Kinetic Model of Gas−Liquid−Liquid Decomposition Extraction

Oct 17, 2002 - Yunzhao Li , Xingfu Song , Shuying Sun , Yanxia Xu , and Jianguo Yu. Journal of Chemical & Engineering Data 2015 60 (10), 3000-3008...
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Kinetic Model of Gas-Liquid-Liquid Decomposition Extraction Liang Hu* and Adeyinka A. Adeyiga Department of Chemical Engineering, Hampton University, Hampton, Virginia 23668

The typical reaction of gas-liquid-liquid decomposition extraction process can be expressed as follows: MA(w) + CO2(g) + H2O(w) + Am(o) ) MHCO3(w,s) + AmHA(o), where M stands for metal ion, such as K+, Na, Mg2+, and so forth. “A” represented acidic anion, for instance, Cl-, SO42-, HCOO-, and so forth. Am means organic amine. This paper investigated the mechanism and kinetics of gas-liquid-liquid decomposition extraction process. With the system of CO2, sodium formate, and organic tertiary amine, the reaction can be expressed as follows: HCOONa(w) + CO2(g) +H2O(w) + NR3(o) ) NaHCO3(s,w) + HCOOHNR3(o). Author proved that carbon dioxide was absorbed by the organic phase and further transferred into the aqueous phase. Tertiary amine (in the organic phase) is the extractant of acid. On the basis of the mechanism of the process, the kinetic model has been established. A kinetic equation was developed at the 2 experimental conditions: NCO2 ) k23[CCO2(g-o) - (RCHCOOHNR )/(K(C°NR3 - CHCOOHNR3)(C°HCOO- 3 RCHCOOHNR3))] Results showed that the calculation data from kinetic equation well match the experimental data. Introduction Use of a decomposition-extraction method to replace an acidic anion in salt with bicarbonate ion HCO3- has been reported since the early 1980s.1-3 The outstanding work reported by Kosswig and Praun4 can be described by the following reaction:

NaCl(w) + CO2(g) + H2O(w) + Am(o) S NaHCO3(w,s) + AmHCl(o) Aqueous solution of sodium chloride reacted with carbon dioxide in the presence of extractant organic amine; the acidic anion Cl- in NaCl was replaced by HCO3-. Produced HCl was extracted by organic amine into an organic phase. The reported organic amine used was trioctylamine. The purpose of this research was to develop a new route for the manufacture of soda. The reaction we studied is

HCOONa(w) + CO2(g) + H2O(w) + NR3(o) ) NaHCO3(s,w) + HCOOHNR3(o) aqueous solution of sodium formate reacted with carbon dioxide in the presence of extractant tertiary amine; the acidic anion HCOO- in sodium formate was replaced by HCO3- to form sodium bicarbonate. Produced HCl was extracted by tertiary amine into the organic phase. Engineering Analysis of Mechanism 1. System Description. The typical reaction for the decomposition-extraction method can be expressed as follows:

MA(w) + CO2(g) + H2O(w) + Am(o) ) MHCO3(w,s) + AmHA(o) * To whom correspondence should be addressed. Phone: 757/727-5530. Fax: 757/727-5189. E-mail: lianghu59@ yahoo.com.

where M stands for metal ion, such as K+, Na, Mg2+, and so forth. A represented acidic anion, for instance, Cl-, SO42-, HCOO-, and so forth. Am means organic amine. The decomposition-extraction method for replacing an acidic anion in salt with bicarbonate ion HCO3- is a process with the mass transfer and reaction among gasliquid-liquid-solid phases. In the system, Am and AmHA existed in the organic phase, and carbon dioxide existed in the gas phase; MA and MHCO3 existed in the aqueous phase; and MHCO3 also existed in the solid phase. During extraction, carbon dioxide was absorbed into liquids and then reacted with MA in the aqueous phase to form MHCO3. Produced acid HA was extracted into the organic phase. Because the aqueous and organic phases were dispersed by the agitation of the liquid phases, carbon dioxide can be absorbed into the liquid phase in three ways: (1) carbon dioxide was absorbed by the organic phase; (2) carbon dioxide was absorbed by the aqueous phase; and (3) carbon dioxide was absorbed by both the organic and aqueous phases. The different way of absorption would result in different mechanism of the process. In this research, NaOOCH was used as MA; extractant Am was a mixture of C7-C12 tertiary amines, R3N. The composition of the organic phase was Am 50% (V) and 2-ethylhexyl alcohol 50% (V). The process analysis included (1) the mechanism of the decomposition reaction of carbon dioxide with sodium formate; (2) determination of the absorption manner of CO2, which included the comparison of the absorption rate in different liquid phases and the CO2 status in the liquid phases; and (3) determination of the mass transfer pathway of CO2, which means whether CO2 would transfer directly into aqueous phase or transfer into organic phase and then enter into an aqueous phase. 2. Mechanism of the Decomposition Reaction of Carbon Dioxide with Sodium Formate. (1) Determination of the Composition of the Extractive Complex. By the comparison of the FTIR spectra of the organic phases ((a) formic acid was extracted from the

10.1021/ie010922q CCC: $22.00 © 2002 American Chemical Society Published on Web 10/17/2002

Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5585 Table 1. Equilibrium Petitions of the Extraction of Formic Acid formic acid formic acid amine concentration concentration concentration petition in aqueous phase in organic phase in organic phase ratio (M) (M) (M) D 0.002 00 0.004 00 0.007 43 0.012 61 0.019 86 0.028 90

0.1138 0.2087 0.3388 0.4622 0.5858 0.6915

0.9392 0.8441 0.7142 0.5908 0.4672 0.3615

56.90 52.18 45.60 36.65 29.50 23.93

reaction of sodium formate with CO2 and (b) formic acid was extracted from its solution directly), both spectra had the same strong absorption at the wavenumber of 1600 cm-1. This meant that both organic phases had the same extractive complex. The composition of the extractive complex can be determined by using the extraction of formic acid from its solution as long as both concentration ranges of the formic acid were the same. On the basis of this discussion, the equilibrium equation of the extraction of formic acid can be expressed as follows:

HCOOH(w) + pNR3 ) HCOOH‚pNR3 the equilibrium constant Kc

Kc )

[HCOOH‚pNR3] [HCOOH][NR3]

p

)

D [NR3]p

where [ ] meant concentration. Define D as the petition ratio of the extraction

D)

[HCOOH‚pNR3] [HCOOH]

Taking the logarithm on both sides of the equation

ln D ) ln Kc + p ln[NR3] By making the plot of ln D versus ln[NR3], the number p was able to be determined through the slope of the plot. The experimental results of the extraction of formic acid were listed in Table 1. By plotting ln D versus ln[NR3], we can obtain that the slope of the line was about 1, or p ) 1. It can be deduced that the composition of the extractive complex was HCOOHNR3. (2) Determination of the Combined Water Molecule in Extractive Complex HCOOHNR3. MITSUBISHI moisture meter, model CA-02 (Carl Fisher titration) was used to determine water content in the organic phase. The water quantity in the organic phase was titrated before and after the extraction of formic acid. By subtraction, the net water content caused by extraction in the organic phase can be obtained. The experimental results showed that the molecular ratio of formic acid and water in organic phase was less than 0.2. By consideration of the error of the measurement, the extractive complex HCOOHNR3 in the organic phase did not combine the water molecules. (3) Structure of the Extractive Complex HCOOHNR3. The major absorption in the FTIR spectrum of the molecule of carboxylic acid was stretching vibration of the CdO in OdC-O-H group at the wavenum-

ber of 1680-1790 cm-1. For formic acid, its stretching vibration of CdO was at the wavenumber of 1730 cm-1. However, the stretching vibration of CdO moved to the wavenumber of 1600 cm-1 after formic acid was extracted into the organic phase by tertiary amine NR3. This migration of the absorption peak caused by the nonsymmetrical stretching vibration of COO, because formic acid dissociated at the form of [H-COO]- + H+ after formic acid with R3N formed its salt. So, the structure of the extractive complex should be [H-COO]H‚NR3+. (4) General Reaction Equation. On the basis of the previous discussion, the general reaction equation can be established by simple mass balance. For the system we studied, we had

HCOONa(w) + CO2(g) +H2O(w) + NR3(o) ) NaHCO3(s,w) + HCOOHNR3(o) 3. Comparison of Carbon Dioxide Absorption Rate by Organic Phase with That by Aqueous Phase. The CO2 absorption rate by the aqueous and organic phases was measured individually at the same experimental conditions, such as, temperature, pressure (pure CO2 gas used), agitation speed, phase ratio (volume), and liquid volume. The experimental results are shown in Figure 1. From Figure 1, it can be seen that the absorption rate of CO2 by the organic phase is much faster than that by the aqueous phase, which was the aqueous solution of sodium formate, 400 g/L. From Figure 1, it also can be seen that the absorption rate of carbon dioxide by the organic phase was 10 times more than that by the aqueous phase. When the aqueous and organic phases existed in the same absorption system, the absorption of carbon dioxide by the aqueous phase is able to be neglected as long as the surface area between gas and organic phases is larger than or equal to the surface area between gas and aqueous phases. The relationship between the absorption rate of carbon dioxide into the organic and aqueous phases with absorption time is shown in Figure 2. From Figure 2, it is obvious that the absorption of carbon dioxide by the organic phase reached equilibrium much earlier than that by the aqueous phase. So, the organic phase was saturated by carbon dioxide much earlier than the aqueous phase when both were present in the same system at the same experimental conditions. 4. Determination of the Pathway of Carbon Dioxide. As we discussed, the absorption rate of carbon dioxide by the organic phase was much faster than that by the aqueous phase when both phases existed in the same system. However, to determine the pathway of carbon dioxide, there are two additional problems to be solved. (1) Would Absorbed Carbon Dioxide in Organic Phase Be Transferred into Aqueous Phase (Possibility of the Decomposition Reaction of Salt M+OOCH- in the Aqueous Solution with Carbon Dioxide from Organic Phase)? To determine whether the absorbed carbon dioxide in the organic phase is able to be transferred into the aqueous phase and, further, if the decomposition reaction with salt M+A- in its aqueous solution occurred, the following experiment was designed. Calcium chloride was selected because calcium carbonate had little solubility in water. The results

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Figure 1. (a) Comparison of CO2 absorption rate by organic phase with that by aqueous phase. (b) Comparison of CO2 absorption rate by organic phase with that by aqueous phase.

were easy to identify by the white deposits if carbon dioxide was able to enter into the aqueous phase and react with calcium chloride in aqueous solution. As usual, 300 mL of organic extractant (organic phase) was placed into the agitated cell. Carbon dioxide was absorbed into the organic phase. The CO2 gas was stopped after the organic phase was saturated with carbon dioxide. The calcium chloride solution with the concentration of 300 g/L was pored into the agitating cell immediately. The liquid was kept agitated at the rate of 300 r/min. The experimental temperature was 20 °C. The rest of the experiment conditions were pressure, 106 Pa; organic phase volume, 80 mL; phase ratio (o/ w); 4/1. After about 10 min of agitation, a large amount of white deposits appeared in the aqueous phase. This experiment proved that carbon dioxide absorbed into the organic phase was able to be transferred into the aqueous phase and further react with the salt (calcium chloride in this case) in the aqueous phase. (2) Mass Transfer Rate of Carbon Dioxide from Organic Phase to Aqueous Phase. Two experiments were designed to compare the mass transfer rate of two

pathways: (1) carbon dioxide transferred from the gas phase to the aqueous phase through the organic phase; and (2) carbon dioxide transferred from the gas phase into the aqueous phase directly. In the first experiment, 280 mL of sodium formate solution (400 g/L) and 20 mL of organic phase were added into an agitating cell. The organic phase existed on the top layer. Liquid was agitated gently to avoid breaking the organic layer. Carbon dioxide from the gas phase, to react with sodium formate in aqueous phase, would have to pass through the organic phase. In the second experiment, 300 mL of sodium formate solution (400 g/L) was placed into an agitating cell. Both experiments operated under the same experimental conditions. The results are shown in Figure 3. From Figure 3, it can be seen that the absorption rate of carbon dioxide in experiment 1 was higher than that in experiment 2. On the basis of these results, the deduction can be made as follows. If the mass transfer rate of carbon dioxide from the organic phase to the aqueous phase was very slow, the absorption rate of carbon dioxide in experiment 1 would

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Figure 2. (a) Relationship between CO2 absorption rate with absorption time. (b) Relationship between CO2 absorption rate with absorption time.

have been less than that in experiment 2 except in the initial absorption area (the concentration range between 0 to the dotted line, as in Figure 3). The fast absorption rate in the initial absorption area in experiment 1 can be contributed to the reason of absorption by the organic phase. As soon as the organic phase was saturated by carbon dioxide (the concentration at the dotted line, as in Figure 3), the absorption rate of carbon dioxide would have been dropped to below or equal to the absorption rate of experiment 2. However, in the whole range of the absorption process, the absorption rate of experiment 1 was always higher than that of experiment 2. It can be concluded that the mass transfer rate of carbon dioxide from the organic phase to the aqueous phase was higher than that from the gas phase to the aqueous phase directly. In the process of decomposition-extraction, the high dispersion between liquid phases promoted the mass transfer of carbon dioxide from the organic phase to the aqueous phase. The carbon dioxide absorbed into the organic phase was transferred to the interface between the aqueous and organic phases. At the interface, CO2 from the

organic phase combined with water to form H2CO3. Because of the basicity of the organic amine R3N, H2CO3 would react with R3N to form R3NH2CO3. The reaction equation can be expressed as follows:

R3N + H+ + HCO3- ) R3NH+‚HCO3When R3NH+‚HCO3- contacted with NaOOCH in the aqueous phase at the interface, the HCO3- ion in R3NH+HCO3- was replaced with the OOCH- ion because formic acid (HOOCH) was stronger acid than carbonic acid (H2CO3). Replaced HCO3- entered into the aqueous phase and formed NaHCO3 with the Na+ ion in the aqueous phase. When the concentration of sodium bicarbonate in aqueous phase is higher than its solubility, the deposits are produced. The solid product of the reaction was analyzed by a differential thermal analyzer and proved that the solid was sodium bicarbonate. The organic phase was analyzed by a Fourier transform infrared spectrometer. The spectrums showed that formic acid was extracted by the organic phase in the decomposition-extraction process.

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Figure 3. Comparison of the absorption rate of CO2 by organic phase + aqueous phase with that by aqueous phase.

5. Summary of the Pathway of DecompositionExtraction Process. (1) The general reaction equation can be expressed as follows:

HCOONa(w) + CO2(g) +H2O(w) + NR3(o) ) NaHCO3(s,w) + HCOOHNR3(o) (2) Carbon dioxide was absorbed from the gas phase into the organic phase.

CO2(g) ) CO2(o) (3) Carbon dioxide absorbed into the organic phase was transferred to the interface between the organic and aqueous phases by diffusion and convection. At the interface, carbon dioxide combined with water to form H2CO3; further H2CO3 reacted with tertiary amine NR3 to form R3NH+‚HCO3-

NR3(o) + CO2(o) + H2O ) R3NH‚HCO3(o) (4) HCOO- ion in the aqueous phase replaced HCO3in R3NH‚HCO3 and formed R3NHOOCH. Replaced HCO3- entered into the aqueous phase and combined with Na+ to form NaHCO3, that is,

R3NH‚HCO3(o) + HCOO-(w) ) HCOOH‚NR3(o) + HCO3-(w) HCO3-(w) + Na+(w) ) NaHCO3(w) Kinetic Model of Decomposition Extraction Process 1. Characteristics of the Decomposition-Extraction Process. As we described previously, the decomposition-extraction process can be expressed as follows:

CO2(g) + HCOONa(w) + H2O(w) + NR3(o) ) NaHCO3(w) + HCOOH‚NR3(o) | NaHCO3(s)

Figure 4. Concentration profile.

In the experiment, the aqueous phase was dispersed into the organic phase, that is, the aqueous phase was a discontinued phase. The gas-liquid contact mainly occurred on the interface between the gas and organic phases. On the basis of the engineering analysis of the process we discussed previously, carbon dioxide was absorbed into the organic phase and, further, was transferred to the interface between the organic and aqueous phases. The decomposition reaction occurred on the interface. Produced formic acid entered into the organic phase with the form of HCOOHNR3. Produced sodium bicarbonate dissolved into the aqueous phase and crystalized when the concentration of sodium bicarbonate was higher than its saturated concentration. The profile of the concentration of the decomposition-extraction process is shown in Figure 4. 2. Steps of Mass Transfer and Reaction. The steps of mass transfer and reaction of the described decomposition-extraction process can be described as follows. Reactants Mass Transfer. (1) CO2 transferred from the bulk of the gas phase to the interface of the gasorganic phase. The mass transfer rate of CO2 can be expressed as follows:

-dNCO2/dt ) k1Ag-o[CCO2(g,b) - CCO2(g-o)]

(1)

(2) CO2 transferred from the interface of the gasorganic phases to the bulk of the organic phase. The mass transfer rate of CO2 can be expressed as follows:

-dNCO2/dt ) k2Ag-o[CCO2(g-o) - CCO2(o,b)]

(2)

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(3) CO2 transferred from the bulk of the organic phase to the interface of the organic-aqueous phases. The mass transfer rate of CO2 can be expressed as follows:

-dNCO2/dt ) k3Ao-w[CCO2(o,b) - CCO2(o,w)]

(3)

(4) HCOO- transferred from the bulk of the aqueous phase to the interface of the aqueous-organic phases. The mass transfer rate of HCOO- can be expressed as follows:

-dNHCOO-/dt ) k4Ao-w[CHCOO-(w,b) - CHCOO-(o-w)] (4) (5) NR3 transferred from the bulk of the organic phase to the interface of the aqueous-organic phases. The mass transfer rate of NR3 can be expressed as follows:

-dNNR3/dt ) k5Ao-w[CNR3(o,b) - CNR3(o-w)]

(5)

Reaction. (6) The decomposition reaction on the interface of the aqueous-organic phases, which included the reaction of CO2, H2O, with NR3 and the ionexchange reaction of HCO3- with HCOO-. The reaction rate based on the CO2 can be expressed as follows:

-dNCO2/dt ) k6Ao-wf(Ci), (i ) CO2, HCOO-, NR3, HCOOH‚NR3, HCO3-) (6) Products Mass Transfer. (7) HCOOH‚NR3 transferred from the interface of the aqueous-organic phases to the bulk of the organic phase. The mass transfer rate of the product HCOOH‚NR3 can be expressed as follows:

dNHCOOHNR3/dt )

However, in many cases, the process rate is controlled by one or several control steps. The kinetic equation can be simplified by the application of the control step or steps. Several possible control steps and its kinetic equation are discussed as follows according to the characteristics. (1) Gas Film Resistance. The process rate was controlled by the mass transfer in gas film. Because of the high purity of gas CO2, 99.99%, the resistance in the gas film was very low. So, the decompositionextraction process is not controlled by gas film mass transfer. (2) Organic Phase Resistance. The process rate was controlled by the mass transfer in organic film. There are three components in the organic phase which were CO2, HCOOHNR3, NR3. When the process was controlled by the mass transfer of the reactant CO2, the rate of the process can be expressed as follows: NCO2 )

[

k23 CCO2(g-o) -

K(C°NR3 - CHCOOHNR3)(C°HCOO- - RCHCOOHNR3)

(11)

When the process was controlled by the mass transfer of both reactant CO2 and product HCOOHNR3, the kinetic equation can be deduced as follows: NCO2 )

[

k23 CCO2(g-o) -

[

1+

2 RCHCOOHNR 3

]

2 RCHCOOHNR k23 3 k7Ao-w K(C°NR - CHCOOHNR )(C°HCOO- - RCHCOOHNR ) 3 3 3

(12)

where

k23 )

dNHCO3-/dt ) k8Ao-w[CHCO3-(o-w) - CHCO3-(w,b)] (8) K)

(9) the rate of the crystallization of NaHCO3 can be expressed as follows:

crystal nucleation rate dNNaHCO3(m)/dt ) km[CNaHCO3(w,b) - CNaHCO3(s)]q (9) crystal growth rate dNNaHCO3(l)/dt ) kl[CNaHCO3(w,b) - CNaHCO3(s)]r (10) 3. Kinetic Equation. To deduce the kinetic equation of the decomposition extraction process, the assumption of the process was made, as follows. (1) The decomposition extraction process is stable; that is, at any moment, the mass transfer rate and reaction rate for certain component in any step was the same. (2) The heat effect from reaction and solubility is negligible; that is, the process temperature is the controlled experiment temperature. Because of the complexity of the process, it is difficult to deduce the kinetic equation in the analytical formula.

]

K(C°NR3 - CHCOOHNR3)(C°HCOO- - RCHCOOHNR3)

k7Ao-w[CHCOOHNR3(o-w) - CHCOOHNR3(o,b)] (7) (8) HCO3- transferred from the interface of the aqueous-organic phases to the bulk of the organic phase. The mass transfer rate of the product HCO3- can be expressed as follows:

]

2 RCHCOOHNR 3

1 1 1 + k2Ag-o k3Ao-w

[

]

CNaHCO3(o-w)CHCOOHNR3(o-w) CCO2(o-w)CHCOO-(o-w)CNR3(o-w)

(13)

(14)

(3) Water Phase Resistance. The process rate was controlled by the mass transfer in water film. The kinetic equation can be deduced when the process was controlled by the mass transfer of both reactants and products

NCO2 ) CHCOO-(w,b) - CHCOOHNR3CHCO3-(o,b)/(KCCO2CNR3) 1/[k4A(o-w)] + 1/[k8A(o-w)]CHCOOHNR3/(KCCO2CNR3)

(15)

(4) Chemical Reaction Control.

NCO2 ) Ao-w(k6CCO2CNR3CHCOO- - k-6CHCO3-CHCOOHNR3) (16) (5) Process Rate Controlled by Crystallization. The kinetic equation was as described in eqs 9 and 10.

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Figure 5. Relationship between process rate and temperature.

Figure 6. Relationship between process rate and initial concentration of sodium format.

4. Simplification of the Kinetic EquationsModel Identification by Experiment. The material, experimental equipments, and experimental methods have been described in Hu et al.5 On the basis of the characteristics of the process, the control step of the process can be identified by the experiments. Further, a simplified kinetic equation can be obtained. (1) Identification of the Control Step. The absorption rate of carbon dioxide was measured under various experimental conditions, such as, temperature and concentration. The control step of the process was distinguished based on the characteristics of each control step. As stated in the reaction kinetics, the reaction rate with temperature had an exponential relationship. The process rate would be very sensitive to temperature by reaction control than by mass transfer control. Furthermore, for the reversible exothermic reaction, the process rate would pass through a maximum with the increase of temperature because increase of temperature led to

higher forward reaction constant and a lower reaction equilibrium constant. However, both characteristics did not appeared in the Figure 5. It is obvious that the process was not controlled by the chemical reaction step. The experiments were conducted at PCO2 ) 101.3 kPa, C°HCOONa ) 8.824 kmol/m3, and R ) 8. Figure 6 shows the relation of the process rate with the initial concentration of sodium formate at the experimental conditions of PCO2 ) 101.3 kPa, T ) 25 °C, and R ) 8. When the reactant concentration increased (CHCOOHNR3 < 50 mol/m3), the process rate was not affected by the reactant concentration CHCOO-(w,b). So, the process rate was not controlled by the chemical reaction step. If the process rate was controlled by the mass transfer in water film, according to eq 15, the process rate should increase with the increase of C°HCOO- (or CHCOO-). However, the process rate was not changed with the increase of C°HCOO- (or CHCOO-) when CHCOOHNR3 was equal or less than 50 mol/m3 (see Figure 6). So, the process rate was not controlled by water film resistance.

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Figure 7. Relationship between process rate and the concentration of formic acid in organic phase.

Formic acid existed in the organic phase and was at the formation of the complex HCOOHNR3. The influence of the concentration of formic acid in the organic phase on process rate is shown in Figure 7. If the process rate was controlled by crystallization, a maximum rate would appear with the increase of concentration of formic acid in the organic phase, right before the appearance of the solid NaHCO3 in the aqueous phase as in the carbonate step of the Solvay process. However, no such characteristics appeared in Figure 7. It means that the process rate was not controlled by the crystallization step either. By using the characteristics of the process, the process control steps have been narrowed down to the mass transfer control in the organic film. As we discussed early, there were two mechanisms for mass transfer in the organic phase. One was the mass transfer of carbon dioxide in the organic phase; another was the mass transfer of both carbon dioxide and product HCOOHNR3 in the organic phase. Be aware that product HCOOHNR3 was transferred from the interface of the organic and aqueous phases to the bulk of the organic phase. The experiment of the extraction of formic acid showed that the influence of the agitation rate of the liquid phases on the rate of extraction of formic acid was negligible as compared with the influence on the absorption rate of carbon dioxide. This meant that the mass transfer of HCOOHNR3 in the organic phase was not the control step of the process rate. The only possible control step of the process rate was the mass transfer of carbon dioxide in the organic phase. 5. Kinetic Equation. The kinetic curves were divided into three periods: steady period, unsteady period, and transition period. In the steady period, the decomposition-extraction process is stable; that is, at any moment, the mass transfer rate and reaction rate for certain component in any step was the same. This period fit the concentration range CHCOOHNR3 > 30 mol/m3. In the unsteady period, the assumption of steady is not applied. This happens at the initial moment of the process because carbon dioxide was absorbed by the liquid phase (organic phase) rapidly. However, the liquid body is still blank for carbon dioxide. The transition period is between of the steady and unsteady periods. Steady Period. On the basis of the previous discus-

Table 2. Solubility of CO2 in Organic Phase Containing Formic Acid concentration of formic acid in organic phase (M)

CO2 solubility (M)

concentration of formic acid in organic phase (M)

CO2 solubility (M)

0.0000 0.3536

0.0900 0.0690

0.5304 0.7072

0.0635 0.0620

sion, the only possible control step for the process was the mass transfer of carbon dioxide in the organic phase. So, the kinetic equation can be expressed as eq 11. NCO2 )

[

k23 CCO2(g-o) -

2 RCHCOOHNR 3

]

K(C°NR3 - CHCOOHNR3)(C°HCOO- - RCHCOOHNR3)

(11)

The equation only applies to the steady period. The CO2 concentration at the interface between the gas and organic phases, CCO2(g-o), is the solubility of CO2 in the organic phase. Table 2 list the relationship of CO2 solubility with the formic acid content in the organic phase. A regression of the solubility of CO2 with the concentration of HCOOHNR3 in the organic phase was obtained as follows:

CCO2(g-o) ) exp[4.504 - 0.05367 ln(CHCOOHNR3 + 1)] (17) As in eq 11, k23 is the function of temperature and agitation. K is chemical reaction constant, which is the function of temperature. The calculation curve based on the eq 11 has been obtained at the experimental conditions PCO2 ) 101.325 kPa; T ) 25 °C; C°NaHOOCH ) 8.824, 7.353, 5.882, and 2.941 kmol/m3, respectively. In Figure 8, experimental data were expressed by dots, and the line is the calculation based on eq 11. Figure 8 showed that the calculation by the kinetic eq 11 well matched the experimental data at HCOOHNR3 concentration (CHCOOHNR3) range of CHCOOHNR3 > 30 mol/m3. When CHCOOHNR3 < 30 mol/m3, the deviation occurred. The reason was that, at the initial of the process, carbon

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dioxide was absorbed by the liquid phase (organic phase) rapidly. The assumption of steady process cannot be applied. Unsteady Period. This happen at the initial moment of the process because carbon dioxide was absorbed by the liquid phase (organic phase) rapidly. However, the liquid body is still blank for carbon dioxide. In this range (CHCOOHNR3 < 15 mol/m3), the process was similar to the absorption of carbon dioxide by the organic phase. The kinetic equation of the absorption of carbon dioxide at the experimental conditions of T ) 25 °C and PCO2 ) 101.325 kPa was obtained from experiments.

The calculation results were shown in Figure 8 with dotted line. The experimental data with kinetic equation of the absorption of carbon dioxide matched well. Transition Period. Transition period is between of the steady and unsteady periods. The HCOOHNR3 concentration range was in 15 mol/m3 < CHCOOHNR3 < 30 mol/m3. This range of the experimental data was above the calculation by both equations because, in this period, carbon dioxide absorbed into the organic phase was transferring into the aqueous phase.

NCO2(o) ) 6.0 × 10-5[90.00 - CCO2(o,b)]

A ) surface area, m2 Ci ) concentration of component i, mol/m3 D ) petition ratio of the extraction, D ) [HCOOH‚pNR3]/ [HCOOH] K ) reaction equilibrium constant kl ) liquid mass transfer coefficient k ) reaction rate coefficient Ni ) mass transfer rate of component i, mol/m2/s P ) pressure, kPa R ) phase ratio by volume, R′ ) V(o)/V(w)

(18)

In gas-liquid-liquid extraction process, the phase ratio of the organic and aqueous phases was 8:1. If the absorption of CO2 by the aqueous phase is neglected, the process rate can be expressed as

NCO2 ) (8/9)NCO2(o) ) (8/9) × 6.0 × 10-5[90.00 - CCO2(o,b)] (19)

Nomenclature

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Figure 8. (a) Comparison of experimental data with calculation results from a kinetic eq 11. (b) Comparison of experimental data with calculation results from the kinetic eq 11. (c) Comparison of experimental data with calculation results from the kinetic eq 11. (d) Comparison of experimental data with calculation results from the kinetic eq 11.

t ) contact time, s T ) temperature, °C (g) ) gas phase (w) ) aqueous phase (o) ) organic phase (s) ) solid phase Superscript ° ) initial, for example, C°NaOOCH means initial concentration of NaOOCH Subscript g,b ) gas bulk o,b ) organic phase bulk w,b ) aqueous phase bulk g-o ) interface of gas and organic phase o-w ) interface of organic and aqueous phase

Literature Cited (1) Hissamori et al., Technol. Rep. Kansai University 1980, 21, 75. (2) Ninane, L.; Breton, C.; Guerdon, C. Device and method for producing an organic solution of a water-insoluble organic base. Ger. Offen. 3,415,303, 1984. (3) Toyo Soda Mfg. Co., Ltd. Sodium bicarbonate. Jpn. Kokai Tokkyo Koho 1982, 57, 7826. (4) Kosswig, K.; Praun, F. V. Sodium carbonate and hydrogen chloride from sodium chloride and carbonic acidsa new process. Chem. Econ. Eng. Rev. 1983, 15 (6), 30. (5) Hu, L.; Adeyiga, A. A. Extraction of formic acid from sodium formate. Ind. Eng. Chem. Res. 1997, 36, 6, 2375.

Received for review November 14, 2001 Revised manuscript received May 9, 2002 Accepted June 8, 2002 IE010922Q