220
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
of the International Fluidization Conference, Asilomer Conference Grounds, Calif., 1975, published as "Fluidization Technology", D. L. Keairns, Ed., Hemisphere Publishing Corporation, 1976. Yang, W -C., Margaritis, P. J., Keairns, D. L., "Simulation and Modeling of Startup and Shutdown in a Pilot-Scale Recirculating Fluidized Bed Coal Devolatilizer", Paper presented at the 69th AlChE Annual Meeting at Chicago, Ill., NOv 28-Dec 2, 1976. Yoshida. K., Fujii, S.,Kunii, D., "Characteristics of Fluidized Beds at High Temperature", Proceedings of the International Fluidization Conference, Asilomar Conference Grounds, Calif., June 15-20, 1975, published as
"Fluidization Technology", D. L. Keairns, Ed., Hemisphere Publishing Corporation. 1976.
Received for review February 3,1977 Accepted December 21,1977 This work is being performed as part of the Westinghouse coal G ~ ~ ification program and has been funded with federal funds from the Energy Research and Development Administration under Contract EF-77-'2-1514. The content of this publication does not necessarily reflect the views or policies of the funding agency.
Representation of NH3-H2S-H20, NH3-C02-H20, and NH3-S02-H20 Vapor-Liquid Equilibria Didier Beutier and Henri Renon* Groupe Commun Reacteurs et Processus, €NSTA-€cole
des Mines, 75006 Paris, France
A new method of calculation of NH3-H2S-H20, NH3-C02-H20, and NH3-S02-H20 vapor-liquid equilibria between 0 and 100 O C in the large range of concentrations encountered in sour water stripping processes is presented. The model is based upon the work by Edwards et al. (1975) on solutions of volatile weak electrolytes and extends its validity by a better representation of activity coefficients. Good prediction of ionic activities is achieved by applying Bromley's and Pitzer's ideas and taking ion-molecule interactions into account. No more than two empirical parameters are adjusted to improve the representation at very high ionic strengths for the acid gas partial pressure.
Introduction An accurate representation of NHs-H~S-H~Oand "3C02-H20 vapor-liquid equilibria is of interest in the calculation of sour water strippers. It was recently attempted with the aid of Van Krevelen's correlation (Beychok, 1967), the validity of which is limited to ammonia rich systems and does not extend up to the high dilution required. A precise representation of dilute solutions is necessary, especially to understand the difficulties commonly encountered in oil refineries to reach very low levels of ammonia. Besides, high concentrations of NH3 and H2S are found in the reflux streams of strippers and Van Krevelen's correlation cannot be extrapolated to such levels (Gantz, 1975).The design of strippers could be achieved with more confidence by a model that is valid in the whole range of concentrations. Vapor-liquid equilibria for these systems and NH3-SO2-HzO as well are needed in the calculation of gas cleaning process involving acid gas absorption. Clearly, a general model for the calculation of all acid gas absorbers and strippers is needed. This work is based upon the thermodynamic framework developed by Edwards et al. (1975). They propose an appropriate reduction of binary equilibrium data for NH3-H20, H2S-H20, C02-H20, the validity of which is confirmed by a fair representation of ternary equilibria NH3-H2S-H20 and NH3-C02-H20 at high dilution. The framework is summed up below.
which expresses the partial pressure of a neutral molecule Pa present in the gas phase, e.g., NH3 as proportional to its activity a t moderate pressures. Edwards estimates Henry's constants, Haas a function of temperature from experimental data. Ionization is expressed by
Binary Solute-Water Equilibria The solubility of volatile weak electrolytes in water results from two equilibria: gas-liquid and ionization. In the case of ammonia, for instance
The functions H,(T), K , ( T ) ,and parameters pa, given by Edwards provide a fair representation of solutes "3, COz, H2S, and water equilibria between 0 and 100 "C. Good agreement was generally found for solutions between 0 and 2 m as shown in Figure 1for the system NH3-H20. Therefore, the adjustment proposed by Edwards for the H2S, and C02 was kept as a basis for this three solutes "3, work on ternary equilibria. For solute S02, a new reduction of vapor-liquid data between 20 and 100 "C is proposed here and results are shown in Figure 2. For all solutes, numerical
The gas-liquid equilibrium is accounted for by
Pa = H,a, 0019-7882/78/1117-0220$01.00/0
a+a-
K, = an In eq 1and 2, activities are expressed on the scale of molalities mk (moles per kg of solvent) and evaluated from the usual reference state for solutes in water. Activities are given, for any molecular or ionic species k , except water, by ak
= mkyk
(3)
with lim y k = 1 Zmi-0
where 1 stands for any solute species. Mass balance, eq 2 and a correct evaluation of activity coefficients Y k allow the calculation of ma,the true molality of the undissociated solute, from mAp,apparent molality of the dissolved solute. Then eq 1and 3 give its partial pressure a t given T and mAp.The activity coefficient of a is estimated by In Y a = 2Paama
0 1978 American Chemical Society
(4)
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
I
20
V
J
10
c5
Figure 1. Ammonia-water system a t atmospheric pressure; partial pressure of ammonia (mmHg) vs. apparent molality of "3; 0 ,data of Polak and Lu (1975); -, calculated curve according to Edwards' model.
parameters necessary to calculate K , are given in Appendix A. General Equations for Ternary Systems The vapor phase is considered ideal a t low pressures. Up to 2 atm, fugacity coefficients calculated by the correlation of Nothnagel et al. (1973) do not depart from unity by more than 1%except for water ( @ ~ =~0.98). 0 The partial pressure of any solute a is given by (1) but, in such systems as "3COz-HzO and NHs-H~S-H~O, the activity a, is lowered significantly by acid-base reactions which shift dissociation equilibria toward more ionization. The following equilibria take place NHs
+ H20
% NH4+
+ OH-
+ HSs H + + S2-
H2S s H+ HS-
+ HC03HC03- 5 C032- + H+ zNHzCOO-
+ H2O
+ HzO 5 H+ + HS03HS03- 5 H + + S032-
SO2
(IV) (VI (VI) (VII) (VIII)
The ionic equilibrium of water
H20 s H+
+ OH-
80
I
I
103
T
Figure 2. S O y H 2 0 system; partial pressure of SO2 (mmHg) vs. temperature; m is the apparent molality of SOz: 0,data of Beuschlein and Simenson (1940); +, data of Rabe and Harris (1963);- - - -, calculated (Edwards' model); -, calculated (this work).
the calculation of activity coefficients and consequently they should be included in the calculation of vapor-liquid equilibria. Van Krevelen's empirical correlation, based on data on a limited range of concentrations, allows no valid extrapolation a t high dilution or at high concentration because it does not take the behavior of ionic activities into account. The accuracy of calculated values of a H 2 S or aC02 depends on the representation of the functions Y k (ml, . . . , rng) for all molecular or ionic species. Dissociation equilibria, mass balances, and electroneutrality provide a nonlinear system of seven equations for the N H ~ - H ~ S - H Z Oand NH3-S02-H20 systems and eight equations for the "3C 0 4 3 2 0 system (details of resolution are given in Appendix
B). Limits of Edwards' Model Edwards uses the simple equation
(111)
+
+ HCO3-
I
1
60
(11)
COZ H 2 0 5 H +
NH3
(1)
LO
221
(1x1
shifts dissociation equilibria toward the right when both acid and base concentrations are of the same order of magnitude. Then, the ionic strength defined by
where zi is the charge of ion i, can reach high values, for instance 4 mol kg-' when both solutes concentrations amount to 10 wt % of the solution. With increasing ionic strength, the contributions of physical ion-ion and ion-molecule interactions become significant in
to evaluate the activity coefficient of any molecular or ionic species k . The first term, a function of the ionic strength I,expresses Debye and Huckel's law and predicts ionic activity coefficients quite well at very high dilution (i.e., I < 0.01). Values of A at any temperature are known (Harned and Owen, 1958). Binary interaction parameters P k l include pa, parameters of eq 4 and Pia parameters for ion-molecule, pi; parameters for ion-ion interactions; the latter are estimated from the correlations developed by Bromley (1972) with standard entropies of ions in water. Interactions between ions of the same sign are neglected and &; is written &, = &* b,*, Le., a specific parameter &* is attached to any ion i. There are two important limitations in that model: (a) eq 6 cannot predict ionic activity coefficients at ionic strengths higher than 0.1 m; (b) Edwards estimates pi; parameters in a rough approximation assuming a unique correlation of pi* for all ions which leads to erroneous values for HCO3- and NH2COO- ions especially. The influence of that assumption at low concentration is small, but a t higher concentrations, a reasonable estimation of interaction parameters becomes crucial to calculate equilibria.
+
222
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
Proposed Model The expression used in this work to derive all activity coefficients is an extension of Pitzer’s equation (1973) for the excess Gibbs free energy of ionic solutions. The total Gibbs free energy of the solution is given by G(T, P, n k , n,) = nw(cLwo(T, P ) + R T In x,)
x k
nk(pko
(T, p ) + R T I n
mk)
-+ GE(T, p, n,,
nk)
(7)
where w represents water and k any other species, n,, n k are numbers of moles, m k is a molality, x , is the mole fraction of water, and Pk0 is the chemical potential of k in the hypothetical ideal solution of unit molality at T, P. The total excess Gibbs free energy GE is given by I?E ”
0.018nR , T
=
f(0+
x k
ion-ion binary interaction coefficients X i j , one from Pitzer’s theory X i j p , and one resulting from ion-neutral solute molecule interaction Xi,D. hia and Xai parameters also result from ion-molecule interaction. A,, coefficients for molecule-molecule interactions are equal to Edwards’s p a , . Only four ternary ion-ion interaction coefficients are taken as adjustable parameters to represent data at high concentration. Molecule-Molecule Interaction Contribution In order to evaluate the term (In Y a ) a a , eq 4 is considered as the limiting form of a more general development, which has been extended to the second power of ma (In Y a ) a a =
2Aaama
+ 3@aaama2
with
Chklmkml 1
Paaa
=
1
-55.5
corresponding to a contribution Here, k, I, h, represent any molecular or ionic species except water, while Pitzer considered only ions when he proposed the same expression. The factor 0.018nWis the mass of water (kg) and the right member of eq 8 calculates the excess Gibbs free energy for 1kg of water; dimensions are kg mol-’ for k k l , kg2 mol+ for &lh, and mol kg-1 for f(1). Matrix p is symmetric. From (8) one obtains the activity coefficients by usual derivations
hama
+ Paaama
in eq 8; paaa is considered as a pseudo-ternary interaction parameter. Ion-ion Interaction Contribution According to Pitzer’s Theory Equation 8, proposed by Pitzer for the treatment of ionic solutions, is characterized by: (a) the term f(Z) which is equivalent a t high dilution to the law of Debye-Huckel and includes an empirical parameter (b = 1.2) common to all salts
(10)
As shown by Pitzer, ion-ion interaction coefficients X must be considered as dependent on ionic strength. Similarly, ion-molecule and molecule-molecule coefficients will be found concentration dependent. At the low concentration of neutral molecules reached in the systems of interest (except for ammonia in some cases), the following assumptions are legitimate: (1)Ternary interactions are neglected between neutral molecules and between molecules and ions. (2) Binary interactions between two different neutral molecules a, a’ are neglected
(b) the parameters X i j p which are functions of the ionic strength I . For a salt MX in solution MX
+
+
UMMZM uxXzX
with
U M Z M+ V X Z X= 0; u = U M + ux Pitzer explains that values of XMM’, AMX’, XxxP cannot be determined from experiment. For example, the activity coefficient YMX of the salt a t molality m is given by
X a a ~= 0
It was verified that this assumption had no effect on the calculation of equilibrium. Additional assumptions are: ( 3 ) The ternary interactions parameters are neglected except Pkll, Pkkl when k stands for NH4+ and 1 for HS-, HC03-, NHzCOO-, HS03-, S2-, C032-, and S0s2-. (4) Binary interactions between ions of the same sign are neglected; this assumption is probably the most serious one and could introduce some discrepancy at higher ionic strengths. The additive form (8) of the excess Gibbs free energy and assumptions 1and 2 justify splitting the expression of all activity coefficients into 2 contributions. For a molecular species a
In y a = (In Y a ) a a + (In Y a ) i a
(11)
and for an ionic species i In
yi
= (In 7i)ij + (In
7i)ia
(12)
where subscript ia refers to the contribution of ion-molecule interactions (“salt effects”) and subscript ij refers to that of pure ionic interactions in water. In eq 8, there are two additive contributions making up
where
9 CMXY = - ( Y M ~ X ) - ~ ’ ~ ( U M P M M+XUX~LMXX) (16) 2 Only two parameters, BMXY and C M X ~can , be fitted on experimental data of salt activities. If, however, it is assumed (assumption 4) that XMM’
= XxxP = O
the knowledge of BMXY is equivalent to that of X M X ~ . It is shown in Appendix C that the functional dependence on I proposed by Pitzer for BMXYis equivalent, with this assumption, to the relation
Ind. Eng. Chem. Process Des. Dev.,Vol. 17, No. 3, 1978
223
O6,
02
! Figure 5. Correlation of parameter S for salts with a common anion 02
00
of Class I1 or 111.
04 PBrOmlGy
Figure 3. Correlation of 1-1 salts, interaction parameters; Pitzer’s vs. Bromley’s parameters.
04-
0.2.O.C
I x
FOHCti$COx HC03-
0
0
t
0.
,.
-yi=t
N+--T+i0.2
Figure 6. Correlation of parameter S for salts with common anion of Class IV. 0.
rameters used by Bromley (1972,1973) and that both sets of parameters are correlated too (Figure 3). However, a unique correlation does not exist for all ions in solution. It is useful to adopt the classification proposed by Harned and Owen (1958) for monovalent ions: Class I, cations -4 0, -30 -10 Li+, Na+, . . . , Cs+; Class 11,halogenide anions C1-, Br-, and k - -%,, I-; Class 111, oxygenated polyatomic anions X03-, X04-, . . . ; Class IV, proton acceptors F-, OH-, HX03-, and Figure 4. Correlation of parameter S for salts with a common catCHBCOO-, . . . . ion. According to this classification, one finds interesting correlations of S parameters for salts with a common cation 2 XMX’(~) = pC0)+ p(l)-(1 - e-adl(l a d ) ) (17) (Figure 4) or a common anion (Figures 5 and 6). CY21 The different behavior of structure-breaking anions (Class where pc0) and p(l) have the values given by Pitzer to fit exI1 and 111)and structure-making anions (Class IV) is evident perimental data, with cy = 2 for all salts. in Figures 5 and 6. Such lines of correlation allow the evaluation of S for a new salt in any class. Moreover, Pitzer (1973) Correlation of Pitzer’s Ion-Ion Binary Interaction observed a correlation between p(0)and p(l);the ratio Coefficient XijP
+
Q =
According to eq C-2 lim (A&) I-0
= p(0)
+ p(1) = S
It was observed that values of S can be correlated with ionic standard entropies in water a t 25 OC as well as similar pa-
pCO)/(p(O)+ p(1))
is often close to the value 0.3 for 1-1 salts, which provides a first approximation. One can predict both parameters p(O) and P(l) from Q and S . The method is applied to the “salts” (NH4+, HS-), (H+,
224
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
Table I. Ionic Interaction Parameters HSH+
0.50 0.36
S
R C*
NH4+
HC03-
S
R C*
NHzCOO-
0.420
0
0.248 0.22 -0.001
0.54 -0.1 -0.01
0.25
0
0.50
0.45
0
0
0.46 0.25
0.0016
0
-0.006
Ion-Ion Ternary Interaction Parameters These parameters are introduced only if they have a significant influence on the representation of the properties of the system considered here. The ionic strength rises to high values only when concentrations of both acid and base are large. Then the predominant ions are NH4,+ and HS- (or (HC03-, HS03-), and the molalities of NH2COO- (or s0s2-) become fairly large; it is ternary interaction contributions between those species which have to be taken into account and corresponding parameters estimated. It is assumed here that
WMMX
= CLMXX
Therefore Cy are given from eq 16 and C* (Pitzer’sparameters for osmotic coefficients) are defined by 9 2
+
3 2
- (CLMMX CLMXX)= Cy = - C*
(for 1-1 salts MX)
(for 1-2 salts M2X) Parameters C* were adjusted for four “salts” only (NH4+, HS-), (NH4+,HCO,-), (NH4+,S032-),and (NH+,HSO3-1; these values, reported in Table I, are in reasonable agreement with those found by Pitzer for similar salts. C* for (NH4+, NHzCOO-) was given the mean value of parameters given by Pitzer for acetate salts. C* for (NH4+,S2-)was given a suitable positive value to give a good representation of system NHs-HzS-HZO at highest molalities ( I > 5 , ~ N >H151, ~ avoiding that activity coefficients of S2- goes to very low values leading to too much ionization. C* for (NH4+, Cos2-) and (NH4+, S2-) could be adjusted only if experimental data on very high pH solutions were available.
0.1
0.059 0.025
0.059
0.16
0.1 0
+ WMYY)
0 0
-0.6
sop.
1 = - (WMXX 2
0 0 0 0.70
S2-
HS-), (NH4+,HC03-), (H+, HC03-), (NH4+,NH2COO-), H+, NH2COO-), (NH4+,OH-), (H+, OH-), (NH4+,HS03-), and (H+, HS03-). Ionic parameters obtained are presented in Table I. To estimate Q, the value for the nearest similar salt has been adopted. For example, it is assumed that Q(NH4HS) = Q(NH4C1) and Q(NH4HC03) = Q(KHC03). Pitzer’s parameters were adjusted for salts LiHC03, NaHC03, and KHCO3 on experimental activity coefficient data (Walker et al., 1927). Values of S obtained are reported in Figure 6. The negative @(O) and high positive @(l)do not fall into Pitzer’s correlation band; some association must occur in view of the vanishing bicarbonate activity coefficient when ionic strength rises. All parameters for interactions involving NH2COO- have been estimated from values for acetate salts (Figure 6). It is justified by the similarity of ions CH3COOand NHzCOO-, confirmed by very close standard entropies in water. Parameters given by Pitzer for the salt (NH4)2S04 have been used for interactions of NH4+ with S2-, C032-, and
CLMXY
S032-
OH-
0.34 0.25
+0.3 0
C032-
HS03-
0
0
0.70 0
1.2
0 0.7
0.059 0.0022
Contribution of Ion-Molecule Interactions: Calculation of Binary Interaction Coefficient Xia, X i j D from Dielectric Effects Ion-molecule interactions and corresponding parameters are not adjusted but estimated using Debye-McAulay’s electrostatic theory (Harned and Owen, 1958). The purpose of this theory was to interpret the elevation of activity coefficients of gases in water when ions are introduced; it predicts the right order of magnitude of the influence of rather “structure-breaking”ions of intermediate size, such as Na+, K+, NH4+, and C1-, Br-, I-. The electrostatic theory cannot represent the variation of the effect with the size of ions for two reasons: it does not take structural effects into account and ionic radii in solution are not known exactly. For our purpose, however, it is sufficient to estimate the overall effect of ionic strength upon undissociated molecules ”3, C02, and H2S neglecting specific effects of ions as far as they belong to intermediate types. It is reasonable to assume that HS-, HC03- behave roughly as C1-, I-. The electrostatic theory gives the electric work necessary to transfer ions from a solution of dielectric constant Di to another of dielectric constant Df
where N is Avogadro’s number, e the charge of electron, and z, and rJ are the charge number and the radius (A) of ion j assimilated to a metallic sphere. The dielectric constant depends on the composition of the solution. If neutral molecules are present in the ionic solution, a contribution given by eq 18 is introduced into GE; it is calculated taking for D fthe dielectric constant of the real ionic solution and for Di the dielectric constant of the ionic solution from which neutral solute molecules would be removed. The dielectric constants D,, Df are functions of all molalities; these functions and the resulting quadratic form of molalities for We,are derived in Appendix D. This contribution to GE yields not only binary interaction coefficients A,, an_d A,, but also XD ,, which are given in Appendix D. Matrix X is symmetric when only ions are present in solution excluding neutral solutes. Although the various contributions to X may appear complex, they are easy to calculate. The complete expressions of the activity coefficients reported in Appendix E are obtained from eq 8, 9, and 10 taking into account the concentration dependence of X coefficients given by eq 17, D-12, and D-14. They bring no more difficulty in computer programming than the simpler Edwards’ equations (6). It must be emphasized to conclude how both works by Pitzer and Bromley on electrolytes are useful. On the one hand, Pitzer’s model is suitable for mixed electrolytes because it provides a generalized expression of the excess Gibbs free energy and therefore consistent activity coefficients; on the other hand, Bromley’s ideas of neglecting interactions between ions of the same sign and correlating binary interaction parameters with standard entropies of ions were incorporated into our model. In the present model, electric contribution is added without adjustable parameters. Only four ternary ionic interaction pa-
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
40°C
1
Table 11. Physical Data for Dielectric Effects ~
3 "
coz
HzS SO2 NH4+ HC03HSC032S2H+
OH-
b
NH2COOHS03SO& a In L mol-'.
Figure 7. Comparison of calculated and experimentalpartial pressure of H2S in the NH3-HzS-HzO system for a ratio of total concentrations C N H ~ J C H=~ S2.1: 0 ,experimental data of Van Krevelen et al. (1949); 0 ,experimental data of Leyko and Piatkewicz (1959);-, calculated curve.
rameters are adjusted for the three ternary systems considered. Applications System N H ~ - H ~ S - H Z OMany . experimental data have been published on this system since the original work by Van Krevelen et al. (1949). They allow a good test of the representation at all temperatures from 20 to 100 "C and all concentrations except in the H2S rich region. Leyko's (1959) equilibrium data a t high concentrations between 20 and 50 "C were used along with those of Van Krevelen to adjust the parameter C* given in Table I for the couple (NH4+, HS-). Figure 7 shows the good agreement obtained for the partial pressure of H2S with both authors. The point with the highest ionic strength of 8 M is especially well represented. However, the partial pressure of NH3 calculated at this point is 40% higher than the experimental value given by Leyko. The mean relative deviation on H2S partial pressure
cT=--E 1 IPcalc - Pexpl n i=l Pexp is 9% on the 14 points reported by Leyko, 12% on more than 60 points reported by Van Krevelen at 20,40, and 60 "C. At higher temperature, static methods have been generally used to investigate vapor-liquid equilibria of this system. It is noteworthy that the model gives the total pressure of such equilibria with no additional adjustment. This is shown in Table I11 for data of Leyko and Piatkewicz (1959) for solutions of 6.15 M NH3 and 1.91 M H2S. The partial pressure of water P, is calculated as P, = Pwsx,yw, where PWs is the pure water saturation pressure and y, is given by eq 10. Equilibrium data are reported between 60 and 90 "C, a t atmospheric pressure, by Ginzburg et al. (1965). Total pressure is calculated with a mean deviation of 2.4% (maximal deviation of 6.5%). The same authors made similar measurements at 600 mmHg; the mean deviation observed is 3%. Typical comparisons are shown in Table IV. The agreement on vapor phase composition is poor but improved in comparison with Edwards' results. Calculated partial pressure of ammonia is systematically lower than the experimental one with a mean deviation of 13%;the mean deviation on partial pressure of H2S is 21% on 40 points, with a strong overestimation at low values of molar ratio W (sulfide/ammonia). Vapor compositions at 70,80, and 90 "C have been obtained
225
b
rj b
uk a
aaa
0.030 0.037 0.034 0.045 0.0134 0.0288 0.0232 0.0065 -0.0037 -0.0047 0.0005 0.0459 0.0375 0.0197
-0.0235 -0.037 -0.031 -0.037
~~
2.5 2.7
2.3 4.0 3.3 3.8 3.5 2.7 2.7 2.8
In A.
Table 111. Total Pressure and Vapor Composition over Solutions Containing 6.15 mol/L of NH3, 1.91 mol/L of HzS. Comparison of Calculated Results with Data of Leyko and Piatkewicz (1964) Exptl Calcd t , " C P , a t m Y N H ~ ~YHzS" P,atm Y N H ~ ' Y H ~ S O 0.576 0.212 1.65 0.558 0.217 90 2.35 0.519 0.234 100 3.20 0.466 0.266 110 4.40 a Mole fraction in vapor phase. 80
1.70 2.43 3.39 4.62
0.564 0.540 0.519 0.502
0.213 0.229 0.241 0.248
by Oratovskii et al. (1964) from a method of evaporation. Table V shows that measured vapor compositions are quite different from Ginzburg's measurements for liquid phases of close molalities a t similar temperatures. The model gives intermediate values of mole fractions. Still the agreement is better with the 30 points of Oratovskii. The absolute mean deviations on vapor weight fractions are 0.015 and 0.059 for NHs and HzS, respectively, when these quantities vary from 0.12 to 0.70. Recent measurements sponsored by API (Brigham Young University, 1975) (Table VI) provide a final test to prove the ability of the model to represent NH3-H2S-H20 equilibria in a very large range of concentrations including molar ratios sulfide/ammonia greater than unity. The mean deviation on NH3 partial pressure is 11%,contrasting with underestimation relative to Ginzburg's data and overestimation relative to some of Leyko's. The largest deviations are found for points with a very high molality of undissociated NH3 when water can hardly be considered as the solvent for the solution. System NH~-COZ-H~O. The improvement achieved over Edwards' calculations is illustrated for CO:! partial pressure in Figure 8. The mean relative deviation on partial pressure of COS is 16%. As shown in Figure 9, NH3 partial pressure is predicted with a mean relative deviation of 5%. System NH3-SO2-HzO. Two parameters C* for (NH4+, HSOB-) and (NH4+, s 0 s 2 - ) were adjusted, minimizing the relative mean deviation on partial pressures of SO:! and "3. Data of Johnstone (1934) a t temperatures of 35,50,70, and 90 "C were used. Figure 10 illustrates the comparison between calculated Pso2and experimental values. Two experimental points of Johnstone for mNHs = 3.2 are erroneous; they are in disagreement with other data points which lie on the calculated curve. Data published by Boublik et al. (1963) for the system N H ~ - S O ~ - S O S - H ~can O be used for comparison of partial pressure of "3, , 9 0 2 , and H20 if the molar ratio (SO3/SO2)
226
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
Table IV. Comparison of Calculated Pressure Using Edwards' Model and the Present Work with Experimental Data of Ginzburg et al. (1966) Molalities H2S partial pressure Total pressure t . "C NH9 HIS Exotl Edwards This work Exotl Edwards This work 62.1 65.3 63.3 75.1 57.6
7.32 6.23 4.91 1.99 5.36
1.08 1.74 2.41 0.95 3.17
2.81 51.47 242.6 196.0 346.5
17.7 94.3 400.5 247.0 712.0
25.3 90.3 250.0 197.5 348.5
600 600 600 600 600
604 600 724 631 958
Table V. Vapor Composition of the NH3-HzS-HzO System between 60 and 90 "C NH3 t mAa mSa Exptl Calcd
604 615 587 576 598
H2S Exptl
Calcd
0.0201 0.3486c 0.289 82.0 1.87 0.30 0.122d 0.269 0.224d 90.0 1.83 0.30 0.1452 0.318 O.432Oc 75.0 3.30 0.975 0.31gd 0.360d 0.367 70.0 3.53 0.962 0.33gd 0.335 0.336d 80.0 3.50 0.962 a Total molalities in solution. b Weight fraction in vapor phase. c Ginzburg et al. (1966). Oratovskii et al. (1964).
0.092 0.104 0.290 0.250 0.277
Table VI. Comparison of'calculated Partial Pressures of.NH3 and HzS with API Data (1975) on the System NHrHzSHzO at 80 O c a Molalities NHs partial pressureb H2S partial pressureb 3 " H2S Exptl Calcd Exptl Calcd
(2
12.0 4.36 136.0 574 72.6 208 597 2285
0.971 1.452 1.151 1.143 5.305 7.935 5.983 5.561
0.960 1.063 2.332 5.112 5.538 9.245 10.201 22.627
2280 9138 304 101 10048 9620 1863 426
2389 8556 319 94.8 12140 9506 1916 241
10.7 3.8 138.0 496 78 235 657 2811
Brigham Young University (1975). b Millimeters of mercury.
02
04
0.6
0.8
w
Figure 8. Comparison of calculated and experimental partial pressure of COn at 20 O C for various ammonia concentrations C, and molal ratios W = CcoJC,: 0 , experimental data of Pexton and Badger (1938);0,experimental data of Van Krevelen et al. (1949);- - - - -, calculated Edwards et al. (1975);-, calculated,this work.
is smaller than 0.02. A comparison between experimental and calculated values is given in Table VII. The partial pressure of SO2 is overestimated because of the disagreement between the data of Boublik e t al. and Johnstone, which was already observed by the former authors. Figure 11shows that partial pressure of SO2 when the molar ratio (S02/NH3) is close to 1and mson= 12 is overestimated by 50% (data of Berdyanskaya (1959) and Sedov (1957). Figure 12 illustrates the comparison of partial pressure of SO2 a t a
t
I
I
0.4
I
I
0.6
N
I
08
1
t
W
Figure 9. Comparison of calculated and experimental partial pressure of NHs at 20 O C at the same conditions as in Figure 8.
given molar ratio (S02/NH,); the calculated curve has the expected molality slope a t high dilution because SO2 is totally dissociated and its activity is proportional to the square of its molality. Experimental points present deviation which can be attributed to large absolute errors because mole fractions of SO;! of the order of were measured in the vapor phase. Conclusion The representation of NHs-H2S-H20, NH3-CO2-Hz0, and NH3-SOz-H20 equilibria has been extended to high ionic
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
227
Table VII. Comparison of Calculated Partial Pressures with Experimental Data of Boublik et al. (1963) When S03/502
< 0.02
Partial pressures, mmHg Molalities
3 "
mNHa
mso,
msozlm "3
Exptl
Calcd
Exptl
3.27 3.39 3.58 3.90 4.89 5.42 8.45
2.62 2.90 3.10 3.46 3.81 4.41 6.55
0.801 0.855 0.866 0.887 0.779 0.814 0.775
2.12 1.08 0.87 0.79 2.97 1.67 3.45
2.00 1.27 1.15 0.94 2.54 2.00 3.51
1.71 3.12 3.81 5.94 2.00 4.01 3.94
Mean deviation
15%
,
so2
HZO Calcd
Exptl
Calcd
1.78 3.59 4.43 6.66 2.42 4.13 4.47
485.6 482.8 480.4 475.8 470.5 460.2 429.0
487.5 483.8 481.2 476.4 471.3 463.3 430.9
