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Modeling the Solubility of Nitrogen Dioxide in Water Using Perturbed-Chain Statistical Associating Fluid Theory Sugata P

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Modeling the Solubility of Nitrogen Dioxide in Water Using Perturbed-Chain Statistical Associating Fluid Theory Sugata P Article pubs.acs.org/IECR Modeling the Solubility of Nitrogen Dioxide in Water Using Perturbed-Chain Statistical Associating Fluid Theory Sugata P. Tan* and Mohammad Piri Department of Chemical and Petroleum Engineering, University of Wyoming, Department 3295, 1000 E. University Avenue, Laramie, Wyoming 82071, United States fl ABSTRACT: NO2 is one of the important components in ue gas from combustion in power plants, which together with CO2 and SO2 pollute the atmosphere if released and cause the undesired acid rains. NO2 reacts immediately with H2O upon dissolution, which prevents direct measurements on the physical phase equilibria of the chemical system. Modeling this reacting system is a challenging task due to the complexities arising from the heterogeneous nature of the chemical reaction, the multiple components that are involved in the phase equilibria, ionic dissociation in water, self- and cross-associations among the molecules, and multiple chemical reactions that may occur before reaching the physicochemical equilibria. Therefore, efforts on modeling this NO2/H2O system have been made so far with no satisfactory progress. In this work, we propose a complete model of the system using Perturbed Chain Statistical Associating Fluid Theory (PCSAFT) equation of state (EOS). The model is found to be able to calculate the solubility curves of NO2 in water at various pressures and temperatures, which provide a strong foundation for a later application in flue gas sequestration into aquifers. ■ INTRODUCTION must be indirectly inferred from kinetic studies, the results of 1 ff which have large uncertainties. Despite its importance in the removal e orts of NOx from the flue gases for a clean environment, in the precipitation processes The buildup of the products in eq 2 complicates the situation. in the atmosphere, and in the manufacture of nitric acid, the At high concentration, HNO3 will tend to dissociate accord- ing to8 absorption of NOx in water is perhaps the least understood in all 1 absorption operations. It is probably the most complex case of 4HNO3222↔++ 4NO 2H O O (3) absorption due to the large number of species and reactions that which is dominant, for example, in the work series of Sage and are involved in the process. NOx is in fact a mixture of all nitrogen 9−14 oxides (N O, NO, NO ,NO ,NO , and N O ), most of which co-workers. 2 2 2 3 2 4 2 5 The resulting oxygen may involve in another reaction with NO react immediately with water upon dissolution resulting in 4 and NO2 following HNO3 (nitric acid) and HNO2 (nitrous acid). Only N2O (nitrous oxide) and NO (nitric oxide) do not react with water 2NO+↔ O22 2NO (4) and hardly dissolve in water. Dozens of chemical equilibria, both in liquid and vapor phases, exist in the absorption and desorption According to this reaction, the availability of O2 is therefore processes that occur simultaneously.2 Therefore, the knowledge required in the production of pure HNO3 using the absorption process eq 2, i.e., to prevent the buildup of NO from halting the Downloaded via UNIV OF WYOMING on July 20, 2018 at 16:56:41 (UTC). of the process’s physicochemical data such as the solubility of those gases in water is still incomplete.1 formation of HNO3. Among the species that react with water, N O (nitrogen At moderate temperatures, the resulting NO or O2 from eq 2 2 3 or eq 3, respectively, builds the system pressure to levels much trioxide) and N2O5 (nitrogen petoxide) are the anhydrate forms See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. 9 of nitrous and nitric acids, respectively, while NO (nitrogen higher than they would have been if the reactions did not occur. 2 Still to worsen the situation, the resulting NO in eq 2 may dioxide) and its dimer N2O4 (nitrogen peroxide or nitrogen 1,2 tetroxide) coexist in equilibrium up to about 150 °C:3 associate with NO2 to form N2O3: NO+↔ NO22 N O3 (5) 2NO22↔ N O4 (1) 7 N2O3 is unstable and reacts with water to form nitrous acid, Generally speaking, the term nitrogen dioxide is meant to include HNO2, which is often considered to involve in intermediate both NO2 and N2O4. In this work we denote them with an reactions for the overall reaction of eq 2. Both acids, HNO and * 2 asterisk to remind us of these duo species, i.e., NO2 . HNO3, in turn also dissociate into their constituting ions in It is customary to summarize the overall chemical equilibrium water.2,7 * 4−7 in the absorption of NO2 in water as Furthermore, the overall reaction eq 1 is in fact a heterogeneous equilibrium, in which the aqueous liquid phase 3NO22*+ H O ↔ 2HNO 3 + NO (2) * The high reactivity of NO2 in water precludes direct Received: July 26, 2013 measurement of physical properties such as the Henry’s Revised: September 24, 2013 coefficient, the magnitude of which is customarily used in the Accepted: October 14, 2013 interpretation of kinetic processes.2 In this case, the coefficient Published: October 14, 2013 © 2013 American Chemical Society 16032 dx.doi.org/10.1021/ie402417p | Ind. Eng. Chem. Res. 2013, 52, 16032−16043 Industrial & Engineering Chemistry Research Article is in equilibrium with the vapor phase above it.1 Therefore, the Whereas K is thermodynamically a function of temperature 21 system has the physical equilibrium of the phases and only as evident in eq 9, it is not the case with K1. Upon simultaneously the chemical reaction equilibrium in eq 2. substituting the fugacities given by eq 8 into eq 7, K1 in the vapor In summary, the complexity makes the modeling of this phase may be calculated as ffi reacting system more di cult. In this work, we attempt to derive 3 ()ϕ̂ ()ϕ̂ y K a model for the physical and chemical equilibria of NO2 in water, K = NO2 H2O H2O 1 ̂ ̂ 2 2 which is needed to describe the absorption of NO2 into aqueous ()ϕ ()ϕ y P (10) solutions. This study will also be the initial step for a later NO HNO3 HNO3 application of the model in flue gas sequestration into aquifers. Therefore, without a reliable EOS, it is not possible to connect We apply an equation of state (EOS), namely the perturbed- the experimentally derived value of K1 with the equilibrium chain statistical associating fluid theory (PCSAFT),15 which has constant K. In this work, we couple eq 9 for K with PCSAFT to been widely used in petrochemical industries due to its reliable calculate K1 and match it with the literature data, and thus accuracy and predictability.16 The kinetics is not considered, as establish the EOS validity before making predictions on the fl we are only concerned with the equilibrium state of the system. solubility of NO2 in water at various conditions relevant to ue To the best of our knowledge, it is the first attempt to model the gas geologic sequestration. physicochemical equilibria of this reacting system using a Physical Equilibrium. The heterogeneous nature of the statistical-mechanics based EOS such as PCSAFT. reaction in eq 1 also requires the system to be in vapor−liquid phase equilibrium (VLE), where the fugacity of component i in ■ THEORY the mixture is the same throughout all phases, in this case vapor Chemical Equilibrium. The most widely used property of (V) and liquid (L) phases: VL the reacting system of NO2 in water or in aqueous nitric acid f ̂ = f ̂ solutions is the partial equilibrium constant of reaction eq 2 ii (11) 4,5 defined as The equality of the fugacities in eq 11 must be solved simultaneously with mass-balance equations to find the ()P ()y 1 K ==NO NO equilibrium compositions in both vapor and liquid phases: 1 ()P 3 ()yP32 NO2 NO2 (6) +− = lxi (1 l ) yi zi (12) which is actually a factor of the reaction equilibrium constant: Here, l is the mole fraction of the liquid phase, and zi is the overall (/)(/ff̂ 0 f̂ f02 ) mole fraction of component i. It is also important to realize that K = NO NO HNO3 HNO3 all mole fractions must sum up to unity: ̂ 03̂ 0 (/)(/)ff ff (7) NO2 NO2 H2O H2O == ∑∑xyi i 1 (13) In eq 6, y and P are the gas mole fractions and the total pressure, respectively, while f ’s with hats in eq 7 are the fugacities in Physicochemical Equilibrium. The VLE of the overall * mixtures and those with superscripts 0 are the fugacities at reaction eq 2 has 4 chemical components: H2O, HNO3,NO2 , * standard states, which are the ideal gas at 1 bar in vapor phase, or and NO. As we will show in the model, NO2 may be treated as a the pure-component fugacities at 1 bar and the system component instead of two in SAFT framework. Therefore, upon temperature in the liquid phase. The fugacity and the mole bookkeeping we have 9 independent equations to solve for 9 fraction of component i are related through variables: {xi}, {yi}, and l. However, the compositions must also satisfy the chemical equilibrium represented by the reaction ̂ = ϕ̂ fi yPi i (8) constant K, eq 7, and, consequently, the mass balance of the chemical reaction, where the overall mole fractions {zi} in fact where ϕ is the fugacity coefficient, which is calculated using an result from the chemical reaction and are calculated through EOS, in our case the PCSAFT. The fugacities in mixtures in eq 7 n + εν may be calculated in either phase because the vapor and liquid 0,ii zi = phases are in equilibrium, where the fugacities are equal in both ∑ ()n0,ii+ εν (14) phases.
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