Membranes for power generation by pressure-retarded osmosis

Lee, K.L.; Baker, Richard W.; Lonsdale, H.K.

doi:10.1016/s0376-7388(00)82088-8

Cited by 683 publications

(505 citation statements)

References 12 publications

Supporting

Mentioning

473

Contrasting

Order By: Relevance

“…(26) and differentiating with respect to P, it can be shown that the maximum power occurs when P = /2. This result was first shown by Lee et al [1] and corresponds to an optimal pressure ratio of * ≡ Δ Δ = 1/2. Therefore, for an exchanger small enough that a zerodimensional model applies, Δπ = Δπ max , and it can be shown that the maximum power per unit mass flow rate of the feed stream is linearly proportional to MTU π and Δπ max Eq.…”

Section: Zero-dimensional Model For a Very Small Exchangersupporting

confidence: 65%

“…The PRO water transport equation for a differential area of membrane, based on the solution-diffusion model [1], is given by…”

Section: Modified Pro Mass Exchanger Flux Performance Modelmentioning

confidence: 99%

“…A one-dimensional model takes into account changing concentrations and net driving pressures along the length of the membrane. This is unlike the classical "zero-dimensional" PRO model [1] which assumes that the net driving pressure is constant throughout the length of the exchanger. That approximation is valid for small, coupon-sized membranes in a benchtop experiment for which the stream compositions are constant along either side of the membrane; but for systems at the scale of a PRO power plant, the flow paths are much longer, so that the streamwise change in salinity, and consequently the change in flux, must usually be considered.…”

Section: Introductionmentioning

confidence: 96%

“…Studies of the power production possible with PRO systems have often been based on the zero-dimensional approximation model [1][2][3][4][5][6][7][8][9][10]. Under that model, the power produced by the system, comprised of an exchanger, a pump, and a turbine, is linearly proportional to the membrane area.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Limits of power production due to finite membrane area in pressure retarded osmosis

Banchik

Sharqawy

Lienhard

2014

Journal of Membrane Science

View full text Add to dashboard Cite

Dimensionless analytical expressions for the power attainable from an ideal counterflow pressure retarded osmosis (PRO) system model are developed using a one-dimensional model that accounts for streamwise variations in concentration. This ideal PRO system has no salt permeation or concentration polarization. The expressions show that the optimal hydraulic pressure difference, for which the maximum power is produced, deviates significantly from the classical solution of one-half of the trans-membrane osmotic pressure difference, Δπ/2, as the dimensionless membrane area (MTU π ) increases and the ratio of draw to feed mass flow rates (MR) varies. The overall maximum power attainable from a PRO membrane is found to occur in the limit of infinitely large MTU π (an effectiveness of unity) and infinite MR. For an ideal PRO system which mixes seawater (35 g/kg) and river water (1.5 g/kg), the overall maximum power of 1.57 kJ per kilogram of feed can be attained at roughly MTU π of 15, an MR of 10, and a pressure of 0.83Δ . Due to economic considerations, a PRO system in practice will have limited membrane area and will operate at an effectiveness of less than unity.The present work can be used to estimate the operating conditions and area required for a PRO system of given performance. The effect of concentration polarization on optimal hydraulic pressure difference and maximum power performance is also investigated using a numerical model.

show abstract

Section: Zero-dimensional Model For a Very Small Exchangersupporting

confidence: 65%

“…The PRO water transport equation for a differential area of membrane, based on the solution-diffusion model [1], is given by…”

Section: Modified Pro Mass Exchanger Flux Performance Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Limits of power production due to finite membrane area in pressure retarded osmosis

Banchik

Sharqawy

Lienhard

2014

Journal of Membrane Science

View full text Add to dashboard Cite

show abstract

“…Internal and external concentration polarization result in significant reductions in flux for osmotic mass exchangers and it is crucial to consider them when designing exchangers [10]. Invoking the van 't Hoff relation can result in additional errors.…”

Section: Solving For βmentioning

confidence: 99%

System scale analytical modeling of forward and assisted forward osmosis mass exchangers with a case study on fertigation

Banchik

Weiner

Al-Anzi

et al. 2016

Journal of Membrane Science

View full text Add to dashboard Cite

Forward osmosis (FO) and assisted forward osmosis (AFO) mass exchangers are currently receiving considerable attention for their potential use in a variety of dilution and concentration applications in resource extraction, fertigation, and pharmaceutical process streams. In this work we develop analytical expressions for parallel and counterflow FO and AFO exchangers which can be used to quickly and accurately estimate the membrane area required for these applications in addition to determining the performance of existing exchangers. Unlike previous models, our analytical model accounts for internal and external concentration polarization in system scale exchangers with overall average errors of less than 10% against a numerical model and less than 35% validated against data from the literature. The performance of FO and AFO exchangers is compared, and an osmotic fertilizer dilution (fertigation) case study is investigated in which the trade-off between energy and membrane area requirements is quantified. We find that AFO exchangers yield a higher recovery relative to FO exchangers for a given energy input especially when the inlet draw-to-feed osmotic pressure ratio is low. Diminishing returns in recovery ratio are attained for increasing membrane area and increasing draw-to-feed mass flow rate ratio. We also find that for the same brackish feed water and recovery ratio, reductions in area of up to 40% relative to FO can be realized with 2 kWh/m 3 of energy input into an AFO system in the fertigation case study.

show abstract

Other Membrane Processes

2012

Membrane Technology and Applications

View full text Add to dashboard Cite

Membranes for power generation by pressure-retarded osmosis

Cited by 683 publications

References 12 publications

Limits of power production due to finite membrane area in pressure retarded osmosis

Limits of power production due to finite membrane area in pressure retarded osmosis

System scale analytical modeling of forward and assisted forward osmosis mass exchangers with a case study on fertigation

Other Membrane Processes

Contact Info

Product

Resources

About