N2O Analogy Using Molecular Simulation

Article pubs.acs.org/IECR

Validation of the CO2/N2O Analogy Using Molecular Simulation Qu Chen,† Sayee Prasaad Balaji,† Mahinder Ramdin,† Juan José Gutiérrez-Sevillano,† André Bardow,‡ Earl Goetheer,§ and Thijs J. H. Vlugt*,† †

Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands ‡ Lehrstuhl für Technische Thermodynamik, RWTH Aachen University, Schinkelstrasse 8, 52062 Aachen, Germany § TNO, Leeghwaterstraat 46, 2628 CA Delft, The Netherlands S Supporting Information *

ABSTRACT: CO2 readily reacts in aqueous amine solutions. The properties of free CO2 in amine solutions are therefore difficult to obtain directly and are often predicted from the nonreacting molecule N2O due to the similarities in mass and structure. This often-used empirical “CO2/N2O analogy” is verified in this work using molecular simulation. Continuous fractional component Monte Carlo (CFCMC) simulations in the osmotic ensemble were used to compute the Henry coefficients of CO2 and N2O in the solvents water, ethanol, n-heptane, and a 30% aqueous MEA solution at a temperature of 303 K. Molecular dynamics (MD) simulations were performed to compute the self-diffusivities of CO2 and N2O in the aforementioned solvents at 303 K. Different force fields for CO2 and water were used. The computed Henry coefficients and self-diffusivities of CO2 and N2O in the solvents are in good agreement with available experimental data. The simulation results indicate that the CO2/N2O analogy is valid for aqueous MEA solution at 303 K. The Henry coefficient and self-diffusivity ratios of CO2 to N2O in water and 30% MEA solution are approximately 0.77 and 1.1, respectively. Additional simulations where all the amines have reacted with CO2 confirm that reactions have little impact on the physical absorption and diffusion properties of CO2.

1. INTRODUCTION As a byproduct of burning fossil fuels, carbon dioxide (CO2) accounts for a large portion of the greenhouse gas emissions.1,2 CO2 capture and storage (CCS) could play a significant role in reducing CO2 emissions from power plants.3−5 The removal of CO2 from natural gas or in the postcombustion process is typically achieved in an absorber using an amine solution.6−8 For example, an aqueous solution containing 30% monoethanolamine (MEA) is a frequently used solvent for CO2 capture.6 For a proper design of a gas absorption unit, it is very important to understand the mass-transfer process of CO2. This requires knowledge of the solubility and diffusivity of CO2 in aqueous amine solutions. Due to reactions between CO2 and amines, the solubility of CO2 measured in experiments is the total solubility, which combines both physical and chemical absorption. However, the physical solubility is needed to obtain the rate of the CO2 absorption.9 When the CO2 molecules absorb into an amine solvent, diffusion and reaction will take place simultaneously. As there is almost no unreacted CO2, it is practically impossible to obtain the solubility and diffusivity of CO2 in amine solutions directly from experiments.10,11 In practice, this problem is usually overcome by substituting CO2 with a similar but inert gas. Nitrous oxide (N2O) can be considered as an ideal candidate since the gases have similar molecular weights, volumes, and structures. Substituting CO2 for N2O to obtain physical properties of CO2 is known as “the CO2/N2O analogy”. According to the CO2/N2O analogy, the solubility and diffusivity of both gases are related by12 © XXXX American Chemical Society

⎡ HCO ⎤ ⎡ HCO ⎤ 2 2 ⎢ ⎥ ⎥ =⎢ ⎢⎣ HN2O ⎥⎦ ⎢ HN2O ⎥⎦ ⎣ in water in amine solution

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⎡ DCO ⎤ ⎡ DCO ⎤ 2 2 ⎢ ⎥ ⎥ =⎢ ⎢⎣ DN2O ⎥⎦ ⎢ DN2O ⎥⎦ ⎣ in water in amine solution

(2)

where H is the Henry coefficient and D is the self-diffusivity. The idea of the CO2/N2O analogy was first conceived by Clarke,13 who studied the absorption kinetics of CO2 in aqueous MEA solutions at short contact times using the laminar liquid jet technique. In this study, it was suggested that the solubility and diffusivity of CO2 in MEA solutions are comparable to those of N2O due to the similarity in their mass and molecular interactions. Joosten and Danckwerts14 presented experimental data on the solubility and diffusivity of N2O in equimolar potassium−potassium bicarbonate solutions of various ionic strengths. These authors indicated that the corresponding properties of CO2 can be reliably predicted by these N2O data. Joosten and Danckwerts showed that the diffusivities of CO2 and N2O in a pure liquid and an electrolyte solution are correlated by ⎡ Dsoln ⎤ ⎡D ⎤ = ⎢ soln ⎥ ⎢ ⎥ ⎣ D0 ⎦CO ⎣ D0 ⎦N O 2

2

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Received: September 3, 2014 Revised: October 23, 2014 Accepted: October 28, 2014

A

dx.doi.org/10.1021/ie503488n | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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molecules fluctuates.25 This can be realized by adding/ removing molecules to/from a so-called “open system”. A system where the number of molecules fluctuates is called an open system. The conventional Monte Carlo schemes are inefficient since they suffer from the low insertion/deletion acceptance probabilities at high densities.26,27 Therefore, methods that can handle open systems at high densities are ́ et required to efficiently compute the Henry coefficient. Lisal al.28 obtained the Henry coefficient for CO2 in water via the Widom test-particle insertion method and the staged freeenergy perturbation method. These authors also compared different interaction models of water and CO2. Cichowski et al.29 determined the Henry coefficient of CO2 in ethanol by transition matrix Monte Carlo simulations coupled with the expanded ensemble technique. A similar study on the CO2 solubility in ethanol was carried out by Zhang and Siepmann,30 who used Gibbs ensemble Monte Carlo simulations to directly calculate the Henry coefficient. The continuous fractional component Monte Carlo (CFCMC) method was recently developed by Shi and Maginn.26,31−33 This method overcomes the difficulties encountered in conventional Monte Carlo (MC) methods by utilizing gradual insertions/deletions of molecules using a continuous coupling parameter and an adaptive bias potential. The CFCMC method in the osmotic ensemble was applied to obtain the Henry coefficient of CO2 in ethanol, and the results are in agreement with previous studies.31 Self-diffusivities of the absorbed CO2 and N2O can be computed by equilibrium molecular dynamics (MD) simulations.34 This approach requires interaction potential models capable of accurately describing the intermolecular and intramolecular interactions of the molecules. Some efforts were made to investigate the influence of different force fields on the diffusion coefficient. In het Panhuis et al.35 used the SPC/E model for water and adjusted the Lennard-Jones size parameters and quadruple moments (partial charges) of the Gromos CO2 potential. This work concluded that, whereas the Lennard-Jones interaction of the CO2 potential has a large impact on the CO2 diffusion behavior, the diffusivity of CO2 is almost independent of the Coulombic interaction of the CO2 potential. Vlcek et al.36 proposed and applied a coupling parameter scheme to optimize the Lennard-Jones cross interactions for the SPC/E−EPM2 models. This successfully improved the accuracy of the predicted mutual diffusion coefficients of CO2 and water in simulations. Zeebe37 presented studies on the diffusivity of dissolved CO2 in water over the temperature range from 273 to 373 K and provided a general power-law equation to predict the diffusivity of CO2 as a function of temperature. Recently, Moultos et al.38 compared different combinations of CO2 and water models to investigate the diffusivity of CO2 over a broad range of temperatures and pressures. These authors found that at normal pressure the TIP4P/2005−EPM2 combination was best to calculate the diffusivity of CO2 at lower temperatures ( 30% MEA aqueous solution > water. To validate the CO2/N2O analogy, the ratios of the Henry coefficients of CO2 and N2O in all investigated solvents were obtained. As listed in Table 2, the CO2/N2O ratios for water Table 2. Ratios of Henry Coefficients of CO2 to N2O in Water, Ethanol, n-Heptane, and a 30% MEA Solution at a Temperature of 303 Ka

Figure 3. Fugacity of CO2 or N2O in the gas phase plotted as a function of mole fraction of CO2/N2O in ethanol and n-heptane at 303 K. The EPM2 and TraPPE models were used for CO2.

solvent water (TIP4P) water (TIP5P) ethanol n-heptane 30% MEA (TIP4P) 30% MEA (TIP5P)

and N2O in the gas phase are plotted as a function of the solute mole fraction in solution. By extrapolating to low pressures, the Henry coefficient can be obtained. As shown in Table 1, all the simulation results for the Henry coefficients of CO2 and N2O in ethanol and n-heptane underestimate the experimental values. To the best of our knowledge, experimental data for the Henry coefficients of CO2 and N2O in ethanol have been reported only at 293 K as 16.28 and 13.72 MPa, respectively.19 The two models of CO2 (EPM2 and TraPPE) in ethanol and heptane, unlike in water, result in Henry coefficients that are very similar. The Henry coefficient of N2O is always lower than that of CO2 in both ethanol and heptane. Note that the solubility is higher when the Henry coefficient is lower. This trend for ethanol was also observed in the work by Kierzkowska-Pawlak et al.,19 although their experiments were conducted at 293 K. Finally, we performed simulations for the CO2 and N2O solubilities in a 30% (w/w) MEA solution. Note that at this stage the reactions between CO2 and MEA have been “switched off” in the MC simulations. In section 3.2 a case will be presented where the reactions between CO2 and MEA have been taken into consideration. On the basis of our results of CO2 solubility in water, we only used the TIP4P and TIP5P models for water and the TraPPE model for CO2. The results are shown in Figure 4 and Table 1. Although a certain deviation from the experiment can be observed, the simulation data show that 30%

[HCO2/HN2O]sim

[HCO2/HN2O]exp

diff (%)

± ± ± ± ± ±

0.7712 0.7712 n/a 1.4760,61 n/a n/a

−7.8 +1.3 n/a −29 n/a n/a

0.71 0.78 1.11 1.05 0.82 0.84

0.02 0.02 0.05 0.02 0.02 0.04

a

Simulation results are compared with the experimental data reported with the difference presented. We only used the TraPPE model for CO2 and the TIP4P/TIP5P model for H2O for comparison.

and MEA solution are all below unity while the CO2/N2O ratios for ethanol and heptane are both above unity. The differences between simulations and experiments for the CO2/ N2O Henry coefficient are below 10% for the TIP4P and TIP5P water models, but for heptane the difference is nearly 30%. The explanation could be that the experimental ratio for heptane is in fact calculated from data of two different studies.60,61 For solvents with larger dipole moments (e.g., water), more CO2 molecules are likely to be absorbed. Solvents with smaller dipole moments (e.g., heptane) tend to absorb more N2O molecules. The validity of eq 1 can be verified by comparing the CO2/N2O ratios for the Henry coefficients in water and in 30% MEA solution. Li and Lai12 reported the ratio HCO2/HN2O in water to be 0.77 at a temperature of 303 K and E



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the other solvents was also investigated, and again no notable differences could be observed for the different system sizes (results not shown). As for the solubility, a comparison of the performance for the different models for H2O with respect to the diffusivity is provided. Three water models (i.e., SPC/E, TIP4P, and TIP5P) were tested using the EPM2 CO2 model. From the diffusivity regime up to 20 ns, the diffusivity of CO2 in the SPC/E, TIP4P, and TIP5P water was obtained as (2.727 ± 0.071) × 10−9, (2.428 ± 0.080) × 10−9, and (3.500 ± 0.079) × 10−9 m2/s, respectively, compared to the experimental value of 2.120 × 10−9 m2/s reported by Li and Lai.12 It is obvious that the combination EPM2−TIP5P performs poorly, and therefore we used the SPC/E and TIP4P models for further research. Simulations were then performed in an ensemble containing 1 CO2 solvated in 500 water molecules, 500 ethanol molecules, 500 heptane molecules, and a 30% MEA solution (56 MEA plus 444 H2O), respectively, at 303 K. Similar simulations were performed with 1 N2O molecule in the aforementioned solvents as well. Two models for H2O (SPC/E and TIP4P) and two models for CO2 (EPM2 and TraPPE) lead to four combinations. Table 3 shows the results for all simulations at

applied this ratio for calculating the Henry coefficient of CO2 in amine solutions. We found that this ratio is in agreement with our simulation results, since all the data points for water and MEA solution fall within 10% of 0.77. The CO2/N2O analogy for the Henry coefficient is therefore supported at a temperature of 303 K. So far, all the MC simulations assume that CO2 does not react with the MEA molecules; hence the solubility of CO2 in the MEA solution was purely due to physisorption. In reality, CO2 will react with MEA and it is therefore very important to understand how reactions or reaction products affect the Henry coefficients of CO2 and N2O. Assuming that all MEA molecules have been reacted with CO2, a simulation of a fully reacted s y s t e m w i t h 2 8 H O C H 2 C H 2 N H CO O − i o n s , 2 8 HOCH2CH2NH2+ ions, and 444 water molecules was performed. In experiments, CO2 can fully react with MEA molecules even at low temperatures (e.g., 293 K).62 At 303 K, the MC simulations were performed to compute the Henry coefficient of CO2. The best performing combination for CO2− H2O (TraPPE−TIP5P) was used. The Henry coefficient of free CO2 in this fully reacted MEA solution is calculated to be 107.2 ± 5.6 MPa, while the Henry coefficient in the nonreacted MEA solution is 92.3 ± 1.9 MPa. This indicates that the Henry coefficient of the MEA solution increases when the reaction products are formed. In other words, the Henry coefficient of CO2 is higher in an unreacted MEA solution than in a solution containing their reaction products. However, there is no huge impact of reaction products on the physical solubility of CO2. As a result, the CO2/N2O analogy for the physical solubility may also hold during the whole chemical reaction process. 3.2. Diffusivity. The self-diffusivity was calculated from Einstein’s equation in three dimensions: 1 1 Di = lim 6Ni m →∞ mΔt

Table 3. Self-Diffusivities of CO2 in Water, Ethanol, nHeptane, and 30% MEA Solution at 303 Ka solute CO2 (EPM2) CO2 (TraPPE) N2O CO2 (EPM2) CO2 (TraPPE) N2O CO2 (EPM2) CO2 (TraPPE) N2O CO2 (EPM2) CO2 (TraPPE) N2O CO2 (EPM2)

Ni

∑ ⟨[rl ,i(t + mΔt ) − rl ,i(t )]2 ⟩ l=1

(6)

where Ni is the total number of molecules of component i, m is the number of time steps, and Δt is the time step used in MD simulations. rl,i(t) is the position of the lth molecule of type i at time t.63 Moultos et al.38 showed that the error bar of the CO2 diffusivity in water is considerably large (>10%). This accuracy is not suitable for the purpose of this study, because the diffusivity ratio of CO2 and N2O will then have an even larger error bar and it will not be possible to obtain a value statistically different from unity. In this work, we carried out at least 50 parallel simulations, from which the statistical uncertainty was determined. An order-n algorithm64 was used to compute the mean squared displacement (MSD). The average MSDs of CO2 as a function of time for each simulation were plotted. In a log−log plot, the different distinct regimes can be observed. Before molecules collide with each other, they undergo ballistic diffusion, which occurs in a very short time ( ethanol > 30% MEA > water. Molecular dynamics simulations also correctly predict the observed CO2/ N2O diffusivities in the solvents, which obey the following order: heptane > ethanol > water > 30% MEA. The simulation results indicate that the CO2/N2O analogy is valid for water and 30% MEA solution at 303 K. The ratio of the Henry coefficients CO2/N2O is approximately 0.77 (±10%), and the ratio of the self-diffusivities CO2/N2O is around 1.1 (±10%). Additional simulations were performed to investigate the effect of a chemical reaction between CO2 and MEA on the physical solubility and self-diffusivity of CO2. The simulation results indicate that both the physical solubility and the self-diffusivity of CO2 are lower in the system containing reaction products of CO2 and MEA, which is a result of the reaction between CO2 and MEA.

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ASSOCIATED CONTENT

S Supporting Information *

Force field parameters of all components; comparison of densities for 30% MEA solution at different CO2 loadings. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed as a part of the CATO-2 program, the Dutch national R&D program on CO2 capture, transport and storage, funded by the Dutch Ministry of Economic Affairs (Q.C. and S.P.B.). Financial support by ADEM, a green Deal in Energy Materials, a program of the Dutch Ministry of Economic Affairs, is also acknowledged (M.R.). This work was also supported by NWO Exacte Wetenschappen (Physical Sciences) for the use of supercomputer facilities, with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organization for Scientific Research, NWO).

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N2O Analogy Using Molecular Simulation

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