacetonate)3 in supercritical COZ at 400C and 600C hasalready been presented in F&ures 4-6. The solubilities increase with increasing pressure, asexpected. Moreover, the system exhibits a “crossover” pressure at around 200 bm~ & describedabove. We ako measured the volubility increase of Fe(acetylacetonate)a in supercridcal CC4when 3 mol YOof chloroform was added to the system. This data is shown in Fi=qre 7 and, toour knowledge, is the first complete isotherm of the volubility increase of a metal chelate when acosolvent is present. We chose CHC13 as a typical organic co-contaminant that might be presentwith radioactive or heavy metals at a DOE site. As can be seen in the figure, the presence of theCHC13 increases the volubility of Fe(acetylacetonate)3 by about a factor of three. Thus, for agiven volume of material that had to be cleaned, this would represent a significant reduction inthe size of the vessel needed. Since pressure vessels are expensive, representing the majority ofthe capital investment cost of most supercritical extraction processes, this would substantiallydecrease the cost associated with a COz-based decontamination process. The modeling of thissystem is discussed below.
C) Local Composition Measurements
To better understand the Fe(acetylacetonate)3/co-contaminant/SC COZ system, we undertooka program to use -spectroscopy to measure the local composition of CHC13 around
7
Fe(acetylacetonate)J in SC COZ. Based on literature results for polar organic solutes in SCFmixtures, it appeared that an important contributor to the increased solubilities and increasedextraction efficiencies of metal chelates in C02/cosolvent mixtures might be the preferentialsolvation of the metal chelate by the cosolvent. We used UV-vis spectroscopy to measure the
preferential solvation of Fe(acetylacetonate)3 by chloroform in SC C02 at 60”C. Initially, wehad planned to measure preferential solvation by solvatochromic shifts since there was a reportof this method being used with Fe(acetylacetonat@3 in the literature (Tingey et al. 1989).Unfortunately, the UV-visible absorption peaks of Fe(acetylacetonate)3 do not shift withchanging solvent environment. Fortunately, Fe(acetylacetonate)3 does show significant changesin the intensity of the metal to Iigand charge transfer band -431 nm, with higher intensitiesobserved in nonpolar solvents. Thus, the ratio of the intensity of a more stable intraligand band-272 nm to the intensity of the 431 nm band is a sensitive measure of the local environmentaround the metal chelate complex. We have used this technique to measure the preferentialsolvation of Fe(acetylacetonate)3 in SC C02/3 mole % chloroform mixtures. The results indicatethat the local environment around the Fe(acetylacetonate)3 is highly enriched with chloroform(up to seven times the bulk composition) and that it is largest at lower pressures, as shown inFigure 7. This is very similar to trends observed for the preferential solvation of polar organicsolutes in SCFS but is the first measurement of preferential solvation of a metal chelate in asupercritical fluid “mixture. Thus, the local environment around the metal chelate is substantiallyenriched with the chloroform and this is particularly pronounced at the lower pressures.
These results suggest that the volubility increase of Fe(acetylacetonate)3 in SC C02 when 3mol % CHC13 is added to the C02 may be due to the increased local composition of the CHC13around the metal chelate. To determine the extent to which is phenomenon is important, wepredicted the volubility increase that one would expect based solely upon the density increasethat one gets at a particular pressure and temperature when one adds 3 mol % chloroform to C02.This can be done simply with the equation of state modeling. Using the best fit kti forFe(acetylacetonate)3/C02 from the binary volubility d~ta, a kti for CHC13/C02 estimated frombinary data in the literature, and a k. of zero for the CHC13/Fe(acetylacetonate)~ pair, weestimated the volubility of Fe(acetylacetonate)3 in a COz/3 mol% CHC13 mixture. As can be seenin Figure 7, the Peng-Robinson equation very accurately predicts the volubility increase observedfor this system with the addition of a co-contaminant. Since the Peng-Robinson equation of statedoes not incorporate any knowledge of local composition increases, at least for”this system, thisresult suggests that the main factor in determining the volubility increase is the increase densityof the C02/chloroform mixture. Nonetheless, the preferential solvation of the metal chelate bythe co-conthrninant does exist, and it may play some role in determining the volubility of themetal chelate in C02/co-contaminant mixtures.
D) Computational Methods
As mentioned above, conventional flash algorithms can fail to converge or converge toincorrect solutions for the types of high pressure phase equilibrium calculations that are neededto design and optimize processes to extract metals with supercritical C02. Whether determiningthe best-fit k. from experimental data, or calculating the volubility of a solid at new conditionsusing a particular EOS model, there are two computational pitfalls that can be encountered in thecalculation of solid-fluid equilibrium:
I.
2.
Solid solubilities in SCFS are usually computed by locating a mole fraction whichsatisfies the equifigacity equation relating the solute fugacity in the supercritical fluid,as predicted by the EOS, and the fugacity of the pure solid (see equation in modelingsection above). However, at certain values of temperature, pressure, and kti, there canexist multiple solutions to the equifugacity condition. A common method for solving theequiiigacity equation is successive substitution or some similar approach (McHugh andKrukonis, 1990), using some small value of the solid volubility in the fluid phase as theinitial guess. In general, this strategy will only find the smallest volubility root and maymiss any larger values, if present, that satisfy the equifugacity equation. Thus, what isneeded is a completely reliable method to determine all the roots to the equifugacityequation.Equifugacity is a necessary but not sufficient condition for stable solid-fluid equilibrium.Solutions to the equifugacity equation must be tested for global thermodynamic phasestability. One widely used technique to determine phase stability is based on tangentplane analysis (Baker et al., 1982); this method can distinguish the stable case from themetastable or unstable cases, but cannot distinguish metastable from unstable. Since weare interested in determining the thermodynamically stable solutions to the equifbgacityequations, we have used the tangent’ plane analysis. Tangent plane analysis itself,however, presents a difficult computational problem, which again can be addressed byusing a completely reliable equation solving technique.
To address these problems, we have developed a completely reliable method for determiningall the solutions to the equifugacity equation, and then using a method that can test thosesolutions for stability with complete certainty. Thus, we present a methodology that isguaranteed to identify the correct, thermodynamically stable composition of a fluid phase inequilibrium with a pure solute, as will be encountered in the extraction of metals from solidmatrices with C02.
The method that we have used to formulate this problem is given in detail by Xu et aL(2000). It is based on the equifugacity condition for the solute, which is given above in themodeling section. We have used the Peng-Robinson equation of state with standard van derWaals mixing rules. The computation of phase stability is based on the tangent plane distance D,which is simply the distance from the tangent plane to the Gibbs energy surface. The applicationof this method to solid/fluid equilibrium is discussed in more detail in Xu et al. (2000).
To solve this problem, we have applied interval mathematics, in particular an intervalNewton/generalized bisection (IN/GB) technique, to find, or, more precisely, to find very narrowenclosures of, all solutions of a nonlinear equation system, or to demonstrate that there are none.The algorithm that we used k been described by Hua et aL (1998a,b), and it is given in moredetail by Schnepper and Stadtherr (1996). Properly implemented, this technique provides thepower to find, with mathematical and computational certainty, enclosures of all solutions of asystem of nonlinear equations (Kearfoot, 1996), or to determine with cefiainty that there arenone, provided that initial upper and lower bounds are available for all variables. This is madepossible through the use of the powerful existence and uniqueness test provided by the intervalNewton method. The technique can also be used to enclose with certainty the global minimumof a nonlinear objective function.
9
We have applied the IN/GB algorithm to the solution of the equifugacity condition, thusdetermining with certainty alf the roots within the given initial interval, or determining withcertainty that there are none. In the latter case, this is mathematical proof that there is no solid
phase present at equilibrium. The second step in the method we developed is the testing of theequifugacity roots, just found, for stability. Again this is done using the IN/GB algorithm, thusguaranteeing that all the station~ points of the tangent plane distance D, or equivalently, theglobal minimum of D, are enclosed.
This method is the first application of a global optimization method to the solid/fluidequilibrium problem. The solid/fluid phase equilibria computed as part of this grant exploitedthis new method to make sure that the correct solutions were identified. The application of thisnew method to a variety of problems, several of which exhibit very complex behavior, can befound in Xu et al. (2000).
In summary, we have produced four major accomplishments under the auspices of thisgrant. First, we have shown that Regular Solution Theory gives both quantitatively andqualitatively incorrect predictions of the volubility of metal chelates in supercritical COZ.Conversely, we have shown that cubic equation of state models provide a very goodrepresentation of the phase behavior with just one parameter fit to limited metal chelate/COzvolubility measurements. In addition, from new .mlubility measurements, we have shown for thefirst time that over a wide range of pressures and temperatures the presence of organic co-contaminants would actually increase the sohibility of metal chelates in supercritica.1 C02.Although we found that on a microscopic level organic co-contaminants that are dissolved in theC02 will enrich the immediate area around a solubilized metal chelate complex, this has nosignificant affect in determining the volubility enhancement that is observed when the co-contaminants are ~present. Finally, we have developed a completely reliable computationaltechnique, based on interval analys’is, to compute the phase behavior of COI mixtures thatcontain metal chelates and chelating agents using cubic equations of state. Unlike anyconventional method (that may be prone to error through failure to converge or convergence toan incorrect solution), the new method that we have developed is guaranteed to provide thecorrect phase behavior for any’ particular cubic equation of state model. Through a combinationof phase behavior measurements, spectroscopy and the development of a new computationaltechnique, we have achieved a completely reliable way to model metal chelate volubility insupercritical COZ and COz/co-contaminant mixtures. Thus, we can now design and optimizeprocesses to extract metals from solid matrices using supercritical COZ, as an alternative tohazardous organic soivents that create their own environmental problems, even while helping inmetals decontamination.
5. List of Publi@tions and Presentations
Below are lists of publications and presentations that acknowledged at least partial support fromthis Department of Energy grant.
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Publications
1,
2.
3.
4.
5.
6.
7.
8.
9.
James Z. Hua, Joan F. Brennecke and Mark A. Stadtherr, “Reliable Computation of PhaseStability Usiqg Interval Analysis: Cubic Equation of State Models,’’ Computers and ChemicalEngineering, 22, 1998, p. 1207-1214.
James Z. Hua, Joan F. Brennecke and Mark A. Stadtherr, “Enhanced Interval Analysis forPhase Stability: Cubic Equation of State Models,” Ind. En~. Chem. Res., 37, 1998, p. 1519-1527.
Robert W. Maier, Joan F. Brennecke and Mark A. Stadtherr, “Reliable Computation ofHomogeneous Azeotropes,” AIChE J., 44, 1998, 1745-1755.
Erik J. Roggeman, Aaron M. Scurto, Mark A. Stadtherr, and Joan F. Brennecke,“Spectroscopy, Measurement and Modeling of Metal Chelate Volubility in Supercritical C02,”
Proceedings of the 8th International Symposium on Supercritical Fluid Chromatography andExtraction, St. Louis, MO, July 12-16, 1998.
James Z. Hua, Robert W. Maier, Steven R. Tessier, Joan F. Brennecke and Mark A. Stadtherr,“Interval Analysis for Thermodynamic Calculations in Process Design: A Novel andCompletely Reliable Approach,” Fluid Phase Ectuilibria, 158-160, 1999,607-615.
Joan F. Brennecke and John E. Chateauneuf, “Homogeneous Organic Reactions asMechanistic’ Probes in Sttpercritical Fluids,” Chemical Reviews, 99 (2), 1999,433-452.
Mark A. Stadtherr, “High Performance Computing: Are We Just Getting Wrong AnswersFaster?” AIChE CAST Conzwumications, 22(l), 6-14 (1999).
Mary J. Kremer, Karen A., Connery, Matthew M. DiPippo, Junbo Feng, John E. Chateauneufand Joan F. Brennecke, “Spectroscopy to Measure Solvation, Kinetics, and Equilibrium inSupercritical Fluids: Proceedings of the 6th Meeting on Supercritical Fluids: Chemistry andMaterials, Nottingham, UK April 10-13, 1999.
Stephan R. Tessier, Joan F. Brennecke and Mark A. Stadtherr, “Reliable Phase StabilityAnalysis for Excess Gibbs Energy Models; Chemical Engineerhw Science, in press, 1999.
10. R. W. Maier, J. F. Brennecke and M. A. Stadthem, “Computing Homogeneous AzeotropesUsing Interval Analysis: Chem. Eng. & Tech., in press, 1999.
311. Chao-Yang Gau, Joan F. Brennecke and Mark A. Stadtherr, “Reliable Nonlinear Parameter
Estimation in VLE Modeling;’ sub~tted to Fluid Phase Equilibri~ 1999.
12. Robert W. Maier, Joan F. Brennecke and Mark A. Stadtherr, “Reliable Computation ofReactive Azeotropes,” submitted to Computers and Chemical Engineering, 1999.
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13. Gang Xu, Aaron M. Scurto, Marcelo Castier, Joan F. Brennecke and Mark A. Stadtherr,“Reliable Computation of High Pressure Solid-Fluid Equilibrium,” Ind. Eng. Chem. Res., inpress, 1999.
Invited Presentations
i.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Mark A. Stadtherr, James Z. Hua, and Joan F. 13rennecke, “Phase Stability AnaIysis forEquation of State ModeIs,” Institute for Operations Research and the Management Sciences,National Meeting, Dallas, October 26-29, 1997.
Joan F. Brennecke, “Supercritical Fluids for Environmental Applications: A ChemicalEngineering Perspective;’ Department of Chemistry, Western Michigan University,November 6, 1997.
Mark A. Stadtherr, “Reliable Process Modeling Using Interval Analysis,” Department ofChemical Engineering Seminar, Carnegie-Mellon University, Pittsburgh,. PA, February 24,1998.
Joan F. Brennecke, “Dense Phase Fluids: Phase Behavior,” Department ofEnergy/Environmental Protection Agency Dense Phase Fluids and Alternative ReactionMedia Workshop, Sante Fe, NM, April 13-16, 1998.
Joan F. Brennecke, “Thermodynamic and Kinetic Studies in Supercritical Fluids,”Department of Chemistry, Loyola-University of Chicago, April 16, 1998. -
Erik J. Roggeman, Aaron M. Scurto, Mark A. !%adtherr, and Joan F. Brennecke“Spectroscopy, Measurement and Modeling of Metal Chelate Volubility in SupercriticalC02,” 8th International Symposium on Supercritical Fluid Chromatography and Extraction,
St. Louis, MO, July 12-16, 1998.
Joan F. Brennecke, Mark A. Stadtherr and John E. Chateauneuf, “Spectroscopy, Modelingand Computation of Metal Chelate Volubility in Supercriticd C02”, Department of Energy
EMSP Scientific Workshop, Rosemont, IL, July 27-30, 1998.
Joan F. Brennecke, “Understanding Metal Chelates in Supercritical C02,” Department ofChemical Engineering, University of Texas at Austin, Austin, TX, September 9, 1998.
Joan F. Brennecke, “Using Spectroscopy to Understand Metal Chelates in SupercriticalC02,” Department of Chemical Engineering, University of Massachusetts, Amherst, MA,October 1, 1998.
Mark A. Stadtherr, “High Performance Computing Are We Just Getting Wrong AnswersFaster?”, Computing and Systems Technology Division Awards Dinner, AIChE AnnualMeeting, Miami Beach, FL, November 15-20, 1998.
12
11. John E. Chateauneuf, “The Use of Reaction Intermediates to Investigate Supercritical FluidSolvent Effects: The Development of Supercritical Fluids as Environmentally BenignReaction Media,” Department of Chemistry, Central Michigan University, Mt. Pleasant, MI,
March 1 (1999).
12. John E. Chateauneuf, ‘The Development of Supercritical Fluids as Environmentally BenignReaction Media The Influence of SCF Solvation on Chemical Reactivity,” Department ofChemistry and the Center for Photochemical Sciences, Bowling Green State University, OH,March 3 (1999).
13. John E. Chateauneuf, J. Zhang, J. Brink, M. Slominis and M. Perkovic, “Investigation ofFree Radical and Radical Ion Reactivity with Supercritical Carbon Dioxide,” (posterpresentation) American Chemical Society 217th National Meeting, Anaheim, CA, March 22(1999). Sci-Mix,
14. Joan F. Brennecke, “Spectroscopy to Measure Solvation, Kinetics, and Equilibrium inSupercritical Fluids, “ 6th Meeting on Supercritical Fluids: Chemistry and Materials,Nottingham, UK, April 10-13, 1999.
15. Joan F. Brennecke, “Pollution Prevention with Supercritical COZ,” Department of CivilEngineering, Northwestern University, Evanston, IL, April 30, 1999.
16. Mark A. Stadtherr, Gang Xu, Benito Stradi, Robert W. Maier and Joan F. Brennecke,“Reliable Computation of Phase Behavior Using Interval Methods,” SIAM Annual Meeting,Atkmt& GA, May 12-15, 1999.
17. John E. Chateauneuf, “Reactions in Supercritical Fluids: The Development of SupercriticalFluids as Environmentally Benign Reaction Media,” Department of Chemistry, AndrewsUniversity, Berriep Springs, MI, May 19, (1999).
18. Joan F. Brennecke, “Environmental Applications of Supercritical Fluids,” Escola deQuimica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil, May 25, 1999.
19. Joan F. Brennecke and Mark A. Stadtherr, “Reliable Computation of Phase Behavior UsingInterval Analysis~ Escola de Quimica, Universidade Federal do Rio de Janeiro, Rio deJaneiro, Brazil, May 27, 1999.
20.Joan F. Brennecke, “Spectroscopic Measurements of Local Compositions,” PLAPIQUI,Universidad ~acional del Sur, Bahia Blanca, Argentina, June 1, 1999.
21. Joan F. Brennecke, “Application of Supercritical Chemical Engineering Processes inEnvironmental Protection and Remedlation,” PLAPIQUI, Universidad National del Sur,Bahia Blanca, Argentina, June 4, 1999.
13
22. John E. Chateauneuf, “Reactionsi nSupercritical Fluids: Thedevelopment of SupercriticalFluids as Environmentally Benign Reaction Media,” Department of Chemistry, ArgonneNational Laboratory, Argonne, IL, June 30, (1999).
23. John E. Chateauneuf, “Free Radical Reactions in Supercritical Fluids,” Gordon ResearchConference on Free Radical Reactions, Holderness School, Plymouth, NH, July 11-16,( 1999).
24.John E. Chateauneuf, “The Use of Reaction Intermediates to Probe Supercritical Fluid .Solvent Effects~’ American Chemical Society 218th National Meeting, New Orleans, LA,August 22-26(1999). Symposium on Chemistry of Reactive Intermediates and ModelinginHydrocarbon Conversion.
25. MarkA. Stadtherr, “RecentAdvances in Reliable Nonlinear Equation Solving~’ AspenWorld2000, Orlando, FL, tobepresented Feb. 6-11,2000.
26. Mark A. Stadthem, “Reliable Process Modeling Using Interval Analysis: Department ofChemical Engineering Seminar, University of Kansas, Lawrence, KS, to be presented March—29,2000. -
Contributed Presentations
1.
2..
3.
4.
5.
Jianwei Zhang, Erik J. Roggeman, John E. Chateauneuf and Joan F. Brennecke, “CosolventEffects on Metal Chelates in Supercritical C02,” Annual AIChE Meeting, Los Angeles, CA,
NOV. 16-21, 1997.
Robert W. Maier, Joan F. Brennecke and Mark A. Stadtherr, “A New Approach for ReliableComputation of Homogeneous Azeotropes in Multicomponent Mixtures,” Annual AIChE .Meeting, Los Angeles, CA, Nov. 16-21, 1997.
James Z. Hua, Joan F Brennecke &-id Mark A. Stadtherr,Approach to Reliable Computation of Phase Equilibria,”Angeles, CA, Nov, 16-21, 1997.
“Combined Local and GlobalAnnual AIChE Meeting, Los
James Z. Hua, Robert W. Maier, Steven R. Tessier, Joan F. Brennecke and Mark A.Stadtherr, “Interval Analysis for Thermodynamic Calculations in Process Design: A Noveland Completely Reliable Approach,” (poster presentation) Eighth International Conferenceon Properties’ band Phase Equilibria for Product and Process Design, Noordwijkerhout, TheNetherlands, April 26-May 1, 1998.
Erik J. Roggeman, Aaron M. Scurto, Joan F. Brennecke and John. E. Chateauneuf,“Spectroscopic Measurements of Preferential Solvation and Novel Volubility Measurementsof Metal Chelate Complexes in Pure and Modified Supercritical C02,” 1998 Midwest
Thermodynamics and Statistical Mechanics Conference, Notre Dame, IN, May 18-19, 1998.
6.
7.
8.
9.
14
Robert W. Maier, Mark A. Stadtherr and Joan F. Brennecke, “Reliable Computation ofHomogeneous Azeotropes,” 1998 Midwest Thermodynamics and Statistical MechanicsConference, Notre Dame, IN, May 18-19, 1998.
Erik J. Roggeman, Aaron M. Scurto, John E. Chateauneuf and Joan F. Brennecke,“Cosolvent Effects to Enhance Metal Extraction with Supercritical C02,” Annual AIChE
Meeting, Miami, FL, Nov. 15-20, 1998.
Mark A. Stadtherr, Robert W. Maier, Benito A. Stradi, Gang Xu and Joan F. Brennecke,“Reliable Computation of High Pressure Phase Behavior,” Annual AIChE Meeting, Miami,FL, NOV. 15-20, 1998.
Robert W. M~er, Joan F. Brennecke and Mark A. Stadtherr, “Computation of ReactiveAzeotropes Using Interval Analysis,” Annual AIChE Meeting, Miami,@ Nov. 15-20, 1998.
10. John E. Chateauneuf, J. Zhang, J. Brink, M. Slominis and M. Perkovic, “Investigation ofFree Radical and Radical Ion Reactivity with Supercritical Carbon Dioxide,” (posterpresentation) American Chemical Society 217th National Meeting, Anaheim, CA, March 24(1999). Physical Chemistry Division, Free Radicals in the Condensed Phase Symposium.
11. Gang Xu, Joan F. Brennecke and Mark A. Stadtherr, “Reliable Computation of Solid-FluidEquilibria Using Interval Analysis,” Midwest Thermodynamics and Statistical MechanicsConference, Detroit, MI, May 17-18, 1999.
12. John E. Chateauneuf, ‘The Use of Reaction Intermediates to Probe Supercritical FluidSolvent Effects,” (poster presentation) American Chemical Society 218th National Meeting,New Orleans, LA, August 23 (1999).
13. Robert W. Maier, Joan F. Brennecke, and Mark A. Stadtherr, “A New Approach for ReliablyComputing All Azeotropes of Multicomponent Mixtures:’ Annual AIChE Meeting, Dallas,TX, Oct. 31 – NOV.5, 1999.
14. Mark A. Stadtherr, Robert W. Maier, and C.-Y. Gau, “New Interval Methodologies forReliable Process Modeling”, AIChE Annual Meeting, Dallas, TX, Oct.31–Nov. 5, 1999.
15. Gang Xu, Joan F. Brennecke and Mark A. Stadtherr, “Reliable Computation of Solid-Supercritical Fluid Equilibria Using Interval Analysis,” Annual AIChE Meeting, Dallas, TX,Oct. 31 – Nov. 5, 1999.
16. Gang Xu, Aa~on M. Scurto, Marcelo. Castier, Mark A. Stadtherr, and Joan F. Brennecke“Reliable Computation of High Pressure Solid-Fluid Equilibrium”, 5[h InternationalSymposium on Supercritical Fluids, Atlanta, GA, to be presented April 8-12,2000.
17. Gang Xu, Aaron M. Scurto, Marcelo. Cas{ier, Mark A. Stadtherr, and Joan F. B~ennecke“Reliable Computation of High Pressure Solid-Fluid Equilibrium”, COBEQ 2000, Aguas deSiio Pedroz Brazil, to be presented Sept. 24-27,2000.
15
6. Listof Personnel Involved with This Project
University of Notre Dame
Graduate Students:Erik J. Roggeman, M.S. Thesis: Spectroscopy and Solubility Measurements of Metal Chelate
Complexes in SupercriticaI Carbon Dioxide Solutions, 7/98Gang Xu, Ph.D. expected 2001Aaron M. Scurto, Ph.D. expected 2002William D. Haynes, Ph.D. expected 2002
Postdoctoral Associates:Jianwei Zhang, currently employed at Monsanto in St. Louis, MO
Faculty: .Joan F. Brennecke, Professor of Chemical Engineering ~Mark A. Stadtherr, Professor of Chemical Engineering
Western Michigan University (subcontract)
Graduate Students:Jingsheng Zhang, M.S. expected 2000Honshu Jin M. S. Thesis: Spectroscopic Investigations of Carbonation Reactivity in
Supercritical Carbon Dioxide, 7/99 .
Faculty:John E. Chateauneuf, Assistant Professor of Chemistry
Literature Cited in Report
Baker, L. E.; Pierce, A. C.; Luks, K. D. (1982), “Gibbs Energy Analysis of Phase Equilibria,”Sot. Petrol. Engrs. J., 22,731.
Beech, G.; Lintonbon, R. M. (1971), “Thermal and Kinetic Studies of Some Metal Complexes of2,4-Pentanedione~ Thermochim. Acts., 3,97-105.
Fedotova, N. E.; Morozova, N. B.; Igurnenov, I. K.; Gerasimov, P. A.; Gerasimova, A. I. (1992),“Thermodynamic @estimation of Iron(III) Tris(beta-diketonates),” Koordinatsionnays Khinziya,19,622-629.
Giddings, J. C; Myers, M. N.; McLaren, L.; Keller, R. A. (1968), “High Pressure GasChromatography of Nonvolatile Species: Nature, 162; 67-73.
Hua, J. Z.; Brennecke, J. F.; Stadtherr, M. A. (1998a), “Reliable Computation of Phase StabilityUsing Interval Analysis: Cubic Equation of State Models,” Comput. Chem. Eng., 22, 1207.
16
Hua, J. Z.; Brennecke, J. F.; Stadtherr, M. A. (1998b), “Enhanced Interval Analysis for PhaseStability: Cubic Equation of State Models,” Ind Eng. .Chem. Res., 37, 1519.
Johnston, K. P., Peck, D. G., and Kim, S. (1989). Modeling Supercritical Mixtures-HowPredictive Is It? M. Eng. Chem. Res., 28, 1115-1125.
Kearfott, R. B.” (1996), Rigorous Global Search: Continuous Problems; Kluwer AcademicPublishers: Dordrecht, The Netherlands.
Koshimura, H. (1978), “Effect of Substituents on the Volubility and the Distribution of Alkyl-Substituted ~Diketone Iron Chelates:’ J. hzorg. AM. Chem., 40,865-874.
Lagalante, A. F.; Hansen, B. N.; Bruno, T. J.; Sievers, R. E. (1995), “Solubilities of Copper(II)and Chromium(III) ~-Diketonates in Supercritical Carbon Dioxide,” Inorg. Chern., 34, 5781-5785.
McHugh, M. A; Krukonis, V. J. (1990), Supercritical Fluid Extraction: Principles and Practice;Butterworth-Heinemann: Boston.
Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. (1999) Molecular Thermodynamicsof Fluid-Phase Equilibria, 3rdcd., Prentice Hall: New Jersey.
Ribeiro da Silva, M. A. V; Monte, M. J. S.; Huinink, J. (1996), “Vapour Pressures and StandardMolar Enthalpies of Sublimation of Two Crystalline Iron(III) beta-Diketonates. The MewMolar (Fe-O) Bond-Dissociation Enthaipies~ J. Chem. Thermo., 28,413-419.
Roof, Jr., R. B. (1956), ‘The Crystal Structure of Ferric Acetylacetonate,” Acts Cryst., 9, 781-786
Schnepper, C. A.; Stadtherr, M. A. (1996), “Robust Process Simulation Using IntervalMethods,” Comput. Chem. Eng., 20, 187.
Span, R.; Wagner, W. (1996), “A New Equation of State for Carbon Dioxide Covering the FluidRegion from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa~’ J. Phys.Chem. Re$ Data, 25, 1509-1596.
Tingey, J. M.; Yonker, C. R.; Smith, R. D. (1989), “Spectroscopic Studies of Metal-Chelates inSupercritical Fluids,” J. Phys. Chem., 93,2140-2143.
Wai, C. M.; Wang, S.; Yu, J-J. (1996), “Volubility Parameters and Solubilities of MetalDithiocarbamates in Supercritical Carbon Dioxide,” Anal. Chem., 68, 3516-3519.
Xu, G.; Scurto, A. M.; Castier, M.; Brennecke, J. F.; Stadtherr, M. A. (2000), “ReliableComputation of High Pressure Solid-Fluid Equilibrium,” hzd. Eng. Chem. Res., in press.
17
Contaminated
Extractor
-1%~Chelating Agent
+
Cleaned Organic4Solid SC CC)2 Recycle
I
Chelating Agent and C02 Makeup
Chelating agent less volatile than organic contaminant
Figure 1 Schematic of metal extraction process using chelating agents dissolved in supercriticalC02, in which the chelating agent is less volatile than any organic co-contaminants thatmight be present.
i
18
Solid
Extractor MetalCheiate
4 Cleaned I u—Solid
7
Organic
SC C02 + ChelatingAgent Recycle
Chelating Agent a’nd C02 Makeup
Chelating agent more volatile than organic contaminant
Figure 2 Schematic of metal extraction process using chelating agents dissolved in supercriticalC02, in which the ‘chelating agent is significantly more volatile than any organic co-contaminants that might be present.
19
------ ------ ------ ------ ------ ------ ------ .-. .. . . .. -- . .. . . . .. . . . .. —... — . .. —... — . .. . . . .. . . . .. .
10-3
[/–-1
...................................................... ...........................#,#..:.
-*--""-""""--8---""--"?""---"-"n-"--"""":"""-"-""----"-"-"----""""""-"-"",0-5 .— -. .. . . . . . . . . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . .. . . ------------ . .. .. . . .. . .. ...=.-/
. . . . . . . . . . . . . . . . . . . . . .. .. . ... . . . . ..y..?.- . . . .. . . . . . . . . . . .. . . . . . . . . . .. . .. . . . . .,0-7 .............. /“---------.-.->---------........................................--....-
/
10-9
,.-11
10-’3
, *-15
10-’7
,0-19
I
1(.................................................................................../..................................................................................../..............................//.........................................................../ 1. . . . . . . . . . . . . . . . . . . . . . . . . . . .
/. . . . . . . . . . . . . . . . . . . . . . . . .. . . .#. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
, t t , , I , , 1 t , I t I I I , [ I , I , I I
80 120 160 200 240 280 320 360 400
Pressure [bar]
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
----
-.——
●
m
_—
Ideal Volubility: T= 60 C
Ideal Volubility: T= 40 C
Experimental Data: T= 60 C
Experimental Data: T= 40 C
RST: T= 40 C
f?ST: T= 60 C
. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .
Figure 3 Volubility of Fe(acetylacetonate)3 in supercritical C02 as predicted by Regular SolutionTheory at 40”C and 60°C. Also included at the top of the graph are the predictions fromideal solution theory, in which the activity coefficient is assumed to be one.
20
7104 I , I , I I .J.Regressed EOS Constants
.
Tc= 747.97 K.* “
610-4*
............ ..... ........ .......................... .................Pc= 18.31 bar
,.C...... ........._#
W=.8144 ,*’5 10“4 . ........... ... .......................................2/ .. ..........
4104 ............. ............................ ................ ........... .........
310-4 ....... ..... ..... ......... #--.................. ..............................
Experimental Data: T= 60 C2 10“4 ----- T= 60 C; k12=0.0686; %AARD=16.70
● Experimental Data: T= 40 C
110-4 ....... ...a’................ — T= 40 C; k12=0.0517 : ?4AARD=16.31
100 150 200 250 300
Figure 4
Pressure [bar]
Modeling of the volubility of Fe(acetylacetonate)3 in supercritical C02 at 40°C and60°C with the Peng-Robinson equation using van der Waal 1 mixing rules. Here three purecomponent parameters for the Fe(acetylacetonate)3, as well as the binary interactionparameter, kv, are regressedregressed values, as well asexperimental data.
from the experimental data. Shown on the graph are thethe average relative deviation between the model and the
i
21
7104
610-4
510-4
410”4
310”4
210-4
110”4
010°
I I I , I I r , I I I-“Regressed EOS Constant .“
W=.5849 *.. .. .. .. .. ... . ...... .. ... .. ..... ......... .. ..... .... .. .. .. ..... ... ..>.?... ..... ... ... ..
Joback EOS ConstantsTc= 799.95 K
++
... . . .... . . .... .. .. . ... . ... ... .. . ................ ..... .Pc= 19.56 bar
E.---.-.--------.--------.--.-----.-.----=/--.----------.-.----,----.--.-------.---4
b“”/+/ !....................................../f ● Experimental Data: T= 60 C “
/8 ----- T= 60 C: k12=0.0594 ; %AARD=16.71
--------------- ----------- *----------- ● Experimental Data: T= 40 C## — T= 40 C: k12=0.0391 ; %AARD=l 6.37
#
h---/--;-a'................................................................-1
100 150 200 250 300
Pressure [bar]
Modeling of the volubility of Fe(acety1acetonate)3 in supex-critical COZ at 40°C and60”C with the Peng-Robinson equation using van der Ward 1 mixing rules. Here only onepure component parameter (the acentric factor) for the Fe(acetylacetonate)3, and the binaryinteraction parameter, ICU,are regressed from the experimental data. Shown on the graph arethe values of the critical temperature and pressure that were estimated with the Jobackmethod, the regressed values of the acentric factor, and kti, as well as the average relativedeviation between the model and the experimental data.
..
22
710-’
6104
5104
4104
310-4
210-”
1104
010°
1 1 I 8 1 { c I , I , , , I JH“
Joback EOS Constants.U “
.. .... .....~c=.ng:95.K ....... .............................z.< .. .... ........ . -
Pc= 19.56 barW=.983. .. ............. ......................... ...
.. .. ... .. .. . . . ... ... . .. ... .. . .. .... .. .. .. . ....-. . ... .. .. .. ... . .. .. .. . .. .. .. .. .
p -------------------------- . . .. .. .. .. .. . . ... ... .. .
● Experimental Data: T= 60 C............... -.. ---. ----)------------ ----- T= 60: k12=0.1546 ; %AARD=16.70Experimental Data: T= 40 C
— T= 40 C: k12=0.1394 %AARD=l 6.15... .......X. . ........ ........
100 . 150 200 250 300
Pressure [bar]
Modeling of the volubility of Fe(acetylacetonate)3 in supercfitical C02 at 40”C and60”C with the Peng-Robinson equation using van der Waal 1 mixing rules. Here only thebinary interaction parameter, kti, was regressed from the experimental data. Shown on thegraph are the values of the critical temperature and pressure that were estimated with theJoback method, the acentric factor determined from pure component data, and the regressedvalue of kU,as well as the average relative deviation between the model and the experimentaldata.
23
75Q Fe(acac) ~“ wo4 0.1 , 1 I 1
100 150 200
Pressure (bar)
250. 3(H)
Figure 7 Local compositions of chloroform around Fe(acetylacetonate)s at 60°C, as measured byUV-visible spectroscopy.
