Novel Dual-Membrane Gas−Liquid Contactors - American Chemical

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SEPARATIONS Novel Dual-Membrane Gas-Liquid Contactors: Modelling and Concept Analysis Shunyu Wang, Kelly Hawboldt, and Majid Abedinzadegan Abdi* Faculty of Engineering and Applied Science, Memorial UniVersity of Newfoundland, NL, A1B 3X5, Canada

Absorption processes have traditionally been used in the removal of contaminants from natural gas. A dualmembrane concept is proposed to improve the performance of membrane gas-liquid contactors. In the proposed configurations, a second membrane was added to a single-membrane system and a sweeping gas or a lower pressure applied on the permeate side of either a porous or nonporous second membrane. Theoretically, the new configurations can partially regenerate the solvent stream simultaneously with the absorption process, and, therefore, better absorption efficiencies can be obtained. The proposed configurations and the ordinary single-membrane contactor were simulated using partial differential equations based on a single-component absorption scheme. The solutions showed that the proposed dual-membrane contactor could remove gas components more efficiently, when compared to the ordinary contactor. A significant improvement in solvent flow rate and regeneration efficiency and, therefore, overall gas purification performance will be achieved using a dual-membrane absorption system. 1. Introduction 1.1. Membrane Gas Absorption. During the past 30 years, solvent absorption has dominated the field of natural gas treatment (including acid gas removal, dehydration, etc.). The solvent can be various amines or formulated mixed or glycol solutions, depending on the purpose of the treatment, and the absorption process can be physical, chemical, or a combination of the two. Membrane-based gas absorption systems show potential in providing an alternative to the traditional absorption processes in the natural gas industry. The separation in membrane gas absorption devices is dependent on the difference in solubilities of various components of the gas mixture in the absorbent liquid. Membranes provide a larger interfacial area, compared to traditional gas absorption processes, and this larger interfacial area results in better performance. For instance, packed and trayed columns can supply an interfacial area of ∼30-300 m2/m3, whereas membrane contactors can provide a surface area of 1600-6600 m2/m3.1 Membrane contactors can reduce the size of equipment required for gas absorption by a factor of more than 20, which is advantageous for offshore gas processing applications where space is a critical parameter in the design of topside facilities. The membrane modules are small and light, making them ideal for offshore applications. In addition, there are no operational limitations such as flooding, loading, weeping, etc. In a membrane contactor, the density difference of the contacting phases is irrelevant, and, therefore, the orientations of the contactor and the sway have little impact on the performance. This property makes it ideal for offshore processing applications. Finally, the scaleup of the membrane system is linear to its modular number, so the treatment capacities can be easily adjusted according to the production.2 Figure 1 illustrates the mechanism for ordinary membrane contactors. For simplicity, this paper will address the plate-andframe membrane contactors. * To whom correspondence should be addressed. Tel.: 001(709)737-3965. Fax: 001(709)737-4042. E-mail address: [email protected].

Figure 1. Schematic drawing of an ordinary single-membrane contactor.

Membrane materials can be hydrophobic or hydrophilic. The pores of the membrane can be filled with either gas or liquid, depending on membrane material, the physicochemical properties of the absorbent liquid, and the operating pressures that are used.3 When a hydrophobic membrane is used with an aqueous solvent, the membrane is under the nonwetted mode (i.e., the pores are filled with gases and the liquid does not wet the membrane). When hydrophilic membranes are used with aqueous absorbents, liquid will wet the membrane spontaneously (i.e., the pores are filled with liquid). Figure 2 shows the wetted and nonwetted modes schematically. In this paper, the focus is only on the nonwetted mode. 1.2. Dual-Membrane Gas-Liquid Contact Concept. The removal efficiency of gaseous contaminants is a strong function of their concentration differential between the liquid and gas phases. Because of the different operating conditions, the absorption and regeneration systems in conventional gas treatment processes are separate. In most cases, the high-pressure solvent from the absorption system is depressurized and routed to a steam or gas stripping system, where the absorbed gaseous contaminants are stripped off the solvent.4 A large number of recent studies have been conducted on modeling membrane contactors.5-17 These studies have focused on the characterization of membranes and modeling of absorption efficiencies in hollow fiber contactors. Various researchers have studied the use of physical solvent for removal of acid gases by membrane contactors. Dindore and co-workers9-11 studied various mass-

10.1021/ie051368d CCC: $33.50 © 2006 American Chemical Society Published on Web 10/04/2006

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Figure 2. Wetted and nonwetted modes of membrane-based gas-liquid contact.

transfer effects, including the type of physical solvents on the performance of membrane contactors. Physical solvents were selected for the present study, because the partial regeneration effects in a dual-membrane system are more pronounced. Masstransfer coefficients in the liquid phase for flat and hollow membrane contactors were determined by Dindore and his colleagues. In a recent work, Kosaraju et al.17 studied the stripping behavior of a novel solvent using microporous membranes for CO2 removal. However, this study was concentrated on the performance of membranes during absorption and stripping cycles in two separate modules. The use of more than one membrane was introduced by Ohno and co-workers.15,16 The membranes in Ohno’s studies were used in a gas separation for increased selectivity, rather than in a gas-liquid contact mode. No use of solvent absorption was introduced by Ohno’s group. Different membrane contactor configurations have been explored for applications as diverse as water and carbon dioxide removal from natural gas to the separation of olefin/paraffin mixtures.19-23 For carbon dioxide removal, most of the systems require both an absorber and stripper. On offshore applications, the space required for these two systems is often limited and may not be practical. Ideally, merging the contactor and stripper into one unit operation would be preferred for remote or offshore applications. In response to this, immobilized liquid membrane (ILM) contactors have been proposed where the solvent is contained within the membrane. Typical problems with these systems have revolved around regenerating the liquid membrane, humidity control, and flooding.24 Variations on this type of membrane include hollow-fiber-containing liquid membranes (HFLCM) where the LM is maintained at a higher pressure than the feed gas and stripping gas streams.25,26 However, these membranes seem to be ideal in situations where the feed gas pressures are similar to atmospheric. Papadopolous studied the configuration for feed gas pressures that were higher than atmospheric within a range of 10-15 MPag.27 Flow swing absorption permeation membranes, which operate in a manner similar to PSA units, have also been proposed.25 Again, the contactor and stripping sections are contained within the same unit; however, the process operates in a semi-continuous mode. Matsumiya et al. have proposed an absorber/stripper combination where the feed gas and solvent are supplied to the feed side (pressure slightly higher than atmospheric) of the hollow fibers of the membrane and the solvent with the absorbed gas permeates through the membrane to the low pressure (shell side).26 In all of the aforementioned applications, except Matsumia’s, where the solvent permeates through the membrane, the solvent is stationary. Other groups have used mobile absorbents between two nonporous membranes. Beckman et al. proposed the Selective Membrane Valve concept, in which a

flowing solvent is used to increase the selectivity of membrane separation.28 A simplified mass-transfer model was also presented. Bessarabov et al. used nonporous membranes in two(single membrane) and three-channel (two parallel membranes) configurations with flowing solvent.29 These systems all have their advantages and disadvantages. However, for produced gas treatment on offshore platforms or at remote locations, the key issues are the footprint, the ability to perform with variable stability, and possibly high feed pressures. A configuration where two membranes are incorporated into a single unit within which the circulating solvent is partially regenerated during the absorption is proposed. The proposed configuration can potentially reduce the overall size and increase the efficiency of gas processing facilities, which would make them more suitable for offshore applications. 1.3. This Work. The purpose of this research is to demonstrate the efficiency of a dual-membrane gas-liquid system for the removal of gaseous contaminants using basic principles governing the absorption and stripping processes. This research proposes two novel configurations to improve the performance of the ordinary porous single-membrane contactor. In configuration 1, a second porous membrane is added and a flow of sweeping gas is introduced on the permeate side of a second porous membrane (see Figure 3a). In configuration 2, the second membrane is a nonporous one, and a low pressure (slightly higher than atmosphere pressure in this study) is applied on the permeate side of the nonporous membrane (see Figure 3b). The sweeping gas in configuration 1, or the differential pressure across the nonporous membrane in configuration 2, can partially strip the acid gas components from the circulating solvent, thereby partially regenerating the solvent stream simultaneously and potentially reducing the load on the solvent regeneration systems. Because the rate of absorption is a function of the concentration of gas components in the liquid phase, by continuous removal of these components from the solvent, better absorption efficiency can be obtained. The differential partial pressure across the second membrane can strip the absorbed gas components from the solvent, thereby partially regenerating the solvent stream simultaneously with the absorption process. To demonstrate the performance of the proposed dual-membrane system a mixture of N2 and CO2 was used with methanol as the absorbing solvent. To show the performance of the dualmembrane system and to simplify the basic modeling, in our study, we assumed that N2 does not participate in the absorption; therefore, the modeling reduces to a single-component absorption process. When several components are absorbed, only the number of differential equations to be solved increases.

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through the desorption membrane, because of the low-pressure employed on permeate side, so it is assumed that, in configuration 2, a nonporous membrane with a low permeability to the solvent should be chosen, to make the vaporization negligible, compared to the flux of CO2. In the following equations, CO2 and methanol (CH3OH) are denoted as A and B, respectively. The governing material balance equation for an incompressible flow can be written as

∂CA ∂CA ∂CA ∂CA +u +V +w ) ∂t ∂x ∂y ∂z ∂2CA ∂2CA ∂2CA + + 2 + RA (1) DAB ∂x2 ∂y2 ∂z

(

)

In our study, a physical solvent was used, so RA is set to a value of zero. 2.1. Absorbing Membrane. For the membrane contactors studied in this paper, based on the assumptions previously mentioned, the mass-transfer model in the liquid phase can be simplified as

u

∂2CA ∂CA ) DAB ∂x ∂y2

(2)

u)

y h2 dPl y 2 2µl dx h h

(3)

where30

Figure 3. Schematic arrangements of membranes in the proposed novel dual-membrane system.

2. Model Development To demonstrate the improvement that the novel dualmembrane system can make, both an ordinary membrane contactor and a dual-membrane contactor with porous and nonporous regenerating membranes (configurations 1 and 2) were modeled. Numerical methods were used to solve the governing equations. The fully developed laminar flow in liquid phase is a reasonable assumption for the study of membrane contactors;5-8 therefore, the study was limited to the fully developed laminar flow in the liquid phase. Typically, the gas is assumed to be in plug flow.8 The models were constructed based on the following assumptions: (1) The membranes were considered as infinite parallel plates. (2) The membrane contactor was operated under steady state and isothermal conditions at 298.15 K and the pressure in the gas phase was constant along the membrane. (3) The physical properties, including the diffusion coefficient, Henry’s constant, density, andviscosity, were constant along the membrane. (4) At the interface of gas and liquid, Henry’s law was assumed to be applicable, and equilibrium was instantaneously obtained. (5) The liquid flow between two plates was fully developed laminar flow. (6) The x-direction diffusion and y-direction convection were negligible. (7) The membranes were under the nonwetted mode (gasfilled pores). Mass-transfer effects that were due to membrane swelling and concentration polarization were also ignored at this stage of the proof of concept. The solvent will inevitably evaporate

[( ) ( )]

In the gas phase, the concentration distribution of CO2 in the y-direction can be assumed to be negligible, because the diffusion coefficient in the gas phase is typically much larger than in the liquid phase. That is, the gas phase is completely mixed in the y-direction and the concentration profile of CO2 in the gas phase is a function of only x. Taking a differential segment of the mixture gas side of the upper porous membrane, according to material balance, the number of moles of CO2 absorbed by the solvent is equal to that diffusing through the boundary:

-dNg1 ) φdxDAl

|

∂CAl ∂y

y)h

(4)

Neglecting the variation of flow rate of gas mixture along the membrane, we can write

dNg1 ) Qg1dCAg1

(5)

Thereby, we have the equation

-Qg1

|

dCAg1 ∂CAl ) φDAl dx ∂y

y)h

(6)

Based on the assumption that the Henry’s law is applicable at the boundary, we have the following equation:

|

Qg1 ∂CAl HA ∂x

y)h

) φDAl

|

∂CAl ∂y

y)h

(7)

This expression is the boundary condition on the mixture gas side. 2.2. Regenerating Membrane. The boundary conditions for the second membrane can be demonstrated as follows. 2.2.1. Configuration 1. Similar to modeling for the absorbing membrane, we can obtain the boundary condition on the

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membrane contactor, the ordinary membrane contactor was also modeled using the same principles. The governing equation in the liquid phase and the boundary condition on the absorbing membrane in configuration 1 can be carried over here. The lower boundary condition is quite straightforward, because there is no mass transfer across this boundary. Figure 4. Depiction of the partial differential equation and the inlet and boundary conditions for configuration 1.

Figure 5. Depiction of the partial differential equation and the inlet and boundary conditions for configuration 2.

sweeping gas side:

|

Qg2 ∂CAl HA ∂x

y)0

|

∂CAl ∂y

) φDAl

y)0

(8)

When combined with the governing partial differential equation in the liquid phase, we have the partial differential equation, inlet, and boundary conditions that are shown in Figure 4. 2.2.2. Configuration 2. The boundary condition on the absorbing membrane can be obtained in the same way as that in configuration 1. For the nonporous membrane, we keep a constant CO2 pressure (Pout) on the permeate side of the membrane.

|

∂CAl dNg2 ) DAl φ dx ∂y

y)0

(9)

|

∂CAl ∂y

y)0

)

PerA(P* - Pout) δ

(11)

According to the Henry’s law, the following equation can be derived:

P* )

CAl(x,0)RT H

(12)

The resulting boundary condition on the nonporous membrane side is

DAl

|

∂CAl ∂y

) y)0

PerA[(CAl(x,0)RT/HA) - Pout] δ

y)0

)0

(14)

Thereby, we have the partial differential equation and the inlet and boundary conditions that are shown in Figure 6. The mixture gas can flow in a co-current or a counter-current scheme with the solvent. Under the co-current condition, Qg1 is positive and CAg1 is given at x ) 0. Under the counter-current condition, Qg1 is negative and CAg1 is given at x ) L (the length of the membrane). According to Henry’s law, we can obtain the CA1 at point (x ) 0,y ) h) for the co-current scheme and at point (x ) L,y ) h) for the counter-current scheme. This can be used as the inlet condition for the material balance equations. The partial differential equations were solved numerically.31 Both explicit and implicit methods can be used to solve the partial differential equations. Implicit methods provide more accuracy, so the Crank-Nicholson method32 was used. The solutions showed the concentration distribution of the CO2 in the solvent phase; thereby, the CO2 concentration profile in the mixture gas phase can be obtained based on Henry’s law and removal efficiencies can be calculated. 3. Results and Discussions The assumed values of parameters used in the following calculations are listed in Table 1. Note that the local concentration distribution in the solvent in the y-direction is not of interest; therefore, the formula

(15)

(10)

Combining eqs 9 and 10, we have

DAl

|

∂CAl ∂y

∫0h u(y)CAl(x,y) dy CAl ) ∫0h u(y) dy

Meanwhile,

dNg2 PerA(P* - Pout) ) φ dx δ

y ) 0, DAl

(13)

The governing equation in the solvent phase and the upper boundary condition that is derived in configuration 1 are still valid here, so we have the partial differential equation and the inlet and boundary conditions that are shown in Figure 5. 2.2.3. Ordinary Membrane Contactor. To compare the novel dual-membrane contactors with an ordinary single-

was used to obtain the average CO2 concentration in the solvent phase. Therefore, the CO2 concentration in the solvent phase shown in the following diagrams will be a function of x only. 3.1. Novel Dual-Membrane Contactor Performance. 3.1.1. Configuration 1. The result for co-current and counter-current flow patterns are shown in Table 2. This table clearly shows that the counter-current flow pattern gives better CO2 removal performance with the same solvent and sweeping gas flow rate. However, it should also be noticed that the solvent from the counter-current model is richer in CO2 than that of the co-current model. This may result in a higher duty on the solvent regeneration unit. Figures 7 and 8 show the CO2 concentration profiles under co-current and counter-current conditions, respectively. Unlike Beckman et al., who used a simplified model where the variation of concentration along the membrane length (x-direction) was assumed linear,29 we used the general masstransfer partial differential equations and showed that the variation of the concentration in the x-direction is, indeed, very nonlinear. 3.1.2. Configuration 2. The results are outlined in Table 3. Again, by comparing these two models (counter-current versus co-current flow models), the counter-current flow pattern clearly has a better CO2 removal performance with the same flow rate of solvent and permeate side pressure. Figures 9 and 10 show

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Figure 6. Depiction of the partial differential equation and the inlet and boundary conditions for an ordinary membrane contactor.

Figure 7. Averaged CO2 concentration profiles under co-current flow conditions for configuration 1. Table 1. Parameters Used in the Calculations parameter

value

channel height (m) dimensions of the membrane (m2) solvent (methanol) flow rate (10-8 m3/s) mixture gas flow rate (10-7 m3/s) CO2 inlet concentration (kg mol/m3) Henry’s Law constant (CO2 in methanol) diffusivity of CO2 in methanol (10-9 m2/s) mixture gas pressure (106PaA) permeability of nonporous membrane (Barrer) pressure (permeate side) (105 PaA)

0.001 0.165 × 0.165 7.12 6.25 0.4034 (20 vol %) 3.89 8.37 5.0 33,100 2.0

Table 2. CO2 Inlet and Outlet Concentration for Configuration 1 Cout (kg mol/m3) component mixture gas solvent sweeping gas

Cin (kg

mol/m3)

0.4034 0 0

co-current

counter-current

0.2397 0.9194 0.2380

0.1572 1.4123 0.3426

the trends and variation of CO2 concentration in the gas and liquid phases for co-current and counter-current flow patterns. 3.1.3. Ordinary Membrane Contactor. For the co-current model, the CO2 concentration in the mixture gas decreases from 0.4034 kg mol/m3 to 0.2808 kg mol/m3, and the average CO2 concentration in solvent increases from 0 kg mol/m3 to 1.0813 kg mol/m3. The counter-current model indicates that the CO2 concentration in the mixture gas decreases from 0.4034 kg mol/

Figure 8. Averaged CO2 concentration profiles under counter-current flow conditions for configuration 1. Table 3. CO2 Inlet and Outlet Concentration for the Dual-Membrane Contactor in Configuration 2 Cout (kg mol/m3) component

Cin (kg mol/m3)

co-current

counter-current

mixture gas solvent

0.4034 0

0.1628 0.4866

0.1235 0.9291

m3 to 0.2277 kg mol/m3, whereas the average CO2 concentration in the solvent increases from 0 kg mol/m3 to 1.545 kg mol/m3 (see Table 4). Again, the counter-current flow pattern has superior CO2 removal performance. Figure 11 shows the CO2 concentration profiles in the mixture gas under the counter-current condition for configuration 1, configuration 2, and the ordinary membrane contactor. The comparison of CO2 removal efficiencies between the cocurrent and counter-current flow patterns for the aforementioned membrane contactors indicate that counter-current flow can result in better CO2 removal performance. As such, only the counter-current flow pattern is considered in the remainder of this study. Figure 12 shows the CO2 concentration profiles in the mixture gas and the solvent under counter-current conditions for the novel membrane contactor with the nonporous second membrane and the ordinary membrane contactor. The dual-membrane contactor can improve CO2 removal performance from the

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Figure 9. Averaged CO2 concentration profiles under co-current flow conditions for configuration 2. Figure 11. Averaged CO2 concentration profiles in the mixture gas under counter-current flow conditions.

Figure 10. Averaged CO2 concentration profiles under counter-current flow conditions for configuration 2. Table 4. CO2 Inlet and Outlet Concentrations for the Ordinary Membrane Contactor Cout (kg mol/m3) component

Cin (kg mol/m3)

co-current

counter-current

mixture gas solvent

0.4034 0

0.2808 1.0813

0.2277 1.545

mixture gas by a factor of 1.59, when compared to the ordinary membrane contactor under the same solvent flow rate. In addition, the outlet CO2 concentration in the solvent from the dual-membrane contactor is much lower than that from the ordinary single-membrane contactor. This can potentially make regeneration of the solvent and, consequently, the entire gas

Figure 12. Averaged CO2 concentration profiles under counter-current flow conditions for dual-membrane (configuration 2) and single-membrane contactors.

removal process less costly, which indicates a clear advantage over ordinary single-membrane contactors. Both configurations 1 and 2 show advantages over the ordinary single-membrane contactor. The dual-membrane contactors can improve CO2 removal performance by a factor of ∼1.7-2, in comparison to the ordinary membrane contactor

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under the same solvent flow rate. In addition, the outlet CO2 concentration in the solvent from either of the dual-membrane contactors is less than that from the ordinary single-membrane contactor, which can potentially make regeneration of the solvent less costly. The previously discussed diagrams also show that configuration 2 is preferable to configuration 1, in terms of outlet CO2 concentration in both the mixture gas and the solvent phase. Nevertheless, it cannot generally be concluded that configuration 2 is a better choice, because if the sweeping gas flow rate is increased, better CO2 removal performance can also be achieved with configuration 1. However, configuration 2 is a more practical choice than configuration 1. The first reason is that applying a low pressure on the permeate side of the nonporous membrane, in many applications, is an easier task, compared to finding the suitable source for the sweeping gas. In addition, the flow rate of permeate gas from configuration 2 is much less than that of the sweeping gas, which make it easier to dispose of. Thereby, we will focus our study on configuration 2 in the remainder of the paper. The advantage of the dual-membrane contactor can be examined from a different perspective. Under counter-current conditions in the dual-membrane contactor, to reduce CO2 concentration in the mixture gas from 0.4034 kg mol/m3 to 0.1235 kg mol/m3, the flow rate of solvent should be kept at 7.12 × 10-8 m3/s. To achieve the same CO2 removal, an ordinary single-membrane contactor requires a solvent rate of 1.25 × 10-7 m3/s. In this case, the novel membrane contactor can reduce the required solvent flow rate by 43%. This will reduce the energy and size requirements for the regeneration system, as well as chemical use. 3.1.4. Effect of Permeate Pressure. Obviously, the pressure on the low permeate side of the second membrane will have a dramatic effect on the performance of the membrane and the feasibility/cost of the system. Therefore, the permeate pressure was varied from the base case of 200 kPa to a value in the range of 10-700 kPa. The single-membrane contactor is included for the sake of comparison but obviously is not affected by the change. As expected, the CO2 in the mixture gas increases with the permeate pressure, as a result of the decrease in regeneration of the solvent (see Figure 13). As expected, the CO2 in the mixture gas increases with permeate pressure, as a result of the decrease in regeneration of the solvent. In fact, at ∼630 kPa, the single membrane performs as well as the dual membrane. Note that these simply show trends, because the actual change in performance, as a function of any of the parameters, will also be affected by the values of the other parameters (i.e., membrane permeability, diffusivities, etc.) 3.1.5. Effect of Diffusivity and Henry’s Constant. Both the diffusion coefficients and the Henry’s Law constant (HLC) are a function of the gas mixture and solvent. By changing these values, we can qualitatively compare the impact of changing the solvent on gas removal. Figure 14 outlines the impact of the HLC. The first part of the figure shows the expected increase in performance for both membrane models as the HLC increases. The increase in performance is much more dramatic for the single membrane. This is not unexpected: as the HLC increases, the flux of the CO2 from the solvent to the permeate gas is reduced. Initially, the reduction is outweighed by the low partial pressure in the permeate side; however, as the HLC increases, the effect of the low pressure is reduced. For this case, at HLC values of >8.6, the single membrane actually outperforms the dual membrane, likely because of the high affinity of the gas

Figure 13. Effect of permeate pressure on acid gas removal.

Figure 14. Effect of Henry’s Law constant (HLC) on acid gas removal.

for the solvent, which results in the reabsorption of CO2 from the permeate side and reduced capacity to absorb from the mixture gas. The diffusion coefficient impact is much more straightforward, as demonstrated in Figure 15. The diffusion coefficient was varied from 3 × 10-9 m2/s to 10 × 10-9 m2/s. As expected, as the diffusion coefficient increased, the performance increased for both membranes, although much more dramatically for the dual membrane. Because the diffusion coefficient only affects the solvent flux (and not both the solvent and the permeate, as

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Figure 15. Effect of diffusivity on acid gas removal.

with the HLC), the dual membrane shows much better performance over the range of diffusion coefficients. Ultimately, to maximize the dual-membrane performance, we want to optimize both the diffusion coefficient and the HLC. However, although this means we want a high diffusion coefficient, it does not also mean that we want the highest possible HLC. The aforementioned study assists in selecting the right solvent for the dual-membrane system. 3.1.6. Mixture Gas Pressure. Critical to the practical application of the membrane is the mixture gas pressure. In gas operations, this is often a function of the upstream equipment (e.g., wellhead and/or separators). To determine the impact of pressure accurately, the actual volumetric flow rate (rather than STP flow) and the inlet concentration of CO2 were kept constant. As Figure 16 demonstrates, the single membrane contactor is relatively unaffected by the change in mixture pressure. However, the dual-membrane contactor shows an increase in removal efficiency. This is not unexpected, because the mass transfer through the nonporous membrane is a function of partial pressure of CO2 on the two sides of the membrane. Again, these numbers are not absolute, but they do show trends rather than magnitude and guide us in the proper selection of the membrane and solvent. 3.1.7. Solvent Flow Rate. Figure 17 shows the impact of solvent flow in the membrane modules. In all previous dualmembrane studies,23-26 the absorbing liquid was kept stationary. The stationery liquid film can enhance the selectivity of separation; however, this results in mass transfer that is controlled largely by diffusion. In our design, the moving solvent can reduce the transfer resistance and improve the mass transfer to the solvent through convection. As Figure 17 demonstrates, no significant mass transfer occurs in a single-membrane contactor at a zero solvent flow rate. However, the dualmembrane configuration can reduce the CO2 concentration from 20% to ∼8%, even in a stationary (no solvent circulation) state. The contactor efficiency can be further improved by flowing the solvent between the two membranes, which further enhances convective mass transfer. Note that the proposed contactor concept will be eventually used in a closed-loop gas processing

Figure 16. Effect of mixture gas pressure on acid gas removal.

Figure 17. Effect of solvent flow rate on CO2 removal.

system, where the solvent should be continuously regenerated in a pressure or temperature swing arrangement. The partial regeneration of the solvent in the dual-membrane contactor (absorber) can also significantly improve the efficiency of the solvent regeneration, improve the overall efficiency, and greatly reduce the size of the system. 4. Conclusions and Recommendations Based on the analysis and the comparison between the proposed new dual-membrane configuration and the ordinary single-membrane contactor, it can be concluded that the countercurrent flow pattern can result in better gas removal efficiency,

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compared to the co-current flow pattern. The novel dualmembrane configuration can substantially improve the gas removal efficiency of the ordinary single-membrane contactor, given suitable choice of parameter and under the proper operating conditions. To achieve the same CO2 removal level, the novel dual-membrane contactor can reduce the required solvent flow rate. All the analysis and predictions regarding the novel dualmembrane contactor are based on mathematical models and, therefore, are at a conceptual stage. To verify whether and how the configurations can realistically improve the performance, experimental studies are required which are currently planned and will be conducted in the future. The experimental work will focus on operating and membrane impacts that are difficult to capture in the model. For instance, membrane stability, with respect to the solvent and gas composition and pressure, is not considered in the model. However, in practice, these parameters may result in membrane swelling and/or degradation and affect the overall efficiencies. For simplicity, at the proof of concept stage, we also ignored important conditions such as polarization effects. The presented mathematical model will also lead to a more-accurate design of the experimental system. In addition, the study will be extended to hollow fiber modules in the next step of the work, because hollow fiber modules have more advantages over the plate-and-frame modules, which were only used for the proof of concept at this stage. Acknowledgment The authors wish to thank the financial supports form the Natural Science and Engineering Research Council of Canada (NSERC) and the Faculty of Engineering and Applied Science, Memorial University of Newfoundland (MUN). Nomenclature C ) molar concentration (kg mol/m3) D ) diffusion coefficient (m2/s) H ) Henry’s constant h ) height of channel (m) L ) length of membrane (m) Ng1 ) mole flow rate of solute in mixture gas (kg mol/s) Ng2 ) molar flow rate of solute diffusing through nonporous membrane (kg mol/s) P ) pressure (Pa) P* ) solute partial pressure in equilibrium with the solute concentration in solvent at the interface (Pa) Per ) permeability coefficient (Barrer) Q ) volumetric flow rate (m3/s) R ) gas constant (m3Pa/(kmol K)) RA ) rate of reaction T ) temperature (K) u ) velocity in the x-direction (m/s) V ) velocity in the y-direction (m/s) w ) velocity in the z-direction (m/s) x ) length coordinate position (m) y ) height coordinate position (m) z ) width coordinate position (m) Greek Symbols δ ) thickness of membrane (m) φ ) width of membrane (m) Subscripts A ) solute A B ) solvent B

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ReceiVed for reView December 8, 2005 ReVised manuscript receiVed August 11, 2006 Accepted September 5, 2006 IE051368D