Ind. Eng. Chem. Res. 2002, 41, 153-163
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Characterization of the SO2-N-Formylmorpholine Complex: Application to a Regenerative Process for Waste Gas Scrubbing Richard de Kermadec,† Franc¸ ois Lapicque,*,† Denis Roizard,‡ and Christine Roizard† Laboratoire des Sciences du Ge´ nie Chimique and Laboratoire de Chimie Physique Macromole´ culaire, CNRS-ENSIC, 1 rue Grandville, BP 451, F-54001 Nancy, France
This paper presents the results of fundamental investigations on physical and chemical interactions between sulfur dioxide and N-formylmorpholine (NFM), with a view to the development of a regenerative process for waste gas scrubbing. This solvent is a promising medium for such processes because of its high absorption capacity, its low-to-moderate vapor pressure for temperatures below 100 °C, and its reduced toxicity. The existence of a chemical interaction between SO2 and NFM, with the formation of a 1:1 complex, was demonstrated by absorption tests, melting curve measurements, and the determination of vapor-liquid equilibrium from 25 to 80 °C. Further characterization was carried out by IR spectrometry. The formation of a solid complex with a melting point at 5.7 °C allows for the transport of absorbed sulfur dioxide under a convenient solid state; in addition, its stability was shown to decrease with temperature, which enables the solvent to be regenerated at high temperatures. The existence of a second complex with a 2:1 stoichiometry was suggested by modeling the gasliquid equilibrium using the Harris and Prausnitz approach but could not be put into evidence by the other techniques. The parameters deduced by the above-mentioned model were successfully used for the prediction of the melting curve of an SO2-NFM system. I. Introduction The removal of sulfur dioxide from industrial waste gases is of increasing importance because of the lowering of the admissible emission and the poorly defined future of the products formed in most current desulfurization processes. Among the various existing routes, the absorption of sulfur dioxide in liquids through regenerative processes allows for its further reuse in valuable applications. Recent examples are the Clintox/ Solinox process involving the use of tetraethyleneglycol dimethyl ether1 or the Clausmaster process with dibutyl phosphonate. Since the pioneering work of Gleason et al.,2 who patented the use of dimethylaniline, scrubbing processes involving the chemical absorption of sulfur dioxide have been developed; famous examples are the Wellman-Lord process with solutions of sodium bisulfite and the Cansolv process with diamine derivatives of aliphatic chains. Numerous organic solvents have been considered as absorption media (e.g., amines,3,4 alcohols, ketones, glycol ethers,5,6 thioureas,7 and various heterocyclic compounds).7,8 Chemical absorption in organic solvents involves, in most cases, the formation of a charge-transfer complex between sulfur dioxide, being an electron-pair acceptor, and the solvent, acting as the electron-pair donor. Such a reaction allows for high selectivity to sulfur dioxide in comparison to other gases such as CO2, H2O, or NOx. The melting points of the complexes formed are usually much higher than those of the initial compounds. * Corresponding author. E-mail: Francois.Lapicque@ ensic.inpl-nancy.fr. † Laboratoire des Sciences du Ge ´ nie Chimique, CNRSENSIC. ‡ Laboratoire de Chimie Physique Macromole ´ culaire, CNRSENSIC.
The investigations reported here were directed to the design of an absorption process relying upon the formation of a solid SO2-solvent complex and allowing for the thermal regeneration of both sulfur dioxide and the solvent. Following the method suggested in a previous paper,9 the selection of organic solvents for SO2 absorption was carried out considering the following criteria: a high absorption capacity, high SO2 selectivity with respect to other gases (e.g., CO2), low toxicity, a melting point of the complex formed at ambient or moderately low temperatures, and finally, the reversibility of the complex formation. Most amines allow for the formation of very stable complexes, which renders the regeneration step by pressure reduction or temperature rise more difficult. Less basic solvents such as amides and ureas, being cyclic or not, can fulfill the previously mentioned requirements and appear to be promising candidates. On the basis of donor-acceptor considerations, we suggested previously the use of N-methylpyrrolidone (NMP) and N,N′-dimethylpropyleneurea (DMPU) for the selective absorption of sulfur dioxide, and the occurrence of complex formation was put into evidence. However, NMP has an appreciable vapor pressure at 80-100 °C, which affects the achievement of the regeneration step. In addition, the 1:1 SO2-DMPU complex has a melting point of approximately -21 °C,9 and the energy consumed for crystallization, separation, and storage of an SO2-DMPU system may hinder the viability of a regenerative process for gas scrubbing. N-Formylmorpholine (NFM) was then considered as an alternative; the presence of a carbonyl group on the nitrogen atom of the cycle, in addition to the oxygen atom of the morpholine heterocycle, was expected to allow for significant interactions with sulfur dioxide. This solvent is selective to SO2 in comparison to CO2, which is only moderately soluble.10 Furthermore, NFM had been used
10.1021/ie010173c CCC: $22.00 © 2002 American Chemical Society Published on Web 12/21/2001
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as a physical solvent for years by Krupp Uhde for recovery of high-purity aromatics and more recently for the treatment of subquality natural gas or natural gas.11 In addition, NFM appears to be a more promising candidate than NMP and DMPU, thanks to its lower partial pressure of approximately 10 Pa at 25 °C and melting point of the 1:1 SO2-solvent complex near 5 °C. This paper presents the results of fundamental investigations of the interactions between SO2 and NFM. The existence of a complex formed between the two species was first demonstrated by IR spectroscopy and determination of the melting enthalpy of the SO2-NFM system. Extensive experimental vapor-liquid equilibrium (VLE) data of the binary system for temperatures up to 80 °C were interpreted by a model relying upon the occurrence of a liquid-phase chemical reaction and taking into account the nonideal behavior of the organic solution. The values of the parameters involved in the model, namely, the equilibrium constants, and the parameters for the activity coefficients were used to model the melting curves of an SO2-NFM system. Chemicals. NFM (analytical grade from Aldrich, Milwaukee, WI) is a liquid above 23 °C with a boiling point at atmospheric pressure close to 240 °C. Its viscosity at 25 °C was measured with an Ubbelohde apparatus at 6.2 10-6 m2 s-1. Its partial pressure at 25 and 75 °C was measured at 16 and 366 Pa using gasliquid chromatography by Weidlich et al.,12 in fair agreement with estimations using Joback and Pitzer’s method of group contribution.13 This solvent is of low toxicity, with a lethal dose of 6500 mg/kg for rats,14 which represents an additional advantage for its possible use in a process. Carbon dioxide has moderate solubility in NFM with a Henry constant at 298 K reported at approximately 7 MPa.10,15 In addition, the VLE curves of the CO2-NFM system are fairly linear in a large domain of pressure, indicating the poorly significant interactions between the molecules. NFM has a polar structure and is miscible with water at any rate. The 8.6 pH value in a 1:1 mixture indicates an alkaline noncorrosive condition.11 Water vapor is present in most waste-containing gases, and the high affinity of water toward the solvent results in the side absorption of water in the scrubbing process. The presence of water in the absorption medium may reduce the absorption capacity, as observed with other solvents,16 as well as the boiling point of the solvent phase; the boiling point of a 10% water solvent phase was measured at approximately 190 °C. For the present investigation, a water-free solvent was used. Traces of water from the purchased solvent were removed using 3-5 Å molecular sieves (Fluka, Sigma-Aldrich) which were freshly regenerated by thermal drying at 250 °C under reduced pressure for 12 h. II. Affinity of NFM to SO2: Evidence of Complex Formation II.1. SO2 Solubility in NFM. The solubility in NFM was measured using a laboratory Pyrex cell with a volume of approximately 30 cm3. The cell was operated batchwise to the solvent, and pure SO2 under atmospheric pressure was continuously fed through a sintered glass. The cell design and the experimental procedure were described in ref 9. The cell was im-
Figure 1. Melting curve of SO2-NFM system.
mersed in a thermostated bath, and the temperature was varied from 25 to 80 °C. The solubility was attained from the steady value of the weight of the cell containing the SO2-NFM mixture. The high absorption capacity was shown by the measurements and, for instance, 1 g of solvent absorbed nearly 0.85 g of SO2 at 25 °C. The global mole fraction of sulfur dioxide x2 (being either as free sulfur dioxide or in the form of a complex) was deduced from weighing measurements and taking into account the molar weight of both compounds. As expected, x2 decreases with temperature, passing from 0.604 at 25 °C to 0.268 at 80 °C under atmospheric pressure. II.2. Melting Curve Measurements. SO2-NFM mixtures with various compositions were prepared using the previously mentioned cell. The global amount of SO2 absorbed by the solvent was varied by varying the temperature of the thermostated bath, the time of gas absorption, and the pressure of the gas up to 200 kPa. The amount of absorbed SO2 was determined by weighing, and the technique was of sufficient accuracy for x2 over 2%. A trial-and-error technique was used in the experiments to reach the desired composition of the binary mixture, and adjustment to the desired x2 value was achieved either by further absorption of pure SO2 or by its desorption from the liquid by means of a vacuum pump; the pressure was followed as a function of time until steady state was obtained. The prepared mixtures were rapidly solidified by immersion of the cell into liquid nitrogen for a few minutes. Then, the cell was placed into the cryostat reservoir at a chosen temperature, and melting of the crystals could be eventually observed. The temperature corresponding to the total melting of the mixture investigated (liquidus) was experimentally determined by the trial-and-error method (i.e., by shifting the cryostat temperature by half of a degree) and by observation of the physical state of the SO2-NFM system. Although tedious, the technique was shown to yield reproducible results, and the accuracy in the liquidus determination was estimated at 0.5 °C. As shown in Figure 1, the melting point of the SO2-NFM system decreases regularly with x2 up to approximately 33%. The sharp change in variation observed at x2 around 0.33 indicates the existence of a eutectic point E1 at approximately -8 °C. The liquidus exhibits a welldefined maximum at 5.7 °C for x2 ) 0.5; this maximum may correspond to the formation of a 1:1 SO2-NFM complex. Further increasing x2 resulted in the regular decrease of the melting temperature. No second eutectic
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Figure 2. (a) Characterization of the SO2-NFM complex by FTIR: absorption bands recorded in the wavenumber domain of 750-450 cm-1 for pure NFM and from SO2-solvent complexes with an SO2 mole content of 48%, 58%, and 63%. (b) Characterization of the SO2NFM complex by FTIR: absorption bands recorded in the wavenumber domain of 1500-1000 cm-1 and its SO2 complex with an SO2 mole content of 63% (solid line). (c) Characterization of the SO2-NFM complex by FTIR: carbonyl bands (asymmetric and symmetric) recorded for pure NFM (dotted line) and its SO2 complex with a SO2 mole content of 63% (solid line).
point could be put into evidence by the measurements. The solid formed by cooling SO2-NFM mixtures was a pure solvent for x2 below 0.33 and the 1:1 complex beyond eutectic point E1. II.3. IR Spectrophotometrical Measurements. NMF solutions of sulfur dioxide were prepared at ambient temperature in the gas-liquid stirred reactor described in section II.4. Three samples were drawn at regular intervals (2, 4, and 6 h) to obtain solutions at different contents. The amount of sulfur dioxide was estimated by pumping off the more volatile compound and weighing. The sample was placed in a vacuum drier at 30 mbar, and sulfur dioxide was allowed to desorb for a few hours. A reference vessel filled with dehydrated NFM was submitted to the same procedure so that the loss of NFM by vaporization at low pressure was shown to be negligible. The desorption procedure was repeated until steady state was attained. Fractions x2 in the samples were estimated at 48%, 58%, and 63%. Spectra of SO2-NFM solutions were recorded from a thin film of the mixture between two KBr pellets at ambient temperature. The spectrum of sulfur dioxide was obtained by dissolving sulfur dioxide into a noncomplexating solvent such as CCl4. The spectrum of this
pure solvent was subtracted from that of the SO2-CCl4 solution. The presence of dissolved SO2 in NFM was clearly demonstrated by three characteristic peaks in the recorded spectra (Figure 2a,b). Using normalized spectra with respect to the area of the aliphatic massif, the areas of these bands were shown to increase with the global mole fraction of SO2, x2. Figure 2a shows an example at 529 cm-1. Besides, if one considers the SO2 absorption band at 529 cm-1 with the values for fractions x2, it is clear that the variation deviates strongly from linearity, especially for the highest SO2 content (63%). In addition, the stretching band of sulfur dioxide at 1145 cm-1 was also observed, while the second band was shifted toward a lower frequency to 1323 cm-1 (Figure 2b); such a shift was observed previously with NMP and DMPU9 and was attributed to the interactions with the carbonyl group of the three solvents. From the NFM point of view, the stretching vibrations of the amide carbonyl group of the SO2-NFM solutions were examined. For the pure solvent, two bands at 1674 and 1662 cm-1, corresponding to antisymmetrical and symmetrical vibrations, were observed, the first one being slightly larger than the second (Figure 2c). The
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Figure 3. (a) VLE of the SO2-NFM system depending on temperature. Symbols are for the experimental data, and lines are for Raoult’s law at 25 °C (- ‚‚ -), 45 °C (- -), 64 °C (‚‚‚), and 80 °C (s). (b) VLE of the SO2-NFM system in the low-pressure domain. Symbols are for the experimental data, and the solid lines are for Henry’s law.
presence of sulfur dioxide induced two noticeable changes: first, it affected the relative importance of the twin bands, with the symmetrical one becoming the stronger one, and second, the wavenumbers of the two bands were decreased by a few reciprocal centimeters. This later effect is far different from that observed formerly with NMP and DMPU, for which the large amide band was shifted by more than 20 cm-1 to the higher frequency by the presence of sulfur dioxide. The difference observed might be due to the different positions of the carbonyl group; the concerned carbon atom belongs to the heterocycle for NMP and DMPU, whereas it is exocyclic for NFM. Besides these significant effects due to SO2, no marked change could be seen on the absorption of the ether bands; the most characteristic one at 1118 cm-1 appeared unaffected either in strength or in position. The SO2 molecule is known to be polar and the sulfur atom to be electropositive; thus, SO2 behaves as an electron acceptor by the sulfur atom, and its interaction with NFM should occur with the oxygen of the carbonyl group. Such an interaction should decrease the doublebond character of the carbonyl group and so induce a lower absorption frequency, as is observed. Furthermore, interactions of the nitrogen atom of NFM with electron-withdrawing groups are predicted17 to give the opposite effect on the carbonyl frequency. From the IR results recorded on the three solvents (NMP, DMPU, and NFM), one can suppose that the SO2-NFM complex is the less stable, as suggested by its lower downshifted frequency. II.4. Measurements of VLE. The VLE of a SO2NFM system was investigated from 25 to 80 °C using two experimental setups, depending on the pressure of sulfur dioxide. The first device was a stirred tank reactor machined out of poly(tetrafluoroethylene) and glass, with a volume of 50 cm3; temperature control of the liquid phase was allowed by the water jacket of the reactor. Sulfur dioxide diluted into a continuous stream of nitrogen upstream from the reactor was introduced at a partial pressure of below 1 kPa, with a global flow rate of the gas phase of approximately 25 cm3 s-1 STP and a total pressure close to 1 atm. The outlet concentration was monitored by UV spectrophotometry (Rosemount NGA 2000) and
continuously recorded. The run was stopped when the outlet concentration attained the level of the inlet stream, corresponding to the saturation of the solvent, with an initial volume of around 30 cm3. Taking into account the inlet pressure, the integration of the variations of the outlet pressure over time led to the amount of absorbed sulfur dioxide. The second device used was the Pyrex cell described in section II.1. Pure sulfur dioxide was introduced at an absolute pressure ranging from 100 to 200 Pa. Investigations with pressures from 2 to 100 kPa were carried out by pumping off sulfur dioxide and connecting the cell to a manometer. For all of the cases, equilibrium was attained for steady values of pressure. The cell was then disconnected and weighed for an estimation of the amount of SO2 absorbed. The experimental variations of PSO2 with global mole fraction x2 are shown in Figure 3a, in comparison with the application of Raoult’s law sat PSO2 ) x2PSO 2
(1)
sat , the vapor pressure of pure liquid SO2, fits where PSO 2 the Antoine equation as follows:18
sat ) ) 10.512 ln(PSO 2
2515.25 T - 23.68 sat with PSO in bar and T in K (2) 2
The significant deviation from Raoult’s law shown in Figure 3a expresses the high affinity of SO2 to the solvent. Besides, the pressure was shown to vary linearly with the global mole fraction up to 1 kPa (Figure 3b). The overall Henry coefficient of sulfur dioxide is defined as
He2 ) lim
( ) PSO2 x2
xf0
(3)
The Henry coefficient was estimated by linear regression of the low-concentration data at 20, 45, 100, and 210 kPa for temperatures of 25, 45, 64, and 80 °C, respectively.
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III. Modeling the Vapor-Liquid SO2-NFM System The absorption of sulfur dioxide into NFM was shown to involve the formation of a complex. The chemical absorption was modeled following the approach suggested by Harris and Prausnitz;19 the absorption consists of the physical absorption in the solvent yielding molecular SO2 under the liquid form (A), followed by its chemical complexation by the solvent (B) as follows:
A+BTC
(4a)
By analogy with other SO2-solvent systems reported in the literature (e.g., SO2-DMF system),20 other reactions may also be considered:
2A + C T D, corresponding to the 2:1 complex (4b) A + 2B T D′, corresponding to the 1:2 complex (4c) The nonideal behavior of the solution was described regardless of the chemical interactions by the simple van Laar model because chemical processes are taken as accounted for by relations (4). III.1. Equations and the Calculation Procedure. The equations given here are related to the ternary system, corresponding to the formation of the 1:1 complex only. The equilibrium constant of complex formation is defined as
K)
γC xC γAγB xAxB
(5)
where γi denotes the activity coefficient of species i. Mole fractions xj are calculated from the global fraction x2 as follows. Fraction x2 is defined from the initial number of moles of solvent and SO2, n1 and n2, respectively, before the occurrence of the reaction
x2 )
n2 n1 + n2
and
x1 ) 1 - x2
(6)
Because of complex formation, the number of moles of solvent at equilibrium, nB, is a function of conversion ζ
nB ) n1(1 - ζ)
(7a)
The complexation stoichiometry led to the number of moles of species A and C
nA ) n2 - n1ζ
(7b)
nC ) n1ζ
(7c)
The expressions for the mole fractions xj at gas-liquid equilibrium (GLE) could then be derived from these relations. The model for activity coefficients involves the volume fractions of the various species, zj, defined from mole fractions xj and by taking into account the effective molar volumes qj
zj )
xjqj
∑k xkqk
(8)
The model was derived from the second-order Wohl expansion of the excess free enthalpy. As considered in ref 19, interaction coefficients Rij were assumed to be symmetrical and were calculated from solubility parameters and molar volumes, as explained by the following:
ln γj )
qj RT
Ri,m - Rkl)] ∑i Rijz2i + k,l*j ∑ xkxl(∑ m
[
(9)
where the interaction parameters are functions of solubility parameters δi
Rij ) (δi - δj)2
(10)
The effective molar volumes were approximated by the molar volumes of pure component Vj. Solubility parameters were defined from the vaporization energy and the molar volumes
δi ) x∆Uv/Vi
(11)
where ∆Uv can be calculated from the vaporization energy (Appendix 1)
∆Uv ) ∆Hv - RT
(12)
The molar volumes of pure species (VA and VB) were obtained from the literature or deduced from other physical properties. The molar volume of the complex VC was estimated from the volumes of pure substances following Harris and Prausnitz19
VC ) VB + 0.75VA
(13)
expressing the noticeable reduction of volume in the complex formation. The values of the physicochemical parameters required in the model are reported in Appendix 1. The equilibrium constant K at temperature T was estimated by fitting the experimental data, consisting of a series of couples (x, PSO2), to the previous model by minimization of error function F defined as
F)
(Pth,SO2 - PSO2)2
∑i
PSO2
(14)
where the theoretical pressure of SO2 was deduced from the activity of molecular sulfur dioxide in the liquid phase and the vapor pressure of pure SO2 at T, neglecting the contribution of the fugacity coefficient in the gas phase sat Pth,SO2 ) xAγAPSO 2
(15)
The particular expression for the error function represents a compromise between the sum of squared deviations and that of the relative squared deviations; use of this peculiar error function was shown to yield accurate fitting for the absorption of both dilute and concentrated sulfur dioxide. Calculation of the theoretical pressure corresponding to the considered fraction x2 was carried out using an iterative scheme starting from an ideal liquid phase; convergence to stable values of xi, γi, and Pth,SO2 was usually obtained after a few iterations. III.2. Development of the Model. The model involving the 1:1 complex and relying upon the previously
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Figure 4. VLE of the SO2-NFM system at 25 °C. Comparison of experimental data with the prediction of the model involving the formation of a 1:1 complex only (dotted line) or the formation of both 1:1 and 2:1 complexes (solid line).
mentioned equations did not allow for satisfactory fitting of the experimental data, as shown in Figure 4. Whereas the fitting was perfect in the low-pressure domain, strong deviations were observed over 50 kPa (i.e., in a concentration range where a 2:1 complex type is more likely to occur). Thus, starting equations related to the quaternary SO2-NFM system and reported in Appendix 2 were developed, giving as results the best fitting of the whole set of data (Figure 4). Although not clearly demonstrated by the analytical measurements obtained up to now (IR and melting experiments), the nonlinear variations of SO2 absorption bands with its concentration in NFM seem to confirm the existence of a 2:1 complex. The estimation of equilibrium constants K1 and K2 at T (see Appendix 2) was carried out by minimization of the error function, and estimates for K1 were obtained by direct fitting for pressures below 10-20 kPa, depending on temperature; as a matter of fact, the 2:1 complex was scarcely present in the low SO2 content domain, and the 1:1 complex predominated. The effect of K2 on VLE curves becomes significant over 30-50 kPa. Confidence Intervals. Confidence intervals were not calculated directly, because of the highly nonlinear character of the equations. Calculation of VLE with postulated values for K1 and K2 showed the existence of a narrow valley situation in the (K1 and K2) plan. From the exact location of the optimal locus, the error function remained weakly changed by decreasing K1 by a few percent and increasing K2 by the same factor. In contrast, changing only one constant resulted in a larger increase in the error function. From the various simulations carried out, confidence intervals for two constants were estimated at approximately 5% for K1 and 8% for K2. Sensitivity to Physicochemical Parameters. Values of solubility parameters were changed within 10% from their reference value to observe their effect on the model prediction. The activity coefficients were shown to be changed significantly, and, for instance, a 10% reduction in δA was accompanied by a 15-30% increase in these values. However, the effect of activity coefficients on VLE is moderate, and the optimal values for
Figure 5. VLE of the SO2-NFM system at various temperatures. Comparison of experimental data with the prediction of the model involving the formation of both 1:1 and 2:1 complexes (solid line).
constants K1 and K2 were changed by a few percent only. The uncertainty in the estimation of the physical parameters such as Vi and ∆Hi was, therefore, of a limited effect on the determination. In addition, the sensitivity of the model with respect to volumes VC and VD was investigated considering other expressions of VA and VB. In particular, it was considered that the interactions between A and B might be stronger in dilute solutions than in more concentrated media, because of steric hindrance in the complex formation; the weighing factor at 0.75 appearing in eq 13 was replaced by increasing functions of x2. Despite the significant difference in values for VC and VD, changes in the predicted pressures were only of secondorder. III.3. Results. The experimental and predicted variations of the pressure of sulfur dioxide with x2 are compared in Figure 5; good agreement was obtained in all cases. Both constants K1 and K2 as determined by fitting decreased with temperature, expressing the fact that the complexes are looser at high temperatures. In addition, constant K2 is nearly on the order of unity, whereas K1 is approximately 1 order of magnitude larger than K2 (Figure 6). Similar treatment of the VLE curves of the SO2-DMPU system in the same temperature range gave values for K1 nearly 2.5 times higher, with comparable K2 values16 indicating that a 1:1 complex is stronger with the urea than with NFM. The equilibrium constants can be related to the enthalpy difference and to the entropy difference of the complexation after van’t Hoff’s relation
ln(Ki) ) -
∆Hi ∆Si ∆Gi )+ RT RT R
(16)
The Arrhenius plot of the two constants enabled ∆Hi and ∆Si of the two complexations to be estimated
∆H1 ) -10.9 kJ mol-1 ∆H2 ) -19.2 kJ mol-1
∆S1 ) -14.4 J mol-1 K-1 ∆S2 ) -55 J mol-1 K-1
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sulfur dioxide, γ2, defined as
γ2 ) γA
Figure 6. Temperature dependence of the equilibrium constants of the formation of a 1:1 complex (K1) and a 2:1 complex (K2) for the SO2-NFM system.
The low absolute value of ∆H1 shows the fair stability of complex C, even at temperatures on the order of 100 °C, and higher temperatures would be required in the regeneration tower. In contrast, complex D is far less stable than C, and the 2:1 complex should be of minor importance over 100 °C. Although less accurate in the high-concentration domain, the ternary model was also used for fitting the experimental data, and the temperature variation of equilibrium constant K yielded estimates for ∆H and ∆S
∆H ) -14.2 kJ mol-1
∆S ) -25.2 J mol-1 K-1
As shown in Figure 7a, the activity coefficient of noncomplexed sulfur dioxide, γA, was slightly above unity in most cases and decreased regularly with x2. In addition, more significant deviations from ideal behavior were observed at high temperatures. Although not given in here, the activity coefficients for the other chemical species (solvent and complexes) were of the same order of magnitude as γA. The overall activity coefficient of
xA x2
(17)
was calculated and plotted versus x2; the variations given in Figure 7b express the significance of chemical reactions in the liquid phase, whereas the effects of physical interactions are less visible.19 The ratios of activity coefficients Kγ1 and Kγ2, respectively, were generally in the range of 0.87-1 at room temperature. As the activity coefficients of the various species were very close to each other, activity ratios Kγ1 and Kγ2 usually had identical values within 1%. The deviation of both ratios from unity was enhanced by increasing temperature, and the lowest Kγ values encountered for a low fraction of sulfur dioxide were at approximately 0.86, 0.82, 0.76, and 0.71 at 25, 45, 64, and 80 °C, respectively. For dilute SO2-containing gases, the ratio x2/xA can be compared to the ratio of the slopes of Raoult’s and Henry’s laws, neglecting the deviation of the activity coefficients from unity sat
x2 PSO2 ≈ xA He2
for xA f 0
(18)
The approximate relation valid for low concentrations of sulfur dioxide was verified within 12% for the four temperatures investigated, and the high x2/xA ratio expresses that the complex form predominates in the organic solution. IV. Modeling the Solid-Liquid SO2-NFM System The experimental melting curve of the investigated system was modeled using the values of the physicochemical parameters determined previously. Thermodynamical variables related to fusion had to be determined by additional measurements prior to development of the model. IV.1. Determination of Fusion Enthalpy. Calorimetric measurements were carried out using a computercontrolled DSC 92 apparatus. The sample was either pure NFM or a 1:1 SO2-NFM mixture. A small quantity
Figure 7. Calculated activity coefficients in the liquid phase versus global mole fraction of sulfur dioxide, x2, and variation of the temperature: (a) coefficients of molecular sulfur dioxide, γA, and (b) global activity coefficient of dissolved sulfur dioxide, γ2.
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of liquid (approximately 20 mg) was introduced in the stainless steel crucible using a syringe. Weighing was carried out using a microbalance. This procedure, although achieved rapidly, resulted in slight loss of sulfur dioxide, and the actual stoichiometry could differ from that in the glass absorption cell. The crucible was sealed by mechanical compression and introduced into the analysis chamber. The sample was frozen in liquid nitrogen for complete solidification. The temperature was then allowed to vary from -100 to +90 °C at 10 °C min-1 after a delay at the initial temperature. Three successive scans were carried out, and the results given were the average values. The heat flux supplied to the sample was continuously recorded. Fusion of the liquid was observed by a well-defined peak of heat flux, and the temperature of the phase change was detected by the onset of the peak. IV.2. Interpretation of the Measurements. Melting of a Pure Solvent. The melting temperature of NFM was determined at 19.8 °C, to be compared with the reference temperature at 23 °C. Replicate measurements confirmed the experimental value, and the deviation observed might be due to the purity of the solvent and to the calibration of the apparatus. For the pure solvent, integration of the heat-flux peak led to the fusion enthalpy, ∆Hfus,NFM, at 12.76 kJ mol-1. The entropy of fusion of the solvent was then deduced
∆Sfus,NFM )
∆Hfus,NFM ) 43.1 J mol-1 K-1 (19) Tfus,NFM
Melting of an SO2-NFM Mixture. The melting of mixtures resulted in two successive phase transitions, as indicated by the presence of two peaks on the recorded heat-flux profiles: the first one expressed the transition through the solidus line, and the second one at higher temperatures was due to the melting of the last crystals (liquidus). Melting of the 1:1 complex, at the maximum of the liquidus curve, should be observed by only one peak. However, the losses of sulfur dioxide caused in the sample preparation resulted in a deviation from 1:1 stoichiometry, and two peaks were observed. Numerous experiments were carried out, and the curve selected exhibited two peaks, but the area of the liquidus peak was nearly 20 units larger than that of the second one. The average heat supplied by melting the binary mixture was measured at 122.7 J g-1. The fusion temperature could not be determined with accuracy, probably because of the deviation of composition from theoretical stoichiometry. The heat supplied for the sample for its melting does not correspond only to the fusion enthalpy of a 1:1 complex. As a matter of fact, the overall change consists of two steps: (i) fusion of the solid to obtain a 1:1 complex under the liquid form, with the molar enthalpy of fusion ∆Hfus,C, and (ii) partial decomposition of the liquid complex to equilibrium between SO2, NFM, and the complexes, involving the enthalpy of complexation determined by modeling of gas-liquid measurements. Consider, for the sake of simplicity, the case of ternary systems, with the presence of only one complex; the mole fractions were calculated at xA ) xB ) 0.1362 and xC ) 0.7276. One mole of liquid mixture at this composition was formed by fusion of a 1:1 complex with a number of moles of xA + xC, and the heat transferred for the
reaction was -xA∆H. The heat balance was then written as follows:
(xA + xC)∆Hmeas ) (xA + xC)∆Hfus,C - xA∆H
(20)
Taking into account the enthalpy of the complexation at -14.2 kJ mol-1 for the ternary system calculated previously, ∆Hfus,C,III could be deduced at 19.6 kJ mol-1. Similar calculations were carried out assuming the existence of two complexes. Complex C splits into A and B and reacts partly with A to form D, after the thermodynamic equilibrium. The fusion enthalpy, ∆Hfus,C,IV, was then estimated at 23.1 kJ mol-1. Besides, attempts in preparing samples at a 2:1 composition did not allow for reliable calorimetric curves; complex D could not be put into evidence, and its enthalpy of fusion could not be determined. Contrary to the case of pure substances, the entropy of fusion of a mixture cannot be deduced from the enthalpy of fusion and its melting point. IV.3. Modeling of the Melting Curves. The experimental curve consisted of two sections: first, a decreasing variation with temperature from A to E1 and then a parabole-looking section with a maximum corresponding to complex C. These two sections of the liquids were modeled from the enthalpy of fusion and the data of the VLE of the system as follows. The principle of the model consisted of calculating the chemical composition of the system from its melting temperature. For the sake of simplicity, only equations to the ternary system were given here. Solid-liquid equilibrium was considered, and its corresponding constant, Kfus, was expressed after the van’t Hoff relationship
( )
ln(Kfus) ) ln
∆Gfus asolid )aliquid RT
(21)
Low-Concentration Section (x2 < xE1). The solid formed below this liquidus section is pure NFM. Relation (21) was applied to species B and, because the activity of solids is unity,
ln γBxB )
∆Hfus,NFM ∆Sfus,NFM RT R
(22)
In addition, the liquid phase is at thermodynamic equilibrium with the vapor, after eq 5. Activity coefficients are functions of temperature T and fractions xi, which were expressed as functions of global fractions x1 and x2 and variable ζ
K)
ζ(1 - x1ζ) γC γAγB (x2 - x1ζ)(1 - ζ)
with x1 ) 1 - x2 (23)
The composition of the liquid phase of the liquidus at T was calculated by solving relations (22) and (23). High-Concentration Section (x2 > xE1). The solid in this region is a 1:1 NFM complex. Use of relation (21) is not straightforward because ∆Sfus,C could not be determined by experiment. The entropy of fusion was estimated by the adjustment of the predicted melting curve at the experimental melting point Tfus,C at x2 ) 0.5. The entropy difference obtained at this point was
Ind. Eng. Chem. Res., Vol. 41, No. 2, 2002 161
Figure 8. Melting curve of the SO2-NFM system: comparison of experimental data with the model predictions, with the formation of a 1:1 complex (solid line) or of two complexes (dotted line).
then used for application of relation (21) for the prediction of the rest of the curve
ln γCxC )
∆Hfus,C,III ∆Sfus,C,III RT R
(25)
IV.4. Results and Discussion. The previously given model allowed for satisfactory predictions of the liquidus, as shown in Figure 8, in particular in the lowconcentration domain. In this region, the temperature variations yielded by the ternary model were slightly below the experimental data, and the deviations varied from 2 °C for x2 near 0.10 to less than 1% close to eutectic point E1. Assuming the existence of a second complex affected to some extent the model predictions for x2 over 0.20; corresponding predicted temperatures exceeded the experimental data by a few degrees. As explained previously, the second section of the liquidus was fitted at x2 ) 0.50 for T ) 5.7 °C. The liquidus profile allowed by the ternary model was shown to be in good agreement with the experimental data, with deviations below 1.5 °C except for concentrated mixtures with x2 over 0.67. Predictions by the quaternary model were far less consistent with experimental practice; the theoretical temperature profile peak differed largely from the experimental variations, and the solidus temperature was overestimated by nearly 5 °C. This discrepancy may be explained as follows. First, assuming the existence of the second complex, the previous approach is only valid beyond the second eutectic point E2, the existence of which could not be demonstrated. In addition, complexation through a 1:1 compound in the quaternary model is less significant than that with the ternary system, corresponding to a less pronounced peak of temperature at x2 of around 0.50. Taking into account the existence of eutectic E2, with available values for the enthalpy of fusion and the melting point of a 2:1 complex, would improve the performance of the model. To the present state of knowledge, better predictions of the liquidus are allowed considering the formation of a 1.1 complex only. V. Conclusion and Significance We suggest in this paper the use of NFM as a solvent for a regenerative process for SO2 abatement from waste gases. This solvent seems to fulfill the defined requirements for use in such a process. In particular, the solvent was shown to form a reversible complex with
sulfur dioxide by use of cross-linked techniques. Both vapor-liquid and solid-liquid equilibria were investigated by thorough measurements. The results of the model developed for interpretation of the VLE were successfully used for modeling the melting curve without further adjustment. Though suggested by the profiles of the P versus x2 curves, the possible formation of a 2:1 SO2-NFM complex could not be fully established by the other techniques used. For concentrated solutions of sulfur dioxide, chemical interactions might exist between sulfur dioxide and a 1:1 complex, which would allow for the formation of a loose (A-C) association in the liquid phase. Such an association would be of actual significance for VLE but could not be observed in the solid state. Further fundamental work would be required to highlight the speculative formation of the 2:1 complex. At this point, it is also interesting to compare the results obtained with NFM with respect to the other solvents examined previously (i.e., NMP and DMPU). From the absorption capacity point of view, the formamide does not exhibit the best performance; with 0.85 g of SO2/g of NFM, performance is 1.5% and 12% lower than that with DMPU or NMP, respectively. However, what makes NFM much more attractive are the physical properties of the SO2-NFM complex. Indeed, with a melting point near 6 °C and a lower stability than those of the complexes formed with amines or even with DMPU, two major advantages can appear: first, the possibility to trap SO2 in a solid state, enabling its transport in fairly safe conditions, and second, an easier regeneration of the solvent at moderate temperatures and reasonable costs. Furthermore, the absorption kinetics of the liquid-phase reaction was shown to be very fast,21 and chemical equilibrium can be assumed even near the gas-liquid interface; this point is an additional positive point for the use of NFM. Additional investigations also have to be conducted for the development of a process relying upon the use of NFM. In particular, the side absorptions of other species (e.g., CO2, H2O, or NOx) present in most waste gases have to be taken into account for this purpose. Nevertheless, the Lewis basicity of the solvent should reduce its affinity to CO2 and NOx, as shown by theoretical considerations (ref 9) and the results of preliminary measurements. In addition, the regeneration step of the scrubbing process with the issue of the solvent stability in the stripping tower has to be investigated. The absorption process with the recovery of a solid SO2-NFM complex is now under investigation by process simulation before complementary tests and measurements. Acknowledgment The authors are indebted to the French Ministery of Education and Research for the Ph.D. Grant allocated to R.deK. Thanks are also due to Henri Lenda for his careful assistance in spectrophotometrical measurements. Appendix 1: Values of Physicochemical Parameters The molar volume of SO2 was provided from the literature (DIPPR database). No reliable data could be found for NFM, and volume VB was estimated from the compound density at liquid state at 25 °C, FB, and its
162
Ind. Eng. Chem. Res., Vol. 41, No. 2, 2002
total number of moles is equal to
Table 1. Parameter Values Used for the Model variables and parameters
SO2
NFM
liquid molar volumes (cm3 mol-1) critical temperature (K) A1 (kJ mol-1) B1 C1, D1, E1
44.7 430.8 36.76 0.40 0
100.6 803 72.8 0.375 0
nT ) n1 + n2 - n1(ζ1 + 2ζ2) with ζ defined as the sum ζ1 + 2ζ2, taking into account the stoichiometry of D formation. Expressions for the mole fractions were then deduced
molecular weight MB
VB ) FB/MB
This technique was controlled for several compounds with published values for Vi. In particular, the volume obtained by the above-mentioned technique is consistent with the literature data. The vaporization enthalpy was usually calculated at T using the following relation:
∆Hv ) A1[(1 - Tr)B1+C1Tr+D1Tr +E1Tr ] 2
3
Appendix 2: SO2 Absorption Involving Two Complexes Consider the existence of the two complexation processes
2A + C T D
xB )
K1 K2
where constants K1 and K2 are of thermodynamic meaning
γc xc xc K1 ) Kγ1 ) xAxB γAγB xAxB
(A2.1)
γD xD xD K2 ) Kγ2 ) xAxC γAγC xAxC
(A2.2)
The overall mole fractions of NFM and SO2, x1 and x2, respectively, were defined on the basis of initial conditions (i.e., regardless of the formation of complexes C and D). Conversions ζ1 and ζ2 were introduced on the basis of the two chemical reactions
nC ) n1ζ1
(A2.3)
nD ) n1ζ2
(A2.3′)
Numbers of moles of sulfur dioxide and 1:1 complex, nA and nB, respectively, were deduced. At equilibrium, the
x2 - x1ζ 1 - x1σ
x1(1 - ζ1 - ζ2) 1 - x1σ
xC )
x1ζ1 1 - x1σ
xD )
x1ζ2 1 - x1σ
(A1.2)
where Tr is the reduced temperature, defined by the ratio of the temperature to the critical temperature Tc. Parameter A1 is an energy, whereas parameters B1, C1, D1, and E1 are real numbers. Values of all parameters for SO2 were taken from the DIPPR database. Data for NFM were estimated from those for morpholine (DIPPR database), taking into account the additional H-CdO group; analogy with other couples (e.g., pentane/hexanal and hexane/heptanal) was used for estimation of the critical temperature and parameter A1. Parameters B1, C1, D1, and E1 were assumed to be unaffected by the introduction of the carbonyl group and were kept at their level for morpholine. The set of values used are reported in Table 1.
A+BTC
xA )
(A1.1)
(A2.4)
The equations involved for calculations of activity coefficients are similar to those for the case of a ternary system. The molar volume of D was estimated as
VD ) VB + 1.5VA
(A2.5)
corresponding to the existence of two molecules of SO2 in the 2:1 complex. List of Symbols A ) SO2 in NFM after physical absorption aj ) activity of species j B ) liquid NFM C ) SO2 complexed in NFM with 1:1 stoichiometry D ) SO2 complexed in NFM with 2:1 stoichiometry F ) objective function (Pa) He ) Henry constant (Pa) K ) equilibrium constant of complexation K1 ) equilibrium constant of formation of 1:1 complex K2 ) equilibrium constant of formation of 2:1 complex n ) number of moles (mol) n1 ) number of moles of SO2 n2 ) number of moles of solvent nT ) total number of moles (mol) P ) pressure (Pa) Psat ) vapor pressure of pure liquid at T (Pa) qj ) effective volume of species j (cm3 mol-1) R ) gas constant (J mol-1 K-1) T ) temperature (K) Tc ) critical temperature (K) Vj ) molar volume of species j (cm3 mol-1) xj ) mole fraction of species j x2 ) global mole fraction of sulfur dioxide zj ) volume fraction of species j Rij ) interaction parameter involved in the van Laar model (J cm-3) δj ) solubility parameter of species j [(J cm-3)1/2] ∆Gi ) difference of free enthalpy of reaction i (J mol-1) ∆Hi ) enthalpy difference of reaction i (J mol-1) ∆Hfus,j ) enthalpy of fusion of species j (J mol-1) ∆Hv ) vaporization enthalpy (J mol-1) ∆Si ) entropy difference of reaction i (J mol-1 K-1) ∆Sfus,j ) entropy of fusion of species j (J mol-1 K-1) ∆Uv ) vaporization energy (J mol-1)
Ind. Eng. Chem. Res., Vol. 41, No. 2, 2002 163 γj ) activity coefficient of species j γ2 ) global activity coefficient of dissolved sulfur dioxide ζi ) conversion of reaction i
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Received for review February 21, 2001 Revised manuscript received August 27, 2001 Accepted October 13, 2001 IE010173C
