How to Manage Complexity in Phase Equilibria Modeling? Application to the Bunsen Reaction

10th International Symposium on Process Systems Engineering - PSE2009 Rita Maria de Brito Alves, Claudio Augusto Oller do Nascimento and Evaristo Chalbaud Biscaia Jr. (Editors) 333

© 2009 Elsevier B.V. All rights reserved.

How to Manage Complexity in Phase Equilibria Modeling? Application to the Bunsen Reaction Mohamed K. Hadj-Kali,a Vincent Gerbaud,a,* Patrick Lovera,b Jean-Marc Borgard,b Pascal Floquet,a Xavier Joulia,a Philippe Carles b a

Université de Toulouse INP- UPS- LGC, Laboratoire de Génie Chimique, 5 rue Paulin Talabot, 31106 Toulouse, France.* [email protected] b CEA, DEN, Physical Chemistry Department, F-91191 Gif sur Yvette, France.

Abstract The present work focuses on the thermodynamic modeling of the Bunsen section of the Iodine-Sulfur thermochemical cycle for hydrogen production on the basis of a combination of UNIQUAC activity coefficient and solvation models. The complexity of the material system, two immiscible electrolyte aqueous phases (H2SO4 rich and HI rich), is managed by defining an equivalent material system able to capture the main physical phenomena. Only the key species involved and their mutual interactions are taken into account, reducing the number of parameters to be estimated from a hundred to only 15. Results show a good agreement with published experimental data, with a better description of the impurities in the HIx phase than in the sulfuric acid phase. Keywords: H2 production, IS thermo-cycle, Bunsen section, liquid–liquid equilibria.

1. The Sulfur–Iodine Thermochemical cycle Hydrogen is considered to be one of the best energy carriers for the future. It can be produced from water by thermo-chemical cycles. The Iodine–Sulfur (IS) thermochemical water splitting cycle is one of the most promising (O’Keefe et al., 1982), chosen among one hundred other possible cycles and expected to become a major source of massive hydrogen production combined with nuclear energy. This cycle, depicted in figure 1, is divided into three sections, namely: 1. The Bunsen section (I), where sulfur dioxide reacts with excess water and iodine to produce two immiscible electrolyte aqueous phases: the upper phase containing mainly water and sulfuric acid (H2SO4 rich phase) and the heavy phase with water, hydroiodic acid and iodine (HIx phase). 2. The sulfuric acid concentration and decomposition section (II), 3. The hydroiodic acid concentration and decomposition section (III). In the two last sections, intermediate acids break down upon heating to release oxygen and hydrogen respectively while water, iodine and sulfur dioxide are recycled in the system. After modeling the phase equilibria of the HIx section (Hadj-Kali et al., 2009), we focus in this paper on the complex liquid – liquid equilibrium occurring in the Bunsen section.

2. The Bunsen reaction The starting point of the IS cycle is the Bunsen reaction: 2 H2O + SO2 + I2 ↔ H2SO4 + 2 HI

(R1)

[1]

334

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TEMPERATURE (°C)

O2

1000

II 800

H2SO4 DECOMPOSITION

H2SO4 ⇒ SO2 + H2O + ½ O2

600

H2O

H2

H2SO4

400

SO2

HI DECOMPOSITION III

2HI ⇔ H2 + I2

HI 200

I2 I

BUNSEN REACTION

H2O

I2 + SO2 + 2H2O ⇒ H2SO4 + 2HI

0

H2O

Figure 1. Sulfur – Iodine thermo-chemical cycle scheme.

This reaction is carried out at 120°C. With standard stoichiometry, its standard Gibbs free energy is positive: ΔG°(400 K) = +82 kJ.mol-1. In the late 1970s and early 1980s, General Atomics (GA, Normann et al., 1981) found that the conversion is greatly improved by using excess iodine and water. Excess iodine not only shifts equation [1] equilibrium towards the production of acids, but also causes the two acids to spontaneously separate into two aqueous solutions: hydroiodic rich (HIx) heavy phase and sulfuric acid (SA) rich light phase. However, when this excess is too large, the compositions of the two phases stop changing because the iodine saturation point is reached. Like iodine, the excess of water causes the equilibrium to be shifted forward but it also causes a substantial change in the reaction Gibbs free energy due to acids dilution. The sulfuric acid complexes with water and hydroiodic acid complexes with water and iodine, according to the following equations (Elder et al., 2005):

ΔG°,400 K = -66 kJ.mole-1

H2SO4 + 4H2O ↔ (H2SO4 + 4H2O)aq

(R2) [2]

2HI + 8I2 + 10H2O ↔ (2HI + 10H2O + 8I2)aq ΔG° = -104 kJ.mole (R3) [3] Combining the three reactions (R1), (R2) and (R3) leads to a modified Bunsen reaction proposed by GA which has a negative Gibbs free energy: ΔG°(400 K) = -88 kJ.mol-1: ,400 K

-1

9 I2 + SO2 + 16 H2O ↔ (2 HI + 10 H2O + 8 I2)aq + (H2SO4 + 4 H2O)aq

(R4) [4]

3. Bunsen section thermodynamic modeling 3.1. Liquid – liquid equilibrium calculation basis The liquid – liquid equilibrium between phases involves activities equality of each component i present in both phases, expressed in terms of activity coefficients γi by: i = 1, Nc [5] Equilibrium equations: γ i (T , x ) ⋅ x i − γ i (T , x ′) ⋅ x' i = 0 At given temperature, pressure and global compositions z, the compositions of each phase at equilibrium (x and x') and the split ratio τ are calculated by solving an isothermal liquid-liquid equilibrium flash model which includes equations [5-7]: Partial mass balances:

z i − (1 − τ ) ⋅ xi − τ ⋅ x'i = 0

Summation equation:

∑x −∑x i

i

' i

=0

i = 1, Nc

[6] [7]

i

An excess Gibbs free energy model is then needed to calculate the activity coefficients.

How to Manage Complexity in Phase Equilibria Modeling? Application to the Bunsen Reaction

335

3.2. The new model versus previous models In order to compute activity coefficients, a symmetric convention is adopted that combines the UNIQUAC model (Abrams and Prausnitz, 1975) with Engel’s electrolytic solvation model (Engels, 1990): the first model accounts for short range interactions by means of two terms (combinatorial and residual) and the second model accounts for complexes formation. Until this work, all published models for this system were derived from a classical electrolyte approach. First, Davis and Conger (1980) proposed to apply the PitzerDebye-Hückel model (Pitzer, 1980). Later Mathias (2002) has used the electrolyteNRTL model developed by Chen and Evans, (1986) that combines the Pitzer-DebyeHückel model for long-range ion-ion electrostatic interactions with the NRTL theory (Renon and Prausnitz, 1968) for short-range energetic interactions. Recently, O’Connell (2008) proposed an improvement of Mathias’ model. 3.3. Model description The proposed model considers three solvation reactions: 1. Solvation of HI by H2O: m1H2O + HI ↔ 2C1

(RS1)

[8]

(RS2)

[9]

(RS3)

[10]

with {2C1} ≡ {[H3O ,(m1-1)H2O]; I } 2. Solvation of H2SO4 by H2O: +

-

m2H2O + H2SO4 ↔ 2C2 with {2C2} ≡ {[H3O ,(m2-1)H2O]; HSO4 } 3. Solvation of HI by I2 in the presence of water: +

-

m1H2O + m3I2 + HI ↔ 2C3

with {2C3} ≡ {[H3O ,(m1-1)H2O]; [I3 ,(m3-1) I2]} where Ci are the resulting complexes, as defined by Engels (1990), and mi the solvation numbers. The corresponding solvation constants Ki are function of the temperature: +

(

K i = exp AKi + BK i / T

-

)

[11]

Each solvation equilibrium introduces a new species, the complex Ci, and requests 3 parameters to be estimated: mi, AKi and BKi. Therefore, the whole system with NC=7 species (I2, HI, H2O, H2SO4, C1, C2, C3), has 93 parameters to be estimated from experimental data: 84 parameters to estimate n×(n-1) UNIQUAC binary interaction parameters with their temperature dependence and 9 parameters for the three solvation equilibria. This number is too high in view of available experimental data. 3.4. Model assumptions On the basis of the operating conditions of Bunsen reaction (water and iodine in large excess (O’Keefe et al., 1982)), the very large immiscibility gap between these two species (Kracek, 1931) and the presence of I3- ions in the solution (Palmer and Lietzke, 1982), a first series of hypotheses can be formulated: a. Total dissociation of both acids (HI and H2SO4) in the presence of an excess of water; the second acidity of H2SO4 being neglected. b. Solvation of all H+ ions by three H2O molecules, independently whether they come from HI or H2SO4 totally dissociated. The hypotheses a and b enable to substitute the measured species HI and H2SO4 by two apparent species, that we write [HI,3H2O] and [H2SO4,3H2O]. They correspond to the complexes {[H3O+,(m1-1)H2O]; I-} and {[H3O+,(m2-1)H2O]; HSO4-} of solvation reactions (RS1) and (RS2) with m1= m2=3.

336

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c. Solvation of each hydrated complex [HI,3H2O] by one mole of I2 (m3=1) following the reaction (RS3). The resulting complex is noted {[HI,3H2O]; I2} and corresponds to {[H3O+,(m1-1)H2O]; [I3-,(m3 – 1) I2]} with m1=3 and m3=1. As a result, the number of species drops from 7 to 5 whereas the number of parameters to identify drops from 84 to 40, with only 2 solvation parameters. It is still too much regarding the number of available experimental data. Thus, a second series of hypotheses is formulated about binary interactions: d. The [H2SO4,3H2O] hydrated complex interacts like water with other species. Engels’ results (1990) on H2O–H2SO4 vapor-liquid equilibria modeling showed that the interaction between water and the solvation complex of H2SO4 by H2O is negligible. e. The complex {[HI,3H2O]; I2]} interacts like iodine with other species. Note that the hypotheses d and e imply that the chemical theory alone allows to partially represent the non ideal behavior of the solution. Finally, the number of parameters of the reduced model drops to 14 (including temperature dependency of UNIQUAC Aij binary interaction parameters and 2 solvation parameters) and the binary interaction parameters matrix becomes: Table 1. Binary interaction parameters matrix. I2 I2 {[HI,3H2O]; I2} H 2O [H2SO4,3H2O] [HI,3H2O]

{[HI,3H2O]; I2}

H 2O

[H2SO4,3H2O]

[HI,3H2O]

0

A12

A13

A21

0

A23

A31

A32

0

The new species [HI,3H2O], [H2SO4,3H2O] and {[HI,3H2O]; I2} are created in the data base of Simulis® Thermodynamics properties server and their UNIQUAC parameters ri and qi are estimated according to Bondi’s group contribution method (Bondi, 1964).

4. Available experimental data Nowadays, available experimental data were published by Sakurai et al., 1999, 2000; Giaconia et al., 2007; Lee et al., 2008. The influence of HI (k), I2 (m) and H2O (n) mole numbers for one sulfuric acid mole on liquid-liquid equilibria is studied. The data points are noted 1/k/m/n. General Atomic typical stoichiometry of reaction (R4) corresponds to a 1/2/8/14 data point. Most of those data are compiled in Lee et al. (2008). Covering the largest temperature range from 25°C to 120°C, they are used in this work.

5. Results and discussion The reduced model reproduces demixtion for all experimental data. Table 2 reports the mean and median relative differences between experimental and calculated molar fractions at each temperature. The results highlight that the relative errors are smaller for the main species (H2O, HI, I2 in HIx phase and H2O, H2SO4 in SA phase) than for impurities (HI, I2 in SA phase and H2SO4 in HIx phase) in both phases. That is because impurities experimental absolute values are small and lead automatically to larger relative errors and they likely bear larger uncertainties. Otherwise, there are no significant differences between the various temperature sets, hinting at a reasonable temperature dependency of the parameters.

How to Manage Complexity in Phase Equilibria Modeling? Application to the Bunsen Reaction

337

Table 2. Mean and median relative differences between experimental and calculated molar fractions upon the data of Lee et al. (2008) All species

Impurities

Main species

T (°C) mean

Median

mean

Median

Mean

median

25

13.5%

3.4%

30.5%

30.6%

3.3%

1.9%

40

17.1%

6.6%

32.7%

18.2%

7.7%

3.1%

60

20.0%

9.9%

41.9%

30.2%

6.9%

3.7%

80

16.0%

7.3%

31.8%

27.1%

6.5%

3.3%

100

20.5%

7.6%

45.6%

37.8%

5.5%

1.6%

120

15.9%

4.2%

33.2%

27.9%

5.6%

1.5%

Figure 2 present results by comparing the calculated and experimental molar fractions for HIx phase at 80°C. The histograms below detail the variation of errors with variables ‘m’ and ‘n’ for a given composition (HI/H2SO4/I2/H2O) = (1/2/m/n). Iodine

Water 1,0

0,9

0,9

0,8

0,8

0,7

0,7

0,6 0,5

0,5 0,4

0,3

0,3

0,2

0,2

0,1

0,1 0,7 0,8 0,9

0,08

0,6

0,4

0,3 0,4 0,5 0,6

0,10

xH2S O4 cal

1,0

0,1 0,2

0,2 0,3 0,4



I2 total dans la phase HIx (80°C)

1,0

0,00

5,11

6,14



H2O libre dans la phase HIx (80°C)

7,20

7,70

0% 3,12

5,11

6,14

7,20

7,70

-20%

3,12

5,11

20,66

6,14

7,20

7,70

m

H2SO4 dans la phase HIx (80°C)

40%

0% 14,26

16,13

18,31

-20% n

0% -20%



20,66

erreur relative (%)

18,31

erreur relative (%)

16,13

0,10

20%

H2O libre dans la phase HIx (80°C)

20%

0%

0,08

H2SO4 dans la phase HIx (80°C)

m



20%

0,06

-40%

m

I2 total dans la phase HIx (80°C)

14,26

0,04

40%

-20%



0,02

xH2SO4 exp

erreur relative (%)

0%

-20%

erreur relative (%)

0,7 0,8 0,9

20% erreur relative (%)

erreur relative (%)

0,5 0,6 xH2O exp

20%

3,12

0,04

0,00

0,1

1,0

0,06

0,02

xI2 exp



Sulfuric acid H2SO4 dans la phase HIx (80°C) ^ƵůĨŝƌŝĐĂĐŝĚŝŶ,/ džƉŚĂƐĞ;ϴϬΣͿ

H2O libre dans la džphase HIx (80°C) &ƌĞĞǁĂƚĞƌŝŶ,/ ƉŚĂƐĞ;ϴϬΣͿ

xH 2O cal

xI2 cal

I2 total dans la phase HIx (80°C) dŽƚĂů/ŽĚŝŶĞŝŶ,/ džƉŚĂƐĞ;ϴϬΣͿ

20% 0% 14,26

16,13

18,31

20,66

-20% -40%

-27%

n

n

Figure 2. Calculated compositions versus experimental data for the HIx phase at 80°C: main species are represented by water and iodine and impurities by sulfuric acid.

6. Conclusion To our knowledge, for the first time a thermodynamic model representing the liquidliquid equilibria of the Bunsen section of the Sulfur – Iodine thermochemical cycle over a large temperature range is proposed. This model is based on UNIQUAC’s activity coefficient model combined with solvation equilibria. Due to the high level of complexity of the system and the lack of experimental data, a fine description of all species and phenomena cannot be obtained. The formulation of

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M.K. Hadj-Kali et al.

sound hypotheses, concerning the species present and their interactions, allows to reduce significantly the number of parameters and enables their estimation. The reduced model reproduces demixtion for all data points with an acceptable mean relative error: below 6% for the main species (water and sulfuric acid in the H2SO4 rich phase; water, iodine and hydrogen iodide in the HIx rich phase) and below 30% for the impurities (iodine and hydrogen iodide in the H2SO4 rich phase; sulfuric acid in the HI rich phase).

References Abrams D.S., Prausnitz J.M., 1975, Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems, AIChE Journal, 21(3), 116-128. Bondi A., 1964, van der Waals Volumes and Radii, J. Phys. Chem., 68, 441-451. Chen C.C., Evans L.B., 1986, A local composition model for the excess Gibbs energy of aqueous electrolyte systems, AIChE Journal,32:444-454. Davis M.E., Conger W.L., 1980, An entropy production and efficiency analysis of the Bunsen reaction in the General Atomics sulfur – iodine thermochemical hydrogen production cycle, Int. J. Hydrogen Energy, 5, 475-485. Elder R.H., Priestman G.H., Ewan B.C., Allen R.W.K., 2005, The separation of HIx in the sulphur – iodine thermochemical cycle for sustainable hydrogen production, Trans IChemE, Part B., 7, 343-350. Engels H., 1990, Phase equilibria and phase diagrams of electrolytes, Chemistry data Series, Volume XI, Part I., Published by DECHEMA. Giaconia A., Caputo G., Ceroli A., Diamanti M., Barbarossa V., Tarquini P., Sau S., 2007, Experimental study of two phase separation in the Bunsen section of the sulfur – iodine thermochemical cycle, Int. J. Hydrogen Energy, 32, 531-536. Hadj-Kali, M.K., Gerbaud V., Borgard J.M., Baudouin O., Floquet P., Joulia X., Carles P., 2009, HIx System Thermodynamic model for Hydrogen Production by the Sulfur-Iodine Cycle, Int. J. Hydrogen Energy, In press. Kracek F.C., 1931, Solubilities in the system water-iodine to 200°C, J. Phys. Chem., 35, 417-422. Lee B.J., No H.C., Yoon H.J., Kim S.J., Kim E.S., 2008, An optimal operating window for the Bunsen process in the S-I thermochemical cycle, Int. J. Hydrogen Energy, 33, 2200-2210. Mathias P.M., 2002, Modeling the sulfur-iodine cycle: Aspen Plus building blocks and simulation models, report GA and Sandia National Laboratories. Normann J.H., Besenbuch G.E., Brown L.C., Thermo-chemical water-splitting cycle. Bench scale investigations and process engineering. DOE/ET/26225, 1981 O’Connell J., 2008, Oral Conference at ESAT (29/05/2008 – 01/06/2008), Cannes, France. O’Keefe D., Allen C., Besenbruch G., Brown L., Norman J., Sharp R. and McCorkle K., 1982, Preliminary results from bench-scale testing of a sulfur-iodine thermochemical water-splitting cycle , Int. J. Hydrogen Energy,7(5), 381-392. Palmer A.D., Lietzke M.H., 1982, The equilibria and kinetics of iodine hydrolysis, Radiochimica Acta, 31, 37-44. Pitzer K., 1980, Electrolytes. From dilute solutions to fused salts, J. Am. Chem. Soc.,102, 2902-2906. ProSim, 2004, Simulis® Thermodynamics User Guide, http://www.prosim.net. Renon H., Prausnitz J.M., 1968, Local compositions in thermodynamic excess functions for liquid mixtures, AIChE Journal, 14(3), 135-144. Sakurai M., Nakajima H., Onuki K., Ikenoya K., Shimizu S., Preliminary process analysis for the closed cycle operation of the iodine-sulfur thermochemical hydrogen production process, Int. J. Hydrogen Energy, 1999;24:603-612 Sakurai M., Nakajima H., Onuki K. And Shimizu S., 2000, Investigation of 2 liquid phase separation characteristics on the Sulfur – Iodine thermochemical hydrogen production process, Int. J. Hydrogen Energy, 25, 605-611.