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On the modelling and simulation of sour gas absorption by aqueous amine solutions
Chemical Engineering Science 58 (2003) 3571 – 3578
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On the modelling and simulation of sour gas absorption by aqueous amine solutions Lars Kuckaa , Ivo M-ullerb , Eugeny Y. Kenigb;∗ , Andrzej G3orakb b Department
a Henkel KGaA, 40191 D usseldorf, Germany of Chemical Engineering, University of Dortmund, 44221 Dortmund, Germany
Received 13 March 2003; received in revised form 30 May 2003; accepted 2 June 2003
Abstract A rigorous rate-based model for reactive sour gas absorption by aqueous amine solutions is presented which governs both the coupling of mass transfer and reaction and speci8c features of electrolyte species. The acceleration of mass transfer due to reactions in the liquid phase is taken into account rigorously, without application of enhancement factors. The model is implemented into the simulation environment Aspen Custom Modeler and validated by comparison of published pilot plant data with the simulation results. It is shown, that the model possesses a good predictivity for pilot plant scale as well as for industrial scale applications. In addition, the in:uence of reaction kinetics on the absorber performance is studied. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Rate-based model; Sour gas puri8cation; Reactive absorption; Simulation; Amines
1. Introduction Absorption of gases in liquids accompanied by chemical reaction (reactive absorption) is a fundamental operation in a broad spectrum of chemical process technologies. In oil re8neries, :ue and tail gases need to be puri8ed to meet pollution standards, in fertiliser and petrochemical plants acid gases have to be removed from the feed to ammonia synthesis plants and polymerisation units to avoid catalyst poisoning (Chakravaty, Phukan, & Weiland, 1985). Aqueous amine solutions are proven to be feasible solvents for the treatment of natural, synthesis and re8nery gas streams. Traditionally modelling and simulation of reactive absorption units have been based on the well-known equilibrium stage model which subdivides the column into arti8cial height segments using height equivalent to a theoretical plate (HETP) and assumes the equilibrium state between the streams leaving each stage (Taylor & Krishna, 1993). In reality equilibrium is rarely attained at a stage since absorption is a rate controlled phenomenon (Chakravaty et al., 1985). This means that mass and heat transfer are kinetically limited ∗ Corresponding author. Tel.: +49-231-755-2357; fax: +49-231-755-3035. E-mail address: [email protected] (E. Y. Kenig).
0009-2509/03/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0009-2509(03)00255-0
processes driven by gradients of the chemical potential and temperature. Due to these facts traditional equilibrium-based models and eFciency approaches are usually inadequate (Schneider, Kenig, & G3orak, 1999). Resistances to mass and heat transfer can only be considered by rate-based models, in which gas and liquid phase are balanced separately under consideration of mass and heat :uxes across the interface (Taylor & Krishna, 1993). In addition rigorous predictive models have to regard the accelerating eGect of chemical reactions on mass transfer (Kenig, Schneider, & G3orak, 2001). For a single irreversible reaction, this eGect can be described by enhancement factors (Van Swaaij & Versteeg, 1992). However, enhancement factors resulting from theoretical derivations are exact only for few simple reaction types, otherwise they are based on several simpli8cations, e.g., all binary diGusion coeFcients are equal, only one component is transported through the interface, gas phase resistance is negligible, absorption is isothermal, etc. (see, e.g., DeCoursey, 1982; Suenson, Georgakis, & Evans, 1985; Zarzycki & Chacuk, 1993). Thus, the application of enhancement factors may not be accurate enough in case of complex reaction schemes, with several parallel and consecutive reversible reactions. As this is the case in the sour gas puri8cation by aqueous amine solutions, in the present work a rate-based process
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description is suggested which involves the 8lm model equations combined with relevant reaction and diGusion kinetics for all reactions and components as well as the special features of electrolyte solutions. The proposed model is applicable to all kinds of sour gas puri8cation processes involving aqueous amine solutions.
2. Process description In absorption processes using aqueous amine solutions mainly carbon dioxide and hydrogen sul8de have to be withdrawn from gas streams. Amines are subdivided into primary (e.g. monoethanolamine), secondary (e.g. diethanolamine) and tertiary (e.g. methyldiethanolamine) amines according to the number of hydrogen atoms substituted by organic groups. Depending on the composition and operation conditions of the raw gas streams to be treated aqueous primary, secondary or tertiary amine solutions or aqueous blends of amines are used to meet the sweet gas speci8cations (Chakma, 1999). Fig. 1 shows a simpli8ed :ow diagram of an amine gas treating process and the major equipment needed. The raw gas stream is fed to the bottom of an absorption tower with structured or random packing internals and is sweetened by the counter-currently :owing amine solvent. The dissolved sour gases are removed from the solvent in the subsequent stripping column. The regenerated amine solution is re-circulated to the top of the absorber for further removal of acid gas impurities. Optionally, the loaded solvent can be :ashed after leaving the washing tower to remove hydrocarbons possibly contained in the raw gas stream. In this work, we focus on one solvent type and one sour gas, and consider the reactive absorption of carbon dioxide into aqueous solutions of monoethanolamine keeping in mind that system is a representative of all reactive amine gas treating processes. In the chemical process industries monoethanolamine has been proven to be a feasible solvent, widely used in numerous absorption plants throughout the world. In 1990 monoethanolamine was the most
commonly used amine in CO2 separations, reaching 40% of the total market (DeMontigny, Tontiwachwuthikul, & Chakma, 2001). 2.1. Chemical reactions The absorption of carbon dioxide by aqueous monoethanolamine solutions involves a complex system of parallel and consecutive reactions in the liquid phase: Kinetically controlled reversible reactions CO2 + MEAH + H2 O MEACOO− + H3 O+ ;
(R1)
CO2 + OH− HCO− 3 :
(R2)
Instantaneous reversible reactions 2− + HCO− 3 + H2 O CO3 + H3 O ;
(R3)
MEAH + H3 O+ MEAH+ 2 + H2 O;
(R4)
− MEAH + HCO− 3 MEACOO + H2 O;
(R5)
2H2 O OH− + H3 O+ :
(R6)
Carbon dioxide forms ionic species in the liquid phase via two diGerent reactions (R1), (R2). Reaction R1 is more important, as the monoethanolamine concentration is signi8cantly higher than that of the hydroxide ions. Instantaneous reactions (R3) – (R6) are taken into consideration via the mass action law based on activities: p; r p; r xp p p Kr = e; r e; r : (1) x e e e
Expressions for the calculation of the chemical equilibrium constants in this electrolyte system are available in Austgen, Rochelle, Peng, and Chen (1989). For the calculation of the reaction rate of the kinetically controlled reactions (R1), (R2), the forward and reverse reaction rate constants are important. The forward constants are taken from Kucka, Kenig, and G3orak (2002) and Kucka, Richter, Kenig, and G3orak (2003): c 11 kR1; for = 4:495 × 10 exp(−44940=(RT));
(2)
c 13 kR2; for = 3:279 × 10 exp(−54971=(RT)):
(3)
The reverse reaction rate constants are calculated using Eq. (1). Since a kinetic description must yield the same chemical equilibrium state as the mass action law, the molarity-based constants have to be converted into activity-based ones: kr; for =
( kr;c for ct
e
e; r )
e
Fig. 1. Simpli8ed :ow diagram of an amine absorption unit.
1 : ee; r
(4)
The reaction rate constant for the reverse reaction is given by kr; for kr; rev = : (5) Kr
L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
3. Rigorous rate-based model In the investigated process several components are present in both, gas and liquid phases. These components comprise neutral molecules and electrolyte species. All components participate in complex liquid-phase consecutive and parallel reactions, which lead to a coupling of multicomponent mass transfer and multiple reactions. As a consequence, a specially developed rigorous mathematical model which considers mass transfer resistances, electrolyte thermodynamics and the reaction system as well as the column con8guration is required (Kenig, Kucka, & G3orak, 2002). In the literature, several simulation studies of amine-based absorption of carbon dioxide are available. Some of them use simpli8ed concepts, e.g. equal diGusivities (Glasscock, Critch8eld, & Rochelle, 1991; Hagewiesche, Ashour, Al-Ghawas, & Sandall, 1995) or enhancement factors (Sivasubramanian & Sardar, 1985; Tontiwachwuthikul, Meisen, & Lim, 1992; Pintola, Tontiwachwuthikul, & Meisen, 1993; Pacheco & Rochelle, 1998; Al-Baghli, Pruess, Yesavage, & Selim, 2001), other are restricted by the consideration of only one column stage or segment (Rascol, Meyer, & Prevost, 1996; Cadours & Bouallou, 1998). In this work a model is suggested that balances gas and liquid phase separately and considers mass and heat transfer resistances according to the 8lm theory by explicit calculation of the interfacial :uxes. The 8lm model equations are combined with relevant reaction and diGusion kinetics and include the speci8c features of electrolyte solutions. An important advantage of this model is that the hydrodynamics in the column can be directly involved via correlations for hold-up, pressure drop, interfacial area and mass transfer coeFcients (Schneider et al., 1999). The model provides a direct description of the concentration and temperature pro8les in the absorber, both in 8lm and bulk regions. The reaction rates are implemented as source terms into the transport equations describing 8lm phenomena and into the balances describing liquid bulk behaviour. Therefore the use of the enhancement factor concept is avoided. The whole system of equations is solved simultaneously, and thus the interactions between the 8lm pro8les and the bulk values as well as the mass transfer acceleration by reaction are taken into account. 3.1. Bulk phase equations In the liquid bulk balance equation the axial change of the total molar stream and the compositions are considered: @Lxilb i lb l = nlb i a A c + R i Ac ; @z
i = 1; : : : ; nl :
i=1
= 1:
@Lhlb = qlf ai Ac : @z
(8)
Similar equations are valid for the gas bulk phase, except for the consideration of chemical reactions: @Gyigb i = ngb i a Ac ; @z
i = 1; : : : ; ng ;
(9)
g
n
yigb = 1;
(10)
i=1
@Ghgb = qgf ai Ac : @z
(11)
Furthermore, the pressure drop is considered in the gas bulk phase via relevant correlations (see Billet & Schultes, 1999): @p = f(L; G; l ; g ; : : :): @z
(12)
3.2. Film region equations Contrary to the equilibrium stage model, in the rigorous rate-based model the calculation of interfacial :uxes is required. For dilute electrolyte solutions the diGusional interactions can be neglected and the Maxwell–Stefan relations, generally applied for the description of multicomponent mass transfer, are reduced to the Nernst–Planck equation (Taylor & Krishna, 1993): l ctlf DeG @xilf F @’ ;i lf lf ni = − + xilf nlft ; + x i zi !l @"l RG T @"l i = 1; : : : ; nl − 1:
(13)
The introduction of the electrical potential requires the application of an additional equation, to assure that the liquid phase is electroneutral everywhere: l
n
xi zi = 0:
(14)
i=1
In the liquid 8lm region mass transfer and chemical reactions occur simultaneously. Therefore a diGerential component balance has to be considered: 1 @nlfi − Rlfi = 0; !l @"l
i = 1; : : : ; nl :
(15)
(6)
(7)
&lf @T l lf lf q =− l + ni hi : ! @"l
l
xilb
The enthalpy balance for the liquid bulk phase neglecting heat losses reads as follows:
Due to chemical conversion in the 8lm the component molar :uxes at the interface and at the boundary between 8lm and bulk phase are not equal. The heat :ux through the liquid 8lm comprises the conductive and convective terms:
The liquid bulk mole fractions sum to unity: n
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lf
nl
i=1
(16)
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In the gas 8lm region (no reaction) the component :uxes are described by ngf i =−
g gf ctgf DeG ; i @yi + yigf ngf t ; g ! @"g
i = 1; : : : ; ng − 1: (17)
The heat :ux through the gas 8lm is given by q
gf
ng
&gf @T g gf gf =− g + ni hi : ! @"g
diGerential and algebraic equation system. Altogether, the model can contain approximately 50,000 equations, the exact number depending on the axial discretisation step. The model is implemented into the commercial software package Aspen Custom Modeler (see http://www.aspentech.com/). This simulation environment oGers the opportunity to calculate all physical properties required in the model equations by using the program package Aspen Properties.
(18)
i=1
The thermodynamic equilibrium at the gas–liquid interface is used for the connection of the gas and liquid phase compositions: yii
=
KD; i xii ;
g
i = 1; : : : ; n :
(19)
The liquid 8lm thickness is an important parameter in the rate-based model. Usually it is estimated via empirical mass transfer correlations taking into account the type of column internals, hydraulics and transport properties. These correlations (e.g. Kolev, 1976; Billet & Schultes, 1999) have to be created simultaneously with all other model equations. 3.3. Thermodynamics The non-idealities of the gas phase are taken into account via application of the well-known Soave–Redlich–Kwong equation of state (Reid, Prausnitz, & Poling, 1987), for the liquid phase the three-parametric electrolyte-NRTL method is used. The latter model is based on the local composition concept and satisfactorily represents physical interactions of true species in aqueous multicomponent electrolyte solutions (Chen & Evans, 1986). All required parameters are available in Austgen et al. (1989). The KD -values required for the description of the gas–liquid equilibrium state (Eq. (19)) comprise fugacity and activity coeFcients. For the calculation of enthalpies the standard state of elements is used and heat of reaction and absorption is directly taken into account. The thermal conductivities in the gas phase are calculated by the Stiel–Thodos model whereas in the liquid phase the Sato–Riedel model with the Riedel electrolyte correction is used (see Reid et al., 1987). The liquid phase diGusion coeFcients are determined by the Wilke–Chang method for molecular species (Reid et al., 1987) and the Nernst–Hartley equation for electrolytes (Horvath, 1985), the gas phase diGusion coeFcients are estimated according to the Chapman–Enskog–Wilke–Lee model at low pressures and the Dawson-Khoury-Kobayashi model is applied at higher pressures (see Reid et al., 1987).
4. Simulation results 4.1. Film discretisation analysis A subdivision of the liquid 8lm into several balance regions is necessary to describe the accelerating eGect of the chemical reactions on mass transfer with a suFcient accuracy. Using this discretisation allows for calculation of concentration pro8les in the 8lm region (Schneider et al., 1999). For the determination of the required number of liquid 8lm grid points, several discretisation types have been tested. It has been found out, that when the number of segments exceeds 10 no noticeable changes in the calculated component mass :uxes and the concentrations pro8les occur. In order to investigate a possible calculation time reduction, the segment width has been varied to check whether the results calculated with 10 segments can be obtained with a lower number of grid points. It has been shown that at the boundaries of the liquid 8lm the segments have to be thinner than in the middle of the 8lm and that 8ve grid points between the interface and bulk (altogether six segments) with this type of non-equidistant distribution provide a very good agreement with the results obtained with 9 equidistantly distributed points (Fig. 2). With this type of the liquid 8lm discretisation, non-linear concentration pro8les are obtained as shown in Fig. 3. The discretisation method is tested for diGerent gas and liquid feed compositions and found to be well suited over the parameter range occurring in the investigated process.
3.4. Simulation environment The suggested model consists of partial diGerential and algebraic equations. To obtain a numerical solution of such problems, a discretisation in regard to the axial and normal co-ordinates should be carried out to yield an ordinary
Fig. 2. Liquid 8lm CO2 concentration pro8les: Dependence on the type of discretisation.
L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
Fig. 3. Liquid 8lm concentration pro8les.
Fig. 4. In:uence of axial discretisation on the sweet gas composition for T20.
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Fig. 5. Simulated and experimental gas phase composition pro8le for T20.
Fig. 6. Simulated and experimental liquid phase temperature pro8le for T20.
4.2. Validation of the rigorous model The validation of the suggested model is performed by comparison of simulation results with experimental data. A good model predictivity can only be stated, if the model is able to describe composition and temperature pro8les along the washing tower suFciently, rather than only calculate the correct values at the top and the bottom. To test the model two diGerent operating states are simulated, in which highly loaded gas feeds are treated to give clean gas streams with remaining impurities in the ppm range. Both data sets (runs T20 and T16) taken from Tontiwachwuthikul et al. (1992) were obtained using the same experimental set-up. The absorption at atmospheric pressure is performed in a column of 0:1 m in diameter 8lled with 12:7 mm ceramic Berl saddles, with a total packing height of 6:6 m. In the 8rst run (T20), an air stream containing 19.2% of carbon dioxide is cleaned by an amine solution with a monoethanolamine concentration of 2:55 kmol=m3 . First of all, to reach acceptable computation times, the minimum number of axial segments has to be determined. As can be seen from Fig. 4, with increasing number of segments the sweet gas concentration reaches an asymptotic value. The minimum number of axial segments which provides results
of suFcient accuracy for T20 is found to be 15. Note that the concentration pro8le of MEAH is not shown in this 8gure, because the MEAH-concentration for this special case is very high and changes of its value can hardly be seen. For this pilot plant data set a good agreement between simulated and experimental data for the gas phase concentrations (Fig. 5) and the liquid phase temperatures (Fig. 6) can be observed. It should be noted that no adaptive parameters are needed for the simulation with the model. In the second data set (T16), a monoethanolamine concentration of 2:08 kmol=m3 and an entering gas concentration of 15.1% carbon dioxide are applied. Simulations of this data set are of special interest since enhancement factor models were not able to describe the process properly (Tontiwachwuthikul et al., 1992). Here the same number of axial segments (15) as in the previous run is used. A good agreement between the experimental and simulated values for the gas composition (Fig. 7) and liquid phase temperature (Fig. 8) as well as the results obtained for the previous pilot plant data set (T20) demonstrate a suFcient predictivity of the proposed model for the diFcult case of high purity applications, which could not be obtained by simpler models (Tontiwachwuthikul et al., 1992).
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L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
Fig. 7. Simulated and experimental gas phase composition pro8le for T16.
Fig. 9. Gas phase composition pro8le of industrial absorber.
Fig. 10. Liquid phase temperature pro8le of industrial absorber. Fig. 8. Simulated and experimental liquid phase temperature pro8le for T16.
4.3. Model testing using an industrial scale application Simulation of an industrial application data set (Pintola et al., 1993) is performed to check whether a successful scale-up from the pilot plant scale is possible. In this operating state a natural gas stream is cleaned at 6:88 bar by an amine solution with a monoethanolamine concentration of 4:4 kmol=m3 . The carbon dioxide load of the gas feed is 2.53%. Oppositely to the pilot plant data sets, the liquid feed has a carbon dioxide pre-load of 0.1 mole carbon dioxide per mole amine. A column of 1:9 m in diameter 8lled with 50 mm Pall rings with a total packing height of 14:1 m is used in an ole8n plant to reduce the carbon dioxide content in the natural gas to less than 10 ppm. The gas and the liquid compositions and temperatures as well as the :owrate are measured only at the top and the bottom of the absorber. Similar to the pilot plant case, the agreement between the experimental and simulated data for the gas phase composition (Fig. 9) and liquid phase temperature (Fig. 10) is very good. Application of an enhancement factor based model does not yield such satisfying results, e.g. the gas phase composition at the top of the absorber is more than eight times higher than the experimental value (Pintola et al., 1993). From the results of the pilot plant and the industrial application simulations it can be concluded that the suggested
Fig. 11. Gas phase composition pro8le for T20: Kinetic vs. instantaneous reaction description.
model has a good predictivity for the whole range of industrial applications. 4.4. Sensitivity analysis A sensitivity study of the reaction kinetics in:uence on the simulated absorber performance has been performed. In the literature three approaches can be found for the kinetics of reaction (R1), the most important reaction for the removal of carbon dioxide in this process. Since reactions of dissolved gases in liquids are usually very rapid, a kinetic description was compared with an instantaneous reaction description. Fig. 11 clearly shows, that
L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
Fig. 12. In:uence of reaction kinetics on gas phase composition pro8le for T20.
Fig. 13. In:uence of reaction kinetics on gas phase composition pro8le for T16.
the usage of an equilibrium reaction in the simulation of run T20 leads to completely wrong results, this proves that the kinetic description is essential. In Fig. 12 results obtained with diGerent kinetic descriptions are presented. The kinetics of Kucka et al. (2003) and Hikita, Asai, Ishikawa, and Honda (1977) give similar pro8les, which deviate signi8cantly from those obtained with the kinetics by Danckwerts and Sharma (1966). Taking the sweet gas composition calculated by usage of the kinetics suggested in Kucka et al. (2003) as the design speci8cation value, the application of the kinetic description obtained from Danckwerts and Sharma (1966) leads to a column height, that is too small by 15%. The same investigations are performed for the other pilot plant data set (run T16). In this case, the kinetics of Kucka et al. (2003) and Hikita et al. (1977) give almost identical column pro8les, so that the results obtained by application of the latter expression are not shown in Fig. 13. On the other hand, usage of the kinetics suggested by Danckwerts and Sharma (1966) leads to an underestimation of the column height of 17%. 5. Conclusions In this work, a rigorous rate-based model for reactive sour gas absorption by aqueous amines is suggested. This model
3577
is based on the two-8lm theory and considers the acceleration of mass transport due to a complex system of chemical reactions without using simpli8ed enhancement factor concepts. The precise description of the accelerating eGect is established via the implementation of liquid 8lm reactions. The latter allows for the calculation of non-linear concentration pro8les within the liquid 8lm. Multicomponent mass transfer is taken into account as well as peculiarities of electrolyte solutions and the column hydrodynamics. The model is tested against literature pilot plant data for carbon dioxide absorption by aqueous monoethanolamine solutions. Good agreement between experimental and simulated data is obtained for high purity operations, which are usually diFcult to describe accurately. Furthermore, an industrial scale application containing the same components is investigated and, again, good agreement between operational and calculated values is gained. Thus the suggested model can be regarded as predictive in a wide range. A comparison with the equilibrium approach for the description of the decisive kinetically controlled reaction shows that the kinetic description of reactions is essential. Sensitivity analyses of the in:uence of reaction kinetics on simulation results are carried out. It is found out, that diGerent kinetic expressions lead to signi8cant deviations in the design of column heights (up to 17%). This clearly demonstrates the importance of a proper choice of the reaction kinetics description. The presented model equations can be implemented into any equation-based solver environment and used for arbitrary amine solution systems by modifying the reaction system including kinetics and thermodynamic data. Model application for the simulation of sour gas absorption enables accurate design calculations of complete columns. By implementing diGerent hydrodynamic and mass transfer correlations, the performance of diGerent column internals can readily be tested against each other.
Notation a AC ct DeG F G h k K KD L n ni p q R
speci8c area, m2 =m3 cross-section area of column, m2 total molar concentration, mol=m3 eGective diGusion coeFcient, m2 =s Faraday’s constant, 96; 500 C=mol total gas molar :ow, mol/s molar enthalpy, J/mol reaction rate constant, m3 =mol s equilibrium reaction constant phase distribution coeFcient total liquid molar :ow, mol/s number of components molar :ux of component i; mol=m2 s pressure, Pa heat :ux, J=m2 s reaction rate, mol=m3 s
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RG T x y z z
L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
gas constant (8:3144 J=mol K) temperature, K liquid phase mole fraction gas phase mole fraction axial co-ordinate, m electrical charge
Greek letters ! " & ’
activity coeFcient 8lm thickness, m dimensionless 8lm co-ordinate thermal conductivity, W=m K stoichiometric coeFcient electrical potential, V volumetric hold-up
Subscripts e for i p r rev
educt forward reaction component index product reaction index reverse reaction
Superscripts b c f g i l
bulk molarity based 8lm gas phase interface liquid phase
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On the modelling and simulation of sour gas absorption by aqueous amine solutions Lars Kuckaa , Ivo M-ullerb , Eugeny Y. Kenigb;∗ , Andrzej G3orakb b Department
a Henkel KGaA, 40191 D usseldorf, Germany of Chemical Engineering, University of Dortmund, 44221 Dortmund, Germany
Received 13 March 2003; received in revised form 30 May 2003; accepted 2 June 2003
Abstract A rigorous rate-based model for reactive sour gas absorption by aqueous amine solutions is presented which governs both the coupling of mass transfer and reaction and speci8c features of electrolyte species. The acceleration of mass transfer due to reactions in the liquid phase is taken into account rigorously, without application of enhancement factors. The model is implemented into the simulation environment Aspen Custom Modeler and validated by comparison of published pilot plant data with the simulation results. It is shown, that the model possesses a good predictivity for pilot plant scale as well as for industrial scale applications. In addition, the in:uence of reaction kinetics on the absorber performance is studied. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Rate-based model; Sour gas puri8cation; Reactive absorption; Simulation; Amines
1. Introduction Absorption of gases in liquids accompanied by chemical reaction (reactive absorption) is a fundamental operation in a broad spectrum of chemical process technologies. In oil re8neries, :ue and tail gases need to be puri8ed to meet pollution standards, in fertiliser and petrochemical plants acid gases have to be removed from the feed to ammonia synthesis plants and polymerisation units to avoid catalyst poisoning (Chakravaty, Phukan, & Weiland, 1985). Aqueous amine solutions are proven to be feasible solvents for the treatment of natural, synthesis and re8nery gas streams. Traditionally modelling and simulation of reactive absorption units have been based on the well-known equilibrium stage model which subdivides the column into arti8cial height segments using height equivalent to a theoretical plate (HETP) and assumes the equilibrium state between the streams leaving each stage (Taylor & Krishna, 1993). In reality equilibrium is rarely attained at a stage since absorption is a rate controlled phenomenon (Chakravaty et al., 1985). This means that mass and heat transfer are kinetically limited ∗ Corresponding author. Tel.: +49-231-755-2357; fax: +49-231-755-3035. E-mail address: [email protected] (E. Y. Kenig).
0009-2509/03/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0009-2509(03)00255-0
processes driven by gradients of the chemical potential and temperature. Due to these facts traditional equilibrium-based models and eFciency approaches are usually inadequate (Schneider, Kenig, & G3orak, 1999). Resistances to mass and heat transfer can only be considered by rate-based models, in which gas and liquid phase are balanced separately under consideration of mass and heat :uxes across the interface (Taylor & Krishna, 1993). In addition rigorous predictive models have to regard the accelerating eGect of chemical reactions on mass transfer (Kenig, Schneider, & G3orak, 2001). For a single irreversible reaction, this eGect can be described by enhancement factors (Van Swaaij & Versteeg, 1992). However, enhancement factors resulting from theoretical derivations are exact only for few simple reaction types, otherwise they are based on several simpli8cations, e.g., all binary diGusion coeFcients are equal, only one component is transported through the interface, gas phase resistance is negligible, absorption is isothermal, etc. (see, e.g., DeCoursey, 1982; Suenson, Georgakis, & Evans, 1985; Zarzycki & Chacuk, 1993). Thus, the application of enhancement factors may not be accurate enough in case of complex reaction schemes, with several parallel and consecutive reversible reactions. As this is the case in the sour gas puri8cation by aqueous amine solutions, in the present work a rate-based process
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description is suggested which involves the 8lm model equations combined with relevant reaction and diGusion kinetics for all reactions and components as well as the special features of electrolyte solutions. The proposed model is applicable to all kinds of sour gas puri8cation processes involving aqueous amine solutions.
2. Process description In absorption processes using aqueous amine solutions mainly carbon dioxide and hydrogen sul8de have to be withdrawn from gas streams. Amines are subdivided into primary (e.g. monoethanolamine), secondary (e.g. diethanolamine) and tertiary (e.g. methyldiethanolamine) amines according to the number of hydrogen atoms substituted by organic groups. Depending on the composition and operation conditions of the raw gas streams to be treated aqueous primary, secondary or tertiary amine solutions or aqueous blends of amines are used to meet the sweet gas speci8cations (Chakma, 1999). Fig. 1 shows a simpli8ed :ow diagram of an amine gas treating process and the major equipment needed. The raw gas stream is fed to the bottom of an absorption tower with structured or random packing internals and is sweetened by the counter-currently :owing amine solvent. The dissolved sour gases are removed from the solvent in the subsequent stripping column. The regenerated amine solution is re-circulated to the top of the absorber for further removal of acid gas impurities. Optionally, the loaded solvent can be :ashed after leaving the washing tower to remove hydrocarbons possibly contained in the raw gas stream. In this work, we focus on one solvent type and one sour gas, and consider the reactive absorption of carbon dioxide into aqueous solutions of monoethanolamine keeping in mind that system is a representative of all reactive amine gas treating processes. In the chemical process industries monoethanolamine has been proven to be a feasible solvent, widely used in numerous absorption plants throughout the world. In 1990 monoethanolamine was the most
commonly used amine in CO2 separations, reaching 40% of the total market (DeMontigny, Tontiwachwuthikul, & Chakma, 2001). 2.1. Chemical reactions The absorption of carbon dioxide by aqueous monoethanolamine solutions involves a complex system of parallel and consecutive reactions in the liquid phase: Kinetically controlled reversible reactions CO2 + MEAH + H2 O MEACOO− + H3 O+ ;
(R1)
CO2 + OH− HCO− 3 :
(R2)
Instantaneous reversible reactions 2− + HCO− 3 + H2 O CO3 + H3 O ;
(R3)
MEAH + H3 O+ MEAH+ 2 + H2 O;
(R4)
− MEAH + HCO− 3 MEACOO + H2 O;
(R5)
2H2 O OH− + H3 O+ :
(R6)
Carbon dioxide forms ionic species in the liquid phase via two diGerent reactions (R1), (R2). Reaction R1 is more important, as the monoethanolamine concentration is signi8cantly higher than that of the hydroxide ions. Instantaneous reactions (R3) – (R6) are taken into consideration via the mass action law based on activities: p; r p; r xp p p Kr = e; r e; r : (1) x e e e
Expressions for the calculation of the chemical equilibrium constants in this electrolyte system are available in Austgen, Rochelle, Peng, and Chen (1989). For the calculation of the reaction rate of the kinetically controlled reactions (R1), (R2), the forward and reverse reaction rate constants are important. The forward constants are taken from Kucka, Kenig, and G3orak (2002) and Kucka, Richter, Kenig, and G3orak (2003): c 11 kR1; for = 4:495 × 10 exp(−44940=(RT));
(2)
c 13 kR2; for = 3:279 × 10 exp(−54971=(RT)):
(3)
The reverse reaction rate constants are calculated using Eq. (1). Since a kinetic description must yield the same chemical equilibrium state as the mass action law, the molarity-based constants have to be converted into activity-based ones: kr; for =
( kr;c for ct
e
e; r )
e
Fig. 1. Simpli8ed :ow diagram of an amine absorption unit.
1 : ee; r
(4)
The reaction rate constant for the reverse reaction is given by kr; for kr; rev = : (5) Kr
L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
3. Rigorous rate-based model In the investigated process several components are present in both, gas and liquid phases. These components comprise neutral molecules and electrolyte species. All components participate in complex liquid-phase consecutive and parallel reactions, which lead to a coupling of multicomponent mass transfer and multiple reactions. As a consequence, a specially developed rigorous mathematical model which considers mass transfer resistances, electrolyte thermodynamics and the reaction system as well as the column con8guration is required (Kenig, Kucka, & G3orak, 2002). In the literature, several simulation studies of amine-based absorption of carbon dioxide are available. Some of them use simpli8ed concepts, e.g. equal diGusivities (Glasscock, Critch8eld, & Rochelle, 1991; Hagewiesche, Ashour, Al-Ghawas, & Sandall, 1995) or enhancement factors (Sivasubramanian & Sardar, 1985; Tontiwachwuthikul, Meisen, & Lim, 1992; Pintola, Tontiwachwuthikul, & Meisen, 1993; Pacheco & Rochelle, 1998; Al-Baghli, Pruess, Yesavage, & Selim, 2001), other are restricted by the consideration of only one column stage or segment (Rascol, Meyer, & Prevost, 1996; Cadours & Bouallou, 1998). In this work a model is suggested that balances gas and liquid phase separately and considers mass and heat transfer resistances according to the 8lm theory by explicit calculation of the interfacial :uxes. The 8lm model equations are combined with relevant reaction and diGusion kinetics and include the speci8c features of electrolyte solutions. An important advantage of this model is that the hydrodynamics in the column can be directly involved via correlations for hold-up, pressure drop, interfacial area and mass transfer coeFcients (Schneider et al., 1999). The model provides a direct description of the concentration and temperature pro8les in the absorber, both in 8lm and bulk regions. The reaction rates are implemented as source terms into the transport equations describing 8lm phenomena and into the balances describing liquid bulk behaviour. Therefore the use of the enhancement factor concept is avoided. The whole system of equations is solved simultaneously, and thus the interactions between the 8lm pro8les and the bulk values as well as the mass transfer acceleration by reaction are taken into account. 3.1. Bulk phase equations In the liquid bulk balance equation the axial change of the total molar stream and the compositions are considered: @Lxilb i lb l = nlb i a A c + R i Ac ; @z
i = 1; : : : ; nl :
i=1
= 1:
@Lhlb = qlf ai Ac : @z
(8)
Similar equations are valid for the gas bulk phase, except for the consideration of chemical reactions: @Gyigb i = ngb i a Ac ; @z
i = 1; : : : ; ng ;
(9)
g
n
yigb = 1;
(10)
i=1
@Ghgb = qgf ai Ac : @z
(11)
Furthermore, the pressure drop is considered in the gas bulk phase via relevant correlations (see Billet & Schultes, 1999): @p = f(L; G; l ; g ; : : :): @z
(12)
3.2. Film region equations Contrary to the equilibrium stage model, in the rigorous rate-based model the calculation of interfacial :uxes is required. For dilute electrolyte solutions the diGusional interactions can be neglected and the Maxwell–Stefan relations, generally applied for the description of multicomponent mass transfer, are reduced to the Nernst–Planck equation (Taylor & Krishna, 1993): l ctlf DeG @xilf F @’ ;i lf lf ni = − + xilf nlft ; + x i zi !l @"l RG T @"l i = 1; : : : ; nl − 1:
(13)
The introduction of the electrical potential requires the application of an additional equation, to assure that the liquid phase is electroneutral everywhere: l
n
xi zi = 0:
(14)
i=1
In the liquid 8lm region mass transfer and chemical reactions occur simultaneously. Therefore a diGerential component balance has to be considered: 1 @nlfi − Rlfi = 0; !l @"l
i = 1; : : : ; nl :
(15)
(6)
(7)
&lf @T l lf lf q =− l + ni hi : ! @"l
l
xilb
The enthalpy balance for the liquid bulk phase neglecting heat losses reads as follows:
Due to chemical conversion in the 8lm the component molar :uxes at the interface and at the boundary between 8lm and bulk phase are not equal. The heat :ux through the liquid 8lm comprises the conductive and convective terms:
The liquid bulk mole fractions sum to unity: n
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lf
nl
i=1
(16)
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In the gas 8lm region (no reaction) the component :uxes are described by ngf i =−
g gf ctgf DeG ; i @yi + yigf ngf t ; g ! @"g
i = 1; : : : ; ng − 1: (17)
The heat :ux through the gas 8lm is given by q
gf
ng
&gf @T g gf gf =− g + ni hi : ! @"g
diGerential and algebraic equation system. Altogether, the model can contain approximately 50,000 equations, the exact number depending on the axial discretisation step. The model is implemented into the commercial software package Aspen Custom Modeler (see http://www.aspentech.com/). This simulation environment oGers the opportunity to calculate all physical properties required in the model equations by using the program package Aspen Properties.
(18)
i=1
The thermodynamic equilibrium at the gas–liquid interface is used for the connection of the gas and liquid phase compositions: yii
=
KD; i xii ;
g
i = 1; : : : ; n :
(19)
The liquid 8lm thickness is an important parameter in the rate-based model. Usually it is estimated via empirical mass transfer correlations taking into account the type of column internals, hydraulics and transport properties. These correlations (e.g. Kolev, 1976; Billet & Schultes, 1999) have to be created simultaneously with all other model equations. 3.3. Thermodynamics The non-idealities of the gas phase are taken into account via application of the well-known Soave–Redlich–Kwong equation of state (Reid, Prausnitz, & Poling, 1987), for the liquid phase the three-parametric electrolyte-NRTL method is used. The latter model is based on the local composition concept and satisfactorily represents physical interactions of true species in aqueous multicomponent electrolyte solutions (Chen & Evans, 1986). All required parameters are available in Austgen et al. (1989). The KD -values required for the description of the gas–liquid equilibrium state (Eq. (19)) comprise fugacity and activity coeFcients. For the calculation of enthalpies the standard state of elements is used and heat of reaction and absorption is directly taken into account. The thermal conductivities in the gas phase are calculated by the Stiel–Thodos model whereas in the liquid phase the Sato–Riedel model with the Riedel electrolyte correction is used (see Reid et al., 1987). The liquid phase diGusion coeFcients are determined by the Wilke–Chang method for molecular species (Reid et al., 1987) and the Nernst–Hartley equation for electrolytes (Horvath, 1985), the gas phase diGusion coeFcients are estimated according to the Chapman–Enskog–Wilke–Lee model at low pressures and the Dawson-Khoury-Kobayashi model is applied at higher pressures (see Reid et al., 1987).
4. Simulation results 4.1. Film discretisation analysis A subdivision of the liquid 8lm into several balance regions is necessary to describe the accelerating eGect of the chemical reactions on mass transfer with a suFcient accuracy. Using this discretisation allows for calculation of concentration pro8les in the 8lm region (Schneider et al., 1999). For the determination of the required number of liquid 8lm grid points, several discretisation types have been tested. It has been found out, that when the number of segments exceeds 10 no noticeable changes in the calculated component mass :uxes and the concentrations pro8les occur. In order to investigate a possible calculation time reduction, the segment width has been varied to check whether the results calculated with 10 segments can be obtained with a lower number of grid points. It has been shown that at the boundaries of the liquid 8lm the segments have to be thinner than in the middle of the 8lm and that 8ve grid points between the interface and bulk (altogether six segments) with this type of non-equidistant distribution provide a very good agreement with the results obtained with 9 equidistantly distributed points (Fig. 2). With this type of the liquid 8lm discretisation, non-linear concentration pro8les are obtained as shown in Fig. 3. The discretisation method is tested for diGerent gas and liquid feed compositions and found to be well suited over the parameter range occurring in the investigated process.
3.4. Simulation environment The suggested model consists of partial diGerential and algebraic equations. To obtain a numerical solution of such problems, a discretisation in regard to the axial and normal co-ordinates should be carried out to yield an ordinary
Fig. 2. Liquid 8lm CO2 concentration pro8les: Dependence on the type of discretisation.
L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
Fig. 3. Liquid 8lm concentration pro8les.
Fig. 4. In:uence of axial discretisation on the sweet gas composition for T20.
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Fig. 5. Simulated and experimental gas phase composition pro8le for T20.
Fig. 6. Simulated and experimental liquid phase temperature pro8le for T20.
4.2. Validation of the rigorous model The validation of the suggested model is performed by comparison of simulation results with experimental data. A good model predictivity can only be stated, if the model is able to describe composition and temperature pro8les along the washing tower suFciently, rather than only calculate the correct values at the top and the bottom. To test the model two diGerent operating states are simulated, in which highly loaded gas feeds are treated to give clean gas streams with remaining impurities in the ppm range. Both data sets (runs T20 and T16) taken from Tontiwachwuthikul et al. (1992) were obtained using the same experimental set-up. The absorption at atmospheric pressure is performed in a column of 0:1 m in diameter 8lled with 12:7 mm ceramic Berl saddles, with a total packing height of 6:6 m. In the 8rst run (T20), an air stream containing 19.2% of carbon dioxide is cleaned by an amine solution with a monoethanolamine concentration of 2:55 kmol=m3 . First of all, to reach acceptable computation times, the minimum number of axial segments has to be determined. As can be seen from Fig. 4, with increasing number of segments the sweet gas concentration reaches an asymptotic value. The minimum number of axial segments which provides results
of suFcient accuracy for T20 is found to be 15. Note that the concentration pro8le of MEAH is not shown in this 8gure, because the MEAH-concentration for this special case is very high and changes of its value can hardly be seen. For this pilot plant data set a good agreement between simulated and experimental data for the gas phase concentrations (Fig. 5) and the liquid phase temperatures (Fig. 6) can be observed. It should be noted that no adaptive parameters are needed for the simulation with the model. In the second data set (T16), a monoethanolamine concentration of 2:08 kmol=m3 and an entering gas concentration of 15.1% carbon dioxide are applied. Simulations of this data set are of special interest since enhancement factor models were not able to describe the process properly (Tontiwachwuthikul et al., 1992). Here the same number of axial segments (15) as in the previous run is used. A good agreement between the experimental and simulated values for the gas composition (Fig. 7) and liquid phase temperature (Fig. 8) as well as the results obtained for the previous pilot plant data set (T20) demonstrate a suFcient predictivity of the proposed model for the diFcult case of high purity applications, which could not be obtained by simpler models (Tontiwachwuthikul et al., 1992).
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L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
Fig. 7. Simulated and experimental gas phase composition pro8le for T16.
Fig. 9. Gas phase composition pro8le of industrial absorber.
Fig. 10. Liquid phase temperature pro8le of industrial absorber. Fig. 8. Simulated and experimental liquid phase temperature pro8le for T16.
4.3. Model testing using an industrial scale application Simulation of an industrial application data set (Pintola et al., 1993) is performed to check whether a successful scale-up from the pilot plant scale is possible. In this operating state a natural gas stream is cleaned at 6:88 bar by an amine solution with a monoethanolamine concentration of 4:4 kmol=m3 . The carbon dioxide load of the gas feed is 2.53%. Oppositely to the pilot plant data sets, the liquid feed has a carbon dioxide pre-load of 0.1 mole carbon dioxide per mole amine. A column of 1:9 m in diameter 8lled with 50 mm Pall rings with a total packing height of 14:1 m is used in an ole8n plant to reduce the carbon dioxide content in the natural gas to less than 10 ppm. The gas and the liquid compositions and temperatures as well as the :owrate are measured only at the top and the bottom of the absorber. Similar to the pilot plant case, the agreement between the experimental and simulated data for the gas phase composition (Fig. 9) and liquid phase temperature (Fig. 10) is very good. Application of an enhancement factor based model does not yield such satisfying results, e.g. the gas phase composition at the top of the absorber is more than eight times higher than the experimental value (Pintola et al., 1993). From the results of the pilot plant and the industrial application simulations it can be concluded that the suggested
Fig. 11. Gas phase composition pro8le for T20: Kinetic vs. instantaneous reaction description.
model has a good predictivity for the whole range of industrial applications. 4.4. Sensitivity analysis A sensitivity study of the reaction kinetics in:uence on the simulated absorber performance has been performed. In the literature three approaches can be found for the kinetics of reaction (R1), the most important reaction for the removal of carbon dioxide in this process. Since reactions of dissolved gases in liquids are usually very rapid, a kinetic description was compared with an instantaneous reaction description. Fig. 11 clearly shows, that
L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
Fig. 12. In:uence of reaction kinetics on gas phase composition pro8le for T20.
Fig. 13. In:uence of reaction kinetics on gas phase composition pro8le for T16.
the usage of an equilibrium reaction in the simulation of run T20 leads to completely wrong results, this proves that the kinetic description is essential. In Fig. 12 results obtained with diGerent kinetic descriptions are presented. The kinetics of Kucka et al. (2003) and Hikita, Asai, Ishikawa, and Honda (1977) give similar pro8les, which deviate signi8cantly from those obtained with the kinetics by Danckwerts and Sharma (1966). Taking the sweet gas composition calculated by usage of the kinetics suggested in Kucka et al. (2003) as the design speci8cation value, the application of the kinetic description obtained from Danckwerts and Sharma (1966) leads to a column height, that is too small by 15%. The same investigations are performed for the other pilot plant data set (run T16). In this case, the kinetics of Kucka et al. (2003) and Hikita et al. (1977) give almost identical column pro8les, so that the results obtained by application of the latter expression are not shown in Fig. 13. On the other hand, usage of the kinetics suggested by Danckwerts and Sharma (1966) leads to an underestimation of the column height of 17%. 5. Conclusions In this work, a rigorous rate-based model for reactive sour gas absorption by aqueous amines is suggested. This model
3577
is based on the two-8lm theory and considers the acceleration of mass transport due to a complex system of chemical reactions without using simpli8ed enhancement factor concepts. The precise description of the accelerating eGect is established via the implementation of liquid 8lm reactions. The latter allows for the calculation of non-linear concentration pro8les within the liquid 8lm. Multicomponent mass transfer is taken into account as well as peculiarities of electrolyte solutions and the column hydrodynamics. The model is tested against literature pilot plant data for carbon dioxide absorption by aqueous monoethanolamine solutions. Good agreement between experimental and simulated data is obtained for high purity operations, which are usually diFcult to describe accurately. Furthermore, an industrial scale application containing the same components is investigated and, again, good agreement between operational and calculated values is gained. Thus the suggested model can be regarded as predictive in a wide range. A comparison with the equilibrium approach for the description of the decisive kinetically controlled reaction shows that the kinetic description of reactions is essential. Sensitivity analyses of the in:uence of reaction kinetics on simulation results are carried out. It is found out, that diGerent kinetic expressions lead to signi8cant deviations in the design of column heights (up to 17%). This clearly demonstrates the importance of a proper choice of the reaction kinetics description. The presented model equations can be implemented into any equation-based solver environment and used for arbitrary amine solution systems by modifying the reaction system including kinetics and thermodynamic data. Model application for the simulation of sour gas absorption enables accurate design calculations of complete columns. By implementing diGerent hydrodynamic and mass transfer correlations, the performance of diGerent column internals can readily be tested against each other.
Notation a AC ct DeG F G h k K KD L n ni p q R
speci8c area, m2 =m3 cross-section area of column, m2 total molar concentration, mol=m3 eGective diGusion coeFcient, m2 =s Faraday’s constant, 96; 500 C=mol total gas molar :ow, mol/s molar enthalpy, J/mol reaction rate constant, m3 =mol s equilibrium reaction constant phase distribution coeFcient total liquid molar :ow, mol/s number of components molar :ux of component i; mol=m2 s pressure, Pa heat :ux, J=m2 s reaction rate, mol=m3 s
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RG T x y z z
L. Kucka et al. / Chemical Engineering Science 58 (2003) 3571 – 3578
gas constant (8:3144 J=mol K) temperature, K liquid phase mole fraction gas phase mole fraction axial co-ordinate, m electrical charge
Greek letters ! " & ’
activity coeFcient 8lm thickness, m dimensionless 8lm co-ordinate thermal conductivity, W=m K stoichiometric coeFcient electrical potential, V volumetric hold-up
Subscripts e for i p r rev
educt forward reaction component index product reaction index reverse reaction
Superscripts b c f g i l
bulk molarity based 8lm gas phase interface liquid phase
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