Gas mixtures can be effectively separated by synthetic membranes made from polymers such as polyamide or cellulose acetate, or from ceramic materials.
While polymeric membranes are economical and technologically useful, they are bounded by their performance, known as the Robeson limit (permeability must be sacrificed for selectivity and vice versa). This limit affects polymeric membrane use for CO2 separation from flue gas streams, since mass transport becomes limiting and CO2 separation becomes very expensive due to low permeabilities. Membrane materials have expanded into the realm of silica, zeolites, metal-organic frameworks, and perovskites due to their strong thermal and chemical resistance as well as high tunability (ability to be modified and functionalized), leading to increased permeability and selectivity. Membranes can be used for separating gas mixtures where they act as a permeable barrier through which different compounds move across at different rates or not move at all. The membranes can be nanoporous, polymer, etc. and the gas molecules penetrate according to their size, diffusivity, or solubility.
Basic process Gas separation across a membrane is a pressure-driven process, where the driving force is the difference in pressure between inlet of raw material and outlet of product. The membrane used in the process is a generally non-porous layer, so there will not be a severe leakage of gas through the membrane. The performance of the membrane depends on permeability and selectivity. Permeability is affected by the penetrant size. Larger gas molecules have a lower diffusion coefficient. The polymer chain flexibility and free volume in the polymer of the membrane material influence the diffusion coefficient, as the space within the permeable membrane must be large enough for the gas molecules to diffuse across. The solubility is expressed as the ratio of the concentration of the gas in the polymer to the pressure of the gas in contact with it. Permeability is the ability of the membrane to allow the permeating gas to diffuse through the material of the membrane as a consequence of the pressure difference over the membrane, and can be measured in terms of the permeate flow rate, membrane thickness and area and the pressure difference across the membrane. The selectivity of a membrane is a measure of the ratio of permeability of the relevant gases for the membrane. It can be calculated as the ratio of permeability of two gases in binary separation. The membrane gas separation equipment typically pumps gas into the membrane module and the targeted gases are separated based on difference in diffusivity and solubility. For example, oxygen will be separated from the ambient air and collected at the upstream side, and nitrogen at the downstream side. As of 2016, membrane technology was reported as capable of producing 10 to 25 tonnes of 25 to 40% oxygen per day.
Membrane governing methodology
There are three main diffusion mechanisms. The first (b), Knudsen diffusion holds at very low pressures where lighter molecules can move across a membrane faster than heavy ones, in a material with reasonably large pores. The second (c), molecular sieving, is the case where the pores of the membrane are too small to let one component pass, a process which is typically not practical in gas applications, as the molecules are too small to design relevant pores. In these cases the movement of molecules is best described by pressure-driven convective flow through capillaries, which is quantified by Darcy's law. However, the more general model in gas applications is the solution-diffusion (d) where particles are first dissolved onto the membrane and then diffuse through it both at different rates. This model is employed when the pores in the polymer membrane appear and disappear faster relative to the movement of the particles. In a typical membrane system the incoming feed stream is separated into two components: permeant and retentate. Permeant is the gas that travels across the membrane and the retentate is what is left of the feed. On both sides of the membrane, a gradient of chemical potential is maintained by a pressure difference which is the driving force for the gas molecules to pass through. The ease of transport of each species is quantified by the permeability, Pi. With the assumptions of ideal mixing on both sides of the membrane, ideal gas law, constant diffusion coefficient and Henry's law, the flux of a species can be related to the pressure difference by Fick's law:
J i = D i K i ( p i ′ − p i ″ ) l = P i ( p i ′ − p i ″ ) l {\displaystyle J_{i}={\frac {D_{i}K_{i}(p_{i}'-p_{i}'')}{l}}={\frac {P_{i}(p_{i}'-p_{i}'')}{l}}}
where, (Ji) is the molar flux of species i across the membrane, (l) is membrane thickness, (Pi) is permeability of species i, (Di) is diffusivity, (Ki) is the Henry coefficient, and (pi') and (pi") represent the partial pressures of the species i at the feed and permeant side respectively. The product of DiKi is often expressed as the permeability of the species i, on the specific membrane being used.
P i = D i K i {\displaystyle P_{i}=D_{i}K_{i}}
The flow of a second species, j, can be defined as:
J j = P j ( p j ′ − p j ″ ) l {\displaystyle J_{j}={\frac {P_{j}(p_{j}'-p_{j}'')}{l}}}
With the expression above, a membrane system for a binary mixture can be sufficiently defined. it can be seen that the total flow across the membrane is strongly dependent on the relation between the feed and permeate pressures. The ratio of feed pressure (p') over permeate pressure (p") is defined as the membrane pressure ratio (θ).
θ = P ′ P ″ {\displaystyle \theta ={\frac {P'}{P''}}}
It is clear from the above, that a flow of species i or j across the membrane can only occur when:
p i ′ − p i ″ = p ′ n i ′ − p ″ n i ″ ≠ 0 {\displaystyle p_{i}'-p_{i}''=p'n_{i}'-p''n_{i}''\neq 0}
In other words, the membrane will experience flow across it when there exists a concentration gradient between feed and permeate. If the gradient is positive, the flow will go from the feed to the permeate and species i will be separated from the feed.
p ′ n i ′ − p ″ n i ″ > 0 → n i ″ n i ′ ≤ p ′ p ″ {\displaystyle p'n_{i}'-p''n_{i}''>0\rightarrow {\frac {n_{i}''}{n_{i}'}}\leq {\frac {p'}{p''}}}
Therefore, the maximum separation of species i results from:
n i ″ , m a x ″ = p ′ p ″ n i ′ = θ n i ′ {\displaystyle n_{i}'',max''={\frac {p'}{p''}}n_{i}'=\theta n_{i}'}
Another important coefficient when choosing the optimum membrane for a separation process is the membrane selectivity αij defined as the ratio of permeability of species i with relation to the species j.
α i j = P i P j {\displaystyle \alpha _{ij}={\frac {P_{i}}{P_{j}}}}
This coefficient is used to indicate the level to which the membrane is able to separates species i from j. It is obvious from the expression above, that a membrane selectivity of 1 indicates the membrane has no potential to separate the two gases, the reason being, both gases will diffuse equally through the membrane. In the design of a separation process, normally the pressure ratio and the membrane selectivity are prescribed by the pressures of the system and the permeability of the membrane . The level of separation achieved by the membrane (concentration of the species to be separated) needs to be evaluated based on the aforementioned design parameters in order to evaluate the cost-effectiveness of the system.
Membrane performance The concentration of species i and j across the membrane can be evaluated based on their respective diffusion flows across it.
n i ″ = J i ∑ J k , n j ″ = J j ∑ J k {\displaystyle n_{i}''={\frac {J_{i}}{\sum {J_{k}}}},\quad n_{j}''={\frac {J_{j}}{\sum {J_{k}}}}}
In the case of a binary mixture, the concentration of species i across the membrane:
n i ″ = J i J i + J j {\displaystyle n_{i}''={\frac {J_{i}}{J_{i}+J_{j}}}}
This can be further expanded to obtain an expression of the form:
n i ″ = n i ″ ( ϕ , α i j , n i ′ ) {\displaystyle n_{i}''=n_{i}''(\phi ,\alpha _{ij},n_{i}^{'})}
n i ″ = J i J i + J j = P i ( p i ′ − p i ″ ) P i ( p i ′ − p i ″ ) + P j ( n j ′ − 1 ϕ n j ″ ) {\displaystyle n_{i}''={\frac {J_{i}}{J_{i}+J_{j}}}={\frac {P_{i}(p_{i}'-p_{i}'')}{P_{i}(p_{i}'-p_{i}'')+P_{j}(n_{j}'-{\frac {1}{\phi }}n_{j}'')}}}
Using the relations:
p i ′ = p ′ n i ′ , p j ′ = p ′ n j ′ = p ′ ϕ n i ′ {\displaystyle p_{i}'=p'n_{i}',\quad p_{j}'=p'n_{j}'={\frac {p'}{\phi }}n_{i}'}
p i ″ = p ″ n i ′ , p j ″ = p ″ n j ″ = p ′ ϕ n i ″ {\displaystyle p_{i}''=p''n_{i}',\quad p_{j}''=p''n_{j}''={\frac {p'}{\phi }}n_{i}''}
The expression can be rewritten as:
n i ″ = P i p ′ ( n i ′ − 1 ϕ n i ″ ) P i p ′ ( n i ′ − 1 ϕ n i ″ ) + P j p ′ ( n j ′ − 1 ϕ n j ″ ) {\displaystyle n_{i}''={\frac {P_{i}p'(n_{i}'-{\frac {1}{\phi }}n_{i}'')}{P_{i}p'(n_{i}'-{\frac {1}{\phi }}n_{i}'')+P_{j}p'(n_{j}'-{\frac {1}{\phi }}n_{j}'')}}}
Then using n j ′ = 1 − n i ′ a n d n j ″ = 1 − n i ″ {\displaystyle n_{j}'=1-n_{i}'\quad and\quad n_{j}''=1-n_{i}''}
n i ″ = P i p ′ ( n i ′ − 1 ϕ n i ″ ) P i p ′ ( n i ′ − 1 ϕ n i ″ ) + P j p ′ ( ( 1 − n i ′ ) − 1 ϕ ( 1 − n i ″ ) ) {\displaystyle n_{i}''={\frac {P_{i}p'(n_{i}'-{\frac {1}{\phi }}n_{i}'')}{P_{i}p'(n_{i}'-{\frac {1}{\phi }}n_{i}'')+P_{j}p'((1-n_{i}')-{\frac {1}{\phi }}(1-n_{i}''))}}}
( 1 − α ) ( n i ″ ) 2 + ( ϕ + ϕ ( α − 1 ) n i ′ + α − 1 ) n i ″ − α ϕ n i ′ = 0 {\displaystyle (1-\alpha )(n_{i}'')^{2}+(\phi +\phi (\alpha -1)n_{i}'+\alpha -1)n_{i}''-\alpha \phi n_{i}'=0}
The solution to the above quadratic expression can be expressed as:
n i = − ( ϕ + ϕ ( α − 1 ) n i ′ + α − 1 ) ± ϕ + ϕ ( α − 1 ) n i ′ + α − 1 ) 2 + 4 ( 1 − α ) α ϕ n i ′ 2 ( 1 − α ) {\displaystyle n_{i}={\frac {-(\phi +\phi (\alpha -1)n_{i}'+\alpha -1)\pm {\sqrt {\phi +\phi (\alpha -1)n_{i}'+\alpha -1)^{2}+4(1-\alpha )\alpha \phi n_{i}'}}}{2(1-\alpha )}}}
Finally, an expression for the permeant concentration is obtained by the following:
n i ″ ( ϕ α n i ′ ) = ϕ 2 ( n i ′ + 1 ϕ + 1 α − 1 − ( n i ′ + 1 ϕ + 1 α − 1 ) 2 − 4 α n i ′ ( α − 1 ) ϕ ) {\displaystyle n_{i}''(\phi \alpha n_{i}')={\frac {\phi }{2}}\left(n_{i}'+{\frac {1}{\phi }}+{\frac {1}{\alpha -1}}-{\sqrt {\left(n_{i}'+{\frac {1}{\phi }}+{\frac {1}{\alpha -1}}\right)^{2}-{\frac {4\alpha n_{i}'}{(\alpha -1)\phi }}}}\right)}
Along the separation unit, the feed concentration decays with the diffusion across the membrane causing the concentration at the membrane to drop accordingly. As a result, the total permeant flow (q"out) results from the integration of the diffusion flow across the membrane from the feed inlet (q'in) to feed outlet (q'out). A mass balance across a differential length of the separation unit is therefore:
q ′ ( x ) = q ′ ( x + d x ) + ∫ x x + d x q ″ ( x ) d x {\displaystyle q'(x)=q'(x+dx)+\int _{x}^{x+dx}q''(x)dx}
where:
q ″ ( x ) = J i ( x ) + J j ( x ) {\displaystyle q''(x)=J_{i}(x)+J_{j}(x)}
Because of the binary nature of the mixture, only one species needs to be evaluated. Prescribing a function n'i=n'i(x), the species balance can be rewritten as:
q ′ ( x ) n i ′ ( x ) = q ′ ( x + Δ x ) n i ′ ( x + Δ x ) + ∫ x x + d x q ″ ( x ) d x n i ″ ¯ {\displaystyle q'(x)n'_{i}(x)=q'(x+\Delta x)n'_{i}(x+\Delta x)+\int _{x}^{x+dx}q''(x)dx{\bar {n_{i}''}}}
Where:
∫ x x + d x q ″ ( x ) d x = δ q ″ , n i ″ ¯ = n i ″ ( x ) + n i ″ ( x + Δ x ) 2 {\displaystyle \int _{x}^{x+dx}q''(x)dx=\delta q'',\quad {\bar {n_{i}''}}={\frac {n_{i}''(x)+n_{i}''(x+\Delta x)}{2}}}
δ q ″ = n i ′ ( x ) − n i ′ ( x + Δ x ) n i ″ ¯ − n i ′ ( x + Δ x ) q ′ ( x ) {\displaystyle \delta q''={\frac {n'_{i}(x)-n'_{i}(x+\Delta x)}{{\bar {n_{i}''}}-n'_{i}(x+\Delta x)}}q'(x)}
Lastly, the area required per unit membrane length can be obtained by the following expression:
A = δ q ″ J i + J j {\displaystyle A={\frac {\delta q''}{J_{i}+J_{j}}}}
Membrane materials for carbon capture in flue gas streams The material of the membrane plays an important role in its ability to provide the desired performance characteristics. It is optimal to have a membrane with a high permeability and sufficient selectivity and it is also important to match the membrane properties to that of the system operating conditions (for example pressures and gas composition). Synthetic membranes are made from a variety of polymers including polyethylene, polyamides, polyimides, cellulose acetate, polysulphone and polydimethylsiloxane.
Polymer membranes Polymeric membranes are a common option for use in the capture of CO2 from flue gas because of the maturity of the technology in a variety of industries, namely petrochemicals. The ideal polymer membrane has both a high selectivity and permeability. Polymer membranes are examples of systems that are dominated by the solution-diffusion mechanism. The membrane is considered to have holes which the gas can dissolve (solubility) and the molecules can move from one cavity to the other (diffusion). It was discovered by Robeson in the early 1990s that polymers with a high selectivity have a low permeability and opposite is true; materials with a low selectivity have a high permeability. This is best illustrated in a Robeson plot where the selectivity is plotted as a function of the CO2 permeation. In this plot, the upper bound of selectivity is approximately a linear function of the permeability. It was found that the solubility in polymers is mostly constant but the diffusion coefficients vary significantly and this is where the engineering of the material occurs. Somewhat intuitively, the materials with the highest diffusion coefficients have a more open pore structure, thus losing selectivity. There are two methods that researchers are using to break the Robeson limit, one of these is the use of glassy polymers whose phase transition and changes in mechanical properties make it appear that the material is absorbing molecules and thus surpasses the upper limit. The second method of pushing the boundaries of the Robeson limit is by the facilitated transport method. As previously stated, the solubility of polymers is typically fairly constant but the facilitated transport method uses a chemical reaction to enhance the permeability of one component without changing the selectivity.
Nanoporous membranes
Nanoporous membranes are fundamentally different from polymer-based membranes in that their chemistry is different and that they do not follow the Robeson limit for a variety of reasons. The simplified figure of a nanoporous membrane shows a small portion of an example membrane structure with cavities and windows. The white portion represents the area where the molecule can move and the blue shaded areas represent the walls of the structure. In the engineering of these membranes, the size of the cavity (Lcy x Lcz) and window region (Lwy x Lwz) can be modified so that the desired permeation is achieved. It has been shown that the permeability of a membrane is the production of adsorption and diffusion. In low loading conditions, the adsorption can be computed by the Henry coefficient. If the assumption is made that the energy of a particle does not change when moving through this structure, only the entropy of the molecules changes based on the size of the openings. If we first consider changes the cavity geometry, the larger the cavity, the larger the entropy of the absorbed molecules which thus makes the Henry coefficient larger. For diffusion, an increase in entropy will lead to a decrease in free energy which in turn leads to a decrease in the diffusion coefficient. Conversely, changing the window geometry will primarily effect the diffusion of the molecules and not the Henry coefficient. In summary, by using the above simplified analysis, it is possible to understand why the upper limit of the Robeson line does not hold for nanostructures. In the analysis, both the diffusion and Henry coefficients can be modified without affecting the permeability of the material which thus can exceed the upper limit for polymer membranes.
Silica membranes Silica membranes are mesoporous and can be made with high uniformity (the same structure throughout the membrane). The high porosity of these membranes gives them very high permeabilities. Synthesized membranes have smooth surfaces and can be modified on the surface to drastically improve selectivity. Functionalizing silica membrane surfaces with amine containing molecules (on the surface silanol groups) allows the membranes to separate CO2 from flue gas streams more effectively. Surface functionalization (and thus chemistry) can be tuned to be more efficient for wet flue gas streams as compared to dry flue gas streams. While previously, silica membranes were impractical due to their technical scalability and cost (they are very difficult to produce in an economical manner on a large scale), there have been demonstrations of a simple method of producing silica membranes on hollow polymeric supports. These demonstrations indicate that economical materials and methods can effectively separate CO2 and N2. Ordered mesoporous silica membranes have shown considerable potential for surface modification that allows for ease of CO2 separation. Surface functionalization with amines leads to the reversible formation of carbamates (during CO2 flow), increasing CO2 selectivity significantly.
Zeolite membranes
Zeolites are crystalline aluminosilicates with a regular repeating structure of molecular-sized pores. Zeolite membranes selectively separate molecules based on pore size and polarity and are thus highly tunable to specific gas separation processes. In general, smaller molecules and those with stronger zeolite-adsorption properties are adsorbed onto zeolite membranes with larger selectivity. The capacity to discriminate based on both molecular size and adsorption affinity makes zeolite membranes an attractive candidate for CO2 separation from N2, CH4, and H2. Scientists have found that the gas-phase enthalpy (heat) of adsorption on zeolites increases as follows: H2 < CH4 < N2 < CO2. It is generally accepted that CO2 has the largest adsorption energy because it has the largest quadrupole moment, thereby increasing its affinity for charged or polar zeolite pores. At low temperatures, zeolite adsorption-capacity is large and the high concentration of adsorbed CO2 molecules blocks the flow of other gases. Therefore, at lower temperatures, CO2 selectively permeates through zeolite pores. Several recent research efforts have focused on developing new zeolite membranes that maximize the CO2 selectivity by taking advantage of the low-temperature blocking phenomena. Researchers have synthesized Y-type (Si:Al>3) zeolite membranes which achieve room-temperature separation factors of 100 and 21 for CO2/N2 and CO2/CH4 mixtures respectively. DDR-type and SAPO-34 membranes have also shown promise i