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Energy Procedía 1 (2009) 1 3343-1350

Energy Procedía

www.elsevier.com/locate/procedia

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Kinetics, Modeling, and Simulation of the Experimental Kinetics Data of Carbon Dioxide Absorption into Mixed Aqueous Solutions of MDEA and PZ using Laminar Jet Apparatus with a Numerically Solved Absorption-Rate/Kinetic Model

Raphael Idema* , Mohamed Edalia, Ahmed Aboudheirb

aProcess Systems Engineering, Faculty of Engineering,, University of Regina, 3737 Wascana Parkway,Regina, Saskatchewan, Canada S4S 0A2. bHTC Purenergy, 001, 2305 Victoria Avenue, Regina, SK, S4P 0S7 Canada

Abstract. The kinetics of the reaction between carbon dioxide (CO2) and mixed solutions of Methyldiethanolamine (MDEA) and Piperazine (PZ) was investigated experimentally in a laminar jet apparatus. The experimental kinetic data were obtained under no interfacial turbulence and over a temperature range from 313 to 333 K, MDEA/PZ wt% concentration ratio of 27/3, 24/6 and 21/9, and CO2 loading from 0.0095 to 0.33 mole of CO2 per mole of amine. A new comprehensive absorption-rate/kinetics model for mixed solvents was developed, which takes into account the coupling between chemical equilibrium, mass transfer, and the chemical all possible chemical reactions involved in the CO2 reaction with MDEA/PZ solvent. The partial differential equations of this model were solved numerically using the finite element method (FEM) based on COMSOL software. The obtained experimental kinetics data were interpreted with this new developed absorption-rate/kinetics model in order to obtain the kinetics parameters for the CO2 absorption into MDEA/PZ solutions. There was excellent agreement between the experimental and predicted absorption rate values from the 1-D comprehensive kinetics model.

© 2009 Elsevier Ltd. All rights reserved.

Keywords: Absorption; Carbon dioxide; Kinetics; Numerical Modeling; Piperazine; Methyldiethanolamine

1. Introduction

Recently, Piperazine (PZ) has been shown to be an effective promoter in MEA, MDEA, and potassium carbonate due to its rapid formation of carbamates with CO2. PZ is more effective than the conventional rate accelerators that have been used as activator in the activated MDEA technology of BASF (Appl et al., 1982). Literature on aqueous PZ solvent system is limited, whereas there is extensive literature on the use of primary, secondary or tertiary

* Corresponding author. Tel.: (306) 585-4470; Fax: 1-306-585-4855. Email address: raphael.idem@uregina.ca (R. Idem).

doi:10.1016/j.egypro.2009.01.176

alkanolamines for removal of CO2. This is so due to the fact that the industrial use of PZ is mainly as an accelerator in other amines.

There is limited experimental data in the literature on the rate or kinetics of CO2 absorption into the blended amine of PZ activated MDEA solvents, and most especially, no data exist for experiments conducted using the laminar jet absorber which has the advantage of its very short gas and liquid contact times where high reactive solvents are involved. This enables the determination of the kinetics more accurately. Xu et al. (1992) used a disk column to study the absorption rates of CO2 into aqueous MDEA-PZ solutions. Bishnoi and Rochelle [2002a] reported experimental absorption rates in a wetted-wall column for 4.0 kmol m 3 MDEA and 0.6 kmol m 3 PZ, at different temperatures, CO2 liquid loadings and partial pressures. Derks et al. (2006), performed experimental data presented on the rate of absorption of CO2 into aqueous solutions containing both PZ and MDEA. The absorption experiments were carried out in a stirred cell contactor, operated with a flat gas-liquid interface. CO2 fluxes were determined in 4.0 kmol m 3 MDEA solutions activated with either 0.5 or 1.0 kmol m 3 PZ, at various CO2 loadings and partial pressures. PZ-activated aqueous MDEA and AMP solutions combine the relatively high rate of reaction of the former with CO2 with the lower heat of reaction of the later with CO2. From these considerations, (MDEA-PZ) and (AMP-PZ) solutions appear to be attractive new blended solvents for acid gas removal. While absorption of CO2 into MDEA and AMP has been studied extensively in the past, only few publications have dealt with absorption of CO2 into the blends of PZ with MDEA or AMP (Bishnoi and Rochelle 2000, and 2002; Seo and Hong 2000; Sun 2005; Xu et al 1992, 1995, and 1998; Zhang et al 2001). The density and viscosity of aqueous solutions of (MDEA-PZ) was published, for the first time in the work of Paul and Mandal (2006). This has provided more accurate thermophysical properties used for the evaluation of the absorption rate/kinetics of absorption of CO2 in MDEA-PZ in the present paper. The total amine mass fraction in the solution was kept at 30%. The BASF activated MDEA technology used PZ as an activator in order to accelerate the absorption or desorption rate. Appl et al. (1982) reported that PZ would be more effective than the conventional absorption accelerators. Xu et al. (1992) investigated the kinetics of CO2 absorption in activated MDEA solutions that contain Piperazine as an activator. They proposed a rapid pseudo-first-order reversible reaction between CO2 and PZ in parallel with the reaction between CO2 and MDEA. Matin et al. (2007) studied the effect of PZ concentration on CO2 loading in MDEA solutions using PZ concentration of 0.36, 0.86 and 1.36 kmol/m3. The interaction parameters of activity coefficient model for these systems were determined using the experimental data in various temperatures. Their results show the model consistency with experimental and literature data and stated that PZ is beneficial for the CO2 loading. In the work of Matin et al. (2007), the VLE model was further developed for the prediction of CO2 solubility into the CO2-MDEA-PZ-H2O system in electrolyte systems using the extended Debye- Huckel model for determining the activity coefficients of the liquid phase species. The interaction parameters of the applied model were obtained for the studied system. The gas phase fugacity coefficients were calculated using the Peng-Robinson equation of state.

In this work, the rates of absorption of CO2 into aqueous solutions of PZ activated MDEA were measured in a laminar jet contactor over the temperature range of 303-333K. Three different mixed amine ratios (27wt. % / 3wt. %, 24wt. %/6wt. %, and 21wt. %/ 9wt. %) with total concentration of 30 weight of MDEA/PZ solutions were considered for experimental work. The CO2 loading into the solution was varied from 0.005 to 0.33 mole of CO2 per mol of amine. The absorption rates were utilized to determine the kinetics of the reaction. The effect of loading on the physical properties is required in order to interpret the kinetics. Based on the proposed mechanisms for the reaction between CO2 and PZ activated MDEA presented, a Vapor-Liquid Equilibrium model and an Absorption Rate/kinetics model to predict the kinetics of reaction were developed. In addition, a coupled mass transfer-kinetics equilibrium mathematical model based on Higbie's penetration theory (Higbie, 1935) is developed with the assumption that all reactions are reversible. The model is used to estimate the reaction rate constants of the reaction between CO2 and aqueous PZ activated MDEA.

2. Theory

The Vapor-Liquid Equilibrium model and an Absorption Rate/kinetics model to predict the kinetics of reaction were developed based on the proposed mechanisms for the reaction between CO2 and PZ activated MDEA presented.

2.1. Reaction scheme in case PZ-MDEA-CO2 reaction system

In general, amines are subdivided into primary, secondary, and tertiary amines according to the number of alkyl groups attached to the N atom in the molecular structure of the compound. MDEA and PZ belong, respectively, to tertiary and secondary amines. The reaction mechanisms of carbon dioxide with alkanolamines have generally been agreed upon. A zwitterion mechanism and proton transfer can describe the reactions of CO2 with primary, secondary, and tertiary amines (Caplow 1968, and Rinker 2000). For activated MDEA mixed with PZ, the reaction mechanism with CO2 can be explained by a homogeneous activation mechanism (Xu et al. 1992). The reactions of CO2 with aqueous PZ activated MDEA to form piperazine carbamate and piperazine dicarbamate primarily account for the rate of absorption of CO2 in aqueous PZ activated MDEA. The following reactions are considered for the absorption of CO2 into an aqueous solution of PZ activated MDEA based on the speciation studies conducted by Bishnoi and Rochelle (2002a):

CO 2 + RRCH 3N + H2O < ^ > RRCH 3 NH ++ HCO 3" (1)

CO2 + OH ~< ^ > HCO3~ (2)

CO2 + PZ + H2O < K3'"23 > PZCOO -+ H3O+ (3)

CO2 + PZCOO -+ H2O < 1-4 > PZ (COO - )2 + H3O+ (4)

HCO 3- + H 2 O ^ CO 32 - + H 3 O * (5)

RRCH3N + H3O+ < 1-6 >RRCH3NH + + H2O (6)

PZ + H 3O+ < 1-1 > PZH+ + H 2O (7)

PZCOO + H3O+ ^^ PZH+COO + H2O (8)

2H, O OH - + H3O+ (9)

Reactions (1)-(3) are considered to be reversible with finite reaction rates, and reactions (5), (6), (1), and (9) are considered to be reversible and instantaneous with respect to mass transfer and at equilibrium, since they involve only proton transfer.

The zwitterion mechanism originally proposed by Caplow (1968) and reintroduced by Danckwerts (1919) is the generally accepted mechanism for reaction of CO2 with the primary and secondary amines (Blauwhoff et al., 1984; Versteeg and van Swaaij, 1988; Glasscock et al., 1991, Littel et al., 1992; Rinker et al., 1996). The same mechanism is assumed to be valid for the reaction of aqueous PZ with CO2 (Bishnoi and Rochelle, 2000; Sun et al., 2005; Derks et al., 2006). This mechanism involves the reaction of CO2 with PZ to form a zwitterion ion intermediate (PZH+COO ) which is subsequently deprotonated by a base (e.g. PZ, PZH+, PZCOO , OH , H2O) present in the solution to produce Piperazine carbamate (PZCOO ) and protonated PZ. Since PZ has a pKa value of 9.13 at 298K (Hetzer et al., 1961), it is not unrealistic to assume that the deprotonation rate is instantaneous. Several authors have arrived at the same conclusion (Bishnoi and Rochelle, 2000; Sun et al., 2005; Derks et al., 2006). Therefore, the rate coefficient, k23 is considered the global rate coefficient for the formation of zwitterions and zwitterion deprotonation for reaction (3).

2.2 Bulk liquid equilibrium model

A vapour-liquid equilibrium model has been developed to estimate the initial liquid bulk concentrations of all chemical species from the initial concentration of PZ, the initial CO2 loading, of the PZ solution and with the assumption that all reactions are at equilibrium. For the 12 liquid bulk concentrations, the equations are as follows:

Overall MDEA balance: [RRCH 3N ] + [RRCH 3NH + ] = [MDEA ]0 Overall PZ balance: [PZ ] + [PZH + ] + [PZCOO - ] = [PZ ]0 Overall CO2 balance:

[CO2] + [HCO3~ ] + [CO32~ ] + [PZCOO- ] = ([MDEA]0 + [PZ ]0)a Electroneutrality balance:

[RRCH 3 NH + ] + [PZH+] + [ H3O+ ] = [ HCO~ ] + [OH " ]

+ 2[CO32" ] + [ PZCOO ~ ]

All reactions are in equilibria:

[HCO3" ]

[CO 2][OH - ] [PZCOO - ][HQ* ]

[ PZ ][CO2, [CO,2- ][H,O+] [HCO,- ] [RRCH 3NH+] [RRCH 3N ][H3O + ]

[ PZH+]

(18) (19)

[PZ ][ H3O+ ] K9 = 1/[H3O+][OH ]

In addition to these mass balance equations, Henry's law relationship between the equilibrium partial pressure and the free concentration of CO2 is required:

P°°2 =He[CO2] (20)

The 11 simultaneous nonlinear algebraic equations (Eqns. (10) - (20)) have been solved using the in-house coded finite difference method using Fortran 90 and the finite elements methods using COMSOL software for the 11 unknowns of the liquid bulk concentrations.

2.3 Absorption-rate/kinetics model interpreting the absorption data of CO2 into MDEA-PZ solutions:

A comprehensive absorption-rate/kinetics model was developed for interpreting the absorption data of CO2 into PZ_MDEA solutions, from which the kinetics data were extracted. The model takes into account the coupling between chemical equilibrium, mass transfer, and chemical kinetics of all possible chemical reactions. The mathematical model is capable of predicting gas absorption rates and enhancement factors from the system hydrodynamics and the physico-chemical properties, as well as predicting the kinetics of reaction from experimental absorption data.

The chemical species in reactions 1-9 have been renamed for convenience in the numerical treatment as follows:

Cj= [CO2], C2= [RRCH3N], C3= [RRCH3NH+], C4= [HCO3"], C5= [OH"], C6= [CO32"] , C7= [H3O+], C8= [PZ], C9= [PZH+], and C10= [PZCOO"].

The partial differential equations and non-linear algebraic equations describing the diffusion -reaction processes can be presented as follows:

CO2 balance:

d C 8 2 C

St 1 Sx2 1 2 3

Total carbon (from CO2) balance:

riC riC SC,, QC

l,[CO2] ^ 4'[HCO3-j ^ 6 [CO3 2 ] ^ 1Q.[PZCOO -

dt dt dt dt D + d +d. +d ^2 ciq

1 dx2 4 dx2 6 dx2 1Q dx2 Total PZ balance:

8C8.[ ^ ] , dC PZH * ] , 8C1Q.[ PZCOO - ] = D + D + D S 2C,r

St ôt St 8 dx2 9 dx2 10 Sx2 (23)

Total MDEA balance:

dC dC d2C d2C

2.[RRCH3N] ^ 3.[RRCH3NH+] _ d 2 ^ D 3

dt dt " 2 dx2 3 ~âxr

Carbamate balance:

3C p,2r

1Q.[PZCOO-] _ O C1Q n

-SZ--D1Q — ~R3 (25)

Electroneutrality balance:

®C3_[ RRCH 3 AT] + ®C7_[ H3O* ] + ^C9.[ PZH * ] ^C4_[ HCO3] ^C5_[OH " ]

dt dt dt dt dt

2 aC6.[CO32-] gC1Q.[PZCOO-] = D dC + D d 'C7 + D d2C9 _ (26)

St St 3 dx2 7 dx2 9 dx2

3 C _ D _ 2d. _ D 5 2C1Q

4 dx2 5 dx2 6 Sx2 10 dx2 Instantaneous reactions assumed to be at equilibrium:

C 6 x C 7 K _ C 3 C 9 K - C x C

K5 = ^ (27), K 6 - ^ x ^ (28), K 7 = Cg x(29), K 9 " 5 x C 7 (30)

Where Ri, R2, R3, and R4 are:

R1 = - k 21C1C 2 + ( k 21/ K1) C 3C 4 (31)

R 2 = - k 22 C1C 5 + ( k 22 / K 2) C 4 (32)

R 3 =- k23 C1C 8 + ( k23/ K 3)C 7 C10 (33)

Thus, there are 10 partial differential-algebraic equations (Eqns. 21-30) solving for the MDEA-PZ aqueous solutions chemical species, C1-C10, excluding C11, H2O concentration.

Initial conditions:

for all chemical species, j = 1, ...,12. (34)

Cj(x,0) = C°j at t=0 and 0 < x > œ

Boundary condition:

for all chemical species, j = 1, ...,12. (35)

Cj(ro,t)=C°j at x=t» and 0 < t < x for all volatile chemical species, j = 1.

Cj(0,t)=C* = Pj / Hej at x=0 and 0 < t < x (36)

For all non-volatile chemical species, j = 2, .,12.

SC-(°, t) = ° at x=0 and 0 < t <x (37)

Then using Eq. (42), the local absorption rate per unit area was calculated from the concentration profile data of the absorbed gas, C1.

N = - D t( ^-J-), = 0 (38)

Eq. 42 represents the concentration gradient at the surface and it is a function of time. The average absorption rate per unit area of solute gas by the liquid jet of length h is obtained by integrating Eq. (38) over the contact time as shown in Eq. (39) (Aboudheir et al., 2003, and Edali et al. 2007).

N„ =- ^ & (0, t ) *. (39)

X 10 St

The effect of a chemical reaction in terms of the enhancement factor, E, defined as the ratio of the absorption rate of a gas into a reacting liquid to that if there was no reaction, is given in Eq. (40).

E = N ae__(40)

k L ( C * - C 0 ) .

Where k\ = 4/dtfyj D1L / h is an expression valid in the case of laminar jet absorber. For each absorption rate

experiment, the predicted enhancement factor (Epred) is fitted to the experimentally observed enhancement factor (Eexp), with the forward reaction-rate constants (k23) as adjustable parameter.

f (M = Eexp- Epred (41)

where ^ is the contact time (as given by T = n d2l/4Q; d and l are the diameter and length of the laminar jet, respectively, and Q is the volumetric flow rate), klo is the physical mass transfer coefficient, pA is the partial pressure of CO2, H is the Henry's law constant, Di is the diffusivity.

The equilibrium constants used for Eqs. (1) - (9) were taken from open literature sources. This speciation vapour liquid Equilibrium and solubility model has been used to predict the partial pressure of carbon dioxide and the Concentrations of species in solution as a function of amine loading.

3. Experimental Data

Absorption experiments are performed to obtain reliable data of CO2 absorption into aqueous solution of partly loaded MDEA-PZ. The experimental data obtained and discussed in this chapter are under the conditions of no interfacial turbulence (Aboudheir, 2002). The data thus generated were obtained by the dynamic method, in which a jet of liquid moves continuously though the gas for a known contact time. From the literature, it is observed that only few experiments were performed in the area of chemical absorption of CO2 into MDEA and PZ. Most of these experiments were restricted only to aqueous solution mixtures without CO2 loading and only two or three temperatures. In this study, three different mixed amine ratios (27wt. % - 3wt. %, 24wt. % - 6wt. %, 21wt. % - 9wt. %) were considered. The CO2 loading into the solution was varied from 0.0095 to 0.33 moles of CO2 per mol of amine. The absorption rates were utilized to determine the kinetics of the reaction. The absorption rates were measured with a digital soap-film meter.

4. Results and Discussion

The experimental absorption rate data obtained in the laminar jet absorber was interpreted by numerically solved comprehensive 1-D absorption-rate/kinetics models (using FEM). In general, the partial differential equations for

unsteady molecular diffusion for the system of mixed solvent system of MDEA/PZ represented by Equations (21 -30) in 1-D format were solved numerically. For each absorption rate data obtained, the calculated enhancement factor was fitted to the experimentally observed enhancement factor with the forward reaction-rate constant kPZ as an adjustable parameter. The values of kPZ obtained by solving the model equations for the comprehensive 1-D format using FEM solution method is presented in Table 1 compared with literature. Figure 1 shows the estimated liquid bulk concentration profile of all chemical species resulted from the vapor-liquid-equilibrium (VLE) model. The parity chart in Figure 2 shows excellent agreement between the experimental and predicted absorption rate values from the 1-D comprehensive kinetics model.

Table 1: kPZ comparison with literature for CO2 in MDEA_PZ mixed Amine system

Composition (kmol m-3) T (C) Experimental Technique Solving method kPZ, at 333 k (m3/kmol s ) Reference

0.6 M (PZ) - 4 M (MDEA) 313 - 343 K wetted wall contactor numerical model 4.60E+05 Bishnoi and Rochelle 2002

2.296 + 0.353 2.044 + 0.707 1.792 + 1.062 313-333 K laminar jet absorber numerical model 4.38E+05 This work

Figure 1: Liquid-phase speciation and concentration in aqueous MDEA-PZ (27wt. % - 3wt. %) solution with CO2 loading (a) at 313K.

Figure 2: Parity Chart for comparison of the kinetics model solved by FEM for loaded 30 wt% MDEA_PZ solution (temperature range of 313-333K).

5. Conclusions

A new comprehensive numerically solved absorption rate/kinetic model was developed for the absorption of CO2 in CO2 loaded aqueous PZ/ MDEA solution conducted on the experimental kinetics data using a laminar jet absorber. Experimental kinetic data were then interpreted with the aid of the numerically solved absorption-rate/kinetics model by the finite element method using COMSOL software. There was excellent agreement between the experimental and predicted absorption rate values from the 1-D comprehensive kinetics model.

6. Acknowledgements

The first author (M. Edali) would like to thank and appreciates the scholarship support from the Libyan Higher Educational studies through the cultural section of the Libyan Embassy in Ottawa, Canada. Also, the partial financial support from HTC Purenergy is highly appreciated. The ITC centre at the University of Regina is acknowledged for using its scientific facilities.

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