Federico
Milella
and
Marco
Mazzotti
*
Institute of Process Engineering, ETH Zurich, 8092 Zurich, Switzerland. E-mail: marco.mazzotti@ipe.mavt.ethz.ch
First published on 14th May 2019
The knowledge of the speciation and of the supersaturation of aqueous solutions of CO2 and NH3 is pivotal for the design and optimization of unit operations, e.g. absorption or crystallization, in the framework of ammonia-based CO2 capture systems. For this information to be available, however, complex analytical techniques and significant experimental effort are required. This work introduces a methodology for the estimation of the concentration of species in aqueous ammonia solutions of ammonium bicarbonate by using attenuated total reflection infrared spectroscopy (ATR-FTIR) and spectral modeling based on least squares methods. In particular, the methodology can be exploited for the on-line monitoring of the liquid composition of crystallizing suspensions of ammonium bicarbonate for which the information on the speciation is combined with a rigorous thermodynamic model to compute the activity-based supersaturation. Finally, this work paves the way for the estimation of the crystallization kinetics of ammonium bicarbonate formation in aqueous ammonia solutions which is of great importance for the design of industrial CO2 capture absorption processes that exploit solid formation.
The call for an improved accuracy in the description of the solid–liquid equilibrium of BC in aqueous ammonia solutions motivated this work in which a methodology for the measurement of the speciation of aqueous ammonia solutions of ammonium bicarbonate is developed. attenuated total reflection Fourier-transform infrared spectroscopy (ATR-FTIR)12,13 has been used to measure the overall carbon concentration, as well as the equilibrium speciation in solution. The advantage of such a technique over Raman spectroscopy, also used to study properties of this system,14–17 is that it allows for liquid-phase concentration monitoring exclusively, in spite of the presence of a solid phase suspended. The analysis of the IR spectrum of the mixtures reveals complex overlaps of the bands of the individual components that have been resolved by means of a simple but effective classical least squares (CLS) method. Then, the information retrieved has been used to estimate the solutes concentration while fulfilling the mass and charge balances in solution.
The BC solubility and the concentration estimates of the species in saturated aqueous ammonia solutions of BC at different nominal ammonia concentrations in the solvent (between 0 and 3% wt) have been, at first, compared to the literature data in the temperature range 8–23 °C. Then, they have been used to improve the accuracy of the description of the liquid–solid equilibrium of ammonium bicarbonate by using a thermodynamic model.
The article is organized as follows: section 2 introduces the thermodynamics of the system and, in particular, it discusses the electrolyte species that form in aqueous solutions of ammonia and CO2 and the chemical reactions involved. In section 3, the experimental setup, the analytical methods and the characterization techniques used are discussed with particular emphasis on the preparation of the standard analytes for the ATR-FTIR calibration measurements. Section 4 provides a description of the mathematical model used to resolve complex overlapping spectra and the estimation of the concentration of the individual species. Finally, in section 5 the methodology is applied to the case of real mixtures containing CO2, NH3, and H2O and a rigorous thermodynamic framework for the estimation of the supersaturation of aqueous ammonia solutions of ammonium bicarbonate is established.
Vapor–liquid equilibria:
CO2(g) ⇌ CO2(aq) | (1) |
NH3(g) ⇌ NH3(aq) | (2) |
H2O(g) ⇌ H2O | (3) |
Liquid speciation:
NH3(aq) + H2O ⇌ NH4+ + OH− | (4) |
CO2(aq) + H2O ⇌ H+ + HCO3− | (5) |
HCO3− ⇌ H+ + CO32− | (6) |
H2O ⇌ H+ + OH− | (7) |
NH3(aq) + HCO3− ⇌ NH2COO− + H2O | (8) |
Solid–liquid equilibria:
NH4+ + HCO3− ⇌ NH4HCO3(s) | (9) |
NH4+ + NH2COO− ⇌ NH2COONH4(s) | (10) |
2NH4+ + CO32− + H2 ⇌ (NH4)2CO3·H2O(s) | (11) |
4NH4+ + CO32− + 2HCO3− ⇌ (NH4)2CO3·2NH4HCO3(s) | (12) |
Due to the operating conditions adopted, the formation of H2O(s) (ice) has not been included in the set of solid–liquid equilibria considered.
Each of the equilibrium reaction of eqn (1) and (12) can be expressed as an equation of the form
(13) |
mNH4+ + mH+ − mOH− − mHCO3− − 2mCO32− − mNH2COO− = 0 | (14) |
After the equilibrium composition is found, eqn (9)–(12) are consulted to verify the presence of any solid phase. If one or more solid phases are formed, the corresponding equation(s) must be solved together with eqn (1)–(8).
Despite the fact that water and ammonia are completely miscible in the range of operating conditions explored, ammonia is considered a solute rather than a solvent. This choice allows for the application of the traditional tabulated standard state chemical potentials (NIST Tables) to ions and non-dissociated molecules for the equilibria calculations in water–ammonia–salt mixtures performed with the extended-UNIQUAC model as well as for the computation of the activity of NH3(aq) in solution.
This work uses molality, m, as solute concentration (mole of component per unit mass of water), where the solvent itself is a reactive species. Additionally, the concentrations of the components must satisfy the following overall mass balances, in addition to the charge balance of eqn (14).
(15a) |
(15b) |
In eqn (17), mC,OL and mN,OL are the overall concentration of carbon and nitrogen in the system, m(s)j, νj,C and νj,N are respectively the concentration of the j-th solid in the system (eqn (9)–(12)) and its carbon and nitrogen stoichiometric coefficients.
In our experimental setup, the presence of a gas phase, consisting mainly of inert air, leads to the evaporation of CO2, NH3, and H2O. This phenomenon can be minimized by reducing the dead gas volume of the reactor (see sec. 3.2.1), thus allowing to neglect the presence of a gas phase in the mass balances.
In this work, mixtures containing CO2, NH3, and H2O have been obtained by dissolving BC in aqueous ammonia solutions at different nominal ammonia concentrations in the solvent (up to 3% wt). While ammonium bicarbonate in water dissociates by forming equimolar mixtures of CO2 and NH3 (before speciation), the presence of an excess of ammonia shifts the ratio between the total nitrogen and carbon content, ζ, to values greater than one, and significantly affects the speciation in solution.
The overall composition of such systems can be identified in the ternary diagram shown in Fig. 1; each point in the diagram corresponds to the overall mass fraction of equivalent CO2, NH3, and H2O (regardless of the liquid speciation and of the number of phases present at a given temperature and pressure). Additionally, the composition of the solid compounds (eqn (9)–(12)) are shown as black points. Mixtures characterized by a molar ratio ζ of one are represented by the isopleth (dashed black line) that connects the composition of the BC salt to the pure water vertex, while the other two isopleths drawn represent systems that are characterized by a molar ratio ζ of 1.3 and 2.0.
Fig. 1 Ternary phase diagram for the CO2–NH3–H2O system at 15 °C and 1 bar obtained using the thermodynamic model proposed by Darde et al.6 The compositions are expressed in weight fractions and its construction and use have been described in detail elsewhere.18 The black dots (●) indicate the composition of the stable solid phases, namely ammonium bicarbonate (BC), ammonium carbonate monohydrate (CB), ammoniumsesquicarbonate (SC), and ammonium carbamate (CM). The dashed isopleths (black lines) refer to CO2, NH3, and H2O mixtures characterized by a constant ratio, ζ, between the nitrogen and carbon species, while a colorcode is used to indicate the pH of the liquid phase calculated using the thermodynamic model proposed by Darde et al.6 |
As a consequence of the equilibria of eqn (1)–(8), when comparable amounts of nitrogen and carbon are present in the system (ζ ≈ 1), the equilibria of eqn (4)–(5) leads to mildly alkaline solutions in which the ammonium and bicarbonate ions are the main species present (see sec. 5.6). As the value of ζ becomes larger than one, the mixture becomes more and more alkaline (see the pH of the liquid phase shown in Fig. 1 using a color code) shifting the carbon speciation towards the carbonate and carbamate species.
The formation of potassium carbonate hydrates has been minimized by exploiting a drying step of the raw material at 100 °C under vacuum for a period of about 5 hours.
Ammonia solutions have been prepared by diluting commercial ammonium hydroxide solutions (Sigma-Aldrich, puriss. p.a., reag. ISO, reag. Ph. Eur. 25% wt).
The immersion probes of the monitoring tools such as the ATRFTIR and FBRM have been connected to the reactor by means of custom-made pressure connectors installed in the lid of the vessel (the interested reader is referred to the ESI† for an illustration of the experimental setup).
The concentration of commercial ammonium hydroxide solutions has been measured by acid–base titration using a 702 SM Titrino (METROHOM, Switzerland) and a 1 M HCl solution as titrant.
m(l)C,OL = m(l)BC = mCO2 + mHCO3− + mCO32− + mNH2COO− | (16) |
(17) |
Binary subsystems consisting of an inorganic salt and water in which the ionic species of interest dissociate completely with negligible speciation have therefore been selected. It has to be acknowledged that, due to the electrolytic nature of the solutes, the measurement of the IR spectrum necessarily embeds the absorbance of the solvent that can be removed during post-processing.26 In this work the subsystems NH4Cl(aq), KHCO3(aq), K2CO3(aq), and NH3(aq) have been used to isolate the characteristic peaks of the ammonium, bicarbonate, carbonate ions, and ammonia respectively.11 This was possible thanks to the negligible extent of speciation of the single components within each subsystem. The presence of spectator ions such as K+ and Cl− is accounted for in the electroneutrality condition and does not affect the relevant dissociation equilibria. Moreover, their effect on the absorbance of the solute of interest has not been significant in the range of concentrations investigated.27 ATR-FTIR polythermal measurements12 have been performed using the aforementioned subsystems in the thermostated, stirred and sealed vessel described in section 3.2.1. The range of temperatures and concentrations selected for the different subsystems is representative of the range of equivalent CO2 and NH3 concentrations investigated in this study and it is reported in Table 2. Samples of pure water, in the same temperature range, have also been collected for background subtraction.
Compound | Concentration [mol kgw−1] | Temperature [°C] | ||||||
---|---|---|---|---|---|---|---|---|
Sample no. | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
a ATR-FTIR detection limit for the NH3(aq). b Temperature value corresponding to the onset of primary nucleation (see the ESI for further information. | ||||||||
NH4HCO3(aq) ( = 0 m) | 1.76 | 2.02 | 2.31 | 2.64 | 5–25 | 10b−25 | 10b−25 | 16b−25 |
NH4HCO3(aq) ( = 1.2 m) | 2.64 | 2.89 | 3.05 | 3.17 | 5–25 | 8b−25 | 12b−25 | 14b−25 |
NH4HCO3(aq) ( = 1.8 m) | 3.06 | 3.27 | 3.42 | 3.53 | 5–25 | 6b−25 | 8b−25 | 13b−25 |
KHCO3(aq) | 1.79 | 2.14 | 2.48 | 2.83 | 5–25 | |||
K2CO3(aq) | 0.25 | 0.35 | 0.45 | 0.55 | 5–25 | |||
NH4Cl(aq) | 1.71 | 2.14 | 2.48 | 2.83 | 5–25 | |||
NH3(aq) | 0.61a | 1.25 | 1.93 | n/a | 5–25 |
The dissolution of KHCO3 in aqueous solution leads to a slightly alkaline environment in a wide range of salt concentrations.28 The formation of CO32− and CO2(aq) according to the equilibria of eqn (5)–(7) occurs as well, and a spontaneous depletion of HCO3− in the liquid phase, albeit minimal, is expected until the vapor pressure of CO2 in the sealed reactor reaches the equilibrium partial pressure of CO2(aq). Because of these phenomena, the analytical concentration of the KHCO3(aq) standards has been corrected accounting for the presence of CO32− and CO2(aq) in solution using the geochemical equilibrium software package EQ3/6 v. 8.0.29 The extent of speciation of the HCO3− ion has been found anyhow to be less than 5% wt. Similarly, the speciation of CO32− in the standard samples of K2CO3(aq) has not been observed given the detection limit of the ATR-FTIR spectrometer.
Due to the acidic nature of NH4Cl(aq) solutions, the speciation of the NH4+ into NH3(aq) is virtually absent, thus facilitating the isolation of the characteristic NH4+ peak. Conversely, the alkaline environment of aqueous ammonia solutions inhibits the hydrolysis of NH3(aq) into NH4+, thus allowing the extraction of the NH3(aq) peak from the infrared spectrum.
The asymmetric CO stretching band of the CO2 located at 2343 cm−1 in the infrared spectrum does not overlap with the spectrum of any other species in solution and has good analytical potential for the determination of the carbon dioxide concentration in water 30 (see the ESI† for further information). However the extent of CO2(aq) formation has been found negligible in the range of operating conditions explored (see sec. 5.6), and its concentration has been determined by using a mass balance on the liquid phase instead of developing a dedicated calibration model.
The formation of carbamate ions (NH2COO−) due to the reaction of eqn (8) yields several characteristic peaks associated to this species located respectively at 1545 cm−1, at ∼1400 cm−1, and at 1120 cm−1 in the infrared spectrum10,11,23 (see Fig. 2b). The segregation of these peaks is complicated by the pronounced overlap with the spectrum of the other species; the extent of speciation, in general, does not allow for a direct measurement of the actual concentration of the carbamate ion. In light of these considerations, two of the three characteristic peaks of the carbamate ion have been modeled, after subtraction of the spectrum of the solvent, using Gaussian functions such as:
(18) |
Fig. 2 (a) Exemplary cases of single-point baseline correction (red circle) applied to all the IR spectra collected in this study (see sec. 3.5). The examples refer to the IR spectrum of the NH4+ ion (red curves) and to the spectrum of H2O (black curves), respectively. The region of interest of the infrared spectrum of this study is indicated by dashed lines. (b) Examples of solvent (water) background subtraction from the measured spectrum of different ionic species in aqueous solution, i.e. NH3(aq), NH4+, HCO3−, and CO32−. Note that the characteristic bands of the NH2COO− (green spectra) have been modeled, net of the spectrum of the solvent, as Gaussian functions using eqn (18) (see sec. 3.4 for further details). |
in which the location of each peak, μ, has been set based on the available literature data10,11 and its broadness, σ, has been chosen by appling an optimization procedure discussed in sec. 5.6.1. In eqn (18), a is the infrared absorbance function of the wavenumber , and the values of m and s are respectively equal to 1545 cm−1 and 1413 cm−1, and 43.1 cm−1 and 19.2 cm−1 for the two modeled peaks of the carbamate ion. The carbamate band located at 1120 cm−1, characterized by a much lower absorptivity compared to the other characteristic peaks,10,11 has been neglected from the modeling procedure without significantly affecting the representation of the system.
This work uses a multivariate classical least squares method26,31 to model the multicomponent spectrum of mixtures of CO2, NH3, and H2O. It assumes the Beer–Lambert law for the spectrum of each pure component, ai, to be valid and the effect of intermolecular interactions on the IR spectrum to be negligible:
ai() = qici | (19) |
In eqn (19), ai, ci, and qi are the absorbance, the concentration, and the absorptivity respectively of the i-th component in solution.
Additionally, the method requires a calibration step that relates the spectra of a given set of standards to their known concentration.
(20) |
(21) |
(22) |
Therefore, the vector estimator (with [n − 1] elements) of the unknown parameters is calculated as:32
= (ATA)−1ATa* | (23) |
Then, the set of optimal parameters allows to estimate the spectrum of the mixture, â, as:
â = A + w | (24) |
Eventually, the concentration estimate of the i-th solute, ĉi, can be calculated using a calibration model fi that relates its estimated IR spectrum, the vector , to its concentration.
ĉi = fi(âi) i = 2,…,n | (25) |
The CLS algorithm is illustrated in Fig. 3, while the derivation of the calibration models is discussed, in detail, in sec. 5.3.
Fig. 3 Graphical representation of the algorithm used to resolve overlapping ATR-FTIR bands of aqueous species in solution. The algorithm includes a modeling step of the spectrum of the mixture represented by a classical least squares (CLS) method, and uses calibration functions (eqn (25)) for the computation of the concentration estimates. |
Fig. 4 Set of normalized and overlapped spectra of pure electrolyte species in aqueous solution in the concentration and temperature ranges investigated in this work (see Table 2). The main deviations are indicated by arrows. (a–d) IR spectra relative to the NH4+, HCO3−, CO32−, and NH3(aq) species respectively. |
Fig. 5 Measured absorptivities and positions of the maximum IR peaks of the solutes as a function of temperature, at constant solute concentration. The analyses are relative to the IR bands corresponding to the minimum value of the standard concentrations of NH4Cl(aq), KHCO3(aq), K2CO3(aq), and NH3(aq) reported in Table 2. The discontinuity in the maximum IR peak position of the NH4+ ion is due to the finite resolution of the IR spectrum recorded. (a)–(d) Refer to the ammonium ion, the bicarbonate ion, the carbonate ion, and the aqueous ammonia, respectively. |
(26) |
Before discussing the details of each method, it is useful to introduce the operator S that extracts the specific features of a generic IR spectrum, s, used by the different calibration methods:
(27) |
Species | Method | Wavenumber [cm−1] | r [−] | RMSE [mol kgw−1] | R 2 [−] |
---|---|---|---|---|---|
NH4+ | Peak area | 1324 ≤ ≤ 1522 | n/a | 0.0404 | 0.9985 |
Maximum peak height | = 1458 | n/a | 0.030 | 0.9918 | |
PLSR | 1324 ≤ ≤ 1522 | 2 | 0.0207 | n/a | |
HCO3− | Peak area | 1156 ≤ ≤ 1466 | n/a | 0.1104 | 0.9990 |
Maximum peak height | = 1365 | n/a | 0.1042 | 0.9937 | |
PLSR | 1156 ≤ ≤ 1466 | 5 | 0.0317 | n/a | |
CO32− | Peak area | 1208 ≤ ≤ 1492 | n/a | 0.0090 | 0.9974 |
Maximum peak height | = 1395 | n/a | 0.0068 | 0.9943 | |
PLSR | 1208 ≤ ≤ 1492 | 3 | 0.0060 | n/a | |
NH3 | Peak area | 1033 ≤ ≤ 1178 | n/a | 0.0898 | 0.9988 |
Maximum peak height | = 1111 | n/a | 0.0397 | 0.9976 | |
PLSR | 1033 ≤ ≤ 1178 | 6 | 0.0022 | n/a | |
BC(aq) | PLSR | 980 ≤ ≤ 1036 | 7 | 7.97 × 10−5 (*) | 0.9999 |
BC ( = 1.2 m) | PLSR | 980 ≤ ≤ 1036 | 10 | 0.0070 (*) | 0.9982 |
BC ( = 1.8 m) | PLSR | 980 ≤ ≤ 1036 | 10 | 0.0062 (*) | 0.9978 |
(28) |
Fig. 6 ATR-FTIR calibrations based on the maximum peak height and temperature for the concentration estimate of the HCO3−, CO32−, NH4+, and NH3(aq) respectively. |
The good quality of the fitting is confirmed by the values of the coefficient of determination, R2 (see Table 3). This is also indicative of the validity of the Beer–Lambert law in the range of operating conditions explored in this work.
Ultimately, the regressed models can be used to estimate the concentration of the i-th component as:
ĉi = 0,i + 1,iS(âi, T) + 2,iT i = 2,…,n | (29) |
Ki = SiWi | (30) |
The method allows to reduce the collinearity of the raw spectral data and leads to a score matrix Ki that contains a set of linearly independent combinations of the original k wavenumbers that still carry the relevant information about the spectra. Similarly to eqn (28), the PLS regressor vector bi is estimated by solving the following minimization problem:
(31) |
(32) |
Finally, the PLSR model can be used to estimate the concentration of the i-th component as:
ĉi = S(âi,T)TWii | (33) |
The optimal number of linearly independent combinations of the original k wavenumbers (latent variables of the PLS model), r, has been chosen so as the root mean squared error of 10-fold cross-validation, RMSECV10, of the PLS model is minimized12 (see Table 3).
Fig. 7 Comparison of the root mean squared errors (RMSEs) of prediction of the concentration of solutes obtained using the different ATR-FTIR calibration methods discussed in sec. 5.3. |
In light of these considerations, this work adopts a set of multivariate PLS calibration models fi (eqn (25)) to estimate solute concentrations, unless explicitly stated otherwise.
An analysis on the accuracy of the concentration estimates for the case of mixtures of CO2, NH3, and H2O characterized by the formation of more than 2 main species cannot be directly performed due to the lack of information on the actual concentration of the species in solution. However, meaningful insights can be provided about the robustness of the CLS algorithm and on its capability of resolving the spectrum of mixtures containing more than 2 overlapping components. In this regard, fictitious quaternary spectra containing the overlapping peaks of NH4+, HCO3−, CO32−, and NH3(aq) have been simulated by combining the experimental spectral data of the pure standards. Then, the CLS methodology has been applied to the in silico generated spectral data.
Based on the outcome of the model, provided in the parity plots of Fig. 9, the CLS algorithm is capable of resolving effectively overlapping bands in the IR spectrum of the mixture with a maximum error in the concentration estimates of ±10%. These errors stem primarily from the difference that exists between the set of reference spectra ā used by the algorithm and the fitted spectra of the standards, a°. Based on the choice of reference spectra, the quality of the estimates may also decrease for mixtures whose species' concentrations significantly differ from those selected as a reference in the CLS method.
Fig. 9 Parity plots of the reference vs. estimated concentrations for multicomponent virtual mixtures: (a–d) concentration estimates of the NH4+, HCO3−, CO32− and NH3(aq) species, respectively. |
The highest absolute error related to the prediction of the NH3(aq) concentration can be justified by the low signal-to-noise ratio that characterizes the peak of this species (see Fig. 6) and that therefore renders its concentration estimates less accurate compared to that of the other components.
Fig. 10 (a) IR reference peak of the HCO3− ion (blue spectrum) used for the estimation of the overall ammonium bicarbonate concentration in aqueous ammonia solutions. The peak has good analytical potential for the estimation of the HCO3− ion concentration in solution. The spectrum of the solvent (gray spectrum) is reported for reference. (b) Percent distribution of the HCO3− species as a function of temperature and total nitrogen to carbon ratio ζ at a fixed total carbon concentration (2 mol kgw−1) in solution. Calculations have been performed using the thermodynamic model proposed by Darde et al.6 |
In this work, a total of three PLS regression models have been computed at values of nominal ammonia concentration in the solvent equal to 0, 2, and 3% wt, respectively. The training sets of the PLS calibrations are represented by the spectra of BC in aqueous ammonia solutions in a temperature range that covers both the undersaturated and the supersaturated conditions (see Tables 2 and 3). The models have been regressed including the information of the spectra of pure water, as well as the dependence of the IR spectra on temperature. During each experiment, a known amount of ammonium bicarbonate has been dissolved in the solution and spectral acquisition has been started shortly after reaching equilibrium. Then, a cooling rate of 10 °C h−1 has been applied to the system, while measuring ATR-FTIR spectra every minute. The onset of primary nucleation has been monitored using FBRM measurements so that spectra measured after nucleation could be rejected from the training set of the PLSR models. For the sake of completeness the whole training data set is reported in the ESI.†
The prediction capability of the ATR-FTIR calibration models has been assessed using independent BC solubility measurements. A first type of experiment consists in heating saturated aqueous ammonia solutions in presence of suspended BC at a rate of 2 °C h−1 while collecting spectral data. A second type of experiment is based on the measurement of the temperature at which the solid phase disappears.19 In this case, the FBRM signal has been used to detect complete dissolution of particles while slowly heating the suspension at a rate of 1 °C h−1.
Fig. 11a shows the ATR-FTIR-based solubility measurements (circles) carried out at a nominal ammonia content in the solvent equal to 0%, 2%, and 3% wt (indicated with a colorcode), while the measurements based on the temperature at which the solid phase disappears are shown as filled dots. The effect of an ammonia enrichment of the solution results in a remarkable increase of the ammonium bicarbonate solubility.
Fig. 11 Ammonium bicarbonate solubility in aqueous ammonia solutions as a function of temperature and nominal ammonia concentration in the solvent, , (see blue colorcode). The solubility is based on a pure water mass basis. (a) ATR-FTIR-based solubility measurements (see arrows) and FBRM measurements of complete solid disappearance (filled dots). Solid curves are the interpolated solubility data, while the dotted red curve refers to the BC solubility in aqueous solution of Sutter and Mazzotti9 (b) representation of the BC solubility data of Fig. 11a in the ternary diagram for the CO2–NH3–H2O system as a function of temperature. The blue lines are the operating lines that connect the composition of ammonium bicarbonate (BC) to aqueous ammonia solutions at different nominal ammonia concentration (see dashed lines). |
The good agreement of the solubility measurements obtained with independent methods supports the applicability of the ATRFTIR calibration for the estimation of the overall BC concentration in solution. Fig. 11b provides a different representation of the BC solubility data in the CO2–NH3–H2O ternary diagram as function of temperature and gives an indication of the operating region investigated experimentally.
Systems in which the ζ ratio is less than unity (see Fig. 1) are characterized by a higher CO2(aq) concentration in the liquid phase (compared to systems in which ζ is greater or equal to one) that leads to an increase of the value of CO2 partial pressure. The investigation of such systems, not addressed in this work, is therefore limited by the maximum pressure of the vessel.
(34) |
In principle, the proposed CLS methodology can be applied to any aqueous solution containing unknown amounts of CO2 and NH3 as long as the validity of the Beer–Lambert law is preserved for each component's spectrum and the interactions among the individual spectra are negligible. In practice, the CLS approach is not applicable in a fully predictive mode since the overall nitrogen and carbon concentrations in solution are unknown.
In the specific case of aqueous ammonia solutions of ammonium bicarbonate the total carbon concentration, mC,OL has been estimated from ATR-FTIR measurements exploiting the calibration method discussed in sec. 5.5, whereas the total nitrogen concentration mN,OL has been computed using the information on the nominal ammonia concentration in the solvent, which is assumed to be known. Then, the overall carbon and nitrogen concentrations have been used together with the concentration estimates of the ammonium and bicarbonate ions, ĉNH4+ and ĉHCO3−, (retrieved by applying the CSL methodology proposed in sec. 4 to the spectrum of the unknown mixture) to solve the charge and mass balances in the liquid phase, eqn ((14)–(16), and eqn (17)), thus retrieving the concentration of the unknown species. Although the solution of the latter system of equations allows to obtain the complete speciation of the system, the values of the remaining degrees of freedom have been specified by introducing the following simplifications. For the case of aqueous solutions of BC the presence of NH3(aq) has been neglected due to mild alkalinity of the system28,35 (see Fig. 1). Analogously, for the case of aqueous ammonia solutions of BC the contribution of the CO2(aq) has been neglected in the material balance due to the basicity of these mixtures. Finally, the presence of H+ and OH− ions has been omitted in the charge balance due to their low concentration in solution, typically in the order of 10−7 mol kgw−1.
Note that the choice of using the ammonium and bicarbonate concentration estimates as an input for the material and charge balances stems from the fact that the CLS concentration estimates of these species are the most reliable ones due the spectroscopic properties of their characteristic IR peaks, i.e. the high absorptivity and the high signal-to-noise ratio in the region of wavenumbers of interest.
An alternative method to estimate the concentration of the bicarbonate ion relies on a PLS calibration based on the HCO3− peak located at 1005 cm−1 that, compared to the CLS methodology, does not require any intermediate modeling step of the spectrum of the mixture. Nevertheless, the estimation of the NH4+ ion concentration, due to the high degree of overlap of the IR peak of this species with the spectra of the other solutes in solution, requires a modeling step of the spectrum of the unknown mixture.
Aqueous solutions of BC are equimolar mixtures of CO2 and NH3 whose overall composition in the ternary diagram of Fig. 1 and 11b lies on the operating line that connects the composition of the BC salt to the vertex of pure water (0% wt ammonia in the solvent or ζ = 1). The measured speciation, indicated as dots in Fig. 13, reveals that the dominant species present in solution are the NH4+ and HCO3− ions, thus confirming the congruent solubility of ammonium bicarbonate in aqueous solution reported by Jänecke.1 The ratio ĉHCO3−/ĉNH4+ is 0.95 at 6 °C; it decreases for increasing values of temperature reaching a value of 0.92 at 23 °C due to the concomitant increment of the concentration of CO2(aq) and NH2COO− whose presence slightly shifts the carbon and nitrogen distributions towards these species. Evidence of dissolved CO2 is confirmed by the presence of a marked antisymmetric stretching fundamental peak of CO2(aq) located at 2343 cm−1 in the infrared spectrum (the interested reader is referred to the ESI† for further details). Finally, the trend followed by the estimated speciation is in agreement with the predictions of the thermodynamic models (indicated as dashed lines) in both qualitative and quantitative ways. Note that the concentrations of the NH3(aq) and the CO32− ion have not been represented due to their negligible level in all these cases.
Fig. 13 Comparison of the ATR-FTIR speciation data (dots) of saturated aqueous ammonia solutions of ammonium bicarbonate and the predictions of thermodynamic models (dashed lines) in the temperature range 5–23 °C. (a) Comparison to the Thomsen model.5 (b) Comparison to the Darde model.6 The range of investigated ammonia concentration in the solvent varies between 0–1.8 mol kgw−1. |
Fig. 13 shows (moving from left to right) how the carbon distribution in saturated aqueous ammonia solutions of BC changes from essentially bicarbonate only to an equilibrium mixture of bicarbonate, carbonate and carbamate ions10,11,33 as the concentration of non-stoichiometric ammonia increases. The concentration estimates of the different species (indicated as dots) are relative to a nominal ammonia concentration in the solvent of 1.2 mol kgw−1 and 1.8 mol kgw−1 respectively, in the temperature range 6–23 °C. Note that in these two cases, the experimental values of the NH4+ concentration exceed slightly the range of concentrations used to build the model calibration for this species. However, literature data confirm the validity of the Beer–Lambert law for this species up to 5 mol kgw−1.10,11
Compared to the case of a pure aqueous solutions of BC ( = 0 mol kgw−1), the presence of additional species such as CO32−, NH2COO−, and NH3(aq) can also be noticed by analyzing the IR spectra shown in Fig. 12. The carbonate ion peak appears as highly convoluted while the appearance of a visible carbamate peak (located at 1545 cm−1), which is pronounced even at low concentrations, indicates a high absorptivity of this band.11 Aqueous ammonia is present at a much lower concentration compared to its nominal value in the solvent, thus indicating that speciation into NH4+ and NH2COO− occurred. Despite the low absorptivity of the aqueous ammonia band (see Fig. 5) and its overlap with one of the weakest NH2COO− peaks, the discrepancy between the reconciled concentration of aqueous ammonia and its CLS estimate has been found to be between ±5%. For the case of CO32− the difference lies between 15%.
In general, both thermodynamic models from the literature describe the experimental trends quite well with the best quantitative agreement offered by the Thomsen model. Instead, Darde model slightly overestimates the carbamate concentration in the entire range of experimental conditions investigated, thus leading to a different distribution of the remaining nitrogen and carbon species in solution.
(35) |
(36) |
Fig. 14 shows a comparison between the experimental solubility of ammonium bicarbonate2 at 20 °C (black boxes and circles) and those computed using the Thomsen model (green curve), the Darde model (blue curve), and a refitted version of the Thomsen model (red curve) built in this work and discussed in the following. The solid–liquid envelopes of the CO2–NH3–H2O system have been obtained by performing solid–liquid flash calculations using the abovementioned models (see ESI† for further details).
Fig. 14 Solubility curves of the different salts in the CO2–NH3–H2O system at 20 °C and 1 bar computed with the Darde model6 (blue curve), the Thomsen model5 (green curve), and the refitted Thomsen model (red curve) respectively. Black boxes (□) indicate the solid–liquid equilibrium data by Jänecke,2 while black circles (○) indicate the ammonium bicarbonate solubility measured in this work. |
As it can be noted in Fig. 14, both Thomsen and Darde models slightly underpredict the measured ammonium bicarbonate solubility (see magnification of the ternary diagram region). Such local inaccuracies, although negligible in the context of overall process simulations,7,39 must be minimized for the monitoring and the kinetic investigation of BC crystallization processes for which an accurate computation of the supersaturation is required. To achieve this, we performed a re-estimation of the parameters of the Thomsen model (that provides the best representation of the speciation data measured in this work) with the aim of increasing the accuracy of the description of the solid–liquid equilibrium of BC in aqueous ammonia solutions. In detail, a subset of extended-UNIQUAC interaction parameters, represented by the matrices u0 and uT of the Thomsen model reported in Tables 4 and 5, has been optimized while keeping unaltered the remaining parameters and thermodynamic properties of the model.
u 0 ij | H2O | NH3(aq) | CO2(aq) | NH4+ | H+ | OH− | CO32− | HCO3− | NH2COO− |
---|---|---|---|---|---|---|---|---|---|
H2O | 0 | ||||||||
NH3 (aq) | 774.41 | 1140.20 | |||||||
CO2(aq) | 205.32 | 2500.00 | 40.52 | ||||||
NH4+ | 142.58 | 1010.60 | −5.05 | 0 | |||||
H+ | 105 | 1010 | 1010 | 1010 | 0 | ||||
OH− | 600.50 | 2046.80 | 2500.00 | 1877.90 | 1010 | 1562.90 | |||
CO32− | 232.71 | 1662.40 | 2500.00 | 226.60 | 1010 | 1588.00 | 1458.30 | ||
HCO3− | 625.93 | 3641.90 | 767.81 | 643.24 | 1010 | 2500.00 | 800.01 | 771.04 | |
NH2COO− | 1.27 | 1006.40 | 2500.00 | 85.21 | 1010 | 2500.00 | 2500.00 | 612.95 | 1405.20 |
u T ij | H2O | NH3(aq) | CO2(aq) | NH4+ | H+ | OH− | CO32− | HCO3− | NH2COO− |
---|---|---|---|---|---|---|---|---|---|
H2O | 0 | ||||||||
NH3(aq) | 0.0996 | 4.0165 | |||||||
CO2(aq) | 11.8880 | 0 | 13.6290 | ||||||
NH4+ | 0.0052 | 19.6218 | 14.8936 | 0 | |||||
H+ | 0 | 0 | 0 | 0 | 0 | ||||
OH− | 8.5455 | 0.0904 | 0 | 0.3492 | 0 | 5.6169 | |||
CO32− | 2.6495 | −0.1314 | 0 | 4.0556 | 0 | 2.5176 | −1.3448 | ||
HCO3− | −1.9399 | 0.2249 | 0.0437 | −0.0002 | 0 | 0 | 1.7241 | −0.0198 | |
NH2COO− | 6.8968 | 6.1568 | 0 | 5.6035 | 0 | 0 | 0 | 3.4233 | 0 |
Experimental data of aqueous ammonia solutions of BC at saturated conditions have been used in the following optimization problem:
(37) |
The first term of the objective function in eqn (37) accounts for the speciation data to be regressed, while the second term is used to impose the values of the BC solubility product to be fitted during the optimization. The speciation has been computed by solving the liquid speciation equilibria (eqn (4)–(8)) while neglecting all the solid–liquid equilibria (eqn (9)–(12)). The unconstrained optimization has been performed using the optimizer fmincon in the Matlab Optimization Toolbox40 with an initial guess provided by the extended-UNIQUAC parameter set of the Thomsen model.
As shown in Fig. 15, the optimal set of regressed parameters allowed for a good fitting of the experimental speciation data as well as of the solubility product of BC in the entire range of operating conditions investigated.
Fig. 15 Performance of the refitted speciation model (see sec. 5.7) over the temperature range 6–20 °C. (a) ATR-FTIR speciation data (dots) and model predictions (lines) of the species' concentration in saturated aqueous ammonia solutions of ammonium bicarbonate. The ammonia concentration in the solvent varies from 0 to 1.8 mol kgw−1 moving from left to right. (b) Ionic product of BC (dots) computed along the solubility curves of BC in Fig. 11a using the refitted Thomsen model presented in this work. The colorcode indicates the value of the nominal ammonia concentration in the solvent. The good overlap with the thermodynamic solubility product (dashed black line), KSP, indicates that the capacity of the model of describing accurately the solid–liquid equilibrium of ammonium bicarbonate in aqueous ammonia solutions. |
It is worth noting that since the optimization procedure does not include any solubility data of the additional solids that might form, the refitted Thomsen model proposed in this work is unable to describe accurately the solubilities of the different salts outside the ammonium bicarbonate region. Although being able to capture the experimental BC solubility2 (black boxes and circles) significantly well (see Fig. 14), it progressively underestimates the salts' solubilities as the equivalent ammonia content in the system increases. Not surprisingly, Darde model, by being fitted on a much larger set of experimental data,6 is capable of describing effectively the entire set of solid–liquid equilibria.
For the purposes of our experimental investigation, the quality of the CLS fitting of the spectra has been used as the main criterion to assess the reliability of the concentration estimates, and the agreement between the ATR-FTIR measurements and the results of the speciation models available in the literature5,6 confirms the validity of the proposed methodology that could be applied for reaction kinetics monitoring purposes, for instance.
The solubility and speciation data measured for saturated aqueous ammonia solutions of BC have been used to improve the accuracy of the available thermodynamic models in the description of the BC solid–liquid equilibrium in aqueous ammonia solutions, thus allowing for a precise estimation of the BC supersaturation during crystallization processes.
Ultimately, this work paves the way for the estimation of the crystallization kinetics of ammonium bicarbonate in aqueous ammonia solutions essential for the design and control of solid formation in ammonia-based CO2 capture processes.7,8
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9re00137a |
This journal is © The Royal Society of Chemistry 2019 |