Absorption of CO2 in Aqueous Diglycolamine - Industrial

Michael J. O'Brien , Rachel L. Farnum , and Robert J. Perry. Energy & Fuels ... Burcu E. Gurkan , Thomas R. Gohndrone , Mark J. McCready , Joan F. Bre...
0 downloads 0 Views 249KB Size
Download PDF
Ind. Eng. Chem. Res. 2006, 45, 2473-2482

2473

Absorption of CO2 in Aqueous Diglycolamine Mohammed Al-Juaied and Gary T. Rochelle* Department of Chemical Engineering, The UniVersity of Texas, Austin, Texas 78712

Absorption of CO2 into aqueous DGA (Diglycolamine) was performed at 25-60 °C in a wetted-wall column. The absorption data were analyzed using a rigorous model based on eddy diffusivity theory and approximations assuming pseudo-first-order (PFO) and interface pseudo-first-order (IPFO) reactions. The PFO is a good approximation for CO2 absorption into DGA at a CO2 loading of less than 0.2 mol/mol DGA. At CO2 loadings greater than 0.4, instantaneous reactions are approached. The IPFO model matches the rigorous model very well. The second-order rate constant in 65 wt % DGA at 25 °C for the reaction with CO2 is four times larger than previously published values, but 25 wt % DGA yields a rate constant which is in good agreement with literature values. This finding suggests that the second-order rate constant is probably a function of DGA concentration. The second-order rate constant in 65 wt % DGA increases by a factor of 5 from 0 to 0.4 mol CO2/mol DGA. Experiments with 65 wt % DGA + glycolic acid and 65 wt % DGA + potassium formate at 25 °C and 40 °C showed similar trends. The rate constant increases a factor of 2 to three in these solutions, suggesting that the rate constant is a function of ionic strength. 1. Introduction

RCO2 ) -

The most widely employed gas-treating process for removing acidic gas in the natural gas and petroleum processing industries is the chemical solvent process using the various alkanolamines. These processes use a solvent, either an alkanolamine or an alkali-salt (hot carbonate processes) in an aqueous solution, which reacts with the acid gas (H2S and CO2) to form a complex or bond. This complex is subsequently reversed in the regenerator at elevated temperatures, and the reduced acid gas partial pressures release the acid gas and allow the solvent to regenerate for reuse. The alkanolamines most commonly used in industrial applications are monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), and Diglycolamine (DGA, both registered trademarks of Huntsman Corporation). The use of DGA for the purpose of acid gas removal was patented by Blohm and Riesenfeld1 and commercialized in the late sixties by Fluor and Jefferson Chemical Company. DGA is a primary amine that can be used at 50-60 wt % amine, resulting in significantly lower circulation rates and energy requirements. For the reaction of CO2 with primary and secondary amines, the zwitterion reaction mechanism, originally proposed by Caplow2 and reintroduced by Danckwerts3, is generally accepted as the reaction mechanism k-1

8 R2NH+ COOCO2 + R2NH 9 k

(1)

1

k-b

R2NH+ COO- + B 9 8 R2NCOO- + BH+ k

(2)

b

This mechanism has two steps: formation of the CO2-amine zwitterion (reaction 1), followed by base-catalyzed deprotonation of this zwitterion (reaction 2). This mechanism leads to the following expression for CO2 * To whom correspondence should be addressed. Tel.: (512) 4717230. Fax: (512) 475-7824. E-mail: [email protected].

k2[R2NH][CO2] k-1 1+ kb[B]

(3)

∑

where ∑ kb[B] is the contribution to the removal of the proton by all bases present in the solution. For two asymptotic cases, eq 3 can be simplified if the second term in the denominator is much less than one. This results in the simple second-order kinetic expression

RCO2 ) -k2[R2NH][CO2]

(4)

If the second term in the denominator is much greater than one, this results in the following third-order kinetic expression

RCO2 ) -

k2 [R NH][CO2] k-1 2

∑ kb[B]

(5)

The reaction kinetics of DGA with CO2 have been studied by few investigators. There is general agreement as to the order and rate of reaction with respect to DGA in the temperature range of 25-40 °C. However, there is disagreement on the rate data at 60 °C. Hikita et al.4 studied the CO2 kinetics in DGA solutions up to 40 °C and at very low amine concentrations in a stopped flow reactor. Alper5 studied the reaction rate with 0.1 and 0.2 M DGA at 25 °C in a stopped flow reactor and found that his results compared very well with those of Hikita et al.4 Littel6 extended the temperature and the concentration range by studying kinetics up to 60 °C and over the concentration range of 0-5 M in a stirred cell reactor. Littel6 found a value of two for the overall reaction order at temperatures below 40 °C and a higher value at 60 °C for the overall reaction order and therefore used the zwitterion mechanism to explain the CO2/ DGA kinetics. They concluded that their data showed good agreement with previous authors. Overall it can be concluded that below 40 °C, the kinetics of DGA are well established. Recently, Pacheco7,8 studied DGA/CO2 kinetics in a wettedwall column, and his results are comparable to those of previous investigators at temperatures below 40 °C; however, the activation energy was found to be higher than the previously published values. All of the previous work was in unloaded

10.1021/ie0505458 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/17/2005

2474

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006

solutions near zero ionic strength, except for that of Pacheco in solutions with 0.0 to 0.5 mol CO2/mol DGA. In this paper, the work of Pacheco7 is reanalyzed and extended to include more data at 65 wt % DGA from 25-60 °C at 0-0.4 mol CO2/mol DGA. This work also uses the mass transfer model developed by Bishnoi,9 which is based on the eddy diffusivity theory. The rate model depends on speciation from the VLE model developed by Al-Juaied and Rochelle.10,20 The pseudofirst-order and interface pseudo-first-order approximation models are also compared to the rigorous model. Glycolic acid and potassium formate were added to determine the effect of ionic strength on the rate constant.

The diffusivity of CO2 in DGA solutions was estimated using the modified Stokes-Einstein equation to correct the diffusivity of CO2 in pure water for the change in viscosity with the addition of DGA as follows

()

DCO2 ) D°CO2

0.6

(10)

where D°CO2 is the diffusivity of CO2 in pure water, DCO2 is the diffusivity of CO2 in DGA solutions, µ0 is the viscosity of pure water and µL is the viscosity of the DGA solution. For diffusivity of DGA, the following equation was given by Hikita et al.14

DDGA ) 2.868 × 10- 8µL- 0.449T

2. Experimental Methods The absorption rate of carbon dioxide was determined in the wetted-wall column used by Bishnoi9 and others. The use of this apparatus to provide data for CO2 absorption in DGA solutions has been described in detail by Al-Juaied.10,20 Solution flowed down the outside of a stainless steel tube that was 9.1 cm long with a contact area of 38.52 cm2. The column operated at 1-8 atm with nitrogen gas rates of 4-6 standard L/min. Loaded amine solution was recirculated at 2 cm3/s from reservoirs with a 1 L volume. The absorption rate was determined from continuous infrared analysis of the gas leaving the system. The reported CO2 partial pressure is the log mean average of the gas entering and leaving the contactor. The liquidfilm mass-transfer coefficient was determined by CO2 desorption from water and ethylene glycol mixtures. The gas film coefficient was determined by the absorption of sulfur dioxide into sodium hydroxide solutions.9 3. Physical Properties

(11)

where DDGA is in cm2/s and T in K. Diffusion coefficients of all other ions were set at the same value as DGA. The solution viscosity and density were taken from Jefferson.15 Viscosity of DGA/glycolic acid and DGA/potassium formate solutions was measured by a Cannon-Fenske viscometer. 4. Description of Models 4.1. Rigorous Model. The model developed by Bishnoi,9 based on the eddy diffusivity theory, was used in this work. The following two reactions were assumed to be kinetically controlled and reversible

CO2 + OH- T HCO3-

(12)

DGA:H2O + CO2 T DGACOO- + H3O+

(13)

For example, the rate of DGA reaction with CO2 is given by

The Henry’s law constant for CO2 (HCO2) is obtained using N2O analogy. Versteeg and van Swaaij11 measured the solubilities of N2O in aqueous DGA solutions up to about 35% DGA (65 wt % only at 25 °C) from 25-60 °C. Using the Henry’s constant of N2O in DGA solutions from this source and the N2O/CO2 analogy

HN2O,DGA HCO2,DGA ) H HN2O,H2O CO2,H2O

HCO2,H2O (atm cm3/mol) ) 1.71 × 1007 exp{-1886/T (K)} (7) The Henry’s constant for N2O in loaded DGA solutions is given by Danckwerts13

(H*H ) ) (k′ + k′ + k′ )I +

-

g

(9)

where ci is the ion concentration and zi is the the ion charge.

)

[DGACOO-][H3O+] K13

(14)

where kDGA is given by

[ (

Ea 1 1 R T 298.15

kDGA ) k25°C exp -

)]

(15)

and the equilibrium constant is calculated by the ratio of the species in the bulk solution

K13 )

[DGACOO-][H3O+]

(16)

[DGA][CO2]

The rate constant for reaction 12 is the expression presented by Pinsent et al.16 The rate constant, kDGA, for reaction 13 is fit to match absorption data into loaded and unloaded solutions. To avoid having H3O+ as a species in the model, the rates of reaction for carbamate formation are described as

(

(8)

The parameters k′+, k′-, and k′g (van-Krevelen coefficients) are specific to the cations, anions, and gas, respectively, and are assumed to be ion concentration independent; Ii is the partial ionic strength of each ion, given as

1 Ii ) cizi2 2

(

R13 ) kDGA [DGA][CO2] -

(6)

Pacheco7 correlated the Henry’s Law constant for carbon dioxide in pure water measured by Versteeg and van Swaaij11 and reported by Al-Ghawas et al.12

log10

µ µL

Kw R13 ) kDGA [DGA][CO2] - [DGACOO-] K13[OH-]

)

(17)

where

Kw ) [H3O+][OH-] and K13 )

[DGACOO-][H3O+] [DGA][CO2]

Reactions involving only a proton transfer are always considered

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2475 Table 1. Model Equations and Boundary Conditions

NCO2 ) xk2,DGA[DGA]bulkDCO2

conservation equations at each node overall species material balance ∇2[DGA] + ∇2[DGACOO-] + ∇2[DGAH+] ) 0 ∇2[CO2] + ∇2[HCO3-] + ∇2[CO3)] + ∇2[DGACOO-] ) 0

/ (PCO2,i - PCO2,i ) HCO2

(21)

P/CO2,i is the partial pressure of CO2 that would be in equilibrium with the composition at the interface. It is clear that eq 20 can be applied explicitly to calculate the flux because [DGA]bulk can be calculated with the equilibrium model described in Al-Juaied and Rochelle.10,20 Equation 21 presents the problem that the concentration of DGA at the interface, [DGA]i, is not known a priori. The diffusion of reactants and products needs to be accounted for with mass transfer coefficients for those species. The calculation of [DGA]i and P/CO2,i was performed using the equilibrium model in AlJuaied and Rochelle10 and knowing also the CO2 loading at the interface, ldgi, which can be calculated using the following equation

material balance for molecular CO2 ∇2[CO2] - (R12 + R13) ) 0 carbamate balance ∇2[DGACOO-] + R13 ) 0 electroneutrality [DGAH+] ) [HCO3-] + 2[CO3)] + [OH-] + [DGACOO-] boundary conditions at x)0 [CO2])[CO2]I DHCO3-∇[HCO3-] + DCO3)∇[CO3)] ) 0 DDGA∇[DGA] + DDGAH+∇[DGAH+] ) 0 ∇[DGACOO-] ) 0 K[HCO3-][OH-] - [CO3)] ) 0 K[DGA] - [DGAH+][OH-] ) 0 [DGAH+] ) [HCO3-] + 2[CO3)] + [OH-] + [DGACOO-]

ldgi )

at x ) ∞ [i] ) [i]o for all species i in solution

NCO2

+ ldgbulk

kl,prod[DGA]T

(22)

where kl,prod is the liquid mass-transfer coefficient of the DGA products. Generally

to be in equilibrium. These reactions are

HCO3- + OH- T CO3) + H2O

(20)

NCO2 ) xk2,DGA[DGA]iDCO2

equilibrium relationships K18 ) ([DGAH+][OH-])/[DGA] K18 ) [CO3)]/([HCO3-][OH-])

DGA:H2O T DGAH+ + OH-

/ (PCO2,i - PCO2,bulk ) HCO2

(18) (19)

All equilibrium constants are calculated directly from the ratio of products and reactants in the bulk solution. The bulk solution is speciated using the electrolyte NRTL model described in AlJuaied and Rochelle.10,20 Along with these seven equations, we define boundary conditions at the interface and in the bulk solution. The equations to be solved and the boundary conditions used in this work are presented in Table 1. The thermodynamic model neglects the presence of inert nitrogen pressure in the experiments. Addicks et al.17 have shown that 200 bar of methane pressure can increase CO2 vapor pressure over MDEA solutions by a factor of 10. Assuming that ln P/CO2 is proportional to the inert pressure, the CO2 vapor pressure in our experiments at 8 bar nitrogen may be underestimated by as much as 10%. 4.2. Approximate Models. Assumptions 1 and 2 listed below lead to the pseudo-first-order and interface pseudo-first-order approximations, respectively. Assumption 1. The liquid-phase driving force (PCO2,i P/CO2,bulk) is very small. This means that the flux is so small that the PCO2,i ≈ P/CO2,bulk and that [DGA]i ≈ [DGA]bulk. Assumption 2. The reaction of CO2 + DGA is fast enough that CO2 reaches equilibrium with the rest of the solution near the interface. Both approximations, PFO and IPFO, assume that the concentration profiles of all the species in the reaction sublayer, except CO2, are constant. The IPFO differs from the PFO approximation in that the profiles are assumed to be constant at their interface value instead of at the bulk value. The advantage of the PFO and IPFO models is that the flux of CO2 can be derived from the analytical solution, as shown by Freguia,18 for PFO and IPFO, respectively

kl,prod ) kl,CO2

x

Dprod DCO2

(23)

where Dprod is the diffusion coefficient of products and is set at the same value as DGA. The mass-transfer rates of CO2 measured in the wetted-wall column contactor were interpreted using the three models described above. The rigorous model was coupled to a generalized regression package, GREG,19 to estimate the parameter values and confidence intervals. Reaction rate constants and diffusion coefficients of reactants and products were extracted from the experimental measurements. 5. Results and Discussion Table 2 presents a subset of the absorption data into aqueous DGA. The data included had less than 50% gas film resistance, 20-50% CO2 removal, and 0-50% approach to equilibrium. The detailed data and error analysis are given in Al-Juaied.20 The rigorous, PFO, and IPFO models were used to extract the second-order rate constant from the rate data in loaded solutions. The regressions were done for each temperature instead of for all temperatures simultaneously. Figure 1 shows that the second-order rate constant at 40 °C increases with an increase in CO2 loading. The IPFO model matches the rigorous model very well. Similar results were obtained at 25 and 60 °C. The knowledge of good values for the DGA diffusivities would allow the use of the IPFO model, which has the advantage of converging faster than the rigorous integration. It can be seen also that the PFO model follows the rigorous model well at low loading, as expected, whereas it underestimates the second-order rate constant at loadings greater than 0.25. At low CO2 loading, the reaction rate with CO2 is not instantaneous but fast enough for most of the reaction to occur in the boundary layer. The PFO model is valid at these conditions when the DGA concentration at the gas-liquid interface is not significantly different from that in the bulk solution. At high CO2 loading, the DGA can be

2476

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006

Table 2. Subset of the Experimental Rate Measurements with 65 wt % DGA/Watera loading (mol CO2/mol DGA)

T (°C)

POUT CO2 (kPa)

flux (×106 kmol m-2 s-1)

k°g (×109 kmol m-2 Pa-1 s-1)

k°l (×105 m/s)

PIN CO2 (kPa)

k′G (×109 kmol m-2 Pa-1 s-1

∼0 ∼0 ∼0 ∼0 ∼0 ∼0 0.109 0.112 0.234 0.228 0.390 0.391 0.115 0.117 0.236 0.242 0.384 0.387 0.104 0.106 0.253 0.257

24.3 24.7 40.4 41.0 60.6 60.7 25.9 26.2 24.0 24.0 25.1 24.8 40.2 40.6 39.3 39.4 40.0 40.0 59.2 58.8 60.1 59.9

1.57 2.26 1.36 2.04 0.59 1.23 6.11 8.29 10.35 14.03 80.43 44.92 6.05 8.26 20.93 9.77 65.87 84.07 5.17 7.22 8.54 11.56

3.05 5.61 4.34 6.84 2.55 5.42 8.78 11.55 7.51 10.04 34.31 18.15 8.78 11.43 19.92 10.61 14.07 16.80 10.96 14.19 11.55 15.39

7.34 7.38 7.56 7.60 7.45 7.48 2.30 2.31 1.70 1.69 1.04 0.89 2.33 2.34 1.53 1.51 1.01 1.00 2.31 2.30 1.61 1.62

2.53 2.52 3.30 3.38 6.20 6.35 2.81 2.68 3.77 3.73 1.67 1.65 2.74 2.84 2.87 2.89 2.49 2.48 5.13 5.07 3.97 3.90

1.97 2.99 1.92 2.91 0.92 1.93 9.91 13.23 14.95 20.17 114.6 68.56 9.82 13.11 34.54 17.32 81.33 101.9 9.94 13.38 16.26 21.73

2.27 3.04 4.13 4.42 6.40 6.56 2.18 2.08 0.93 0.92 0.54 0.52 2.19 2.04 1.42 1.74 0.24 0.22 4.52 3.84 3.13 2.83

a

Total pressure from 100 to 650 kPa.

resistance is determined by the resistances of the two regions in series.

Rliquid ) RIPFO + Rinst

(24)

RIPFO is the resistance of the reaction sublayer, and Rinst is the resistance of the diffusion region, where the reactions are instantaneous. Equation 24 can be written in the following form in terms of normalized flux, kIg

1 1 1 ) I + I I kg kg,IPFO kg,inst

(25)

The IPFO (kinetic controlled) term is given by I ) kg,IPFO

Figure 1. Second-order rate constant for the reaction between CO2 and 65 wt % DGA at 40 °C.

depleted at the gas-liquid interface, and therefore, the PFO model no longer applies. Under these conditions, it is necessary to correct for the diffusion of DGA and DGA products. The rigorous model and IPFO models account for this correction but the PFO corrects only for the diffusion of CO2 and not for that of DGA and DGA products. At 60 °C, the deviation is more pronounced, and the PFO model at 0.25 mol CO2/mol DGA gives a value of k2 that is 10 times less than that of the other two models.20 This is related to the slope of the equilibrium curve that is increasing as the temperature increases, and therefore, the deviation between the total concentration of DGA at the interface and in the bulk solution increases. The reaction rate at high CO2 loading and high-temperature becomes instantaneous. An analysis was done to estimate the relative importance of the kinetic term to the total reaction rate. The approximation is good if the fraction of the kinetic term is close to 1 and the instantaneous term is close to 0. The IPFO approximation divides the boundary layer into two regions, one controlled by reaction rates and one controlled by the diffusion of reactants and products. The liquid-phase mass-transfer

xk2[DGA]iDCO2 HCO2

(26)

The instantaneous coefficient can be calculated using eq 30, derived in Dang,21 and valid for small driving forces

kIg,inst )

1 k0l,prod ∂P/CO2

(27)

∂[CO2]* The instantaneous coefficient depends on the partial derivative of the equilibrium partial pressure with respect to the CO2 total concentration. It also depends on the physical mass-transfer coefficient of the reaction products and DGA, k0l,prod. The derivative was obtained using the electrolyte-NRTL model described in Al-Juaied and Rochelle;10,20 k0l,prod was obtained using eq 23. The error introduced by extracting the second-order rate constant from the rate data at high loading can be estimated by calculating the fractional resistance of the kinetic term

fraction kinetic )

kIg I kg,IPFO

(28)

Table 3 shows the result of the analysis done for 25, 40, and 60 °C. At low loading for the three temperatures, the instan-

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2477 Table 3. Analysis of Importance of the Kinetics at Low and High Loading for 25 °C, 40 °C, and 60 °C T loading 1/k′g,IPFO 1/k′g,inst fraction (°C) (mol CO2/mol DGA) (cm2s atm/mol) (cm2 s atm/mol) IPFO 25 39 59 25 39 60

0.078 0.101 0.100 0.390 0.385 0.257

4.39 × 104 4.66 × 104 2.06 × 104 2.52 × 105 1.06 × 105 3.14 × 104

1.27 × 101 1.26 × 102 9.23 × 102 1.13 × 104 1.61 × 104 3.57 × 103

0.999 0.997 0.957 0.957 0.868 0.898

Table 4. Results for the Regression of DDGA, Dprod, and k2 parameter

value

A B C R

0.30 × 102 ( 0.71 × 101 0.42 × 101 ( 1.51 × 100 -0.61 × 104 ( 1.60 × 103 0.75 × 100 ( 0.31 × 100

taneous resistance is always negligible. At high loading, it accounts for 5-15% of the total resistance. Figure 2 shows the sensitivity of the second-order rate constant and the diffusion of products and reactants to the flux predicted by the rigorous model with 65 wt % DGA at 40 °C. The results in Figure 2 can be divided into two regions. The first region is where the CO2 loading is less than 0.10 (low loading). The second region is where the CO2 loading is greater than 0.10 (high loading). At low loading (region 1), the rate constant of DGA and the diffusion of reactants and products is least sensitive. As the loading increases and the concentration of DGA drops, the rate constant of DGA and the diffusion coefficient of reactants and products becomes most sensitive (region 2). This shows that the removal of reaction products and the diffusion of DGA to the interface have become important phenomena at high loading. The results in Table 3 and Figure 2 show that the rate data contain a source of error that tends to overpredict the second-order rate constant, since part of the resistance is neglected. This problem becomes more important as CO2 loading and temperature increase. Because of the importance of the diffusion of reactants and products at high CO2 loading, the parameters Dion and DDGA were regressed from the experimental data along with the second-order rate constant. The second-order rate constant was regressed as a function of CO2 loading and temperature

ln k2 ) A + Bldg + C/T

(29)

where A, B, and C are the fitting parameters and ldg is the CO2 loading in mol CO2/mol DGA. A limited set of data, shown in Table 2, was regressed to minimize the computation time using the rigorous model. This work used 38 nodes with small spacing to achieve the desired accuracy. The values of the diffusion coefficients of the reactants and products used in the initial guess are those obtained by Pacheco.7 We regressed these values using the same temperature and viscosity dependence as obtained by Pacheco.7 The following equations for the diffusion of reactants and products were used in the regression

DDGA ) 2.845E - 8Rµ-0.5752(cP)T(K)

(30)

Dprod ) 2.845E - 8Rµ-0.5752(cP)T(K)

(31)

Table 4 presents the regressed values and confidence intervals obtained during the regression of DDGA, Dprod, and k2. Figure 3

Figure 2. Sensitivity of calculated CO2 flux to values of the diffusion coefficients of reactants and products and second-order rate constant: 40 °C, k°l ) 2.74 × 10-3 m/s, Pi ) 10P*.

Figure 3. Effect of CO2 loading on the second-order rate constant for the 65 wt % DGA. Lines are model predictions.

shows the effect of CO2 loading and temperature on the rate constant. The small confidence interval of the regressed Dprod and DDGA gives some confidence in the estimated values of the secondorder rate constant. The results in Figure 3 show that k2 is indeed increasing with CO2 loading since the effects of the diffusion of reactants and products are accounted for in the regression of k2. Figure 3 includes additional data from Al-Juaied19 that were not regressed. Figure 4 is the parity plot for the calculated and measured fluxes of CO2 for the DGA system at various CO2 loadings and three temperatures. For most experiments the measured flux is within 15% of the calculated flux. We might also choose to express the rate of reaction in terms of activity. The true rate expression is a function of activity rather than concentration. The equilibrium model in Al-Juaied19 and Rochelle was used to calculate the activity coefficients of CO2 and DGA in the 65 wt % DGA. Figure 5 show the activity coefficients at 40 °C for 65 wt % DGA. As can be seen in Figure 5, the activity coefficients of the ions depart farther from unity as CO2 loading increases. From

2478

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006

Figure 4. Comparison of measured and calculated interfacial fluxes of CO2 with 65 wt % DGA at various CO2 loadings.

Figure 6. Effect of CO2 loading on the second rate constant calculated on the basis of concentration and activity at 40 °C for the DGA/water/CO2 system. Lines are model predictions.

Figure 7. Normalized CO2 flux with 65 wt % DGA at low and high driving force at 40 °C. Figure 5. Predicted activity coefficients for 65 wt % DGA at 313 K.

eq 1 and eq 2, we can write RCO2 as

RCO2 ) kb[DGAH+ COO-] where

Keq )

aDGAH+COO- γDGAH+COO- [DGAH+COO-] ) aDGAaCO2 γDGAγCO2 [DGA][CO2]

Therefore

γDGAγCO2 RCO2 ) kbKeq[DGA][CO2] γDGAH+COOThe rate-based activity constant can be written as a function of CO2 loading as follows

( (

kA ) kldg)0

) )

γDGAγCO2 γDGAH+COO- loaded γDGAγCO2 γDGAH+COO- unloaded

(32)

It should be noted that the CO2 activity coefficient is calculated using the nitrous oxide analogy. In eq 32, the activity coefficient of the zwitterion complex is assumed to be the same as DGA carbamate. Figure 6 shows the rate-based activity constant as a function of CO2 loading at 40 °C using the model fit in Figure 3 and eq 32. The results in Figure 3 at 40 °C are also included. It can be seen that the concentration-based rate constant calculated using eq 32 shows a factor-of-four increase in k2 compared to the second-order rate constant regressed from the kinetic data. Figure 7 shows the model prediction of the normalized flux for 65 wt % DGA at 40 °C with low and high driving forces. The CO2 flux should depend on the concentration of free DGA. Therefore the normalized flux decreases as the loading increases and DGA is depleted in the bulk solution. Furthermore, with the larger driving force DGA is also depleted at the gas-liquid interface giving a reduced normalized flux. 5.1. CO2 Reactive Absorption into Low-Loading Aqueous DGA. Table 5 and Figure 8 show the comparison between the results of the 65 wt % DGA in this work and that of other investigators. There is a good agreement between the activation energy for the DGA reaction found in this work and that reported

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2479 Table 5. Kinetic Data for DGA ref 4 21 5 22 8 reanalyzed this work

T (K)

DGA (mol/L)

k298 (m3kmol-1 s-1)

Ea (kJ/mol)

278-313 298 278-298 298-318 298-333 298-313 298-333

0.015-0.032 0-0.050 0.1, 0.2 0.1-3 4.8 (50 wt %) 2.4 (25 wt %) 6.2 (65 wt %)

5923 4480 4517 3990

40.7 39.4 44.3 47.8 40.1 51.7

6663 17300

technique stopped flow stopped flow stirred cell wetted-wall column wetted-wall column

Table 6. Subset of Rate Measurements with 25 wt % DGA at Zero Loadinga [DGA]T (kmol/ m3)

T (°C)

POUT CO2 (kPa)

flux (×106 kmol m-2 s-1)

k°g (×109 kmol m-2 Pa-1 s-1)

k°l (× 105m/s)

PIN CO2 (kPa)

k′G (×109 kmol m-2 Pa-1 s-1)

2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38

24.5 24.5 24.5 24.6 24.9 40.2 40.9 40.8 41.0 41.1 60.9 61.0 61.2 61.2 61.3

2.54 5.24 8.03 10.98 13.76 2.24 4.59 7.22 10.12 12.90 2.25 4.72 7.41 10.22 12.76

2.68 5.78 8.66 11.15 13.84 2.96 6.44 9.62 12.42 15.06 2.54 5.57 8.29 10.47 13.07

1.98 2.00 2.02 2.04 2.06 2.11 2.13 2.10 2.08 2.10 2.32 2.28 2.25 2.27 2.30

6.63 6.63 6.63 6.64 6.65 8.88 8.91 8.91 8.92 8.92 12.16 12.16 12.18 12.18 12.18

4.09 8.52 12.82 17.01 21.07 3.86 8.03 12.36 16.76 20.77 3.51 7.49 11.55 15.33 19.00

1.41 1.50 1.46 1.34 1.33 1.89 2.06 1.93 1.73 1.61 1.45 1.56 1.47 1.31 1.31

a

Total pressures from 100 to 400 KPa.

by other researchers. Pacheco et al.8 reported an activation energy of 66.1 kJ/mol greater than other researchers. However, the rate constant in 65 wt % DGA is approximately four times larger than the rate constants reported by other researchers. To understand the effect of the DGA concentration on mass transfer, the absorption rate of CO2 into 25 wt % DGA was investigated. Table 6 presents the absorption data in 65 wt % DGA at zero solution loading. Figure 8 shows the temperature dependence of the rate constant. The results are also shown in Table 5. There is an excellent agreement between the rate constants for the 25 wt % DGA reaction and those reported by other researchers. For 25 wt % DGA in the temperature range of 25-40 °C, the second-order rate constant is given by

( (

Ea 1 1 R T 298 K

k2(m3 kmol-1 s-1) ) k2(298K) exp -

))

(33)

k2(T)298K) ) 6.66 × 103 m3 kmol-1 s-1 Ea ) 40.1 kJ/mol The activation energy will be smaller for 25 wt % DGA if the data set at 60 °C were included. For 65 wt % DGA, the relation is valid from 25-60 °C. The data of Pacheco7 at low loading for 50 wt % DGA were also analyzed (Figure 8). The activation energy obtained in 50 wt % DGA is approximately 47.8 kJ/mol; however, the rate constant is approximately two times greater than previously published values. Results with 25, 50, and 65 wt % DGA suggest that the second-order rate constant increases as DGA concentration increases. The most probable explanation for this observation is that the reaction of DGA with CO2 follows the zwitterion mechanism and that DGA catalyzes itself. Recently, Alboudheir et al.24 found similar results. They obtained kinetic data using a laminar jet apparatus for CO2 absorption into loaded and concentrated MEA solutions. They found, for low MEA concentrations within the temperature range of 20-40 °C, that the reaction order is one and that the

Figure 8. Second-order rate constant for the reaction between CO2 and DGA at zero loading.

simple second-order kinetic model r ) k2[RNH2][CO2] is applicable. For concentrated MEA solutions ([MEA] ) 1.4055.498 M), they found that the apparent reaction order in MEA increases with increasing amine concentration and that the temperature effect follows Arrhenius behavior from 20-60 °C, and therefore they used the zwitterion mechanism to explain the CO2/MEA kinetics. Results with 25, 50, and 65 wt % DGA are given in Figure 9 in terms of normalized flux, k′G. Figures 8 and 9 show that k′G varies with DGA less than k2 since k′G is proportional to the square root of k2. Figure 9 shows that the normalized flux is also a function of DGA concentration, especially at 60 °C. 5.2. Effect of Ionic Strength on the Reation Rate Constant for DGA and CO2. When CO2 is absorbed into aqueous

2480

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006

Table 7. Results for the Fit of k2 as a Function of Ionic Strength

65 wt % DGA 65 wt % DGA 65 wt % DGA 65 wt % DGA + potassium formate 65 wt % DGA + potassium formate 65 wt % DGA + glycolic acid

T (°C)

ko (m3 kmol-1 cm-2 s-1)

C (m6 kmol-2 cm-2 s-1)

25 40 60 25 40 40

1.73 × 104 5.00 × 104 1.51 × 105 1.41 × +104 3.84 × 104 8.90 × 104

0.674 0.674 0.674 0.730 0.230 0.510

Table 8. Rate Measurements in 65 wt %DGA/Water/Glycolic Acid at Zero CO2 Loadinga glycolic acid/DGA (mol/mol)

T (°C)

POUT CO2 (kPa)

0 0 0 0 0 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4

39.5 39.9 39.9 39.9 39.8 39.6 39.7 39.7 39.8 39.6 40.4 40.3 40.0 39.8 39.8 39.2 39.8 39.6 39.9 40.1 39.2 39.7 39.6 39.7 39.7

0.84 1.67 2.54 3.59 4.67 0.98 1.99 3.00 4.15 5.31 1.12 2.28 3.45 4.76 6.08 1.30 2.57 4.06 5.45 6.91 1.60 3.20 4.85 6.70 8.40

a

flux m-2 s-1)

(×106 kmol

(×109

2.49 5.72 8.71 11.3 14.1 2.50 5.58 8.61 11.3 13.9 2.50 5.58 8.61 11.3 13.9 2.15 5.31 8.01 10.7 13.1 2.56 5.84 8.95 11.5 14.3

k°g kmol m-2 Pa-1 s-1) 5.50 5.53 5.56 5.40 5.25 4.69 4.71 4.73 4.69 4.64 4.09 4.11 4.13 4.09 4.06 3.79 3.77 3.66 3.67 3.69 2.84 2.86 2.87 2.88 2.90

k°l (×105 m/s)

PIN CO2 (kPa)

k′G (×109 kmol m-2 Pa-1 s-1)

4.39 4.39 4.39 4.39 4.39 3.95 3.95 3.95 3.95 3.95 3.42 3.42 3.42 3.42 3.42 2.89 2.89 2.89 2.89 2.89 2.61 2.61 2.61 2.61 2.61

1.29 2.71 4.10 5.67 7.31 1.52 3.18 4.82 6.53 8.27 1.74 3.65 5.53 7.48 9.46 1.88 3.98 6.25 8.34 10.4 2.51 5.26 7.97 10.6 13.3

4.18 5.14 5.15 4.61 4.38 3.60 4.12 4.26 3.96 3.79 3.14 3.59 3.71 3.45 3.31 2.14 2.93 2.78 2.77 2.64 2.28 2.78 2.83 2.52 2.51

Total pressures from 305 to 490 kPa. Table 9. Henry’s Constants and Viscosities Used for Glycolic Acid/DGA and Potassium Formate (CHKO2)/DGA

Figure 9. Comparison of CO2 flux measurements at zero loading.

solutions, including alkanolamines, it combines with water and dissociates into positive and negative ions. Depending on the components in the solution, different species may end up carrying positive and negative charges (typically protonated amines and negatively charged carbamates and bicarbonates in DGA solutions). Usually, in such solutions, ionic strength is an important parameter because each ion is surrounded by an extended solvation shell which can affect ionic activities and

solution

T (°C)

HCO2 (atm.cm3/mol-1)

µ (cP)

0.1 glycolic acid/mol DGA 0.2 glycolic acid/mol DGA 0.3 glycolic acid/mol DGA 0.4 glycolic acid/mol DGA 0 M CHKO2/6.5 M DGA 1 M CHKO2/6.5 M DGA 0 M CHKO2/6.5 M DGA 1 M CHKO2/6.5 M DGA 3 M CHKO2/6.5 M DGA

40 40 40 40 25 25 40 40 40

67500 75000 81000 90000 45981 54836 62397 72773 98396

8.5 11.7 16.7 20.5 11.3 11.3 6.7 6.7 6.7

rate constants. Davies25 pointed out that ion association can modify the reaction in two ways: first, ion pair formation affects the total ionic strength of the medium and second, one (or more) such ion pairs may be involved in the rate-determining step, thus altering the charge of the activated complex and reaction rate. In the last section, it was shown that the second-order rate constant is increasing with CO2 loading or ionic strength. Therefore, the results in the previous section can be reinterpreted in terms of the following equation

log k ) log ko + Cµ

(34)

Figure 10 shows the second-order rate constant presented in Figure 3 as a function of ionic strength. Table 7 shows the values of k0 and C for the three temperatures. Table 8 presents more detailed experimental results with the addition of glycolic acid to 65 wt % DGA at zero CO2 loading

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2481 Table 10. 65 wt % DGA/Water/Potassium Formate Subset of the Experimental Rate Measurements Kformate (kmol/m3)

T (°C)

POUT CO2 (kPa)

flux (×106 kmol m-2 s-1)

k°g (×109 kmol m-2 Pa-1 s-1)

k°l (×105 m/s)

PIN CO2 (kPa)

k′G (×109 kmol m-2 Pa-1 s-1)

0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 3 3 3 3 3

25.2 25.2 25.1 25.2 24.4 39.3 39.5 39.6 39.4 24.9 25.4 26.0 39.7 40.0 25.9 39.8 25.7 39.9 39.6 39.7 40.0 40.3 40.1 40.2 40.2

1.1 2.4 3.7 4.9 6.2 1.0 3.0 4.0 1.9 0.9 2.1 3.2 5.1 1.1 5.5 2.2 4.4 5.8 4.6 3.4 1.1 2.2 3.4 4.6 5.8

1.7 4.1 6.1 8.3 9.9 2.1 7.7 10.3 5.1 1.6 4.4 6.5 12.4 2.0 10.7 4.8 8.6 11.3 9.2 6.8 2.0 5.1 7.6 10.1 12.1

5.4 4.9 4.9 5.0 5.0 5.5 5.5 5.6 5.5 6.5 5.4 5.4 5.6 5.0 5.5 5.0 5.5 5.1 5.1 5.0 4.8 4.9 4.9 4.9 4.9

2.72 2.72 2.72 2.72 2.72 3.02 3.02 3.02 3.02 2.61 2.61 2.61 3.02 3.03 2.61 3.03 2.61 3.03 3.03 3.03 3.46 3.46 3.46 3.46 3.46

1.4 3.2 4.9 6.5 8.1 1.4 4.3 5.8 2.9 1.2 2.9 4.4 7.2 1.5 7.4 3.2 5.9 8.0 6.4 4.8 1.6 3.3 5.0 6.6 8.2

1.77 2.07 2.04 2.09 1.91 2.62 3.47 3.45 3.56 2.01 2.64 2.48 3.20 2.24 2.41 2.80 2.45 2.47 2.53 2.51 2.29 3.07 2.98 2.95 2.72

Total pressures from 170 to 225 KPa.

summarizes the results. The results with no added potassium formate are included here for comparison. The Henry’s constants and viscosities in the DGA-potassium formate solutions are given in Table 10. Figure 10 shows the second-order rate constant as a function of ionic strength at 25 and 40 °C. The present results suggest that ionic strength has a strong effect on the second-order rate constant. The results in 65 wt % DGA showed increases by a factor of 5 over the range of loading from 0 to 0.4 mol CO2/mol DGA. Table 6 shows the slope of the line from eq 34. The results with potassium formate and 65 wt % DGA at 25 °C compare well to the results with 65 wt % DGA; however, at 40 °C, the potassium formate and glycolic acid and 65 wt % DGA increases by a factor of 2 to 3 with ionic strength compared with 65 wt % DGA which increases by a factor of 5 over the range studied. Conclusions Figure 10. Effect of ionic strength on k2 for the DGA/water/CO2, DGA/ glycolic acid/water/CO2, and DGA/potassium formate/water/CO2 systems. (b) Experimental points for 65 wt % DGA + glycolic acid at 40 °C. (9) Experimental points for 65 wt % DGA + potassium formate at 40 °C. (2) Experimental points for 65 wt % DGA + potassium formate at 25 °C. Lines are the curve fit of eq 34.

to quantify the effect of ionic strength on the reaction rate constant. Glycolic acid will react to form DGAH+ glycolate-. Glycolic acid was added to give up to 0.4 mol glycolic acid/ mol DGA. These data were evaluated with the pseudo-firstorder assumption for kinetics, eq 20, to extract the second-order rate constant of DGA/glycolic acid with carbon dioxide. Figure 10 shows the second-order rate constant for the system DGA/ glycolic acid/CO2/water at 40 °C. The Henry’s constant and viscosities used in the calculation of the second-order rate constant are given in Table 9. Increasing the glycolic acid concentration increases the second-order rate constant by a factor of 2 from 0 to 0.4 mol glycolic acid per mol DGA. Systematic experiments were also performed at ionic strengths up to 3 M by adding potassium formate to 65 wt % DGA solutions at zero loading. Table 10

Absorption experiments of CO2 into aqueous 65 and 25 wt % DGA solutions were performed at 25-60 °C in a wettedwall column. The eddy diffusivity theory was used to simulate liquid-phase hydrodynamic characteristics. Two approximate models were used: the pseudo-first-order approximation and the interface pseudo-first-order model. The electrolyte-NRTL model was used to represent the activity coefficients of the species in solution. In Al-Juaied,19 the NRTL model was verified using 13C NMR data, physical and chemical solubility data. Kinetic rate constants have been regressed from the currently obtained experimental data. The following conclusions can be made. • CO2 absorption in DGA shows a zwitterion mechanism. Our results in low concentration DGA (25 wt % DGA) show a close agreement with published data and a deviation at high concentration (50 and 65 wt % DGA). In the low concentration solution, a temperature maximum of 40 °C was found on the applicability of the second-order kinetic model. • The IPFO model matches the rigorous model very well. The PFO model underestimates the second-order rate constant, especially at high loading.

2482

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006

• The reaction of DGA with CO2 is the dominant effect at low loading. At high loading, instantaneous reactions are approached and the diffusion of reactants and products becomes an important phenomenon. • Two models were proposed for the increase in k2 with ionic strength. The first one assumes that natural log of k2 increases linearly with ionic strength. This model was used to fit kinetic data in loaded solutions. The second model is predictive where k2 at zero loading is corrected for the activities of CO2, DGA, and DGACOO- as a function of CO2 loading. • Experiments with 65 wt % DGA, glycolic acid, and potassium formate show a comparable increase (a factor of 2-3) in rate constant with ionic strength as in 65 wt % DGA (a factor of 5 with ionic strength) at 25 and 40 °C. Acknowledgment M. Al-Juaied received scholarship support from Saudi Aramco while performing this work. Nomenclature ai ) activity of species i ci ) concentration of species i (mol/L) Di ) diffusion coefficient of species i (m2/s) Ea ) activation energy (kJ/mol) Hi ) Henry’s constant for species i (L atm/mol) Ii ) ionic strength for species i (mol/L) k2 ) second-order rate constant (L mol-1 s-1) k°l ) liquid film mass transfer coefficient (m/s) kg ) gas film mass transfer coefficient (kmol m-2 atm-1 s-1) k′+ ) Van-Krevelen coefficient for cations k′- ) Van-Krevelen coefficient for anions k′g ) Van-Krevelen coefficient for gas ldg ) mol CO2/mol DGA K ) equilibrium constant k′G ) gas-phase mass transfer coefficient (kmol m-2 Pa-1 s-1) NCO2 ) flux of CO2 (mol cm-2 s-1) P ) pressure (Pa, kPa, atm) P/CO2 ) equilibrium partial pressure of CO2 (Pa) PCO2,i ) interfacial partial pressure of CO2 (Pa) RCO2 ) rate of reaction of CO2 (mol s-1 m-3) T ) temperature (°C, K) zi ) ion charge for species i R ) correction factor for diffusion coefficients, eq 30. Greek Symbols γ ) activity coefficient µ ) solution viscosity (cP) Subscripts i ) interface prod ) products Literature Cited (1) Blohm, C. L.; Riesenfeld, F. C. Removal of hydrogen sulfide and carbon dioxide from hydrocarbon gases. U.S. Patent 2,712,978, 1955. (2) Caplow, M. Kinetics of carbamate formation and breakdown. J. Am. Chem. Soc. 1968, 90, 6795-6803. (3) Dankwerts, P. V. The reaction of CO2 with ethanolamines. Chem. Eng. Sci. 1979, 34, 443-446.

(4) Hikita, H.; Asai, S.; Ishikawa, H.; Honda, M. The kinetics of reactions of carbon dioxide with mono-2-propanolamine, diglycolamine, and ethylenediamine by a rapid mixing method. Chem. Eng. J. 1977, 14, 27-30. (5) Alper, E. Kinetics of reactions of carbon dioxide with diglycolamine and morpholine. Chem. Eng. J. 1990, 44, 107-111. (6) Littel, R. J. Selective carbonyl sulfide removal in acid gas treating processes. Ph.D. Dissertation, University of Twente, Enschede, The Netherlands, 1991. (7) Pacheco, M. A. Mass transfer, kinetics and rate-based modeling of reactive absorption. Ph.D. Dissertation, The University of Texas, Austin, TX, 1998. (8) Pacheco, M. A.; Kaganoi, S.; Rochelle, G. T. CO2 absorption into aqueous mixtures of diglycolamine and methyldiethanolamine. Chem. Eng. Sci. 2000, 55, 5125-5140. (9) Bishnoi, S. Carbon dioxide absorption and solution equilibrium in piperazine activated methyldiethanolamine. Ph.D. Dissertation, The University of Texas, Austin, TX, 2000. (10) Al-Juaied, M. A.; Rochelle, G. T. Thermodynamics of diglycolamine/morpholine/water/carbon dioxide. J. Chem. Eng. Data 2005, Submitted for publication. (11) Versteeg, G. F.; Swaaij, W. P. M. Solubility and diffusivity of acid gases (CO2, N2O) in aqueous alkanolamine solutions. J. Chem. Eng. Data 1988, 33, 29-34. (12) Al-Ghawas, H. A.; Hagewiesche, D. P.; Ruiz-Ibanez, G.; Sandall, O. C. Physicochemical properties important for carbon dioxide absorption in aqueous methyldiethanolamine. J. Chem. Eng. Data 1989, 34, 385391. (13) Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: New York, 1970. (14) Hikita, H.; Ishikawa, H.; Murakami, T.; Ishii, T. Densities, viscosities and amine diffusivities of aqueous MIPA, DIPA, DGA and EDA solutions. J. Chem. Eng. Jpn 1981, 14, 5. (15) Jefferson Chemical Company, Inc., Gas Treating Data Book, No. 337, 1969. (16) Pinsent, B. R.; Pearson, L.; Roughton, F. J. W. The kinetics of combination of carbon dioxide with hydroxide ions. Trans. Faraday Soc. 1956, 52, 15. (17) Addicks, J.; Owren, G. A.; Fredheim, A. O.; Tangvik, K. Solubility of carbon dioxide and methane in aqueous methyldiethanolamine solutions. J. Chem. Eng. Data 2002, 47, 855-860. (18) Freguia, S. Modeling of CO2 removal from flue gases with monoethanolamine. MS Thesis, The University of Texas, Austin, TX, 2002. (19) Caracotsios, M. Model parametric sensitivity analysis and nonlinear parameter estimation. Theory and applications. Ph.D. Dissertation, The University of Wisconsin, Madison, WI, 1986. (20) Al-Juaied, M. A. Carbon dioxide removal from natural gas by membranes in the presence of heavy hydrocarbons and by aqueous diglycolamine/morpholine. Ph.D. Dissertation, The University of Texas, Austin, TX, 2004. (21) Dang, H. CO2 absorption rate and solubility in MEA/PZ/H2O. MS Thesis, The University of Texas, Austin, TX, 2001. (22) Barth, D.; Tondre, C.; Delpuech, J. J. Stopped-flow investigations of the reaction kinetics of carbon dioxide with some primary and secondary alkanolamines in aqueous solutions. Int. J. Chem. Kinet. 1986, 18, 445457. (23) Littel, R. J.; Versteeg, G. F.; Van Swaaij, W. P. M. Kinetics of carbon dioxide with primary and secondary amines in aqueous solutions. II. Influence of temperature on zwitterion formation and deprotonation rates. Chem. Eng. Sci. 1992, 47, 2037-2045. (24) Aboudheir, A.; Tontiwachwuthikul, P.; Chakma, A.; Idem, R. Kinetics of the reactive absorption of carbon dioxide in high CO2-loaded, concentrated aqueous monoethanolamine solutions. Chem. Eng. Sci. 2003, 58, 5195-5210. (25) Davies, C. W. Salt effects in solution kinetics. Prog. React. Kinet. 1961, 1, 163.

ReceiVed for reView May 10, 2005 ReVised manuscript receiVed October 14, 2005 Accepted October 15, 2005 IE0505458