Estimating speciation of aqueous ammonia solutions of ammonium bicarbonate: application of least squares methods to infrared spectra†

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

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1 Introduction

The characterization of the CO₂–NH₃–H₂O system in terms of the liquid phase reactions and of the solid–liquid equilibria that can be established at the relevant operating conditions is based on extensive experimental work carried out almost one hundred years ago.^1–4 Furthermore, thermodynamic models capable of computing such equilibria have been developed with the aim of designing and optimizing relevant industrial processes such as wastewater and flue gas treatment, and enhanced oil recovery.^5,6 As an example, the Chilled Ammonia Process (CAP) developed by Alstom Power captures greenhouse gases from large CO₂ point sources such as power plants by means of aqueous ammonia solutions.⁷ Several variants of the process exist; among them the so-called Controlled Solid Formation-Chilled Ammonia Process (CSF-CAP) allows for the precipitation of ammonium bicarbonate (NH₄HCO₃, in the following also “BC”) to lower the specific energy demand of the process by increasing the CO₂ uptake capacity of the solvent system.⁷ In this process, the information about the phase equilibria and the kinetic effects of chemical reactions and mass transfer are key for the design and optimization of a continuous crystallization section fully integrated with the rest of the capture plant.⁸ Retrieving crystallization kinetics of BC for this system is complicated by the high volatility of the solutes,⁹i.e. NH₃ and CO₂, and requires the information on the speciation of the solution for the computation of the driving force of the crystallization process, i.e. the supersaturation. In this regard, the use of available thermodynamic models,^5,6 usually fitted on vapor–liquid equilibrium data and only on a limited amount of liquid speciation data,^10,11 leads to inaccurate estimates of the BC solubility.

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.

2 The CO₂–NH₃–H₂O system

The CO₂–NH₃–H₂O system is a highly volatile system characterized by the following vapor–liquid–solid equilibria.^1,3,5,14

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)

where is the change in standard state Gibbs free energy for reaction j at the temperature T, a_i is the activity of the i-th component, and ν_i,j is the stoichiometric coefficient of component i in the reaction j. In order to compute the equilibrium phase composition of a mixture of CO₂, NH₃, and H₂O, eqn (1)–(8) must be brought in a form like eqn (13) and solved simultaneously. Extent of reactions can be used as iteration variables instead of the amounts of individual components to fulfill automatically the electroneutrality condition:

mNH4+ + mH+ − mOH− − mHCO3− − 2mCO32− − mNH2COO− = 0	(14)

where m_i is the molality of the i-th component in the liquid phase.

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), m_C,OL and m_N,OL are the overall concentration of carbon and nitrogen in the system, m^(s)_j, ν_j,C and ν_j,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.

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.

3 Experimental section

3.1 Materials

Electrolyte solutions have been prepared using analytical grade chemicals purchased from Sigma-Aldrich (Buchs, Switzerland) and Milli-Q water (18.2 MΩcm at 25 °C). Ammonium bicarbonate (NH₄HCO₃, BioUltra, ≥99.5% pure), ammonium chloride (NH₄Cl, BioUltra, ≥99.5% pure), potassium bicarbonate (KHCO₃, BioUltra, ≥99.5% pure), and potassium carbonate (K₂CO₃, BioUltra, ≥99% pure) have been used without further purification.

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).

3.2 Experimental setup and analytical methods

3.3 In situ characterization techniques

3.4 IR peaks indentification

ATR-FTIR spectroscopic analyses of aqueous solutions are challenging due to the strong water absorption over the entire mid-infrared spectral region. Nevertheless, characteristic and well distinct IR-active bending modes of the species investigated in this work, i.e. NH₄⁺, NH₃(aq), CO₂(aq), HCO₃⁻, CO₃²⁻, and NH₂COO⁻ are observable in the spectrum of aqueous solutions containing CO₂ and NH₃ (ref. 10, 11 and 25) (see Table 1). The first step towards the resolution of such mixtures is represented by the isolation of the characteristic IR modes of each individual component. Then, a set of ATR-FTIR standards of the solute of interest can be prepared for calibration purposes.

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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.

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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 spectrum^10,11,23 (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)

in which the location of each peak, μ, has been set based on the available literature data^10,11 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.

3.5 Preprocessing techniques

As illustrated in Fig. 2a, the ATR-FTIR pre-processing technique for all the raw IR spectra collected consisted of a single-point baseline correction applied at 1033 cm⁻¹ of the spectrum (red circle), The technique has been developed in our laboratory and implemented in MATLAB. The use of this constant baseline correction is effective in removing the background signal of the solvent (water) that appears almost as an off-set over the range of wavenumbers of interest, i.e. 1033–1610 cm⁻¹. Fig. 2b shows how the IR spectrum of each pure component has been isolated from the background signal of the solvent by subtracting the baseline-corrected spectrum of water from the measured spectrum of the electrolytes in aqueous solution at the relevant temperature (see below for the details).

4 Modeling

4.1 Model equations

From a mathematical point of view the infrared absorbance of a multicomponent liquid mixture of given composition is a continuous function a(,T) defined on the wavenumber, , and temperature, T, domains. However, from a practical point of view, due to the instrument finite resolution, the measured spectrum can be described as a vector of data points recorded at m discrete wavenumber values, i.e.a(,T) = [a(₁,T),…,a(_m,T)]^T, at a given temperature.

This work uses a multivariate classical least squares method^26,31 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, a_i, to be valid and the effect of intermolecular interactions on the IR spectrum to be negligible:

ai() = qici	(19)

In eqn (19), a_i, c_i, and q_i 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.

4.2 Classical least squares method

The linear model of an ATR-FTIR spectrum discretized over m wavenumbers, the vector a, which embeds n overlapping components is, at a given temperature T:

	(20)

where the index i associated with the solvent (water) is 1; the vector a*(T) is the spectrum of the mixture after subtracting the contribution of the solvent, i.e. the vector w(T); k_i is the CLS weight parameter relative to the i-th component; the vector is the CLS reference spectrum of the i-th component; and the vector ε is the residual error of the model. The CLS reference spectra are defined as the spectra of the standards at the lowest concentration value of the calibration set reported in Table 2. Since m ≫ n, the optimal set of parameters, = [₂,…,_n]^_T, that minimizes the residual error of eqn (20) can be computed by solving the following optimization problem:

	(21)

where the CLS reference spectra of the pure components (solutes) are collected column-wise into the matrix A. The set of reference spectra also accounts for the temperature dependence of the spectrum of each species in solution:

	(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, ĉ_i, can be calculated using a calibration model f_i 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.

5 Results and discussion

The following sections address important aspects related to the application of the CLS method to real mixtures containing CO₂, NH₃, and H₂O. At first, the validity of the Beer–Lambert law and the capability of the CLS model to resolve complex overlapping spectra are investigated. Then, different calibration approaches are compared in terms of accuracy and reliability of the concentration estimates. Against this background, the speciation of aqueous ammonia solutions of BC have been assessed, investigating, in particular, the effect of a stoichiometric excess of ammonia, on the equilibria established in solution. Additionally, the solid–liquid equilibrium of ammonium bicarbonate has been characterized and modeled, thus establishing a rigorous thermodynamic framework for the estimation of the solution supersaturation.

5.1 Validity of the Beer–Lambert law

The validity of the Beer–Lambert law for the pure components, in the range of concentrations explored in this work, is a prerequisite for the application of the CLS method to the spectrum of a mixture of unknown composition. In this regard, Fig. 4 shows the sets of normalized (and overlapping) spectra of the pure species in aqueous solution corresponding to the different concentrations used for calibration (see Table 2). The overlapping of spectra is indicative of systems for which the Beer–Lambert law applies, i.e. a linear relationship between the absorbance and the concentration. However, in this system deviations from the linear behavior can be noticed especially for the NH₄⁺ and the HCO₃⁻ ions. More in detail, Fig. 4a shows a slight shift of the absorption bands of NH₄⁺, while in Fig. 4b a certain absorbance variability is noticeable in the proximity of the lower shoulder of the HCO₃⁻ peak; deviations in the wavenumber range between 1350–1450 cm⁻¹ may be attributed to the concomitant presence of CO₃²⁻ in solution, while no significant deviations could be reported in the case of CO₃²⁻ and of NH₃(aq).

5.2 Effect of temperature on the spectrum of a pure solute

As described in section 4, the proposed modeling approach accounts also for the temperature dependence of the spectrum of the unknown mixture, in order to improve the accuracy of the concentration estimates. To prove the relevance of this effect, Fig. 5 shows a cursory analysis on the temperature behavior of the maximum peak height and position of the characteristic IR bands of the pure species. As a general trend, the maximum peak heights decrease linearly with increasing values of temperature, for all the species, at fixed concentration values. This phenomenon is probably due to the weakening of the H-bonds between water and solutes with increasing temperature;¹⁶ it is distinct in the case of the CO₃²⁻ spectrum, while the decreasing trend is negligible for the remaining species. The peak position of the NH₄⁺ ion slightly shifts to lower values with increasing temperature as shown in Fig. 5a.

5.3 ATR-FTIR calibration methods

Several functional forms for the general calibration model presented in eqn (25) have been suggested and analyzed in order to identify the most accurate method for the estimation of the solute concentrations. The screening carried out in this study considered calibration models based on the maximum absorbance peak height (model I), on the maximum absorbance peak area (model II), and on a partial least squares regression (PLSR) of spectral data (model III). The root mean squared error of prediction, RMSE, has been used to compare the performance of the different calibration models of each component as follows:

	(26)

where E is the mean operator; and are respectively the vector of concentration estimates of the standards of the i-th component, and the vector of the relative standard concentrations.

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)

where s(_j,T) is the absorbance at a specific wavenumber _j and temperature T; Δ_j is the fixed interval between two discretized wavenumbers; and [a,b] is a generic range of wavenumbers. Details on the maximum peak positions and wavenumber ranges adopted for each component are reported in Table 3.

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5.4 Model validation

First, the predictive capability of the proposed CLS methodology has been assessed for the case of binary mixtures of known composition, namely NH₄Cl(aq) and KHCO₃(aq). In detail, the validation exploits a set of in silico generated IR spectra of NH₄Cl(aq) and KHCO₃(aq) obtained by combining the spectra of the pure standards, as well as a set of real spectra of aqueous mixtures of NH₄Cl(aq) and KHCO₃(aq), and of aqueous solutions of NH₄HCO₃ (BC). For the real mixtures ¹³C-NMR spectroscopic analyses^33,34 (reported in the ESI†) have been used to select the solutions that exhibit a low degree of speciation (e.g. absence of carbamate ion formation) to be included in the validation set. Then, the spectral data, both the simulated and experimental, has been processed using the CLS method proposed in sec. 4, and the resulting concentration estimates have been compared with the reference values. Fig. 8 shows that the absolute error of prediction for the NH₄⁺ and HCO₃⁻ ions in virtual binary mixtures (red and blue dots, respectively) is below 5%. Similar results are obtained for real mixtures of NH₄Cl(aq) and KHCO₃(aq) indicated by stars, and for aqueous solutions of BC indicated by triangles. The underprediction of the HCO₃⁻ concentrations for the case of real mixtures may be attributed to the formation of CO₂(aq) and CO₃²⁻ in solution.

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.

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.

5.5 Estimation of the ammonium bicarbonate concentration in aqueous ammonia solutions

In aqueous ammonia solutions of ammonium bicarbonate (i.e. solutions whose representative point is on a isopleth line with ζ ≥ 1 in Fig. 1) the distribution of carbon species changes significantly according to the overall nitrogen to carbon ratio of the system.³³ This phenomenon leads to spectral data that cannot be easily correlated to the overall BC concentration in the liquid phase, m⁽¹⁾_BC, using a single PLS calibration model. Such challenge has therefore been overcome by building dedicated PLS calibrations for different nominal ammonia concentration in the solvent (i.e. different values of ζ). These models implictly account for the liquid speciation and correlate the overall BC concentration to the baseline corrected C–OH stretching band of the HCO₃⁻ ion located at 1005 cm⁻¹ in the infrared spectrum³⁰ (Fig. 10a). In fact, this peak overlaps with the solvent band only, thus minimizing the interference with any other ionic species in solution. As shown in Fig. 10b, the ratio between the concentration of the HCO₃⁻ ion and of the total carbon species steadily decreases with increasing overall nitrogen content, thus reducing accordigly the intensity of the HCO₃⁻ peak. Nevertheless, the method can potentially be used to estimate reliably the BC concentration in a wide range of nominal ammonia concentrations in the solvent. It must be acknowledged that the proposed calibration models are inherently dependent on the solvent composition, the information on the nominal ammonia concentration in the solvent must be known in order to properly exploit the model.

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.

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.

5.6 Speciation of ammonium bicarbonate in solution

The speciation of saturated aqueous ammonia solutions of ammonium bicarbonate has been measured by applying the proposed CLS methodology for a nominal ammonia concentration in the solvent in the range 0–3% wt. For these mixtures the ratio between nitrogen to carbon species roughly spans values from 1 to 1.5.

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.

5.7 Estimation of the Supersaturation of aqueous ammonia solutions of ammonium bicarbonate

The speciation process occurring in the CO₂–NH₃–H₂O system affects the several solid–liquid equilibria that can be established at the relevant conditions of temperature, pressure and composition of the system. In this study, the most stable solid that could form is ammonium bicarbonate^1–3 and, as stated in sec. 2, the strong non-ideality of the liquid phase requires an activity-based approach for the description of all the phase equilibria. An important thermodynamic property involved in the description of the BC solid–liquid equilibrium, and of any solid–liquid equilibria in general, is the supersaturation S defined as:^37,38

	(35)

where the superscript * indicates quantities at solubility (solid–liquid phase equilibrium), a_i is the activity of the i-th species, K_SP(T) is the thermodynamic solubility product of BC defined as:

	(36)

and K_IP is often referred to as the ionic product of ammonium bicarbonate in solution, function of the temperature and composition of the system. Its dependence on pressure is typically weak and for this reason neglected in this study. The term ΔG_BC(T) in eqn (36) is the increment in standard state Gibbs free energy of formation of BC in aqueous solution,⁶ at temperature T and R is the ideal gas constant.

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).

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 u^T 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.

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Experimental data of aqueous ammonia solutions of BC at saturated conditions have been used in the following optimization problem:

	(37)

where c^calc_i, c^exp_i, and K_IP are the model predictions of the concentration of the i-th species, the one measured, and the ionic product of ammonium bicarbonate. The variables n, N_e and N_obv are the number of species, the number of experimental conditions investigated (i.e. different nominal concentrations of ammonia in the solvent), and the number of observations of each species at the relevant experimental conditions, respectively. The data set to be fitted consisted of 13 concentration data points (N_obv) for each species collected in the temperature range 6–20 °C at three different nominal ammonia concentration in the solvent, i.e. 0, 2, and 3% wt.

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.

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.

6 Conclusions

In this article, a methodology that allows to determine the speciation of aqueous ammonia solutions of ammonium bicarbonate using in situ ATR-FTIR spectroscopy measurements has been presented. The determination of the liquid composition of such systems, regardless of the type of analytical technique exploited to measure it, poses several challenges. Among them, the high volatility of the solutes, i.e. CO₂ and NH₃, requires to operate in a sealed reactor to minimize the material loss to the vapor phase, and the extent of the speciation in the liquid phase results, in general, in a complex overlap of the IR bands of the solutes in the infrared spectrum. A CLS methodology has therefore been used to segregate the contribution of each species to the IR signal of the mixture, and to estimate the concentration of the individual components in solution. This modeling approach, although simplified, is grounded on a physical description of the system and requires the estimation of fewer model parameters when compared to more complex modeling techniques such as the ones proposed by Lichtfers and Rumpf^10,11 and Kriesten et al.^41,42 As a matter of fact, the model's accuracy is expected to decrease as the absorbance of the individual species deviates from the values used as an internal reference of the CLS model (see eqn (20)), thus making it difficult to extend the use of the proposed methodology to a wide range of compositions in the CO₂–NH₃–H₂O system.

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 literature^5,6 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

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Support from the Swiss Commission for Technology and Innovation (KTI. 1155000150) within the SCCER-EIP (Swiss Competence Center for Energy Research - Efficiency of Industrial Processes) is gratefully acknowledged. Additionally, the authors thank Prof. Kaj Thomsen (Department of Chemical and Biochemical Engineering, Technical University of Denmark) for making the thermodynamic model available, Daniel Sutter, José Francisco Peréz Calvo and Ashwin Kumar Rajagopalan for the many fruitful discussions, Daniel Sutter again for a careful reading of the manuscript, and Daniel Trottmann, Markus Huber and the ETH NMR Service for the technical support.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9re00137a

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