National Academies Press: OpenBook

Desalination: A National Perspective (2008)

Chapter: Appendix B: Mass and Energy Balance on Reverse Osmosis System

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Suggested Citation:"Appendix B: Mass and Energy Balance on Reverse Osmosis System." National Research Council. 2008. Desalination: A National Perspective. Washington, DC: The National Academies Press. doi: 10.17226/12184.
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Page 275
Suggested Citation:"Appendix B: Mass and Energy Balance on Reverse Osmosis System." National Research Council. 2008. Desalination: A National Perspective. Washington, DC: The National Academies Press. doi: 10.17226/12184.
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Page 276
Suggested Citation:"Appendix B: Mass and Energy Balance on Reverse Osmosis System." National Research Council. 2008. Desalination: A National Perspective. Washington, DC: The National Academies Press. doi: 10.17226/12184.
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Page 277
Suggested Citation:"Appendix B: Mass and Energy Balance on Reverse Osmosis System." National Research Council. 2008. Desalination: A National Perspective. Washington, DC: The National Academies Press. doi: 10.17226/12184.
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Page 278

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Appendix B Mass and Energy Balance on Reverse Osmosis System 275

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 Energy Used ≅ 0.6QO (1 − ηeff ) + 0.4Q O ( O − PP ) . 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 ) 0.6Q O (1 − η eff ) + 0.4Q O ON Energy New 2 2 = Energy Baseline (PO + PR ) (PO + PR ) 0.6Q O (1 − η eff ) + 0.4Q O 2 2

Appendix B 277 This equation can be factored as follows, (PON + PRN ) (0.6Q O (1 − η eff ) + 0.4Q O ) Energy New 2 = Energy Baseline (PO + PR ) (0.6Q O (1 − η eff ) + 0.4Q O ) 2 and further simplified to the following equation: (PON + PRN ) Energy New 2 PAvg. Applied New PAvg. Driving New + POsmotic = = = Energy Baseline (PO + PR ) PAvg. Applied Baseline PAvg. Applied Baseline + POsmotic 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)

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, Energy New PAvg. Driving New + POsmotic 140 + 656 = = = 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.

Next: Appendix C: Desalination Economics Summary Data »
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There has been an exponential increase in desalination capacity both globally and nationally since 1960, fueled in part by growing concern for local water scarcity and made possible to a great extent by a major federal investment for desalination research and development. Traditional sources of supply are increasingly expensive, unavailable, or controversial, but desalination technology offers the potential to substantially reduce water scarcity by converting the almost inexhaustible supply of seawater and the apparently vast quantities of brackish groundwater into new sources of freshwater.

Desalination assesses the state of the art in relevant desalination technologies, and factors such as cost and implementation challenges. It also describes reasonable long-term goals for advancing desalination technology, posits recommendations for action and research, estimates the funding necessary to support the proposed research agenda, and identifies appropriate roles for governmental and nongovernmental entities.

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