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Electrodialysis for water desalination

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Electrodialysis for water desalination ( electrodialysis-water-desalination )

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In the practical design of an ED unit, the process path length can be derived from this equation when working below the limiting current density and including a correction factor to take into account the shadow effects: h 𝐶𝐶􏰠 𝐿 􏱁 􏰩 􏰫 􏰝 = 􏱅 𝑙 𝑛 􏰶 􏰏 + ( 𝑟 􏱀 􏰾 􏰿 + 𝑟 􏰶 􏰾 􏰿 ) 􏰦 𝐶 􏰏􏰠 − 𝐶 􏰏 􏰪 􏱆 𝑧𝐹𝑄 􏱁 􏰩 􏰫 􏰝 𝜁∆𝑉𝐹􏰕𝑏 (51) 𝜆 𝐶􏰏 𝐶􏰠 􏰶 where 𝐹􏰕 is the shadow factor, 𝑏 is the cell width and 𝑄􏱁􏰩􏰫􏰝 = 𝑄𝜎, with 𝜎 being a factor expressing the fluid volume % of a cell (i.e. the porosity of the spacer). In a subsequent work, Brauns [361] modified this equation by replacing the shadow factor with a general experimentally determined model parameter which can account for additional phenomena. Another example of simplified model was presented in 2007 by Sadrzadeh et al. [360]. In this empirical regression-based model, a current efficiency is used to include all phenomena leading to an incomplete current utilisation, without explicitly considering the various contributions different from the migrative flux for the mass transfer through membranes. In this way, the mass balance can be written as 𝑢h􏰏𝑑𝐶 = 𝜁 𝐼 𝑑𝑥 𝐹𝐴 (52) where 𝑢 is the fluid velocity, h􏰏 is the thickness of the diluate compartment, 𝜁 is the current efficiency, 𝐹 is the Faraday constant, 𝐼 is the electrical current, while I/A represent the current density and 𝐴 is the effective area of an IEM. dC and dx represent the differential variation of concentration for a differential increase in the stack length, respectively. In addition, membrane resistances as well as Nernst potentials are not explicitly calculated but all included in fitting parameters. The result is a lumped model characterised by a single design equation that gives the outlet diluate concentration as a function of the various parameters: 𝛽 𝑄􏰣⁄􏰼 h􏰏􏰣 𝐹 􏰣⁄􏰼 ∆𝑉 𝐴 􏰶 􏰯 𝑓(𝐶􏱇,𝐶)= 􏱈𝑑𝑥 􏱇 1 (53) (54) 𝑓(𝐶􏱇, 𝐶) = 􏱈 𝐶(12.64 − 8.92𝐶􏱇.􏱉 + 8.21 𝐶) 𝑑𝐶 􏰶􏱊 where 𝑄 is the flow rate and 𝛽 is a parameter that is fitted by experimental data, resulting in a function of flow rate and applied voltage. As it was shown, simplified models result in a limited number of equations that can easily be used to estimate the main design parameters. However, a simplified design tool does not provide details on the variables distribution along the channel, such as current profiles, and approximates all non-ideal 65

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