Modeling water flux in forward osmosis: Implications for improved membrane design

McCutcheon, Jeffrey R.; Elimelech, Menachem

doi:10.1002/aic.11197

Cited by 342 publications

(226 citation statements)

References 22 publications

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“…Figure 7 shows that the average CP moduli (βd and βf) in the exchanger decrease and approach unity as MTUπ increases for a range of MR in the case of combining seawater and river water. For the case of seawater and river water, the feed-side internal CP is a larger issue than the draw CP, a result in agreement with literature [2,4,25,27]. Figure 7 also shows that the largest deviation of β from unity is for high values of MR at low…”

Section: Performancesupporting

confidence: 80%

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

Banchik

Sharqawy

Lienhard

2014

Journal of Membrane Science

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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.

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Section: Performancesupporting

confidence: 80%

“…More details on the concentration polarization model used can be found in [25]. Equation (34) assumes an asymmetric membrane with the active layer facing the draw stream and no concentrative external CP on the feed side, which is acceptable for relatively dilute feed streams.…”

Section: Performancementioning

confidence: 99%

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

Banchik

Sharqawy

Lienhard

2014

Journal of Membrane Science

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“…This equation, however, assumes a well-stirred system without the presence of boundary layers, which in ODMPs occur on both the feed and draw solution sides of the membrane and inside the porous support layer of the membrane. McCutcheon et al [30,31] presented a model for osmotic flux across a dense, symmetric membrane: (2) where π D,b and π F,b are the bulk osmotic pressures of the draw and feed solutions, respectively, and k D and k F are the mass transfer coefficients on the draw and feed solution sides of the membrane, respectively. This implicit flux model incorporates concentration polarization moduli that account for boundary layer phenomenon on both sides of the membrane.…”

Section: Governing Equations In Odmpsmentioning

confidence: 99%

Standard Methodology for Evaluating Membrane Performance in Osmotically Driven Membrane Processes

et al. 2013

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Osmotically driven membrane processes (ODMPs) such as forward osmosis (FO) and pressure retarded osmosis (PRO) are extensively investigated for utilization in a broad range of applications. In ODMPs, the operating conditions and membrane properties play more critical roles in mass transport and process performance than in pressure-driven membrane processes. Search of the literature reveals that ODMP membranes, especially newly developed ones, are tested under different temperatures, draw solution compositions and concentrations, flow rates, and pressures. In order to compare different membranes, it is important to develop standard protocols for testing of membranes for ODMPs. In this article we present a standard methodology for testing of ODMP membranes based on experience gained and operating conditions used in FO and PRO studies in recent years. A round-robin testing of two commercial membranes in seven independent laboratories revealed that water flux and membrane permeability coefficients were similar when participants performed the experiments and calculations using the same protocols. The thin film composite polyamide membrane exhibited higher water and salt permeability than the asymmetric cellulosebased membrane, but results with the high permeability thin-film composite membrane were more scattered. While salt rejection results in RO mode were relatively similar, salt permeability coefficients for both membranes in FO mode were more varied. Results suggest that high permeability ODMP membranes should be tested at lower hydraulic pressure in RO mode and that RO testing be conducted with the same membrane sample used for testing in FO mode. AbstractOsmotically driven membrane processes (ODMP) such as forward osmosis (FO) and pressure retarded osmosis (PRO) are extensively investigated for utilization in a broad range of applications. In ODMPs, the operating conditions and membrane properties play more critical roles in mass transport and process performance than in pressure-driven membrane processes.Search of the literature reveals that ODMP membranes, especially newly developed ones, are tested under different temperatures, draw solution compositions and concentrations, flowrates, and pressures. In order to compare different membranes, it is important to develop standard protocols for testing of membranes for ODMP. In this article we present a standard methodology for testing of ODMP membranes based on experience gained and operating conditions used in FO and PRO studies in recent years. A round-robin testing of two commercial membranes in seven independent laboratories revealed that water flux and membrane permeability coefficients were similar when participants performed the experiments and calculations using the same protocols. The thin film composite polyamide membrane exhibited higher water and salt permeability than the asymmetric cellulose-based membrane, but results with the high permeability thin-film composite membrane were more scattered. While salt rejection results in RO mode were...

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“…Designers can choose whether the support layer of the FO/AFO membrane faces the feed solution (referred to as PRO mode) or draw solution (FO mode) [28]. This choice affects where and to what extent internal and external concentration polarization play a role in reducing the net driving pressure, and consequently flux, through the membrane.…”

Section: Step 1 Solve For Rr Of a Small Membrane With Concentration mentioning

confidence: 99%

“…For the numerical model, we will also use representative values for the average external mass transfer coefficient for the draw side (k d = 1.74 × 10 −5 m/s [28]), and average solute resistance to mass transfer for a membrane operated in PRO mode (K = 2.24 × 10 5 s/m [28]). The local permeate mass flow rate through a section of membrane with area A s is given by the well known solution diffusion equation with concentration polarization moduli for a membrane operated in PRO mode:…”

Section: Numerical Modelmentioning

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

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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.

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Modeling water flux in forward osmosis: Implications for improved membrane design

Cited by 342 publications

References 22 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

Standard Methodology for Evaluating Membrane Performance in Osmotically Driven Membrane Processes

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

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