Executive summary
This experiment seeks to compute the overall mass transfer coefficients for nitrogen gas and oxygen gas via a polymer membrane under different experimental conditions. The calculation of the overall mass transfer coefficient of the gasses will aid in establishing how the permeability of the polymer membrane is affected by altering these conditions. The experiment employs the calculation of the separation factor in determining the efficiency of a membrane in separating oxygen gas from nitrogen gas. It uses the measured values of flow rates, exit streams and flow rate composition of the membrane component to calculate the mass transfer coefficients. It was determined that altering the flow rate and pressure affects the concentration ratio inside the membrane, thus the coefficients of oxygen gas and nitrogen gas changes in each experimental trial.
Introduction
Membranes are applied in medical, commercial and industries for the separation of gasses. The application of membranes in segregation of gasses such as oxygen and nitrogen has grown tremendously since its inception (Robeson 164). This tremendous growth in the demand is attributed to the several benefits and advantages of this technique. 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.
The movement of gasses from one point to another through a membrane occurs if there is a gradient. That is, there must be a difference in concentration or pressure of gas before it can diffuse to its surrounding until equilibrium. The difference in pressure or concentration of gasses makes the gasses move to regions of low concentration or pressure from areas of high concentration or pressure until the pressure gradient is equalized. Where there is no more gradient about the concentration or pressure of gas, the gas is said to be at equilibrium, thus, no more transportation or diffusion can occur (Robeson 167). The rate at which a gas can diffuse through the membrane can be obtained by calculating the mass transfer coefficient of the gasses involved.
This experiment seeks to determine the overall mass transfer coefficients for nitrogen and oxygen (Ko2 and KN2) via a polymer membrane subjected to different experimental conditions. As a consequence, the overall mass transfer coefficients for nitrogen and oxygen through a polymer membrane will be computed to establish how altering these experimental circumstances affect the permeability of the polymer membrane. There two factors used to determine the permeability of a membrane; the rate at which gas diffuse through the membrane and the solubility of gas in the membrane (Stern 34). Both the rate of gas diffusion through the membrane and the solubility of gas in the membrane are part of the mass transfer coefficient. These two factors can be used to compute the expected amount of gas penetrating through a specific area per unit time (the expected flux). The separation factor can be defined as the gradient of the permeability of the membrane to each gas in the assortment of gasses. The exit stream that passes through the membrane is known as permeate while the exit stream that is retained within the membrane is known as retentate.
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. Both oxygen and nitrogen gasses exhibit similar shapes, are diatomic in nature and demonstrate equivalent root mean square value under the same temperature (Stern 35).
However, it is imperative to note that the solubility of oxygen gas is five times that of nitrogen gas in some polymers. The solubility property difference between oxygen and nitrogen in some polymer membrane is utilized in attained separation of the two gasses in most industrial processes and application. The property is one of the design factors employed in the production of air separation membrane for industrial use (Stern 44). For the separation of these two gasses, a dual layered, asymmetric membrane is employed. One porous layer beneath and a thin, non-porous discriminating skin make up the membrane used in the separation of nitrogen and oxygen gas. The membrane acquires its mechanical properties from the porous structure while the thin skin allows the membrane to be permeable (Robeson 163).
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. The molar flow rate is determined regarding differences in pressure (Robeson 167).
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.
Appendix
Figure 1: Graph indicating the ideal flow rate of both oxygen and nitrogen gas. Retrieved from https://permselect.com
Figure 2: Oxygen enrichment graph. Retrieved from https://permselect.com
Works Cited
Robeson, Lloyd M. "Correlation of separation factor versus permeability for polymeric membranes." Journal of membrane science 62.2 (1991): 165-185.
Stern, S. Alexander. "Polymers for gas separations: the next decade."Journal of Membrane Science 94.1 (1994): 1-65.
