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gas membrane contactors – An emerging membrane unit operation
Journal of Membrane Science 462 (2014) 131–138
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Gas/gas membrane contactors – An emerging membrane unit operation Pingjiao Hao n, J.G. Wijmans, Jay Kniep, Richard W. Baker Membrane Technology and Research, Inc., 39630 Eureka Drive, Newark, CA 94560, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 17 January 2014 Received in revised form 13 March 2014 Accepted 17 March 2014 Available online 21 March 2014
Gas/gas membrane contactors are devices in which a feed gas and a sweep gas are circulated on either side of a membrane. The pressures of the two gas streams are often approximately equivalent, so the principal driving force for permeation is the concentration difference between the feed and sweep gas components. This type of contactor has been commercialized for energy recovery devices in air conditioning applications. More recently, these contactors have been suggested for use in carbon dioxide capture and sequestration. In this paper, the performance of an ideal contactor using perfectly selective membranes is examined. For this type of ideal contactor, analytical equations can be derived that allow the partial pressure profiles within the contactor to be calculated. The effect of the sweep ratio (sweep flow rate/feed flow rate) and feed pressure on separation performance of the contactors has been calculated. In the final section of the paper, the performance of contactors fitted with membranes permeable to other components of the feed gas is described. & 2014 Elsevier B.V. All rights reserved.
Keywords: Membrane contactors CO2 capture Gas separation
1. Introduction This paper describes the operation of gas/gas membrane contactors. These are typically low-pressure devices in which a feed gas is circulated across one surface of a permeable membrane, and an approximately equal volume of another gas, at a similar pressure, is circulated countercurrently on the other side of the membrane. Permeation occurs because of the partial pressure difference between components in the feed and sweep gases. Most of this partial pressure difference occurs because of concentration rather than pressure differences across the membrane. This type of contactor has been commercialized for energy recovery devices in air conditioning and fuel cell humidity control applications [1–3]. More recently, these contactors have been suggested for use in carbon dioxide capture [4,5]. Most membrane gas separation processes do not use a permeate side sweep gas. In conventional processes, a feed gas mixture flows across the surface of a permselective membrane; a portion of the mixture permeates the membrane and is removed as lower pressure permeate gas. The remaining gas, depleted in the permeating components, is removed from the feed side of the membrane as a residue gas. One stream enters the membrane module (the feed), two streams leave (the residue and permeate).
n
Corresponding author. Tel.: þ 1 650 543 3344. E-mail address: [email protected] (P. Hao).
http://dx.doi.org/10.1016/j.memsci.2014.03.039 0376-7388/& 2014 Elsevier B.V. All rights reserved.
A few membrane processes have been developed in which a small flow of sweep gas is introduced on the permeate side of the membrane. This gas usually flows countercurrently to the incoming feed. Two streams enter the module (the feed and sweep) and two streams leave (the residue and permeateþ sweep). This type of sweep process has been used when the membrane selectivity is much higher than the pressure ratio across the membrane, and a small amount of an extremely permeable component must be removed. A well-known example is the removal of water vapor from compressed air, first commercialized in the 1990s [6,7]. In this process, the membrane performance is pressure ratio limited, and the separation can be much improved by using a small fraction of dry gas as a permeate side sweep to reduce the partial pressure of the permeating component (water) on the permeate side of the membrane. In these applications, the volume of sweep gas used is only a few percent of the volume of the feed gas to be separated. A few years ago, Membrane Technology and Research, Inc. (MTR) proposed using a gas/gas membrane contactor to separate carbon dioxide (CO2) from fossil fuel power plant flue gas [4,5]. If successfully developed, this could be an important membrane application. In this process, CO2-rich flue gas passes across the feed side of a membrane, while an approximately equal volume of air passes as a sweep gas on the membrane permeate side. In this way, the partial pressure of CO2 on the permeate side is maintained at a lower level than on the feed side. Because of this partial pressure difference, CO2 passes from the flue gas into the sweep air stream. If membranes are used that are very permeable to CO2,
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but relatively impermeable to oxygen and nitrogen, very little nitrogen passes from the flue gas into the sweep air and very little oxygen passes from the air sweep into the flue gas. Because the feed and permeate pressures are low, blowers are the only compression equipment needed to circulate the gases across the membrane. A useful separation is performed at a minimal energy cost. A block diagram illustrating the application of this device to CO2 capture in a coal-fired power plant is shown in Fig. 1. Air passing countercurrently to the flue gas strips CO2 out of the gas. The CO2-laden air is then used to burn coal in the power plant boiler. This combustion process is used to produce steam to drive a turbine and make electricity; it also generates a CO2-enriched flue gas. A portion of this flue gas is separated as a CO2-enriched stream by a conventional membrane unit. The remaining gas passes across the feed surface of the membrane contactor and becomes the CO2-depleted gas (2% CO2) that is discarded through the chimney. By using the membrane contactor, the CO2 concentration in the flue gas from the boiler can be enriched from the normal concentration of 10–13% CO2 to 20% CO2 or more. Enhancing the CO2 concentration of the flue gas from the coal combustor increases the efficiency of the selective CO2 purge step. A more concentrated CO2 purge is produced because only a portion of the CO2 must be removed in this step. The remaining CO2 is recycled by the membrane contactor. The use of a membrane contactor significantly reduces the cost of separating a CO2 concentrate stream from the flue gas. This process is under development by MTR as a potential CO2 capture technology. In this paper, a gas/gas contactor of the type shown in Fig. 1 is treated as a unit operation. The impacts of different process parameters on unit performance are examined. The paper is divided into two sections. In the first section, we will show calculations for an ideal contactor; that is, a contactor fitted with a membrane permeable to one of the components of the feed gas (CO2), but impermeable to all other components. We will also assume the component to be removed is present at a low concentration ( 1%) so that the volume change in the feed and sweep streams caused by permeation can be ignored. The properties of a gas/gas contactor will then be illustrated using this ideal device. In the second section of the paper, we will illustrate the complications that result when real membranes with limited selectivity are used and permeation of other components is possible. The changes in performance that occur when permeation through the membrane causes volume changes to the feed and sweep flows will also be examined. This type of contactor is closer to the type that would be used for the application shown in Fig. 1.
2. Ideal contactor performance The base case operating conditions for an ideal contactor that forms the starting point of this analysis are shown in Fig. 2. The base case contactor is assumed to have an area of 5000 m2, and contains a membrane having a CO2 permeance of 1000 gpu. The feed stream contains 1% CO2, and the sweep stream is pure nitrogen. The feed and sweep streams are both at atmospheric pressure. The device achieves 80% CO2 removal from the feed to the sweep gas when the feed and sweep flows are set at 1 m3(STP)/s. One concern with high permeance membranes of the type shown in Fig. 2 is that concentration polarization effects may occur in stagnant boundary layers on either side of the membrane. The problem is expected to be most significant on the side in contact with the microporous support layer of the composite membrane. This support creates a stagnant layer which is significantly thicker
Fig. 1. Block diagram illustrating the use of a selective membrane contactor to recycle CO2 to the boiler of a coal power plant. In this way, the concentration of CO2 in the flue gas exiting the boiler increases from 10–13% to 20% at very little energy cost [4].
Fig. 2. Base case conditions used in this paper for an ideal gas/gas membrane contactor.
than the gas boundary layers in the gas channels. The likelihood of concentration gradients forming in the stagnant layer can be estimated by calculating the Peclet number, Jvδ/D, where Jv is the actual gas velocity or volume flux in the layer, δ is the stagnant layer thickness and D is the gas diffusion coefficient in the stagnant layer gas at the stagnant layer pressure [8]. This dimensionless number represents the ratio of the convective transport Jv and the diffusive transport D/δ. When the Peclet number is large (Jv Z D/δ), the convective flux through the membrane cannot easily be balanced by diffusion in the boundary layer, and concentration gradients form in the boundary layers. When the Peclet number is small (Jv rD/δ), convection is easily balanced by diffusion in the boundary layer and significant concentration gradients do not form in the boundary layer. The CO2 permeance of the membranes shown in Fig. 2 is 1000 gpu (1000 10 6 cm3(STP)/cm2 s cmHg). Under typical operating conditions of the process in a power plant type of environment (1–2 bar feed, 1 bar permeate and 10% CO2 in the feed gas), the volume flux through the membrane is about 1.5 10 2 cm3(STP)/cm2 s. Assuming the stagnant layer is at atmospheric pressure, the superficial velocity through the microporous support in the layer is 1.5 10 2 cm/s. The actual velocity, Jv, will be higher because of the effects of porosity and tortuosity; we will assume here that the actual velocity is about six times higher and equal to 1.0 10 1 cm/s. Assuming the microporous support layer that separates the selective membrane layer from the well-mixed counter-flowing gas is 200 μm thick (δ), and taking the gas diffusion coefficient at atmospheric pressure to be 0.2 cm2/s, it follows that the permeate-side Peclet number Jvδ/D is 1 10 2. A Peclet number this small implies that diffusion is
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Fig. 3. CO2 partial pressures on the feed and sweep sides of the ideal base case membrane contactor shown in Fig. 2. The driving force for permeation is constant because the two flow rates are equal.
dominant over convection and that concentration gradients in the stagnant layer are small and can be ignored.
One of the most important parameters affecting the operation of a membrane contactor is the sweep ratio, defined as the volumetric flow of the inlet sweep gas divided by the volumetric flow of the inlet feed gas (both as standard m3/s, not actual m3/s).
2.1. Factors affecting ideal contactor performance One of the best ways to understand the influence of process operating conditions on contactor performance is to calculate the partial pressure difference between the gases on either side of the membrane. The equations required to make this possible are derived in an appendix to this paper. These equations have been formulated into an Excel program that allows the partial pressure on the feed and permeate side of the membrane to be calculated at any point. This program is given in the supplemental material to the paper. The results obtained using these equations, for the base case process shown in Fig. 2, are given in Fig. 3 below. The feed gas at a concentration of 1% CO2 enters on the feed side of the membrane at the left end of the module. An equal volume of nitrogen sweep gas enters on the permeate side of the membrane at the right end of the module. Because of the difference in partial pressure created across the membrane, CO2 permeates from the feed to the permeate side. In the base case process illustrated in Fig. 3, the flows on either side of the membrane are equal. This means an incremental flow of CO2 from the feed to the permeate side of the membrane causes a decrease in the feed side CO2, while simultaneously producing an equal increase in the CO2 concentration of the sweep gas on the other side of the membrane. The result (derived mathematically in Appendix 1) is that the partial pressure of CO2 decreases linearly on the feed side of the membrane and increases linearly on the counter-flowing sweep gas side. The difference between the feed and sweep side partial pressure is the driving force for CO2 permeation, and is equal at all points in the membrane module.
Sweep ratio ¼
Inlet sweep flow rate ðm3 ðSTPÞ=sÞ Inlet feed flow rate ðm3 ðSTPÞ=sÞ
ð1Þ
The definition of sweep ratio given in Eq. (1) is a reliable way of characterizing the ideal membrane contactor shown in Fig. 2, where only a small fraction of the feed and sweep gas flow permeate the membrane (the process stage-cut is small). In the second half of this paper, we will show a modified definition might be used when a significant volume flow takes place across the membrane. Fig. 4 shows the calculated partial pressure profiles within modules when the sweep flow is increased or decreased to produce a sweep ratio of 0.5 or 2.0. Consider first the case when the sweep ratio is 0.5, shown in Fig. 4(a). Because the volume of sweep gas is half that of the feed, only half of the CO2 in the feed can permeate, even when an infinitely permeable membrane is used. If more than half of the feed gas CO2 permeates the membrane, the sweep gas leaving the module would have a higher concentration than the feed gas entering. CO2 would then flow from the sweep to the feed. As Fig. 4(a) shows, a sweep ratio of 0.5 removes almost half of the CO2 from the feed, reducing the CO2 concentration of the feed to just a little over 0.5% CO2. Concurrently, the CO2 concentration in the sweep gas increases, reaching a little under 1.0% CO2 in the sweep gas leaving the module. The driving force for CO2 permeation is the difference in CO2 partial pressure (concentration) across the membrane, and as the figure shows, the driving force is highest at the incoming sweep end of the module. The bulk of CO2 permeation occurs at the sweep input end.
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Fig. 4. CO2 concentration profiles in the base case membrane module shown in Fig. 2, except that the sweep flow rate, and thus the sweep ratio, is changed. (a) Sweep flow rate 0.5 m3/s, sweep ratio 0.5: most CO2 permeation occurs at the incoming sweep end of the module. (b) Sweep flow rate 2.0 m3/s, sweep ratio 2.0: most CO2 permeation occurs at the incoming feed end of the module.
When the sweep ratio is 2.0, shown in Fig. 4(b), the situation is reversed. There is now more than enough sweep gas to remove all of the CO2 from the feed. With a membrane having the base case properties, the feed gas leaving the module contains less than 0.1% CO2. The permeated CO2 leaves with the sweep air at a concentration of just under 0.5% CO2. The driving force is highest at the incoming feed end of the module and the bulk of CO2 permeation occurs at the feed input end. An alternative way to show the effect of sweep ratio on CO2 removal from the feed is shown in Fig. 5. The calculations shown in Fig. 5 and those reported elsewhere in this paper were performed using a computer process simulator (ChemCad 6.3, Chemstations, Inc., Austin, TX), enhanced with differential element code for the membrane separation step, written at MTR. In the Fig. 5 calculation, the base case module is operated with various sweep gas flow rates to change the sweep ratio. The fractional removal of CO2 from the feed gas is calculated at each sweep ratio. Plots determined this way are shown for membranes with different CO2 permeances. The base case membrane has a CO2 permeance of 1000 gpu and the performance of this module (already illustrated in Figs. 3 and 4) is shown on the line marked CO2 permeance ¼1000 gpu. At a sweep ratio of 0.5, the fractional removal of this module is 49.6%; at a ratio of 1.0 (the base case), the removal is 80%; and at a sweep ratio of 2.0, the removal increases to 93.4%. Two limiting regions are shown in Fig. 5. The first limiting region is to the left of the bold line that shows the fractional CO2 removal achieved by an infinitely permeable membrane. This boundary is defined by Fractional removal ¼ Sweep ratio
ð2Þ
In pressure driven processes, two similar limiting regions are also known, governed by the pressure ratio of the processes and called the pressure ratio limited region and the selectivity limited
Fig. 5. Effect of sweep ratio on CO2 removal from the feed, calculated for membranes of different CO2 permeance. The feed flow rate is maintained constant at 1 m3/s, while the sweep flow rate is changed to adjust the sweep ratio. The base case membrane module (Fig. 2) is shown as a dot on the 1000 gpu membrane line. Two limiting regions are shown: one is in the region below a sweep ratio of 1.0, where the CO2 removal is limited at least in part by the sweep ratio, and the other is a region at higher sweep ratios where the CO2 removal is limited at least in part by the inability of the membranes to permeate sufficient CO2.
region [9]. The sweep ratio, like the pressure ratio, provides a link between the driving force, selectivity and separation. The boundary of the sweep ratio limited region can be derived from simple mass balance considerations. As the curves in Fig. 5 show, at a sweep ratio of 0.5, all membranes with a permeance
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Fig. 6. Feed and sweep concentration profiles within the ideal contactor (Fig. 2), operated with membranes having a permeance of 200 gpu. The sweep ratio is fixed at 100. Under these conditions, the exiting sweep gas contains very little CO2 ( o 0.01%) and the driving force for CO2 permeation reaches the maximum possible value.
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Fig. 7. Contactor membrane permeances required to achieve 50% and 80% CO2 removal as a function of sweep ratio for the ideal 5000 m2 contactor illustrated in Fig. 2.
above 1000 gpu produce essentially the same fractional CO2 removal; that is, very close to 0.5. Increasing the membrane permeance above 1000 gpu does not produce a higher CO2 removal. The contactor performance is limited by the sweep ratio. This limit occurs at all sweep ratios below 1.0. In this region, the maximum fractional removal is set by the sweep ratio, no matter how high the membrane permeance. A second limiting region is also shown in Fig. 5. This region, on the right-hand side of the figure, occurs when low membrane permeance limits the removal of CO2. Performance in this region is best explained by calculating the partial pressure on the feed and sweep side of the membrane. This calculation is shown in Fig. 6, for a membrane with a permeance of 200 gpu. The sweep ratio is set at 100. Because of the very high sweep ratio, the partial pressure of CO2 on the sweep side of the module is almost zero at all points along the module. The driving force for permeation is therefore at its maximum value and cannot be further improved by increasing the sweep flow rate. The fractional removal of CO2 from the feed is then also at its maximum value, set by the permeation rate of CO2 through the membrane. In the example illustrated, a membrane with a permeance of 200 gpu achieves a limiting maximum removal (xmax) of 55%. The limiting (maximum possible) removal of CO2 at high sweep ratios is linked to the contactor membrane permeance, area and the operating conditions of the device. In Appendix 2 at the end of this paper, it is shown that the term xmax is given by the expression:
membrane permeance required increases asymptotically. In this region, the separation reaches the sweep ratio limit set by Eq. (2). Similarly at high sweep ratios, the membrane permeance required to achieve 80% CO2 removal asymptotically approaches a limiting value of 480 gpu. The plot for 50% CO2 removal has the same form. The sweep ratio limit is at a ratio of 0.5, and the limiting permeance is at 195 gpu. Thus far, the discussion of contactor performance has been limited to units operating with equal pressures on either side of the membrane. The driving force for permeation in these units is only due to the concentration differences between components of the feed and sweep gases. However, the concentration driving forces can be enhanced by creating a pressure difference across the membrane. This effect is illustrated in Fig. 8, which compares the partial pressure driving force profiles for the base case shown in Fig. 3, and the same device operating at a feed pressure of 2 bar. When the pressure is equal on either side of the membrane (1 bar/1 bar) [Fig. 8(a)], the partial pressure driving force feed-tosweep is uniform across the module at 0.002 bar. However, when the same volume of feed gas is compressed to 2 bar [Fig. 8(b)], the partial pressure driving force is significantly higher. At the feed end of the module, the driving force (feed-to-sweep) increases fivefold to 0.011 bar, and then decreases steadily as feed CO2 concentration falls. The net result is to increase CO2 removal from 80% to 95%.
! ðP CO2 =lÞpft A xmax ¼ 1 exp Ff
In the description of contactor performance given thus far, we have made two significant assumptions. First, the membranes are permeable to one component and impermeable to all others. Second, the volume of gas permeating the membrane is small compared to the feed flow. These assumptions are realistic for some contactor applications. For example, in many dehydration applications, the permeability of water can be several-hundredfold higher than that of the other components in the feed. Also, the feed often contains only 1–2% water, so the volume flow through the membrane is small. However, in other applications, including CO2 separation from flue gas, the simplifying assumptions are no longer valid, so the separation performance will deviate from the ideal contactor behavior described thus far. The consequences of these effects are described below. For this section of the paper, we will use a new base case contactor operating under the conditions shown in Fig. 9. Comparing this case to the ideal base case (Fig. 2):
ð3Þ
where ðP CO2 =lÞ is the membrane permeance, ptt is the total feed pressure of the contactor, A is the contactor surface area and Ff is the feed volume flow rate (STP) to the contactor. One final way to illustrate this interaction of sweep ratio and permeance is to replot the data in Fig. 5 as a plot of permeance against sweep ratio for various levels of CO2 removal. Two scenarios are shown in Fig. 7, one for 80% CO2 removal and the other for 50% removal. On the line marked 80% removal, the base case is marked as a solid point (black circle) at a permeance of 1000 gpu and a sweep ratio of 1.0. Increasing the permeance of the membrane used in the base case device above 1000 gpu allows lower sweep ratios to be used while still reaching the target of 80% removal. However, as the sweep ratio approaches 0.8, the
2.2. Non-ideal contactors
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Fig. 8. Effect of increasing the feed side pressure on the partial pressure profiles through the base case membrane contactor. Increasing the feed pressure from 1 bar [Figs. 8 (a)] to 2 bar [Fig. 8(b)] increases the driving force (partial pressure difference, feed-to-sweep) fivefold at the feed end of the module. The fractional CO2 removal achieved with the same size module then increases from 80% to 95%.
Fig. 9. Non-ideal base case membrane contactor.
The concentration of CO2 in the feed gas has been increased tenfold.
The sweep gas is air containing 21% oxygen. The membrane still has a CO2 permeance of 1000 gpu, but is now also permeable to nitrogen (25 gpu) and oxygen (50 gpu). The permeances of these membranes are comparable to membranes currently available for CO2 separations at industrial operating conditions. Comparing the new base case contactor performance assumptions in Fig. 9 with the ideal contactor in Fig. 2 shows three main differences. First, the definition of the sweep ratio used in Eq. (1) for the ideal contactor no longer reflects the reality of the new contactor. Using the Eq. (1) definition, the contactor has a sweep ratio of 1.0 [sweep flow rate 1 m3(STP/s) and feed flow 1 m3(STP/ s)], but at the feed end of the contactor, the sweep-to-feed ratio is 1.08 (m3/s)/1.0 (m3/s) or 1.08, while at the sweep end of the contactor the ratio is 1.0 (m3/s)/0.92 (m3/s), or 1.09. Defining the sweep ratio as the average of the inlet and exit sides of the sweep ratio is clearly a better method to use than the ratio of the inlet sweep and feed flows. Second, because of the volume flow through the membrane, 80% CO2 removal from the feed means the residue gas concentration is 2.1% CO2. The membrane area required to achieve the same fractional removal is then slightly less, at 4800 m2 rather than 5000 m2. Finally, some oxygen from the sweep side permeates into the feed side and some nitrogen from the feed permeates to the sweep. This effect is described below.
Fig. 10. Calculated oxygen concentration of sweep gas in a non-ideal membrane contactor used to remove 80% CO2 from flue gas with a countercurrent air sweep stream. The performance obtained with different hypothetical membranes is plotted as a function of the flue gas feed pressure. The sweep ratio is maintained at 1.0 in all the calculations shown.
3. The effect of membrane selectivity The calculations for the ideal contactor described in the first section of this paper assumed the contactor membrane was permeable to CO2 and impermeable to all other gases. Fig. 9 shows what might be expected when a membrane with more realistic properties is used. The membrane still achieves the required removal of CO2 from the feed, but a significant amount of nitrogen also permeates with the CO2 to the sweep, and some oxygen back permeates from the sweep into the feed. A consequence of these additional flows is that when this contactor is used in the CO2 separation scheme illustrated in Fig. 1, the oxygen concentration in the air sweep sent to the coal boiler decreases from 21% to approximately 18%. Fortunately, an oxygen level of 18% in the boiler air stream will still provide efficient combustion, although minor changes to the boiler burner may be required [10]. Fig. 10 shows a plot of the oxygen concentration in the sweep gas leaving the contactor on its way to the boiler as a function of feed gas pressure. The performance profiles of several different hypothetical membranes are shown. The CO2 flue gas feed pressure is varied from a pressure of 1 bar (the base case shown in Fig. 9) to a feed pressure of 3 bar. As described earlier in the
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discussion of Fig. 8, increasing the feed pressure has a very significant impact on the driving force for CO2 permeation and contactor performance. This means the membrane area required to perform the target separation decreases from 4800 m2 at a feed gas pressure of 1 bar (the base case) to 850 m2 at a feed gas pressure of 3 bar. The top line in Fig. 10 is a reference line showing the normal oxygen concentration of air (21%). The next line down, marked CO2 ¼1000 gpu, N2 ¼0 gpu, O2 ¼0 gpu, is the calculated performance of a contactor fitted with a membrane that permeates CO2, but is impermeable to nitrogen and oxygen. The oxygen concentration in the sweep air leaving a contactor fitted with this membrane is 19.3%. This decrease in oxygen concentration from 21% to 19.3% is due to the dilution effect of CO2 permeating the membrane into the sweep gas, thus increasing its volume. The next line in Fig. 10, marked CO2 ¼1000 gpu, N2 ¼25 gpu, O2 ¼0 gpu, shows the dilution effect due to permeation of both CO2 and nitrogen from the feed into the sweep gas. The nitrogen contribution to dilution increases slightly as the feed pressure increases, reflecting the effect of pressure on the driving force for nitrogen permeation. Finally, the bottom line in Fig. 10, marked CO2 ¼1000 gpu, N2 ¼25 gpu, O2 ¼ 50 gpu, shows the sweep gas concentration when the base case membrane from Fig. 9 is used. The difference between this line and the one immediately above it is the contribution of oxygen loss from the sweep gas to the feed. This loss is small compared to the combined dilution effects of CO2 and nitrogen, and decreases as the feed pressure increases because the membrane area needed to perform the target separation decreases with increasing feed pressure.
4. Conclusions In this paper, we have shown the effect of operating parameters on the performance of a gas/gas membrane contactor used for CO2 removal. These devices are not in common use today, but could find future use in CO2 capture processes. The most important operating parameters affecting the gas/gas contactor performance are the sweep gas-to-feed gas volume ratio, the relative pressures of the feed and sweep gases, and the permeance and selectivity of the membranes used.
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Starting from the expression for gas permeation of individual components1: Ji ¼
Pi f ðp psi Þ ℓ i
ðA1Þ
we obtain the following equation for the partial pressure gradients: ! f dJ i P i dpi dpsi ¼ ðA2Þ dа ℓ dа dа The partial pressure gradients can also be obtained from the mass balance in each differential element: J i da ¼
J i da ¼
dpfi pf f dp or ¼ Ji t i f d а Ff pt
ðA3Þ
dps Fs s ps dp or i ¼ J i t ps i dа Fs
ðA4Þ
Ff
Combining Eqs. (A2)–(A4) gives ! dJ i P i pst pft ¼ J dа ℓ i F s F f
ðA5Þ
Integrating Eq. (A5) over the membrane area, the expression for the permeate flux as a function of the membrane area then gives f
J i;a ¼ J i;0 eP i =ℓððpt =F s Þ ðpt =F f ÞÞa ¼ J i;0 eba s
with P ps pf b¼ i t t ℓ Fs Ff
ðA6Þ
! ðA7Þ
Inserting Eq. (A6) into Eqs. (A3) and (A4) and integrating over the membrane area then give the following expression for the partial pressures in the two exit streams: pfi;A ¼ pfi;0 þ J i;0
psi;0 ¼
pft 1 ebA Ff b
psi;A pfi;0 P i =ℓpst =F s ðð1 ebA Þ=bÞ 1 ðP i =ℓÞpst =F s ðð1 ebA =bÞ
ðA8Þ
ðA9Þ
Combining with following equation, Pi f ðp ps i;o Þ ℓ i;0
Acknowledgments
J i;0 ¼
This work was performed as part of a research program supported by the U.S. Department of Energy Project no. DE-FE0007553.
we obtain for the partial pressure in the sweep outlet stream: psi;0 ¼
psi;A pfi;0 P i =ℓpst =F s ðð1 ebA Þ=bÞ 1 ðP i =ℓÞpst =F s ðð1 ebA Þ=bÞ
ðA10Þ
ðA11Þ
and for the partial pressure in the feed outlet stream: Appendix 1 Equations used to calculate the partial pressure difference between the gases on either side of a gas/gas membrane contactor (Fig. A1).
pfi;A ¼ pi;0 f
pft =F f s ðp psi;A Þ pst =F s i;0
ðA12Þ
An Excel file based on these equations, which calculates the pressure profiles and local permeate fluxes, is attached in the supplementary material to this paper. The graphics in the file will auto-adjust if the inputs are changed.
Appendix 2 The limiting (maximum possible) removal of CO2 is linked to the contactor membrane permeance, membrane area and the Fig. A1. Model for the countercurrent sweep module. Pressure drops in the feed and sweep channels are ignored. The permeating compound is assumed to be present at a low concentration, which means that the feed and sweep flow rates can be assumed to be constant throughout the module.
1 In the equations that follow the superscripts f and s represent the feed and sweep side of the membrane, and the terms 0 and A represents positions along the membrane module from the feed entrance (0) to the feed exit (A).
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operating conditions of the device. The CO2 removal (x) is the ratio of the amount of CO2 permeating the membrane divided by the amount of the CO2 that enters the contactor; that is, RA J CO2 dA ðA13Þ x¼ 0 F f nCO2 where J CO2 is the flux through the membrane at any point in the contactor area A. Ff is the volumetric feed flow of gas into the contactor at standard temperature and pressure conditions (STP), and nCO2 is the molar fraction of CO2 in the feed gas. The maximum CO2 removed (xmax) is obtained at infinite sweep ratio, in which case the membrane flux at any point is proportional to membrane permeance ðP CO2 =lÞ and the feed side CO2 partial pressure pfCO2 (the permeate side CO2 partial pressure is close to zero and can be ignored). Eq. (A13) can then be written2 R0 f A ðP CO2 =lÞpCO2 dA xmax ¼ ðA14Þ F f nCO2
Jv J CO2 i nCO2 ðP CO2 =lÞ pfCO2 ;0 pfCO2 ;A pft xmax
and since nCO2 ¼
pfCO2 ;0
ðA15Þ
pft
where pft is the total pressure on the feed side of the module, R0 pft ðP CO2 =lÞ A pfCO2 dA xmax ¼ ðA16Þ F f pCO2 ;0 f R0 The integral of the partial pressure driving force A pfCO2 dA has the familiar form for the log mean and Eq. (A16) can become xmax ¼
pft ðP CO2 =lÞA F f pfCO2 ;0
U
pfCO2 ;0 pfCO2 ;A lnðpfCO2 ;0 =ppfCO2 ;A Þ
ðA17Þ
Because the fractional removal (xmax) can be also be written as xmax ¼
pfCO2 ;0 pfCO2 ;A
ðA18Þ
pfCO2 ;0
Combining Eqs. (A17) and (A18) gives 0 1 pfCO2 ;0 P CO2 =l pft A @ A ¼ ¼ lnð1 xmax Þ ln f Ff p
ðA19Þ
CO2 ;A
which can be rearranged to xmax ¼ 1 exp
ðP CO2 =lÞ U pft UA Ff
! ðA20Þ
This expression shows the dependence of the limiting value for CO2 removal on the permeance, pressure, area and feed flow rate of an ideal contactor.
Nomenclature A Ff
Fs
actual gas velocity through the membrane support, cm3/cm2 s carbon dioxide flux through the membrane at any point in the contactor, cm3(STP)/cm2 s ith component in the feed or sweep side. molar fraction of CO2 in the feed gas CO2 permeance, gpu [1 10 6 cm3(STP)/ (cm2 s cmHg)] CO2 partial pressure at the feed entrance of the module (point 0), cmHg CO2 partial pressure at the residue exit end of the module (point A), cmHg total feed pressure, cmHg maximum possible fractional removal of a component from the feed gas, that is, the ratio of the amount of a gas permeating the membrane divided by the amount of the gas that enters the contactor. For this paper, xmax is discussed and calculated only for CO2.
area of the membrane contactor, m2 volumetric feed flow of gas into the contactor at standard temperature and pressure conditions, m3(STP)/s volumetric sweep flow of gas into the contactor at standard temperature and pressure conditions, m3(STP)/s
2 In the equations that follow the superscripts f and s represent the feed and sweep side of the membrane, and the terms 0 and A represents positions along the membrane module from the feed entrance (0) to the feed exit (A).
References [1] D. Chen, W. Li, H. Peng, An experimental study and model validation of a membrane humidifier for PEM fuel cell humidification control, J. Power Sources 180 (2008) 461–467. [2] K. Mahmud, G.I. Mahmood, C.J. Simonson, R.W. Besant, Performance testing of a counter-cross-flow run-around membrane energy exchanger (RAMEE) system for HVAC applications, Energy Build. 42 (2010) 1139–1147. [3] Y. Kusano, H. Shimanuki, T. Katagiri, M. Suziki, Humidifiers, US patent 6,659,433, Dec 2003. [4] T.C. Merkel, H. Lin, X. Wei, R.W. Baker, Power plant post-combustion carbon dioxide capture: an opportunity for membranes, J. Membr. Sci. 359 (2010) 126–139. [5] T.C. Merkel, X. Wei, Z. He, L.S. White, J.G. Wijmans, R.W. Baker, Selective exhaust gas recycle with membranes for CO2 capture from natural gas combined cycle power plants, Ind. Eng. Chem. Res. 52 (2013) 1150–1159. [6] K.L. Wang, S.H. McCray, D.D. Newbold, E.L. Cussler, Hollow fiber air drying, J. Membr. Sci. 72 (1992) 231–244. [7] H. Lin, S.M. Thompson, A. Serbanescu-Martin, J.G. Wijmans, K.D. Amo, K. A. Lokhandwala, B.T. Low, T.C. Merkel, Dehydration of natural gas using membranes, Part II: sweep/countercurrent design and field test, J. Membr. Sci. 432 (2013) 106–114. [8] P.L.T. Brian, in: U. Merten (Ed.), Mass Transport in Reverse Osmosis in Desalination by Reverse Osmosis, MIT Press, Cambridge, MA, 1966, p. 161. [9] R.W. Baker, J.G. Wijmans, Molecular separation of organic vapor from gas streams, in: D.R. Paul, Y. Yampolskii (Eds.), Polymeric Gas Separation Membranes, CRC Press, Boca Raton, FL., 1994. [10] T.C. Merkel, Pilot Testing of a Membrane System for Post-Combustion CO2 Capture, DOE NETL CO2 Capture Technology Meeting Presentation, Pittsburg, PA, July 10, 2013.
Contents lists available at ScienceDirect
Journal of Membrane Science journal homepage: www.elsevier.com/locate/memsci
Gas/gas membrane contactors – An emerging membrane unit operation Pingjiao Hao n, J.G. Wijmans, Jay Kniep, Richard W. Baker Membrane Technology and Research, Inc., 39630 Eureka Drive, Newark, CA 94560, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 17 January 2014 Received in revised form 13 March 2014 Accepted 17 March 2014 Available online 21 March 2014
Gas/gas membrane contactors are devices in which a feed gas and a sweep gas are circulated on either side of a membrane. The pressures of the two gas streams are often approximately equivalent, so the principal driving force for permeation is the concentration difference between the feed and sweep gas components. This type of contactor has been commercialized for energy recovery devices in air conditioning applications. More recently, these contactors have been suggested for use in carbon dioxide capture and sequestration. In this paper, the performance of an ideal contactor using perfectly selective membranes is examined. For this type of ideal contactor, analytical equations can be derived that allow the partial pressure profiles within the contactor to be calculated. The effect of the sweep ratio (sweep flow rate/feed flow rate) and feed pressure on separation performance of the contactors has been calculated. In the final section of the paper, the performance of contactors fitted with membranes permeable to other components of the feed gas is described. & 2014 Elsevier B.V. All rights reserved.
Keywords: Membrane contactors CO2 capture Gas separation
1. Introduction This paper describes the operation of gas/gas membrane contactors. These are typically low-pressure devices in which a feed gas is circulated across one surface of a permeable membrane, and an approximately equal volume of another gas, at a similar pressure, is circulated countercurrently on the other side of the membrane. Permeation occurs because of the partial pressure difference between components in the feed and sweep gases. Most of this partial pressure difference occurs because of concentration rather than pressure differences across the membrane. This type of contactor has been commercialized for energy recovery devices in air conditioning and fuel cell humidity control applications [1–3]. More recently, these contactors have been suggested for use in carbon dioxide capture [4,5]. Most membrane gas separation processes do not use a permeate side sweep gas. In conventional processes, a feed gas mixture flows across the surface of a permselective membrane; a portion of the mixture permeates the membrane and is removed as lower pressure permeate gas. The remaining gas, depleted in the permeating components, is removed from the feed side of the membrane as a residue gas. One stream enters the membrane module (the feed), two streams leave (the residue and permeate).
n
Corresponding author. Tel.: þ 1 650 543 3344. E-mail address: [email protected] (P. Hao).
http://dx.doi.org/10.1016/j.memsci.2014.03.039 0376-7388/& 2014 Elsevier B.V. All rights reserved.
A few membrane processes have been developed in which a small flow of sweep gas is introduced on the permeate side of the membrane. This gas usually flows countercurrently to the incoming feed. Two streams enter the module (the feed and sweep) and two streams leave (the residue and permeateþ sweep). This type of sweep process has been used when the membrane selectivity is much higher than the pressure ratio across the membrane, and a small amount of an extremely permeable component must be removed. A well-known example is the removal of water vapor from compressed air, first commercialized in the 1990s [6,7]. In this process, the membrane performance is pressure ratio limited, and the separation can be much improved by using a small fraction of dry gas as a permeate side sweep to reduce the partial pressure of the permeating component (water) on the permeate side of the membrane. In these applications, the volume of sweep gas used is only a few percent of the volume of the feed gas to be separated. A few years ago, Membrane Technology and Research, Inc. (MTR) proposed using a gas/gas membrane contactor to separate carbon dioxide (CO2) from fossil fuel power plant flue gas [4,5]. If successfully developed, this could be an important membrane application. In this process, CO2-rich flue gas passes across the feed side of a membrane, while an approximately equal volume of air passes as a sweep gas on the membrane permeate side. In this way, the partial pressure of CO2 on the permeate side is maintained at a lower level than on the feed side. Because of this partial pressure difference, CO2 passes from the flue gas into the sweep air stream. If membranes are used that are very permeable to CO2,
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but relatively impermeable to oxygen and nitrogen, very little nitrogen passes from the flue gas into the sweep air and very little oxygen passes from the air sweep into the flue gas. Because the feed and permeate pressures are low, blowers are the only compression equipment needed to circulate the gases across the membrane. A useful separation is performed at a minimal energy cost. A block diagram illustrating the application of this device to CO2 capture in a coal-fired power plant is shown in Fig. 1. Air passing countercurrently to the flue gas strips CO2 out of the gas. The CO2-laden air is then used to burn coal in the power plant boiler. This combustion process is used to produce steam to drive a turbine and make electricity; it also generates a CO2-enriched flue gas. A portion of this flue gas is separated as a CO2-enriched stream by a conventional membrane unit. The remaining gas passes across the feed surface of the membrane contactor and becomes the CO2-depleted gas (2% CO2) that is discarded through the chimney. By using the membrane contactor, the CO2 concentration in the flue gas from the boiler can be enriched from the normal concentration of 10–13% CO2 to 20% CO2 or more. Enhancing the CO2 concentration of the flue gas from the coal combustor increases the efficiency of the selective CO2 purge step. A more concentrated CO2 purge is produced because only a portion of the CO2 must be removed in this step. The remaining CO2 is recycled by the membrane contactor. The use of a membrane contactor significantly reduces the cost of separating a CO2 concentrate stream from the flue gas. This process is under development by MTR as a potential CO2 capture technology. In this paper, a gas/gas contactor of the type shown in Fig. 1 is treated as a unit operation. The impacts of different process parameters on unit performance are examined. The paper is divided into two sections. In the first section, we will show calculations for an ideal contactor; that is, a contactor fitted with a membrane permeable to one of the components of the feed gas (CO2), but impermeable to all other components. We will also assume the component to be removed is present at a low concentration ( 1%) so that the volume change in the feed and sweep streams caused by permeation can be ignored. The properties of a gas/gas contactor will then be illustrated using this ideal device. In the second section of the paper, we will illustrate the complications that result when real membranes with limited selectivity are used and permeation of other components is possible. The changes in performance that occur when permeation through the membrane causes volume changes to the feed and sweep flows will also be examined. This type of contactor is closer to the type that would be used for the application shown in Fig. 1.
2. Ideal contactor performance The base case operating conditions for an ideal contactor that forms the starting point of this analysis are shown in Fig. 2. The base case contactor is assumed to have an area of 5000 m2, and contains a membrane having a CO2 permeance of 1000 gpu. The feed stream contains 1% CO2, and the sweep stream is pure nitrogen. The feed and sweep streams are both at atmospheric pressure. The device achieves 80% CO2 removal from the feed to the sweep gas when the feed and sweep flows are set at 1 m3(STP)/s. One concern with high permeance membranes of the type shown in Fig. 2 is that concentration polarization effects may occur in stagnant boundary layers on either side of the membrane. The problem is expected to be most significant on the side in contact with the microporous support layer of the composite membrane. This support creates a stagnant layer which is significantly thicker
Fig. 1. Block diagram illustrating the use of a selective membrane contactor to recycle CO2 to the boiler of a coal power plant. In this way, the concentration of CO2 in the flue gas exiting the boiler increases from 10–13% to 20% at very little energy cost [4].
Fig. 2. Base case conditions used in this paper for an ideal gas/gas membrane contactor.
than the gas boundary layers in the gas channels. The likelihood of concentration gradients forming in the stagnant layer can be estimated by calculating the Peclet number, Jvδ/D, where Jv is the actual gas velocity or volume flux in the layer, δ is the stagnant layer thickness and D is the gas diffusion coefficient in the stagnant layer gas at the stagnant layer pressure [8]. This dimensionless number represents the ratio of the convective transport Jv and the diffusive transport D/δ. When the Peclet number is large (Jv Z D/δ), the convective flux through the membrane cannot easily be balanced by diffusion in the boundary layer, and concentration gradients form in the boundary layers. When the Peclet number is small (Jv rD/δ), convection is easily balanced by diffusion in the boundary layer and significant concentration gradients do not form in the boundary layer. The CO2 permeance of the membranes shown in Fig. 2 is 1000 gpu (1000 10 6 cm3(STP)/cm2 s cmHg). Under typical operating conditions of the process in a power plant type of environment (1–2 bar feed, 1 bar permeate and 10% CO2 in the feed gas), the volume flux through the membrane is about 1.5 10 2 cm3(STP)/cm2 s. Assuming the stagnant layer is at atmospheric pressure, the superficial velocity through the microporous support in the layer is 1.5 10 2 cm/s. The actual velocity, Jv, will be higher because of the effects of porosity and tortuosity; we will assume here that the actual velocity is about six times higher and equal to 1.0 10 1 cm/s. Assuming the microporous support layer that separates the selective membrane layer from the well-mixed counter-flowing gas is 200 μm thick (δ), and taking the gas diffusion coefficient at atmospheric pressure to be 0.2 cm2/s, it follows that the permeate-side Peclet number Jvδ/D is 1 10 2. A Peclet number this small implies that diffusion is
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Fig. 3. CO2 partial pressures on the feed and sweep sides of the ideal base case membrane contactor shown in Fig. 2. The driving force for permeation is constant because the two flow rates are equal.
dominant over convection and that concentration gradients in the stagnant layer are small and can be ignored.
One of the most important parameters affecting the operation of a membrane contactor is the sweep ratio, defined as the volumetric flow of the inlet sweep gas divided by the volumetric flow of the inlet feed gas (both as standard m3/s, not actual m3/s).
2.1. Factors affecting ideal contactor performance One of the best ways to understand the influence of process operating conditions on contactor performance is to calculate the partial pressure difference between the gases on either side of the membrane. The equations required to make this possible are derived in an appendix to this paper. These equations have been formulated into an Excel program that allows the partial pressure on the feed and permeate side of the membrane to be calculated at any point. This program is given in the supplemental material to the paper. The results obtained using these equations, for the base case process shown in Fig. 2, are given in Fig. 3 below. The feed gas at a concentration of 1% CO2 enters on the feed side of the membrane at the left end of the module. An equal volume of nitrogen sweep gas enters on the permeate side of the membrane at the right end of the module. Because of the difference in partial pressure created across the membrane, CO2 permeates from the feed to the permeate side. In the base case process illustrated in Fig. 3, the flows on either side of the membrane are equal. This means an incremental flow of CO2 from the feed to the permeate side of the membrane causes a decrease in the feed side CO2, while simultaneously producing an equal increase in the CO2 concentration of the sweep gas on the other side of the membrane. The result (derived mathematically in Appendix 1) is that the partial pressure of CO2 decreases linearly on the feed side of the membrane and increases linearly on the counter-flowing sweep gas side. The difference between the feed and sweep side partial pressure is the driving force for CO2 permeation, and is equal at all points in the membrane module.
Sweep ratio ¼
Inlet sweep flow rate ðm3 ðSTPÞ=sÞ Inlet feed flow rate ðm3 ðSTPÞ=sÞ
ð1Þ
The definition of sweep ratio given in Eq. (1) is a reliable way of characterizing the ideal membrane contactor shown in Fig. 2, where only a small fraction of the feed and sweep gas flow permeate the membrane (the process stage-cut is small). In the second half of this paper, we will show a modified definition might be used when a significant volume flow takes place across the membrane. Fig. 4 shows the calculated partial pressure profiles within modules when the sweep flow is increased or decreased to produce a sweep ratio of 0.5 or 2.0. Consider first the case when the sweep ratio is 0.5, shown in Fig. 4(a). Because the volume of sweep gas is half that of the feed, only half of the CO2 in the feed can permeate, even when an infinitely permeable membrane is used. If more than half of the feed gas CO2 permeates the membrane, the sweep gas leaving the module would have a higher concentration than the feed gas entering. CO2 would then flow from the sweep to the feed. As Fig. 4(a) shows, a sweep ratio of 0.5 removes almost half of the CO2 from the feed, reducing the CO2 concentration of the feed to just a little over 0.5% CO2. Concurrently, the CO2 concentration in the sweep gas increases, reaching a little under 1.0% CO2 in the sweep gas leaving the module. The driving force for CO2 permeation is the difference in CO2 partial pressure (concentration) across the membrane, and as the figure shows, the driving force is highest at the incoming sweep end of the module. The bulk of CO2 permeation occurs at the sweep input end.
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Fig. 4. CO2 concentration profiles in the base case membrane module shown in Fig. 2, except that the sweep flow rate, and thus the sweep ratio, is changed. (a) Sweep flow rate 0.5 m3/s, sweep ratio 0.5: most CO2 permeation occurs at the incoming sweep end of the module. (b) Sweep flow rate 2.0 m3/s, sweep ratio 2.0: most CO2 permeation occurs at the incoming feed end of the module.
When the sweep ratio is 2.0, shown in Fig. 4(b), the situation is reversed. There is now more than enough sweep gas to remove all of the CO2 from the feed. With a membrane having the base case properties, the feed gas leaving the module contains less than 0.1% CO2. The permeated CO2 leaves with the sweep air at a concentration of just under 0.5% CO2. The driving force is highest at the incoming feed end of the module and the bulk of CO2 permeation occurs at the feed input end. An alternative way to show the effect of sweep ratio on CO2 removal from the feed is shown in Fig. 5. The calculations shown in Fig. 5 and those reported elsewhere in this paper were performed using a computer process simulator (ChemCad 6.3, Chemstations, Inc., Austin, TX), enhanced with differential element code for the membrane separation step, written at MTR. In the Fig. 5 calculation, the base case module is operated with various sweep gas flow rates to change the sweep ratio. The fractional removal of CO2 from the feed gas is calculated at each sweep ratio. Plots determined this way are shown for membranes with different CO2 permeances. The base case membrane has a CO2 permeance of 1000 gpu and the performance of this module (already illustrated in Figs. 3 and 4) is shown on the line marked CO2 permeance ¼1000 gpu. At a sweep ratio of 0.5, the fractional removal of this module is 49.6%; at a ratio of 1.0 (the base case), the removal is 80%; and at a sweep ratio of 2.0, the removal increases to 93.4%. Two limiting regions are shown in Fig. 5. The first limiting region is to the left of the bold line that shows the fractional CO2 removal achieved by an infinitely permeable membrane. This boundary is defined by Fractional removal ¼ Sweep ratio
ð2Þ
In pressure driven processes, two similar limiting regions are also known, governed by the pressure ratio of the processes and called the pressure ratio limited region and the selectivity limited
Fig. 5. Effect of sweep ratio on CO2 removal from the feed, calculated for membranes of different CO2 permeance. The feed flow rate is maintained constant at 1 m3/s, while the sweep flow rate is changed to adjust the sweep ratio. The base case membrane module (Fig. 2) is shown as a dot on the 1000 gpu membrane line. Two limiting regions are shown: one is in the region below a sweep ratio of 1.0, where the CO2 removal is limited at least in part by the sweep ratio, and the other is a region at higher sweep ratios where the CO2 removal is limited at least in part by the inability of the membranes to permeate sufficient CO2.
region [9]. The sweep ratio, like the pressure ratio, provides a link between the driving force, selectivity and separation. The boundary of the sweep ratio limited region can be derived from simple mass balance considerations. As the curves in Fig. 5 show, at a sweep ratio of 0.5, all membranes with a permeance
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Fig. 6. Feed and sweep concentration profiles within the ideal contactor (Fig. 2), operated with membranes having a permeance of 200 gpu. The sweep ratio is fixed at 100. Under these conditions, the exiting sweep gas contains very little CO2 ( o 0.01%) and the driving force for CO2 permeation reaches the maximum possible value.
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Fig. 7. Contactor membrane permeances required to achieve 50% and 80% CO2 removal as a function of sweep ratio for the ideal 5000 m2 contactor illustrated in Fig. 2.
above 1000 gpu produce essentially the same fractional CO2 removal; that is, very close to 0.5. Increasing the membrane permeance above 1000 gpu does not produce a higher CO2 removal. The contactor performance is limited by the sweep ratio. This limit occurs at all sweep ratios below 1.0. In this region, the maximum fractional removal is set by the sweep ratio, no matter how high the membrane permeance. A second limiting region is also shown in Fig. 5. This region, on the right-hand side of the figure, occurs when low membrane permeance limits the removal of CO2. Performance in this region is best explained by calculating the partial pressure on the feed and sweep side of the membrane. This calculation is shown in Fig. 6, for a membrane with a permeance of 200 gpu. The sweep ratio is set at 100. Because of the very high sweep ratio, the partial pressure of CO2 on the sweep side of the module is almost zero at all points along the module. The driving force for permeation is therefore at its maximum value and cannot be further improved by increasing the sweep flow rate. The fractional removal of CO2 from the feed is then also at its maximum value, set by the permeation rate of CO2 through the membrane. In the example illustrated, a membrane with a permeance of 200 gpu achieves a limiting maximum removal (xmax) of 55%. The limiting (maximum possible) removal of CO2 at high sweep ratios is linked to the contactor membrane permeance, area and the operating conditions of the device. In Appendix 2 at the end of this paper, it is shown that the term xmax is given by the expression:
membrane permeance required increases asymptotically. In this region, the separation reaches the sweep ratio limit set by Eq. (2). Similarly at high sweep ratios, the membrane permeance required to achieve 80% CO2 removal asymptotically approaches a limiting value of 480 gpu. The plot for 50% CO2 removal has the same form. The sweep ratio limit is at a ratio of 0.5, and the limiting permeance is at 195 gpu. Thus far, the discussion of contactor performance has been limited to units operating with equal pressures on either side of the membrane. The driving force for permeation in these units is only due to the concentration differences between components of the feed and sweep gases. However, the concentration driving forces can be enhanced by creating a pressure difference across the membrane. This effect is illustrated in Fig. 8, which compares the partial pressure driving force profiles for the base case shown in Fig. 3, and the same device operating at a feed pressure of 2 bar. When the pressure is equal on either side of the membrane (1 bar/1 bar) [Fig. 8(a)], the partial pressure driving force feed-tosweep is uniform across the module at 0.002 bar. However, when the same volume of feed gas is compressed to 2 bar [Fig. 8(b)], the partial pressure driving force is significantly higher. At the feed end of the module, the driving force (feed-to-sweep) increases fivefold to 0.011 bar, and then decreases steadily as feed CO2 concentration falls. The net result is to increase CO2 removal from 80% to 95%.
! ðP CO2 =lÞpft A xmax ¼ 1 exp Ff
In the description of contactor performance given thus far, we have made two significant assumptions. First, the membranes are permeable to one component and impermeable to all others. Second, the volume of gas permeating the membrane is small compared to the feed flow. These assumptions are realistic for some contactor applications. For example, in many dehydration applications, the permeability of water can be several-hundredfold higher than that of the other components in the feed. Also, the feed often contains only 1–2% water, so the volume flow through the membrane is small. However, in other applications, including CO2 separation from flue gas, the simplifying assumptions are no longer valid, so the separation performance will deviate from the ideal contactor behavior described thus far. The consequences of these effects are described below. For this section of the paper, we will use a new base case contactor operating under the conditions shown in Fig. 9. Comparing this case to the ideal base case (Fig. 2):
ð3Þ
where ðP CO2 =lÞ is the membrane permeance, ptt is the total feed pressure of the contactor, A is the contactor surface area and Ff is the feed volume flow rate (STP) to the contactor. One final way to illustrate this interaction of sweep ratio and permeance is to replot the data in Fig. 5 as a plot of permeance against sweep ratio for various levels of CO2 removal. Two scenarios are shown in Fig. 7, one for 80% CO2 removal and the other for 50% removal. On the line marked 80% removal, the base case is marked as a solid point (black circle) at a permeance of 1000 gpu and a sweep ratio of 1.0. Increasing the permeance of the membrane used in the base case device above 1000 gpu allows lower sweep ratios to be used while still reaching the target of 80% removal. However, as the sweep ratio approaches 0.8, the
2.2. Non-ideal contactors
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Fig. 8. Effect of increasing the feed side pressure on the partial pressure profiles through the base case membrane contactor. Increasing the feed pressure from 1 bar [Figs. 8 (a)] to 2 bar [Fig. 8(b)] increases the driving force (partial pressure difference, feed-to-sweep) fivefold at the feed end of the module. The fractional CO2 removal achieved with the same size module then increases from 80% to 95%.
Fig. 9. Non-ideal base case membrane contactor.
The concentration of CO2 in the feed gas has been increased tenfold.
The sweep gas is air containing 21% oxygen. The membrane still has a CO2 permeance of 1000 gpu, but is now also permeable to nitrogen (25 gpu) and oxygen (50 gpu). The permeances of these membranes are comparable to membranes currently available for CO2 separations at industrial operating conditions. Comparing the new base case contactor performance assumptions in Fig. 9 with the ideal contactor in Fig. 2 shows three main differences. First, the definition of the sweep ratio used in Eq. (1) for the ideal contactor no longer reflects the reality of the new contactor. Using the Eq. (1) definition, the contactor has a sweep ratio of 1.0 [sweep flow rate 1 m3(STP/s) and feed flow 1 m3(STP/ s)], but at the feed end of the contactor, the sweep-to-feed ratio is 1.08 (m3/s)/1.0 (m3/s) or 1.08, while at the sweep end of the contactor the ratio is 1.0 (m3/s)/0.92 (m3/s), or 1.09. Defining the sweep ratio as the average of the inlet and exit sides of the sweep ratio is clearly a better method to use than the ratio of the inlet sweep and feed flows. Second, because of the volume flow through the membrane, 80% CO2 removal from the feed means the residue gas concentration is 2.1% CO2. The membrane area required to achieve the same fractional removal is then slightly less, at 4800 m2 rather than 5000 m2. Finally, some oxygen from the sweep side permeates into the feed side and some nitrogen from the feed permeates to the sweep. This effect is described below.
Fig. 10. Calculated oxygen concentration of sweep gas in a non-ideal membrane contactor used to remove 80% CO2 from flue gas with a countercurrent air sweep stream. The performance obtained with different hypothetical membranes is plotted as a function of the flue gas feed pressure. The sweep ratio is maintained at 1.0 in all the calculations shown.
3. The effect of membrane selectivity The calculations for the ideal contactor described in the first section of this paper assumed the contactor membrane was permeable to CO2 and impermeable to all other gases. Fig. 9 shows what might be expected when a membrane with more realistic properties is used. The membrane still achieves the required removal of CO2 from the feed, but a significant amount of nitrogen also permeates with the CO2 to the sweep, and some oxygen back permeates from the sweep into the feed. A consequence of these additional flows is that when this contactor is used in the CO2 separation scheme illustrated in Fig. 1, the oxygen concentration in the air sweep sent to the coal boiler decreases from 21% to approximately 18%. Fortunately, an oxygen level of 18% in the boiler air stream will still provide efficient combustion, although minor changes to the boiler burner may be required [10]. Fig. 10 shows a plot of the oxygen concentration in the sweep gas leaving the contactor on its way to the boiler as a function of feed gas pressure. The performance profiles of several different hypothetical membranes are shown. The CO2 flue gas feed pressure is varied from a pressure of 1 bar (the base case shown in Fig. 9) to a feed pressure of 3 bar. As described earlier in the
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discussion of Fig. 8, increasing the feed pressure has a very significant impact on the driving force for CO2 permeation and contactor performance. This means the membrane area required to perform the target separation decreases from 4800 m2 at a feed gas pressure of 1 bar (the base case) to 850 m2 at a feed gas pressure of 3 bar. The top line in Fig. 10 is a reference line showing the normal oxygen concentration of air (21%). The next line down, marked CO2 ¼1000 gpu, N2 ¼0 gpu, O2 ¼0 gpu, is the calculated performance of a contactor fitted with a membrane that permeates CO2, but is impermeable to nitrogen and oxygen. The oxygen concentration in the sweep air leaving a contactor fitted with this membrane is 19.3%. This decrease in oxygen concentration from 21% to 19.3% is due to the dilution effect of CO2 permeating the membrane into the sweep gas, thus increasing its volume. The next line in Fig. 10, marked CO2 ¼1000 gpu, N2 ¼25 gpu, O2 ¼0 gpu, shows the dilution effect due to permeation of both CO2 and nitrogen from the feed into the sweep gas. The nitrogen contribution to dilution increases slightly as the feed pressure increases, reflecting the effect of pressure on the driving force for nitrogen permeation. Finally, the bottom line in Fig. 10, marked CO2 ¼1000 gpu, N2 ¼25 gpu, O2 ¼ 50 gpu, shows the sweep gas concentration when the base case membrane from Fig. 9 is used. The difference between this line and the one immediately above it is the contribution of oxygen loss from the sweep gas to the feed. This loss is small compared to the combined dilution effects of CO2 and nitrogen, and decreases as the feed pressure increases because the membrane area needed to perform the target separation decreases with increasing feed pressure.
4. Conclusions In this paper, we have shown the effect of operating parameters on the performance of a gas/gas membrane contactor used for CO2 removal. These devices are not in common use today, but could find future use in CO2 capture processes. The most important operating parameters affecting the gas/gas contactor performance are the sweep gas-to-feed gas volume ratio, the relative pressures of the feed and sweep gases, and the permeance and selectivity of the membranes used.
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Starting from the expression for gas permeation of individual components1: Ji ¼
Pi f ðp psi Þ ℓ i
ðA1Þ
we obtain the following equation for the partial pressure gradients: ! f dJ i P i dpi dpsi ¼ ðA2Þ dа ℓ dа dа The partial pressure gradients can also be obtained from the mass balance in each differential element: J i da ¼
J i da ¼
dpfi pf f dp or ¼ Ji t i f d а Ff pt
ðA3Þ
dps Fs s ps dp or i ¼ J i t ps i dа Fs
ðA4Þ
Ff
Combining Eqs. (A2)–(A4) gives ! dJ i P i pst pft ¼ J dа ℓ i F s F f
ðA5Þ
Integrating Eq. (A5) over the membrane area, the expression for the permeate flux as a function of the membrane area then gives f
J i;a ¼ J i;0 eP i =ℓððpt =F s Þ ðpt =F f ÞÞa ¼ J i;0 eba s
with P ps pf b¼ i t t ℓ Fs Ff
ðA6Þ
! ðA7Þ
Inserting Eq. (A6) into Eqs. (A3) and (A4) and integrating over the membrane area then give the following expression for the partial pressures in the two exit streams: pfi;A ¼ pfi;0 þ J i;0
psi;0 ¼
pft 1 ebA Ff b
psi;A pfi;0 P i =ℓpst =F s ðð1 ebA Þ=bÞ 1 ðP i =ℓÞpst =F s ðð1 ebA =bÞ
ðA8Þ
ðA9Þ
Combining with following equation, Pi f ðp ps i;o Þ ℓ i;0
Acknowledgments
J i;0 ¼
This work was performed as part of a research program supported by the U.S. Department of Energy Project no. DE-FE0007553.
we obtain for the partial pressure in the sweep outlet stream: psi;0 ¼
psi;A pfi;0 P i =ℓpst =F s ðð1 ebA Þ=bÞ 1 ðP i =ℓÞpst =F s ðð1 ebA Þ=bÞ
ðA10Þ
ðA11Þ
and for the partial pressure in the feed outlet stream: Appendix 1 Equations used to calculate the partial pressure difference between the gases on either side of a gas/gas membrane contactor (Fig. A1).
pfi;A ¼ pi;0 f
pft =F f s ðp psi;A Þ pst =F s i;0
ðA12Þ
An Excel file based on these equations, which calculates the pressure profiles and local permeate fluxes, is attached in the supplementary material to this paper. The graphics in the file will auto-adjust if the inputs are changed.
Appendix 2 The limiting (maximum possible) removal of CO2 is linked to the contactor membrane permeance, membrane area and the Fig. A1. Model for the countercurrent sweep module. Pressure drops in the feed and sweep channels are ignored. The permeating compound is assumed to be present at a low concentration, which means that the feed and sweep flow rates can be assumed to be constant throughout the module.
1 In the equations that follow the superscripts f and s represent the feed and sweep side of the membrane, and the terms 0 and A represents positions along the membrane module from the feed entrance (0) to the feed exit (A).
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P. Hao et al. / Journal of Membrane Science 462 (2014) 131–138
operating conditions of the device. The CO2 removal (x) is the ratio of the amount of CO2 permeating the membrane divided by the amount of the CO2 that enters the contactor; that is, RA J CO2 dA ðA13Þ x¼ 0 F f nCO2 where J CO2 is the flux through the membrane at any point in the contactor area A. Ff is the volumetric feed flow of gas into the contactor at standard temperature and pressure conditions (STP), and nCO2 is the molar fraction of CO2 in the feed gas. The maximum CO2 removed (xmax) is obtained at infinite sweep ratio, in which case the membrane flux at any point is proportional to membrane permeance ðP CO2 =lÞ and the feed side CO2 partial pressure pfCO2 (the permeate side CO2 partial pressure is close to zero and can be ignored). Eq. (A13) can then be written2 R0 f A ðP CO2 =lÞpCO2 dA xmax ¼ ðA14Þ F f nCO2
Jv J CO2 i nCO2 ðP CO2 =lÞ pfCO2 ;0 pfCO2 ;A pft xmax
and since nCO2 ¼
pfCO2 ;0
ðA15Þ
pft
where pft is the total pressure on the feed side of the module, R0 pft ðP CO2 =lÞ A pfCO2 dA xmax ¼ ðA16Þ F f pCO2 ;0 f R0 The integral of the partial pressure driving force A pfCO2 dA has the familiar form for the log mean and Eq. (A16) can become xmax ¼
pft ðP CO2 =lÞA F f pfCO2 ;0
U
pfCO2 ;0 pfCO2 ;A lnðpfCO2 ;0 =ppfCO2 ;A Þ
ðA17Þ
Because the fractional removal (xmax) can be also be written as xmax ¼
pfCO2 ;0 pfCO2 ;A
ðA18Þ
pfCO2 ;0
Combining Eqs. (A17) and (A18) gives 0 1 pfCO2 ;0 P CO2 =l pft A @ A ¼ ¼ lnð1 xmax Þ ln f Ff p
ðA19Þ
CO2 ;A
which can be rearranged to xmax ¼ 1 exp
ðP CO2 =lÞ U pft UA Ff
! ðA20Þ
This expression shows the dependence of the limiting value for CO2 removal on the permeance, pressure, area and feed flow rate of an ideal contactor.
Nomenclature A Ff
Fs
actual gas velocity through the membrane support, cm3/cm2 s carbon dioxide flux through the membrane at any point in the contactor, cm3(STP)/cm2 s ith component in the feed or sweep side. molar fraction of CO2 in the feed gas CO2 permeance, gpu [1 10 6 cm3(STP)/ (cm2 s cmHg)] CO2 partial pressure at the feed entrance of the module (point 0), cmHg CO2 partial pressure at the residue exit end of the module (point A), cmHg total feed pressure, cmHg maximum possible fractional removal of a component from the feed gas, that is, the ratio of the amount of a gas permeating the membrane divided by the amount of the gas that enters the contactor. For this paper, xmax is discussed and calculated only for CO2.
area of the membrane contactor, m2 volumetric feed flow of gas into the contactor at standard temperature and pressure conditions, m3(STP)/s volumetric sweep flow of gas into the contactor at standard temperature and pressure conditions, m3(STP)/s
2 In the equations that follow the superscripts f and s represent the feed and sweep side of the membrane, and the terms 0 and A represents positions along the membrane module from the feed entrance (0) to the feed exit (A).
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