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KINETICS, CATALYSIS, AND REACTION ENGINEERING Kinetic Study of Carbonyl Sulfide (COS) Absorption by Methyldiethanolamine Aqueous Solutions from 415 mol/m3 to 4250 mol/m3 and 313 K to 353 K Rodrigo Rivera-Tinoco and Chakib Bouallou* Centre EÄ nerge´ tique et Proce´ de´ s (CEP) Ecole des Mines de Paris; 60 BouleVard Saint Michel, 75006 Paris, France
In this work, we present the rigorous modeling of carbonyl sulfide (COS) absorption by N-methyldiethanolamine (MDEA) aqueous solutions, taking into account the experimental data of our previous works, for an extended temperature range of 313-353 K and an amine concentration range of 415-4250 mol/m3. We intend to clarify the discrepancies on the kinetic data and the validation of new kinetic data for the extended temperature range. The modeling of COS absorption data is based on the COS mass transfer and chemical reaction at the liquid/gas interface, considering Henry’s law and the zwitterion mechanism. Reaction rate constants were estimated using a Downhill simplex optimization procedure. The enhancement factor was estimated as a function of temperature and amine concentration. The water dissociation rate was assumed to be negligible. In this work, the determined values for the reaction rate constants allow a satisfactory concordance between experimental and modeled data for the entire temperature range and validate the few data reported previously for low temperatures. Introduction The removal of acid and sulfur compound gases prevents equipment damage and catalyst empoisoning in several processes, such as methane reforming and oil refining. Furthermore, the increasingly strict regulations regarding the emission of this type of gas demands technical improvements in the processes used to remove them. The technical development of the removal of these gases is dependent directly on scientific progress. Therefore, in this work, we present the modeling of carbonyl sulfide (COS) absorption, using N-methyldiethanolamine (MDEA) aqueous solutions, to extend the current COS absorption kinetic data and clarify the discrepancies found between them. Experimental data for COS absorption were obtained from the experiments performed by Amararene and Bouallou1 in a thermoregulated, constant-interfacial-area Lewis-type cell, operated batchwise, with respect to both gas and liquid phases. Our modeling work is based on the zwitterion reaction mechanism proposed by Littel et al.2 However, the enhancement factor (E ) was considered as a system variable and it was modeled as a function of temperature and amine concentration. Literature Early works on COS absorption can be found in the literature. Philipp and Dautzenberg3 and Donaldson and Nguyen4 studied the hydrolysis of COS in water and the COS analogies with CO2 chemical absorption, respectively. However, a reaction mechanism that described the COS absorption was not proposed until the work by Al-Ghawas et al.,5,6 which included the estimation of physicochemical properties for COS-MDEA * To whom correspondence should be addressed. Tel.: (+33) 1-40519111. Fax: (+33) 1-46342491. E-mail address: chakib.
[email protected].
absorption, at temperatures in the range of 288.15-313.15 K and MDEA concentrations up to a weight fraction of 0.3. The work reported by Al-Ghawas et al.5,6 showed that the reaction rate of COS absorption was slower than that of CO2 absorption. Afterward, the COS absorption by MDEA aqueous solutions, using a stirred reactor, under saturated bulk conditions, was studied by Littel et al.2,7 In their works, the pressure profile of the COS absorption was modeled using a zwitterion reaction mechanism in two steps, improving the Al-Ghawas5 model, which was based on a one-step zwitterion mechanism. The reaction rate constants of the two-step zwitterion mechanism were estimated through the solution of a differential equation system for amine and COS chemical species. As in the work by Littel et al.,2 we considered the water reaction with MDEA to be negligible. Ulteriorly, Amararene and Bouallou1 experimentally measured the rates for COS absorption by MDEA aqueous solutions in a temperature range of 313-353 K and alkanolamine concentrations in the range of 415-4250 mol/ m3. A Lewis cell with a constant interfacial surface area was used to measure the COS mass transfer. They considered the absorbed COS in the liquid phase to modify the amine concentration negligibly; therefore, a constant value for the amine concentration could be set. They do not present the reaction rate constants in their work. However, they do reveal that a rigorous model that considers the chemical reactions could validate the reaction mechanism that is proposed. For other COS absorption systems, we determined that the MDEA and diethanolamine (DEA) absorptions were studied by Cadours et al.,8 considering a two-step zwitterion mechanism to model the COS absorption. Furthermore, Lammers et al.9 modeled the COS absorption using MDEA-polyhydroxyalcohol solutions, considering the same zwitterion mechanism, and they conceived an outstanding industrial application in a natural gas sweetening plant. Taking into account that the zwitterion
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reaction mechanism has been validated by several authors, we decided to apply it to model the COS-MDEA absorption for temperature and amine concentration ranges that previously have not been published. The properties of different chemical species were estimated using different correlations. Based on the work of Hsu and Li,10,11 we estimated the density and viscosity of MDEA aqueous solutions, and, based on the work by Pani et al.,12 the diffusivity coefficients were estimated. Henry constants for COS were estimated in analogy with N2O behavior, based on the works of Wang et al.13 and Sandall.14 Moreover, the diffusivity coefficient of N2O was estimated in a manner similar to that described in the works of Versteeg and Swaaij15 and Tsai et al.16 The experimental data studied in this work were collected from Amararene and Bouallou.1 In their work, pure COS was introduced during a very short time in the upper part of the stirred Lewis cell, which is noted as Vg; the pressure must not exceed 2.5 × 105 Pa. The data then were collected as pressuretime values until the system reached equilibrium. The estimated maximum experimental error in their COS absorption data was 8%. The MDEA was supplied by Fluka, with a certified minimum mass purity of 98%. COS was supplied by Air Liquide, with a certified volume purity of 99.997%. The aqueous solutions used doubly distilled water.
where
β)
kLEaRT VgHCOS
(5)
presents a linear behavior of global absorption, in which the initial COS pressure data PT,0 (at t0) are included. The mass-transfer coefficient kL was calculated using the Sherwood, Reynolds, and Schmidt correlations. We estimated an initial value of the enhancement factor E, using the experimental data set and a β value, as shown in eq 6.
E)
βVgHCOS aRT
(6)
The reaction mechanism proposed by Littel et al.2 involves four chemical reactions, the reactions rates of which are expressed as R1,1, R2,1, R2,1, and R2,2. They are represented as a chemical balance in eqs 7 and 8. k1,1
COS + MDEA + H2O 79 8 MDEAH+ + HCO2Sk k2,1
MDEA + HCO2S- + H2O 79 8 MDEAH+ + HCO3- + k 2,2
HS- (8)
Results and Discussion The COS concentration at the interface, which participates in all chemical reactions, defines the COS absorption rate, as shown in the following equation:
dCCOS,g kLECCOS,inta )Vg dt
PCOS - CCOS,L CCOS,int ) HCOS
Taking into account the differential equations of COS presented by Littel et al.2 and the mass-transfer equations (eqs 4 and 5) of this work, we propose the following differential equations for the COS gas and liquid concentrations:
[
As assumed in the work by Amararene and Bouallou,1 the COS-amine reaction negligibly modifies the amine bulk concentration. Therefore, we are able to consider that kL, HCOS, and E become constant values over time, according to the works of Littel et al.2,7 Thus, the integration of eq 1, as shown in eqs 4 and 5,
(
)
P T - PI ) -β(t - t0) PT,0 - PI
(4)
]
(9)
The diffusion of ionic molecules and parallel reactions between amine and water were neglected; thus, the differential equations for the other chemical species were the same as those proposed by Littel et al.2
dCMDEA ) -R1,1 + R1,2 - R2,1 + R2,2 dt
(2)
(3)
]
PCOS dCCOS,L 1 - CCOS,L - R1,1 + R1,2 (10) ) kLaE dt HCOS Vg
dCCHCO2S-
(11)
) R1,1 - R1,2 - R2,1 + R2,2
(12)
dCMDEAH+ ) R1,1 - R1,2 + R2,1 - R2,2 dt
(13)
dCHCO- dCHS) ) R2,1 - R2,2 dt dt
(14)
R1,1 ) k1,1CCOS,LCMDEA
(15)
R1,2 ) k1,2CHCO2S-CMDEAH+
(16)
R2,1 ) k2,1CHCO2S-CMDEA
(17)
R2,2 ) k2,2CHCO3-CHS-CMDEAH+
(18)
dt
The initial value of the COS concentration in the liquid phase assumed that, at t ) 0, there is no dissolved COS. Ulteriorly, at t ) ∞, the COS consumption by chemical reaction reaches the equilibrium of the system. At any time, PCOS could be estimated from the total pressure (PT) and inert pressure (PI) values:
PCOS ) PT - PI
[
PCOS VL dCCOS,g ) -kLaE - CCOS,L 2 dt HCOS Vg
(1)
The variables of eq 1 are the enhancement factor (E), the masstransfer coefficient (kL), and the gas volume in the cell (Vg). The interface presents a surface of area a in which vapor-liquid equilibrium is assumed. The COS gas concentration was estimated assuming ideal behavior of the gas phase. The COS concentration at the interface (CCOS,int) is composed of the partial pressure (PCOS) values, the Henry’s coefficient for COS (HCOS), and the concentration of unreacted COS dissolved in the bulk liquid phase (CCOS,L), as shown in eq 2:
ln
(7)
1,2
with
The differential equations were solved using a fourth-order Runge-Kutta procedure. The optimum values for the reaction
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Figure 1. Estimated reaction rate constants versus the inverse experimental temperature (1/T) for COS absorption by MDEA aqueous solutions. Table 1. Experimental Parameters of COS Absorption by MDEA Aqueous Solutions. temperature, T (K)
CMDEA (mol m-3)
Vg (× 10-6 m3)
PT,0
HCOS (Pa m3/mol)
313.98 313.80 313.90 313.84 314.09 323.66 323.60 323.83 333.57 333.46 333.54
1264.41 2126.23 2126.13 3435.33 4324.79 416.15 2115.89 4267.71 1252.37 2104.24 2104.14
184.10 180.53 183.99 184.01 183.27 183.62 183.54 183.79 182.13 181.99 182.57
143328 147015 120975 184193 194490 127841 125522 191105 132116 135401 128422
7331.39 7563.72 7580.68 7929.40 7984.39 9149.02 9356.54 9572.25 11398.62 11440.29 11458.40
rate constant modeling for COS absorption were estimated using a Downhill Simplex multivariable method, minimizing the difference between COS experimental and modeled pressure data, as represented in eq 19.
Figure 2. Modeling of COS absorption at 313.98 K and CMDEA ) 1264.41 mol/m3 using the enhancement factor (E) estimated with eq 6.
quite similar to those presented in the work by Littel et al.,2 which were 10896 K and 6891 K. Nevertheless, we observed that the data modeling using the enhancement factor E, estimated using eq 6, does not agree as well as that estimated in this work. Littel et al.2 did not use this enhancement factor, but, normally, this factor should fit both data sets. Using eqs 20-22, we estimated, by extrapolation, the reaction rate constants for higher temperatures. Afterward, the iterative procedure applied on the enhancement factor allowed the modeling of COS absorption at temperatures up to 353 K. Finally, using the results of the iterative procedure, we estimated the enhancement factor E as a function of temperature (T) and amine concentration (CMDEA). In our work, we observed that the E behavior is significantly affected by the amine concentration, so we estimated one equation for each of two amine concentration ranges. The first range goes from 415 mol/m3 to 2000 mol/m3, with eq 23, and the second one goes from 2001 mol/m3 to 4250 mol/m3, with eq 24.
n
∆P )
(PCOS,g ∑ i)0
-Experimental
- PCOS,g-Calculated)ti2
(19)
Moreover, an iterative sequence of values for the enhancement factor E was examined to improve the modeling of COS absorption. The estimation of the Arrhenius law coefficients was performed, considering all experimental data at temperatures from 313 K to 333 K. The experimental conditions for these data sets are presented in Table 1. The results of the reaction rate constant estimation are presented in Figure 1. Between 313 K and 333 K, we observe that the values of the reaction rate constants k1,1 and k1,2 are between 4.71 × 10-5 and 9.97 × 10-4, and the k2,1 values are between 8.87 × 10-7 and 8.65 × 10-6 for the mentioned temperatures. We found that reaction rate constant k2,2 has a value of zero, as in the work of Littel et al.2 We estimated the coefficients of the Arrhenius law equation, using a quasi-Newton minimization method, based on the minimization results for temperatures increasing from 313 K to 333 K. We present the Arrhenius equations as expressed in Littel et al.2 for the reaction rate constants as follows:
ln k1,1 )
-10983 -1.4599pKa + 37.33 T
(20)
ln k1,2 )
-10810 -1.4369pKa + 36.66 T
(21)
ln k2,1 )
-7202.3 -1.2960pKa + 20.17 T
(22)
The values of the ratio between activation energy and the ideal gas constant (Ea/R), for k1,1 and k2,1, presented in this work are
E ) 0.5386T0.6 - 0.17149CMDEA0.5 + 728.961eR + 0.03301T0.5eγ + 1.0058 ×10-7T2.5CMDEA0.5 - 749.5233 (23) and
E ) 15.3082T0.6 - 9116.71CMDEA0.05 + 48617.63eR + 0.001T0.6eγ + 1.1817 × 10-7T2.5CMDEA0.6 - 39980.2 (24) with
R)
CMDEA0.1 γ ) -1.5996CMDEA T
γ ) -409.601CMDEA
The modeling of the pressure profiles of COS absorption, using the reaction rates estimated in this work under the experimental conditions shown in Table 1, are presented and compared in the following figures. First, Figure 2 shows the modeling of COS absorption with the enhancement factor E estimated by eq 6. Figure 3 presents the successful validation of the modeling of COS pressure profile using our enhancement factor E, using eq 23. Lastly, in Figure 4, we observe that the enhancement factor E estimated in this work allows the best modeling of experimental data, even at high temperatures and amine concentrations. Satisfactory modeling of the COS absorption by MDEA aqueous solutions was achieved. A minimal difference was observed between the literature and our reaction rate constants.
Ind. Eng. Chem. Res., Vol. 46, No. 20, 2007 6433
Figure 3. Modeling of COS absorption at 313.98 K and CMDEA ) 1264.41 mol/m3 using the enhancement factor (E) estimated in this work.
Figure 4. Modeling of COS absorption at 353.14 K and CMDEA ) 4215.65 mol/m3 using the enhancement factor (E) estimated in this work.
Figure 6. Reaction rate constants estimated in this work and presented in previous works for COS-MDEA absorption. Table 2. Comparison of the Reaction Rate Constants Presented in This Work and in Littel et al.2 for COS Absorption by MDEA Aqueous Solutions.
Figure 5. Comparison between the experimental and modeled pressure profiles of COS absorption, at 313.8 K and CMDEA ) 445 mol/m3, using the reaction rate constants of Littel et al.2 and those obtained from this work.
However, to evaluate this slight difference between the values of the reaction rate constants, we conducted the modeling of experimental data under the same conditions as those that were fixed in the work of Littel et al.2 Its enhancement factor E was fixed at 1.2. The initial pressure was 123 512 Pa. The modeling of the COS pressure profile compares the Littel et al.2 reaction rate constants and the reaction rate constants that have been estimated in this work. In Figure 5, we graphically observed the difference between both pressure profiles. The difference that can be observed between the experimental and the modeled data, using our reaction rate constants, is less important than the difference of modeling with reaction rate constants of the work of Littel et al.2 The value of eq 19, using the Littel et al.2 reaction rate constants, is 9.6041 × 1010; using the reaction rate constants that have been estimated in this work, we obtained a value of 1.8636 × 109. This represents that, if we consider a constant value difference for each experimental and modeled pressure data point, only a deviation of 5 Pa per experimental point would be observed, using the reaction rate constants
k1,1 at 313 K at 323 K k1,2 at 313 K at 323 K k2,1 at 313 K at 323 K
this work
Littel et al.2
4.822 × 10-5 1.886 × 10-4
5.800 × 10-5 1.410 × 10-4
5.194 × 10-5 1.988 × 10-4
5.200 × 10-5 1.480 × 10-4
1.168 × 10-6 3.047 × 10-6
1.400 × 10-6 4.770 × 10-6
estimated in this work, versus a deviation of 34 Pa, which would be observed using the constants from the work of Littel et al.2 Table 2 compares the reaction constant values of Littel et al.2 and those estimated in this work (using eqs 20-22). Taking into account previous works about COS absorption by MDEA aqueous solutions, which were performed to estimate the reaction rate constants at temperatures in the range of 293323 K, we can enlarge the reaction constant rates values for temperatures up to 353 K, as shown in Figure 6. For values of 1/T ) 0.00319 and 0.00309 (313 and 323 K, respectively), the reaction rates correspond to those indicated in Table 2. For smaller values of 1/T, the use of eqs 20-22 allowed us to estimate the reaction rate constants for temperatures in the range of 333-353 K. This last temperature range could expand modeling for industrial applications. The Arrhenius equations that describe the temperature and pKa influence on reaction rate constants become totally linear in a logarithmic representation, as represented in Littel et al.,2 considering the Brønsted theory. However, as shown in Figure 6, an important deviation of linear behavior at higher values of 1/T exists for the reaction rate constants from previous works.
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Furthermore, as written in the work by Al-Ghawas et al.,5 the COS absorption is a slow reaction system and our work presents that the reaction rate constant for R1,2 is higher than the constant value of R1,1. This means that, after the chemical reaction starts and the ionic species appear in the interface, a decrease in the COS reaction rate R1,1 will occur. This leads to a logical decrease in the reaction rates until a chemical equilibrium is reached. Conclusion Considering the two-step zwitterion reaction mechanism, the reaction rate constants of carbonyl sulfide (COS) absorption by N-methyldiethanolamine (MDEA) aqueous solutions were estimated and validated for temperatures in the range of 313.15353.15 K and amine concentrations in the range of 415-4250 mol/m3. These reaction constants were used successfully in the modeling of COS absorption at higher temperatures than previous works on COS absorption. Comparing the values of the reaction constants estimated in this work and those from literature, a minor difference could be found. However, our reaction rate constants allows a highly accurate modeling of COS pressure for all the temperature and amine concentration ranges. Besides, the literature about COS-MDEA absorption is scarce and does not permit validation of the estimation of the enhancement factor equations proposed in this work; future studies would validate this point. Nomenclature a ) interface area (m2) C ) concentration (mol/m3) E ) enhancement factor H ) molar scale Henry’s law constant (Pa m3/mol) k1,1, k1,2, k2,1 ) reaction rate constants (m3 mol-1 s-1) k2,2 ) reaction rate constants (m6 mol-2 s-1) kL ) liquid-side mass transfer coefficient of unreacted COS (m/ s) Pi ) pressure (Pa) R ) gas constant; R ) 8.3143 J K-1 mol-1 Ri,j ) reaction rate (mol m-3 s-1) T ) absolute temperature (K) t ) time (s) V ) volume (m3) Greek Letters β ) slope (s-1) Subscripts g ) gas int ) interface I ) inert
L ) liquid T ) total 0 ) initial Literature Cited (1) Amararene, F.; Bouallou, C. Kinetics of Carbonyl Sulfide (COS) Absorption with Aqueous Solutions of Diethanolamine and Methyldiethanolamine. Ind. Eng. Chem. Res. 2004, 43, 6136. (2) Littel, R. J.; Versteeg, G. F.; van Swaaij, W. M. P. Kinetics Study of COS with Tertiary Alkanolamine Solutions. 1. Experiments in an Intensely Stirred Batch Reactor. Ind. Eng. Chem. Res. 1992, 31, 1262. (3) Philipp, B.; Dautzenberg, H. Kinetische Untersuchungen zur Bildung and Zetsetzung von Monothiocarnonat in wa¨ssrige Lo¨sung. Z. Phys. Chem. 1965, 229, 210. (4) Donaldson, T. L.; Nguyen, Y. N. Carbon dioxide reaction and transportation in aqueous amine membranes. Ind. Eng. Chem. Fundam. 1980, 19, 260-266. (5) Al-Ghawas, H. A.; Ruiz-Ibanez, G.; Sandall, O. C. Absorption of Carbonyl Sulfide in Aqueous Methyldiethanolamine. Chem. Eng. Sci. 1989, 44, 631. (6) Al-Ghawas, H. A.; Ruiz-Ibanez, G.; Sandall, O. C. Absorption of Carbonyl Sulphide in Aqueous Methyldiethanolamine. Presented at the American Institute of Chemical Engineers Spring National Meeting, New Orleans, LA, 1988. (7) Littel, R. J.; Versteeg, G. F.; van Swaaij, W. M. P. Kinetics Study of COS with Tertiary Alkanolamine Solutions. 2. Modelling and Experiments in a Stirred Cell Reactor. Ind. Eng. Chem. Res. 1992, 31, 1269. (8) Cadours, R.; Magne´-Drisch, J.; Normand, L.; Roquet, D.; Perdu, G. COS removal from natural gases by absorption in alkanolamine solutions. Presented at the 85th Annual GPA Convention, Grapevine, TX, 2006. (9) Lammers, J. N. J. J.; Haringa, J.; Littel, R. J. Effect of polyhydroxyalcohols on COS absorption in aqueous methyldiethanolamine. Chem. Eng. J. Biochem. Eng. 1995, 60, 123-129. (10) Hsu, C. H.; Li, M. H. Densities of aqueous blended amines. J. Chem. Eng. Data 1997, 42, 502. (11) Hsu, C. H.; Li, M. H. Viscosities of aqueous blended amines. J. Chem. Eng. Data 1997, 42, 714. (12) Pani, F.; Gaunand, A.; Cadours, R.; Bouallou, C.; Richon, D. Kinetics of Absorption of CO2 in Concentrated Aqueous Methyldiethanolamine Solutions in the Range 296 K to 343 K. J. Chem. Eng. Data 1997, 42, 353. (13) Wang, Y. W.; Xu, S.; Otto, F. D.; Mather, A. E. Solubility of N2O in Alkanolamines and in Mixed Solvents. Chem. Eng. J. 1992, 48, 31. (14) Sandall, O. C. Kinetics of Sulfur Species-Hydrocarbon-Aqueous Amine Systems, Research Report No. RR-182, Gas Processors Association, Tulsa, OK, 2002. (15) Versteeg, G. F.; van Swaaij, W. M. P. Solubility and Diffusivity of Acid Gases (CO2, N2O) in Aqueous Alkanolamine Solutions. J. Chem. Eng. Data 1988, 33, 29. (16) Tsai, T. C.; Ko, J. J.; Wang, H. M.; Lin, C. Y.; Li, M. H. Solubility of Nitrous Oxide in Alkanolamine Aqueous Solutions. J. Chem. Eng. Data 2000, 45, 341.
ReceiVed for reView April 11, 2007 ReVised manuscript receiVed July 5, 2007 Accepted July 23, 2007 IE070516S
