Thermodynamic Study of Four {Methylpiperidine + Water} Systems

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Thermodynamic Study of Four {Methylpiperidine + Water} Systems: New Experimental Data and Challenging Modeling for the Simultaneous Representation of Liquid−Liquid Equilibrium and Energetic Properties Edouard Moine,‡ Yohann Coulier,*,† Jean-Yves Coxam,† Karine Ballerat-Busserolles,*,† and Romain Privat*,‡ Downloaded via TULANE UNIV on February 8, 2019 at 15:26:34 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

Institut de Chimie (ICCF), Université Clermont Auvergne, CNRS, SIGMA Clermont, F-63000 Clermont−Ferrand, France Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), Ecole Nationale Supérieure des Industries Chimiques, Université de Lorraine, 1 rue Grandville, 54000 Nancy, France

‡

S Supporting Information *

ABSTRACT: In carbon capture processes based on chemical absorption, the solution used for absorbing carbon dioxide plays a central role and must be carefully selected. It is expected to have the potential to capture large amounts of carbon dioxide on the one hand, and to be fully regenerated at the lowest energy price on the other hand. As a continuation of a study initiated by Coulier et al. some years ago, the present work focuses on the measurement and modeling of thermodynamic properties of aqueous solvents containing methylpiperidines (a class of amines), potentially usable in carbon capture processes and leading to liquid−liquid phase split in process conditions. To complete liquid−liquid equilibrium (LLE), excess enthalpy and excess heat capacity data previously measured by Coulier et al. for the N-methylpiperidine + water and 2-methylpiperidine + water systems, LLE data, and excess-enthalpy data were measured for the 3-methylpiperidine + water and 4-methylpiperidine + water systems. To model all these data, a nonrandom two-liquid type activity-coefficient model was identified among tens of models as the most reliable one. Owing to the complex nature of interactions governing this type of systems, no less than 10 binary interaction parameters were necessary to ensure qualitative and quantitative correlations of our experimental data.

I. INTRODUCTION Carbon dioxide (CO2) issued from anthropogenic emissions, strongly takes part in the adverse effects of global warming. The Carbon Capture and Storage (CCS) process based on chemical absorption in an aqueous solution of alkanolamine is considered as one of the most mature technologies.1 However, this process is energy intensive and needs to be improved in order to lower energy requirements in the regeneration unit.2 For that purpose, novel solvents have been proposed and phase-change solvents were considered as a promising alternative to aqueous solutions of alkanolamines for the decarbonation of industrial effluents.3−5 These solvents undergo a liquid−liquid phase separation. Then, a phase separation unit could be integrated in the process to reduce the energetic cost of the solvent regeneration step. For example, in the DMX process developed by IFP Energies Nouvelles,6−8 a decantation step is added before the CO2 desorption step. The liquid−liquid phase separation makes it possible to treat only the CO2-rich phase in the desorption unit; the CO2-lean phase is reinjected into the absorption unit. This phase separation © XXXX American Chemical Society

aims to concentrate CO2 into the water-rich phase, lowering thus the amount of absorbent to be treated in the regeneration step and reducing the energy requirements. These absorbents used in the DMX process are aqueous solutions of amine capable of phase separation according to particular conditions of temperatures (higher than the absorption temperature) and CO2 loading charges in order to avoid any liquid−liquid mass transfer limitation.9 The development of such a process including the sizing of operation units, the estimation of process parameters, and the simulation of the process plant requires an appropriate thermodynamic model capable of reproducing phase equilibria and energetic properties (i.e., enthalpies and heat capacities of the flowing {amine + water} mixtures) with accuracy. This accuracy strongly depends on the selected thermodynamic model and model-parameter estimation, as well. To benchmark Received: October 26, 2018 Accepted: January 18, 2019

A

DOI: 10.1021/acs.jced.8b00974 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Other Experimental Data Found in the Open Literature Concerning the Four Binary Mixtures under Investigationa property {NMPD + Water} LLE:(T, xαamine, xβamine)

VLE: (T, P, xamine) excess enthalpy: (T, xamine, hE) excess heat capacity: (T, xamine, cEP) {2-MPD + Water} LLE: (T, xαamine, xβamine)

VLE: (T, P, xamine) excess enthalpy: (T, xamine, hE) excess heat capacity: (T, xamine, cEP) {3-MPD + Water} LLE: (T, xαamine, xβamine)

{4-MPD + Water} LLE: (T, xαamine, xβamine)

denomination

ref

N points

(T/K) range

Coulier et al. Flaschner Stephenson Marczak et al. Góral et al. Schneider Dergal Coulier et al. Coulier et al.

11 10 14 15 20 16 21 17 17

19 20 17 24 2 1 18 62 36

[315.6−348.1] [321.4−509.2] [317.15−367.85] [316.65−342.56] [319.4; 544.4] 319.15 [273.13−314.8] [308.15−333.15] [283.15; 288.15; 293.15; 298.15; 303.15; 308.15]

Coulier et al. Flaschner et al. Stephenson Schneider Dergal Nakanishi et al. Coulier et al. Coulier et al.

11 12 14 16 21 22 17 17

7 20 18 1 26 22 107 55

[339.35−376.65] [352.45−500.15] [343.15−365.65] 344.85 [273.13−333] [298.15; 308.15] [303.15−338.15] [283.15−333.15]

101325

Flaschner Stephenson Schneider Gòral et al.

13 14 16 20

18 5 12

[330.05−508.15] [340.15−363.15] 340.25 [329.7−507.0]

101325

Flaschner Stephenson Schneider Gòral et al.

13 14 16 20

19 512

[358.05−462.65] [359.15−368.15] 360.15 [358.4 462.2]

101325

(P/Pa) range 101325

[1045−14480]

[685−28420] [2632−7173]

a

Notation: VLE, vapor−liquid equilibrium; LLE, liquid−liquid equilibrium.

from literature. More details about the capabilities of the selected model and model-parameter determination are provided in the last part of this article.

potentially usable thermodynamic models for identifying the most appropriate one and fit model parameters, experimental data are an imperious prerequisite. In this study, four aqueous systems containing isomers of methylpiperidine are investigated. These are N-methylpiperidine (NMPD), 2-methylpiperidine (2MPD), 3-methylpiperidine (3MPD), and 4-methylpiperidine (4MPD) that are known to give birth to a liquid−liquid phase split in the water solvent.10−16 For the {NMPD + water} and {2MPD + water} binary systems, molar excess enthalpy (hE) data and liquid− liquid equilibrium (LLE) data were reported previously by Coulier et al.17 to complement some LLE data measured by other authors. For the two remaining systems ({3MPD + water} and {4MPD + water}), only LLE data were found in the literature. In the present work, new experimental values of LLE data are provided for both systems, as well as, excess enthalpy data. These new data were obtained from the heat of mixing measurements, using a flow-calorimeter technique. For each of the four binary mixtures investigated, a thermodynamic model capable of reproducing both LLE and energetic experimental data with a unique parameter set was searched. It was observed that the modeling of such systems is highly challenging because of the difficulty for a model to describe simultaneously LLE and excess enthalpy behaviors resulting from the complex interactions present in the system. Among the various kinds of thermodynamic model approaches that we considered, only an extended version of the NRTL activity coefficient model led to an acceptable reproduction of the thermodynamic properties stemming from this work and

II. LITERATURE REVIEW OF EXPERIMENTAL DATA In this section, experimental thermodynamic properties related to the four binary systems {methylpiperidine + water} (i.e., {NMPD + water}, {2MPD + water}, {3MPD + water}, {4MPD + water}) are reviewed. Thermodynamic properties of interest are phase equilibrium and energetic data (hE and cEP). These literature data are reported in Table 1. Note that calorimetric measurements performed in this study or in other literature studies make it possible to measure M enthalpy (hM liq) or heat capacity (cP,liq) changes on the mixing of liquid solutions. According to a recent discussion,18,19 in the particular case for which pure species and their related mixtures are in the same aggregation state at given temperature and pressure (liquid state in the present case), enthalpy and heat capacity changes on mixing are strictly equal to excess enthalpies (hEliq) and excess heat capacities (cEP,liq), respectively. p M z liq =

liq stable state E ∑ xi[z pure (T , P)] + z liq i(T , P) − z pure i i=1

for z ∈ {h; cP} E = z liq , if pure i are stable liquids at (T , P)

(1)

Thus, the terms “excess enthalpy” and “excess heat capacity” will be used thereafter to designate the measured data. B



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al.11 for amine mole fractions lower than 0.0211 and for temperatures below 385.15.K. Deviations between experimental amine mole fractions in water published by different authors appear at higher concentrations. LLE data measured by Coulier et al.11 are in agreement with those determined by Stephenson for amine mole fractions x2MPD up to 0.05. Above this value, temperature deviations remain in the experimental uncertainty range. The representation of all the available LLE data for the {2MPD + water} system is given in section IV.4. LCST values reported in the literature or deduced from LLE measurements are shown in Table 3.

To better identify the lack of experimental information, a description of the experimental data collected by authors in previous studies is first proposed for each of these four binary mixtures. It is followed by a description of the data measured in the present study. II.1. {NMPD + Water} System. The LLE behavior was first investigated by Flaschner10 and Stephenson.14 A critical evaluation of these LLE data was proposed by Goral et al.20 Recently, Coulier et al.11 on the one hand, and Marczak et al.,15 on the other hand, published new LLE data. LLE data reported by Marczak et al.15 are similar to those by Coulier et al.11 in the mole fraction range 0 < xNMPD < 0.3. At higher concentrations, slight deviations appear. A significant scatter of deviations is observed among all the published LLE data (see section IV.4). Coulier et al.11 pointed out that these discrepancies could be ascribed to a lack of purity of the Nmethylpiperidine compound used for the measurements. Goral et al. reported two liquid−liquid critical points for this system: the lower critical solution temperature (LCST) and the upper critical solution temperature (UCST) were estimated at 319.4 K, for an amine mole fraction xNMPD = 0.035, and 544.4 K for xNMPD = 0.10, respectively,20 as mentioned in Table 2.

Table 3. Comparison between the LCST Values and Corresponding Critical Composition of the {2MPD + Water} System Reported by Different Authors or Deduced from LLE Data authors 11

(LCST) (K)

Coulier et al.11 Marczak et al.

15

xLCST NMPD (mol/mol)

315

0.07

316.7

0.06

Stephenson14

317.2

Flaschner10

321.4

0.07 0.04

Goral et al.20

319.4

0.035

Schneider16

319.2

0.05

xLCST 2MPD (mol/mol)

339

0.07

Schneider

344.9

0.05

Stephenson14

343.2

Flaschner and MacEwen12

352.5

Coulier et al. 16

Table 2. Comparison between the LCST Values and Corresponding Critical Composition of the {NMPD + Water} System Reported by Different Authors or Deduced from LLE Data authors

(LCST) (K)

0.06 0.04

comments explicitely provided in ref 11 explicitely provided in ref 16 explicitely provided in ref 14 deduced from LLE data explicitly provided in ref 12

As previous, isoplethic VLE data (measured at the following mole fractions: xNMPD = 0.0591, xNMPD = 0.0722, xNMPD = 0.1538) were reported by Dergal.21 Moreover, isothermal VLE data (for temperatures equal to 298.15 and 308.15 K) were reported for various amine mole fractions by Nakanishi et al.22 Regarding energetic properties, Coulier et al.17 reported molar excess enthalpy and molar excess heat capacity data measured at [0.5 MPa; (303.15 to 338.15) K] and [0.1 MPa; (283.15 to 333.15) K], respectively. II.3. {3MPD + Water} System. LLE data related to the {3MPD + water} system were investigated by Flaschner13 and Stephenson.14 A critical evaluation of these LLE data was proposed by Goral et al.20 As for the {NMPD + water} system, Goral et al.20 reported liquid−liquid critical data: the LCST was estimated at 329.7 K, for an amine mole fraction x3MPD = 0.045 and the UCST was estimated at 507.0 Kfor x3MPD = 0.095, respectively. The representation of all of these data is given in section IV.4. LCST values reported in the literature or deduced from LLE measurements are shown in Table 4. To the best of our knowledge, no hE or cEP data and no VLE data were published in the literature for this system.

comments explicitly provided in ref 11 explicitly provided in ref 15 explicitly provided in ref 14 deduced from LLE data explicitly provided in ref 10 explicitly provided in ref 20 explicitly provided in ref 16

In Table 2, a good agreement between LCST values deduced from Marczak et al.,15 Coulier et al.,11 and Stephenson14 measurements was found while Flaschner10 reported a 7 K lower LCST value. Note that particularly interesting is the article by Schneider,16 describing how LCST moves with pressure. Such a study was repeated for the three other systems investigated here. Isoplethic vapor−liquid equilibrium (VLE) data (measured at the following mole fractions: xNMPD = 0.0591, xNMPD = 0.0722, xNMPD = 0.1538) were reported by Dergal.21 In addition, molar excess enthalpies were reported for various amine mole fractions and temperatures in the range (308.15 to 328.15) K at a fixed pressure of 0.5 MPa by Coulier et al.17 Molar excess heat capacities were measured by the same authors for various amine mole fractions at 0.1 MPa in the temperature range (283.15 to 308.15) K. II.2. {2MPD + Water} System. LLE data were first studied by Flaschner and MacEwen,12 Stephenson,14 and lately by Coulier et al.11 Data measured by Flaschner and MacEwen agree well with data reported by Stephenson and Coulier et

Table 4. Comparison between the LCST values and Corresponding Critical Composition of the {3MPD + Water} System Reported by Different Authors or Deduced from LLE Data (LCST) (K)


Schneider16

340.3

0.05

Stephenson14 Flaschner13 Goral et al.20

340.2 330.1 329.7

0.05 0.04 0.045

authors

C

comments explicitly provided in ref 16 deduced from LLE data deduced from LLE data explicitly provided in ref 20



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III.1.B. Techniques. B.1. LLE. Liquid−liquid equilibrium data were obtained using the cloud point method. It consists in determining the temperature at which a second liquid phase appears or disappears in the binary liquid system {amine + water}. For that purpose, two apparatuses designed by Coulier et al.23 were used. The main difference between these two techniques is the arrangements of the liquid−liquid equilibrium cells employed to visualize the appearance of the turbidity in the liquid mixture. The first technique uses an equilibrium cell SPM20 from Thar Technologies and the second one uses a sapphire cell. More details of the experimental arrangements are given in ref 23. The experimental protocol consists of steeply increasing the temperature by small increments inside the liquid−liquid equilibrium cell filled with the {amine + water} solution beforehand. The phase separation is visually determined when clear solution goes through a cloud point. The uncertainty of the temperature of the cloud point estimated from reproducibility tests is less than 2 K while the uncertainty of such a temperature determination for one experiment is better than 0.5 K. B.2. Excess Enthalpy. As mentioned above, in the experimental conditions under which the measurements were performed, excess enthalpies of {amine−water} systems are equal to enthalpy changes on mixing. These latter were estimated from heat of mixing measurements, as described previously by Coulier et al.17 Briefly the heat of mixing is determined as a function of the amine composition using a flow-mixing cell custom-made for a BT2.15 calorimeter from Setaram. Experiments were performed at constant temperature (±0.01 K) and pressure. Pure amine and water mixed into the mixing cell located in the calorimetric block where the heat flux due to mixing is measured. The two fluids flow at constant volume flow rate using two high-pressure syringe pumps (Isco model 100 DM). In order to maintain the constant molar flow rate, the pumps are temperature controlled at 303.15 ± 0.1 K. The molar flow rates are derived from the volume flow rates of the pumps using fluid densities. The densities of water are calculated using the equation of state from REFPROP24 and the densities of pure amines are issued from Lowe.25 The excess enthalpy is derived from the calorimetric signal, detected by the thermopile surrounding the mixing cell. This calorimetric signal Δ signal (mV) is first converted into heat power using a calibration constant K (mV·mW−1) and then, into molar enthalpy using the molar flow rates of the fluids (nȧ for the amine and n ̇w for water) as indicated in eq 2.

II.4. {4MPD + Water} System. The LLE behavior of the {4MPD + water} system was studied by Flaschner13 and Stephenson.14 A critical evaluation of these LLE data was proposed by Goral et al.20 The LCST and the UCST were estimated by these latter at (358.4 K, x4MPD = 0.06) and (462.2 K, x4MPD = 0.085), respectively. LCST values reported in the literature or deduced from LLE measurements are shown in Table 5. Table 5. Comparison between the LCST Values and Corresponding Critical Composition of the {4MPD + Water} System Reported by Different Authors or Deduced from LLE Data (LCST) (K)


Schneider16

360.2

0.07

Stephenson14

359.2

Flaschner13

358.1

0.05 0.05

Goral et al.20

358.4

0.06

authors

comments explicitly provided in ref 16 explicitly provided in ref 14 deduced from LLE data explicitly provided in ref 13 explicitly provided in ref 20

To the best of our knowledge, no hE or cEP data and no VLE data was published in the literature for this system. II.5. New Measured Data. To complete the database of {methylpiperidine + water} systems, excess enthalpy and LLE data were measured for the {3MPD + water} and {4MPD + water} systems. They are reported in Part A of the Supporting Information. A summary of the new measured data is presented in Table 6. Table 6. New Experimental Data Published in the Present Paper property {3-MPD + Water} LLE: (T, xαamine, xβamine) Excess enthalpy: (T, xamine, hE) {4-MPD + Water} LLE: (T, xαamine, xβamine) Excess enthalpy: (T, xamine, hE)

N points

(T/K)

9 88

[339.9−355.4] [303.15; 313.15; 323.15; 333.15]

9 90

[360−365] [303.15; 313.15; 323.15; 333.15]

III. MEASUREMENTS OF LIQUID−LIQUID EQUILIBRIA AND ENERGETIC PROPERTIES FOR THE {3-MPD + WATER} AND {4-MPD + WATER} SYSTEMS III.1. Experimental Section. III.1.A. Materials. 3-Methylpiperidine (3MPD) and 4-methylpiperidine (4MPD) were used without further purification. Water was distilled and degassed under vacuum before use (resistivity 18.2 MΩ·cm). Aqueous solutions used for LLE measurements were prepared by mass with an uncertainty on mass fraction estimated to be better than ±10−4. Aqueous solutions were stored in a glass bottle in an opaque cabinet to prevent any photodegradation. Suppliers, purities, and CAS numbers of all chemicals used in this study are given in the Supporting Information in Table S1. The amount of water contained in methylpiperidines samples was not considered in calculation of the mole fraction.

hE =

Δ signal K (na + n w )

(2)

The relative uncertainty on amine composition and excess enthalpies are less than 3% and 5%, respectively. III.2. Results. III.2.A. LLE. LLE data for the {3MPD + water} and {4MPD + water} systems are reported in Part A of the Supporting Information and are represented in Figure 4a and Figure 5a, respectively. According to our measurements, the temperature versus mole fraction phase diagram for the {3MPD + water} system exhibits a LCST at 340 K for an amine molar fraction x3MPD = 0.043. This LCST agrees well with the values given by Stephenson14 and Schneider16 but is about 10 K above the value reported by Flaschner.13 D



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other words, it has been observed throughout this study that if a model can properly describe LLE behavior, it has always the capacity to describe properly VLE behavior (this statement is illustrated by the results presented below) • There is no abundant experimental VLE experimental data in the literature for these systems (VLE experimental data are available only for {2MPD + water} systemsee Table 1) Molar excess heat capacity data were also disregarded for the following reasons: • Their absolute experimental value is rather low in comparison with pure component heat capacity values. In other words, experimental cEP terms have a low contribution to the total cP of the mixture, • It has been observed that the reproduction of the cEP evolution with the amine mole fraction and the temperature is especially difficult for a thermodynamic model. According to classical thermodynamics:

Our measurements also highlight that the phase diagram of the {4MPD + water} system exhibits a LCST at 361 K and an amine molar fraction x4MPD = 0.05. By taking into account the experimental uncertainties, it is possible to claim that this LCST agrees well with the values deduced from Stephenson14 and Flaschner13 measurements. It can be observed that changing the methyl group piperidine ring from the meta position (3MPD) to the para position (4MPD) entails a significant temperature increase of the LCST (of around 20 K). This LCST increase can be explained in terms of hydrogen bonding between water molecules and the substituted piperidines. In the case of the 3MPD compound, the free electron pair may be hindered by the methyl group due to the conformation of the amine molecule contrary to the case of the 4MPD compound. III.2.B. Excess Enthalpy. Molar excess enthalpy data for the {3MPD + water} and {4MPD + water} systems were measured for various amine mole fractions, at the following temperatures: (303.15, 313.15, 323.15, 333.15) K and at a constant pressure of 1.0 MPa. Experimental data are provided in Part A of the Supporting Information and shown in Figure 4b and Figure 5b, respectively. All these data were measured at temperatures such that the liquid phase remains stable over the entire composition range, that is, at temperatures lower than the LCST (340 and 361 K for the {3MPD + water} and {4MPD + water} systems, respectively). Figure 4b and Figure 5b show negative excess enthalpies which increase when the temperature increases. The isothermal hE versus amine mole fraction curves all exhibit a minimum characterized by a nearly constant amine mole fraction (xamine remains in the mole fraction range 0.40−0.45). The magnitude of the minima of excess enthalpies varies from −3130 J·mol−1 at 303.15 K to −2540 J·mol−1 at 333.15 K for the {3MPD + water} system, and from −3155 J·mol−1 at 303.15 K to −2500 J·mol−1 at 333.15 K for the {4MPD + water} system. For both systems, an exothermic effect is observed, resulting from the interaction of the amine and −OH groups in water. This effect softens as temperature increases.

ij ∂cPE yz i 2 Ey jj zz = jjj ∂ h zzz jj zz jj 2 zz k ∂T { P , x k ∂T { P , x

(3)

• While reproducing hE data with a reasonable order of magnitude was already a challenging task, reproducing how cEP data move with the temperature is even more difficult since it is only made possible at the condition that the concavity of the hE versus T curve is properly predicted. On the contrary, all the available experimental data were used to evaluate the model performances (LLE, VLE, hE and cEP data). More details can be found below (see section IV.4.D). IV.2. On the Selection of an Appropriate Modeling Approach. A thermodynamic model (i.e., a set of equations and corresponding parameters) is now searched for reproducing the experimental data points related to the four {amine + water} binary systems that were either measured in the frame of this study or collected in the open literature. To perform this modeling study, various thermodynamic approaches were considered. At this step, let us mention that for the sake of simplicity and applicability through chemical-engineering simulation software, it has been decided to ignore chemical reactions taking place between piperidines and water. Considering such reactions would considerably increase the modeling complexity and the number of input parameters for a limited gain of accuracy. In our opinion, the addition of chemical reaction contributions will be justified if, and only if, the present modeling approach does not provide accurateenough results. To the best of our knowledge, this study is the first attempt to model simultaneously the LLE, hE, cEP (and VLE, when available) property behaviors for the four binary systems of interest. This task is actually highly challenging not only because it is expected from the model to account for phaseequilibrium properties (LLE) as well as one derivative property (in the sense that hE is a first-order temperature derivative of the excess Gibbs energy characteristic function), but also, above all, due to the inner thermodynamic complexity of the systems. From a methodologic viewpoint, it was decided to only consider equations of state (EoS) and activity coefficient models (g E models) which are the unique types of

IV. SIMULTANEOUS CORRELATION OF ENERGETIC AND LLE DATA IV.1. Data Used for Model-Parameter Estimation, Data Used for Model Evaluation. As discussed above, the thermodynamic behavior of the four {amine + water} systems considered is complex, which entails real difficulties to describe simultaneously LLE and energetic data with a unique set of model parameters. More details are given in the last part of this paper. For fitting model parameters, only LLE and hE data were considered. VLE data were disregarded for the following reasons: • Even if the considered systems present high deviations from ideal behavior (highlighted by the instability of their liquid phases), their reproduction stays governed in a larger extent by the vapor-pressure values of pure species and in a lesser extent, by the activity-coefficient or fugacity values. In other words, similar VLE predictions were obtained regardless of the considered thermodynamic model while very different LLE or hE behaviors were obtained depending on the chosen model and the corresponding parameters. Consequently, adding VLE data in the objective function does not improve significantly the capabilities of the model. In E



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Table 7. Presentation of the Thermodynamic Models Investigated and Summary of the Model-Selection Procedure (i.e., Capability for Each Model to Predict LLE and Energetic Experimental Data for the {NMP + water} System)a

a

Notation: EoS, equation of state; MR: mixing rule, SRK; Soave−Redlich−Kwong; PR, Peng−Robinson.

thermodynamic models present in chemical-engineering simulation software. To do so, 10 different thermodynamic models, available in the ProSim Plus simulation software, were tested out and are listed in Table 7. These models were selected because they were deemed as well representative of the approaches likely to provide accurate-enough results in the present case. More precisely: 8 cubic EoS involving different types of mixing rules (including classical and advanced mixing rules) and 2 gE models were considered. A short description of the mixing rules (i.e., the expressions for the attractive parameter am and covolume bm) used in the 8 cubic EoS is presented in Scheme 1. As mentioned above, the candidate-model parameters were fit to LLE and hE data exclusively. The model selection procedure is graphically described in Figure 1 and was Scheme 1. Description of Mixing Rules Presented in Table 7

Figure 1. Methodology to select an appropriate thermodynamic model capable of reproducing both LLE and hE.

implemented for each thermodynamic model mentioned in Table 7. For each model candidate, (i) its capacity to reproduce separately LLE and energetic (hE) data (i.e., with specific model parameters for each kind of properties) is tested first; (ii) if the first test passed, a unique set of model parameters was searched for reproducing simultaneously LLE and energetic properties (first, at a given temperature and then, at any temperature). Note that for each test, success or failure was evaluated qualitatively, by looking at LLE phase diagrams and isothermal hE-composition planes. At each step of the procedure, the search for optimal parameters was performed using the regression procedure described in the next section. F



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Figure 2. Modeling of LLE, hE, cPE and VLE data for the {NMPD + water} system. Continuous line, NRTL. (a) LLE: +, Coulier et al.;11 ×, Flaschner;10 □, Stephenson;14 ◊, Marczak et al.;15 ∗, Goral et al.;20 ■, Schneider.16 (b) VLE isopleths: +, xNMPD = 0.0591; ×, xNMPD = 0.0722; □, xNMPD = 0.1538, experimental data from Dergal.21 (c) hE: +, T = 308.15 K; ×, T = 318.15 K; □, T = 328.15 K, experimental data from Coulier et al.17 Liquid−liquid phase split areas are highlighted with a bold line. (d) cEP: +, T = 283.15 K; ×, T = 293.15 K; □, T = 303. 15 K; ◊, 313.15 K; ∗, 323.15 K; ○, 333.15 K, experimental data from Coulier et al.17 Demixtion areas are highlighted with a bold line.

As a last step, the two model candidates were benchmarked over all the data (LLE and hE, at any temperature) and only the multiparameter NRTL gE model passed the test (the EoS failed in reproducing the temperature behavior of the h E experimental data). To conclude, the multiparameter NRTL gE model was selected for the rest of this study and is succinctly described in the Supporting Information. IV.3. Methodology for Model Parametrization. The multiparameter NRTL model includes 14 adjustable binary parameters at the most. One of the main issues investigated in this part of the study was to determine, for each binary system, how many parameters among the 14 ones available are strictly necessary for ensuring a proper representation of LLE and hE experimental data points. In other words, it was necessary to evaluate the sensitivity of experimental properties to each model parameter, which was performed following a trial-anderror procedure. The determination of the model parameter was performed using an optimization procedure. Equation 4 shows the expression selected for the objective function:

As the four binary mixtures studied exhibit similar LLE and energetic-property behaviors, the thermodynamic-model choice procedure was only performed one time, by considering the {NMPD + water} system as a reference system and by assuming that the model selected for this system remains optimal for the three other ones. Details related to the modelselection procedure can be found in Table 7. As observed in Table 7, for most of the investigated models, it was possible to find one set of parameters making it possible to reproduce only energetic experimental data (hE in the present case) at any temperature. For a notably less copious number of models, sets of model parameters could be found for representing LLE data only. Nevertheless, and as expected, most of the models failed in reproducing simultaneously LLE and energetic data. Among the 10 investigated models, only 2 of them were able to offer an acceptable (at least, qualitatively) thermodynamic representation of the binary-system behaviors (using a unique set of model parameters) at one temperature: (i) the SRK EoS using the MHV2 mixing rules coupled with an activity coefficients model (a multiparameter NRTL model version was selected) and (ii) a multiparameter NRTL gE model (see Supporting Information). Both these models involve a maximum number of adjustable binary parameters equal to 14. G



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Table 8. NRTL Binary Parameter Values for the Four Considered Binary Mixtures {NMPD-water} a b c d e f g

{2MPD-water}

{3MPD-water}

{4MPD-water}

ij

ji

ij

ji

ij

ji

ij

ji

−1.8862309 389.60375 −56856.407 0.24311981 0 −15.110399 0

168.51859 −13066.792 707852.42 −22.985245 0 0.19247733 0

−1.7965896 295.7578 −37031.217 0.24343123 0 −15.746035 0

167.39657 −12198.144 491023.74 −22.991251 0 0.34515729 0

−1.7889543 294.11216 −37099.904 0.24343904 0 −15.742225 0

167.50981 −12287.513 491757.17 −22.991118 0 0.34585011 0

−1.79 294.11216 −37099.904 0.24343904 0 −15.742225 0

167.29 −12287.513 491757.17 −22.991118 0 0.34585011 0

l LLE hE o o Fob = wLLEfob + w hMf ob o o o o o o Nptprop o o propiexp − propicalc 1 m prop o f = ∑ o ob o o Nptprop i = 1 propiexp o o o o LLE o o with prop = {hE ; xamine } n

adjusted with the {NMPD + water} system and then applied in a similar way to the three remaining binary systems. Note however that the optimal model-parameter values determined for the {NMPD + water} system were systematically included in the set of initial parameter values tested out with the three other systems. It should be reported that for the four binary systems investigated, the eij, eji, gij, and gji parameters (see Supporting Information) have no effect on the modeling efficiency and were consequently set to 0. IV.4. Results and Discussion. Experimental data points are now compared to data estimated from the multiparameter NRTL gE model and the corresponding parameter sets determined in the previous section. In Figures 2−5, LLE data are represented in a temperaturemole fraction phase diagram, hE data are reported in an isobaric−isothermal hE-mole fraction projection. For the sake of clarity, error bars were not represented in the figures showing hE and cEP data but can be seen in a file provided as Supporting Information. As mentioned above, VLE and cEP data found in the literature are also considered to benchmark the predictive capability of the proposed model. Binary parameter values for the four binary systems are reported in Table 8. A. {NMPD + Water} System. A scatter of deviation is first observed among the various LLE data sets measured by the various authors (Figure 2a). As an example, Flaschner predicts a minimum water solubility in the amine-rich phase near xamine = 0.65 while we did not find an experimental evidence of such a behavior. The model makes it possible to predict rather accurately the global LLE behavior including the UCST and LCST at the price of a high number of binary model parameters. Isopleth VLE experimental data (at fixed composition) are also perfectly reproduced by the model (Figure 2b). In addition, the model represents properly the temperature evolution of hE data and predicts rather accurately the composition of the minima in the hE-amine mole fraction planes (Figure 2c). As previously mentioned, although the multiparameter NRTL model predicts properly the order of magnitude of cEP data, it fails in reproducing the correct temperature evolution trend (see Figure 2d). This failure is discussed in section IV.3.D. B. {2MPD−Water}. As previously observed for the {NMPD + water} system, the experimental LLE behaviors measured by different authors are not in perfect agreement. Note that Flaschner was the only experimentalist to observe a minimum water solubility in the amine-rich phase (probably, because of the large temperature range covered by his measurements). It seems that the fitted parameters of the multiparameter NRTL

(4)

where the amine mole fraction in the aqueous phase at fixed LLE temperature and pressure is denoted xamine , w denotes prop weighting factors, and Npt denotes the number of considered points for each property. Note that relative deviations were considered in the objective function making it possible to sum deviations on LLE mole fraction and deviations on excess enthalpy data. As model parameters are much more sensitive to LLE data than to hE data, weighting factors were initially set to wLLE = 50 and whE = 1 and then, manually adjusted (if necessary) to ensure the best compromise between the reproduction of LLE and hE data. It is recalled that the data not used in the fitting procedure (i.e., VLE and cEP data) were used in order to validate the optimal model parameters a posteriori. Moreover, regarding hE data, since: (i) one of the main objectives of the model-parameter fitting procedure was to find a parameter set enabling an accurate reproduction of the minima located in the Moreover, regarding hE data, since: (i) one of the main objectives of the model-parameter fitting procedure was to find a parameter set enabling an accurate reproduction of the minima located in the isothermal hE versus amine mole fraction curves; (ii) such curves are constrained to pass through the (xamine = 0; hE = 0) point, (iii) high relative deviations are systematically obtained at low amine concentration (because hE values are low); it was decided to disregard data when the amine mole fraction was lower than 0.1. For fitting model parameters, two different optimization methods were implemented, and their results were compared: these are the Nelder−Mead and Gauss−Newton methods. When mutually agreeing, solutions returned by both algorithms were kept. Regarding the determination of the appropriate number of model parameters, we proceeded as follows: the 3-parameter NRTL model (these three parameters are aij, aji, and f ij = f ji) was investigated first. Observing the impossibility to get accurate results using only three parameters, model parameters were gradually added until a proper description of the target properties was obtained. Note that this procedure relies essentially on a visual analysis of the LLE phase diagrams and excess enthalpy−composition diagrams. The optimization procedure (including also the search for efficient initial values and the number of optimization runs with different initialization sets for each binary system) was H



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Figure 3. Modeling of LLE, hE, cPE, and VLE data for the {2MPD + water} system. Continuous line, NRTL. (a) LLE: +, Coulier et al.;11 ×, Flaschner;12 □, Stephenson;14 ◊, Schneider.16 (b) VLE isopleths: + , x2MPD = 0.0591; ×, x2MPD = 0.0722; □, x2MPD = 0.1538, experimental data from Dergal.21 (c) VLE isotherms: +, T = 298.15K; ×, T = 308.15 K, experimental data, Nakanishi et al.22 (d) hE: +, T = 303.15 K; ×, T = 308.15 K; □, T = 318.15 K; ◊, 328.15 K; ∗, 333.15 K; ○, 338.15 K, experimental data from Coulier et al.17 Demixtion areas are highlighted by a bold line. (e) cEP: +, T = 283.15 K; ×, T = 293.15 K; □, T = 303.15 K; ◊, 313.15 K; ∗, 323.15 K; ○, 333.15 K, experimental data from Coulier et al.17.

predicting the evolution of cEP data with temperature. More details are provided in section IV.3.D. C. {3MPD − Water} and {4MPD − Water}. Similar conclusions can be drawn for these two systems by comparison with previous ones. The multiparameter NRTL model provides a satisfactory representation of experimental LLE data in spite of a significant scatter of deviation between measurements made by different authors (Figures 4a and 5a). The hE property of these two binary systems are well predicted by the model (Figures 4b and 5b)), and especially at low temperature (in particular in terms of order of magnitude,

model induce a compromise between the conflicting experimental behaviors. VLE isopleths and isothermal pressure−composition projections are well predicted by the model (Figure 3b). The representation of hE experimental data for this system are satisfactory since the order of magnitude, the minimum location, and the temperature evolutions of this property are properly reproduced by the model (Figure 3d). Regarding the prediction of cEP data (Figure 3e), deviations are more important than for the {NMPD + water} system, especially at low temperature. Moreover, the model fails in I



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Figure 4. Modeling of LLE and hE data for the {3MPD + water} system. Continuous line, NRTL. (a) LLE: +, this study; ×, Flaschner;13 □, Stephenson;14 ◊, Schneider;16 ∗, Goral et al.20 (b) hE. +, T = 303.15 K; ×, T = 313.15 K; □, T = 323.15 K; ◊, 333.15 K, experimental data measured in this study..

Figure 5. Modeling of LLE and hE for the {4MPD + water} system. Continuous line, NRTL. (a) LLE: +, Coulier et al.; ×, Flaschner;13 □, Stephenson;14 ◊, Schneider;16 ∗, Goral et al.20 (b) hE. +, T = 303.15 K; ×, T = 313.15 K; □, T = 323.15 K; ◊, 333.15 K, experimental data measured in this study..

minimum location, and evolution with increasing temperature). D. Comment on the Evolution of cEP with Temperature Predicted from the Model for the {NMPD + Water} and {2MPD + Water} Systems. Experimental values of cEP increase with increasing temperature for both systems. Consequently, according to eq 5, experimental excess enthalpy data should exhibit a convex behavior in the (hE, T) plane. ij ∂cPE yz i 2 Ey jj zz = jjj ∂ h zzz jj zz jj 2 zz k ∂Ö≠TÖÖÖÖÖÖÖÖÖ { PÖÆ, x k ∂T { P , x ´ÖÖÖÖÖÖÖÖÖ >0

(5)

Nevertheless, in practice, it is highly difficult to determine whether hE is a convex function for both systems, as illustrated in Figure 6. The reason is that the concave/convex character of the hE versus temperature data is rather mild and furthermore, that experimental data are affected by experimental uncertainty. While the model predicts slightly concave hE versus temperature behavior, it should actually predict a slightly convex behavior in order to be in agreement with c PE measurements. If cEP data had been used as target property for fitting model parameters, the temperature evolution of cEP

Figure 6. Representation of experimental hE vs T data at fixed amine mole fractions for the {NMPD + water} and {2MPD + water} systems. For the sake of clarity, experimental data are connected with straight lines. Continuous line, {2MPD + water}; dashed line, {NMPD + water}: ○, xamine = 0.5; ×, xamine = 0.6; ◊, xamine = 0.7. Data were obtained by smoothing experimental data.

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ProSim Company, for their help and support during the modelling phase of the present study.

data would have been properly predicted at the price of a slight deterioration of hE predictions. In this study, it was decided to favor the reproduction of hE data with respect to the reproduction of cEP data.

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(1) Bui, M.; Adjiman, C. S.; Bardow, A.; Anthony, E. J.; Boston, A.; Brown, S.; Fennell, P. S.; Fuss, S.; Galindo, A.; Hackett, L. A.; Hallett, J. P.; Herzog, H. J.; Jackson, G.; Kemper, J.; Krevor, S.; Maitland, G. C.; Matuszewski, M.; Metcalfe, I. S.; Petit, C.; Puxty, G.; Reimer, J.; Reiner, D. M.; Rubin, E. S.; Scott, S. A.; Shah, N.; Smit, B.; Trusler, J. P. M.; Webley, P.; Wilcox, J.; Mac Dowell, N. Carbon capture and storage (CCS): the way forward. Energy Environ. Sci. 2018, 11, 1062− 1176. (2) Sreedhar, I.; Nahar, T.; Venugopal, A.; Srinivas, B. Carbon capture by absorption − Path covered and ahead. Renewable Sustainable Energy Rev. 2017, 76, 1080−1107. (3) Liebenthal, U.; Pinto, D. D. D.; Monteiro, J.G.M.-S.; Svendsen, H. F.; Kather, A. Overall Process Analysis and Optimisation for CO2 Capture from Coal Fired Power Plants based on Phase Change Solvents Forming Two Liquid Phases. Energy Procedia 2013, 37, 1844−1854. (4) Shen, Y.; Jiang, C.; Zhang, S.; Chen, J.; Wang, L.; Chen, J. Biphasic solvent for CO2 capture: Amine property-performance and heat duty relationship. Appl. Energy 2018, 230, 726−733. (5) Zhuang, Q.; Clements, B.; Dai, L.; Carrigan, J. Ten years of research on phase separation absorbents for carbon capture: Achievements and next steps. Int. J. Greenhouse Gas Control 2016, 52, 449−460. (6) Raynal, L.; Alix, P.; Bouillon, P.-A.; Gomez, A.; de Nailly, M. le F.; Jacquin, M.; Kittel, J.; di Lella, A.; Mougin, P.; Trapy, J. The DMXTM process: An original solution for lowering the cost of postcombustion carbon capture. Energy Procedia 2011, 4, 779−786. (7) Raynal, L.; Bouillon, P.-A.; Gomez, A.; Broutin, P. From MEA to demixing solvents and future steps, a roadmap for lowering the cost of post-combustion carbon capture. Chem. Eng. J. 2011, 171, 742−752. (8) Raynal, L.; Briot, P.; Dreillard, M.; Broutin, P.; Mangiaracina, A.; Drioli, B. S.; Politi, M.; La Marca, C.; Mertens, J.; Thielens, M.-L.; Laborie, G.; Normand, L. Evaluation of the DMX Process for Industrial Pilot Demonstration − Methodology and Results. Energy Procedia 2014, 63, 6298−6309. (9) Aleixo, M.; Prigent, M.; Gibert, A.; Porcheron, F.; Mokbel, I.; Jose, J.; Jacquin, M. Physical and chemical properties of DMXTM solvents. Energy Procedia 2011, 4, 148−155. (10) Flaschner, O. Die gegenseitige Löslichkeit der Piperidine mit Wasser. Z. Phys. Chem. 1908, 62U, DOI: 10.1515/zpch-1908-6228. (11) Coulier, Y.; Ballerat-Busserolles, K.; Rodier, L.; Coxam, J.-Y. Temperatures of liquid−liquid separation and excess molar volumes of {N-methylpiperidine−water} and {2-methylpiperidine−water} systems. Fluid Phase Equilib. 2010, 296, 206−212. (12) Flaschner, O.; MacEwen, B. XCVI.The mutual solubility of 2-methylpiperidine and water. J. Chem. Soc., Trans. 1908, 93, 1000− 1003. (13) Flaschner, O. LXXXI.The miscibility of the pyridine bases with water and the influence of a critical-solution point on the shape of the melting-point curve. J. Chem. Soc., Trans. 1909, 95, 668−685. (14) Stephenson, R. M. Mutual solubility of water and pyridine derivatives. J. Chem. Eng. Data 1993, 38, 428−431. (15) Marczak, W.; Łȩzṅ iak, M.; Zorȩbski, M.; Lodowski, P.; Przybyła, A.; Truszkowska, D.; Almásy, L. Water-induced aggregation and hydrophobic hydration in aqueous solutions of N-methylpiperidine. RSC Adv. 2013, 3, 22053. (16) Schneider, G. Druckeinfluß auf die Entmischung flüssiger Systeme. Z. Phys. Chem. 1963, 39, 187−197. (17) Coulier, Y.; Ballerat-Busserolles, K.; Mesones, J.; Lowe, A. R.; Coxam, J.-Y. Excess Molar Enthalpies and Heat Capacities of {2Methylpiperidine−Water} and {N -Methylpiperidine−Water} Systems of Low to Moderate Amine Compositions. J. Chem. Eng. Data 2015, 60, 1563−1571.

V. CONCLUSION In this article, the modeling of the thermodynamics (and in particular, LLE and energetic properties) of four amine + water systems that could be of interest for CCS processes, is investigated. Energetic data refer here to hE and cEP data. In addition to the VLE, LLE, and energetic data that were found in the literature, it was decided to complete the database by measuring new LLE and energetic data for the {3MPD + water} and {4MPD + water} systems. As a result, 18 new experimental LLE data and 178 new hE data are reported. Different modeling approaches were tested involving equations of state and activity-coefficient models. The multiparameter NRTL activity coefficient model was selected for its capacity to reproduce VLE, LLE solubility, and energetic data. To the best of our knowledge, this paper is the first proposed study attempting to correlate simultaneously all these kinds of property data for the four considered {amine−water} systems. Eventually, four sets of NRTL parameters were found for the four binary systems. Despite the high difficulty to model such systems, the proposed model describes satisfactorily VLE, LLE (including the LCST and UCST), and hE data. Prediction of cEP data are however less accurate.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00974.

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REFERENCES

Tables of the chemicals, the experimental LLE, and excess enthalpie; figures illustrating the abilities of the thermodynamic model to reproduce experimental excess enthalpies and to predict excess heat capacities at different temperatures; description of the multiparameter NRTL gE model selected in this work to represent the thermodynamics properties of four amine + water systems (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID

Yohann Coulier: 0000-0002-1434-3974 Romain Privat: 0000-0001-6174-9160 Funding

This work is realized with the financial support of ANR and NSERC through an international collaborative project between France and Canada named DACOOTA (No. ANR-12-IS090001-01). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Romain Privat and Edouard Moine would like to thank warmly Mr. Olivier Baudouin and Mr. Stéphane Déchelotte, from the K



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Thermodynamic Study of Four {Methylpiperidine + Water} Systems

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