Absorption of Carbon Dioxide into Aqueous Blends of Diethanolamine

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Ind. Eng. Chem. Res. 2000, 39, 4346-4356

Absorption of Carbon Dioxide into Aqueous Blends of Diethanolamine and Methyldiethanolamine Edward B. Rinker, Sami S. Ashour, and Orville C. Sandall* Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080

In this work, a comprehensive model is developed for the absorption of carbon dioxide into aqueous mixtures of primary or secondary alkanolamines with tertiary alkanolamines. The model, which is based on penetration theory, incorporates an extensive set of important reversible reactions and takes into account the coupling between chemical equilibrium, mass transfer, and chemical kinetics. The reaction between CO2 and the primary or secondary amine is modeled according to the zwitterion mechanism. The key physicochemical properties that are needed for the model are the CO2 physical solubility, the CO2 and amine diffusion coefficients, and the reaction rate coefficients and equilibrium constants. Data for carbon dioxide absorption into aqueous mixtures of diethanolamine and methyldiethanolamine are compared to model predictions. Introduction Removal of acid gas impurities, such as CO2, is important in natural gas processing. Natural gas, depending on its source, can have varying concentrations of CO2. Some of the CO2 is often removed from natural gas because, when present at high levels, it reduces the heating value of the gas, and because it is costly to pump this extra volume when it does not have any heating value. Aqueous solutions of alkanolamines are the most widely used solvents for removing CO2. The most commonly used alkanolamines are the primary amine monoethanolamine (MEA), the secondary amine diethanolamine (DEA), and the tertiary amine methyldiethanolamine (MDEA). Primary and secondary amines react rapidly with CO2 to form carbamates. By the addition of a primary or secondary amine to a purely physical solvent such as water, the CO2 absorption capacity and rate is enhanced manyfold. However, because there is a relatively high heat of absorption associated with the formation of carbamate ions, the cost of regenerating primary and secondary amines is high. Primary and secondary amines also have the disadvantage of requiring 2 mol of amine to react with 1 mol of CO2; thus, their loadings are limited to 0.5 mol of CO2/mol of amine. Tertiary amines lack the N-H bond required to form the carbamate ion and therefore do not react directly with CO2. However, in aqueous solutions, tertiary amines promote the hydrolysis of CO2 to form bicarbonate and the protonated amine. Amine-promoted hydrolysis reactions are much slower than the direct reactions of primary and secondary amines with CO2, and therefore, the kinetic selectivity of tertiary amines toward CO2 is poor. However, the heat of reaction associated with the formation of bicarbonate ions is much lower than that associated with carbamate formation, and thus, the regeneration costs are lower for tertiary amines than for primary and secondary amines. Another advantage with tertiary amines is that the stoichiometry is 1:1, which allows for very high equilibrium CO2 loadings. * Corresponding author: [email protected].

Chakravarty et al.1 suggested that, by mixing a primary or secondary amine with a tertiary amine, the CO2 selectivity in the presence of H2S could be improved and regeneration costs minimized. These blended amine solutions also offer the advantage of setting the selectivity of the solvent toward CO2 by judiciously mixing the amines in varying proportions, which results in an additional degree of freedom for achieving the desired separation for a given gas mixture. This approach could dramatically reduce capital and operating costs while providing more flexibility in achieving specific purity requirements. Because of the need to exploit poorer quality crude and natural gas coupled with increasingly strict environmental regulations, highly economical and selective acid gas treatment is more important today than at any time in the past. As a result, there has been a resurgence of interest in improved alkanolamine solvents and particularly in aqueous blends of alkanolamines. Design methods for acid-gas-treating processes employing aqueous blends of alkanolamines vary widely in their effectiveness at predicting process performance. Many acid-gas-treating processes are still designed by experience and heuristics, resulting in overdesign, excessive energy consumption, and often failure to meet purity requirements entirely (Chakravarty et al.1). Another common method uses equilibrium stage models modified by tray efficiencies. This method, however, requires the use of existing plant data and lumps all uncertainties about the finite reaction rates of the gases in the solvent into one parameter, the tray efficiency. Such a model cannot be predictive and will not capture the essential interplay of mass transfer, chemical kinetics, and chemical thermodynamics that occur in complex chemical solvents such as aqueous blends of alkanolamines. The third method of design is to develop models based on the chemistry and physics of the process, which accounts for rates of mass transfer coupled with chemical kinetics and thermodynamics. These models, while still requiring some experimental hydrodynamic information specific to different types of contacting devices, are capable of predicting column performance, thus minimizing the costs of design, equipment, and energy consumption.

10.1021/ie990850r CCC: $19.00 © 2000 American Chemical Society Published on Web 09/27/2000

Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4347

The objective of the work presented here is to develop a comprehensive model for the absorption of CO2 into aqueous blends of tertiary and primary or secondary amines. Experiments to test the model using methyldiethanolamine (MDEA) as the tertiary amine and diethanolamine (DEA) as the secondary amine are described.

Reaction Mechanism When CO2 is absorbed into an aqueous solution of a tertiary alkanolamine, R(1)R(2)R(3)N, and a primary or a secondary alkanolamine, R(4)R(5)NH, the following reactions may occur: K1,k1

CO2 + H2O 798 H2CO3

(1)

K2,k2

CO2 + OH- 798 HCO-

(2)

K15

HCO3- + H3O+ 798 H2CO3 + H2O

(15)

K16

2H2O 798 OH- + H3O+

(16)

For MDEA, we have R(1) ) -CH3 and R(2) ) R(3) ) -CH2CH2OH, and for DEA, we have R(4) ) R(5) -CH2CH2OH. Ki, ki, and k-i are the equilibrium constant, the forward rate coefficient, and the reverse rate coefficient for reaction i. Reactions 1-11 are considered to be reversible with finite reaction rates. Whereas reactions 12-16 are considered to be reversible and instantaneous with respect to mass transfer and at equilibrium, since they involve only proton transfers. Note that not all of the reaction equilibrium constants are independent. Only eight equilibrium constants (K2, K4, K5, K12, K13, K14, K15, and K16) are independent. The remaining eight can be obtained by appropriate combinations of the independent equilibrium constants. The interaction between the protonated and unprotonated amines according to the reaction

K3,k3

CO2 + R(1)R(2)R(3)N + H2O 798

K17

R(1)R(2)R(3)NH+ + HCO3- (3) (4)

(5)

K4,k4,k-4

(4)

(5)

+

CO2 + R R NH 798 R R NH COO

-

(4)

K5,k5,k-5

R(4)R(5)NH+COO- + R(4)R(5)NH 798 R(4)R(5)NH2+ + R(4)R(5)NCOO- (5) K6,k6,k-6

R(4)R(5)NH+COO- + R(1)R(2)R(3)N 798 R(1)R(2)R(3)NH+ + R(4)R(5)NCOO- (6) K7,k7,k-7

R(4)R(5)NH+COO- + H2O 798 H3O + R(4)R(5)NCOO- (7) K8,k8,k-8

R(4)R(5)NH+COO- + OH- 798 H2O + R(4)R(5)NCOO- (8) K9,k9,k-9

R(4)R(5)NH+COO- + HCO3- 798 H2CO3 + R(4)R(5)NCOO- (9) K10,k10,k-10

R(4)R(5)NH+COO- + CO32- 798 HCO3- + R(4)R(5)NCOO- (10) K11,k11

R(4)R(5)NCOO- + H2O 798 R(4)R(5)NH + HCO3- (11) K12

R(1)R(2)R(3)NH+ + OH- 798 R(1)R(2)R(3)N + H2O (12) K13

R(4)R(5)NHH2+ + OH- 798 R(4)R(5)NH + H2O (13) K14

HCO3- + OH- 798 CO32- + H2O

(14)

R(4)R(5)NH2+ + R(1)R(2)R(3)N 798 R(4)R(5)NH + R(1)R(2)R(3)NH+ (17) involves only a proton transfer and is considered to be instantaneous and at equilibrium. Reaction 17 is implicitly included in the reaction scheme above, as it can be obtained by properly combining the instantaneous equilibria reactions 12 and 13. Hence, we have K17 ) K13/K12. The proposed mechanism for the reaction between CO2 and tertiary alkanolamines, R(1)R(2)R(3)N, indicates that they do not react directly with CO2. Instead, tertiary alkanolamines act as bases that catalyze the hydration of CO2 (Donaldson and Nguyen,2 Haimour et al.,3 Versteeg and van Swaaij,4 Littel et al.,5 Rinker et al.6). In contrast, the proposed mechanism for the reaction between CO2 and a primary or secondary alkanolamine, R(4)R(5)NH, involves the formation of a zwitterion, R(4)R(5)NH + COO- (see reaction 4), followed by the deprotonation of the zwitterion by a base to produce carbamate, R(4)R(5)NCOO-, and protonated base (see reactions 5-10) (Caplow,7 Danckwerts,8 Blauwhoff et al.,9 Versteeg and van Swaaij,10 Versteeg and Oyevaar,11 Versteeg et al.,12 Glasscock et al.,13 Littel et al.,14 Rinker et al.15). Any base present in the solution might contribute to the deprotonation of the zwitterion. The contribution of each base would depend on its concentration as well as its strength. Hence, the main contribution to the deprotonation of the zwitterion in an aqueous solution of a mixture of a primary or secondary alkanolamine, R(4)R(5)NH, and a tertiary alkanolamine, R(1)R(2)R(3)N, would come from R(4)R(5)NH, R(1)R(2)R(3)N, and to a lesser extent OH- and H2O. There are two limiting cases in the zwitterion mechanism. When the zwitterion formation reaction is rate-limiting, the reaction rate appears to be first-order in both the amine and CO2 concentrations. In the case of monoethanolamine (MEA), a primary alkanolamine, the formation of the zwitterion has been shown to be the rate-determining step (Danckwerts,8 Sada et al.,16 Versteeg and van Swaaij,10 Littel et al.14). On the other hand, when the zwitterion deprotonation reactions are

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rate-limiting, the overall reaction rate appears to be of order 2 in the amine concentration. For the secondary alkanolamines diethanolamine (DEA) and diisopropanolamine (DIPA), the rate-determining step is the deprotonation of the zwitterion (Littel et al.13). Several authors have reported some rate coefficients for this limiting case of the zwitterion mechanism for DEA and DIPA for a few temperatures (Blauwhoff et al.,9 Versteeg and van Swaaij,16 Versteeg and Oyevaar,10 Glasscock et al.,12 Rinker et al.14). Similarly, if neither reaction in the zwitterion mechanism is rate-limiting, the reaction rate exhibits a fractional order between 1 and 2 with respect to the amine concentration. However, the rate expression is more complicated than the limiting cases. Fractional orders are usually only observed for reactions between CO2 and secondary amines (Sada et al.,16 Versteeg and Oyevaar,11 Littel et al.14); however fractional orders have also been observed for sterically hindered primary amines such as 2-amino-2-methylpropanol (AMP) (Bosch et al.,17 Alper18).

All reactions at equilibrium (only independent equilibrium constants) K2 )

u04

K4K5K13K16 ) K12 ) K13 ) K14 )

u07 u010

u02 u08 u06

u2 ) [R(1)R(2)R(3)N] -

+

u4 ) [HCO3 ]

u3 ) [R R R NH ] u5 ) [OH-]

u6 ) [CO32-]

u7 ) [H3O+]

u8 ) [R(4)R(5)NH]

u9 ) [R(4)R(5)NH2+] u11 ) [H2CO3]

u10 ) [R(4)R(5)NCOO-] u12 ) [H2O]

Liquid Bulk Concentrations of All Chemical Species. The liquid bulk concentrations of all chemical species can be estimated from the initial concentrations of R(1)R(2)R(3)N and R(4)R(5)NH; the initial CO2 loading of the solution, L1; and the assumption that all reactions are at equilibrium. Because the concentration of water is much larger than the concentrations of all other chemical species, changes to its concentration over very short contact times are negligible, and we assume that its concentration remains constant. Hence, we only need to solve for the concentrations of the remaining 11 chemical species. We have the following equations for 0 the liquid bulk concentrations u01, ... , u11 :

u011

+

u03

(1)

(2)

(3)

)[R R R N]initial

R1 ) -k1u1 +

(18)

(19)

R3 ) -k3u1u5 +

u01 + u04 + u06 + u010 + u011 + L1{[R(1)R(2)R(3)N]initial +

R4,...,10 )

[R R NH]initial} (20) (5)

Electroneutrality balance u03 + u07 + u09 - u04 - u05 - 2u06 - u010 ) 0

(21)

k1 u K1 11

where

(29)

k2 u K2 4

(30)

k3 uu K3 3 4

(31)

R2 ) -k2u1u5 +

Overall carbon (from CO2) balance (4)

(28)

0 ) and 11 nonlinear We have 11 unknowns (u01, ... , u11 algebraic equations that we can solve for the liquid bulk concentrations. We have found that Newton’s method did not converge unless the initial guesses for the liquid bulk concentrations were very close to the (unknown) solution. We, therefore, used the Newton homotopy continuation method (Hanna and Sandall19), which exhibited better convergence behavior. The Partial Differential and Nonlinear Algebraic Equations That Describe the Diffusion/ Reaction Processes. Higbie’s penetration model (Higbie,20 Danckwerts21) was used to set up the diffusion/ reaction partial differential equations that describe the absorption/desorption of CO2 into/from aqueous solutions of tertiary amines, R(1)R(2)R(3)N, and primary or secondary amines, R(4)R(5)NH, in a laminar-liquid-jet absorber or a stirred-cell absorber. All reactions were treated as reversible reactions. The first 11 reactions have finite reaction rates, which are given by the following reaction rate expressions, where Ri is the reaction rate expression for reaction i:

Overall primary or secondary amine, R(4)R(5)NH, balance u08 + u09 + u010 )[R(4)R(5)NH]initial

(27)

u04 u07

Overall tertiary amine, R(1)R(2)R(3)N, balance u02

(26)

u04 u05

K16 ) u05 u07

(3)

(25)

u09 u05

For convenience, the concentrations of the chemical species are renamed as follows:

(2)

(24)

u03 u05

K15 )

(1)

(23)

u01 u08

Mathematical Model

u1 ) [CO2]

(22)

u01 u05

[

-k4 u1u8 1+

1 B

(BA)u ] 10

(32)


( )

A)

( ) ( ) ( ) ( ) ( )

k5 u 9 + k-4 K4K5 k8 k-4

k6 u3 + k-4 K4K6 u12 k9 + K4K8 k-4

k7 u7 + k-4 K4K7 u11 k10 u4 + (33) K4K9 k-4 K4K10

and

B)

( ) ( ) ( ) ( ) ( ) ( )

k5 k6 k7 k8 u + u + u + u + k-4 8 k-4 2 k-4 12 k-4 5 k9 k10 u + u (34) k-4 4 k-4 6 R11 ) -k11u10 +

k11 uu K11 4 8

(35)

Note that eq 32 was derived with the assumption of a pseudo-steady-state approximation for the zwitterion reaction intermediate, R(4)R(5)NH+COO-. The partial differential equations that describe the diffusion/reaction processes were combined so as to eliminate the very large reaction rates for the instantaneous reactions 1216. Because these reactions are assumed to be at equilibrium, their equilibrium constant expressions were used to complete the equations that are required to solve for the concentration profiles of all chemical species. Furthermore, the diffusion coefficients of the ionic species were assumed to be equal. With this assumption, the electrostatic potential gradient terms in the diffusion/reaction partial differential equations for the ionic species can be neglected, while the electroneutrality of the solution is preserved. The more rigorous approach of taking into account the electrostatic potential gradient terms with unequal diffusion coefficients for the ionic species requires much greater computational effort with essentially intangible effects on the predicted rates of absorption. The following equations describe the diffusion/reaction processes:

∂u10 ∂2u10 ) D10 2 + R11 - R4,...10 ∂t ∂x

(41)

Instantaneous reactions assumed to be at equilibrium

K12 )

u2 u3u5

(42)

K13 )

u8 u9u5

(43)

K14 )

u6 u4u5

(44)

K15 )

u11 u4u7

(45)

K16 ) u5u7

(46)

We have 11 partial differential/algebraic equations that we can solve for the concentrations of the 11 chemical species, u1, ... , u11. Initial Condition and Boundary Condition at x ) ∞. At t ) 0 (for all x ) 0) and at x ) 8 (for all t ) 0), the concentrations of all chemical species are equal to their liquid bulk concentrations.

ui ) u0i , i ) 1, ... , 11

∂ui ) 0 at x ) 0, t > 0 ∂x

∂2u1 ∂2u4 ∂u1∂u4 ∂u6 ∂u10 ∂u11 + + + ) D1 2 + D4 2 + ∂t ∂t ∂t ∂t ∂t ∂x ∂x ∂2u6 ∂2u10 ∂2u11 D6 2 + D10 2 + D11 2 (37) ∂x ∂x ∂x Total tertiary amine, R(1)R(2)R(3)N, balance (38)

Total primary or secondary amine, R(4)R(5)N, balance ∂u8 ∂u9 ∂u10 ∂2u8 ∂2 u 9 ∂2u10 + + ) D8 2 + D9 2 + D10 2 ∂t ∂t ∂t ∂x ∂x ∂x

Carbamate, R(4)R(5)NCOO-, balance

(47)

(36)

Total carbon (from CO2) balance

∂u2 ∂u3 ∂2 u 2 ∂2 u 3 + ) D2 2 + D 3 2 ∂t ∂t ∂x ∂x

∂u3 ∂u7 ∂u9 ∂u4 ∂u5 ∂u6 ∂u10 + + -2 ) ∂t ∂t ∂t ∂t ∂t ∂t ∂t ∂2u3 ∂2u7 ∂2 u 9 ∂2 u 4 ∂2u5 D3 2 + D7 2 + D9 2 - D4 2 - D5 2 ∂x ∂x ∂x ∂x ∂x 2 2 ∂ u6 ∂ u10 2D6 2 - D10 2 (40) ∂x ∂x

Boundary Condition at Gas-Liquid Interface (x ) 0). At x ) 0 (gas-liquid interface), the fluxes of the nonvolatile chemical species are equal to zero, which leads to the following equations:

CO2 balance ∂2u1 ∂u1 ) D1 2 + R1 + R2 + R3 + R4,...10 ∂t ∂x

Electroneutrality balance

(39)

(48)

for all i except i ) 1 (CO2). For the volatile component, CO2, the mass transfer rate in the gas near the interface is equal to the mass transfer rate in the liquid near the interface.

∂u1 ) kg,1[P1 - H1u1(0,t)] at x ) 0, t > 0 -D1 ∂x

(49)

H1 is the physical equilibrium constant (Henry’s law constant) of CO2, which is defined as the interfacial partial pressure of CO2 in the gas phase, P/1, divided by the interfacial concentration of CO2 in the liquid, u/1. For the case of pure CO2 in the gas phase, the interfacial partial pressure of CO2, P/1, is the same as the bulk partial pressure of CO2, P1, and there is not any mass transfer resistance in the gas-phase (kg,1 f ∞). Hence,

4350


the boundary condition for CO2 at the gas-liquid interface reduces to

u1(0,t) ) u/1 )

P1 at x ) 0, t > 0 H1

πd2l 4Q

x

D1 πτ

D1 τ

∫0τ

∂u1 (0,t) dt ∂x

(52)

RA1 0 kl,1 (u/1- u01)

Table 1 gives the values of the equilibrium constants used in the model calculations, with the exception of K15. The value of K15 at 298 K was taken to be 2 × 10-4 m3/kmol (Cotton and Wilkinson31). K15 was then corrected for temperature dependence according to the following equation:

[

K15(T)

K15(298.15)

]

)

(

1 -∆H0 1 R T 298.15

)

(57)

where the standard enthalpy change of reaction, ∆H0, is assumed to be independent of T and is approximated 0 (Smith and Van by its value at 298.15 K, ∆H298.15 0 Ness32). ∆H298.15 values were calculated from values reported in the CRC Handbook of Chemistry and Physics (Lide33). Experimental Apparatus and Procedure

(53)

The enhancement factor of CO2 is determined according to the following equation:

E1 )

(56)

ln

The average rate of absorption of CO2 per unit interfacial area is then computed from the following equation:

RA1 ) -

2895 T

log10(k2) ) 13.635 -

(51)

where Q is the volumetric liquid flow rate, and d and l are the diameter and length of the laminar-liquid jet, respectively. For Higbie’s penetration model, the liquidphase mass transfer coefficient for physical absorption of CO2 is defined as 0 )2 kl,1

17265.4 (55) T

(50)

The differential equations are integrated from t ) 0 to t ) τ, the contact time. For the laminar-liquid-jet absorber, the contact time is given by

τ)

log10(k1) ) 329.85 - 110.54 log10(T) -

(54)

where u/1 and u01 are the interfacial and bulk concentrations of CO2 in the liquid, respectively. Method of Solution for the Partial Differential/ Algebraic Equations. The method of lines was used to transform each partial differential equation into a system of ordinary differential equations in t (Hanna and Sandall19). The systems of partial differential/ algebraic equations were transformed into larger systems of ordinary differential/algebraic equations, which were then solved by using the code DDASSL (Petzold22) in double-precision Fortran on an HP-735 computer. Model Parameters The nitrous oxide analogy method was used to estimate the CO2 solubility (Rinker and Sandall23) and the CO2 diffusivity (Ashour et al.24) in the aqueous amine solutions. The kinetics for CO2/MDEA were measured by Rinker et al.,6 and the kinetics for the CO2/DEA reaction were determined by Rinker et al.15 The diffusion coefficients of MDEA and DEA were estimated from the diffusivity data of Hikita et al.25 We include here correlations that were used to estimate various other reaction rate coefficients and equilibrium constants that were obtained from the literature. Values for the forward rate coefficient of reactions 1 and 2, k1 and k2, respectively, were calculated from the following correlations, which were reported by Pinsent et al.26 for the temperature ranges of 273-311 K and 273-313 K, respectively:

The rates of absorption of CO2 into aqueous solutions of DEA and MDEA were measured in a laminar-liquidjet absorber and a stirred-cell absorber. A schematic drawing of the laminar-liquid-jet absorber is shown in Figure 1. The laminar-liquid-jet absorber and its operation are described in detail by Rinker et al.15 The stirredcell absorber is shown schematically in Figure 2. The absorption chamber is made of a 30.5 cm long, 10.1 cm i.d. Pyrex cylinder and is enclosed in a constanttemperature heating jacket constructed from a 31 cm long, 24 cm i.d. Lucite cylinder. The ends of the Lucite cylinder are sealed with rubber O-rings between two anodized aluminum flanges, and the glass cylinder is sandwiched between two stainless steel flanges with the ends sealed by Teflon gaskets. Cooling or heating water is supplied to the jacket and recycled to a constanttemperature circulating bath. Two separate stainless steel coils are placed in the heating/cooling jacket and are used to control the temperatures of the liquid and gas feeds. The liquid supply is introduced into the chamber by a 0.635 cm o.d. stainless steel tube that can slide in the vertical direction through the bottom flange and can be locked in position by a Swagelok nut with Teflon ferrules. The end of this tube is plugged, and the liquid is discharged into the absorption chamber from perforations on the side of the tube near the plugged end. This assembly makes it possible to discharge the liquid at different heights if so desired. The absorption chamber is also equipped with four flat stainless steel baffles, which help in reducing vortex formation and promoting better mixing of the liquid phase. The baffles are 12.7 cm long, 1.0 cm wide, and 0.1 cm thick and are pinned to the bottom flange, and their top ends are connected by a wire ring. The distance between the baffles and the glass wall of the chamber is about 0.35 cm. When the liquid height in the chamber is 11.0 cm, the baffles extend about 1.7 cm above the liquid surface. The absorber has two concentric shafts that protrude into the chamber through the top flange. The inner shaft is 0.6 cm in diameter and 36.5 cm long and is made of stainless steel. This shaft extends to a Teflon bushing in the bottom flange and is supported at the top end by a pin bearing held in a cup on a crossbar. There are


Figure 1. Schematic drawing of the laminar-liquid-jet absorber. Table 1. Equilibrium Constant Correlations Used for Model Calculations equilibrium constant

temp range (K)

equation

reference

293-573

Olofsson and Hepler27

273-523

Read28

K14K16

log10(K16) ) 8909.483 - 142613.6/T -4229195 log10(T) + 9.7384 T -0.012 963 8T2 + (1.150 68 × 10-5)T3 -(4.602 × 10-9)T4 log10(K2K16) ) 179.648 + 0.019 244T -67.341 log10(T) - 7 495.441/T log10(K14K16) ) 6.498 - 0.023 8T - 2 902.4/T

273-323

K4K5K13K16 K13K16 K12K16

log10(K4K5K13K16) ) -10.549 2 + 1 526.27/T log10(K13K16) ) -4.030 2 - 1 830.15/T + 0.0043T log (K12K16) ) -14.01 + 0.018T

298-333 298-333 298-333

Danckwerts and Sharma29 Barth et al.30 Barth et al.30 Barth et al.30

K16

K2K16

two liquid-phase impellers mounted on the shaft, one with a diameter of 7.5 cm mounted at a height of 8.0 cm from the bottom flange, and another with a diameter of 6.0 cm mounted at a height of 3.0 cm from the bottom flange. The second shaft, which is a hollow stainless steel tube 20.0 cm long with a 1.1 cm i.d., is supported by a concentric tubular extension welded onto the top flange and extends 10.0 cm into the chamber. Mounted on the second shaft are two impellers for stirring the gas phase, a 7.5 cm diameter impeller at 10.5 cm from the top flange, and a 9.5 cm diameter impeller at 17.5 cm from the top flange. When the liquid height in the chamber is 11.0 cm, the bottom edge of the second gas impeller is 2.0 cm away from the gas-liquid interface. Two sets of ball bearings, Teflon packings, and springloaded Teflon seals support the tubular shaft. Two similar assemblies support the liquid shaft. The two shafts are driven independently by two variable-speed motors. The liquid feed is pumped to a surge tank and then through a calibrated rotameter and through a stainless steel coil in the constant-temperature jacket. It is then

introduced into the absorption chamber through the bottom flange and is discharged into the chamber by seven perforations about 8 cm from the bottom of the chamber. The liquid leaves the chamber through the bottom flange and goes to a liquid-leveling reservoir. The leveling device is similar to that used in the laminar-liquid-jet absorber. The gases pass through two sets of regulators (high and low pressure) and then through mass flow controllers in order to maintain constant gas feed rates. The gases subsequently pass through soap bubble meters so that their volumetric flowrates can be measured. The gases are next mixed in a T-fitting and fed to a saturator. After the saturator, the overall gas flow rate is measured with a bubble meter. The temperature of the gas mixture is measured and recorded at this point with a type-J thermocouple. The gas mixture then passes through the stainless steel heating/cooling coil in the constant-temperature jacket before being introduced into the absorption chamber through the tube in the top flange. The gas mixture is sampled just before it enters the absorption chamber and is analyzed with

4352


Figure 2. Schematic drawing of stirred-cell absorber.

a gas chromatograph. The gas is discharged just above the larger impeller through perforations near the end of the feed tube. The gas exits the chamber through a fitting in the top flange and is sampled for composition by a gas chromatograph. The volumetric flow rate of the exit gas is measured with a soap bubble meter and the temperature of the exit gas is measured with a type-J thermocouple. The gas samples were analyzed using a model 5890 Hewlett-Packard gas chromatograph equipped with a thermal conductivity detector. The column used in the GC was a 6 ft. long, 0.085 in. i.d., stainless steel column packed with Poropak Q with a mesh size of 80/100. The run conditions were 70 °C for 1.5 min, ramp to 90 °C at 5 °C per minute, cool, and equilibrate for 2 min. Experimental Results (A) Absorption Measurements at Short Contact Times Using a Laminar-Liquid-Jet Absorber. According to the zwitterion mechanism, any base can contribute to the deprotonation of the zwitterion. For the aqueous DEA case, the potential bases are R2NH, OH-, H2O, HCO, and CO. In an earlier study (Rinker et al.15), the contributions of OH-, H2O, HCO, and CO to the deprotonation of the zwitterion were found to be insignificant for the reaction of CO2 with aqueous DEA in the laminar-liquid-jet absorber. However, if CO2 is absorbed into aqueous blends of DEA and MDEA, it is possible that MDEA could contribute significantly to the

Table 2. CO2 Absorption Data in 10 wt % Blends of DEA and MDEA Obtained in the Laminar-Liquid-Jet Absorber at 25 °C [MDEA] (kmol/m3)

[DEA] (kmol/m3)

RCO2 × 105 measured (kmol/m2s)

RCO2 × 105 predicted (kmol/m2s)

0.844 0.808 0.692 0.586 0.532 0.232 0

0 0.040 0.173 0.293 0.355 0.696 0.959

1.22 1.29 1.45 1.65 1.71 2.40 3.28

1.22 1.35 1.44 1.65 1.76 2.69 3.32

deprotonation of the zwitterion. Littel et al.14 report that MDEA makes a measurable contribution to the deprotonation of the zwitterion for CO2 absorption into aqueous blends of DEA and MDEA. To test the hypothesis that MDEA contributes to the deprotonation of the zwitterion, the rates of CO2 absorption into aqueous blends of DEA and MDEA were measured in the laminar-liquid-jet absorber at 25 °C. The total weight percents of the aqueous DEA/MDEA blends were 10, 30, and 50 wt %, and the molar ratios of DEA to MDEA were varied from zero to infinity. The absorption data are listed in Tables 2-4. The rates of CO2 absorption were predicted using the numerical model developed in this work without taking into account the contribution of MDEA to the deprotonation of the zwitterion. The predicted and measured rates of CO2 absorption are compared in the parity plot shown

Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4353 Table 3. CO2 Absorption Data in 30 wt % Blends of DEA and MDEA Obtained in the Laminar-Liquid-Jet Absorber at 25 °C [MDEA] (kmol/m3)

[DEA] (kmol/m3)



2.581 2.118 1.376 0.712 0 2.581 2.118 1.376 0.712 0

0 0.529 1.376 2.135 2.947 0 0.529 1.376 2.135 2.947

1.12 1.97 3.08 3.77 4.86 1.06 1.73 3.06 3.72 4.65

0.870 1.49 2.83 3.80 4.75 0.850 1.51 2.82 3.80 4.71

Table 4. CO2 Absorption Data in 50 wt % Blends of DEA and MDEA Obtained in the Laminar-Liquid-Jet Absorber at 25 °C [MDEA] (kmol/m3)

[DEA] (kmol/m3)



4.217 4.217 3.722 3.719 3.722 3.034 3.034

0.202 0.202 0.772 0.771 0.772 1.517 1.517

0.753 0.868 1.10 1.15 1.09 1.67 1.50

0.692 0.783 1.11 1.12 1.09 1.72 1.74

in Figure 3. From this plot, it is clear that there is good agreement between the measured rates of CO2 absorption and the rates of CO2 absorption predicted by the model neglecting the contribution of MDEA to the deprotonation of the zwitterion. The average deviation of the predicted rates from the measured rates is 6.8%. On the basis of these experiments, it appears that MDEA does not significantly contribute to the deprotonation of the zwitterion. A possible explanation for the difference in the results of this study and the work of Littel et al.14 is that we used a laminar-liquid-jet absorber whereas they used a batch stirred-tank reactor. The laminar-jet absorber operates at steady state, with a gas-liquid contact time of about 0.005 s, whereas the reactor used by Littel et al. operates under transient conditions and over much longer gas-liquid contact times. For very short contact times, the deprotonation reaction with MDEA may not have time to contribute significantly to the overall rate of absorption. (B) Absorption Measurements at Long Contact Times Using a Stirred-Cell Absorber. To predict rates of CO2 absorption obtained using the stirred-cell apparatus, accurate values of the liquid-phase mass transfer coefficient for physical absorption must be determined from experimental absorption data obtained for a model system. The liquid-phase physical mass transfer coefficient was determined by measuring the concentration of dissolved CO2 in the liquid effluent from the stirred-cell absorber using wet-chemical analysis. The liquids used for these experiments were pure deionized water and pure poly(ethylene glycol) (PEG400). The gas phase was pure CO2 saturated with the vapor pressure of the liquid. The liquid feedstocks were degassed at elevated temperatures. The concentration of CO2 dissolved in the liquid was determined by titration of samples of effluent. The water samples were drawn slowly into a syringe and injected into an equal volume of 0.05 M NaOH to convert all of the dissolved

Figure 3. Comparison of predicted and measured rates of CO2 absorption into aqueous blends of DEA and MDEA at 25 °C in the laminar-liquid-jet absorber. The total amine concentrations were 10, 30, and 50 mass %.

CO2 into carbonate. The carbonate was precipitated with barium chloride, and the remaining NaOH was titrated with 0.05 M HCl. This method was reproducible to within 1%, and it was accurate enough to measure the small rates of CO2 absorption over liquid stirring speeds of 30-140 rpm. For the pure PEG400 experiments, the samples were injected into twice their volume of 0.05 M NaOH in order to convert the CO2 to carbonate and dilute the PEG400 so that the samples were mostly water (on a molar basis) for accurate pH determination. Pure PEG400 was used to check the viscosity dependence of the mass transfer coefficient as it has a viscosity of 0.9527 P at 25 °C and water has a viscosity of 0.00895 P at 25 °C. The physical mass transfer coefficients were calculated from the measured data using the following equations:

RA1 ) k°l,1(C/A- CA0) RA1 )

(58)

C0A L As

(59)

where C/A is the interfacial concentration of CO2, C0A is the bulk or effluent concentration of CO2, L is the volumetric liquid flowrate, As is the area of the gasliquid interface (79.64 cm2), and k is the physical liquidphase mass transfer coefficient. The mass transfer coefficients were correlated in dimensionless form as follows:

Sh ) 0.0193Re0.845Sc0.5

(60)

where

Sh )

k°l,1da DA

Re )

FNLdi2 µ

Sc )

µ FDA

(61)

The dimensionless mass transfer coefficients used to obtain the correlation given above are plotted in Figure 4. (i) CO2 Absorption into Aqueous MDEA. Rates of CO2 absorption into aqueous solutions of MDEA were measured in the stirred-cell absorber at 25 °C. The CO2 partial pressure was varied from 0.15 to 0.5 atm, and the diluent was N2. The measured absorption rates are

4354


Figure 4. Liquid-phase physical absorption mass transfer coefficient correlation.

Figure 5. Comparison of predicted and measured rates of CO2 absorption into aqueous MDEA at 25 °C in the stirred-cell absorber.

Figure 7. Comparison of predicted and measured rates of CO2 absorption into aqueous 50 mass % blends of DEA and MDEA at 25 °C in the stirred-cell absorber.

with an average deviation of 10.2% from the measured rates. (iii) Absorption of CO2 into Aqueous Blends of DEA and MDEA. Rates of absorption of CO2 into aqueous blends of DEA and MDEA were measured in the stirredcell absorber at 25 °C. The total amine concentration was approximately 50 wt %, and the molar ratios of DEA to MDEA were 0.050, 0.207, 0.250, and 0.500. The model predictions are compared to the measured absorption rates in Figure 7. The average deviation of the predictions from the measured rates of absorption is 17.6%. The predicted rates of absorption were made by neglecting the contribution of MDEA to the deprotonation of the zwitterion. Some of the absorption rates are overpredicted and some are underpredicted when the MDEA contribution is neglected. As a result, the CO2 absorption data obtained in the stirred-cell absorber support the findings for CO2 absorption into blends in the laminar-liquid-jet absorber that MDEA does not significantly contribute to the deprotonation of the zwitterion. Conclusions

Figure 6. Comparison of predicted and measured rates of CO2 absorption into aqueous DEA at 25 °C in the stirred-cell absorber.

compared to the model predictions in the parity plot shown in Figure 5. The average deviation of the model predictions from the measured rates is 24%. (ii) CO2 Absorption into Aqueous DEA. Rates of CO2 absorption into 10 wt % aqueous DEA were measured in the stirred-cell absorber at 25 °C. The CO2 partial pressure was varied from 0.088 to 0.712 atm, and the diluent was N2. The measured and predicted rates of CO2 absorption are compared in the parity plot shown in Figure 6. In this case, there is fairly good agreement between the model predictions and the measurements,

The model developed in this work for the rates of absorption of carbon dioxide into a aqueous mixed amine solutions was found to agree reasonably well with the experiments. The reaction between carbon dioxide and the secondary amine, DEA, was described by the zwitterion mechanism in this model. For our experiments with gas-liquid contact times varying from approximately 0.005 to 10 s, it appears that the tertiary amine, MDEA, does not contribute significantly to the deprotation of the zwitterion. The only species that contributes significantly to the deprotonation of the zwitterion is DEA, and thus, eqs 6-10 in the reaction model could be deleted according to the results obtained in this study. The key physicochemical property needed for the model calculations is the physical solubility of CO2. Any uncertainty in this property translates to an equivalent error in the predicted absorption rate. Acknowledgment This work was sponsored by the Gas Research Institute and the Gas Processors Association.


Notation As ) gas-liquid interface area, m2 CA ) diameter of the laminar-liquid jet, m Di ) coefficient of species i in the aqueous alkanolamine solution, m2/s DEA ) diethanolamine DIPA ) diisopropanolamine E1 ) factor of CO2, defined by eq 54 h0 ) spacing next to the gas-liquid interface for the discretized spatial variable x, m H1 ) physical equilibrium constant (Henry’s law constant) for CO2, H1 ) P/1/u/1, (kPa m3)/kmol kapp ) rate coefficient for the reaction between CO2 and a secondary or a primary alkanolamine, defined by eq 70, m3/(kmol s) kg,1 ) gas-phase mass transfer coefficient for CO2, kmol/ (kPa m2 s) k0l,1 ) mass transfer coefficient for CO2 in the liquid phase, defined by equation (52), m/s ki ) rate coefficient of reaction i, s-1 for first-order reactions, m3/(kmol s) for second-order reactions k-i ) rate coefficient of reaction i Ki ) constant for reaction i l ) length of the laminar-liquid jet, m L1 ) CO2 loading of the aqueous amine solution, (kmol CO2)/(kmol amine) MDEA ) N-methyldiethanolamine MEA ) monoethanolamine NL ) impeller speed, rev/s P1 ) pressure of CO2 in the gas phase, kPa P/1) partial pressure of CO2 in the gas phase, kPa Q ) volumetric flow rate of the liquid, m3/s Ri ) reaction rate of reaction i, kmol/(m3 s) RA1 ) rate of absorption of CO2 per unit interfacial area, defined by equation (53), kmol/(m2 s) Re ) Reynolds number defined by eq 80 Sc ) Schmidt number defined by eq 80 Sh ) Sherwood number defined by eq 80 t ) independent time variable, s T ) absolute temperature, K ui ) concentration of species i in the liquid phase (which is a function of x and t), kmol/m3 0 ui ) liquid bulk concentration of s pecies i (which is a constant), kmol/m3 u/1 ) interfacial concentration of CO2 in the liquid, kmol/ m3 x ) independent spatial variable, m Greek letters µ ) viscosity of the aqueous alkanolamine solution, kg/(m s) F ) density of the aqueous alkanolamine solution, kg/m3 τ ) gas-liquid contact time, defined by eq 51 for a laminarliquid-jet absorber, s

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Received for review November 22, 1999 Revised manuscript received July 17, 2000 Accepted July 20, 2000 IE990850R

Absorption of Carbon Dioxide into Aqueous Blends of Diethanolamine

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