Thermodynamic Modeling of the NH - American Chemical Society

ARTICLE pubs.acs.org/IECR

Thermodynamic Modeling of the NH3CO2H2O System with Electrolyte NRTL Model Huiling Que† and Chau-Chyun Chen*,‡ † ‡

AspenTech Limited, Pudong, Shanghai 201203, China Aspen Technology, Inc., Burlington, Massachusetts 01803, United States ABSTRACT: To facilitate simulation, design, and optimization of chilled ammonia processes for CO2 capture, we develop a thermodynamic model for the NH3CO2H2O system with the electrolyte NRTL activity coefficient model. The thermodynamic model explicitly accounts for the solution chemistry which includes dissociations of H2O, NH3, and CO2, formation of ammonium carbamate, and precipitation of ammonium bicarbonate. The electrolyte NRTL activity coefficient model parameters are identified by fitting against selected experimental data for vaporliquid equilibrium, heat of solution, and heat capacity of the NH3H2O binary, solidliquid equilibrium of the NH4HCO3H2O binary, and vaporliquid equilibrium and speciation of the NH3CO2H2O ternary. The model is further validated with additional VLE, speciation, heat capacity, and heat of solution data for the NH3CO2H2O system. Overall the model satisfactorily represents the thermodynamic properties of the NH3CO2H2O system with temperature up to 473 K, pressure up to 7 MPa, NH3 concentration up to 30 wt %, and CO2 loading up to unity.

’ INTRODUCTION With the potential advantages of lower energy cost for solvent regeneration and free of solvent degradation, chilled ammonia has been considered as an attractive alternative to traditional amines for postcombustion CO2 capture in power plants.1 The process absorbs CO2 mainly by precipitation of ammonium bicarbonate as well as some other possible solids such as ammonium carbonate.2,3 The absorber is operated at low temperatures, typically from 273 to 283 K. The ammonia concentration can be up to 28 wt %. The lean solvent loading is at the point of imminent precipitation of solids,2 with a range from 0.25 to 0.67.3 The CO2 removal efficiency can reach 90%, resulting in rich solvent loadings between 0.67 and 1. The rich solvent is then sent to the stripper for solvent regeneration at preferably between 373 and 423 K. The stripper operates around 3 MPa2 or in the range of 0.2 to 14 MPa.3 The phase behavior of the NH3CO2H2O system has been studied extensively primarily because of industrial interests in modeling sour water stripper systems.4,5 Typically these models involve equations of state for the vapor phase, activity coefficient models for the aqueous phase, Henry’s law for NH3 and CO2 solubility in the aqueous phase, chemical equilibrium for dissociations of H2O, NH3, and CO2 and formation of ammonium carbamate, and precipitation of solids such as ammonium bicarbonate. According to the models for aqueous phase activity coefficients, the prior studies can be grouped into three categories: (1) Pitzer model,411 (2) electrolyte NRTL model,2 and (3) extended UNIQUAC model.3 Among these models, the electrolyte NRTL model is most suitable for process modeling and simulation applications as it requires only binary interaction parameters and makes use of mole fraction concentration scale consistently for both the short-range local composition interactions and the long-range DebyeH€uckel expression.12,13 In this work, we choose to use the 2009 version of the electrolyte NRTL model13,14 as the aqueous phase activity coefficient model. r 2011 American Chemical Society

To cover typical process conditions for chilled ammonia processes, we aim at developing a thermodynamic model for the NH3 CO2H2O system that encompasses temperature up to 473 K, pressure up to 7 MPa, NH3 concentration up to 30 wt % (∼25 m), and CO2 loading up to 1. The model should support calculations of all thermodynamic properties of interest to process simulation, that is, VLE, SLE, speciation, heat of solution, and heat capacity. Available experimental data are compiled and regressed to obtain and validate the model parameters.

’ THERMODYNAMIC FRAMEWORK Chemical Equilibrium. In aqueous solutions, H2O, NH3, and CO2 undergo partial dissociation K1

2H2 O S H3 Oþ þ OH K2

ð1Þ

NH3 þ H2 O S NHþ 4 þ OH

ð2Þ

þ CO2 þ 2H2 O S HCO 3 þ H3 O

K3

ð3Þ

K4

ð4Þ

2 þ HCO 3 þ H2 O S CO3 þ H3 O

In addition, ammonia and bicarbonate ion form carbamate K5

NH3 þ HCO 3 S NH2 COO þ H2 O

ð5Þ

Received: June 15, 2011 Accepted: August 23, 2011 Revised: August 16, 2011 Published: August 23, 2011 11406

dx.doi.org/10.1021/ie201276m | Ind. Eng. Chem. Res. 2011, 50, 11406–11421

Industrial & Engineering Chemistry Research

ARTICLE

As results of the aqueous phase reactions, there are three molecular species including solvent water and molecular solutes NH3 and CO2. In addition, there are six ionic species, H3O+, NH4+, OH, HCO3, CO32, and NH2COO in the aqueous solution. Ionic species may form solid precipitates, such as NH4HCO3(s) K6

NH4 HCO3ðsÞ S NHþ 4 þ HCO3

ð6Þ

The chemical equilibrium constants K1K6 can be calculated from reference state Gibbs energy change of reaction, ΔG°j . RT ln Kj ¼ ΔG°j , j ¼ 1 6

ð7Þ

where R is the gas constant, T is the system temperature, and Kj is the chemical equilibrium constant for reaction j. Reference state Gibbs energy for solvent water is calculated from ideal gas Gibbs energy and fugacity of pure liquid water Glw ðTÞ ¼ Gigw ðTÞ þ RT ln

fw° ðTÞ Pref

T ig ig ðΔf Hi, 298 Δf Gi, 298 Þ 298 Z T Z T ig Cp, i ðTÞ ig þ dT Cp, i ðTÞdT T T 298 298 ig

Gi ðTÞ ¼ Δf Hi, 298

ð9Þ

where ΔfHigi,298 is the ideal gas enthalpy of formation for component i at 298 K, ΔfGigi,298 is the ideal gas Gibbs energy of formation for component i at 298 K, and Cigp,i is the ideal gas heat capacity. Cigp,i is calculated with the DIPPR correlation15 2 Ci =T ig Cp, i ðTÞ ¼ Ai þ Bi sinhðCi =TÞ 2 Ei =T þ Di ð10Þ coshðEi =TÞ where Ai, Bi, Ci, Di, and Ei are correlation parameters for component i. f°w is calculated with the following equation: fw° ¼ Pw° j°w θ°w

ð11Þ

where P°w is the vapor pressure of water; j°w is the vapor fugacity coefficient of water at the system temperature and P°w, and θ°w is the Poynting pressure correction from P°w to system pressure P. P°w is calculated with the extended Antoine equation: 7258:2 7:3037ln T ln ¼ 73:649 T þ 4:1653 106 T 2 Pwo ðTÞ

ð12Þ

The reference state Gibbs energy for molecular solutes, that is, NH3 and CO2, is chosen to be the Gibbs energy of molecular solute in aqueous phase infinite dilution. It is calculated from the ideal gas Gibbs energy and Henry’s law constant: ∞, aq

Gi

ig

¼ Gi þ RT ln

Hi, w , i ¼ NH3 or CO2 Pref

b þ c ln T þ dT T Z P Vi,∞w dp e p°w þ 2 þ ð14Þ T RT where a, b, c, d, and e are the Henry’s law constant correlation parameters and V∞ i,w is the infinite dilution partial molar volume of molecular solute i in water. V∞ i,w is calculated with the Brelvi O’Connell model:16 ln Hi, w ðT, PÞ ¼ a þ

Vi,∞w ¼ f ðViBO , VwBO , Vwol Þ

ð8Þ

where Glw is the Gibbs energy for liquid water, Gigw is the ideal gas Gibbs energy for water, f°w is the fugacity of liquid water, and Pref is the reference pressure, that is, 101325 Pa. Ignoring pressure dependency, we calculate the ideal gas Gibbs energy for component i with the following equation: ig

is the Gibbs energy for component i at aqueous where G∞,aq i phase infinite dilution, Gigi is the ideal gas Gibbs energy and calculated with eq 9, and Hi,w is the mole fraction scale Henry’s law constant for component i with water. Hi,w is calculated with the following equation:

VBO i

ð15Þ

VBO w

where and are the characteristic volume for solute i and for solvent water, respectively, and Vo,l w is the liquid molar volume of water. The characteristic volume is assumed to be linear with temperature ViBO ¼ v1, i þ v2:i T

ð16Þ

where v1,i and v2,i are the correlation parameters. The reference state Gibbs energy for ionic species i is chosen to be the Gibbs energy at aqueous phase infinite dilution and is calculated with the following equation: ∞, aq

Gi

∞, aq

ðTÞ ¼ Hi

∞, aq

ðTÞ TSi

þ RT ln

1000 Mw

ð17Þ

where G∞,aq , H∞,aq , and S∞,aq are the Gibbs energy, enthalpy, i i i and entropy of ionic species i at aqueous phase infinite dilution, respectively, and Mw is the molecular weight of water. Note that the last term in eq 17, RT ln((1000)/(Mw)), is introduced to convert the molality scale Gibbs energy to the mole fraction scale Gibbs energy. is calculated with the following equation: H∞,aq i Z T ∞, aq ∞, aq ∞, aq Hi ðTÞ ¼ Δf Hi, 298 þ Cp, i dT ð18Þ 298

ΔfH∞,aq i,298

where is the enthalpy of formation for ionic species i at is the heat aqueous phase infinite dilution at 298 K and C∞,aq p,i capacity of ionic species i at aqueous phase infinite dilution. C∞,aq p,i is assumed to be temperature-independent. is calculated with the following equation: S∞,aq i Z T ∞, aq ∞, aq ∞, aq Cp, i Δf Hi, 298 Δf Gi, 298 ∞, aq þ dT ð19Þ Si ¼ 298 298 T where ΔfG∞,aq i,298 is the Gibbs energy of formation for ionic species i at aqueous phase infinite dilution at 298 K. The reference state Gibbs energy for solid component i is chosen to be the Gibbs energy for crystalline solid. It can be calculated as follows: T ðΔf Hi,cr298 Δf Gcr i, 298 Þ 298 Z T Z T cr Cp, i þ dT Ccr dT T p, i 298 298 T

cr Gcr i ðTÞ ¼ Δf Hi, 298

ð13Þ 11407

ð20Þ

dx.doi.org/10.1021/ie201276m |Ind. Eng. Chem. Res. 2011, 50, 11406–11421


ARTICLE

where Gcr i is the crystalline solid Gibbs energy for component i, cr ΔfHcr i,298 and ΔfGi,298 are the enthalpy of formation and the Gibbs energy of formation at crystalline solid state at 298 K, and Ccr p,i is the crystalline solid heat capacity. Ccr p,i is assumed to be independent of temperature. VaporLiquid Equilibria. For vaporliquid equilibria, the solvent water is treated with Raoult’s law (eq 21), while NH3 and CO2 are treated with Henry’s law (eq 22): yi ji P ¼ xi γi fi° , i ¼ H2 O

ð21Þ

yi ji P ¼ xj γkj, w Hj, w , j ¼ CO2 or NH3

ð22Þ

where y is the vapor phase mole fraction, j is the vapor phase fugacity coefficient, x is the liquid phase mole fraction, γ is the liquid phase activity coefficient, f°i is the fugacity of pure liquid component i, calculated with eq 11, Hj,w is the Henry’s law constant for component j with water, calculated with eq 14, and γ*j,w is the unsymmetric activity coefficient of component j in aqueous solution, calculated with eq 23: γj, w ¼

γj, w

ð23Þ

γ∞ j, w

where γj,w is the activity coefficient of component j in water at the system conditions and γ∞ j,w is the activity coefficient of component j at aqueous phase infinite dilution. The dielectric constant of water is required for the calculation of the long-range ionion interaction contribution of the electrolyte NRTL model. It is correlated to temperature with the following equation: 1 1 ð24Þ ε ¼ 78:51 þ 31989 T 298 where ε is the dielectric constant. The electrolyte NRTL model requires nonrandomness factor αij and asymmetric binary interaction energy parameter τij. τij is expressed as the following temperature-dependent correlation: τij ¼ τ1, ij þ

τ2, ij T

ð25Þ

where τ1,ij and τ2,ij are correlation parameters. The PC-SAFT equation of state17,18 is used to calculate fugacity coefficients for the vapor phase. Enthalpy, Heat Capacity, and Heat of Solution. Liquid phase enthalpy of the system can be calculated with the following equation: H l ¼ xw Hwo, l þ

∑i

∞, aq xi H i

þ

∑j

∞, aq xj Hj

i ¼ ionic species, j ¼ NH3 or CO2 l

þ HE, ð26Þ

where H is the molar enthalpy of the liquid phase, xw is the liquid phase mole fraction of water, Ho,l w is the molar enthalpy of liquid water, xi is the liquid phase mole fraction of ionic species is the molar enthalpy of ionic species i at aqueous i, H∞,aq i phase infinite dilution, xj is the liquid phase mole fraction of is the molar enthalpy of molecular molecular solute j, H∞,aq j solute j at aqueous phase infinite dilution, and HE is the excess enthalpy of the liquid solution calculated with the electrolyte NRTL model.

Molar enthalpy of liquid water is calculated with the following equation: Z T ig Cigp, w dT þ ΔHwv Hwo, l ðTÞ ¼ Δf Hw, 298 þ 298

þ Δvap Hw ðTÞ

ð27Þ

where ΔfHigw,298 is the ideal gas enthalpy of formation of water at 298 K, Cigp,w is the ideal gas heat capacity of water, calculated with eq 10, ΔHvw is the vapor phase enthalpy departure for water, calculated with the PC-SAFT equation of state, and ΔvapHw is the heat of vaporization of water, calculated with the DIPPR correlation15 Δvap Hw ðTÞ ¼ 5:5146 10

7

T 1 Tc, w

!ð0:28402 0:15843T þ 0:2375T 2 Þ

ð28Þ where Tc,w is the critical temperature of water. Molar enthalpy of ionic species i at aqueous phase infinite , is calculated with eq 18. Molar enthalpy of dilution, H∞,aq i , is molecular solute j at aqueous phase infinite dilution, H∞,aq j calculated with the equation ∞, aq

Hj

ig

ðTÞ ¼ Δf Hj, 298 Z T ∂ ln Hj, w ig þ Cp, j dT RT 2 ∂T 298

ð29Þ

where ΔfHigj,298 is the ideal gas enthalpy of formation for component j at 298 K, Cigp,j is the ideal gas heat capacity, calculated with eq 10, and Hj,w is the Henry’s law constant for component j with water, calculated with eq 14. Excess enthalpy is calculated with the following equation: H E ¼ RT 2

∑i xi

∂ ln γi ∂T

ð30Þ

Liquid phase heat capacity is derived as temperature derivatives of liquid phase enthalpy. Heat of solution for CO2 gas in the system is calculated from the enthalpy balance of the dissolving process, during which nCO2 moles of CO2 gas are dissolved into an initial NH3CO2H2O solution of ninitial moles to form a final solution of nfinal moles: ΔHs ¼

l l ν nfinal Hfinal ninitial Hinitial nCO2 HCO 2 nCO2

ð31Þ

where ΔHs is the heat of solution per mole of CO2 gas in the system, Hlfinal and Hlinitial are the molar enthalpies of the final solution and the initial solution respectively, calculated with eq 26, and HCO2v is the molar enthalpy of CO2 gas added to the initial solution, calculated with Z T ig ig v ðTÞ ¼ Δ H þ Cp, CO2 dT HCO f CO2 , 298 2 298

v þ ΔHCO 2

ð32Þ

where ΔfHigCO2,298 is the ideal gas enthalpy of formation of CO2 at 298 K, Cigp,CO2 is the ideal gas heat capacity of CO2, calculated 11408



ARTICLE

Table 1. Model Parameters parameters

components

ref

ΔfGig298

H2O, CO2, NH3

15

ΔfHig298

H2O, CO2, NH3

15

Cigp

H2O, CO2, NH3

15

ΔfG∞,aq 298

H3O+, OH, HCO3, CO32, NH4+

15

NH2COO

this work

ΔfH∞,aq 298

+

H3O , OH , HCO3 ,

CO32,

NH4

+

NH2COO C∞,aq p

+

15 this work

chemical equilibrium constant19 chemical equilibrium constant19

H3O , OH , NH4+ HCO3, CO32 NH2COO

15 20 this work

chemical equilibrium constant19

ΔfGcr 298 ΔfHcr 298 Ccr p

NH4HCO3(s)

this work

SLE of the NH4HCO3H2O system

NH4HCO3(s)

this work

SLE of the NH4HCO3H2O system

NH4HCO3(s)

this work

Henry’s law constant

CO2

21

NH3

this work

CO2 NH3

21 15

VBO i

NRTL binary parameters

PC-SAFT pure component parameters PC-SAFT binary parameters

H2O

16

CO2H2O pair

21

VLE, heat capacity, heat of solution of the NH3H2O system

NH3H2O pair

this work

VLE, heat capacity, heat of solution of the NH3H2O system

moleculeelectrolyte pairs

this work

VLE, SLE, and speciation of the NH3CO2H2O system

CO2

15

NH3

15

H2O moleculemolecule pairs

18 this work

Table 2. Reference State Thermodynamic Property Parameters

a

experimental data for regression

fixed at 0

Table 3. DIPPR Correlation Parameters for Ideal Gas Heat 15 Capacity Cig p in J/kmol 3 K (eq 10)

ΔfG298 kJ/

ΔfH298 kJ/

Cp J/

mol

mol

mol 3 K

A

33363

33427

29370

ig

228.59

241.81

15

B

26790

48980

34540

NH3 CO2

ig ig

16.400 394.37

45.898 393.51

15 15

C D

2610.5 8896.0

2036.0 22560

1428.0 26400

H3O+

∞,aq

237.13

285.83

15

E

1169.0

OH

∞,aq

157.24

229.99

HCO3

∞,aq

586.77a

691.99a

CO32 NH4+

∞,aq

527.81

677.14

∞,aq

79.31

132.51

79.962

15

NH2COO

∞,aq

376.39

499.38

30.710

19

NH4HCO3(s)

cr

665.67

844.86

50.702

components

state

H2O

a

a

parameters

75.291 148.45

H2O

NH3

882.00

CO2

588.00

15

29.260b 397.10

ref

b

15, 20 15, 20

this work

From ref 15. b From ref 20.

with eq 10, and ΔHvCO2 is the vapor phase enthalpy departure for CO2, calculated with the PC-SAFT equation of state.

’ MODEL PARAMETERS Table 1 summarizes the required model parameters associated with the thermodynamic framework. Also given in Table 1 are the sources of the model parameter values and the experimental data used to identify the model parameters. ΔfGig298, ΔfHig298, and Cigp for molecules are taken from the ∞,aq Aspen databank.15 ΔfG∞,aq 298 and ΔfH298 for ions, with the exception of NH2COO , are taken from the Aspen databank.15

∞,aq ∞,aq ΔfG∞,aq for NH2COO are calculated from 298 , ΔfH298 , and Cp reported chemical equilibrium constants for carbamate formafor H3O+, OH, and NH4+ tion by Lichtfers and Rumpf.19 C∞,aq p are taken from the Aspen databank.15 C∞,aq for HCO3 and p 20 2 CO3 are taken from Criss and Cobble. cr ΔfGcr 298 and Δ fH 298 for solid ammonium bicarbonate are regressed against related experimental solubility data. Ccr p for solid ammonium bicarbonate is derived from Cp values of NH4+ and HCO3 and the assumption of zero ΔCp for reaction 6. Tables 2 and 3 summarize the values used for various reference state thermodynamic property constants. Henry’s law constant parameters are taken from Yan and Chen21 for CO2 with water and are regressed for NH3 with water against related experimental data. Characteristic volume parameters for the Brelvi and O’Connell model16 are taken from the Aspen databank15 for NH3, from Yan and Chen21 for CO2 and from Brelvi and O’Connell16 for H2O. The values of these parameters are summarized in Tables 4 and 5.

11409



ARTICLE

Table 4. Parameters for Henry’s Law Constant in Pa (eq 14) components

a

CO2

100.65

NH3

b

c

d

e

6147.7 10.191 0.010

34.995 3148.3

ref

11.418 0.02665 0.0 this work

vBO 1,i

vBO 2,i

ref

H2O

0.0464

0.0

16

NH3

0.07234

0.0

15

0.177

CO2

4

3.42 10

21

Table 6. Adjusted NRTL Binary Interaction Parameters (eq 25) component i H2O NH3

NH3 H2O (NH4+, HCO3)

H2O (NH4+,

HCO3 )

H2O (NH4+,CO32)

H2O (NH4+,

component j

CO32)

H2O

τ1,ij 0.5275 3.0173

components

H2O

ref

18

15

15

association energy ε(AB), K effective association volume k(AB), Å3

2500.7 0.034868

0.0 0.0

1772.5 0.12051

segment number m

1.0656

2.5692

1.0

segment energy parameter ε, K

366.51

152.1

144.28

segment diameter σ, Å

3.0007

2.5637

3.1725

0.0 21

Table 5. BrelviO’Connell Characteristic Volume Parameters in m3/kmol (eq 16) components

Table 7. PC-SAFT Equation of State Pure Component Parameters

τ2,ij

αij

1022.3 726.72

0.1 0.1

3.9505

2860.2

0.2

3.4774

1850.6

0.2 0.2

3.4273

0.0

2.7182

0.0

0.2

9.7292

0.0

0.2

H2O

(NH4+, NH2COO)

(NH4+, NH2COO)

H2O

4.3814

0.0

0.2

NH3 (NH4+, NH2COO)

(NH4+, NH2COO) NH3

7.3696 4.8826

0.0 0.0

0.1 0.1

The NRTL binary parameters for the waterCO2 pair are set to zero.21 The binary parameters for the waterNH3 pair are regressed with nonrandomness factor αij fixed at 0.1. The binary parameters for the pairs between water and (NH4+, HCO3), (NH4+, CO32), and (NH4+, NH2COO), and for the pair between NH3 and (NH4+, NH2COO) are regressed against experimental data with αij fixed at 0.2 for the former three pairs and 0.1 for the last pair. These electrolytes are the major species in the solution and the binary parameters associated with these electrolytes should have dominant effects on the thermodynamic properties calculated with the electrolyte NRTL model. The binary parameters for all other pairs of waterelectrolyte and CO2electrolyte are assumed to be 8 and 4 with αij fixed at 0.2.13,14 The binary parameters for pairs of NH3electrolyte are assumed to be 15 and 8 with αij fixed at 0.1. The adjusted NRTL binary parameters are summarized in Table 6. The PC-SAFT pure component parameters are summarized in Table 7. They include association energy ε(AB), effective association volume k(AB), segment number m, segment energy parameter ε, and segment diameter σ. They are taken from Gross and Sadowski18 for water and from the Aspen databank15 for CO2 and NH3. All the binary interaction parameters associated with the PC-SAFT EOS are set to zero.

’ DATA REVIEW An extensive amount of experimental data for vaporliquid equilibrium (VLE), solidliquid equilibrium (SLE), speciation, heat capacity, and heat of solution of the NH3CO2H2O system and the NH3H2O subsystem is available to identify

CO2

NH3

model parameters and to validate model results. Tables 8 and 9 summarize some of the more readily accessible literature data for the NH3H2O system and the NH3CO2H2O system, respectively. There are abundant VLE data for the NH3H2O system.2243 They cover a wide temperature range from 200 to 600 K and the whole concentration range. Good agreement is found among them. We select several data sets to cover temperature from 250 to 450 K. Specifically the low temperature data of Sherwood25 are chosen to cover temperature from 273 to 333 K, pressure up to 0.13 MPa and NH3 concentration up to 50 mol %. To extend the data to lower temperatures, we use the isobaric VLE data of Hoshino et al.33 with pressure at 0.1 MPa and temperature from 250 to 363 K. The isobaric VLE data from Clifford and Hunter28 at 0.02 MPa are also selected to provide more data below 273 K. The isobaric data of Kogan et al.31 at 1 MPa are also included to extend the temperature up to 450 K. The isothermal VLE data from Rizvi and Heidemann36 at 399 and 405 K further supplement the database with pressure up to 5 MPa. The heat of solution data for the NH3H2O system at 298 K from Wagman et al.44 are included in the regression. The data cover NH3 mole fraction up to 0.5. Rumpf et al.45 reported the enthalpy change upon dilution of 26 g aqueous NH3 solution at concentrations of approximately 6, 12, and 18 m with 16 g water at temperatures from 313 to 373 K. These data from Rumpf et al.45 are used for model validation. There are six sets of heat capacity data4651 for the binary NH3H2O system. The data from Chernen’kaya46 at room temperature and NH3 concentrations up to 21 wt % and the data from Chan and Giauque47 for a 32 wt % NH3 solution from 200 to 288 K are included in the regression. The data from Magee and Kagawa48 are not used as they are isochoric values for vapor phase. The data from Allred and Woolley49 are for very dilute aqueous NH3 solutions. These data are deemed questionable when compared against the heat capacity of pure water. Hildenbrand and Giauque50 reported heat capacity data for concentrated NH3 solutions, that is, above 50 wt % NH3, too high for chilled ammonia processes. These data are dropped from the regression as we find no satisfactory fit to the data. The data of Hnedkovsky and Wood51 are also excluded from the regression because the temperatures for these data are too high for chilled ammonia processes. An extensive amount of data is also available for the NH3 CO2H2O system. Trypuc and Kielkowska52 reported solubility data from 293 to 323 K for the NH4HCO3H2O system, equivalent to the NH3CO2H2O system with a CO2 loading of unity. These SLE data are used in the regression. Chernen’kaya46 measured heat capacity of aqueous NH4HCO3 solutions with NH4HCO3 concentration ranging from 2 to 12 wt % at 298 K. These heat capacity data are used for model validation. Rumpf et al.11 measured enthalpy change on partial vaporization of the NH3CO2H2O system from 313 to 393 K with NH3 11410



ARTICLE

Table 8. Experimental Data for the NH3H2O Binary System data type

T, K

P, MPa

NH3 mole fraction

data points

ref

VLE

273334

0.00020.24

0.030.36

77

22

VLE

283303

0.0050.21

0.290.53

17

23

VLE

273313

0.0980.49

0.250.67

31

24

VLE

273333

0.00020.13

0.010.5

95

25

VLE

283313

0.0710.13

0.0040.015

VLE

267476

0.022.03

0.150.99 01

14

26

378

27

82

28

6 26

29 30

VLE

212454

0.021.01

VLE VLE

298 283446

0.0050.007 0.1, 1 0.1, 1

0.020.81

26

31

0.0020.38

0.050.9

10

32

0.020.04 0.020.81

VLE

283446

VLE

273

VLE

241363

0.1

0.0250.975

21

33

VLE

373473

0.193.12

0.0420.32

40

34

VLE

403503

0.786.71

25

35

VLE

305618

0.00522.5

01

0.1950.974 (vapor)

307

36

VLE VLE

313588 333

0.00721.8 0.162.07

01 0.200.83

183 6

37 38

VLE

389613

1.2921.5

0.190.80

111

39

VLE

293413

0.0063.1

0.0460.96

198

40

VLE

305379

1.015.45

9

41

VLE

303337

0.0040.25

VLE

310400

0.0034.50

heat of solution

298

heat of dilution Cp

313373 298

Cp

200288

Cv

441522

Cp

283313

Cp

201258

Cp

303623

0.84, 0.91 less than 0.0001

0.1

16

42

0.100.90

51

43

0.000010.5

13

44

0.10.24 0.020.19

27 9

45 46

13

47

0.33 13.619.9

0.81, 0.90

28

concentration up to 12 m and CO2 concentration up to 6 m. These data are used for model validation. Qin et al.53 measured differential heat of solution of CO2 in aqueous NH3 solution of ∼2.5 wt % with CO2 loading up to 0.95. These heat of solution data are also used for model validation. Note that the Qin et al.53 data at higher temperatures, 333 and 353 K, exhibit peculiar and questionable trends. Numerous VLE data sets are available for the NH3 CO2H2O system.6,8,10,34,5460 We choose to use the comprehensive and reliable data sets reported by Maurer and co-workers from 1983 to 1995.8,10,34 G€oppert and Maurer8 reported experimental VLE data for aqueous solutions of NH3 and CO2 at temperature between 333 and 393 K, pressure up to 7 MPa, and concentrations up to 16 m for NH3 and 13 m for CO2. Kurz et al.10 measured the solubilities of NH3 and CO2 in water at 313, 333, and 353 K, pressures up to 0.7 MPa, NH3 concentration of 6 and 12 m, and CO2 concentration up to 10 m. Precipitation of solid NH4HCO3 was detected at 313 and 333 K. For the 6 m aqueous NH3 solution, NH4HCO3 precipitation only occurred at 313 K when CO2 concentration was greater than 5.2 m. For the 12 m aqueous NH3 solution, NH4HCO3 precipitation occurred both at 313 K for CO2 concentration greater than 7.6 m and at 333 K for CO2 concentration greater that 8.8 m. M€uller et al.34 reported VLE data for the NH3CO2H2O ternary at temperature between 373 and

146

48

0.00060.006

39

49

0.600.65

29

50

0.0030.05

35

51

473 K, NH3 concentration up to 25 m and CO2 concentration up to 13 m. Together these three studies provide comprehensive VLE data for the NH3CO2H2O system from 313 to 473 K. The VLE data from Kurz et al.10 at 313, 333, and 353 K and those of M€uller et al.34 at 373 K are used in regression. The data of G€oppert and Maurer8 from 333 to 393 K and those of M€uller et al. 34 at temperatures from 393 to 473 K serve as validation data. Also used as validation data are those of Pawilkowski et al. 6 at 373 K. The vaporliquidsolid equilibrium data points of Kurz et al.10 are excluded from regression. Multiple sets of speciation data19,6164 are available for the NH3CO2H2O system. Lichtfers and Rumpf19 presented a systematic study by means of infrared spectroscopy on speciation of the NH3CO2H2O system and reported results for a 4.44 m NH3 solution at 333 K. Wen and Brooker61 performed a Raman spectra study of the (NH4)2CO3H2O solution at temperature from 295 to 373 K with (NH4)2CO3 concentration varied from 0.65 to 3.45 m. The (NH4)2CO3H2O solution is equivalent to a NH3CO2H2O system with CO2 loading of 0.5. Wen and Brooker reported concentrations of various species in the solution. Holmes II et al.62 studied ionic concentrations in the NH3CO2H2O system by 13C NMR spectroscopy and reported the experimental results at 298 K. The NH3 concentration for these data varies from 11411



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Table 9. Experimental Data for the NH3CO2H2O Ternary System T, K

data type SLE

P, MPa

data points

ref

1

4

298

1

6

46

106

53

heat of solution

308353

enthalpy of vaporization

313393

0.022

373, 423

0.153

1.5

VLE

333393

0.17

VLE

313353

0.030.7

VLE VLE

373473 293373

0.29 0.0040.4

VLE

312367

0.1

VLE

343372

1.96

VLE

383, 393

0.050.95

6, 12 0.310 0.716.5

0.250.5

56

11

0.314

19

6

0.0382.058

6, 12

886

8

63

10

294 78

34 54 55

0.070.95

2.426 0.915

01 0.10.97

0.2412.5

52

0.1751

24

58120

0.10.25

21

56

1.82.6

106197

0.330.37

8

57

7236

VLE

301333

0.022

VLE

413433

0.7

VLE

296

0.1

speciation speciation

CO2 loading

293323

Cp

VLE

NH3 molality

333 295373

0.0250.25

10

58

0.45

0.020.3

36

59

2

60

4.44 1.36

0.160.90 0.5

5 12

19 61

speciation

298

0.698.95

0.330.72

17

62

speciation

293

0.8713

0.040.5

5

63

speciation

298

0.692.1 (molar)

0.180.67

5

64

Table 10. Selected Data for Regression for the NH3H2O System T, K data type

P, MPa

data

data

σ

XNH3 ARD, %

σ

data

YNH3 ARD,%

data

σ

prop ARD, %

σ

ARD, %

ref

VLE

399

0.374.86

1%

0.31

0.05∼.58

0.01

2.66

0.340.95

0.01

2.38

36

VLE VLE

405 263323

0.294.23 0.02

1% 3%

1.20 0.84

0.11∼.51 0.03∼.32

0.01 0.01

13.89 5.12

0.110.93 0.380.99

0.01 0.01

10.28 0.39

36 28

VLE

250363

0.1

1%

0.21

0.03∼.70

0.01

2.22

0.311

0.01

0.35

33

VLE

305446

1

1%

0.78

0.02∼.81

0.01

2.14

0.141

0.01

2.07

VLE

273

0.002∼.13

5%

2.76

0.05∼.51

0.01

5.15

0.1

25

VLE

283

0.003∼.133

5%

2.19

0.03∼.46

0.01

6.34

0.1

25

VLE

293

0.004∼.138

5%

1.86

0.02∼.39

0.01

8.00

0.1

25

VLE

303

0.006∼.1

5%

1.55

0.01∼.30

0.01

8.56

0.1

25

VLE VLE

313 323

0.01∼.1 0.02∼.122

5% 5%

1.89 1.28

0.03∼.24 0.03∼.21

0.01 0.01

8.54 8.07

0.1 0.1

25 25

VLE

333

0.02∼.13

5%

0.84

0.01∼.17

0.01

11.04

0.1

heat of solution

298

0.1

0

0.00001∼.50

0.1%

0.0002

1%

1.16

Cp

200288

0.1

0

0.33

0.01

1.12

1%

0.93

47

Cp

298

0.1

0

0.02∼.21

0.01

0.11

3%

0.39

46

0.69 to 8.95 mol/L-solvent. One CO2 loading is studied for each NH3 concentration and the CO2 loading varies from 0.33 to 0.72. Mani et al. 63 performed a 13C NMR study at 293 K for the NH 3CO2H2 O system and reported speciation data as a function of pH for a 2.5 M NH3 solution loaded with increasing CO2. They also reported speciation for solutions with NH3 concentration changing from 0.85 to 10 M with CO2 loading fixed at 0.01 mol. Zhao et al.64 measured speciation in the NH 3 CO2H2 O solution at 298 K with NH3 concentration varying from 0.69 to 2.1 molar. For each NH3 concentration, the CO2 loading is varied from 0.18 to 0.67.

31

25 44

Some of the above speciation studies reported similar results. For example, Lichtfers and Rumpf,19 Mani et al.,63 and Zhao et al.64 all reported increasing relative concentration for HCO3 but decreasing relative concentration for NH2COO as the CO2 loading increases and the temperature and the NH3 concentration are fixed. However, these studies do not agree with each other well in values. Wen and Brooker61 reported much higher concentration for HCO3 and much lower concentration for NH2COO in comparison with the results from the other studies. We choose to use the latest speciation data from Zhao et al.64 in the regression. The other speciation data are used to validate the model. 11412



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Table 11. Selected data for regression for the NH3CO2H2O system T, K data type

data

σ

ARD, %

ref

0.050.12

0.001

2.50

52

data

SLE

293323 T, K

data type

XNH4HCO2

P, MPa

data

data

σ

XNH3 ARD, %

data

σ

XCO2 ARD, %

a

σ

data

prop ARD, %

a

ARD, %

ref

PCO2

373

0.0030.75

10%

0.32

0.060.31

0.01

0.23

0.0040.12

0.01

5.54

34

PNH3

373

0.020.85

10%

1.06

0.060.31

0.01a

1.01

0.0040.12

0.01a

5.54

34

PCO2

353

0.0010.62

10%

2.35

0.100.18

0.001

0.05

0.010.1

0.001

1.21

10

PNH3

353

0.010.2

10%

3.67

0.100.18

0.001

0.08

0.010.1

0.001

0.25

10

PCO2 PNH3

333 333

0.0020.65 0.0010.11

10% 10%

4.89 4.56

0.090.18 0.090.18

0.001 0.001

0.15 0.14

0.0080.13 0.0080.13

0.001 0.001

1.76 0.35

10 10

PCO2

313

0.00010.5

10%

0.17

0.090.19

0.01a

0.46

0.010.13

0.01a

5.20

10

0.090.19

a

0.01

1.52

0.010.13

0.01a

6.46

10

0.023

0.001

1.30

0.0040.015

0

3.34

PNH3

313

0.00020.03

speciation

298

0.1

10% 0

1.54

CO32 HCO3

NH2COO a

σ

64 2.6b 9b 7.5b

11.82

64

19.94

64

17.74

64

Larger standard deviations assigned to reflect larger uncertainties. b Standard deviations reported by Zhao et al.64

Figure 1. Henry’s law constants: (—) NH3 with water, (- - -) CO2 with water.

Tables 10 and 11 summarize the selected data sets used in the regression for the NH3H2O binary system and the NH3 CO2H2O ternary system respectively.

’ DATA REGRESSION As summarized in Table 1, the crystalline solid state Gibbs energy and enthalpy of formation at 298 K for ammonium bicarbonate, the Henry’s law constants for NH3 with water, and the NRTL binary interaction parameters for the pairs between NH3 and water, between water and electrolytes (NH4+, HCO3), (NH4+, CO32), and (NH4+, NH2COO), and between NH3 and (NH4+, NH2COO) are to be identified through regression against experimental data.

Figure 2. Comparison of the experimental Pxy data from Rizvi and Heidemann36 (symbols) for vaporliquid equilibrium of the NH3H2O system and the model calculations (lines): (O and b) 305 K, (Δ and 2) 341 K, (0 and 9) 376 K, (—) 305 K, (- - -) 341 K, ( ) 376 K.

Among these parameters, the Henry’s law constants for NH3 with water and the NRTL binary parameters for the NH3H2O pair are to be determined from data for the NH3H2O binary on VLE, heat capacity, heat of solution, as summarized in Table 10. Also given in Table 10 are the standard deviations, σ, applied to the various data types. The remaining parameters are to be determined from data for the NH3CO2H2O ternary on SLE, VLE, and liquid phase speciation. Table 11 summarizes the experimental ternary system data used to identify the NRTL binary parameters for the pairs between water and electrolytes (NH4+, HCO3), (NH4+, CO32), and (NH4+, NH2COO) and between NH3 and electrolyte (NH4+, NH2COO), and the crystalline solid state Gibbs energy and 11413



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Figure 3. Comparison of the experimental Txy data (symbols) for vaporliquid equilibrium of the NH3H2O system and the model correlations at 0.1 MPa and the model calculations at 1 MPa (lines): (O and b) 0.1 MPa from Hoshino et al.,33 (Δ and 2) 1 MPa from Chu et al.,30 (—) 0.1 MPa, ( ) 1 MPa.

Figure 4. Comparison of the experimental data from Wagman et al.44 (O) for heat of solution of NH3 in water at 298 K and the model correlations (—).

enthalpy of formation for ammonium bicarbonate at 298 K. The standard deviations, σ, applied to the data are also given in Table 11. A measure for fitting quality is residual root-mean-square error, RRMSE, defined in eq 33 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u u k m Z ZM 2 ij ij u u σij ti ¼ 1 j ¼ 1

∑∑

Figure 5. Comparison of the experimental data from Rumpf et al.45 (symbols) for heat of dilution of NH3 in water on enthalpy change when 26 g aqueous NH3 solutions at various initial NH3 concentration are diluted with 16 g water and the model calculations (lines): (O) 313 K, (Δ) 333 K, (0) 353 K, () 373 K, (—) 313 K, (— —) 333 K, (- - -) 353 K, ( 3 3 3 ) 373 K.

Figure 6. Comparison of the experimental data from Trypuc and Kielkowska52 (O) for solubility of NH4HCO3 in water and the model correlations (—).

Furthermore, average relative deviations (ARDs) between the experimental data and the model results are also calculated n EST EXP i i 100% EXPi i¼1 ð34Þ ARD, % ¼ n

∑

ð33Þ

where ESTi is the estimated value for data point i, EXPi is the experimental value of data point i, and n is the number of data points.

where ZM is the measured experimental value; Z is the calculated value; σ is the standard deviation; i is the data point number; k is the total number of data points; j is the measured variable for a data point (such as temperature, pressure, or mole fraction); m is the number of measured variables for a data point and n is the total number of adjustable parameters.

’ RESULTS AND DISCUSSION Simultaneous data regression of all the data listed in Table 10 for the NH3H2O binary system yields RRMSE of 1.50. The resulting parameters are summarized in Tables 5 and 6. The ARDs of this data regression are summarized in Table 10.

RRMSE ¼

kn

11414



Figure 7. Comparison of the experimental data from Chernen’kaya46 (symbols) for heat capacity of aqueous NH4HCO3 solution and the model calculations (lines): (O) 298 K, (—) 298 K, ( ) 323 K, (- 3 -) 348 K, (- - -) 373 K, ( 3 3 3 )393 K, (- 3 3 -) 423 K.

Figure 8. Comparison of the experimental data from Qin et al.53 (O) for differential heat of solution for CO2 in 2.5 wt % aqueous NH3 solution at 313 K and the model calculations (—).

Figure 1 shows the Henry’s law constant for NH3 with water as function of temperature. The Henry’s law constant for CO2 with water is also included for comparison purposes. Figure 2 shows the calculation results against the experimental isothermal VLE data of Rizvi and Heidemann36 at 305, 341, and 376 K. Figure 3 shows the correlation results against the isobaric VLE data of Hoshino et al.33 at 0.1 MPa and the model calculations at 1 MPa against the VLE data of Chu et al.30 The model correlation results match within 1% the experimental data of Chernen’kaya46 for heat capacity of aqueous NH3 solution at 298 K and the experimental data of Chan and Giauque47 for heat capacity of 32 wt % aqueous NH3 solution from 200 to 300 K. The model correlations for heat of solution data at 298 K and the experimental data of Wagman et al.44 are shown in Figure 4. The model calculations for heat of dilution of aqueous NH3 solutions are also checked and compared well with the data of Rumpf et al.,45 as shown in Figure 5. Overall the model satisfactorily represents the thermodynamic properties for the NH3H2O binary system

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with temperature from 250 to 450 K, pressure up to 5 MPa and NH3 mole fraction up to unity. Simultaneous data regression of all the experimental data listed in Table 11 for the NH3CO2H2O system results in RRMSE of 0.82. The identified model parameters are summarized in Tables 2 and 6. The ARDs of this data regression are also given in Table 11. Figure 6 shows the excellent match between the model correlations and the experimental data of Trypuc and Kielkowska52 on NH4HCO3(s) solubility in water. Figure 7 shows the comparison between the model calculations and the experimental data of Chernen’kaya46 on heat capacity of aqueous NH4HCO3 solution. Figures 810 show the model calculations for differential heat of solution for CO2 in 2.5 wt % aqueous NH3 solution at 313, 333, and 353 K, respectively, in comparison to the data of Qin et al.53 The model results indicate the heat of solution for CO2 does not change significantly with temperature. The relatively large discrepancies between the model calculations and the data at higher temperatures suggest the difficulties in getting reliable experimental data for the heat of solution especially at high temperatures. Figure 11 shows the parity plot 11415



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Figure 11. Parity plot for the model calculations for enthalpy change on partial vaporization of the NH3CO2H2O system and data from Rumpf et al.11 at temperatures between 313 and 393 K, NH3 concentrations up to 12 m and CO2 concentrations up to 6 m.

Figure 13. Comparison of the experimental data of Kurz et al.10 (symbols) for NH3 partial pressure of the NH3CO2H2O system at 313 K and the model results (lines): (O) 11.8 m NH3, (Δ) 6.3 m NH3, (—) 11.8 m NH3, (- - -) 6.3 m NH3. Filled symbols and bold lines stand for precipitations of solid NH4HCO3.

Table 12. Validation Results for VLE of the NH3CO2H2O System (Data Points with pi < 0.05 MPa Omitted) ref

T, K

mNH3

6

373

3.12, 9.57

8

333

0.7211.79

ΔpCO2, %

ΔpNH3, %

1.345.44

43.26

23.57

0.101.82

22.47

mCO2

8

353

0.5912.17

0.0111.39

13.55

7.78

8

373

0.9514.31

0.0510.42

8.82

12.39

8 34

393 393

0.6911.96 2.8325.88

0.047.41 0.2212.69

9.74 11.84

22.61 11.34

34

413

2.5025.24

0.2211.59

21.39

30.84

34

433

2.7224.62

0.259.76

27.40

19.15

34

453

2.5212.68

0.193.80

33.95

16.74

34

473

2.4110.73

0.262.09

37.84

13.01

Figure 14. Comparison of the experimental data of G€oppert and Maurer8 (empty symbols) and Kurz et al.10 (filled symbols) for CO2 partial pressure of the NH3CO2H2O system at 353 K and the model results (lines): (O) 12.17 m NH3, (b) 11.8 m NH3, (Δ) 9.03 m NH3, (0) 5.93 m NH3, () 2.01 m NH3, ()) 0.6 m NH3, (—) 12.17 m NH3, ( ) 9.03 m NH3, (- 3 -) 5.93 m NH3, () 2.01 m NH3, ( 3 3 3 ) 0.6 m NH3.

Figure 12. Comparison of the experimental data of Kurz et al.10 (symbols) for CO2 partial pressure of the NH3CO2H2O system at 313 K and the model results (lines): (O) 11.8 m NH3, (Δ) 6.3 m NH3, (—) 11.8 m NH3, (- - -) 6.3 m NH3. Filled symbols and bold lines stand for precipitations of solid NH4HCO3.

for the model calculations and the data of Rumpf et al.11 for enthalpy change on partial vaporization of the NH3CO2H2O ternary. Excellent match is achieved. To further validate the model, we calculate the differential CO2 heat of solution in 8 wt % aqueous NH3 solution at 100 °F for CO2 loadings of 0.1 to 0.7. Here the differential heat of solution is reported in terms of Btu/ lb so that it is directly comparable to the earlier study of Mathias et al.2 Our model calculates the heat of solution to be ∼740 Btu/ lb at CO2 loading of 0.1 which drops to ∼440 Btu/lb at CO2 loading of 0.7. In contrast, Mathias et al.2 reported ∼700 Btu/lb at CO2 loading of 0.1 and ∼600 Btu/lb at CO2 loading of 0.7. The model generates satisfactory VLE results for temperature up to 473 K. Table 11 presents the quality of fit to the VLE data in terms of average relative deviations (ARDs). The ARDs are less than 5% for both CO2 partial pressure and NH3 partial pressure, 11416



Figure 15. Comparison of the experimental data of G€ oppert and Maurer8 (empty symbols) and Kurz et al.10 (filled symbols) for NH3 partial pressure of the NH3CO2H2O system at 353 K and the model results (lines): (O) 12.17 m NH3, (b) 11.8 m NH3, (Δ) 9.03 m NH3, (0) 5.93 m NH3, (—) 11.8 m NH3, ( ) 9.03 m NH3, (- 3 -) 5.93 m NH3.

Figure 16. Comparison of the experimental data of G€oppert and Maurer8 (empty symbols) and M€uller et al.34 (filled symbols) for CO2 partial pressure of the NH3CO2H2O system at 393 K and the model calculations (lines): (b) 25.7 m NH3, (2) 20.4 m NH3, (0) 11.8 m NH3, (9) 8.1 m NH3, ()) 3.8 m NH3, (+) 0.7 m NH3, (—) 25.7 m NH3, ( ) 20.4 m NH3, (- 3 -) 11.8 m NH3, (- - -) 8.1 m NH3, ( 3 3 3 ) 3.8 m NH3, (- 3 3 -) 0.7 m NH3.

typically less than 1.5% for NH3 concentration, and less than 6.5% for CO2 concentration, indicative of satisfactory fit to the data. In addition, Table 12 summarizes the ARDs of the model calculations for the VLE data of Pawilkowski et al.,6 G€oppert and Maurer,8 and M€uller et al.34 that are not included in the regression. Considering the large uncertainties in low pressure measurements, we follow the treatment of Kurz et al.10 and report in Table 12 the statistics only for data points with the partial pressures greater than 0.05 MPa. ARDs for the data from G€oppert and Maurer8 at 333, 353, 373, and 393 K are 822% for both CO2 partial pressure and NH3 partial pressure. ARDs for the data from M€uller et al.34 at 393, 413, 433, 453, and 473 K vary from 11 to 38% for CO2 partial pressure and from 11 to 31% for NH3 partial pressure. Interestingly, ARDs for the partial pressure

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Figure 17. Comparison of the experimental data of G€oppert and Maurer8 (empty symbols) and M€uller et al.34 (filled symbols) for NH3 partial pressure of the NH3CO2H2O system at 393 K and the model calculations (lines): (b) 25.7 m NH3, (2) 20.4 m NH3, (0) 11.8 m NH3, ()) 3.8 m NH3, (+) 0.7 m NH3, (—) 25.7 m NH3, ( ) 20.4 m NH3, (- 3 -) 11.8 m NH3, ( 3 3 3 ) 3.8 m NH3, (- 3 3 -) 0.7 m NH3.

Figure 18. Comparison of the experimental data from M€uller et al.34 (symbols) for CO2 partial pressure of the NH3CO2H2O system at 433 K and the model calculations (lines): (O) 24.6 m NH3, (Δ) 18 m NH3, (0) 12.6 m NH3, () 7.6 m NH3, ()) for 2.7 m NH3, (—) 24.6 m NH3, ( ) 18 m NH3, (- 3 -) 12.6 m NH3, (- - -) 7.6 m NH3, ( 3 3 3 ) 2.7 m NH3.

data from Pawilkowski et al.6 at 373 K are much higher, 43% for CO2 partial pressure and 24% for NH3 partial pressure. We suspect the 373 K data from Pawilkowski et al.6 are slightly inconsistent with the 373 K data from G€oppert and Maurer,10 for which the ARDs are merely 9% and 12%, respectively, for CO2 partial pressure and NH3 partial pressure. Figures 1219 show the VLE results at temperatures 313, 353, 393, and 433 K, in terms of CO2 partial pressure and NH3 partial pressure versus CO2 loading for a number of aqueous NH3 solutions. Figures 12 and 13 compare the model results for CO2 partial pressure and NH3 partial pressure, respectively, with the experimental data from Kurz et al.10 for the NH3 CO2H2O system at 313 K and NH3 concentrations at 6 and 12 m. Note that the data show abrupt changes in the partial pressures when solid NH4HCO3 is formed. The model achieves 11417



Figure 19. Comparison of the experimental data from M€uller et al.34 (symbols) for NH3 partial pressure of the NH3CO2H2O system at 433 K and the model calculations (lines): (O) 24.6 m NH3, (Δ) 18 m NH3, (0) 12.6 m NH3, () 7.6 m NH3, ()) 2.7 m NH3, (—) 24.6 m NH3, ( ) 18 m NH3, (- 3 -) 12.6 m NH3, (- - -) 7.6 m NH3, ( 3 3 3 ) 2.7 m NH3.

Figure 20. Comparison of the experimental data from Lichtfers and Rumpf19 (symbols) for liquid phase speciation of the NH3CO2H2O system with 4.44 m NH3 at 333 K and the model calculations (lines): (O) NH3, (Δ) NH4+, (0) HCO3, () NH2COO, ()) CO32, (+) CO2, (—)NH3, ( ) NH4+, (- 3 -) HCO3, (- - -) NH2COO, ( 3 3 3 ) CO32, (- 3 3 -) CO2.

satisfactory match to the data of Kurz et al.10 not only for the partial pressures but also for solid precipitation even though the vaporliquidsolid phase equilibrium data are excluded from the regression. Figures 14 and 15 show the comparisons of the model results on CO2 partial pressure and NH3 partial pressure, respectively, with the experimental data from G€oppert and Maurer8 and from Kurz et al.10 for the NH3CO2H2O system at 353 K with the NH3 concentration ranging from 0.6 to 12.17 m. Even though the data from G€oppert and Maurer8 are not included in the regression, good agreement is achieved between the model results and the experimental data from G€oppert and Maurer.8 Figures 16 and 17 show the comparisons of the model calculations on CO2 partial pressure and NH3 partial pressure, respectively, with the experimental data from G€oppert and Maurer8 and M€uller et al.34 for the NH3CO2H2O

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Figure 21. Parity plot for carbon distribution in liquid phase for the NH3CO2H2O system at 298 K and NH3 concentration from 0.69 mol/L-solvent to 8.95 mol/L-solvent and CO2 concentration from 0.24 mol/L-solvent to 4.27 mol/L-solvent, the experimental data from Holmes II et al.:62 (O) HCO3, (Δ) NH2COO, (0) CO32.

Figure 22. Comparison of the experimental data from Mani et al.63 (symbols) for liquid phase speciation of the NH3CO2H2O system at 293 K and NH3 concentration from 0.8 to 10 M and the model calculations (lines): (O) HCO3, (Δ) NH2COO, (0) CO32, (—) HCO3, ( ) NH2COO, (- 3 -) CO32.

system at 393 K with NH3 concentration ranging from 0.7 to 25.7 m. Satisfactory agreement is achieved between the model results and the experimental data for CO2 partial pressure. The model results for NH3 partial pressure are less satisfactory but still considered acceptable. Figures 18 and 19 compare the model calculations for CO2 partial pressure and NH3 partial pressure, respectively, with the experimental data from M€uller et al.34 for the NH3CO2H2O system at 433 K and NH3 concentration from 2.7 to 24.6 m. Acceptable agreement is achieved for both CO2 partial pressure and NH3 partial pressure. The model results for liquid phase speciation of the NH3 CO2H2O system generally match the experimental data19,6164 well, except for those of Wen and Brooker.61 Figure 20 shows the comparison of the experimental data from Lichtfers and Rumpf19 and the model calculations at 333 K with 4.44 m NH3 solution. Absolute concentrations of various true species, that is, NH3, 11418



Figure 23. Comparison of the experimental data from Zhao et al.64 (symbols) for carbon distribution in liquid phase in the NH3 CO2H2O system at 298 K and 1.34 molar NH3 and the model correlations (lines): (O) HCO3, (Δ) NH2COO, (0) CO32, (—) HCO3, ( ) NH2COO, (- 3 -) CO32.

Figure 24. Comparison of the experimental data from Wen and Brooker61 (symbols) for liquid phase speciation of the (NH4)2CO3H2O system at 295 K and the model calculations (lines): (O) HCO3, (Δ) NH2COO, (0) CO32, (—) HCO3, ( ) NH2COO, (- 3 -) CO32.

NH4+, HCO3, NH2COO, CO32, and CO2, are generated and plotted versus CO2 loading. The model calculations show excellent matches with the data both in values and in trends. Figure 21 is a parity plot showing the comparison between the model calculations and the data of Holmes II et al.62 for liquid phase speciation of the NH3CO2H2O system at 298 K, NH3 concentrations from 0.69 to 8.95 mol/L-solvent and CO2 concentrations from 0.24 to 4.27 mol/L-solvent. The data were reported in terms of carbon distribution, which is the percentage of a carbon-containing ion over the total carbon in the liquid phase. The model yields reasonable calculations for the carbon distribution in terms of HCO3, NH2COO, and CO32 ions. Figure 22 shows the comparison of the experimental data from Mani et al.63 and the model calculations for the NH3CO2H2O system at 293 K with NH3 concentrations in the range of 0.8 to 10 M. The model calculations exhibit trends consistent with the data of Mani et al.,63

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Figure 25. Comparison of the experimental data from Wen and Brooker 61 (symbols) for liquid phase speciation of a 2.9 m (NH4)2CO3H2O solution and the model calculations (lines): (O) HCO3, (Δ) NH2COO, (0) CO32, (—) HCO3, ( ) NH2COO, (- 3 -) CO32.

Figure 26. Chemical equilibrium constants for reactions 16: (- - -) Edwards et al.4 for reactions 14 and Lichtfers and Rumpf19 for reaction 5, (—) model calculations. Mole fraction based Q chemical equilibrium constants are shown here, which are defined as: K = i (xiγi)vi, where xi is the mole fraction of component i; γi is the activity coefficient of component i; and vi is the stoichiometric number for component i in the reaction.

also in terms of carbon distribution. Figure 23 shows the comparison of the experimental data from Zhao et al.,64 also in terms of carbon distribution, and the model correlations for the NH3CO2H2O system at 298 K and 1.34 molar NH3. The model generally reproduces the reported concentration trends versus CO2 loading. Figures 24 and 25 show the comparisons of the experimental data from Wen and Brooker61 and the model calculations for the (NH4)2CO3H2O binary system at 295 K for different (NH4)2CO3 concentrations and at 2.9 m (NH4)2CO3 for different temperatures, respectively. These two figures show the model calculations for the CO32 concentration match the data of Wen and Brooker61 well. However, the model calculates much higher concentrations for NH2COO and much lower 11419


Industrial & Engineering Chemistry Research concentrations for HCO3. Given that the model calculations seem consistent with all the other speciation data shown above, we suspect the data of Wen and Brooker61 may be less reliable. Figure 26 shows an excellent match between the chemical equilibrium constants as calculated from the reference state Gibbs energies and those of Edwards et al.4 for reactions 14 and those of Lichtfers and Rumpf19 for reaction 5. The chemical equilibrium constants for Reaction 6 are also shown in this figure. The crystalline solid state Gibbs energy of formation and enthalpy of formation at 298 K for NH4HCO3(s) are 665.67 kJ/mol and 844.86 kJ/mol, respectively, as determined in this work through data regression. In contrast, the values reported by Wagman et al.44 are 665.9 and 849.4 kJ/mol, respectively.

’ CONCLUSION The electrolyte NRTL activity coefficient model has been successfully applied to model the thermodynamic properties of the NH3CO2H2O system. Necessary experimental data on vaporliquid equilibrium, solidliquid equilibrium, heat capacity, heat of dilution, and speciation have been regressed to identify the model parameters and additional experimental data have been used to validate the model results. The model enables efficient and reliable calculations of all thermodynamic properties of interest to process simulation, that is, VLE, VLSE, speciation, and calorimetric properties with temperature up to 473 K, pressure up to 7 MPa, NH3 concentration up to 30 wt % (25 m) and CO2 loading up to unity. The electrolyte NRTL model for the NH3CO2H2O system should provide a sound thermodynamic foundation for modeling and simulation of chilled ammonia processes. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Phone: 781-221-6420. Fax: 781-221-6410.

’ ACKNOWLEDGMENT The authors are grateful to our colleagues Yuhua Song and Joe DeVincentis for their careful reviews of the manuscript. ’ REFERENCES (1) Gal, E. Ultra cleaning of combustion gas including the removal of CO2. World Intellectual Property, Patent WO 2006022885. 2006 (2) Mathias, P. M.; Reddy, S.; O’Connell, J. P. Quantitative evaluation of the chilled-ammonia process for CO2 capture using thermodynamic analysis and process simulation. Int. J. Greenhouse Gas Control 2010, 4, 174–179. (3) Darde, V.; Thomsen, K.; van Well, W. J. M.; Stenby, E. H. Chilled ammonia process for CO2 capture. Energy Procedia 2009, 1, 1035–1042. (4) Edwards, T. J.; Maurer, G.; Newman, J.; Prausnitz, J. M. Vapor liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. AIChE J. 1978, 24, 966–976. (5) Chen, C.-C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Extension and application of the Pitzer equation for vaporliquid equilibrium of aqueous electrolyte systems with molecular solutes. AIChE J. 1979, 25, 820–831. (6) Pawilkowski, E. M.; Newman, J.; Prausnitz, J. M. Phase equilibria for aqueous solutions of ammonia and carbon dioxide. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 764–770.

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Thermodynamic Modeling of the NH - American Chemical Society

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