Exp 3-Reverse Osmosis Calculation

CHE 415- Unit Operations Lab II-Fall 2021 Objectives: To show the pressure gradient across the membrane and the solvent flux is proportional To show that increasing recycling the reject stream yields a higher rejection efficiency Exp 3. Reverse Osmosis Data Results and Discussion: Table 1 Result Table Figure 1. Mass flowrate (kg/s) vs. Pressure Difference (atm) for Recycle Valve Fully Open Figure 2. Mass flowrate (kg/s) vs. Pressure Difference (atm) for Recycle Valve 90% Open Figure 3. Mass flowrate (kg/s) vs. Pressure Difference (atm) for Recycle Valve 80% Open Figure 4. Mass flowrate (kg/s) vs. Pressure Difference (atm) for Recycle Valve 70% Open Figure 5. Rejection Efficiency vs. Recycle Valve Open Percentage The relation between the mass flowrate of the permeate and the pressure difference across the reverse osmosis membrane is expected to be linear. When the recycle valve is fully open the plot of mass flow rate vs. pressure difference shows a nearly linear correlation. When the recycle valve is opened at 90%, 80% and 70% the plot shows various error from the linear trendlines. The mass flow rate of permeate is supposed to be increase with the increase of pressure difference. However, it is observed from the plots that the mass flow rate only follows this trend when the recycle valve is fully open and 70% open. When the recycle valve is 90% and 80% open the mass flow rate decreases with the increase of pressure difference. The relation of rejection efficiency is expected to increase with the increase of the open percentage of the recycle valve, since the purpose of recycling the reject stream is to improve the particle removal efficiency of the reverse osmosis membrane unit. It is observed in figure 5 that the trendline of rejection efficiency vs. recycle valve open percentage is linear and has a positive coefficient. Therefore, the result fulfilled the expectation. Possible source of error will be discussed in the error analysis section. Sample calculations: Concentration (mg/l) TDS (ppm) Total Feed TDS (ppm) calcium 33.3 33.3 113.79 magnesium 8.5 8.5 sodium 15.4 15.4 potassium 1.6 1.6 chloride 29.4 29.4 nitrate 0.39 0.39 sulfate 25.2 25.2 Table of Ion Concentrations of Toronto Tap Water 2020 (City of Toronto) TDS in ppm is considered the same with concentration in mg/L since tap water is a very diluted aqueous solution. Mass water flow rate conversion (assume water density at 25C is 997kg/m3): 0.5 gpm=0.5gallonminute×m3264 gallon×997kgm3×minute60s=0.0315kg/s 6Lpm=6Lminute×m31000L×997kgm3×minute60s=0.0997kg/s Pressure difference: ?P=Phigh-Plow=15psi-5psi=10psi=0.68046atm Osmotic pressure: ?=RTnV Osmotic pressure of the feed: ?feed=RTnV=8.314L kpaK mol×298K×0.00299molL=7.408 kpa Assume osmotic pressure of the permeate is 0: ??=?feed-?permeate=7.408 kpa Water flux: Jw=PwLm(?P-??) Jw=QwA, where Qw is the volumetric flow rate of water and A is the membrane area in m2. Since the area is unknown this method was not used in the report. Rejection efficiency of recycle valve fully open: Average TDSproduct=11+11+10+9+75=9.6ppm TDSfeed= Rejection efficiency=TDSfeed-TDSproductTDSfeed=113.79-9.6113.79×100%=91.56% Raw data: Recycle Valve Fully Open High Pressure Gauge (psi) Low Pressure Gauge (psi) Product flow rate (gpm) Reject flow rate (gpm) Product TDS (ppm) 15 5 0.5 2.5 11 30 7 0.75 1.75 11 40 7 0.75 1.2 10 50 8 1 1.6 9 60 10 1 1.2 7 Recycle Valve 90% Open High Pressure Gauge (psi) Low Pressure Gauge (psi) Product flow rate (Lpm) Reject flow rate (gpm) Product TDS (ppm) 30 7.5 6 2 10 40 7.5 4.5 1.5 10 55 8 3 1 7 70 10 1.5 1 7 Recycle Valve 80% Open High Pressure Gauge (psi) Low Pressure Gauge (psi) Product flow rate (Lpm) Reject flow rate (Lpm) Product TDS (ppm) 70 4 5.5 9.25 9 75 5 3 4.5 9 80 6 4.5 4.5 9 90 7.5 4.5 3.7 9 Recycle Valve 70% Open High Pressure Gauge (psi) Low Pressure Gauge (psi) Product flow rate (Lpm) Reject flow rate (Lpm) Product TDS (ppm) 75 2 3.7 5.55 10 80 4 3.7 5.55 11 90 4 6 4.5 12 100 5 6 3.7 10 Ref: City of Toronto. Tap Water Quality & System Reports https://www.toronto.ca/services-payments/water-environment/tap-water-in-toronto/tap-water-quality-system-reports/ (accessed Oct 12, 2021). Water - density, specific weight and thermal expansion coefficients https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html (accessed Oct 12, 2021).