Model Building Methodology for Multiphase Reaction Systems

Article pubs.acs.org/IECR

Model Building Methodology for Multiphase Reaction SystemsModeling of CO2 Absorption in Monoethanolamine for Laminar Jet Absorbers and Packing Beds Rameshwar Hiwale,† Sungwon Hwang,*,‡ and Robin Smith† †

Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, P.O. Box 88, Manchester, M60 1QD, U.K. ‡ Catalysts, Adsorbents and Specialties, UOP Ltd., Liongate, Ladymead, Guildford, Surrey, GU1 1AT, U.K. ABSTRACT: This research has focused on a new methodology to develop a rigorous reactor model for gas−liquid chemical reactions in absorption processes. This involves simultaneous chemical reaction and mass transfer between two phases. In particular, all feasible chemical reaction mechanisms and kinetics are considered for the modeling to improve the accuracy of the simulation results. Detailed mathematical modeling is developed to identify physical properties of the key components. For a reactor design, a packed bed reactor has been developed with two different types of modeling approaches. The results of two separate models are compared with the laboratory experimental data. For a case study, CO2 absorption to monoethanolamine (MEA) solution is used based on a wide range of experimental data from both laminar jet absorber and packed bed column. • Chemical reaction and its effect on mass and heat transfer coefficients (iii) Reactor modeling of the system is developed for simulation and compared with laboratory experimental results. (iv) A methodology is developed to identify the scope for further experiments, especially when it requires further clarification for reaction kinetics or mechanism. For example, multiple sets of kinetics are developed to explain the same system behavior without much noticeable deviation. In such cases, the modeling provides more systematic guidelines to what experimental data is required and what operating conditions are the most suitable to clarify between rival models. By doing this, a more optimized reactor design can be achieved by making full use of experimental information, saving unnecessary laboratory and pilot plant experiments. In this paper, we have focused on item numbers i, ii, and iii above, while number iv is discussed in a separate paper. In our earlier research, details for the new methodology of developing reactive absorption process are illustrated by using a laminar jet absorber with a case study of oleic acid chlorination.1 In this research, the methodology has been extended further to detail modeling of a packed bed reactor with a case study of CO2 absorption to monoethanolamine (MEA) solution. In particular, two different models are used for the design of a packed bed reactor, and generated concentration and temperature profiles along the reactor bed are compared with experimental data.

1. INTRODUCTION Multiphase reactions are common in chemical processes. However, the design of such reactors remains a difficult task due to its highly complex nature. In particular, among the many different types of multiphase chemical reactions, reactive absorption is regarded as one of the most complex systems due to interactions between chemical reaction and mass transfer involving the gas and liquid. Chemical engineers and scientists from both academia and industry have attempted to develop optimized reactive absorption systems. However, the following challenges still remain: (i) Increased complexity due to mass and heat transfer between different phases occurring simultaneously with multiple chemical reactions. (ii) Reaction mechanism and kinetics are mainly developed by chemists without consideration of reactor design, and the mechanism and kinetic data are not validated by simulation of the process. (iii) Inconsistency between conditions for laboratory experiments carried out by chemists and reactor design by chemical engineers. Early involvement of chemical engineers is required to analyze laboratory experiments for the systematic development of reaction mechanism and kinetics, to ensure it is appropriate for reactor design. For these reasons, this research has focused on a new approach for the model building of multiphase reactions: (i) Feasible reaction mechanisms are identified on the basis of sets of experimental data, and the kinetics are developed. (ii) Rigorous modeling is adopted to increase the accuracy of the simulation results by considering the following aspects simultaneously. • Physical properties of the major key components • Mass and heat transfer phenomena © 2012 American Chemical Society

Received: Revised: Accepted: Published: 4328

August 20, 2011 December 22, 2011 February 24, 2012 February 24, 2012 dx.doi.org/10.1021/ie201869w | Ind. Eng. Chem. Res. 2012, 51, 4328−4346

Industrial & Engineering Chemistry Research

Article

2. BACKGROUNDS OF CO2 ABSORPTION TO MONOETHANOLAMINE (MEA) SOLUTION

Liu et al. proposed a model to predict the concentration, temperature and velocity distribution with heat effects for the chemical absorption of CO2 in NaOH aqueous solution by using a randomly packed column.20 The model was able to predict simultaneously velocity, temperature, and concentration profiles, as well as the turbulent mass transfer diffusivity. The enhancement factor of chemical absorption, which is predicted from the models, varied significantly along the packed bed column. The model results illustrated good agreement with the experimental data, which was reported by Tontiwachwuthikul et al. and Pintola et al.21,22 Aboudheir et al. developed a model to predict the packing height in absorption columns.23 The model was used for the simulation of absorption of carbon dioxide into aqueous 2amino-2-methyl-1-propanol (AMP) solutions in a packed bed column. The model developed takes into account the heat effects on the absorption system. The model is based on Pandya’s procedure, and it predicts concentration and temperature profiles of CO2−AMP system. The reported average absolute deviations between the predicted and experimental data in terms of concentration and temperature profiles were about 9.2% and 2.3%, respectively.

Many researchers have used a solution of a chemical base to remove carbon dioxide from a gas. The most widely used chemical solvents are aqueous alkanolamines and alkaline salt solution. Monoethanolamine (MEA) is one of the most commonly used chemicals for the purpose of gas purification. For this reason, the MEA reaction with CO2 has been extensively studied by a number of researchers since the early 1960s. The related research and its significance are summarized in the work of Hiwale.2 For study of the kinetics of carbon dioxide−alkanolamine reactions, it has been found quite difficult to compare literature data since researchers have used different experimental techniques, physicochemical data, and amine purities.3 For example, many researcher have conducted absorption rate experiments to generate the kinetic data for the carbon dioxide− monoethanolamine system by using various types of laboratory units such as laminar jet absorbers, short wetted-wall columns, stirred cells or avone-sphere units for mass transfer.3−5 Many researchers have investigated the reaction kinetics between carbon dioxide and monoethanolamine systems, but considerable discrepancies have been found among these works. For illustration, many studies on the reaction kinetics of carbon dioxide and monoethanolamine have been analyzed by using the methodology of gas absorption with a pseudo-first-order reaction previously. However, the reported values of the reaction rate constant ranges from 3880 to 8400 L/mol and the activation energy varies from 39.7 to 46.7 kJ/mol.6−13 This discrepancy might be attributed to (1) different types of experimental techniques, (2) the inability to determine the exact interfacial area, (3) the assumption of a pseudo-first-order reaction, (4) difficulties of obtaining solubility and the diffusivity of CO2 in MEA solutions, and (5) the possible existence of interfacial turbulence driven by surface tension gradients.3−5 With regard to the type of reactor for absorption processes, packing has been used to enhance the performance of absorption columns. In general, packings are classified into the categories of random packing and structured packing. In comparison with random packing, structured packing offers excellent mass transfer performance with lower pressure drops because of regular geometric structures.14,15 In recent years, packed bed columns have become more popular for a wide range of applications, because of enhanced performance. In the design of absorption process, one of the most important items to be considered should be the temperature variation within the absorption column.17 The temperature distribution within the absorber column is important because it influences the solubilities of the gas phase components, the vapor pressure of the solvent and the values of the transport properties.17 For example, the rate of chemical reaction between the reactive solvent and solute gas, and the solubility of the solute gas strongly depends on temperature.18 For the simulation of CO2 absorption into MEA solutions, DeMontigny et al. developed a model to predict the absorption of carbon dioxide into aqueous solutions of monoethanolamine in a packed bed column, containing Sulzer DX structured packing.19 The model is based on Pandya’s material and energy balance model.18 A new correlation for the effective surface area was developed and the model was validated by comparing experimental data with the simulation results.16

3. EXPERIMENTAL DATA For the mathematical modeling of CO2−MEA process in this research, the available experimental data of the process was mainly obtained from the work of Aboudheir, which were investigated over a wide range of operating conditions.24 Aboudheir conducted experiments to measure the absorption rate of carbon dioxide into aqueous monoethanolamine solution by using both a laminar jet absorber and a packed bed column. Summaries of both cases are given below.24 First, a laminar jet absorber was used to measure the absorption rate of gas into reactive liquid under predetermined variables of the operating conditions such as concentration, pressure, temperature, and contact time. Variation of the absorber jet length and the liquid flow rate was applied to investigate the effect of change of contact time. In his research, a wide range of operating conditions was used for the experiments for the laminar jet absorber: • Total monoethanolamine concentration: 3.0−9.0 mol/L • Total CO2 loading in solution: 0.1−0.49 mol CO2/mol MEA • Contact time: 0.005−0.02 s • Temperature: 293−333 K All experiments were conducted at atmospheric pressure. The absorption rate, by volume, was measured using a digital soap-film meter. In his experimental work, the temperature of the liquid and gas which entered and left the jet chamber was controlled by external heating/cooling circular units. The gas flow rate entering the jet chamber was measured using a gas flow meter. Second, in his experimental work with a packed bed column, the absorption of CO2 from air into MEA solution was performed in a pilot plant. This consisted of three identical absorption columns and a regenerator. Three different types of packing materials such as pall rings-16 mm, IMTP#15, and A4structured packings were used separately in three individual absorber columns. The absorption experiments were conducted in a counter-current mode at different operating conditions. The following range of the operating conditions was applied to the experiments: 4329

dx.doi.org/10.1021/ie201869w | Ind. Eng. Chem. Res. 2012, 51, 4328−4346


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Table 1. Experimental Data Using a Packed Bed Column with IMTP#15 Packing24 parameters inlet gas flow rate (kmol/m2·h) inlet gas temperature (°C) liquid flow rate (m3/m2·h) MEA concentration (kmol/m3) inlet CO2 loading (mol CO2/mol MEA) outlet CO2 loading (mol CO2/mol MEA) CO2 removal (%) parameters inlet gas flow rate (kmol/m2·h) inlet gas temperature (°C) liquid flow rate (m3/m2·h) MEA concentration (kmol/m3) inlet CO2 loading (mol CO2/mol MEA) outlet CO2 loading (mol CO2/mol MEA) CO2 removal (%)

B001

B002

B004

B007

B008

B009

B012

31.80 25 15.40 3.00 0.174 0.347 94.8 B013

31.80 25 21.10 3.00 0.185 0.306 97.5

31.80 25 15.40 3.00 0.353 0.488 72.5

31.80 24.5 7.50 3.00 0.195 0.420 91.4

31.80 24.5 15.20 3.00 0.195 0.315 96.6

31.80 23.5 7.40 3.00 0.195 0.268 99.20 B033 46.8 27.7 7.4 9.0 0.204 0.323 92.8

50.50 26.5 14.70 4.00 0.105 0.191 96.0

B015

B016

B020

31.80 24.5 20.90 3.00 0.328 0.441 85.70 B031

31.80 25.8 7.40 5.00 0.195 0.331 96.2

50.5 26 6.6 5.1 0.078 0.399 89.9

50.50 26 16.90 5.10 0.078 0.214 96.8

31.8 27.9 7.4 9.0 0.204 0.289 98.0

• Total monoethanolamine solution concentration: 3.0− 9.0 kmol/m3 • CO2 loading in the liquid feed: 0.078−0.353 mol CO2/ mol MEA • Superficial liquid flow rate: 6.6−24.0 m3/m2·h • Superficial gas flow rate: 28.1−65.5 kmol/m2·h • Feed CO2 concentration in air: 5.0−20.3% At steady state operation, the gas concentration and temperature profiles along the column height were reported. For a case study in this research, sets of experimental data, which were obtained from INTALOX Metal Tower Packing (IMTP#15), a high performance random packing, are adopted as shown in Table 1. Aboudheir provides a more detailed description of these experiments and the data obtained from them.24

Since carbon dioxide reacts with monoethanolamine solution, its physical solubility and diffusivity cannot be measured directly. Therefore, N2O is used as an alternative of CO2. The N2O analogy has been frequently used to estimate the solubility and diffusivity of CO2 in amine solutions.13,25−31 The N2O analogy for the solubility of CO2 in amine solution is given as (HCO2)amine = (HN2O)amine (HCO2/HN2O)water

where, HN2O is the solubility of N2O in amine solution. Calculating the physical solubility of CO2 in monoethanolamine solution by using the N2O analogy requires two experimental measurements: (1) the physical solubility of CO2 and N2O in water and (2) the solubility of N2O in monoethanolamine. Since the effect of the reaction between CO2 and H2O on solubility is very small, it can, in general, be neglected.4,32 Versteeg and Van Swaaij4 proposed the following correlations for the solubility of N2O and CO2 in water:

4. MODELING 4.1. Physical Properties. The estimation of the appropriate physical properties of the fluid, involved in the absorption process is one of the most important factors for the mathematical modeling of the absorption process with chemical reaction. Physical properties such as density, viscosity, solubility, and diffusivity of the CO2−MEA system are carefully considered for the modeling in this research. 4.1.1. Solubility and Diffusivity. Physical solubility and diffusivity of the solute gases in the solvents are very important parameters, both for the analysis of the observed absorption rate from experiments and its mathematical modeling. However, the complexity of the absorption process significantly increases when the gas absorption is accompanied by chemical reaction, since it is impossible to measure the solubility of the substance directly. In such cases, it is often required to meaure the solubility of the inert gas in a solution, which has similar properties to the target solute. Solubility of CO2 in Amine Solution. Solubility is given by Henry’s law, which relates the equilibrium concentration of the gas in the liquid phase as a function of its partial pressure in the gas phase. Pi = HiCi

(2)

⎛ 2044 ⎞ ⎟ (HCO2)water = 2.8249 × 106 exp⎜ − ⎝ T ⎠

(3)

⎛ 2284 ⎞ ⎟ (HN2O)water = 8.7470 × 106 exp⎜ − ⎝ T ⎠

(4)

Where, the units of the solubility are kilopascal cubic meters per kilomole, and temperature is in kelvin. Versteeg and Van Swaaij4 and Mandal et al.31 experimentally measured the solubility of CO2 in water at various temperatures. Predicted solubilities of CO2 in water using eq 3 shows good agreement with the experimentally measured values, with an average deviation of 3%. Versteeg and Van Swaaij4 and Mandal et al.31 also experimentally measured the solubility of N2O in water at various temperatures. Predicted solubilities of CO2 in water using eq 4 show good agreement with the experimentally measured values, with an average deviation of 3.6%. Wang et al. experimentally measured solubility of N2O in pure MEA over the temperature range of 20−85 °C and proposed the solubility of N2O in pure amine as follows.33

(1)

where, Hi is the Henry’s law constant for the gas component i, and Ci is the equilibrium concentration of the absorbed gas i in the liquid.

⎛ 1136.5 ⎞ ⎟ (HN2O)pure MEA = 1.207 × 104 exp⎜ − ⎝ T ⎠ 4330

(5)



Article

agreement with the experimentally measured values, with an average difference of 6.1%. The scattered and inconsistent diffusivity data of N2O in amine may contribute to the inconsistent results for the reaction kinetics.3 The correct diffusivity of N2O in amine is essential to estimate the correct free molecular diffusivity of CO2 in monoethanolamine solution, which can be used in developing the reaction kinetic models. Ko et al.35 developed a correlation to determine the diffusivity of N2O in amine solution at temperatures of 303, 308, and 313 K, along with different amine concentrations, as shown in eq 13:

Where, (HN2O)MEA is the solubility of N2O in kilopascal cubic meters per kilomole, and T is in kelvin. Wang et al.33 proposed to calculate the solubility of N2O in monoethanolamine semiempirically: 3

(HN2O)MEA solution = R23 +

∑ φj ln((HN2O)pure MEA, j ) j=2

(6)

where, (1) (HN2O)MEA solution is Henry’s constant of N2O in MEA solvent, (2) (HN2O)pure MEA is Henry’s constant of N2O in pure MEA solvent, (3) 2 refers to the pure amine, (4) 3 refers to water, and (5) φj is the volume fraction of solvent. The volume fraction is calculated by the following equation:33

⎛ b + b4Camine ⎞ D N2O = (b0 + b1Camine + b2Camine2) exp⎜ 3 ⎟ ⎝ ⎠ T (13)

3

Where, DN2O is a diffusivity of N2O in amine solution, and Camine is a concentration of amine in solution. The units of diffusivity, concentration, and temperature are squared meters per second, kilomoles per cubic meter, and kelvin, respectively. 4.1.2. Density. Weiland et al. studied the effect of carbon dioxide loading on density and viscosity of industrial strength alkanolamines solutions and developed an empirical equation below to describe the density of the alkanolamine solutions as a function of CO2 loading and temperature.36

φj = xjVj/ ∑ xjVj j=2

(7)

where Vj is the molar volume of pure solvent j, The excess Henry’s quantity for a binary system is defined as a function of volume fraction:34 R23 = φ N Oφpure MEA α23 2

(8)

where α23 is a two-body interaction parameter. It is temperature-dependent and described by the following expression.34 2

α23 = a + bT + cT + d φ3

ρ=

(9)

(14)

Where, ρ is a solution density (g/cm ), V is a molar volume of the solution (cm3/mol), and xi and Mi are a mole fraction and a molecular weight of amine, water, and carbon dioxide. The molar volume of an ideal solution shall be the sum of the molar volumes of the components multiplied by their respective mole fractions under the assumption of neither reaction nor ionization. However, the amine solution, loaded with CO2, is not ideal. Therefore, additional terms need to be added to account for interactions between components such as “amine + water” and “amine + carbon dioxide”, as described in eq 15.36 3

Where, φ3 is the volume fraction of water, and a, b, c, and d are parameters for each binary system.34 Tsai et al. compared the predicted solubility of N2O in aqueous monoethanolamine solution within the concentration range of 1−6 M from eq 6 with experimental data and reported 4.5% deviation.34 Predicted solubilities of N2O in pure MEA using eq 5 are in good agreement with the experimentally measured values, with an average deviation of 1.4%. Diffusivity of CO2 in Amine Solution. Diffusivity of CO2 in amine solution can be obtained in a similar manner to the solubility of CO2 in amine solution as shown below. ⎛ DCO ⎞ 2⎟ (DCO2)amine = (D N2O)amine ⎜⎜ ⎟ ⎝ D N2O ⎠ water

xAmMAm + x H2OM H2O + xCO2MCO2 V

V = xAmVAm + x H2OVH2O + xCO2VCO2 + xAmx H2OV * + xAmxCO2V * *

(10)

where, (DCO2)amine is the diffusivity of N2O in amine solution. Versteeg and Van Swaaij4 proposed the following correlations for the diffusivity of N2O and CO2 in water: ⎛ 2119 ⎞ ⎟ (DCO2)water = 2.35 × 10−6 exp⎜ − ⎝ T ⎠

(11)

⎛ 2371 ⎞ ⎟ (D N2O)water = 5.07 × 10−6 exp⎜ − ⎝ T ⎠

(12)

(15)

Where, (1) xAm, xH2O, and xCO2 are mole fractions of pure monoethanolamine, water, and carbon dioxide, respectively, (2) VAm, VH2O, and VCO2 are molar volumes of pure monoethanolamine, water, and carbon dioxide, respectively, (3) V* is a molar volume associated with the interaction between water and monoethanolamine, and (4) V** is a molar volume associated with the interaction between carbon dioxide and monoethanolamine.36 Al-Ghawas et al.27 and DeGuillo et al.37 developed the following correlation for the density of pure amine.

Where, the units of the diffusivity are squared meters per second, and temperature is in kelvin. Versteeg and Van Swaaij4 and Mandal et al.31 reported experimentally measured diffusivity of CO2 in water. The predicted diffusivities of CO2 in water from eq 11 were in good agreement with the experimentally measured values, with an average difference of 3.2%. Versteeg and Van Swaaij,4 Ko et al.,35 and Mandal et al.31 reported experimentally measured diffusivities of N2O in water, and predicted diffusivities of N2O from eq 12 were in a good

ρpure component = a1 + a2T + a3T 2

(16)

Where, a1, a2, and a3 are constants, T is temperature in kelvin, ρpure component is the density of pure amine in kilograms per cubic meter. Predicted densities of pure MEA using eq 16 show good agreement with the experimentally measured values, with an average deviation of 0.035%.37 4331



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For a binary system, the δν12 is a function of temperature and mole fraction:39

The molar volume of pure monoethanolamine, VAm, is

1

δν12 = x1x2

described below.37 VAm =

i=0

a1 + a2T + a3T

(21)

where Ai is a pair parameter, which is a function of temperature.

MAm 2

(17)

Ai = a +

Where, (1) VAm is the molar volume of pure amine, (2) MAm is the molecular weight of amine, and (3) a1, a2, and a3 are constants. Hsu and Li also developed an expression to calculate the density of the pure components.38 ρi = a1 + a2T + a3T 2

(18)

(22)

where a1, a2, and a3 are the constants that are determined from the kinematic viscosities of pure fluids. The viscosity of the solution is a product of density and kinematic viscosity of the solution. The overall average absolute percentage deviation of the predicted viscosity from experimental data is about 1.0%.39 DiGuillo et al. developed a correlation to determine the viscosities of the monoethanolamine, as described in eq 24.40 ln νi = b1 +

b2 T − b3

(24)

Predicted viscosities of pure MEA using eq 24 are in good agreement with the experimentally measured values with an average deviation of 0.25%.40,41 The correlation and constants for the viscosities of pure MEA, which are given by DiGuillo et al.,40 showed better agreement with experimentally measured values, as compared with the correlation from Hsu and Li.39 Surface Tension. Surface tension is one of the main parameters which affect the mass transfer rates. The surface tension, σ, of aqueous monoethanolamine solutions is obtained from the correlation developed by Vazquez et al. as described in eq 25.42

[(aΩ + b)T + (c Ω + d)][α(e Ω + fT + g ) + 1]Ω η = exp ηH O T2 2

(19)

Where, η and ηH2O are the viscosities (mPa·s) of the amine solution and water, respectively, Ω is the mass percent of amine, T is the temperature (K), and α is the CO2 loading (mole of CO2/mol of amine). This equation can be used to calculate MEA solution viscosities up to the following level: • Maximum amine concentrations of 40 wt % • CO2 loading up to 0.6 mol of CO2/mol of MEA • Maximum temperature of 398 K The standard deviation to published experimental data is 0.0732.36 However, the correlation that was developed by Weiland et al. is not applicable for concentrations higher than 40 wt % MEA.36 Therefore, Hsu and Li developed a correlation for the estimation of the viscosity, based on the Redlich−Kister equation, which can be used for concentrations higher than 40 wt % MEA.39 The kinematic viscosity νm of the solution can be calculated from the following expression:39

∑ xi ln νi

b T+c

Here a, b, and c are constant parameters. Hsu et al. developed a correlation for the viscosity of pure fluids, νi:39 a2 ln νi = a1 + T + a3 (23)

Where, (1) ρi are the densities of pure components in grams per cubic centimeter, (2) T is the temperature in kelvin, and (3) a, b, and c are constant factors. This density expression covers a wide range of temperatures, from 15 to 200 °C, and the average percentage deviation is about 0.038% for 115 data points.38 4.1.3. Viscosity and Surface Tension. Viscosity. Viscosity of the solution is one of the important factors in the modeling of the mass-transfer rate of absorbers and regenerators because it affects the liquid-film coefficient of mass transfer. Weiland et al. developed an empirical equation to calculate the viscosity of an amine solution at a given temperature, amine concentration, and CO2 loading, as described in eq 19.36

ln νm = δv12 +

∑ Ai(x1 − x2)

σ = σH2O − (σH2O − σMEA )x ⎛ (0.63036 − 1.3 × 10−5(T − 273.15))x H2O ⎞ ⎟ × ⎜1 + ⎜ 1 − (0.947 − 2 × 10−5(T − 273.15))x H2O ⎟⎠ ⎝ × x MEA

(25)

where xH2O and xMEA denote the mole fractions of water and MEA in aqueous monoethanolamine solution. The maximum deviation between experimentally measured values and predicted surface tension from eq 25 was reported to be less than 0.5% for MEA solutions.42 The pure liquid surface tensions of water and monoethanolamine are obtained from the following correlations:42 σH2O = 76.0852 − 0.1609(T − 273.15)

(26)

σMEA = 53.082 − 0.1648(T − 273.15)

(27)

The predicted surface tensions of pure water and MEA from eqs 26 and 27 are in good agreement with the experimentally measured values, with an average difference of 0.09% and 0.07%, respectively.42 4.2. Identification of Feasible Reaction Mechanisms and Kinetics. Although the reactions between CO2 and

(20)

Where, ν the kinematic viscosity, and the subscripts m and i represent the kinematic viscosity of the solution and the pure fluid. 4332



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RNH2+COO− + H2O

monoethanolamine have been extensively studied for more than 50 years, they are still not fully understood yet.6−8,12,22,24,43,44 Danckwerts and McNeil proposed the reaction mechanism between carbon dioxide and primary and secondary alkanolamines with two-step reactions as shown below.45

k 6 , k−6 , K 6

←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ H3O+ + RNHCOO−

(37)

RNH2+COO− + OH− k 7 , k−7 , K7

←⎯⎯⎯⎯⎯⎯⎯⎯⎯→ H2O + RNHCOO−

Step 1: carbamate formation CO2 + R1R2NH ⇔ R1R2NHCOO− + H+

(8) Carbamate reversion to bicarbonate (hydrolysis reaction)

(28)

k8,k−8 , K8

RNHCOO− + H2O ←⎯⎯⎯⎯⎯⎯⎯⎯⎯→ RNH2 + HCO3−

Step 2: protonated alkanolamine formation R1R2NH + H+ ⇔ R1R2NH2+

(39)

(29)

(9) Dissociation of protonated MEA

With second-order, the overall reaction becomes the following: CO2 + 2R1R2NH ⇔ R1R2NCOO− + R1R2NH2+

k 9 , k−9 , K 9

RNH3+ + H2O ←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ RNH2 + H3O+

(30)

2H2O ↔ OH− + H3O

k10 , k−10 , K10

(32)

k r2 = − k2[CO2 ] + 2 [HCO3−][H3O] K2

(33)

(41)

k r10 = − k10[CO2 ][OH−] + 10 [HCO3−] K10

(42)

RNH2+COO− + HCO3− k11,k−11, K11

←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ H2CO3 + RNHCOO−

k12,k−12 , K12

←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ HCO3− + RNHCOO−

K3

k ∑ k−b[BH+] [CO2 ][RNH2] − −4 [RNHCOO−]

rCO2 =

(34)

(4) Zwitterion formation from MEA and CO2 reaction The intermediate zwitterion is formed by reaction between carbon dioxide and monoethanolamine solution.46 The zwitterion mechanism is generally defined as a reaction mechanism for the formation of carbamate from carbon dioxide and monoethanolamine.3,4,51−53 k4 , k−4,K 4

CO2 + RNH2 ←⎯⎯⎯⎯⎯⎯⎯⎯⎯→ RNH2+COO−

k4

∑ kb[B]

k−4 1 + k4 k4 ∑ kb[B] (45)

When CO2 reacts with aqueous MEA, the formation of the zwitterion has been shown to be the rate determining step, and the zwitterion deprotonation is considered to be much faster than the reverse rate to CO2 and MEA, which can be defined as k−4/(k4 ∑kb[B]) ≪ (1/k4). For this reason, the above rate can be simplified to the following expression, where the reaction rate appears to be the first order in both the amine and the CO2 concentrations:3,54

(35)

(5−7) Carbamate formation by deprotonation of the zwitterion Subsequent removal of the proton by a base that could be amine, OH−, or H2O RNH2+COO− + RNH2 k5 , k−5 , K5 ←⎯⎯⎯⎯⎯⎯⎯⎯⎯→ RNH3+ + RNHCOO−

(44)

Where, Ki is the equilibrium constant, ki is the forward rate coefficient, and k−i is the reverse rate coefficient of reaction i. From the zwitterion mechanism, the general reaction rate of CO2 with monoethanolamine is described as follows:3,54

(3) Dissociation of bicarbonate HCO3− + H2O ↔ CO32 − + H3O+

(43)

RNH2+COO− + CO32 −

(2) Dissociation of dissolved carbon dioxide through carbonic acid k2,k−2K2

CO2 + OH− ←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ HCO3−

Since temperature, concentration, and CO2 loading are the operating variables in absorption process, the following reversibility between reactants and products should not be ignored in the kinetic studies.24

(31)

CO2 + 2H2O ←⎯⎯⎯⎯⎯⎯⎯→ HCO3− + H3O+

(40)

(10) Bicarbonate formation The reaction of CO2 with hydroxyl ion is considered as the bicarbonate formation.

Where, R1 represents the −(CH2)2− group, and R2 represents the −R1−OH group. The reactions between CO2 and MEA solution have been described in the literature by two mechanisms: (1) the zwitterion mechanism, which was introduced by Danckwerts,46 and (2) the termolecular mechanism, which was introduced by Crooks and Donnellan.11 Extensive literature on the reaction between CO2 and alkanolamines in aqueous solutions have been published so far and were reviewed well by Blauwhoff et al. in 1984.3 All feasible reactions are identified from the published literatature and are summarized below:24,47−50 (1) Ionization of water K1

(38)

rCO2 = k4[CO2 ][RNH2]

(46)

where, k4 is the second-order rate constant. The termolecular mechanism assumes that the reaction is a single step, where the initial product is not a zwitterion. The

(36) 4333



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Jou et al.; Liu et al.; Park et al.; Ma’mun et al.; Jakobsen et al.; Barreau et al.; and Bottinger et al.45,47,48,55−68 Details of this research are summarized in the work of Hiwale.2 4.3.2. Equilibrium Constants. Reactions of eq 31, 32, and 34 have been common, which have been studied and reported in the literature over a wide range of temperatures and pressures.48,59,69 The equilibrium constants for dissociation or ionization of water (eq 31), dissociation of carbon dioxide (eq 32), and dissociation of the carbonate ion (eq 34) are calculated by the correlations developed by Edwards et al.69 The equilibrium constant, Ki, is a function of temperature, as described in eq 53.69

forward reaction rate of this mechanism is presented as follows:11,24,54 rCO2 = − (kRNH2[RNH2] + k H2O[H2O])[RNH2][CO2 ] (47)

where kRNH2 and kH2O are the constants of the forwarding third-order reaction rate for MEA and H2O, respectively. Aboudheir obtained the reaction rate constants of kRNH2 and kH2O by a linear regression analysis of the absorption rate:24 ⎛ −4412 ⎞ ⎟ kRNH2 = 4.61 × 109 exp⎜ ⎝ T ⎠ ⎛ −3287 ⎞ ⎟ k H2O = 4.55 × 10 exp⎜ ⎝ T ⎠

(48)

ln K i =

6

(49)

(50)

⎡ B C D E ⎤ K i = exp⎢A + + 2 + 3 + 4⎥ ⎣ T T ⎦ T T

For aqueous monoethanolamine solutions, the overall reaction order has a value of two, and the partial order in the amine is equal to one. However, the reported values of the reaction rate constant, k4, are relatively scattered.54 ⎛ 5400 ⎞ ⎟ k4 = 4.4 × 1011 exp⎜ − ⎝ T ⎠

2152 T

(54)

where parameters A, B, C, D, and E are constants. The input data of the thermodynamic model for CO2−amine solution includes (1) initial concentration of the MEA solution, [MEA]0, (2) the initial CO2 loading in the MEA solution, α, (3) the equilibrium constants of the reactions, and (4) the solubility of CO2 in MEA solution as a function of both amine concentration and temperature. It has been assumed that all of the chemical reactions are at equilibrium.24,31,41,50,70,71 The concentration of water is assumed to remain constant because it is much larger than the concentration of all the other species and also because of the short contact time in the laminar jet absorber.24,41,70 The concentrations of the remaining eight chemical species, which are shown in the above chemical reactions, are calculated by solving the following mass balance equations with the Henry’s law correlation.

(51)

Where, k4 is in cubic meters per mole second, and T is in kelvin. Therefore, the reaction rate constant for the CO2−MEA system that was characterized by Hikita et al.43 is adopted: log(k4) = 10.99 −

(53)

where parameters A1, A2, A3, and A4 are constants. The equilibrium constants for carbamate reversion (hydrolysis reaction) (eq 39) and dissociation of protonated MEA (eq 40) are calculated by the correlations developed by Kent and Eisenberg, as shown in eq 5456

The rate constant of the termolecular mechanism is presented by Aboudheir:24 k4 = kRNH2[RNH2]2 + k H2O[H2O][RNH2]

A1 + A2 ln T + A3 + A 4 T

(52)

4.3. Bulk Liquid Equilibrium Model. 4.3.1. Background on Equilibrium Modeling. A thermodynamic model to estimate CO2 partial pressure and liquid bulk concentrations of all the chemical species present in the solution is required for the kinetic analysis. The liquid bulk concentrations of all chemical species can be estimated from the initial concentration of amine, the initial CO2 loading, and the assumption of that all reactions are at equilibrium.41 In the carbon dioxide−monoethanolamine system, the first step is the dissolution of CO2 gas, which is purely a physical process and occurs prior to chemical reaction in the amine solution. In the formation of bicarbonate, amine reacts with the carbonic acid, which is formed from the dissolution of carbon dioxide in water. The bicarbonate formation takes place at the ratio of 1:1 for the reaction of carbon dioxide to monoethanolamine, and the enthalpy of absorption is very low. The bicarbonate is also in equilibrium with carbonate and carbonic acid. The carbamate formation takes place at the ratio of 0.5:1 for the reaction of carbon dioxide to monoethanolamine; two molecules of monoethanolamine are required to absorb one molecule of carbon dioxide. In this step, one molecule is required for the formation of carbamate, while the second molecule acts as a base to react with the proton released. A number of experiments on vapor−liquid equilibrium in CO2 and amine solution system and its mathematical analysis have beed carried out by many researchers since the 1960s: Danckwerts and McNeil; Lawson and Garst; Kent and Eisenberg; Deshmukh and Mather; Jou et al.; Austgen et al.; Shen and Li; Weiland et al.; Li and Shen; Li and Mather;

MEA balance [RNH2] + [RNH3+] + [RNHCOO−] = [MEA]0

(55)

Carbon balance [CO2 ] + [HCO3−] + [CO3−] + [RNHCOO−] = α[MEA]0

(56)

Charge balance [RNH3+] + [H3O+] = [HCO3] + [OH−] + 2[CO3−] + [HCO3−] + [RNHCOO−]

(57)

Independent equilibrium constants

4334

K1 = [OH−][H3O+]

(58)

K2 = [HCO3][H3O+]/[CO2 ]

(59)

K3 = [CO−][H3O+]/[HCO3]

(60)

K8 = [RNH2][HCO3]/[RNHCOO−]

(61)


Industrial & Engineering Chemistry Research K 9 = [RNH2][H3O+]/[RNH3+]

Article

The above nine algebraic eqs, 55−62, and 1 are solved for the nine unknown variables of the bulk concentrations and the equilibrium partial pressure. The program utilizes the subroutine C05NCF from Numerical Algorithms Group (NAG) library. 4.4. Mass Transfer. 4.4.1. Interfacial Area and Mass Transfer Coefficients. Mass transfer coefficients for gas absorption, desorption, and vaporization are important factors for the design of packed bed column since it directly affects absorption performance of the column. Most of the packing models are based on empirical or semiempirical correlations, which are developed mainly through absorption/distillation experiments. Meanwhile, generalized correlations to estimate the individual mass transfer coefficients have been proposed for widely used packings such as Raschig rings, Berl saddles, and Pall rings by Onda et al., Bolles and Fair, and Bravo and Fair.72−74 For example, Bravo et al. developed correlations for structured packings.75 Onda’s correlations have been well-described in many publications, including Perry’s Handbook.76 The correlations of Onda et al. provided separate effects of the operating conditions on the coefficients and specific area.18,72 The effective interfacial area is an important parameter for accurate modeling, design, and scale-up of the absorption processes. Onda developed equations for the wetted surface area (ae), taking into account the liquid surface tension, as shown in eq 64.72

(62)

where R = CH2OHCH, RNH2 = CH2OHCH2NH2C2H7NO, RNHCOO− = C3H6NO3−, and RNH3+ = C2H8NO

The equilibrium constants of K1, K2, and K3 are calculated by the correlations developed by Edwards et al.69 These correlations are well established and have been utilized by Austgen et al. and Li and Mather.48,61 For K8 and K9, the equilibrium constants are expressed as a function of temperature only by Kent and Eisenberg, as described in eq 54.56 On the other hand, Li and Shen developed an alternative correlation that is a function of temperature, amine concentration, and CO2 loading as shown in Table 2.60 Aboudheir reported that the K8 and K9 Table 2. Equilibrium Constants, as a Function of Temperature, Amine Concentration, and CO2 Loadinga 60 ln K = b1 + b2 /T + b3/T 3 + b4a + b5/a + b6 /a2 + b7 ln M K8 (mol/L) (for reaction 39)

K9 (mol/L) (for reaction 40)

−13.071 7.617 * 103 −3.221 * 103 0.8808 −2.537 0.8293 −1.0935

13.24 −1.221 * 104 2.157 * 108 2.502 −2.643 0.2628 −0.067

b1 b2 b3 b4 b5 b6 b7 a

−0.05 ⎤ ⎡ 0.1 ⎛ L2 ⎞0.2 ⎥ ⎛ σ ⎞0.75⎛ L ⎞ ⎛ L2a t ⎞ ae ⎢ ⎟ ⎜ ⎟ ⎟⎟ ⎜⎜ = 1 − exp⎢− 1.45⎜ c ⎟ ⎜⎜ ⎜ ⎟ ⎥ at ⎝ σL ⎠ ⎝ a tμL ⎠ ⎝ ρ L 2g ⎟⎠ ⎝ ρ LσLa t ⎠ ⎥ ⎢⎣ ⎦

⎤ ⎡ ⎛ σ ⎞0.75 = 1 − exp⎢− 1.45⎜ c ⎟ (Re)0.1(Fr )−0.05 (We)0.2 ⎥ ⎥ ⎢ ⎝ σL ⎠ ⎦ ⎣

The temperature range used is 313−373 K.

(64)

correlations of the Kent and Eisenberg prediction showed good agreement with the measured equilibrium partial pressure at CO2 loading with a deviation of less than 0.6%, while K8 and K9 correlations from Li and Shen showed good agreement with deviation of greater than 0.6%.24,56,60 For this reason, the equilibrium constant correlations K8 and K9 of Kent and Eisenberg are applied to the bulk liquid equilibrium model in this research.56 An accurate thermodynamic model to estimate the CO2 partial pressure and the liquid bulk concentrations of all of the chemical species involved in the system is important to produce accurate results from the simulation model. Therefore, an understanding of the equilibrium behavior is essential for the absorption processes in aqueous amine solution. For the distribution of solute gas A (CO2) across the interphase, the concentration can be calculated from the following expression:

The above equation can be applied with ±20% error to a column packed with Raschig rings, berl saddles, spheres, and rode, made from ceramic glass and polyvinylchloride.72 The liquid-side mass transfer coefficient correlation is described as follows.72 ⎛ L ⎞0.67 ⎛ μ ⎞−0.5 ⎛ ρ ⎞−0.33 0.4 L ⎟⎟ ⎜⎜ ⎟⎟ kL = 0.0051⎜⎜ (a tDp) ⎜⎜ L ⎟⎟ ⎝ a tμL ⎠ ⎝ ρ LDL ⎠ ⎝ μLg ⎠ (65)

The gas phase individual mass transfer coefficient (kG) can be estimated from the correlation, proposed by Onda.72 The gas side mass transfer coefficient correlation is described as ⎞0.7 ⎛ μ ⎞0.33 ⎟⎟ ⎜⎜ G ⎟⎟ (a tDp)−2.0 G ⎠ ⎝ ρGDG ⎠

⎛ D a ⎞⎛ G k G = 5.23⎜ G t ⎟⎜⎜ ⎝ RT ⎠⎝ a tμ

0

pA, i =

k E pA + LA Ci k

(66)

GA

0

k E 1 + LA Hi k GA

4.4.2. Enhancement Factor. When dissolved gas reacts with liquid, an enhancement factor is often used to describe the effect of a chemical reaction on the absorption. The enhancement factor is defined as the ratio of “the mass transfer coefficient for the absorption with chemical reaction” to “the mass transfer coefficient for purely physical absorption”.77 Wellek et al. derived the following correlation for the calculation of enhancement factor, E, with deviation of less than

(63)

where Hi, Ci, E, and kL0 are the Henry’s law constant, the equilibrium concentration, the enhancement factor which is described in section 4.4.2, and the physical mass transfer coefficient, respectively. The liquid phase interfacial concentration can be obtained from eq 1. 4335



Article

3%.19,21−23,78−80 The explicit expression for the enhancement factor is described in eq 67.78 E=

E12 ( 1 + 4(Ei − 1)Ei /E12 − 1) 2(Ei − 1)

used.6,12,13,24,27,49,50,70,77,83−85 Therefore, mass transfer in the liquid phase is described by the penetration theory model. (2) The curvature effect of the cylindrical liquid jet is neglected, and the gas-absorbing liquid is considered to be infinitely deep with a flat surface. Aboudheir reported that the penetration depth for gas absorption, accompanied by chemical reaction as occurs in the CO2−MEA system, was much smaller than 1.5% of the MEA-jet diameter. The same assumption is applied to the models developed in this work.24 (3) The reaction occurs within the liquid mass transfer film, which has a thickness of xf, and the bulk liquid is in equilibrium. (4) Carbon dioxide and water are the main components, which are transported across the interface. (5) Axial dispersion in the liquid layer can be neglected. (6) Heat transfer resistance in the liquid phase is relatively small, compared with the gas phase. (7) Mass transfer resistance for water in the liquid phase is negligible. (8) Major operating variables, including temperature are taken into account for the calculation of diffusivity, solubility, and chemical rate constants. (9) The termolecular mechanism and its kinetic reaction rates reported by Aboudheir are considered in this model. The objectives in this work are (a) both models will take into account all physical and chemical phenomena in the process including mass transfer, chemical kinetics of all identified reactions, and chemical equilibrium and (b) both models will predict accurately carbon dioxide absorption rates and kinetics of all identified reactions. 4.5.1. Model 1 for Laminar Jet Absorber. The basic mathematical models of the absorption process with chemical reactions are previously discussed in the paper of “Model Building Methodology for Multiphase Reaction System” and the same models are extended further to the carbon dioxide− monoethanolamine system in this research.1 In model 1, total volume is equally divided into a number of identical elemental volumes, which are considered as a compartment. The mass balance equations for the gas and the liquid are separately written for each compartment. At each compartment, gas and liquid enters with information of temperature, molar flow rate, and composition. Solute gas i crosses the interface into the liquid phase with a flux Ni. Both the liquid and gas in each section are assumed to be well mixed. The liquid and the gas leaving the section are assumed to have the same temperature and composition as the liquid and the gas in the compartment. The film thickness of xf is calculated from penetration theory and varies along the length of jet with respect to contact time. For the laminar jet absorber, the interfacial area is measured accurately. For the solute gas of CO2, physical equilibrium at the interface is expressed by eq 1. The flux of the solute gas i satisfies the following relation:

(67)

where Ei =

DCO2 DMEA

+

CMEA * zCCO 2

DMEA DCO2

(68)

Ei, an enhancement factor shows a deviation of less than 2% for instantaneous reaction compared with penetration theory, which is one of major theories to describe the behavior of highly complex absorption and desorption processes. 78 Higbie81 proposed a model for the gas exchange between a liquid and adjust gaseous phase, and many researchers have successfully used Higbie penetration theory to describe gas absorption process. For example, Scriven and Pigford82 have used penetration theory to predict absorption rates of carbon dioxide in water jet. The phase equilibrium was assumed at gas−liquid interface. The penetration depth of the diffusing carbon dioxide molecules was assumed very small compared with liquid jet diameter. The model predictions showed good agreement with experimental measurement, which validated assumption of phase equilibrium at the freshly formed carbon dioxide−water interfaces. Also, the enhancement factor of a pseudo-first-order reaction showed a deviation of less than 2%, compared with the Hatta number:78 E1 =

M tanh

M

(69)

The Hatta Number is a dimensionless parameter that compares the rate of absorption of a solute in a reactive system to the rate of absorption of the same solute in the case of physical absorption. It is given as78 M=

k4DCO2CMEA kL 0

(70)

where, k4, DCO2, CMEA is the second-order reaction rate constants for the CO2−MEA system, diffusivity of carbon dioxide in aqueous monoethanolamine solution, and concentration of MEA, respectively. 4.5. Reactor Modeling and Simulation of Laminar Jet Absorber. According to the research results of Mandal et al., most of the commercial simulators available today have been developed based on rather simple assumptions and approximations.41 However, a rigorous mathematical modeling is required especially for the absorption process with chemical reaction in order to produce accurate results of the products. In this research, two mathematical models were developed based on different modeling approaches, using experimental data obtained with a laminar jet apparatus. For both modeling approaches, the following principles are adopted: (1) Many researchers have confirmed that penetration theory is able to correctly represent the behavior of different gas absorption systems such as CO2−MEA, Cl2−aqueous bicarbonate solutions and aqueous hydroxide solutions, CO2−MEA + MDEA, CO2−MDEA, CO2− DEA, etc. in particular when a laminar jet absorber is

Ni = k l0aEi(Ci ,int − Ci ,bulk )

(71)

Where, (1) kl0 is the physical mass transfer coefficient of the solute gas i in the liquid phase, (2) a is the area of the interface, (3) Ei is the enhancement factor of the dissolved gas i. 4336



Article

For the CO2−MEA system, eqs 31−41 are used for the equilibrium reactions, which occur in the bulk of the liquid. 4.5.2. Model 2 for Laminar Jet Absorber. Model 2 for a laminar jet absorber has been developed based on unsteadystate partial differential equations. From the laminar jet absorber experiments, the interfacial area is measured, and the physical mass transfer coefficient is obtained from solution of the hydrodynamic equations. Many researchers have developed models based on numerical solutions of a set of partial differential equations to predict the absorption rates.24,41,52,71,87,88 The diffusion−reaction processes are modeled according to Higbie’s penetration theory with the assumption of that all reactions are reversible. The model involves all possible reversible reactions and partial differential equations. In laminar jet absorber experiments, the contact time between the gas and the liquid jet is very short; hence, the penetration depth of the absorbed molecules is much smaller than the laminar jet diameter. For convenience, the chemical species in the reactions are named as follows:

(5) Carbamate balance ∂C8 ∂ 2C8 = D8 + r8 − rCO2 ∂t ∂x 2

The instantaneous reactions of eqs 31, 34, and 40 are assumed to be in equilibrium, and the equilibrium constants are presented as follows:24,71

All reactions are assumed to be at equilibrium for the above nine liquid bulk concentrations of C1,bulk−C9,bulk. For nine unknown variables (C1,bulk, ..., C9,bulk), nine nonlinear algebraic equations from 55 to 62 and 1 are solved. The following equations represent the gas diffusion, accompanied by chemical reaction in the liquid near the interface.5,24,41,70,71 (1) Carbon dioxide reaction balance

(72)

log10 k10 = 13.635 − (2895/T )

(74)

Ci(x, 0) = Ci0

at t = 0 and 0 ≤ x ≤ ∞

Ci(∞ , t ) = Ci0

∂ 2C3

∂ 2C4 ∂C ∂C7 + − − D5 25 D D 7 4 2 2 2 ∂x ∂x ∂x ∂x

(83)

(84)

(85)

at x = 0 and 0 ≤ t ≤ τ

(86)

For all volatile chemical species, i = 1, 2, ..., 8

2

∂ C8 ∂x

(82)

Boundary Conditions For all chemical species, i = 1, 2, ..., 8

∂C3 ∂C4 ∂C5 ∂C7 ∂C ∂C8 + − − −2 6 − ∂t ∂t ∂t ∂t ∂t ∂t

∂x

(81)

Thus, there are eight partial differential−algebraic equations, which can be solved for the concentration of the eight chemical species (C1, C2, ..., C8), subject to the following initial and boundary conditions. Initial and Boundary Conditions. For all chemical species, i = 1, 2, ..., 8

(4) Charge balance

2

(80)

The reaction rate constant for the reaction between CO2 and OH− is taken from the work of Pinsent et al. as described in eq 84.32

∂ 2C2

− D8

(79)

k r10 = −k10C1C5 + 10 C4 K10

∂C3 ∂C8 ∂C2 + + ∂t ∂t ∂t

2

C2C7 C3

The reaction constants kRNH2 and kH2O can be calculated from eq 49 and 50, respectively.5,24 The reaction rate of CO2 with OH− is given by Pinsent et al.:32

(3) Total MEA balance

∂ C6

K9 =

rCO2 − term = −(kRNH2C2 + k H2OC9)C2C1

(73)

− 2D6

(78)

Second, the reaction rate of CO2 with MEA is represented via the termolecular mechanism.54 The termolecular mechanism is given by

∂C4 ∂C6 ∂C8 ∂C1 + + + ∂t ∂t ∂t ∂t 2 ∂C4 ∂ 2C6 ∂C ∂ C1 = D1 + D + + D8 28 D 4 6 2 2 2 ∂x ∂x ∂x ∂x

2

C6C7 C4

log10 k2 = 329.850 − 110.541log T − (17265.4/T )

(2) Total carbon dioxide balance

= D3

K3 =

The reaction rate constant of k2 for the reaction between CO2 and H2O is taken from the work of Pinsent et al., and is described as follows.32

C7 = [H3O+], C8 = [RNHCOO−], C9 = [H2O]

∂C3 ∂ 2C8 + D + D 3 8 ∂x 2 ∂x 2 ∂x 2

(77)

k r2 = −k2C1 + 2 C4C7 K2

C4 = [HCO3], C5 = [OH−], C6 = [CO3−],

= D2

K1 = C5C7

The finite reaction rates are described by the following expressions. First, the reaction rate of CO2 with H2O (reaction 2) is described by

C1 = [CO2 ], C2 = [RNH2], C3 = [RNH3+],

∂C1 ∂ 2C1 = D1 + r2 + rCO2 + r10 ∂t ∂x 2

(76)

Ci(0, t ) = Ci* =

(75) 4337

Pi Hi

at x = 0 and 0 ≤ t ≤ τ (87)



Article

For nonvolatile chemical species, i = 1, 2, ..., 8 dC i (0, t ) = 0 dx

at x = 0 and 0 ≤ t ≤ τ

solutions of monoethanolamine absorption in a packed absorption column is proposed based on Pandya’s modeling methodology.18 The Pandya’s modeling is based on Treybal’s research on adiabatic, physical gas absorption and Danckwerts’ work on isothermal gas absorption with chemical reaction.18,77,90 Recently many studies have successfully implemented Pandya’s approach to model the absorption process in a packed bed column.19,21−24,91,92 The procedure developed by Pandya accounts for heats of absorption, chemical reaction in the liquid phase, solvent evaporation and condensation, and also heat and mass transfer resistances in both gas and liquid phases. The temperature distribution within the packed bed column influences the vapor pressure of the solvents, the solubilities of the gas phase components, and the mass tansfer properties. Mass transfer at the gas−liquid interface can be described by using the two-film model. In the two-film model, it is assumed that the resistance to mass transfer is concentrated entirely in the thin film, adjacent to the phase interface, and that mass transfer occurs within these films by steady-state molecular diffusion. It is assumed that there is no concentration gradient in the bulk phase, which is the outside of the film, because of perfect mixing.93 In the film, the film thickness can be estimated by using the mass transfer coefficient correlations, which govern the mass transport dependence on physical properties and process hydrodynamics. Liquid and gas side film thickness depends strongly on the flow pattern in the column, the type of column internals and gas and liquid physical properties, including surface tension, diffusivity, and viscosity. Another important parameter of the film model is the interfacial area, which can be estimated from experimental data. In general, data of film thickness, interfacial area, and mass transfer coefficients area most often are determined by empirical correlations.93 In this research work, computer models are developed based on the following: (1) A material and energy balance model developed by Pandya is used because the model accounts for the major heat effects (absorption, reaction, solvent evaporation, and condensation).18 (2) A bulk liquid equilibrium model is used to determine the concentration of all the chemical species present in the bulk liquid, as described in section 4.3. (3) Feasible reactions (eq 31−44) and the forward reaction rates are used based on the termolecular mechanism (eq 47−50). The available experimental data for CO2− MEA system from pilot plant scale packed columns was taken from the work of Aboudheir.24 (4) Physical properties of CO2−MEA system such as solubilities, diffusivities, solution density, and solution viscosity are obtained from the published literature as presented in previous section 4.1.1 for solubility and diffusivity, section 4.1.2 for density, and section 4.1.3 for viscosity. (5) The diffusivity of MEA molecule in aqueous monoethanolamine solutions is given by correlations given by Snijder et al.96 (6) Surface tension of the monoethanolamine is used to correlate the interfacial area in a packed bed column (eqs 25−27 and 64).42,72 (7) The gas side mass transfer coefficient (eq 66), the liquid side mass transfer coefficient (eq 65), and the interfacial area (eq 64) are calculated by the correlations, proposed

(88)

The differential equations are integrated from t = 0 to τ, the contact time. From the obtained concentration profile data of the absorbed gas, C1, the local absorption rate per unit area can be calculated. ⎛ ∂C ⎞ N = −D1⎜ ⎟ ⎝ ∂x ⎠x = 0

(89)

The term of (∂C/∂x)x=0 is the concentration gradient at the surface and is a function of time. The average absorption rate per unit interfacial area of the solute gas through the liquid jet length of L is obtained by integrating the equation over the contact time as shown below:77,86 τ ⎛ ∂C1 ⎞ D ⎜ Navg = − 1 (0, t )⎟ dt ⎠ τ 0 ⎝ ∂x

∫

(90)

For Higbie’s penetration model, the physical mass transfer coefficient, kL0 , can be obtained from the following equation in the case of laminar jet absorber:77,84 kL0 =

4 πd

Dν L

(91)

In general, absorption of the gas into the liquid is described with constant diffusivity and density.86 The molecular transport is shown in eq 92. D∇2 C = uΔC +

∂C +r ∂t

(92)

where, D is diffusivity, u is liquid velocity, C is the concentration of absorbed gas in the liquid, t is time, and r is reaction rate. Equation 92 can be simplified to the following diffusion eq 93, which is most frequently used to represent the absorption of gas into liquid jets.5,24,41,70,71 D

∂ 2C ∂x 2

=

∂C +r ∂t

(93)

where, x is a distance from the gas−liquid interface into the liquid bulk. In order to solve the ordinary differential equations, an LSODE (Livermore solver for ordinary differential equations) was used in the model. Partial differential equations are transformed into sets of ordinary differential equations with time variable of t. An important feature of LSODE is its capability of solving “stiff” ordinary differential equations. The difficulty with stiff problems is the prohibitive amounts of computer time required for their solution by using explicit Runge−Kutta and Adams methods. Therefore, the LSODE package uses the backward differentiation formula to solve stiff problems. For the nonstiff problems, the LSODE package uses an implicit Adams−Moulton method.89 4.6. Reactor Modeling and Simulation of a Packed Bed Column. Rigorous theories of absorption with chemical reactions are well-documented by Danckwerts and Astarita.77,86 Their research primarily focused on developing expressions for the local mass transfer coefficients. In this work, a rigorous ratebased process model to predict the behavior of CO2−aqueous 4338



Article

by Onda et al.72 It has been demonstrated that the correlations provide satisfactory results.20,79,94,95 (8) The enhancement factor expression developed by Wellek et al. (eq 67) is applied to the modeling.78 (9) The specific heats of the liquid and gas components, the heat of vaporization of water and the heat of chemical reaction are obtained from Pandya’s research (Table 3).18

where P, a, and kG are the pressure, interfacial area, and the gas side mass transfer coefficient. The absorption of CO2 into the aqueous monoethanolamine solution results in release of heat. At the bottom of the column, the liquid effluent heats up the gas feed. After the temperature of the gas reaches to a maximum point, the gas temperature profile follows closely that of the liquid temperature profile. A volatile solvent is evaporated at the bottom of the column, whereas it is condensed at the top of the column. The balance of temperature in the liquid and gas phases are expressed by the thermal energy equations, as described below.18

Table 3. Physical and Chemical Properties of the CO2−MEA System18 CPCO2

36.8

J/mol·K

heat capacity of CO2

CPH2O

33.9

J/mol·K

heat capacity of H2O

CPsolution CPair λH2O

4.2 29.3 45.0

J/mol·K J/mol·K kJ/mol

heat capacity of a liquid solution heat capacity of air latent heat of vaporization of H2O

ΔHR

84431.0

hGa

103.7

J/mol CO2 absorbed J/s·m2·K

heat of chemical reaction between CO2 and MEA heat transfer coefficient

Gas phase energy balance dTG −hGa(TG − TL) = dZ GB(CPB + YACPA + YSCPS)

Liquid phase energy balance dT dTL (LMCL) = GB[CPB + YACPA + YSCPS] G dZ dZ dYS + GB[CPS(TG − TO) + λS] dZ

The major assumptions of the present models are the following: (1) The gas absorption process is adiabatic, which means that there is no heat exchange between the column and environment. This was earlier demonstrated by Pandya and Treybal.18,90 (2) The reaction is rapid enough to satisfy the assumption of that the reaction takes place only in the film and the species involved in this system are in equilibrium in bulk of the liquid. (3) Heat transfer resistance in the liquid phase is relatively small compared to that of the gas phase. (4) Only CO2 and water vapor can cross the gas/liquid interface. (5) The liquid phase mass transfer resistance for volatile liquid solvent are negligible. (6) The interfacial area of heat and mass transfer is identical. (7) Axial dispersion of either gas or liquid flows is not accounted for since it has been shown by Pandya that this effect would be minor.18 The same approach that is used to laminar jet absorber is applied to the modeling of a packed bed columnmodel 1 and model 2. For model 1, a packed bed column is equally divided into a number of identical elemental compartments along its height, and mass and heat balance is considered at each compartment. On the other hand, model 2 is developed based on partial differential equations with a height of dZ. Figure 1 represents material and engery balance around a differential height, dZ, of a packed bed column. The following material and energy equations are applied to the modeling: The system is assumed to be in steady state conditions. The concentration gradients of the gas species, component A (CO2) and component S (water vapor), in each differential section are described by the following equations −k G,AaP(yA − yA, i ) dYA = dZ GB

(94)

−k G, SaP(yS − yS, i ) dYS = dZ GB

(95)

(96)

+ GB[CPA(TG − TO) − ΔHR (TO , P)]

dYA dZ (97)

where h, λ, CP, and ΔHR are the heat transfer coefficient, the latent heat of vaporization, the heat capacity, and the heat of chemical reaction between CO 2 and aqueous monoethanolamine. In order to calculate the enthalpy of the solution, the equilibrium constants and ΔHR values as a function of temperature for each of the reactions are required.97 Various physical and chemical properties such as the specific heats of the gas components and liquid, heat of vaporization of solvent (S), and heat of chemical reaction for the CO2−MEA system are taken from the research of Pandya as shown in Table 3.18 For the mass and heat balance across the bed in countercurrent mode, a two-boundary value problem is solved by using a shooting method (“shooting” at the target terminal points).94 For example, the value obtained at the top of the column is compared with the initially assumed values of CO2 concentration at the outlet vapor stream. If the deviation is within an acceptable range, the calculation for the balance will be completed. The process iterates until the deviation reaches an acceptable range. 4.7. Algorithm. The following computation procedures are used for the simulation of a packed bed column. (1) Assume temperature and moisture content of the outlet gas. The temperature and moisture content of the outlet gas are assumed to be in equilibrium with the entering liquid. (2) The composition of the outlet liquid and its temperature is determined via the material (eq 94 and 95) and energy balances (eq 96 and 97). The calculation now starts from the bottom of the packed bed column. (3) The necessary physical and chemical properties of the liquid and gas such as density, viscosity, thermal conductivity, heat capacity, diffusivities, vapor pressure of water, and chemical equilibrium constant are obtained from density eq 14, viscosity eq 19, and surface tension eq 25. 4339



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Figure 1. Differential section of absorber or stripper for a multicomponent system.18

(9) Choose a suitable small value of ΔYA so that the gradients of dYA/dZ, dYS/dZ, dTG/dZ, and dTL/dZ do not change too significantly. Next the value of Z is obtained as follows:

(4) Forward reaction rate constant k4 in the second-order form for the CO2−MEA system, which are obtained from a termolecular mechanism by Aboudheir24 and Hikita et al.43 are solved via eqs 48−50 and 52. (5) The following coefficients are calculated via eqs 65 and 66: • Mass transfer coefficient of component CO2 in the liquid phase for physical absorption • Mass transfer coefficient of component CO2 in the gas phase • Mass transfer coefficient of component H2O in the gas phase • Heat transfer coefficient in the gas phase (6) Enhancement factor E is computed based on the assumption of pAi by the correlations, given by Wellek et al.78 (eqs 63 and 67). (7) Calculate pAi from eq 1. Steps 6 and 7 are iterated until

Znext = Z + ΔZ

(98)

where Z = 0 for the bottom of the packed bed column. ΔZ =

ΔYA dYA dZ

( )

(99)

(10) Compute values at Znext:

the assumed and calculated pAi become identical. (8) Compute dYA/dZ, dYS/dZ, dTG/dZ, and dTL/dZ. 4340

YA,next = YA + ΔYA

(100)

⎛ dY ⎞ YS,next = YS + ΔZ ⎜ A ⎟ ⎝ dZ ⎠

(101)



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⎛ dT ⎞ TG,next = TG + ΔZ ⎜ G ⎟ ⎝ dZ ⎠

(102)

⎛ dT ⎞ TL,next = TL + ΔZ ⎜ L ⎟ ⎝ dZ ⎠

(103)

⎛ dY dY ⎞ LM,next = LM + GBΔZ ⎜ A + S ⎟ ⎝ dZ dZ ⎠

(104)

L x + νNAa dZ x R,next = M R LM,next

(105)

L x − νNAa dZ x P,next = M P LM,next

(106)

by the N2O analogy. The liquid phase physical mass transfer coefficients are obtained by penetration theory. During the laboratory experiments, the contact time is varied by two independent variables of the length of the jet and the liquid flow rate. The performance of the developed mathematical models was evaluated under various operating conditions such as temperature, molarity of monoethanolamine

(11) Repeat 1−10 until the deviation of YA between the assumed and calculated figures falls into the acceptable range in the outlet gas. (12) In this step, check the assumed value of moisture content and the outlet gas temperature. If the values are within specified tolerance, then the calculation is complete. Otherwise, it continues with new values of moisture content until the balance is completed. A FORTRAN 77 computer program was written to simulate CO2 absorption into aqueous solutions of monoethanolamine in a packed column with random packing.

Figure 2. Absorption of carbon dioxide into monoethanolamine solution at 293 K.

5. SUMMARY OF RESULTS A detailed modeling procedure for multiphase packed bed reactors with reactive absorption processes has been illustrated in this paper by using a case study of CO2 absorption to monoethanolamine (MEA) solution. Comprehensive data on the absorption rate of carbon dioxide into monoethanolamine solutions using a laminar jet absorber is taken from the work of Aboudheir.24 The simulation results are compared with the laboratory experiments with a laminar jet absorber under the same operating conditions in order to check the validity of the proposed mathematical models. Two different mathematical models were developed to predict the absorption rates in this research. In both models, the termolecular reaction mechanism, reported by Aboudheir4,23 is used as a kinetic model. Mathematical model 1 for laminar jet absorber uses an iterative procedure to solve the equations. The film thickness is considered to vary along the jet length and the effect of reactions on mass transfer is considered by using an enhancement factor. Meanwhile, in model 2, the LSODE method is used for the modeling of laminar jet absorber to solve ordinary differential equations and film thickness is considered to be constant along with jet length. Although the rigorous model is believed to be very accurate, it is worthwhile to note that it has the disadvantage of high computational burden due to the complex numerical methods, and it significantly increases computing time consumption. In this research, both mathematical models take into account the interaction between mass transfer and chemical kinetics of all suitable chemical reactions, and chemical equilibrium of components. Physical properties of the fluids such as density, viscosity, solubility, and diffusivity of the system are calculated based on the correlations, which are from published data. The solubility and diffusivity of CO2 in aqueous monoethanolamine solutions cannot be found out directly because CO2 undergoes reaction with the MEA. Hence, these properties are estimated


solution, loading of CO2, varying liquid jet length and liquid volumetric flow rates. The predicted restults of the model for carbon dioxide absorption rates are compared with experimental results in parity plots as shown in Figure 2−6. The parity plots prove good agreement between the experimental and predicted results with average deviation of 7% and 13% for models 1 and 2, respectively. The main reason for higher deviation from the experimental results of model 2 is that the film thickness variation along the length of the jet is considered in model 1 for a laminar jet absorber, while film thickness is assumed to be constant in model 2. The modeling of a packed bed column takes into account the thermodynamics and its impact on the system such as mass and heat transfer coefficients, phase equilibrium, and chemical reaction rates, etc. An appropriate estimation of the enhancement 4341



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Figure 4. Absorption of carbon dioxide into monoethanolamine solution at 303 K. Figure 7. Simulation and experimental results for the CO2−MEA system using packed bed column (experiment number B002 in Table 1).


Figure 8. Simulation and experimental results for the CO2−MEA system using packed bed column (experiment number B008 in Table 1).


Figure 6. Absorption of carbon dioxide into monoethanolamine solution at 333 K. 4342



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by adopting CO2 absorption to MEA solution as a case study. Meanwhile, a separate research was carried out to identify suitable reaction mechanisms and kinetics by using a two-stage method, which was developed by Zhang.98 In addition, a methodology is developed to identify further required experimental scope to finetune the developed kinetics. Its methodology will be discussed in detail in a separate paper. Lastly, it should be noted that this case study is limited to gas− liquid apsortion system. Therefore, appropriate modeling should be developed for different system such as multiphase liquid system.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +44 1483 466251. Fax: +44 1483 466259. E-mail: sungwon. [email protected].

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factor plays a critical role for the accuracy of the simulation results. Aboudheir’s experimental data is used to compare with the simulation results and demonstrates that the model predictions show good agreement with experimental data in terms of temperature and concentration profile through the packed bed column height.24 A comparison between the experimental results and the model predictions under various operating conditions is illustrated in Figures 7−10. The average deviation in terms of concentration and temperature profiles between the simulation results from model 1 with a packed bed column and experimentally measured data are 8.2% and 6.0%, respectively. The average deviation of model 2 is 12% and 5.8%, respectively. The validity of the computer model developed has been confirmed by comparing a wide range of experimental data results with simulation results for the CO2−MEA system. On the basis of the results obtained, it appears that the models developed based on Pandya’s procedure and reaction rate constant for CO2−MEA system from Aboudheir24 and Hikita et al.43 can be used successfully to predict packed absorption column performance in terms of CO2 concentration and temperature profiles along the packed bed column under wide range of operating conditions.

6. CONCLUSION It is worthwhile to emphasize that the simultaneous development of reaction system modeling and reactor design is crucial for the success of chemical industry nowadays. This is particularly important in industries such as specialty chemicals where delivery of new product to market within short period is critical. Therefore, this research has focused on the objective of making the experimental work relevant to the conditions in the final reactor design, minimizing experimental work to the essential relevant measurements, shortening process development, and developing reactor modeling on a more rigorous basis. The problems are compounded with multiphase systems, where mass transfer and chemical reaction are both important. In our research, two separate studies have been considered individually, and they are integrated: (1) rigorous modeling of the system and reactor design and (2) identification of reaction mechanism and development of kinetics on the basis of minimum required experimental data. In this paper, we have focused on rigorous modeling of the system and reactor design

NOTATION a = interfacial area (m2) CP = heat capacity (kJ/kg·K) Ci or CAe = concentration of component i, interfacial concentration of component i (kmol/m3) Di or D = diffusivity of component i (m2/s) E = enhancement factor, activation energy (−, kJ/mol) E1 = enhancement factor for a pseudo-first-order reaction (−) Ei = enhancement factor for instantaneous reactions (−) G = total molar gas flow rate (kmol/m2·s) GB = molar gas flow rate of carrier gas Hi = Henry’s law constant of component i or solubility of component i (kPa·m3/kmol) HG = enthalpy of gas (kJ/kmol) HL = enthalpy of liquid (kJ/kg) hG = heat transfer coefficient (kcal/s·m2·K) i,j,k = integer indices kl = mass transfer coefficient (m/s) k4 = second-order reaction rate constant (m3/kmol·s) kRNH = third-order reaction rate constant for MEA (m6/ kmol2·s) kH2O = third-order reaction rate constant for H2O (m6/ kmol2·s) ki = first- or second-order reaction rate constant for component i (1/s, m3/kmol·s) kg or kG = gas phase mass transfer coefficient (kmol/ m2·s·kPa) LM = mass liquid flow rate (kg/m2·s) M, MH = molecular weight, Hatta number (kg/kmol, −) Ni = mass transfer flux of component (kmol/s·m2·interfacial area) P = total pressure (kPa) Pi = partial pressure of component i (kPa) T = temperature (K, °C) Vj = molar volume of component j (m3/mol) xf = film thickness (m) Yi = gas concentration of gas component i (kmol i/kmol B)

Greek Letters

α = CO2 loading (mol/mol) ∇ or ∇2 = math operators λ = latent heat of vaporization (kJ/kmol) μ or η = viscosity (cP) ν = kinematic viscosity, reaction stoichiometric coefficient vector (m2/s, −) 4343



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ν1,2 = kinematic viscosity in a binary system of pure fluid 1 and 2 ρ = density (kg/m3) σ = surface tension, standard deviation of the objective function (mN/m, −) Φi = volume fraction of solvent Ω = mass percent of amine

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Abbreviations

AMP = 2-amino-2-methyl-1-propanol DEA = diethanolamine MDEA = methyldiethanolamine MEA = monoethanolamine OA = oleic acid

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