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Appendix B Mass and Energy Balance on Reverse Osmosis System

The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001

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Appendix B Mass and Energy Balance on Reverse Osmosis System 275

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276 Desalination: A National Perspective Mass and Energy Balance on Reverse Osmosis System: Feed: Concentrate: Flow = Qo Flow (@ 40% Recovery) = 0.6Qo Pressure = Pfeed Pressure = PR Energy ~ 0.6Qo(Pfeed+PR)/2 x (1-fraction of Energy Recovered) Permeate: Flow (@ 40% Recovery) = 0.4Qo Pressure = PP Energy ~ 0.4Qo((Pfeed+PR)/2 - PP) Following is an approximation of the energy used in a typical RO process operating at 40% recovery and an energy recovery device operating at an efficiency of η eff . (PO + PR ) P + PR − PP ) . (1 − ηeff ) + 0.4Q O ( O Energy Used ≅ 0.6QO 2 2 Making the assumption that Pp is significantly less than the applied average operating pressure, (i.e., that PP = 14.7 at atmospheric pressure and P0 + PR because this term is << this term is presumed to be negligible and ≅ 0) 2 and taking a ratio of a future, new energy balance based on a new membrane with new properties relative to a baseline energy balance we get the following equation: (PON + PRN ) (P + PRN ) (1 − η eff ) + 0.4Q O ON 0.6Q O Energy New 2 2 = (PO + PR ) (PO + PR ) Energy Baseline (1 − η eff ) + 0.4Q O 0.6Q O 2 2

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Appendix B 277 This equation can be factored as follows, (PON + PRN ) (0.6Q O (1 − η eff ) + 0.4Q O ) Energy New 2 = (PO + PR ) Energy Baseline (0.6Q O (1 − η eff ) + 0.4Q O ) 2 and further simplified to the following equation: (PON + PRN ) PAvg. Driving New + POsmotic PAvg. Applied New Energy New 2 = = = (PO + PR ) PAvg. Applied Baseline + POsmotic Energy Baseline PAvg. Applied Baseline 2 . As shown above, the average applied pressure can be broken down into two components: (1) the osmotic pressure required to overcome the osmotic energy barrier and (2) the net driving pressure required to overcome the native resistance of the membrane permeability. For the purposes of illustrating the sensitivity of membrane permeability on potential future energy reductions, the following system operating data is taken from “The Guidebook to Membrane Desalination Technology,” p. 472, Balaban Desalination Publications, 2007: Average Total Dissolved Solids (TDS): 59,921 ppm Temperature: 26 °C PAvg Osmotic = 656 psi (at the average TDS of 59,053 ppm and Temperature of 28 °C; calculated by using the Van’t Hoff equation) PAvg Applied Baseline = 936 psi (Pfeed = 947 psi; Pconcentrate = 924 psi) PAvg Driving Baseline = (936 – 656) = 280 psi PAvg Driving New = 0.5 x 280 = 140 psi (Reflecting a doubling of membrane permeability)

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278 Desalination: A National Perspective Assuming that the membrane permeability can be doubled without sacrificing salt rejection, the average driving pressure for the new membrane can be reduced by 50 percent (shown above). Substituting these values into the equation above, PAvg. Driving New + POsmotic 140 + 656 Energy New = = = 0.85 Energy Baseline PAvg. Applied Baseline + POsmotic 280 + 656 results in an energy ratio of new to baseline of 0.85. This translates into a net reduction of energy equal to 15 percent from today’s baseline.