Thermodynamic Modeling of CaSO4-(NH4)2SO4-NH3-H2O

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Thermodynamics, Transport, and Fluid Mechanics

Thermodynamic Modeling of CaSO4-(NH4)2SO4-NH3H2O Quaternary System with Asymmetric E-NRTL model Teng Pan, Yan Liu, Wei Qin, Youwei Cheng, Lijun Wang, and Xi Li Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 25 Mar 2019 Downloaded from http://pubs.acs.org on March 31, 2019

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Industrial & Engineering Chemistry Research

Thermodynamic Modeling of CaSO4-(NH4)2SO4-NH3H2O Quaternary System with Asymmetric E-NRTL model Teng Pan, Yan Liu, Wei Qin, Youwei Cheng, Lijun Wang and Xi Li

Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, P. R. China

ABSTRACT: Ammonium sulfate [(NH4)2SO4], an undesired by-product in caprolactam process, can be converted into recyclable NH3 by the substitution reaction with lime milk to reduce the ammonia consumption and produce high quality gypsum. However, the thermodynamic mechanism of this process has not been clarified, which results in the unpredictable crystal phase of calcium sulphate products. In this work, a thermodynamic



Corresponding author. E-mail: [email protected].

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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model for the CaSO4-(NH4)2SO4-NH3-H2O quaternary system with the asymmetric E-NRTL activity coefficient model was developed to understand the thermodynamic behavior. The modeling works involved the data fitting of binary solubility, osmotic coefficient, enthalpy of solution and heat capacity data, as well as ternary solubility data. It was shown that the model could predict the solubility of ammonia and calcium sulfate in aqueous ammonium sulfate solution with temperature range from 0 to 160 ℃ and pressure up to 1.0 MPa. Furthermore, the constructed model for the quaternary system was proved to be reliable for predicting the phase transition behavior of solid CaSO4 in the electrolyte mixtures of (NH4)2SO4-NH3-H2O solution. For the regeneration process of NH3 from ammonium sulfate, this work will offer a reliable model for the reactors design and process optimization.

1. INTRODUCTION Ammonium sulfate [(NH4)2SO4] has finite application and is usually used as an inferior fertilizer that can lead to soil acidification, which seriously limits its market and demand. However, large amounts of (NH4)2SO4 is produced in the typical caprolactam process, and one ton of caprolactam product will release 1.5-2.0 tons of ammonium sulfate as an undesirable by-product.1 Additionally, the production and demand of caprolactam is


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increasing rapidly every year, resulting in the overproduction of ammonium sulfate.2 Therefore, several new caprolactam technologies with less or non-(NH4)2SO4 by-product had been investigated and brought forward,3 such as vapor-phase Beckmann rearrangement over solid catalysts4-6, and the liquid-phase Beckmann rearrangement over solid7-9 or organic catalysts.10-12 Unfortunately, very few industrial applications have been reported about these technologies, due to the practical problems including serious catalyst deactivation, poor catalytic efficiency, low selectivity, etc. A different solution recycling NH3 from ammonium sulfate had been proposed to eliminate the overcapacity of ammonium sulfate, as shown in Figure 1.13 OH O

N NH2OH

O H2SO4

H N

+ (NH4)2SO4

NH3

CaSO4

Ca(OH)2

Figure 1. Ammonia cycle process route diagram for caprolactam production process.

In the caprolactam production process, ammonia is recovered from ammonium sulphate solution by adding lime milk (hydrated calcium oxide), and the recycled NH3 can be reused to neutralize the excess sulfuric acid. NH3 is liberated by the reaction of the ammonium ion



Page 4 of 45

with the hydroxide ions in the lime milk, and could be separated from the slurry by hot steam. While the insoluble gypsum can be converted into high quality gypsum by crystallization separation. In aqueous solution containing ammonium sulfate and ammonia, there exist six possible solid gypsum phases (Table 1), and the crystallization behaviors of gypsum are very complicated. Among these gypsum crystals, the mixed sulfate double salts (mono-calcium, di-calcium and penta-calcium) are undesirable, as the ammonia nitrogen is fixed at solid phase, reducing the ammonia recovery. In the remaining calcium sulfate hydrates (dihydrate, hemihydrate and anhydrite), hemihydrate is the most valuable product for its gel properties, and can be widely used in the construction industry. Therefore, hemihydrate is the high quality gypsum by-product in the investigated crystallization process, and it is necessary to gain the solubility information and phase transition behavior of gypsum in the system consisting of calcium sulfate, ammonium sulfate, ammonia and water (CaSO4(NH4)2SO4-NH3-H2O). Then a thermodynamic model should be constructed to describe this mixed electrolyte solution system, which will offer the reliable data and model for the design and optimization of the process.


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Table 1. Names and Chemical Formulas of Calcium Sulfate

name

formula

dihydrate

CaSO4·2H2O

hemihydrate

CaSO4·1/2H2O

anhydrite

CaSO4

mono-calcium salt

CaSO4·(NH4)2SO4·H2O

di-calcium salt

2CaSO4·(NH4)2SO4

penta-calcium salt

5CaSO4·(NH4)2SO4

The previous modeling works about the solubility of calcium sulfate have been mostly carried out in other electrolyte solutions. Li and his coworkers successfully used their OLIbased chemical model to investigate the phase-transition diagrams of calcium sulfate in the HCl-CaCl2-H2O system at a temperature of 0 to 100 ℃.13 Based on non-random two liquid (NRTL) formulas, Barba et al. developed a thermodynamic model to calculate the dihydrate solubility in Na2SO4-MgCl2-H2O system.15,

16

Yuan and Wang using Pitzer’s model to

evaluate the dihydrate solubility in multi-component alkali solutions on the basis of experimental solubility values at 25-75 ℃.17 Pitzer’s framework was also used by Christov and Moller who proposed a thermodynamic model to calculate the solubility of calcium sulfate hydrates and its double salt in aqueous solution of Na2SO4 about H-Na-K-Ca-OH-Cl-



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HSO4-SO4-H2O system.18 Azimi et al. used the mixed solvent electrolyte activity coefficient model to calculate the solubility of CaSO4 and its scaling potential in sulfate systems.19 The solubility of dihydrate and anhydrite in (NH4)2SO4 aqueous solution was determined, but the double salts were not considered in their research. In conclusion, there is no comprehensive study on the solubility of calcium sulfate hydrates and its double salts in (NH4)2SO4 aqueous solution or more complicated electrolyte solution so far. In this work, the asymmetric E-NRTL model20-22 was used to investigate the thermodynamic behavior of CaSO4-(NH4)2SO4-NH3-H2O quaternary system on Aspen Plus platform. Compared with Pitzer model23,

24

and extended UNIQUAC model,25,

26

the

asymmetric E-NRTL model is more suitable for the process modeling and optimization as it requires only binary interaction parameters and makes use of mole fraction concentration scale consistently for each item in the equation.25, 26 Model parameters are regressed and validated by the available thermodynamic experimental data in the literature including solubility, osmotic coefficient, enthalpy of solution and heat capacity. The model will be helpful for the reactors design and process optimization of the NH3 regeneration from


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ammonium sulfate, and that is an important contribution to the new caprolactam technologies with non-(NH4)2SO4 by-product. 2. THERMODYNAMIC MODELING 2.1. Activity Coefficient Model. The asymmetric E-NRTL activity coefficient model,28 which is based on the two parts of the long-range and short-range terms, uses the asymmetric reference state for ions and molecular solutes (infinite dilution in aqueous solution). The Pitzer-Debye-Hückel (PDH) formula is adopted for the electrostatic interaction forces as long-range term, and the electrolyte NRTL expression is used to describe the local interactions that exist at the immediate neighborhood of any species. The E-NRTL asymmetric coefficient of electrolyte specie is given by29: (1)

∗ ∗ + 𝑙𝑛𝛾𝑖,𝐿𝑅 𝑙𝑛𝛾𝑖∗ = 𝑙𝑛𝛾𝑖,𝑆𝑅

where the subscripts SR and LR stand for the short-range and the long-range interactions, respectively. The long-range contribution of the activity coefficient is used as the electrostatic theory of the PDH23: ∗ = ― 𝐴𝜑 𝑙𝑛𝛾𝑖,𝐿𝑅

1000 0.5 2𝑧2𝑖 𝜌 𝑙𝑛 𝑀𝑤

( ) (

(1 + 𝜌𝐼1/2 𝑥 )+

)

3/2 𝑧2𝑖 𝐼1/2 𝑥 ― 2𝐼𝑥

1 + 𝜌𝐼1/2 𝑥

with


(2)


1

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(3)

𝐼𝑥 = 2∑𝑖𝑧2𝑖 𝑥𝑖

where Aφ is the Debye-Hückel parameter, Ix is the mole fraction ionic strength, ρ is the closest approach parameter, Mw is the molecular weight. For ionic components with infinite dilution aqueous as reference state, the asymmetric activity coefficients is given as: (4)

∞ ∗ = 𝑙𝑛𝛾𝑖,𝑆𝑅 ― ∑𝑐𝑥𝑐𝑙𝑛𝛾∞ 𝑙𝑛𝛾𝑖,𝑆𝑅 𝑐 ― ∑𝑎𝑥𝑎𝑙𝑛𝛾𝑎

where subscript a and c indicate cation and anion, respectively. The superscript “∞” denotes infinity dilution reference state. For multicomponent electrolyte solution, the symmetric activity coefficient expressions for cation, anion and molecular, respectively, are written as28: 1 𝑆𝑅 𝑍𝑐𝑙𝑛𝛾𝑐

+

𝑖 𝑖 𝑖𝑚

∑𝑖 ≠ 𝑐𝑋𝑖𝐺𝑖𝑐𝜏𝑖𝑐 ∑𝑖 ≠ 𝑐𝑋𝑖𝐺𝑖𝑐

1 𝑆𝑅 𝑍𝑎𝑙𝑛𝛾𝑎

+

𝑋𝑚𝐺𝑐𝑚

= ∑ 𝑚∑ 𝑋 𝐺

+ ∑ 𝑎∑

(

𝑙𝑛𝛾𝑆𝑅 𝑚 =

𝑖 𝑖 𝑖𝑚

+ ∑ 𝑐∑

∑𝑖𝑋𝑖𝐺𝑖𝑚𝜏𝑖𝑚 ∑𝑖𝑋𝑖𝐺𝑖𝑚

𝜏𝑐𝑎 ―

𝑋𝐺 𝑖 ≠ 𝑎 𝑖 𝑖𝑎

𝑋𝑚𝐺𝑎𝑚

∑𝑖 ≠ 𝑎𝑋𝑖𝐺𝑖𝑎

∑𝑖𝑋𝑖𝐺𝑖𝑚

(

𝑋𝑎𝐺𝑐𝑎

= ∑ 𝑚∑ 𝑋 𝐺

∑𝑖 ≠ 𝑎𝑋𝑖𝐺𝑖𝑎𝜏𝑖𝑎

∑𝑖𝑋𝑖𝐺𝑖𝑚𝜏𝑖𝑚

𝜏𝑐𝑚 ―

(

(

𝑋𝐺 𝑖 ≠ 𝑐 𝑖 𝑖𝑐

𝑋𝑚′𝐺𝑚𝑚′

+ ∑ 𝑚′ ∑ 𝑋 𝐺

𝑖 𝑖 𝑖𝑚′

(

(5)

)

(6)

∑𝑖 ≠ 𝑎𝑋𝑖𝐺𝑖𝑎

∑𝑖𝑋𝑖𝐺𝑖𝑚

𝜏𝑎𝑐 ―

)

∑𝑖 ≠ 𝑎𝑋𝑖𝐺𝑖𝑎𝜏𝑖𝑎

∑𝑖𝑋𝑖𝐺𝑖𝑚𝜏𝑖𝑚

𝜏𝑎𝑚 ―

𝑋𝑐𝐺𝑎𝑐

)

)


𝜏𝑚𝑚′ ―

∑𝑖𝑋𝑖𝐺𝑖𝑚′𝜏𝑖𝑚′ ∑𝑖𝑋𝑖𝐺𝑖𝑚′

)


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+ ∑ 𝑐∑

𝑋𝑐𝐺𝑚𝑐

(

𝑋𝐺 𝑖 ≠ 𝑐 𝑖 𝑖𝑐

+ ∑ 𝑎∑

𝑋𝑎𝐺𝑚𝑎

𝜏𝑚𝑐 ―

(

𝑋𝐺 𝑖 ≠ 𝑐 𝑖 𝑖𝑎

𝜏𝑚𝑎 ―

)


∑𝑖 ≠ 𝑎𝑋𝑖𝐺𝑖𝑎𝜏𝑖𝑎 ∑𝑖 ≠ 𝑎𝑋𝑖𝐺𝑖𝑎

)

(7)

with 𝑛𝑖

(8)

𝑋𝑖 = 𝐶𝑖𝑥𝑖 = 𝐶𝑖 𝑛 , 𝑖 = 𝑚, 𝑐, 𝑎

where x is local mole fraction, G and τ are local binary quantities related to each other by the NRTL non-random factor parameter α: (9)

𝐺 = 𝑒𝑥𝑝( ―𝛼𝜏) The parameters τij are written versus temperature as: 𝜏𝑖𝑗 = 𝜏1,𝑖𝑗 +

𝜏2,𝑖𝑗 𝑇

+ 𝜏3,𝑖𝑗

(

𝑇0 ― 𝑇 𝑇

𝑇0

+ 𝑙𝑛 𝑇

)

(10)

where τ1,ij, τ2,ij and τ3,ij are the coefficients of the adjustable parameters and T0 = 298.15K. These coefficients of adjustable parameters are determined in regression procedures from various types of thermodynamic data. 2.2. Phase Equilibrium. In the current electrolyte system, there are two types of phase equilibrium. The first type is solid-liquid equilibrium (SLE) between an aqueous solution and a hydrated salt with x water molecules, vc cations and va anions, which is described by the precipitation/dissolution reaction:



𝑀𝑣𝑐𝑋𝑣𝑎 ∙ 𝑥𝐻2𝑂 = 𝑣𝑐𝑀𝑧𝑐 + 𝑣𝑎𝑀𝑧𝑎 +𝑥𝐻2𝑂

Page 10 of 45

(11)

The equilibrium constant of this reaction is determined from the Gibbs free energy relation:

(

𝐾 = 𝑒𝑥𝑝 ―

∆𝐺0𝑟 𝑅𝑇

)

(

= 𝑒𝑥𝑝 ―

∑𝑣𝑖𝜇0𝑖 𝑅𝑇

)

(12)

Nevertheless, the equilibrium constant for the solid-liquid equilibrium evaluated from the standard chemical potential μ0 of individual species is not always accurate or available. Thus, the equilibrium constant in this work is regressed from experimental data, and expressed as a function of temperature: 𝐵

(13)

𝑙𝑛𝐾(𝑇) = 𝐴 + 𝑇 +𝐶 ∗ 𝑙𝑛𝑇 + 𝐷 ∗ 𝑇

where A-D are the equilibrium constant correlation parameters, determined in regression procedures from various types of electrolyte data. It is noted that the equilibrium constants used in this work are in mole fraction scale. The second type is vapor-liquid equilibrium (VLE), for which the solvent water is treated using Raoult’s law, while NH3 are described using Henry’s law: 𝑦𝑖𝜑𝑖𝑃 = 𝑥𝑖𝛾𝑖𝑓0𝑖 , 𝑖 = 𝐻2𝑂

(14)

∗ 𝑦𝑗𝜑𝑗𝑃 = 𝑥𝑗𝛾𝑗,𝑤 𝐻𝑗,𝑤, 𝑗 = 𝑁𝐻3

(15)


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where y is the vapor phase mole fraction, φ is the vapor phase fugacity coefficient, x is the liquid phase mole fraction, γ is the liquid phase activity coefficient, fi0 is the fugacity of pure liquid component i. Hj,w is the Henry’s law constant for component j with water, calculated as follows: 𝑃

𝐵 𝑇

2

𝑙𝑛𝐻𝑖,𝑤(𝑇) = 𝐴 + +𝐶 ∗ 𝑙𝑛𝑇 + 𝐷 ∗ 𝑇 + 𝐸 ∗ 𝑇 +

∫ 𝑃0 𝑉 ∞ 𝑖,𝑤𝑑𝑃 𝑤

𝑅𝑇

(16)

where A-E are the Henry’s law constant correlation parameters and Vi,w ∞ is the infinite dilution partial molar volume of molecular solute i in water, this constant existing in the databank of Aspen Plus was directly used. 2.3. Other Thermodynamic Relations. In addition to using SLE and VLE data, the asymmetric E-NRTL activity coefficient model parameters are identified by fitting against other experimental data for osmotic coefficient, heat capacity and heat of solution. These relations are listed as follows: 𝑙𝑛𝑎𝑤

𝜑(𝑚) = ―55.50844 ∑𝑚

(17)

𝑖

where φ is the osmotic coefficient. The superscript (m) denotes the molality scale which can be converted to the mole fraction scale by the following relation: 𝑥 𝑖 = (∑ 𝑣 𝑚 𝑗 𝑗

𝑚𝑖 𝑗

(18)

+ 55.508)



Page 12 of 45

In binary solutions, solution enthalpies and heat capacities are usually given by apparent molar quantities φL and φCp: 𝐿

𝜑

𝐿=𝑚

𝜑

𝐶𝑝 =

(19)

𝐶𝑠𝑝 ― 𝐶0𝑝,𝑙

(20)

𝑚

where Csp is the measured specific heat capacity, 𝐶0𝑝,𝑙 is the molar heat capacity of pure solvent, and L is the relative enthalpy given by ∂𝑙𝑛𝛾𝑖

𝐿 = ―𝑅𝑇2∑𝑖𝑥𝑖

(21)

∂𝑇

2.4 Data Regression. In CaSO4-(NH4)2SO4-NH3-H2O quaternary system, there are three binary subsystems (CaSO4-H2O, (NH4)2SO4-H2O and NH3-H2O) and three ternary subsystems (CaSO4-(NH4)2SO4-H2O, CaSO4-NH3-H2O and (NH4)2SO4-NH3-H2O). To study and predict the phase behavior of this quaternary system, a lot of parameters need to be determined including the equilibrium constants of salt-water system, Henry's constants of ammonia-water system and binary interaction parameters between species. Among these parameters, the equilibrium constants for the three CaSO4 hydrates and the NRTL binary parameters for the (NH4)2SO4-H2O and CaSO4-H2O pairs are to be determined from the available thermodynamic data including the solubility, osmotic


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coefficient, heat capacity and heat of solution. The equilibrium constants for (NH4)2SO4 with water are taken from Clegg.33 The binary interaction parameters and the Henry’s constants of NH3-H2O system are taken from Que.27 The equilibrium constants of double salts and the salt-salt binary parameters are to be regressed from data for the corresponding ternary systems on SLE or VLE. The adjusted equilibrium constant, Henry’s constant and NRTL binary interaction parameters are listed in Tables 2-4 respectively. Sources of available thermodynamic data used to regress the model parameters are summarized in Supporting Information. Table 2. Regressed Equilibrium Constant of Chemical Reaction (eq 13)

components

A

B

C

D

ref

ammonium sulfate

-1102.02

23931.46

197.35

-0.3845

33

dihydrate

252.59

-9758.68

-43.63

0.0356

this work

hemihydrate

-860.44

22113.86

149.38

-0.2736

this work

anhydrite

-850.47

21937.95

147.30

-0.2690

this work

mono-salt

478.37

-20939.58

-78.46

0.0260

this work

di-salt

-847.67

0

168.88

-0.5488

this work

penta-salt

-777.27

0

147.04

-0.5493

this work



Page 14 of 45

Table 3. Regressed parameters for Henry’s Constant in Pa (eq 16)

component

A

B

C

D

E

ref

NH3

-34.995

-3148.3

11.428

-0.02665

0

27

The following general objective function, based on the maximum-likelihood principle, is used to regress the parameters:

[ (

OF = Min∑𝑖 𝑤1

2 𝑇𝑒𝑥𝑝 ― 𝑇𝑐𝑎𝑙 𝑖 𝑖 𝜎𝑇

)

(

+ 𝑤2

2 𝑃𝑒𝑥𝑝 ― 𝑃𝑐𝑎𝑙 𝑖 𝑖 𝜎𝑃

)

(

+ 𝑤3

2 𝑥𝑒𝑥𝑝 ― 𝑥𝑐𝑎𝑙 𝑖 𝑖 𝜎𝑥

)]

(22)

The average relative deviation (ARD) between the experimental value Zexp and the calculated value Zcal is defined as follows: 𝑛

|

∑𝑖 = 1

ARD =

|

𝑍𝑒𝑥𝑝 ― 𝑍𝑐𝑎𝑙 𝑍𝑒𝑥𝑝

(23)

𝑛

where n is the number of data points.

Table 5. Regressed Binary Interaction Parameters of NRTL model (eq 10)

component i

component j

τ1,ij

τ2,ij

τ3,ij

αij

ref

H 2O

(NH4+,SO42-)

9.6399

-584.81

-19.68

0.2

this work

(NH4+,SO42-)

H 2O

-4.7058

285.36

10.18

0.2

this work


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NH3

(NH4+,SO42-)

-3.4832

3428.74

37.78

0.2

this work

(NH4+,SO42-)

NH3

7.1049

-3216.63

-31.32

0.2

this work

H 2O

(Ca2+,SO42-)

-0.5855

0

114.45

0.2

this work

(Ca2+,SO42-)

H 2O

3.1915

0

-67.73

0.2

this work

NH3

(Ca2+,SO42-)

-2.6179

1160.74

173.32

0.2

this work

(Ca2+,SO42-)

NH3

4.6767

-1642.42

-55.63

0.2

this work

(Ca2+,SO42-)

(NH4+,SO42-)

24.8246

0

-619.91

0.2

this work

(NH4+,SO42-)

(Ca2+,SO42-)

-9.1273

0

215.19

0.2

this work

H 2O

NH3

0.5275

-1022.3

0

0.1

27

NH3

H 2O

3.0173

-726.72

0

0.1

27

3. RESULTS AND DISCUSSION 3.1. Binary System. 3.1.1. (NH4)2SO4-H2O system. There are a plenty of solubility data for the (NH4)2SO4-H2O system. The solubility data from physical handbook30, 31 are selected to regress the model parameters. There is a good agreement between experimental data and calculated values derived from the thermodynamic model with the ARD of 0.38 % and the maximum relatively deviation (MRD) is 1.18%, as shown in Figure 2.



8.0

7.5

7.0

m / mol·kg-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 45

6.5

6.0

5.5

5.0

0

20

40

60

80

100

120

T/℃

Figure 2. Experimental values of Perry30 (●) and Lidde31 (■) for (NH4)2SO4 solubility in water and model calculations (—).

Numerous osmotic coefficients data are available for the (NH4)2SO4-H2O system and have a good consistency.32-35 Clegg et al. reported osmotic coefficients by an isopiestic method at 25 ℃ and 50 ℃ with (NH4)2SO4 concentration varied from 0 to 6 mol/kg for the (NH4)2SO4-H2O system.33 Guendouzi et al. measured the osmotic coefficients at a temperature of 25 ℃ with a hygrometric method, at molality in the range from 0.1 mol/kg to saturation.32 These osmotic coefficients data are used in the regression. As shown in Figure 3, the calculated values can accurately match the experimental results, since the ARD is 0.83%. The model predictions indicate that temperature has little influence on the osmotic coefficient of (NH4)2SO4-H2O system.


Page 17 of 45

1.00 25℃ 25℃ 50℃

0.95 0.90 0.85

φ(m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.80 0.75 0.70 0.65 0.60 0

1

2

3

4

m / mol·kg-1

5

6

7

Figure 3. Experimental data of Clegg33 (● and ×) and Guendouzi32 (■) for osmotic coefficient of (NH4)2SO4-H2O system and model calculations at 25 ℃ and 50 ℃.

The variation of the thermodynamic properties of (NH4)2SO4-H2O system with temperature is dependent on heat capacities and enthalpies. Figure 4 shows the comparison between the model results on heat of solution with experimental data from Benrath et al36 at 25 ℃ and (NH4)2SO4 molality from 0 to 5.5 mol/kg. Three data sets of heat capacity are available for the (NH4)2SO4-H2O system.37-39 The experimental data from Schneider and Muller37 from 23 to 92 ℃ and (NH4)2SO4 concentration from 24.6-40 wt % and the data from D’ans et al.38 at 20℃ and (NH4)2SO4 molality from 0.28-3.70 mol/kg are used to fit the parameters. The experimental data from Sukhatme are not adopted as they are grossly discordant with other measurements, and are probably in error.39 Figure 5



shows the comparison of the calculated and experimental apparent molar heat capacity data. It is noted that enthalpy data at 25 ℃ are determined from early measurements and only provide eight values.36 As can be seen Figure 4, the accuracy of these data is limited. The same is true for the 𝜑𝐶𝑝 (Figure 5) with nine values. Model validation are therefore important for verifying the accuracy and prediction performance of the model.

L / kJ·mol-1

2

1



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 45

0

0

1

2

3

m / mol·kg-1

4

5

6

Figure 4. Comparison of the experimental data of Benrath36 (■) for enthalpy of (NH4)2SO4H2O system and the model calculations (—) at 25 ℃.


Page 19 of 45

150

Cp / J·mol-1·K-1

100

50



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

-50

0

1

2

3

4

5

6

m / mol·kg-1

Figure 5. Comparison of the experimental data of Schneider37 (●), D’ans38 (■) and Beggerow40 (▲) for heat capacity of (NH4)2SO4-H2O system and model predictions (—) at 25 ℃.

The boiling point data of (NH4)2SO4-H2O system are adopted for model validation. Multiple sets of boiling point data are available for the (NH4)2SO4-H2O system.41, 42 To show the predictive accuracy of the present model, the calculated and the experimental boiling point as a function of (NH4)2SO4 molality are compared and plotted in Figure 6. There are three curves predicted by different binary interaction parameters which are fitted by three types of data sets. Data set I contains solubility data only, data set II contains solubility and osmotic coefficient data, data set III contains solubility, osmotic coefficient, heat of solution and heat capacity data. Figure 6 shows that the model regressed by data set I has poor



predictive performance, the boiling point calculated at high (NH4)2SO4 concentration is significantly higher than the experimental value. The addition of the osmotic coefficient data (data set II) improves the predictive performance, the predicted results are basically in accordance with the experimental data. Moreover, the accuracy of the model is further improved by adding the enthalpy and heat capacity data in the regression. The results indicate that it is necessary to adopt multiple types of data to regress thermodynamic model parameters as more information can be obtained in this way. 114

Data set I Data set II Data set III

112 110 108

T/℃

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 45

106 104 102 100 98

0

1

2

3

4

5

6

7

8

m / mol·kg-1

Figure 6. Comparison of the experimental data of Liu41 (■) and Emons42 (●) for boiling point of (NH4)2SO4-H2O system and model predictions (—).


Page 21 of 45

Dihydrate Anhydrite Hemihydrate

0.08

0.06

m / mol·kg-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Hemihydrate

0.04

0.02 Dihydrate Anhydrite

0

0

20

40

60

80

100

120

140

160

180

200

220

T/℃

Figure 7. Experimental data for CaSO4 solubility in aqueous solution and model calculations: (□) Dihydrate43, 44, (○) Hemihydrate43-45 , (▲) Anhydrite43, 44, 46-48.

3.1.2. CaSO4-H2O system. In pure water, the solubility of the CaSO4 solid phases is low and decreases with increasing temperature. Numerous solubility data of CaSO4-H2O system can be found in the literatures.43-48 Figure 7 compares the model results and experiment data for the solubility of CaSO4 in the three phases (dihydrate, hemihydrate and anhydrite) at temperature range from 0 to 200 ℃. Good agreement is achieved with the exception of solubility of hemihydrate at low temperature, where the experimental data are scattered due to the hemihydrate is the most unstable phase in this temperature range. At a certain temperature the solid phase that has the lowest solubility is the stable phase. The calculated phase transition point between dihydrate-anhydrite is 41.3 ℃ close to the 40 ℃,



which is reported by Hill48, Bock47 and Power et al49. And the transition point between dihydrate-hemihydrate is 101.3 ℃, this value lies between the 98 ℃ reported by Partridge et al.50 and 104 ℃ reported by Dahlgren’s51.

1.00 0.95

φ(m)

0.90 0.85 0.80 0.75 0.70 0

0.002

0.004

0.006

0.008

0.01

0.012

m / mol·kg-1

Figure 8. Comparison of the experimental data of Pitzer52 (■) and Malatesta53 (●) for osmotic coefficient of CaSO4-H2O system and model predictions (—) at 25 ℃.

3

L / kJ·mol-1

2



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 45

1

0

0

0.002

0.004

0.006

m / mol·kg-1

0.008

0.01

0.012

Figure 9. Experimental data of Wagman et al.54 (■) for enthalpy of CaSO4-H2O system and model calculations (—) at 25 ℃.


Page 23 of 45

-220

Cp / J·mol-1·K-1

-240

-260

-280



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-300

-320

0

0.005

0.01

0.015

0.02

m / mol·kg-1

Figure 10. Comparison of the estimated data of Toner et al.55 (■) for heat capacity of CaSO4-H2O system and the model calculations (—) at 25 ℃.

For osmotic coefficients, the data measured by freezing point depression method,

53

which are consistent with later electromotive force measurements, are included in the regression. The enthalpy data of Wagman et al54 and the heat capacity data reported by Toner et al55 are also used in this work. The calculated results of osmotic coefficients, enthalpy and heat capacity can match the reported values satisfactorily, as shown in Figures 8-10 respectively. It is noted that the heat capacity data of CaSO4-H2O system from Toner et al were estimated by analogy the MgSO4 system up to 0.02 mol/kg. 55 3.1.3. NH3-H2O system. For the asymmetric E-NRTL model of NH3-H2O system, the researchers have done a lot of valuable work. Que27 applied the asymmetric E-NRTL



Page 24 of 45

activity coefficient model to accurately describe the NH3-H2O system, the model parameters including Henry’s constant and binary interaction parameters are determined by data fitting against the experimental values for VLE, heat capacity and enthalpies of the NH3-H2O system. These results are directly applied to our work and listed in Tables 3 and 4. 3.2. Ternary System. 3.2.1 CaSO4-(NH4)2SO4-H2O system. The solubility behavior of CaSO4(NH4)2SO4-H2O system is very complicated because of the presence of hydrates (dihydrate, hemihydrate and anhydrite) and double salts (mono-calcium salt, di-calcium salt and pentacalcium salt). Hill and Yanick presented a systematic study on the solubility of all solid phases mentioned above except hemihydrate in CaSO4-(NH4)2SO4-H2O system from 25 to 100 ℃ with (NH4)2SO4 concentration between 0 and saturation.56 Their data are adopted to evaluate the NRTL binary interaction parameters for the pair between electrolytes (Ca+, SO42-) and (NH4+, SO42-). Ge et al. investigated the effect of the concentration (0 ～ 2.5 mol·kg−1) of (NH4)2SO4 on the solubility of gypsum by means of ICP-AES under the conditions of 25-75 ℃.57 These data are adopted for validating the model. Figure 11 presents a comparison of the model calculations and the experimental results of Hill and Yanick56 on solubility of dihydrate, anhydrite, mono-calcium, di-calcium and


Page 25 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


penta-calcium as a function of (NH4)2SO4 molality at 25, 50, 75 and 100 ℃, respectively. The solubility of hemihydrate predicted by the model at 75 and 100 ℃ are also plotted for comparison. The model results is in excellent agreement with the experimental values except for the solubility of di-salt and penta-salt at high concentration of (NH4)2SO4. Both of them are higher than the experimental data with the max relative deviation is 18.2% and 24.6% respectively. In addition, the anhydrite is the most stable phase with temperature above 75 ℃ at the (NH4)2SO4 concentration range from 0 to saturation. While the temperature is relatively low, an interesting phenomenon was observed. With the increase of (NH4)2SO4 concentration, the most stable phase is dihydrate first at low (NH4)2SO4 molality (0-2 mol/kg), then turns into penta-salt with increasing (NH4)2SO4 molality (2-4.8 mol/kg), and finally becomes mono-calcium (4.8-7.6 mol/kg) at 50 ℃. And the most stable phase is dihydrate and mono-calcium at low and high (NH4)2SO4 concentration respectively at 25 ℃. The model calculations for solubility of dihydrate in ammonium sulfate solution from 25 to 75 ℃ are examined and compared with the experimental results of Ge et al.57, as shown in Figure 12. Generally, the solubility behavior for the CaSO4-(NH4)2SO4-H2O ternary system can be satisfactorily described by the constructed model.



Dihydrate Anhydrite Mono-calcium Di-calcium Penta-calcium

m

m

lcium

0.02

He m ih yd ra t

iu

CaSO4 / mol·kg-1

He m ih yd ra t

rat e yd Di h

a Penta-c

lc

0.06

h Di

0.04

yd

e rat

0.02

0

1

2

3

4

5

(NH4)2SO4 / mol·kg-1

6

7

0

8

ri Anhyd

0

1

2

3

al c

iu m

M

on

0.02

oca

lc

iu

m

ih D

yd

t ra

e

iu m

Penta-calcium

0.03

al c

y

Dihydrate Mono-calcium

o-c

ih D

7

on

0.03

6

0.04

0.04

e at dr

5

D: 25℃

CaSO4 / mol·kg-1

Dic

4

M

CaSO4 / mol·kg-1

0.05

m

te


0.05 Dihydrate Mono-calcium Di-calcium Penta-calcium

C: 50℃

0.06

Di-ca lciu

Penta-calcium

rite Anhyd 0

iu m

0.04

oca

al c

Di-ca lciu

on

o-c

CaSO4 / mol·kg-1

e

M

Dihydrate Anhydrite Mono-calcium Di-calcium Penta-calcium

on

0.06

B: 75℃

0.08

e

A: 100℃

0.08

M

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 45

0.02

0.01 0.01

0

0

1

2

3

4

-1

5

6

7

0

0

1

(NH4)2SO4 / mol·kg

2

3

4


5

6

Figure 11. Experimental data of Hill et al.56 (symbols) for solubility of dihydrate, anhydrite, mono-calcium salt, di-calcium salt and penta-calcium salt in aqueous (NH4)2SO4 solution and the model calculations (lines) at 25, 50, 70, 100 ℃, respectively.


Page 27 of 45

0.05

0.04

CaSO4 / mol·kg-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25℃ 30℃ 40℃ 50℃ 60℃ 75℃

0.03

0.02

0.01 0.0

0.5

1.0

1.5

2.0

2.5

3.0


Figure 12. Experimental data of Ge et al.57 (symbols) for solubility of dihydrate in (NH4)2SO4 solution and the model predictions (lines) at 25-75 ℃.

3.2.2 NH3-(NH4)2SO4-H2O system. The binary interaction parameters of the E-NRTL model for the pair between NH3 and electrolyte (NH4+, SO42-) were determined in NH3-(NH4)2SO4H2O system. Two types of data can be used for regression of parameters, one is the VLE data of NH3 in aqueous solution of (NH4)2SO4, the other is the solubility data of (NH4)2SO4 in aqueous solution of NH3. The experimental results of Rumpf and Maurer58 for the solubility of NH3 in aqueous solution of (NH4)2SO4 with temperature ranging from 60 to 160 ℃ and pressure up to 3 MPa are used in this work. Figure 13 exhibits the predicted and experimental bubble point pressure of NH3-(NH4)2SO4-H2O system as a function of the NH3 concentration at various temperatures with fixed (NH4)2SO4 molality. The results indicate



that the obtained model can accurately describe the thermodynamic behavior of NH3 in aqueous solution of (NH4)2SO4 with the overall ARD of 6.8%. Only limited data points for (NH4)2SO4 in aqueous solution of NH3 are available.59,

60

As shown in Figure 14, good

agreement between experimental results and calculated values at 25 and 40 ℃ is achieved. 1.2

A: m(NH4)2SO4=2 mol/kg

B: m(NH4)2SO4=4 mol/kg

60℃ 80℃ 120℃ 140℃ 160℃

1

60℃ 80℃ 120℃ 140℃ 160℃

1

0.8 0.8

P / MPa

0.6

P / MPa

0.4

0.2

0

0.6

0.4

0.2

0

5

10

15

NH3 / mol·kg

20

0

25

0

5

10

NH3 / mol·kg-1

-1

15

Figure 13. Experimental data of Rumpf et al.58 (symbols) for solubility of NH3 in aqueous (NH4)2SO4 solution and model predictions (lines) at (NH4)2SO4 molality of 2 and 4 mol/kg, respectively.

25℃ 40℃

6

5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 45

4

3

2

1

0

2

4

6

8

10

12

NH3 / mol·kg-1


14

16

Page 29 of 45

Figure 14. Experimental data of Cao59 (■) and Shu60 (●) for solubility of (NH4)2SO4 in NH3 solution and the model calculations (—).

3.2.3 CaSO4-NH3-H2O System. The only data we found in the literature for gypsum solubility in CaSO4-NH3-H2O system are reported by Behij et al,61 which are available to 28% ammonia aqueous solution at temperature range from 5 to 30 ℃. Figure 15 displays the comparison between the experimental results and the model calculation. The calculated dihydrate solubility are consistent with the experimental values with the ARD of 0.35%. 0.04 0.035 0.03

CaSO4 / mol·kg-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.025 0.02

0.015 0.01 0.005 0

0

5

10

15

20

25

30

35

40

T/℃

Figure 15. Experimental data of Behij et al.61 (■) for solubility of dihydrate in 28 wt % aqueous NH3 solution and model predictions (—) as a function of temperature.

3.3 Prediction of Quaternary System. After all adjustable parameters have been regressed successfully, the solubility of CaSO4 in (NH4)2SO4-NH3-H2O mixed electrolyte solution can



Page 30 of 45

be predicted by the constructed model. Figures 16 and 17 show the predicted solubility of dihydrate, hemihydrate, anhydrite, mono-calcium, di-calcium salt and penta-calcium salt as a function of (NH4)2SO4 molality at 90 and 30 ℃ with NH3 molality fixed at 2 mol/kg (solid line) and 6 mol/kg (dashed line) respectively. It can be seen that the increase in NH3 concentration reduces the solubility of each form of calcium sulfate, but it has little effect on the shape of the solubility phase diagram. In Figure 16, when the temperature is fixed at 90 ℃, the only stable two-salt coexistence point is anhydrite-mono salt at both NH3 molality. When the temperature decreases to 30 ℃ (Figure 17), there are three stable two-salt coexistence points that are dihydrate-anhydrite, anhydrite-penta salt, penta salt-mono salt at NH3 molality of 2 mol/kg. As the NH3 molality increases to 6 mol/kg, the dihydrateanhydrite coexistence point disappears. The reason is that the increasing of the NH3 concentration decreases the dielectric constant of mixed solvent, thus causing lower levels of the CaSO4 salts dissociation. In addition, the water activity reduces with the increasing of NH3 concentration as well. Therefore, compared with anhydrite, the solubility of dihydrate containing two H2O molecules is more significantly affected by the NH3 concentration.


Page 31 of 45

It should be noted that the temperature range of the data available for the CaSO4-NH3H2O system is 5-30°C, the predicted results at 90 °C can only be used as a reference. Additional experimental data about the CaSO4-NH3-H2O ternary system, particularly around 100 °C, are required to improve the model’s reliability. 90 ℃

0.06

0.05 d ra te

M on

Di hy

0.04

ca

lc

iu

m

m

yd

ra te

0.03

Di-calc iu

o-

He m ih

CaSO4 / mol·kg-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.02

alcium Penta-c

ri Anhyd

0.01

0

0

1

te

2

3

4

5


6

7

Figure 16. Predicted solubility of dihydrate, hemihydrate, anhydrite, mono-calcium salt, dicalcium salt and penta-calcium salt in (NH4)2SO4-NH3-H2O mixed electrolyte solution with NH3 molality of 2 mol/kg (solid lines) and 6 mol/kg (dash lines) at 90 ℃.



0.04

30 ℃

0.03

Di-ca lcium

alcium

o-

CaSO4 / mol·kg-1

-c Penta

on M ca lc iu m

te ra yd

An hy dr it

e

0.02

Di h

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 45

0.01

0

0

1

2

3

4


5

6

Figure 17. Predicted solubility of dihydrate, hemihydrate, anhydrite, mono-calcium salt, dicalcium salt and penta-calcium salt in (NH4)2SO4-NH3-H2O mixed electrolyte solution with NH3 molality of 2 mol/kg (solid lines) and 6 mol/kg (dash lines) at 30 ℃.

4．CONCLUSIONS The asymmetric E-NRTL activity coefficient model was used to describe the thermodynamic behaviors of the CaSO4-(NH4)2SO4-NH3-H2O quaternary system. The thermodynamic data of SLE, VLE, osmotic coefficient, heat of solution and heat capacity were used to determine the model parameters including the chemical reaction equilibrium constant and NRTL binary interaction parameters. The developed E-NRTL model was proved to be a reliable model for calculating the phase equilibrium of NH3 and CaSO4 in aqueous solution of (NH4)2SO4. The predictive performance of the model was also


Page 33 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


examined by comparing the experimental data and calculated values. With the increasing of NH3 concentration, the solubility of CaSO4 salts will decrease. The proposed model with provision of fitted parameters can serve as a tool to design and optimize the NH3 regeneration process from ammonium sulfate.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications. Table S1 summarizes the source of thermodynamic data used in this work for the parameter regression.

References:



Page 34 of 45

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(5) Kumar, R.; Chowdhury, B., Comprehensive study for vapor phase Beckmann rearrangement reaction over zeolite systems. Ind. Eng. Chem. Res. 2014, 53, 1658716599.


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(6) Mandal, S.; Santra, C.; Kumar, R.; Pramanik, M.; Rahman, S.; Bhaumik, A.; Maity, S.; Sen, D.; Chowdhury, B., Niobium doped hexagonal mesoporous silica (HMS-X) catalyst for vapor phase Beckmann rearrangement reaction. Rsc. Adv. 2013, 4, 845-854.

(7) Ghiaci, M.; Ghazaie, M., Modification of a heterogeneous catalyst: sulfonated graphene oxide coated by SiO2 as an efficient catalyst for Beckmann rearrangement. Catal.

Commun. 2016, 87, 70-73.

(8) Li, D.; Dan, M.; Jing, L.; Yu, Z.; Wang, J., In situ functionalized sulfonic copolymer toward recyclable heterogeneous catalyst for efficient Beckmann rearrangement of cyclohexanone oxime. Appl. Catal. A- Gen. 2016, 510, 125-133.

(9) Mao, D.; Long, Z.; Zhou, Y.; Li, J.; Wang, X.; Wang, J., Dual-sulfonated dipyridinium phosphotungstate catalyst for liquid-phase Beckmann rearrangement of cyclohexanone oxime. Rsc. Adv. 2014, 4, 15635-15641.

(10) Jain, S.; Dwivedi, J.; Jain, P.; Kishore, D., Use of 2,4,6-trichloro-1,3,5-triazine (TCT) as organic catalyst in organic synthesis. Synth. Commun. 2016, 46, 1155-1174.



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(11) Zhang, J.; Lu, Y.; Kai, W.; Luo, G., Novel one-step synthesis process from cyclohexanone to caprolactam in trifluoroacetic acid. Ind. Eng. Chem. Res. 2013, 52, 63776381.

(12) Augustine, J. K.; Kumar, R.; Bombrun, A.; Mandal, A. B., An efficient catalytic method for the beckmann rearrangement of ketoximes to amides and aldoximes to nitriles mediated by propylphosphonic anhydride (T3P®). Tetrahedron Lett. 2011, 52, 1074-1077.

(13) Youwei, C.; Teng, P.; Wei, Q.; Lijun, W.; Xi, L., A method for recovering ammonia and high quality gypsum from ammonium sulfate. CN108706610A, 2018.

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Thermodynamic Modeling of CaSO4-(NH4)2SO4-NH3-H2O

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