Introduction
Using membrane for gas separation by numerous industries and fields is highly associated with easy operability, low energy costs, light weight and compactness of the process.
Organizational need
There is an organizational need by Learning Curve Consultants’ client to generate relatively pure nitrogen and oxygen gasses within the organization for the application in various processes through the use of high-pressure air as feed. The client has the need to investigate the possibility of employing the use of polymer membranes to produce both nitrogen and oxygen gasses. As a consequence, the customer has presented the team with two bench scale gas membrane severance components from the manufacturer.
Technical need
The technical need for this team is to acquire data pertaining to the performance of the membrane in addition to the impact of feed pressure on overall mass transfer coefficients of both nitrogen and oxygen. This performance data of the membrane and the effects of feed pressure will be used to generate a mathematical model of the membrane separation capabilities. The proposed model will be utilized as the basic for exploration of different designs used to construct plant scale units which will be used to attain the air-separation requirements for the client’s pilot plant.
Figure 1
Figure 2
Theory
Separations for porous membranes can be modeled through the use of three dissimilar methods; slip flow, Knudsen diffusion, and viscous flow. The root mean square speed of the penetrant molecule and the size of the membrane pore determine the kind of diffusion taking place. The root mean square speed is determined by establishing the square root of the average of the squared velocities of all the particles in the gas. The similarities in nature of oxygen and nitrogen gas present a daunting task for their separation.
In this experiment, the membrane applied is nonporous. The nonporous membrane functions through diffusion/ solution system. The surface of the membrane absorbs the gas molecule. The molecule diffuses via the membrane through a random walk system. After diffusion, the gas molecule desorbs on the opposite side of the membrane. There are two primary factors that determine the equilibrium concentration of the gas (C); the solubility coefficient of the gas in the membrane (S) and the fractional pressure of the gas (p). As a consequence, the concentration of the gas is directly proportional to both the pressure of the gas and the solubility coefficient of the gas.
C= p.S
The efficiency of the membrane is measured by calculating the flux. Flick’s la of diffusion is applied in the computation of the flux of the gas passing through the membrane. All factors constant, the concentration in diffusion volume remain constant with respect to time in steady state diffusion. According to Fick’s first law, the molar flux, J is directly proportional to the concentration ratio C in the membrane and the diffusivity D. A uniform membrane structure and failure of the gasses to interact allows for the expression of flux regarding alteration in the concentration via width of the membrane, z.
n= -QA (pp- pr)
The ideal separation factor, a, is determined by the ration of permeabilities of two or more gasses in a mixture. The ideal separation factor of the gasses determines the gas that will permeate through the membrane more than the other.
Procedure
A mass flow rate meter is used to measure the standard volumetric flow rates of the retentate and the permeate streams. The meter acquires data in standard liters per minute and passes it via an oxygen analyzer that calibrates the volume percentage of oxygen.
The experiment was started by pressing the black switch situated on the bottom of the power strip. The switch turned on the pressure gauges and the flow meters. The oxygen sensor was turned on and calibrated to read 20.9 percent O2. The calibration of the oxygen sensor was done through adjusting the calibration knob on the left. The oxygen analyzer close to valve B was set to measure the composition of the permeate stream while the oxygen analyzer close to valve C was set to measure the composition of the retentate stream.
The flow rate meters were set to read zero by depressing the switch located on the meters until the flow rate reading was close to zero. The tare button on the Omega pressure gauge was hit so as to set the pressure gauge to zero. The apparatus was set to run in a series configuration which allowed the feed to flow through the first unit and then through the second unit for additional separation.
After the apparatus had been set up, the valve on top of the air cylinder was opened to allow air to flow into the membrane component. The pressure was adjusted using the blue knob on the Bourdon pressure gauge. The flow rate of the tube-side was adjusted using the needle point valve situated closer to the bottom flow meter. The system was simultaneously adjusted until it attained a steady state.
The feed, retentate, and the permeate pressures were recorded. Additionally, the percentage oxygen of permeate and retentate alongside the retentate and permeate flow rates were also recorded. These values were used to calculate the flux and the overall mass transfer coefficients.
Discussion
According to the results obtained from the experiment, it is apparent that there is a clear correlation between the feed pressure and the quality of the membrane in separation of both oxygen and nitrogen. There is a direct relationship between the feed pressure and the mass transfer coefficient. An increase in the feed pressure result to an increase in the overall mass transfer coefficient of both oxygen gas and nitrogen gas. While there is a fluctuation in overall mass coefficient of oxygen gas, the overall mass transfer coefficient of nitrogen gas steadily increases with increase in feed pressure. Generally, there is an increase in the overall mass transfer coefficient with a corresponding increase in feed pressure.
At a constant configuration and the tube flow rate, the mass transfer coefficient of oxygen gas fluctuates with increase of feed pressure. On the other hand, the mass transfer coefficient of nitrogen gas increases steadily with an increase in the feed pressure.
Figure 3: oxygen mol fraction in relation to feed pressure
It is therefore rational to assert that increasing the feed pressure increases the amount of nitrogen gas that pass through the membrane. The overall mass transfer coefficient is directly proportional to the amount of feed pressure applied.
Figure 4: Nitrogen mol fraction in relation to feed pressure
Pressure highly affects the rate of diffusion of these gases through the membrane. However, it is apparent that pressure escalates the rate of diffusion of nitrogen through the membrane. Additionally, the figures and results obtained on the retentate and the mol fraction of both gasses, it is evident that the oxygen mole fraction decreases with increase in feed pressure. On the other hand, nitrogen mole fraction increases with the increasing feed pressure. As a consequence, it is rational to conclude that increasing feed pressure increases the purity of the nitrogen gas as well as the molar production rate.
Figure 5: molar production rate of nitrogen
Recommendation
Since the client is particularly interested in enriched nitrogen steam, it is imperative to maintain the factors that ensures the generation of more nitrogen gas than oxygen from the separation. It is evident from the results obtained by the experiment that more nitrogen gas is diffused by increasing the feed pressure. The molar fraction of nitrogen gas increases with increase in feed pressure. On the other hand, the molar production rate of nitrogen gas fluctuates with increase in feed pressure. As a consequence, it is imperative to maintain the feed pressure at a desirable level so as to ensure the production of high amount of enriched nitrogen at good molar production rate.
Works Cited
Robeson, Lloyd M. "Correlation of separation factor versus permeability for polymeric membranes." Journal of membrane science 62.2 (1991): 165-185.
Appendix
List of figures
Figure 1: A graph indicating the relationship between feed pressure and mass transfer coefficient
Figure 2: A graph indicating the relationship between feed pressure and the ideal separation factor
Figure 3: oxygen mol fraction in relation to feed pressure
Figure 4: Nitrogen mol fraction in relation to feed pressure
Figure 5: molar production rate of nitrogen
The overall mass transfer coefficient for Oxygen and Nitrogen
