Scaling Model: CO2-CaCO3-H2O

Aspen Plus

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Revision History 1

Revision History

Version Description

V7.2 First version

V7.3 Some parameters updated

V7.3.2 Databanks are updated, results are updated with V7.3.2

V8.0 Update the model to V8.0

2 Contents

Contents

Revision History ......................................................................................................1

Contents..................................................................................................................2

Introduction............................................................................................................3

1 Components .........................................................................................................4

2 Physical Properties...............................................................................................5

3 Reactions ...........................................................................................................10

4 Simulation Approach ..........................................................................................12

5 Simulation Results .............................................................................................14

6 Conclusion..........................................................................................................15

References ............................................................................................................16

Introduction 3

Introduction

This file describes an Aspen Plus model for the scaling prediction of CO2-CaCO3–H2O ternary system at 398.15 K, and the scaling mineral CaCO3 isincluded in this model. This model consists of a flash block to simulate theliquid-solid equilibrium for CO2-CaCO3–H2O at 398.15 K. The thermophysicalproperties are studied intensively, wherever possible, model parameters havebeen estimated and validated against experimental data from open literature.

The model includes the following key features:

True species including ions

Unsymmetric electrolyte NRTL activity coefficient model[1-3] for liquidphase nonideality and PC-SAFT equation of state for vapor phase

Thermodynamic equilibrium between solid and liquid phase

4 1 Components

1 Components

The following components represent the chemical species present in theprocess:

Table 1. Components Used in the CO2-CaCO3–H2O Model

ID Type Name Formula

CA+2 Conventional CA++ CA+2

CO3-2 Conventional CO3-- CO3-2

HCO3- Conventional HCO3- HCO3-

H2O Conventional WATER H2O

H3O+ Conventional H3O+ H3O+

CO2 Conventional CARBON-DIOXIDE CO2

OH- Conventional OH- OH-

CACO3(S) SOLID STRONTIUM-CARBONATE

CACO3

2 Physical Properties 5

2 Physical Properties

The unsymmetric electrolyte NRTL method and PC-SAFT equation of state areused to compute liquid and vapor properties respectively in this model. Forapplying this model, the option code for model should be specified as follows:

Model ESPSAFT with 10 as the second option code should be used forPHIVMX, DHVMX, DGVMX, DSVMX, VVMX. Model ESPSAFT0 with10 as the second option code should be used for PHIV, DHV, DGV,DSV, VV. That means the Copolymer PC-SAFT equation of state isused to calculate the vapor fugacity coefficient, vapor molar enthalpydeparture, molar Gibbs free energy departure, molar entropydeparture, molar volume for both mixture and pure component. Thesecond option code 10 is implemented to find the true density at thegiven condition of T, P, compositions regardless of the specified phase.

Note that, the specification of the databanks should be: ASPENPCD,AQUEOUS, SOLID, INORGANIC, PURE27, PC-SAFT.

Henry’s law is applied to CO2. Henry’s constant parameters and Brelvi-O’Connell characteristic volume parameters of CO2 required for pressurecorrection of Henry’s constant are identified against the experimentalsolubility of CO2 in water[4-10]. The NRTL interaction parameters for the CO2-H2O pair are set to zero, assuming the interactions between CO2 and waterare negligible.

Henry’s constant can be calculated from the following equations:

dpVRT

pTHPTHP

p

ijl

jijijl

w,

1exp,, ,

(1)

2

, ln,lnT

ETDTC

T

BApTH

ij

ijij

ij

ijl

jij for HL TTT

(2)

Where:

PTH ij , - Henry’s constant of i in j at system temperature and pressure

ljji pTH ,, - Henry’s constant of i in j at system temperature and vapor

pressure of j

6 2 Physical Properties

ijV - Infinite dilution partial molar volume of i in solvent j obtained from the

Brelvi-O’Connell model[11]

Aij, Bij, Cij, Dij, Eij, TL, TH - Correlation parameters

Table 2 shows the Henry’s constant parameters of CO2 in water at systemtemperature and water vapor pressure.

Table 2. Henry’s Constant Parameters for CO2 in H2O (SI)

Component i CO2

Component j H2O

Aij 100.650

Bij -6147.7

Cij -10.191

Dij -0.010

TLOWER 273

TUPPER 500

Eij 0.0

The general form of the Brelvi-O’Connell model is expressed as:

lj

BOj

BOiij VVVfcnV ,,,

2

(3)

Where:

BOj

BOi VV , - Characteristic volume for solute i and solvent j, respectively

ljV ,

- Liquid molar volume of solvent j

Brelvi and O’Connell (1972)[11] presented the universal functions relating thecompressibility to the reduced density and the solute partial molal volume tothe reduced solvent density. Based on these empirical correlations, thecompressibility of a liquid and the partial molal volume of a solute at infinitedilution in the solvent can be calculated with only the characteristic volumesfor the solute and the solvent being required. The characteristic volumes aretreated as temperature dependent with the following equation:

TvvV BO21 (4)

Where:

1v , 2v - Correlation parameters for a solute or a solvent

Table 3 summarized the Brelvi-O’Connell characteristic volume parametersrequired in this model.

Table 3. Brelvi-O’Connell characteristic volumeparameters (SI)

Component Water[11] CO2a

1v 0.0464 0.177

2 Physical Properties 7

2v 0 -3.42E-04

a Parameters regressed.

Extended Antoine equation is used instead of a steam table for the calculationof vapor pressure for water, because practice shows that the predictions fromsteam tables at high temperatures are not accurate enough. To implementthis change, route PHIL04 should be used for property PHIL.

Because of the low ionization rate of CO2 in water and the minor solubility ofCaCO3, the interactions between species are negligible. So, zero is used forthe NRTL binary parameters between CO2 and H2O. The default values areused for the NRTL parameters for electrolyte and electrolyte or molecule.

Based on the liquid activity coefficient, the enthalpy of aqueous solution canbe calculated from the following equations:

Em

kkkwwm HHxHxH **

(5)

wvapvw

Tig

wpigwfw HHdTCHH

15.298

,

(6)

dTCHHT

kpkfk

15.298

,

(7)

alli

ii

Em

TxRTH

*2* ln

(8)

Where:

aqkpC ,

,

- Infinite dilution aqueous phase heat capacity, J/kmol-K

igwpC , - Ideal gas heat capacity of water, J/kmol-K

kH

- Aqueous infinite dilution thermodynamic enthalpy, J/kmol

EmH *

- Molar excess enthalpy defined with the asymmetrical reference state,J/kmol

wH- Water molar enthalpy, J/kmol

igwf H

- Standard ideal gas enthalpy of formation for water, J/kmol

vwH

- Vapor phase enthalpy departure for water, J/kmol

wvap H- Heat of vaporization of water, J/kmol

kf H- Infinite dilution aqueous phase enthalpy of formation for ions and

molecules, J/kmol

8 2 Physical Properties

*i - Liquid activity coefficient

The infinite dilution aqueous phase heat capacity (

aqkpC ,

,

) is estimated by thefollowing equation:

T

C

T

C

T

CTCTCCC iii

iiiaqkp

6

2

542321

,,

for ii CTC 87 (9)

Where: parameters C1i to C8i are equivalent to the CPAQ0/1…8 in Aspen Plus.i indicated molecules, cations and anions.

Criss and Cobble (1964)[12] show that the Cp of ions changes little from298.15 K to 473.15 K. That means considering the Cp of ions as a constant atthis temperature range is more reasonable than using the existingspecification in Aspen Plus. For this reason, we updated the CPAQ0 for anionsin this work as shown in Table 4.

Table 4. Heat Capacity Parameters Used in Eq. 9

Component Ca++ CO2 H3O+ OH-

C1i 873.222 132230.718 75291 -148445.904

C2i 0 0 0.0 0

C3i 0 0 0.0 0

C4i 0 0 0.0 0

C5i 0 0 0.0 0

C6i 0 0 0.0 0

C7i 0 0 0.0 0

C8i 2000 2000 2000 2000

The estimated VLE behavior of CO2-H2O using the regressed equilibriumconstant parameters is plotted in Figure 1:

2 Physical Properties 9

Figure 1.CO2 Solubility in water. The symbols are experimental data[4-10], thelines are model results: (×) 298.15 K; (♦) 323.15 K; (∆) 373.15 K; (○) 423.15K; (◊) 473.15 K.

0

25

50

75

100

125

150

175

0 0.02 0.04 0.06 0.08

To

tal

P,M

Pa

CO2, mole fraction

10 3 Reactions

3 Reactions

The solid-liquid equilibrium chemistry and the equilibrium reactions betweenCO2 and water have been represented as a CHEMISTRY model named Global.The chemistry is specified to be Global on the Global sheet of the Properties| Methods | Specifications form. This chemistry also can be used tosimulate the SLE for CaCO3-H2O binary systems at similar conditions.

A. Chemistry ID: SLE1

1 Equilibrium OHCOHCOOH 3

2332

2 Equilibrium OHHCOCOOH 33222

3 Equilibrium OHOHOH 322

4 Salt2

32

3 )( COCasCaCO

The built-in chemical equilibrium expression as follows is used for theequilibrium reactions:

DTTCTBAK )ln(/ln (10)

Where: K is the equilibrium constant; A, B, C and D are adjustableparameters; T is the temperature in Kelvin.

The parameters for the first three equilibrium reactions are retrieved fromAspen Plus databank.

The parameters for the Salt reaction were regressed against Solid-LiquidEquilibrium data for both binary CaCO3-H2O and CO2-CaCO3-H2O from openliterature[13-15], and the regressed parameters are given in Table 5.

Table 5. Parameters Required in Eq. 10

Reaction A B C D

CaCO3 289.994 -12626.5 -48.259 0

The parameters in Table 5 can be used to estimate the solubility of CaCO3(s) inCO2-H2O at different pressures. That is because comparing to the pressureeffect on solubility product, the influence of CO2 concentration on thesolubility of carbonate minerals is more considerable. It means that thedramatic increase of CaCO3 in CO2-H2O is caused by the reaction between

3 Reactions 11

dissolved CO2 and CaCO3(s). So, the influence of pressure on Ksp is ignored inthis model.

The predictions of the solubilities for CaCO3 in water and solutions saturatedwith CO2 are plotted in Figures 2 and 3 along with the experimental data[13-15]:

Figure 2. Solubility of CaCO3(s) in water up to 573.15 K: (∆) Linke (1958)[13];the line is a prediction.

Figure 3. Solubility of CaCO3(s) in CO2-H2O. The points are the data from Linke(1958)[13] and Portier (2005)[15]: (○) 298.15 K; (□) 323.15 K; (◊) 348.15 K; (∆) 373.15 K; (×) 398.15 K; (ж) 423.15 K; (●) 448.15 K; (■) 473.15 K. The lines

are predictions.

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

7.0E-04

8.0E-04

9.0E-04

273 323 373 423 473 523 573 623

CaC

O3,m

T, K

0.0001

0.001

0.01

0.1

1E-05 0.001 0.1 10

Ca

CO

3,m

PCO2, MPa

12 4 Simulation Approach

4 Simulation Approach

Because of the reaction between CO2 and CO3-2, the solubility of CaCO3(s) in

CO2-H2O is much greater than that in water at the same conditions. As thereare no industrial or pilot plant data available for barite precipitationprocesses, we use the equilibrium model (flash calculations) to simulate thescaling potential of the stable minerals. The scaling potential is estimated withsolubility index of a salt, and the solubility index can be expressed as:

sp

p

K

ISOLINDEX (11)

Where:

Ip – Activity product in liquid phase

Ksp – Solubility product.

Simulation Flowsheet – In the following simulation flowsheet in Aspen Plus(Figure 4), solid-liquid equilibrium for CO2-CaCO3–H2O at 398.15 K issimulated by a FLASH2 block.

Figure 4. CO2-CaCO3-H2O Solid-liquid Equilibrium Flowsheet in Aspen Plus

4 Simulation Approach 13

Unit Operations - Major unit operations in this model have been representedby Aspen Plus blocks as outlined in Table 6.

Table 6. Aspen Plus Unit Operation Blocks Used in theCO2-CaCO3-H2O Model

Unit Operation Aspen Plus Block Comments / Specifications

SLE Flash21.Temperature is set at 398.15 K

2. Pressure is set at 1.5 MPa

Note that Gibbs is used as the flash convergence algorithm. It can bespecified on the Setup | Simulation Options | Flash Convergence form.The Gibbs algorithm is based on Gibbs energy minimization, as in the RGibbsunit operation model. It calculates mass and energy balances, true-specieschemistry (if applicable), and properties simultaneously. It is recommended ifthe default inside-out algorithm exhibits convergence difficulties, especiallywhen solving three-phase problems, and almost all vapor electrolytechemistry with salts.

Streams - Feeds to SLE are the liquid stream CaCO3IN containing Ca+2, CO3-2

and H2O, and vapor stream CO2IN containing pure CO2. Feed conditions aresummarized in Table 7.

Table 7. Feed Specifications

Stream ID CO2IN CACO3IN

Substream: MIXED

Temperature: K 398.15 398.15

Pressure: MPa 1.5 1.5

Mole-Flow kmol/hr

CA+2 0 1

CO3-2 0 1

HCO3- 0 0

H2O 0 55.508

H3O+ 0 0

CO2 0.5 0

OH- 0 0

CACO3(S) 0 0

Prop-Sets – Two Prop-Set properties are used: SOLINDEX to monitorprecipitation of possible scaling minerals, and PPMX to report the partialpressure of CO2 and H2O in the vapor phase.

14 5 Simulation Results

5 Simulation Results

The simulation was performed using Aspen Plus V8.0. Key simulation resultsare presented in Table 8. All the compositions are true compositions.

Table 8. Key Simulation Results

Stream ID CO2IN CACO3IN GASOUT LIQUIOUT

Substream: MIXED

Temperature: K 398.15 398.15 398.15 398.15

Pressure: MPa 1.5 1.5 1.5 1.5

Mole flow kmol/hr

CA+2 0 1.5981E-4 0 0.0037

CO3-2 0 1.2279E-06 0 1.2345E-07

HCO3- 0 1.5432E-4 0 0.0074

H2O 0 55.5083 0.0740 55.43073

CACO3(S) 0 0.9998 0 0.9963

H3O+ 0 8.1834E-09 0 5.9335E-06

CO2 0.5 4.2584E-06 0.3759 0.1204

OH- 0 1.6284E-4 0 2.7633E-07

Total Flow kmol/hr 0.5 56.5086 0.4499 56.5585

SOLINDEX

CACO3(S) 1 1

PPMX MPa

CO2 1.5 1.253

H2O 0.247

We can see from Tables 7 and 8 that about 0.376 kmol/h CO2 goes to thevapor phase, which means the solution is saturated with CO2. And thesolubility of CaCO3(s) increases from 1.60E-04 molal to 3.7E-03 molal afterCO2 is bubbled into the solution. The results are consistent with theexperimental data[15].

The SOLINDEX in Table 8 shows that the streams CACO3IN and LIQUIOUT aresaturated with CaCO3(s).

6 Conclusion 15

6 Conclusion

The CO2-CaCO3-H2O model provides a starting point for the potentialprediction of precipitation of carbonate minerals in CO2 aqueous solution. Thekey features of this simulation model include electrolyte thermodynamics andsolution chemistry. Since the main factor influencing the solubility ofcarbonate minerals is the solubility of CO2, just one set of parameters is usedto estimate the SLE at different pressures.

The model is meant to be used as a guide for modeling calcium carbonateprecipitation potential from the CO2-CaCO3-H2O ternary system at differentpressures and temperatures. This simple SLE model has been validated withexperimental solubility data for CaCO3-H2O and CO2-CaCO3-H2O up to 10 MPaand 548.15 K. Further validation of this CO2-CaCO3-H2O model will be donewhen industrial or pilot plant data become available.

16 References

References

[1] Y. Song, C.-C. Chen, “Symmetric Electrolyte Nonrandom Two-LiquidActivity Coefficient Model”, Ind. Eng. Chem. Res., 48, 7788-7797, (2009)

[2] C.-C. Chen, L.B. Evans, “A Local Composition Model for the Excess GibbsEnergy of Aqueous Electrolyte Systems”, AIChE Journal, 32, 444-454, (1986)

[3] C.-C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, “Local Composition Modelfor Excess Gibbs Energy of Electrolyte Systems. Part I: Single Solvent, SingleCompletely Dissociated Electrolyte Systems”, AIChE J., 28, 588-596, (1982)

[4] S. Takenouchi and G.C. Kennedy, “The binary system H2O–CO2 at hightemperatures and pressures”. Am. J. Sci. 262, 1055–1074, (1964)

[5] K. Tödheide and E.U. Franck, Zeitschrift fur physikalische chemie neuefolge, BD. 37, S.387-401 (1963)

[6] W.S. Dodds, L.F. Stutzman and B.J. Sollami, "Carbon dioxide solubility inwater", industrial and engineering chemistry, 1 (1), 92-95, (1956)

[7] S.E. Drummond, “Boiling and mixing of hydrothermal fluids: chemicaleffects on mineral precipitation”, Ph.D. Thesis, Pennsylvania State University,(1981)

[8] A. Zawisza and B. Malesiska, “Solubility of carbon dioxide in liquid waterand of water in gaseous carbon dioxide in the range 0.2-5 Mpa and attemperature up to 473K" J. Chem. Eng. Data, 26, 388-391 (1981)

[9] R. Wiebe and V.L. Gaddy, “The solubility of carbon dioxide in water atvarious temperatures from 12 to 40 ◦C and at pressures to 500 atm”, J. Am. Chem. Soc. 62, 815–817, (1940)

[10] G. Houghton, A.M. Mclean, and P.D. Ritchie, "Compressibility, fugacity,and water-solubility of carbon dioxide in the region 0-36 atm and 0-100 C",Chemical engineering science, 6, 132-137 (1957)

[11] S.W. Brelvi and J.P. O’Connell, “Corresponding states correlations forliquid compressibility and partial molal volumes of gases at infinite dilution inliquids”, AIChE J., 18, 1239-1243 (1972)

[12] C.M. Criss, J.W. Cobble, “The Thermodynamic Properties of HighTemperature Aqueous Solutions. V. The Calculation of Ionic Heat Capacitiesup to 200 °. Entropies and Heat Capacities above 200 °”, J. Am. Chem. Soc.,86, 5390-5393, (1964)

References 17

[13] W.F. Linke, “Solubilities of inorganic and metal-organic compound”, D.Van Nostrand Company, Inc., Princeton, New Jersey (1958)

[14] O.I. Martynova, L.G. Vasina, S.A. Pozdnyakova, “Determination of theSolubility Product of Calcium Carbonate in the Temperature Range from 22 to98 C”, Dokl. Chem., 201, 1022-1024 (1971)

[15] S. Portier, “Solubilite De CO2 Dans Les Saumures Des BassinsSedimentaires : Application au stockage de CO2 (gaz à effet de serre)”,Universite Louis Pasteur – Strasbourg I, (2005)