Rigorous modelling of adiabatic multicomponent CO2 post-combustion capture using hollow fibre membrane contactors

Chemical Engineering Science 145 (2016) 45–58

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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces

Rigorous modelling of adiabatic multicomponent CO2 post-combustion capture using hollow fibre membrane contactors David Albarracin Zaidiza, Seth Gabriel Wilson, Bouchra Belaissaoui, Sabine Rode, Christophe Castel, Denis Roizard, Eric Favre Laboratoire Réactions et Génie des Procédés (LRGP) (UMR 7274), Université de Lorraine, ENSIC, 1, rue Grandville – BP 20451, 54001 Nancy Cedex, France

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T


In the considered domain, 1D and 2D approaches give similar results.
A high temperature peak, related to huge trans-membrane water flux is evidenced.
For both, water and MEA, transmembrane flux reversal occurs.
Significant solvent losses are shown, when industrial conditions are applied.
Simulation results with average- or distributed-membrane resistances are comparable.

art ic l e i nf o

a b s t r a c t

Article history: Received 28 October 2015 Received in revised form 20 January 2016 Accepted 25 January 2016 Available online 8 February 2016

The modelling of adiabatic multicomponent chemical absorption of carbon dioxide by means of hollow fibre membrane contactors is presented. One-dimensional and two-dimensional approaches are compared. A relatively wide operating domain was covered, ranging from fresh solvent and partial MEA conversions which correspond to experimental data, to partially loaded solvent and almost complete MEA conversion which represent industrial conditions. Both models predicted solvent flux reversal through the membrane and significant temperature peaks, up to 75 °C. Moreover, important solvent losses are expected for the absorption unit. For considerably reduced calculation times, the onedimensional model provided average results that compared well with those of the two-dimensional model. A relative difference of only 2.88% was found in the average absorbed specific flux of CO2. In the considered operating domain, the diffusion of the complex reaction product, protonated-amine-carbamate, could be considered non-limiting. Furthermore, the use of an average equivalent membrane masstransfer coefficient was found to be adequate. Finally comparison with the packed bed technology evidenced similar trends and significant process intensification. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Carbon dioxide capture Adiabatic modelling Hollow fibre membrane contactor Chemical absorption

1. Introduction Post-combustion capture (PCC) is convenient to achieve greenhouse gas emission reductions, as it can be retrofitted to existing power stations and can be integrated into new ones. The robustness of packed columns makes it the standard technology of choice for the gas–liquid absorption of CO2, using aqueous amine solutions as liquid absorbents. Even though it is not the best http://dx.doi.org/10.1016/j.ces.2016.01.053 0009-2509/& 2016 Elsevier Ltd. All rights reserved.

performing chemical solvent, monoethanolamine (MEA) at 30 wt% is currently considered as the benchmark solvent in PCC (Liang et al., 2015). However, the treatment of large quantities of flue gases requires itself equipment of a large size. Hollow fibre membrane contactors (HFMC) are an increasingly more attractive alternative because they allow for a reduction of the equipment size. Indeed, the specific interfacial area for mass-transfer in a typical HFMC is many times greater than that of a typical packed

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column, approximately in the range of 2500–12,000 m  1 and 200–500 m  1, respectively (Tobiesen et al., 2007). Moreover, contrary to packed columns, the contact between gas and liquid is indirect thereby avoiding liquid entrainment and flooding, both of which limit the operational range of packed columns. In spite of this, HFMC technology is subject to membrane wetting which is a principal concern of membrane contactor performance. HFMC has been widely investigated both experimentally and theoretically. When a low absorbent conversion (e.g. less than 0.2 for the MEA system), is imposed, simulations and experiments indicate that the contactor may be considered to operate isothermally. If, in addition, the inlet liquid absorbent is unloaded, the reaction may be considered pseudo-first order and irreversible. In this case, the mass balance equations can be solved for only one species (i.e. CO2) (Albarracin Zaidiza et al., 2015). However in an industrial context, which implies high absorbent conversion and partially loaded inlet liquid absorbent, temperature gradients and liquid evaporation and condensation are significant and reaction rates are limited by chemical equilibrium. Hence, energy balances, multi-component transfer and reversible reaction kinetics need to be considered. Most of the investigations have been performed considering mild conditions (i.e. low conversions and fresh liquid absorbent). A literature review is given in Albarracin Zaidiza et al. (2014), Cui and deMontigny (2013) and Zhang et al. (2014). Process models of various complexities have been developed; however, for the most part, isothermal behaviour and irreversible reactions are considered, and water transfer is neglected. Isothermal one-dimensional (1D) models, based on an average overall mass-transfer coefficient have been suggested (Chabanon et al., 2013). The principal assumption of these models is the invariance in conductance for each of the gas, membrane- and liquid-side, over the entire fibre length. They cannot be applied to operating conditions in which the liquid-side conductance varies widely over the reactor length (Rode et al., 2012). For this case, models based on resistance in series approaches were proposed, taking into consideration the variation of the gas- and liquid-side conductance (Rode et al., 2012). Simultaneously, supported by the rapid development of CFD facilities, two-dimensional (2D) isothermal models were published (Albarracin Zaidiza et al., 2014; Boucif et al., 2008; Faiz et al., 2011). These models are based on the resolution of the convective diffusion equations coupled with the equations of the chemical reactions, using cylindrical geometry coordinates. To our knowledge, few research papers tackle the adiabatic multi-component modelling of HFMC for chemical absorption of CO2 (Albarracin Zaidiza et al., 2015; Ghasem et al., 2013; Hoff et al., 2004; Hoff and Svendsen, 2014; Iliuta et al., 2014; Rongwong et al., 2013). Rongwong et al. (2013) developed an adiabatic onedimensional model including membrane wetting. The model was validated using experimental data from literature. However, the operating and simulation conditions were far from being industrially relevant and accordingly the temperature variations were lower than 2 K. In a previous paper, a 1D adiabatic multicomponent model has been discussed. Under severe operating conditions, significant local temperature peaks appeared together with important water vapor fluxes across the membrane (Albarracin Zaidiza et al., 2015). Hoff et al. (2004) and Hoff and Svendsen (2014) developed and validated an adiabatic twodimensional diffusion-reaction model in a large range of operation conditions. No temperature profiles were shown. The authors considered that in HFMC with reversible chemical reactions, the liquid-phase product diffusion was the limiting factor. For scaling purposes, it was pointed out that 2D models are too complicated and that 1D models are preferable, provided that they have been validated with more rigorous approaches. A similar 2D model, but

including for membrane wetting, has been proposed by Iliuta et al. (2014). It was concluded that non-isothermal simulations reveal that the hollow-fibre membrane module operation can be considered as quasi-isothermal. However, the operating and simulation conditions were far from industrial context (i.e. very high liquid-to-gas flow ratio and MEA conversions lower than 0.2). Finally the solvent evaporation in CO2 absorption using HFMC has been addressed by Ghasem et al. (2013). In their model, free convection of water inside the membrane pores was considered to evaluate the mass flux across the membrane. Since an aqueous solution of NaOH was used as solvent, the water evaporation was mainly due to the use of dry inlet gas. This is different from CO2 post-combustion capture by amine solvents. The main advantage of the 2D over the 1D approach is that more rigorous computations of transfer fluxes and reaction rates are possible. The main drawback is that model resolution requires significant calculation time and a high processor performance. It is therefore tedious and not appropriate for the investigation of large parameter domains. Identification of an efficient model strategy, ideally both rigorous yet robust while not overly complex, is key. In a previous paper (Albarracin Zaidiza et al., 2014), a comparison of 1D and 2D approaches assuming isothermal behaviour, irreversible reactions and neglecting water transfer was performed for CO2 capture with amine solution using membrane contactors. The aim was to identify the most efficient model strategy. The results showed comparable simulation results, with a maximum relative deviation of 2.2%, thus indicating the quality of the 1D approach. In this paper, 1D and 2D approaches are compared applying more realistic assumptions, i.e. adiabatic behaviour, multi-component transfer and reversible reactions. Both mild and severe operating conditions are considered. Indeed, unloaded solvent and relatively low amine conversion are representative of most of the available experimental data; whereas preloaded solvent and high amine conversion illustrate an industrial context. In addition, use of an average and a distributed equivalent membrane mass-transfer coefficient are compared. Finally simulations of the packed bed technology are presented and compared to those made in the HFMC.

2. System characteristic The mass- and heat-transfer within a membrane module with a microporous membrane is described as a three step process, as illustrated in Fig. 1. Mass-transfer is considered for three species (i¼CO2, H2O or MEA). The illustrated reactive species (i¼CO2) is transferred from the gas phase to the external face of the membrane, it then diffuses through the membrane pores, and is finally absorbed by the liquid solution where it reacts. The mass and heat flux lead to radial concentration and temperature gradients, as illustrated in Fig. 1. The shell-side flow section is commonly represented using equivalent annulus geometry. The radial velocity gradients correspond, in general, to developed laminar flow. The membrane contactor consists of a bundle of cylindrical hollow fibres, made of hydrophobic microporous membranes. The contactor has an effective length, Z, an external radius, re, a fibre volume fraction, φ, and a relative thickness, δ/re. The geometric characteristics of the HFMC are calculated as shown in Table 1. Since content of particles (e.g. ashes) in the post-combustion gases is significant, the amine solvent flows in the lumen to prevent fibre closure. The gas mixture (a mixture of saturated air and carbon dioxide) flows in the shell surrounding the hollow fibre in a counter-current flow arrangement.

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47

Fig. 1. Schematic representation of the hollow fibre membrane contactor for CO2 capture in amine solutions.

3.2. Physicochemical properties, phase and chemical equilibria and reaction kinetics

Table 1 Definition and expression of geometrical characteristics of the HFMC. Parameter

Mathematical expression External volume

Hydraulic diameter

dh  ext ¼ 2r e 1 φ φ

Specific interfacial area

aext ¼

Specific membrane area

 re  aM ¼ 2φ re

2φ re δ

ln

Units

m1

The physicochemical properties were estimated using correlations available in literature, references to which are given in Table 3. Since the ionic components are considered to be nonvolatile, the phase equilibria are established for the considered molecular species, i.e. CO2, MEA, H2O and N2, as follows:

m1

C i;L ¼ mi C i;G

Internal volume
 dh  int ¼ 2r e 1 rδe   2φ 1  rδe aint ¼ re

m

1 1  rδ e

ð1Þ

For CO2 and N2, the partition coefficient, m, is defined as mi ¼

RT Hi

ð2Þ

3. Modelling approaches

Whereas for MEA and H2O, it is defined as

3.1. Model assumptions

mi ¼

The assumptions made in this work are mostly based on the general consensus found in other published work. The two models consider the non-isothermal nature of the overall absorption process, including the solvent transfer across the membrane. The membrane mass-transfer coefficient used for simulation correspond to the range of data which have been reported for carbon capture by membrane contactors (Chabanon et al., 2013). In the choice of the value, partial wetting of the membrane was assumed. The model assumptions made for both 1D and 2D approaches are summarised in Table 2. The main differences between the models reside in the assumptions made in the mass- and heattransfer and reaction. The 1D model simplifies the partial differential balance equations used in the 2D modelling approach by employing an enhancement factor, a local overall mass-transfer coefficient and transfer analogies. The enhancement factor describes the chemical reaction in the liquid-side diffusion boundary layer, and its definition and implementation involves numerous assumptions. Only CO2 is considered capable of diffusing through the gas–liquid phase boundary, and hence the membrane. Furthermore the liquid-side diffusion coefficient of each species is considered to be constant (Chang and Rochelle, 1982). Finally, liquid mixing-cup concentrations, which are assumed to be at chemical equilibrium, are considered. In contrast, the 2D model considers local concentrations.

where Hi , P sat and C T;L stand for the Henry constant (Crovetto, i 1991), the saturating pressure and the total molar liquid concentration, respectively. The chemical speciation of the aqueous MEA-CO2 solution is characterised by the following reactions: Water ionisation:

RTC T;L P sat i

ð3Þ

K1

2H2 O 3 HO  þ H3 O þ

ð4Þ

Dissolved CO2 dissociation: K2

CO2 þ 2H2 O 3 HCO3 þ H3 O þ

ð5Þ

Bicarbonate dissociation: K3

HCO3  þ H2 O 3 CO3 2 þ H3 O þ

ð6Þ

Carbamate reversion to bicarbonate: K4

RNHCOO  þ H2 O 3 RNH2 þHCO3 

ð7Þ

Dissociation of protonated MEA: K5

RNH3þ þ H2 O 3 RNH2 þH3 O þ

ð8Þ

The correlations of the equilibrium constants used in this work are given in Appendix A. It is worth mentioning that the nonideality of the system was lumped into the expressions of K4 and

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Table 2 1D and 2D modelling assumptions. Hydrodynamics 1. Steady state (Boucif et al., 2012; Chabanon et al., 2013; Eslami et al., 2011; Faiz and Al-Marzouqi, 2009; Ghasem et al., 2013; Hoff et al., 2004; Hoff and Svendsen, 2014; Keshavarz et al., 2008; Wang et al., 2004; Zhang et al., 2006) 2. Laminar liquid and gas flow with fully developed velocity profiles, i.e. no radial velocity components (Chabanon et al., 2013; Eslami et al., 2011; Faiz and Al-Marzouqi, 2009; Ghasem et al., 2013; Hoff et al., 2004; Hoff and Svendsen, 2014; Keshavarz et al., 2008; Wang et al., 2004; Zhang et al., 2006) 3. Plug flow, i.e. non-uniform flow distribution due to random packing neglected (Boucif et al., 2012; Chabanon et al., 2013; Eslami et al., 2011; Faiz and Al-Marzouqi, 2009; Ghasem et al., 2013; Hoff et al., 2004; Hoff and Svendsen, 2014; Keshavarz et al., 2008; Wang et al., 2004; Zhang et al., 2006) Thermodynamics 4. Henry’s law used to represent the gas–liquid equilibrium (Boucif et al., 2012; Chabanon et al., 2013; Eslami et al., 2011; Faiz and Al-Marzouqi, 2009; Ghasem et al., 2013; Keshavarz et al., 2008; Wang et al., 2004; Zhang et al., 2006) 5. Solubility of N2 neglected 6. Semi-empirical liquid speciation (Hoff and Svendsen, 2014) 7. Ideal gas behaviour (Boucif et al., 2012; Chabanon et al., 2013; Eslami et al., 2011; Faiz and Al-Marzouqi, 2009; Ghasem et al., 2013; Hoff et al., 2004; Hoff and Svendsen, 2014; Keshavarz et al., 2008; Wang et al., 2004; Zhang et al., 2006) Reaction and mass- and heat-transfer 8. Kinetics including reaction reversibility (Albarracin Zaidiza et al., 2015; Chabanon et al., 2015; Hoff and Svendsen, 2014) 9. Ionic products considered as one complex-product with a single apparent diffusion coefficient (Albarracin Zaidiza et al., 2015; Hoff and Svendsen, 2014) 10. Membrane mass transfer modelled using Fick diffusion through porous media, thus neglecting convective contributions. Equivalent membrane mass-transfer coefficient value as reported in literature. For heat transfer, solid conduction is added. (Boucif et al., 2012; Chabanon et al., 2013; Eslami et al., 2011; Faiz and Al-Marzouqi, 2009; Hoff et al., 2004; Hoff and Svendsen, 2014; Keshavarz et al., 2008; Wang et al., 2004; Zhang et al., 2006) 11. Condensation or evaporation of water occurs only at the liquid–membrane interface (Albarracin Zaidiza et al., 2015; Hoff and Svendsen, 2014) 12. Adiabatic behaviour thus neglecting heat-losses One dimensional: Two dimensional: 13. Axial diffusion neglected in all phases 13. Axial diffusion considered for gas, liquid and membrane. 14. Sherwood and Nusselt numbers calculated using the Graetz equation for the gas 14. Contributions of advection, diffusion and reaction to mass balances solved using and the liquid phase. Mixing-cup-concentrations and temperatures are conlocal concentrations. Analogously, contributions of convection, conduction and sidered. Uniform wall flux is taken as boundary condition (Beek et al., 1999). heat of reaction to energy balances solved using local temperatures. Reaction taken into account by an enhancement factor using liquid mixing-cup concentrations at chemical equilibrium. Kinetically controlled reversible reaction restricted to a reaction boundary-layer.

Table 4 Reaction kinetics constants of the forward and backward reaction between CO2 and MEA.

Table 3 Physicochemical properties of both, the gas and liquid phases. Property

Symbol [units]

Gas Reference

Cp [J mol  1 K  1] Reid et al. (1987) Ideal gas Density ρ [kg m  3] 1 Viscosity m [Pa s ] Reid et al. (1987) Fuller et al. Diffusion coefficients Di [m  2 s  1] (1966) Thermal λ [W m  1 K  1] Reid et al. conductivity (1987) 1 Heat of absorption of ΔHabs [J mol ] CO2 Water and MEA ΔHvap [J mol  1] latent heat Surface tension γ [N m  1] Specific heat

Liquid Reference

Kinetic constant

Expression

6

Forward, kr [m mol

Hilliard (2008) Weiland et al. (1998) Weiland et al. (1998) Talbot (1987), Wilke and Chang (1955) Cheng et al. (1996) Kim and Svendsen (2007) Hilliard (2008) Jayarathna et al. (2013)

2

s

1

]

Backward, kr’ [m3 mol  1 s  1]

4:2919  103 exp

h

3:1792  1010 exp

 4389:8 TðKÞ

h

i

 12687 TðKÞ

i

0

where kr and kr are the reaction constants for the forward and backward reaction, respectively. The expressions of the kinetics constants, which are obtained with experimental data from Aboudheir et al. (2003), are summarised in Table 4. The influence of the temperature on the reaction kinetics was taken into account using the Arrhenius model, within the temperature range of the experimental data, i.e. between 290 and 330 K. 3.3. Model equations

K5. The estimation procedures of the CO2 solubility and of the chemical speciation are described in Appendix B. The kinetic controlled reaction, Eq. (9), is the result of combining of Eqs. (5), (7) and (8). K6

2RNH2 þ CO2 3 RNHCOO  þ RNH3þ ; where U K 6 ¼

K3 K5K6

ð9Þ

The termolecular reaction mechanism has been used to describe the reaction kinetics as it is suitable for partially loaded primary amines (Aboudheir et al., 2003). The overall reaction kinetics is described as follows: 0

r CO2 ¼ kr C CO2 C MEA 2  kr C RNHCOO  C RNH þ ; where U K 6 ¼ kr1 =kr1 3

0

ð10Þ

The balance equations that characterise the system are presented in this section for both, the 1D and 2D modelling approaches. Mass- energy- and momentum differential balances are established in steady state. 3.3.1. One dimensional (1D) model approach The 1D model is detailed in Albarracin Zaidiza et al. (2015), hence, the model equations are summarised in this section. – Gas molar balance d G ¼  N i ; where U Gi ¼ uG C i;G dz i

ð11Þ

D. Albarracin Zaidiza et al. / Chemical Engineering Science 145 (2016) 45–58

– Gas thermal balance

49

3.3.2. Two dimensional (2D) model approach

dT G q P ¼ CpG Gi dz

ð12Þ

i

– Gas molar balance:

     ∂C ∂C ∂ 1∂ ∂ vG C i;G  rDi;G i;G þ Di;G i;G ¼0 ∂z r ∂r ∂z ∂r ∂z

ð21Þ

– Gas momentum balance (Happel, 1959) d PG 8φ   ¼  μG v G K koz ; where U K koz ¼  dz 2 ln 1=φ  3 þ4φ  φ2 r 2e ð13Þ

where Di;M ¼ Di;G

– Liquid molar balance d L ¼  N i ; where U Li ¼ u L C i;L dz i – Liquid thermal balance P q þ i N i ΔH abs=vap dT L P ¼ dz CpL i Li

2

DCO

ref 2 ;G

δ

ð22Þ

– Liquid molar balance:

     ∂C ∂C ∂ 1∂ ∂ vL C i;L  rDi;L i;L þ Di;L i;L ¼ ri ∂z r ∂r ∂z ∂r ∂z

ð23Þ

ð15Þ

dP L 8μ v L ¼  L2 dz ri

ð16Þ

The local flux of the species i, Ni, as well as the local heat flux, q, are computed using a resistance in series approach, as follows: 1 1 1 1 ¼ þ þ aM ki;ov aext ki;G aM ki;M aint mi Ei ki;L

ð17Þ   1 1 1 1 ¼ q ¼ aM U T G  T L ; where U þ þ aM U aext hG aM hM aint hi;L

ð18Þ

T and C i denote the mixing-cup temperature and concentration respectively at a given axial position, z. u f and v f signify, respectively, for the mean superficial and interstitial velocity at a given axial position z. Ei is the enhancement factor related to the chemical reaction (DeCoursey, 1982; Weiland et al., 1982). The gas and liquid-side mass-transfer coefficients, ki,G, and ki,L are computed locally, using the Sherwood number estimated using Graetz’s equation as follows:
1=3 3 Shi;f ¼ a3 þ b Gzi;f With the material Graetz number defined as

– Gas thermal balance:  

 ∂T 1 ∂ ∂T G ∂2 T G r þ 2 ¼0 ρG CpG vG G  λG r ∂r ∂z ∂r ∂z

vf dh;f Uniform wall flux Di;f z

ð24Þ

– Membrane thermal balance:  

 1 ∂ ∂T M ∂2 T M r þ λM;ef f ¼ 0; where λM;ef f ¼ λM ð1  εÞ þ λG ε 2 r ∂r ∂r ∂z ð25Þ – Liquid thermal balance:  

 ∂T 1 ∂ ∂T L ∂2 T L r þ 2 þ r CO2 ΔH abs ρL CpL vL L ¼ λL r ∂r ∂z ∂r ∂z

ð26Þ

The momentum equations of the 2D model are the same as those used in the 1D model. For the fluid in the lumen-side, the integration of the Hagen‐Poiseuille equation with no-slip conditions leads to the fully developed velocity profile. For the fluid in the shell-side, the Happel free surface approach is used (Happel, 1959). "  2 # r ð27Þ vL ¼ 2vL 1  r1

2

Gzi;f ¼

kM;COeq

ð14Þ

– Liquid momentum balance


 N i ¼ aM ki;ov C i;G  miC i;L ; where U

– Membrane molar balance:

    ∂C ∂C 1∂ ∂ rDi;M i;M þ Di;M i;M ¼ 0; r ∂r ∂z ∂r ∂z



vG ¼ 2vG r 2s r 2e

boundary condition :



2 4




3  r 2e pffiffiffiffiffiffiffiffiffi
5; where r s ¼ r e 1=φ rs 4 2 2 4 4 3r s  4r s r e þ r e  4r s ln re r 2  2r 2s ln

r re

ð19Þ

ð28Þ

For heat-transfer calculations, the membrane porosity was set to 0.5 and the membrane thermal conductivity to 0.15 W m  1 K  1. The wetting phenomena caused by liquid breakthrough and/or capillary condensation are lumped in the value of the kM,CO2eq. In addition, it is considered that all components are affected in the same way. For this reason, the mass-transfer coefficient of the specie i was determined by

The increase in the solvent loading is accompanied by an increase of liquid density. The volumetric liquid flow rate is thus almost invariant over the fibre length and hence, the variation of the axial velocity of the liquid can be neglected. Conversely, the variation of the axial gas velocity may be important due to the high CO2 capture ratio expected. From a molar balance for the inert compounds (i.e. N2), the local gas velocity can be expressed as follows:

a ¼ 4:36 and b ¼ 1:30

kM;i ¼

kM;CO2 DCO2 ;G

eq

D ref i;G

ð20Þ

vG ¼ vzG ¼ 0

P C T;G z ¼ 0  i  N2 C zi;G¼ 0 P C T;G  i  N2 C i;G

ð29Þ

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4. Numerical resolution Since the flow configuration was set to counter-current, the 1D model is a boundary value problem of an ordinary differential equation system. Due to the relatively high heat of absorption, the solution can be stiff and hence, a collocation method from the routine bvp5c of Matlabs was used. The 2D model is a boundary value problem of a partial differential equation system (PDES). It was developed in COMSOL Multiphysicss, which uses the Finite Element Method which itself employs the concept of piecewise polynomial interpolation over the model domain; and hence, the numerical resolution of simultaneous equations at each of the nodes. Due to the important ratio between the fibre length and the fibre inner diameter, the PDES was scaled in reduced form to prevent an extremely high number of elements in the axial direction. Details of the this scaling are given in Albarracin Zaidiza et al. (2014). 4.1. Mesh sizing An appropriate mesh is necessary for conducting the finite element analysis. It is sufficiently understood that the absorption process is controlled by liquid-side resistance to mass-transfer and that modelling requires a rigorous absorption model and ensured sufficient discretisation of the liquid phase in the radial direction. One must also take into account the fact that the chemical absorption reaction occurs very close to the liquid–membrane interface. Consequently, the space-scale of the mesh was selected as being of the same order of magnitude as that of the coupled mass-transfer and reaction phenomena (Albarracin Zaidiza et al., 2014; Hoff and Svendsen, 2014). The elements are rectangular in shape in accordance with the two main directions of transport, as schematised in Fig. 2. Around boundaries, where the mass-transfer layers are extremely thin, the meshes are refined using arithmetic progressions, except for the liquid–membrane boundary where a geometric progression proved to be more efficient. Finally, a vast number of elements, i.e. about 3 million, require solutions. 4.2. Boundary conditions The boundary conditions and corresponding expressions for the mass and energy balance equations across the domains are summarised in Table 5. With reference to Fig. 2, the positive direction is taken from left to right, e.g. from the liquid to membrane to gas phase. The inlet liquid phase at boundary B-3, an aqueous solution of MEA, is assumed to be pre-loaded with carbon dioxide and at chemical equilibrium.

Fig. 2. Schematic representation of the meshing, domains and boundaries in the 2D model.

Table 5 Boundary conditions for 2D mass- and energy-transport equations. Boundary Condition

Mass-transfer Heat-transfer

B-1



B-5

Axialsymmetry Convective flux at liquid outlet Initial liquid conditions Continuity at interface & evaporation of liquid No-flux

B-6

No-flux

B-7

Continuity at interface Initial gas conditions Convective flux at gas outlet Axialsymmetry

B-2

B-3 B-4

B-8 B-9

B-10

dC i;L dr

L ¼0  dT dr

¼0 ¼0

L ¼0  λL dT dz

C i;L ¼ C i;L z ¼ Z

TL ¼ TLz ¼ Z

C i;L ¼ m:C A;M

TL ¼ TM

P i sat :yi R:T L

L  λL dT ¼  λM dTdrM  DW;M dr

 Di;L

dC i;L dz

¼ C i;M

 Di;M

dC i;M dz dC

¼0

 dT M dz  dT M dz

¼0 ¼0

 Di;M dzi;M ¼ 0 C i;M ¼ C i;G

TM ¼ TG

C i;G ¼ C i;G z ¼ 0

TG ¼ TGz ¼ 0

 Di;G



dC i;G dr

dC i;G dz

¼0

¼0

dC W;M :ΔHvap dr

G ¼0  λG dT dz

G ¼0  dT dr

5. Simulations and discussion This section discusses the results obtained from the simulations of the 1D and 2D models. Severe as well as mild operating conditions are considered. Indeed, preloaded solvent and high amine conversion are chosen for a detailed 1D–2D comparison, as they illustrate an industrial context. In addition unloaded solvent and relatively low amine conversion conditions are simulated and overall simulation results are compared to available experimental data. It should be mentioned that the simulation time of the 1D model was about 100 times less that of the 2D model. There is still a lack of experimental data from membrane contactors in relevant industrial operating conditions. Therefore, the use of the thermodynamic approach, of the physico-chemical properties and of the reaction kinetics was tested by modelling the CO2 chemical absorption using packed columns. The simulation results were in excellent agreement with packed-column experimental data from pilot plants, as shown in Section 5.4.1.

5.1. Comparison of 1D and 2D approaches under industrial operating conditions Operating conditions that would be present in an industrial MEA absorption plant are characterised by a nearly complete solvent conversion as well as a partially loaded lean solvent. These conditions, reported in Table 6 together with geometrical parameters, are recommended by literature to minimise overall energy requirements (Tobiesen et al., 2007). In addition, the liquid pressure should always be higher than that of the gas phase in order to prevent bubbling; hence, the liquid-side pressure is fixed to that of the inlet gas pressure. Simulations were performed using a microporous membrane with an equivalent membrane masstransfer coefficient between that of a dry and a partially wetted membrane (Chabanon et al., 2013). In order to meet both gas-phase pressure drop requirements, i.e. 50 mbar, and CO2 capture ratio, i.e. 89.5%, the contactor length is of only 0.32 m for a superficial inlet gas velocity of 0.19 m s  1 when simulated in the 2D model. This fibre length and superficial inlet gas velocity were then input into the 1D model.

D. Albarracin Zaidiza et al. / Chemical Engineering Science 145 (2016) 45–58

5.1.1. Radial concentration profiles Radial profiles can only be computed using the 2D approach as the 1D approach utilises average radial values. In Fig. 3 and Fig. 4, only radial profiles of the liquid phase are plotted, as this is where the main transfer resistance of the system is located. Radial concentration profiles of CO2, MEA and reaction product (MEAH þ MEACOO–) in the liquid phase are shown in Fig. 3a–c respectively for different axial positions. At the contactor inlet section, the liquid phase was assumed to be at chemical equilibrium and concentrations were homogeneous. The radial concentration profiles for all components and for all positions were relatively flat, except those close to the liquid–membrane interface for CO2. The almost homogenous radial concentration distributions indicate that the diffusion of the different species was not limiting. Fig. 3a shows the gradual enrichment of the solvent by CO2 along the fibre length. This demonstrates that the reversibility of the reaction must be taken into account when high solvent conversions are required. Fig. 3b and c illustrate the depletion of MEA and the enrichment of reaction products respectively along the fibre length.

51

Fig. 4 illustrates radial profiles of the overall reaction rate of CO2, rCO2, and for different axial positions. In order to observe trends, the reaction rate was normalised by its maximal value at the corresponding axial position. The maximal penetration depth of CO2 into the liquid phase was observed at the liquid inlet and corresponded to about 20 μm. This value is almost two times higher than that estimated when an irreversible reaction was assumed (Albarracin Zaidiza et al., 2014). Since the reaction rate rapidly reached values close to zero, for nearly the entire liquid domain, the mixed-cup concentrations can be considered to be at chemical equilibrium. The influence of reaction–products diffusion on the local reaction rate can be observed in the additional char shown in Fig. 4. The curvature of the reaction rate profiles is typical for a diffusion-reaction system where concentration profiles are observed. However the reaction rate far from the liquid– membrane interface is very small and its influence on the overall absorption rate can thus be neglected. The published work of Hoff et al. (2004) and Hoff and Svendsen (2014) suggest that the diffusivity of complex-products should have a significant impact on the overall CO2 absorption. However the operating conditions in that study were very different to those used in this work, where a

Table 6 Operating conditions and geometrical characteristics of the HFMC used in the simulation with typical industrial operating conditions. Parameter

Value

Units

Gas (shell side) CO2 molar fraction H2O molar fraction (saturated flue gas) Inlet temperature Inlet pressure Pressure drop Superficial inlet gas velocity

0.14 0.07 313 1.05  105 5  103 0.19

–– –– K Pa Pa m s1

Liquid (lumen side) MEA total mass fraction CO2 loading of lean solvent Outlet pressure Inlet temperature Superficial inlet liquid velocity

0.3 0.242 1.05  105 313 8.6  10  4

kgMEA kgL  1 molCO2 molMEA  1 Pa K m s1

Contactor (counter-current parallel flow) External fibre radius 2  10  4 Relative fibre thickness 0.2 Packing fraction 0.6 Fibre length 0.32 CO2 mass-transfer coefficient in kM,CO2ref ¼ 10  3 membrane

m – – m m s1 Fig. 4. Dimensionless overall reaction kinetics as a function of the relative internal radius, 2D approach.

Fig. 3. Dimensionless liquid phase species concentration as a function of the relative internal radius, 2D approach: (a) CO2, (b) MEA and (c) RNH3 þ RNHCOO– complex. Curves for z/Z¼ 1 are almost superimposed with the abscissa axis for (a) and (c), while for (b) this curve is a horizontal line with value equal to unity.

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Fig. 5. Local trans-membrane specific flux of species: (a) CO2, (b) H2O and (c) MEA, estimated from both 1D and 2D modelling approaches, using industrial conditions (see Table 6).

Table 7 Averaged specific fluxes estimated from both 1D and 2D approaches. 1D Specific flux (mol m  3 s  1) CO2 3.13 H2O  3.50 MEA  1.76  10  2

Fig. 6. Liquid phase temperature profile estimated from both 1D and 2D modelling approaches.

much faster liquid velocity is present (between 1 and 5 cm s  1), allowing for the build-up of radial concentration gradients. 5.1.2. Axial profiles of temperature and trans-membrane flux Fig. 5a–c show axial profiles of the specific trans-membrane fluxes of CO2, water and MEA, respectively. Positive values indicate the absorption or condensation of the component at the membrane–liquid interface; conversely, negative values indicate desorption or evaporation. Simulation results of the 1D and the 2D model are illustrated. Similar trends are obtained, however the profiles do not correspond exactly. For CO2 (Fig. 5a), both models render profiles that pass through a maximum value of the absorbed specific flux close to half-way along the length of the fibre. For low of the axial coordinate values, near the liquid outlet, the 1D model overestimates relative to the 2D model; in particular at the liquid outlet, z/Z¼0, where the local absorbed flux for the 1D and 2D models were approximately 3 and 1.5 mol m  3 s  1, respectively. However, the 2D model itself passes through a greater maximum of 5 mol m  3 s  1. For both water and MEA vapours (Fig. 5b and c), flux reversal occurred, i.e. vapour condensation, at the vicinity of the liquid inlet. Since the local specific trans-membrane molar flux of water is more than 10 and 100 times higher than that of CO2 and of MEA, respectively, the condensate is mainly composed of water. The

2D Specific flux (mol m  3 s  1)

Relative difference (%)

3.04  3.60  2.20  10  2

2.96  2.78  20.0

transfer of water across the membrane is crucial because the more water that passes through the membrane the more likely it is for the membrane to become wet as a result of the condensation of water vapour (Albarracin Zaidiza et al., 2015). Fig. 6 compares the liquid phase axial temperature profiles predicted by the 1D and 2D adiabatic models. The temperature shown is that of the fibre centre. As a result of the excellent radial heat-transfer between the phases, there exists virtually no radial temperature gradient. Both models predict that along the length of the hollow fibre, the temperature profile passes through a maximum temperature of approximately 80 °C, near the liquid inlet. In fact, the liquid is warmed up near the liquid inlet by the water condensation and then, it is cooled by the water evaporation (Albarracin Zaidiza et al., 2015). Compared to the 2D model, the 1D temperature profile passes through its maximum further away from the liquid inlet. Furthermore, the outlet temperature of the liquid phase predicted by the 2D model shows a cooler temperature than that of the 1D model, approximately 50 ºC and 55 ºC, respectively. It should be noted that, as illustrated in Section 5.4.2, the temperature peak value is comparable to that measured in packed beds when using similar boundary conditions and CO2 capture ratios. This is related to the fact that the systems, developing counter-current plug flow, are very similar in nature. 5.1.3. Average specific trans-membrane fluxes Table 7 shows the averaged trans-membrane molar fluxes per unit contactor volume for CO2, water and MEA. Even if the profiles for the specific flux of CO2 and water do not correspond exactly, they lead to comparable values for the average specific flux with relative differences lower than 3%. No further information was obtained using the 2D approach in terms of CO2 capture ratio. Moreover, the estimation of the amount of transferred water from the solvent to the gas is similar using both models. However, MEA fluxes across the membrane differed. The 1D model under predicted MEA losses in the absorption unit with a relative difference of 20%. Given that the MEA is a relatively non-volatile solvent, this

D. Albarracin Zaidiza et al. / Chemical Engineering Science 145 (2016) 45–58

difference must be considered when using more volatile solvents, e.g. NH3. Solvent loss is important to consider in terms of running costs and contactor performance, especially for long periods of continuous operation. The predicted MEA concentrations in the outlet gas were 1.4 and 2.1 g/N m3, from the 1D and 2D model respectively. Both values far exceeded the maximum limit for the design of post-combustion CO2 capture plants (i.e. 12 mg/N m3 for MEA) (Khakharia et al., 2013). In addition, water losses were significant. For illustration purposes, considering solely the absorption operation unit, the total solvent losses would be of about 0.5 ton H2O and 4.6 kg of MEA per ton of CO2 captured. For a model coal power plant of 500 MW including carbon capture, these outputs would correspond to losses of around 5000 ton of water and 50 ton of MEA per day. Therefore, in practical terms, a scrubbing section following the HFMC would be required to solvent recovery. This issue represents an opportunity for possible advancements in membrane contactor technology. Indeed, a dense-film composite membrane, being selective to the MEA, would reduce the amine vapour outflow. Such a study is however out of the scope of this paper. 5.2. Comparison between experimental and simulation results Both models were compared against experimental data to identify the most appropriate model. The compared variables of simulation results are the CO2 capture ratio and the liquid outlet temperature. These variables are of particular interest because they provide important information, such as process intensification factors and increasing solvent temperatures, which are essential to performing process energy consumption calculations. The experimental data were taken from the EnergiCapt project, funded by the Agence Nationale de la Recherche (ANR) grant Energicapt. The small pilot plant consists of a 10 m2 exchangesurface HFMC in which the aqueous solution, approximately 30 wt% of MEA, was fed in the lumen, whereas the flue gas from a natural gas power plant, a mixture of 10% of CO2 and water saturated air, flowed through the shell in a counter-current arrangement. Since the combustible was natural gas, NOx and SOx concentrations were neglected. As a result of the liquid-to-gas ratio fixed during the experiments, relatively low MEA conversions were obtained, i.e. lower than 0.6. In addition, it should be noted that for a total of 11 experiments, 10 were performed using fresh solvent. Despite the use of real flue gases and an important exchange area, these conditions are still far from actual industrial conditions. The membrane contactor had been previously used intermittently for several months. The kM,CO2ref value was set to 5  10  4 m s  1, as found in a previous work (Albarracin Zaidiza et al., 2015). Overall contactor features and operating conditions are presented in Table 8. Fig 7a and b show parity plots between experiments and simulations of the CO2 capture ratio and the liquid outlet temperature respectively. Simulation results of both the 1D and 2D models are shown. From Fig 7a it can be seen that both models predict the CO2 capture ratio within an agreement of 10% with respect to experiments. Moreover, the simulation results of the 1D and the 2D approach are almost superimposed. Fig 7b demonstrates the non-isothermal nature of the process, since the solvent is shown to be heated by at least 18 K. The 2D model estimates a solvent warming of at least 30 K, whereas the warming estimated of the 1D model is significantly lower. Even though, the predicted capture ratios of the 1D and the 2D models are close. It seems, as though the average volumetric absorption flux was not very sensitive to the liquid outlet temperature, as multiple compensations are likely to occur over the contactor

53

Table 8 Operating conditions and geometrical characteristics of the HFMC used in EnergiCapt project. Parameter

Value

Units

Gas (shell side) CO2 molar fraction 0.102 H2O molar fraction (saturated flue gas) 0.1 Inlet temperature 323–326 Inlet pressure 1  105 Gas flow rate 11–18

– – K Pa N m3 h  1

Liquid (lumen side) MEA total mass fraction CO2 loading of lean solvent Inlet temperature Inlet pressure Liquid flow rate

kgB kgL  1 molCO2 molMEA  1 K Pa [L h  1]

0.3 0–0.16  289 1.05  105 30–80

Contactor (PTFE fibres, counter-current parallel flow) External fibre radius 4.35  10  4 Relative fibre thickness 0.5 Packing fraction 0.58 Effective contactor length 0.88 Contactor diameter 0.105 CO2 mass-transfer coefficient in kM,CO2ref ¼5  10  4 membrane

m – – m m m s1

length. The experimental temperature increase is in-between. The temperature variation is closely related to the trans-membrane water transfer. The important temperature increase shows that the understanding of the latter is crucial and needs to be improved. 5.3. Influence of axial distribution of the membrane mass-transfer coefficient The previous simulations were performed assuming an equivalent membrane mass-transfer coefficient, kM,CO2eq, which is constant over the contactor length. However, membrane wetting may occur, leading to an axial distribution. Indeed, liquid breakthrough and capillary condensation are likely to occur in the vicinity of the liquid inlet due to, respectively, the increase of transmembrane pressure (PL PG), and water condensation. This section aims to investigate the influence of the distribution of the membrane mass-transfer coefficient on simulation results. The estimation of membrane wetting due to liquid breakthrough and capillary condensation is extremely complex, as it depends on many parameters unknown in industrial conditions, such as, for example, the pore size geometry and distribution and the membrane–liquid contact angle. Nevertheless, in order make a first guess about the influence of an axial distribution of the membrane mass-transfer coefficient on the overall process performance, a simple distribution was set, as follows:   eq kM;i ¼ kM;CO2 1 þ β 1  2

z=Z



Di;G DCO2 ;G ref

ð30Þ

where β stands for the deviation from the equivalent membrane mass-transfer coefficient. Simulations were performed with the 1D model using conditions shown in Table 6, however by setting a gas pressure drop of 50 mbar and a CO2 capture ratio of 0.9, obtained by the 1D approach. Fig. 8a and b illustrate respectively the variation of the membrane mass-transfer coefficient (estimation using Eq. (30)) and the liquid temperature with the contactor length. Two scenarios are presented. The base case with an almost uniform distribution, β ¼0, and the case in which membrane wetting leads to a deviation of 90% from the average value, β ¼ 0.9. In the latter, as shown

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Fig. 7. Comparison of simulation results and experimental data taken from EnergiCapt project: (a) CO2 capture ratio and (b) liquid outlet temperature. kM, m s  1.

4 eq CO2 ¼ 5  10

Fig. 8. Axial profiles obtained using the 1D model; CO2 capture ratio of 0.9; gas pressure drop of 50 mbar; kM,CO2eq ¼ 10  3 m s  1 with a distribution given by Eq. (30): (a) membrane mass-transfer coefficient and (b) liquid temperature.

in Fig. 8a, one part of the module exhibits high mass-transfer coefficients (kM,CO2 410  3 m s  1 for z/Z o0.5) standing for almost totally dry membranes, whereas the other part exhibits much lower mass-transfer coefficients (kM,CO2 ¼10  4 m s  1 for z/Z¼1) standing for partially wetted membranes. Fig. 8b shows that the values of the liquid temperature peaks obtained for both, almost uniform and non-uniform distribution of kM,CO2, are shown to be close. However, in the non-uniform distribution the peak is shifted to the module zone with higher membrane mass-transfer coefficients. Indeed, since the transfer through the membrane has been deteriorated in the zone near the liquid inlet, the condensation zone is extended. Fig. 9 illustrates the variation of the average CO2 specific absorbed flux with the equivalent membrane mass-transfer coefficient for the two scenarios β ¼ 0 and 0.9. The reduction of the equivalent membrane mass-transfer coefficient by one order of magnitude significantly impacts the contactor performance. Moreover, the non-uniform distribution of kM,CO2 decreases the average performance of the module. However, the deviation from the base case is less than 15% which is of the same order of experimental uncertainty (i.e. about 10%). Hence, the use of an

Fig. 9. Influence of the mass-transfer coefficient of the membrane on the average CO2 specific absorbed flux, applying a local distribution of kM, CO2ref. CO2 capture ratio of 0.9 and gas pressure drop of 50 mbar.

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55

Fig. 10. Simulation results of the packed column model. Solid and dotted lines: model predictions. Dots: experimental data: (a) temperature profile of the absorber for the Run 1A and (b) parity plot of CO2 capture ratio.

average equivalent membrane mass-transfer coefficient appears to be adequate for modelling of the membrane contactor. 5.4. Comparison of HFMC with packed columns At this stage, the absorption using HFMC could be compared to that using packed columns under an industrial context. Such study allows to identify possible additional advantages of membrane contactors. The packed column model was developed by setting the adequate mass-transfer correlations (Hanley and Chen, 2012) and removing the terms related to the membrane from the 1D HFMC approach described in this work. Details of packed columns modelling are found in Neveux et al. (2013), Tobiesen et al. (2007), von Harbou et al. (2014). The Esbjerg pilot plant was taken as reference. The absorber column of 17 m height with a diameter of 1.1 m, was filled with IMPT-50 packing. While operating at its energetic optimum at 2 bar of reboiler pressure, the pilot plant was able to absorb 0.46 mole of CO2 per cubic meter of absorber volume, with a corresponding reboiler heat duty of 3.74 GJ per ton of absorbed CO2. Model validation as well as simulations at industrial conditions are presented in the following subsections. 5.4.1. Verification of the rate-based model of the contactor Modelling packed columns not only allowed to compare their performance with HFMC technology, but also allowed to validate the HFMC model. Indeed, experimental data of use HFMC in applicable industrial operating condition is lacking. Therefore, use of the thermodynamic approach, physicochemical properties and reaction kinetics, was tested with the packed column model. The tests performed in the CASTOR campaign at the Esbjerg pilot plant were simulated (Dugas et al., 2009). These experimental tests are characterised by partially loaded lean solvent, high CO2 capture ratio as well as high MEA conversions. The comparison between simulations and experiments are illustrated in Fig. 10. The model predicts correctly the temperature profiles, as shown in Fig. 10a, which evidences the non-isothermal behaviour of the absorption unit. Moreover, as shown in Fig. 10b, the packing column performances are predicted within an uncertainty lower than 5%, thus demonstrating the quality of the CO2 solubility approach used in this work. It is worthwhile mentioning that the temperature peak measured in packed beds when using a high MEA conversion and a high CO2 capture ratio is significant, as it reaches 75 °C. Similar

Fig. 11. Gas and liquid temperature profiles. Solid lines, 1D model of HFMC (gas and liquid profiles are superimposed). Dashed lines, 1D model of Esbjerg packed column. Simulation conditions given in Table 6.

high peaks can be expected to occur in membrane contactors with similar boundary conditions. This is in accordance with simulation results obtained in this work.

5.4.2. Simulations results of energetic optimum The absorber column of the Esbjerg pilot plant was computed under conditions similar to that shown in Table 6, corresponding to a CO2 capture ratio of 0.9 and inlet and outlet CO2 solvent loadings of 0.242 and 0.484, respectively. The simulation results were compared to those shown in Section 5.1 for HFMC using the 1D model. The temperature profiles are shown in Fig. 11 for both HFMC and packed columns. As the radial heat transfer is very efficient in the HFMC technology, the gas and the liquid temperature profiles are almost superimposed, by difference with the packed column technology, where radial temperature gradients are obtained. The outlet gas and liquid temperatures are respectively higher and lower for the packed bed for an identical enthalpy output. Significant temperature peaks are observed

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Table 9 Predicted CO2 captured and solvent losses for both HFMC and packed column technologies under industrial conditions (given in Table 6).

CO2 (molcaptured m3 s  1) H2O (ton tonCO2 captured  1) MEA (kg tonCO2 captured  1)

HFMC

Esbjerg packed column

3.13 0.50 4.60

0.45 0.55 7.20

in the two technologies, with a slightly higher peak in the HFMC model. Accordingly, the profiles of interfacial fluxes computed for HFMC (illustrated in Fig. 5) and packed columns (not shown) depict similar shapes. However the absolute values corresponding to the latter are nearly one order of magnitude lower, due to the intensification provided by HFMC. The averaged CO2 flux and solvent losses from simulations of the two technologies are given in Table 9. The solvent losses in the packed columns are higher than those obtained when using HFMC. This is due to the higher gas outlet temperature, resulting in higher MEA and water vapour concentrations. Again, the HFMC technology seems to be promising. It is worth to mention that the emissions correspond to the total amount of solvent that would be present in the gas phase, whether in vapour state or as aerosol or fog. No general conclusions can be drawn since solvent emissions (mist and vapour) for flue gases are site-specific as well as specific to the conditions in which the tests are performed. Further analysis of solvent emissions modelling are out of the scope of this paper. Details of solvent emissions in the Esbjerg pilot plant are given in Mertens et al. (2013) and Mertens et al. (2014).

6. Concluding remarks and outlook The aim of the present work was to compare 1D and 2D adiabatic modelling approaches for the chemical absorption of CO2 using hollow fibre membrane contactors. The effects of the temperature variation on the mass-transfer and on reaction kinetics were taken into account by both models. The comparison was performed considering the absorption of CO2 using an aqueous solution of MEA under severe and mild operating conditions. When severe operating conditions are applied, the estimated average specific fluxes of both, CO2 and water are very close between the 1D and the 2D approach, the relative difference being lower than 3%. Both models predict temperature peaks inside the contactor and describe the condensation/evaporation of water similarly. The simulated outlet temperatures are comparable. For the pilot plant experiments, the simulation results from both models, in terms of CO2 capture, are very close and in agreement with measurements. A discrepancy in the liquid temperature outlet between the models is observed, the measured temperature being in the range of the 1D approach. The good performance of the 1D approach can be explained by the fact that, as the reaction film is very thin, the concentrations of the reactants and products in the liquid phase are almost flat. In addition, the influence of the diffusion of the reaction products on the reaction rate was found to be almost negligible. The radial heat transfer being rapid, the radial temperature profiles are also flat. Hence, the 1D approach, using mixing-cup values and neglecting diffusion of reaction products is quite correct in the investigated domain. Consequently the 1D model might be applied preferably for scaling purposes as the

simulation time in comparison to the 2D approach is significantly reduced. However, slower reaction systems might lead to significant radial gradients and to situations where the 2D approach is necessary. To our opinion, the consistency of the 1D approach should always be checked by 2D calculations and hence, both, 1D and 2D approaches are valuable. It is worth mentioning that industrial absorption conditions are severe, as they are characterised by pressure fluctuations, high reactant concentrations and important temperature peaks. Still, both, modelling as well as experimental investigations performed using severe conditions are sparse. Thus, additional experimental and theoretical work is needed in industrial conditions, in order to assess the feasibility of the technology. More generally, to our belief, the key to success of HFMC technology is the control of the membrane wetting which influences strongly the overall absorption performance. Simulations indicate that membrane wetting can be simulated conveniently, using an average equivalent membrane mass-transfer coefficient rather than local values. Nonetheless, fundamental understanding of the wetting mechanisms in relevant industrial conditions would be helpful in order to develop reliable and still simple wetting models that could be implemented in the reactor model.

Nomenclature Latin symbols Ci Cp dh Di E G Gz h H ΔH K k L m M Ni P q re rCO2 R Sh T U u v Z

molar concentration (molm  3) specific heat (J mol  1 K  1) hydraulic diameter diffusion coefficient (m  2 s  1) enhancement factor (dimensionless) molar flux of gas phase (mol m  2 s  1) Graetz number (dimensionless) heat transfer coefficient (W m  2 K  1) enthalpy (J) enthalpy difference (J mol  1) chemical equilibrium constant (molar scale) or Kozeny constant (m  2) mass-transfer coefficient (m s  1) or kinetic constant (molar scale) molar flux of liquid phase (mol m  2 s  1) the partition coefficient (dimensionless) molecular mass (mol kg  1) molar flux (mol m  2 s  1) pressure (Pa) heat flux (W m  2) external fibre radius (m) reaction rate relative to CO2 (mol m  3 s  1) gas constant (J  mol  1K  1) Sherwood number ¼ kDF j;Fdh (dimensionless) temperature (K) overall heat transfer coefficient (W m  2 K  1) superficial fluid velocity (m s  1) interstitial fluid velocity (m s  1) effective contactor length (m)

Greek symbols

α δ φ λ

CO2 solvent loading (molCO2 molMEA  1) fibre thickness (m) fibre volume fraction (dimensionless) thermal conductivity (W m  1 K  1)

D. Albarracin Zaidiza et al. / Chemical Engineering Science 145 (2016) 45–58

m

ρ

H

57

The values of the correlation parameters C1σC4 regressed in this work are reported in Table A1. Data from Aronu et al. (2011), Ma’mun et al. (2005), Tong et al. (2012), Wagner et al. (2013) and Xu and Rochelle (2011).

viscosity (Pa s  1) density (kg m  3) Henry constant (Pa m3 mol  1)

Subscripts i G F L M abs cond int ext vap

Appendix B. Estimation of CO2 solubility and chemical speciation

compound relative to gas relative to fluid relative to liquid relative to the membrane absorption relative to condensation internal surface of the fibres external surface of the fibres vaporisation

The chemical equilibria describing the species distribution, or speciation, of the liquid phase is based on the formulation given by Astarita et al. (1983). In such a way, the solution of the chemical equilibrium is straightforward and can be described in terms of temperature, total apparent mass fraction, wi, and CO2 loading, ɑ.

C MEACOO  ¼ C tot MEA þ 1=K 4 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  tot 2 2_ C MEA þ1=K 4  4C tot MEA α ð1  αÞ ðB:1Þ

Superscripts ref eq

relative to reference relative to equivalent membrane mass transfer coefficient

Appendix A. Estimation of equilibrium constants The equilibrium constants Kj are expressed in molar concentration units. C1 ln K j ¼ þC 2 lnðT Þ þ C 3 T þ C 4 T

ðA:1Þ

Table A.1 Temperature dependence of the equilibrium constants for Reactions 1–5.

K1 K2 K3 K4 K5

2

C1

C2

C3

C4

 13,445.9  12,092.1  12,431.7  3084.32  5844.22

 22.4773  36.7816 35.4819  39.254  40.358

0 0 0 0.1311 0.125

140.932 235.482 220.067 189.56 191.51

C MEAH þ ¼ C tot MEA α

ðB:2Þ

 C MEA ¼ C tot MEA ð1  αÞ  C MEACOO

ðB:3Þ

 _ C HCO3 ¼ C tot MEA α  C MEACOO

ðB:4Þ

tot  _ C H2 O ¼ C tot H 2 O  C MEA α þ C MEACOO

ðB:5Þ

C tot i ¼ wi ρL =M i

ðB:6Þ

    C CO2 ¼ C MEAH þ C MEACOO  =C MEA K 2 K 4 =K 5

ðB:7Þ

Model predictions are illustrated in Fig. B1 together with experimental data from literature. Fig. B1a shows the solubility of CO2 in an aqueous solution of MEA 30 wt% at different temperatures, whereas Fig. B1b depicts the chemical speciation for the same solution at 333 K. Good agreement between experimental data and model prediction is obtained. Therefore, this approach provides correct estimation of CO2 solubility as well as true composition of the liquid phase. This is crucial for rate based models.

Fig. B.1. Comparison between model predictions and experiments. Solid lines: model predictions. Dots: experimental data: (a) CO2 solubility in 30 wt%. MEA. Data from Aronu et al. (2011), Ma’mun et al. (2005), Tong et al. (2012), Wagner et al. (2013), and Xu and Rochelle (2011). (b) Chemical speciation of 30 wt%. MEA. T ¼ 333 K (Wagner et al., 2013).

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