Prediction of H2S and CO2 Solubilities in Aqueous Triethanolamine

Apr 17, 2012 - Department of Chemical Engineering, Petroleum Institute 2533, Abu Dhabi, UAE ... The model can be used to correlate mixed acid gases so...
16 downloads 11 Views 1014KB Size
Download PDF
Correlation pubs.acs.org/IECR

Prediction of H2S and CO2 Solubilities in Aqueous Triethanolamine Solutions Using a Simple Model of Kent−Eisenberg Type Wael A. Fouad*,†,‡ and Abdallah S. Berrouk† †

Department of Chemical Engineering, Petroleum Institute 2533, Abu Dhabi, UAE Department of Chemical and Biomolecular Engineering, Rice University, 6100 S. Main, Houston, Texas 77005, United States

‡

ABSTRACT: Absorption of acid gases (H2S and CO2) by aqueous solutions of alkanolamines is the most commonly used process in the gas treatment industry. Recent process investigations on the use of triethanolamine (TEA) show its potential to render the gas sweetening operation more energy efficient in particular when mixed to methyldiethanolamine (MDEA). This paper presents a simple model of Kent−Eisenberg type that computes the dissociation of the protonated triethanolamine (TEA) equilibrium constant. The model can be used to correlate mixed acid gases solubility data over 2, 3.5, and 5 M of aqueous TEA solutions at 50, 75, and 100 °C. Results for the new model shows high fitting percentage errors for both acid gases; however, the model was able to predict H2S and CO2 partial pressures accurately for another set of unfitted data. Despite the highly fitted percentage errors, the model was used as an initial guess for a different Kent−Eisenberg model which resulted into a significantly lower percentage error at 50 °C.

1. INTRODUCTION Amine gas sweetening is a widely used technology to remove H2S and CO2 from natural gas and liquid hydrocarbon streams through absorption and chemical reaction. Amines have a natural affinity for both H2S and CO2 rendering the aminesweetening process efficient in producing transportable and marketable natural gas and hydrocarbons liquids. Different types of amines have been developed over the years to respond to different specific hydrocarbon treating problems. Methyldiethanolamine (MDEA) has been the widely used solvent for full absorption of H2S and partial absorption of CO2 through chemical reactions. It has the ability to remove H2S and CO2 down to the 4 ppmv and 3 mol % levels respectively. However, it is well-known that its regeneration counts for approximately 70% of the unit’s energy requirement. Recently, Fouad et al. (2011)1 tested the effect of replacing part of the MDEA solvent by triethanolamine (TEA) solvent for the energy requirement of an industrial absorption unit. Through optimization of certain process parameters, it was found that the (40 wt % MDEA + 5 wt % TEA) mixture decreased the regeneration energy requirement of the unit by 5% (equivalent to 3% annual reduction in the operating cost of the unit) while still meeting the same sweet gas specifications. To capitalize on this interesting finding for further optimization of the amine sweetening process, it is therefore crucial to study the thermodynamic behavior of such nonideal MDEA−TEA−H2O−H2S−CO2 system for better understanding of its vapor−liquid equilibrium (VLE) over wide ranges of operating conditions and thus better process design and simulation. Currently used experimental techniques have failed to measure accurately VLE data for low acid gas partial pressures and loadings. This has triggered a substantial research activity on VLE modeling that can accurately predict H2S and CO2 solubilities in various amine solutions for different operating conditions. © 2012 American Chemical Society

These thermodynamic models are of two classes: those derived from the original Kent and Eisenberg model2 and those based on the activity coefficients model. The latter are relatively rigorous since they take into account the mixture nonidealities but they require the solution of a large number of nonlinear equations and are hard to converge. Their superiority over Kent and Eisenberg type of models has not been demonstrated at low loadings and still they have not been successfully applied to model commercial absorption units.3 Although they assume mixture ideality through neglecting activity coefficients, models based on Kent and Eisenberg equations have been widely used for their simplicity and reasonable prediction power beyond the range of experimental data for which they were fitted. Extensive research work has been generated using various versions of Kent and Eisenberg model and activity coefficients model to predict the thermodynamic behavior of MEA−, DEA−, and MDEA−H2O−H2S−CO2 systems whereas very few investigations have been dedicated to the TEA−H2O− H2S−CO2 system. The original Kent and Eisenberg model was validated for mixed acid gas systems in aqueous solutions of monoethanolamine (MEA) and diethanolamine (DEA).2 The model was subsequently developed and tested for MDEA solution by Patil et al.3 based on the equilibrium constants of the six reactions taking place in the system as well as Henry’s law. Through a series of experiments, Jou et al.4 have demonstrated that equilibrium constants do not depend only on temperature but also on amine concentration and amine loading. This finding was accounted for by Chakma and Meisen5 who developed an extended variant of Kent and Eisenberg model to predict phase equilibria behavior of DEA− H2O−CO2 systems. Posey et al.6 developed later a simple Received: Revised: Accepted: Published: 6591

November 13, 2011 April 4, 2012 April 17, 2012 April 17, 2012 dx.doi.org/10.1021/ie202612k | Ind. Eng. Chem. Res. 2012, 51, 6591−6597

Industrial & Engineering Chemistry Research

Correlation

variant of Kent and Eisenberg model by combining reactions taking place in the absorption process into two chemical formulas while neglecting species with low concentration in the mixture such as CO32−, S2−, and OH−. Consequently, the number of needed parameters in the original Kent and Eisenberg model was reduced from 22 to 4. The model was successfully validated against experimental data on H2S and CO2 solubilities in aqueous solutions of both MDEA and DEA systems. Patil et al.3 also succeeded in predicting H2S and CO2 partial pressures in aqueous MDEA solutions through deriving an equation of Kent and Eisenberg type for the dissociation of protonated alkanolamine equilibrium constant. Models of Kent and Eisenberg class has been also designed to predict acid gas solubilities in aqueous solutions of mixed amines. Li et al.7 and Haji−Sulman et al.8 designed a thermodynamic model that predicted CO2 solubility in an aqueous solution of MDEA/MEA and MDEA/DEA mixtures respectively using an extended version of the Kent and Eisenberg model. Later, Li et al.9 applied the developed model to predict the solubility of H2S and CO2 in aqueous MEA/AMP solution. The model was also used by Park et al.10 to compute CO2 partial pressures in aqueous MEA/AMP and DEA/AMP solutions and provide analytical approximate expressions for the concentration of the neutral and ionic species. Recently, Yang et al.11 and Chung et al.12 used the modified model to predict the equilibrium solubility of CO2 in aqueous AMP/PZ and TEA/PZ solutions. As far as the knowledge of the authors is concerned, very few thermodynamic models have been developed to predict acid gases solubility in aqueous TEA solutions. Indeed, Jou et al.13 is the only work found in literature that used Kent−Eisenberg model type of model to predict solubility of both H2S and CO2 in aqueous TEA solutions. For the same purpose, a VLE model was developed by Li and Mather14 based on the activity coefficients class of models. The model was derived from the Clegg−Pitzer equation,15 and it is the only one in its kind that was validated for TEA systems. The present work aims to develop a simple model of Kent and Eisenberg class of models to use to predict H2S and CO2 solubilities in aqueous TEA solution. The model elaborates on Posey et al.6 and Patil et al.3 VLE models to allow an accurate estimate of H2S and CO2 partial pressures in aqueous TEA solutions over a wide range of operating conditions. The model should estimate accurately the enthalpy of TEA solutions and serve as a good initial guess for more complex models.

Dissociation of bicarbonate H 2O + HCO3− ↔ H3O+ + CO32 −

Dissociation of protonated alkanolamine H 2O + RNR′R″H+ ↔ H3O+ + RNR′R″

amineH+ + HS− ↔ amine + H 2S

(8)

B + C[CO2 ] + D ln Camine + E ln αCO2 T

+ F ln[CO2 ] + G(αCO2 + αH2S) + H ln([CO2 ] + [H 2S])

(9)

This model is an improved form of the original Kent and Eisenberg model2 since it depends on temperature, amine concentration, and amine loading. A simplified thermodynamic model can also be derived using eq 7 or 8 to approximate H2S and CO2 partial pressures in aqueous amine solutions. It reads6 ″ =A+ ln K acidgas

B ° + D(L TXamine ° )0.5 + CL TXamine T

(10)

6

This model was used by Posey et al. to predict acid gas partial pressures in aqueous solutions of DEA and MDEA. Parameters for both models can be regressed using equilibrium VLE data for both single and mixed acid gas systems. However, the equilibrium constant of the dissociation of protonated alkanolamine shown in eq 9 should be obtained through solving simultaneously a system of 12 nonlinear equations with 22 parameters. Patil et al.3 used eq 9 to model acid gases solubility in aqueous MDEA solution. The model compared reasonably well with the measured partial pressures reported by Jou et al.17,18 for 35% wt and 48.9% wt aqueous MDEA solutions. Posey et al.6 used eq 10 to predict CO2 and H2S partial pressures in DEA and MDEA systems. Compared to the experimental data provided by Ho and Eguren19 and Jou et al.,4,17,20,21 the model was accurate within an error margin of 205 and 22% for CO2 and H2S, respectively. On the basis of the above two models herein, a new empirical correlation be derived and used to approximate the equilibrium constant of the dissociation of protonated alkanolamine (K1). This can be done by combining both models through the acid gas dissociation equilibrium constant and Henry’s Law constant. The model chemistry is mainly based on eqs 2, 4, 7, and 8. Chemical equilibria of the developed model are described below. Posey et al.6 defined an equilibrium constant, K′, based on eq 7 that combines all intermediate chemical reactions for CO2 into a single step:

(1)

(2)

(3)

Dissociation of carbon dioxide 2H 2O + CO2 ↔ H3O+ + HCO3−

(7)

ln K1 = A +

Hydroxylation of bisulphide H 2O + HS− ↔ H3O+ + S2 −

amineH+ + HCO3− ↔ amine + CO2 + H 2O

2.2. Thermodynamic Expressions. On the basis of the equation network (eqs 1−6), a thermodynamic model can be developed to predict H2S and CO2 partial pressures in aqueous TEA solutions through the dissociation of protonated alkanolamine equilibrium constant.3 It reads

Dissociation of water H 2O + H 2S ↔ H3O+ + HS−

(6)

This network can be generalized to all similar tertiary amine reactions including MDEA. It can also be approximated by a single equilibrium (eq 7 or 8) neglecting species produced with small concentrations such as CO32−, S2−, and OH−:6

2. THERMDODYNAMIC FRAMEWORK 2.1. Chemical Equilibria. The following reaction network represents the equilibrium reactions taking place in a system of TEA−H2O−H2S−CO2:16 Ionization of water 2H 2O ↔ H3O+ + OH−

(5)

(4) 6592

dx.doi.org/10.1021/ie202612k | Ind. Eng. Chem. Res. 2012, 51, 6591−6597

Industrial & Engineering Chemistry Research

Correlation

Table 1. Regressed Parameters for TEA Equilibrium Constant present model (eq 19, mixed acid gas)

present model (eq 19, CO2 only)

Patil model (eq 9, mixed acid gas)

parameter

H2S

CO2

CO2

H2S

CO2

A B C D E F G H

−107.72 −4407.94 5.11 −10.02 21.51 0.0060

102.13 −9719.89 17.89 −14.92 −14.82 0.0058

97.51 −9148.22 −173.54 31.28 −14.82 0.0058

−5.7449 −3083.4 1.0015 −0.47914 −0.21844 0.090151 −4.0476 0.15602

−12.040 −741.43 0.71660 −0.72789 −0.80491 0.74484 −3.1524 −0.27615

′ 2= K CO

[CO2 ][amine] [HCO3−][amineH+]

The negative sign of the last term in eq 19 resulted from the model derivation. Table 1 shows the values of the regressed parameters for TEA equilibrium constants in eqs 9 and 19. The [amine] and [amineH+] terms can be approximated on a basis of total loading, LT, as follows:

(11)

The dissociation of protonated alkanolamine can be expressed as: K1 =

[H+][amine] [amineH+]

(12)

By combining eqs 11 and 12, we obtain: ′ 2= K CO

[CO2 ]K1 [HCO3−][H+]

(13)

PCO2 =

(14)

PCO2 =

[HCO3−][H+] [CO2 ]

PCO2 =

(15)

(16)

ln K1 = A +

(23)

″ 2)2 K CO2XCO2 (K CO K1HCO2

LT 1 − LT

(24)

dln PCO2 d(1/T )

(26)

3. RESULTS AND DISCUSSION 3.1. Prediction of Acid Gases Partial Pressures in Aqueous TEA Solutions. To define the present model parameters (A, B, C, D, E, and F in eq 19) designed to predict acid gas vapor−liquid equilibrium in aqueous TEA solution, regression was performed based on 105 mixed acid gas equilibrium data points provided by Jou et al.22 These data points pertain to three TEA solutions of 2, 3.5, and 5 M at temperatures of 50, 75, and 100 °C. Data points with amine loading greater than one were discarded. The reason is that models of Kent and Eisenberg type such as the Posey et al.6

(18)

B ° + D(L TXamine ° )0.5 + E ln T + CL TXamine T

− FT

K1

LT 1 − LT

Derivation of the H2S system is identical and H2S predictions are made by replacing the CO2 subscripts in eqs 19 and 25 with H2S subscripts.

On the basis of eqs 9 and 10, the defined Kent and Eisenberg temperature dependent model for CO2 dissociation equilibrium constant, and Henry’s Law, eq 17 can be expanded to be a function of temperature, total amine loading, and gas free amine mole fraction: B + C ln T + DT T

″ 2K CO ′ 2K CO2XCO2 K CO

ΔHabs = − R

(17)

ln K CO2 /HCO2 = A +

(22)

The heat of absorption of CO2 in aqueous TEA solution can be obtained using eq 25 and the Clausius−Clapeyron equation:

″ 2K CO2 K CO HCO2

K1

LT 1 − LT

Combining eq 24 with eq 17 will yield the final pressure equation form: K1XCO2HCO2 L T PCO2 = K CO2 1 − LT (25)

Henry’s Law can be used to express the free aqueous CO2 concentration in terms of partial pressure and Henry’s Law constant to get the final Equilibrium Equation form: K1 =

″ 2K CO2K CO ′ 2[HCO32 −] K CO

Substituting K′CO2 by K″CO2/HCO2, we obtain:

″ 2K CO2[CO2 ] K CO K1

(21)

XCO2 can be used to approximate [HCO32−]

If we combine K′CO2 and H′CO2 terms into a single constant, K″CO2 and eliminate the [H+] term through defining the equilibrium constant of the dissociation of CO2 expressed by eq 4, we obtain the following: K CO2 =

° [amineH+] = (L T)Xamine

PCO2 =

K ′CO2 HCO2[HCO3−][H+] K1

(20)

An equation of the CO2 partial pressure can be obtained by combining eqs 11 and 16 and using eqs 20 and 21:

Rearranging eq 13 and using Henry’s Law, the CO2 partial pressure can be derived: PCO2 =

° [amine] = (1 − L T)Xamine

(19) 6593

dx.doi.org/10.1021/ie202612k | Ind. Eng. Chem. Res. 2012, 51, 6591−6597

Industrial & Engineering Chemistry Research

Correlation

Results of Table 2 show also the ability of Patil’s model to predict both acid gases partial pressures with nearly a zero percentage error for the low absorption temperature of 50 °C and this using the present model equilibrium constants. At this temperature, a wide range of partial pressures (0.40−465 kPa for H2S and 0.38−2520 kPa for CO2) were covered. Such accuracy was not achieved by the more complex activity coefficient model used by Li and Mather14 though it embeds all the nonidealities into its interaction parameters. It is important to mention that in Patil et al.,3 the dissociation constant for the protonated alkanolamine was calculated by solving numerically 12 nonlinear equations containing 22 parameters while only one equation involving 6 fitted parameters was solved in the present model which reduces the computational cost significantly while maintaining the model good performance in particular at low temperatures. Figures 1 and 2 compare the predictions of the present model to the measured H2S and CO2 partial pressures as

model tend to diverge at total loading close to unity as demonstrated by Dicko et al.23 Also, VLE data available for TEA−H2O−H2S and TEA−H2O−CO2 systems were excluded for better accuracy. Indeed, systems containing a single acid gas have a different VLE behavior from the one of mixed acid gas systems. Adding or removing an acid gas from the system will generally affect the reaction kinetics and mass transfer. The reason is that, in mixed acid gas systems, H2S and CO2 compete for the available base in the solution as demonstrated by Jou et al.22 Consequently, single acid gas systems’ VLE data were not included in the regression work to reduce fitting errors while fitting the model parameters for the mixed acid gas system. In this section, we compare the predictions of the present model against the experimental findings of Jou et al.22 using 14 unfitted VLE data points. The model will be also used to calculate equilibrium constants and plug them into the Patil et al.3 model as an initial guess to regress Patil model parameters using the multivariable Newton−Raphson method. The performance of the Patil model is measured based on its average percentage error in predicting fitted and unfitted VLE data. Table 2 shows the absolute fitting percentage error calculated for TEA system using the present model, Patil et al.3 model, Table 2. Comparison of the Present, Clegg−Pitzer, and Patil Models’ Predictions in Terms of Absolute Percentage Errors TEA−H2O−H2S−CO2 (2, 3.5, 5 M) source Li and Mather model11 (116 data points) present model (105 data points) Patil model3 (105 data points) Li and Mather11

50 °C 20.7% (CO2) 22.5% (H2S) 45.7% (CO2) 32.0% (H2S) 0.205% (CO2) 0.554% (H2S) total average error

present model total average error Patil model total average error

75 °C

100 °C

15.6% (CO2) 23.7% (H2S)

17.8% (CO2) 16.1% (H2S)

Figure 1. Comparison of predicted H2S partial pressures using the present model to experimental data of Jou et al.22

46.1% (CO2) 46.1%(CO2) 66.7% (H2S) 37.6% (H2S) 32.6% (CO2) 41.9% (CO2) 29.9% (H2S) 47.0% (H2S) 18.03% (CO2) 20.8% (H2S) 46.1% (CO2) 47.8% (H2S) 31.7% (CO2) 28.4% (H2S)

and the Li and Mather14 model based on Clegg−Pitzer15 activity coefficient model. Posey et al.6 results are not shown in Table 2 since it records the same percentage error as the present model. Referring to Table 2, the significant errors recorded by both the present and Patil et al.3 models were also observed in Posey et al.6 predictions of H2S solubility in DEA systems (absolute error up to 60%) and in Dicko et al.23 in predictions of H2S solubility in 50% wt MDEA (absolute error of 44%). The superiority shown by the Clegg−Pitzer activity coefficient model used by Li and Mather14 over both the present and Patil et al.3 models can be attributed on one hand to the fact that Kent and Eisenberg type of models do not take into account mixtures nonidealities that are well embedded in activity coefficients type of models. In the other hand, Li and Mather14 used only single acid gas VLE data to regress the interaction parameters of the model used to model an aqueous mixed acid gas quaternary system. This provided them with a larger set of data points which might have played a role in decreasing the average absolute error.

Figure 2. Comparison of predicted CO2 partial pressures using the present model to experimental data of Jou et al.22

function of the total TEA loading. Most of the data points were fit within a factor of 2 over several orders of magnitude of pressure and amine loading. Figures 3 and 4 compare the predicted acid gases partial pressures based on the present model to the measured data for TEA concentrations of 2, 3.5, and 5 M at temperatures of 50− 100 °C and H2S and CO2 partial pressures ranging from 0.09255 to 2878.3 kPa (neglecting the single data point measured at approximately 5000 kPa) and 0.134−5490 kPa, respectively. Figures 5 and 6 illustrate the ability of the present model to predict the experimental results of Jou et al.22 using a set of 14 unfitted data points at acid gas partial pressures of 10 and 100 kPa in a solution of 3.5 M TEA at 100 °C. Figure 5 depicts the good agreement the present model has with Jou et al.22 6594

dx.doi.org/10.1021/ie202612k | Ind. Eng. Chem. Res. 2012, 51, 6591−6597

Industrial & Engineering Chemistry Research

Correlation

experimental results compared to Patil et al.3 model performance. The present model scores an average absolute error of 11.7% in predicting H2S partial pressures. As far as CO2 partial pressure predictions are concerned, an absolute error of 12.1% and 14.0% are recorded for the present model and Patil’s model, respectively. 3.2. Prediction for the Heats of Absorption in Aqueous TEA Systems. Posey et al.6 demonstrated that their model’s second coefficient (B) (see eq 10) is directly related to the heat of absorption of H2S and CO2. This fact can be used to further examine the accuracy of the regressed parameters for the TEA system. Table 3 compares the

Figure 3. Comparison of predicted H2S partial pressures using the present model (solid line) with experimental data: (○) Jou et al.22

Table 3. Average Heat of Absorption of H2S and CO2 in a TEA solution heat of absorption (kJ/gmol gas) source

TEA−H2S

TEA−CO2

Kohl et al.24 Jou et al.13 present model (H2S + CO2) Posey model (H2S + CO2) present model (CO2) Posey model (CO2)

−38.7 −34.9 −38.6 −37.7

−47.6 −48.5 −50.8 −50.9 −46.0 −46.0

predicted average heat of absorption for H2S and CO2 in TEA solution to the average values provided by literature for an amine loading of 0−0.4 at 100 °F. The results show that the present model predictions reasonably match the experimental data and other model predictions given the accuracy of the data and the error introduced by the use of average experimental conditions. 3.3. Prediction of the Equilibrium Constant in TEA Single Acid Gas Systems. The predictive power of the present model was also examined for single acid gas solubility in aqueous TEA solutions. Experimental data of Jou et al.13 on TEA−H2O−CO2 system are unavailable because they are copyrighted by the Depository for Unpublished Data, CISTI, National Research Council of Canada. Therefore, we rely only on published data provided by Cheng et al.25 for 2 M TEA solutions at temperatures of 40, 60, 80, and 100 °C and CO2 partial pressures ranging from 1.7−109 kPa to fit the model parameters. Equilibrium constants calculated using the present model for data by Chung et al.12 dealing with 2 M TEA solutions at 40, 60, and 80 °C were compared to calculation performed using Jou et al.13 model for single acid gas systems. Figure 7 shows an increasing discrepancy between the predictions as the temperature increases and this for the three different CO2 loadings tested. 3.4. Evaluation of the Present Model Errors and Assumptions. It is deemed that the new model can help in better process design and optimization of industrial absorbers which mainly operate within conditions covered by the model (50−75 °C). It is worth noting that the average absolute percentage error of the model increases with temperature. This can be attributed to the assumption made that the equilibrium constants, KH2S and KCO2, are temperature dependent. However, this assumption gets weaker at higher absorption temperatures. Also, an increase in the concentrations of the neglected CO32−, S2−, and OH− ions with temperature increase could have played a role in deviating the model predictions from the experimental data. Finally, the assumption made of having a single combined

Figure 4. Comparison of predicted CO2 partial pressures using the present model (solid line) with experimental data: (◊) Jou et al.22

Figure 5. Comparison of predicted H2S partial pressures using the present model and Patil model with experimental data in a 3.5 M TEA solution at 100 °C: (○) Jou et al.;22 (⧫) Patil’s model; (△) present model.

Figure 6. Comparison of predicted CO2 partial pressures using the present model and Patil model with experimental data in a 3.5 M TEA solution at 100 °C: (○) Jou et al.;22 present model (solid curve); Patil model (dashed curve).

6595

dx.doi.org/10.1021/ie202612k | Ind. Eng. Chem. Res. 2012, 51, 6591−6597

Industrial & Engineering Chemistry Research

Correlation

HCO2 = Henry’s constant for CO2, Pa P = partial pressure, kPa T = absolute temperature, °C or K as noted LT = total acid gas loading, gmol of acid gas/gmole of amine KCO2 = dissociation of CO2 temperature dependent equilibrium constant, gmol/L Xamine ° = gas free amine mole fraction, gmol of amine/(gmol of amine + gmol of water) K′CO2 = acid gas equilibrium constant for the single combined reaction Camine = alkanolamine concentration, gmol/L [CO2] = CO2 concentration in liquid phase, gmol/L [H2S] = H2S concentration in liquid phase, gmol/L A−H = parameters in Table 1

Figure 7. Comparison of equilibrium constants predicted by the present model (solid line) and Jou et al.13 model (dashed line) for a range of conditions: (black) αCO2 = 0.1, (red) αCO2 = 0.2, (blue) αCO2 = 0.3.

Amine Abbreviations

MDEA = methyldiethanolamine TEA = triethanolamine DEA = diethanolamine MEA = monoethanolamine PZ = piperazine AMP = 2-amino-2-methyl-1-propanol

reaction for each of the acid gases might not be adequate at high temperature conditions.

4. CONCLUSIONS A new model is derived to approximate the dissociation of protonated TEA equilibrium constant with only 6 regressed parameters. Parameters are fitted initially using only mixed acid gas data. Results show an average absolute fitting error of 46.1% and 47.8% for H2S and CO2 predicted partial pressures respectively. The model is integrated into Patil model to be used as a good initial guess to estimate protonated alkanolamine dissociation equilibrium constants. These values were used to regress Patil model’s parameters for a wide range of operating temperatures, concentrations and amine loadings. As a result, Patil model succeeds in predicting H2S and CO2 partial pressures at low temperatures with nearly zero percentage error. This reduces the computational time needed to solve Kent and Eisenberg set of nonlinear equations. The present model capabilities in predicting acid gas partial pressures was further tested for another set of unfitted data. Results were in good agreement with experimental values and better than Patil model predictions. In addition, a new set of parameters were regressed for the usage of the present model in predicting single acid gas systems. Equilibrium constants and heat of reaction predicted for the TEA−H2O−CO2 system were compared to that calculated using Jou et al.13 model. We expect that the present model performance in prediction acid gas solubility in TEA systems can be further improved if more experimental data will be provided for similar VLE systems.

■

Greek Symbols

αCO2 = CO2 loading in the liquid phase, gmol of CO2/ gmol of TEA αH2S = H2S loading in the liquid phase, gmol of H2S/gmol of TEA Subscripts

■

exp = experimental pred = predicted abs = absorption

REFERENCES

(1) Fouad, W. A.; Berrouk, A. S.; Peters, C. J. Mixing MDEA, TEA shows benefit for gas-sweetening operations. Oil Gas J. 2011, 109 (45), 112−118. (2) Kent, R. L.; Eisenberg, B. Better Data for Amine Treating. Hydrocarbon Process. 1976, 55, 87. (3) Patil, P.; Malik, Z.; Jobson, M. Prediction of CO2 and H2S Solubility in Aqueous MDEA Solutions Using an Extended Kent and Eisenberg Model; Distillation and Absorption: London, 2006. (4) Jou, F. Y.; Mather, A. E.; Otto, F. D. Solubility of H2S and CO2 in aqueous methyldiethanolamine solutions. Ind. Eng. Chem Process. Des. Dev. 1982, 21, 539−544. (5) Chakma, A.; Meisen, A. Improved Kent-Eisenberg Model for predicting CO2 solubilities in aqueous diethanolamine (DEA) solutions. Gas. Sep. Purif. 1990, 4, 37−40. (6) Posey, M. L.; Tapperson, K. G.; Rochelle, G. T. A Simple Model for Prediction of Acid Gas Solubilities in Alkanolamines. Gas. Sep. Purif. 1996, 10 (3), 181−186. (7) Li, M.-H.; Shen, K.-P. Calculation of equilibrium solubility of carbon dioxide on aqueous mixtures of monoethanolamine with methyldiethanolamine. Fluid Phase Equilib. 1993, 85, 129−140. (8) Haji−Sulman, M. Z.; Aroua, M. K.; Pervez, M. I. Equilibrium concentration profiles of species in CO2 − alkanolamine − water system. Gas. Sep. Purif. 1996, 10 (1), 13−18. (9) Li, M.-H.; Chang, B.-C. Solubility of Mixtures of Carbon Dioxide and Hydrogen Sulfide in Water + Monoethanolamine + 2-Amino-2methyl-1-propanol. J. Chem. Eng. Data 1995, 40, 328−331. (10) Park, S. H.; Lee, K. B.; Hyun, J. C.; Kim, S. H. Correlation and Prediction of the Solubility of Carbon Dioxide in Aqueous Alkanolamine and Mixed Alkanolamine Solutions. Ind. Eng. Chem. Res. 2002, 41, 1658−1665.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +1-832-660-8660. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We express our appreciation to Mohammed Adnan, PhD student at Rice University, for providing technical support needed for this research.

■

NOMENCLATURE AND SYMBOLS K1 = dissociation of protonated alkanolamine equilibrium constant, gmol/L Kacidgas ″ = acid gas equilibrium constant 6596

dx.doi.org/10.1021/ie202612k | Ind. Eng. Chem. Res. 2012, 51, 6591−6597

Industrial & Engineering Chemistry Research

Correlation

(11) Yang, Z.-Y.; Soriano, A. N.; Caparanga, A. R.; Li, M.-H. Equilibrium solubility of carbon dioxide in (2-amino-2-methyl-1propanol + piperazine + water). J. Chem. Thermodynamics 2010, 42, 659−665. (12) Chung, P. Y.; Soriano, A. N.; Leron, R. B.; Li, M. H. Equilibrium solubility of carbon dioxide in the amine solvent system of (triethanolamine + piperazine + water). J. Chem. Thermodynamics 2010, 42, 802−807. (13) Jou, F.-Y.; Otto, F. D.; Mather, A. E. Equilibria of H2S and CO2 in triethanolamine solutions. Can. J. Chem. Eng. 1985, 63, 122−125. (14) Li, Y.-G.; Mather, A. E. Correlation and Prediction of the Solubility of CO2 and H2S in Aqueous Solutions of Triethanolamine. Ind. Eng. Chem. Res. 1996, 35, 4804−4809. (15) Clegg, S. L.; Pitzer, K. S. Thermodynamics of Multicomponent, Miscible, Ionic Solutions: Generalized Equations for Symmetrical Electrolytes. J. Phys. Chem. 1992, 96, 3513. (16) Austegen, D. M.; Rochelle, G. T.; Chen, C. C. Model of vaporliquid equilibria for aqueous acid gas − alkanolamine systems. 2. Representation of H2S and CO2 solubility in aqueous MDEA and CO2 solubility in mixtures of MDEA with MEA or DEA. Ind. Eng. Chem. Res. 1991, 30, 543−555. (17) Jou, F.-Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D. Solubility of carbon dioxide and hydrogen sulfide in a 35 wt% aqueous solution of methyldiethanolamine. Can. J. Chem. Eng. 1993, 71, 264−268. (18) Jou, F.-Y.; Otto, F. D.; Mather, A. E. The Solubility of Mixtures of H2S and CO2 in an MDEA Solution. Can. J. Chem. Eng. 1997, 75, 1138−1141. (19) Ho, B. S.; Eguren, R. R. Solubility of acidic gases in aqueous DEA and MDEA solutions. Amoco Production Company. Presented at the 1988 Spring National Meeting of the American Institute of Chemical Engineers, New Orleans, LA, Mar 6−10, 1988; paper no. 69-a. (20) Jou, F.-Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D. Solubility of mixtures of hydrogen sulfide and carbon dioxide in aqueous Nmethyldiethanolamine solutions. J. Chem. Eng. Data 1993, 38, 75−77. (21) Jou, F.-Y.; Otto, F. D.; Mather, A. E. Vapor-liquid equilibrium of carbon dioxide in aqueous mixtures of monoethanolamine and methyldiethanolamine. Ind. Eng. Chem. Res. 1994, 33, 2002−2005. (22) Jou, F.-Y.; Otto, F. D.; Mather, A. E. Solubility of Mixtures of Hydrogen Sulfide and Carbon Dioxide in Aqueous Solutions of Triethanolamine. J. Chem. Eng. Data 1996, 41, 1181−1183. (23) Dicko, M.; Coquelet, C.; Jarne, C.; Northrop, S.; Richon, D. Acid gases partial pressure above a 50wt% aqueous methyldiethanolamine solution: Experimental work and modelling. Fluid Phase Equilib. 2010, 289, 99−109. (24) Kohl, A. L.; Nielsen, R. B. Alkanolamines for Hydrogen Sulfide and Carbon Dioxide Removal; Gas Purification: Houston, 1997. (25) Cheng, M. D.; Caparanga, A. R.; Soriano, A. N.; Li, M. H. Solubility of CO2 in the solvent system (water + monoethanolamine + triethanolamine). J. Chem. Thermodynamics 2010, 42, 342−347.

6597

dx.doi.org/10.1021/ie202612k | Ind. Eng. Chem. Res. 2012, 51, 6591−6597