Kinetics of CO2 Desorption from Highly Concentrated and CO2

Then where HCO2 is the apparent Henry's law constant in the concentration scale. Very small ..... This result agrees with the conclusions of Bosch et ...
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5384

Ind. Eng. Chem. Res. 1997, 36, 5384-5391

Kinetics of CO2 Desorption from Highly Concentrated and CO2-Loaded Methyldiethanolamine Aqueous Solutions in the Range 312-383 K Renaud Cadours,† Chakib Bouallou,† and Alain Gaunand† Centre de Recherche en Proce´ de´ s de Transformation de la Matie` re, Ecole Nationale Supe´ rieure des Mines de Paris, 60 bd Saint-Michel, 75006 Paris, France

Dominique Richon* Laboratoire de Thermodynamique des Equilibres entre Phases, Ecole Nationale Supe´ rieure des Mines de Paris, 35 rue Saint Honore´ , 77305 Fontainebleau, France

Kinetics of CO2 desorption from CO2-loaded methyldiethanolamine (MDEA) aqueous solutions were measured in the following conditions: 312-383 K, 25-50 wt % MDEA aqueous solutions, CO2 loadings from 5 to 85%. A thermoregulated constant interfacial area reaction cell was operated by measuring the pressure over the solution. Producing a very slight depression in the cell, the time-dependent equilibrium pressure recovery is accurately recorded during batch desorption. Kinetics are in agreement with a fast reaction regime of desorption according to the film theory. For CO2 loadings below 0.50 mol of gas/mol of amine, desorption rates are well predicted by using the kinetic constant and orders determined from absorption experiments for the reaction between CO2 and MDEA. Some discrepancies were pointed out for loadings above 0.50 mol of gas/mol of amine. Introduction Absorption by aqueous alkanolamine solutions is the dominant industrial process for acid gases removal, in particular CO2 and H2S, from natural gas. Such washing processes are also used in petroleum refining, coal gasification, and hydrogen production. Methyldiethanolamine (MDEA) and its blends with primary or secondary amines or with sterically hindered amines are the main systems of interest, already studied at the laboratory and sometimes industrial scales. A number of workers have measured absorption kinetics of acid gases in various alkanolamine solutions. Although desorption processes often act as regenerative processes for absorption systems, studies devoted to desorption are not as numerous as those concerning absorption. The regeneration often uses steam or heated inert gas as stripping agents, and then an accurate design based on proper chemical and masstransfer data could lead to significant energy savings. Among the few works dealing with CO2 desorption from aqueous alkanolamine solutions, Critchfield (1988), Bosch et al. (1990), and Xu et al. (1995) have studied the desorption of CO2 from MDEA solutions at various temperatures in a stirred-cell reactor or in packed columns. These investigations are limited to CO2 loadings lower than 0.50 mol of CO2/mol of amine and temperatures lower than 343 K. Experiments and analyses show that the absorption theory can also be applied to desorption in these ranges of temperatures, MDEA concentrations, and CO2 loadings. There are no data between 343 K and the temperatures found in strippers, i.e., 383 K. This paper describes the apparatus developed to measure acid gases desorption kinetics from amine * Telephone: 33-1-64-69-49-65. Fax: 33-1-64-69-49-68. E-mail: [email protected]. † Telephone: 33-1-45-52-54-70. Fax: 33-1-45-52-55-87. E-mail: [email protected], [email protected], [email protected]. S0888-5885(97)00354-0 CCC: $14.00

solutions. Experiments of CO2 desorption from MDEA aqueous solutions have been achieved with CO2 loadings in the range 0.05-0.85 mol of gas/mol of amine, in an extended range of temperatures, 313-383 K, and with 25-50 wt % MDEA aqueous solutions. Experimental Section The (6.20 ( 0.02) × 10-2 m internal diameter thermostated glass reactor shown in Figure 1 is provided with a (4.25 ( 0.02) × 10-2 m diameter six-bladed Rushton turbine in its lower part, a (4.00 ( 0.02) × 10-2 m diameter propeller in its upper part, and four equally spaced vertical PTFE baffles to prevent vortexing. A horizontal PTFE plate and a ring are put midway between the bottom and the top of the cell to set both level and area A of the gas-liquid interface and to make sure of their stability during stirring. A is (13.64 ( 0.05) × 10-4 m2. The shafts are maintained vertically between two pivots supported by two sapphire bearings on the flanges of the cell and the horizontal PTFE plate; they are driven magnetically by adjustable speed motors. This technique avoids leaking, friction, and heat generation which appear when using stems crossing the cell bottom and top. The Rushton turbine speed is checked with a stroboscope; it remains constant within 1 rpm during each test. The total volume available for gas and liquid is (0.3648 ( 0.0005) × 10-3 m3. The temperature in the reactor is known within 0.05 K through a 100 Ω platinum probe, calibrated between 273 and 398 K by the Laboratoire National d’Essais. It is controlled through a thermostatic fluid circulated into the glass double jacket. The upper flange is kept at a temperature slightly higher than the temperature in the reactor, in order to avoid water condensation. The whole cell is placed inside a thermoregulated air bath. A tube settled through the upper flange allows one either to degas the cell or to connect the cell to a variable-volume device originally under a vacuum. The lower flange is equipped with a hypodermic needle for liquid and gas loading. © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5385

pressure PI:

PCO2 ) PT,eq - PI

(2)

Then stirring is started, a vacuum is created in the small external volume, and this one is connected during a short time to the upper part of the reaction cell. The resulting small pressure drop leads water to evaporate and CO2 to desorb, to go back to the initial pressure; the corresponding pressure increase is recorded, up to the vapor-liquid equilibrium value. Small pressure drops are achieved in order to avoid bubble desorption and to keep the initial liquid composition constant during the whole experiment. Water evaporation takes place in a very short time at the beginning of experiment, and CO2 desorption rates are carefully measured once this first step is finished. The apparatus and the method chosen allow one to use small amounts of amine solution and gas, compared to semibatch or batch apparatuses generally used. Kinetics of CO2 desorption from loaded MDEA-water solutions are adequately measured during a period ranging between 500 and 20 000 s (Figure 2). Materials. Twice-distilled water and reagent-grade MDEA are used. MDEA is from Aldrich, with a 99 wt % certified minimum purity. Carbon dioxide is from L’Air Liquide, with a certified purity of 99.995 vol %. Theory Figure 1. Experimental apparatus: (DA) data acquisition, (DE) transparent thermostated double envelope, (HR) heating rod, (MR) magnetic rod, (MS) magnetic stirrer, (N) needle, (Pt 100) platinum probe, (S) septum, (PT) pressure transducer, (TJ) thermostated jacket, (VP) vacuum pump, (VV) variable volume.

Kinetics of gas desorption are measured, just after performing a slight depression inside the cell, by recording the absolute pressure increase up to equilibrium pressure through a SEDEME pressure transducer, working in the range 0-200 kPa. This transducer is thermostated at 408 K, a temperature higher than that in the reaction cell, in order to avoid liquid condensation in its measuring chamber. It is calibrated within (10 Pa against a mercury manometer. A microcomputer fitted with a data acquisition card is used to record the pressure transducer and platinum probe signals. Procedure. Water and MDEA are degassed independently, and aqueous solutions are prepared under a vacuum. The amounts of water and MDEA are known separately by differential weighings within 10-2 g. The flask containing the solution is connected to the reaction cell needle in order to transfer the solution by gravity under a vacuum. Accurate weighings of the flask before and after transfer yield the mass of solution present in the cell and the liquid phase volume through the density correlation used in Glasscock (1990). At a given temperature and under the solution vapor pressure PI, pure CO2 from a homemade gas cylinder is bubbled into the solution through the hypodermic needle (see Figure 1), under stirring to speed up the loading and reach the vapor-liquid equilibrium. The CO2 amount absorbed nCO2,abs is known from weighings of the homemade gas cylinder before and after loading and from the equilibrium CO2 partial pressure PCO2:

nCO2,abs )

PCO2VG

mCO2 MCO2

-

RTK

Most of the previous works on CO2 absorption or desorption by and from tertiary alkanolamine solutions consider the reaction mechanism proposed by Donaldson and Nguyen (1980): ka1

MDEA + CO2 + H2O S MDEAH+ + HCO3kd1

Such a mechanism leads to the generally accepted rate expression

r ) ka1CMDEACCO2 - kd1CMDEAH+CHCO3-

(3)

In the frame of the stagnant film theory, Fick’s law for CO2 transfer leads to the usual stationary balance at distance x from the interface:

DCO2

d2CCO2 dx2

)r

(4)

For each experiment, the interfacial gradients of all species concentrations except CO2 can be easily estimated from (1) the corresponding measured initial desorption rate, (2) diffusivities of each species, (3) CO2 Henry’s law constant, and (4) CO2 mass-transfer coefficient (see Appendix A). The gradients calculated in this way are always lower than 3% and then can be neglected. Equation 4 becomes

DCO2

d2CCO2 dx2

) ka1CMDEA,eq[CCO2 - CCO2,eq]

(5)

where

(1)

PCO2 is obtained from the difference between the total pressure at equilibrium PT,eq and the solution vapor

(I)

CCO2,eq )

CMDEAH+,eqCHCO3-,eq K1CMDEA,eq

(6)

is the CO2 bulk concentration at equilibrium with the

5386 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997

Figure 2. Typical CO2 pressure versus time profiles at high temperature, CMDEA ) 2079 mol‚m-3 and R ) 0.10 molCO2/molMDEA: (thick line) pressure, (s) temperature.

Figure 3. Treatment of a desorption acquisition curve: (thick line) pressure, (s) temperature.

bulk concentrations of the three other species. K1 is the apparent equilibrium constant of reaction I. Using Fick’s law at x ) 0, the analytical solution of eq 5 yields the CO2 desorption rate

Ha φ0 ) kL,CO2(CCO2,in - CCO2,eq) th(Ha)

(7)

which is negative in the case of the desorption. Ha is the dimensionless Hatta number:

Ha )

1 k D C kL,CO2x a1 CO2 MDEA,eq

(8)

From the experiments achieved at various gas stirring speeds, it is assumed that there is no gas-side mass-

transfer resistance. Then

CCO2,in ) PCO2/HCO2

(9)

where HCO2 is the apparent Henry’s law constant in the concentration scale. Very small amounts of CO2 are transferred to the gas phase, leaving quasi-unchanged the CO2 liquid bulk concentration during experiments. Then, the bulk concentration CCO2,eq is assumed constant and calculated from Henry’s law at equilibrium pressure, Peq (see Figure 3). This assumption leads to

φ0 )

kL,CO2

Ha (P - PCO2,eq) HCO2 th(Ha) CO2,in

(10)

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5387 Table 1. Conditions of CO2 Desorption from 25 wt % MDEA Solutionsa

no.

temperature, K

CMDEA,total, mol‚m-3

R, molCO2/ molMDEA

VG, 10-6 m3

1 2 3 4 5 6 7 8 9 (b) 10 (b) 11 12 13 14 (c) 15 (c) 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 (a) 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 (a)

312.3 312.3 312.3 312.3 312.3 313.5 313.6 313.6 313.5 313.5 313.6 313.5 313.5 313.6 313.6 313.5 313.5 313.6 313.6 313.6 313.6 313.6 322.4 322.4 322.4 322.4 322.4 322.6 322.3 322.3 322.4 322.4 322.3 321.8 321.8 321.9 322.2 322.0 322.0 322.0 333.7 333.6 333.6 333.9 333.5 333.6 333.6 333.5 333.6 333.6 333.4 364.2 364.2 382.9 382.9 383.0 383.0

2109 2108 2108 2107 2107 2193 2193 2193 2190 2190 2190 2189 2189 2189 2189 2188 2188 2186 2186 2185 2184 2184 2195 2191 2191 2189 2189 2188 2187 2187 2186 2186 2185 2086 2086 2086 2086 2086 2086 2086 2322 2321 2321 2320 2319 2319 2319 2317 2316 2316 2314 2216 2214 2013 2013 2079 2079

0.16 0.27 0.27 0.27 0.30 0.24 0.24 0.24 0.43 0.43 0.43 0.47 0.47 0.47 0.47 0.58 0.58 0.71 0.71 0.76 0.83 0.83 0.16 0.45 0.45 0.57 0.57 0.66 0.72 0.72 0.78 0.78 0.85 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.20 0.31 0.31 0.31 0.43 0.43 0.43 0.52 0.62 0.62 0.70 0.08 0.21 0.06 0.06 0.10 0.10

181.30 181.17 181.17 181.17 181.14 178.72 178.72 178.71 178.50 178.50 178.50 178.45 178.45 178.44 178.44 178.32 178.32 178.17 178.16 178.11 178.03 178.03 175.26 174.91 174.91 174.76 174.76 174.63 174.59 174.58 174.51 174.50 174.58 179.76 179.76 179.76 179.74 179.75 179.75 179.75 174.05 173.91 173.91 193.88 173.76 173.75 173.75 173.63 173.48 173.48 173.39 177.50 177.32 174.03 174.03 176.76 176.76

∆P, Pa

experimental desorption rate, mol‚m-2‚s-1

calculated desorption rate, mol‚m-2‚s-1

98 185 145 169 169 151 87 148 333 305 276 343 355 266 340 474 592 1278 1470 1779 2148 2220 115 118 740 1157 1202 1732 2490 2829 3178 3198 3445 387 347 307 249 393 443 399 341 489 686 673 1081 1188 1185 1848 2481 2789 4564 190 900 1680 1180 1711 752

3.63 × 10-6 4.15 × 10-6 3.42 × 10-6 3.83 × 10-6 3.80 × 10-6 4.47 × 10-6 3.39 × 10-6 4.74 × 10-6 1.15 × 10-5 8.41 × 10-6 8.66 × 10-6 8.44 × 10-6 7.25 × 10-6 5.78 × 10-6 7.09 × 10-6 9.42 × 10-6 1.11 × 10-5 1.62 × 10-5 1.83 × 10-5 1.85 × 10-5 2.07 × 10-5 1.96 × 10-5 3.65 × 10-6 4.09 × 10-6 1.92 × 10-5 2.06 × 10-5 1.87 × 10-5 2.83 × 10-5 3.12 × 10-5 3.11 × 10-5 4.33 × 10-5 3.94 × 10-5 3.98 × 10-5 1.13 × 10-5 1.09 × 10-5 1.23 × 10-5 6.81 × 10-6 1.01 × 10-5 1.17 × 10-5 1.12 × 10-5 1.50 × 10-5 2.31 × 10-5 2.28 × 10-5 2.04 × 10-5 3.01 × 10-5 3.80 × 10-5 3.38 × 10-5 4.45 × 10-5 4.95 × 10-5 4.48 × 10-5 5.49 × 10-5 1.21 × 10-5 3.93 × 10-5 1.11 × 10-4 7.68 × 10-5 1.08 × 10-4 6.30 × 10-5

3.40 × 10-6 5.85 × 10-6 4.58 × 10-6 5.34 × 10-6 5.21 × 10-6 5.00 × 10-6 2.88 × 10-6 4.93 × 10-6 9.31 × 10-6 8.51 × 10-6 7.71 × 10-6 9.10 × 10-6 9.42 × 10-6 7.07 × 10-6 9.04 × 10-6 1.11 × 10-5 1.38 × 10-5 2.47 × 10-5 2.84 × 10-5 3.12 × 10-5 3.26 × 10-5 3.37 × 10-5 4.89 × 10-6 3.89 × 10-6 2.44 × 10-5 3.32 × 10-5 3.45 × 10-5 4.37 × 10-5 5.71 × 10-5 6.49 × 10-5 6.58 × 10-5 6.62 × 10-5 6.16 × 10-5 1.42 × 10-5 1.28 × 10-5 1.13 × 10-5 9.20 × 10-6 1.45 × 10-5 1.63 × 10-5 1.47 × 10-5 1.74 × 10-5 2.26 × 10-5 3.17 × 10-5 3.12 × 10-5 4.46 × 10-5 4.91 × 10-5 4.90 × 10-5 6.87 × 10-5 8.18 × 10-5 9.20 × 10-5 1.33 × 10-4

a All experiments were realized with liquid- and gas-phase agitation at 100 rpm except the following: (a) N ) 100 rpm, no gas phase agitation. (b) N ) 175 rpm, no gas-phase agitation. (c) N ) 50 rpm, gas-phase and liquid-phase agitation.

Solving the mass balance for CO2 in the gas phase

dnCO2/dt ) -φ0A

(11)

Linear regression of Y over t shows that relation (12) is fulfilled for all experiments. It is then possible to calculate the initial CO2 desorption rates as

VG φ0 ) U ∆P RTKA

where nCO2 ) PCO2VG/RT is the number of CO2 moles in the gas phase at time t, with eq 10, yields

(

Y ) ln

)

PT - PT,eq ) -U(t - tdep) PT,dep - PT,eq

(12)

(14)

where

∆P ) PT,dep - PT,eq

(see Figure 3)

(15)

where Results

RT Ha A U ) kL,CO2 VGHCO2 th(Ha)

(13)

Experiments have been carried out in the temperature range 313-383 K, for 25 and 50 wt % MDEA

5388 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 Table 2. Conditions of CO2 Desorption from 50 wt % MDEA Solutionsa

no.

temperature, K

CMDEA,total, mol‚m-3

R, molCO2/ molMDEA

VG, 10-6 m3

58 59 60 61 62 63 64 65 66 67 68 69 70 (a) 71 (a) 72 (a) 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 (b) 88 (b) 89 (b) 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

312.8 312.8 312.8 312.8 312.7 312.7 312.7 312.9 312.9 312.7 312.7 312.7 313.5 313.5 313.5 313.5 322.1 322.1 322.1 322.4 322.4 322.4 322.4 322.6 322.6 322.4 322.5 322.6 332.9 332.3 332.3 332.3 332.3 332.3 332.3 332.4 332.4 332.4 332.4 332.5 332.5 332.5 332.5 332.6 332.3 332.4 332.4 332.4 332.5 332.6 332.6 364.5 364.3 364.2 364.3 382.7 382.7

4412 4412 4412 4412 4407 4407 4407 4400 4400 4394 4386 4381 4000 4000 4000 3993 4104 4104 4104 4098 4098 4092 4092 4089 4089 4088 4086 4085 4630 4226 4226 4226 4222 4222 4222 4217 4217 4217 4217 4217 4217 4217 4217 4217 4215 4215 4215 4211 4209 4206 4206 4067 4065 4062 4061 4073 4071

0.11 0.11 0.11 0.11 0.20 0.20 0.20 0.33 0.33 0.44 0.59 0.67 0.15 0.15 0.15 0.32 0.28 0.28 0.28 0.39 0.39 0.52 0.52 0.57 0.57 0.59 0.63 0.65 0.23 0.08 0.08 0.08 0.14 0.14 0.14 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.28 0.28 0.28 0.33 0.38 0.42 0.44 0.05 0.10 0.15 0.16 0.02 0.05

175.54 175.54 175.54 175.54 175.34 175.34 175.34 175.01 175.01 174.77 175.28 175.28 180.81 180.81 180.81 180.46 173.03 173.03 173.03 172.75 172.75 172.45 172.46 172.32 172.32 172.27 172.18 172.13 174.72 177.13 177.13 177.13 176.97 176.97 176.97 176.77 176.77 176.77 176.77 176.76 176.76 176.76 176.76 176.76 176.63 176.62 176.62 176.50 176.38 176.28 176.21 167.68 167.49 167.38 167.31 176.47 176.38

∆P, Pa

experimental desorption rate, mol‚m-2‚s-1

predicted desorption rate, mol‚m-2‚s-1

81 58 69 77 194 181 173 342 375 618 1369 2106 158.1 152.9 167.4 381.8 453 679 703 1383 1243 2204 2353 2249 2907 2102 3660 4425 811 233 270 179 459 495 507 884 852 840 658 601 601 422 307 233 1624 1449 1111 1622 2201 2732 2913 982 1854 4013 3157 1029 1287

2.18 × 10-6 1.49 × 10-6 1.71 × 10-6 1.29 × 10-6 4.48 × 10-6 4.48 × 10-6 3.42 × 10-6 6.95 × 10-6 7.16 × 10-6 1.19 × 10-5 1.79 × 10-5 2.32 × 10-5 5.13 × 10-6 5.22 × 10-6 6.04 × 10-6 9.25 × 10-6 1.42 × 10-5 1.45 × 10-5 1.55 × 10-5 3.28 × 10-5 3.26 × 10-5 2.66 × 10-5 3.49 × 10-5 2.97 × 10-5 3.25 × 10-5 1.79 × 10-5 2.93 × 10-5 3.36 × 10-5 2.24 × 10-5 1.09 × 10-5 1.03 × 10-5 8.00 × 10-6 1.59 × 10-5 1.46 × 10-5 1.50 × 10-5 2.35 × 10-5 2.15 × 10-5 2.28 × 10-5 1.67 × 10-5 1.53 × 10-5 1.52 × 10-5 1.24 × 10-5 9.71 × 10-6 7.69 × 10-6 3.34 × 10-5 2.98 × 10-5 2.97 × 10-5 2.66 × 10-5 3.86 × 10-5 4.24 × 10-5 4.81 × 10-5 3.96 × 10-5 4.65 × 10-5 7.22 × 10-5 5.69 × 10-5 4.85 × 10-5 5.07 × 10-5

2.34 × 10-6 1.66 × 10-6 1.99 × 10-6 2.23 × 10-6 5.14 × 10-6 4.81 × 10-6 4.59 × 10-6 8.03 × 10-6 8.81 × 10-6 1.28 × 10-5 2.34 × 10-5 3.16 × 10-5 4.77 × 10-6 4.62 × 10-6 5.06 × 10-6 9.92 × 10-6 1.50 × 10-5 2.25 × 10-5 2.33 × 10-5 4.11 × 10-5 3.70 × 10-5 5.66 × 10-5 6.04 × 10-5 5.45 × 10-5 7.05 × 10-5 4.88 × 10-5 8.07 × 10-5 9.50 × 10-5 3.70 × 10-5 1.18 × 10-5 1.37 × 10-5 9.03 × 10-6 2.19 × 10-5 2.37 × 10-5 2.43 × 10-5 3.94 × 10-5 3.80 × 10-5 3.74 × 10-5 2.94 × 10-5 2.68 × 10-5 2.68 × 10-5 1.88 × 10-5 1.37 × 10-5 1.05 × 10-5 6.84 × 10-5 6.11 × 10-5 4.70 × 10-5 6.49 × 10-5 8.42 × 10-5 1.01 × 10-4 1.05 × 10-4

a All experiments were realized with liquid- and gas-phase agitation at 100 rpm except the following: (a) N ) 100 rpm, no gas-phase agitation. (b) N ) 165 rpm, no gas phase agitation.

aqueous solutions, and for CO2 loadings from 0.05 to 0.85 mol of gas/mol of amine. The different experimental conditions and the corresponding initial desorption rates obtained from eq 14 are shown in Tables 1 and 2 (in these tables, desorption rates and ∆P values are given as absolute values). For given temperature and MDEA concentration, the constant U defined by eq 13 is independent of the depression created. So the desorption rate is proportional to ∆P (see, for instance, experiments 93-101). The influence of ∆P must be taken into account to observe the influence of the experimental parameters, and the ratio χ will be used

to establish further observations:

χ ) -φ0HCO2/∆P

(16)

For given concentrations, temperatures, and CO2 loadings, several experiments have usually been performed. The reproducibility of initial CO2 desorption rates has been found to be better than 10% using the quantity χ for comparisons (see Figure 4). Gas-phase stirring has been found to be of no influence on the CO2 desorption rate as demonstrated by experiments performed at given temperature, given

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5389

Figure 4. Influence of temperature (K) and loading on CO2 desorption rate from 50 wt % MDEA solutions: (×) 313, (+) 323, (*) 333, (O) 364, (4) 383.

MDEA concentration, and given CO2 loading (for example, see experiments 34-39 achieved with gas-phase stirring and experiment 40 without gas-phase stirring). These experiments agree with the previous assumption about the absence of mass-transfer resistance in the gas phase. With a 2189 mol‚m-3 MDEA solution, at 313.6 K, and 47% CO2 loading, reducing the stirring speeds on both liquid and gas sides from 100 to 50 rpm, experiments 12, 13, and 14, 15 respectively, does not lead to a significant decrease of CO2 desorption kinetic rates, as they are within the reproducibility range. These results agree with high values of Ha, between 7 and 89 for our experiments, for which kL,CO2 has no influence on desorption rate. At given temperature and total MDEA concentration, increasing the CO2 loading leads to a decrease of the CO2 desorption rate (see Figure 4). This observation agrees with eq 8: at given experimental conditions except loading, the Hatta number characterizes the enhancement of the desorption processes by the chemical reaction. Increasing the CO2 loading leads to decreasing CMDEA and then the Hatta number. Figure 4 clearly shows the influence of temperature on CO2 desorption from MDEA solutions: the CO2 desorption rate increases with temperature as χ increases faster than the Henry’s constant. This result agrees with the conclusions of Bosch et al. (1990) and Xu et al. (1995). The same observations are obtained with 25 wt % MDEA solutions. Discussion For each experiment at 313, 323, and 333 K, the desorption rates were estimated using correlations of previous works which are given in Appendix A. The CO2 diffusion coefficient is obtained with the relation established for unloaded solutions (see Appendix A); the correlation used for HCO2 was extrapolated up to 333 K. The Arrhenius law is taken from Pani et al. (1997), who studied CO2 absorption by aqueous MDEA solutions in the temperature range 296-343 K:

ka1 ) 4.68 × 105 exp(-5461/TK)

(17)

Let Ω be the ratio of the predicted desorption rate over the measured desorption rate. For 25 wt % MDEA aqueous solutions, CO2 experimental desorption rates are well predicted at low loadings (see Figure 5). This conclusion agrees with the results of Bosch et al. (1990) or Xu et al. (1995). But for loadings higher than 0.5 mol

Figure 5. Influence of the loading on the deviation between experimental and predicted rates of desorption from 25 wt % MDEA solutions: (×) 313 K, (+) 323 K, (*) 333 K.

Figure 6. Influence of the loading on the deviation between experimental and predicted rates of desorption from 50 wt % MDEA solutions: (×) 313 K, (+) 323 K, (*) 333 K.

of CO2/mol of MDEA for which no data are available in the literature, predicted desorption rates are significantly higher than experimental ones. The deviation observed increases with temperature. The same results are observed in Figure 6 for 50 wt % MDEA solutions. The deviation pointed out at 333 K can be explicated by the extrapolation of the correlations used to calculate the CO2 Henry’s law constant (see Appendix A). In the same way, the correlation used for the CO2 diffusivity has been established for unloaded MDEA solutions. The most important deviation is found at high loadings and with 50 wt % MDEA aqueous solutions. In these cases, the ionic species concentrations are quite high; unfortunately, the correlations leading to diffusivity and solubility data did not consider the effect of electrolyte species. According to Rinker et al. (1995), it could be necessary to take into account the reaction between CO2 and OH-. In this work, we have pointed out some difficulties in representing experimental data within experimental accuracy and have given some reasons besides a possible nonanalogy of absorption and desorption. Further modeling works are in progress in our laboratory. At 363 and 383 K, no data are available in the literature, and CO2 diffusivities and Henry’s constants are missing. Consequently, it is not possible to interpret our experimental desorption rates with the model. Conclusion We designed a thermoregulated constant interfacial area reactor for accurate desorption measurements up to 383 K. Desorption rates of CO2 from loaded aqueous

5390 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997

solutions of methyldiethanolamine were measured in the temperature range 313-383 K, for 25 and 50 wt % MDEA solutions, and CO2 loadings from 0.05 to 0.85 mol of gas/mol of amine. For loadings lower than 0.5 mol of CO2/mol of MDEA, the CO2 desorption rates calculated with our model are comparable to experimental ones. These conclusions agree with Bosch et al. (1990) or Xu et al. (1995) results. For higher loadings for which the correlations used for diffusivities or Henry’s law constant are extrapolated, the deviations between experimental and predicted desorption rates are significant. These deviations are more important with 50 wt % MDEA solutions than with 25 wt % MDEA solutions. The lack of diffusivity and Henry’s constant data at temperatures higher than 343 K prevents us from comparing the experimental desorption rates measured at 363 and 383 K with the results obtained with our model. We supposed that neglecting the influence of electrolyte species on the diffusivity and the Henry’s constant could be the principal source of discrepancies. We need a rigorous kinetic and thermodynamic model taking into account the electrolyte species for the representation of the desorption rates measured with high loadings and high temperatures. Nomenclature A ) interfacial area, m2 C ) concentration, mol‚m-3 d ) density of the solution, kg‚m-3 Di ) diffusivity of species i in liquid phase, m2‚s-1 Dag ) Rushton turbine diameter, m DT ) internal cell diameter, m Ha ) Hatta number HCO2 ) Henry’s law constant in the concentration scale, Pa‚m3‚mol-1 K ) equilibrium constant ka1, kd1 ) reaction rate constants for the reaction between CO2 and MDEA, m3‚mol-1‚s-1 kL ) liquid-side mass-transfer coefficient of dissolved CO2, m‚s-1 N ) stirring speed, s-1 mCO2 ) CO2 mass introduced in the reactor, kg M ) molecular weight, kg nCO2,abs ) CO2 moles absorbed in the liquid phase P ) pressure, Pa r ) rate of reaction between CO2 and MDEA, mol‚m-3‚s-1 R ) gas constant, 8.3143 J‚K-1‚mol-1 Re ) dimensionless Reynolds number Sc ) dimensionless Schmidt number Sh ) dimensionless Sherwood number t ) time, s T ) temperature, K or °R U ) defined by eq 17 V ) volume, m3 w ) wt % x ) spatial variable measured from the gas-liquid interface, m z ) dimensionless spatial variable

Subscripts aq sol ) values in aqueous solution CO2 ) carbone dioxide dep ) depression eq ) equilibrium G ) gas HCO3- ) bicarbonate in ) interface I ) inert K ) for temperature in K MDEA ) methyldiethanolamine MDEAH+ ) protoned methyldiethanolamine R ) for temperature in °R T ) total water ) values in pure water R)0 ) unloaded solution R*0 ) loaded solution

Appendix A For calculation of the density and viscosity of the solution, we used the correlations proposed by Glasscock (1990). The viscosity of unloaded solution is obtained by

B1 ) -19.52 - 23.40WMDEA 31.24WMDEA2 + 36.17WMDEA3 B2 ) 3912 + 4894WMDEA + 8477WMDEA2 8358WMDEA3 B3 ) 0.02112 + 0.03339WMDEA + 0.02780WMDEA2 - 0.04202WMDEA3 µaq sol,R)0 ) exp(B1 + B2/TK + B3TK) × 10-3

(A1b)

This correlation is considered to be reasonable for 0-50 wt % total amine and a temperature range of 290-320 K. It is used to estimate the viscosity of loaded solution through the relative viscosity:

µr ) 1.000 + 0.8031R + 0.35786R2

(A2a)

µaq sol,R)0 ) 1.0 + 2.0(µr - 1)WMDEA µaq sol,R)0

(A2b)

The density of loaded solution is given by

1000 ) Wwater × 1.01 × 10-3 × d exp[0.000344(TK - T0)] + WMDEA × 0.918 × 103 × exp[0.000528(TK - T0)] + WCO2 × 0.0636 × 103 × exp[0.0036(TK - T0)] (A3) The diffusion coefficient of CO2 was estimated using the data and the N2O analogy of Versteeg and van Swaaij (1988). It was estimated for unloaded solutions through

Greek Letters R ) loading of the solution, molCO2/molMDEA δ ) laminar film thickness, m ∆P ) pressure drop, Pa φ0 ) CO2 desorption rate at the interface, mol‚m-2‚s-1 µ ) viscosity, Pa‚s-1 µr ) reduced viscosity χ ) defined by eq 16, m‚s-1 Ω ) (predicted desorption rate)/(experimental desorption rate)

}

(A1a)

(

DCO2 ) 2.35 × 10-6 exp -

)( )

2119 µwater TK µaq sol

0.8

(A4)

The relation proposed by Pani et al. (1997) was used to estimate the MDEA coefficient diffusion:

( ) DCO2

DMDEA

( )

) 2.43 aq sol

µwater µaq sol

0.2

(A5)

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5391

The equilibrium constant for eq I is obtained with the ratio of equilibrium constants of the following reactions:

CO2 + 2H2O S H3O+ + HCO3-

(II)

MDEAH+ + H2O S MDEA + H3O+

(III)

The equilibrium constant K2 of eq II is given by Kent and Eisenberg (1976) for temperatures lower than 413 K:

(

K2 ) exp -241.818 +

Acknowledgment

53.6855 × 104 TR

)

4.8123 × 108 1.94 × 1011 2.96445 × 1013 + TR2 TR3 TR4 (A6a) The equilibrium constant of reaction (III) is obtained through the correlation used by Rinker et al. (1995) over the range of 298-333 K:

log(K3) ) -14.01 + 0.018TK

(A6b)

The CO2 Henry constant was determined with the correlation proposed by Al-Ghawas et al. (1989) for temperatures between 288 and 323 K and for MDEA compositions up to 50 wt % MDEA:

B4 ) 2.01874 - 2.37638 × 101WMDEA,R)0 + 2 3 - 4.80196 × 102WMDEA,R)0 2.90092 × 102WMDEA,R)0 B5 ) 3.13549 × 103 + 1.54931 × 104WMDEA,R)0 2 3 + 3.00562 × 105WMDEA,R)0 1.83987 × 105WMDEA,R)0 B6 ) -8.13702 × 105 + -2.4808 × 106WMDEA,R)0 + 2 3 - 4.70852 × 107WMDEA,R)0 2.92013 × 107WMDEA,R)0

(

HCO2,R)0 ) 101.325 exp B4 +

)

}

(A7a)

B5 B6 + 2 (A7b) TK T K

A mass-transfer correlation between dimensionless numbers has been established for our apparatus from the same N2O absorption experiments by MDEA-water solutions used by Pani et al. (1997):

Sh ) 0.25Re0.63Sc0.42

the correlation presented includes N2O-aqueous MDEA solutions and CO2-water absorption experiments. As CO2 absorption may be enhanced by its reaction with hydroxide ions, only the N2O absorption in MDEA solution experiments was considered here, leading to the above correlation. However, the previous choice is of no consequence on Pani et al. (1997) results as their absorption experiments of CO2 in MDEA solutions took place according to a fast regime of reaction, insensitive to the liquid-side mass-transfer resistance.

The authors are grateful to Agence de l’environnement et de la Maitrise de L’ENERGIR (ADEME) and to ELF Aquitaine Production for financial support. Literature Cited 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, 385. Bosch, H.; Versteeg, G. F.; van Swaaij, W. P. M. Desorption of Acid Gases (CO2 and H2S) from Loaded Alkanolamine Solutions. In Gas Separation Technology; Vansant, E. F., Dewolfs, R., eds.; Elsevier Science Publishers B.V.: Amsterdam, The Netherlands, 1990; pp 505-512. Critchfield, J. E. CO2 Absorption/Desorption in Methyldiethanolamine Solutions Promoted with Monoethanolamine and Diethanolamine: Mass Transfer and Reaction Kinetics. Ph.D. Dissertation, The University of Texas, Austin, Austin, TX, 1988. Donaldson, T. L.; Nguyen, Y. N. Carbon Dioxide Reaction and Transport into Aqueous Amine Membranes. Ind. Eng. Chem. Fundam. 1980, 19, 260. Glasscock, D. A. Modelling and Experimental Study of Carbon Dioxide Absorption into Aqueous Alkanolamines. Ph.D. Dissertation, The University of Texas, Austin, Austin, TX, 1990. Kent, R. L.; Eisenberg, B. Better Data for Amine Treating. Hydrocarbon Process. 1976, 55, 87. 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 (2), 353. Rinker, E. B.; Ashour, S. S.; Sandall, O. C. Kinetics and modelling of carbon dioxide absorption into aqueous solutions of Nmethyldiethanolamine. Chem. Eng. Sci. 1995, 50 (5), 755. Versteeg, G. F.; van Swaaij, W. P. M. Solubility and Diffusivity of Acid Gases (CO2, N2O) in Aqueous Alkanolamine Solutions. J. Chem. Eng. Data 1988, 33 (1), 29. Xu, G.-W.; Zhang, C.-F.; Qin, S.-J.; Zhu, B.-C. Desorption of CO2 from MDEA and Activated MDEA Solutions. Ind. Eng. Chem. Res. 1995, 34 (3), 874.

Received for review May 19, 1997 Revised manuscript received July 31, 1997 Accepted August 4, 1997X

(A8)

IE9703548

Sh ) kLDT/DCO2 is the Sherwood number, Re ) dNDAg2/µ is the stirrer Reynolds number, and Sc ) µ/dDCO2 is the Schmidt number. In Pani et al. (1997),

X Abstract published in Advance ACS Abstracts, October 1, 1997.