Process Parameter Influences
The gas separation performance for a given membrane system mainly depends on membrane material properties (i.e., gas permeability and selectivity). However, the operating parameters (i.e., pressure, temperature) for a specific process can also affect the membrane separation performance.
Effect of Pressure
One of the most important parameters is the pressure ratio across a membrane, which is defined as the ratio between feed and permeate pressures. Component i can only transport through membrane when the partial pressure on the feed side (pH) is higher than that on the permeate side (pL), as indicated in Equation 4.12.
It is also found from Equation 4.12 that enrichment of component i can never exceed the pressure ratio regardless of membrane selectivity . The relationship between pressure ratio and membrane selectivity can be derived from Equations 4.2 and 4.4 [9,10].
If membrane selectivity (a) is much larger than pressure ratio (Ф) (i.e., a » Ф), Equation 4.13 can be simplified as,
This is normally called the pressure-ratio-limited region, and membrane separation performance is mainly determined by the pressure ratio across membranes while selectivity has only a minor effect. However, if membrane selectivity is much smaller than pressure ratio (a «: ф), Equation 4.13 becomes,
This is the membrane-selectivity-limited region; membrane separation performance is mainly controlled by membrane selectivity while the pressure ratio has a minor effect. In between these two extremes, both pressure ratio and membrane selectivity will influence membrane system performance.
An example of the dependence of the permeate concentration on pressure ratio and selectivity was reported by Paul et al. . The pressure ratio is very important for gas separation processes at the industrial scale due to practical limitations. Achieving a high pressure ratio by compressing feed gas to high pressure or applying a high vacuum to the permeate side will significantly increase energy costs. Therefore, the practical pressure ratios are typically in the range of 5-20 .
Effect of Temperature
Gas transport through carbon membranes may be considered as an activated process, which can typically be described by an Arrhenius equation ,
where P0, S0 and D0 are the preexponential factors and AHS and Erf are the heat of solution and activation energy for diffusion, respectively. Temperature has a significant effect on gas permeability For small, non-interactive gas molecules, the effect of temperature on gas permeability is mainly determined by diffusivity, as temperature has a minor influence on the solubility coefficient. However, for large gas molecules, the temperature effects on solubility coefficient and diffusivity are in opposition and thus gas permeability will be determined by the dominant parameter. Lei et al. reported the temperature dependence of the separation performance of a cellulose-based carbon membrane operating at a feed pressure of 8 bar . When the temperature was increased from 25 to 60 °C, both C02 and CH4 permeabilities increased, whereas the separation factor decreased, as shown in Figure 4.3. They also reported that increasing the operating temperature enhances the C02 diffusion coefficient but C02 adsorption in the carbon matrix decreases. Overall, it causes a relatively slower increase of C02 permeability compared with that of CH4. The apparent transport activation energies, calculated from
Effects of operation temperature on separation performance of a cellulose-based carbon hollow fiber membrane, (a) Temperature dependence of CO, permeability and CO,/CH4 separation factor; (b) Arrhenius plots according to CO, and CH4 permeability .
the Arrhenius equation (P = P0e RT), are 6.7 and 25.4 kj/mol for C02 and CH4, respectively. The larger E„ of CH4 indicates a lower permeability at the same operating temperature but a more significant effect of temperature.