110th Anniversary: Accurate Modeling of the Simultaneous Absorption

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Thermodynamics, Transport, and Fluid Mechanics

110th Anniversary: Accurate Modelling of the Simultaneous Absorption of H2S and CO2 in Aqueous Amine Solvents Ismail Alkhatib, Luis M.C. Pereira, and Lourdes F. Vega Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b00862 • Publication Date (Web): 28 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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Industrial & Engineering Chemistry Research

110th Anniversary: Accurate Modelling of the Simultaneous Absorption of H2S and CO2 in Aqueous Amine Solvents Ismail I.I. Alkhatib1,2, Luis M.C. Pereira1, Lourdes F. Vega1,2,* 1Gas

Research Center, Chemical Engineering Department, Khalifa University of Science and Technology, P.O. 127788, Abu Dhabi, United Arab Emirates. 2Center for Catalysis and Separation (CeCaS), Research and Innovation Center on CO and H 2 2 (RICH), Khalifa University of Science and Technology, P.O. 127788, Abu Dhabi, United Arab Emirates *

Corresponding Author. E-mail address: [email protected]

Abstract We present results concerning the application of soft-SAFT, a molecular-based equation, for modeling the absorption of carbon dioxide and hydrogen sulfide in several aqueous amines, including MEA, DEA, and MDEA, at conditions of relevance for acid gas separation. The chemisorption of CO2 and H2S in aqueous amines was modeled through the formation of physically bounded CO2-amine and H2S-amine aggregates by explicitly considering strong intermolecular association forces. This approach eliminates the need to consider all speciation reactions, significantly reducing the number of fitted parameters required to describe the absorption process while providing a direct connection between each amine and the chemical reaction with the acid gases. The model predicts the absorption of H2S for different amine concentrations in excellent agreement with experimental data, showing high extrapolative capability. Soft-SAFT is also used to predict the simultaneous absorption of H2S and CO2 in aqueous amines and results compared with experimental literature data and predictions from the recommended thermodynamic models implemented in the Aspen Plus® (V.10) process simulator. Results show that soft-SAFT provides comparable levels of accuracy as the e-NRTL thermodynamic model recommended in the process simulator, with the added advantages of higher transferability and predictive capabilities, being a reliable model for the screening of high performance solvents for acid gas separation when limited experimental data is available. Keywords: acid gas removal, soft-SAFT predictive models, aqueous amines, hydrogen sulfide, carbon dioxide

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1. Introduction Acid gases impurities, mainly hydrogen sulfide (H2S) and carbon dioxide (CO2), are commonly present in various industrial gas streams, being their removal motivated by operational, economic and environmental factors.1 The presence of acid gases in aqueous environments leads to the formation of corrosive acidic solutions that reduces the lifetime and operational integrity of industrial processing facilities, and in extreme cases can lead to tragic accidents.1 Moreover, strict environmental requirements on limiting H2S emissions, owing to their high toxicity and role in acid precipitation, along with stringent regulations on reducing atmospheric CO2 emissions, due to their contribution in global warming phenomena and climate change, are among the main environmental drivers for acid gas removal.2,3 Though acid gas removal is primarily driven by their negative environmental and operational impacts, once these acid gases are separated from industrial streams and recovered, they can be utilized as raw materials for other industrial processes, providing an economic incentive for their removal. For example, CO2 can be used for Enhanced Oil Recovery (EOR), carbonation of beverages, food preservation and supercritical CO2, extraction, among others,4 while H2S can be used, for instance, for the production of elemental sulfur2 and for hydrogen and sulfur production.5,6 Furthermore, CO2 and H2S can be directly converted into fuel using solar energy. The most renowned scheme for acid gases removal is through their chemical absorption using aqueous solutions of amines.1 The favorability of these solvents is due to their natural affinity and selectivity for both H2S and CO2 over nonpolar species, ease of recovery through heating along with their relatively low costs compared to other solvents.7–11 Depending on the type of industry and imposed environmental regulations or product specifications, several amine solvents can be utilized for acid gas removal.12,13 For example, primary amines such as monoethanolamine (MEA) rapidly react with CO2 due to the formation of stable reaction products, making them more suitable for bulk CO2 removal as needed for carbon capture applications. Alternatively, tertiary amines such as N-methyldiethanolamine (MDEA) are more suitable for oil and gas processing, as they are more selective towards H2S absorption compared to CO2 whenever both acid gases co-exist in a stream.14 Additionally, blends of several amines can also be used to overcome the shortcomings of using solutions of single amines.15 By adjusting the composition of blended amines,


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environmental and industrial requirements can be met with enhanced absorption rate without considerably affecting the absorption capacity and regeneration energy.12 The choice of amine solvent (as single or mixed amines) is dictated by several factors such as the quantity of inlet acid gases, extent of acid gas removal requirements, and whether simultaneous or selective acid gases removal is desired.16–18 Given these factors and the array of possible solvents to be utilized, the screening and selection of existing or new amine solvents for industrial applications is quite cumbersome and experimentally demanding. Apart from that, proper design and optimization of acid gas removal processes, as well as, their techno-economic viability are not only dependent on the choice of amine solvents but also on the accurate determination of their acid gas absorption capacity.19 Thus, it is imperative to formulate consistent and reliable thermodynamic models capable not only of accurately describing the phase equilibria of acid gases and aqueous amine solutions over a broad range of industrially applicable conditions, but also function as a robust predictive screening tool for existing or new amine solvents. Several classes of models exist for predicting the absorption of acid gases in aqueous amines, with varying degrees of thermodynamic consistency in terms of accounting for the non-ideality of both liquid and vapor phases, owing to complex interactions between species formed during the chemical absorption process.20 Excess Gibbs models, semi-empirical models, and those based on equations of state (EoSs) are among the most commonly used models for such application.21,22 These models provide reasonable accuracy of acid gases solubility in aqueous amines within the fitted range, making them suitable for implementation in process simulators. Still, this accuracy is achieved on the expenses of predictive capability, transferability and robustness. Most of these models involve the use of a large number of parameters fitted using experimental data in order to achieve a good level of accuracy. These parameters are specific for each system and depend on both composition and temperature,21,23 lacking transferability. The large number of adjustable parameters stems from the explicit consideration of the chemical reactive nature of the absorption process requiring prior knowledge of reaction equilibrium constants, as well as, the reaction equilibria of all relevant ionic species.24–28 Though such modelling treatment is thermodynamically sound, it reduces the wide applicability of these models, being hardly predictive for relatively new systems and inefficient as a screening tool for new solvents.



The development of consistent and robust thermodynamic screening tools for ad-hoc solvents, hinges on a balance between accuracy, transferability, simplicity and predictive capability. The key to achieving this goal is through a simpler modelling approach for the absorption process coupled with the use of a molecular-based EoSs that take into account the molecular structure of the different substances integrating the fluid. In this regard, the Statistical Associating Fluid Theory (SAFT),29–32 and some of its refined variations, have become one of the most wellestablished and successful tool for this purpose, given its high degree of predictability and robustness. One of the most important factors that lead to the success of SAFT and related approaches is their foundation on statistical mechanics, letting quantifying and separating the different molecular structural effects into the macroscopic properties of the system, while, on the practical side, is still relatively simple to be used for engineering calculations, with modest computational time. The three most cited publications on SAFT29–32 and how to implement it as a molecular-based equation of state for engineering purposes were published in Industrial & Engineering Chemistry Research in the early 1990s, marking one of the key contributions of the journal to the scientific and industrial chemical and engineering communities in its 110 years of history. SAFT explicitly considers highly directional associative forces between molecules, allowing the formation of aggregates. The use of a physical approach such as SAFT to model the absorption of acid gases in aqueous amines entails a relatively simpler treatment of the absorption process by modelling the formation of main reaction products through a physical aggregation process rather than a chemical one. Wherein, these products are represented by the formation of acid gas-amine aggregates created by specific and strong physical interactions via associative sites present on the acid gas molecules.33–35 Even though this treatment seems to be an oversimplification, it avoids the need to state all speciation reactions involved in the process and their equilibrium constants. Apart from that, its ingenuity is in its predictive nature, as an accurate description of pure substances and their binary interactions within the investigated system suffices to describe multicomponent systems (ternary, quaternary, etc.) without the need to fit the model to multicomponent system experimental data, assuming the availability of data for all binary systems. The work of Button and Gubbins36 was the first to use SAFT for the study of the CO2 absorption in aqueous MEA. Since then, several other versions of SAFT successfully described the absorption of single acid gases in amine solutions.37–43 The description of the absorption of mixed acid gases 4 ACS Paragon Plus Environment

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with Wertheim’s-based models for association was recently done using the Cubic-PlusAssociation (CPA) EoS.41 A good description of CO2 and H2S solubility in aqueous solutions containing MEA and MDEA over a wide range of thermodynamic conditions was obtained. Moreover, the absorption of mixed acid gases was reasonably predicted without additional parameters, apart from those fitted to each single gas system. Nevertheless, the transferability of these models is still lacking as the number of required adjustable parameters is relatively high. In this contribution, we have modeled the simultaneous absorption of CO2 and H2S in aqueous amine solutions, containing MEA, DEA, and MDEA, at conditions of relevance for acid gas removal by using the soft-SAFT EoS.44,45 This work belongs to a long-term project towards the development of a robust and reliable solvent screening tool for CO2 capture and separation extendable to process simulation. The amine-amine and water-amine hydrogen bonding interactions were modeled as in references33,34 and used here in a transferable manner. A brief description of soft-SAFT is presented in the next section, together with the explanation of the molecular models of the pure substances studied in this work. Afterwards, the soft-SAFT modeling approach used for the main reactions between acid gases and the studied amines is presented. The chemisorption of H2S is described considering the establishment of H2S-amine aggregates created by strong intermolecular association forces, similar to that employed for the chemisorption of CO2 in our previous works.33,35 The models are next used to describe the H2S absorption in single amines over a range of amine concentrations and temperatures along with all relevant binary mixtures needed for the description of mixed acid gases absorption in the studied amines. Finally, the robustness of the model is showcased by predicting the simultaneous absorption of H2S and CO2 in various aqueous amine solutions. Results from soft-SAFT are compared to calculations carried out with Aspen Plus® (V.10), using the e-NRTL thermodynamic model for the same systems under investigation.

2. Theory 2.1 soft-SAFT The Statistical Associating Fluid Theory (SAFT),29–32 based on Wertheim’s first order thermodynamic perturbation theory (TPT1),46–48 is today a well-established EoS model accurately



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describing the thermodynamic behavior of a wide variety of substances and their mixtures, by taking into account specific molecular interactions. The soft-SAFT EoS,44,45 an accurate variation of the original SAFT proposed by Blas and Vega, accounts for the contributions of different intermolecular forces in a fluid in a coarse-grained manner. Molecules are modeled as associating chain molecules composed of connected LennardJones (LJ) segments, where the number of associating sites need to be specified a priori, depending on the system under study. The generalized expression for soft-SAFT EoS is written in terms of the residual Helmholtz free energy density of a fluid, 𝑎𝑟𝑒𝑠, defined as the molar Helmholtz energy density of a fluid, 𝑎, relative to that of an ideal gas, 𝑎𝑖𝑑, at the same temperature and density. The residual Helmholtz free energy density of a fluid is computed in terms of the sum of different independent microscopic contributions to the total free energy, each accounting for different molecular effects: 𝑎𝑟𝑒𝑠 = 𝑎 ― 𝑎𝑖𝑑 = 𝑎𝑟𝑒𝑓 + 𝑎𝑐ℎ𝑎𝑖𝑛 + 𝑎𝑎𝑠𝑠𝑜𝑐 + 𝑎𝑝𝑜𝑙𝑎𝑟

(1)

where 𝑎𝑟𝑒𝑓 refers reference fluid Helmholtz free energy density, denoting the segment-segment interactions of segments forming the molecule, 𝑎𝑐ℎ𝑎𝑖𝑛 is the term accounting for the formation of chains from the connectivity of individual segments, and, 𝑎𝑎𝑠𝑠𝑜𝑐 is the contribution due to association forces emulating short range attractive and localized interactions such as hydrogenbonding, represented in the model as specific interactions between sites placed in the molecule. In soft-SAFT the reference term, 𝑎𝑟𝑒𝑓, uses a LJ intermolecular potential to account for the repulsive and attractive interactions between the spheres making the molecule (or van der Waals interactions), explicitly considered in a single expression.49 The chain and association contribution terms are the same in all SAFT EoS, as derived from Wertheim’s theory (TPT1).46–48 Further details can be found in the original papers.44,45 Finally, 𝑎𝑝𝑜𝑙𝑎𝑟, is a specific term added to account for polarity effects as those due to large dipole or quadrupole moments. This term is computed using the theory of Gubbins and Twu,50,51 modified to consider chain fluids by Jog et al.,52 Further details on the specific equations and implementations can be found in previous works.53 In the soft-SAFT approach molecules are modeled as bonded spheres with a LJ segment diameter, 𝜎𝑖𝑖, and dispersive energy between segments, 𝜀𝑖𝑖 /𝑘𝐵, forming a chain of length mii. In the presence 6 ACS Paragon Plus Environment

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of highly attractive directional forces, association sites are incorporated into the molecules, each 𝐻𝐵 with a specific association volume, 𝜅𝐻𝐵 𝛼 ― 𝛽, 𝑖𝑖, and energy, 𝜀𝛼 ― 𝛽, 𝑖𝑖/𝑘𝐵. In the case of quadrupolar

fluids, an effective quadrupolar moment, 𝑄 and the fraction of segments containing the polar moment, 𝑥𝑝 are explicitly considered. The soft-SAFT molecular parameters are usually regressed against vapor pressure and liquid density of pure substances, although other experimental data such as high pressure data or derivative property data can be considered. They are further used in a transferable manner to calculate other thermodynamic properties of the pure compounds (heat capacities, speed of sound, surface tensions, etc.) and to describe the behavior of the compounds in multicomponent mixtures. The chain and association term explicitly consider mixtures, while the reference term, writing for a pure fluid, is extended to mixtures through the van der Waals one-fluid theory, hence approximating the free energy of the mixture of spheres to that of a pure hypothetical fluid. This implies calculating the crossed size, 𝜎𝑖𝑗, and energy, 𝜀𝑖𝑗, parameters using the generalized LorentzBerthelot (LB) combining rules: 𝜎𝑖𝑗 = 𝜂𝑖𝑗

(𝜎𝑖𝑖 + 𝜎𝑗𝑗)

(2)

2

𝜀𝑖𝑗 = 𝜉𝑖𝑗 𝜀𝑖𝑖𝜀𝑗𝑗

(3)

where 𝜂𝑖𝑗 and 𝜉𝑖𝑗 (𝜂𝑖𝑗 = 1 ― 𝑙𝑖𝑗 and 𝜉𝑖𝑗 =1-𝑘𝑖𝑗 in classical EoS) are the adjustable size and energy binary parameters, respectively. Setting the values of the binary parameters to unity, reduces Equations (2) and (3) to the classical LB combining rules, using the EoS in a fully predictive manner without fitting to binary mixture data. The cross interactions between associating sites located in different types of molecules and between different associating sites within the same molecule, representing different functional groups, are calculated through combining rules similar to those presented in Equations (2) and (3). The mean arithmetic radius of the association site, and the modified geometric average are used to describe the volume and energy of cross-association, respectively, as follows:

(

3

𝜅𝐻𝐵 𝛼 ― 𝛽, 𝑖𝑗 =

3 𝐻𝐵 𝜅𝐻𝐵 𝛼 ― 𝛽, 𝑖𝑖 + 𝜅𝛼 ― 𝛽, 𝑗𝑗

2

3

)


(4)


𝐻𝐵 𝐻𝐵 𝜀𝐻𝐵 𝜀𝐻𝐵 𝛼 ― 𝛽, 𝑖𝑖/𝑘𝐵𝜀𝛼 ― 𝛽, 𝑗𝑗/𝑘𝐵 𝛼 ― 𝛽, 𝑖𝑗/𝑘𝐵 = 𝛼𝑖𝑗

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(5)

where, 𝛼𝐻𝐵 𝑖𝑗 , is a binary parameter added to generalized the cross-association energy. 2.2 Molecular Models The accurate thermodynamic description of any system utilizing a molecular-based EoS such as soft-SAFT requires the prior selection of a simple yet reliable molecular model, representative of the key structural features of the pure compounds under investigation, specifically considering the physical short-range interactions. The molecular models together with soft-SAFT parameters of the MEA, DEA, MDEA, water, CO2 and H2S were transferred from previous works (see Table S1 in the Supporting Information). CO2 was modelled as a homonuclear LJ chain of length m, explicitly considering its quadrupolar moment.53 H2S was modelled as an associating molecule with three association sites, two sites of type H accounting for the hydrogen atoms and one site of type e accounting for the electronegativity of the Sulphur atom.54 Self-association between like-like molecules is allowed in the model only through e-H interactions, thus explicitly considering the hydrogen bonding forces. Water was modeled as a spherical LJ (𝑚𝐻2𝑂= 1.0), with diameter 𝜎𝑖𝑖, and van der Waals dispersive energy of interaction 𝜀𝑖𝑖, containing four association sites: two sites of type H and two of type e representing the H atoms and the lone pair of electrons on the oxygen atom, respectively, (only e-H interactions were allowed).55 Note that the dipolar moment of H2S and water are not explicitly considered in these models, their value is implicitly included in the association model and molecular parameter values. The models have proven to give excellent agreement with experimental data.54,55 MEA, DEA and MDEA were considered as LJ chains with different associating sites accounting for the multifunctional nature of these substances.33,34 Analogous to the modelling approach previously followed for 1-alkanols,56 the hydroxyl group (-OH) in the three amines was modelled with two association sites, one of type H standing for the H atom and one of type O, taking into account the two lone pairs of electrons on the oxygen atom. The amines primary (-NH2), secondary (-NH) and tertiary (-N) groups were represented by three, two or one association site, respectively, with sites of type N signifying the lone electrons pair in the nitrogen atom and sites of type H 8 ACS Paragon Plus Environment

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accounting for the hydrogen atom. Self-association interactions between the functional groups OH-OH and NH2-NH2, NH-NH of two amines were allowed, with association parameters fixed to soft-SAFT values obtained for ethanol, ethylamine and diethylamine. Moreover, cross interactions between different associating sites mimicking functional groups OH-NH2 and OH-NH of two amine molecules were also permitted, using the combining rules (Equations (4) and (5), with 𝛼𝐻𝐵 𝑖𝑗 = 1.0) in a predictive manner. As for the MDEA molecules, specific interactions between the nitrogen atom and the hydrogen atom of the hydroxyl groups were modelled via N-H interactions, optimized by using vapor pressure and liquid density of pure MDEA. In the case of water-amines binary mixtures, cross-association interactions between the water molecule and the OH, NH2, NH, N functional groups of amine molecules were allowed within the model. The association parameters were taken from mixtures of water with ethanol, ethylamine and diethylamine, respectively, or obtained by using combining rules;33,34 the values of these parameters are included in Table S2 in the Supporting Information for completeness. Following previous work,33 the water and CO2 interactions were calculated by using a temperature dependent binary parameter for the unlike segments (𝜂𝑖𝑗): 𝜂𝑖𝑗 = ―0.00031 × 𝑇 + 1.1854

(6)

The interactions between acid gases and each amine are explained in detail in the subsequent sections.

2.3 Acid gases absorption in aqueous amine solutions The development of a model capable of predicting the simultaneous absorption of acid gases in amine solutions with a molecular-based EoS such as soft-SAFT44,45 is highly dependent on a sound representation of the absorption of single acid gases in aqueous amines. To this end, an understanding of the main reaction mechanisms occurring between individual acid gases and aqueous amines is needed to develop their counterpart representation within the soft-SAFT approach. In the absorption of mixed acid gases using aqueous amines it is postulated that several species are formed from the different dissociation and hydrolysis reactions. For the following reactions, 𝑅1𝑅2 9 ACS Paragon Plus Environment


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𝑅3𝑁 represents amine and 𝑅1, 𝑅2, 𝑅3 are hydrocarbon groups or mobile protons depending on the type of amine, for example 𝑅1, 𝑅2, 𝑅3 are organic groups for tertiary amines, 𝑅1, 𝑅2 are organic groups for secondary amines, while 𝑅1 is an organic group for primary amines. The chemisorption of CO2 with amines primarily proceeds through the formation of carbamate (Equation 7) and bicarbonate (Equation 8). The formation of carbamate is the governing chemical reaction for the absorption of CO2 in primary (MEA) and secondary amines (DEA) as shown by NMR spectroscopy studies.57,58 The reaction of CO2 with tertiary amines (MDEA) leads to the formation of bicarbonate through a base-catalyzed hydration mechanism.59 This clear distinction in terms of reaction mechanism with different amines influences the absorption process of CO2. 𝐶𝑂2 + 2𝑅1𝑅2𝐻𝑁 ↔ 𝑅1𝑅2𝑁𝐻2 + + 𝑅1𝑅2𝑁𝐶𝑂𝑂 ―

(7)

𝐶𝑂2 + 𝑅1𝑅2𝑅3𝑁 + 𝐻2𝑂↔ 𝑅1𝑅2𝑅3𝑁𝐻 + + 𝐻𝐶𝑂3 ―

(8)

following the notation previously defined. However, for the chemisorption of H2S in aqueous amines, regardless of the type of amine, the primary reaction proceeds via the same fast proton-transfer reaction leading to the formation of bisulfide (Equation 9).60–62 𝐻2𝑆 + 𝑅1𝑅2𝑅3𝑁 ↔ 𝑅1𝑅2𝑅3𝑁𝐻 + + 𝐻𝑆 ―

(9)

Considering the absorption of mixed acid gases, the acid-base reaction between MDEA and CO2 is slower than that with H2S, hence the MDEA’s selective removal of H2S. However, in most cases, MEA and DEA simultaneously react with H2S and CO2, impeding selective removal of the acid gases.63 Understanding the selectivity of amine solvents to acid gas absorption depends on the difference in reaction pathways for both acid gases with aqueous amines and the driving forces of the absorption process.64,65 The accurate prediction of the simultaneous absorption of acid gases in aqueous amines depends on the accurate description of the absorption of single acid gases (H2S or CO2) in each amine. The absorption of CO2 in aqueous amine solutions have been successfully modelled using soft-SAFT in our previous work with no more than two adjustable parameters, one being linearly temperature dependent.33,35 The carbamate and bicarbonate species formed from the reaction of CO2 with 10 ACS Paragon Plus Environment

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amines was implicitly accounted for by the formation of acid gas-amines aggregates created by strong association interactions, imitating the main reactions involved in the absorption process. This was done by including specific association sites (“reaction sites”) in the acid gas molecule, their number depending on the main reaction pathway, which can only form strong localized crossassociation interactions with the lone electrons pair located in the nitrogen atom in the amines. The required cross-association strength parameters for these sites were either transferred from previous works

33

or fitted to experimental CO2 absorption data for each amine over a wide range of

conditions.35 The number of “reactive sites” and their cross-association strength parameters for the absorption of CO2 in each amine are provided in Table S3 of the supporting information.33,35 The same methodology was carried out in this work for the description of the absorption of H2S in aqueous amine solutions: either one or two association sites, α1 and α2, were incorporated in the H2S molecule, mimicking the reaction mechanisms with each of the examined amines. The crossassociation energy between sites α1 and α2 with each amine was fitted to available H2S + H2O + Amine ternary mixture solubility data, owing to the lack of experimental data for H2S + Amine binary mixtures, while the cross-association volume was transferred from that obtained from the 3 modelling of CO2 absorption in amines (i.e., 𝜅𝐻𝐵 𝑁 ― 𝛼𝑖 = 500 𝐴 ). Fixing cross-association volume

parameter value reduces the number of parameters to be fitted, representing the strength of the interactions between H2S and each amine into the value for the cross-association energy.35 Due to the absence of NMR data or spectroscopic information on the species formed during the reaction of H2S with primary and secondary amines, the absorption of H2S in MEA/DEA was modelled with two different strategies: (1) only one site in H2S (e.g. α1) was considered in the acid gas molecule, capable of forming only a N–α1 bond with either amine molecule, and (2) two sites (α1 and α2) were considered in H2S and are able to cross-associate with MEA/DEA through N–αi interactions, emulating the formation of amine–H2S–amine aggregates. In the case of tertiary amine such as MDEA, only one association site is incorporated in H2S and permitted to interact with the lone electrons pair in the nitrogen atom present in the tertiary amine, forming an N–α1 association bond. The accuracy of these models will be discussed in the next section. 3. Results & Discussion



We present and discuss in this section results concerning the simultaneous absorption of H2S and CO2 in aqueous solutions of various amines, including MEA, DEA and MDEA as predicted by soft-SAFT. As mentioned in Section 2, CO2 absorption in several aqueous amines have been described in previous contributions, 33,35 and therefore models developed therein are directly used in this work, while H2S absorption in aqueous amines with soft-SAFT is studied here for the first time. With the models for describing the absorption of each individual acid gas set, the proposed modelling approach is used to predict the absorption of mixed acid gases without the need to introduce additional adjustable parameters. Results from the model are compared to available experimental data of the quaternary system H2S + CO2 + H2O + amine. The feasibility of the molecular modelling approach is assessed through calculations for the same systems with best available models in the Aspen Plus® (V.10) process simulator, and results compared with those predicted with soft-SAFT. 3.1 H2S + CO2 Binary Mixture Characterizing the binary interaction between H2S and CO2 is the first step in describing the simultaneous absorption of acid gases in aqueous amine solutions. We have studied the mixture with the models and parameters from previous works. Carbon dioxide was modelled explicitly considering its quadrupolar moment, while H2S was modelled as an associating molecule with weak self-association, no cross-association was allowed between both molecules in the mixture. The VLE of CO2 + H2S system at four different pressures (1.38, 2.07, 2.76 and 3.45 MPa) is plotted in Figure 1. Excellent agreement with experimental data

66,67

was obtained for all isobars using

pure component molecular parameters, in a predictive manner (see Figure 1, left), although some slight deviations are observed in the liquid phase. A single constant binary energy parameter equal to ξij=1.04, optimized at a single intermediate isobar, is sufficient to provide excellent agreement with the experimental data at all chosen conditions (see Figure 1, right).


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Fig. 1. Vapor-liquid equilibrium of CO2 and H2S mixture at different isobars: symbols represent the experimental data, 66,67 while lines stand for soft-SAFT calculations. See text for details.

Notice that this system was correlated by Jaubert and coworkers68 using the PPR78 model yielding excellent agreement with experimental data. PPR78 implements a group contribution approach to the Peng-Robinson EoS to predict the temperature dependency of binary interaction parameters in the van der Waals one-fluid mixing rules, since a constant kij are not adequate to predicting the phase equilibria of such highly non-ideal systems with cubic EoS. 3.2 H2S + H2O Binary Mixture Although H2S and water can be deemed structurally equivalent, hydrogen sulfide’s tendency to form weak hydrogen bonds with other H2S molecules or other molecules such as water versus the strong hydrogen bonding nature of water are responsible for their different physicochemical properties.69 Accordingly, the estimated binding energy value for self-association (H2S-H2S) is in the range of -3,766 to -6,276 J/mol,70 whereas the typical value for cross-association (H2S-H2O) is -10,878 J/mol,71 both of which are far lower than the hydrogen bond value of -25,000 J/mol reported for water dimers.71 Modelling the phase equilibria of H2S + water binary mixtures is quite challenging given the extreme non-ideality of the mixture; several works have attempted modelling this system using various approaches focusing on capturing H2S’s tendency to weakly self- and cross-associate with other H2S and water molecules, respectively. For instance, Fouad et al.72 , modelled the water content in H2S rich phase using a solvation model in PC-SAFT, considering H2S as a non-self13 ACS Paragon Plus Environment


associating molecule with two proton donor sites able to cross-associate with proton acceptor sites on water. The cross-association energy was transferred from the experimental binding energy,71 while the volume of cross-association was regressed to experimental VLE data of the binary mixture without using any binary interaction parameters. Nguyen et al.73 used GC-PPC-SAFT to describe the VLE of the binary mixture, modeling H2S as an associating molecule with three sites, wherein fitted cross-association strength parameters (energy and volume) and a binary energy interaction parameter were used to obtain a good agreement with experimental data. Tsivintzelies et al.74 using CPA EoS, obtained good agreement with experimental data for the phase equilibria considering both self- and cross-association of H2S. The cross-association energy was transferred from the experimental binding energy, while they simultaneously fitted the cross-association volume and binary energy parameter to experimental data; however, a large value of the binary interaction parameter was needed for a good representation of the phase equilibria. On a different approach, Qian et al.75 used the PPR78 model with kij temperature dependent parameters, achieving excellent agreement with experimental data. One of the significant factors needed to correctly capture the governing behavior of H2S + water mixture is to explicitly take into account the extent of cross-association, emulating the formation of weak hydrogen bonds between both molecules. In this work, three approaches were considered based on the extent of cross-association between H2S and water shown in Figure 2. In all cases, H2S and water were modelled as associating molecules as previously described (Section 2.2), wherein self-association interactions (e.g. H2S-H2S, H2O-H2O) were allowed in all modelling approaches.

Fig. 2. Cross-association interactions between H2S and H2O considered in this work.


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The first approach (Approach I) did not allow cross-association between unlike molecules (H2SH2O) by setting cross-association parameters equal to zero. In the second approach (Approach II), cross-association was allowed in the model, with cross-association parameters acquired in a predictive manner from Eqs. (4) and (5) with 𝛼𝐻𝐵 𝑖𝑗 = 1.0. In the third approach (Approach III), cross-association was permitted in the model, with the cross-association energy (𝜀𝑖𝑗 𝐻𝐵/𝑘𝐵) calculated directly from the combining rule (Eq. (5) with 𝛼𝐻𝐵 𝑖𝑗 = 1.0), while the cross-association volume (𝜅𝑖𝑗 𝐻𝐵) was transferred from that of pure H2S (i.e., 500.6 𝐴3), in order to describe the localized short range interactions. Interestingly, the cross-association energy parameter (𝜀𝑖𝑗 𝐻𝐵/𝑘𝐵 ) calculated from the mixing rule (1268.46 K) in approaches II and III, is close to that of the experimental value (1308.12 K).71 A binary size parameter ( 𝜂𝑖𝑗) was needed in all cases, obtained by optimizing to experimental VLE data. Table 1 contains the binary parameter values used in this work. Table 1. Binary and cross-association parameters between water and H2S for the different modelling approaches considered in this work (fitted to experimental data at T = 344 K 76,77)

Modelling Approaches

ηij

ξij

Approach I a Approach II Approach III Approach IV

1.118 1.135 1.125 1.085

1.0 1.0 1.0 0.95

Cross-Association strength parameters 𝜺𝒊𝒋 𝑯𝑩/𝒌𝑩(𝑲) 𝜿𝒊𝒋 𝑯𝑩(𝑨𝟑) 0.0 1268.48 b 1268.48 b 1268.48 b

0.0 1377.43 b 500.6 c 500.6 c

a)

Cross-association between H2S and H2O was not allowed (See Text for details) Calculated from Eq. (4) & Eq. (5) with 𝛼𝐻𝐵 𝑖𝑗 = 1.0 c) Transferred from pure H S (see text for details) 2 b)

Results for all approaches tested on experimental data a single isotherm at 344 K 76,77 are presented in Figure 3, using the parameters shown in Table 1. Regardless of the approach used, very good agreement with available experimental data was observed in the vapor-liquid equilibria (VLE) region of the diagram; however, important deviations were observed in the liquid-liquid equilibria (LLE) region, with the model describing a pronounced negative slope for the solubility line of H2S in the water-rich phase in the LLE region, and underestimating the composition of H2S in the nonaqueous phase. The lowest deviations to experimental data in the LLE region were obtained when no cross-association (Approach I) or a localized cross-association (Approach III) were considered in the model. The assumption of a localized cross-association (Approach III) is more 15 ACS Paragon Plus Environment


physically sound, as it mimics the formation of weak hydrogen bonds between both molecules, H2S-H2O; however, an additional correction is required to fully capture the behavior of the LLE region as the description of this region is more sensitive to the use of binary parameters than the VLE region.78 Consequently, Approach IV treats the extent of cross-association in this binary mixture as a localized cross-association, but with an additional binary interaction parameters ξij, related to the unlike van der Waal energy of interactions, in addition to the size binary parameter (see Table 1). With this approach, excellent agreement with experimental data from literature76,77 was achieved in both phases using the same set of parameters.

Fig. 3. Vapor-liquid and liquid-liquid equilibria of water and H2S mixture at 344 K. Symbol represent the experimental data from literature, 76,77 while the lines correspond to the soft-SAFT calculations using different cross-association approaches. See text for details.

The VLE and LLE of the water + H2S mixture over a wide range of temperatures was studied using Approach IV, keeping the value of the binary energy parameter (𝜉𝑖𝑗) at 0.95 (transferred from the one previously optimized at 344 K isotherm), while the size binary parameter was linearly correlated with the temperature ( 𝜂𝑖𝑗 = ―0.00068 × 𝑇 + 1.32412, 𝑅2 = 0.986) using data from 76,77.

Results are presented in Figure 4. The left graph depicts the water-rich phase while the right

graph represents the H2S-rich phase; solid lines stand for the calculated isotherms while the dashed lines correspond to a vapor-liquid-liquid equilibria (VLLE) transition observed at 311 and 344 K (only for isotherms below the critical point of H2S). These results demonstrate that the model accurately describes the experimental solubility data available in literature for temperatures up to 444 K and 10 MPa. 16 ACS Paragon Plus Environment

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To further check the suitability of the developed model for H2S + water, the phase behavior of this system was calculated for temperatures not included in the fitting procedure. As shown in Figure 5, the model predictions agree well with experimental data from the literature79,80 over a wide range of temperatures and pressures.

Fig. 4. Vapor-liquid and liquid-liquid equilibria of water and H2S mixture at five temperatures, ranging from 311444K: experimental data 76,77 (symbols), soft-SAFT calculations (full lines). Dashed lines correspond to the VLLE transition. All soft-SAFT calculation were done using parameters for Approach IV with a temperature dependent binary size parameter. VLE data taken from,75 and LLE data from.76



Fig. 5. Vapor-liquid equilibrium of water and H2S binary mixture at different temperatures: (Top) VLE of water and H2S, (Bottom) solubility of H2S is water rich phase: experimental data 79,80 (symbols), and calculations using softSAFT parameters for Approach IV in Table 1 (lines).

3.3 H2S solubility in aqueous amines Modelling the absorption of H2S in aqueous amines was performed following the methodology developed in our previous works for the CO2 absorption in aqueous amines.33,35 Using this approach, just the parameters characterizing the N–αi association strength for each amine are required to calculate the H2S absorption in aqueous amines with the soft-SAFT approach. Other molecular parameters required to characterize these ternary mixtures were transferred from previous works, as described in Section 2.2. The reaction governing the absorption of H2S in amines was modeled through the formation of physical aggregates composed by one H2S molecule and either one amine molecule (one-site approach) or two amine molecules (two-sites approach). For the two-sites approach, the cross18 ACS Paragon Plus Environment

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association energy of the two sites were considered to be either symmetric, (𝜀𝑁 ― 𝛼1 𝐻𝐵/𝑘𝐵 = 𝜀𝑁 ― 𝛼2 𝐻𝐵/𝑘𝐵), or asymmetric, (𝜀𝑁 ― 𝛼1 𝐻𝐵/𝑘𝐵 ≠ 𝜀𝑁 ― 𝛼2 𝐻𝐵/𝑘𝐵). In all cases, the van der Waals binary size (𝜂𝑖𝑗) and energy (𝜉𝑖𝑗) parameters between H2S and each of the chosen amines were set to unity in a predictive manner. The optimized parameters against solubility data for a fixed amine concentration and temperature are presented in Table S4 in the accompanying Supporting Information. Figure 6 depicts the soft-SAFT calculations compared to experimental data81–83 for a fixed amine concentration and intermediate temperature using the cross-association strength parameters of Table S4 in the Supporting Information. For the absorption of H2S in single aqueous MEA and DEA, the theoretical reaction stoichiometry of 1 mole H2S to 1 mole of amine postulates the use of a one-site model to mimic the formation of H2S-amines aggregates. However, the one-site model seemed unable to describe the solubility of H2S in these amines over the range of loading capacities at the examined conditions, even with adjusting cross-association volume and/or binary interaction parameters. Similar to previous modelling results on the CO2 absorption,35 the best descriptions of the solubility of H2S in aqueous MEA and DEA were obtained when using two association sites with asymmetrical site energy, as also done by Wangler et al. using CPA.41 Conversely, the one-site model was able to capture the absorption of H2S in aqueous MDEA in good agreement with available experimental data, in accordance with the postulated reaction stoichiometry. To enhance the performance of the model over a broad range of temperatures is essential to capture the effect of temperature on the absorption of H2S in aqueous amines, as both equilibrium constants and reaction rates for the absorption process are temperature-dependent. Better agreement with experimental data over a broad range of temperatures was obtained when the cross-association energy parameters for each amine were optimized at each isotherm rather than transferring the cross-association parameters for each amine optimized at a fixed temperature.



Fig. 6. Partial pressure of H2S versus H2S loading in single aqueous solutions of MEA, DEA and MDEA amines at a fixed temperature comparing the different modelling approaches: experimental data 81–83 (symbols), and calculations using soft-SAFT calculations (lines). See text for details.

To reduce the number of fitting parameters and enhance the robustness of the model, the values of the cross-association energy characterizing N–α2 bonds were taken to be those calculated at constant temperature (Table S4) while those characterizing N–α1 bonds were adjusted as function of temperature. The model calculations with the new the cross-association energy parameters versus experimental H2S loading capacities for each aqueous amine over a broad range of temperatures are depicted in Figure. 7. Remarkably, the cross-association energy characterizing N–α1 for each amine + H2S pair is linearly dependent on temperature (𝑅2 > 0.98). However, contrary to what was observed on the models used to describe the CO2 absorption,35 the value of these parameters increases with temperature. The final set of parameters characterizing the interactions between H2S and each of the examined amines within the soft-SAFT approach and


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functions correlating the linear dependence of 𝜀𝑁 ― 𝛼1 𝐻𝐵/𝑘𝐵 parameters on temperature are provided in Table 2. Table 2. Volume and energy cross-association parameters of N–αi interactions using the soft-SAFT framework together with the optimized amine concentration and range of temperatures covered. The size and energy van der Waals binary parameters, 𝜼𝒊𝒋 and 𝝃𝒊𝒋, between H2S and each amine were set to unity.

H2S + MEA DEA MDEA

𝟑 𝛆𝑯𝑩 /𝒌𝑩 (K) 𝛋𝑯𝑩 𝑵 ― 𝛂 (𝑨 ) 𝑵 ― 𝜶𝟏

500a 500a 500a

c 𝛆𝑯𝑩 𝑵 ― 𝜶𝟐/𝒌𝑩 (K)

T range (K)

wt % amine

5600 3959 0b

313‒393 298‒393 313‒373

15.3 20.6 35

7.7  T  1238 1.302  T  4661 0.5  T  4563

Transferred from Lloret et al. 33 and Pereira et al. 35 One-site model for H2S c) Values fitted at a constant temperature (see Supporting Information, Table S4) a)

b)


Reference solubility data 81 82 83


Fig. 7. Partial pressure of H2S as a function of H2S loading capacity in single aqueous solutions of MEA, DEA and MDEA at different temperatures: experimental data 81–83 (symbols) and soft-SAFT calculations (lines). The soft-SAFT calculations were obtained using the functions developed for 𝜺𝑵 ― 𝜶𝟏 𝑯𝑩/𝒌𝑩 shown in Table 2.

As a measure of the robustness of the developed model, the transferability of the association strength parameters between H2S and each amine (Table 2) was tested by predicting the absorption process for different amine concentrations. As depicted in Figure 8, soft-SAFT predictions for the solubility of H2S in aqueous solutions of MEA (20.0 wt%),84 DEA (30 wt%),84 and MDEA (∼11.9 and 23.8 wt%)

85

are in overall good agreement with experimental data over a broad range of

compositions and temperatures. The highest deviations were obtained for the solubility H2S in aqueous solutions of MDEA (∼11.9 and 23.8 wt%),85 particularly for gas loadings lower than 0.3 ―1 . These results demonstrate a good degree of transferability of the cross𝑚𝑜𝑙𝐻s𝑆.𝑚𝑜𝑙𝑚𝑜𝑙𝐴𝑚𝑖𝑛𝑒

association parameters within the examined range of amine concentrations. Though an improved 22 ACS Paragon Plus Environment

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description could be attained by explicitly accounting for the effect of amine concentration on the cross-association energy parameters, the required additional fitting will reduce the model’s robustness and predictive capability,35 contrary to our objective of developing a model as predictive and transferable as possible. Overall, the model in this form uses only a maximum of two adjustable parameters, one of which is linearly temperature-dependent, with demonstrated predictive capability at conditions of interest for industrial gas separation processes.

Fig. 8. Partial pressure of H2S as a function of H2S loading capacity in single aqueous solutions of MEA, DEA & MDEA at different temperatures and amine concentrations: experimental data84,85 (symbols), and soft-SAFT predictions (lines).



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The solubility of H2S in each aqueous amine solution calculated by the proposed approach using soft-SAFT was used to calculate the H2S enthalpy of absorption (∆𝐻𝑎𝑏𝑠) as a function of H2S loading through the approximate form of the Gibbs-Helmholtz thermodynamic relation: ∆𝐻𝑎𝑏𝑠 = 𝑅

[ ] ∂ln 𝑃𝐻2𝑆 1 ∂( ) 𝑇

(10) 𝑃, 𝛼𝐻2𝑆

where 𝑃𝐻2𝑆 is the partial pressure of H2S predicted by soft-SAFT at a given temperature, pressure and H2S loading. Results of the heat of absorption calculated using (Equation 10) in combination with VLE data obtained with the developed soft-SAFT models are compared to experimental values reported in the literature for each amine82,85,86 in Figure 9. As inferred from the figure, excellent agreement with literature values are obtained with an accurate representation of the effect of the acid gas loading on the heat of absorption over a wide range of composition.


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Fig. 9. Calculated enthalpy of absorption as a function of H2S loading: experimental data form MEA86, DEA82 and MDEA85 (symbols), soft-SAFT calculations (lines). The values reported in the literature for each amine were calculated using the Gibbs-Helmholtz equation (Equation 10) from experimental VLE data.

3.4 Mixed acid gases absorption in aqueous amines The previously developed models for each sub-binary system and for the absorption of single acid gases (CO2 or H2S) in aqueous amine solutions are transferred and used here to check the validity of the modelling approach for predicting the simultaneous absorption of both acid gases in aqueous amine solutions. For simplicity, it was assumed that only the direct reactions between each acid gas and each amine proceed according to the previously described reaction mechanisms (Section 2.3). In other words, the formation of aggregates in the absorption of mixed acid gases occurs only via the formation of either H2S-amine or CO2-amine aggregates or a combination of both, which is controlled by the strength of the cross-association interaction between each acid gas and amine molecule as determined from the absorption of single acid gases. In this case, a single amine molecule can only bond to the reactive sites on either H2S or CO2 forming a single N-αi bond. All the model parameters described in previous section were applied without any modification for predicting phase behavior of the quaternary CO2 + H2S + amine + water systems. To quantify the predictive capability of the model, the modified index of agreement (d) was used as it provides an unbiased quantification of the model’s accuracy.87 Although the coefficient of determination (R2) or error measurements such as mean absolute deviation (MAD) or absolute average deviation (AAD) are more commonly used, still they can give misleading results to the accuracy of the model even for a poor model fit as these measures are sensitive to outliers and extreme values.88,89 However, the advantage of the modified index of agreement is that the errors and differences are given their appropriate weighting and not inflated by their squared values, overcoming any deficiencies from other model accuracy measurements.87–89 The modified index of agreement (d) is calculated as:87 𝑁

𝑑 = 1.0 ―

∑𝑖 = 1|𝑃exp ,𝑖 ― 𝑃𝑝𝑟𝑒𝑑, 𝑖| 𝑁

∑𝑖 = 1(|𝑃𝑝𝑟𝑒𝑑, 𝑖 ― 𝑃𝑒𝑥𝑝| + |𝑃exp ,𝑖 ― 𝑃𝑒𝑥𝑝|)

(11)

where 𝑃exp ,𝑖 is the experimental values, 𝑃𝑒𝑥𝑝, is the mean of the experimental values, and 𝑃𝑝𝑟𝑒𝑑, 𝑖 is the predicted values. The modified index of agreement d varies from 0 to 1, with index values closer to 1 indicating a better agreement between predictions from the model and experimental 25 ACS Paragon Plus Environment


partial pressure values. The interpretation of values obtained from the modified index of agreement is similar to that of the coefficient of determination (R2),87 wherein, the closer the value of d to 1, the better the agreement between predictions from the model and experimental values, highlighting the strength of the predictive power of the model. Notice, for instance, than a value of 0.9 gives excellent agreement between the predictions and the experiments, as shown in Figure 10. Predictions obtained from soft-SAFT for the absorption of mixed acid gases in aqueous solutions of MEA, DEA and MDEA are compared with experimental data available in literature90–93 and results presented in Figure 10 in the form of parity plots. In these plots, the soft-SAFT predicted partial pressures of CO2 and H2S are represented as function of the experimental partial pressure of each corresponding acid gas in the examined aqueous amine systems. To allow further discussion, calculated values of the index of agreement d for each amine and acid gas pair are also provided in the parity plots. Based on values of the index of agreement, it can be seen that the partial pressure of H2S is better predicted for MEA, then MDEA and finally DEA, with a d value of, 0.909, 0.875 and 0.719, respectively. Conversely, CO2 partial pressures are better predicted for DEA, followed by MEA and finally MDEA, with a d value of 0.844, 0.766, and 0.705, respectively. Such differences in the performance of the model for predicting the partial pressure of CO2 and H2S might be attributed to the range of amines concentrations selected when optimizing the cross-association energy parameters for each acid gas-amine pair. The selected range of amine concentration used during the fitting of the cross-association energy parameters for each CO2-amine and H2S-amine pair was dictated only by the availability of experimental data on the absorption of each single acid gas in aqueous amines. As previously mentioned, the model can be easily re-parametrized to a broader range of amine concentrations and additional fitting parameters added for a better representation of the effect of changing the amine concentration on the value of the cross-association energy characterizing the interactions of CO2 and H2S with each amine (see Figure S1 in the Supporting Information); however, such a treatment would reduce the model’s functionality in terms of transferability and robustness. Overall, the adopted modelling strategy provides a good compromise between the number of parameters used to describe the complex chemisorption of CO2 and H2S in aqueous amines and the accuracy of the predictions obtained for mixed acid gases.


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Fig. 10. Parity plots of predicted (soft-SAFT) and experimental partial pressure of CO2 and H2S in aqueous amine solutions 90–93 with values of index of agreement (d). Symbols correspond to soft-SAFT predictions.



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In order to gauge the performance of our modeling approach, the absorption of mixed acid gases in the selected aqueous amines was also predicted using Aspen Plus® (V.10) process simulator. Aspen Plus® provides several thermodynamic models capable of calculating the absorption of acid gases in aqueous amine solutions. Among all, the recommended model for describing the separation process of acid gases with aqueous amines is the electrolyte-NRTL (e-NRTL) model coupled with the Redlich-Kwong EoS for an integrated modelling of the non-idealities in the liquid and vapor phases. Contrary to the modelling approach followed in this work, the recommend model in Aspen Plus® (V.10) explicitly takes into account all the main speciation reactions involved in the chemical absorption of CO2 and H2S in aqueous amines. The built-in template (ElecNRTL_Rate_Based_Amine_model) was used as the basis for all VLE calculations with Aspen Plus® (V.10) and the required models parameters pre-specified in this template were used without any modification. As a first step, the absorption of single acid gases in each aqueous amine solutions were calculated with Aspen Plus® (V.10) and compared with experimental data and predictions using the developed soft-SAFT models. Results of these calculations are shown in Figure 11. As can be seen, the description of the absorption of CO2 and H2S in aqueous amines using the in-built models in Aspen Plus® (V.10) and soft-SAFT can attain a comparable levels of accuracy. The same methodology was then applied to predict the absorption of mixed acid gases; the index of agreement for the partial pressure of CO2 and H2S for each aqueous amine solutions calculated from soft-SAFT predictions and Aspen Plus® (V.10) are summarized in Table 3 while the parity plots using the e-NRTL model are provided in Figure S2 in the Supporting Information. Table 3. Index of agreement (d) (Eq. 16) for the prediction of the partial pressure of CO2 and H2S from the absorption of mixed acid gases in aqueous solutions of MEA, DEA and MDEA, using soft-SAFT (this work) and using e-NRTL + RK EoS model from Aspen Plus® (V.10).

soft-SAFT Amine

MEA DEA MDEA

wt % amine T range (K)

15.3 20.6, 25 35

313-393 323, 339 313, 373

𝑷𝑪𝑶𝟐(kPa)

0.766 0.844 0.705

Aspen Plus (e-NRTL + RK EOS) Index of Agreement (d) 𝑷𝑯𝟐𝑺(kPa) 𝑷𝑪𝑶𝟐(kPa) 𝑷𝑯𝟐𝑺(kPa)

0.909 0.719 0.875


0.885 0.887 0.933

0.827 0.718 0.904

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Fig. 11. Partial pressure of acid gases (H2S and CO2) as a function of acid gas loading capacity in single aqueous solutions of MEA, DEA & MDEA at different temperatures: experimental data 81–83,94,95 (symbols), soft-SAFT predictions (full lines), and Aspen Plus® (V.10) predictions (dashed lines). Soft-SAFT predictions were obtained using the functions developed for 𝜺𝑵 ― 𝜶𝟏 𝑯𝑩/𝒌𝑩 shown in Table 2 and Table S3 for H2S absorption and CO2 absorption, respectively.

Based on the results depicted Table 3, Figure 11 and Figure S2 in the Supporting Information, it can be concluded that, both modelling approaches show a comparable level of accuracy for predicting the absorption process of mixed acid gases in aqueous amine solutions. Predictions obtained with Aspen Plus® (V.10) showed a slightly overall higher index of agreement with experimental partial pressure data for mixed CO2 and H2S in aqueous MEA, DEA and MDEA 29 ACS Paragon Plus Environment


solutions. However, the advantages of the proposed approach using soft-SAFT manifest themselves on several fronts. Firstly, the modelling approach based on the physical aggregation process not only provides a simple modelling framework but also eliminates the need for detailed speciation reactions, significantly reducing the number of adjustable parameters and, hence, experimental data required for an accurate representation of the absorption process. This in turn, makes the proposed approach an attractive potential platform for the screening of new solvents. Secondly, the predictive nature of molecular-based models allows transferring fitted parameters to a range of industrially relevant conditions at a good level of accuracy. Finally, the extrapolative power of the proposed approach allows the prediction of mixed acid gases without the need to fit additional parameters, merely from the accurate representation of the absorption of single acid gases. It should be noted that degradation of prediction power is expected whenever the parameters are transferred to predict the absorption process in either dilute or concentrated amine solutions, which could be easily adjusted by re-parametrizing the models at those specific amine concentrations allowing for a more accurate prediction of the absorption of mixed acid gases. With that said, the validity of the proposed soft-SAFT approach in modelling the absorption of single and mixed acid gases in aqueous amines is demonstrated with a simple yet accurate and robust framework. This approach allows for the consistent and reliable screening of existing and new solvents for acid gas removal, applicable for implementation in engineering simulators.

Conclusions In this work, the soft-SAFT molecular-based EoS was used to model the absorption of single and mixed acid gases in aqueous amine solutions over a range of conditions using a simple yet robust and consistent approach, applicable to existing and new solvents for acid gas removal, and results compared to the best available model for this purpose in the Aspen Plus® (V.10) process simulator. The molecular models were built following a systematic approach, from pure fluids to multicomponent mixtures, searching for physical meaning and transferability. Molecular models of pure substances present in acid gases + water + amine systems along with those accounting for water + amine, and CO2 + amine interactions were taken from previous contributions in a fully transferable manner to describe the chemisorption of mixed acid gases. The chemisorption of H2S in aqueous solutions of MEA, DEA and MDEA was described by mimicking the formation of 30 ACS Paragon Plus Environment

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reaction products as physical aggregates of H2S-amine, in a similar manner as done for the chemisorption of CO2. Such a simplified modelling approach reduces the number of parameters required to represent the absorption process and eliminates the need to specify the detailed chemical equilibrium reactions of all species present in the solution. The developed model required a maximum of two adjustable parameters for cross-association energy representing H2S-amine interactions (one of which has a linear temperature dependency), to acquire good agreement with experimental results for the absorption of H2S in aqueous amines over a broad range of temperatures. The transferability of the optimized parameters for the model was tested through predicting the absorption of H2S at different amine concentrations, with an overall good agreement with experimental data. Comparison with experimental absorption data of mixed acid gases in aqueous MEA, DEA and MDEA showed the overall good capabilities of the models for predicting the partial pressure of H2S and CO2 over different thermodynamic conditions. The highest deviations were observed for the partial pressure of CO2 in aqueous MEA and DEA solutions. This degradation in the performance is attributed to the absence of any correction parameter for the effects of changing the amine concentration on the cross-association energy parameters, which in turn appears to be key for achieving a good degree of accuracy over wider ranges of amine concentrations. Finally, comparing these results with those obtained from recommended thermodynamic models in Aspen Plus® (V.10) process simulator showed a comparable level of predictive accuracy; nevertheless, the robustness and transferability of the molecular model developed in this work provides an attractive alternative to current existing models, as discussed in the previous sections. Overall, the results of this work confirm the capabilities of the proposed molecular modelling approach as an effective tool for the methodical assessment of the effects of various process conditions on the absorption of single and mixed acid gases in aqueous amines. Furthermore, it simplifies the description of the chemical equilibrium reactions in the absorption process making it applicable to new amines solvents, and thereby as a powerful framework for the selection of potential solvents for acid gas removal.



Author information Corresponding Author Lourdes. F. Vega, phone +971 2 607 5626, e-mail: [email protected] ORCID Ismail I.I Alkhatib 0000-0002-6769-5383 Luis M. C. Pereira 0000-0001-5168-4922 Lourdes F. Vega 0000-0002-7609-4184 Notes The authors declare no competing financial interest. Acknowledgements Financial support by ADNOC Gas Processing and their shareholders: the Abu Dhabi National Oil Company (ADNOC), Shell Abu Dhabi, Total SA and Partex, through the Gas Research Center (project GRC18003) is gratefully acknowledged. Supporting Information Values of the molecular parameters of the pure components; parameters for the CO2 + amines, amines + water and H2S+ amines parameters. Parity plots for H2S and CO2 in aqueous MDEA for the e-NRTL predicted and experimental partial pressure of H2S and CO2 in aqueous amine solutions. References (1) (2)

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110th Anniversary: Accurate Modeling of the Simultaneous Absorption

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