Multiobjective Evaluation of Amine-Based Absorbents for SO2 Capture Process Using the pK a Mathematical Model.

The screening of high-efficiency and low-energy consumption absorbents is critical for capturing SO2. In this study, absorbents with better performance are screened based on mechanism, model, calculation, verification, and analysis methods. The acidity coefficient (pK a) values of ethylenediamine (EDA), piperazine (PZ), 1-(2-hydroxyethyl)piperazine (HEP), 1,4-bis(2-hydroxyethyl)piperazine (DIHEP), and 1-(2-hydroxyethyl)-4-(2-hydroxypropyl)piperazine (HEHPP) are calculated by quantum chemical methods. A mathematical model of the SO2 cyclic absorption capacity per amine (αc) in the amine-based SO2 capture process is built based on the electroneutrality of the solution. Another model of desorption reaction heat (Q des) is also built based on the van't Hoff equation. Correspondingly, αc and Q des of the above five diamines are calculated and verified with the experimental data. The results show that αc of the diamine changes with the increase in the pK a value, and the increase in the pK a value directly leads to changes in Q des. The order of αc of the above five diamines is EDA > PZ > HEHPP > HEP > DIHEP, and the order of Q des is EDA > PZ > HEHPP > DIHEP > HEP. The multiobjective analysis between αc and Q des suggests that it is not advisable to simply pursue a higher αc while ignoring Q des. The compound quaternary system absorbent has a wider range of αc than the single ternary absorbent, which is the direction of absorbent development. This study is expected to strengthen absorbent screening for the amine-based SO2 capture process from flue gas.

Introduction

Global climate change caused by industrial flue gas emissions (e.g., CO2 and SO2) is the most urgent environmental problem today. For example, CO2 emissions lead to worldwide warming, ocean acidification, and frequent forest fires, which seriously threaten the survival and development of the human race.[1] Excessive emissions of SO2 readily form acid rain, causing water body and soil acidification, agricultural product damage, and the acceleration of building corrosion.[2,3] Reducing flue gas emissions has become the general consensus and trend of the international community. In 2016, China and more than 170 countries around the world signed the Paris Agreement,[4] which pursues efforts to limit the global average temperature increase to 1.5 °C; carbon capture, utilization, and storage is an important part of the technology portfolio to achieve the objectives of the agreement. The organic amine-based postcombustion CO2 capture process is the most widely used and developed carbon capture technology.[5,6] However, SO2 is also an acidic gas whose content is second only to CO2 in industrial flue gas at 500–3000 ppmv. The coexistence of SO2 and CO2 in flue gas is one of the important factors affecting the efficiency of amine-based CO2 capture processes.[7] The main effects of SO2 on the CO2 capture process are as follows: (1) the acidity of SO2 is stronger than CO2, and SO2 is absorbed prior to CO2. The reaction sites of organic amines to absorb CO2 are reduced and thus the efficiency of CO2 removal is also reduced.[8,9] (2) The accumulation of SO2 reduces the pH value of the absorbent solution, so the solubility of CO2 in the absorbent is reduced. (3) SO2 accelerates the degradation of organic amines. Uyanga and Idem[10] showed that SO2 is more likely to lead to the degradation of amine absorbents than O2, and the generated formate and acetate can not only cause corrosion of the device but also produce foam, affecting normal device operation. An International Energy Agency research report suggested that the amine-based CO2 capture process should limit the SO2 concentration to less than 10 ppmv in flue gas.[11] Therefore, highly efficient flue gas desulfurization (FGD) technologies have become a basic requirement for postcombustion CO2 capture.

The traditional FGD process mainly uses alkaline absorbers such as lime, calcium hydroxide, and sodium hydroxide to neutralize SO2 in flue gas.[12] These desulfurizers react with SO2 to form irreversible products such as calcium sulfate and sodium sulfate, whose use value is very low and long-term accumulation will cause secondary pollution. The ammonia desulfurization technology can coproduce an ammonium sulfate fertilizer. However, ammonia is easy to volatilize and causes losses.[13] Recently, ionic liquids (ILs) have attracted extensive attention in the FGD field due to their extremely low vapor pressure, excellent chemical and thermal stability, and adjustable structure.[14] Among them, guanidinium-based and imidazolium-based functional ILs have high absorption capacities for SO2.[15−17] However, there are still many challenges to truly apply ILs to industrial desulfurization processes: (1) the high production cost of functional ILs, (2) poor mass transfer effect due to the high viscosity of ILs, and (3) poor selectivity of ILs for SO2 and CO2 in flue gas. The amine-based SO2 capture process is a green and renewable FGD technology. The efficient recycling of sulfur resources is realized through the efficient capturing of SO2 from flue gas, which further produces sulfuric acid, liquid SO2, and other chemical products. This emerging SO2 capture process from flue gas is critically significant for atmospheric pollution control, carbon capture pretreatment, and economic benefits.

Organic amines play an important role in the field of FGD in the academic and industrial communities. Zhao et al. reported that the amine-organic solvent binary system absorbent captures SO2, and the amines include N,N-dimethylaniline,[18]N,N-dimethylcyclohexylamine,[19] and N,N-dimethylethanolamine.[20] It was found that the high viscosity of the absorbent limits its industrial application in the SO2 capture process. Therefore, SO2 is still mainly captured by aqueous organic amine adsorbents due to the extremely low viscosity of water. Walker evaluated the desulfurization cost of several aqueous solutions of citric acid, glycolic acid, N-methylpyrrolidone, and ethylenediamine (EDA) and found that the total desulfurization cost of the EDA-based aqueous solution was the lowest. However, the cost of lost EDA vapor traveling up the tower was excessive due to its high vapor pressure.[21] The strongly basic amine group first reacts with a strong acid to form a half-salt. The diamine in its half-salt form is used to capture SO2. The vapor pressure of the half-salt form of diamine is almost zero, which solves the shortcomings of volatile amine absorbents.[22] Tang et al.[23] added phosphoric acid (H3PO3) to the EDA-based aqueous solution, which lowered the vapor pressure of EDA. In contrast, the EDA-H3PO3-H2O ternary system absorbent only uses the weakly basic amine group of EDA to capture SO2, which improves the desorption performance of EDA. Khalili et al.[24] determined the acidity coefficient (pKa) values of six piperazine diamines at 298.15, 303.15, 313.15, and 323.15 K by potentiometric titration. It was found that adding different substituents to the piperazine molecule caused the pKa value of piperazine to change. The deprotonation reaction enthalpy (ΔHa) of the abovementioned diamines was predicted using the van’t Hoff equation. It was found that the smaller the pKa, the lower the ΔHa. The ΔHa value can reflect the desorption reaction heat consumption. However, the smaller the pKa, the lower the corresponding SO2 absorption capacity. Therefore, the selection of the SO2 absorbent is a multiobjective optimization problem, which requires not only the pursuit of maximum SO2 absorption capacity but also lower desorption reaction heat consumption and at the same time low vapor pressure. The vapor pressure of organic amines can be lowered using diamine-acid-water ternary system absorbents. Therefore, the focus of this study is to explore the multiobjective relationship between the SO2 absorption capacity and desorption reaction heat consumption.

The pKa of an organic diamine is an important parameter reflecting its SO2 absorption capacity and desorption reaction heat consumption. However, the experimental data on the first acidity coefficient (pKa1) and the second acidity coefficient (pKa2) values of diamines are quite lacking, and it is difficult to experimentally determine the second acidity coefficient (pKa2) of diamines.[25] Therefore, the pKa1 and pKa2 values of organic diamines are predicted by quantum chemistry methods, and two mathematical models of the SO2 absorption capacity and desorption reaction heat consumption are also established. Then, the multiobjective relationship of the diamine-acid-water ternary system absorbent during the SO2 capture process is explored. Finally, alternative organic diamines for SO2 capture are screened. This research has important guiding significance for the development of SO2 trapping solvents with high SO2 absorption capacity and low desorption reaction heat consumption.

Mechanism and Mathematical Model

Reaction Mechanism and Research Framework

The reaction mechanism of the diamine-acid-water ternary system absorbent SO2 capture process is shown as follows in R1–R5. First, SO2 is dissolved in water (R1). Second, SO2 in the water quickly dissociates into HSO3–, SO32–, and H+ (R2 and R3). Third, the monovalent protic amine (BN2H+) combines with the H+ dissociated from SO2 to generate the divalent protic diamine (BN2H22+) (R4), which promotes the positive dissociation of SO2 in the absorbent and realizes the absorption of SO2. The monovalent protic diamine (BN2H+) is obtained by combining the strongly basic amine group (−N) in the diamine (BN2) with a strong acid (HX) (R5). In addition to SO2, there is also acidic gas CO2 in the flue gas, which may lead to reactions R6–R9. The absorption of CO2 should be avoided in the amine-based absorbent capture SO2 process in flue gas. In this study, the dissociation of SO2 and CO2 in aqueous solution is studied. According to the calculation of the dissociation equilibrium constant,[26−28] the dissociation degree of SO2 and CO2 varies with the solution pH value as shown in Figure . As can be seen from Figure , when the pH value of solution is less than 6, only physical dissolution of CO2 in aqueous solution occurs without dissociation reactions, such as R6–R8. Furthermore, the strongly basic amine group in the diamine has already combined with the H+ protons, so there will be no reaction to generate carbamate, such as R9. Therefore, as long as the pH value of the absorbent is less than 6, the purpose of the diamine-acid-water ternary system absorbent to capture only SO2 and not CO2 can be achieved.

Figure 1

Dissociation degree of SO2 and CO2 varies with the solution pH value.

Figure shows the research framework of this study. First, the pKa value of organic diamines is calculated by density functional theory (DFT) and a solvation model based on density (SMD). Then, a mathematical model of the SO2 cyclic absorption capacity per amine (αc) is established using the dissociation equilibrium constant (Ka) of diamine according to the electroneutrality principle of the absorbent solution. The αc value in different amine absorbents is then calculated. Furthermore, another mathematical model of desorption reaction heat (Qdes) is established according to the van’t Hoff equation and the logarithmic dissociation equilibrium constant (lnKa) of the diamine. Then, the Qdes consumption corresponding to different diamine absorbents is calculated. Finally, the multiobjective relationship between αc and Qdes of absorbents based on the amine-based SO2 capture process is evaluated.

Figure 2

Research framework based on the multiobjective relationship of the amine-based SO2 capture process.

The amine-based SO2 capture process is briefly described as follows: after the SO2 from flue gas entering the absorption tower is captured by the absorbent, the absorbent becomes an SO2-rich liquid moving into the desorption tower for high-temperature desorption. The top of the desorption tower contains the SO2 product, and the bottom of the tower contains the recycled SO2-lean absorption liquid. The SO2-lean liquid enters the absorber as a recycled absorbent to start the next cycle.

Mathematical Model of SO2 Absorption Capacity

The above reaction mechanism shows that the SO2 absorption capacity of the diamine-acid-water ternary system absorbent cannot be predicted by Henry’s law relationship. For such a nonideal chemical absorption system, Kent and Eisenberg[29] proposed the “quasi-equilibrium constant method,” which attributes the nonideal form of the gas–liquid two phase to one or more equilibrium constants in the absorption step. This method has been successfully applied to establish solubility models of H2S and CO2 in an alcohol-amine solution.[30,31] In this study, a mathematical model of SO2 absorption capacity of an amine absorbent is established based on absorption phase equilibrium and chemical reaction equilibrium. The organic amine-based SO2 capture process is divided into three steps to quantitatively predict the SO2 absorption capacity of the ternary system absorbent.

SO2 transforms from the gas phase to the liquid phase (as R1). The concentration of SO2 in the gas phase and the liquid phase conforms to Henry’s law. The concentration of SO2 in the solution is proportional to the partial pressure of SO2 in the gas phase,[22] as given in the following equation (eq ).where H is Henry’s coefficient (mol·(m3·Pa)−1), and its relationship with temperature (T) is given by Sander.[32]

The dissociation of SO2 in water (R2 and R3). Among them, R2 is the first dissociation of SO2 to generate HSO3– and H+. R3 is the second dissociation of SO2 (i.e., the dissociation of HSO3–) to generate SO32– and H+. Ks1 and Ks2 are the first and second dissociation equilibrium constants of SO2, respectively, which follows eqs and 4. The relationship between Ks1, Ks2, and temperature is given by Rabe and Harris[27] and Millero et al.[28]

The total concentration of SO2 in the liquid phase is represented by Cs as follows:

The monovalent protic diamine (BN2H+) neutralizes the H+ dissociated from SO2 in the aqueous solution (R4). The absorption of SO2 by organic amines is essentially a proton transfer reaction. The stronger the amine’s ability to neutralize H+, the higher the degree of dissociation of SO2 in water, and the greater the amount of SO2 captured by the amine absorbent.

Diamine has two amine groups (−N) and can undergo a two-stage proton transfer reaction. Strongly basic amine groups combine with H+ dissociated from the strong acid. Then, weakly basic amine groups combine with H+ dissociated from SO2. The two-stage deprotonation reaction equation of diamine conjugate acid and the equilibrium constant Ka are as follows:

The initial concentration of diamine is represented by CN as follows:

The strong acid (HX) dissociation reaction equation and the equilibrium constant Kx are as follows:

The initial concentration of HX is represented by Cx as follows:

The absorbent maintains the overall electrical neutrality of the solution after absorbing SO2. That is, the number of cationic charges is equal to the number of anionic charges. Therefore, the electric neutrality of the solution is used as the closing condition of the above equations, following eq . By knowing the Ka of each reaction, the αc value in the absorbent at different temperatures and partial pressures can be calculated:

The absorbent absorbs SO2 at low temperatures and desorbs SO2 at high temperatures. The absorbent becomes a SO2-rich liquid after absorption, which then becomes a SO2-lean liquid after desorption. The SO2 absorption capacity per amine is α (mol (SO2) mol–1 (BN2)), following eq . The SO2 cyclic absorption capacity per amine is αc (mol (SO2) mol–1 (BN2)), following eq . Among them, Csrich and Cslean are the SO2 absorption capacities in the SO2-rich and the SO2-lean liquids, respectively:

Model of SO2 Desorption Reaction Heat

The high energy consumption for the regeneration of organic amines is a significant shortcoming of the amine-based SO2 capture process. The total energy consumption (Qtot) mainly includes the desorption reaction heat consumption (Qdes), the sensible heat consumption (Qsen) of the absorbent heating up, and the latent heat consumption (Qlat) of the absorbent vaporization. Among them, the Qdes value is the main source of energy consumption for amine regeneration, and its value is only related to the type of the absorbent. Qsen and Qlat belong to process energy consumption, and their values can be reduced by heat integration optimization. Thus, reducing Qdes becomes the key to reducing the energy consumption of the amine-based SO2 capture process, and it is also an important basis for screening absorbents with excellent performance. The Qdes value depends on the desorption heat enthalpy (ΔHdes) of the desorption process, that is, the sum of the reverse reaction enthalpy of R2–R4. Among them, the reverse reaction enthalpies of R2 and R3 are the necessary energy consumption steps, so the key to reduce Qdes is to screen the organic diamine with the smaller divalent diamine deprotonated reaction enthalpy (ΔHa).

ΔHa can be obtained by differentiating the logarithm (lnKa) of the equilibrium constant using the van’t Hoff equation.

Generally, the relationship between Ka and T can be expressed in the form given by Weiland et al.[33] as follows:

To obtain the relationship between ΔHa and T for differential processing, see the following equation:

The equilibrium constant of the desorption reaction corresponding to ΔHdes can be shown as:

Kim pointed out that ΔHdes can also be regarded as a function of α alone.[34] Therefore, the equilibrium constant Ka of the diamine deprotonation reaction is known, and then Qdes can be calculated using the following equation:

Prediction of the Acidity Coefficient (pKa)

The calculations of the above αc and Qdes models are based on the Ka of the protic diamine, and Ka can be calculated using pKa of the diamine conjugate acid, as shown in eq :

The first step in using quantum chemistry to predict pKa is to calculate the reaction free energy (ΔGsoln*) of organic amines in solution.[35] Among them, ΔGsoln*1 corresponds to pKa1 and ΔGsoln*2 corresponds to pKa2.

The calculation of the reaction free energy change in solution is usually carried out under a thermodynamic cycle framework, as shown in Figure .

Figure 3

Thermodynamic cycle framework for calculating the free energy of the reaction.

It can be seen from Figure that the free energy of the reaction in solution is the sum of the free energy of the corresponding gas phase and the free energy of solvation, as shown in eq :where * represents the standard state of 1 mol·L–1, and ΔGsolv*(BNH+) and ΔGsolv*(BN) are the solvation free energies of BNH+ and BN, respectively. ΔGsolv*(H+) is the solvation free energy of H+. ΔG0* is the free energy change when a gas pressure of 1 atm moves to the liquid concentration of 1 mol·L–1,[36] as shown in eq :

When T = 298.15 K and ΔG0* is 7.91 kJ·mol–1, ΔGgas0(BNH+) is the free energy of the gas-phase reaction of BNH+, as shown in eq :

In this study, the Gibbs free energies (ΔGgas) of hydrogen protons, molecular amines, monovalent protic amines, and divalent protic amines in gas phase are calculated via high-level CBS-QB3 combined with thermodynamic methods.[37,38] There are many methods to calculate the solvation free energy (ΔGsolv), including the explicit solvent model and the implicit solvent model. The former requires consideration of various possible different arrangements of solvent molecules, so it is more complicated and requires a large amount of calculation. The latter involves treating the solvent environment simply as a polarizable continuum. The advantage of considering the solvent effect is that it can provide the average effect of the solvent without considering the possible molecular arrangement of the solvent layer like the explicit solvent model, and it does not increase the calculation time very much, so it is widely used in the field of quantum chemistry and molecular simulation. Implicit solvent models include Onsager, PCM, CPCM, IPCM, SCIPCM, COSMO, SMD, SMx series (e.g., SM12), etc.

The implicit solvent model usually divides ΔGsolv into polar contribution (ΔGpolar) and nonpolar contribution (ΔGapolar), as shown in eq . ΔGpolar is calculated by solving the Poisson–Boltzmann equation or the simplified generalized Born equation. For most implicit solvation models (PCM, CPCM, IPCM, SCIPCM, etc.), ΔGapolar is simplified to the product of the empirical surface tension parameter (γ) by fitting the experimental value of the solvation free energy of nonpolar solutes and the accessible surface area of the solvent, as shown in eq . For the SMD model, different atoms are used with different surface tension parameters, and ΔGapolar is split into cavity formation energy (ΔGcav), dispersion contribution (ΔGdis), and local solvent structure contribution (ΔGs), as shown in eq . The SMD is better than the aforementioned model and has higher calculation accuracy. Therefore, the ΔGsolv values of diamines, monovalent protic diamines, and divalent protic diamines in aqueous phase are calculated using the implicit SMD.[39] Since the parameters of the SMD are fitted under the framework of DFT with the M05-2x functional and 6-31g* basis set,[40−42] the calculation method of the solvation energies is also restricted to M05-2x/6-31g*. Finally, the Shermo program is used to calculate the Gibbs free energy at different temperatures.[43] The solvation energy of protons is directly obtained from the published literature,[44] which is −265.9 kcal·mol–1.

Results and Discussion

pKa Value and Parameter Fitting

In conventional amine SO2-capturing plants, the absorber works at 298.15–328.15 K and the stripper works at 378.15–398.15 K. Thus, the pKa1 and pKa2 values of the five diamines are calculated in the temperature range of 298.15–398.15 K, as shown in Table . The five diamines are ethylenediamine (EDA), piperazine (PZ), 1-(2-hydroxyethyl)piperazine (HEP), 1,4-bis(2-hydroxyethyl)piperazine (DIHEP), and 1-(2-hydroxyethyl)-4-(2-hydroxypropyl)piperazine (HEHPP). The above five diamines are considered potential absorbents for the amine-based SO2 capture process. The structure diagram of the five diamines and the free energy change value of the five diamine deprotonation reactions with increasing temperature are shown in the Supporting Information (Appendix 1).

Table 1

Diamine Acidity Coefficients pKa1 and pKa2

T (K)	pKa1					pKa2
	EDA	PZ	HEP	DIHEP	HEHPP	EDA	PZ	HEP	DIHEP	HEHPP
298.15	9.7532	9.8171	9.1537	8.0618	9.7646	6.6503	5.5457	4.5588	3.9649	4.7121
308.15	9.3136	9.3757	8.7272	7.6905	9.3225	6.2894	5.2202	4.2806	3.6833	4.4262
318.15	8.8982	8.9580	8.3233	7.3391	8.9033	5.9464	4.9111	4.0158	3.4160	4.1554
328.15	8.5067	8.5641	7.9421	7.0079	8.5091	5.6222	4.6192	3.7652	3.1616	3.8992
338.15	8.1371	8.1934	7.5834	6.6962	8.1381	5.3173	4.3441	3.5293	2.9236	3.6575
348.15	7.7882	7.8434	7.2446	6.4011	7.7872	5.0292	4.0840	3.3064	2.6974	3.4290
358.15	7.4574	7.5118	6.9236	6.1220	7.4547	4.7554	3.8366	3.0947	2.4832	3.2121
368.15	7.1447	7.1970	6.6200	5.8574	7.1409	4.4958	3.6026	2.8934	2.2800	3.0057
378.15	6.8473	6.8994	6.3313	5.6068	6.8424	4.2494	3.3798	2.7032	2.0865	2.8103
388.15	6.5642	6.6154	6.0564	5.3674	6.5583	4.0141	3.1680	2.5218	1.9023	2.6238
398.15	6.2952	6.3452	5.7952	5.1400	6.2889	3.7905	2.9668	2.3483	1.7274	2.4462

The first step in calculating αc and Qdes is to convert the pKa value into Ka according to eq , as explained in Section . The coefficients for the correlation of the temperature dependency of the above five diamine Ka values used in this study are given in Table . The lnKa and ΔHa values were calculated by using eqs and 23, as explained in Section .

Table 2

Coefficients of lnK (mol·L–1)–T (K) Relation

lnK	A	B	C	D	E	reference
lnKs1 (SO2)	–10.9670	1972.5				Rabe and Harris[27]
lnKs1 (HSO3–)	–358.5700	5477.1	65.31	–0.1624		Millero et al.[28]
lnK (H2SO4)	>10					Sippola[47]
lnK (HSO4–)	–49.7086	178.1142	10.9523	–0.0598		Sippola[47]
lnKa1 (EDAH+)	–1155.4712	16,611.5048	216.1750	–0.6018	2.8158E-04	this work
lnKa1 (PZH+)	–1469.5789	23,157.0111	275.2578	–0.7771	3.6759E-04	this work
lnKa1 (HEPH+)	–1732.5071	29,175.2775	324.4527	–0.9178	4.3445E-04	this work
lnKa1 (DIHEPH+)	–1240.1501	19,624.7054	232.2769	–0.6545	3.0918E-04	this work
lnKa1 (HEHPPH+)	–1253.3912	18,569.1484	234.6655	–0.6566	3.0786E-04	this work
lnKa2 (EDAH22+)	–1574.5134	27,239.3726	295.0325	–0.8323	3.9399E-04	this work
lnKa2 (PZH22+)	–848.7211	12,611.8734	158.7754	–0.4312	1.9757E-04	this work
lnKa2 (HEPH22+)	–1573.8890	29,030.2873	294.5322	–0.8274	3.8922E-04	this work
lnKa2 (DIHEPH22+)	–1315.7710	23,517.2331	246.4046	–0.6865	3.2091E-04	this work
lnKa2 (HEHPPH22+)	–831.7789	12,860.5300	155.8702	–0.4295	1.9995E-04	this work

Model Verification

Verification of the pKa Value

The lnKa values obtained by fitting are used to calculate the values of the acidity coefficients pKa1 and pKa2 of each diamine using eq , and the results are shown in Figures and 5. Comparing Figures and 5, it can be found that pKa1 > pKa2 for each diamine. It is verified that the abovementioned diamine has two amine groups with different basicities and can be used as the diamine-acid-water ternary system absorbent. It can also be seen that pKa1 and pKa2 of each diamine decrease with increasing temperature.

Figure 4

First acidity coefficients (pKa1) of the diamines.

Figure 5

Second acidity coefficients (pKa2) of the diamines.

The accuracy of pKa is a prerequisite for the accuracy of the calculation results of α and Qdes. In order to verify the accuracy of the calculated pKa value (pKa(cal)), the collected experimental pKa values (pKa(exp))[45,46] are plotted on the abscissa and the calculated pKa values on the ordinate, as shown in Figure . It can be seen from Figure that each point is near the diagonal. Letting MRE to be the average relative error between the calculated value of pKa and the experimental value, its value is calculated using eq . The result is 3.18%, which can meet the needs of engineering design and application:

Figure 6

Comparison between calculated and experimental pKa values.

Verification of the SO2 Absorption Capacity Model

In order to verify the accuracy of the SO2 absorption capacity determined by the mathematical model, Figure shows a comparison between the calculated SO2 solubility in EDA-H3PO3-H2O solution and the experimental value obtained from the study of Tang et al.[23] The absorption temperature is 298.15 K, the concentration of EDA is 0.3 mol·L–1, and there are four groups of H3PO3 with different concentrations. It can be found from Figure that the calculated values of the EDA-H3PO3-H2O ternary system absorbent are basically consistent with the experimental values, and the MRE value is 3.21%. Thus, the SO2 absorption capacity values derived from the mathematical model can meet the needs of engineering design and application.

Figure 7

Comparison between the calculated SO2 solubility in the EDA-H3PO3-H2O solution and experimental values.

Analysis of the SO2 Absorption Capacity

In this study, sulfuric acid is used to neutralize the strongly basic amine groups in the diamine, and the diamine-to-sulfuric acid concentration ratio is set to 2:1, and the decomposition constant of sulfuric acid is given by Sippola[47] In order to investigate the α of the weakly basic amine group of the diamine, the concentration of each diamine is set at 1 mol·L–1, and the partial pressure of SO2 is 200 Pa. The α value in the diamine-sulfuric acid-water ternary system absorbent is calculated at 298.15–398.15 K by the mathematical model, as shown in Figure . The concentration of each particle in the absorbent after capturing SO2 and the pH values of the absorbent solution at different temperatures are shown in the Supporting Information (Appendix 2).

Figure 8

SO2 absorption capacity in diamine-sulfuric acid-water solutions at 298.15–398.15 K.

It can be seen from Figure that the order of α is EDA > PZ > HEHPP > HEP > DIHEP. The order of the pKa2 value of each diamine is also EDA > PZ > HEHPP > HEP > DIHEP, as explained in Section . As the temperature increases, the diamine pKa2 and α values decrease simultaneously. The results show that the pKa2 value of the diamines is positively correlated with α. The greater the pKa2 value of the diamine, the more the α value.

The αc value is an important indicator to characterize the SO2 absorption effect of organic amines. In this study, αc is calculated at 298.15 K for adsorption and 398.15 K for desorption, as shown in Figure . It can be found from Figure that the αc values of the above five diamines are 0.95 mol (SO2)·mol–1 (EDA), 0.90 mol (SO2)·mol–1 (PZ), 0.69 mol (SO2)·mol–1 (HEHPP), 0.63 mol (SO2)·mol–1 (HEP), and 0.41 mol (SO2)·mol–1 (DIHEP). From the perspective of absorption capacity, EDA and PZ are the diamine absorbents with the greatest potential.

Figure 9

SO2 cyclic absorption capacity (αc) of the five diamines.

Analysis of the Diamine Deprotonation Reaction Enthalpy

The divalent diamine deprotonation enthalpy (ΔHa) determines the Qdes value in the amine-based SO2 capture process. Through the SO2 desorption reaction heat mathematical model, the ΔHa of the abovementioned divalent diamine is predicted at 298.15–398.15 K, as shown in Figure . It can be inferred from Figure that the order of ΔHa values is EDA > PZ > HEHPP > DIHEP > HEP. The ΔHa value of HEP, DIHEP, and HEHPP is much smaller than that of EDA and PZ, so EDA and PZ are not suitable as absorbents for capturing SO2 from the perspective of ΔHa. The conclusions of this section conflict with those of Section . Thus, the contradictory characteristics of αc and ΔHa of the organic diamine absorbents are demonstrated.

Figure 10

Divalent diamine proton deprotonation reaction enthalpy (ΔHa) at 298.15–398.15 K.

Multiobjective Evaluation between Capacity and Energy

In order to calculate Qdes, the functional relationship between ΔHdes and α is fitted under different desorption temperatures using a polynomial (eq ). The coefficients for the correlation of the ΔHdes – α relationship are shown in Table .

Table 3

Coefficients of ΔHdes (kJ·mol–1) – α (mol (SO2)·mol–1 (HEP)) Relation

diamine	a	b	c	d
EDA	–14.2062	21.63958	–10.8574	83.32186
PZ	–8.10857	11.87724	–6.92186	76.14744
HEP	–23.8924	25.93031	–10.7243	67.61641
DIHEP	–91.1772	66.90022	–18.0294	68.19448
HEHPP	–19.6444	24.56956	–11.1515	68.98485

The multiobjective relationship between the αc of each diamine under different desorption temperatures and the corresponding Qdes is quantified, as shown in Figure . It can be seen from Figure that Qdes increases with the increase in αc for the above five diamines. The αc of DIHEP is much smaller than those of the other diamines, so DIHEP can be excluded from the potential absorbents. For the remaining four diamines, the Qdes values of EDA, PZ, HEHPP, and HEP are 81.23, 74.39, 67.23, and 66.07 kJ·mol–1 (SO2), and αc reaches the maximal value of 0.6 mol (SO2)·mol–1 (BN2). The Qdes values of EDA and PZ are much larger than those of HEP and HEHPP. Therefore, it is concluded that HEP and HEHPP can be selected as absorbents for the amine-based SO2 capture process while meeting a high αc (0.6 mol (SO2)·mol–1 (BN2)) and lower Qdes. However, if we expect a higher αc, such as 0.9 mol (SO2)·mol–1 (BN2), HEHPP and HEP cannot meet the αc requirements. Thus, EDA and PZ can be selected as absorbents for the amine-based SO2 capture. In this situation, the Qdes values of EDA and PZ are 81.44 (SO2) and 74.71 kJ·mol–1 (SO2), respectively. The Qdes value of the EDA absorbent is 9% higher than that of PZ. Therefore, PZ is a high-quality absorbent for capturing SO2 when a higher αc of 0.9 mol (SO2)·mol–1 (BN2) is required.

Figure 11

Multiobjective relationship between capacity and energy in the diamine-sulfuric acid-water ternary absorbent.

Multiobjective Scenario Analysis

The higher the αc of the organic diamines, the smaller the corresponding absorbent dosage. Therefore, an organic diamine absorbent with high αc can reduce the operating cost of the SO2 capture process. However, a higher αc will result in a greater Qdes for the corresponding absorbent. Correspondingly, a much higher thermal utility consumption is required, and the operating cost of the capture process is increased. Therefore, when screening organic diamine absorbents, it is impossible to only pursue high αc while ignoring Qdes value changes. Absorbent screening is a multiobjective optimization problem involving both αc and Qdes in the amine-based SO2 capture process. From Section , it is concluded that the αc value of the PZ absorbent is relatively large, and the Qdes values of HEP and HEHPP absorbents are relatively small. In this study, in order to obtain an absorbent with a larger αc and a smaller Qdes, HEP and HEHPP are compounded with PZ by mole ratio to form HEP-PZ-H2SO4-H2O (HEP:PZ = 1:0, 0.8:0.2, 0.6:0.4, 0.4:0.6, 0.2:0.8, 0:1, HEP + PZ = 1 mol·L–1) and HEHPP-PZ-H2SO4-H2O (HEHPP:PZ = 1:0, 0.8:0.2, 0.6:0.4, 0.4:0.6, 0.2:0.8, 0:1, HEHPP+PZ = 1 mol·L–1) quaternary adsorbents. The multiobjective relationship of the quaternary system absorbent between αc and Qdes is calculated by the above two models, as shown in Figure . It can be found from Figure that the Qdes of the composite absorbent also increases with the increase in αc. The multiobjective absorption performance curves of the HEHPP-PZ-H2SO4-H2O and HEP-PZ-H2SO4-H2O quaternary adsorbents become infinitely closer to the absorption performance data point of PZ-H2SO4-H2O as αc increases; particularly, the HEHPP-PZ-H2SO4-H2O and HEP-PZ-H2SO4-H2O compound absorbents broaden the αc range compared to the HEHPP-H2SO4-H2O and HEP-H2SO4-H2O single absorbents. The Qdes of the HEHPP-PZ-H2SO4-H2O composite absorbent is less than that of the HEP-PZ-H2SO4-H2O composite absorbent under the same αc. For example, the Qdes values of HEP-PZ-H2SO4-H2O and HEP-PZ-H2SO4-H2O are roughly 71.78 and 72.15 kJ·mol–1 (SO2) when αc is 0.8 mol (SO2)·mol–1 (BN2), respectively. Therefore, considering Qdes, the HEHPP-PZ-H2SO4-H2O compound absorbent is better than the HEP-PZ-H2SO4-H2O compound absorbent. The above analysis concludes that the compound quaternary absorbent has a wider range of αc than the single ternary absorbent, which is the direction of absorbent development.

Figure 12

Multiobjective relationship between capacity and energy in the quaternary system absorbent.

Conclusions

The pKa values of the five organic diamines are predicted using DFT and an implicit SMD at the M05-2X/6-31G* base set level at 298.15–398.15 K, which included EDA, PZ, HEP, DIHEP, and HEHPP. Then, a mathematical model of αc during the amine-based SO2 capture process is built based on the electroneutrality of the solution. Correspondingly, another mathematical model of Qdes is also built based on the van’t Hoff equation. Finally, the multiobjective relationship between αc and Qdes is evaluated to guide the screening of potential solvents that can be used in the amine-based SO2 capture process from flue gas. The main research conclusions are as follows:

The mathematical models can quantitatively predict the αc and Qdes values of the diamine-sulfuric acid-water ternary system absorbent during the amine-based capture SO2 process.

The αc value of the organic diamines changes with the increase in the pKa value, and the increase in pKa directly leads to changes in ΔHa. However, αc and ΔHa have a contradiction in their multiobjective characteristics. It is impossible to only pursue high αc while ignoring the change in the enthalpy of the deprotonation reaction in the process of screening organic amine adsorbents.

The multiobjective relationship between αc and Qdes of each diamine is quantified. The order of αc is EDA > PZ > HEHPP > HEP > DIHEP, and the order of Qdes is EDA > PZ > HEHPP > DIHEP > HEP. According to αc, the organic diamine absorbent with the smallest Qdes value can be screened out. The composite quaternary system absorbent has better absorption performance than the single ternary system absorbent. The HEHPP-PZ-H2SO4-H2O composite system absorbent has a lower Qdes value than the HEP-PZ-H2SO4-H2O absorbent under the same αc.