4908
Ind. Eng. Chem. Res. 2004, 43, 4908-4921
Modeling and Experimental Study of Carbon Dioxide Absorption in Aqueous Alkanolamine Solutions Using a Membrane Contactor Karl Anders Hoff,† Olav Juliussen,‡ Olav Falk-Pedersen,§ and Hallvard F. Svendsen*,† Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), Trondheim N-7491, Norway
The performance of a laboratory-scale membrane contactor was investigated for the case of CO2 absorption into separate aqueous solutions of monoethanolamine (MEA) and methyldiethanolamine (MDEA). The variation in the flux of the CO2 absorption rate with the CO2 partial pressure, liquid CO2 loading, liquid velocity, and temperature was studied individually in an apparatus giving well-defined and controlled experimental conditions. A two-dimensional diffusion-reaction model was developed and used to predict the results of the experiments. Initial and boundary conditions for the concentrations of chemical species were calculated by an equilibrium speciation model based on the solution method given by Astarita et al. (Gas Treating with Chemical Solvents; Wiley: New York, 1983). Corrections for nonideality were introduced by using a salting-out correction and by tuning the model to experimental VLE data. It was found that the diffusion of the ionic reaction products had a significant rate-limiting contribution to the observed fluxes and these diffusivities were regressed from parts of the experimental data. 1. Introduction 1.1. Membrane Gas Absorption. Membrane gas absorption (MGA) represents a new way of contacting gas and liquid for industrial-scale bulk gas purification and offers significant advantages compared to the conventional absorption towers. It can be considered a hybrid of a gas absorption technology and membrane technology, as the gas phase is separated from the liquid phase by a microporous membrane. The membrane works only as a physical barrier between the phases, whereas the absorption liquid provides the selectivity for separation and can be similar in type to that used in conventional gas absorption, e.g., an aqueous solution of alkanolamines in the case of CO2 absorption. Because of the separation of the phases by a microporous membrane, the contactor can be operated without limitations caused by flooding, foaming, channeling, and liquid entrainment. These are typical operating boundaries encountered in conventional absorption towers and result to a large extent from the momentum transfer due to the direct contact between the countercurrent gas and liquid flows. By forming the membranes as hollow fibers with diameters of 0.5-1 mm in densely packed membrane modules, very compact units can be made. Specific surface areas of 500-2000 m2/m3 can be achieved, which is higher than the typical values of 100-300 m2/m3 offered by conventional tower packings. This leads to significant savings in weight and space required for the contactor. The possibility of an industrial application of hollowfiber membranes as gas/liquid contactors was first studied by Qi and Cussler.2,3 Since then, a considerable * To whom correspondence should be addressed. E-mail:
[email protected]. † NTNU. ‡ SINTEF Materials and Chemistry, Trondheim, Norway. § Kvaerner Process Systems, Lysaker, Oslo, Norway.
amount of academic research has been performed to study the principle of membrane gas absorption, especially in the application as a contactor for CO2 removal.4-11 1.2. Membrane Properties. As most systems applied in CO2 absorption are controlled by liquid-side mass-transfer resistance, it is of utmost importance to prevent any penetration of liquid into the pores of the membrane. This is dependent on the transmembrane pressure and the wettability of the membrane material. The membrane breakthrough pressure can be described by the Young-Laplace equation as
∆Pbr ) -γl cos θ
(
)
1 1 + r1 r2
(1)
where γl is the liquid surface tension and θ is the contact angle between liquid and solid (the membrane material). r1 and r2 are the two characteristic radii of an ellipseshaped pore. ∆P is here defined as Pliquid - Pgas. The requirement to prevent liquid penetration is that the liquid does not wet the membrane material, as indicated in Figure 1. This does not spontaneously occur if θ > 90°. Liquid penetration into the pores will then occur only if ∆P > ∆Pbr. If 0 < ∆P < ∆Pbr, the gas/liquid interface will be “immobilized” at the liquid-side pore opening, whereas if ∆P < 0, the gas will penetrate as bubbles into the liquid phase. From eq 1, it is seen that a high value of ∆Pbr can be obtained by using a small membrane pore radius and by using a liquid with a high surface tension. A lower practical limit will exist for the pore radius when the contribution from Knudsen diffusion becomes significant, thus reducing the effective diffusivity through the membrane. The pore radii should therefore preferably be higher than the mean free path of CO2, which is 0.07 µm at 40 °C. Otherwise, the membrane resistance will more easily become a significant fraction of the overall
10.1021/ie034325a CCC: $27.50 © 2004 American Chemical Society Published on Web 07/08/2004
Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4909
Figure 1. Principle of membrane gas absorption.
mass-transfer resistance. The use of an aqueous solution ensures that the surface tension is relatively high. However, the surface tension decreases considerably with increasing alkanolamine concentration.12,13 This effect is counteracted by a slight increase with CO2 concentration.11 These aspects should always be considered in a conservative design. Wetting of the polymer by the liquid solution is generally favored by a high polymer surface energy. It has been found that polytetrafluorethylene (PTFE) has the desirable property in terms of a significantly lower surface energy than other typical membrane polymers (see, e.g., Mulder14). Important additional advantages of PTFE are its chemical stability and inertness, which prevent the polymer from changing its properties over time. Tests with CO2 absorption into alkanolamine using polyethylene and polypropylene membranes have shown that the resistance to liquid penetration breaks down after a period of long-term operation. This is probably due to a combination of surface wetting and swelling of the polymer with the elapse of time.5,15 1.3. Kvaerner/Gore Process. Kvaerner Process Systems, in collaboration with W. L. Gore & Associates, has worked for a number of years on the development of membrane contactors based on microporous polytetrafluorethylene (PTFE) hollow-fiber membranes. The aim has been the application in CO2 removal with aqueous alkanolamines, both from exhaust gas (Figure 2a) and from natural gas.16 The technology has also been developed for natural gas dehydration.17 The Kvaerner/ Gore membrane modules essentially consist of layers formed as microporous tubes interconnected by impermeable bridges. The tube layers are separated by a spacer that serves to prevent adjacent layers from coming into direct contact, as illustrated in Figure 2b. The gas flow is thus regularly distributed on the available cross section. The spacer additionally serves to provide a thorough mixing of the gas phase to minimize the presence of gas-phase mass-transfer resistance. Through testing performed on a pilot scale, the important advantages of this technology have been verified.16 These can be summarized as as follows: (i) Equipment size and weight are reduced by 60-75% compared to a conventional tower. (ii) The footprint requirement is reduced by 40% compared to the conventional case. (iii) The contactor is insensitive to motion. (iv) No foaming, channeling, entrainment, or flooding occurs. (v) Corrosion problems are significantly reduced. (vi) Operating cost savings of 38-42% and (vii) capital cost savings of 35-40% can be achieved. 1.4. This Work. The modular and discrete configuration of the membrane gas absorber principally leads to the significant advantage of a linear scale-up. This greatly enhances the value of a fundamental laboratoryscale study of the process to capture the individual
Figure 2. (a) Module design of a hollow-fiber membrane contactor for exhaust gas CO2 removal. (b) Principle of the interconnected tube membrane design, with spacer between the tube layers.
effects of operating variables such as the (i) liquid velocity, (ii) gas velocity, (iii) temperature, (iv) amine type and strength, (v) CO2 concentrations in the liquid and gas, and (vi) membrane properties (not addressed in this work). The present work deals with the experimental study of membrane gas absorption in a laboratory-scale apparatus to investigate the effects of these important operating variables, covering the whole range of operation for an industrial process for exhaust gas CO2 removal using aqueous ethanolamine (MEA) as the absorbent. Additional experiments were performed in aqueous solutions of methyldiethanolamine (MDEA) to cover a system that is typically used in CO2 removal at higher pressures, e.g., from natural gas. MEA and MDEA represent two extremes in amine chemistry and reaction kinetics and can be used to study the operation of the membrane contactor in different reaction- and diffusion-controlled mass-transfer regimes. In parallel to the experimental study, a rigorous mathematical model has been developed to predict the experimental absorption rates and calculate concentration and temperature profiles in a single membrane tube. 2. Model Development 2.1. Chemistry. Alkanolamines have achieved a special position within the field of acid gas absorption, i.e., removal of CO2 and H2S from process gas. They can be distinguished as primary, secondary, or tertiary alkanolamines, depending on the number of hydrogen atoms substituted by organic groups. The amines that have been of principal commercial interest for gas purification are ethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA).18 In an aqueous solution of a primary alkanolamine such as MEA, absorbed CO2 is chemically bound in the form of
4910 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004
a carbamate ion, as given by the following chemical reaction
CO2 + 2RNH2 T RNHCOO- + R2NH3+
(2)
The reaction is found to be first-order in the alkanolamine and thus second-order overall.19 For tertiary alkanolamines such as MDEA, unable to form carbamate, bicarbonate formation is the dominating reaction
CO2 + R3N + H2O T R3NH+ + HCO3-
(3)
The kinetics of reaction 3 is significantly slower than that of reaction 2 and low concentrations of a fasterreaction primary or secondary alkanolamine promoter such as piperazine is often added to MDEA-based solvents to accelerate the mass transfer in the liquid film. Additional CO2-consuming reactions in aqueous solutions are hydration to form carbonic acid and direct reaction with hydroxide, given by
CO2 + 2H2O T H3O+ + HCO3-
(4)
CO2 + OH- T HCO3-
(5)
Because of a low value for the rate constant, the kinetic contribution of reaction 4 to the overall rate of reaction can be neglected. The contribution from reaction 5 can be important at close-to-zero CO2 loading, where the pH of an amine solution typically approaches 12. In this range, the reaction can be treated as irreversible. At increasing loading, the drop in pH implies that the contribution from reaction 5 diminishes to a negligible value compared to the contributions from reactions involving the amine. The rate expression describing the consumption of CO2 by chemical reaction is then given by
rCO2 ) k2,OH- cCO2cOH- + k2,amcam(cCO2 - cCO2,e) (6) The concentration difference (cCO2 - cCO2,e) is here the driving force of the carbamate formation reaction. cCO2,e, the free CO2 concentration in equilibrium with the chemically bound CO2, must be calculated from an equilibrium speciation model. The second-order rate constants for MEA, MDEA, and OH- used in this work are taken from Versteeg et al.,19 Tomcej and Otto,20 and Pinsent et al.,21 respectively. 2.2. Equilibrium Model. 2.2.1. Speciation. The equilibrium model for the CO2/MEA/water and CO2/ MDEA/water systems is based on the model given by Astarita et al.1 The distribution of chemically combined CO2 between the different forms of carbamate, bicarbonate, and carbonate ions is modeled by an “extent of reaction” approach from the following equilibria
1. M(D)EA + HCO3- T M(D)EAH+ + CO32- (7) 2. MEA + HCO3- T MEACOO- + H2O
(8)
Initially, it is assumed that all of the captured CO2 is in the form of bicarbonate, corresponding to reactions 7 and 8 both being shifted to the left. The reactions are then allowed to proceed to equilibrium as given by the extents of reaction ξ1 and ξ2
[M(D)EA] ) m(1 - yj) - ξ1 - ξ2
(9)
[M(D)EAH+] ) myj + ξ1
(10)
[MEACOO-] ) ξ2
(11)
[HCO3-] ) myj - ξ1 - ξ2
(12)
[CO32-] ) ξ1
(13)
Here, m is the total amine molarity, and yj is the loading in terms of chemically bound CO2, so that the following relation holds from the CO2 balance of the system
myj ) my - [CO2] ) [MEACOO-] + [HCO3-] + [CO32-] (14) For the range of CO2 partial pressures encountered in this work, it can always be assumed that yj ) y. Equations 9-13 can be substituted into the equilibrium relations of reactions 7 and 8, with equilibrium constants denoted by Kc1 and Kc2, respectively, and solved for ξ1 and ξ2 as follows. The solution in the MDEA case is simplified because ξ2 ) 0
ξ1 ) roots of(Az4 + Bz3 + Cz2 + Dz + E) ξ2 )
Kc2ξ1(ξ1 + my) Kc1
(15) (16)
with
A ) Kc22 B ) 2Kc22my + 2Kc1Kc2 C ) Kc12 - Kc1 + 2Kc2myKc1 + Kc22m2y2 - Kc2Kc1m D ) -Kc12m - Kc1my - Kc2m2yKc1 E ) Kc12m2y - Kc12m2y2
(17)
From calculating the extents of reaction as a function of only the amine molarity and CO2 loading, the speciation can be calculated from eqs 9-13. The concentration of free CO2 is subsequently calculated from the equilibrium relation of reaction 2 or 3, and by multiplying with the Henry’s law constant for the system under consideration, the equilibrium partial pressure of CO2 can be calculated. 2.2.2. Equilibrium and Henry’s Law Constants. The equilibrium in reaction 7 results from a combination of the equilibria of the deprotonation of bicarbonate to carbonate and the protonation of amine
HCO3- + H2O T CO32- + H3O+
(18)
M(D)EAH+ + H2O T M(D)EA + H3O+
(19)
Austgen et al.22 was used as a source for the temperature-dependent equilibrium constant of reaction 18. For reaction 19, the correlations given by Bates and Pinching23 and Kamps and Maurer24 were used. Austgen et al.22 was also used as a source for the equilibrium constant of reaction 8. The original correlation was referred to pure MEA as the standard state for alkano-
Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4911
lamine and had to be corrected by the infinite-dilution activity coefficient, γ∞MEA, which was calculated by relating the MEA deprotonation constant of Austgen et al.22 to that of Bates and Pinching.23 Austgen et al.22 made the correlation by tuning their equilibrium model to experimental data. The resulting value is lower by a factor of 2 than the experimentally determined value at 40 °C given by Sartori and Savage,24 and this factor was introduced into the model, thus keeping only the temperature dependence from Austgen et al.22 The Henry’s law constant in unloaded MDEA solution was correlated by the model from Al-Ghawas et al.25 In the case of MEA, the values for the pure components (MEA and water), as given by Austgen et al.,22 were combined with a mole-fraction-based mixing rule as recommended by Reid et al.26 2.2.3. Corrections Due to Nonideality. Corrections due to deviations from ideality were introduced through the salting-out correlation for the Henry’s law constant, as given by van Krevelen et al.27
( )
log
HA
HsA
) hAI
(20)
Here, HA and HsA are the Henry’s constants for the electrolyte solution and the corresponding molecular solvent, respectively, at the same temperature. The CO2free mixed alkanolamine/water solvent was adopted as a reference state. We could then make use of the experimentally correlated values for HsA 25 and let the relation HA/HsA denote the salting out due to the absorption of CO2 in the mixed solvent. The factor hA of eq 20 is the sum of contributions from the species of positive and negative ions present and the dissolving gas, referred to as the van Krevelen coefficients
hA )
∑i hB
+
+
i
∑i hB
-
i
+ hAg
(21)
The coefficients hBi+ and hBi- (denoting any positively or negatively charged ion, respectively) and hAg (attributed to the dissolved gas) are independent of concentration and can be assumed to be independent of temperature.28 These constants have been evaluated for a number of common ionic species and dissolved gases.29 Browning et al.28 made solubility measurements on loaded amine (MEA, DEA, and MDEA) solutions and calculated the van Krevelen coefficients for the protonated amines, MEA and DEA carbamates, and bicarbonate ions. For a neutral molecule in an electrolyte solution, the activity coefficient can be determined from the DebyeMcAuley formula30
log γA ) βAI
(22)
By recognizing the salting-out effect as a direct measure of the deviation from ideal behavior for the dissolved molecular species and combination of eqs 20 and 22, we have
γA )
HA HsA
) 10hA
(23)
with hA as given by eq 21. This gives an expression for the activity coefficient of CO2, closely related to experimental data for the Henry’s law constant and the
Figure 3. (a) Equilibrium model and experimental data from Jou et al.32 for a 30 wt % MEA solution. (b) Speciation plot for a 15 wt % MEA solution at 40 °C.
salting-out coefficients. The phase equilibrium determining the solubility of free CO2 in the loaded alkanolamine solution is then given by s pCO2 ) γCO2HCO [CO2] 2
(24)
A temperature- and loading-dependent parameter in the form of an activity coefficient for the free alkanolamine was introduced to tune the model to fit the experimental equilibrium data of Jou et al.31,32 and Lee et al.33 for MDEA (23.5 and 48.8%) and MEA (15 and 30%). The model is shown in Figures 3a and 4a, respectively, together with experimental data for 30% MEA and 23.5% MDEA. The resulting equilibrium speciation (Figures 3b and 4b) was found to give results very similar to those resulting from considerably more rigorous and computer-intensive thermodynamical models, such as the electrolyte-NRTL model by Austgen et al.22 2.3. Membrane Reactor Model. 2.3.1. Balance Equations for the Gas Phase. Early experiments were done with varying gas flow and absorption of CO2 in a 30 wt % MEA solution, and the calculated overall mass-transfer coefficient showed no effect of gas flow (Figure 5). As the gas-side mass-transfer coefficient is expected to vary as vg0.5-1 (Gabelman and Hwang34), it could then be assumed that the gas-side mass-transfer
4912 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004
Figure 6. Results from measurements of pressure drop in the laboratory-scale membrane module.
assume that the gas phase was perfectly mixed laterally and in axial plug flow. It was further assumed that the gas flow was counter- or co-current to the liquid flow. The model is thus not directly representative of the typical flow situation in a single industrial low-pressure membrane module, which would be cross-current (as in Figure 2a). However, normally, the concentration changes in a single module are modest, thus making the difference between counter- and co-current flow very small. Following the plug-flow assumption, the mass balance equation of the gas phase is given by Figure 4. (a) Equilibrium model and experimental data from Jou et al.31 for a 23.5 wt % MDEA solution. (b) Speciation plot for a 23.5 wt % MDEA solution at 40 °C.
dntot dz
)
vg ∂P RTg ∂z
+
P ∂vg RTg ∂z
-
Pvg ∂T RTg2 ∂z
)
a
∑i Ni
(25)
g
where ntot (mol/m2‚s) is the molar flux of the gas phase referred to the free gas cross-sectional area. dntot/dz is expanded by introduction of the ideal gas law, ntot ) Pvg/RTg, where P is the total pressure, vg is the gas velocity, and Tg is the gas temperature. Ni (mol/m2‚s) is the molar flux of component i from the gas through the membrane and into the liquid phase referred to the inner surface area of the membrane tubes. g is the fraction of the total area available for the gas flow, whereas a (m2/m3) is the specific inner surface area of the membrane module. This equation can be solved for the gas velocity derivative
vg ∂P vg ∂Tg RTg a ∂vg N )+ ∂z P ∂z Tg ∂z vg ig Figure 5. Influence of gas flow rate on the overall mass-transfer coefficient, from an experiment with 30% MEA at 40 °C, pCO2 ) 5 kPa, y ) 0.04.
resistance is negligible compared to the membrane and liquid-side resistances. Pressure drop measurements were performed on the membrane module and showed a second-order dependence on the gas flow (Figure 6), which indicates the presence of local shell-side turbulence as discussed by Gabelman and Hwang34 for a similar type of contactor. With a flow length/hydraulic diameter ratio of about 400 and an interstitial gas velocity of about 10 m/s, dispersion effects should be negligible. These observations were used as support to
(26)
The pressure drop gradient, ∂P/∂z, was taken from a correlation based on the measurements shown in Figure 6. The equation describing the partial pressures of gas components is derived in an analogous manner from the balance of component i and introduction of ni ) pivg/ RTg
pi ∂vg pi ∂Tg RTg a ∂pi )+ N ∂z vg ∂z Tg ∂z vg ig
(27)
The thermal balance for the gas phase is straightforward when any frictional heat and heat loss to the surroundings are disregarded
Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4913
∑i
cp,ini
∂Tg
)Q
(28)
∂z
where cp,i is the specific heat of component i. 2.3.2. Flux across the Membrane. The transfer flux across the membrane was modeled using the simple resistance-in-series approach, including the gas-film and membrane mass-transfer coefficients
Ni )
(
RTg
1 1
+
)
Rout ln(Rout/Rin)
ki,g
eff Di,m
(pi - Hici,s) + xi
∑i Ni (29)
where ci,s is the concentration of component i at the liquid/membrane interface. Rout and Rin are the outer and inner radii, respectively, of the membrane tube. The eff , is defined effective diffusivity in the membrane, Di,m as eff ) Di,m
Di τ
1 (T - Tl,s) 1 1 g + hg hm
[ ( )]
2vz,av 1 -
(31)
where hg and hm are the gas-phase and membrane heattransfer coefficients, respectively. Tl,s is the temperature at the liquid/membrane interface. As with the mass transfer, the heat-transfer resistance of the gas phase was considered negligible compared to the membrane resistance. The heat-transfer coefficient of the microporous membrane was calculated from the thermal conductivities of PTFE and of the gas phase, modeled as two resistances in parallel. 2.3.3. Transport Model for the Liquid Phase. The mass-transport model for the liquid phase was derived from the equation of continuity for species in a reacting mixture.35 It was assumed that the transport mechanism in the liquid phase is by convection in the axial direction and diffusion in the radial direction. The diffusional flux was described by Fick’s law in cylindrical coordinates. The diameter of the tubes in the module used for the experiments was 3.0 mm, and the linear liquid velocities were in the range of 0.5-4 cm/s. With the densities and viscosities of the systems under consideration, this gives liquid Reynolds numbers well below 100, which implies that the liquid flow is in the laminar regime. The radial velocity profile will then be parabolic.35 The velocity profile was assumed to be fully developed, which is supported by the fact that the liquid inlet region is covered by membrane fiber potting (see Figure 2b), and the velocity profile then has time to stabilize before the mass-transfer zone is reached. The absorption of CO2 in a liquid leads to an increase in solution density and viscosity, which was correlated by Weiland et al.36 Because the bound CO2 concentration increases toward the wall in the membrane absorber, there will be corresponding gradients in viscosity and
r Rin
2
(
)
∂ci 1 ∂ ∂ci rDi + ri ) ∂z r ∂r ∂r
(32)
The component diffusivity cannot be taken outside the derivative, as significant radial diffusivity gradients can occur. This is a result of the coupling between CO2 loading and viscosity and between viscosity and diffusivity, as given by the Stokes-Einstein relation.19 Expansion of the right-hand side gives
2vz,av (30)
where Di is the molecular diffusivity of component i and and τ are the membrane porosity and tortuosity, respectively. The conductive sensible heat flux is modeled in an analogous manner as
Q)
density. The derivation of the parabolic velocity profile assumes constant viscosity and density,35 and to test whether this assumption would lead to deviations from the assumed profile, a CFD calculation was performed using an in-house program code. The velocity profile calculated with the radial viscosity and density gradients imposed on the flow field showed a negligible deviation from the parabolic velocity profile; see Hoff et al.43 for details. With the parabolic velocity profile, the balance for component i becomes
[
( )]
r 1Rin
(
)
2 ∂Di ∂ci ∂ci 1 ∂ci ∂ ci ) Di + 2 + + ri ∂z r ∂r ∂r ∂r ∂r (33)
2
One such equation is needed for each of the components that influence the rate of absorption of CO2. This includes the free CO2, the free alkanolamine, and the bound CO2 reaction products. The ionic reaction products were modeled as a single diffusing species according to the requirement of electroneutrality. The thermal balance can be formulated similarly, using the thermal conductivity of the amine mixture and the heat of reaction for the CO2/alkanolamine reaction. Thermal conductivity was taken outside the derivative, thus neglecting any possible effect of varying liquid viscosity, which is unknown and expected to be of minor importance
[ ( )]
2vz,av 1 -
r Rin
2
cp,lFl
( )
∂T 1 ∂ ∂T ) λl r + ri(-∆Hr) ∂z r ∂r ∂r (34)
The following boundary conditions are required for eqs 33 and 34
r ) Rin
z)0
ci ) c0i and Tl ) T0l
(35)
r)0
∂ci ∂Tl ) 0 and )0 ∂r ∂r
(36)
∂Tl Q ∂ci Ni ∆Hvap ) ) + Nw and (37) ∂r Di ∂r λl λl
The temperature boundary condition at the liquid/ membrane interface includes the latent heat from the evaporation or condensation of water at the liquid surface, ∆Hvap. 2.3.4. Physical Properties. An overview of the most important physical properties including their functional dependences and literature sources is given in Table 1. The approach chosen in the description of the diffusion of bound CO2 is elaborated in the Appendix. 2.3.5. Model Implementation. The model was programmed in MATLAB, and the system of partial differential equations was solved by the method-of-lines procedure.41 The r derivatives of eqs 33 and 34 were
4914 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 Table 1. Physical Properties Used in the Membrane Gas Absorber Model property
symbol
functional dependence
source
specific heat of gas components specific heat of alkanolamine/ water solution density of alkanolamine/ water solution diffusivity of CO2 and water in the gas phase viscosity of the loaded solution diffusivity of CO2 in the loaded solution diffusivity of the free alkanolamine in the loaded solution diffusivity of chemically bound CO2 thermal conductivity of the gas thermal conductivity of the PTFE
cp,g cp,l
f(T) f(T,wam,yCO2)
Reid et al.26 Cheng et al.37
Fl
f(T,wam,yCO2)
Cheng et al.37
Di,g
f(T,P)
Reid et al.26
µl DCO2,l
f(T,wam,yCO2) f(T,µl)
Weiland et al.36 Versteeg et al.19
Dam,l
f(T,cam,µl)
Snijder et al.39
Dcb λg λPTFE
f(T,µl) f(T,composition) f(T)
thermal conductivity of the alkanolamine solution
λl
f(T,wam)
this work Reid et al.26 Brandrup and Immergut40 Cheng et al.37
calculated from finite-difference approximations. First derivatives were calculated by fourth-order finite differences, while second-order finite differences were used for the second derivatives, using the routines dss004 and dss042.41 To capture the very steep gradients close to the membrane wall, the r domain was divided into two regions with different uniform resolutions. The two zones were typically separated at r/Rin ) 0.995 with 40 grid points in both the “wall” zone and the bulk zone, and the model was thoroughly tested for grid independence in the whole range of conditions examined. The solution for the co-current case was straightforward, whereas for the countercurrent case, an outer iteration loop based on the Broyden method42 was used, as the integration always follows the liquid phase from the inlet to the outlet. See Hoff et al.43 and Hoff44 for details. After integration, the overall average flux from gas to liquid was calculated by independent mass balances on the gas and liquid phases. The liquid inlet and outlet molar flows are, respectively l ni,in ) c0i QL l ni,out ) ntubes2π
∫0R ci(r) vz(r) r dr i
(38) (39)
where c0i is the molar concentration of component i in the inlet liquid and QL is the volumetric flow rate of liquid. ntubes is the number of membrane tubes in the module, and ci(r) and vz(r) are the radial concentration and velocity profiles, respectively. The molar absorption rate of component i in the liquid phase is then given as l l - ni,in . The corresponding absorption rate Rli ) ni,out from the gas-phase balance is given by
Rgi )
Ag [(p v )in - (pivg)out] RTg i g
(40)
The error in the global mass balances was typically within (1%, which reflects the fact that the finitedifference method does not necessarily lead to conservation of the fluxes. This problem can be resolved by building a corresponding model around the finitevolume method, which is inherently mass conserving. The price, however, would be a less robust model with significantly higher computation times.43
comment loading dependence from Weiland et al.38 CO2 taken into account by adding the weight of absorbed molecules44 Fuller equation was used
based on the N2O analogy and a Stokes-Einstein relation viscosity dependence from a StokesEinstein relation see the Appendix
3. Experimental Section 3.1. Apparatus and Procedures. A new laboratoryscale apparatus for the study of the membrane gas absorption of carbon dioxide was constructed. A a schematic diagram and description of the apparatus are given in Figure 7. Data of the PTFE membrane module, delivered by W.L Gore & Associates, Munich, are given in Table 2. The whole gas circulation loop, including the membrane module, was placed inside a heated cabinet for accurate and uniform temperature control. Liquid was pumped through the membrane module from a 20-L feed storage tank with temperature control by a heated water jacket. To keep the liquid-side pressure at a level 0.1-0.5 bar higher than the pressure on the gas side (as required to prevent the formation of gas bubbles), a back-pressure valve placed on the liquid outlet line was used for adjustment. The gas/liquid pressure difference was monitored by a Rosemount differential pressure transmitter. The CO2 makeup stream was mixed with a N2 flow of 1 NL/min, which corresponded to the amount required by the IR CO2 analyzer (Rosemount Binos 100). For this purpose, thermal mass flow controllers from Bronkhorst Hi-Tec were used. The gas temperature was specified to always be at least 1 °C higher than the liquid temperature to prevent any liquid condensate from forming on the gas side of the membrane module. The residence time of the gas in the membrane module was always less than 0.1 s, and this made it possible to hold the gas temperature higher than the liquid temperature both at the inlet and at the outlet. At lower gas velocities than those applied, the outlet gas temperature would equal the inlet liquid temperature because of the efficient heat exchange of the membrane module. The flux of CO2 from gas to liquid was calculated from a CO2 balance on the system as a whole and not from the difference in gas composition between the membrane inlet and outlet. This feature essentialy gave a direct measurement of the absorption flux, as the amount leaving the system through the IR analyzer was very small. This mode of operation was used to do experiments on CO2 absorption from a 0-10% gas mixture with N2 as the inert in a 30% MEA solution. Experiments could also be performed with a pure CO2 (+ solvent vapor) stagnant gas phase. In this mode, the
Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4915
Figure 7. Diagram of the laboratory-scale apparatus: 1, liquid feed tank; 2, liquid sample point (membrane inlet); 3, liquid gear pump; 4, flow meter; 5, membrane drainage; 6, temperature RTD transmitter; 7, differential pressure transmitter; 8, condensate trap; 9, block valves for stagnant gas operation; 10, membrane module; 11, orifice meter; 12, pressure transmitter; 13, heating cabinet; 14, side channel blower; 15, condenser; 16, CO2 gas analyzer; 17, mass flow controllers; 18, back-pressure regulator; 19, liquid sample point (membrane outlet); 20, soap bubble meter; 21, water lock (gas washing bottle); 22, liquid collection tank; 23, centrifugal pump. Table 2. Data on the Membrane Module Used in This Work
Table 3. Base-Case Values and Ranges for the Experiments
parameter
value
variable
base case
range (3-5 values)
number of tubes inner diameter of tubes membrane wall thickness total tube length (incl potting) active tube length active inner surface area, am porosity, tortuosity, τ inner diameter of canister specific inner surface area, a max differential pressure (Pliquid - Pgas)
28 3 mm 240 µm 575 mm 430 mm 0.11 m2 0.50 1.3 28 mm 416 m2/m3 0.5 bar
vol % CO2 liquid flow (L/min) gas flow (m3/h) T (°C) CO2 loading
5 0.2 3 40 parameter
0.5-10 (circulating gas mode) 0.1-0.4 2-5 25-70 0-0.4
block valves in the gas circulation loop before and after the membrane module were closed, defining the volume available for the stagnant gas phase. After a thorough flushing with CO2, the liquid flow was started, and the absorption flux was measured directly using a soap bubble meter. The “stagnant gas phase” was the mode of operation used in this work for experiments with a 15% MEA solution and with a 23.5% MDEA solution. Experiments were done in series with 3-5 levels of a specific variable. The variables tested were gas velocity, liquid velocity, CO2 partial pressure, and temperature. The same liquid batch was pumped back to the feed tank for every new series, thus resulting in a gradual increase in the solution loading. Extra recirculation with absorption was sometimes applied to make a sufficient span in the CO2 loading. The operation required the apparatus to be completely gastight, which was regularly tested by closing the gas outlet, applying a very low N2 flow (
