Scholarly article on topic 'Representation of Piperazine-CO2-H2O System Using Extended-UNIQUAC and Computational Chemistry'

Representation of Piperazine-CO2-H2O System Using Extended-UNIQUAC and Computational Chemistry Academic research paper on "Chemical sciences"

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Abstract of research paper on Chemical sciences, author of scientific article — Hamid Mehdizadeh, Mayuri Gupta, Eirik F. Da Silva, Hallvard F. Svendsen

Abstract Piperazine, an absorbent that has good potential for use as single amine or in mixtures with other amines, is studied in this work. Current measurement devices and methods are not able to measure the concentrations of all species that form during CO2 absorption into this amine and consequently calculation of equilibrium constants are not possible. To overcome this problem, using computational chemistry, optimized shapes of molecules and ions and needed energies of reaction and equilibrium constants are calculated. The eUNIQUAC model is used to model the behavior of the mixture. Results show the capability of the method used for this work and the power of computational chemistry to fill the gap between experimental data and data needed to build an equilibrium model.

Academic research paper on topic "Representation of Piperazine-CO2-H2O System Using Extended-UNIQUAC and Computational Chemistry"

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Energy Procedia 37 (2013) 1871 - 1880

GHGT-11

Representation of Piperazine-CO2-H2O system using extended-UNIQUAC and computational chemistry

Hamid Mehdizadeha, Mayuri Guptaa, Eirik F. Da Silvab, Hallvard F. Svendsena*

aNorwegian University of Science and Technology, Trondheim, Norway _b SINTEF material and Chemistry_

Abstract

Piperazine, an absorbent that has good potential for use as single amine or in mixtures with other amines, is studied in this work. Current measurement devices and methods are not able to measure the concentrations of all species that form during CO2 absorption into this amine and consequently calculation of equilibrium constants are not possible. To overcome this problem, using computational chemistry, optimized shapes of molecules and ions and needed energies of reaction and equilibrium constants are calculated. The eUNIQUAC model is used to model the behavior of the mixture. Results show the capability of the method used for this work and the power of computational chemistry to fill the gap between experimental data and data needed to build an equilibrium model.

© 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of GHGT

Keywords: CO2 capture, Piperazine, Computational Chemistry, extended UNIQUAC, Equilibrium Constant

1. Introduction

Global warming is a threat and one the main reasons of this effect is anthropological production of CO2 that increases the amount CO2 more than can be accepted by the nature on earth[1]. There are different suggestions to overcome this problem and among them, the fastest way is to decrease the release of CO2 through CO2 Capture and Storage, CCS Concepts for CO2 capture from industrial gases are known decades and among these reactive absorption is today believed to be the most viable.

Piperazine with two reaction sites is considered as a good solvent for a thermal swing absorption process. Piperazine has the potential to be used as a single absorbent in low or high concentration^, 3] or in mixtures with potassium carbonate[4], with AMP[5, 6] or with MEA[2]. One of the problems to model

* Corresponding author. Tel.: +47 735 94 100; fax: +47 73 59 40 80. E-mail address: hallvard.svendsen@chemeng.ntnu.no.

1876-6102 © 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of GHGT doi: 10.1016/j.egypro.2013.06.067

the behavior of piperazine is the uncertainty regarding equilibrium constants of the different reactions because of limitations of current measurement devices. e.g. NMR cannot separate piperazine from protonated piperazine and piperazine carbamate from protonated piperazine carbamate. So, measurements of their exact concentrations and subsequent calculation of their equilibrium constants is currently not possible. Different researchers have used these equilibrium constants as tuning parameters. Because of this, the results are different values from different sources, often with a variation over several decades.

2. Computational Chemistry

Computational chemistry offers an alternative route to obtaining equilibrium constants which is used in this work. All calculations were initially done at HF/3-21G* level in vacuum. Single point calculations were done on the optimized gas phase configurations with the SM 5.4 A [7] solvation model. These calculations were done by using Spartan 08. The optimized structures were used for density functional theory calculations using B3LYP functional at 6-311++G (d, p) basis set level for both gaseous phase and solution phase calculations. Gaseous phase calculations were done in Gaussian 03 [8]. The solvent effects were studied by using SM8T continuum solvation model [9] in the Gamessplus software.

Initial conformer search for PZ species was carried out at HF/6-31G* level. Potential conformers were optimized at B3LYP/6-311++G (d, p) level in both gaseous and aqueous phase. Single point energy calculations on this optimized geometry of the molecule obtained were used to study the solvation effects with the SM8T solvation model. The most stable conformers in gaseous and solution phase were taken for further calculations for gaseous phase basicity and solution phase basicity respectively. These molecules are not very flexible because of the ring structure, so the most stable conformer in gaseous phase and solution phase was the same. The most stable conformers used in the calculations are shown in Figure 1.

3. Chemical Reactions and Phase Equilibria

As described earlier, because of the double reaction sites in Piperazine, numbers of possible reactions in this system are more than for primary amines like MEA. These reactions can be presented in different

ways and among them the following are selected for this work:

2 H20^^H30+ +OH~ (1)

C02 + 2 H30+ + HCO~ (2)

HCO~3+h2O^^H3O+ +co32" (3)

PZH+ +H20 < > PZ + H30+ (4)

PZ + C02 + H20< K5 >PZCOO + H30+ (5)

H+PZCOO~ +H20< > PZCOO~ +H30+ (6)

PZC00+C02 +H2O^^PZ{COO)2 +H30+ (7)

Figure 1: Most stable conformers used for calculations in gaseous and solution phase.

Formation of double protonated Piperazine is neglected because of the low pKa value. For reactions (1) through (3) available data from Austgen et al.[10] were used. For reactions (4) through(7), results from computational chemistry were used and optimized to the conventional temperature dependent form of

\nK = A + B/T + C\nT + DT (8)

The non-ideality of the system, for each reaction, is related to the equilibrium constant using the following relation

\n.K = Y\a' =F[ xj'.y?

Beside these reactions in the liquid phase, there are equilibrium between gas and liquid phase. In these equilibriums, ions are considered as non-volatile and water, CO2 and Piperazine have the possibility to migrate to the gas phase.

4. Model Implementation and Optimization

In order to describe non-ideality in the liquid phase the extended-UNIQUAC model described by Thomsen et al.[11] is used. This model is based on the UNIQUAC model presented by Abrams and Prausnitz[12] with the addition of a Debye-Huckel term to take into account long-range interactions.

In yj = In yUNIOUAC + Jn yDH

UN10UAC .

■ In

1 — In

Tkl is a binary interaction type parameter that is given by

Tkl = exp

akl is defined with the following relation

V , 1 rji

= akl+aklxT

uk!=uk!+ukix T-298.5 (14)

As Mehdizadeh et al.[13] have shown this formulation decreases the required number of interaction parameters in systems with a high number of species compared to the ordinary linear temperature dependency formalism.

To solve the equilibrium reaction in liquid phase a free energy minimization approach based on RAND method is used that is described in [14]. Activity coefficients of components are added to describe non-idealities in the liquid phase. Thus, mole fractions of components are calculated from:

M pure

In which X are dimensionless Lagrange multipliers and A is the formation matrix. To solve the system of equations, a conventional Newton method is used with analytically calculated derivatives.

For reactions and species that are previously investigated, UNIQUAC parameteres were taken from the literature[11, 15]. For optimization of parameters (coefficients of equation (8) for each reaction, r and q and interaction parameters of UNIQUAC model and intercept of equilibrium constants) a multi-step approach was used. First, a pattern search approach was used to optimize temperature independent interaction parameters (all temperature dependent parameters, uT, are set to sero in this stage) and r and q parameters and results are used as intial guesses for a bounded Nelder-Mead minimization. Results of this stage were send to the pattern search rutine again and this loop repeated to reach a minimum change of s in the objective function value. In the next stage, all avaiable parameters were used to minimize the objective function including u°, uT, r, q and variables for four re actions, (4) through(7)) of equation (8). Altoghether, 67 parameters were optimized in a nonlinear system.

For binary mixtures of water and Piperazine, total pressure data form Wilson and Wilding[16] and also some in-house measurements of partial pressures were used. Loaded systems were fitted using speciation data from Ermatchkov et al. [17], partial pressure data for CO2 from Hilliard[2], Kamps et al.[18], Bishnoi and Rochelle[19] and some in-house measurements. Partial pressures of water and Piperazine were also taken from the work of Hilliard[2] for tuning of the model.

5. Results and Discussion

5.1. Computational chemistry model

Reaction energies for the various reactions involved in the chemistry of Piperazine reacting with CO2 are studied with density functional theory. The temperature dependency of these reaction energies was also studied with the help of the SM8T continuum solvation model. Piperazine undergoes reactions (4) through (7) in aqueous solution with CO2. The gaseous phase and solution phase reaction energies for

these reactions were calculated by employing a different thermodynamic cycle for each reaction. Thermodynamic cycles help to use different level of theory for calculating various contributions to the total free energy of solution. In 2007, Sadlej-Sosnowska studied the importance of different thermodynamic cycle in calculating reaction energies [20]. Figure 2 lists the thermodynamic cycles employed for reaction (4) to (7) in this study.

Table 1 shows gaseous phase and solution phase contributions for calculating the free energy of solution at 298 K. From these results we can see that piperazine can form several stable species on reaction with CO2 in aqueous solutions. It has the highest tendency to form protonated piperazine carbamate. We can see that there is a negative free energy of solution for reaction(7), i.e. the formation of piperazine di-carbamate, which suggests that there is a tendency also to form stable di-carbamate with piperazine. Using these free energies of solution values, ln^ values were calculated and the values at 298K are given in Table 1.

Table 1 : Gaseous phase and solution phase contributions to calculate free energy of solution for reactions 1 -4 in Kcal/mol at 298 K.

Reaction AG- A^SOlV Aft lnK

Reaction (4) -225.95 -57.45 -13.18 22.33

Reaction (5) 188.92 -156.84 -2.068 3.50

Reaction (6) -136.59 111.30 -12.87 21.82

Reaction (7) 242.01 -215.86 -0.46 0.78

a: Reaction energies for reactions 1,2,3 and 4 calculated in vaccum (DFT, B3LYP/6-311++G(d, p)); b: Solvation energy contribution to free energy of solution for reactions 1, 2, 3 and 4 respectively (SM8T continuum solvation model) ; c: Reaction enegies in solution for different reactions.

Using calculated values of lnK for different temperatures, the parameters of equation (8) were optimized and shown in the following table.

Table 2: Constants of equation (8) for different reactions

Reaction A B C D

Reaction (4) -0.80954 -5845.7 -0.38087 0

Reaction (5) -58.064 9979.1 4.9289 0

Reaction (6) -53.798 -1423.5 8.449 0

Reaction (7) -38.153 8857.6 1.8837 0

5.2. Binary mixture

Data for the binary mixture of water and Piperazine are rare, so tuning of the model using these data is questionable. On the other hand, because of formation of different crystal forms at high concentration of piperazine, the behavior of the system is so complicated and measurements of partial pressures at low temperature is hard and sometimes not practical.

Figure 2: Thermodynamic cycles employed for reactions (4) to (7)respectively.

In Figure 3 and Figure 4 the total pressure above the binary mixture at two different temperatures is shown over a range of concentrations. As the figures show, despite the high complexity of this mixture, the model gives a fairly good prediction, mainly because of high temperature of the mixture.

5.3. Ternary mixture

After tuning the binary system, interaction parameters were used for ternary mixture. Results for different temperatures and concentrations are shown in Figure 5 to Figure 8.

mole fraction of PZ

Figure 3: Prediction of total pressure above the H2O-Piperazine system at 113oC

mole fraction of PZ

Figure 4: Prediction of total pressure above the H2O-Piperazine system at 199oC

PPZ by UNIQUAC PH2O by UNIQUAC

PH2O by Hilliard

* * * * Ф

0.4 0.6

loadina

PPZ by UNIQUAC

-PH2O by UNIQUAC

Ф PPZ by Hilliard PH2O by Hilliard

0.4 0.6

loading

Figure 5: Partial pressure of water and Piperazine in 5.18wt% Figure 6: Partial pressure of water and Piperazine in 5.18

mixture at 40oC

wt% mixture at 60oC

10° -

Ф- Ppz by Hilliard

In Figures 5 and 6 are shown comparisons between experimental and predicted individual water and Piperazine vapor pressure. The model seems to under-predict the Piperazine vapor pressure data at 40oC but the fit at 60oC is good. It should be taken into account that the Piperazine volatility is quite low at 40oC the experimental accuracy will be lower for this case.

It should be noted that data from Kamps et al.[18] at 60oC in Figure 8 are total pressure data. At this temperature with total pressures in the high loading range of 200-2000kPa, the water and piperazine vapor pressures are low and CO2 partial pressure could be a measure of the total pressure of the system. Although there is some scatter in the experimental data it is evident that the model has a problem in representing the data well, in particular for low loadings. This could point to inaccuracies in the carbamate equilibrium constant which will be further studied to have an improved model.

Optimized r and q parameters for UNIQAUC parameters for different pairs is also shown in Table

low ino S" 10 a Q. r 3. 1 O 0.1 5,18wt% a ■ / * / i' a - ' □ i * iT / ■1 * ■ s .. 0 J"" b ^ ^ t, Derksela!,20i£ ^ □ aishnoi, 2000 ^ ^ • --40°C a ^^ ' ......70°C S ■ / " / /

n? 0.4 0.6 o.a 1 12 loading

Figure 7: Representation of partial pressures of CO2 in the 5.18 wt% Piperazine mixture in 40oC (solid shapes) and 70oC (empty shapes)

model are shown in Table 3. Binary interaction

Figure 8: Representation of partial pressures of CO2 in the 15 wt% Piperazine mixture in 40oC (solid shapes) , 60oC (empty shapes), 120oC (filled shapes)

Table 3: r and q parameters of UNIQUAC model for different species in the mixture, the rest of the parameters are taken from the literature[11, 15]

Species r q

Piperazine 3.76 2.95

protonated piperazine 15.443 11.1670

carbamate

protonated piperazine 3.7987 6.9464

piperazine carbamate 15.819 6.7506

piperazine double carbamate 17.922 3.0338

Figure 9: Representation of partial pressures of CO2 in the 1.73 wt% Piperazine mixture in 25oC (solid shapes) , 40oC (filled shapes), 60oC (empty shapes)

Table 4: u0 (temperature independent) parameters of the UNIQUAC model for different binary pairs in the mixture. The rest of the interaction parameters are taken from the literature[11, 15]

Species H+PZCOO- PZH+ PZCOO- PZ(COO-)2

H2O -174.987 -267.746 -389.192 -242.462

PZ 368.7228 23419.63 3.88E+08 2.9E+08

CO2 -272.007 948.2698 -666.859 5.37E+08

H3O+ 1E+09 1E+09 1E+09 1E+09

OH- 1E+09 1E+09 1E+09 1E+09

HCO3- 5.37E+08 -344.975 1E+09 1E+09

CO3= -504.255 5.37E+08 1E+09 1E+09

H+PZCOO- 201.1884 -143.669 617361.9 9.13E+08

PZH+ -143.669 65.18625 9.13E+08 -515.114

PZCOO- 617361.9 9.13E+08 -1214.63 1E+09

PZ(COO-)2 9.13E+08 -515.114 1E+09 62298.62

Table 5: uT (temperature dependent) parameters of the UNIQUAC model for different binary pairs in the mixture. The rest of the interaction parameters are taken from the literature[11, 15]

Species H+PZCOO- PZH+ PZCOO- PZ(COO-)2

H2O 0.175004 0.034366 5.334548 0.100613

PZ -8.5621 -46.5511 0.000783 -49.5515

CO2 9.613207 -7.40423 8.706104 -0.55466

H3O+ 0 0 0 0

OH- 0 0 0 0

HCO3- 16.99984 -2.8055 0 0

CO3= 1.984841 0.000365 0 0

H+PZCOO- -1.66122 -1.03012 -7.36466 6.92E-05

PZH+ -1.03012 23.01202 -0.00023 20.06757

PZCOO- -7.36466 -0.00023 18.5529 0

PZ(COO-)2 6.92E-05 20.06757 0 39.06803

6. Conclusion

An approach for the calculation of equilibrium constants for reactions between species that are not experimentally measureable is introduced. This approach in used with reasonable success for the representation of Piperazine in mixture with water and CO2. The extended UNIQUAC framework was used for equilibrium modeling of the mixture.

Acknowledgements

This work is done under the SOLVit project, performed under the strategic Norwegian research program CLIMIT. The authors acknowledge the partners in SOLVit: Aker Clean Carbon, Gassnova, EON, EnBW and the Research council of Norway for their support.

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