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Procedía

Energy Procedía 4 (2011) 35-42 -

www.elsevier.com/locate/procedia

GHGT-10

Modeling piperazine thermodynamics

Peter Frailiea, Jorge Plazaa, David Van Wagenera, Gary T. Rochellea1* aThe University of Texas at Austin, 1 University Station C0400, Austin, TX 78757, USA

Abstract

A thermodynamic model in Aspen Plus® was developed to predict properties of piperazine (PZ)/H2O and PZ/H2O/CO2. A sequential regression was performed to represent recently acquired loaded and unloaded heat capacity, CO2 solubility, CO2 activity coefficient, speciation, and unloaded and loaded amine volatility data. The resulting model is able to predict each of these properties over operationally significant loading and temperature ranges (0.20—0.40 mol CO2/mol alkalinity and 40 oC—160 oC). The predicted heat of absorption for 8 m PZ solution at 0.35 mol CO2/mol alkalinity between 40 oC and 160 oC was 65±4 kJ/mol CO2. The temperature dependence of the heat of absorption was predicted using three analytical methods, each of which predicted different trends but similar ranges between 40 oC and 160 oC. The sequential regression methodology has also been applied to methyl-diethanolamine (MDEA) and MDEA/PZ. Ultimately this thermodynamic model will be modified in Aspen Plus® to predict kinetic and transport data as well, and the resulting model will be used to design and optimize a post-combustion absorption/stripping process.

(©5 20111 Published by IElsevier Ltd.

Keywords: carbon dioxide; piperazine; modeling

1. Introduction

This work focuses on the development of a piperazine (PZ) thermodynamic model in Aspen Plus® for the evaluation and optimization of a post-combustion absorber/stripper. Previous studies have modeled PZ thermodynamics, but each attempt has been limited by either a lack of available experimental data or the modeling methods employed. Several of these modeling methods introduce thermodynamic inconsistencies, which can lead to conflicting or inaccurate predictions. FORTRAN models developed by Bishnoi [1] and Cullinane [2] calculated equilibrium constants using a polynomial expression rather than thermodynamically significant quantities such as Gibbs free energies of formation (AG°f), enthalpies of formation (AH°f), and heat capacities (CPo). This introduces a thermodynamic inconsistency when calculating quantities such as heat capacities and heats of absorption, which share a fundamental interdependence with

* Gary T. Rochelle. Tel.: +1-512-471-7230; fax: +1-512-471-7060. E-mail address: gtr@che.utexas.edu.

ELSEVIER

doi:10.1016/j.egypro.201L0L020

speciation. Activity-based PZ/H2O and PZ/H2O/CO2 models developed by Hilliard [3] and Dugas [4] in Aspen Plus® do not have this inconsistency, but these models only consider PZ concentrations at or below 5m. This model accurately predicts recently acquired experimental data for CO2 solubility, PZ volatility, heat capacity, activity coefficient of CO2, and speciation over operationally significant temperature, loading, and amine concentration ranges using thermodynamically consistent methods. This model will be identified as 5deMayo version 1.

2. Methods and Theory

2.1 PZ/H2O Regression

Unloaded amine volatility and heat capacity data was fit by adjusting PZ heat capacity, infinite dilution activity coefficient of PZ in H2O, and Henry's constant of PZ in H2O. Modeling PZ as a Henry's component provides a better set of handles for fitting PZ volatility. Even though a plant will never operate with unloaded PZ it is important to fix the model predictions at these conditions to avoid extreme or inexplicable behavior, which could indirectly affect the ability to fit data within the operational loading range. All parameters concerning the PZ/H2O were held constant during all subsequent regressions.

2.2 PZ/H2O/CO2 Regression

There are two equations that may be used to calculate equilibrium constants in Aspen Plus®: (1) a temperature-dependent polynomial and (2) an expression based on AGofrxn, AHofrxn, and ACPorxn. These expressions are shown below as Equations 1 and 2, respectively.

In Kq = A + - + C ln T + DT (1)

- ln Kq ^AGlzAHl+AHl+1 iACCLJT - ¡ACldT (2)

eq RT RT0 RT TT R T R

0 To T0

The major advantage of using Equation 2 is that it maintains thermodynamic consistency between speciation and properties calculated directly from speciation. Equation 2 will always be used in this study. Before regressing CO2 solubility and loaded heat capacity data, the pKa of PZ from 20 oC to 80 oC was fit by adjusting the AGof, AHof, and CPo of PZH+. The pKa values in the literature [5] had to be converted from a symmetric to an asymmetric activity coefficient reference state. The method for accomplishing this conversion can be found in Hilliard [3].

With these values held constant, CO2 solubility and heat capacity data for 2 m to 12 m PZ between 40 oC and 160 oC were regressed by adjusting AGof, AHof, and CPo, for PZCOO-, PZ(COO)22-, and H+PZCOO-, as well as activity coefficients for all true species. Because Aspen Plus cannot model zwitterions, H+PZCOO- was treated as a Henry's component with a Henry's constant on the order of 10-9. Previous studies [3] have treated H+PZCOO- as a cation with a charge of 10-5, but this led to two major problems: (1) a significant charge imbalance as the concentration of H+PZCOO-increased rapidly at high loadings and (2) a constant activity coefficient of 1. Treating H+PZCOO- as a Henry's component corrects these errors by giving it a zero charge.

2.3 CO2 Activity Coefficient Regression

Aspen Plus cannot directly regress activity coefficients. A user-supplied subroutine had to be used to adjust parameters and incorporate them into the model. The experimental data used was for an 8 m PZ solution between 25 oC and 60 oC at loadings of 0.25 and 0.40 mol CO2/mol alkalinity. Because the concentration of free CO2 in the liquid phase is so low, adjusting the activity coefficient of CO2 did not affect the model predictions for other PZ/H2O/CO2 data sets.

CO2 activity coefficients were inferred from N2O solubility measurements using Equation 3.

H(N2O/ ^Q1") „ „ (3)

H ~/CO1/ soln (3)

H (N2O /H2O)

2.4 Calculating Heat of Absorption

There are three methods for calculating the heat of absorption of CO2: (1) applying the Gibbs-Helmholtz equation to CO2 solubility curves, (2) calculating heat duty when CO2 is absorbed in an Aspen Plus® flash block, and (3) integrating the change in the partial heat capacity of CO2 from a reference temperature with a known heat of absorption to another temperature of interest. Equation 4 is the Gibbs-Helmholtz equation.

dln fa d 1/

-AH, R

Methods 1 and 2 should predict similar values for the heat of absorption if thermodynamically consistent methodology is used in Aspen Plus®. Method 3 is based on Equation 5, which is derived from the mass and energy balance depicted in Figure 1. Because it must always be referenced to another value for the heat of absorption, Method 3 can only be used to determine temperature dependence. For this study, the heat of absorption at 80 oC predicted by the Gibbs Helmholtz Method 1 will be used as the reference point for Method 3.

AH „

,(T) — AHabs (Tref )+|

1 mol CO

AHABs(Tref)

1 mol CO2 AHabs(T)

Figure 1: Mass and energy flow diagram used to derive Equation 5. 3. Results and Discussion

Figure 2 compares CO2 solubility from Aspen Plus® predictions (lines) and experimental data (points) for 3.6, 5, 8, and 12 m PZ between 40 oC and 160 oC. Experimental data between 40 oC and 100 oC were collected by Dugas [4], and data between 120 oC and 160 oC were collected by Xu [6]. Figure 1 suggests that the solubility of CO2 in PZ is a strong function of temperature and loading, and it is a weak function of amine concentration. This result is expected with solvents such as PZ, which produce large amounts of carbamate throughout operationally significant loading ranges [4].

Figure 3 compares Aspen Plus® predictions and experimental points [7] for 8 m PZ heat capacity between 40 oC and 150 oC at loadings of 0.21, 0.29, and 0.40 mol CO2/mol alkalinity. Solution heat capacity tends to increase with temperature and decrease with loading. The increase with temperature may be attributed to La Chatelier's principle, which states that a system in equilibrium will shift to counteract any imposed change in temperature, partial pressure, volume, or concentration until equilibrium is re-established. By increasing its heat capacity, the solution is more resistant to temperature changes.

1.e-02

0.2 0.25 0.3 0.35 0.4 0.45 0.5

Loading (mol CO2/mol Alkalinity) Figure 2: Partial Pressure of CO2 as a function of loading for 3.6 m (□), 5 m (A), 8 m (0), and 12 m (x) PZ

Temperature (C)

Figure 3: Experimental (points) and Aspen Plus® predictions (lines) for CP of 8 m PZ between 40 oC and 150 oC at loadings of 0.21, 0.29, and 0.40 mol CO2/equiv PZ. Data from [7].

The parameters used to regress the PZ/H2O and PZ/H2O/CO2 data can be found in Table 1. Table 1: Parameters used for the PZ/H2O and PZ/H2O/CO2 regressions

Parameter Species Std. Dev. Units

PZ/H2O

Cpo/1 pz 1.2E+5 J/kmol.K

Cpo/2 pz 350 J/kmol.K

T /1 umm' 1 h2o/pz 1.8 N/A

T /1 mm pz/h2o 0.10 N/A

T /3 mm h2o/pz 0.018 N/A

Henry/1 pz/h2o 0.96 N/A

Henry/2 pz/h2o 310 K

PZ/H2O/CO2

AG°f h+pzcoo- 1.2E+5 J/kmol

AH°f h+pzcoo- 3.7E+10 J/kmol

Cpo/1 h+pzcoo- 8,610 J/kmol.K

Cpo/2 h+pzcoo- 0.0028 J/kmol.K

AG0f pzcoo- 2.6E+05 J/kmol

AHof pzcoo- 3.7E+10 J/kmol

Cpo/1 pzcoo- 8,278 J/kmol.K

Cpo/2 pzcoo- 0.0052 J/kmol.K

AGof pZ(COO)22- 3.7E+10 J/kmol

AHof pZ(COO)22- 3.73E+10 J/kmol

Cpo/1 pZ(COO)22- 5,002 J/kmol.K

Cpo/2 pZ(COO)22- 0.0054 J/kmol.K

Cpo/1 pzh+ 11,700 J/kmol.K

Cpo/2 pzh+ 37.1 J/kmol.K

Tca/m/1 h+pzcoo-/(pzh+,pzcoo-) 0.46 N/A

Tca/m/1 (pzh+,pzcoo-)/h+pzcoo- 0.040 N/A

Tca/m/1 h+pzcoo-/[pzh+,pz(coo)22-] 0.57 N/A

Tca/m/1 [pzh+, pz(coo)22-]/h+pzcoo- 0.20 N/A

Tca/m/1 h+pzcoo-/(pzh+,hco3-) 0.44 N/A

Tca/m/1 (pzh+, hco3-)/h+pzcoo- 0.29 N/A

T /1 mm h2o/h+pzcoo- 0.018 N/A

T /1 mm h+pzcoo-/h2o 0.0029 N/A

T /2 mm h2o/h+pzcoo- 5.9 K

T /2 mm h+pzcoo-/h2o 4.0 K

T /3 mm h2o/h+pzcoo- 0.0083 N/A

T /5 mm h2o/h+pzcoo- 0.021 N/A

T /5 "■mm7 ^ h+pzcoo-/h2o 0.015 N/A

All activity coefficient tau parameters not mentioned in Table 1 were set to Aspen Plus® default values for the PZ/H2O/CO2 regression. Because Aspen Plus® is not configured to regress speciation data and the model was not generating any HCO3-, two of the Tca/m parameters in Table 1 [H+PZCOO-/(PZH+,HCO3-) and (PZH+,HCO3-)/ H+PZCOO-] were adjusted manually to generate HCO3- at higher loadings.

The final speciation result is shown in Figure 4. Because proton NMR is unable to distinguish between a species and its protonated counterpart (i.e. PZ vs. PZH+, PZCOO- vs. H+PZCOO-), only the concentrations of PZ(COO)22- and HCO3-were known with any precision. Those concentrations are represented by the two points at a loading of 0.4 [8]. These measurements were made with C13 and proton NMR of 8 m PZ loaded with C13O2 at 40oC.

Figure 5 compares the Gibbs-Helmholtz and calorimetric predictions for the heat of absorption of loaded 8 m PZ. Unlike previous studies, which use Equation 1 to represent equilibrium constants, the two methods for calculating heat of absorption seem to be consistent. At the operational ranges for temperature (40 oC—160 oC) and loading (0.3—0.4) the average heat of absorption is about 65 kJ/mol CO2.

0 0.1 0.2 0.3 0.4 0.5

Loading (mol CO2/mol alk) Figure 4: Aspen Plus® predictions (lines) and NMR data (points) for speciation of 8m PZ at 40 oC.

Figure 6 examines the temperature dependence of the heat of absorption of an 8 m PZ solution at a loading of 0.35 mol CO2/mol alkalinity predicted by the Gibbs-Helmholtz equation, calorimetry, and mixture heat capacity. While all three methods predict different temperature dependence, the spread of the values is quite narrow. All three methods between 40 oC and 160 oC predict heats of absorption between 61 and 69 kJ/mol CO2.

Figure 7 compares the Aspen Plus® predictions and experimental points [9] for the activity coefficient of CO2 in loaded 8 m PZ. Just as with MDEA [10], the activity coefficient of CO2 increases with loading and decreases with temperature. Both of these trends may be attributed to the effects of temperature and loading on the ideality of the liquid phase. Aspentech supplied a FORTRAN subroutine for the regression of CO2 activity coefficients.

Figure 8 compares the Aspen Plus® predictions and experimental data for loaded [7] and unloaded [11] 8 m PZ volatility between 40 oC and 60 oC. As the loading approaches 0.5 the volatility drops off rapidly for all temperatures. This trend is easily understood after examining Figure 4. According to stoichiometry, in the absence of HCO3- and CO32- production all of the PZ will be consumed at a loading of 0.5. Both Aspen Plus® predictions and NMR data suggest that HCO3- and CO32- are only present at small concentrations. Therefore, the drop in PZ partial pressure can be directly attributed to the depletion of free PZ.

70 65 ^ 60 55 50

Loading (mol CO2/mol Alk) Figure 5: Comparison of Gibbs-Helmholtz (dashed lines) and calorimetric (solid lines) predictions for heat of CO2 absorption of 8 m PZ at 40 oC to 160

Temperature (C)

Figure 6: Comparison of Gibbs-Helmholtz (0), calorimetric (□), and CP (A) predictions for the heat of CO2 absorption of 8 m PZ at 0.35 mol CO2/mol alkalinity between 40 oC and 160 oC.

1.E-01

Figure 7: Aspen Plus predictions (lines) and experimental data (points) for the activity coefficient of CO2 in a loaded 8 m PZ solution between 25 oC and 60 oC. Data Provided by Svendsen [9].

4. Conclusions

0.1 0.2 0.3 0.4

Loading (mol CO2/mol Alk)

Figure 8: Experimental [7,11] (points) and Aspen Plus® predictions (lines) for volatility of 8 m PZ between 40 oC and 60 oC.

Heat capacity, CO2 solubility, loaded and unloaded amine volatility, speciation, and CO2 activity coefficient data were incorporated into Aspen Plus® for solutions of 2—12 m PZ. The model adequately predicts each of these quantities over operationally significant loading and temperature ranges (0.20—0.40 and 40 oC—160 oC). Modeling H+PZCOO-as a Henry's component eliminated both charge balance and activity coefficient issues experienced with previous models. Just as with other carbamate forming amines, the solubility of CO2 in PZ solutions is a strong function of

temperature and loading, and it is a weak function of amine concentration. The discrepancy between the Gibbs-Helmholtz and calorimetric heat of absorption predictions has been minimized by using thermodynamically consistent methodology. Predicted values for the heat of absorption between 40 oC and 160 oC suggest that the heat of absorption is approximately 65±4 kJ/mol CO2 at a loading of 0.35 over that temperature range. The same sequential regression methodology used to construct this model can be and has been applied to other amines.

5. Acknowledgements

This work was supported by the Luminant Carbon Management Program. Aspen Technology provided the Aspen Plus® software and a FORTRAN subroutine to regress CO2 Activity coefficients. Hallvard Svensen at NTNU provided the data on N2O solubility. Thu Nguyen provided the speciation measurements with NMR. The Aspen Plus® model, experimental methods, and data of Marcus Hilliard provided the starting point for this model development.

6. References

[1] Bishnoi, S. Carbon Dioxide Absorption and Solution Equilibrium in Piperazine Activated Methyldiethanolamine. The University of Texas at Austin. Ph.D. Dissertation. 2000.

[2] Cullinane, JT. Thermodynamics and Kinetics of Aqueous Piperazine with Potassium Carbonate for Carbon Dioxide Absorption. The University of Texas at Austin. Ph.D. Dissertation. 2005.

[3] Hilliard, MD. A Predictive Thermodynamic Model for an Aqueous Blend of Potassium Carbonate, Piperazine, and Monoethanolamine for Carbon Dioxide Capture from Flue Gas. The University of Texas at Austin. Ph.D. Dissertation. 2008.

[4] Dugas, RE. Carbon Dioxide Absorption, Desorption, and Diffusion in Aqueous Piperazine and Monoethanolamine. The University of Texas at Austin. Ph. D. Dissertation. 2009.

[5] Hetzer HB, Robinson RA Bates RG. Dissociation Constants of Piperazinium Ion and Related Thermodynamic Quantities from 0 to 50o. J. Phys. Chem. 1968 ;72(6): 2081—2086.

[6] Xu, Q., Rochelle, GT, Total pressure and CO2 solubility and high temperature in aqueous amines, GHGT-10, 2010.

[7] Freeman SA, Dugas RE, Van Wagener DH, Nguyen T, Rochelle GT. CO2 Capture with Concentrated, Aqueous Piperazine. IJGCC 2010, 4, 119-124.

[8] Nguyen, T. NMR measurements for 8 m PZ, personal communication, 2010.

[9] Svendsen, H. N2O solubility in Piperazine/CO2/H2O, personal communication, 2009.

[10] Rinker EB, Ashour SS, Sandall OC. Physical Property Data Important in Modeling H2S and CO2 Absorption into Aqueous DEA, MDEA and Blends of DEA and MDEA. Gas Processors Association. RR-158. December 1997.

[11] Nguyen, T., Hilliard, M., Rochelle, GT. Amine Volatility in CO2 Capture. doi:10.1016/j.ijggc.2010.06.003, IJGGC 2010.