13.3. GAS PERMEATION MEMBRANE PROCESSES

13.3A. Series Resistances in Membrane Processes

In membrane processes with two gas phases and a solid membrane, similar equations can be written for the case illustrated in Fig. 13.2-1b. The equilibrium relation between the solid and gas phases is given by

Equation 13.3-1

where S is the solubility of A in m³ (STP)/atm · m³ solid, as shown in Eq. (6.5-5), and H is the equilibrium relation in kg mol/m³ · atm. This is similar to Henry's law. The flux equations in each phase are as follows:

Equation 13.3-2

Equation 13.3-3

Equation 13.3-4

The permeability P_M given previously is

Equation 6.5-9

The permeability P_M is given in kg mol units by dividing Eq. (6.5-9) by 22.414 m³/kg mol:

Equation 13.3-5

Then the flux N_A through the membrane given by Eq. (13.3-3) becomes

Equation 13.3-6

Eliminating the interfacial concentrations as before,

Equation 13.3-7

In the case where pure A (p_A1) is on the left side of the membrane, there is no diffusional resistance in the gas phase, and k_c1 can be considered to be infinite. Note that k_G1 = k_c1/RT.

An example of gas permeation in a membrane is the use of a polymeric membrane as an oxygenator for a heart-lung machine to oxygenate blood. In this biomedical application, pure O₂ gas is on one side of a thin membrane and blood is on the other side. Oxygen diffuses through the membrane into the blood and CO₂ diffuses in a reverse direction into the gas stream.

13.3B. Types of Membranes and Permeabilities for Separation of Gases

1. Types of dense-phase symmetric membranes

Early membranes were limited in their use because of low selectivities in separating two gases and quite low permeation fluxes. This low-flux problem was due to the fact that the membranes had to be relatively thick (1 mil or 1/1000 of an inch or greater) in order to avoid tiny holes, which reduced the separation by allowing viscous or Knudsen flow of the feed. Development of silicone polymers (1 mil thickness) increased the permeability by factors of 10–20 or so. These are called dense-phase symmetric membranes.

2. Types of asymmetric membranes

Newer asymmetric membranes include a very thin but dense skin on one side of the membrane supported by a porous substructure (R1). The dense skin has a thickness of about 1000 and the porous support thickness is about 25–100 μm. The flux increase of these membranes is thousands of time higher than the 1-mil-thick original membranes. Some typical materials currently used for asymmetric membranes are a composite of polysulfone coated with silicone rubber, cellulose acetate and modified cellulose acetates, aromatic polyamides or aromatic polyimides, and silicone-polycarbonate copolymer on a porous support.

3. Permeability of membranes

The permeability P_M in Eqs. (6.5-9) and (13.3-6) is defined as D_ABS in m³ (STP)/s · m²C.S. · atm/m. Since mixtures of gases are often present, for gas A and for gas B will be used instead of P_M. The different sets of units used and their conversion factors are given in Table 13.3-1. Sometimes units are given in terms of Barrers, as also defined in Table 13.3-1.

Table 13.3-1. Conversion Factors for Permeability and Permeance /t

Permeability,	Permeance, /t

The accurate prediction of permeabilities of gases in membranes is generally not possible, and experimental values are needed. Experimental data for common gases in some typical dense-phase membranes are given in Table 13.3-2. Note that there are wide differences among the permeabilities of various gases in a given membrane. Silicone rubber exhibits very high permeabilities for the gases in the table.

Table 13.3-2. Permeabilities of Various Gases in Dense-Phase Symmetric Membranes

	Permeability,
Material	Temp. (°C)	He	H2	CH4	CO2	O2	N2	Ref.
Silicone rubber	25	300	550	800	2700	500	250	(S2)
Natural rubber	25	31	49	30	131	24	8.1	(S2)
Polycarbonate (Lexane)	25–30	15	12		5.6,10	1.4		(S2)
Nylon 66	25	1.0			0.17	0.034	0.008	(S2)
Polyester (Permasep)	—		1.65	0.035	0.31		0.031	(H1)
Silicone-polycarbonate copolymer (57% silicone)	25		210		970	160	70	(W2)
Teflon FEP	30	62		1.4			2.5	(S1)
Ethyl cellulose	30	35.7	49.2	7.47	47.5	11.2	3.29	(W3)
Polystyrene	30	40.8	56.0	2.72	23.3	7.47	2.55	(W3)

For the effect of temperature T in K, ln is approximately a linear function of 1/T and increases with T. However, operation at high temperatures can often degrade the membranes. When a mixture of gases is present, reductions of permeability of an individual component of up to 10% or so can often occur. In a few cases, much larger reductions have been observed (R1). Hence, when using a mixture of gases, experimental data should be obtained to determine if there is any interaction between the gases. The presence of water vapor can have similar effects on the permeabilities and can also possibly damage the membranes.

4. Permeance of membranes

In many cases, especially in asymmetric membranes, the thickness t is not measured and only experimental values of permeance /t are given. Conversion factors are also given in Table 13.3-1.

13.3C. Types of Equipment for Gas Permeation Membrane Processes

1. Flat membranes

Flat membranes are mainly used in experiments to characterize the permeability of the membrane. The modules are easy to fabricate and use and the areas of the membranes are well defined. In some cases modules are stacked together like a multilayer sandwich or plate-and-frame filter press. The major drawback of this type is the very small membrane area per unit separator volume. Small commercial flat membranes are used for producing oxygen-enriched air for individual medical applications.

2. Spiral-wound membranes

This configuration retains the simplicity of fabricating flat membranes while increasing markedly the membrane area per unit separator volume up to 100 ft²/ft³ (328 m²/m³) and decreasing pressure drops (R1). The assembly consists of a sandwich of four sheets wrapped around a central core of a perforated collecting tube. The four sheets consist of a top sheet of an open separator grid for the feed channel, a membrane, a porous felt backing for the permeate channel, and another membrane, as shown in Fig. 13.3-1. The spiral-wound element is 100 to 200 mm in diameter and is about 1 to 1.5 m long in the axial direction. The flat sheets before rolling are about 1-1.5 m by about 2-2.5 m. The space between the membranes (open grid for feed) is about 1 mm and the thickness of the porous backing (for permeate) is about 0.2 mm.

The whole spiral-wound element is located inside a metal shell. The feed gas enters at the left end of the shell, enters the feed channel, and flows through this channel in the axial direction of the spiral to the right end of the assembly (Fig. 13.3-1). Then the exit residue gas leaves the shell at this point. The feed stream, which is in the feed channel, permeates perpendicularly through the membrane. This permeate then flows through the permeate channel in a direction perpendicular to the feed stream toward the perforated collecting tube, where it leaves the apparatus at one end. This is illustrated in Fig. 13.3-2, where the local gas flow paths are shown for a small element of the assembly.

3. Hollow-fiber membranes

The membranes are in the shape of very-small-diameter hollow fibers. The inside diameter of the fibers is in the range of 100–500 μm and the outside 200–1000 μm, with the length up to 3-5 m. The module resembles a shell-and-tube heat exchanger. Thousands of fine tubes are bound together at each end into a tube sheet that is surrounded by a metal shell having a diameter of 0.1-0.2 m, so that the membrane area per unit volume is up to 10 000 m²/m³, as in Fig. 13.3-3. A typical large industrial permeator has fibers of 200 μm ID and 400 μm OD in a shell 6 in. in diameter and 10 ft long (P7).

Typically, the high-pressure feed enters the shell side at one end and leaves at the other end. The hollow fibers are closed at one end of the tube bundles. The permeate gas inside the fibers flows countercurrent to the shell-side flow and is collected in a chamber where the open ends of the fibers terminate. Then the permeate exits the device.

In some lower-pressure operations, such as for separation of air to produce nitrogen, the feed enters inside the tubes (P7).

13.3D. Introduction to Types of Flow in Gas Permeation

1. Types of flow and diffusion gradients

In a membrane process, high-pressure feed gas is supplied to one side of the membrane and permeates normal to the membrane. The permeate leaves in a direction normal to the membrane, accumulating on the low-pressure side. Because of the very high diffusion coefficient in gases, concentration gradients in the gas phase in the direction normal to the surface of the membrane are quite small. Hence, gas film resistances compared to the membrane resistance can be neglected. This means that the concentration in the gas phase in a direction perpendicular to the membrane is essentially uniform, whether the gas stream is flowing parallel to the surface or is not flowing.

If the gas stream is flowing parallel to the membrane in essentially plug flow, a concentration gradient occurs in this direction. Hence, several cases can occur in the operation of a membrane module. The permeate side of the membrane can be operated so that the phase is completely mixed (uniform concentration) or so that the phase is in plug flow. The high-pressure feed side can also be completely mixed or in plug flow. Countercurrent or cocurrent flow can be used when both sides are in plug flow. Hence, separate theoretical models must be derived for these different types of operation, as given in Sections 13.4–13.8.

2. Assumptions used and ideal flow patterns

In deriving theoretical models for gas separation by membranes, isothermal conditions and negligible pressure drop in the feed stream and permeate stream are generally assumed. It is also assumed that the effects of total pressure and/or composition of the gas are negligible and that the permeability of each component is constant (i.e., no interactions between different components).

Since there are a number of idealized flow patterns, the important types are summarized in Fig. 13.3-4. In Fig. 13.3-4a, complete mixing is assumed for the feed chamber and the permeate chamber. Similar to a continuous-stirred tank, the reject or residue and the product or permeate compositions are equal to their respective uniform compositions in the chambers.

An ideal cross-flow pattern is given in Fig. 13.3-4b, where the feed stream is in plug flow and the permeate flows in a normal direction away from the membrane without mixing. Since the feed composition varies along its flow path, the local permeate concentration also varies along the membrane path.

In Fig. 13.3-4c, both the feed stream and permeate stream are in plug flow countercurrent to each other. The composition of each stream varies along its flow path. Cocurrent flow of the feed and permeate streams is shown in Fig. 13.3-4d.