Phase equilibria for the oxygen-water system up to elevated temperatures and pressures

Transcription

1 Phase equlbra for the oxygen-water system up to elevated temperatures and pressures Xaoyan J 1, 2, Xaohua Lu 2, Jnyue Yan 1,3* 1 Department of Chemcal Engneerng and Technology / Energy Processes, Royal Insttute of Technology, SE Stockholm, Sweden 2 Department of Chemcal Engneerng, Nanjng Unversty of Chemcal Technology, Nanjng 219, Chna 3 Shangha Jaotong Unversty, Shangha 252, Chna Abstract: A new thermodynamc model was presented to calculate the phase equlbra for the oxygen-water system. The modfed Redlch- Kwong equaton of state wth a new correlated cross nteracton parameter was used to calculate fugacty coeffcents for the vapor phase. The dssolved oxygen followed Henry s law. A new expresson was correlated from the expermental data to calculate Henry s constant of oxygen. The calculaton results of equlbrum composton were compared wth the avalable expermental data and those calculated by other models wth dfferent parameters. The comparson revealed that the new model s sutable for calculatng both lqud and vapor compostons whle the emprcal method s only sutable for estmatng the lqud composton. Furthermore, compared to the model proposed by Rebenovch and Beketov, the calculaton results of the vapor composton wth the new model are better. Keywords: oxygen, water, equaton of state, vapor-lqud equlbrum, Henry s constant Introducton Many natural and ndustral processes occur n aqueous envronments that nvolve or are affected by dssolved oxygen. Such processes range from bologcal and synthess reactons to the corroson and oxdaton of materals. A detaled knowledge of temperature and pressure effects on oxygen solublty enables the related processes to be modelled more accurately and controlled more effectvely. In prevous lterature, oxygen solublty n water was determned expermentally, and Henry s constant of oxygen n water was correlated from ts partal pressure whch was estmated by subtractng the vapor pressure of water from the total pressure [1-2]. Usng the correlaton results n the prevous lterature, t s reasonable to calculate the lqud composton wthn a narrow temperature range. However, such method s unsutable over a wde temperature range. Furthermore, the vapor composton cannot be calculated relably, especally at hgh pressures. Meanwhle, thermodynamc propertes (humdty, enthalpy and entropy) n the vapor phase for the oxygen-water system are of mportance [3]. Saturated vapor * Correspondng author, yanjy@ket.kth.se,

2 composton s often needed n order to calculate saturated propertes. Based on vral equaton of state (EOS), Rabnovch and Beketov [3] proposed a model to calculate thermodynamc propertes ncludng saturated vapor composton for the studed system. Because of the scarcty of the expermental data, the cross nteracton parameter between molecular oxygen and water was estmated from theory and the calculaton results of saturated vapor composton were verfed by comparng wth the expermental data of the ntrogen-water system. The calculaton results of the saturated composton and other propertes n the vapor phase are questonable, and lqud composton cannot be calculated snce the lqud phase was assumed to be pure water. In ths paper, phase equlbra of the oxygen-water system were studed. Fugacty coeffcents of the components n the vapor phase were calculated wth the modfed Redlch-Kwong (RK) EOS [4]. The dssolved oxygen n the lqud phase followed Henry s law. Avalable expermental data were collected and analyzed to obtan a reasonable Henry s constant and to nvestgate the exstng cross nteracton parameter n the modfed RK EOS. Calculaton results n ths paper were compared wth expermental data and those of other models n the lterature. Thermodynamc model The thermodynamc condton for lqud-vapor equlbrum s φ y P = f x γ (1) φ s calculated wth the modfed RK EOS developed by de Sants et al. [4] and y jaj v b j v + b ln φ = ln + 2 ln 1.5 v b v b RT b v (2) ab v + b b Rv + ln ln RT b v v + b RT where a and b are parameters wth the mxng rule [4] and a y y a (3) a = j j j ( T ) 1 = a + a (4) ( a a ). 5 a j = a j = jj (5) b = (6) The temperature-ndependent parameters, a and b, were taken from Wark [5]. The temperature-dependent parameter, a 1, s zero for gaseous oxygen. For water vapor, a 1 was taken from de Sants et al. [4]. Because the modfed RK EOS has not been verfed yet for the oxygen-water system, t was nvestgated n the followng text. The lqud phase reference fugacty of water f w s calculated wth equaton (7). Propertes of pressure and volume were calculated from the ndustral standard IAPWS- IF97 [6]. φ w V (T, P w s ) was calculated from software of Aspen Plus wth STEAMNBS model [7] and correlated wth the polynomal equaton (8). The sum of squares of resduals about the polynomal correlaton s

3 s s 1 L ( T, P ) P ( T ) exp v ( T P) dp V f = P w φ w w w S w, (7) Pw RT V s φw ( T, Pw ) = T T (8) T T The dssolved oxygen follows Henry s law, and f of oxygen s equal to H (Henry s constant). The Henry s constant of oxygen n water can be taken from lterature [1, 2, 8, 9] or calculated from Helgeson EOS wth equaton (9) [1, 11] or recorrelated from the avalable expermental data. It was studed carefully as descrbed as follows. G H = exp ( T, P) G ( T P) 2, g m O2, aq m (9) RT O, Actvty coeffcents were assumed to be unty because the dssolved gas s small. Adjustment of the modfed RK EOS For the model descrbed above, parameters n the modfed RK EOS are often correlated from the expermental data n the vapor phase. For the studed system, most of the expermental data are oxygen solubltes n the lqud phase. Although Zoss [12] determned the vapor composton up to hgh temperatures and pressures, t was proved that there are expermental errors [13]. Subsequently, the modfed RK EOS has not been verfed yet for the oxygen-water system. Recently, Wyle and Fsher [14] determned the enhancement factor from to K and 2 to 14 bar for the oxygen-water system. Saturated vapor compostons were calculated from ths group of expermental data [14] and used to nvestgate the modfed RK EOS n ths paper. Henry s constant of oxygen n water s also needed n order to calculate the saturated vapor composton. For the frst.1 try, the Henry s constant was calculated wth the Helgeson EOS from equaton (9). P (bar) The calculaton results of water vapor composton were compared wth the expermental data [14]. Comparson results are shown n Fgure 1. Obvously, the hgher the pressure and the lower the temperature, the hgher the devaton between the calculaton results and the expermental data of Wyle and Fsher [14]. The devaton s about 15% at K and bar The devaton may be due to two factors, the parameters n the modfed RK EOS and the Henry s constant calculated wth the Helgeson EOS. At low temperature (< 1 ºC), parameters n the Helgeson EOS were correlated from expermental data of Benson y w Fgure 1. Comparson of the water vapor composton., and, expermental data of Wyle and Fsher [14] at , and K, respectvely. and, calculaton results of the modfed RK EOS wth the orgnal and new correlated parameters, respectvely;, calculaton results of Rabnovch and Beketov [3]

4 et al. [8] n whch the Henry s constant of oxygen n water was correlated from the accurate oxygen solublty wth a sem-emprcal method. Therefore, we can conclude that the Henry s constant calculated wth the Helgeson EOS should be correct n the low temperature range. Wyle and Fsher [14] also stated that the effect of oxygen on the concentraton of water vapor wth lqud water s manly caused by ntermolecular forces n the gas phase. The Poyntng effect s about one thrd compared to ntermolecular forces of gas, and the Raoult effect s much less compared to ntermolecular forces of gas and the Poyntng effect. In other words, the effect of Henry s constant on the vapor composton s small. Therefore, the devaton s due to the parameters n the modfed RK EOS. In ths paper, an adjustable parameter k was added n order to calculate the cross nteracton parameter as shown n equaton (1). k was correlated from expermental data of Wyle and Fsher [14]. The correlaton result s also shown n equaton (1). a j j.5 ( a a ) =.783 ( a a ). 5 = a = k (1) jj jj Correlaton of the Henry s constant of oxygen n water Correlaton for each expermental data pont The Henry s constant of oxygen n water can be correlated from solublty data whch have been determned expermentally [1, 8, 9, 12, 13, 15-18]. In most of these studes, the partal pressure of oxygen was reported whch was estmated by subtractng the vapor pressure of water from the total pressure. When a gas dssolves n water, the partal pressure of water wll devate from the saturated pressure of pure water, especally at hgh pressure. It ndcates that the estmated partal pressure of oxygen n the lterature s unreasonable. In ths paper, the Henry s constant of oxygen n water was correlated from the solublty data at the expermental temperature and total pressure. However, n the work of Cramer [1], the total pressure was not reported, thus we have not ncluded the data of Cramer [1] n our correlaton. It was proved that the solublty values of Zoss [12] are more than an order of magntude hgh at low temperature, therefore, they were not consdered n the correlaton and ther expermental errors were checked n the later text. The data of Stephan et al. [9] covered the data of Pray and Stephan [17], so the data of Pray and Stephan [17] were excluded n the correlaton. The data of Rettch et al. [18] were also not consdered because the temperature range s wthn that of Benson et al. [8], and the devaton between them s small. Henry s constant was correlated for each expermental data pont wth the Newton s method. However, for the data of Benson et al. [8], Henry s constant for each expermental data pont has been correlated, and t was used drectly n ths paper. Correlaton of the expresson of H = f (T, P) An approprate expresson, equaton (11), was chosen for the expresson of H. The errors of the avalable expermental data have not been estmated n prevous studes. In order to obtan reasonable correlaton results, each expermental data pont has an equvalent weght n our correlaton. But n ths case a large error n one group wll cause a large devaton n the correlaton. In order to avod ths, each group of data were - 4 -

5 correlated frst wth equaton (11). Snce the number of the data of Pray et al. [16] s less than that of parameters n the correlaton expresson, the data cannot be checked n ths step. The correlaton results for other groups are lsted n Table 1. ln H = 2 2 Q1 + Q2P + Q3P + ( Q4 + Q5P + Q6P ) T ( Q + Q P + Q P ) T + ( Q + Q P + Q P ) ln T Table 1. Correlaton results for each group of data and mult-groups of data No data source R-squared 1 Benson et al. [8] > Stephan et al. [9] Brodén and Smonson [15] case A case B.997 case A, four groups of data (Benson et al. [8]; Stephan et al. [9] Brodén and Smonson [15]; Pray et al. [16]) were used n the correlaton. case B, three groups of data (Benson et al. [8] ; Stephan et al. [9]; Brodén and Smonson [15]) were used n the correlaton As shown n Table 1, the random expermental error for each group of data s small (No. 1 to No. 3). Therefore, all of them combned wth the data of Pray et al. [16] (case A) were used to correlate the parameters n equaton (11). The correlaton results are lsted n Table 1 (No. 4) and Fgure 2. From the correlaton results shown n Fgure 2, t s clear that some expermental data caused large devatons. The data of Pray et al. [16] may be responsble because they had not been checked separately before correlaton. In order to verfy ths concluson, three groups of data [8, 9, 15] (case B) were used to correlate the parameters n equaton (11). The correlaton results are also lsted n Table 1 (No. 5) and shown n Fgure 3. The value of R-squared of case B s near to that of case A, but the dstrbuton of the devaton of case B s much better than that of case A as shown n Fgures 2 and 3. Therefore, the correlaton results of case B are reasonable and the correspondng correlaton results for each parameter are lsted n Table 2. Table 2. Coeffcents n equaton (11) for calculatng the Henry s constant of oxygen symbol value symbol value symbol value symbol value Q Q Q Q Q Q Q Q Q Q Q Q (11) Observed versus Predcted Values Observed versus Predcted Values Observed Values Observed Values Predcted Values Fgure 2. Observed versus predcted values (lnh) wth equaton (11) when four groups of data (case A) were used to correlate the expresson Predcted Values Fgure 3. Observed versus predcted values (lnh) wth equaton (11) when three groups of data (case B) were used to correlate the expresson

6 Comparson and dscusson Drect comparson of the Henry s constant In the paper of Benson et al. [8], the Henry s constant was correlated at the determned total pressure whch s below 1.2 bar. In the studes of Cramer [1] and Tromans [2], the Henry s constant was correlated at hgh temperature. These correlaton results were compared wth those n ths paper. From the comparson results shown n Fgure 4, t s clear that the correlaton results n ths paper are consstent wth those n the lterature. In other words, when the pressure s near or lower than the saturated pressure of water, ts effect on Henry s constant can be neglected H x 4 Hx T(K) Fgure 4. Comparson of Henry s constant at the saturated pressure of water., and, expermental data of Cramer [1], Tromans [2] and Benson et al. [8], respectvely., correlaton results n ths paper. the Helgeson EOS., calculaton results from P (bar) Fgure 5. Comparson of Henry s constant at K., and, expermental data of Stephan et al [9], Brodén and Smonson [15] and Pray and Stephan [17], respectvely., correlaton results of ths paper;, correlaton results of Tromans [2]. Fgure 5 shows the pressure effect on Henry s constant at K. At pressure below 15 bar, the effect of pressure on Henry s constant can be neglected. When the pressure s hgh, the value of Henry s constant ncreases obvously. In ths case, t s necessary to consder the pressure mpact n order to obtan relable results. Correlaton results of Tromans [2] are also plotted as a dashed lne n Fgure 5. Obvously, the results n ths paper are much better than those of Tromans [2] at hgh pressure. In the former text, the Henry s constant of oxygen n water was calculated frst from Helgeson EOS wth equaton (9) n order to correlate the cross nteracton parameter n the modfed RK EOS. Therefore, t s necessary to check the calculaton results of Helgeson EOS. The Henry s constant at the saturated pressure of water was calculated wth equaton (9) and compared wth those correlated n ths paper. The comparson results are depcted n Fgure 4 as a dashed lne. At low temperature (< 4 K), results from Helgeson EOS are very close to those correlated n ths paper snce these two studes are all based on the results of Benson et al. [8] at low temperature. Ths also mples that the correlaton of the cross nteracton parameter for the oxygenwater system n the modfed RK EOS s reasonable. When the temperature s hgh, there s some devaton between the calculaton results of ths paper and those calculated wth the Helgeson EOS. Ths s explaned by - 6 -

7 the followng text. In the Helgeson EOS [1, 11], the parameter of the effectve Born coeffcent (w e ) for the neutral speces (O 2, aq ) was correlated from the equlbrum constant. The equlbrum constant was calculated from the solublty data n whch the partal pressure was estmated by subtractng vapor pressure of water from total pressure [1]. The devaton of the estmated partal pressure caused the devaton n the Henry s constant. Ths also ndcates that t s necessary to make a further study on how to mprove and correct the parameter of the Helgeson EOS. Comparson of the composton Composton was calculated here wth two methods, thermodynamc and emprcal ones, n order to understand the effects of Henry s constant and the method on the equlbrum composton. In the thermodynamc method, the partal pressure of water was calculated when each component satsfed the condtons for phase equlbra. In the emprcal method, the partal pressure of water s the saturated pressure of pure water. In both of these two methods, the Henry s constant of oxygen n water was needed. The Helgeson EOS [1, 11] can be used to calculate the Henry s constant at a certan temperature and pressure. Tromans [2] correlated the Henry s constant from 273 to 613 K and the partal pressure up to 6 bar. In ths paper, a new expresson for Henry s constant was correlated. Therefore, the Henry s constant was calculated or taken from these three studes respectvely to calculate the composton for comparson. In addton, n the thermodynamc method, fugacty coeffcent n the vapor phase was calculated by the modfed RK EOS wth the exstng parameter and the new parameter correlated n ths paper, respectvely. Based on the above dscusson, fve cases were calculated n ths paper: Case 1, thermodynamc method, the Henry s constant was calculated from the correlaton expresson n ths paper and the fugacty coeffcents were calculated by the modfed RK EOS wth the new parameter correlated n ths paper. Case 2, thermodynamc method, the Henry s constant was calculated from the Helgeson EOS and the fugacty coeffcents were calculated by the modfed RK EOS wth the new parameter correlated n ths paper. Case 3, thermodynamc method, the Henry s constant was calculated from the Helgeson EOS and the fugacty coeffcents were calculated from the modfed RK EOS wth the exstng parameter n the lterature [1]. Case 4, emprcal method, x O2 = P O2 φ O2 (T, P)/H, y w = P w s /P. φ O2 was calculated by the modfed RK EOS wth the exstng parameter. The Henry s constant was calculated from the Helgeson EOS. Case 5, emprcal method, x O2 = P O2 /H, y w = P w s /P. The Henry s constant was taken from Tromans [2]. Calculaton results at K and dfferent pressures were shown as an example. The calculaton results of the oxygen solublty n water (x O2 ) were compared wth expermental data of Stephan et al. [9]. However, expermental data n the vapor phase have not been determned at ths temperature. In order to show the dfference between dfferent methods, the calculaton results of ths paper (Case 1) were used as reference - 7 -

8 data because ther accuracy has been checked n the prevous text. The calculaton and comparson results are shown n Table 3. Table 3. Equlbrum composton for the oxygen (1) water (2) system at K* calculated wth dfferent methods and parameters Thermodynamc method Emprcal method P (bar) 1 4 x 1exp Case 1 Case 2 Case 3 Case 4** Case x 1 y 2r 1 4 x 1 y x 1 y x 1 y x 1 y Max. (%) Av. (%) * The saturated pressure P s w s 73.3 bar at K. **If the second pont was excluded, Max. = 4.81 %, Av = 2.79 %. x x Max. = 1 1exp y2 y2 r max or = max x 1exp y 2r ( = 1, 6) 6 1 Av. = x1 x 6 1exp 1 y2 y2r or = 6 = 1 x 1exp = 1 6 y2 r In cases 1 and 2, the Henry s constant was taken from dfferent studes. The water vapor n dfferent cases s nearly the same. The maxmum devaton s about.6 %. However, the calculaton results of oxygen solubltes n case 1 are much better than those n case 2 by comparng wth the expermental data. Ths mples that the effect of the Henry s constant on lqud composton s obvous whle ts effect on vapor composton s small enough to be neglected. In cases 2 and 3, fugacty coeffcents were calculated from the modfed RK EOS wth the new correlated and exstng parameters, respectvely. Comparng the calculaton results of these two cases, one concluson can be drawn. The effects of the parameter n the modfed RK EOS on lqud and vapor compostons are vsble. In cases 4 and 5, the composton of water vapor was calculated by the emprcal method. Comparng the calculaton results of water vapor n these two cases wth those n case 1, the devaton s large and the maxmum value s up to 2 %. However, the calculaton results of lqud composton n these two cases are better than those n case 3. It mples that the emprcal method s sutable for calculatng the lqud composton. Based on the above comparson, we can conclude that the thermodynamc method s better than the emprcal method. Furthermore, wth the new parameter n the modfed RK EOS and the Henry s constant correlated n ths paper, the calculaton results for both lqud and vapor compostons are better than other models

9 Comparson wth the model proposed by Rabnovch and Beketov [3] Rabnovch and Beketov [3] calculated and tabulated saturated vapor composton from 2 to 4 K and 1 to 1 bar. In order to nvestgate the calculaton results of ths model, data at , and K were nterpolated from 2 to 1 bar and compared wth the expermental data of Wyle and Fsher [14]. The comparson results are shown n Fgure 1. The calculaton results of Rabnovch and Beketov [3] are hgher than the expermental data of Wyle and Fsher [14]. The lower the temperature and the hgher the pressure, the lager the devaton. The calculaton results of the new model wth the new correlated parameters are also shown n Fgure 1 for comparson. From to K, the average devaton of the calculaton results n ths paper from the expermental data [14] s wthn.3 %, and the maxmum devaton s only.5 %. It mples that the correlaton s reasonable, and the calculaton results of ths paper are much better than those of Rabnovch and Beketov [3]. Investgaton of the data of Zoss [12] Vapor and lqud compostons were determned expermentally by Zoss [12]. However, t was stated that the data of lqud composton are more than an order of magntude hgh at low temperature. In the lterature [13], t was also proved that the solublty data at the hgher temperatures appears to be relable. We made a comparson of the calculaton results wth the data of Zoss [12]. Fgure 6 gves the comparson results for the lqud composton. At hgh temperatures and pressures, the calculaton results agree wth the expermental data of Zoss [12]. Therefore, the calculaton results are also accurate enough up to 65 K. x T (K) Fgure 6. Comparson of the calcualton results of lqud composton of water wth expermental data of Zoss [1].,,, and, expermental data at 34.5, 68.95, 13.4 and bar, respectvely;, calculaton results n ths paper. Table 4. Comparson of the calcualton results of water vapor composton (y wcal ) n ths paper wth the expermental data of Zoss [12] (y wexp ) bar 13.4 bar bar T(K) y wexp y wcal T(K) y wexp y wcal T(K) y wexp y wcal E E E E E E E E E E E E E E E-1 Table 4 shows the comparson of the water vapor composton calculated n ths paper wth the expermental data of Zoss [12]. The expermental data of Zoss [12] are much hgher than the calculaton results n ths paper. Because our calculaton results - 9 -

10 have been evaluated by the expermental data of Wyle and Fsher [14] from to K and 14 bar, there mght be some errors n the expermental data of Zoss [12]. Conclusons Phase equlbra for the oxygen-water system were studed by the thermodynamc method n whch the modfed Redlch-Kwong EOS wth a new correlated parameter was used to calculate fugacty coeffcents for the vapor phase and the dssolved gas followed Henry s law. A relable expresson was obtaned to calculate fugacty coeffcent of pure saturated water accurately, and a new Henry s constant of oxygen n water was correlated from the expermental data. Furthermore, the nvestgaton of the Henry s constant of oxygen n water calculated wth the Helgeson EOS shows that there are some devatons at hgh temperatures and pressures, whch means that new parameters n Helgeson EOS are to be re-correlated. Equlbrum compostons were calculated by the new model wth the parameters suggested n ths paper and compared wth expermental data and those calculated by other models wth dfferent parameters. The comparson revealed that the new model s relable for calculatng lqud and vapor compostons, and the calculaton results of the vapor composton are much better than those n the study of Rabnovch and Beketov [3], whle the emprcal method s only sutable for estmatng the lqud composton. Meanwhle, there mght be some errors n the expermental data of Zoss [12]. Lst of symbols a, b coeffcents n the modfed RK EOS; f lqud phase reference fugacty; G Gbbs free energy; H Henry s consatnt of oxygen n water; k adjustable parameter n the modfed RK EOS; P total pressure, bar; Q 1 to Q 12 coeffcents n equatons (14); R the gas unversal constant; T temperature, K; v specfc volume; x lqud composton; y vapor composton; φ fugacty coeffcents n the vapor phase; γ actvty coeffcents n the lqud phase; Superscrpts s saturated state; Subscrpts w water;, j component; m molalty bass

11 Acknowledgement Fnancal support from the Swedsh Energy Agency and the outstandng youth of Natonal Nature Scence Foundaton of Chna ( ) s gratefully acknowledged. References [1] S. D. Cramer, Ind. Eng. Chem. Process Des. Dev., 19 (198) [2] D. Tromans, Hydrometallurgy, 48 (1998) [3] V. A. Rabnovch, and V. G. Beketov, Most gases, thermodynamc propertes, Begell: House, 1995 [4] R. de Sants, G. J. F. Breedveld and J. M. Prausntz, Ind. Eng. Chem., Process Des. Devlop., 13 (1974) [5] K. Wark, Advanced thermodynamcs for engneers, McGraw-Hll, Inc., Sngapore, [6] W. Wagner and A. Kruse, Propertes of water and steam, Sprnger, New York, [7] Aspen Plus, UserGude, Aspen Tech. Inc., Cambrdge, MA, 1999 [8] B. B. Benson, D. Krause and M. A. Peterson, J. Solu. Chem., 8 (1979) [9] E. F. Stephan, N. S. Hatfeld, R. S. Peoples and H. A. H. Pray, The solublty of gases n water and n aqueous uranyl solutons at elevated temperature and pressure, BMI, 167, 54, Battelle Mem. Inst., Columbus, OH., [1] E. L. Shock, H. C. Helgeson and D. A. Sverjensky, Geochmca & Cosmochmca Acta, 53 (1989) [11] J. W. Johnson, E. T. Oelkers and H. C. Helgeson, Computers & Geoscences, 18 (1992) [12] L. M. Zoss, 1952, cted n Battno (1981). [13] R. Battno, Oxygen and Ozoner, IUPAC solublty data seres 7, Pergamon Press, Oxford, [14] R. G. Wyle and R. S. Fsher, J. Chem. Eng. Data, 41 (1996), [15] Å. Brodén and R. Smonson, Svensk Parrerstdnng, 81 (1978), [16] H. A. Pray, C. E. Schweckert and B. H. Mnnch, Ind. Eng. Chem., 44 (1952), [17] H. A. Pray and E. F. Stephan, 1953, cted n Battno (1981). [18] T. R. Rettch, R. Battno and E. Wlhelm, J. Chem. Thermodyn., 32 (2)